From 1ce07ee9c1fe12df43431f2ee3db5db5a35a51aa Mon Sep 17 00:00:00 2001 From: jellepoland Date: Fri, 24 Jul 2026 09:59:02 +0200 Subject: [PATCH 01/37] Improve plotting geometry and update tutorial Co-Authored-By: Claude Opus 4.8 (1M context) --- .../struc_geometry_manually_adjusted.yaml | 188 ++++++----- examples/TUDELFT_V3_KITE/tutorial.py | 302 +++++++++--------- src/VSM/plot_geometry_plotly.py | 13 +- 3 files changed, 256 insertions(+), 247 deletions(-) diff --git a/data/TUDELFT_V3_KITE/CAD_derived_geometry/struc_geometry_manually_adjusted.yaml b/data/TUDELFT_V3_KITE/CAD_derived_geometry/struc_geometry_manually_adjusted.yaml index fdc68f0..4987dc6 100644 --- a/data/TUDELFT_V3_KITE/CAD_derived_geometry/struc_geometry_manually_adjusted.yaml +++ b/data/TUDELFT_V3_KITE/CAD_derived_geometry/struc_geometry_manually_adjusted.yaml @@ -1,8 +1,7 @@ - ############################## ## General ################### ############################## -bridle_point_node: [0,0,0] #[x,y,z] --> location of kcu +bridle_point_node: [0, 0, 0] #[x,y,z] --> location of kcu ## Mass pulley_mass: !!float 0.1 #[kg] #TODO: would be better to define these per pulley @@ -15,7 +14,6 @@ dyneema: youngs_modulus: 550000000 #[Pa] -> k = E A / l0 damping_per_stiffness: 0.0 # [/s] -> c = damping_per_stiffness * k - ########################### ## Wing ################### ########################### @@ -117,38 +115,38 @@ wing_elements: # line name, measured rest length "l0" [m], stiffness "k" [N/m], damping "c" [N.s/m], mass "m" [kg], linktype headers: [name, l0, k, c, m, linktype] data: - # leading-edge tube (LE[i] -- LE[i+1]) - - [le_1, 0.984642, 2e3, 0, 1, "default"] - - [le_2, 1.327663, 2e3, 0, 1, "default"] - - [le_3, 1.326240, 2e3, 0, 1, "default"] - - [le_4, 1.323655, 2e3, 0, 1, "default"] - - [le_5, 1.347595, 2e3, 0, 1, "default"] - - # struts (chords) - - [strut_1, 1.074728, 2e3, 0, 1, "default"] - - [strut_2, 1.511911, 2e3, 0, 1, "default"] - - [strut_3, 1.960560, 2e3, 0, 1, "default"] - - [strut_4, 2.154185, 2e3, 0, 1, "default"] - - [strut_5, 2.265501, 2e3, 0, 1, "default"] - - # trailing-edge wire (TE[i] -- TE[i+1]) - - [te_1, 0.903854, 1e3, 0, 0.2, "default"] - - [te_2, 1.351057, 1e3, 0, 0.2, "default"] - - [te_3, 1.350587, 1e3, 0, 0.2, "default"] - - [te_4, 1.350462, 1e3, 0, 0.2, "default"] - - [te_5, 1.321072, 1e3, 0, 0.2, "default"] - - # diagonal springs (both directions per panel) - - [dia_1a, 1.360356, 1e3, 0, 0.1, "default"] - - [dia_1b, 1.780032, 1e3, 0, 0.1, "default"] - - [dia_2a, 2.108078, 1e3, 0, 0.1, "default"] - - [dia_2b, 2.251513, 1e3, 0, 0.1, "default"] - - [dia_3a, 2.449188, 1e3, 0, 0.1, "default"] - - [dia_3b, 2.455523, 1e3, 0, 0.1, "default"] - - [dia_4a, 2.601005, 1e3, 0, 0.1, "default"] - - [dia_4b, 2.563136, 1e3, 0, 0.1, "default"] - - [dia_5a, 2.629214, 1e3, 0, 0.1, "default"] - - [dia_5b, 2.629214, 1e3, 0, 0.1, "default"] + # leading-edge tube (LE[i] -- LE[i+1]) + - [le_1, 0.984642, 2e3, 0, 1, 'default'] + - [le_2, 1.327663, 2e3, 0, 1, 'default'] + - [le_3, 1.326240, 2e3, 0, 1, 'default'] + - [le_4, 1.323655, 2e3, 0, 1, 'default'] + - [le_5, 1.347595, 2e3, 0, 1, 'default'] + + # struts (chords) + - [strut_1, 1.074728, 2e3, 0, 1, 'default'] + - [strut_2, 1.511911, 2e3, 0, 1, 'default'] + - [strut_3, 1.960560, 2e3, 0, 1, 'default'] + - [strut_4, 2.154185, 2e3, 0, 1, 'default'] + - [strut_5, 2.265501, 2e3, 0, 1, 'default'] + + # trailing-edge wire (TE[i] -- TE[i+1]) + - [te_1, 0.903854, 1e3, 0, 0.2, 'default'] + - [te_2, 1.351057, 1e3, 0, 0.2, 'default'] + - [te_3, 1.350587, 1e3, 0, 0.2, 'default'] + - [te_4, 1.350462, 1e3, 0, 0.2, 'default'] + - [te_5, 1.321072, 1e3, 0, 0.2, 'default'] + + # diagonal springs (both directions per panel) + - [dia_1a, 1.360356, 1e3, 0, 0.1, 'default'] + - [dia_1b, 1.780032, 1e3, 0, 0.1, 'default'] + - [dia_2a, 2.108078, 1e3, 0, 0.1, 'default'] + - [dia_2b, 2.251513, 1e3, 0, 0.1, 'default'] + - [dia_3a, 2.449188, 1e3, 0, 0.1, 'default'] + - [dia_3b, 2.455523, 1e3, 0, 0.1, 'default'] + - [dia_4a, 2.601005, 1e3, 0, 0.1, 'default'] + - [dia_4b, 2.563136, 1e3, 0, 0.1, 'default'] + - [dia_5a, 2.629214, 1e3, 0, 0.1, 'default'] + - [dia_5b, 2.629214, 1e3, 0, 0.1, 'default'] ############################# ## Bridle ################### @@ -177,71 +175,71 @@ bridle_particles: bridle_connections: # name, ci, cj, ck (this is the third node, only exist when a pulley) - headers: [name, ci, cj, ck] + headers: [name, ci, cj, ck] data: # front lines - - [a6,25,1,33] # pulley - - [A5,3,21] - - [A3,5,21] - - [A2,7,22] - - [A1,9,22] - - [A1,11,23] - - [A2,13,23] - - [A3,15,24] - - [A5,17,24] - - [a6,26,19,35] # pulley - - [AII,21,25] - - [AI,22,25] - - [AI,23,26] - - [AII,24,26] - - [amain,25,0] - - [amain,26,0] + - [a6, 25, 1, 33] # pulley + - [A5, 3, 21] + - [A3, 5, 21] + - [A2, 7, 22] + - [A1, 9, 22] + - [A1, 11, 23] + - [A2, 13, 23] + - [A3, 15, 24] + - [A5, 17, 24] + - [a6, 26, 19, 35] # pulley + - [AII, 21, 25] + - [AI, 22, 25] + - [AI, 23, 26] + - [AII, 24, 26] + - [amain, 25, 0] + - [amain, 26, 0] # rear lines - - [br6,33,2,36] # pulley - - [br5,4,27] - - [br3,6,27] - - [br2,8,28] - - [br1,10,28] - - [br1,12,29] - - [br2,14,29] - - [br3,16,30] - - [br5,18,30] - - [br6,35,20,37] # pulley - - [BRII,27,31] - - [BRI,28,31] - - [BRI,29,32] - - [BRII,30,32] - - [BR-main-1,31,33] - - [BR-main-1,32,35] - - [M-line,36,33,34] # pulley - - [M-line,34,35,37] # pulley - - [Steering Tape,36,0] - - [Power Tape,34,0] - - [Steering Tape,37,0] + - [br6, 33, 2, 36] # pulley + - [br5, 4, 27] + - [br3, 6, 27] + - [br2, 8, 28] + - [br1, 10, 28] + - [br1, 12, 29] + - [br2, 14, 29] + - [br3, 16, 30] + - [br5, 18, 30] + - [br6, 35, 20, 37] # pulley + - [BRII, 27, 31] + - [BRI, 28, 31] + - [BRI, 29, 32] + - [BRII, 30, 32] + - [BR-main-1, 31, 33] + - [BR-main-1, 32, 35] + - [M-line, 36, 33, 34] # pulley + - [M-line, 34, 35, 37] # pulley + - [Steering Tape, 36, 0] + - [Power Tape, 34, 0] + - [Steering Tape, 37, 0] bridle_lines: # line name, measured rest length "l0" [m], stiffness "k" [N/m], damping "c" [N.s/m], diameter "d" [m], density "rho" [kg/m^3] # dyneema has rho = 970 - headers: [name, l0, diameter, material, linktype] + headers: [name, l0, d, material, linktype] data: - # front lines - - [a6, 11.372, 0.005, dyneema, "pulley"] - - [A5, 2.782, 0.005, dyneema, "noncompressive"] - - [A3, 3.253, 0.005, dyneema, "noncompressive"] - - [A2, 3.352, 0.005, dyneema, "noncompressive"] - - [A1, 3.520, 0.005, dyneema, "noncompressive"] - - [AII, 3.188, 0.01, dyneema, "noncompressive"] - - [AI, 3.420, 0.01, dyneema, "noncompressive"] - - [amain, 4.297, 0.02, dyneema, "noncompressive"] - # rear lines - - [br1, 4.448, 0.002, dyneema, "noncompressive"] - - [br2, 4.300, 0.002, dyneema, "noncompressive"] - - [br3, 4.560, 0.002, dyneema, "noncompressive"] - - [br5, 4.047, 0.002, dyneema, "noncompressive"] - - [br6, 14.172, 0.002, dyneema, "pulley"] - - [BRI, 2.388, 0.002, dyneema, "noncompressive"] - - [BRII, 1.890, 0.002, dyneema, "noncompressive"] - - [BR-main-1, 0.874, 0.002, dyneema, "noncompressive"] - - [M-line, 2.196, 0.002, dyneema, "pulley"] - - [Steering Tape, 1.506, 0.002, dyneema, "noncompressive"] - - [Power Tape, 3.129, 0.002, dyneema, "noncompressive"] \ No newline at end of file + # front lines + - [a6, 11.372, 0.005, dyneema, 'pulley'] + - [A5, 2.782, 0.005, dyneema, 'noncompressive'] + - [A3, 3.253, 0.005, dyneema, 'noncompressive'] + - [A2, 3.352, 0.005, dyneema, 'noncompressive'] + - [A1, 3.520, 0.005, dyneema, 'noncompressive'] + - [AII, 3.188, 0.01, dyneema, 'noncompressive'] + - [AI, 3.420, 0.01, dyneema, 'noncompressive'] + - [amain, 4.297, 0.02, dyneema, 'noncompressive'] + # rear lines + - [br1, 4.448, 0.002, dyneema, 'noncompressive'] + - [br2, 4.300, 0.002, dyneema, 'noncompressive'] + - [br3, 4.560, 0.002, dyneema, 'noncompressive'] + - [br5, 4.047, 0.002, dyneema, 'noncompressive'] + - [br6, 14.172, 0.002, dyneema, 'pulley'] + - [BRI, 2.388, 0.002, dyneema, 'noncompressive'] + - [BRII, 1.890, 0.002, dyneema, 'noncompressive'] + - [BR-main-1, 0.874, 0.002, dyneema, 'noncompressive'] + - [M-line, 2.196, 0.002, dyneema, 'pulley'] + - [Steering Tape, 1.506, 0.002, dyneema, 'noncompressive'] + - [Power Tape, 3.129, 0.002, dyneema, 'noncompressive'] diff --git a/examples/TUDELFT_V3_KITE/tutorial.py b/examples/TUDELFT_V3_KITE/tutorial.py index f5460fd..11ce873 100644 --- a/examples/TUDELFT_V3_KITE/tutorial.py +++ b/examples/TUDELFT_V3_KITE/tutorial.py @@ -49,7 +49,7 @@ def main(): PROJECT_DIR = Path(__file__).resolve().parents[2] ### 2. defining settings - n_panels = 50 + n_panels = 100 spanwise_panel_distribution = "uniform" solver_base_version = Solver(reference_point=np.array([0.0, 0.0, 0.0])) @@ -62,28 +62,30 @@ def main(): file_path=(cad_derived_geometry_dir / "aero_geometry_CAD_CFD_polars.yaml"), spanwise_panel_distribution=spanwise_panel_distribution, ) - body_aero_CAD_CFD_polars_with_bridles = BodyAerodynamics.instantiate( - n_panels=n_panels, - # file_path=(cad_derived_geometry_dir / "config_kite_CAD_CFD_polars.yaml"), - file_path=(cad_derived_geometry_dir / "config_kite_CAD_CFD_polars.yaml"), - spanwise_panel_distribution=spanwise_panel_distribution, - bridle_path=( - cad_derived_geometry_dir / "struc_geometry_manually_adjusted.yaml" - ), - ) - body_aero_CAD_neuralfoil = BodyAerodynamics.instantiate( - n_panels=n_panels, - file_path=(cad_derived_geometry_dir / "aero_geometry_CAD_neuralfoil.yaml"), - spanwise_panel_distribution=spanwise_panel_distribution, - ) - body_aero_masure_regression = BodyAerodynamics.instantiate( - n_panels=n_panels, - file_path=( - cad_derived_geometry_dir / "aero_geometry_CAD_masure_regression.yaml" - ), - ml_models_dir=(Path(PROJECT_DIR) / "data" / "ml_models"), - spanwise_panel_distribution=spanwise_panel_distribution, - ) + # body_aero_CAD_CFD_polars_with_bridles = BodyAerodynamics.instantiate( + # n_panels=n_panels, + # file_path=( + # cad_derived_geometry_dir + # / "config_kite_CAD_CFD_polars_converged_fitted_pchip.yaml" + # ), + # spanwise_panel_distribution=spanwise_panel_distribution, + # bridle_path=( + # cad_derived_geometry_dir / "struc_geometry_manually_adjusted.yaml" + # ), + # ) + # body_aero_CAD_neuralfoil = BodyAerodynamics.instantiate( + # n_panels=n_panels, + # file_path=(cad_derived_geometry_dir / "aero_geometry_CAD_neuralfoil.yaml"), + # spanwise_panel_distribution=spanwise_panel_distribution, + # ) + # body_aero_masure_regression = BodyAerodynamics.instantiate( + # n_panels=n_panels, + # file_path=( + # cad_derived_geometry_dir / "aero_geometry_CAD_masure_regression.yaml" + # ), + # ml_models_dir=(Path(PROJECT_DIR) / "data" / "ml_models"), + # spanwise_panel_distribution=spanwise_panel_distribution, + # ) # Step 2: Set inflow conditions for each aerodynamic object """ @@ -97,40 +99,40 @@ def main(): body_aero_CAD_CFD_polars.va_initialize( Umag, angle_of_attack, side_slip, body_rates=yaw_rate ) - body_aero_CAD_CFD_polars_with_bridles.va_initialize( - Umag, - angle_of_attack, - side_slip, - body_rates=yaw_rate, - body_axis=np.array([0, 0, 1]), - ) - body_aero_CAD_neuralfoil.va_initialize( - Umag, - angle_of_attack, - side_slip, - body_rates=yaw_rate, - body_axis=np.array([0, 0, 1]), - ) - body_aero_masure_regression.va_initialize( - Umag, - angle_of_attack, - side_slip, - body_rates=yaw_rate, - body_axis=np.array([0, 0, 1]), - ) + # body_aero_CAD_CFD_polars_with_bridles.va_initialize( + # Umag, + # angle_of_attack, + # side_slip, + # body_rates=yaw_rate, + # body_axis=np.array([0, 0, 1]), + # ) + # body_aero_CAD_neuralfoil.va_initialize( + # Umag, + # angle_of_attack, + # side_slip, + # body_rates=yaw_rate, + # body_axis=np.array([0, 0, 1]), + # ) + # body_aero_masure_regression.va_initialize( + # Umag, + # angle_of_attack, + # side_slip, + # body_rates=yaw_rate, + # body_axis=np.array([0, 0, 1]), + # ) # Step 3: Plot the kite geometry using Matplotlib """ Visualize the panel mesh, control points, and aerodynamic centers for the selected BodyAerodynamics object. """ - plot_geometry( - body_aero_CAD_CFD_polars, - title="TUDELFT_V3_KITE", - data_type=".pdf", - save_path=".", - is_save=False, - is_show=True, - ) + # plot_geometry( + # body_aero_CAD_CFD_polars, + # title="TUDELFT_V3_KITE", + # data_type=".pdf", + # save_path=".", + # is_save=False, + # is_show=True, + # ) # Step 4: Create an interactive plot using Plotly """ @@ -138,7 +140,7 @@ def main(): This allows for interactive exploration of the geometry and panel arrangement. """ interactive_plot( - body_aero_CAD_CFD_polars_with_bridles, + body_aero_CAD_CFD_polars, vel=Umag, angle_of_attack=angle_of_attack, side_slip=side_slip, @@ -154,105 +156,105 @@ def main(): # / "interactive_plot.html", ) - # Step 5: Plot polar curves for different angles of attack and side slip angles, and save results - """ - Compare the aerodynamic performance of different models by plotting lift, drag, and side force coefficients - as a function of angle of attack (alpha sweep) and side slip (beta sweep). - Literature/CFD data can be included for validation. - """ - save_folder = Path(PROJECT_DIR) / "results" / "TUDELFT_V3_KITE" + # # Step 5: Plot polar curves for different angles of attack and side slip angles, and save results + # """ + # Compare the aerodynamic performance of different models by plotting lift, drag, and side force coefficients + # as a function of angle of attack (alpha sweep) and side slip (beta sweep). + # Literature/CFD data can be included for validation. + # """ + # save_folder = Path(PROJECT_DIR) / "results" / "TUDELFT_V3_KITE" - # Step 5a: Plot alpha sweep (angle of attack) - path_cfd_lebesque_alpha = ( - Path(PROJECT_DIR) - / "data" - / "TUDELFT_V3_KITE" - / "3D_polars_literature" - / "CFD_RANS_Rey_10e5_Poland2025_alpha_sweep_beta_0.csv" - ) - path_wt_data = ( - Path(PROJECT_DIR) - / "data" - / "TUDELFT_V3_KITE" - / "3D_polars_literature" - / "V3_CL_CD_CS_alpha_sweep_for_beta_0_WindTunnel_Poland_2025_Rey_560e4.csv" - ) - plot_polars( - solver_list=[ - solver_base_version, - solver_base_version, - solver_base_version, - solver_base_version, - ], - body_aero_list=[ - body_aero_CAD_CFD_polars, - body_aero_CAD_CFD_polars_with_bridles, - body_aero_CAD_neuralfoil, - body_aero_masure_regression, - ], - label_list=[ - "VSM CAD CFD Polars", - "VSM CAD CFD Polars with Bridles", - "VSM CAD NeuralFoil", - "VSM CAD Masure Regression", - "CFD_RANS_Rey_10e5_Poland2025_alpha_sweep_beta_0", - "Wind Tunnel Data Poland 2025", - ], - literature_path_list=[path_cfd_lebesque_alpha, path_wt_data], - angle_range=[0, 5, 8, 10, 12, 15, 20, 25], - angle_type="angle_of_attack", - angle_of_attack=0, - side_slip=0, - yaw_rate=0, - Umag=Umag, - title="alphasweep", - data_type=".pdf", - save_path=Path(save_folder), - is_save=True, - is_show=False, - ) + # # Step 5a: Plot alpha sweep (angle of attack) + # path_cfd_lebesque_alpha = ( + # Path(PROJECT_DIR) + # / "data" + # / "TUDELFT_V3_KITE" + # / "3D_polars_literature" + # / "CFD_RANS_Rey_10e5_Poland2025_alpha_sweep_beta_0.csv" + # ) + # path_wt_data = ( + # Path(PROJECT_DIR) + # / "data" + # / "TUDELFT_V3_KITE" + # / "3D_polars_literature" + # / "windtunnel_alpha_sweep_beta_00_0_Poland_2025_Rey_5e5.csv" + # ) + # plot_polars( + # solver_list=[ + # solver_base_version, + # solver_base_version, + # solver_base_version, + # solver_base_version, + # ], + # body_aero_list=[ + # body_aero_CAD_CFD_polars, + # body_aero_CAD_CFD_polars_with_bridles, + # body_aero_CAD_neuralfoil, + # body_aero_masure_regression, + # ], + # label_list=[ + # "VSM CAD CFD Polars", + # "VSM CAD CFD Polars with Bridles", + # "VSM CAD NeuralFoil", + # "VSM CAD Masure Regression", + # "CFD_RANS_Rey_10e5_Poland2025_alpha_sweep_beta_0", + # "Wind Tunnel Data Poland 2025", + # ], + # literature_path_list=[path_cfd_lebesque_alpha, path_wt_data], + # angle_range=[0, 5, 8, 10, 12, 15, 20, 25], + # angle_type="angle_of_attack", + # angle_of_attack=0, + # side_slip=0, + # yaw_rate=0, + # Umag=Umag, + # title="alphasweep", + # data_type=".pdf", + # save_path=Path(save_folder), + # is_save=True, + # is_show=False, + # ) - # Step 5b: Plot beta sweep (side slip) - path_cfd_lebesque_beta = ( - Path(PROJECT_DIR) - / "data" - / "TUDELFT_V3_KITE" - / "3D_polars_literature" - / "CFD_RANS_Rey_10e5_Poland2025_beta_sweep_alpha_13_02.csv" - ) - plot_polars( - solver_list=[ - solver_base_version, - solver_base_version, - solver_base_version, - solver_base_version, - ], - body_aero_list=[ - body_aero_CAD_CFD_polars, - body_aero_CAD_CFD_polars_with_bridles, - body_aero_CAD_neuralfoil, - body_aero_masure_regression, - ], - label_list=[ - "VSM CAD CFD Polars", - "VSM CAD CFD Polars with Bridles", - "VSM CAD NeuralFoil", - "VSM CAD Masure Regression", - "CFD_RANS_Rey_10e5_Poland2025_beta_sweep_alpha_13_02", - ], - literature_path_list=[path_cfd_lebesque_beta], - angle_range=[0, 3, 6, 9, 12], - angle_type="side_slip", - angle_of_attack=6.8, - side_slip=0, - yaw_rate=0, - Umag=3.15, - title="betasweep", - data_type=".pdf", - save_path=Path(save_folder), - is_save=True, - is_show=True, - ) + # # Step 5b: Plot beta sweep (side slip) + # path_cfd_lebesque_beta = ( + # Path(PROJECT_DIR) + # / "data" + # / "TUDELFT_V3_KITE" + # / "3D_polars_literature" + # / "CFD_RANS_Re1e6_beta_sweep_alpha_13_Vire2022_CorrectedByPoland2025.csv" + # ) + # plot_polars( + # solver_list=[ + # solver_base_version, + # solver_base_version, + # solver_base_version, + # solver_base_version, + # ], + # body_aero_list=[ + # body_aero_CAD_CFD_polars, + # body_aero_CAD_CFD_polars_with_bridles, + # body_aero_CAD_neuralfoil, + # body_aero_masure_regression, + # ], + # label_list=[ + # "VSM CAD CFD Polars", + # "VSM CAD CFD Polars with Bridles", + # "VSM CAD NeuralFoil", + # "VSM CAD Masure Regression", + # "CFD_RANS_Re1e6_beta_sweep_alpha_13_Vire2022_CorrectedByPoland2025", + # ], + # literature_path_list=[path_cfd_lebesque_beta], + # angle_range=[0, 3, 6, 9, 12], + # angle_type="side_slip", + # angle_of_attack=6.8, + # side_slip=0, + # yaw_rate=0, + # Umag=3.15, + # title="betasweep", + # data_type=".pdf", + # save_path=Path(save_folder), + # is_save=True, + # is_show=True, + # ) if __name__ == "__main__": diff --git a/src/VSM/plot_geometry_plotly.py b/src/VSM/plot_geometry_plotly.py index 236b62b..abf7140 100644 --- a/src/VSM/plot_geometry_plotly.py +++ b/src/VSM/plot_geometry_plotly.py @@ -411,7 +411,7 @@ def add_bridle_system(fig: go.Figure, wing_aero: object, is_first: bool = True) elif hasattr(wing_aero, "_bridle_line_system") and wing_aero._bridle_line_system: # Handle basic bridle line system (backward compatibility) for i, bridle_line in enumerate(wing_aero._bridle_line_system): - p1, p2, _, _, diameter, _ = bridle_line + p1, p2, diameter = bridle_line # Calculate thickness based on diameter (simple scaling) thickness = max(2, min(12, diameter * 1000)) # Assume diameter in meters @@ -859,4 +859,13 @@ def interactive_plot( fig.write_html(save_path) if is_show: - fig.show() + import tempfile + import webbrowser + + with tempfile.NamedTemporaryFile( + suffix=".html", delete=False, mode="w", encoding="utf-8" + ) as f: + tmp_path = f.name + fig.write_html(f, include_plotlyjs=True, full_html=True) + print(f"Interactive plot saved to: {tmp_path}") + webbrowser.open(f"file://{tmp_path}") From 3b92415ccdbb512eb6b8dd8464b17661f9e2b0a9 Mon Sep 17 00:00:00 2001 From: jellepoland Date: Fri, 24 Jul 2026 11:55:02 +0200 Subject: [PATCH 02/37] Add CLAUDE.md with repo guidance for Claude Code Co-Authored-By: Claude Opus 4.8 (1M context) --- CLAUDE.md | 46 ++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 46 insertions(+) create mode 100644 CLAUDE.md diff --git a/CLAUDE.md b/CLAUDE.md new file mode 100644 index 0000000..fe3990e --- /dev/null +++ b/CLAUDE.md @@ -0,0 +1,46 @@ +# CLAUDE.md + +This file provides guidance to Claude Code (claude.ai/code) when working with code in this repository. + +## Repository purpose + +Python implementation of the Vortex Step Method (VSM): an enhanced lifting-line aerodynamic solver coupled with 2D viscous airfoil polars, aimed at low-aspect-ratio wings and leading-edge inflatable (LEI) kites. Scientific software — physical correctness, numerical stability, and reproducibility outrank abstraction and stylistic churn. **Read `AGENTS.md` before changing solver/aerodynamic logic** (sign conventions, reference frames, and circulation definitions must never change silently). + +## Commands + +```bash +source venv/bin/activate # project venv at ./venv — required; system python lacks deps +pip install -e .[dev] # editable install (dev = pytest, pytest-cov, black) + +pytest # full suite (~35 s), config in pytest.ini (testpaths = tests) +pytest tests/Solver/test_solver.py # one file +pytest tests/Solver/test_solver.py::test_name # one test +black src tests # formatting (used by the project) +``` + +Examples run as plain scripts: `python examples/TUDELFT_V3_KITE/tutorial.py`. CI (`.github/workflows/testing.yml`) runs pytest with coverage on Python 3.10. + +## Architecture (big picture) + +Data flow: **geometry YAML → `BodyAerodynamics.instantiate()` → `Wing`/`Panel` mesh → `Solver.solve()` → results dict → plotting**. + +- `src/VSM/core/BodyAerodynamics.py` — central orchestrator. `BodyAerodynamics.instantiate(n_panels, file_path=, spanwise_panel_distribution=..., bridle_path=...)` reads the YAML's `wing_sections` (headers `[airfoil_id, LE_x..z, TE_x..z]`) and `wing_airfoils` tables, builds polars per airfoil, adds sections to a `Wing`, and refines to `n_panels`. YAML readers index columns **by header name**, so extra columns (e.g. `VUP_x..z` from newer SurfplanAdapter exports) are ignored harmlessly. +- `src/VSM/core/AirfoilAerodynamics.py` — polar generation per airfoil type: `breukels_regression`, `masure_regression` (needs `ml_models_dir`; ~2.3 GB models downloaded from Zenodo into `data/ml_models/`, not in git), `neuralfoil`, `polars` (CSV), `inviscid`. Batch entry point: `from_yaml_entry_batch()`. +- `src/VSM/core/WingGeometry.py` (`Wing`), `Panel.py`, `Filament.py`, `Wake.py` — mesh & vortex elements. **Panels retain only LE/TE points + interpolated polar data**; airfoil `info_dict` parameters (`t`, `chord`, …) are discarded during instantiation — anything needing them later must re-read the YAML. +- `src/VSM/core/Solver.py` — iterative circulation (gamma) loop; optional Anderson acceleration and Li/Gaunaa spanwise artificial viscosity for post-stall stabilization. Returns a results dict (forces, moments, distributions). +- Top-level `src/VSM/` modules build on core: `stability_derivatives.py`, `trim_angle.py`, plus plotting: `plotting.py` (polars/distributions), `plot_geometry_matplotlib.py` (`plot_geometry`), `plot_geometry_plotly.py` (`interactive_plot` — the primary interactive 3D wing view, incl. bridle rendering), `plot_styling.py`. +- Performance-critical vector math is `numba`-jitted (`core/utils.py`). + +## Data layout + +`data//` holds per-kite inputs, e.g. `data/TUDELFT_V3_KITE/`: +- `CAD_derived_geometry/` and `Surfplan_derived_geometry/` — `aero_geometry_*.yaml` variants (one per airfoil-model type) + `struc_geometry_*.yaml` (bridle/particle data, used via `bridle_path`). +- `Surfplan_export/` — raw Surfplan export (`.txt` + `profiles/*.dat`). Converted to VSM YAMLs by the sibling [SurfplanAdapter](https://github.com/awegroup/SurfplanAdapter) project, which also handles the Surfplan→VSM coordinate transform. +- Different YAML sources use different global frames (CAD-derived vs Surfplan-derived origins differ by ~10 m in z) — never mix coordinates across YAML families. + +## Conventions that matter + +- Body-fixed reference frame: **x rearward (LE→TE), y right wing, z up**; α positive nose-up, β positive wind from port. Aircraft-frame conversion via `stability_derivatives.map_derivatives_to_aircraft_frame()`. +- Wing sections are ordered/symmetric tip-to-tip; `airfoil_id` in `wing_sections` must match `wing_airfoils`. +- Style (`docs/style_guide.md`): typed Google docstrings, `snake_case`, path variables end `_path`, directories end `_dir`. +- Tests include verification cases against analytical solutions (`tests/verification_cases/`: elliptical, swept, curved wing, horseshoe vortices) — solver changes must keep these passing; add regression tests when numerical behaviour intentionally changes and explain what changed and why in the commit. From 2eb7fe948de6bcb1fda5b9990110b21a9b7b7bb7 Mon Sep 17 00:00:00 2001 From: jellepoland Date: Fri, 24 Jul 2026 11:55:21 +0200 Subject: [PATCH 03/37] Feat: Fancy Plotly plot with inflatable tubes and curved canopy Add an opt-in 'fancy' mode to interactive_plot that renders the physical inflatable structure of a LEI kite: the leading-edge tube, the chordwise strut tubes, and the curved single-skin canopy. Passing surfplan_dir (a raw Surfplan export: a .txt plus profiles/) triggers a cached SurfplanAdapter conversion; the generated tube-diameter tables and airfoil top-surfaces are then drawn on the wing. Omitting it leaves the plain plot unchanged. - src/VSM/plotly/surfplan_runner.py: run + cache the SurfplanAdapter pipeline - src/VSM/plotly/tube_geometry.py: LE tube (diameter from leading_edge_tubes table) and profile-curved strut tubes (paired tip-to-tip with strut_tubes) - src/VSM/plotly/canopy_geometry.py: loft airfoil upper contours into a canopy - All geometry anchored on the drawn panels, so it is independent of the Surfplan export's coordinate frame - interactive_plot gains surfplan_dir / is_with_canopy / is_with_tube_rings - SurfplanAdapter added as a dependency; tests + tutorial step added Co-Authored-By: Claude Opus 4.8 (1M context) --- .gitignore | 5 +- .../Surfplan_export/TUDELFT_V3_KITE.txt | 214 ++++++++++ .../Surfplan_export/profiles/V3D_AVL.avl | 116 +++++ .../Surfplan_export/profiles/prof_1.dat | 151 +++++++ .../Surfplan_export/profiles/prof_1.png | Bin 0 -> 32884 bytes .../Surfplan_export/profiles/prof_10.dat | 150 +++++++ .../Surfplan_export/profiles/prof_10.png | Bin 0 -> 27808 bytes .../Surfplan_export/profiles/prof_11.dat | 147 +++++++ .../Surfplan_export/profiles/prof_11.png | Bin 0 -> 26726 bytes .../Surfplan_export/profiles/prof_12.dat | 150 +++++++ .../Surfplan_export/profiles/prof_12.png | Bin 0 -> 27674 bytes .../Surfplan_export/profiles/prof_2.dat | 151 +++++++ .../Surfplan_export/profiles/prof_2.png | Bin 0 -> 29174 bytes .../Surfplan_export/profiles/prof_3.dat | 151 +++++++ .../Surfplan_export/profiles/prof_3.png | Bin 0 -> 28812 bytes .../Surfplan_export/profiles/prof_4.dat | 151 +++++++ .../Surfplan_export/profiles/prof_4.png | Bin 0 -> 28645 bytes .../Surfplan_export/profiles/prof_5.dat | 151 +++++++ .../Surfplan_export/profiles/prof_5.png | Bin 0 -> 28548 bytes .../Surfplan_export/profiles/prof_6.dat | 150 +++++++ .../Surfplan_export/profiles/prof_6.png | Bin 0 -> 28785 bytes .../Surfplan_export/profiles/prof_7.dat | 150 +++++++ .../Surfplan_export/profiles/prof_7.png | Bin 0 -> 28076 bytes .../Surfplan_export/profiles/prof_8.dat | 150 +++++++ .../Surfplan_export/profiles/prof_8.png | Bin 0 -> 28054 bytes .../Surfplan_export/profiles/prof_9.dat | 150 +++++++ .../Surfplan_export/profiles/prof_9.png | Bin 0 -> 27972 bytes examples/TUDELFT_V3_KITE/tutorial.py | 23 + pyproject.toml | 1 + src/VSM/plot_geometry_plotly.py | 90 +++- src/VSM/plotly/__init__.py | 24 ++ src/VSM/plotly/canopy_geometry.py | 230 ++++++++++ src/VSM/plotly/surfplan_runner.py | 95 +++++ src/VSM/plotly/tube_geometry.py | 397 ++++++++++++++++++ tests/plotting/test_tube_geometry.py | 196 +++++++++ 35 files changed, 3190 insertions(+), 3 deletions(-) create mode 100644 data/TUDELFT_V3_KITE/Surfplan_export/TUDELFT_V3_KITE.txt create mode 100644 data/TUDELFT_V3_KITE/Surfplan_export/profiles/V3D_AVL.avl create mode 100644 data/TUDELFT_V3_KITE/Surfplan_export/profiles/prof_1.dat create mode 100644 data/TUDELFT_V3_KITE/Surfplan_export/profiles/prof_1.png create mode 100644 data/TUDELFT_V3_KITE/Surfplan_export/profiles/prof_10.dat create mode 100644 data/TUDELFT_V3_KITE/Surfplan_export/profiles/prof_10.png create mode 100644 data/TUDELFT_V3_KITE/Surfplan_export/profiles/prof_11.dat create mode 100644 data/TUDELFT_V3_KITE/Surfplan_export/profiles/prof_11.png create mode 100644 data/TUDELFT_V3_KITE/Surfplan_export/profiles/prof_12.dat create mode 100644 data/TUDELFT_V3_KITE/Surfplan_export/profiles/prof_12.png create mode 100644 data/TUDELFT_V3_KITE/Surfplan_export/profiles/prof_2.dat create mode 100644 data/TUDELFT_V3_KITE/Surfplan_export/profiles/prof_2.png create mode 100644 data/TUDELFT_V3_KITE/Surfplan_export/profiles/prof_3.dat create mode 100644 data/TUDELFT_V3_KITE/Surfplan_export/profiles/prof_3.png create mode 100644 data/TUDELFT_V3_KITE/Surfplan_export/profiles/prof_4.dat create mode 100644 data/TUDELFT_V3_KITE/Surfplan_export/profiles/prof_4.png create mode 100644 data/TUDELFT_V3_KITE/Surfplan_export/profiles/prof_5.dat create mode 100644 data/TUDELFT_V3_KITE/Surfplan_export/profiles/prof_5.png create mode 100644 data/TUDELFT_V3_KITE/Surfplan_export/profiles/prof_6.dat create mode 100644 data/TUDELFT_V3_KITE/Surfplan_export/profiles/prof_6.png create mode 100644 data/TUDELFT_V3_KITE/Surfplan_export/profiles/prof_7.dat create mode 100644 data/TUDELFT_V3_KITE/Surfplan_export/profiles/prof_7.png create mode 100644 data/TUDELFT_V3_KITE/Surfplan_export/profiles/prof_8.dat create mode 100644 data/TUDELFT_V3_KITE/Surfplan_export/profiles/prof_8.png create mode 100644 data/TUDELFT_V3_KITE/Surfplan_export/profiles/prof_9.dat create mode 100644 data/TUDELFT_V3_KITE/Surfplan_export/profiles/prof_9.png create mode 100644 src/VSM/plotly/__init__.py create mode 100644 src/VSM/plotly/canopy_geometry.py create mode 100644 src/VSM/plotly/surfplan_runner.py create mode 100644 src/VSM/plotly/tube_geometry.py create mode 100644 tests/plotting/test_tube_geometry.py diff --git a/.gitignore b/.gitignore index cdd06fd..910c9b8 100644 --- a/.gitignore +++ b/.gitignore @@ -177,4 +177,7 @@ cython_debug/ #.idea/ #Ignore old thesis -Aerostructural_model_LEI \ No newline at end of file +Aerostructural_model_LEI + +# Generated cache from the fancy-plot SurfplanAdapter conversion +vsm_processed/ \ No newline at end of file diff --git a/data/TUDELFT_V3_KITE/Surfplan_export/TUDELFT_V3_KITE.txt b/data/TUDELFT_V3_KITE/Surfplan_export/TUDELFT_V3_KITE.txt new file mode 100644 index 0000000..717e097 --- /dev/null +++ b/data/TUDELFT_V3_KITE/Surfplan_export/TUDELFT_V3_KITE.txt @@ -0,0 +1,214 @@ +Filename: TUDELFT_V3.sle +Design name: 14 hydrav1 07 +Revision: 1.0 +Designer: +Export Date: jeu. 13/02/2025 16:57:57 + +3d rib positions + LE X; Y; Z; TE X; Y; Z; VUP X; Y; Z +24 + 4,156287; 0,916618; 0,520832; 4,156287; 0,916618; -0,864107; 1,352509; 0,297952; 0,000000 + 3,967978; 1,791356; 0,709238; 3,955506; 1,787553; -1,011852; 1,646267; 0,501952; -0,013040 + 3,805350; 2,209568; 0,790880; 3,789238; 2,199439; -1,189372; 1,676461; 1,053982; -0,019032 + 3,501223; 2,540205; 0,864219; 3,485499; 2,522089; -1,256822; 1,390325; 1,601815; -0,023989 + 3,134335; 2,796493; 0,929298; 3,116753; 2,773988; -1,310901; 1,379198; 1,765306; -0,028558 + 2,798300; 3,092998; 0,986158; 2,780285; 3,065722; -1,354755; 1,290075; 1,953351; -0,032688 + 2,393198; 3,288677; 1,034831; 2,380855; 3,254511; -1,390237; 0,824015; 2,280780; -0,036327 + 1,959729; 3,398648; 1,075348; 1,946587; 3,361473; -1,418530; 0,831221; 2,351276; -0,039430 + 1,553762; 3,587398; 1,107733; 1,540958; 3,547442; -1,440421; 0,777640; 2,426595; -0,041958 + 1,111239; 3,671702; 1,132004; 1,107796; 3,627957; -1,456442; 0,203071; 2,580468; -0,043881 + 0,664252; 3,658834; 1,148177; 0,660721; 3,613797; -1,466944; 0,204434; 2,607118; -0,045175 + 0,225013; 3,741837; 1,156262; 0,220752; 3,696209; -1,472144; 0,244401; 2,617018; -0,045826 + -0,225013; 3,741837; 1,156262; -0,220752; 3,696209; -1,472144; -0,244401; 2,617018; -0,045826 + -0,664252; 3,658834; 1,148177; -0,660721; 3,613797; -1,466944; -0,204434; 2,607118; -0,045175 + -1,111239; 3,671702; 1,132004; -1,107796; 3,627957; -1,456442; -0,203071; 2,580468; -0,043881 + -1,553762; 3,587398; 1,107733; -1,540958; 3,547442; -1,440421; -0,777640; 2,426595; -0,041958 + -1,959729; 3,398648; 1,075348; -1,946587; 3,361473; -1,418530; -0,831221; 2,351276; -0,039430 + -2,393198; 3,288677; 1,034831; -2,380855; 3,254511; -1,390237; -0,824015; 2,280780; -0,036327 + -2,798300; 3,092998; 0,986158; -2,780285; 3,065722; -1,354755; -1,290075; 1,953351; -0,032688 + -3,134335; 2,796493; 0,929298; -3,116753; 2,773988; -1,310901; -1,379198; 1,765306; -0,028558 + -3,501223; 2,540205; 0,864219; -3,485499; 2,522089; -1,256822; -1,390325; 1,601815; -0,023989 + -3,805350; 2,209568; 0,790880; -3,789238; 2,199439; -1,189372; -1,676461; 1,053982; -0,019032 + -3,967978; 1,791356; 0,709238; -3,955506; 1,787553; -1,011852; -1,646267; 0,501952; -0,013040 + -4,156287; 0,916618; 0,520832; -4,156287; 0,916618; -0,864107; -1,352509; 0,297952; 0,000000 + +3d curved wingtip positions + LE X; Y; Z; TE X; Y; Z; VUP X; Y; Z +7 + 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2,000000 + 3,148563; 2,814703; 0,256835; 2,644934; 1,015550; 0,607355; e3 ; 1,900910; ; 2,000000 + 0,654966; 3,540403; -1,204082; 1,155974; -0,902939; -0,473306; br1 ; 4,530820; ; 2,000000 + 1,920720; 3,288303; -1,167853; 1,155974; -0,902939; -0,473306; br2 ; 4,316681; ; 2,000000 + 3,069960; 2,714095; -1,085876; 1,921865; -1,309919; -0,396111; br3 ; 4,241059; ; 2,000000 + 3,891515; 1,768042; -0,839226; 1,921865; -1,309919; -0,396111; br4 ; 3,680993; ; 2,000000 + 4,142726; 0,875716; -0,615380; 3,821673; 0,392361; -0,630484; br5 ; 0,580461; ; 2,000000 + 4,137746; 0,864315; -0,791897; 3,821673; 0,392361; -0,630484; br6 ; 0,590505; ; 2,000000 + 1,155974; -0,902939; -0,473306; 1,087879; -3,228214; -0,089481; BR1 ; 2,357724; ; 2,000000 + 1,921865; -1,309919; -0,396111; 1,087879; -3,228214; -0,089481; BR2 ; 2,114098; ; 2,000000 + 3,821673; 0,392361; -0,630484; 0,954417; -3,906964; 0,021095; BR3 ; 5,208639; ; 2,000000 + 1,087879; -3,228214; -0,089481; 0,954417; -3,906964; 0,021095; BRI ; 0,700529; ; 3,000000 + 0,954417; -3,906964; 0,021095; 0,910001; -4,099458; 0,052295; brmain ; 0,200000; ; 4,000000 + diff --git a/data/TUDELFT_V3_KITE/Surfplan_export/profiles/V3D_AVL.avl b/data/TUDELFT_V3_KITE/Surfplan_export/profiles/V3D_AVL.avl new file mode 100644 index 0000000..4519c16 --- /dev/null +++ b/data/TUDELFT_V3_KITE/Surfplan_export/profiles/V3D_AVL.avl @@ -0,0 +1,116 @@ +Empty Project +0.0 | Mach +0 0 0.0 | iYsym iZsym Zsym + + 25.000 2.630 11.180 | Sref Cref Bref + 0.00 0.00 0.00 | Xref Yref Zref + 0.00 | CDp (optional) + + + +#================================================= +SURFACE | (keyword) +14 hydrav1 07 +#Nchord Cspace [ Nspan Sspace ] + 10 1.0 + +INDEX | (keyword) +111 | Lsurf + +YDUPLICATE +0.0 + +SCALE +1.0 1.0 1.0 + +TRANSLATE +0.0 0.0 0.0 + +ANGLE +0.0 | dAinc + +#__________________________________ +SECTION | (keyword) + 0.0000 0.2250 0.0000 2.6288 0.9989 3 0 | Xle Yle Zle Chord Ainc [ Nspan Sspace ] + +AFIL 0.0 1.0 +G:\Shared drives\Hardware\01 - Kite and Bridle (KB)\Archived kites\V3.25\V3.25D\VSM Package\prof_1.dat + +#______________ +SECTION | (keyword) + 0.0081 0.6643 -0.0830 2.6155 0.9897 3 0 | Xle Yle Zle Chord Ainc [ Nspan Sspace ] + +AFIL 0.0 1.0 +G:\Shared drives\Hardware\01 - Kite and Bridle (KB)\Archived kites\V3.25\V3.25D\VSM Package\prof_2.dat + +#______________ +SECTION | (keyword) + 0.0243 1.1112 -0.0701 2.5888 0.9712 3 0 | Xle Yle Zle Chord Ainc [ Nspan Sspace ] + +AFIL 0.0 1.0 +G:\Shared drives\Hardware\01 - Kite and Bridle (KB)\Archived kites\V3.25\V3.25D\VSM Package\prof_3.dat + +#______________ +SECTION | (keyword) + 0.0485 1.5538 -0.1544 2.5485 0.9433 3 0 | Xle Yle Zle Chord Ainc [ Nspan Sspace ] + +AFIL 0.0 1.0 +G:\Shared drives\Hardware\01 - Kite and Bridle (KB)\Archived kites\V3.25\V3.25D\VSM Package\prof_4.dat + +#______________ +SECTION | (keyword) + 0.0809 1.9597 -0.3432 2.4942 0.9058 3 0 | Xle Yle Zle Chord Ainc [ Nspan Sspace ] + +AFIL 0.0 1.0 +G:\Shared drives\Hardware\01 - Kite and Bridle (KB)\Archived kites\V3.25\V3.25D\VSM Package\prof_5.dat + +#______________ +SECTION | (keyword) + 0.1214 2.3932 -0.4532 2.4253 0.8582 3 0 | Xle Yle Zle Chord Ainc [ Nspan Sspace ] + +AFIL 0.0 1.0 +G:\Shared drives\Hardware\01 - Kite and Bridle (KB)\Archived kites\V3.25\V3.25D\VSM Package\prof_6.dat + +#______________ +SECTION | (keyword) + 0.1701 2.7983 -0.6488 2.3411 0.8000 3 0 | Xle Yle Zle Chord Ainc [ Nspan Sspace ] + +AFIL 0.0 1.0 +G:\Shared drives\Hardware\01 - Kite and Bridle (KB)\Archived kites\V3.25\V3.25D\VSM Package\prof_7.dat + +#______________ +SECTION | (keyword) + 0.2270 3.1343 -0.9453 2.2404 0.7304 3 0 | Xle Yle Zle Chord Ainc [ Nspan Sspace ] + +AFIL 0.0 1.0 +G:\Shared drives\Hardware\01 - Kite and Bridle (KB)\Archived kites\V3.25\V3.25D\VSM Package\prof_8.dat + +#______________ +SECTION | (keyword) + 0.2920 3.5012 -1.2016 2.1212 0.6480 3 0 | Xle Yle Zle Chord Ainc [ Nspan Sspace ] + +AFIL 0.0 1.0 +G:\Shared drives\Hardware\01 - Kite and Bridle (KB)\Archived kites\V3.25\V3.25D\VSM 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zvKjK0_d#))iC!U72>ZTH596d+#Ze(?Z&oetyqz*h0vLzJTsccWZ>bb4i`OVZ@@s-{ z1;(-Jh^hH>X@CO(;59anLoOeljFQ0h-fy@d=keoP+2jt@bftkbD2nK(TgAvOK>-|5 zJipOICNFUL%sir|2yB1=1DhrUp1WzzN@y^!p@c5He@plD(D|3ZZMv#cpEZDxDzg|0 z)G&it!+H^RAReM!kH78Aa}htX9OOb{;pD4^KX^z>9d!Hh5kc538ibM{bAWSd53$oz zX~rt0Y_h5uZAN#?Xg66jt z9n0d3-YZ3tWv_@;*vA`B^3?b#hd8hI5`h3coW%5^e4Zw(0S84+Sluj{B+#E$@GM5# zkDLS>-A`h;KWxBjQ4w_~f1mJ9B4BUj%HK&1UGCY&)(D~v1Iv#Ufhi&*DJD{pz^Fzj ziR`K-oazvg@_KZ<JO;9{Ba*OHN*V@yqk*!k$Yj_u?YFkuSbw l=tWU_@oiN97p0*6!.txt' export + and its 'profiles/' directory) switches on the physically-detailed plot. The + export is converted with SurfplanAdapter (cached under the export directory), + and the tube diameters + airfoil top-surfaces are drawn on the wing. The plain + plot above is unaffected when ``surfplan_dir`` is omitted. + """ + # interactive_plot( + # body_aero_CAD_CFD_polars, + # vel=Umag, + # angle_of_attack=angle_of_attack, + # side_slip=side_slip, + # title="TUDELFT_V3_KITE (inflatable tubes + canopy)", + # surfplan_dir=Path(PROJECT_DIR) + # / "data" + # / "TUDELFT_V3_KITE" + # / "Surfplan_export", + # is_with_canopy=True, # curved canopy over the tubes; False -> tubes only + # is_with_tube_rings=False, # True -> also show tube construction rings + # ) + # # Step 5: Plot polar curves for different angles of attack and side slip angles, and save results # """ # Compare the aerodynamic performance of different models by plotting lift, drag, and side force coefficients diff --git a/pyproject.toml b/pyproject.toml index 32412c0..6bd7026 100644 --- a/pyproject.toml +++ b/pyproject.toml @@ -51,6 +51,7 @@ dependencies = [ "numba", "screeninfo", "odfpy", + "SurfplanAdapter", ] [project.optional-dependencies] dev = [ diff --git a/src/VSM/plot_geometry_plotly.py b/src/VSM/plot_geometry_plotly.py index abf7140..88cf6b7 100644 --- a/src/VSM/plot_geometry_plotly.py +++ b/src/VSM/plot_geometry_plotly.py @@ -1,5 +1,6 @@ import os -from typing import List, Tuple, Dict, Any +from pathlib import Path +from typing import List, Tuple, Dict, Any, Optional import numpy as np import plotly.graph_objects as go from VSM.core.Solver import Solver @@ -435,6 +436,9 @@ def create_3D_plot( forces_of_panels: List[np.ndarray], is_with_aerodynamic_details: bool, is_with_bridles: bool = False, + tube_data: Optional[Dict[str, Any]] = None, + canopy_grid: Optional[Tuple[np.ndarray, np.ndarray, np.ndarray]] = None, + is_with_tube_rings: bool = False, ) -> go.Figure: """ Creates an interactive 3D plot of wing geometry using Plotly. @@ -444,10 +448,19 @@ def create_3D_plot( forces_of_panels: List of force vectors for each panel is_with_aerodynamic_details: Boolean to show/hide aerodynamic visualization details is_with_bridles: Boolean to show/hide bridle system visualization + tube_data: Optional inflatable-tube geometry from + ``VSM.plotly.build_tube_data``; when given, the leading-edge and strut + tubes are drawn as surfaces. + canopy_grid: Optional ``(X, Y, Z)`` curved-canopy surface from + ``VSM.plotly.build_canopy_grid``; when given, it replaces the flat + panel surfaces. + is_with_tube_rings: Also draw the tube construction rings (for inspection). Returns: plotly.graph_objects.Figure """ + from VSM.plotly.tube_geometry import add_tube_surfaces, add_tube_rings + panels = wing_aero.panels chord_average = np.max([panel.chord for panel in panels]) @@ -460,6 +473,8 @@ def create_3D_plot( if is_with_bridles: add_bridle_system(fig, wing_aero, is_first=True) + draw_flat_surface = canopy_grid is None + # Add geometric elements for i, panel in enumerate(panels): is_first = False @@ -473,7 +488,8 @@ def create_3D_plot( add_filaments(fig, panel, is_first) add_panel_edges(fig, panel, is_first, is_last) - add_panel_surface(fig, panel, is_first) + if draw_flat_surface: + add_panel_surface(fig, panel, is_first) add_aerodynamic_vectors( fig, panel, @@ -483,9 +499,39 @@ def create_3D_plot( max_force=max_force, ) + # Curved single-skin canopy replaces the flat panel surfaces. + if canopy_grid is not None: + add_canopy_surface(fig, canopy_grid) + + # Inflatable tubes (leading-edge tube + struts). + if tube_data is not None: + add_tube_surfaces(fig, tube_data) + if is_with_tube_rings: + add_tube_rings(fig, tube_data) + return fig +def add_canopy_surface( + fig: go.Figure, canopy_grid: Tuple[np.ndarray, np.ndarray, np.ndarray] +) -> None: + """Add the curved single-skin canopy as a uniformly coloured surface.""" + x, y, z = canopy_grid + fig.add_trace( + go.Surface( + x=x, + y=y, + z=z, + surfacecolor=np.zeros_like(z), + colorscale=[[0, "lightgrey"], [1, "lightgrey"]], + showscale=False, + opacity=0.85, + name="Canopy", + showlegend=True, + ) + ) + + def compute_kite_geometry_ranges(panels: List[Any]) -> Tuple[Dict[str, float], float]: """Calculate axis ranges and tick spacing.""" all_points = [] @@ -754,6 +800,9 @@ def update_plot( is_with_aerodynamic_details: bool, is_with_bridles: bool, title: str, + tube_data: Optional[Dict[str, Any]] = None, + canopy_grid: Optional[Tuple[np.ndarray, np.ndarray, np.ndarray]] = None, + is_with_tube_rings: bool = False, ): # Update AoA and rerun VSM results = running_VSM( @@ -773,6 +822,9 @@ def update_plot( results["F_distribution"], is_with_aerodynamic_details, is_with_bridles, + tube_data=tube_data, + canopy_grid=canopy_grid, + is_with_tube_rings=is_with_tube_rings, ) fig = add_case_information( fig, @@ -804,6 +856,9 @@ def interactive_plot( is_save: bool = False, filename="wing_geometry", is_show: bool = True, + surfplan_dir: Optional[Path] = None, + is_with_canopy: bool = True, + is_with_tube_rings: bool = False, ): """ Creates and optionally saves multiple views of the wing geometry with interactive AoA slider. @@ -823,8 +878,34 @@ def interactive_plot( is_save: Whether to save the plot filename: Base filename for saved files is_show: Whether to display the plot + surfplan_dir: Optional path to a raw Surfplan export (a ``.txt`` plus + a ``profiles/`` directory). When given, the "fancy" plot is drawn: the + export is converted with SurfplanAdapter (cached) and the inflatable + leading-edge and strut tubes -- and, by default, the curved single-skin + canopy -- are rendered on the wing. Leaving it ``None`` keeps the plain + plot unchanged. + is_with_canopy: When a Surfplan export is given, draw the curved canopy + (lofted airfoil top-surfaces) in place of the flat panel surfaces. + is_with_tube_rings: Also draw the tube construction rings (for inspection). + + Returns: + plotly.graph_objects.Figure: The created figure. """ + # Build the optional fancy-plot geometry once (reused on every slider update). + tube_data = None + canopy_grid = None + if surfplan_dir is not None: + from VSM.plotly.surfplan_runner import ensure_surfplan_processed + from VSM.plotly.tube_geometry import build_tube_data + from VSM.plotly.canopy_geometry import load_contour_table, build_canopy_grid + + processed_dir = ensure_surfplan_processed(Path(surfplan_dir)) + tube_data = build_tube_data(wing_aero.panels, processed_dir) + if is_with_canopy: + contour_table = load_contour_table(processed_dir) + canopy_grid = build_canopy_grid(wing_aero.panels, contour_table) + # Create the figure with a default orientation fig = go.Figure() fig.update_layout( @@ -848,6 +929,9 @@ def interactive_plot( is_with_aerodynamic_details, is_with_bridles, title, + tube_data=tube_data, + canopy_grid=canopy_grid, + is_with_tube_rings=is_with_tube_rings, ) # Save or show the plot if requested @@ -869,3 +953,5 @@ def interactive_plot( fig.write_html(f, include_plotlyjs=True, full_html=True) print(f"Interactive plot saved to: {tmp_path}") webbrowser.open(f"file://{tmp_path}") + + return fig diff --git a/src/VSM/plotly/__init__.py b/src/VSM/plotly/__init__.py new file mode 100644 index 0000000..a204699 --- /dev/null +++ b/src/VSM/plotly/__init__.py @@ -0,0 +1,24 @@ +"""Helpers for the interactive Plotly wing plot. + +The public ``interactive_plot`` entry point lives in ``VSM.plot_geometry_plotly`` +(unchanged location for backward compatibility). This subpackage holds the +supporting machinery for the opt-in "fancy" plot that renders the inflatable +tubes and the curved single-skin canopy of a LEI kite from a raw Surfplan export. +""" + +from VSM.plotly.surfplan_runner import ensure_surfplan_processed +from VSM.plotly.tube_geometry import ( + add_tube_rings, + add_tube_surfaces, + build_tube_data, +) +from VSM.plotly.canopy_geometry import build_canopy_grid, load_contour_table + +__all__ = [ + "ensure_surfplan_processed", + "build_tube_data", + "add_tube_surfaces", + "add_tube_rings", + "build_canopy_grid", + "load_contour_table", +] diff --git a/src/VSM/plotly/canopy_geometry.py b/src/VSM/plotly/canopy_geometry.py new file mode 100644 index 0000000..ae4e98c --- /dev/null +++ b/src/VSM/plotly/canopy_geometry.py @@ -0,0 +1,230 @@ +"""Curved single-skin canopy geometry for the interactive Plotly wing plot. + +The canopy is rendered as a loft of the real airfoil top-surfaces (the ``.dat`` +profiles produced by SurfplanAdapter) placed on the *drawn* wing panels. Only the +upper contour is used (LEI kites are single-skin), so the inflatable tubes stay +visible from below. See ``VSM.plotly.tube_geometry`` for the tubes and +``VSM.plotly.surfplan_runner`` for how the source files are generated. + +All geometry is anchored on the drawn ``Panel`` objects (their LE/TE points and +local frame), so the result is independent of the coordinate frame of the source +Surfplan export. +""" + +from pathlib import Path +from typing import Any, List, Tuple + +import numpy as np +import yaml + + +def read_upper_contour(dat_file_path: Path) -> np.ndarray: + """Read an airfoil ``.dat`` file and return its upper contour, LE-to-TE. + + The ``.dat`` files use the standard ordering starting at the trailing edge + ``(1, 0)``, running forward over the upper surface to the leading edge + ``(0, 0)``, then back over the lower surface to the trailing edge. The upper + surface is the run up to the minimum-x (leading edge) point. + + Args: + dat_file_path (Path): Path to the airfoil coordinate file. The first line + is a name label and is skipped; remaining lines are ``x y`` pairs + normalised by the chord. + + Returns: + np.ndarray: Upper contour as an ``(n, 2)`` array ordered from the leading + edge ``(0, 0)`` to the trailing edge ``(1, 0)``. + """ + points = [] + for line in Path(dat_file_path).read_text().splitlines(): + parts = line.split() + if len(parts) != 2: + continue + try: + points.append((float(parts[0]), float(parts[1]))) + except ValueError: + continue + points = np.asarray(points, dtype=float) + le_index = int(np.argmin(points[:, 0])) + upper = points[: le_index + 1] # TE -> LE + return upper[::-1] # LE -> TE + + +def resample_contour(contour: np.ndarray, n_points: int = 40) -> np.ndarray: + """Resample a contour to a fixed point count by arc length. + + Uses cumulative chord-length parameterisation so that the leading- and + trailing-edge endpoints are preserved. This lets contours from different + airfoils be blended point-by-point. + + Args: + contour (np.ndarray): ``(n, 2)`` contour ordered LE-to-TE. + n_points (int): Number of output points. Defaults to 40. + + Returns: + np.ndarray: ``(n_points, 2)`` resampled contour. + """ + segment_lengths = np.linalg.norm(np.diff(contour, axis=0), axis=1) + arc_length = np.concatenate([[0.0], np.cumsum(segment_lengths)]) + total = arc_length[-1] + if total <= 0: + return np.repeat(contour[:1], n_points, axis=0) + sample = np.linspace(0.0, total, n_points) + x = np.interp(sample, arc_length, contour[:, 0]) + y = np.interp(sample, arc_length, contour[:, 1]) + return np.column_stack([x, y]) + + +def load_contour_table( + processed_dir: Path, n_points: int = 40 +) -> List[Tuple[float, np.ndarray]]: + """Build a span-fraction -> upper-contour table from the generated aero yaml. + + Reads ``aero_geometry.yaml`` written by SurfplanAdapter: each wing section + provides its span position (``LE_y``) and an ``airfoil_id`` whose + ``info_dict`` carries the ``dat_file_path``. Span positions are normalised to + fractions of the half-span so the table can be sampled against any drawn wing + regardless of scale or frame. + + Args: + processed_dir (Path): Directory holding ``aero_geometry.yaml`` and the + ``profiles/`` referenced by relative ``dat_file_path`` entries. + n_points (int): Point count each contour is resampled to. Defaults to 40. + + Returns: + List[Tuple[float, np.ndarray]]: ``(span_fraction, contour)`` pairs sorted + by ascending span fraction, each contour an ``(n_points, 2)`` array. + """ + processed_dir = Path(processed_dir) + aero = yaml.safe_load((processed_dir / "aero_geometry.yaml").read_text()) + sections = aero["wing_sections"] + airfoils = aero["wing_airfoils"] + + section_headers = sections["headers"] + idx_id = section_headers.index("airfoil_id") + idx_le_y = section_headers.index("LE_y") + + airfoil_headers = airfoils["headers"] + a_idx_id = airfoil_headers.index("airfoil_id") + a_idx_info = airfoil_headers.index("info_dict") + dat_by_id = { + row[a_idx_id]: row[a_idx_info]["dat_file_path"] for row in airfoils["data"] + } + + contour_cache = {} + span_y = np.array([abs(row[idx_le_y]) for row in sections["data"]]) + half_span = span_y.max() if span_y.max() > 0 else 1.0 + + table = [] + for row in sections["data"]: + airfoil_id = row[idx_id] + if airfoil_id not in contour_cache: + dat_path = processed_dir / dat_by_id[airfoil_id] + contour_cache[airfoil_id] = resample_contour( + read_upper_contour(dat_path), n_points + ) + fraction = abs(row[idx_le_y]) / half_span + table.append((fraction, contour_cache[airfoil_id])) + + table.sort(key=lambda item: item[0]) + return table + + +def interpolate_contour_at( + span_fraction: float, contour_table: List[Tuple[float, np.ndarray]] +) -> np.ndarray: + """Linearly blend the two contours bracketing a span fraction. + + Args: + span_fraction (float): Target fraction of the half-span, in ``[0, 1]``. + contour_table (List[Tuple[float, np.ndarray]]): Output of + :func:`load_contour_table`; contours share a common point count. + + Returns: + np.ndarray: Interpolated contour, clamped to the end contours outside the + table's fraction range. + """ + fractions = [f for f, _ in contour_table] + if span_fraction <= fractions[0]: + return contour_table[0][1] + if span_fraction >= fractions[-1]: + return contour_table[-1][1] + upper = int(np.searchsorted(fractions, span_fraction)) + lower = upper - 1 + f_lo, c_lo = contour_table[lower] + f_hi, c_hi = contour_table[upper] + weight = (span_fraction - f_lo) / (f_hi - f_lo) if f_hi > f_lo else 0.0 + return (1.0 - weight) * c_lo + weight * c_hi + + +def _edge_stations(panels: List[Any]) -> List[dict]: + """Collect the ``n_panels + 1`` spanwise edge stations of the drawn wing. + + Each station carries its leading- and trailing-edge points, the chord vector + and length, and the local up-vector (averaged across adjacent panels), all + taken from the ``Panel`` objects so the canopy sits exactly on the drawn wing. + """ + stations = [] + + def make_station(le_point, te_point, up_vectors): + chord_vector = np.asarray(te_point) - np.asarray(le_point) + chord_length = float(np.linalg.norm(chord_vector)) + chord_hat = chord_vector / max(chord_length, 1e-12) + up = np.mean(up_vectors, axis=0) + up = up / max(np.linalg.norm(up), 1e-12) + return { + "le_point": np.asarray(le_point, dtype=float), + "te_point": np.asarray(te_point, dtype=float), + "chord_length": chord_length, + "chord_hat": chord_hat, + "up": up, + } + + stations.append( + make_station(panels[0].LE_point_1, panels[0].TE_point_1, [panels[0].x_airf]) + ) + for index, panel in enumerate(panels): + neighbours = [panel.x_airf] + if index + 1 < len(panels): + neighbours.append(panels[index + 1].x_airf) + stations.append(make_station(panel.LE_point_2, panel.TE_point_2, neighbours)) + return stations + + +def build_canopy_grid( + panels: List[Any], contour_table: List[Tuple[float, np.ndarray]] +) -> Tuple[np.ndarray, np.ndarray, np.ndarray]: + """Build the lofted canopy surface grid over the drawn wing panels. + + For every panel-edge station the local upper contour (blended from the rib + profiles at that span fraction) is placed on the drawn chord: the contour's + chordwise coordinate runs along the station chord and its height along the + local up-vector, both scaled by the station chord length. + + Args: + panels (List[Any]): Drawn ``Panel`` objects, ordered tip to tip. + contour_table (List[Tuple[float, np.ndarray]]): Output of + :func:`load_contour_table`. + + Returns: + Tuple[np.ndarray, np.ndarray, np.ndarray]: ``X``, ``Y``, ``Z`` arrays of + shape ``(n_panels + 1, n_points)`` suitable for a Plotly surface. + """ + stations = _edge_stations(panels) + all_y = np.array([abs(station["le_point"][1]) for station in stations]) + half_span = all_y.max() if all_y.max() > 0 else 1.0 + + rows = [] + for station in stations: + fraction = abs(station["le_point"][1]) / half_span + contour = interpolate_contour_at(fraction, contour_table) + chord_length = station["chord_length"] + points = ( + station["le_point"][None, :] + + contour[:, 0:1] * chord_length * station["chord_hat"][None, :] + + contour[:, 1:2] * chord_length * station["up"][None, :] + ) + rows.append(points) + + grid = np.stack(rows, axis=0) # (n_stations, n_points, 3) + return grid[:, :, 0], grid[:, :, 1], grid[:, :, 2] diff --git a/src/VSM/plotly/surfplan_runner.py b/src/VSM/plotly/surfplan_runner.py new file mode 100644 index 0000000..f7680fb --- /dev/null +++ b/src/VSM/plotly/surfplan_runner.py @@ -0,0 +1,95 @@ +"""Run SurfplanAdapter to produce the geometry files the fancy plot needs. + +The interactive "fancy" plot needs physical tube diameters and airfoil profiles +that are not present in a plain VSM aero-geometry yaml. They live in a raw +Surfplan export (a ``.txt`` plus a ``profiles/`` directory). This module drives +SurfplanAdapter to convert that export into VSM-readable yaml files, caching the +result so the conversion only runs when the export changes. +""" + +from pathlib import Path +from typing import Optional + + +def _find_surfplan_txt(surfplan_dir: Path) -> Path: + """Return the single ``.txt`` export in ``surfplan_dir`` (error if not one).""" + txt_files = sorted(surfplan_dir.glob("*.txt")) + if not txt_files: + raise FileNotFoundError( + f"No Surfplan '.txt' export found in {surfplan_dir}. Expected a raw " + "Surfplan export (a '.txt' plus a 'profiles/' directory)." + ) + if len(txt_files) > 1: + raise ValueError( + f"Multiple '.txt' files found in {surfplan_dir}: " + f"{[f.name for f in txt_files]}. Keep only the Surfplan export." + ) + return txt_files[0] + + +def ensure_surfplan_processed( + surfplan_dir: Path, output_dir: Optional[Path] = None +) -> Path: + """Convert a raw Surfplan export into VSM geometry yamls, with caching. + + Args: + surfplan_dir (Path): Directory containing the Surfplan ``.txt`` export and + a ``profiles/`` subdirectory of airfoil ``.dat`` files. + output_dir (Optional[Path]): Where to write the generated files. Defaults + to ``surfplan_dir / "vsm_processed"``. + + Returns: + Path: The directory holding the generated ``aero_geometry.yaml``, + ``struc_geometry_all_in_surfplan.yaml`` and ``profiles/``. + + Raises: + ImportError: If SurfplanAdapter is not installed. + FileNotFoundError: If the export ``.txt`` or ``profiles/`` is missing. + """ + surfplan_dir = Path(surfplan_dir) + if output_dir is None: + output_dir = surfplan_dir / "vsm_processed" + output_dir = Path(output_dir) + + txt_path = _find_surfplan_txt(surfplan_dir) + profile_load_dir = surfplan_dir / "profiles" + if not profile_load_dir.is_dir(): + raise FileNotFoundError( + f"No 'profiles/' directory in {surfplan_dir}; the fancy plot needs the " + "airfoil '.dat' files from the Surfplan export." + ) + + aero_yaml = output_dir / "aero_geometry.yaml" + struc_yaml = output_dir / "struc_geometry_all_in_surfplan.yaml" + if ( + aero_yaml.exists() + and struc_yaml.exists() + and aero_yaml.stat().st_mtime >= txt_path.stat().st_mtime + and struc_yaml.stat().st_mtime >= txt_path.stat().st_mtime + ): + return output_dir + + try: + from SurfplanAdapter.process_wing import main_process_wing + from SurfplanAdapter.process_bridle_lines import main_process_bridle_lines + from SurfplanAdapter.generate_yaml import main_generate_yaml + except ImportError as error: + raise ImportError( + "The fancy plot requires SurfplanAdapter to convert the raw Surfplan " + "export. Install it with 'pip install SurfplanAdapter'." + ) from error + + output_dir.mkdir(parents=True, exist_ok=True) + ribs_data = main_process_wing.main( + surfplan_txt_file_path=txt_path, + profile_load_dir=profile_load_dir, + profile_save_dir=output_dir / "profiles", + is_make_plots=False, + ) + bridle_lines = main_process_bridle_lines.main(txt_path) + main_generate_yaml.main( + ribs_data=ribs_data, + bridle_lines=bridle_lines, + yaml_file_path=output_dir / "config_kite.yaml", + ) + return output_dir diff --git a/src/VSM/plotly/tube_geometry.py b/src/VSM/plotly/tube_geometry.py new file mode 100644 index 0000000..f6fad66 --- /dev/null +++ b/src/VSM/plotly/tube_geometry.py @@ -0,0 +1,397 @@ +"""Inflatable-tube geometry for the interactive Plotly wing plot. + +Builds lofted 3D surfaces for the leading-edge tube and the chordwise strut tubes +of a LEI kite, using the physical tube-diameter tables produced by SurfplanAdapter +(``leading_edge_tubes`` and ``strut_tubes`` in +``struc_geometry_all_in_surfplan.yaml``) together with the airfoil top-surface +contours (see ``VSM.plotly.canopy_geometry``). + +Diameters are physical (metres) and sourced from the generated tables; positions +are anchored on the *drawn* ``Panel`` objects, so tubes always sit on the wing +that is actually plotted, independent of the Surfplan export's coordinate frame: + +* Leading-edge tube: centred just aft of the drawn LE polyline, diameter + interpolated from the ``leading_edge_tubes`` table by span fraction (this + captures the tapering tip, which ``t * chord`` does not). +* Struts: placed at the ``is_strut`` rib span fractions, shaped to follow the + local airfoil top-surface and offset downward so the tube top touches the + canopy underside. Per-strut LE/TE diameters come from the ``strut_tubes`` table + paired tip-to-tip with the strut ribs (both are symmetric and span-ordered, so + the pairing does not rely on the table's node indices). +""" + +from pathlib import Path +from typing import Any, Callable, Dict, List, Tuple + +import numpy as np +import plotly.graph_objects as go +import yaml + +from VSM.plotly.canopy_geometry import interpolate_contour_at, load_contour_table + +TUBE_COLOR = "#2c7fb8" +TUBE_OPACITY = 0.5 +RING_COLOR = "#08306b" + + +def circle_points( + center: np.ndarray, axis: np.ndarray, diameter: float, n: int = 24 +) -> np.ndarray: + """Ring of ``n`` points of the given diameter, perpendicular to ``axis``. + + Args: + center (np.ndarray): Ring centre, shape ``(3,)``. + axis (np.ndarray): Tube axis at this station; the ring lies in the plane + normal to it. + diameter (float): Ring diameter. + n (int): Number of points around the ring. Defaults to 24. + + Returns: + np.ndarray: ``(n, 3)`` ring points, closed (first point repeated at end). + """ + axis = np.asarray(axis, dtype=float) + axis = axis / max(np.linalg.norm(axis), 1e-12) + helper = np.array([0.0, 0.0, 1.0]) + if abs(axis @ helper) > 0.9: + helper = np.array([0.0, 1.0, 0.0]) + e1 = np.cross(axis, helper) + e1 = e1 / max(np.linalg.norm(e1), 1e-12) + e2 = np.cross(axis, e1) + theta = np.linspace(0.0, 2.0 * np.pi, n) + radius = 0.5 * float(diameter) + return ( + np.asarray(center, dtype=float)[None, :] + + radius * np.cos(theta)[:, None] * e1[None, :] + + radius * np.sin(theta)[:, None] * e2[None, :] + ) + + +def load_le_diameter_interp(processed_dir: Path) -> Callable[[float], float]: + """Return a leading-edge diameter(span-fraction) interpolator. + + Builds the interpolator from the ``leading_edge_tubes`` segment table: each + segment midpoint gives a ``(|y| fraction, diameter)`` sample. Fractions are + of the half-span so the curve can be sampled against any drawn wing. + + Args: + processed_dir (Path): Directory holding + ``struc_geometry_all_in_surfplan.yaml``. + + Returns: + Callable[[float], float]: Function mapping a span fraction in ``[0, 1]`` + to a leading-edge tube diameter in metres. + """ + struc = yaml.safe_load( + (Path(processed_dir) / "struc_geometry_all_in_surfplan.yaml").read_text() + ) + particles = { + int(row[0]): np.asarray(row[1:4], dtype=float) + for row in struc["wing_particles"]["data"] + } + le = struc["leading_edge_tubes"] + idx_ci = le["headers"].index("ci") + idx_cj = le["headers"].index("cj") + idx_d = le["headers"].index("diameter") + + y_mid = [] + diam = [] + for row in le["data"]: + ci = particles[int(row[idx_ci])] + cj = particles[int(row[idx_cj])] + y_mid.append(0.5 * (ci[1] + cj[1])) + diam.append(float(row[idx_d])) + y_mid = np.abs(np.asarray(y_mid)) + diam = np.asarray(diam) + half_span = y_mid.max() if y_mid.max() > 0 else 1.0 + fractions = y_mid / half_span + + order = np.argsort(fractions) + frac_sorted = fractions[order] + diam_sorted = diam[order] + + def interp(span_fraction: float) -> float: + return float(np.interp(span_fraction, frac_sorted, diam_sorted)) + + return interp + + +def load_strut_diameter_table(processed_dir: Path) -> List[Tuple[float, float]]: + """Per-strut ``(diam_le, diam_te)`` pairs in span order (tip to tip). + + Args: + processed_dir (Path): Directory holding + ``struc_geometry_all_in_surfplan.yaml``. + + Returns: + List[Tuple[float, float]]: Leading- and trailing-edge strut-tube diameters + in metres, in the table's listed (span) order. + """ + struc = yaml.safe_load( + (Path(processed_dir) / "struc_geometry_all_in_surfplan.yaml").read_text() + ) + st = struc["strut_tubes"] + idx_le = st["headers"].index("strut_diam_le") + idx_te = st["headers"].index("strut_diam_te") + return [(float(row[idx_le]), float(row[idx_te])) for row in st["data"]] + + +def load_strut_span_fractions(processed_dir: Path) -> np.ndarray: + """Signed span fractions of the strut ribs, from the generated aero yaml. + + Uses the ``is_strut`` flag in each section's airfoil ``info_dict``. Fractions + are ``LE_y`` normalised by the half-span, returned sorted by descending span + (``+tip`` to ``-tip``) to match the ``strut_tubes`` table order. + + Args: + processed_dir (Path): Directory holding ``aero_geometry.yaml``. + + Returns: + np.ndarray: Signed span fractions of the strut ribs, high to low. + """ + aero = yaml.safe_load((Path(processed_dir) / "aero_geometry.yaml").read_text()) + sections = aero["wing_sections"] + airfoils = aero["wing_airfoils"] + idx_id = sections["headers"].index("airfoil_id") + idx_le_y = sections["headers"].index("LE_y") + a_idx_id = airfoils["headers"].index("airfoil_id") + a_idx_info = airfoils["headers"].index("info_dict") + is_strut_by_id = { + row[a_idx_id]: bool(row[a_idx_info].get("is_strut", False)) + for row in airfoils["data"] + } + + span_y = np.array([abs(row[idx_le_y]) for row in sections["data"]]) + half_span = span_y.max() if span_y.max() > 0 else 1.0 + strut_y = [ + row[idx_le_y] + for row in sections["data"] + if is_strut_by_id.get(row[idx_id], False) + ] + fractions = np.array(sorted(strut_y, reverse=True)) / half_span + return fractions + + +def _drawn_stations(panels: List[Any]) -> Dict[str, np.ndarray]: + """Spanwise edge stations of the drawn wing as stacked arrays. + + Returns leading/trailing points, chord lengths, chord and up unit vectors, and + signed span fractions for the ``n_panels + 1`` panel edges, sorted by span. + """ + le = [panels[0].LE_point_1] + [p.LE_point_2 for p in panels] + te = [panels[0].TE_point_1] + [p.TE_point_2 for p in panels] + up = [panels[0].x_airf] + for index, panel in enumerate(panels): + neighbours = [panel.x_airf] + if index + 1 < len(panels): + neighbours.append(panels[index + 1].x_airf) + up.append(np.mean(neighbours, axis=0)) + + le = np.asarray(le, dtype=float) + te = np.asarray(te, dtype=float) + up = np.asarray(up, dtype=float) + up = up / np.linalg.norm(up, axis=1, keepdims=True).clip(1e-12) + chord_vec = te - le + chord_len = np.linalg.norm(chord_vec, axis=1) + chord_hat = chord_vec / chord_len[:, None].clip(1e-12) + + half_span = np.abs(le[:, 1]).max() + half_span = half_span if half_span > 0 else 1.0 + fraction = le[:, 1] / half_span + + order = np.argsort(fraction) + return { + "le": le[order], + "te": te[order], + "up": up[order], + "chord_len": chord_len[order], + "chord_hat": chord_hat[order], + "fraction": fraction[order], + } + + +def _station_at(stations: Dict[str, np.ndarray], signed_fraction: float) -> dict: + """Interpolate a drawn-wing station at a signed span fraction.""" + frac = stations["fraction"] + le = np.array( + [np.interp(signed_fraction, frac, stations["le"][:, i]) for i in range(3)] + ) + te = np.array( + [np.interp(signed_fraction, frac, stations["te"][:, i]) for i in range(3)] + ) + up = np.array( + [np.interp(signed_fraction, frac, stations["up"][:, i]) for i in range(3)] + ) + up = up / max(np.linalg.norm(up), 1e-12) + chord_vec = te - le + chord_len = float(np.linalg.norm(chord_vec)) + chord_hat = chord_vec / max(chord_len, 1e-12) + return { + "le": le, + "te": te, + "up": up, + "chord_len": chord_len, + "chord_hat": chord_hat, + } + + +def build_le_tube( + panels: List[Any], le_diameter_interp: Callable[[float], float] +) -> List[np.ndarray]: + """Build the leading-edge tube as a list of cross-section rings. + + The tube runs spanwise along the drawn LE polyline; each ring is centred just + aft of the LE point (so the tube front touches the drawn leading edge) and its + diameter is looked up from the LE table at the local span fraction. + + Args: + panels (List[Any]): Drawn ``Panel`` objects, ordered tip to tip. + le_diameter_interp (Callable[[float], float]): Output of + :func:`load_le_diameter_interp`. + + Returns: + List[np.ndarray]: One ``(n, 3)`` ring per spanwise station. + """ + stations = _drawn_stations(panels) + le = stations["le"] + fraction = np.abs(stations["fraction"]) + diameters = np.array([le_diameter_interp(f) for f in fraction]) + centers = le + 0.5 * diameters[:, None] * stations["chord_hat"] + + rings = [] + for index in range(len(centers)): + lo = max(index - 1, 0) + hi = min(index + 1, len(centers) - 1) + tangent = centers[hi] - centers[lo] + rings.append(circle_points(centers[index], tangent, diameters[index])) + return rings + + +def build_strut( + stations: Dict[str, np.ndarray], + contour_table, + signed_fraction: float, + diam_le: float, + diam_te: float, +) -> List[np.ndarray]: + """Build one chordwise strut tube hugging the canopy underside. + + The local airfoil top-surface is placed on the drawn wing at the strut span, + then each chord station is offset downward by the local strut radius so the + tube top touches the canopy. Diameter tapers linearly from ``diam_le`` at the + leading edge to ``diam_te`` at the trailing edge. + + Args: + stations (Dict[str, np.ndarray]): Output of :func:`_drawn_stations`. + contour_table: Output of ``canopy_geometry.load_contour_table``. + signed_fraction (float): Signed span fraction of the strut rib. + diam_le (float): Strut-tube diameter at the leading edge, metres. + diam_te (float): Strut-tube diameter at the trailing edge, metres. + + Returns: + List[np.ndarray]: One ``(n, 3)`` ring per chordwise station. + """ + station = _station_at(stations, signed_fraction) + contour = interpolate_contour_at(abs(signed_fraction), contour_table) + chord_len = station["chord_len"] + + canopy_points = ( + station["le"][None, :] + + contour[:, 0:1] * chord_len * station["chord_hat"][None, :] + + contour[:, 1:2] * chord_len * station["up"][None, :] + ) + chord_fraction = contour[:, 0] + diameters = diam_le + (diam_te - diam_le) * chord_fraction + centers = canopy_points - 0.5 * diameters[:, None] * station["up"][None, :] + + rings = [] + for index in range(len(centers)): + lo = max(index - 1, 0) + hi = min(index + 1, len(centers) - 1) + tangent = centers[hi] - centers[lo] + rings.append(circle_points(centers[index], tangent, diameters[index])) + return rings + + +def build_tube_data(panels: List[Any], processed_dir: Path) -> Dict[str, Any]: + """Assemble leading-edge and strut tube rings for the drawn wing. + + Args: + panels (List[Any]): Drawn ``Panel`` objects, ordered tip to tip. + processed_dir (Path): Directory of SurfplanAdapter-generated files. + + Returns: + Dict[str, Any]: ``{"le": [rings], "struts": [[rings], ...]}``. + """ + processed_dir = Path(processed_dir) + le_interp = load_le_diameter_interp(processed_dir) + contour_table = load_contour_table(processed_dir) + strut_fractions = load_strut_span_fractions(processed_dir) + strut_table = load_strut_diameter_table(processed_dir) + + le_rings = build_le_tube(panels, le_interp) + + stations = _drawn_stations(panels) + struts = [] + for index, signed_fraction in enumerate(strut_fractions): + if index < len(strut_table): + diam_le, diam_te = strut_table[index] + else: + # Fallback: size the strut from the local LE tube diameter. + diam_le = le_interp(abs(signed_fraction)) + diam_te = 0.6 * diam_le + struts.append( + build_strut(stations, contour_table, signed_fraction, diam_le, diam_te) + ) + return {"le": le_rings, "struts": struts} + + +def _rings_to_surface( + rings: List[np.ndarray], +) -> Tuple[np.ndarray, np.ndarray, np.ndarray]: + """Stack a list of rings into ``X``, ``Y``, ``Z`` surface arrays.""" + grid = np.stack(rings, axis=0) # (n_rings, n_circle, 3) + return grid[:, :, 0], grid[:, :, 1], grid[:, :, 2] + + +def _add_surface(fig: go.Figure, rings: List[np.ndarray], name: str, show_legend: bool): + """Add one tube as a uniformly coloured, semi-transparent surface.""" + x, y, z = _rings_to_surface(rings) + fig.add_trace( + go.Surface( + x=x, + y=y, + z=z, + surfacecolor=np.zeros_like(z), + colorscale=[[0, TUBE_COLOR], [1, TUBE_COLOR]], + showscale=False, + opacity=TUBE_OPACITY, + name=name, + showlegend=show_legend, + ) + ) + + +def add_tube_surfaces(fig: go.Figure, tube_data: Dict[str, Any]) -> None: + """Add the leading-edge and strut tube surfaces to the figure.""" + _add_surface(fig, tube_data["le"], "Leading-edge tube", show_legend=True) + for index, strut in enumerate(tube_data["struts"]): + _add_surface(fig, strut, "Strut tube", show_legend=(index == 0)) + + +def add_tube_rings(fig: go.Figure, tube_data: Dict[str, Any]) -> None: + """Add the construction rings (wireframe circles) for inspection.""" + all_rings = list(tube_data["le"]) + [ + r for strut in tube_data["struts"] for r in strut + ] + for index, ring in enumerate(all_rings): + fig.add_trace( + go.Scatter3d( + x=ring[:, 0], + y=ring[:, 1], + z=ring[:, 2], + mode="lines", + line=dict(color=RING_COLOR, width=1), + name="Tube rings", + showlegend=(index == 0), + ) + ) diff --git a/tests/plotting/test_tube_geometry.py b/tests/plotting/test_tube_geometry.py new file mode 100644 index 0000000..2bc5cff --- /dev/null +++ b/tests/plotting/test_tube_geometry.py @@ -0,0 +1,196 @@ +"""Tests for the fancy Plotly plot: inflatable tubes and curved canopy. + +Unit tests cover the pure geometry helpers (ring math, contour handling, +interpolation). The integration tests exercise the full SurfplanAdapter +conversion and figure assembly against the bundled TUDELFT V3 Surfplan export; +they are skipped if SurfplanAdapter or the export data are unavailable. +""" + +from pathlib import Path + +import numpy as np +import pytest + +from VSM.plotly.canopy_geometry import ( + interpolate_contour_at, + read_upper_contour, + resample_contour, +) +from VSM.plotly.tube_geometry import circle_points + +REPO_ROOT = Path(__file__).resolve().parents[2] +SURFPLAN_DIR = REPO_ROOT / "data" / "TUDELFT_V3_KITE" / "Surfplan_export" +DRAWN_YAML = ( + REPO_ROOT + / "data" + / "TUDELFT_V3_KITE" + / "CAD_derived_geometry" + / "aero_geometry_CAD_breukels_regression.yaml" +) + + +def _has_surfplan(): + try: + import SurfplanAdapter # noqa: F401 + except ImportError: + return False + return SURFPLAN_DIR.is_dir() + + +requires_surfplan = pytest.mark.skipif( + not _has_surfplan(), reason="SurfplanAdapter or Surfplan export data unavailable" +) + + +# --------------------------------------------------------------------------- # +# Unit tests -- pure geometry helpers +# --------------------------------------------------------------------------- # + + +def test_circle_points_radius_and_orthogonality(): + center = np.array([1.0, 2.0, 3.0]) + axis = np.array([0.0, 1.0, 0.0]) + diameter = 0.4 + ring = circle_points(center, axis, diameter, n=32) + + # Every point lies at the radius from the centre. + radii = np.linalg.norm(ring - center, axis=1) + assert np.allclose(radii, 0.5 * diameter, atol=1e-9) + + # The ring lies in the plane normal to the axis (constant projection). + projections = (ring - center) @ axis + assert np.allclose(projections, 0.0, atol=1e-9) + + +def test_circle_points_axis_normalisation_invariant(): + center = np.zeros(3) + ring_unit = circle_points(center, np.array([0.0, 0.0, 1.0]), 1.0) + ring_scaled = circle_points(center, np.array([0.0, 0.0, 5.0]), 1.0) + assert np.allclose(ring_unit, ring_scaled, atol=1e-9) + + +def test_resample_contour_count_and_endpoints(): + contour = np.array([[0.0, 0.0], [0.3, 0.08], [0.7, 0.05], [1.0, 0.0]]) + resampled = resample_contour(contour, n_points=25) + assert resampled.shape == (25, 2) + assert np.allclose(resampled[0], contour[0], atol=1e-9) + assert np.allclose(resampled[-1], contour[-1], atol=1e-9) + + +def test_interpolate_contour_at_blends_and_clamps(): + c_lo = np.array([[0.0, 0.0], [1.0, 0.0]]) + c_hi = np.array([[0.0, 0.0], [1.0, 1.0]]) + table = [(0.0, c_lo), (1.0, c_hi)] + + # Midpoint is the average of the two contours. + mid = interpolate_contour_at(0.5, table) + assert np.allclose(mid, 0.5 * (c_lo + c_hi)) + + # Outside the range clamps to the end contours. + assert np.allclose(interpolate_contour_at(-1.0, table), c_lo) + assert np.allclose(interpolate_contour_at(2.0, table), c_hi) + + +def test_read_upper_contour_ordering(tmp_path): + # Minimal Selig-style .dat: TE -> upper -> LE -> lower -> TE. + dat = tmp_path / "prof.dat" + dat.write_text( + "test_profile\n" "1.0 0.0\n" "0.5 0.08\n" "0.0 0.0\n" "0.5 -0.04\n" "1.0 0.0\n" + ) + upper = read_upper_contour(dat) + # Ordered LE (x=0) to TE (x=1), all upper-surface points. + assert upper[0, 0] == pytest.approx(0.0) + assert upper[-1, 0] == pytest.approx(1.0) + assert np.all(np.diff(upper[:, 0]) > 0) + assert np.all(upper[:, 1] >= 0.0) + + +# --------------------------------------------------------------------------- # +# Integration tests -- full conversion + figure assembly +# --------------------------------------------------------------------------- # + + +@requires_surfplan +def test_ensure_surfplan_processed_and_cache(): + from VSM.plotly.surfplan_runner import ensure_surfplan_processed + + processed = ensure_surfplan_processed(SURFPLAN_DIR) + aero = processed / "aero_geometry.yaml" + struc = processed / "struc_geometry_all_in_surfplan.yaml" + assert aero.exists() and struc.exists() + + # Second call is a cache hit: the generated file is not rewritten. + first_mtime = aero.stat().st_mtime + ensure_surfplan_processed(SURFPLAN_DIR) + assert aero.stat().st_mtime == first_mtime + + +@requires_surfplan +def test_build_tube_and_canopy_shapes(): + from VSM.core.BodyAerodynamics import BodyAerodynamics + from VSM.plotly.surfplan_runner import ensure_surfplan_processed + from VSM.plotly.tube_geometry import build_tube_data, load_strut_span_fractions + from VSM.plotly.canopy_geometry import build_canopy_grid, load_contour_table + + n_panels = 36 + body = BodyAerodynamics.instantiate( + n_panels=n_panels, + file_path=DRAWN_YAML, + spanwise_panel_distribution="uniform", + ) + panels = body.panels + processed = ensure_surfplan_processed(SURFPLAN_DIR) + + tube = build_tube_data(panels, processed) + n_struts = len(load_strut_span_fractions(processed)) + assert len(tube["le"]) == n_panels + 1 + assert len(tube["struts"]) == n_struts + + x, y, z = build_canopy_grid(panels, load_contour_table(processed)) + assert x.shape[0] == n_panels + 1 + assert x.shape == y.shape == z.shape + + # Tubes track the drawn wing span (within a tube radius at the tips). + wing_le = np.array([p.LE_point_1 for p in panels] + [p.LE_point_2 for p in panels]) + tube_pts = np.vstack(list(tube["le"])) + assert abs(tube_pts[:, 1].max() - wing_le[:, 1].max()) < 0.2 + + +@requires_surfplan +def test_interactive_plot_fancy_traces(): + import plotly.graph_objects as go + from VSM.core.BodyAerodynamics import BodyAerodynamics + from VSM.plot_geometry_plotly import interactive_plot + from VSM.plotly.tube_geometry import load_strut_span_fractions + from VSM.plotly.surfplan_runner import ensure_surfplan_processed + + body = BodyAerodynamics.instantiate( + n_panels=36, + file_path=DRAWN_YAML, + spanwise_panel_distribution="uniform", + ) + n_struts = len(load_strut_span_fractions(ensure_surfplan_processed(SURFPLAN_DIR))) + + # Fancy plot with canopy: surfaces = canopy + LE tube + struts, no flat panels. + fig = interactive_plot(body, surfplan_dir=SURFPLAN_DIR, is_show=False) + surfaces = [t for t in fig.data if isinstance(t, go.Surface)] + flat_panels = [ + t for t in fig.data if isinstance(t, go.Mesh3d) and t.name == "Panel Surface" + ] + assert len(surfaces) == 1 + 1 + n_struts + assert len(flat_panels) == 0 + + # Tubes only: flat panels kept, no canopy surface. + fig2 = interactive_plot( + body, surfplan_dir=SURFPLAN_DIR, is_with_canopy=False, is_show=False + ) + surfaces2 = [t for t in fig2.data if isinstance(t, go.Surface)] + flat_panels2 = [ + t for t in fig2.data if isinstance(t, go.Mesh3d) and t.name == "Panel Surface" + ] + assert len(surfaces2) == 1 + n_struts + assert len(flat_panels2) == len(body.panels) + + # Plain plot is unchanged: no surfaces at all. + fig3 = interactive_plot(body, is_show=False) + assert not [t for t in fig3.data if isinstance(t, go.Surface)] From f3005aa806095098b38a6e8d50f8c0578ae63d84 Mon Sep 17 00:00:00 2001 From: jellepoland Date: Fri, 24 Jul 2026 13:20:48 +0200 Subject: [PATCH 04/37] Refine inflatable tube geometry: strut-to-LE join, tip wrap, framing - Struts now start at the leading-edge tube's aft edge (buried half a tube depth in) instead of passing straight through it - Leading-edge tube wraps around each wingtip and continues to the trailing edge of the outer panel (constant-diameter, tip-to-tip continuous) - Twist-free parallel-transport ring framing (rings_along_centerline) so the swept surfaces do not pinch where the tube turns at the tips - Solid (opaque) tubes so the leading-edge tube reads clearly over the canopy - Split add_tube_surfaces into add_strut_surfaces / add_le_tube_surface so the leading-edge tube can be drawn last (on top) Co-Authored-By: Claude Opus 4.8 (1M context) --- src/VSM/plotly/tube_geometry.py | 190 ++++++++++++++++++++++----- tests/plotting/test_tube_geometry.py | 3 +- 2 files changed, 160 insertions(+), 33 deletions(-) diff --git a/src/VSM/plotly/tube_geometry.py b/src/VSM/plotly/tube_geometry.py index f6fad66..adafdda 100644 --- a/src/VSM/plotly/tube_geometry.py +++ b/src/VSM/plotly/tube_geometry.py @@ -29,13 +29,17 @@ from VSM.plotly.canopy_geometry import interpolate_contour_at, load_contour_table -TUBE_COLOR = "#2c7fb8" -TUBE_OPACITY = 0.5 +TUBE_COLOR = "black" +TUBE_OPACITY = 1.0 RING_COLOR = "#08306b" def circle_points( - center: np.ndarray, axis: np.ndarray, diameter: float, n: int = 24 + center: np.ndarray, + axis: np.ndarray, + diameter: float, + n: int = 24, + ref: np.ndarray = None, ) -> np.ndarray: """Ring of ``n`` points of the given diameter, perpendicular to ``axis``. @@ -45,15 +49,27 @@ def circle_points( normal to it. diameter (float): Ring diameter. n (int): Number of points around the ring. Defaults to 24. + ref (np.ndarray): Optional reference vector fixing the azimuthal origin of + the ring. Passing the *same* ``ref`` for every ring of a tube keeps + consecutive rings consistently oriented, which avoids the surface + twisting where the tube tangent swings (e.g. at a wingtip). Falls back + to an automatic helper when ``ref`` is parallel to the axis. Returns: np.ndarray: ``(n, 3)`` ring points, closed (first point repeated at end). """ axis = np.asarray(axis, dtype=float) axis = axis / max(np.linalg.norm(axis), 1e-12) - helper = np.array([0.0, 0.0, 1.0]) - if abs(axis @ helper) > 0.9: - helper = np.array([0.0, 1.0, 0.0]) + if ref is not None: + helper = np.asarray(ref, dtype=float) + if abs(axis @ (helper / max(np.linalg.norm(helper), 1e-12))) > 0.98: + helper = np.array([0.0, 0.0, 1.0]) + if abs(axis @ helper) > 0.9: + helper = np.array([0.0, 1.0, 0.0]) + else: + helper = np.array([0.0, 0.0, 1.0]) + if abs(axis @ helper) > 0.9: + helper = np.array([0.0, 1.0, 0.0]) e1 = np.cross(axis, helper) e1 = e1 / max(np.linalg.norm(e1), 1e-12) e2 = np.cross(axis, e1) @@ -66,6 +82,61 @@ def circle_points( ) +def rings_along_centerline( + centers: np.ndarray, diameters: np.ndarray, n: int = 24 +) -> List[np.ndarray]: + """Sweep circular rings along a centreline with twist-free framing. + + The ring frame is parallel-transported from one station to the next (the + previous in-plane axis is projected onto the new normal plane) instead of + being chosen independently per ring. This keeps the swept surface from + twisting or pinching where the centreline curves sharply -- e.g. where the + leading-edge tube turns chordwise at a wingtip. + + Args: + centers (np.ndarray): ``(m, 3)`` centreline points. + diameters (np.ndarray): ``(m,)`` local tube diameters. + n (int): Number of points around each ring. Defaults to 24. + + Returns: + List[np.ndarray]: One ``(n, 3)`` ring per centreline station. + """ + centers = np.asarray(centers, dtype=float) + diameters = np.asarray(diameters, dtype=float) + m = len(centers) + + tangents = np.zeros_like(centers) + tangents[1:-1] = centers[2:] - centers[:-2] + tangents[0] = centers[1] - centers[0] + tangents[-1] = centers[-1] - centers[-2] + tangents /= np.linalg.norm(tangents, axis=1, keepdims=True).clip(1e-12) + + def _seed_axis(tangent): + ref = np.array([0.0, 0.0, 1.0]) + if abs(tangent @ ref) > 0.9: + ref = np.array([0.0, 1.0, 0.0]) + axis = ref - (ref @ tangent) * tangent + return axis / max(np.linalg.norm(axis), 1e-12) + + theta = np.linspace(0.0, 2.0 * np.pi, n) + e1 = _seed_axis(tangents[0]) + rings = [] + for index in range(m): + # Parallel-transport the previous in-plane axis onto this normal plane. + e1 = e1 - (e1 @ tangents[index]) * tangents[index] + if np.linalg.norm(e1) < 1e-8: + e1 = _seed_axis(tangents[index]) + e1 /= max(np.linalg.norm(e1), 1e-12) + e2 = np.cross(tangents[index], e1) + radius = 0.5 * diameters[index] + rings.append( + centers[index][None, :] + + radius * np.cos(theta)[:, None] * e1[None, :] + + radius * np.sin(theta)[:, None] * e2[None, :] + ) + return rings + + def load_le_diameter_interp(processed_dir: Path) -> Callable[[float], float]: """Return a leading-edge diameter(span-fraction) interpolator. @@ -234,36 +305,59 @@ def _station_at(stations: Dict[str, np.ndarray], signed_fraction: float) -> dict } +def _tip_extension(le_center, te_point, le_diameter, n=8, taper=1.0): + """Centreline points + diameters continuing from a tip LE to the TE. + + Extends the leading-edge tube at the wingtip so it runs on to the trailing + edge of the outer panel, at (by default) constant diameter for a clean tube. + """ + ts = np.linspace(0.0, 1.0, n + 1)[1:] # exclude 0 (the LE centre already exists) + le_center = np.asarray(le_center, dtype=float) + te_point = np.asarray(te_point, dtype=float) + points = [le_center + t * (te_point - le_center) for t in ts] + diams = [le_diameter * (1.0 - (1.0 - taper) * t) for t in ts] + return points, diams + + def build_le_tube( - panels: List[Any], le_diameter_interp: Callable[[float], float] + panels: List[Any], + le_diameter_interp: Callable[[float], float], + extend_tips: bool = True, ) -> List[np.ndarray]: """Build the leading-edge tube as a list of cross-section rings. The tube runs spanwise along the drawn LE polyline; each ring is centred just aft of the LE point (so the tube front touches the drawn leading edge) and its - diameter is looked up from the LE table at the local span fraction. + diameter is looked up from the LE table at the local span fraction. With + ``extend_tips`` the tube wraps around each wingtip and continues toward the + trailing edge, tapering closed. Args: panels (List[Any]): Drawn ``Panel`` objects, ordered tip to tip. le_diameter_interp (Callable[[float], float]): Output of :func:`load_le_diameter_interp`. + extend_tips (bool): Wrap the tube from each tip toward the trailing edge. Returns: - List[np.ndarray]: One ``(n, 3)`` ring per spanwise station. + List[np.ndarray]: One ``(n, 3)`` ring per centreline station. """ stations = _drawn_stations(panels) le = stations["le"] + te = stations["te"] fraction = np.abs(stations["fraction"]) diameters = np.array([le_diameter_interp(f) for f in fraction]) centers = le + 0.5 * diameters[:, None] * stations["chord_hat"] - rings = [] - for index in range(len(centers)): - lo = max(index - 1, 0) - hi = min(index + 1, len(centers) - 1) - tangent = centers[hi] - centers[lo] - rings.append(circle_points(centers[index], tangent, diameters[index])) - return rings + center_list = list(centers) + diam_list = list(diameters) + if extend_tips: + neg_pts, neg_d = _tip_extension(centers[0], te[0], diameters[0]) + pos_pts, pos_d = _tip_extension(centers[-1], te[-1], diameters[-1]) + # Prepend the -tip wrap (reversed: TE -> LE) and append the +tip wrap. + center_list = neg_pts[::-1] + center_list + pos_pts + diam_list = neg_d[::-1] + diam_list + pos_d + + return rings_along_centerline(np.array(center_list), np.array(diam_list)) def build_strut( @@ -272,6 +366,7 @@ def build_strut( signed_fraction: float, diam_le: float, diam_te: float, + le_tube_diameter: float = 0.0, ) -> List[np.ndarray]: """Build one chordwise strut tube hugging the canopy underside. @@ -280,12 +375,19 @@ def build_strut( tube top touches the canopy. Diameter tapers linearly from ``diam_le`` at the leading edge to ``diam_te`` at the trailing edge. + The strut starts at the aft edge of the leading-edge tube (chord fraction + ``le_tube_diameter / chord`` -- the LE tube spans that far back from the drawn + LE) rather than at the leading edge, so it butts against the LE tube instead + of passing straight through it. + Args: stations (Dict[str, np.ndarray]): Output of :func:`_drawn_stations`. contour_table: Output of ``canopy_geometry.load_contour_table``. signed_fraction (float): Signed span fraction of the strut rib. diam_le (float): Strut-tube diameter at the leading edge, metres. diam_te (float): Strut-tube diameter at the trailing edge, metres. + le_tube_diameter (float): Local leading-edge tube diameter, metres; sets + where the strut starts. Zero means start at the leading edge. Returns: List[np.ndarray]: One ``(n, 3)`` ring per chordwise station. @@ -294,22 +396,27 @@ def build_strut( contour = interpolate_contour_at(abs(signed_fraction), contour_table) chord_len = station["chord_len"] + # Start the strut partway into the leading-edge tube (half its depth) so the + # forward cap is buried inside the LE tube -- no gap, no through-poke. + le_tube_depth_fraction = le_tube_diameter / max(chord_len, 1e-12) + start_fraction = min(0.5 * le_tube_depth_fraction, 0.9) + cx = contour[:, 0] + cy = contour[:, 1] + keep = cx > start_fraction + if start_fraction > 0 and keep.any(): + cx = np.concatenate([[start_fraction], cx[keep]]) + cy = np.concatenate( + [[float(np.interp(start_fraction, contour[:, 0], cy))], cy[keep]] + ) + canopy_points = ( station["le"][None, :] - + contour[:, 0:1] * chord_len * station["chord_hat"][None, :] - + contour[:, 1:2] * chord_len * station["up"][None, :] + + cx[:, None] * chord_len * station["chord_hat"][None, :] + + cy[:, None] * chord_len * station["up"][None, :] ) - chord_fraction = contour[:, 0] - diameters = diam_le + (diam_te - diam_le) * chord_fraction + diameters = diam_le + (diam_te - diam_le) * cx centers = canopy_points - 0.5 * diameters[:, None] * station["up"][None, :] - - rings = [] - for index in range(len(centers)): - lo = max(index - 1, 0) - hi = min(index + 1, len(centers) - 1) - tangent = centers[hi] - centers[lo] - rings.append(circle_points(centers[index], tangent, diameters[index])) - return rings + return rings_along_centerline(centers, diameters) def build_tube_data(panels: List[Any], processed_dir: Path) -> Dict[str, Any]: @@ -339,8 +446,16 @@ def build_tube_data(panels: List[Any], processed_dir: Path) -> Dict[str, Any]: # Fallback: size the strut from the local LE tube diameter. diam_le = le_interp(abs(signed_fraction)) diam_te = 0.6 * diam_le + le_tube_diameter = le_interp(abs(signed_fraction)) struts.append( - build_strut(stations, contour_table, signed_fraction, diam_le, diam_te) + build_strut( + stations, + contour_table, + signed_fraction, + diam_le, + diam_te, + le_tube_diameter=le_tube_diameter, + ) ) return {"le": le_rings, "struts": struts} @@ -367,17 +482,28 @@ def _add_surface(fig: go.Figure, rings: List[np.ndarray], name: str, show_legend opacity=TUBE_OPACITY, name=name, showlegend=show_legend, + lighting=dict(ambient=0.75, diffuse=0.8, specular=0.05, roughness=0.9), ) ) -def add_tube_surfaces(fig: go.Figure, tube_data: Dict[str, Any]) -> None: - """Add the leading-edge and strut tube surfaces to the figure.""" - _add_surface(fig, tube_data["le"], "Leading-edge tube", show_legend=True) +def add_strut_surfaces(fig: go.Figure, tube_data: Dict[str, Any]) -> None: + """Add the strut tube surfaces to the figure.""" for index, strut in enumerate(tube_data["struts"]): _add_surface(fig, strut, "Strut tube", show_legend=(index == 0)) +def add_le_tube_surface(fig: go.Figure, tube_data: Dict[str, Any]) -> None: + """Add the leading-edge tube surface to the figure.""" + _add_surface(fig, tube_data["le"], "Leading-edge tube", show_legend=True) + + +def add_tube_surfaces(fig: go.Figure, tube_data: Dict[str, Any]) -> None: + """Add the leading-edge and strut tube surfaces to the figure.""" + add_le_tube_surface(fig, tube_data) + add_strut_surfaces(fig, tube_data) + + def add_tube_rings(fig: go.Figure, tube_data: Dict[str, Any]) -> None: """Add the construction rings (wireframe circles) for inspection.""" all_rings = list(tube_data["le"]) + [ diff --git a/tests/plotting/test_tube_geometry.py b/tests/plotting/test_tube_geometry.py index 2bc5cff..2d43889 100644 --- a/tests/plotting/test_tube_geometry.py +++ b/tests/plotting/test_tube_geometry.py @@ -143,7 +143,8 @@ def test_build_tube_and_canopy_shapes(): tube = build_tube_data(panels, processed) n_struts = len(load_strut_span_fractions(processed)) - assert len(tube["le"]) == n_panels + 1 + # LE tube has one ring per panel edge, plus the wrap-around tip extensions. + assert len(tube["le"]) >= n_panels + 1 assert len(tube["struts"]) == n_struts x, y, z = build_canopy_grid(panels, load_contour_table(processed)) From 7f4d749e9f4f4aa4724b9e4cd21b8d3d62017a42 Mon Sep 17 00:00:00 2001 From: jellepoland Date: Fri, 24 Jul 2026 13:21:01 +0200 Subject: [PATCH 05/37] Fancy plot: panel toggle, surface-normal force grid, draw order - interactive_plot gains is_with_panels (default off in fancy mode); when off the panel outlines are hidden and drawn thin/blue when on - Replace the per-panel force arrows over the canopy with a grid of equal, surface-normal vectors: one row per panel x 10 chordwise nodes placed at the true 5%-95% chord fractions (clear of the LE tube and trailing edge) - Draw order: struts under the canopy, then canopy, then the vector grid, then the leading-edge tube last so it is never occluded - Canopy recoloured grey; matte surface lighting - Make the figure axis-range helper skip None/NaN gap separators Co-Authored-By: Claude Opus 4.8 (1M context) --- src/VSM/plot_geometry_plotly.py | 297 ++++++++++++++++++++++----- tests/plotting/test_tube_geometry.py | 15 +- 2 files changed, 254 insertions(+), 58 deletions(-) diff --git a/src/VSM/plot_geometry_plotly.py b/src/VSM/plot_geometry_plotly.py index 88cf6b7..99ba553 100644 --- a/src/VSM/plot_geometry_plotly.py +++ b/src/VSM/plot_geometry_plotly.py @@ -7,41 +7,56 @@ import yaml -def add_panel_edges(fig: go.Figure, panel: Any, is_first: bool, is_last: bool) -> None: - """Add panel edges to the figure with different thicknesses.""" - leadinge_edge_line_color = "black" - leadinge_edge_line_width = 15 - # Leading edge - if is_first: - # Include 1-side edge - fig.add_trace( - go.Scatter3d( - x=[panel.LE_point_1[0], panel.TE_point_1[0]], - y=[panel.LE_point_1[1], panel.TE_point_1[1]], - z=[panel.LE_point_1[2], panel.TE_point_1[2]], - mode="lines", - line=dict( - color=leadinge_edge_line_color, width=leadinge_edge_line_width - ), - name="Leading Edge", - showlegend=False, +def add_panel_edges( + fig: go.Figure, + panel: Any, + is_first: bool, + is_last: bool, + is_thin_outline: bool = False, +) -> None: + """Add panel edges to the figure. + + By default the leading edge is drawn as a thick black line. With + ``is_thin_outline`` (used by the fancy plot, where the inflatable leading-edge + tube already marks the leading edge) all panel edges are thin grey outlines + and the thick leading-edge line is omitted. + """ + edge_color = "blue" if is_thin_outline else "black" + if is_thin_outline: + leadinge_edge_line_color = "blue" + leadinge_edge_line_width = 1.5 + else: + leadinge_edge_line_color = "black" + leadinge_edge_line_width = 15 + # Thick tip edges only make sense for the thick leading-edge style. + if is_first: + fig.add_trace( + go.Scatter3d( + x=[panel.LE_point_1[0], panel.TE_point_1[0]], + y=[panel.LE_point_1[1], panel.TE_point_1[1]], + z=[panel.LE_point_1[2], panel.TE_point_1[2]], + mode="lines", + line=dict( + color=leadinge_edge_line_color, width=leadinge_edge_line_width + ), + name="Leading Edge", + showlegend=False, + ) ) - ) - elif is_last: - # Include 1-side edge - fig.add_trace( - go.Scatter3d( - x=[panel.LE_point_2[0], panel.TE_point_2[0]], - y=[panel.LE_point_2[1], panel.TE_point_2[1]], - z=[panel.LE_point_2[2], panel.TE_point_2[2]], - mode="lines", - line=dict( - color=leadinge_edge_line_color, width=leadinge_edge_line_width - ), - name="Leading Edge", - showlegend=False, + elif is_last: + fig.add_trace( + go.Scatter3d( + x=[panel.LE_point_2[0], panel.TE_point_2[0]], + y=[panel.LE_point_2[1], panel.TE_point_2[1]], + z=[panel.LE_point_2[2], panel.TE_point_2[2]], + mode="lines", + line=dict( + color=leadinge_edge_line_color, width=leadinge_edge_line_width + ), + name="Leading Edge", + showlegend=False, + ) ) - ) # Standard leading edge fig.add_trace( go.Scatter3d( @@ -62,7 +77,7 @@ def add_panel_edges(fig: go.Figure, panel: Any, is_first: bool, is_last: bool) - y=[panel.TE_point_1[1], panel.TE_point_2[1]], z=[panel.TE_point_1[2], panel.TE_point_2[2]], mode="lines", - line=dict(color="black", width=2), + line=dict(color=edge_color, width=2), name="Trailing Edge", showlegend=is_first, ) @@ -78,7 +93,7 @@ def add_panel_edges(fig: go.Figure, panel: Any, is_first: bool, is_last: bool) - y=[points[0][1], points[1][1]], z=[points[0][2], points[1][2]], mode="lines", - line=dict(color="black", width=0.8), + line=dict(color=edge_color, width=0.8), name=( "Side Edge" if is_first and i == 0 else None ), # Legend only for the first side edge @@ -176,6 +191,7 @@ def add_aerodynamic_vectors( force_vector: np.ndarray, scale: float = 0.5, max_force: float = 1.0, + origin: np.ndarray = None, ): """ Add aerodynamic force vectors to a given panel on the plot. @@ -185,9 +201,12 @@ def add_aerodynamic_vectors( panel: Panel object force_of_panel: Aerodynamic force vector scale: Scaling factor for the force vector + origin: Optional vector origin. Defaults to the panel aerodynamic centre; + pass a point on the canopy surface to make the vectors emanate from + the surface when the panels are hidden. """ # Compute vector endpoint - aerodynamic_center = panel.aerodynamic_center + aerodynamic_center = panel.aerodynamic_center if origin is None else origin vector = (force_vector / max_force) * scale * 0.5 vector_endpoint = aerodynamic_center + vector @@ -439,6 +458,7 @@ def create_3D_plot( tube_data: Optional[Dict[str, Any]] = None, canopy_grid: Optional[Tuple[np.ndarray, np.ndarray, np.ndarray]] = None, is_with_tube_rings: bool = False, + is_with_panels: bool = True, ) -> go.Figure: """ Creates an interactive 3D plot of wing geometry using Plotly. @@ -455,11 +475,18 @@ def create_3D_plot( ``VSM.plotly.build_canopy_grid``; when given, it replaces the flat panel surfaces. is_with_tube_rings: Also draw the tube construction rings (for inspection). + is_with_panels: Draw the panel outlines. When ``False`` and a canopy is + present, the force vectors are lifted onto the canopy surface instead + of starting at the flat panel aerodynamic centres. Returns: plotly.graph_objects.Figure """ - from VSM.plotly.tube_geometry import add_tube_surfaces, add_tube_rings + from VSM.plotly.tube_geometry import ( + add_strut_surfaces, + add_le_tube_surface, + add_tube_rings, + ) panels = wing_aero.panels @@ -474,6 +501,12 @@ def create_3D_plot( add_bridle_system(fig, wing_aero, is_first=True) draw_flat_surface = canopy_grid is None + # In the fancy plot the inflatable LE tube marks the leading edge, so draw the + # panels as thin grey outlines instead of the thick black leading-edge line. + is_thin_outline = tube_data is not None + # On the canopy the per-panel force vectors are replaced by a set of equal, + # surface-normal vectors distributed across the span (see below). + use_distributed_vectors = canopy_grid is not None # Add geometric elements for i, panel in enumerate(panels): @@ -487,25 +520,39 @@ def create_3D_plot( if is_with_aerodynamic_details: add_filaments(fig, panel, is_first) - add_panel_edges(fig, panel, is_first, is_last) - if draw_flat_surface: + if is_with_panels: + add_panel_edges( + fig, panel, is_first, is_last, is_thin_outline=is_thin_outline + ) + if draw_flat_surface and is_with_panels: add_panel_surface(fig, panel, is_first) - add_aerodynamic_vectors( - fig, - panel, - is_first, - np.array(forces_of_panels[i]), - scale=chord_average, - max_force=max_force, - ) - # Curved single-skin canopy replaces the flat panel surfaces. + if not use_distributed_vectors: + add_aerodynamic_vectors( + fig, + panel, + is_first, + np.array(forces_of_panels[i]), + scale=chord_average, + max_force=max_force, + ) + + # Draw order (so the leading-edge tube ends up rendered on top): struts sit + # under the canopy, then the canopy, then the force vectors, and finally the + # leading-edge tube last so it is never occluded by the semi-transparent canopy. + if tube_data is not None: + add_strut_surfaces(fig, tube_data) + if canopy_grid is not None: add_canopy_surface(fig, canopy_grid) - # Inflatable tubes (leading-edge tube + struts). + if use_distributed_vectors: + add_distributed_surface_vectors( + fig, canopy_grid, forces_of_panels, scale=chord_average + ) + if tube_data is not None: - add_tube_surfaces(fig, tube_data) + add_le_tube_surface(fig, tube_data) if is_with_tube_rings: add_tube_rings(fig, tube_data) @@ -516,6 +563,7 @@ def add_canopy_surface( fig: go.Figure, canopy_grid: Tuple[np.ndarray, np.ndarray, np.ndarray] ) -> None: """Add the curved single-skin canopy as a uniformly coloured surface.""" + canopy_color = "lightgrey" x, y, z = canopy_grid fig.add_trace( go.Surface( @@ -523,11 +571,138 @@ def add_canopy_surface( y=y, z=z, surfacecolor=np.zeros_like(z), - colorscale=[[0, "lightgrey"], [1, "lightgrey"]], + colorscale=[[0, canopy_color], [1, canopy_color]], showscale=False, opacity=0.85, name="Canopy", showlegend=True, + lighting=dict(ambient=0.75, diffuse=0.8, specular=0.05, roughness=0.9), + ) + ) + + +def add_distributed_surface_vectors( + fig: go.Figure, + canopy_grid: Tuple[np.ndarray, np.ndarray, np.ndarray], + forces_of_panels: List[np.ndarray], + scale: float, + n_chord: int = 10, + n_span: int = None, +) -> None: + """Draw a grid of equal, surface-normal force vectors on the canopy. + + One row of ``n_chord`` nodes is placed at each panel centre (uniformly over + the chord); every node carries one equal-length arrow oriented along the local + canopy surface normal (the outward/suction side). This gives a regular + ``n_span x n_chord`` grid of vectors covering the whole canopy. + + Args: + fig: Plotly figure. + canopy_grid: ``(X, Y, Z)`` canopy surface arrays, each ``(S, P)`` with + ``S`` spanwise stations and ``P`` chordwise points. + forces_of_panels: Per-panel aerodynamic force vectors (used only to skip + drawing when there is no force). + scale: Length scale (typically the average chord). + n_chord: Nodes per row, distributed over the chord. Defaults to 10. + n_span: Number of spanwise rows. Defaults to one row per panel (the + midpoints between the ``S`` canopy stations, i.e. ``S - 1`` rows). + """ + x, y, z = canopy_grid + grid = np.stack([x, y, z], axis=-1) # (S, P, 3) + + force_magnitudes = np.linalg.norm(np.asarray(forces_of_panels), axis=1) + if force_magnitudes.size == 0 or np.max(force_magnitudes) <= 0: + return + + # One row per panel: use the midpoints between adjacent canopy stations. + panel_grid = 0.5 * (grid[:-1] + grid[1:]) # (S - 1, P, 3) + n_rows, n_points, _ = panel_grid.shape + + if n_span is None: + n_span = n_rows + span_rows = np.unique( + np.clip(np.round(np.linspace(0, n_rows - 1, n_span)), 0, n_rows - 1).astype(int) + ) + + # Surface-normal field over the panel-centre grid. + d_chord = np.gradient(panel_grid, axis=1) + d_span = np.gradient(panel_grid, axis=0) + normal_field = np.cross(d_chord, d_span) + normal_field /= np.linalg.norm(normal_field, axis=-1, keepdims=True).clip(1e-12) + normal_field[normal_field[:, :, 2] < 0] *= -1 # outward (suction) side + + # Sample each row at the exact target chord fractions (5%-95%). The grid + # columns are arc-length spaced, so interpolate by true chord fraction rather + # than snapping to columns -- this keeps vectors clear of the leading-edge + # tube (near 0%) and the trailing edge (near 100%). + targets = np.linspace(0.05, 0.95, n_chord) + origins = [] + normals = [] + for row in span_rows: + pts = panel_grid[row] # (P, 3) + chord_vector = pts[-1] - pts[0] + chord_length = np.linalg.norm(chord_vector) + chord_hat = chord_vector / max(chord_length, 1e-12) + chord_fraction = ((pts - pts[0]) @ chord_hat) / max(chord_length, 1e-12) + order = np.argsort(chord_fraction) + frac_sorted = chord_fraction[order] + pts_sorted = pts[order] + nrm_sorted = normal_field[row][order] + for target in targets: + point = np.array( + [np.interp(target, frac_sorted, pts_sorted[:, k]) for k in range(3)] + ) + normal = np.array( + [np.interp(target, frac_sorted, nrm_sorted[:, k]) for k in range(3)] + ) + norm = np.linalg.norm(normal) + if norm < 1e-9: + continue + origins.append(point) + normals.append(normal / norm) + + if not origins: + return + origins = np.array(origins) + normals = np.array(normals) + + # Equal arrow length, scaled to the chordwise node spacing so the grid reads + # cleanly without the arrows overlapping badly. + length = 0.9 * scale / max(n_chord, 1) + endpoints = origins + normals * length + + # All stems as one trace (None-separated segments), all heads as one cone trace. + stem_x, stem_y, stem_z = [], [], [] + for start, end in zip(origins, endpoints): + stem_x += [start[0], end[0], None] + stem_y += [start[1], end[1], None] + stem_z += [start[2], end[2], None] + fig.add_trace( + go.Scatter3d( + x=stem_x, + y=stem_y, + z=stem_z, + mode="lines", + line=dict(color="red", width=3), + name="Aerodynamic Vectors", + showlegend=True, + ) + ) + fig.add_trace( + go.Cone( + x=endpoints[:, 0], + y=endpoints[:, 1], + z=endpoints[:, 2], + u=normals[:, 0] * length, + v=normals[:, 1] * length, + w=normals[:, 2] * length, + sizemode="absolute", + sizeref=length / 3, + anchor="tip", + colorscale=[[0, "red"], [1, "red"]], + showscale=False, + name="Arrowheads", + showlegend=False, ) ) @@ -553,14 +728,18 @@ def compute_axis_parameters_from_fig( fig: go.Figure, ) -> Tuple[Dict[str, float], float]: """Calculate axis ranges and tick spacing based on the figure's data.""" - # Extract all data points from the figure traces + # Extract all data points from the figure traces, skipping gap separators + # (``None``/NaN) that traces may use to draw multiple segments at once. all_points = [] for trace in fig.data: if isinstance(trace, go.Scatter3d): - all_points.extend(zip(trace.x, trace.y, trace.z)) + for px, py, pz in zip(trace.x, trace.y, trace.z): + if px is None or py is None or pz is None: + continue + all_points.append((px, py, pz)) # Convert to numpy array for calculations - all_points = np.array(all_points) + all_points = np.array(all_points, dtype=float) # Calculate ranges for each axis ranges = { @@ -803,6 +982,7 @@ def update_plot( tube_data: Optional[Dict[str, Any]] = None, canopy_grid: Optional[Tuple[np.ndarray, np.ndarray, np.ndarray]] = None, is_with_tube_rings: bool = False, + is_with_panels: bool = True, ): # Update AoA and rerun VSM results = running_VSM( @@ -825,6 +1005,7 @@ def update_plot( tube_data=tube_data, canopy_grid=canopy_grid, is_with_tube_rings=is_with_tube_rings, + is_with_panels=is_with_panels, ) fig = add_case_information( fig, @@ -859,6 +1040,7 @@ def interactive_plot( surfplan_dir: Optional[Path] = None, is_with_canopy: bool = True, is_with_tube_rings: bool = False, + is_with_panels: Optional[bool] = None, ): """ Creates and optionally saves multiple views of the wing geometry with interactive AoA slider. @@ -887,10 +1069,16 @@ def interactive_plot( is_with_canopy: When a Surfplan export is given, draw the curved canopy (lofted airfoil top-surfaces) in place of the flat panel surfaces. is_with_tube_rings: Also draw the tube construction rings (for inspection). + is_with_panels: Draw the panel outlines. Defaults to ``False`` for the + fancy plot (a Surfplan export is given) and ``True`` otherwise. When + off, the force vectors are lifted onto the canopy surface. Returns: plotly.graph_objects.Figure: The created figure. """ + # Default: hide the panel outlines for the fancy plot, show them otherwise. + if is_with_panels is None: + is_with_panels = surfplan_dir is None # Build the optional fancy-plot geometry once (reused on every slider update). tube_data = None @@ -932,6 +1120,7 @@ def interactive_plot( tube_data=tube_data, canopy_grid=canopy_grid, is_with_tube_rings=is_with_tube_rings, + is_with_panels=is_with_panels, ) # Save or show the plot if requested diff --git a/tests/plotting/test_tube_geometry.py b/tests/plotting/test_tube_geometry.py index 2d43889..26c4236 100644 --- a/tests/plotting/test_tube_geometry.py +++ b/tests/plotting/test_tube_geometry.py @@ -172,18 +172,24 @@ def test_interactive_plot_fancy_traces(): ) n_struts = len(load_strut_span_fractions(ensure_surfplan_processed(SURFPLAN_DIR))) - # Fancy plot with canopy: surfaces = canopy + LE tube + struts, no flat panels. + # Fancy plot with canopy (panels default off): surfaces = canopy + LE + struts. fig = interactive_plot(body, surfplan_dir=SURFPLAN_DIR, is_show=False) surfaces = [t for t in fig.data if isinstance(t, go.Surface)] flat_panels = [ t for t in fig.data if isinstance(t, go.Mesh3d) and t.name == "Panel Surface" ] + le_outline = [t for t in fig.data if getattr(t, "name", None) == "Leading Edge"] assert len(surfaces) == 1 + 1 + n_struts assert len(flat_panels) == 0 + assert len(le_outline) == 0 # panel outlines hidden by default in fancy mode - # Tubes only: flat panels kept, no canopy surface. + # Tubes only with panels explicitly on: flat panels kept, no canopy surface. fig2 = interactive_plot( - body, surfplan_dir=SURFPLAN_DIR, is_with_canopy=False, is_show=False + body, + surfplan_dir=SURFPLAN_DIR, + is_with_canopy=False, + is_with_panels=True, + is_show=False, ) surfaces2 = [t for t in fig2.data if isinstance(t, go.Surface)] flat_panels2 = [ @@ -192,6 +198,7 @@ def test_interactive_plot_fancy_traces(): assert len(surfaces2) == 1 + n_struts assert len(flat_panels2) == len(body.panels) - # Plain plot is unchanged: no surfaces at all. + # Plain plot is unchanged: panels shown, no surfaces at all. fig3 = interactive_plot(body, is_show=False) assert not [t for t in fig3.data if isinstance(t, go.Surface)] + assert [t for t in fig3.data if getattr(t, "name", None) == "Leading Edge"] From 282cbbc90fc88faa177e68f20431d8d0eb55e846 Mon Sep 17 00:00:00 2001 From: jellepoland Date: Fri, 24 Jul 2026 14:39:03 +0200 Subject: [PATCH 06/37] Fancy plot: Cp-distributed chord-normal force vectors from AoA database Replace the equal surface-normal vector grid with a physically-scaled loading: - New VSM.plotly.cp_distributions: treat data/.../cpx_distributions as a Cp database keyed by AoA; select the closest available angle to the operating point and extract the upper (suction) surface |Cp|(x/c) - Each panel's VSM force is distributed chordwise, weighted by |Cp| (even split without a Cp dir); the node forces of a panel sum back to that panel's force - Vectors point normal to the local chord line (flat-panel up), constant per section, at the true 5%-95% chord fractions - Normalise force->length so the largest panel force plots at the maximum chord length; modest fixed-size arrowheads - interactive_plot gains cp_distributions_dir; add the V3 Cp/Cf data files and Cp-database tests Co-Authored-By: Claude Opus 4.8 (1M context) --- .../cpx_distributions/README.md | 34 +++++ .../cpx_distributions/cf_AOA_2.dat | 78 +++++++++++ .../cpx_distributions/cf_AOA_6.dat | 103 +++++++++++++++ .../cpx_distributions/cf_AOA_8.dat | 104 +++++++++++++++ .../cpx_distributions/cp_AOA_2.dat | 45 +++++++ .../cpx_distributions/cp_AOA_6.dat | 55 ++++++++ .../cpx_distributions/cp_AOA_8.dat | 59 +++++++++ src/VSM/plot_geometry_plotly.py | 124 +++++++++++++----- src/VSM/plotly/cp_distributions.py | 97 ++++++++++++++ tests/plotting/test_tube_geometry.py | 57 ++++++++ 10 files changed, 724 insertions(+), 32 deletions(-) create mode 100644 data/TUDELFT_V3_KITE/cpx_distributions/README.md create mode 100644 data/TUDELFT_V3_KITE/cpx_distributions/cf_AOA_2.dat create mode 100755 data/TUDELFT_V3_KITE/cpx_distributions/cf_AOA_6.dat create mode 100644 data/TUDELFT_V3_KITE/cpx_distributions/cf_AOA_8.dat create mode 100644 data/TUDELFT_V3_KITE/cpx_distributions/cp_AOA_2.dat create mode 100755 data/TUDELFT_V3_KITE/cpx_distributions/cp_AOA_6.dat create mode 100644 data/TUDELFT_V3_KITE/cpx_distributions/cp_AOA_8.dat create mode 100644 src/VSM/plotly/cp_distributions.py diff --git a/data/TUDELFT_V3_KITE/cpx_distributions/README.md b/data/TUDELFT_V3_KITE/cpx_distributions/README.md new file mode 100644 index 0000000..d328489 --- /dev/null +++ b/data/TUDELFT_V3_KITE/cpx_distributions/README.md @@ -0,0 +1,34 @@ +# TU Delft V3 kite — 2D Cp(x/c) distributions + +Chordwise pressure-coefficient (`cp_AOA_*.dat`) and skin-friction (`cf_AOA_*.dat`) +distributions for the **TU Delft V3 LEI kite midspan airfoil section** (rigid 2D), +from RANS CFD (Thijs/Kasper). + +File format: whitespace columns `# x y Cp` (or `... Cf`), i.e. column 0 = x/c, +column 1 = y/c, column 2 = Cp (or Cf). + +## Contents + +| Angle of attack | Cp file | Cf file | +|---|---|---| +| 2° | `cp_AOA_2.dat` | `cf_AOA_2.dat` | +| 6° | `cp_AOA_6.dat` | `cf_AOA_6.dat` | +| 8° | `cp_AOA_8.dat` | `cf_AOA_8.dat` | + +These are the only angles for which the genuine V3 midspan section Cp distribution +is available locally. + +## Provenance + +Copied from `WES_aero_sim_for_kite_design/data/`: +- AoA 2° and 8°: `cp_cf_kasper/` +- AoA 6°: `THIJS_CFD_alpha_6_V3_turbulent/postProcessing/surfaces/624/` + +The V3 section is identified by its airfoil geometry embedded in the files: +~13.4% thickness, max camber y ≈ 0.0953 (chord normalised to 1). + +## Not included + +`Pointwise-Openfoam-toolchain/.../cp_AOA_10.dat` was **excluded**: it is a generic +demo LEI profile from the Pointwise→OpenFOAM toolchain (~12.4% thickness, +`tube_size=0.08, c_x=0.15, c_y=0.08`), **not** the V3 section. diff --git a/data/TUDELFT_V3_KITE/cpx_distributions/cf_AOA_2.dat b/data/TUDELFT_V3_KITE/cpx_distributions/cf_AOA_2.dat new file mode 100644 index 0000000..2d874b9 --- /dev/null +++ b/data/TUDELFT_V3_KITE/cpx_distributions/cf_AOA_2.dat @@ -0,0 +1,78 @@ +# x y Cf +0.04276388755929555 0.06356556861711357 -5.3685492635529e-05 +0.03309840970977389 0.04825624850833229 -3.582704828999522e-08 +0.06326602268098154 0.03073779662338421 6.167786129151704e-05 +0.07384327410599092 0.01793640188203612 -0.0003192609764164146 +0.07660775307689469 0.01104437306879618 -0.000228764133061211 +0.07819996384396966 4.127780662861551e-05 -2.991057168005374e-06 +0.07202763627549755 -0.02108505542368243 -0.0004650481933519364 +0.06030740026776515 -0.03284898406007216 -0.000575092613061699 +0.05197415418742954 -0.03691972333053082 -0.0009533577132157866 +0.04841011551193194 -0.03797539582415126 -0.0012756171634708763 +0.04106259222822374 -0.03905070100038476 -0.002640959490398662 +0.0392041678823387 -0.03909985971367359 -0.002617383818930308 +0.03734550757143083 -0.03906061142774211 -0.0019512487320989223 +0.03549081466558211 -0.03893305307143092 -0.0004661649781977114 +0.02999235773064849 -0.03802447036198644 0.005671899478682422 +0.02819522910180473 -0.03754856560901278 0.007255265503267772 +0.02642274895181671 -0.03698778874565389 0.008437998523398466 +0.02467892578294952 -0.03634339841365394 0.009272998170146079 +0.02296771065963648 -0.03561683055468438 0.009818887434565653 +0.0212929661235993 -0.034809744871696 0.010121505031131855 +0.01965847119772771 -0.03392397792845034 0.010215736624071617 +0.01652493718577972 -0.03192453294918682 0.00988329670009842 +0.01503298224681096 -0.03081537691891334 0.009500925488249457 +0.01221552866592811 -0.02839075860041346 0.008406802228970986 +0.009641067793166569 -0.0257095339280482 0.00700174990074151 +0.0073328241508335 -0.02279597455813496 0.005439446132599986 +0.0004212849451338721 -0.0057241591407998 -9.821423814390917e-05 +0.0001929063854338941 -0.00387916574954884 -0.0001677770129790615 +3.715759961701779e-07 -0.000167057565479412 8.866677575636765e-06 +0.0003737770984357588 0.005393438845063324 0.0009648191807615032 +0.00106093352703043 0.009046469258067052 0.001906286770070402 +0.002091866108723892 0.01261774277269358 0.002862841031091262 +0.002733467311930074 0.01436259362075018 0.003226329655069884 +0.003457264975454637 0.01607498180921493 0.003373864267305056 +0.005118832334056953 0.01943119745211363 0.003244479859277398 +0.01551627563955031 0.03736815990984928 0.00640642847178748 +0.01999837151218267 0.04343539867217488 0.00746451057835034 +0.02363912034760315 0.04776628085227682 0.008134354582056486 +0.03738856887789012 0.0606405766812684 0.009765309341371863 +0.04832587972692123 0.06818926940941658 0.0116451778915289 +0.05399675986092924 0.07144915477192883 0.012011259579708933 +0.06072447947721454 0.07485584093822345 0.012147363864742813 +0.07472263851285585 0.08065345333266476 0.011970806903965334 +0.08887221045490147 0.08513218823611196 0.011442401741641892 +0.1793062895712234 0.09530077013388079 0.006856086486232446 +0.2117339898587441 0.09495067176705572 0.006628380949299338 +0.2581032333418144 0.09215324744689607 0.005192207194632046 +0.2996809993542806 0.08811305015450889 0.004457266541411632 +0.3567078053717327 0.08168243973732783 0.00394706807980882 +0.4309247818702319 0.07270373419804112 0.003581264429982738 +0.859748396615083 0.01806363700433209 0.002415898765630274 +0.990135014604125 0.00127095875812223 0.0018193027298150943 +0.9980660976826226 0.000249320580680477 0.00202920416730058 +0.9995004786446735 6.447374315074194e-05 0.002407312125848668 +0.9998066004065816 2.499749945161417e-05 0.002663732027943266 +1.0 0.0 0.003108088175078052 +1.000175570344442 -0.0003873748714666402 -0.0005394350261954327 +0.9999361185511577 -0.0004959023699215505 0.007227548955785272 +0.9997426931776413 -0.0004710692940610273 0.006070740947186466 +0.9992898615857166 -0.0004127908100313096 0.00523084111183753 +0.9984027748023451 -0.0002985631337174143 0.004596763351448572 +0.9969850747884935 -0.0001159634273836383 0.004125445965553146 +0.9925102286323966 0.0004604996516486448 0.003608634550155278 +0.9828366693570219 0.001706780446830773 0.003290951256256768 +0.8007931164398834 0.02514688172946307 0.0015438641554223705 +0.6227248105276376 0.04799391426786268 -0.000934765929254101 +0.5467873640304859 0.05766507732352074 -0.0017082583043725305 +0.4557607131227709 0.06912084908337753 -0.002057381475396368 +0.3439219432772413 0.08267370547347265 -0.001909630199411214 +0.2878908640215147 0.0888395395812468 -0.0016403223905841638 +0.2472404119045495 0.0925291412707685 -0.0012439644700339358 +0.2284148315498924 0.09375889647752622 -0.0008998106920897766 +0.1938680582880188 0.09475868486167134 6.862163771827565e-05 +0.1565453765113058 0.0943433883278578 3.083217355968188e-05 +0.1049056581150844 0.0884277941269339 0.0003608467874276816 +0.0596424493908252 0.07383844242791567 -7.284237499479304e-05 +0.04571639419151958 0.06586873418008751 -7.147357452011414e-05 diff --git a/data/TUDELFT_V3_KITE/cpx_distributions/cf_AOA_6.dat b/data/TUDELFT_V3_KITE/cpx_distributions/cf_AOA_6.dat new file mode 100755 index 0000000..a415d17 --- /dev/null +++ b/data/TUDELFT_V3_KITE/cpx_distributions/cf_AOA_6.dat @@ -0,0 +1,103 @@ +# x y Cf +0.04276388755929555 0.06356556861711357 -0.0001879585975700373 +0.03309840970977389 0.04825624850833229 -5.458507980308168e-07 +0.04467938624112796 0.03869402682902678 0.0002106766326490412 +0.06326602268098154 0.03073779662338421 0.00010683943074351959 +0.06739054964049444 0.0269898872199461 -5.94499259365639e-05 +0.07295141860002202 0.01956758285390561 -0.000747380127932433 +0.07465658066274587 0.01626466884529217 -0.000804869041349509 +0.07660775307689469 0.01104437306879618 -0.0005439448493615928 +0.07819996384396966 4.127780662861551e-05 -7.537638609578638e-06 +0.07606735331573551 -0.0127367285437733 -0.0003803835335502698 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0.297013291348983 +0.04571639419151958 0.06586873418008751 0.284032411033685 diff --git a/data/TUDELFT_V3_KITE/cpx_distributions/cp_AOA_8.dat b/data/TUDELFT_V3_KITE/cpx_distributions/cp_AOA_8.dat new file mode 100644 index 0000000..ce2f14c --- /dev/null +++ b/data/TUDELFT_V3_KITE/cpx_distributions/cp_AOA_8.dat @@ -0,0 +1,59 @@ +# x y Cp +0.04276388755929555 0.06356556861711357 0.369754792445869 +0.05363791167027467 0.03629681937611275 0.369512825076681 +0.06023799864411321 0.03289369258862966 0.3803300404656592 +0.07295141860002202 0.01956758285390561 0.4525002946292716 +0.07538949147001935 0.0145561611100228 0.4564693840993162 +0.07801937057148131 0.003753985959382214 0.446882922242024 +0.07780867321095557 -0.005517988661109592 0.4783581156255348 +0.06613535838326418 -0.02824710359527738 0.5311348004808492 +0.05709225787431717 -0.03471437303988962 0.484086890575362 +0.05197415418742954 -0.03691972333053082 0.508181593031596 +0.04106259222822374 -0.03905070100038476 0.42315148127032 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0.06300526498795977 -0.5230590187758586 +0.5859002138042717 0.05319596110636245 -0.4121258594586978 +0.6824259822772941 0.04085560183950949 -0.298421444448391 +0.8093373719000714 0.02455167460498058 -0.17313674963583736 +0.9660562316502389 0.004372544645865283 -0.0386406821187513 +0.993768270458061 0.000802973252239986 -0.02128853044019792 +1.000216009864362 -0.000279890227385287 -0.03062803960527396 +0.9943997089817618 0.0002170811127827793 0.0244731662116314 +0.9818912176243451 0.001828584093814853 0.06971150300101164 +0.960286674485311 0.004611622190581761 0.11726533977474018 +0.9274984236403104 0.00883501341243748 0.1677274935281196 +0.8530499807859604 0.01842190075726221 0.2484797697022198 +0.6588094047445807 0.04337787974553729 0.4164065158335706 +0.5852500607119644 0.05277533327406693 0.4895377938887346 +0.5208166631398357 0.06095334182358406 0.571407956570911 +0.4173409525953314 0.07387363386197163 0.7448626251611238 +0.3922624879189146 0.07693223386512749 0.7709991898354575 +0.3799297067584973 0.0784194374404138 0.7726402699823532 +0.3677534071070601 0.07987434616211128 0.7634659759410414 +0.3557467275473164 0.08129361982160917 0.741382005954384 +0.3322904223011696 0.08401082699279248 0.654753629482031 +0.2570330318015585 0.09174362234289557 0.14088055807058458 +0.237700137204438 0.09320459962989104 0.05907810318650006 +0.2284148315498924 0.09375889647752622 0.04303112368943488 +0.2193869169365694 0.09418446720371103 0.04419401824806442 +0.2106187027457731 0.09448229827809655 0.06265088115711293 +0.1707025886246218 0.09474637369056492 0.2715407898968978 +0.1565453765113058 0.0943433883278578 0.2872016129793902 +0.09590926783756276 0.08644641392015195 0.2638217468843654 +0.0596424493908252 0.07383844242791567 0.350286588153118 +0.04571639419151958 0.06586873418008751 0.3689025452585844 diff --git a/src/VSM/plot_geometry_plotly.py b/src/VSM/plot_geometry_plotly.py index 99ba553..35ace20 100644 --- a/src/VSM/plot_geometry_plotly.py +++ b/src/VSM/plot_geometry_plotly.py @@ -459,6 +459,7 @@ def create_3D_plot( canopy_grid: Optional[Tuple[np.ndarray, np.ndarray, np.ndarray]] = None, is_with_tube_rings: bool = False, is_with_panels: bool = True, + cp_magnitude_fn=None, ) -> go.Figure: """ Creates an interactive 3D plot of wing geometry using Plotly. @@ -548,7 +549,11 @@ def create_3D_plot( if use_distributed_vectors: add_distributed_surface_vectors( - fig, canopy_grid, forces_of_panels, scale=chord_average + fig, + canopy_grid, + forces_of_panels, + scale=chord_average, + cp_magnitude_fn=cp_magnitude_fn, ) if tube_data is not None: @@ -588,24 +593,34 @@ def add_distributed_surface_vectors( scale: float, n_chord: int = 10, n_span: int = None, + cp_magnitude_fn=None, ) -> None: - """Draw a grid of equal, surface-normal force vectors on the canopy. + """Draw a grid of chord-normal force vectors on the canopy. One row of ``n_chord`` nodes is placed at each panel centre (uniformly over - the chord); every node carries one equal-length arrow oriented along the local - canopy surface normal (the outward/suction side). This gives a regular - ``n_span x n_chord`` grid of vectors covering the whole canopy. + the chord); every node carries one arrow oriented normal to the local chord + line (the flat-panel "up", perpendicular to chord and span), pointing to the + outward/suction side. This gives a regular ``n_span x n_chord`` grid of + vectors covering the whole canopy. + + Each panel's VSM force is distributed over its chord nodes: the arrow lengths + reflect both the spanwise loading (the panel force from VSM) and the chordwise + shape (the ``|Cp|`` weighting, or an even split without a Cp distribution). + The node forces of a panel sum back to that panel's force. Args: fig: Plotly figure. canopy_grid: ``(X, Y, Z)`` canopy surface arrays, each ``(S, P)`` with ``S`` spanwise stations and ``P`` chordwise points. - forces_of_panels: Per-panel aerodynamic force vectors (used only to skip - drawing when there is no force). + forces_of_panels: Per-panel aerodynamic force vectors from VSM; their + magnitudes set the total per panel that is distributed chordwise. scale: Length scale (typically the average chord). n_chord: Nodes per row, distributed over the chord. Defaults to 10. n_span: Number of spanwise rows. Defaults to one row per panel (the midpoints between the ``S`` canopy stations, i.e. ``S - 1`` rows). + cp_magnitude_fn: Optional callable mapping chord fraction ``x/c`` to a + (positive) pressure-coefficient magnitude, used as the chordwise + weighting of each panel's force. Without it the force is spread evenly. """ x, y, z = canopy_grid grid = np.stack([x, y, z], axis=-1) # (S, P, 3) @@ -624,52 +639,75 @@ def add_distributed_surface_vectors( np.clip(np.round(np.linspace(0, n_rows - 1, n_span)), 0, n_rows - 1).astype(int) ) - # Surface-normal field over the panel-centre grid. - d_chord = np.gradient(panel_grid, axis=1) - d_span = np.gradient(panel_grid, axis=0) - normal_field = np.cross(d_chord, d_span) - normal_field /= np.linalg.norm(normal_field, axis=-1, keepdims=True).clip(1e-12) - normal_field[normal_field[:, :, 2] < 0] *= -1 # outward (suction) side + # Spanwise direction field, used to build the per-row chord-normal. + d_span = np.gradient(panel_grid, axis=0) # (R, P, 3) + + # Chordwise weights: how each panel's force is spread over its nodes. With a + # Cp distribution the weights follow the local |Cp| loading; otherwise the + # force is spread evenly. Normalised so the weights sum to one (the node + # forces of a panel add back up to that panel's VSM force). + targets = np.linspace(0.05, 0.95, n_chord) + if cp_magnitude_fn is not None: + chord_weights = np.asarray(cp_magnitude_fn(targets), dtype=float) + else: + chord_weights = np.ones(n_chord) + chord_weights = chord_weights / max(chord_weights.sum(), 1e-12) # Sample each row at the exact target chord fractions (5%-95%). The grid # columns are arc-length spaced, so interpolate by true chord fraction rather # than snapping to columns -- this keeps vectors clear of the leading-edge # tube (near 0%) and the trailing edge (near 100%). - targets = np.linspace(0.05, 0.95, n_chord) origins = [] normals = [] + node_forces = [] # per-node share of the panel's VSM force magnitude for row in span_rows: pts = panel_grid[row] # (P, 3) chord_vector = pts[-1] - pts[0] chord_length = np.linalg.norm(chord_vector) chord_hat = chord_vector / max(chord_length, 1e-12) + + # Chord-normal: perpendicular to the chord line and the span, in the + # airfoil plane (the flat-panel "up"). Constant along the chord, so every + # vector in this row points the same way rather than following the local + # surface curvature. + span_vector = d_span[row].mean(axis=0) + chord_normal = np.cross(chord_vector, span_vector) + cn = np.linalg.norm(chord_normal) + if cn < 1e-9: + continue + chord_normal = chord_normal / cn + if chord_normal[2] < 0: # orient toward the outward (suction) side + chord_normal = -chord_normal + + # Row r is the centre of panel r, so its total is that panel's force. + panel_force = force_magnitudes[row] if row < len(force_magnitudes) else 0.0 + chord_fraction = ((pts - pts[0]) @ chord_hat) / max(chord_length, 1e-12) order = np.argsort(chord_fraction) frac_sorted = chord_fraction[order] pts_sorted = pts[order] - nrm_sorted = normal_field[row][order] - for target in targets: + for k, target in enumerate(targets): point = np.array( - [np.interp(target, frac_sorted, pts_sorted[:, k]) for k in range(3)] + [np.interp(target, frac_sorted, pts_sorted[:, j]) for j in range(3)] ) - normal = np.array( - [np.interp(target, frac_sorted, nrm_sorted[:, k]) for k in range(3)] - ) - norm = np.linalg.norm(normal) - if norm < 1e-9: - continue origins.append(point) - normals.append(normal / norm) + normals.append(chord_normal) + node_forces.append(panel_force * chord_weights[k]) if not origins: return origins = np.array(origins) normals = np.array(normals) + node_forces = np.array(node_forces) - # Equal arrow length, scaled to the chordwise node spacing so the grid reads - # cleanly without the arrows overlapping badly. - length = 0.9 * scale / max(n_chord, 1) - endpoints = origins + normals * length + # Normalise force (N) to plotted length (m): the largest panel force over all + # panels plots at the maximum chord length (``scale``). Each panel's total + # plotted length is then this per-panel length spread across the chord, so a + # panel's node lengths add up to ``|F_panel| / max_force * max_chord``. + max_force = float(force_magnitudes.max()) + newton_to_metre = scale / max(max_force, 1e-12) + lengths = (node_forces * newton_to_metre)[:, None] + endpoints = origins + normals * lengths # All stems as one trace (None-separated segments), all heads as one cone trace. stem_x, stem_y, stem_z = [], [], [] @@ -693,11 +731,11 @@ def add_distributed_surface_vectors( x=endpoints[:, 0], y=endpoints[:, 1], z=endpoints[:, 2], - u=normals[:, 0] * length, - v=normals[:, 1] * length, - w=normals[:, 2] * length, + u=normals[:, 0] * lengths[:, 0], + v=normals[:, 1] * lengths[:, 0], + w=normals[:, 2] * lengths[:, 0], sizemode="absolute", - sizeref=length / 3, + sizeref=0.06 * scale, anchor="tip", colorscale=[[0, "red"], [1, "red"]], showscale=False, @@ -983,6 +1021,7 @@ def update_plot( canopy_grid: Optional[Tuple[np.ndarray, np.ndarray, np.ndarray]] = None, is_with_tube_rings: bool = False, is_with_panels: bool = True, + cp_magnitude_fn=None, ): # Update AoA and rerun VSM results = running_VSM( @@ -1006,6 +1045,7 @@ def update_plot( canopy_grid=canopy_grid, is_with_tube_rings=is_with_tube_rings, is_with_panels=is_with_panels, + cp_magnitude_fn=cp_magnitude_fn, ) fig = add_case_information( fig, @@ -1041,6 +1081,7 @@ def interactive_plot( is_with_canopy: bool = True, is_with_tube_rings: bool = False, is_with_panels: Optional[bool] = None, + cp_distributions_dir: Optional[Path] = None, ): """ Creates and optionally saves multiple views of the wing geometry with interactive AoA slider. @@ -1072,6 +1113,11 @@ def interactive_plot( is_with_panels: Draw the panel outlines. Defaults to ``False`` for the fancy plot (a Surfplan export is given) and ``True`` otherwise. When off, the force vectors are lifted onto the canopy surface. + cp_distributions_dir: Optional directory of ``cp_AOA_.dat`` chordwise + pressure-coefficient files. When given, the closest available angle of + attack is selected and its ``|Cp|(x/c)`` scales the chordwise force + vector magnitudes (the single mid-span distribution is applied at + every span station). Returns: plotly.graph_objects.Figure: The created figure. @@ -1094,6 +1140,19 @@ def interactive_plot( contour_table = load_contour_table(processed_dir) canopy_grid = build_canopy_grid(wing_aero.panels, contour_table) + # Optional Cp-based scaling of the chordwise force vectors. + cp_magnitude_fn = None + if cp_distributions_dir is not None: + from VSM.plotly.cp_distributions import build_cp_magnitude_fn + + cp_magnitude_fn, matched_aoa = build_cp_magnitude_fn( + Path(cp_distributions_dir), angle_of_attack + ) + print( + f"Cp loading from closest available AoA = {matched_aoa:g} deg " + f"(operating AoA = {angle_of_attack:g} deg)" + ) + # Create the figure with a default orientation fig = go.Figure() fig.update_layout( @@ -1121,6 +1180,7 @@ def interactive_plot( canopy_grid=canopy_grid, is_with_tube_rings=is_with_tube_rings, is_with_panels=is_with_panels, + cp_magnitude_fn=cp_magnitude_fn, ) # Save or show the plot if requested diff --git a/src/VSM/plotly/cp_distributions.py b/src/VSM/plotly/cp_distributions.py new file mode 100644 index 0000000..29c1ad0 --- /dev/null +++ b/src/VSM/plotly/cp_distributions.py @@ -0,0 +1,97 @@ +"""Chordwise pressure-coefficient (Cp) database for the fancy Plotly plot. + +A directory of ``cp_AOA_.dat`` files (whitespace columns ``x/c, y/c, Cp`` +around the 2D airfoil section) is treated as a small database keyed by angle of +attack. Given an operating angle of attack, the closest available distribution is +selected and its **upper (suction) surface** ``|Cp|(x/c)`` is used to scale the +magnitude of the chordwise force vectors on the canopy. + +Per the modelling assumption in use, the single mid-span section distribution is +applied to every spanwise station (all airfoils share this geometry). +""" + +import re +from pathlib import Path +from typing import Callable, Dict, Tuple + +import numpy as np + + +def load_upper_surface_cp(dat_file_path: Path) -> Tuple[np.ndarray, np.ndarray]: + """Extract the upper (suction) surface ``Cp(x/c)`` from a Cp ``.dat`` loop. + + The file lists ``x/c, y/c, Cp`` around the closed airfoil section. The upper + surface is the leading-edge-to-trailing-edge branch with the more negative + (suction) mean Cp; it is returned sorted by ``x/c``. + + Args: + dat_file_path (Path): Path to a ``cp_AOA_*.dat`` file. + + Returns: + Tuple[np.ndarray, np.ndarray]: ``x/c`` (ascending) and ``Cp`` arrays. + """ + data = np.loadtxt(dat_file_path) + x = data[:, 0] + cp = data[:, 2] + n = len(x) + i_le = int(np.argmin(x)) + i_te = int(np.argmax(x)) + + def branch(a: int, b: int) -> np.ndarray: + if a <= b: + return np.arange(a, b + 1) + return np.concatenate([np.arange(a, n), np.arange(0, b + 1)]) + + branch_a = branch(i_le, i_te) + branch_b = branch(i_te, i_le) + upper = branch_a if cp[branch_a].mean() < cp[branch_b].mean() else branch_b + + x_upper = x[upper] + cp_upper = cp[upper] + order = np.argsort(x_upper) + return x_upper[order], cp_upper[order] + + +def load_cp_database(cp_dir: Path) -> Dict[float, Tuple[np.ndarray, np.ndarray]]: + """Load all ``cp_AOA_.dat`` files, keyed by angle of attack in degrees. + + Args: + cp_dir (Path): Directory of ``cp_AOA_*.dat`` files. + + Returns: + Dict[float, Tuple[np.ndarray, np.ndarray]]: Mapping ``aoa_deg -> (x/c, Cp)`` + for the upper surface. + """ + database = {} + for path in sorted(Path(cp_dir).glob("cp_AOA_*.dat")): + match = re.search(r"AOA_(-?\d+(?:\.\d+)?)", path.stem) + if not match: + continue + database[float(match.group(1))] = load_upper_surface_cp(path) + if not database: + raise FileNotFoundError(f"No 'cp_AOA_*.dat' files found in {cp_dir}.") + return database + + +def build_cp_magnitude_fn( + cp_dir: Path, angle_of_attack: float +) -> Tuple[Callable[[np.ndarray], np.ndarray], float]: + """Return a ``|Cp|(x/c)`` interpolator for the closest available AoA. + + Args: + cp_dir (Path): Directory of ``cp_AOA_*.dat`` files. + angle_of_attack (float): Operating angle of attack in degrees. + + Returns: + Tuple[Callable, float]: A function mapping ``x/c`` (array) to ``|Cp|`` and + the matched database angle of attack. + """ + database = load_cp_database(cp_dir) + available = np.array(sorted(database)) + matched_aoa = float(available[np.argmin(np.abs(available - angle_of_attack))]) + x_upper, cp_upper = database[matched_aoa] + + def magnitude(x_over_c: np.ndarray) -> np.ndarray: + return np.abs(np.interp(x_over_c, x_upper, cp_upper)) + + return magnitude, matched_aoa diff --git a/tests/plotting/test_tube_geometry.py b/tests/plotting/test_tube_geometry.py index 26c4236..a518998 100644 --- a/tests/plotting/test_tube_geometry.py +++ b/tests/plotting/test_tube_geometry.py @@ -20,6 +20,7 @@ REPO_ROOT = Path(__file__).resolve().parents[2] SURFPLAN_DIR = REPO_ROOT / "data" / "TUDELFT_V3_KITE" / "Surfplan_export" +CP_DIR = REPO_ROOT / "data" / "TUDELFT_V3_KITE" / "cpx_distributions" DRAWN_YAML = ( REPO_ROOT / "data" @@ -202,3 +203,59 @@ def test_interactive_plot_fancy_traces(): fig3 = interactive_plot(body, is_show=False) assert not [t for t in fig3.data if isinstance(t, go.Surface)] assert [t for t in fig3.data if getattr(t, "name", None) == "Leading Edge"] + + +# --------------------------------------------------------------------------- # +# Cp distribution database +# --------------------------------------------------------------------------- # + + +@pytest.mark.skipif(not CP_DIR.is_dir(), reason="Cp distributions unavailable") +def test_load_upper_surface_cp_ordering(): + from VSM.plotly.cp_distributions import load_upper_surface_cp + + x, cp = load_upper_surface_cp(CP_DIR / "cp_AOA_8.dat") + assert np.all(np.diff(x) >= 0) # ascending x/c + assert x.min() >= 0.0 and x.max() <= 1.01 # normalised chord (small CFD overshoot) + assert cp.min() < 0 # suction side has negative Cp + + +@pytest.mark.skipif(not CP_DIR.is_dir(), reason="Cp distributions unavailable") +def test_build_cp_magnitude_fn_closest_aoa(): + from VSM.plotly.cp_distributions import build_cp_magnitude_fn + + # Exact and nearest matches over the available {2, 6, 8} degrees. + assert build_cp_magnitude_fn(CP_DIR, 8)[1] == 8 + assert build_cp_magnitude_fn(CP_DIR, 5)[1] == 6 + assert build_cp_magnitude_fn(CP_DIR, 3)[1] == 2 + assert build_cp_magnitude_fn(CP_DIR, 100)[1] == 8 + + magnitude, _ = build_cp_magnitude_fn(CP_DIR, 8) + values = magnitude(np.array([0.05, 0.5, 0.95])) + assert np.all(values >= 0) + # Loading is front-heavy: near-LE |Cp| exceeds near-TE |Cp|. + assert values[0] > values[-1] + + +@pytest.mark.skipif( + not (_has_surfplan() and CP_DIR.is_dir()), + reason="SurfplanAdapter or data unavailable", +) +def test_interactive_plot_cp_scaled_vectors_run(): + from VSM.core.BodyAerodynamics import BodyAerodynamics + from VSM.plot_geometry_plotly import interactive_plot + + body = BodyAerodynamics.instantiate( + n_panels=36, + file_path=DRAWN_YAML, + spanwise_panel_distribution="uniform", + ) + fig = interactive_plot( + body, + angle_of_attack=8, + surfplan_dir=SURFPLAN_DIR, + cp_distributions_dir=CP_DIR, + is_show=False, + ) + # The vector grid is still drawn (stems + arrowheads present). + assert [t for t in fig.data if getattr(t, "name", None) == "Aerodynamic Vectors"] From 1cfe544053b88474582c128e9ff5815b25fc4e08 Mon Sep 17 00:00:00 2001 From: jellepoland Date: Fri, 24 Jul 2026 17:16:40 +0200 Subject: [PATCH 07/37] Fancy plot: Cp-scaled force field, tube end-caps, high-res render, example - Distribute each panel's VSM force over the chord weighted by the closest-AoA |Cp|(x/c); per-vector size anchored to a base of 10 nodes (extract the shared distributed_surface_vector_field into canopy_geometry) - Cap the open tube ends (leading-edge + struts) so junctions read cleanly - save_high_res_render: render on a square canvas (Plotly only renders a 3D scene undistorted when square), strip legend/axes/annotations, and auto-crop to the kite -> a clean, to-scale PNG - Drop the forced cube aspectratio in the layout so the scene stays true-to-scale - Add examples/TUDELFT_V3_KITE/fancy_interactive_plot.py running the pipeline and writing the high-res render; embed docs/plotly_render.png in the README Co-Authored-By: Claude Opus 4.8 (1M context) --- README.md | 2 + docs/plotly_render.png | Bin 0 -> 96855 bytes .../TUDELFT_V3_KITE/fancy_interactive_plot.py | 85 ++++++++ src/VSM/plot_geometry_plotly.py | 187 +++++++++--------- src/VSM/plotly/canopy_geometry.py | 102 ++++++++++ src/VSM/plotly/tube_geometry.py | 42 +++- 6 files changed, 326 insertions(+), 92 deletions(-) create mode 100644 docs/plotly_render.png create mode 100644 examples/TUDELFT_V3_KITE/fancy_interactive_plot.py diff --git a/README.md b/README.md index 1d42c90..1bb6935 100644 --- a/README.md +++ b/README.md @@ -3,6 +3,8 @@ The Vortex Step Method (VSM) is an enhanced lifting line method that improves up A Julia version of this project is available at [VortexStepMethod.jl](https://github.com/Albatross-Kite-Transport/VortexStepMethod.jl) + +![](docs/plotly_render.png) ## Reference Frame diff --git a/docs/plotly_render.png b/docs/plotly_render.png new file mode 100644 index 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z`Y*p@Rt8ys*2l>zirb0Pc5R*p_2GA1w5?*%BqTR%5x=e(-{ly>h=G{ zOa<1Nsuwimp;ZHjyNtRRYm+shNik@#LR%lI%4qO&Gn2`i(75Q7e zOihUAFwZSpvsuaoC4wR3b(EqHhOz+x00mS9u2S3mEXq>myC#$jwA?hl%<3`{vFY#W zO5Q5URf~5P_|BG>cI70Isy2|pyRLlU)>74uR?IRLR7mStG;x*Ts+$fRs=zkJk}pYf zDbHjovQ^?Z5H.txt`` plus a ``profiles/`` directory, + - (optional) a directory of ``cp_AOA_.dat`` chordwise Cp distributions. + +SurfplanAdapter must be installed (a dependency of VSM) -- it converts the raw +export into the VSM geometry the plot needs (cached on first run). +""" + +from pathlib import Path + +from VSM.core.BodyAerodynamics import BodyAerodynamics +from VSM.plot_geometry_plotly import interactive_plot, save_high_res_render + +PROJECT_DIR = Path(__file__).resolve().parents[2] +DATA_DIR = PROJECT_DIR / "data" / "TUDELFT_V3_KITE" +RESULTS_DIR = PROJECT_DIR / "results" / "TUDELFT_V3_KITE" + +# Set True to also write a high-resolution PNG (results/.../plotly_render.png) +SAVE_HIGH_RES_PNG = True + + +def main(): + # --- inflow / operating point ------------------------------------------- + Umag = 10.0 # [m/s] + angle_of_attack = 8.0 # [deg] + side_slip = 0.0 # [deg] + + # --- build the aerodynamic model ---------------------------------------- + # The Breukels-regression CAD geometry needs no ML models, so it runs + # out of the box. Any other aero_geometry_*.yaml works too. + aero_geometry = ( + DATA_DIR / "CAD_derived_geometry" / "aero_geometry_CAD_breukels_regression.yaml" + ) + body_aero = BodyAerodynamics.instantiate( + n_panels=36, + file_path=aero_geometry, + spanwise_panel_distribution="uniform", + ) + + # --- data for the fancy plot -------------------------------------------- + # Raw Surfplan export (tubes + airfoil profiles) and the Cp database. + surfplan_dir = DATA_DIR / "Surfplan_export" + cp_distributions_dir = DATA_DIR / "cpx_distributions" + + # --- interactive fancy plot --------------------------------------------- + # Passing ``surfplan_dir`` switches on the inflatable tubes + curved canopy. + # Passing ``cp_distributions_dir`` distributes each panel's VSM force over the + # chord using the closest-AoA measured Cp(x/c). Omit either to fall back. + fig = interactive_plot( + body_aero, + vel=Umag, + angle_of_attack=angle_of_attack, + side_slip=side_slip, + title="TUDELFT_V3_KITE", + surfplan_dir=surfplan_dir, + cp_distributions_dir=cp_distributions_dir, + is_with_canopy=True, # curved canopy over the tubes (False -> tubes only) + is_with_tube_rings=False, # True -> also draw the tube construction rings + is_show=True, # open the interactive plot in a browser + # is_save=True, # uncomment to also write an interactive .html + # save_path=str(RESULTS_DIR / "fancy_plot.html"), + ) + + # --- optional: high-resolution PNG (matches the interactive view) -------- + if SAVE_HIGH_RES_PNG: + save_high_res_render( + fig, + RESULTS_DIR / "plotly_render.png", + base_size=2000, # square canvas -> undistorted; then cropped to the kite + scale=4, + show_legend=False, + show_axes=False, + show_annotations=False, + ) + + +if __name__ == "__main__": + main() diff --git a/src/VSM/plot_geometry_plotly.py b/src/VSM/plot_geometry_plotly.py index 35ace20..0d99386 100644 --- a/src/VSM/plot_geometry_plotly.py +++ b/src/VSM/plot_geometry_plotly.py @@ -622,91 +622,19 @@ def add_distributed_surface_vectors( (positive) pressure-coefficient magnitude, used as the chordwise weighting of each panel's force. Without it the force is spread evenly. """ - x, y, z = canopy_grid - grid = np.stack([x, y, z], axis=-1) # (S, P, 3) - - force_magnitudes = np.linalg.norm(np.asarray(forces_of_panels), axis=1) - if force_magnitudes.size == 0 or np.max(force_magnitudes) <= 0: - return - - # One row per panel: use the midpoints between adjacent canopy stations. - panel_grid = 0.5 * (grid[:-1] + grid[1:]) # (S - 1, P, 3) - n_rows, n_points, _ = panel_grid.shape - - if n_span is None: - n_span = n_rows - span_rows = np.unique( - np.clip(np.round(np.linspace(0, n_rows - 1, n_span)), 0, n_rows - 1).astype(int) + from VSM.plotly.canopy_geometry import distributed_surface_vector_field + + origins, normals, lengths_1d = distributed_surface_vector_field( + canopy_grid, + forces_of_panels, + scale, + n_chord=n_chord, + n_span=n_span, + cp_magnitude_fn=cp_magnitude_fn, ) - - # Spanwise direction field, used to build the per-row chord-normal. - d_span = np.gradient(panel_grid, axis=0) # (R, P, 3) - - # Chordwise weights: how each panel's force is spread over its nodes. With a - # Cp distribution the weights follow the local |Cp| loading; otherwise the - # force is spread evenly. Normalised so the weights sum to one (the node - # forces of a panel add back up to that panel's VSM force). - targets = np.linspace(0.05, 0.95, n_chord) - if cp_magnitude_fn is not None: - chord_weights = np.asarray(cp_magnitude_fn(targets), dtype=float) - else: - chord_weights = np.ones(n_chord) - chord_weights = chord_weights / max(chord_weights.sum(), 1e-12) - - # Sample each row at the exact target chord fractions (5%-95%). The grid - # columns are arc-length spaced, so interpolate by true chord fraction rather - # than snapping to columns -- this keeps vectors clear of the leading-edge - # tube (near 0%) and the trailing edge (near 100%). - origins = [] - normals = [] - node_forces = [] # per-node share of the panel's VSM force magnitude - for row in span_rows: - pts = panel_grid[row] # (P, 3) - chord_vector = pts[-1] - pts[0] - chord_length = np.linalg.norm(chord_vector) - chord_hat = chord_vector / max(chord_length, 1e-12) - - # Chord-normal: perpendicular to the chord line and the span, in the - # airfoil plane (the flat-panel "up"). Constant along the chord, so every - # vector in this row points the same way rather than following the local - # surface curvature. - span_vector = d_span[row].mean(axis=0) - chord_normal = np.cross(chord_vector, span_vector) - cn = np.linalg.norm(chord_normal) - if cn < 1e-9: - continue - chord_normal = chord_normal / cn - if chord_normal[2] < 0: # orient toward the outward (suction) side - chord_normal = -chord_normal - - # Row r is the centre of panel r, so its total is that panel's force. - panel_force = force_magnitudes[row] if row < len(force_magnitudes) else 0.0 - - chord_fraction = ((pts - pts[0]) @ chord_hat) / max(chord_length, 1e-12) - order = np.argsort(chord_fraction) - frac_sorted = chord_fraction[order] - pts_sorted = pts[order] - for k, target in enumerate(targets): - point = np.array( - [np.interp(target, frac_sorted, pts_sorted[:, j]) for j in range(3)] - ) - origins.append(point) - normals.append(chord_normal) - node_forces.append(panel_force * chord_weights[k]) - - if not origins: + if len(origins) == 0: return - origins = np.array(origins) - normals = np.array(normals) - node_forces = np.array(node_forces) - - # Normalise force (N) to plotted length (m): the largest panel force over all - # panels plots at the maximum chord length (``scale``). Each panel's total - # plotted length is then this per-panel length spread across the chord, so a - # panel's node lengths add up to ``|F_panel| / max_force * max_chord``. - max_force = float(force_magnitudes.max()) - newton_to_metre = scale / max(max_force, 1e-12) - lengths = (node_forces * newton_to_metre)[:, None] + lengths = lengths_1d[:, None] endpoints = origins + normals * lengths # All stems as one trace (None-separated segments), all heads as one cone trace. @@ -721,7 +649,7 @@ def add_distributed_surface_vectors( y=stem_y, z=stem_z, mode="lines", - line=dict(color="red", width=3), + line=dict(color="red", width=3.9), name="Aerodynamic Vectors", showlegend=True, ) @@ -735,7 +663,7 @@ def add_distributed_surface_vectors( v=normals[:, 1] * lengths[:, 0], w=normals[:, 2] * lengths[:, 0], sizemode="absolute", - sizeref=0.06 * scale, + sizeref=0.048 * scale, anchor="tip", colorscale=[[0, "red"], [1, "red"]], showscale=False, @@ -861,12 +789,15 @@ def update_fig_layout( f"{kite_geometry_ranges['z'][1]:.2f}", ], # Label for the ticks ), - aspectmode="data", # Allow different axis lengths - aspectratio=dict(x=1, y=1, z=1), # Keep aspect ratio 1:1:1 + # "data" keeps the scene true-to-scale (equal units on every axis); + # do NOT force a cube aspectratio here, that squeezes the wide wing. + aspectmode="data", camera=dict( up=dict(x=0, y=0, z=1), center=dict(x=0, y=0, z=0), - eye=dict(x=1.5, y=1.5, z=1.5), + eye=dict( + x=-1.92, y=-1.44, z=0.30 + ), # rotated ~180 deg, low and further out ), bgcolor="white", ), @@ -1204,3 +1135,83 @@ def interactive_plot( webbrowser.open(f"file://{tmp_path}") return fig + + +def save_high_res_render( + fig: go.Figure, + save_path, + base_size: int = 2000, + scale: int = 4, + show_legend: bool = False, + show_axes: bool = False, + show_annotations: bool = False, + transparent_background: bool = False, + pad_frac: float = 0.02, +) -> str: + """Export a clean, to-scale high-resolution PNG of the kite. + + A Plotly 3D scene is only rendered undistorted on a **square** canvas (on a + non-square canvas Plotly stretches it, which squeezes the kite). So this + renders on a square canvas -- guaranteeing correct proportions -- then crops + tightly to the drawn content. The legend, axes and annotations are removed by + default for a clean figure. + + Args: + fig: The Plotly figure (e.g. from :func:`interactive_plot`). + save_path: Output ``.png`` path; parent directories are created. + base_size: Square canvas size in pixels before supersampling. + scale: Supersampling factor (final render is ``base_size * scale`` square, + then cropped). Defaults to 4. + show_legend: Keep the trace legend. Defaults to False. + show_axes: Keep the 3D axes. Defaults to False. + show_annotations: Keep the corner case-info text. Defaults to False. + transparent_background: Transparent instead of white background. + pad_frac: Padding around the cropped content, as a fraction of its size. + + Returns: + str: The path the PNG was written to. + """ + import io + from PIL import Image + + render_fig = go.Figure(fig) + render_fig.update_layout(showlegend=show_legend, margin=dict(l=0, r=0, t=0, b=0)) + if not show_annotations: + render_fig.layout.annotations = () + render_fig.layout.title = None + if not show_axes: + render_fig.update_scenes( + xaxis_visible=False, yaxis_visible=False, zaxis_visible=False + ) + bg = "rgba(0,0,0,0)" if transparent_background else "white" + render_fig.update_layout(paper_bgcolor=bg, plot_bgcolor=bg) + + # Square canvas => Plotly does not distort the 3D scene. + png = render_fig.to_image( + format="png", width=base_size, height=base_size, scale=scale + ) + image = Image.open(io.BytesIO(png)).convert("RGBA") + + # Crop tightly to the drawn content (non-background pixels). + rgb = np.asarray(image)[:, :, :3].astype(int) + alpha = np.asarray(image)[:, :, 3] + if transparent_background: + content = alpha > 0 + else: + content = rgb.sum(axis=2) < 3 * 250 # anything not near-white + ys, xs = np.where(content) + if len(xs): + pad = int(pad_frac * max(xs.max() - xs.min(), ys.max() - ys.min())) + left = max(xs.min() - pad, 0) + right = min(xs.max() + pad, image.width) + top = max(ys.min() - pad, 0) + bottom = min(ys.max() + pad, image.height) + image = image.crop((left, top, right, bottom)) + + save_path = Path(save_path) + save_path.parent.mkdir(parents=True, exist_ok=True) + image.save(str(save_path)) + print( + f"High-resolution render saved to: {save_path} ({image.width} x {image.height} px)" + ) + return str(save_path) diff --git a/src/VSM/plotly/canopy_geometry.py b/src/VSM/plotly/canopy_geometry.py index ae4e98c..419c6bc 100644 --- a/src/VSM/plotly/canopy_geometry.py +++ b/src/VSM/plotly/canopy_geometry.py @@ -228,3 +228,105 @@ def build_canopy_grid( grid = np.stack(rows, axis=0) # (n_stations, n_points, 3) return grid[:, :, 0], grid[:, :, 1], grid[:, :, 2] + + +def distributed_surface_vector_field( + canopy_grid: Tuple[np.ndarray, np.ndarray, np.ndarray], + forces_of_panels: List[np.ndarray], + scale: float, + n_chord: int = 10, + n_span: int = None, + cp_magnitude_fn=None, +) -> Tuple[np.ndarray, np.ndarray, np.ndarray]: + """Chord-normal force-vector field over the canopy (origins, directions, lengths). + + One row of ``n_chord`` nodes is placed at each panel centre, uniformly over + the chord (at the true 5%-95% chord fractions). Every node's arrow points + normal to the local chord line (the flat-panel "up", outward/suction side). + Each panel's VSM force is distributed over its chord nodes, weighted by the + ``|Cp|`` chordwise loading (an even split without a Cp distribution) and + normalised to length so the largest panel force plots at the maximum chord + length (``scale``). + + Args: + canopy_grid: ``(X, Y, Z)`` canopy arrays, each ``(S, P)``. + forces_of_panels: Per-panel VSM force vectors. + scale: Length scale (typically the maximum chord); the largest panel + force plots at this length. + n_chord: Nodes per row over the chord. Defaults to 10. + n_span: Number of spanwise rows. Defaults to one per panel (``S - 1``). + cp_magnitude_fn: Optional ``x/c -> |Cp|`` weighting callable. + + Returns: + Tuple[np.ndarray, np.ndarray, np.ndarray]: ``origins`` ``(N, 3)``, + unit ``directions`` ``(N, 3)`` and ``lengths`` ``(N,)``. Empty arrays + if there is no force. + """ + x, y, z = canopy_grid + grid = np.stack([x, y, z], axis=-1) # (S, P, 3) + + force_magnitudes = np.linalg.norm(np.asarray(forces_of_panels), axis=1) + if force_magnitudes.size == 0 or np.max(force_magnitudes) <= 0: + return np.empty((0, 3)), np.empty((0, 3)), np.empty((0,)) + + panel_grid = 0.5 * (grid[:-1] + grid[1:]) # (S - 1, P, 3), one row per panel + n_rows, n_points, _ = panel_grid.shape + + if n_span is None: + n_span = n_rows + span_rows = np.unique( + np.clip(np.round(np.linspace(0, n_rows - 1, n_span)), 0, n_rows - 1).astype(int) + ) + d_span = np.gradient(panel_grid, axis=0) # (R, P, 3) + + targets = np.linspace(0.05, 0.95, n_chord) + if cp_magnitude_fn is not None: + chord_weights = np.asarray(cp_magnitude_fn(targets), dtype=float) + else: + chord_weights = np.ones(n_chord) + chord_weights = chord_weights / max(chord_weights.sum(), 1e-12) + + origins = [] + directions = [] + node_forces = [] + for row in span_rows: + pts = panel_grid[row] + chord_vector = pts[-1] - pts[0] + chord_length = np.linalg.norm(chord_vector) + chord_hat = chord_vector / max(chord_length, 1e-12) + + span_vector = d_span[row].mean(axis=0) + chord_normal = np.cross(chord_vector, span_vector) + cn = np.linalg.norm(chord_normal) + if cn < 1e-9: + continue + chord_normal = chord_normal / cn + if chord_normal[2] < 0: # outward (suction) side + chord_normal = -chord_normal + + panel_force = force_magnitudes[row] if row < len(force_magnitudes) else 0.0 + + chord_fraction = ((pts - pts[0]) @ chord_hat) / max(chord_length, 1e-12) + order = np.argsort(chord_fraction) + frac_sorted = chord_fraction[order] + pts_sorted = pts[order] + for k, target in enumerate(targets): + point = np.array( + [np.interp(target, frac_sorted, pts_sorted[:, j]) for j in range(3)] + ) + origins.append(point) + directions.append(chord_normal) + node_forces.append(panel_force * chord_weights[k]) + + if not origins: + return np.empty((0, 3)), np.empty((0, 3)), np.empty((0,)) + + origins = np.array(origins) + directions = np.array(directions) + node_forces = np.array(node_forces) + newton_to_metre = scale / max(float(force_magnitudes.max()), 1e-12) + # Anchor the per-vector size to a base of 10 chordwise nodes, so adding more + # nodes makes the field denser without shrinking each arrow (at n_chord=10 the + # factor is 1 and the largest panel's arrows still sum to the max chord). + lengths = node_forces * newton_to_metre * (n_chord / 10.0) + return origins, directions, lengths diff --git a/src/VSM/plotly/tube_geometry.py b/src/VSM/plotly/tube_geometry.py index adafdda..0609302 100644 --- a/src/VSM/plotly/tube_geometry.py +++ b/src/VSM/plotly/tube_geometry.py @@ -487,15 +487,49 @@ def _add_surface(fig: go.Figure, rings: List[np.ndarray], name: str, show_legend ) +def _add_ring_cap(fig: go.Figure, ring: np.ndarray) -> None: + """Close an open tube end with a filled (fan-triangulated) cap disc.""" + ring = np.asarray(ring)[:-1] # drop the duplicated closing point + n = len(ring) + center = ring.mean(axis=0) + verts = np.vstack([center[None, :], ring]) # index 0 is the centre + i = [0] * n + j = [1 + t for t in range(n)] + k = [1 + (t + 1) % n for t in range(n)] + fig.add_trace( + go.Mesh3d( + x=verts[:, 0], + y=verts[:, 1], + z=verts[:, 2], + i=i, + j=j, + k=k, + color=TUBE_COLOR, + opacity=TUBE_OPACITY, + name="Tube cap", + showlegend=False, + ) + ) + + +def _add_tube_with_caps( + fig: go.Figure, rings: List[np.ndarray], name: str, show_legend: bool +): + """Add a tube surface and close both open ends with caps.""" + _add_surface(fig, rings, name, show_legend) + _add_ring_cap(fig, rings[0]) + _add_ring_cap(fig, rings[-1]) + + def add_strut_surfaces(fig: go.Figure, tube_data: Dict[str, Any]) -> None: - """Add the strut tube surfaces to the figure.""" + """Add the strut tube surfaces (with end caps) to the figure.""" for index, strut in enumerate(tube_data["struts"]): - _add_surface(fig, strut, "Strut tube", show_legend=(index == 0)) + _add_tube_with_caps(fig, strut, "Strut tube", show_legend=(index == 0)) def add_le_tube_surface(fig: go.Figure, tube_data: Dict[str, Any]) -> None: - """Add the leading-edge tube surface to the figure.""" - _add_surface(fig, tube_data["le"], "Leading-edge tube", show_legend=True) + """Add the leading-edge tube surface (with end caps) to the figure.""" + _add_tube_with_caps(fig, tube_data["le"], "Leading-edge tube", show_legend=True) def add_tube_surfaces(fig: go.Figure, tube_data: Dict[str, Any]) -> None: From 3c680eba4fc3ad3b3e33300d7c2f426f16ca3fda Mon Sep 17 00:00:00 2001 From: jellepoland Date: Fri, 24 Jul 2026 17:28:34 +0200 Subject: [PATCH 08/37] readme --- README.md | 22 +++++++++++----------- 1 file changed, 11 insertions(+), 11 deletions(-) diff --git a/README.md b/README.md index 1bb6935..7028e4c 100644 --- a/README.md +++ b/README.md @@ -3,9 +3,20 @@ The Vortex Step Method (VSM) is an enhanced lifting line method that improves up A Julia version of this project is available at [VortexStepMethod.jl](https://github.com/Albatross-Kite-Transport/VortexStepMethod.jl) + +## Key Features ![](docs/plotly_render.png) +- **Accurate low-aspect-ratio wing modeling** with enhanced lifting line theory +- **Viscous-inviscid coupling** using 2D airfoil polars (inviscid, CFD, ML-based) +- **Complex geometry support**: sweep, dihedral, anhedral, leading-edge inflatable (LEI) kites +- **Rigid-body stability derivatives**: automatic computation of dCx/dα, dCMy/dq, etc. +- **Trim angle solver**: automatic determination of trimmed angle of attack +- **Non-dimensional rate derivatives**: controls-friendly output (hat_p, hat_q, hat_r) +- **Reference point flexibility**: correctly handles moment reference point for rotational velocities +- **Interactive visualization**: Plotly and Matplotlib geometry and results plotting + ## Reference Frame The VSM uses a body-fixed reference frame with the following conventions: @@ -32,17 +43,6 @@ The reference frame is illustrated below for the open-source example kite, the [ **Aircraft Frame Transformation:** For stability derivatives in standard aircraft coordinates (x-forward, y-right, z-down), use `map_derivatives_to_aircraft_frame()` from the `VSM.stability_derivatives` module. See `examples/TUDELFT_V3_KITE/evaluate_stability_derivatives.py` for usage. -## Key Features - -- **Accurate low-aspect-ratio wing modeling** with enhanced lifting line theory -- **Viscous-inviscid coupling** using 2D airfoil polars (inviscid, CFD, ML-based) -- **Complex geometry support**: sweep, dihedral, anhedral, leading-edge inflatable (LEI) kites -- **Rigid-body stability derivatives**: automatic computation of dCx/dα, dCMy/dq, etc. -- **Trim angle solver**: automatic determination of trimmed angle of attack -- **Non-dimensional rate derivatives**: controls-friendly output (hat_p, hat_q, hat_r) -- **Reference point flexibility**: correctly handles moment reference point for rotational velocities -- **Interactive visualization**: Plotly and Matplotlib geometry and results plotting - ## Documentation For detailed documentation, please refer to the following resources. From 3cc38965868081e39dfececc8de214e816bb76bc Mon Sep 17 00:00:00 2001 From: jellepoland Date: Fri, 24 Jul 2026 17:41:07 +0200 Subject: [PATCH 09/37] radme --- README.md | 5 ++--- 1 file changed, 2 insertions(+), 3 deletions(-) diff --git a/README.md b/README.md index 7028e4c..2376db6 100644 --- a/README.md +++ b/README.md @@ -5,9 +5,6 @@ A Julia version of this project is available at [VortexStepMethod.jl](https://gi ## Key Features - -![](docs/plotly_render.png) - - **Accurate low-aspect-ratio wing modeling** with enhanced lifting line theory - **Viscous-inviscid coupling** using 2D airfoil polars (inviscid, CFD, ML-based) - **Complex geometry support**: sweep, dihedral, anhedral, leading-edge inflatable (LEI) kites @@ -16,6 +13,8 @@ A Julia version of this project is available at [VortexStepMethod.jl](https://gi - **Non-dimensional rate derivatives**: controls-friendly output (hat_p, hat_q, hat_r) - **Reference point flexibility**: correctly handles moment reference point for rotational velocities - **Interactive visualization**: Plotly and Matplotlib geometry and results plotting + +![](docs/plotly_render.png) ## Reference Frame From c58337d997bc574d1a7f41a2db89b3967558a3b3 Mon Sep 17 00:00:00 2001 From: jellepoland Date: Wed, 2 Sep 2026 11:16:15 +0200 Subject: [PATCH 10/37] Release v2.2.0: fix body_axis in angle-derivative evaluation, drop debug plot, add changelog - stability_derivatives._evaluate_with_angles now passes body_axis so baseline roll/pitch rates are not silently mapped to the z-axis - trim_angle: remove leftover matplotlib debug plot/plt.show() in coarse sweep - changelog: add 2.2.0 entry (rotational-inflow sign fix, body_rates/body_axis API, bridle 'd' key, solver/filament changes, plotly plotting) Co-Authored-By: Claude Fable 5.1 Claude-Session: https://claude.ai/code/session_01GmKZURQ7nvjtTzZXXqE6ze --- changelog.md | 52 ++++++++++++++++++++++++++++++++ src/VSM/stability_derivatives.py | 1 + src/VSM/trim_angle.py | 4 --- 3 files changed, 53 insertions(+), 4 deletions(-) diff --git a/changelog.md b/changelog.md index 410043c..3daddb9 100644 --- a/changelog.md +++ b/changelog.md @@ -4,6 +4,58 @@ All notable changes to this project will be documented in this file. The format is based on [Keep a Changelog](http://keepachangelog.com/) and this project adheres to [Semantic Versioning](http://semver.org/). +## [2.2.0] - 02/09/2026 + +Release cut from the `improve_plotting` branch. This is the version used to +generate the rigid-body stability derivatives (Table 8) of Poland et al. (2026), +Wind Energ. Sci., "Computational aerodynamics for soft-wing kite design". + +### Fixed +- `BodyAerodynamics.va` setter: the rotational inflow due to body rates is now + `va -= omega x (r - r0)` (apparent wind = freestream minus body-point velocity). + v2.1.2 used `+=`, i.e. the body rotating at `-omega`. **This flips the sign of + every rate derivative** (`d/dp_hat`, `d/dq_hat`, `d/dr_hat`) computed with + `stability_derivatives.py`; angle derivatives and trim angles are unaffected. + Roll, pitch and yaw damping derivatives are now negative, as physics requires. +- `stability_derivatives.py::_evaluate_with_angles` now passes `body_axis`, so a + non-zero baseline roll/pitch rate is no longer silently applied about the z-axis. +- `trim_angle.py`: removed leftover debug `matplotlib` plot/`plt.show()` from the + coarse sweep (blocked headless pipelines). +- `Filament`: vortex-core regularization uses the radial projection of the + evaluation point onto the filament. +- `WingGeometry`: section meshing is orientation-agnostic. +- Elliptical-wing y-offset bug in tests fixed; bridle line index handling fixed. + +### Changed +- **Breaking:** `BodyAerodynamics.va_initialize` / `va` setter no longer accept + `roll_rate`, `pitch_rate`, `yaw_rate`. Use `body_rates` (scalar or list of + magnitudes, rad/s), `body_axis` (matching axes, default +z) and + `rates_in_body_frame`. `compute_trim_angle` and + `compute_rigid_body_stability_derivatives` keep their `roll_rate/pitch_rate/yaw_rate` + keyword arguments. +- **Breaking:** bridle-line dictionaries use header key `d` (line diameter) + instead of `diameter`, matching the SurfPlanAdapter export. +- `BodyAerodynamics.instantiate` accepts `aerodynamic_center_location` and + `control_point_location` (chord fractions, defaults 0.25 / 0.75); AC and CP + chord weights are decoupled. +- `Solver`: opt-in Anderson-accelerated inner circulation loop; opt-in + Li/Gaunaa spanwise artificial viscosity for post-stall stabilization; + `relaxation_factor` default restored to 0.01. +- `Solver.solve` results include `q_ref` (reference dynamic pressure); coefficients + are normalised with an area-weighted reference velocity for distributed inflow. +- Quasi-steady-state solver API and examples added and subsequently removed. + +### Added +- `BodyAerodynamics.rotate(angle_deg|angle_rad, axis, point)` to rotate the full + geometry; body rates follow the geometry unless `rates_in_body_frame=True`. +- `BodyAerodynamics.compute_flat_area`. +- `src/VSM/plotly/`: interactive Plotly geometry plots with inflatable tubes, + curved canopy, Cp-scaled force fields (`fancy_interactive_plot.py` example). +- Examples: `compute_trim_angle.py`, `calculate_max_roll.py`, + `attitude_and_yaw_rate_optimize.py`, `cmz_sensitivity_default.py`, + `varying_spanwise_va.py`. +- Tests for gamma initialization, tube geometry, updated filament/solver tests. + ## [2.1.0] - 11/02/2026 ### Added diff --git a/src/VSM/stability_derivatives.py b/src/VSM/stability_derivatives.py index 0489689..527008c 100644 --- a/src/VSM/stability_derivatives.py +++ b/src/VSM/stability_derivatives.py @@ -183,6 +183,7 @@ def _evaluate_with_angles(alpha_deg: float, beta_deg: float) -> CoeffDict: angle_of_attack=alpha_deg, side_slip=beta_deg, body_rates=[rates["r"], rates["q"], rates["p"]], + body_axis=[[0, 0, 1], [0, 1, 0], [1, 0, 0]], reference_point=reference_point, ) return _solve_and_extract() diff --git a/src/VSM/trim_angle.py b/src/VSM/trim_angle.py index 1207c8c..cb2402e 100644 --- a/src/VSM/trim_angle.py +++ b/src/VSM/trim_angle.py @@ -132,10 +132,6 @@ def _compute_derivative(alpha_deg: float, delta_deg: float) -> float: cmy_coarse.append(cmy_value) cmy_coarse_array = np.asarray(cmy_coarse) - import matplotlib.pyplot as plt - - plt.plot(alpha_coarse, cmy_coarse_array, marker="o") - plt.show() valid_mask = ~np.isnan(cmy_coarse_array) valid_alphas = alpha_coarse[valid_mask] valid_cmy = cmy_coarse_array[valid_mask] From f43bcdbe0cd0554a30d374f4fd29075e625c7a84 Mon Sep 17 00:00:00 2001 From: ocayon Date: Thu, 17 Sep 2026 17:25:38 +0200 Subject: [PATCH 11/37] feat(solver): chord-regularised curved bound vortex at the quarter chord The quarter-chord flow that sets the force directions (TAT3) held the other panels' bound segments evaluated on the bound line itself. On a curved or swept line that self-induction is logarithmically singular (Li, Gaunaa, Pirrung, Ramos-Garcia & Horcas 2020, "LL-P&S"), and because the on-blade induced drag is rho*Gamma*(w cos a + u sin a) with w only ~1 deg of induced angle, the chordwise u it produces moved the V3 drag by 10% and kept moving it with the panel count: on-blade over Trefftz 0.93 / 0.90 / 0.86 at 20 / 50 / 150 panels. Leaving the term out is worse (swept wings collapse, because the streamwise legs carry the opposite singularity), and reusing Li's 3/4-chord difference at the quarter chord breaks straight wings here. Replace the term by the difference between the actual vortex system and the same wing unrolled onto each panel's tangent line, with the bound vorticity and the leg starting points of every ring spread along the chord with the thin-airfoil distribution sqrt((c-x)/x). The quarter-chord velocity is then Prandtl's downwash of the unrolled wing plus a bracket that is identically zero on straight wings, finite on curved ones (the distribution fixes the cut-off at 0.15 c, no tunable length) and mesh-independent. Same mechanism as the effective-lifting-line / jointed-vortex method of Reid & Hunsaker (2020), whose two empirical lengths it removes; discrete counterpart of the inner solution of curved lifting-line theory (Guermond 1990). On-blade over Trefftz induced drag, inviscid: straight 1.000 (unchanged); arc R=4c 0.999 at 40, 80 and 160 panels; V3 1.007 / 1.008 / 1.010; swept 30 deg 0.97 -> 0.99; swept-anhedral elliptic wing of Gaunaa et al. 1.01. V3 viscous polars: lift unchanged, CD +0.001 at 5 deg, +0.006 at 10 deg, +0.011 at 13 deg, onto the RANS values. Cost: one numba kernel evaluated once per solve (about 1 s at 80 panels). Docs: Solver.md section on the consistent coupling, figures 03 (regenerated), 08 (mechanism and fix) and 09 (V3 polars) with README entries. Co-Authored-By: Claude Fable 5.1 --- docs/Solver.md | 35 ++++- docs/figures/03_trefftz_check.png | Bin 70933 -> 70455 bytes .../08_curved_bound_vortex_regularisation.png | Bin 0 -> 366040 bytes .../09_v3_polars_curved_bound_vortex_fix.png | Bin 0 -> 240220 bytes docs/figures/README.md | 35 ++++- src/VSM/core/BodyAerodynamics.py | 48 ++++-- src/VSM/core/utils.py | 142 +++++++++++++++--- .../test_curved_bound_vortex.py | 88 +++++++++++ 8 files changed, 307 insertions(+), 41 deletions(-) create mode 100644 docs/figures/08_curved_bound_vortex_regularisation.png create mode 100644 docs/figures/09_v3_polars_curved_bound_vortex_fix.png create mode 100644 tests/BodyAerodynamics/test_curved_bound_vortex.py diff --git a/docs/Solver.md b/docs/Solver.md index 440a434..5affc04 100644 --- a/docs/Solver.md +++ b/docs/Solver.md @@ -244,9 +244,30 @@ non-uniform grid (the paper derives it for uniform rectangular wings). drag directions come from the flow at the quarter chord (TAT3, the paper's LL-Gaunaa), **`is_aoa_corrected=True`**, now the default. False keeps the 3/4-chord directions (the paper's LL-3/4): those overestimate the induced - drag by 20-40% against the Trefftz plane (figure 03), but historically gave - a better match to the V3 wind-tunnel drag, for reasons not yet understood, - which is why it used to be the default. + drag by 20-40% against the Trefftz plane (figure 03). They historically + matched the V3 wind-tunnel drag better, but only because that overshoot has + the same lift-dependent shape as the drag the wind tunnel measures beyond + every simulation, RANS included (Poland et al. 2026 attribute it to the + model's thick canopy and the flow behind the leading-edge tube); a + compensating error, not a physical effect. +- **Curved bound vortex at the quarter chord.** The quarter-chord flow is the + trailed system (Prandtl's downwash, exact on straight wings) plus the + influence of the curved or swept bound vortex. Evaluating the other panels' + bound segments on the line itself is logarithmically singular (Li, Gaunaa, + Pirrung, Ramos-Garcia & Horcas 2020), which showed up as an on-blade induced + drag that kept falling with the panel count on the V3 (0.93, 0.90, 0.86 of + the Trefftz value at 20, 50, 150 panels). The solver instead adds, for each + panel, the difference between the actual vortex system and the same wing + unrolled onto the panel's tangent line, with the bound vorticity and the leg + starting points spread along the chord with the thin-airfoil distribution + `sqrt((c-x)/x)` (`assemble_curved_bound_correction_AIC`). The correction is + identically zero on straight wings, has no tunable length (the distribution + fixes the cut-off at 0.15 c), and brings the on-blade induced drag within 1% + of the Trefftz plane on an arc wing, the V3 and the paper's swept-anhedral + elliptic wing at every resolution (figure 08). It shares its mechanism with + the effective-lifting-line method of Reid & Hunsaker (2020), whose two + empirical lengths it replaces. On the V3 it raises the drag by about 5% of the + induced drag at 10 deg, onto the RANS value (figure 09). - **`is_with_attached_trailed_vortex_force`** (default True): Kutta-Joukowski force on the chordwise vortex legs between the bound vortex and the trailing edge (Sec. 3 of the paper). Zero net effect on unswept wings, needed for swept @@ -257,9 +278,11 @@ Every solve of a wing in one uniform inflow also reports `results["drag_induced_trefftz"]`, the Trefftz-plane induced drag (`BodyAerodynamics.compute_trefftz_plane_induced_drag`): the far-wake value that does not depend on where the forces are evaluated on the blade. With -quarter-chord directions and the attached-trailed force the on-blade drag of -an inviscid straight wing matches it to four digits; with 3/4-chord -directions it does not. It is `None` for per-panel inflow or body rates. +quarter-chord directions, the attached-trailed force and the curved +bound-vortex regularisation the on-blade drag of an inviscid straight wing +matches it to four digits and that of curved wings and the V3 within 1%, +independently of the panel count; with 3/4-chord directions it does not. It +is `None` for per-panel inflow or body rates. 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zeiUXC+M@vkDFb*RPy2c8Ni-s}aM)Z>*Mv900?0*&z9-e3bJe7ddztX#24F6yF%jSf z(EK&?0U9&_R|{heyvTTdF8U0eNJZN%hvi|5%e1wOawlqQ5t^ z>|wMA>O$(hnO_^z;Qnfv%!8-tmcRG=_g~z>+VDLV_n`8EV+;6jEdXHUtu6<8TNAu@ z3Umvi13NpJkYzIfa}dm-$;yYNHgb9Zww3`XwJkNP+??O!6s#V`B5$R#A814dEK7dk zYX&hXG`l*{q-p`(h=wb6-X(6?GV77bI1$a(An;gdB+S-Y3Fxy$;M4Offf5D^vXHDU z_q%W6=nK3$=sn={%@MiabRsC2(XLCSbq*k=yju4W zN|*xQ%ePy4fG}SZOoM3%i@-pm6{7F7qv0P&jL$+;%z1&4UBNaF7{rp%_G`mY=}{c4 zia%42oCKr^Q7Z}pYf47$rn7RGv-cKL&1_&!S66bgsX}!NkLF_|GHj9vg2}9Kgzzr4 zHCID>NTE*ngPf<+1{N1TvaA+6-+JJ{drIJAYOhF9N@ohqWou8igQL4y!wU=whVgjI zpI@m~A_xfYrT}seXA{qMAXhFP-6j(u5ZWFX-#rUhz?**XYFYMJ0W|SNt~}JGTf`K! zluFznLPf;|p@@J5{+eRG})) zF|(1uo4iu+HK=$#$Uw~>pN9}k(}TV;roX_KXtzA9{q^fteTWb@Tol*7-%+ZY0auK} z;(~hdIg}DFQbwmCvX&quhY1Fz8|PQp;W*Gx`_PH%AS<_`BZ bp1. + fwd = True + if n > 1: + fwd = np.linalg.norm(bound_point_1[0] - bound_point_2[1]) < np.linalg.norm( + bound_point_2[0] - bound_point_1[1] + ) + sgn = 1.0 if fwd else -1.0 + s_node = np.zeros(n + 1) + for j in range(n): + s_node[j + 1] = s_node[j] + L[j] + for i in range(n): + ep = eval_points[i] + t = seg[i] / L[i] + c_i = chord_dir[i] + s_P = 0.5 * (s_node[i] + s_node[i + 1]) + U = va_norm[i] + for j in range(n): + ra = ep + sgn * (s_node[j] - s_P) * t + rb = ep + sgn * (s_node[j + 1] - s_P) * t + if fwd: + rb2 = ra + rb1 = rb + else: + rb2 = rb + rb1 = ra + leg = (1.0 - ac_fraction) * chords[j] * c_i + rte1 = rb1 + leg + rte2 = rb2 + leg + bp1 = bound_point_1[j] + bp2 = bound_point_2[j] + te1 = TE_point_1[j] + te2 = TE_point_2[j] + # unrolled legs (single filaments) minus actual legs (single filaments) + v = _vel_trailing_vortex(rb1, rte1, ep, 1.0, U) + _vel_trailing_vortex( + rte2, rb2, ep, 1.0, U ) - AIC[0, icp, jring] = vel[0] - AIC[1, icp, jring] = vel[1] - AIC[2, icp, jring] = vel[2] - return AIC + v = v - _vel_trailing_vortex(bp1, te1, ep, 1.0, U) - _vel_trailing_vortex( + te2, bp2, ep, 1.0, U + ) + # chordwise-spread actual system minus chordwise-spread unrolled system + for q in range(n_strips): + f = (strip_x[q] - ac_fraction) / (1.0 - ac_fraction) + w = strip_w[q] + n1 = bp1 + f * (te1 - bp1) + n2 = bp2 + f * (te2 - bp2) + u1 = rb1 + f * (rte1 - rb1) + u2 = rb2 + f * (rte2 - rb2) + v = v + w * ( + _vel_bound_vortex(n2, n1, ep, 1.0, core_radius_fraction) + - _vel_bound_vortex(u2, u1, ep, 1.0, core_radius_fraction) + + _vel_trailing_vortex(n1, te1, ep, 1.0, U) + + _vel_trailing_vortex(te2, n2, ep, 1.0, U) + - _vel_trailing_vortex(u1, rte1, ep, 1.0, U) + - _vel_trailing_vortex(rte2, u2, ep, 1.0, U) + ) + A[0, i, j] = v[0] + A[1, i, j] = v[1] + A[2, i, j] = v[2] + return A + + +def thin_airfoil_strips(n_strips=24): + """Chordwise stations x/c and weights of the thin-airfoil bound vorticity + distribution gamma(x) ~ sqrt((c - x)/x), via x = c sin^2(phi) with phi at + the midpoints of n_strips equal intervals on (0, pi/2), so that + sqrt((c - x)/x) dx = 2 c cos^2(phi) dphi. The centroid of the weights is at + x/c = 1/4, so the far field of the spread vorticity equals that of the + single quarter-chord filament.""" + phi = (np.arange(n_strips) + 0.5) * (np.pi / 2) / n_strips + x = np.sin(phi) ** 2 + w = np.cos(phi) ** 2 + return np.ascontiguousarray(x, dtype=float), np.ascontiguousarray(w / w.sum(), dtype=float) @jit(nopython=True, cache=True) diff --git a/tests/BodyAerodynamics/test_curved_bound_vortex.py b/tests/BodyAerodynamics/test_curved_bound_vortex.py new file mode 100644 index 0000000..3d36256 --- /dev/null +++ b/tests/BodyAerodynamics/test_curved_bound_vortex.py @@ -0,0 +1,88 @@ +"""The quarter-chord direction velocity on curved lifting lines. + +A lifting line evaluated on itself has a logarithmically singular +self-induction wherever it is curved. The regularised correction in +``assemble_curved_bound_correction_AIC`` must (a) vanish on a straight wing, +so the classical exact result is kept, and (b) make the on-blade induced drag +equal to the Trefftz-plane value on curved wings independently of the panel +count. Inviscid polars, so the on-blade drag is pure induced drag. +""" + +import numpy as np +import pytest + +from VSM.core.BodyAerodynamics import BodyAerodynamics +from VSM.core.Solver import Solver +from VSM.core.WingGeometry import Wing +from VSM.core.utils import assemble_curved_bound_correction_AIC, thin_airfoil_strips + +_alpha = np.radians(np.linspace(-25, 25, 101)) +INVISCID = np.column_stack((_alpha, 2 * np.pi * _alpha, 0 * _alpha, 0 * _alpha)) + + +def _straight(n_panels, half_span=4.0): + wing = Wing(n_panels=n_panels, spanwise_panel_distribution="uniform") + for y in np.linspace(-half_span, half_span, n_panels + 1): + wing.add_section(np.array([0.0, y, 0.0]), np.array([1.0, y, 0.0]), INVISCID) + body = BodyAerodynamics([wing]) + body.va_initialize(20.0, 5.0, 0.0) + return body + + +def _arc(n_panels, radius=4.0, half_angle_deg=55.0): + """Circular-arc wing (kite-like anhedral), constant chord 1 along x.""" + wing = Wing(n_panels=n_panels, spanwise_panel_distribution="uniform") + for th in np.radians(np.linspace(-half_angle_deg, half_angle_deg, n_panels + 1)): + le = np.array([0.0, radius * np.sin(th), radius * np.cos(th)]) + wing.add_section(le, le + np.array([1.0, 0.0, 0.0]), INVISCID) + body = BodyAerodynamics([wing]) + body.va_initialize(10.0, 8.0, 0.0) + return body + + +def _ratio(body): + results = Solver(allowed_error=1e-7, max_iterations=4000).solve(body) + assert results["gamma_converged"] + return results["drag"] / results["drag_induced_trefftz"] + + +def test_strip_weights_are_thin_airfoil_with_quarter_chord_centroid(): + x, w = thin_airfoil_strips(24) + assert np.isclose(w.sum(), 1.0) + assert np.isclose(np.sum(w * x), 0.25, atol=2e-3) + # effective cut-off exp() of the distribution is 0.15 c + assert np.isclose(np.exp(np.sum(w * np.log(np.abs(x - 0.25)))), 0.15, atol=0.02) + + +def test_correction_vanishes_on_a_straight_wing(): + body = _straight(20) + panels = body.panels + ep = np.array([p.aerodynamic_center for p in panels]) + bp1 = np.array([p.bound_point_1 for p in panels]) + bp2 = np.array([p.bound_point_2 for p in panels]) + te1 = np.array([p.TE_point_1 for p in panels]) + te2 = np.array([p.TE_point_2 for p in panels]) + y_airf = np.array([p.y_airf for p in panels]) + chords = np.array([p.chord for p in panels]) + x, w = thin_airfoil_strips() + A = assemble_curved_bound_correction_AIC( + ep, bp1, bp2, te1, te2, y_airf, chords, np.full(20, 20.0), 0.25, 0.05, x, w + ) + assert np.max(np.abs(A)) < 1e-9 + + +def test_straight_wing_on_blade_drag_equals_trefftz(): + assert np.isclose(_ratio(_straight(40)), 1.0, atol=2e-3) + + +@pytest.mark.parametrize("n_panels", [20, 40, 80]) +def test_arc_wing_on_blade_drag_equals_trefftz_at_every_resolution(n_panels): + # Before the regularisation this ratio was 0.977 / 0.957 / 0.937 at + # 20 / 40 / 80 panels and kept falling (log-singular self-induction). + assert np.isclose(_ratio(_arc(n_panels)), 1.0, atol=1e-2) + + +def test_arc_wing_ratio_is_mesh_independent(): + r40 = _ratio(_arc(40)) + r80 = _ratio(_arc(80)) + assert abs(r80 - r40) < 3e-3 From a4ca2ca9755a48d9b51bfded88a7e5c161c15d4b Mon Sep 17 00:00:00 2001 From: ocayon Date: Mon, 12 Oct 2026 17:12:17 +0200 Subject: [PATCH 12/37] docs(validation): report and reproducible validation of the curved bound-vortex regularisation docs/validation/curved_bound_vortex_validation.py reproduces every table of the report from the committed solver: on-blade over Trefftz induced drag against panel count for a straight wing, skewed ribs, a 30 deg swept wing, a circular arc, the TORQUE 2026 swept-anhedral elliptic wing and the V3, for the regularisation and for the alternatives that were tried and rejected (trailed system only, bound segments on the line as on develop before, the literal Li et al. 2020 recipe, the Reid & Hunsaker 2020 effective-line construction with its joint and blending parameters), the arc mid-span self-induction (polyline vs chordwise-spread sheet), the V3 viscous polars, and figures 08 and 09. Full run 193 s; results in the JSON next to it. docs/validation/curved_bound_vortex_report.tex/.pdf: problem statement, cause, literature (Li 2018/2020, Gaunaa 2026 and its online appendix, Reid & Hunsaker, Guermond 1990, core methods), the formulation, the verification tables and the V3 polars against RANS and the wind tunnel, plus the two points where the code still deviates from the published Li/Gaunaa prescription. Co-Authored-By: Claude Fable 5.1 --- .../08_curved_bound_vortex_regularisation.png | Bin 366040 -> 368756 bytes .../09_v3_polars_curved_bound_vortex_fix.png | Bin 240220 -> 243602 bytes docs/figures/README.md | 3 + .../validation/curved_bound_vortex_report.pdf | Bin 0 -> 831839 bytes .../validation/curved_bound_vortex_report.tex | 230 +++++ .../curved_bound_vortex_validation.json | 971 ++++++++++++++++++ .../curved_bound_vortex_validation.py | 563 ++++++++++ 7 files changed, 1767 insertions(+) create mode 100644 docs/validation/curved_bound_vortex_report.pdf create mode 100644 docs/validation/curved_bound_vortex_report.tex create mode 100644 docs/validation/curved_bound_vortex_validation.json create mode 100644 docs/validation/curved_bound_vortex_validation.py diff --git a/docs/figures/08_curved_bound_vortex_regularisation.png b/docs/figures/08_curved_bound_vortex_regularisation.png index ce876b96f42c2c40a4c011c66cf789d87b9d390d..8a586f7db4ba0e9a430a666981770ddd303fc4f7 100644 GIT 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+\usepackage[margin=2.2cm]{geometry} +\usepackage{amsmath,amssymb} +\usepackage{graphicx} +\usepackage{booktabs} +\usepackage{array} +\usepackage[hidelinks]{hyperref} +\usepackage{caption} +\usepackage{enumitem} +\usepackage{microtype} +\graphicspath{{../figures/}} +\setlength{\parskip}{4pt} +\setlength{\parindent}{0pt} +\title{On-blade induced drag of curved lifting lines in the Vortex Step Method:\\ +problem statement, literature, and a parameter-free regularisation} +\author{Working document, awegroup/Vortex-Step-Method, branch \texttt{feature/curved-bound-vortex-regularisation}} +\date{17 September 2026 (rebuilt 12 October 2026)} + +\begin{document} +\maketitle + +\begin{abstract} +The \texttt{develop} branch of the Python Vortex Step Method (VSM) was aligned with the coupling rules of Gaunaa, Li and Pirrung (TORQUE 2026): force magnitudes from the three-quarter-chord flow, force directions from the quarter-chord flow, and a Kutta--Joukowski force on the attached-trailed vortex legs. With these rules the on-blade induced drag equals the Trefftz-plane value exactly on straight wings, but on the TU~Delft V3 kite it is 7--15\,\% low and decreases without bound as the number of spanwise panels increases. This document states the problem, identifies its cause (the logarithmically singular self-induction of the curved bound vortex, evaluated on its own line to set the force direction, entering the drag through $\rho\Gamma\,u\sin\alpha$), reviews how the literature treats the singularity, tests the two published remedies inside the VSM framework, and describes the parameter-free regularisation now implemented: the quarter-chord velocity is built from the classical lifting-line downwash of the wing unrolled onto the local tangent line, plus the difference between the actual and the unrolled vortex systems with the bound vorticity and the leg starting points spread chordwise with the thin-airfoil distribution. The result is identically zero on straight wings, mesh-independent, and within 1\,\% of the Trefftz-plane induced drag on an arc wing, a swept wing, the swept--anhedral elliptic wing of Gaunaa et al., and the V3 kite. All tables are reproduced by \texttt{docs/validation/curved\_bound\_vortex\_validation.py}. +\end{abstract} + +\section{Status of the implementation with respect to Li and Gaunaa} +\label{sec:status} + +The \texttt{develop} branch (commits \texttt{233a238}\ldots\texttt{62c53af}) implements the following elements of Gaunaa, Li and Pirrung~\cite{gaunaa2026} and Li, Gaunaa, Pirrung and L{\o}nb{\ae}k~\cite{li2026}: +\begin{itemize}[nosep] + \item CP1: the inner 2D velocity is the component perpendicular to the local quarter-chord line, and the chord is measured perpendicular to that line; + \item TAT1: the section's own 2D bound-vortex induction is subtracted at the three-quarter-chord point (the VSM \texttt{subtract\_bound\_2D} term, which the code has had since its inception); + \item TAT2: force magnitudes from the three-quarter-chord angle of attack, with $\Gamma_i = \tfrac12 |V_{\mathrm{inner},i}|\, c_i\, C_l(\alpha_{3/4,i})$ (eq.~4 of~\cite{gaunaa2026}); + \item TAT3: force directions from the undisturbed relative flow at the quarter chord (\texttt{is\_aoa\_corrected=True}, now the default); + \item the attached-trailed (AT) vortex force $\rho\,\Delta\Gamma_j\, \mathbf V_{3D,\mathrm{rel},j}\times \mathbf l_{AT,j}$ evaluated at the three-quarter-chord point of the leg; + \item the implicit artificial viscosity with the tip closures and the relaxation-factor bound of~\cite{li2026}, the latter halved for the VSM after measurement of the fixed-point Jacobian. +\end{itemize} + +\textbf{Two elements do not follow the published prescription.} +\begin{enumerate}[nosep] + \item \emph{The curved bound-vortex influence on the direction velocity.} Reference~\cite{gaunaa2026} states that LL-Gaunaa includes ``the influence of the curved bound vortex'' according to~\cite{li2020}. In~\cite{li2020} (Section~2.2) that influence is the induction of the 3D bound vortex minus that of an infinitely long 2D vortex of the section's own strength, evaluated at the \emph{three-quarter} chord, assumed constant along the chord, and added to the quarter-chord velocity. \texttt{develop} instead evaluated the other panels' bound segments \emph{on the quarter-chord line itself} (commit \texttt{9c43c1a}), which~\cite{li2020} calls LL-P\&S and shows to be log-singular and non-convergent. This is the cause of the problem treated here (Section~\ref{sec:problem}). A literal implementation of the~\cite{li2020} recipe in this code was also tested and fails on straight wings (Section~\ref{sec:lit}); the 2026 paper and its online appendix~\cite{appendix2026} do not specify the quarter-chord term further, so the form used in the authors' code needs clarification with them. The branch replaces the term by the regularisation of Section~\ref{sec:fix}. + \item \emph{The direction of the attached-trailed legs.} Reference~\cite{gaunaa2026} aligns the bound part of the trailed vortex with the local chordwise direction, i.e.\ perpendicular to the quarter-chord line (CP1). The code keeps the legs along the section ribs. On the V3 the two differ by up to 0.77 in chord-to-span skew at the tips. Perpendicular legs were tried and rejected because they produced coincident filaments on a streamwise-ribbed swept wing and a worse comparison with RANS for the V3 (mean $|\Delta C_D|/C_D$ 4.7\,\% instead of 1.5\,\%). This remains a deviation; the regularisation of Section~\ref{sec:fix} works with either leg direction. +\end{enumerate} + +\section{Problem statement} +\label{sec:problem} + +\subsection{Observation} +For steady, uniform inflow the induced drag can be computed in two ways from the same converged circulation $\Gamma(s)$: on the blade, by projecting the panel forces (lift tilted by the quarter-chord flow angle, plus the AT force) onto the freestream, or in the Trefftz plane from the momentum in the far wake. The Trefftz value depends only on $\Gamma(s)$ and the wake geometry; for a consistent force evaluation the two must agree. Table~\ref{tab:conv} shows the ratio for inviscid polars ($C_l = 2\pi\alpha$) with the bound segments evaluated on the line. + +\begin{table}[h]\centering\small +\caption{On-blade over Trefftz-plane induced drag, bound segments on the quarter-chord line (\texttt{develop} as of \texttt{62c53af}), inviscid polars.} +\label{tab:conv} +\begin{tabular}{lcccccc} +\toprule +case & $N=10$ & 20 & 40 & 80 & 160 & trend\\ +\midrule +straight rectangular, AR 8 & -- & 1.000 & 1.000 & 1.000 & -- & exact\\ +swept $30^\circ$, AR 8, streamwise ribs & 0.933 & 0.937 & 0.939 & 0.940 & 0.936 & converged, 6\,\% low\\ +circular arc, $110^\circ$, $R=4c$ & 0.998 & 0.977 & 0.957 & 0.937 & 0.917 & $-0.02$ per doubling\\ +elliptic, 10\,\% sweep, 25\,\% anhedral (\cite{gaunaa2026}) & -- & -- & 0.980 & 0.967 & 0.954 & $-0.013$ per doubling\\ +V3 kite, CAD geometry & -- & 0.933 & 0.907 & 0.881 & 0.854 & $-0.026$ per doubling\\ +\bottomrule +\end{tabular} +\end{table} + +Lift is converged to four digits in all cases; only the drag drifts. The drift is a clean logarithm in $N$ on every wing with out-of-plane curvature. + +\subsection{Cause} +The quarter-chord direction velocity of panel $i$ was assembled as +\begin{equation} +\mathbf V_{1/4,i} = \mathbf V_\infty + \sum_j \Gamma_j\,\mathbf K^{\mathrm{trailed}}_j(\mathbf P_i) + \sum_{j\neq i} \Gamma_j\, \mathbf K^{\mathrm{bound}}_j(\mathbf P_i), +\label{eq:current} +\end{equation} +with $\mathbf P_i$ on the bound line. The last sum is needed: without it a swept wing with streamwise legs diverges (ratio 0.43 at $N=40$, 0.25 at $N=160$), because the legs carry a logarithmic term of their own that only the bound segments cancel. But on a line curved out of its own plane the neighbouring segments induce, at $\mathbf P_i$, a velocity perpendicular to the plane of curvature, i.e.\ along the chord, +\begin{equation} +u \simeq \frac{\Gamma\kappa}{4\pi}\ln\frac{L}{\epsilon},\qquad \epsilon\sim\frac{\text{panel width}}{2}, +\end{equation} +which has no counterpart in the legs and grows as the panels shrink. Figure~\ref{fig:explain}(b) shows this on the arc: the polyline value at mid-span grows by 0.05\,m/s per doubling of $N$ ($U=10$\,m/s). + +The drag is exceptionally sensitive to this component. With the lift perpendicular to $\mathbf V_{1/4}$ and $\mathbf V_{1/4}=(U\cos\alpha+u,\; U\sin\alpha-w)$ in chord/normal components, the freestream component of the force is +\begin{equation} +D_i = \rho\,\Gamma_i\,(w\cos\alpha + u\sin\alpha). +\label{eq:drag} +\end{equation} +The downwash $w$ corresponds to about one degree of induced angle, so a chordwise $u$ of 3\,\% of $U$ at $\alpha=8^\circ$ moves the induced drag by about 12\,\%. This is the whole V3 shortfall: on the arc the ratio is 1.08 with the bound term removed and drifts from 0.96 to 0.92 with it included; the physically correct value of $u$ lies in between and is finite. + +\begin{figure}[p]\centering +\includegraphics[width=\textwidth]{08_curved_bound_vortex_regularisation.png} +\caption{Mechanism and fix (\texttt{docs/figures/08}). (a) Front view of the curved bound polyline with the quarter-chord point of panel $i$. (b) Arc wing, mid-span: chordwise self-induction from the polyline (grows logarithmically with $N$) and from the chordwise-spread sheet (finite); grey band: value at which on-blade drag equals Trefftz. (c) Why a chordwise velocity changes the drag, eq.~\eqref{eq:drag}. (d) The thin-airfoil bound vorticity distribution used for the regularisation; effective cut-off $\exp\langle\ln|x-c/4|\rangle_\gamma = 0.15\,c$. (e) The unrolled reference construction. (f) Convergence of on-blade over Trefftz drag before and after.} +\label{fig:explain} +\end{figure} + +\section{How the literature treats the singularity} +\label{sec:lit} + +\subsection{Li, Gaunaa, Pirrung, Ramos-Garc\'ia, Horcas (2020): evaluate at the three-quarter chord} +Reference~\cite{li2020} identifies the LL-P\&S evaluation (bound vortex on its own line, as in Phillips and Snyder~\cite{phillips2000}) as log-singular and demonstrates its mesh dependence numerically (their Figs.~3--4). Their remedy (LL-mod) evaluates the bound-vortex induction at the three-quarter-chord point, subtracts the 2D infinite-vortex induction of the section's own strength, treats the difference as constant along the chord and adds it to the quarter-chord velocity that sets the force direction. The trailed vortices are also evaluated at the three-quarter chord in LL-mod, which they note makes the iteration less stable. This is the reference cited by~\cite{gaunaa2026} for LL-Gaunaa; neither the 2026 paper nor its online appendix~\cite{appendix2026} (results for ten planforms at 120 sections, no convergence study) adds implementation detail. + +\emph{Test in the VSM framework.} The recipe was implemented literally: for every panel $j$, the finite bound segment at the control point $\mathbf C_i$ minus (for $j=i$) the infinite line, reused at $\mathbf P_i$. Results (on-blade/Trefftz): straight AR\,8 wing 0.848, straight AR\,4 wing 0.815, arc 0.84, swept--anhedral elliptic wing with perpendicular legs 0.865, swept $30^\circ$ wing $0.50\to0.35$. The straight-wing failure is decisive: for a finite wing with spanwise-varying $\Gamma$ the ``3D minus 2D'' difference at the three-quarter chord is not zero (it contains the finite-span tails and the $\Gamma$-variation of the bound vortex; $+0.02$\,m/s at mid-span and $+0.11$\,m/s near the tips at $U=20$\,m/s on the AR\,8 wing), and eq.~\eqref{eq:drag} amplifies it. The same quantity used for the three-quarter-chord angle of attack, which the VSM has always done, is correct and untouched; only its reuse as a quarter-chord velocity fails. Since~\cite{gaunaa2026} reports LL-Gaunaa within 0.6\,\% of a VLM on straight wings, the authors' implementation must differ from this literal reading, most plausibly by taking ``curved minus straight'' (as first described in~\cite{li2018}) rather than ``3D minus 2D''. This should be confirmed with the authors. In their appendix the on-blade Oswald factor sits 5.6\,\% and 1.1\,\% above the Trefftz one for the 15\,\% and 25\,\% swept wings, within 0.6\,\% for the dihedral, anhedral and combined wings. + +\subsection{Reid and Hunsaker (2020), Goates and Hunsaker (2021, 2023): effective lifting line and jointed legs} +References~\cite{reid2020,goates2021,goates2023} (open-source implementation MachUpX) prove that the induced velocity on a lifting line is finite only where the line's second derivative vanishes and the trailing vortices leave it perpendicularly. Their construction: each control point sees an \emph{effective} lifting line, straight (tangent) near the point and blended into the true curve with a Gaussian of prescribed width (``blending distance'', recommended $\gtrsim 25\,\%$ of the span, MachUpX default one semispan); each trailing vortex has a finite \emph{joint} of length $\delta c$ perpendicular to the effective line before turning along the freestream (recommended $\delta\gtrsim0.15$, MachUpX default 0.15). Bound segments of the other sections are kept. Validation is on circulation distributions and $C_L$ of planar swept wings against panel methods and experiment; induced drag and non-planar wings are not examined. + +\emph{Test in the VSM framework.} The construction was implemented for the quarter-chord direction velocity, everything else unchanged (Table~\ref{tab:rh}). It is mesh-independent, as claimed, but the induced drag depends on the two lengths, by 17\,\% on the V3 and 12\,\% on the arc across reasonable choices, because the blending distance is precisely the cut-off of the curvature logarithm; the authors' insensitivity statement concerns lift, which is far less sensitive. With streamwise rib legs the swept wing fails (0.2--0.7), since the perpendicular joints no longer represent the vortex system that carries the force. + +\begin{table}[h]\centering\small +\caption{Reid--Hunsaker construction in the VSM framework: on-blade over Trefftz drag at $N=80$. Joint length and blending distance in local chords, except the MachUpX column (defaults: joint 0.15\,$c$, blending one semispan). Last column: the regularisation of Section~\ref{sec:fix} at the same $N$.} +\label{tab:rh} +\begin{tabular}{lccccccc} +\toprule +case & 0.25\,/\,1 & 0.5\,/\,1 & 1.0\,/\,1 & 0.5\,/\,0.5 & 0.5\,/\,2 & MachUpX & regularised\\ +\midrule +straight AR 8 & 1.000 & 1.000 & 1.000 & 1.000 & 1.000 & 1.001 & 1.000\\ +swept $30^\circ$, rib legs & 0.642 & 0.471 & 0.198 & 0.191 & 0.637 & 0.688 & 0.982\\ +arc, $R=4c$ & 1.049 & 1.025 & 1.004 & 1.003 & 1.052 & 1.117 & 0.999\\ +elliptic, 10\,\% sweep, 25\,\% anhedral & 1.007 & 0.988 & 0.968 & 0.968 & 1.008 & 1.042 & 1.015\\ +V3 kite & 1.003 & 0.966 & 0.930 & 0.885 & 1.032 & 1.053 & 1.008\\ +\bottomrule +\end{tabular} +\end{table} + +\subsection{Other approaches} +\begin{itemize}[nosep] + \item \emph{Li et al.\ 2018}~\cite{li2018}: correct a straight-blade model by the difference between the curved and an imaginary straight bound vortex. Same subtraction idea as below, but with single filaments, hence mesh dependent; abandoned in~\cite{li2020}. + \item \emph{Guermond 1990}~\cite{guermond1990}: matched-asymptotic lifting-line theory for curved and swept wings. Shows analytically that the curvature term is finite once the inner (airfoil-scale) problem is accounted for, using Hadamard finite-part integrals. It is the theoretical basis for a chord-scale cut-off but is not a numerical scheme with horseshoes and polars. + \item \emph{Vortex core on the bound vortex} (e.g.\ QBlade~\cite{qblade}, core radius a fraction of chord): Reid and Hunsaker note these are ``very sensitive to the cutoff/core distance''. Tested here with the code's Vatistas kernel: the projection of an on-line point to the core boundary produces spurious velocities of order $\Gamma/(4\pi\epsilon)$ and unusable results. + \item \emph{Three-quarter-chord directions} (Weissinger, Ranneberg~\cite{ranneberg2015}, the VSM default before the \texttt{develop} branch): no singularity, but the induced drag is overestimated by 20--40\,\% on the V3~\cite{gaunaa2026}. + \item \emph{Trefftz-plane drag only} (Ranneberg): exact for the total in steady uniform inflow, unavailable with body rates or distributed inflow, no spanwise distribution. +\end{itemize} + +\section{The regularisation implemented on the branch} +\label{sec:fix} + +\subsection{Formulation} +Let $\mathbf K^{\mathrm{LL}}_j(\mathbf P)$ denote the induction at $\mathbf P$ of ring $j$ without its bound segment (two legs and two semi-infinite wake filaments; this is what the code's LLT influence matrix holds), and let $\mathbf K^{\mathrm{sheet}}_j(\mathbf P)$ denote the induction of ring $j$ with its bound vorticity and its leg starting points spread along the chord: +\begin{equation} +\mathbf K^{\mathrm{sheet}}_j(\mathbf P)=\sum_{q=1}^{M} w_q\Big[\mathbf K^{\mathrm{seg}}\big(\mathbf n_{2,jq}\to\mathbf n_{1,jq};\mathbf P\big) + \mathbf K^{\mathrm{leg}}\big(\mathbf n_{1,jq}\to\mathbf T_{1,j}\big)+\mathbf K^{\mathrm{leg}}\big(\mathbf T_{2,j}\to\mathbf n_{2,jq}\big)\Big] + \mathbf K^{\mathrm{wake}}_j(\mathbf P), +\end{equation} +where the strip nodes lie on each node's own leg line, +\begin{equation} +\mathbf n_{k,jq} = \mathbf b_{k,j} + \frac{x_q - x_{ac}}{1-x_{ac}}\,(\mathbf T_{k,j}-\mathbf b_{k,j}),\qquad x_{ac}=\tfrac14, +\end{equation} +so that the strip legs are collinear with the actual legs, and the chordwise stations and weights follow the thin-airfoil distribution $\gamma(x)\propto\sqrt{(c-x)/x}$ through $x_q=\sin^2\phi_q$, $w_q\propto\cos^2\phi_q$, $\phi_q=(q-\tfrac12)\pi/(2M)$, $M=24$ (\texttt{thin\_airfoil\_strips}). The distribution has its centroid at $c/4$, so the far field of the sheet equals that of the single filament. + +For each evaluation panel $i$, the \emph{unrolled} reference wing is built on the tangent line $\mathbf t_i$ of panel $i$ through $\mathbf P_i$: every node keeps its arc-length coordinate along the bound line, the legs are perpendicular to the line in panel $i$'s chord direction with the panel's own chord length, and the wake keeps its direction. The quarter-chord velocity is then +\begin{equation} +\boxed{\; +\mathbf V_{1/4,i}=\mathbf V_\infty+\sum_j\Gamma_j\Big[\mathbf K^{\mathrm{LL}}_{j,\mathrm{unrolled}(i)}(\mathbf P_i) ++\mathbf K^{\mathrm{sheet}}_{j}(\mathbf P_i)-\mathbf K^{\mathrm{sheet}}_{j,\mathrm{unrolled}(i)}(\mathbf P_i)\Big].\;} +\label{eq:fix} +\end{equation} +The first term is Prandtl's classical downwash of the straight wing with the actual $\Gamma(s)$, exact for straight wings (ratio 1.000). The bracket is the curvature, sweep and skew effect; it is identically zero on a straight wing with perpendicular legs, finite because both sheets regularise the near field at the chord scale, and convergent because no filament is evaluated on its own line. The semi-infinite wake filaments cancel identically between the actual and unrolled systems, so the wake model plays no role. Nothing else changes: the three-quarter-chord magnitude (which already contains the LL-mod term of~\cite{li2020}), the circulation map, the AT force and the wake are untouched. The single-filament limit of the bracket recovers the curved-minus-straight idea of~\cite{li2018}; the chordwise spreading is the discrete counterpart of the inner solution in~\cite{guermond1990}; the local straightening is the mechanism of~\cite{reid2020} without its two empirical lengths. The effective cut-off implied by the distribution is $\exp\langle\ln|x-c/4|\rangle_\gamma=0.1515\,c$; the number of strips does not matter beyond $M\approx 20$ (24 and 32 strips give the same arc self-induction to three digits). Implementation: \texttt{assemble\_curved\_bound\_correction\_AIC} in \texttt{src/VSM/core/utils.py}, called once per solve from \texttt{BodyAerodynamics.update\_effective\_angle\_of\_attack\_if\_VSM}; about 1\,s at 80 panels. + +\subsection{Verification against the Trefftz plane} + +\begin{table}[h]\centering\small +\caption{On-blade over Trefftz-plane induced drag with eq.~\eqref{eq:fix}, inviscid polars (\texttt{curved\_bound\_vortex\_validation.py}).} +\label{tab:fix} +\begin{tabular}{lccccc} +\toprule +case & $N=10$ & 20 & 40 & 80 & 160\\ +\midrule +straight rectangular, AR 8 & -- & -- & 1.000 & 1.000 & --\\ +straight, ribs skewed $22^\circ$ & -- & -- & 1.029 & 1.030 & --\\ +swept $30^\circ$, streamwise ribs & -- & -- & 0.971 & 0.982 & 0.988\\ +circular arc, $110^\circ$, $R=4c$ & 1.008 & 1.001 & 0.999 & 0.999 & 0.999\\ +elliptic, 10\,\% sweep, 25\,\% anhedral, rib legs & -- & -- & 1.014 & 1.015 & 1.017\\ +elliptic, same, perpendicular legs & -- & -- & 1.024 & 1.024 & --\\ +V3 kite, rib legs & -- & 1.011 & 1.007 & 1.008 & 1.010\\ +V3 kite, perpendicular legs & -- & -- & 1.042 & 1.038 & --\\ +\bottomrule +\end{tabular} +\end{table} + +Two residuals remain and are unrelated to the bound vortex: the swept wing converges to 0.99 rather than 1.00, and the straight wing with skewed ribs sits at 1.03 with or without the fix. Both point to the attached-trailed force on non-perpendicular legs and are a separate, smaller item. The 4\,\% excess with perpendicular legs on the V3 is likewise not caused by the bound-vortex term (it is the same with the bound segments on the line). + +\subsection{Independent evidence: the arc self-induction} +On the arc the chordwise self-induction that makes on-blade equal Trefftz is $u\approx-0.19$\,m/s (interpolating between the trailed-only value, ratio 1.079 at $u=0$, and the on-line value at $N=80$, ratio 0.951 at $u=-0.34$\,m/s). The chordwise-spread sheet gives $u=-0.186$\,m/s at every $N$ from 40 to 320 (Figure~\ref{fig:explain}b). Nothing was tuned to obtain this agreement. + +\subsection{Effect on the V3 kite polars} +Figure~\ref{fig:polars} and Table~\ref{tab:polars} show the V3 (CAD geometry, 2D RANS polars at Re $5\times10^5$, 50 panels, 2.82\,m/s) with the old three-quarter-chord directions, the quarter-chord directions with the bound segments on the line and the regularisation, against RANS~\cite{poland2026} and the wind-tunnel data of Poland et al.~\cite{poland2026}. Lift is unchanged; the drag rises by a fraction of the induced drag, most at high lift and in sideslip, and lands on the RANS values up to $10^\circ$. + +\begin{table}[h]\centering\small +\caption{V3 kite drag coefficient, $\beta=0$.} +\label{tab:polars} +\begin{tabular}{cccccc} +\toprule +$\alpha$ & old 3/4-chord & bound on the line & regularised & RANS (Re $10^6$) & wind tunnel (Re $5\times10^5$)\\ +\midrule +$5^\circ$ & 0.061 & 0.054 & 0.055 & 0.052 ($4^\circ$) & 0.076 ($5.4^\circ$)\\ +$7^\circ$ & 0.075 & 0.063 & 0.065 & 0.064 & 0.090 ($7.3^\circ$)\\ +$9^\circ$ & 0.094 & 0.074 & 0.079 & 0.084 ($10^\circ$) & 0.107 ($9.4^\circ$)\\ +$13^\circ$ & 0.148 & 0.110 & 0.120 & 0.110 & 0.217 ($13.4^\circ$)\\ +\bottomrule +\end{tabular} +\end{table} + +\begin{figure}[p]\centering +\includegraphics[width=\textwidth]{09_v3_polars_curved_bound_vortex_fix.png} +\caption{V3 kite polars (\texttt{docs/figures/09}) with the old three-quarter-chord directions, the quarter-chord directions with the bound segments on the line, and the regularisation, against RANS and the wind-tunnel data of Poland et al.\ (1:6.5 rigid model, no bridles, open-jet corrections applied).} +\label{fig:polars} +\end{figure} + +The remaining gap to the wind tunnel is lift-dependent, $\Delta C_D\approx0.003+0.037\,C_L^2$, and is shared by RANS ($C_D=0.043+0.052\,C_L^2$ versus $0.041+0.085\,C_L^2$ measured). Poland et al.\ attribute it to the 3--4\,mm model canopy, the flow behind the leading-edge tube and transition. It is not a lifting-line issue and the fix is not meant to close it; the old three-quarter-chord directions appeared to close part of it only because they overestimate the induced drag by 20--40\,\%. + +\section{Assessment and open items} +\begin{itemize}[nosep] + \item The mechanism of the fix (straighten locally, regularise the legs, keep the far field) is that of Reid and Hunsaker~\cite{reid2020}; the difference-form goes back to Li et al.~\cite{li2018}. The contribution here is the replacement of the two empirical lengths by the thin-airfoil chordwise distribution, which fixes the cut-off at $0.15\,c$ from theory, and the demonstration that this yields Trefftz-consistent induced drag on curved kites. It should be presented as such, with~\cite{reid2020,li2020,guermond1990} cited. + \item To be confirmed with the authors of~\cite{gaunaa2026,li2020}: how the curved bound-vortex influence is applied at the quarter chord in their code, and how it behaves when the number of sections is doubled. + \item Open: the attached-trailed force on skewed legs (swept wing 0.99, skewed ribs 1.03), and the choice between rib and perpendicular legs (Section~\ref{sec:status}, item~2). +\end{itemize} + +\begin{thebibliography}{99}\small +\bibitem{gaunaa2026} M.~Gaunaa, A.~Li, G.~R.~Pirrung, From thin airfoil theory to finite wings: consistent implementation of Lifting Line-based models, J.\ Phys.: Conf.\ Ser.\ 3224 (2026) 042030. +\bibitem{appendix2026} M.~Gaunaa, A.~Li, G.~R.~Pirrung, Internet appendix for ``From thin airfoil theory to finite wings'', Zenodo, doi:10.5281/zenodo.18222326 (2026). +\bibitem{li2026} A.~Li, M.~Gaunaa, G.~R.~Pirrung, K.~L{\o}nb{\ae}k, Relaxation limits and artificial viscosity for lifting line methods, TORQUE 2026. +\bibitem{li2020} A.~Li, M.~Gaunaa, G.~R.~Pirrung, N.~Ramos-Garc\'ia, S.~G.~Horcas, The influence of the bound vortex on the aerodynamics of curved wind turbine blades, J.\ Phys.: Conf.\ Ser.\ 1618 (2020) 052038. +\bibitem{li2018} A.~Li, G.~Pirrung, H.~Aa.~Madsen, M.~Gaunaa, F.~Zahle, Fast trailed and bound vorticity modeling of swept wind turbine blades, J.\ Phys.: Conf.\ Ser.\ 1037 (2018) 062012. +\bibitem{reid2020} J.~T.~Reid, D.~F.~Hunsaker, A general approach to lifting-line theory, applied to wings with sweep, J.\ Aircraft 58 (2021), doi:10.2514/1.C035994. +\bibitem{goates2021} C.~D.~Goates, D.~F.~Hunsaker, Practical implementation of a general numerical lifting-line method, AIAA SciTech 2021, paper 2021-0118. +\bibitem{goates2023} C.~D.~Goates, D.~F.~Hunsaker, Modern implementation and evaluation of lifting-line theory for complex geometries, J.\ Aircraft (2023), doi:10.2514/1.C036748. Code: \url{https://github.com/usuaero/MachUpX}. +\bibitem{guermond1990} J.-L.~Guermond, A generalized lifting-line theory for curved and swept wings, J.\ Fluid Mech.\ 211 (1990) 497--513. +\bibitem{phillips2000} W.~F.~Phillips, D.~O.~Snyder, Modern adaptation of Prandtl's classic lifting-line theory, J.\ Aircraft 37 (2000) 662--670. +\bibitem{ranneberg2015} M.~Ranneberg, Direct wing design and inverse airfoil identification with the nonlinear Weissinger method, arXiv:1501.04983 (2015). +\bibitem{qblade} QBlade documentation, Lifting line free vortex wake, \url{https://docs.qblade.org/src/theory/aerodynamics/lifting_line/lifting_line.html}. +\bibitem{poland2026} J.~A.~W.~Poland, J.~M.~van Spronsen, M.~Gaunaa, R.~Schmehl, Wind tunnel load measurements of a leading-edge inflatable kite rigid-scale model, Wind Energ.\ Sci.\ 11 (2026) 911. +\end{thebibliography} + +\end{document} diff --git a/docs/validation/curved_bound_vortex_validation.json 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inviscid polars, as a + function of the number of spanwise panels, for a straight wing, a straight + wing with skewed ribs, a 30 deg swept wing with streamwise ribs, a circular + arc wing, the swept-anhedral elliptic wing of Gaunaa, Li & Pirrung (TORQUE + 2026) and the TU Delft V3 kite; +* the same ratio for the alternatives that were tried and rejected: no bound + term at the quarter chord (trailed system only), the other panels' bound + segments evaluated on the line (Phillips & Snyder, "LL-P&S" in Li et al. + 2020; the develop branch before this work), the literal Li et al. 2020 + recipe (3D minus 2D bound induction at the 3/4 chord reused at the quarter + chord) and the effective-lifting-line / jointed-vortex construction of Reid + & Hunsaker (2020) for several joint lengths and blending distances; +* the chordwise self-induction at the mid-span of the arc from the bound + polyline (log-divergent) and from the chordwise-spread sheet (finite); +* the V3 viscous polars (figure 09) and the mechanism figure (figure 08). + +Every alternative is a drop-in replacement of +``assemble_curved_bound_correction_AIC`` installed by monkeypatching the name +in ``VSM.core.BodyAerodynamics``; the solver is otherwise unchanged. + +Usage (from the repository root; the full run takes about 20 minutes, most +of it in the pure-Python Reid-Hunsaker loops):: + + python docs/validation/curved_bound_vortex_validation.py # tables + python docs/validation/curved_bound_vortex_validation.py --quick # regularised + on-line + none only + python docs/validation/curved_bound_vortex_validation.py --figures # tables + figures 08, 09 +""" + +from __future__ import annotations + +import argparse +import json +import logging +import sys +import time +from pathlib import Path + +import numpy as np +import pandas as pd +import yaml + +import VSM.core.BodyAerodynamics as BA +from VSM.core.BodyAerodynamics import BodyAerodynamics +from VSM.core.Solver import Solver +from VSM.core.WingGeometry import Wing +from VSM.core.utils import ( + _vel_bound_vortex, + _vel_semiinfinite, + _vel_trailing_vortex, + thin_airfoil_strips, +) + +logging.disable(logging.CRITICAL) +ROOT = Path(__file__).resolve().parents[2] +OUT = Path(__file__).resolve().parent +FIG = ROOT / "docs" / "figures" +DATA = ROOT / "data" / "TUDELFT_V3_KITE" +REGULARISED = BA.assemble_curved_bound_correction_AIC + +_a = np.radians(np.linspace(-25, 25, 101)) +INVISCID = np.column_stack((_a, 2 * np.pi * _a, 0 * _a, 0 * _a)) + + +# -------------------------------------------------------------------------- +# Geometries +# -------------------------------------------------------------------------- +def straight(n, half_span=4.0, skew=0.0): + wing = Wing(n_panels=n, spanwise_panel_distribution="uniform") + for y in np.linspace(-half_span, half_span, n + 1): + wing.add_section(np.array([0.0, y, 0.0]), np.array([1.0, y + skew, 0.0]), INVISCID) + body = BodyAerodynamics([wing]) + body.va_initialize(20.0, 5.0, 0.0) + return body + + +def swept(n, sweep_deg=30.0, half_span=4.0): + """Kinked 30 deg sweep, sections (ribs) along the freestream x axis.""" + wing = Wing(n_panels=n, spanwise_panel_distribution="uniform") + for y in np.linspace(-half_span, half_span, n + 1): + x = abs(y) * np.tan(np.radians(sweep_deg)) + wing.add_section(np.array([x, y, 0.0]), np.array([x + 1.0, y, 0.0]), INVISCID) + body = BodyAerodynamics([wing]) + body.va_initialize(20.0, 5.0, 0.0) + return body + + +def arc(n, radius=4.0, half_angle_deg=55.0): + """Circular arc in the y-z plane (kite-like), chord 1 along x.""" + wing = Wing(n_panels=n, spanwise_panel_distribution="uniform") + for th in np.radians(np.linspace(-half_angle_deg, half_angle_deg, n + 1)): + le = np.array([0.0, radius * np.sin(th), radius * np.cos(th)]) + wing.add_section(le, le + np.array([1.0, 0.0, 0.0]), INVISCID) + body = BodyAerodynamics([wing]) + body.va_initialize(10.0, 8.0, 0.0) + return body + + +def elliptic_swept_anhedral(n, aspect_ratio=8.0, sweep=0.10, anhedral=0.25): + """Elliptic chord, root chord 1, tip offsets of 10 % (back) and 25 % (down) + of the semispan, parabolic; the TORQUE 2026 combined case.""" + s = aspect_ratio * (np.pi / 4) / 2 + wing = Wing(n_panels=n, spanwise_panel_distribution="uniform") + for y in np.linspace(-s, s, n + 1): + eta = min(abs(y) / s, 0.999999) + c = np.sqrt(1 - eta**2) + x = sweep * s * eta**2 + z = -anhedral * s * eta**2 + wing.add_section(np.array([x, y, z]), np.array([x + c, y, z]), INVISCID) + body = BodyAerodynamics([wing]) + body.va_initialize(10.0, 10.0, 0.0) + return body + + +_V3 = None + + +def v3_inviscid(n, alpha=10.0): + global _V3 + if _V3 is None: + _V3 = yaml.safe_load(open(DATA / "CAD_derived_geometry" / "aero_geometry_CAD_CFD_NF_combined.yaml")) + wing = Wing(n_panels=n, spanwise_panel_distribution="uniform") + for row in _V3["wing_sections"]["data"]: + wing.add_section(np.array(row[1:4], float), np.array(row[4:7], float), INVISCID) + body = BodyAerodynamics([wing]) + body.va_initialize(2.82, alpha, 0.0) + return body + + +# -------------------------------------------------------------------------- +# Alternatives for the quarter-chord bound-vortex term (drop-in replacements) +# -------------------------------------------------------------------------- +STATE = {"body": None, "U": None, "wake": None, "delta": 0.15, "blend": 1.0} + + +def _seg(x1, x2, p): + """Unit-strength straight segment x1 -> x2, zero on the line (to round-off).""" + r1 = p - x1 + r2 = p - x2 + r0 = x2 - x1 + c = np.cross(r1, r2) + L = np.linalg.norm(r0) + n = np.linalg.norm(c) + if n < 1e-9 * L * max(np.linalg.norm(r1), L): + return np.zeros(3) + return c / (4 * np.pi * n * n) * (r0 @ (r1 / np.linalg.norm(r1) - r2 / np.linalg.norm(r2))) + + +def _none(eval_points, bp1, bp2, *args): + """Trailed system only at the quarter chord.""" + n = eval_points.shape[0] + return np.zeros((3, n, n)) + + +def _on_line(eval_points, bp1, bp2, te1, te2, cdir, chords, va_norm, ac, core, sx, sw): + """Other panels' bound segments evaluated on the quarter-chord line + (Phillips & Snyder; develop before this work).""" + n = eval_points.shape[0] + A = np.zeros((3, n, n)) + for i in range(n): + for j in range(n): + if i != j: + A[:, i, j] = _vel_bound_vortex(bp2[j], bp1[j], eval_points[i], 1.0, core) + return A + + +def _li2020_literal(eval_points, bp1, bp2, te1, te2, cdir, chords, va_norm, ac, core, sx, sw): + """3D bound induction minus the section's own 2D infinite vortex, evaluated + at the 3/4-chord control point and reused at the quarter chord.""" + P = STATE["body"].panels + cps = np.array([p.control_point for p in P]) + n = eval_points.shape[0] + A = np.zeros((3, n, n)) + for i in range(n): + for j in range(n): + v = _seg(bp2[j], bp1[j], cps[i]) + if i == j: + r0 = bp1[j] - bp2[j] + t = r0 / np.linalg.norm(r0) + r1 = cps[i] - bp2[j] + dp = r1 - (r1 @ t) * t + v = v - np.cross(t, r1) / (2 * np.pi * (dp @ dp)) + A[:, i, j] = v + return A + + +def _ring_trailed(bp1, bp2, te1, te2, ep, wake, U): + return ( + _vel_trailing_vortex(bp1, te1, ep, 1.0, U) + + _vel_trailing_vortex(te2, bp2, ep, 1.0, U) + + _vel_semiinfinite(te1, wake, ep, 1.0, U, 1.0) + + _vel_semiinfinite(te2, wake, ep, 1.0, U, -1.0) + ) + + +def _reid_hunsaker(eval_points, bp1, bp2, te1, te2, cdir, chords, va_norm, ac, core, sx, sw): + """Reid & Hunsaker (2020): for each control point the lifting line is + straightened near the point (Gaussian blend of width STATE['blend'] times + the local chord, or an absolute length if STATE['blend'] is a tuple + ('abs', metres)), every trailing vortex gets a joint of STATE['delta'] + chords perpendicular to the effective line before turning along the + freestream, and the bound segments of the other rings are kept.""" + U = STATE["U"] + wake = STATE["wake"] + n = eval_points.shape[0] + seg = bp1 - bp2 + L = np.linalg.norm(seg, axis=1) + s_node = np.concatenate([[0.0], np.cumsum(L)]) + fwd = n == 1 or np.linalg.norm(bp1[0] - bp2[1]) < np.linalg.norm(bp2[0] - bp1[1]) + sgn = 1.0 if fwd else -1.0 + nodes = np.vstack([bp2, bp1[-1:]]) if fwd else np.vstack([bp1, bp2[-1:]]) + A = np.zeros((3, n, n)) + for i in range(n): + ep = eval_points[i] + t = seg[i] / L[i] + s_P = 0.5 * (s_node[i] + s_node[i + 1]) + blend = STATE["blend"] + ds = blend[1] if isinstance(blend, tuple) else blend * chords[i] + w = np.exp(-((s_node - s_P) / ds) ** 2) + eff = (1 - w)[:, None] * nodes + w[:, None] * (ep + sgn * (s_node - s_P)[:, None] * t) + for j in range(n): + e2, e1 = (eff[j], eff[j + 1]) if fwd else (eff[j + 1], eff[j]) + tj = e1 - e2 + tj = tj / np.linalg.norm(tj) + d = cdir[j] - (cdir[j] @ tj) * tj + d = d / np.linalg.norm(d) + j1 = e1 + STATE["delta"] * chords[j] * d + j2 = e2 + STATE["delta"] * chords[j] * d + v = (0.0 if i == j else 1.0) * _seg(e2, e1, ep) + v = v + _ring_trailed(e1, e2, j1, j2, ep, wake, U) + A[:, i, j] = v - _ring_trailed(bp1[j], bp2[j], te1[j], te2[j], ep, wake, U) + return A + + +VARIANTS = { + "regularised (this work)": REGULARISED, + "trailed only (no bound term)": _none, + "bound segments on the line (develop before)": _on_line, + "Li 2020 literal (3/4c difference reused)": _li2020_literal, +} +RH_PARAMS = [ # (joint length / chord, blending distance / chord) + (0.25, 1.0), + (0.5, 1.0), + (1.0, 1.0), + (0.5, 0.5), + (0.5, 2.0), +] + + +def solve(body, variant, **rh): + BA.assemble_curved_bound_correction_AIC = variant + STATE["body"] = body + va = body.va if np.ndim(body.va) == 1 else body.va[0] + STATE["U"] = float(np.linalg.norm(va)) + STATE["wake"] = va / STATE["U"] + STATE.update(rh) + try: + r = Solver(allowed_error=1e-7, max_iterations=4000).solve(body) + finally: + BA.assemble_curved_bound_correction_AIC = REGULARISED + return r + + +def ratio(body, variant, **rh): + r = solve(body, variant, **rh) + return float(r["drag"] / r["drag_induced_trefftz"]), float(r["cl"]) + + +# -------------------------------------------------------------------------- +# Tables +# -------------------------------------------------------------------------- +CASES = [ + ("straight AR 8", straight, (40, 80)), + ("straight, ribs skewed 22 deg", lambda n: straight(n, skew=0.4), (40, 80)), + ("swept 30 deg, streamwise ribs", swept, (40, 80, 160)), + ("arc 110 deg, R = 4c", arc, (20, 40, 80, 160)), + ("elliptic, 10% sweep, 25% anhedral", elliptic_swept_anhedral, (40, 80, 160)), + ("V3 kite, inviscid, 10 deg", v3_inviscid, (20, 40, 80, 160)), +] + + +def table_variants(quick): + names = ["regularised (this work)", "bound segments on the line (develop before)", "trailed only (no bound term)"] + if not quick: + names.append("Li 2020 literal (3/4c difference reused)") + rows = {} + print("\non-blade / Trefftz induced drag (CL), inviscid polars") + for case, mk, Ns in CASES: + for name in names: + vals = [] + for N in Ns: + t0 = time.time() + try: + rt, cl = ratio(mk(N), VARIANTS[name]) + except Exception as e: # degenerate geometry etc. + rt, cl = float("nan"), float("nan") + vals.append((N, rt, cl)) + rows[f"{case} | {name}"] = vals + print(f" {case:36s} {name:44s} " + " ".join(f"N={N}: {rt:.3f}" for N, rt, _ in vals), flush=True) + return rows + + +def table_reid_hunsaker(): + rows = {} + print("\nReid & Hunsaker construction, on-blade / Trefftz (joint/chord, blending/chord)") + for case, mk, Ns in CASES: + if "skewed" in case: + continue + N = min(max(Ns), 80) + for delta, blend in RH_PARAMS: + try: + rt, _ = ratio(mk(N), _reid_hunsaker, delta=delta, blend=blend) + except Exception: + rt = float("nan") + rows[f"{case} | RH {delta}/{blend}"] = [(N, rt)] + print(f" {case:36s} joint {delta:4.2f} c, blend {blend:3.1f} c N={N}: {rt:.3f}", flush=True) + # MachUpX defaults: joint 0.15 c, blending distance one semispan + body = mk(N) + y = np.array([p.aerodynamic_center[1] for p in body.panels]) + semispan = 0.5 * (y.max() - y.min()) + try: + rt, _ = ratio(body, _reid_hunsaker, delta=0.15, blend=("abs", semispan)) + except Exception: + rt = float("nan") + rows[f"{case} | RH MachUpX defaults"] = [(N, rt)] + print(f" {case:36s} MachUpX defaults (0.15 c, semispan) N={N}: {rt:.3f}", flush=True) + return rows + + +def arc_self_induction(): + """Chordwise induced velocity at the arc mid-span quarter-chord point from + the other panels' bound vortices: polyline (log-divergent) and chordwise- + spread sheet (finite). Circulation from the 80-panel solution.""" + b80 = arc(80) + r80 = solve(b80, REGULARISED) + gam80 = np.asarray(r80["gamma_distribution"]) + th80 = np.array([np.arctan2(p.aerodynamic_center[1], p.aerodynamic_center[2]) for p in b80.panels]) + order = np.argsort(th80) + sx, sw = thin_airfoil_strips() + out = {"N": [], "polyline": [], "sheet": []} + for N in (10, 20, 40, 80, 160, 320): + b = arc(N) + P = b.panels + i = N // 2 + ep = P[i].aerodynamic_center + th = np.array([np.arctan2(p.aerodynamic_center[1], p.aerodynamic_center[2]) for p in P]) + gam = np.interp(th, th80[order], gam80[order]) + u_poly = np.zeros(3) + u_sheet = np.zeros(3) + for j in range(N): + if j == i: + continue + u_poly += gam[j] * _vel_bound_vortex(P[j].bound_point_2, P[j].bound_point_1, ep, 1.0, 1e-20) + for x, w in zip(sx, sw): + sh = np.array([x - 0.25, 0.0, 0.0]) + u_sheet += gam[j] * w * _vel_bound_vortex(P[j].bound_point_2 + sh, P[j].bound_point_1 + sh, ep, 1.0, 1e-20) + out["N"].append(N) + out["polyline"].append(float(u_poly[0])) + out["sheet"].append(float(u_sheet[0])) + print("\narc mid-span chordwise self-induction u [m/s] (U = 10 m/s):") + for N, up, us in zip(out["N"], out["polyline"], out["sheet"]): + print(f" N={N:4d}: polyline {up:+.4f} sheet {us:+.4f}") + return out + + +# -------------------------------------------------------------------------- +# V3 viscous polars (figure 09) +# -------------------------------------------------------------------------- +def v3_polars(): + ref = np.array([0.422646, 0.0, 9.3667]) + U = 2.82 + body = BodyAerodynamics.instantiate( + n_panels=50, + file_path=DATA / "CAD_derived_geometry" / "aero_geometry_CAD_CFD_NF_combined.yaml", + spanwise_panel_distribution="uniform", + ) + alphas = [-3, -1, 1, 3, 5, 7, 9, 10, 11, 12, 13, 14, 15, 17, 19] + betas = [0, 4, 8, 12, 14, 20] + runs = { + "old34": (dict(is_aoa_corrected=False), REGULARISED), + "on_line": (dict(is_aoa_corrected=True), _on_line), + "fix": (dict(is_aoa_corrected=True), REGULARISED), + } + pol = {"alpha": {}, "beta": {}} + for tag, (kw, variant) in runs.items(): + s = Solver(reference_point=ref, **kw) + BA.assemble_curved_bound_correction_AIC = variant + rows = [] + for al in alphas: + body.va_initialize(U, float(al), 0.0) + r = s.solve(body) + rows.append((al, float(r["cl"]), float(r["cd"]))) + pol["alpha"][tag] = rows + rows = [] + for be in betas: + body.va_initialize(U, 7.4, float(be)) + r = s.solve(body) + rows.append((be, float(r["cl"]), float(r["cd"]), float(r["cs"]))) + pol["beta"][tag] = rows + BA.assemble_curved_bound_correction_AIC = REGULARISED + print(f" V3 polars {tag} done", flush=True) + return pol + + +# -------------------------------------------------------------------------- +# Figures 08 and 09 +# -------------------------------------------------------------------------- +def figure_08(conv, ux): + import matplotlib + + matplotlib.use("Agg") + import matplotlib.pyplot as plt + from matplotlib.patches import FancyArrowPatch + + plt.rcParams.update({"font.size": 9}) + fig, ax = plt.subplots(2, 3, figsize=(15, 9)) + A = ax[0, 0] + R = 4 + th = np.radians(np.linspace(-55, 55, 13)) + y, z = R * np.sin(th), R * np.cos(th) + A.plot(y, z, "o-", color="k", lw=2, ms=4, label="bound vortex (polyline) on the quarter-chord line") + i = 6 + P = (0.5 * (y[i] + y[i + 1]), 0.5 * (z[i] + z[i + 1])) + A.plot(*P, "r*", ms=14, label="quarter-chord point P of panel i") + for k in (4, 5, 7, 8): + m = (0.5 * (y[k] + y[k + 1]), 0.5 * (z[k] + z[k + 1])) + A.annotate("", xy=P, xytext=m, arrowprops=dict(arrowstyle="->", color="tab:blue", lw=1.2)) + A.text(0.0, 1.55, "neighbouring segments induce a velocity at P\nperpendicular to the arc plane, i.e. along the chord:\nu ~ (Gamma kappa / 4 pi) ln(span / panel width)\n-> grows without bound as the panels shrink", + ha="center", va="top", fontsize=8.5, bbox=dict(fc="w", ec="0.7")) + A.set_xlim(-3.6, 3.6); A.set_ylim(0.3, 4.6); A.set_xlabel("y (span)"); A.set_ylabel("z") + A.legend(loc="upper left", fontsize=8); A.set_title("(a) Front view: curved bound vortex evaluated on itself") + B = ax[0, 1] + B.semilogx(ux["N"], ux["polyline"], "o-", color="tab:red", label="polyline segments (bound on the line)") + B.semilogx(ux["N"], ux["sheet"], "s-", color="tab:green", label="chordwise-spread sheet (thin-airfoil weight)") + B.axhspan(-0.20, -0.18, color="0.85", label="value for which on-blade drag = Trefftz") + B.set_xlabel("number of spanwise panels N"); B.set_ylabel("chordwise induced velocity u at mid-span [m/s] (U = 10 m/s)") + B.set_title("(b) Arc wing: the self-induction diverges, the sheet value is finite"); B.legend(fontsize=8); B.grid(alpha=0.3) + C = ax[0, 2] + al = np.radians(20) + C.plot([-0.1, 1.1], [0, 0], "k-", lw=3); C.text(1.12, 0, "chord", va="center") + e = np.array([np.cos(al), np.sin(al)]); nvec = np.array([-np.sin(al), np.cos(al)]); o = np.array([0.25, 0.0]) + + def arr(p, v, c, lab, dy=0.02): + C.add_patch(FancyArrowPatch(p, p + v, arrowstyle="->", mutation_scale=14, color=c, lw=1.8)) + C.text(*(p + v + np.array([0.02, dy])), lab, color=c, fontsize=9) + + arr(o, 0.9 * e, "k", "freestream U\n(angle alpha to the chord)") + w = 0.12; u = -0.10 + arr(o + 0.9 * e, -w * nvec, "tab:blue", "downwash w (from the trailed wake)") + arr(o + 0.9 * e - w * nvec, u * e, "tab:red", "chordwise u (curved bound vortex)", dy=-0.06) + V = 0.9 * e - w * nvec + u * e; arr(o, V, "tab:purple", "quarter-chord flow V", dy=-0.12) + Vh = V / np.linalg.norm(V); Lv = np.array([-Vh[1], Vh[0]]) * 0.55 + arr(o, Lv, "tab:green", "lift, perpendicular to V", dy=0.0) + C.text(-0.1, -0.62, "the lift component along U is the\non-blade induced drag:\nD = rho Gamma (w cos(alpha) + u sin(alpha))\n\nw is small (about 1 deg of induced angle),\nso u = 3% of U changes D by about 12%", + fontsize=8.5, bbox=dict(fc="w", ec="0.7")) + C.set_xlim(-0.15, 1.75); C.set_ylim(-0.7, 0.9); C.set_aspect("equal"); C.axis("off"); C.set_title("(c) Why a chordwise velocity changes the drag") + Dd = ax[1, 0] + x = np.linspace(0.002, 0.998, 400); g = np.sqrt((1 - x) / x); g /= np.trapezoid(g, x) + Dd.plot(x, g, color="tab:green", lw=2, label="thin-airfoil bound vorticity gamma(x) ~ sqrt((c-x)/x)") + Dd.fill_between(x, 0, g, color="tab:green", alpha=0.15) + sx, _ = thin_airfoil_strips() + for xq in sx: + Dd.plot([xq, xq], [0, np.interp(xq, x, g)], color="tab:green", lw=0.6, alpha=0.6) + Dd.plot([0.25], [0], "ro", ms=9, label="single bound vortex at c/4 (lifting line)"); Dd.plot([0, 1], [0, 0], "k-", lw=3) + Dd.text(0.5, 2.2, "same total circulation, same centroid (c/4);\nspreading it over the chord makes the curved\nsheet self-induction finite (effective cut-off 0.15 c)", + ha="center", fontsize=8.5, bbox=dict(fc="w", ec="0.7")) + Dd.set_xlabel("x / c"); Dd.set_ylabel("gamma(x) c / Gamma"); Dd.set_ylim(-0.3, 3.2); Dd.legend(fontsize=8, loc="upper right") + Dd.set_title("(d) The regularisation: bound vortex spread over the chord") + E = ax[1, 1] + s = np.linspace(-1, 1, 9); yy = 3.0 * s; zz = -1.2 * s**2 + E.plot(yy, zz, "o-", color="k", lw=2, ms=4, label="actual curved system (bound + legs), smeared") + for k in range(9): + E.plot([yy[k], yy[k]], [zz[k], zz[k] - 0.6], color="k", lw=0.8) + E.plot(yy, 0 * yy + 0.9, "o-", color="tab:orange", lw=2, ms=4, label="same panels unrolled onto the tangent line of P") + for k in range(9): + E.plot([yy[k], yy[k]], [0.9, 0.3], color="tab:orange", lw=0.8) + E.plot([0], [0], "r*", ms=14); E.plot([0], [0.9], "r*", ms=14) + E.text(0, -2.1, "V(1/4c) = classical lifting-line downwash of the UNROLLED wing\n + [ smeared actual system - smeared unrolled system ]\n\nstraight wing: the bracket is exactly zero (nothing changes)\ncurved wing: the bracket is the finite curvature effect", + ha="center", fontsize=8.5, bbox=dict(fc="w", ec="0.7")) + E.set_xlim(-3.6, 3.6); E.set_ylim(-4.4, 1.5); E.axis("off"); E.legend(fontsize=8, loc="lower left") + E.set_title("(e) The fix: reference straight wing + regularised difference") + F = ax[1, 2] + for key, c, lab in (("arc 110 deg, R = 4c", "tab:blue", "arc wing"), ("V3 kite, inviscid, 10 deg", "tab:red", "V3 kite (inviscid)")): + for name, ls, m, lab2 in (("bound segments on the line (develop before)", "--", "o", "bound on the line"), ("regularised (this work)", "-", "s", "regularised")): + rows = np.array([(N, rt) for N, rt, _ in conv[f"{key} | {name}"]]) + F.semilogx(rows[:, 0], rows[:, 1], ls, marker=m, color=c, label=f"{lab}: {lab2}") + F.axhline(1.0, color="k", lw=0.8); F.set_xlabel("number of spanwise panels N"); F.set_ylabel("on-blade induced drag / Trefftz-plane induced drag") + F.set_title("(f) Result: mesh-independent and equal to Trefftz"); F.legend(fontsize=8); F.grid(alpha=0.3); F.set_ylim(0.8, 1.08) + fig.suptitle("Why the V3 on-blade induced drag disagrees with the Trefftz plane, and the fix", fontsize=13) + fig.tight_layout() + fig.savefig(FIG / "08_curved_bound_vortex_regularisation.png", dpi=150) + plt.close(fig) + + +def figure_09(pol): + import matplotlib + + matplotlib.use("Agg") + import matplotlib.pyplot as plt + + plt.rcParams.update({"font.size": 9}) + D = DATA / "3D_polars_literature" + cfd = pd.read_csv(D / "CFD_RANS_Rey_10e5_Poland2025_alpha_sweep_beta_0.csv") + wt = pd.read_csv(D / "windtunnel_alpha_sweep_beta_00_0_Poland_2025_Rey_5e5.csv") + wtb = pd.read_csv(D / "windtunnel_beta_sweep_alpha_07_4_Poland_2025_Rey_5e5.csv") + fig, ax = plt.subplots(2, 2, figsize=(12, 9)) + sty = { + "old34": dict(color="0.5", ls="--", label="develop before this work (3/4-chord directions)"), + "on_line": dict(color="tab:blue", ls="-", label="quarter-chord directions, bound segments on the line"), + "fix": dict(color="tab:red", ls="-", lw=2, label="quarter-chord directions, regularised curved bound vortex"), + } + for tag in ("old34", "on_line", "fix"): + r = np.array(pol["alpha"][tag]) + ax[0, 0].plot(r[:, 0], r[:, 1], **sty[tag]); ax[0, 1].plot(r[:, 0], r[:, 2], **sty[tag]); ax[1, 0].plot(r[:, 0], r[:, 1] / r[:, 2], **sty[tag]) + rb = np.array(pol["beta"][tag]); ax[1, 1].plot(rb[:, 0], rb[:, 2], **sty[tag]) + ax[0, 0].plot(cfd.alpha, cfd.CL, "k^", label="RANS Re 1e6 (Poland 2025)"); ax[0, 1].plot(cfd.alpha, cfd.CD, "k^"); ax[1, 0].plot(cfd.alpha, cfd.CL / cfd.CD, "k^") + m = (wt.alpha > -4) & (wt.alpha < 20) + ax[0, 0].errorbar(wt.alpha[m], wt.CL[m], yerr=wt.CL_ci[m], fmt="ko", mfc="w", label="wind tunnel Re 5e5 (Poland 2026), 99% CI") + ax[0, 1].errorbar(wt.alpha[m], wt.CD[m], yerr=wt.CD_ci[m], fmt="ko", mfc="w"); ax[1, 0].plot(wt.alpha[m], wt.CL[m] / wt.CD[m], "ko", mfc="w") + mb = wtb.beta >= -0.5 + ax[1, 1].errorbar(wtb.beta[mb], wtb.CD[mb], yerr=wtb.CD_ci[mb], fmt="ko", mfc="w", label="wind tunnel, +beta") + mb2 = wtb.beta <= 0.5 + ax[1, 1].errorbar(-wtb.beta[mb2], wtb.CD[mb2], yerr=wtb.CD_ci[mb2], fmt="kd", mfc="w", label="wind tunnel, -beta (mirrored)") + ax[0, 0].set_ylabel("CL"); ax[0, 1].set_ylabel("CD"); ax[1, 0].set_ylabel("L/D"); ax[1, 1].set_ylabel("CD at alpha 7.4 deg") + for a_ in ax[0]: + a_.set_xlabel("angle of attack [deg]") + ax[1, 0].set_xlabel("angle of attack [deg]"); ax[1, 1].set_xlabel("sideslip [deg]") + for a_ in ax.ravel(): + a_.grid(alpha=0.3) + ax[0, 0].legend(fontsize=8); ax[1, 1].legend(fontsize=8); ax[0, 1].set_ylim(0, 0.35) + fig.suptitle("TU Delft V3 kite, CAD geometry, 2D RANS Re 5e5 polars, 50 panels, 2.82 m/s: effect of the fix", fontsize=12) + fig.tight_layout() + fig.savefig(FIG / "09_v3_polars_curved_bound_vortex_fix.png", dpi=150) + plt.close(fig) + + +# -------------------------------------------------------------------------- +def main(argv=None): + ap = argparse.ArgumentParser(description=__doc__, formatter_class=argparse.RawDescriptionHelpFormatter) + ap.add_argument("--quick", action="store_true", help="only the regularised, on-line and trailed-only variants") + ap.add_argument("--figures", action="store_true", help="also regenerate docs/figures/08 and 09") + args = ap.parse_args(argv) + out = {} + t0 = time.time() + out["variants"] = table_variants(args.quick) + out["arc_self_induction"] = arc_self_induction() + if not args.quick: + out["reid_hunsaker"] = table_reid_hunsaker() + if args.figures: + print("\nV3 viscous polars for figure 09") + out["v3_polars"] = v3_polars() + figure_08(out["variants"], out["arc_self_induction"]) + figure_09(out["v3_polars"]) + print("figures 08 and 09 written to docs/figures") + json.dump(out, open(OUT / "curved_bound_vortex_validation.json", "w"), indent=1) + print(f"\nresults written to {OUT / 'curved_bound_vortex_validation.json'} ({time.time() - t0:.0f} s)") + + +if __name__ == "__main__": + main() From 118e91d7bb859017c9e5020323ac90f779b095c2 Mon Sep 17 00:00:00 2001 From: ocayon Date: Mon, 12 Oct 2026 17:34:20 +0200 Subject: [PATCH 13/37] docs(validation): rib versus perpendicular attached-trailed legs with the regularisation in place docs/validation/leg_direction_study.py repeats the September leg-direction comparison with the curved bound-vortex regularisation (f43bcdb) instead of the singular bound-on-line term: on-blade over Trefftz induced drag on the arc, the swept-anhedral elliptic wing, the inviscid V3 and a kinked 30 deg swept wing, with the attached-trailed force on and off, and the V3 viscous polars against RANS, for rib legs and for span-perpendicular (CP1) legs. Results in leg_direction_study.json (149 s). Outcome: the rib legs stay. Perpendicular legs cannot be built on the kinked planform (adjacent perpendiculars cross, NaN), lower the V3 inviscid lift by 6% and the agreement with RANS (mean |dCL| 0.031 against 0.020), and with the attached-trailed force sit 2.5-4% above the Trefftz plane on the swept V3 and elliptic lines, the same excess the TORQUE 2026 appendix shows on the authors' swept wings. Rib legs are within 1.5% on every curved case. No solver change. Report: new Section 4.3 with the table, status item 2 and the open items updated; PDF rebuilt (10 pages). Figures README entry 07 carries the new numbers. Co-Authored-By: Claude Fable 5.1 --- docs/figures/README.md | 9 + .../validation/curved_bound_vortex_report.pdf | Bin 831839 -> 846835 bytes .../validation/curved_bound_vortex_report.tex | 28 +- docs/validation/leg_direction_study.json | 362 ++++++++++++++++++ docs/validation/leg_direction_study.py | 150 ++++++++ 5 files changed, 547 insertions(+), 2 deletions(-) create mode 100644 docs/validation/leg_direction_study.json create mode 100644 docs/validation/leg_direction_study.py diff --git a/docs/figures/README.md b/docs/figures/README.md index acc5e01..47224b1 100644 --- a/docs/figures/README.md +++ b/docs/figures/README.md @@ -96,3 +96,12 @@ inboard, and on a swept wing with streamwise ribs the legs cross neighbouring panels and their control points (NaN). Against RANS the V3 mean errors are 0.020 in CL and 1.5% in CD with rib legs, 0.031 / 4.7% with fixed-length perpendicular legs and 0.057 / 9.4% with legs to the trailing edge. +Repeated with the curved bound-vortex regularisation in place +(`docs/validation/leg_direction_study.py`, results in the JSON next to it): +against RANS the V3 mean errors are 0.020 / 3.0% with rib legs and +0.031 / 3.8% with perpendicular legs (the 13 deg point carries most of the +drag error in both); on-blade over Trefftz induced drag is 1.01 with ribs +and 1.04 with perpendicular legs on the V3, 1.015 against 1.025 on the +swept-anhedral elliptic wing, identical on the arc, and the perpendicular +legs still fail on the kinked swept wing. The ribs stay; the report +`docs/validation/curved_bound_vortex_report.pdf` has the table. diff --git a/docs/validation/curved_bound_vortex_report.pdf b/docs/validation/curved_bound_vortex_report.pdf index 62379404babfc18506af850456500df286c8e50e..af39d533fb509c7219f64c26a7e5bac6d7d4275c 100644 GIT binary patch delta 92173 zcmZ_VbzBtR!#8|t>F#D}klJ0Ag+&@c8l*uHB&0(c1r`ti0jUL+l9uj9rKB4Pm6C30 zkP>_r{r&Fi`@OH{{$t09bIzPOGsDZ*dp>7j8FKtpv?_*}SN9PJ1hT(fSl%ukfuQIg z2;_acu(@5h-!44jpU@Jy{m(vRCNVwkpITN(Od={wcVq=VHx?8gPfm{Q)Qm{4RWDHpPfBnJs4qeE#q00_v$_<=Gqgf=eLu9gmjFc7i>lNwn>8ifgq zC!@oD2!kNC$Y?ReQ4ibzRJFcjs^nPcUDdikYH@KO2&hXaqHE*f>g8@_;{gLObt)R66*nn*+VpPl4L6E1bsC4!h3a1V&?R`L!$KczSveXiSn zOGy!m{Mn5>;F7rQ;T>*%l+ruEpWfPV-$8Ae6B8rTxk(Tbpxf>NMUvUMZhmv$+IHZJFJ}GvD)p2H+7&fYUNaRR2X%Ljrmh1|Vf_1v z+N>V}J$R8QAII{ed^>T(x4s0++Ttd-_b;LeRso0KyT&J0QG}SSw=8dSy#(#gK#Wi4`FC;eAROa~r(DeIRXU#m z7j>KAO^v|6 z7{h~nA0Js`mlmA1fC&5$h%I?&F8e6=7$6UVh-C)FXELCOV_EL>_XfY0|GJ360i@bH 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z01TW{_}4@k(@-mD@z7o6FlkhwRcpDJQc1FC8U<3&+|oo^hJP$4X}1S0JWdSehYP%VOZyXW)TAg38X`|Z;^A8tf^leK4tEIr z+c>>Ot6!%mX#T-l|6ZyRGz7RNzKM+kG)+v~L;{m=+9t*{7(CmjX3E``P;vCEMHB>0(z(Qu96g>WgC0#W#X(Op%T-bc=2Z|Stz!rMlO`c( zI69C`T(mE`v5R|ul7x=yI5bR70VSqyb)s?7MVC;hWP$3Wi`$RCY_vI%vUx^Bmlpl)*-iW-Xt62LMd^; Date: Mon, 12 Oct 2026 17:44:42 +0200 Subject: [PATCH 14/37] docs(validation): correct the sign of the authors' swept-wing Trefftz discrepancy 118e91d stated that the TORQUE 2026 appendix shows the same 1-6% excess of on-blade over Trefftz induced drag that perpendicular legs give here. The sign is the opposite: in Gaunaa, Li & Pirrung (2026) Table 2 and the appendix the on-blade induced drag of LL-Gaunaa is 1-5% below the Trefftz plane on the swept wings (e_Osw,Blade above e_Osw,Trefftz), and their VLM reference is 3% below as well. The report now states this, quotes the paper's own wording that the leg direction is a modelling choice not fixed by theory, and notes that the paper runs the legs up to the trailing edge while the perpendicular legs tested here have a fixed length. 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z6}V#|a}d0-0g`&X@9(Mu4#%KOBL@T<#{a-*dD>C3pP{acp$3&jz|hP-hj%6 z$Sr{3XlFvAIUEBya7IBY0Siu}m<;M7QVxg_5mkqTCDUx;03%TUFYsqx0*vNXPsNZI zC4iBzG)n@u*MFCeT6MfVtsI^0Jed_0Mdgn=p0N|fVlaSi-ObG#`~^G%IJD*WyV|>f zSD@;yy#gfXiX@ySxGQUd+YgGQh2E& WX-_+QW)cns-cn+gkkHiCV*Wo?$U?gS diff --git a/docs/validation/curved_bound_vortex_report.tex b/docs/validation/curved_bound_vortex_report.tex index 74d0fcd..927a394 100644 --- a/docs/validation/curved_bound_vortex_report.tex +++ b/docs/validation/curved_bound_vortex_report.tex @@ -39,7 +39,7 @@ \section{Status of the implementation with respect to Li and Gaunaa} \textbf{Two elements do not follow the published prescription.} \begin{enumerate}[nosep] \item \emph{The curved bound-vortex influence on the direction velocity.} Reference~\cite{gaunaa2026} states that LL-Gaunaa includes ``the influence of the curved bound vortex'' according to~\cite{li2020}. In~\cite{li2020} (Section~2.2) that influence is the induction of the 3D bound vortex minus that of an infinitely long 2D vortex of the section's own strength, evaluated at the \emph{three-quarter} chord, assumed constant along the chord, and added to the quarter-chord velocity. \texttt{develop} instead evaluated the other panels' bound segments \emph{on the quarter-chord line itself} (commit \texttt{9c43c1a}), which~\cite{li2020} calls LL-P\&S and shows to be log-singular and non-convergent. This is the cause of the problem treated here (Section~\ref{sec:problem}). A literal implementation of the~\cite{li2020} recipe in this code was also tested and fails on straight wings (Section~\ref{sec:lit}); the 2026 paper and its online appendix~\cite{appendix2026} do not specify the quarter-chord term further, so the form used in the authors' code needs clarification with them. The branch replaces the term by the regularisation of Section~\ref{sec:fix}. - \item \emph{The direction of the attached-trailed legs.} Reference~\cite{gaunaa2026} aligns the bound part of the trailed vortex with the local chordwise direction, i.e.\ perpendicular to the quarter-chord line (CP1). The code keeps the legs along the section ribs; the panel frame, the chord and the three-quarter-chord control point do follow CP1. On the V3 the two directions differ by up to 0.77 in chord-to-span skew at the tips. Perpendicular legs were compared again with the regularisation of Section~\ref{sec:fix} in place (Section~\ref{sec:legs}): they cannot be built on a kinked planform (adjacent perpendiculars cross and the solve returns NaN), they lower the V3 lift by 6\,\% and worsen the comparison with RANS (mean $|\Delta C_L|$ 0.031 instead of 0.020), and with the attached-trailed force the on-blade induced drag sits 2.5--4\,\% above the Trefftz plane, as the authors' own swept wings do in their appendix (1--6\,\%), whereas rib legs sit within 1.5\,\%. The ribs are kept. This remains a documented deviation; the regularisation works with either leg direction. + \item \emph{The direction of the attached-trailed legs.} Reference~\cite{gaunaa2026} aligns the bound part of the trailed vortex with the local chordwise direction, i.e.\ perpendicular to the quarter-chord line (CP1). The code keeps the legs along the section ribs; the panel frame, the chord and the three-quarter-chord control point do follow CP1. On the V3 the two directions differ by up to 0.77 in chord-to-span skew at the tips. Perpendicular legs were compared again with the regularisation of Section~\ref{sec:fix} in place (Section~\ref{sec:legs}): they cannot be built on a kinked planform (adjacent perpendiculars cross and the solve returns NaN), they lower the V3 lift by 6\,\% and worsen the comparison with RANS (mean $|\Delta C_L|$ 0.031 instead of 0.020), and with the attached-trailed force the on-blade induced drag sits 2.5--4\,\% above the Trefftz plane, whereas rib legs sit within 1.5\,\%. (The authors' own swept wings show a discrepancy of the same size but of the opposite sign: on-blade induced drag 1--5\,\% \emph{below} the Trefftz plane, Table~2 of~\cite{gaunaa2026} and the appendix~\cite{appendix2026}; their VLM reference is 3\,\% below as well.) The ribs are kept. This remains a documented deviation; the regularisation works with either leg direction. \end{enumerate} \section{Problem statement} @@ -197,7 +197,7 @@ \subsection{Rib versus perpendicular legs} \end{tabular} \end{table} -On the arc the ribs are perpendicular and the two coincide; there the AT force is required (0.946 to 0.999). On the elliptic wing and the V3 both the AT contribution ($+0.04$ and $+0.09$ with ribs, $+0.02$ and $+0.04$ with perpendicular legs) and the remainder depend on the leg direction, and their sum is within 1.5\,\% of the Trefftz plane with ribs but 2.5--4\,\% high with perpendicular legs. Dropping the AT force with perpendicular legs gives 1.00 on those two wings but 0.946 on the arc, so no rule is consistent on all three. The excess with perpendicular legs is not a bound-vortex effect (Table~\ref{tab:fix} shows it with the bound segments on the line as well); it is a property of chordwise legs on a swept quarter-chord line, where the leg carries a Kutta--Joukowski force from the downwash with a streamwise component, and the appendix of~\cite{gaunaa2026} shows the same 1--6\,\% excess on the authors' swept wings. On the V3 the perpendicular legs also lower the inviscid lift from 0.639 to 0.600 (the fixed-length leg at the curved tips ends far from the trailing edge), which moves the viscous $C_L$ away from RANS at every angle below $10^\circ$. On the kinked swept wing they cannot be built. The rib legs are therefore kept: constructible on every input planform, within 1.5\,\% of the far-wake drag on all curved cases, and the best V3 agreement with RANS (within 3\,\% in $C_D$ up to $10^\circ$; the 13$^\circ$ point, 10\,\% high, is near the RANS stall). +On the arc the ribs are perpendicular and the two coincide; there the AT force is required (0.946 to 0.999). On the elliptic wing and the V3 both the AT contribution ($+0.04$ and $+0.09$ with ribs, $+0.02$ and $+0.04$ with perpendicular legs) and the remainder depend on the leg direction, and their sum is within 1.5\,\% of the Trefftz plane with ribs but 2.5--4\,\% high with perpendicular legs. Dropping the AT force with perpendicular legs gives 1.00 on those two wings but 0.946 on the arc, so no rule is consistent on all three. The excess with perpendicular legs is not a bound-vortex effect (Table~\ref{tab:fix} shows it with the bound segments on the line as well); it is a property of chordwise legs on a swept quarter-chord line, where the leg carries a Kutta--Joukowski force from the downwash with a streamwise component. The authors' results on swept wings differ from the Trefftz plane by a similar amount but in the opposite direction: for the swept--anhedral elliptic wing, Table~2 of~\cite{gaunaa2026} gives $e_{\mathrm{Osw,Blade}}=1.101$ against $e_{\mathrm{Osw,Trefftz}}=1.080$ for LL-Gaunaa, i.e.\ on-blade induced drag 1.9\,\% \emph{below} the Trefftz plane, and their VLM reference is 2.8\,\% below (1.106 against 1.075); the appendix~\cite{appendix2026} gives 5\,\% and 1\,\% below for the 15\,\% and 25\,\% swept wings. The authors read this as a limitation of the Trefftz-plane analysis for curved wings. Note also that~\cite{gaunaa2026} (Section~3) runs the chordwise legs ``up to the trailing edge'', whereas the perpendicular legs tested here have the fixed length $(1-a)\bar c$ and end on the trailing edge only where it is parallel to the quarter-chord line; the paper states explicitly that the leg direction ``is not specified by theoretical results'' and ``is effectively a modeling choice''. On the V3 the perpendicular legs also lower the inviscid lift from 0.639 to 0.600 (the fixed-length leg at the curved tips ends far from the trailing edge), which moves the viscous $C_L$ away from RANS at every angle below $10^\circ$. On the kinked swept wing they cannot be built. The rib legs are therefore kept: constructible on every input planform, within 1.5\,\% of the far-wake drag on all curved cases, and the best V3 agreement with RANS (within 3\,\% in $C_D$ up to $10^\circ$; the 13$^\circ$ point, 10\,\% high, is near the RANS stall). \subsection{Independent evidence: the arc self-induction} On the arc the chordwise self-induction that makes on-blade equal Trefftz is $u\approx-0.19$\,m/s (interpolating between the trailed-only value, ratio 1.079 at $u=0$, and the on-line value at $N=80$, ratio 0.951 at $u=-0.34$\,m/s). The chordwise-spread sheet gives $u=-0.186$\,m/s at every $N$ from 40 to 320 (Figure~\ref{fig:explain}b). Nothing was tuned to obtain this agreement. From bf07a8b9e29dd28b46e50e479bcba9b942d6cd95 Mon Sep 17 00:00:00 2001 From: ocayon Date: Mon, 12 Oct 2026 21:05:56 +0200 Subject: [PATCH 15/37] feat(solver): leg_direction option for the attached-trailed legs, judged with a vortex-lattice referee BodyAerodynamics(..., leg_direction="rib" | "streamwise" | "perpendicular"), also on instantiate(). "rib" (default, unchanged behaviour) keeps the legs along the interpolated input sections. "perpendicular" is the TORQUE 2026 recipe: legs along the CP1 chord direction, perpendicular to the quarter-chord line, up to the trailing-edge curve; the line tangent is averaged over one leg length so the legs fan out instead of crossing at a planform kink (no free parameter), the leg ends at the closest point of the trailing-edge curve (extended at its ends for skewed tips), and the control point moves between the panel's own legs (without that, kinked wings diverge). "streamwise" projects the apparent velocity onto the surface and rebuilds the legs whenever va is set. utils.perpendicular_leg_end_points, Panel.set_leg_end_points. Legs that still cross raise ValueError. Referee: docs/validation/vlm_referee.py runs the AeroSandbox VLM (flat-plate sections) on straight, yawed, kinked-swept, arc, swept-anhedral elliptic wings and the inviscid V3, with the Trefftz drag of the VLM circulation (its near-field drag is low on non-planar wings). Rib and streamwise legs reproduce the VLM lift within 1% on all planar and curved wings (streamwise 2% low on the arc); the perpendicular legs lose 9% on the kinked wing and 8% on the V3, where they also cross at the tips above 80 panels. On the V3 against RANS the streamwise legs give the closest polars (drag within 0.3% up to 10 deg). The rib legs stay the default; the earlier fixed-length perpendicular test (118e91d) is superseded. Docs: report Section 4.3 rewritten with the three constructions, the referee tables and figures 10 (geometry: legs, aerodynamic centres, control points, VLM lattice) and 11 (referee); status item 2 and open items updated; docs/Solver.md and figures README. Tests: tests/BodyAerodynamics/ test_leg_direction.py (11 tests: equality with ribs where ribs are perpendicular or streamwise, skewed ribs give the straight wing, kinked wing builds and converges, crossing raises, legs follow the inflow). Full suite 181 passed, 5 skipped. Co-Authored-By: Claude Fable 5.1 --- docs/Solver.md | 23 +- docs/figures/10_leg_direction_geometry.png | Bin 0 -> 448239 bytes docs/figures/11_leg_direction_referee.png | Bin 0 -> 269776 bytes docs/figures/README.md | 53 +- .../validation/curved_bound_vortex_report.pdf | Bin 850022 -> 1557473 bytes .../validation/curved_bound_vortex_report.tex | 78 +- .../curved_bound_vortex_validation.py | 31 +- docs/validation/leg_direction_study.json | 710 +- docs/validation/leg_direction_study.py | 389 +- docs/validation/vlm_referee.json | 7509 +++++++++++++++++ docs/validation/vlm_referee.py | 253 + src/VSM/core/BodyAerodynamics.py | 100 +- src/VSM/core/Panel.py | 21 + src/VSM/core/utils.py | 145 + tests/BodyAerodynamics/test_leg_direction.py | 173 + 15 files changed, 9293 insertions(+), 192 deletions(-) create mode 100644 docs/figures/10_leg_direction_geometry.png create mode 100644 docs/figures/11_leg_direction_referee.png create mode 100644 docs/validation/vlm_referee.json create mode 100644 docs/validation/vlm_referee.py create mode 100644 tests/BodyAerodynamics/test_leg_direction.py diff --git a/docs/Solver.md b/docs/Solver.md index 5affc04..937e0e0 100644 --- a/docs/Solver.md +++ b/docs/Solver.md @@ -273,6 +273,27 @@ non-uniform grid (the paper derives it for uniform rectangular wings). edge (Sec. 3 of the paper). Zero net effect on unswept wings, needed for swept ones. Reported per section boundary in `F_attached_trailed_distribution` and folded into `F_distribution` and the totals. +- **Direction of the attached-trailed legs**, + `BodyAerodynamics(..., leg_direction=...)` (also on `instantiate`). The paper + states that theory does not fix this direction and chooses the chordwise + direction of CP1, perpendicular to the quarter-chord line, up to the + trailing edge. Three constructions are available (figure 10): `"rib"` + (default) runs the legs along the interpolated input sections to their + trailing-edge points, with the control point on the section; `"streamwise"` + runs them along the apparent velocity projected onto the surface, up to the + trailing-edge curve, and rebuilds them whenever `va` is set; `"perpendicular"` + is the paper's choice, with the tangent of the quarter-chord line averaged + over one leg length so that the legs do not cross at a planform kink. With + the last two the control point moves with the legs so that it stays between + the panel's own two legs. Against a vortex-lattice method (AeroSandbox, + `docs/validation/vlm_referee.py`, figure 11) rib and streamwise legs + reproduce the lift of straight, yawed, kinked-swept, arc and + swept-anhedral elliptic wings within 1% (streamwise: 2% low on the arc) and + the induced drag within 1-4%; perpendicular legs lose 9% of the lift on the + kinked swept wing and 8% on the V3, where they also cross at the tips above + 80 panels. On the V3 the rib legs are the ribs of the real kite; streamwise + legs give the closest V3 polars to RANS. Details in + `docs/validation/curved_bound_vortex_report.pdf`, Section 4.3. Every solve of a wing in one uniform inflow also reports `results["drag_induced_trefftz"]`, the Trefftz-plane induced drag @@ -293,7 +314,7 @@ chord directions, the red line with quarter-chord directions ![V3 polars before and after the consistency fixes](consistency_fixes_V3_polars.png) More figures (frame, Trefftz check, attached-trailed force, relaxation, -wake direction) with their descriptions are in [figures/README.md](figures/README.md). +wake direction, leg direction) with their descriptions are in [figures/README.md](figures/README.md). ### Frozen wake direction diff --git a/docs/figures/10_leg_direction_geometry.png b/docs/figures/10_leg_direction_geometry.png new file mode 100644 index 0000000000000000000000000000000000000000..87a224a3346470cc8f8dd173141fceaabd17795f GIT binary patch literal 448239 zcmeEuc{r5s|F0I5qDAE+4V8*iWM?FlQrY+HmBzk>AJ%@b{Y&b z#*i#CV@%eGF`Rq)p7S~9T-W*IT<6bo{pPv~EzdmjJoo*6zqa=iZJ?*c%X5;4gM)+j 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zAlZ>HB<#9y1I(z!ZS`DWaXblOUlO>sj>LO?&dS&kF90ps0)mB^PhDM=~000&wtTQBhN`49L#E zE;+qYtH3}ab+fiwK)?h??GF$%5Zvo%MCxt`F^)u95s>nqxiDB1bx*c-AZQrYO~zu^ zYX?L`#3u@aC9G2pgC$Wrk^guogFi7i>^isvJGpfA7DZzV&UI6Arat73=Ty` z*d544Mq(_Uj6qRv`TS1`YWW}%sNFb%MnoaB2R#Fcgvbs+BjeB%#AG}*bl1{A5D?bk zE(W*GbW~#^v4@HZNbP|i@c-fh^QW-^8i08I!}wnS;R$49Uq){Ti^-H?J9zXLnbGfOF*_8pt^#Jh+Gdyz8vPO5CDruFE{T9CPZXgKrIud;>lXqR zLqV22ECEYICLIt4hs1DTR?NQz|2QAaT~~;yH1c1@|BVBov+NR$e+U2u0>>l#1cX5* zB9=fRBVh&$;tOmGSnoojbl`6obr(d|{}6?YC#}hUka+|$Xzr0*$z&9gMg;kURD(!G zM#NlD068i;(*)F5df!Pe7A6l5C#N*dS@Atw_+?OaC# zxWA5uqh80mT0pQK2#<9%;vcB_ueN}JWMuyU5EpDhkdtws)j`rw>+=xo3y^y@upThi z>bb!FBn%mg?CiimEYk0w#3VW*uWP=-<~0 zLjVN~ITwh$4!8gf(OH50F$iBQGJ*k(xHe4ytYSgdtx26_8Ua~x2zbz0AT$QeJ!%~f z5DXx;sQC9^>Jac`{Mz0RFadjFB$@#l0a>&Opll#JZ!iqBduy#lL;>PI8fB$>21GLT zq5P(GWBY*vunoATklIBVx#)mq(1lfiqd;Tnb1WKq7(e8M)IZfj)0F%rE;NoOb{^k}=pVBQ?g7z{V3f4)n$UgSO79 zIFQLmtKvZYLq`tanx}xaZrcxNB>cMdKrAfB7SR8n`Eg+H zjtn?(1WElQkosCR4v#D_0MUua;sj` 1: + wing = wing.subdivide_sections(n_span) + points, faces = wing.mesh_thin_surface(method="quad", chordwise_resolution=n_chord, add_camber=False) + return np.asarray(points)[np.asarray(faces)] + + +def _draw(ax, body, legs, ij, lattice=None, outline=True, lw=1.2): + i, j = ij + bound, te, ac, cp, le_sec, te_sec = _geometry(body) + if lattice is not None: + for q in lattice: + q = np.vstack([q, q[:1]]) + ax.plot(q[:, i], q[:, j], color="0.8", lw=0.5, zorder=0) + if outline: + ax.plot(le_sec[:, i], le_sec[:, j], color="0.45", lw=0.8, zorder=1) + ax.plot(te_sec[:, i], te_sec[:, j], color="0.45", lw=0.8, zorder=1) + for a, b in zip(le_sec, te_sec): + ax.plot([a[i], b[i]], [a[j], b[j]], color="0.75", lw=0.5, zorder=1) + ax.plot(bound[:, i], bound[:, j], color="k", lw=2.0, zorder=3) + for a, b in zip(bound, te): + ax.plot([a[i], b[i]], [a[j], b[j]], color=COLOR[legs], lw=lw, zorder=2) + ax.plot(ac[:, i], ac[:, j], "o", color="k", ms=2.5, zorder=4) + ax.plot(cp[:, i], cp[:, j], "+", color=COLOR[legs], ms=6, mew=1.3, zorder=4) + ax.set_aspect("equal") + + +def figure_10(): + import matplotlib + + matplotlib.use("Agg") + import matplotlib.pyplot as plt + from matplotlib.lines import Line2D + + try: + import aerosandbox as asb + + FLAT = asb.Airfoil("naca0010") + xs = lambda pts, c=1.0: [asb.WingXSec(xyz_le=p, chord=c, twist=0.0, airfoil=FLAT) for p in pts] + except ImportError: + asb = None + + plt.rcParams.update({"font.size": 9}) + fig, ax = plt.subplots(2, 3, figsize=(15, 9.5)) + tan30 = np.tan(np.radians(30.0)) + + # (a) straight wing with skewed ribs, tip region: rib vs streamwise (= perpendicular) + A = ax[0, 0] + lat = _vlm_quads(xs([[0, -4, 0], [0, 4, 0]]), 4, 20) if asb else None + _draw(A, cbv.straight(20, skew=0.4), "rib", (1, 0), lattice=lat) + _draw(A, cbv.straight(20, skew=0.4, leg_direction="streamwise"), "streamwise", (1, 0), outline=False) + A.set_xlim(2.0, 4.6); A.set_ylim(1.6, -0.3) + A.set_title("(a) straight wing, ribs drawn 22 deg skewed: tip") + A.set_xlabel("y"); A.set_ylabel("x (flow downwards)") + + # (b) kinked swept wing, root region: rib (= streamwise) vs perpendicular + B = ax[0, 1] + lat = _vlm_quads(xs([[4 * tan30, -4, 0], [0, 0, 0], [4 * tan30, 4, 0]]), 4, 10) if asb else None + _draw(B, cbv.swept(40), "rib", (1, 0), lattice=lat) + _draw(B, cbv.swept(40, leg_direction="perpendicular"), "perpendicular", (1, 0), outline=False) + B.set_xlim(-1.6, 1.6); B.set_ylim(2.0, -0.4) + B.set_title("(b) kinked 30 deg swept wing: root") + B.set_xlabel("y"); B.set_ylabel("x (flow downwards)") + + # (c) elliptic swept-anhedral wing, right half, top view + C = ax[0, 2] + s = 8.0 * (np.pi / 4) / 2 + pts, chords = [], [] + for y in np.linspace(-s, s, 41): + eta = min(abs(y) / s, 0.999999) + pts.append([0.10 * s * eta**2, y, -0.25 * s * eta**2]); chords.append(np.sqrt(1 - eta**2)) + lat = None + if asb: + lat = _vlm_quads([asb.WingXSec(xyz_le=p, chord=c, twist=0.0, airfoil=FLAT) for p, c in zip(pts, chords)], 4, 1) + for legs in ("rib", "streamwise", "perpendicular"): + _draw(C, cbv.elliptic_swept_anhedral(40, leg_direction=legs), legs, (1, 0), lattice=lat if legs == "rib" else None, outline=legs == "rib", lw=1.0) + C.set_xlim(0.0, 3.3); C.set_ylim(1.4, -0.2) + C.set_title("(c) elliptic, 10% sweep, 25% anhedral: right half, top view") + C.set_xlabel("y"); C.set_ylabel("x (flow downwards)") + + # (d) arc wing, side view of the upper tip: streamwise legs climb with the flow + D = ax[1, 0] + for legs in ("rib", "streamwise"): + _draw(D, cbv.arc(40, leg_direction=legs), legs, (0, 2), outline=legs == "rib", lw=1.0) + D.set_xlim(-0.2, 1.4); D.set_ylim(2.1, 4.2) + D.set_title("(d) arc wing, 8 deg: side view of the tip region (x-z)") + D.set_xlabel("x"); D.set_ylabel("z") + + # (e) V3 kite, top view, whole wing, with the VLM lattice + E = ax[1, 1] + lat = None + if asb: + import vlm_referee + + lat = _vlm_quads(vlm_referee.v3_xsecs(), 4, 2) + v3 = {legs: cbv.v3_inviscid(40, leg_direction=legs) for legs in ("rib", "streamwise", "perpendicular")} + for legs, body in v3.items(): + _draw(E, body, legs, (1, 0), lattice=lat if legs == "rib" else None, outline=legs == "rib", lw=0.8) + E.invert_yaxis() + E.set_title("(e) V3 kite, 10 deg: top view") + E.set_xlabel("y"); E.set_ylabel("x (flow downwards)") + + # (f) V3 kite, the +y tip, top view + F = ax[1, 2] + for legs, body in v3.items(): + _draw(F, body, legs, (1, 0), outline=legs == "rib", lw=1.2) + bound = _geometry(v3["rib"])[0] + F.set_xlim(bound[:, 1].max() - 2.2, bound[:, 1].max() + 0.3) + xr = bound[:4, 0] + F.set_ylim(xr.max() + 1.8, xr.min() - 0.5) + F.set_title("(f) V3 kite: tip region") + F.set_xlabel("y"); F.set_ylabel("x (flow downwards)") + + handles = [ + Line2D([], [], color="k", lw=2, label="bound vortex (quarter-chord line)"), + Line2D([], [], color="0.45", lw=0.8, label="section outline (LE, TE, ribs)"), + Line2D([], [], color="0.8", lw=0.6, label="VLM lattice (AeroSandbox, coarse)"), + Line2D([], [], color="k", marker="o", ls="", ms=3, label="aerodynamic centre"), + Line2D([], [], color="tab:blue", lw=1.5, marker="+", ms=7, label="rib legs, control point"), + Line2D([], [], color="tab:green", lw=1.5, marker="+", ms=7, label="streamwise legs, control point"), + Line2D([], [], color="tab:red", lw=1.5, marker="+", ms=7, label="perpendicular legs, control point"), + ] + fig.legend(handles=handles, loc="lower center", ncol=4, frameon=False, bbox_to_anchor=(0.5, 0.0)) + fig.suptitle("Attached-trailed legs: along the ribs, along the flow, or perpendicular to the quarter-chord line", y=0.995) + fig.tight_layout(rect=(0, 0.05, 1, 0.98)) + fig.savefig(FIG / "10_leg_direction_geometry.png", dpi=150) + print(f"figure 10 written to {FIG / '10_leg_direction_geometry.png'}") + + +def figure_11(): + import matplotlib + + matplotlib.use("Agg") + import matplotlib.pyplot as plt + + ref = json.load(open(OUT / "vlm_referee.json")) + plt.rcParams.update({"font.size": 9}) + fig, ax = plt.subplots(2, 3, figsize=(15, 8.5)) + + # top: circulation distributions, finest VLM vs VSM at the finest N + panels = [("kinked swept 30 deg", "kinked 30 deg swept wing, 5 deg", 20.0), + ("elliptic", "elliptic, 10% sweep, 25% anhedral, 10 deg", 10.0), + ("V3", "V3 kite, flat-plate sections, 10 deg", 2.82)] + for A, (case, title, U) in zip(ax[0], panels): + row = ref[case] + vkeys = [k for k in row if k.startswith("VLM")] + v = row[vkeys[-1]] + o = np.argsort(v["y"]) + A.plot(np.array(v["y"])[o], np.array(v["gamma"])[o] / U, "k-", lw=2, label=f"VLM ({vkeys[-1][4:]})") + for legs in LEGS: + keys = [k for k in row if k.startswith(f"VSM {legs}")] + if not keys: + continue + r = row[keys[-1]] + o = np.argsort(r["y"]) + A.plot(np.array(r["y"])[o], np.array(r["gamma"])[o] / U, color=COLOR[legs], lw=1.3, label=f"VSM, {legs} legs ({keys[-1].split()[-1]})") + A.set_title(title); A.set_xlabel("y"); A.set_ylabel("Gamma / U") + A.legend(fontsize=8, frameon=False) + + # bottom: CL and induced drag relative to the VLM (Trefftz drag of the VLM circulation) + cases = ["straight AR 8", "yawed 30 deg", "kinked swept 30 deg", "arc", "elliptic", "V3"] + labels = ["straight", "yawed 30", "kinked 30", "arc", "elliptic", "V3"] + for A, quantity, ylabel in zip(ax[1, :2], ("CL", "CDi"), ("CL / CL_VLM", "CDi (on-blade) / CDi_VLM (Trefftz)")): + x = np.arange(len(cases)) + for k, legs in enumerate(LEGS): + vals = [] + for case in cases: + row = ref[case] + vkeys = [kk for kk in row if kk.startswith("VLM")] + v = row[vkeys[-1]] + keys = [kk for kk in row if kk.startswith(f"VSM {legs}")] + if not keys: + vals.append(np.nan) + continue + r = row[keys[-1]] + vals.append(r["CL"] / v["CL"] if quantity == "CL" else r["CDi_blade"] / v["CDi_trefftz"]) + A.bar(x + (k - 1) * 0.26, vals, 0.26, color=COLOR[legs], label=f"{legs} legs") + A.axhline(1.0, color="k", lw=0.8) + A.set_xticks(x); A.set_xticklabels(labels) + A.set_ylim(0.85, 1.15); A.set_ylabel(ylabel); A.legend(fontsize=8, frameon=False, ncol=3, loc="upper left") + ax[1, 0].set_title("lift relative to the VLM") + ax[1, 1].set_title("induced drag relative to the VLM") + + # bottom right: the V3 viscous polars against RANS for the three leg options + A = ax[1, 2] + st = json.load(open(OUT / "leg_direction_study.json"))["v3_vs_rans"] + for legs in LEGS: + rows = np.array(st[f"{legs} | AT=True"]["rows"]) + A.plot(rows[:, 0], rows[:, 2], "-o", color=COLOR[legs], ms=3, label=f"VSM, {legs} legs") + A.plot(rows[:, 0], rows[:, 4], "k--s", ms=3, label="RANS (Poland 2025)") + A.set_title("V3 viscous drag against RANS (2D RANS polars, 50 panels)") + A.set_xlabel("alpha [deg]"); A.set_ylabel("CD"); A.legend(fontsize=8, frameon=False) + fig.suptitle("Leg direction against a vortex-lattice referee (AeroSandbox) and RANS", y=0.995) + fig.tight_layout(rect=(0, 0, 1, 0.97)) + fig.savefig(FIG / "11_leg_direction_referee.png", dpi=150) + print(f"figure 11 written to {FIG / '11_leg_direction_referee.png'}") + + +def main(argv=None): + import argparse + + ap = argparse.ArgumentParser(description="rib / streamwise / perpendicular attached-trailed legs") + ap.add_argument("--figures", action="store_true", help="only draw figures 10 and 11 from the stored results") + args = ap.parse_args(argv) + if args.figures: + figure_10() + figure_11() + return t0 = time.time() - out = {"trefftz": trefftz_table(), "v3_vs_rans": v3_vs_rans()} + out = {"trefftz": trefftz_table(), "geometry": geometry_table(), "v3_vs_rans": v3_vs_rans()} json.dump(out, open(OUT / "leg_direction_study.json", "w"), indent=1) print(f"\nresults written to {OUT / 'leg_direction_study.json'} ({time.time() - t0:.0f} s)") + figure_10() + if (OUT / "vlm_referee.json").exists(): + figure_11() if __name__ == "__main__": diff --git a/docs/validation/vlm_referee.json b/docs/validation/vlm_referee.json new file mode 100644 index 0000000..d08a292 --- /dev/null +++ b/docs/validation/vlm_referee.json @@ -0,0 +1,7509 @@ +{ + "straight AR 8": { + "VLM 8x40": { + "CL": 0.40416905089811733, + 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-3.940297445900068, + -3.980882665942608, + -4.010357312989299, + -4.036893946993906, + -4.060187903515944, + -4.080593267564084, + -4.0980419116068685, + -4.1114466538155465 + ] + } + } +} \ No newline at end of file diff --git a/docs/validation/vlm_referee.py b/docs/validation/vlm_referee.py new file mode 100644 index 0000000..925c91e --- /dev/null +++ b/docs/validation/vlm_referee.py @@ -0,0 +1,253 @@ +"""Lifting-surface referee for the attached-trailed leg direction. + +The Trefftz plane checks the induced drag of a given circulation but cannot +judge the lift. A vortex-lattice method (VLM) can: for inviscid flat-plate +sections it solves the same potential-flow problem as the lifting line with +``Cl = 2 pi alpha``, with full chordwise resolution. This script runs the VLM +of AeroSandbox (Sharpe, MIT, ``pip install aerosandbox``; horseshoe vortices, +trailing legs along the body x axis, near-field forces) and the VSM with the +three leg options (``rib``, ``streamwise``, ``perpendicular``) on + +* a straight AR 8 wing, a yawed wing (uniform 30 deg sweep, no kink) and a + kinked 30 deg swept wing, chord 1, span 8, at 5 deg; +* the circular-arc wing (110 deg, R = 4 c) at 8 deg; +* the TORQUE 2026 swept-anhedral elliptic wing at 10 deg; +* the inviscid V3 kite (CAD leading and trailing edges, flat-plate sections) + at 10 deg. AeroSandbox takes its sections perpendicular to the local span, + so the skewed V3 ribs are unskewed there (chord = rib length, twist from + the rib's x-z angle); the surface differs from the VSM one at the tips. + +For the induced drag two VLM numbers are given: AeroSandbox's near-field +value, and the Trefftz-plane drag of the VLM's own strip circulation on the +wake trace. The two agree on planar wings; on the non-planar wings the +near-field value is low (the trailing legs are not aligned with the wind), +so the Trefftz value is the one to compare with. + +Results go to ``vlm_referee.json`` and into the report. About 4 minutes. +""" + +from __future__ import annotations + +import json +import logging +from pathlib import Path + +import numpy as np +import yaml + +import curved_bound_vortex_validation as cbv +from VSM.core.Solver import Solver + +try: + import aerosandbox as asb +except ImportError as err: # pragma: no cover + raise SystemExit("vlm_referee.py needs AeroSandbox: pip install aerosandbox") from err + +logging.disable(logging.CRITICAL) +OUT = Path(__file__).resolve().parent +FLAT = asb.Airfoil("naca0010") # symmetric: the VLM sees a flat camber line +LEGS = ("rib", "streamwise", "perpendicular") +RHO = 1.225 + + +def strip_circulation(vlm, n_chord, n_segments): + """Chordwise sum of the horseshoe strengths per spanwise strip, with the + strip's trailing-edge corners; handles the three panel orderings + AeroSandbox produces.""" + G = np.asarray(vlm.vortex_strengths) + te = np.asarray(vlm.is_trailing_edge, bool) + n_strip = len(G) // n_chord + if np.all(te.reshape(n_strip, n_chord)[:, -1]): + Gs = G.reshape(n_strip, n_chord).sum(axis=1) + te_idx = np.arange(n_strip) * n_chord + (n_chord - 1) + elif np.all(te.reshape(n_chord, n_strip)[-1]): + Gs = G.reshape(n_chord, n_strip).sum(axis=0) + te_idx = (n_chord - 1) * n_strip + np.arange(n_strip) + else: + ns_seg = n_strip // n_segments + te3 = te.reshape(n_segments, n_chord, ns_seg) + if not np.all(te3[:, -1, :]): + raise RuntimeError("AeroSandbox panel ordering not recognised") + Gs = G.reshape(n_segments, n_chord, ns_seg).sum(axis=1).ravel() + te_idx = np.array( + [(g * n_chord + n_chord - 1) * ns_seg + j for g in range(n_segments) for j in range(ns_seg)] + ) + bl = np.asarray(vlm.back_left_vertices)[te_idx] + br = np.asarray(vlm.back_right_vertices)[te_idx] + return Gs, bl, br + + +def trefftz_drag(G, bl, br, alpha_deg): + """Trefftz-plane induced drag of strip circulations ``G`` whose wake + leaves at the strip corners ``bl -> br``, projected onto the plane + perpendicular to the freestream (sideslip zero). Each strip edge sheds + a line vortex of strength equal to the jump in ``G``.""" + al = np.radians(alpha_deg) + ex = np.array([np.cos(al), 0.0, np.sin(al)]) + ey = np.array([0.0, 1.0, 0.0]) + ez = np.cross(ex, ey) + proj = lambda p: np.column_stack((p @ ey, p @ ez)) + L, R = proj(bl), proj(br) + order = np.argsort(0.5 * (L[:, 0] + R[:, 0])) + G, L, R = G[order], L[order], R[order] + edges = np.vstack([L[:1], 0.5 * (R[:-1] + L[1:]), R[-1:]]) + dG = np.concatenate(([G[0]], G[1:] - G[:-1], [-G[-1]])) + mid = 0.5 * (L + R) + tang = R - L + ds = np.linalg.norm(tang, axis=1) + tang = tang / ds[:, None] + nrm = np.column_stack((-tang[:, 1], tang[:, 0])) + drag = 0.0 + for j in range(len(G)): + r = mid[j][None, :] - edges + r2 = np.einsum("ij,ij->i", r, r) + v = (dG / (2 * np.pi * r2))[:, None] * np.column_stack((-r[:, 1], r[:, 0])) + drag += 0.5 * RHO * G[j] * float(np.sum(v @ nrm[j])) * ds[j] + return drag + + +def run_vlm(xsecs, area, U, alpha, n_chord, n_span_per_segment): + airplane = asb.Airplane( + wings=[asb.Wing(symmetric=False, xsecs=xsecs)], s_ref=area, c_ref=1.0, b_ref=1.0 + ) + vlm = asb.VortexLatticeMethod( + airplane=airplane, + op_point=asb.OperatingPoint(velocity=U, alpha=alpha), + spanwise_resolution=n_span_per_segment, + chordwise_resolution=n_chord, + align_trailing_vortices_with_wind=False, + ) + r = vlm.run() + G, bl, br = strip_circulation(vlm, n_chord, len(xsecs) - 1) + q = 0.5 * RHO * U**2 * area + return { + "CL": float(r["CL"]), + "CDi_near": float(r["CD"]), + "CDi_trefftz": float(trefftz_drag(G, bl, br, alpha) / q), + "gamma": G.tolist(), + "y": (0.5 * (bl[:, 1] + br[:, 1])).tolist(), + } + + +def run_vsm(make, N, legs, area, U): + body = make(N, leg_direction=legs) + r = Solver(allowed_error=1e-7, max_iterations=4000).solve(body) + q = 0.5 * RHO * U**2 * area + return { + "CL": float(r["cl"]), + "CDi_blade": float(r["drag"] / q), + "CDi_trefftz": float(r["drag_induced_trefftz"] / q), + "converged": bool(r["gamma_converged"]), + "gamma": np.asarray(r["gamma_distribution"]).ravel().tolist(), + "y": [float(p.aerodynamic_center[1]) for p in body.panels], + } + + +def show(name, key, v): + if "CDi_near" in v: + print(f" {name:22s} {key:22s}: CL {v['CL']:.4f} CDi near {v['CDi_near']:.5f} Trefftz {v['CDi_trefftz']:.5f}") + else: + print(f" {name:22s} {key:22s}: CL {v['CL']:.4f} CDi blade {v['CDi_blade']:.5f} Trefftz {v['CDi_trefftz']:.5f}") + + +def v3_xsecs(): + data = yaml.safe_load(open(cbv.DATA / "CAD_derived_geometry" / "aero_geometry_CAD_CFD_NF_combined.yaml")) + ribs = [(np.array(r[1:4], float), np.array(r[4:7], float)) for r in data["wing_sections"]["data"]] + ribs.sort(key=lambda t: t[0][1]) + xsecs = [] + for le, te in ribs: + cvec = te - le + xsecs.append(asb.WingXSec(xyz_le=le.tolist(), chord=float(np.linalg.norm(cvec)), + twist=float(np.degrees(np.arctan2(-cvec[2], cvec[0]))), airfoil=FLAT)) + return xsecs + + +def main(): + out = {} + tan30 = np.tan(np.radians(30.0)) + cases = { + "straight AR 8": ([[0.0, -4.0, 0.0], [0.0, 4.0, 0.0]], cbv.straight), + "yawed 30 deg": ([[-4.0 * tan30, -4.0, 0.0], [4.0 * tan30, 4.0, 0.0]], cbv.yawed), + "kinked swept 30 deg": ([[4.0 * tan30, -4.0, 0.0], [0.0, 0.0, 0.0], [4.0 * tan30, 4.0, 0.0]], cbv.swept), + } + print("planar wings, chord 1, span 8, 5 deg, U = 20 m/s") + for name, (le_points, make) in cases.items(): + xsecs = [asb.WingXSec(xyz_le=p, chord=1.0, twist=0.0, airfoil=FLAT) for p in le_points] + n_seg = len(le_points) - 1 + row = {} + for n_chord, n_span in ((8, 40), (16, 80)): + key = f"VLM {n_chord}x{n_span}" + row[key] = run_vlm(xsecs, 8.0, 20.0, 5.0, n_chord, n_span // n_seg) + show(name, key, row[key]) + for legs in LEGS: + for N in (40, 80): + key = f"VSM {legs} N={N}" + row[key] = run_vsm(make, N, legs, 8.0, 20.0) + show(name, key, row[key]) + out[name] = row + + print("\ncircular arc, 110 deg, R = 4 c, 8 deg, U = 10 m/s") + xsecs = [] + for th in np.radians(np.linspace(-55.0, 55.0, 23)): + xsecs.append(asb.WingXSec(xyz_le=[0.0, 4.0 * np.sin(th), 4.0 * np.cos(th)], chord=1.0, twist=0.0, airfoil=FLAT)) + body = cbv.arc(40) + area = float(body.wings[0].compute_projected_area()) + row = {"projected_area": area} + for n_chord, n_seg in ((8, 2), (16, 4)): + key = f"VLM {n_chord}x{22 * n_seg}" + row[key] = run_vlm(xsecs, area, 10.0, 8.0, n_chord, n_seg) + show("arc", key, row[key]) + for legs in LEGS: + for N in (40, 80): + key = f"VSM {legs} N={N}" + row[key] = run_vsm(cbv.arc, N, legs, area, 10.0) + show("arc", key, row[key]) + out["arc"] = row + + print("\nelliptic, 10% sweep, 25% anhedral, 10 deg, U = 10 m/s") + s = 8.0 * (np.pi / 4) / 2 + ys = np.linspace(-s, s, 41) + xsecs, chords = [], [] + for y in ys: + eta = min(abs(y) / s, 0.999999) + c = np.sqrt(1 - eta**2) + chords.append(c) + xsecs.append(asb.WingXSec(xyz_le=[0.10 * s * eta**2, y, -0.25 * s * eta**2], chord=c, twist=0.0, airfoil=FLAT)) + area = float(np.trapz(chords, ys)) + row = {} + for n_chord, n_seg in ((8, 1), (16, 2), (16, 4)): + key = f"VLM {n_chord}x{40 * n_seg}" + row[key] = run_vlm(xsecs, area, 10.0, 10.0, n_chord, n_seg) + show("elliptic", key, row[key]) + for legs in LEGS: + for N in (80, 160): + key = f"VSM {legs} N={N}" + row[key] = run_vsm(cbv.elliptic_swept_anhedral, N, legs, area, 10.0) + show("elliptic", key, row[key]) + out["elliptic"] = row + + print("\nV3 kite, flat-plate sections, 10 deg, U = 2.82 m/s") + xsecs = v3_xsecs() + area = float(cbv.v3_inviscid(40).wings[0].compute_projected_area()) + row = {"projected_area": area} + for n_chord, n_seg in ((8, 2), (16, 4)): + key = f"VLM {n_chord}x{(len(xsecs) - 1) * n_seg}" + row[key] = run_vlm(xsecs, area, 2.82, 10.0, n_chord, n_seg) + show("V3", key, row[key]) + for legs in LEGS: + for N in (40, 80): + key = f"VSM {legs} N={N}" + try: + row[key] = run_vsm(cbv.v3_inviscid, N, legs, area, 2.82) + except ValueError as err: + print(f" V3 {key}: {err}") + continue + show("V3", key, row[key]) + out["V3"] = row + + json.dump(out, open(OUT / "vlm_referee.json", "w"), indent=1) + print(f"\nresults written to {OUT / 'vlm_referee.json'}") + + +if __name__ == "__main__": + main() diff --git a/src/VSM/core/BodyAerodynamics.py b/src/VSM/core/BodyAerodynamics.py index c3a7e13..124835d 100644 --- a/src/VSM/core/BodyAerodynamics.py +++ b/src/VSM/core/BodyAerodynamics.py @@ -13,6 +13,7 @@ assemble_AIC_matrices, induced_velocity_at_points, assemble_curved_bound_correction_AIC, + perpendicular_leg_end_points, thin_airfoil_strips, ) from . import jit_cross, jit_norm, jit_dot @@ -60,10 +61,39 @@ def __init__( bridle_line_system: list = None, aerodynamic_center_location: float = 0.25, control_point_location: float = 0.75, + leg_direction: str = "rib", ): + """ + Args: + wings (list): Wing instances. + bridle_line_system (list, optional): bridle lines as [p1, p2, diameter]. + aerodynamic_center_location (float): chord fraction of the bound vortex. + control_point_location (float): chord fraction of the control point. + leg_direction (str): direction of the attached-trailed legs, the + chordwise vortex segments between the bound vortex and the + trailing edge. ``"rib"``: along the (interpolated) input + sections, ending at their trailing-edge points. ``"perpendicular"``: + perpendicular to the local quarter-chord line, up to the + trailing-edge curve, as in Gaunaa, Li & Pirrung (TORQUE 2026, + Sec. 3), with the control point between the panel's two legs; + see ``utils.perpendicular_leg_end_points``. ``"streamwise"``: + along the apparent velocity projected onto the local surface, + up to the trailing-edge curve, rebuilt whenever ``va`` is set + (a Weissinger-type lattice; identical to ``"rib"`` on wings whose + ribs are drawn along the flow). The panel frame + and the chord length are the span-perpendicular ones (CP1) in + both cases; with ``"rib"`` the control point lies on the + interpolated rib at the control-point chord fraction. + """ + if leg_direction not in ("rib", "perpendicular", "streamwise"): + raise ValueError( + "leg_direction must be 'rib', 'perpendicular' or 'streamwise', " + f"got {leg_direction!r}" + ) self._wings = wings self._aerodynamic_center_location = aerodynamic_center_location self._control_point_location = control_point_location + self._leg_direction = leg_direction self._bridle_line_system = bridle_line_system self._reference_point = np.zeros(3, dtype=float) @@ -86,6 +116,7 @@ def __init__( def _build_panels(self): """Helper method to build the panel list from the current wing geometry.""" panels = [] + wing_panel_groups = [] for wing in self.wings: section_list = wing.refine_aerodynamic_mesh() n_panels_per_wing = len(section_list) - 1 @@ -105,8 +136,9 @@ def _build_panels(self): self._aerodynamic_center_location, self._control_point_location, ) + wing_panels = [] for j in range(n_panels_per_wing): - panels.append( + wing_panels.append( Panel( section_list[j], section_list[j + 1], @@ -119,9 +151,68 @@ def _build_panels(self): z_airf_list[j], ) ) + if self._leg_direction == "perpendicular": + self._apply_perpendicular_legs(wing_panels, section_list) + wing_panel_groups.append((wing_panels, section_list)) + panels.extend(wing_panels) + self._wing_panel_groups = wing_panel_groups self._panels = panels self._n_panels = len(panels) + def _apply_perpendicular_legs(self, wing_panels, section_list, direction=None): + """Replace the rib legs of one wing by legs perpendicular to the + quarter-chord line (or along ``direction``, projected onto the + surface) that end on the trailing-edge curve.""" + bound_nodes = np.array( + [p.bound_point_1 for p in wing_panels] + [wing_panels[-1].bound_point_2], + dtype=float, + ) + te_nodes = np.array([sec.TE_point for sec in section_list], dtype=float) + normals = None + if direction is not None: + normals = np.array([p.x_airf for p in wing_panels], dtype=float) + ends = perpendicular_leg_end_points( + bound_nodes, + te_nodes, + np.array([p.y_airf for p in wing_panels], dtype=float), + np.array([p.chord for p in wing_panels], dtype=float), + float(self._aerodynamic_center_location), + direction=direction, + normals=normals, + ) + # The control point goes between the panel's own two legs, at the + # control-point fraction along them, with the same spanwise weights + # that place the aerodynamic centre on the bound segment. Between + # parallel perpendicular legs this is the 3/4-chord point of the CP1 + # section (the paper's control point); where the legs fan out near a + # kink or a tip it stays between them, as it does between the rib + # legs in the default construction. + t_leg = (self._control_point_location - self._aerodynamic_center_location) / ( + 1.0 - self._aerodynamic_center_location + ) + for j, panel in enumerate(wing_panels): + b1, b2 = panel.bound_point_1, panel.bound_point_2 + w1 = np.linalg.norm(panel.aerodynamic_center - b2) / np.linalg.norm(b1 - b2) + control_point = w1 * (b1 + t_leg * (ends[j] - b1)) + (1.0 - w1) * ( + b2 + t_leg * (ends[j + 1] - b2) + ) + panel.set_leg_end_points(ends[j], ends[j + 1], control_point) + + def _apply_streamwise_legs(self, va_distribution): + """Streamwise legs: along the mean apparent velocity, projected onto + the local surface, up to the trailing-edge curve. Called whenever + ``va`` is set, since the legs follow the inflow.""" + va_mean = np.mean(np.atleast_2d(np.asarray(va_distribution, dtype=float)), axis=0) + norm = np.linalg.norm(va_mean) + if norm < 1e-12: + raise ValueError("streamwise legs need a non-zero apparent velocity") + for wing_panels, section_list in self._wing_panel_groups: + self._apply_perpendicular_legs(wing_panels, section_list, direction=va_mean / norm) + + @property + def leg_direction(self): + return self._leg_direction + #################### ## CLASS METHODS ### #################### @@ -137,6 +228,7 @@ def instantiate( ml_models_dir=None, aerodynamic_center_location: float = 0.25, control_point_location: float = 0.75, + leg_direction: str = "rib", ): """ Instantiate a BodyAerodynamics object from either a provided wing_instance or a YAML config file. @@ -151,6 +243,7 @@ def instantiate( center / bound vortex (default: 0.25). control_point_location (float): Chord fraction (from LE) of the control point (default: 0.75). + leg_direction (str): ``"rib"`` or ``"perpendicular"``, see ``BodyAerodynamics.__init__``. Returns: BodyAerodynamics instance. @@ -348,12 +441,14 @@ def instantiate( bridle_lines, aerodynamic_center_location=aerodynamic_center_location, control_point_location=control_point_location, + leg_direction=leg_direction, ) else: return cls( [wing_instance], aerodynamic_center_location=aerodynamic_center_location, control_point_location=control_point_location, + leg_direction=leg_direction, ) def rotate( @@ -562,6 +657,9 @@ def va( va_distribution += -np.cross(self._body_rates, control_points - r0) # push to panels + if self._leg_direction == "streamwise": + self._apply_streamwise_legs(va_distribution) + for i, panel in enumerate(self.panels): panel.va = va_distribution[i] diff --git a/src/VSM/core/Panel.py b/src/VSM/core/Panel.py index c71f4fe..650326b 100644 --- a/src/VSM/core/Panel.py +++ b/src/VSM/core/Panel.py @@ -98,6 +98,27 @@ def __init__( self._filaments.append(BoundFilament(x1=bound_point_1, x2=self._TE_point_1)) self._filaments.append(BoundFilament(x1=self._TE_point_2, x2=bound_point_2)) + def set_leg_end_points(self, te_point_1, te_point_2, control_point=None): + """Move the ends of the two attached-trailed legs, and with them the + start of the wake, to the given points on the trailing-edge curve, + and optionally the control point. + + The section corners, chord and frame are kept. Used when the legs are + built perpendicular to the quarter-chord line instead of along the + input ribs (``BodyAerodynamics(..., leg_direction="perpendicular")``); + the control point then moves with the legs so that it stays between + the panel's own two legs. + """ + self._TE_point_1 = np.asarray(te_point_1, dtype=float) + self._TE_point_2 = np.asarray(te_point_2, dtype=float) + if control_point is not None: + self._control_point = np.asarray(control_point, dtype=float) + self._filaments = [ + BoundFilament(x1=self._bound_point_2, x2=self._bound_point_1), + BoundFilament(x1=self._bound_point_1, x2=self._TE_point_1), + BoundFilament(x1=self._TE_point_2, x2=self._bound_point_2), + ] + ########################### ## GETTER FUNCTIONS ########################### diff --git a/src/VSM/core/utils.py b/src/VSM/core/utils.py index aa2cc37..d4c4643 100644 --- a/src/VSM/core/utils.py +++ b/src/VSM/core/utils.py @@ -484,3 +484,148 @@ def point_in_quad(pt, corners): return point_in_triangle( pt, corners[0], corners[1], corners[2] ) or point_in_triangle(pt, corners[0], corners[2], corners[3]) + + +def perpendicular_leg_end_points( + bound_nodes, te_nodes, chord_dir, chords, ac_fraction, direction=None, normals=None +): + """End points of attached-trailed legs perpendicular to the quarter-chord line. + + Gaunaa, Li & Pirrung (TORQUE 2026, Sec. 3) run the attached part of the + trailed vortex from the bound vortex "along the local chordwise direction + up to the trailing edge", the chordwise direction being that of the + Crossflow Principle (CP1): perpendicular to the local quarter-chord line. + The legs then depend only on the quarter-chord line and the trailing-edge + curve, not on where the input ribs were drawn. + + Where the line turns by more than about one radian within one leg length + (a planform kink, a tip whose curvature radius is below a chord) plain + perpendiculars cross. The line tangent is therefore averaged over plus and + minus one leg length, ``(1 - ac) c``, of arc length around each node before + the perpendicular is taken. On a straight or uniformly swept line this is + the plain perpendicular. At a kink it turns the leg at the kink into the + bisector (streamwise at the root of a symmetric swept wing) and blends to + the perpendicular within one leg length. The averaging length is the leg's + own scale, not a free parameter. Legs that still cross raise an error. + + Args: + bound_nodes (np.ndarray): (n+1, 3) bound-vortex nodes in panel order + (node ``k`` is ``bound_point_1`` of panel ``k``; node ``n`` is + ``bound_point_2`` of the last panel). + te_nodes (np.ndarray): (n+1, 3) section trailing-edge points in the + same order; their polyline is the trailing-edge curve. + chord_dir (np.ndarray): (n, 3) span-perpendicular chord directions of + the panels, leading edge to trailing edge (``Panel.y_airf``). + chords (np.ndarray): (n,) perpendicular chords of the panels. + ac_fraction (float): chord fraction of the bound vortex. + direction (np.ndarray, optional): a fixed leg direction (3,), e.g. the + apparent-velocity direction for streamwise legs. It is projected + onto the local surface (perpendicular to ``normals``) at each + node and used instead of the perpendicular to the quarter-chord + line; the tangent averaging is then not needed. + normals (np.ndarray, optional): (n, 3) panel normals (``Panel.x_airf``), + required with ``direction``. + + Returns: + np.ndarray: (n+1, 3) leg end points, on the trailing-edge polyline + (or on the straight extension of its first or last segment, for a + leg that leaves a skewed tip through the tip edge). + + Raises: + ValueError: if a leg does not reach the trailing-edge curve or two + neighbouring legs cross (end points not ordered along the edge). + """ + B = np.asarray(bound_nodes, dtype=float) + T = np.asarray(te_nodes, dtype=float) + Y = np.asarray(chord_dir, dtype=float) + c = np.asarray(chords, dtype=float).ravel() + n = len(c) + if B.shape != (n + 1, 3) or T.shape != (n + 1, 3) or Y.shape != (n, 3): + raise ValueError("perpendicular_leg_end_points: inconsistent array shapes") + + seg = B[1:] - B[:-1] + seg_len = np.linalg.norm(seg, axis=1) + if np.any(seg_len < 1e-12): + raise ValueError("repeated bound-vortex nodes") + tangent = seg / seg_len[:, None] + s_node = np.concatenate(([0.0], np.cumsum(seg_len))) + + te_seg = T[1:] - T[:-1] + te_len = np.linalg.norm(te_seg, axis=1) + if np.any(te_len < 1e-12): + raise ValueError("repeated trailing-edge points") + s_te = np.concatenate(([0.0], np.cumsum(te_len))) + + ends = np.zeros_like(B) + s_end = np.zeros(n + 1) + for k in range(n + 1): + adjacent = [j for j in (k - 1, k) if 0 <= j < n] + leg_length = (1.0 - ac_fraction) * float(np.mean(c[adjacent])) + + # tangent of the quarter-chord line averaged over +- one leg length + lo, hi = s_node[k] - leg_length, s_node[k] + leg_length + overlap = np.minimum(s_node[1:], hi) - np.maximum(s_node[:-1], lo) + overlap = np.clip(overlap, 0.0, None) + t_avg = overlap @ tangent + if np.linalg.norm(t_avg) < 1e-12: + t_avg = tangent[adjacent].sum(axis=0) + t_avg = t_avg / np.linalg.norm(t_avg) + + if direction is None: + # leg direction: the chord direction with its component along the + # averaged tangent removed (points from the bound vortex aft) + y = Y[adjacent].sum(axis=0) + d = y - np.dot(y, t_avg) * t_avg + else: + # fixed direction projected onto the local surface + nrm = np.asarray(normals, dtype=float)[adjacent].sum(axis=0) + nrm = nrm / np.linalg.norm(nrm) + d = np.asarray(direction, dtype=float) + d = d - np.dot(d, nrm) * nrm + d_norm = np.linalg.norm(d) + if d_norm < 1e-9: + raise ValueError(f"leg direction at node {k} is degenerate (along the span or the normal)") + d = d / d_norm + + # The leg ends at the point of the trailing-edge curve closest to the + # ray B_k + t d, t > 0. A ray in 3D does not meet a polyline on a + # curved surface exactly, so the closest point is used rather than an + # intersection; it lies on a segment, or on the straight extension of + # the first or last segment, so that a leg leaving a skewed tip + # through the tip edge still ends on the trailing-edge line. + w0 = B[k][None, :] - T[:-1] + b = te_seg @ d + cc = te_len**2 + dd = w0 @ d + e0 = np.einsum("ij,ij->i", te_seg, w0) + denom = cc - b * b + regular = denom > 1e-10 * cc + u = np.where(regular, (e0 - b * dd) / np.where(regular, denom, 1.0), 0.0) + lower = np.zeros(len(te_len)) + upper = np.ones(len(te_len)) + lower[0], upper[-1] = -np.inf, np.inf + u = np.clip(u, lower, upper) + P = T[:-1] + u[:, None] * te_seg + t = (P - B[k][None, :]) @ d + ahead = t > 0.0 + if not np.any(ahead): + raise ValueError( + f"the perpendicular attached-trailed leg of node {k} does not reach " + "the trailing-edge curve; use leg_direction='rib'" + ) + dist = np.linalg.norm(B[k][None, :] + t[:, None] * d[None, :] - P, axis=1) + dist[~ahead] = np.inf + m = int(np.argmin(dist)) + u_clip = u + ends[k] = P[m] + s_end[k] = s_te[m] + u_clip[m] * te_len[m] + + crossing = np.where(np.diff(s_end) <= 0.0)[0] + if crossing.size: + k = int(crossing[0]) + raise ValueError( + f"attached-trailed legs cross between nodes {k} and {k + 1}: the " + "quarter-chord line turns by more than one leg length there; use " + "leg_direction='rib'" + ) + return ends diff --git a/tests/BodyAerodynamics/test_leg_direction.py b/tests/BodyAerodynamics/test_leg_direction.py new file mode 100644 index 0000000..84a1e55 --- /dev/null +++ b/tests/BodyAerodynamics/test_leg_direction.py @@ -0,0 +1,173 @@ +"""Direction of the attached-trailed legs: along the ribs or perpendicular to +the quarter-chord line or along the flow (``BodyAerodynamics(leg_direction=...)``). + +Perpendicular legs depend only on the quarter-chord line and the +trailing-edge curve, so (a) they coincide with the ribs wherever the ribs are +perpendicular, (b) a straight wing whose ribs are drawn skewed gives the same +vortex system and the same forces as the same wing with straight ribs, and +(c) a kinked swept wing builds without crossing legs, with the root leg on the +symmetry plane. Inviscid polars. +""" + +import numpy as np +import pytest + +from VSM.core.BodyAerodynamics import BodyAerodynamics +from VSM.core.Solver import Solver +from VSM.core.WingGeometry import Wing +from VSM.core.utils import perpendicular_leg_end_points + +_alpha = np.radians(np.linspace(-25, 25, 101)) +INVISCID = np.column_stack((_alpha, 2 * np.pi * _alpha, 0 * _alpha, 0 * _alpha)) + + +def _straight(n, skew=0.0, **kw): + wing = Wing(n_panels=n, spanwise_panel_distribution="uniform") + for y in np.linspace(-4.0, 4.0, n + 1): + wing.add_section(np.array([0.0, y, 0.0]), np.array([1.0, y + skew, 0.0]), INVISCID) + body = BodyAerodynamics([wing], **kw) + body.va_initialize(20.0, 5.0, 0.0) + return body + + +def _swept(n, sweep_deg, **kw): + """Kinked swept wing, chord 1, ribs along the freestream.""" + wing = Wing(n_panels=n, spanwise_panel_distribution="uniform") + for y in np.linspace(-4.0, 4.0, n + 1): + x = abs(y) * np.tan(np.radians(sweep_deg)) + wing.add_section(np.array([x, y, 0.0]), np.array([x + 1.0, y, 0.0]), INVISCID) + body = BodyAerodynamics([wing], **kw) + body.va_initialize(20.0, 5.0, 0.0) + return body + + +def _arc(n, **kw): + wing = Wing(n_panels=n, spanwise_panel_distribution="uniform") + for th in np.radians(np.linspace(-55.0, 55.0, n + 1)): + le = np.array([0.0, 4.0 * np.sin(th), 4.0 * np.cos(th)]) + wing.add_section(le, le + np.array([1.0, 0.0, 0.0]), INVISCID) + body = BodyAerodynamics([wing], **kw) + body.va_initialize(10.0, 8.0, 0.0) + return body + + +def _legs(body): + P = body.panels + bound = np.array([p.bound_point_1 for p in P] + [P[-1].bound_point_2]) + te = np.array([p.TE_point_1 for p in P] + [P[-1].TE_point_2]) + return bound, te + + +def _solve(body): + r = Solver(allowed_error=1e-7, max_iterations=4000).solve(body) + assert r["gamma_converged"] + return r + + +def test_unknown_leg_direction_raises(): + with pytest.raises(ValueError): + _straight(8, leg_direction="diagonal") + + +@pytest.mark.parametrize("make", [_straight, _arc]) +def test_perpendicular_legs_equal_ribs_where_ribs_are_perpendicular(make): + rib = make(16) + perp = make(16, leg_direction="perpendicular") + assert perp.leg_direction == "perpendicular" + for p_rib, p_perp in zip(rib.panels, perp.panels): + assert np.allclose(p_rib.TE_point_1, p_perp.TE_point_1, atol=1e-10) + assert np.allclose(p_rib.TE_point_2, p_perp.TE_point_2, atol=1e-10) + assert np.allclose(p_rib.control_point, p_perp.control_point, atol=1e-10) + assert np.isclose(p_rib.chord, p_perp.chord) + + +def test_skewed_ribs_give_the_straight_wing(): + """The surface is the same rectangle whichever way the ribs are drawn.""" + reference = _straight(20) + skewed = _straight(20, skew=0.4, leg_direction="perpendicular") + bound, te = _legs(skewed) + # legs along x, ending on the trailing-edge line x = 1 at the node's own y + assert np.allclose(te[:, 0], 1.0, atol=1e-10) + assert np.allclose(te[:, 1], bound[:, 1], atol=1e-10) + r_ref = _solve(reference) + r_skw = _solve(skewed) + assert np.isclose(r_skw["cl"], r_ref["cl"], rtol=1e-6) + assert np.isclose(r_skw["cd"], r_ref["cd"], rtol=1e-5) + assert np.isclose(r_skw["drag"] / r_skw["drag_induced_trefftz"], 1.0, atol=1e-3) + + +def test_skewed_rib_legs_are_not_the_straight_wing(): + """The reference behaviour: rib legs carry the skew into the result.""" + reference = _solve(_straight(20)) + skewed = _solve(_straight(20, skew=0.4)) + assert abs(skewed["cd"] / reference["cd"] - 1.0) > 5e-3 + + +def test_kinked_swept_wing_builds_without_crossing_legs(): + body = _swept(40, 30.0, leg_direction="perpendicular") + bound, te = _legs(body) + # ends ordered along the trailing edge (panels run from +y to -y) + assert np.all(np.diff(te[:, 1]) < 0.0) + # root leg on the symmetry plane, streamwise; away from the root the legs + # turn towards the perpendicular (aft and inboard), one leg length away + k = len(bound) // 2 + assert np.isclose(bound[k, 1], 0.0, atol=1e-12) + assert np.isclose(te[k, 1], 0.0, atol=1e-10) + leg = te - bound + j = k - 6 # 1.2 chords from the root at 0.2 panel width, outside the averaging window + inboard = -np.sign(bound[j, 1]) * leg[j, 1] + assert np.isclose(inboard / np.linalg.norm(leg[j]), np.sin(np.radians(30.0)), atol=1e-6) + r = _solve(body) + assert np.isfinite(r["cl"]) and np.isfinite(r["cd"]) + assert 0.9 < r["drag"] / r["drag_induced_trefftz"] < 1.1 + + +def test_crossing_legs_raise(): + with pytest.raises(ValueError, match="cross|does not reach"): + _swept(40, 75.0, leg_direction="perpendicular") + + +def test_leg_end_points_function_on_a_uniformly_swept_line(): + """On a line of constant sweep the legs are the plain perpendiculars.""" + sweep = np.radians(30.0) + n = 10 + s = np.linspace(0.0, 5.0, n + 1) + bound = np.column_stack((s * np.sin(sweep), s * np.cos(sweep), 0 * s)) + perp = np.array([np.cos(sweep), -np.sin(sweep), 0.0]) + te = bound + 0.75 * perp + np.array([0.0, 0.0, 0.0]) + chord_dir = np.tile(perp, (n, 1)) + ends = perpendicular_leg_end_points(bound, te, chord_dir, np.ones(n), 0.25) + assert np.allclose(ends, te, atol=1e-10) + + +def test_streamwise_legs_equal_ribs_drawn_along_the_flow(): + """On the kinked swept wing the ribs are along x, as are streamwise legs.""" + rib = _swept(40, 30.0) + stream = _swept(40, 30.0, leg_direction="streamwise") + for p_rib, p_s in zip(rib.panels, stream.panels): + assert np.allclose(p_rib.TE_point_1, p_s.TE_point_1, atol=1e-10) + assert np.allclose(p_rib.control_point, p_s.control_point, atol=1e-10) + + +def test_streamwise_legs_on_skewed_ribs_give_the_straight_wing(): + reference = _solve(_straight(20)) + skewed = _solve(_straight(20, skew=0.4, leg_direction="streamwise")) + assert np.isclose(skewed["cl"], reference["cl"], rtol=1e-6) + assert np.isclose(skewed["cd"], reference["cd"], rtol=1e-5) + + +def test_streamwise_legs_follow_the_inflow(): + """Setting a sideslip rebuilds the legs along the new apparent velocity.""" + body = _straight(16, skew=0.4, leg_direction="streamwise") + te_0 = np.array([p.TE_point_1 for p in body.panels]) + body.va_initialize(20.0, 5.0, 15.0) + te_1 = np.array([p.TE_point_1 for p in body.panels]) + bound = np.array([p.bound_point_1 for p in body.panels]) + legs = te_1 - bound + # legs lie in the plane of the flat wing and point along the yawed flow + assert np.allclose(legs[:, 2], 0.0, atol=1e-12) + va = np.atleast_2d(body.va)[0] + expected_yaw = np.degrees(np.arctan2(va[1], va[0])) + yaw = np.degrees(np.arctan2(legs[:, 1], legs[:, 0])) + assert np.allclose(yaw, expected_yaw, atol=1e-9) + assert not np.allclose(te_0, te_1) From def20bb66f2de789adeb02f66fc67cc1d0fdd658 Mon Sep 17 00:00:00 2001 From: ocayon Date: Mon, 12 Oct 2026 21:18:14 +0200 Subject: [PATCH 16/37] feat(solver): streamwise attached-trailed legs by default BodyAerodynamics(leg_direction="streamwise") becomes the default (was "rib"). The legs run along the apparent velocity projected onto the surface, up to the trailing-edge curve, and are rebuilt whenever va is set; they depend only on the quarter-chord line, the trailing edge and the flow, not on how the input sections were drawn, follow the inflow in sideslip, and give the closest V3 polars to RANS (drag within 0.3% up to 10 deg, lift slope equal to the RANS one). Known cost, from the AeroSandbox referee: 1-3% less lift than a lifting surface on the nearly vertical tips of an arc wing at 4-15 deg (rib legs: -0.2 to +1.6%), with the induced drag closer; up to 7% less lift at high angle of attack on the thesis curved-wing case. The change is physical: the vortex system differs where the ribs are not aligned with the flow (kite tips, sideslip); identical results on wings whose ribs are drawn along the flow. An inflow without a mean direction (pure rotation about the centroid) has no streamwise legs: the rib legs are used for that inflow and a warning is logged (Panel.reset_legs_to_ribs). After a geometry rebuild (rotate, update_from_points) the legs follow the stored inflow distribution. Tests that verify the thesis vortex system (tests/utils.py, the create_geometry_general oracle, the curved-wing and V3 verification cases) and the regularisation tests (chordwise legs isolate the bound-vortex term) now pass leg_direction="rib" explicitly; make_pr_figures.py and the regularisation validation script likewise, so figures 01-09 and the report's Sections 2-4 stay reproducible. New test: fallback for pure rotation. Report (decision paragraph, status, open items), Solver.md and the figures README state the new default and its cost. Suite: 182 passed, 5 skipped. Co-Authored-By: Claude Fable 5.1 --- docs/Solver.md | 22 +++++-- docs/figures/README.md | 6 +- docs/figures/make_pr_figures.py | 6 +- .../validation/curved_bound_vortex_report.pdf | Bin 1557473 -> 1559286 bytes .../validation/curved_bound_vortex_report.tex | 10 +-- .../curved_bound_vortex_validation.py | 16 +++-- src/VSM/core/BodyAerodynamics.py | 61 +++++++++++++----- src/VSM/core/Panel.py | 16 +++++ .../test_curved_bound_vortex.py | 4 +- tests/BodyAerodynamics/test_leg_direction.py | 31 +++++++-- ..._object_against_create_geometry_general.py | 2 +- tests/utils.py | 4 +- 12 files changed, 129 insertions(+), 49 deletions(-) diff --git a/docs/Solver.md b/docs/Solver.md index 937e0e0..9d96e26 100644 --- a/docs/Solver.md +++ b/docs/Solver.md @@ -277,11 +277,12 @@ non-uniform grid (the paper derives it for uniform rectangular wings). `BodyAerodynamics(..., leg_direction=...)` (also on `instantiate`). The paper states that theory does not fix this direction and chooses the chordwise direction of CP1, perpendicular to the quarter-chord line, up to the - trailing edge. Three constructions are available (figure 10): `"rib"` - (default) runs the legs along the interpolated input sections to their - trailing-edge points, with the control point on the section; `"streamwise"` - runs them along the apparent velocity projected onto the surface, up to the - trailing-edge curve, and rebuilds them whenever `va` is set; `"perpendicular"` + trailing edge. Three constructions are available (figure 10): `"streamwise"` + (default) runs the legs along the apparent velocity projected onto the + surface, up to the trailing-edge curve, and rebuilds them whenever `va` is + set; `"rib"` (the default until October 2026) runs them along the + interpolated input sections to their trailing-edge points, with the control + point on the section; `"perpendicular"` is the paper's choice, with the tangent of the quarter-chord line averaged over one leg length so that the legs do not cross at a planform kink. With the last two the control point moves with the legs so that it stays between @@ -291,8 +292,15 @@ non-uniform grid (the paper derives it for uniform rectangular wings). swept-anhedral elliptic wings within 1% (streamwise: 2% low on the arc) and the induced drag within 1-4%; perpendicular legs lose 9% of the lift on the kinked swept wing and 8% on the V3, where they also cross at the tips above - 80 panels. On the V3 the rib legs are the ribs of the real kite; streamwise - legs give the closest V3 polars to RANS. Details in + 80 panels. Streamwise legs are the default because they depend only on the + quarter-chord line, the trailing edge and the flow (not on how the input + sections were drawn), follow the inflow in sideslip, and give the closest V3 + polars to RANS (and the RANS lift slope); their known cost is 1-3% of lift + on the nearly vertical tips of an arc wing at 4-15 deg, where the chordwise + rib legs are within 2%. An inflow without a mean direction (pure rotation) + falls back to the rib legs with a warning. The thesis-based verification + tests keep `leg_direction="rib"` because they check the thesis vortex + system. Details in `docs/validation/curved_bound_vortex_report.pdf`, Section 4.3. Every solve of a wing in one uniform inflow also reports diff --git a/docs/figures/README.md b/docs/figures/README.md index ee18510..a1986f9 100644 --- a/docs/figures/README.md +++ b/docs/figures/README.md @@ -1,7 +1,8 @@ # Figures: consistent lifting-line coupling Generated by `make_pr_figures.py` (run from the repository root, a few -minutes). They document the changes that align the solver with Gaunaa, Li & +minutes; figures 01-07 use rib legs explicitly, the default when they were +made, see 10 and 11 for the leg direction). They document the changes that align the solver with Gaunaa, Li & Pirrung (TORQUE 2026, "From thin airfoil theory to finite wings"), Li, Gaunaa, Pirrung & Lønbæk (TORQUE 2026, "Relaxation limits and artificial viscosity") and Gaunaa, Sørensen & Li (2024, spanwise-flow viscous correction). @@ -98,7 +99,8 @@ figures 10 and 11 and Section 4.3 of Generated by `docs/validation/leg_direction_study.py --figures`. Top views (flow downwards) and one side view of the three leg constructions of `BodyAerodynamics(leg_direction=...)`: along the input ribs (blue, the -default), along the flow projected onto the surface (green), or +default until October 2026), along the flow projected onto the surface +(green, now the default), or perpendicular to the quarter-chord line as in the TORQUE 2026 paper (red), with the bound vortex (black), the aerodynamic centres (dots), the control points (crosses in the colour of their legs) and, in grey, the lattice of the diff --git a/docs/figures/make_pr_figures.py b/docs/figures/make_pr_figures.py index 78945d1..78fff5a 100644 --- a/docs/figures/make_pr_figures.py +++ b/docs/figures/make_pr_figures.py @@ -45,7 +45,7 @@ def rect_wing(n, aspect_ratio, sweep_deg=0.0, dist="uniform"): for y in np.linspace(-aspect_ratio / 2, aspect_ratio / 2, n + 1): x = abs(y) * np.tan(np.radians(sweep_deg)) w.add_section(np.array([x, y, 0.0]), np.array([x + 1.0, y, 0.0]), polar) - return BodyAerodynamics([w]) + return BodyAerodynamics([w], leg_direction="rib") def elliptic_wing(n, aspect_ratio): @@ -55,11 +55,11 @@ def elliptic_wing(n, aspect_ratio): for y in np.linspace(-b / 2, b / 2, n + 1): c = np.sqrt(max(1e-6, 1 - (2 * y / b) ** 2)) w.add_section(np.array([-c / 4, y, 0.0]), np.array([3 * c / 4, y, 0.0]), polar) - return BodyAerodynamics([w]) + return BodyAerodynamics([w], leg_direction="rib") def v3(n=50, geom=V3_GEOM): - return BodyAerodynamics.instantiate(n_panels=n, file_path=geom, spanwise_panel_distribution="uniform") + return BodyAerodynamics.instantiate(n_panels=n, file_path=geom, spanwise_panel_distribution="uniform", leg_direction="rib") # -------------------------------------------------------------------------- diff --git a/docs/validation/curved_bound_vortex_report.pdf b/docs/validation/curved_bound_vortex_report.pdf index 665f50ef3c746be343ac93a941e7ac43e94f7eb0..dfdd7c6cf354edb6cff49259a222b059873d3df1 100644 GIT binary patch delta 51152 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z+>RhZZGaEUKqC@xM?WIOBghmTAI4XPEq_d`sc(ZT<>m%Y*siq9c(4bt|q8fIA@;0ag#!8G;_JaK$c);4KmyANV=`6b?Q; z@odUerv@5Sq|^JtL4rMD%>I8&4MYZhA47!*DG=A0NQaXMjz*$lZw+GO{*wor7?@MCg zD{Dxf5J2$Czzs9UOyJs=!>o`g|Ltw|HikIO#4eAgD-9Ewm>kUi?@TDz4FHajLL}ki zH(a%XKj8Vu1YFw2j(iYS@O)I-G)u$ySayPUbMTDdg?LkASD1LqP~ajD?;jLMm3W7v z&>`#K$AJ9Dv35`e;0~prAl$lgD9C_Hg+n0c(qYk&Lut^3-S=<(2ZO*9nj8Y*)`w#z zaP7w_kcO+4F?rLDEFr@GE#4Ja)jc4Ge@|IkJC)D5PT+;1vkp zKs@&AdNX*{MxSC#U$%4wc!setfrg#VC`%bjO_syeKY1yYZbCIw`2SfpD8K_3TSHuf ZL&AeSy@a6Ngxf!Ykg~D~kJSpH{{t=Y1v~%% diff --git a/docs/validation/curved_bound_vortex_report.tex b/docs/validation/curved_bound_vortex_report.tex index 1c75bd3..8a107b1 100644 --- a/docs/validation/curved_bound_vortex_report.tex +++ b/docs/validation/curved_bound_vortex_report.tex @@ -39,7 +39,7 @@ \section{Status of the implementation with respect to Li and Gaunaa} \textbf{Two elements do not follow the published prescription.} \begin{enumerate}[nosep] \item \emph{The curved bound-vortex influence on the direction velocity.} Reference~\cite{gaunaa2026} states that LL-Gaunaa includes ``the influence of the curved bound vortex'' according to~\cite{li2020}. In~\cite{li2020} (Section~2.2) that influence is the induction of the 3D bound vortex minus that of an infinitely long 2D vortex of the section's own strength, evaluated at the \emph{three-quarter} chord, assumed constant along the chord, and added to the quarter-chord velocity. \texttt{develop} instead evaluated the other panels' bound segments \emph{on the quarter-chord line itself} (commit \texttt{9c43c1a}), which~\cite{li2020} calls LL-P\&S and shows to be log-singular and non-convergent. This is the cause of the problem treated here (Section~\ref{sec:problem}). A literal implementation of the~\cite{li2020} recipe in this code was also tested and fails on straight wings (Section~\ref{sec:lit}); the 2026 paper and its online appendix~\cite{appendix2026} do not specify the quarter-chord term further, so the form used in the authors' code needs clarification with them. The branch replaces the term by the regularisation of Section~\ref{sec:fix}. - \item \emph{The direction of the attached-trailed legs.} Reference~\cite{gaunaa2026} (Section~3) states that the framework ``does not indicate how the trailed vorticity should connect from the 1/4 chord junctions to the trailing edge'', that this ``is not specified by theoretical results'' and ``is effectively a modeling choice'', and aligns the legs ``with the local chordwise direction up to the trailing edge'', i.e.\ perpendicular to the quarter-chord line (CP1). The code's default keeps the legs along the input ribs; the paper's construction and a streamwise one are now available as options (\texttt{leg\_direction}), and the three were compared against a vortex-lattice referee (Section~\ref{sec:legs}, Figures~\ref{fig:legs} and~\ref{fig:referee}). The perpendicular legs lose 9\,\% of the lift on a kinked swept wing and 8\,\% on the V3, where they also cross at the tips above 80 panels; rib and streamwise legs reproduce the lifting-surface lift within 1\,\% on straight, yawed, kinked, arc and swept--anhedral elliptic wings (streamwise: 2\,\% low on the arc). The ribs are kept as the default. This is now a documented choice backed by a referee rather than an untested deviation. + \item \emph{The direction of the attached-trailed legs.} Reference~\cite{gaunaa2026} (Section~3) states that the framework ``does not indicate how the trailed vorticity should connect from the 1/4 chord junctions to the trailing edge'', that this ``is not specified by theoretical results'' and ``is effectively a modeling choice'', and aligns the legs ``with the local chordwise direction up to the trailing edge'', i.e.\ perpendicular to the quarter-chord line (CP1). The code kept the legs along the input ribs; the paper's construction and a streamwise one were implemented (\texttt{leg\_direction}) and the three were compared against a vortex-lattice referee (Section~\ref{sec:legs}, Figures~\ref{fig:legs} and~\ref{fig:referee}). The perpendicular legs lose 9\,\% of the lift on a kinked swept wing and 8\,\% on the V3, where they also cross at the tips above 80 panels; rib and streamwise legs reproduce the lifting-surface lift within 1\,\% on straight, yawed, kinked, arc and swept--anhedral elliptic wings (streamwise: 2\,\% low on the arc). The streamwise legs are now the default (Section~\ref{sec:legs}, Decision); rib legs remain available. This is now a documented choice backed by a referee rather than an untested deviation. \end{enumerate} \section{Problem statement} @@ -179,8 +179,8 @@ \subsection{Direction of the attached-trailed legs} \label{sec:legs} Theory fixes the inner 2D section (CP1: velocity, chord and angle of attack perpendicular to the quarter-chord line) but not the path of the attached-trailed vorticity from the bound vortex to the trailing edge; reference~\cite{gaunaa2026} calls it a modelling choice and takes the CP1 chord direction. Three constructions are implemented (\texttt{BodyAerodynamics(leg\_direction=...)}, Figure~\ref{fig:legs}): \begin{itemize}[nosep] - \item \texttt{rib} (default): along the interpolated input sections to their trailing-edge points, control point on the section at the control-point chord fraction. On a kite these are the ribs of the real wing; on the test wings they are drawn along the flow (swept wings), along the chord (arc) or deliberately skewed (straight wing). - \item \texttt{streamwise}: along the apparent velocity projected onto the local surface, up to the trailing-edge curve, rebuilt whenever the inflow is set; a Weissinger-type lattice. + \item \texttt{rib} (the default until this branch): along the interpolated input sections to their trailing-edge points, control point on the section at the control-point chord fraction. On a kite these are the ribs of the real wing; on the test wings they are drawn along the flow (swept wings), along the chord (arc) or deliberately skewed (straight wing). + \item \texttt{streamwise} (now the default): along the apparent velocity projected onto the local surface, up to the trailing-edge curve, rebuilt whenever the inflow is set; a Weissinger-type lattice. \item \texttt{perpendicular}: the paper's choice. The tangent of the quarter-chord line is averaged over plus and minus one leg length, $(1-a)c$, before the perpendicular is taken, so that the legs fan out instead of crossing at a planform kink (Figure~\ref{fig:legs}b); the averaging length is the leg's own scale, not a free parameter. Legs that still cross raise an error. \end{itemize} In the last two the leg ends at the point of the trailing-edge curve closest to the leg's ray (a ray does not meet a polyline on a curved surface exactly), the curve being extended beyond its ends so that a leg leaving a skewed tip still ends on the trailing-edge line, and the control point moves with the legs so that it stays between the panel's own two legs (midway between parallel legs this is the paper's 3/4-chord point of the CP1 section; without this move the control points of a kinked wing land on neighbouring legs and the solve diverges). The curved bound-vortex regularisation of Section~\ref{sec:fix} and the AT force follow whichever legs are built. @@ -242,7 +242,7 @@ \subsection{Direction of the attached-trailed legs} The on-blade over Trefftz ratio is not a criterion between rib and streamwise legs (both are within 2\,\% except the streamwise arc at 1.035, where the climbing legs carry an attached-trailed force the flow-aligned legs of the other options do not); it does reject the perpendicular legs on the kinked wing (1.09, rising with $N$) and the singular earlier construction. The skewed-rib straight wing shows what the rib legs cost when the ribs are not aligned with the flow: the same wing, drawn with skewed ribs, gives 1.03 and 0.7\,\% less lift, whereas streamwise and perpendicular legs return the straight-wing result exactly. -\paragraph{Decision.} The perpendicular legs are rejected with evidence. Between rib and streamwise legs the referee does not decide: each is within 1\,\% of the VLM lift on four of the five wings it can judge, the ribs win on the arc and the streamwise legs on the elliptic wing and against RANS on the V3. The ribs stay the default, because on the V3 they are the physical ribs, they need no inflow to be built, and nothing in the evidence shows them wrong; the streamwise construction is one keyword away and is the one to use when the ribs of an input geometry are drawn obliquely to the flow. The argument that chord and legs should follow the same direction has been tested in the one form the theory allows, the all-perpendicular CP1 construction, and it loses to the CP1 frame with flow-aligned legs; the paper itself separates the two choices. +\paragraph{Decision.} The perpendicular legs are rejected with evidence. Between rib and streamwise legs the referee does not decide sharply: each is within 1\,\% of the VLM lift on four of the five wings it can judge, the ribs win on the arc and the streamwise legs on the elliptic wing and against RANS on the V3. The streamwise legs are made the default: they depend only on the quarter-chord line, the trailing edge and the flow, not on how the input sections were drawn (the skewed-rib wing shows what that costs), they follow the inflow in sideslip, and on the real kite they give the closest polars to RANS. Their known cost is on wings with nearly vertical tips, where the climbing legs lower the lift: on the arc wing $-1.3$, $-2.1$ and $-3.0\,\%$ against the VLM at $4$, $8$ and $15^\circ$ (rib legs: $-0.2$, $+0.3$, $+1.6\,\%$), while in induced drag at the same angles the streamwise legs are the closer ones ($-1.3$, $-1.3$, $-1.0\,\%$ against $-2.4$, $-3.5$, $-4.8\,\%$); on the thesis curved-wing verification case the lift at high angle of attack drops by up to 7\,\%. On the V3 the streamwise lift slope ($0.065$ per degree) matches the RANS slope, the rib one ($0.078$) does not. An inflow without a mean direction (pure rotation) has no streamwise legs; the code then uses the rib legs for that inflow and logs a warning. Rib legs remain available (\texttt{leg\_direction="rib"}) and are what the tables of Sections~2--4 and Figures~\ref{fig:explain}--\ref{fig:polars} were made with; the quarter-chord regularisation itself is the same under either. The argument that chord and legs should follow the same direction has been tested in the one form the theory allows, the all-perpendicular CP1 construction, and it loses to the CP1 frame with flow-aligned legs; the paper itself separates the two choices. \paragraph{The authors' numbers.} For the swept--anhedral elliptic wing Table~2 of~\cite{gaunaa2026} gives $e_{\mathrm{Osw,Blade}}=1.101$ against $e_{\mathrm{Osw,Trefftz}}=1.080$ for LL-Gaunaa, i.e.\ on-blade induced drag 1.9\,\% \emph{below} the Trefftz plane, and their VLM reference is 2.8\,\% below (1.106 against 1.075); the appendix~\cite{appendix2026} gives 5\,\% and 1\,\% below for the 15\,\% and 25\,\% swept wings. The authors read this as a limitation of the Trefftz-plane analysis for curved wings. Here the near-field drag of the VLM is likewise below its own Trefftz drag on the non-planar wings (8\,\% on the elliptic wing), for the same reason: trailing legs that are not aligned with the wind carry a force that the near-field evaluation drops. @@ -279,7 +279,7 @@ \section{Assessment and open items} \begin{itemize}[nosep] \item The mechanism of the fix (straighten locally, regularise the legs, keep the far field) is that of Reid and Hunsaker~\cite{reid2020}; the difference-form goes back to Li et al.~\cite{li2018}. The contribution here is the replacement of the two empirical lengths by the thin-airfoil chordwise distribution, which fixes the cut-off at $0.15\,c$ from theory, and the demonstration that this yields Trefftz-consistent induced drag on curved kites. It should be presented as such, with~\cite{reid2020,li2020,guermond1990} cited. \item To be confirmed with the authors of~\cite{gaunaa2026,li2020}: how the curved bound-vortex influence is applied at the quarter chord in their code, and how it behaves when the number of sections is doubled. - \item Settled with a referee (Section~\ref{sec:legs}): the paper's perpendicular legs are rejected; rib legs stay the default, streamwise legs are available and preferable when the input ribs are oblique to the flow. Open: the attached-trailed force on legs that are not aligned with the flow (kinked wing 0.98, skewed ribs 1.03, streamwise legs on the arc 1.035), and a V3 referee with the exact skewed tips (AeroSandbox unskews them). Not quantified: the section polars are rib-section polars while CP1 applies them in the span-perpendicular plane. + \item Settled with a referee (Section~\ref{sec:legs}): the paper's perpendicular legs are rejected; streamwise legs are the default, rib legs remain available. Open: the attached-trailed force on legs that are not aligned with the flow (kinked wing 0.98, skewed ribs 1.03, streamwise legs on the arc 1.035), and a V3 referee with the exact skewed tips (AeroSandbox unskews them). Not quantified: the section polars are rib-section polars while CP1 applies them in the span-perpendicular plane. \end{itemize} \begin{thebibliography}{99}\small diff --git a/docs/validation/curved_bound_vortex_validation.py b/docs/validation/curved_bound_vortex_validation.py index ad6a033..f247195 100644 --- a/docs/validation/curved_bound_vortex_validation.py +++ b/docs/validation/curved_bound_vortex_validation.py @@ -60,6 +60,10 @@ FIG = ROOT / "docs" / "figures" DATA = ROOT / "data" / "TUDELFT_V3_KITE" REGULARISED = BA.assemble_curved_bound_correction_AIC +# The geometries below use rib legs unless told otherwise: the tables of the +# report's Sections 2-4 isolate the quarter-chord bound-vortex term and were +# made with rib legs (the default until October 2026). The leg direction is +# compared separately in leg_direction_study.py and vlm_referee.py. _a = np.radians(np.linspace(-25, 25, 101)) INVISCID = np.column_stack((_a, 2 * np.pi * _a, 0 * _a, 0 * _a)) @@ -72,7 +76,7 @@ def straight(n, half_span=4.0, skew=0.0, **body_kwargs): wing = Wing(n_panels=n, spanwise_panel_distribution="uniform") for y in np.linspace(-half_span, half_span, n + 1): wing.add_section(np.array([0.0, y, 0.0]), np.array([1.0, y + skew, 0.0]), INVISCID) - body = BodyAerodynamics([wing], **body_kwargs) + body = BodyAerodynamics([wing], **{"leg_direction": "rib", **body_kwargs}) body.va_initialize(20.0, 5.0, 0.0) return body @@ -83,7 +87,7 @@ def swept(n, sweep_deg=30.0, half_span=4.0, **body_kwargs): for y in np.linspace(-half_span, half_span, n + 1): x = abs(y) * np.tan(np.radians(sweep_deg)) wing.add_section(np.array([x, y, 0.0]), np.array([x + 1.0, y, 0.0]), INVISCID) - body = BodyAerodynamics([wing], **body_kwargs) + body = BodyAerodynamics([wing], **{"leg_direction": "rib", **body_kwargs}) body.va_initialize(20.0, 5.0, 0.0) return body @@ -94,7 +98,7 @@ def yawed(n, sweep_deg=30.0, half_span=4.0, **body_kwargs): for y in np.linspace(-half_span, half_span, n + 1): x = y * np.tan(np.radians(sweep_deg)) wing.add_section(np.array([x, y, 0.0]), np.array([x + 1.0, y, 0.0]), INVISCID) - body = BodyAerodynamics([wing], **body_kwargs) + body = BodyAerodynamics([wing], **{"leg_direction": "rib", **body_kwargs}) body.va_initialize(20.0, 5.0, 0.0) return body @@ -105,7 +109,7 @@ def arc(n, radius=4.0, half_angle_deg=55.0, **body_kwargs): for th in np.radians(np.linspace(-half_angle_deg, half_angle_deg, n + 1)): le = np.array([0.0, radius * np.sin(th), radius * np.cos(th)]) wing.add_section(le, le + np.array([1.0, 0.0, 0.0]), INVISCID) - body = BodyAerodynamics([wing], **body_kwargs) + body = BodyAerodynamics([wing], **{"leg_direction": "rib", **body_kwargs}) body.va_initialize(10.0, 8.0, 0.0) return body @@ -121,7 +125,7 @@ def elliptic_swept_anhedral(n, aspect_ratio=8.0, sweep=0.10, anhedral=0.25, **bo x = sweep * s * eta**2 z = -anhedral * s * eta**2 wing.add_section(np.array([x, y, z]), np.array([x + c, y, z]), INVISCID) - body = BodyAerodynamics([wing], **body_kwargs) + body = BodyAerodynamics([wing], **{"leg_direction": "rib", **body_kwargs}) body.va_initialize(10.0, 10.0, 0.0) return body @@ -136,7 +140,7 @@ def v3_inviscid(n, alpha=10.0, **body_kwargs): wing = Wing(n_panels=n, spanwise_panel_distribution="uniform") for row in _V3["wing_sections"]["data"]: wing.add_section(np.array(row[1:4], float), np.array(row[4:7], float), INVISCID) - body = BodyAerodynamics([wing], **body_kwargs) + body = BodyAerodynamics([wing], **{"leg_direction": "rib", **body_kwargs}) body.va_initialize(2.82, alpha, 0.0) return body diff --git a/src/VSM/core/BodyAerodynamics.py b/src/VSM/core/BodyAerodynamics.py index 124835d..14f3fe8 100644 --- a/src/VSM/core/BodyAerodynamics.py +++ b/src/VSM/core/BodyAerodynamics.py @@ -61,7 +61,7 @@ def __init__( bridle_line_system: list = None, aerodynamic_center_location: float = 0.25, control_point_location: float = 0.75, - leg_direction: str = "rib", + leg_direction: str = "streamwise", ): """ Args: @@ -71,16 +71,20 @@ def __init__( control_point_location (float): chord fraction of the control point. leg_direction (str): direction of the attached-trailed legs, the chordwise vortex segments between the bound vortex and the - trailing edge. ``"rib"``: along the (interpolated) input - sections, ending at their trailing-edge points. ``"perpendicular"``: + trailing edge. ``"streamwise"`` (default): along the apparent + velocity projected onto the local surface, up to the + trailing-edge curve, rebuilt whenever ``va`` is set; depends + only on the quarter-chord line, the trailing edge and the + flow, not on how the input sections were drawn, and follows + the inflow in sideslip. ``"rib"``: along the (interpolated) + input sections, ending at their trailing-edge points (the + behaviour before October 2026). ``"perpendicular"``: perpendicular to the local quarter-chord line, up to the trailing-edge curve, as in Gaunaa, Li & Pirrung (TORQUE 2026, Sec. 3), with the control point between the panel's two legs; - see ``utils.perpendicular_leg_end_points``. ``"streamwise"``: - along the apparent velocity projected onto the local surface, - up to the trailing-edge curve, rebuilt whenever ``va`` is set - (a Weissinger-type lattice; identical to ``"rib"`` on wings whose - ribs are drawn along the flow). The panel frame + see ``utils.perpendicular_leg_end_points``. Streamwise and rib + legs coincide on wings whose ribs are drawn along the flow. + The panel frame and the chord length are the span-perpendicular ones (CP1) in both cases; with ``"rib"`` the control point lies on the interpolated rib at the control-point chord fraction. @@ -157,6 +161,14 @@ def _build_panels(self): panels.extend(wing_panels) self._wing_panel_groups = wing_panel_groups self._panels = panels + # after a rebuild (rotate, update_from_points) streamwise legs must + # follow the inflow already set; before the first va they are ribs + va_distribution = getattr(self, "_va_distribution", None) + if self._leg_direction == "streamwise" and va_distribution is not None: + if len(va_distribution) == len(panels): + self._apply_streamwise_legs(va_distribution) + else: # panel count changed: only the mean direction is meaningful + self._apply_streamwise_legs(np.mean(va_distribution, axis=0, keepdims=True)) self._n_panels = len(panels) def _apply_perpendicular_legs(self, wing_panels, section_list, direction=None): @@ -201,13 +213,28 @@ def _apply_perpendicular_legs(self, wing_panels, section_list, direction=None): def _apply_streamwise_legs(self, va_distribution): """Streamwise legs: along the mean apparent velocity, projected onto the local surface, up to the trailing-edge curve. Called whenever - ``va`` is set, since the legs follow the inflow.""" - va_mean = np.mean(np.atleast_2d(np.asarray(va_distribution, dtype=float)), axis=0) + ``va`` is set, since the legs follow the inflow. + + An inflow without a usable mean direction (pure rotation, a flow + that does not run from the bound vortex towards the trailing edge) + has no streamwise legs; the rib legs are then used and a warning is + logged, so that such a case still solves.""" + va = np.atleast_2d(np.asarray(va_distribution, dtype=float)) + va_mean = np.mean(va, axis=0) norm = np.linalg.norm(va_mean) - if norm < 1e-12: - raise ValueError("streamwise legs need a non-zero apparent velocity") - for wing_panels, section_list in self._wing_panel_groups: - self._apply_perpendicular_legs(wing_panels, section_list, direction=va_mean / norm) + speed = float(np.mean(np.linalg.norm(va, axis=1))) + try: + if speed <= 0.0 or norm < 1e-3 * speed: + raise ValueError("the mean apparent velocity is zero (pure rotation?)") + for wing_panels, section_list in self._wing_panel_groups: + self._apply_perpendicular_legs(wing_panels, section_list, direction=va_mean / norm) + except ValueError as err: + logging.warning( + "streamwise attached-trailed legs cannot be built for this inflow " + f"({err}); using the rib legs for this inflow" + ) + for panel in self._panels: + panel.reset_legs_to_ribs() @property def leg_direction(self): @@ -228,7 +255,7 @@ def instantiate( ml_models_dir=None, aerodynamic_center_location: float = 0.25, control_point_location: float = 0.75, - leg_direction: str = "rib", + leg_direction: str = "streamwise", ): """ Instantiate a BodyAerodynamics object from either a provided wing_instance or a YAML config file. @@ -243,7 +270,7 @@ def instantiate( center / bound vortex (default: 0.25). control_point_location (float): Chord fraction (from LE) of the control point (default: 0.75). - leg_direction (str): ``"rib"`` or ``"perpendicular"``, see ``BodyAerodynamics.__init__``. + leg_direction (str): ``"streamwise"`` (default), ``"rib"`` or ``"perpendicular"``, see ``BodyAerodynamics.__init__``. Returns: BodyAerodynamics instance. @@ -657,6 +684,8 @@ def va( va_distribution += -np.cross(self._body_rates, control_points - r0) # push to panels + # kept for a rebuild of the panels (rotate, update_from_points) + self._va_distribution = np.array(va_distribution, dtype=float) if self._leg_direction == "streamwise": self._apply_streamwise_legs(va_distribution) diff --git a/src/VSM/core/Panel.py b/src/VSM/core/Panel.py index 650326b..7aca671 100644 --- a/src/VSM/core/Panel.py +++ b/src/VSM/core/Panel.py @@ -92,6 +92,12 @@ def __init__( # Conceptually, you should mulitply by the width of the bound vortex and thus take the average width. self._width = jit_norm(bound_point_2 - bound_point_1) + # rib legs and control point as built from the sections, kept so that + # another leg construction can be undone (set_leg_end_points) + self._rib_TE_point_1 = np.array(self._TE_point_1, dtype=float) + self._rib_TE_point_2 = np.array(self._TE_point_2, dtype=float) + self._rib_control_point = np.array(control_point, dtype=float) + ### Setting up the filaments (order used to reversed for right-to-left input) self._filaments = [] self._filaments.append(BoundFilament(x1=bound_point_2, x2=bound_point_1)) @@ -113,6 +119,16 @@ def set_leg_end_points(self, te_point_1, te_point_2, control_point=None): self._TE_point_2 = np.asarray(te_point_2, dtype=float) if control_point is not None: self._control_point = np.asarray(control_point, dtype=float) + self._rebuild_filaments() + + def reset_legs_to_ribs(self): + """Restore the rib legs and the section control point.""" + self._TE_point_1 = self._rib_TE_point_1.copy() + self._TE_point_2 = self._rib_TE_point_2.copy() + self._control_point = self._rib_control_point.copy() + self._rebuild_filaments() + + def _rebuild_filaments(self): self._filaments = [ BoundFilament(x1=self._bound_point_2, x2=self._bound_point_1), BoundFilament(x1=self._bound_point_1, x2=self._TE_point_1), diff --git a/tests/BodyAerodynamics/test_curved_bound_vortex.py b/tests/BodyAerodynamics/test_curved_bound_vortex.py index 3d36256..d84b44a 100644 --- a/tests/BodyAerodynamics/test_curved_bound_vortex.py +++ b/tests/BodyAerodynamics/test_curved_bound_vortex.py @@ -24,7 +24,7 @@ def _straight(n_panels, half_span=4.0): wing = Wing(n_panels=n_panels, spanwise_panel_distribution="uniform") for y in np.linspace(-half_span, half_span, n_panels + 1): wing.add_section(np.array([0.0, y, 0.0]), np.array([1.0, y, 0.0]), INVISCID) - body = BodyAerodynamics([wing]) + body = BodyAerodynamics([wing], leg_direction="rib") # chordwise legs isolate the bound-vortex term body.va_initialize(20.0, 5.0, 0.0) return body @@ -35,7 +35,7 @@ def _arc(n_panels, radius=4.0, half_angle_deg=55.0): for th in np.radians(np.linspace(-half_angle_deg, half_angle_deg, n_panels + 1)): le = np.array([0.0, radius * np.sin(th), radius * np.cos(th)]) wing.add_section(le, le + np.array([1.0, 0.0, 0.0]), INVISCID) - body = BodyAerodynamics([wing]) + body = BodyAerodynamics([wing], leg_direction="rib") # chordwise legs isolate the bound-vortex term body.va_initialize(10.0, 8.0, 0.0) return body diff --git a/tests/BodyAerodynamics/test_leg_direction.py b/tests/BodyAerodynamics/test_leg_direction.py index 84a1e55..702c3ae 100644 --- a/tests/BodyAerodynamics/test_leg_direction.py +++ b/tests/BodyAerodynamics/test_leg_direction.py @@ -1,5 +1,6 @@ -"""Direction of the attached-trailed legs: along the ribs or perpendicular to -the quarter-chord line or along the flow (``BodyAerodynamics(leg_direction=...)``). +"""Direction of the attached-trailed legs: along the flow (default), along +the ribs, or perpendicular to the quarter-chord line +(``BodyAerodynamics(leg_direction=...)``). Perpendicular legs depend only on the quarter-chord line and the trailing-edge curve, so (a) they coincide with the ribs wherever the ribs are @@ -25,7 +26,7 @@ def _straight(n, skew=0.0, **kw): wing = Wing(n_panels=n, spanwise_panel_distribution="uniform") for y in np.linspace(-4.0, 4.0, n + 1): wing.add_section(np.array([0.0, y, 0.0]), np.array([1.0, y + skew, 0.0]), INVISCID) - body = BodyAerodynamics([wing], **kw) + body = BodyAerodynamics([wing], **{"leg_direction": "rib", **kw}) body.va_initialize(20.0, 5.0, 0.0) return body @@ -36,7 +37,7 @@ def _swept(n, sweep_deg, **kw): for y in np.linspace(-4.0, 4.0, n + 1): x = abs(y) * np.tan(np.radians(sweep_deg)) wing.add_section(np.array([x, y, 0.0]), np.array([x + 1.0, y, 0.0]), INVISCID) - body = BodyAerodynamics([wing], **kw) + body = BodyAerodynamics([wing], **{"leg_direction": "rib", **kw}) body.va_initialize(20.0, 5.0, 0.0) return body @@ -46,7 +47,7 @@ def _arc(n, **kw): for th in np.radians(np.linspace(-55.0, 55.0, n + 1)): le = np.array([0.0, 4.0 * np.sin(th), 4.0 * np.cos(th)]) wing.add_section(le, le + np.array([1.0, 0.0, 0.0]), INVISCID) - body = BodyAerodynamics([wing], **kw) + body = BodyAerodynamics([wing], **{"leg_direction": "rib", **kw}) body.va_initialize(10.0, 8.0, 0.0) return body @@ -171,3 +172,23 @@ def test_streamwise_legs_follow_the_inflow(): yaw = np.degrees(np.arctan2(legs[:, 1], legs[:, 0])) assert np.allclose(yaw, expected_yaw, atol=1e-9) assert not np.allclose(te_0, te_1) + + +def test_streamwise_legs_fall_back_to_ribs_for_pure_rotation(caplog): + """A body that only rotates has no mean inflow direction: the rib legs + are used, with a warning, and the solve goes through.""" + import logging + + body = _straight(12, skew=0.4, leg_direction="streamwise") + rib_te = np.array([p._rib_TE_point_1 for p in body.panels]) + centre = np.mean([p.control_point for p in body.panels], axis=0) + with caplog.at_level(logging.WARNING): + body.va_initialize(Umag=0.0, angle_of_attack=0.0, side_slip=0.0, + body_rates=[0.3, -0.2, 0.1], + body_axis=[[0, 0, 1], [0, 1, 0], [1, 0, 0]], + reference_point=centre) + assert any("rib legs" in m for m in caplog.messages) + assert np.allclose(np.array([p.TE_point_1 for p in body.panels]), rib_te) + # a proper inflow restores the streamwise legs + body.va_initialize(20.0, 5.0, 0.0) + assert not np.allclose(np.array([p.TE_point_1 for p in body.panels]), rib_te) diff --git a/tests/BodyAerodynamics/test_wing_aero_object_against_create_geometry_general.py b/tests/BodyAerodynamics/test_wing_aero_object_against_create_geometry_general.py index 4bd33fb..5c86206 100644 --- a/tests/BodyAerodynamics/test_wing_aero_object_against_create_geometry_general.py +++ b/tests/BodyAerodynamics/test_wing_aero_object_against_create_geometry_general.py @@ -216,7 +216,7 @@ def create_geometry(model="VSM", wing_type="rectangular", plotting=False, N=40): coord_left_to_right[2 * idx + 1], polar_data, ) - wing_aero = BodyAerodynamics([wing]) + wing_aero = BodyAerodynamics([wing], leg_direction="rib") # thesis vortex system wing_aero.va = Uinf if plotting: wing_aero.plot() diff --git a/tests/utils.py b/tests/utils.py index 92d3844..e44e0c2 100644 --- a/tests/utils.py +++ b/tests/utils.py @@ -508,10 +508,10 @@ def compute_new_for_alpha_range( # airfoil_input, # ) - wing_aero = BodyAerodynamics([wing]) + wing_aero = BodyAerodynamics([wing], leg_direction="rib") # thesis vortex system # initializing zero lists - wing_aero = BodyAerodynamics([wing]) + wing_aero = BodyAerodynamics([wing], leg_direction="rib") # thesis vortex system CL_LLT_new = np.zeros(len(aoas)) CD_LLT_new = np.zeros(len(aoas)) gamma_LLT_new = np.zeros((len(aoas), N - 1)) From deef069df201efe7a495a326a55480c1bf0b5da1 Mon Sep 17 00:00:00 2001 From: ocayon Date: Mon, 12 Oct 2026 21:24:04 +0200 Subject: [PATCH 17/37] fix(solver): rib legs stay the default; streamwise remains an option Reverts the default of def20bb. The code's main use is trim finding with an inflow that varies along the span (body rates, distributed va), where the streamwise construction can only use the mean inflow direction and is rebuilt at every inflow; the rib legs give a fixed vortex system of the same accuracy (better on arc-shaped tips against the VLM). The streamwise and perpendicular constructions, the referee, the tests and the figures are unchanged; the report, Solver.md and the figures README state the reasoning and the mean-direction limitation. Suite: 182 passed, 5 skipped. Co-Authored-By: Claude Fable 5.1 --- docs/Solver.md | 30 +++++++++--------- docs/figures/README.md | 7 ++-- .../validation/curved_bound_vortex_report.pdf | Bin 1559286 -> 1559958 bytes .../validation/curved_bound_vortex_report.tex | 10 +++--- src/VSM/core/BodyAerodynamics.py | 24 +++++++------- tests/BodyAerodynamics/test_leg_direction.py | 4 +-- 6 files changed, 38 insertions(+), 37 deletions(-) diff --git a/docs/Solver.md b/docs/Solver.md index 9d96e26..489788f 100644 --- a/docs/Solver.md +++ b/docs/Solver.md @@ -277,12 +277,12 @@ non-uniform grid (the paper derives it for uniform rectangular wings). `BodyAerodynamics(..., leg_direction=...)` (also on `instantiate`). The paper states that theory does not fix this direction and chooses the chordwise direction of CP1, perpendicular to the quarter-chord line, up to the - trailing edge. Three constructions are available (figure 10): `"streamwise"` - (default) runs the legs along the apparent velocity projected onto the - surface, up to the trailing-edge curve, and rebuilds them whenever `va` is - set; `"rib"` (the default until October 2026) runs them along the - interpolated input sections to their trailing-edge points, with the control - point on the section; `"perpendicular"` + trailing edge. Three constructions are available (figure 10): `"rib"` + (default) runs the legs along the interpolated input sections to their + trailing-edge points, with the control point on the section, a fixed + vortex system independent of the inflow; `"streamwise"` runs them along + the mean apparent velocity projected onto the surface, up to the + trailing-edge curve, and rebuilds them whenever `va` is set; `"perpendicular"` is the paper's choice, with the tangent of the quarter-chord line averaged over one leg length so that the legs do not cross at a planform kink. With the last two the control point moves with the legs so that it stays between @@ -292,15 +292,15 @@ non-uniform grid (the paper derives it for uniform rectangular wings). swept-anhedral elliptic wings within 1% (streamwise: 2% low on the arc) and the induced drag within 1-4%; perpendicular legs lose 9% of the lift on the kinked swept wing and 8% on the V3, where they also cross at the tips above - 80 panels. Streamwise legs are the default because they depend only on the - quarter-chord line, the trailing edge and the flow (not on how the input - sections were drawn), follow the inflow in sideslip, and give the closest V3 - polars to RANS (and the RANS lift slope); their known cost is 1-3% of lift - on the nearly vertical tips of an arc wing at 4-15 deg, where the chordwise - rib legs are within 2%. An inflow without a mean direction (pure rotation) - falls back to the rib legs with a warning. The thesis-based verification - tests keep `leg_direction="rib"` because they check the thesis vortex - system. Details in + 80 panels. The rib legs stay the default: same accuracy, a fixed vortex + system, and the code's main use is trim finding with an inflow that varies + along the span, where the streamwise construction can only use the mean + direction. Streamwise legs are the option for uniform-inflow studies of + wings whose sections are drawn obliquely to the flow, or in sideslip: they + give the closest V3 polars to RANS (and the RANS lift slope) at a cost of + 1-3% of lift on the nearly vertical tips of an arc wing at 4-15 deg, where + the chordwise rib legs are within 2%. An inflow without a mean direction + (pure rotation) falls back to the rib legs with a warning. Details in `docs/validation/curved_bound_vortex_report.pdf`, Section 4.3. Every solve of a wing in one uniform inflow also reports diff --git a/docs/figures/README.md b/docs/figures/README.md index a1986f9..8ac9dd8 100644 --- a/docs/figures/README.md +++ b/docs/figures/README.md @@ -1,8 +1,8 @@ # Figures: consistent lifting-line coupling Generated by `make_pr_figures.py` (run from the repository root, a few -minutes; figures 01-07 use rib legs explicitly, the default when they were -made, see 10 and 11 for the leg direction). They document the changes that align the solver with Gaunaa, Li & +minutes; figures 01-07 pass `leg_direction="rib"` explicitly, see 10 and 11 +for the leg direction). They document the changes that align the solver with Gaunaa, Li & Pirrung (TORQUE 2026, "From thin airfoil theory to finite wings"), Li, Gaunaa, Pirrung & Lønbæk (TORQUE 2026, "Relaxation limits and artificial viscosity") and Gaunaa, Sørensen & Li (2024, spanwise-flow viscous correction). @@ -99,8 +99,7 @@ figures 10 and 11 and Section 4.3 of Generated by `docs/validation/leg_direction_study.py --figures`. Top views (flow downwards) and one side view of the three leg constructions of `BodyAerodynamics(leg_direction=...)`: along the input ribs (blue, the -default until October 2026), along the flow projected onto the surface -(green, now the default), or +default), along the mean flow projected onto the surface (green), or perpendicular to the quarter-chord line as in the TORQUE 2026 paper (red), with the bound vortex (black), the aerodynamic centres (dots), the control points (crosses in the colour of their legs) and, in grey, the lattice of the diff --git a/docs/validation/curved_bound_vortex_report.pdf b/docs/validation/curved_bound_vortex_report.pdf index dfdd7c6cf354edb6cff49259a222b059873d3df1..d85cb4936728d622f09a4b6cb34297c88d9ba489 100644 GIT binary patch delta 28722 zcmZ6SV{j%wx2fJwk*HgP+ zQVdeF4C>P;fH~6|V!){YGq{_vhpo@PeS?(q>Or;W_wr=pBAM)nzvD|M@+s@rA!A6r zn{8xjO>a#z^KQ9#!y1oV*&kj4jRV-E62f?2VY&MH0QVCb(zT+gCtCFCuUSzy(#09^ 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influence on the direction velocity.} Reference~\cite{gaunaa2026} states that LL-Gaunaa includes ``the influence of the curved bound vortex'' according to~\cite{li2020}. In~\cite{li2020} (Section~2.2) that influence is the induction of the 3D bound vortex minus that of an infinitely long 2D vortex of the section's own strength, evaluated at the \emph{three-quarter} chord, assumed constant along the chord, and added to the quarter-chord velocity. \texttt{develop} instead evaluated the other panels' bound segments \emph{on the quarter-chord line itself} (commit \texttt{9c43c1a}), which~\cite{li2020} calls LL-P\&S and shows to be log-singular and non-convergent. This is the cause of the problem treated here (Section~\ref{sec:problem}). A literal implementation of the~\cite{li2020} recipe in this code was also tested and fails on straight wings (Section~\ref{sec:lit}); the 2026 paper and its online appendix~\cite{appendix2026} do not specify the quarter-chord term further, so the form used in the authors' code needs clarification with them. The branch replaces the term by the regularisation of Section~\ref{sec:fix}. - \item \emph{The direction of the attached-trailed legs.} Reference~\cite{gaunaa2026} (Section~3) states that the framework ``does not indicate how the trailed vorticity should connect from the 1/4 chord junctions to the trailing edge'', that this ``is not specified by theoretical results'' and ``is effectively a modeling choice'', and aligns the legs ``with the local chordwise direction up to the trailing edge'', i.e.\ perpendicular to the quarter-chord line (CP1). The code kept the legs along the input ribs; the paper's construction and a streamwise one were implemented (\texttt{leg\_direction}) and the three were compared against a vortex-lattice referee (Section~\ref{sec:legs}, Figures~\ref{fig:legs} and~\ref{fig:referee}). The perpendicular legs lose 9\,\% of the lift on a kinked swept wing and 8\,\% on the V3, where they also cross at the tips above 80 panels; rib and streamwise legs reproduce the lifting-surface lift within 1\,\% on straight, yawed, kinked, arc and swept--anhedral elliptic wings (streamwise: 2\,\% low on the arc). The streamwise legs are now the default (Section~\ref{sec:legs}, Decision); rib legs remain available. This is now a documented choice backed by a referee rather than an untested deviation. + \item \emph{The direction of the attached-trailed legs.} Reference~\cite{gaunaa2026} (Section~3) states that the framework ``does not indicate how the trailed vorticity should connect from the 1/4 chord junctions to the trailing edge'', that this ``is not specified by theoretical results'' and ``is effectively a modeling choice'', and aligns the legs ``with the local chordwise direction up to the trailing edge'', i.e.\ perpendicular to the quarter-chord line (CP1). The code kept the legs along the input ribs; the paper's construction and a streamwise one were implemented (\texttt{leg\_direction}) and the three were compared against a vortex-lattice referee (Section~\ref{sec:legs}, Figures~\ref{fig:legs} and~\ref{fig:referee}). The perpendicular legs lose 9\,\% of the lift on a kinked swept wing and 8\,\% on the V3, where they also cross at the tips above 80 panels; rib and streamwise legs reproduce the lifting-surface lift within 1\,\% on straight, yawed, kinked, arc and swept--anhedral elliptic wings (streamwise: 2\,\% low on the arc). The rib legs remain the default (Section~\ref{sec:legs}, Decision); the streamwise construction is available as an option. This is now a documented choice backed by a referee rather than an untested deviation. \end{enumerate} \section{Problem statement} @@ -179,8 +179,8 @@ \subsection{Direction of the attached-trailed legs} \label{sec:legs} Theory fixes the inner 2D section (CP1: velocity, chord and angle of attack perpendicular to the quarter-chord line) but not the path of the attached-trailed vorticity from the bound vortex to the trailing edge; reference~\cite{gaunaa2026} calls it a modelling choice and takes the CP1 chord direction. Three constructions are implemented (\texttt{BodyAerodynamics(leg\_direction=...)}, Figure~\ref{fig:legs}): \begin{itemize}[nosep] - \item \texttt{rib} (the default until this branch): along the interpolated input sections to their trailing-edge points, control point on the section at the control-point chord fraction. On a kite these are the ribs of the real wing; on the test wings they are drawn along the flow (swept wings), along the chord (arc) or deliberately skewed (straight wing). - \item \texttt{streamwise} (now the default): along the apparent velocity projected onto the local surface, up to the trailing-edge curve, rebuilt whenever the inflow is set; a Weissinger-type lattice. + \item \texttt{rib} (default): along the interpolated input sections to their trailing-edge points, control point on the section at the control-point chord fraction; a fixed vortex system, independent of the inflow. On a kite these are the ribs of the real wing; on the test wings they are drawn along the flow (swept wings), along the chord (arc) or deliberately skewed (straight wing). + \item \texttt{streamwise}: along the mean apparent velocity projected onto the local surface, up to the trailing-edge curve, rebuilt whenever the inflow is set; a Weissinger-type lattice. With a spanwise-varying inflow (body rates, distributed inflow) only the mean direction is used. \item \texttt{perpendicular}: the paper's choice. The tangent of the quarter-chord line is averaged over plus and minus one leg length, $(1-a)c$, before the perpendicular is taken, so that the legs fan out instead of crossing at a planform kink (Figure~\ref{fig:legs}b); the averaging length is the leg's own scale, not a free parameter. Legs that still cross raise an error. \end{itemize} In the last two the leg ends at the point of the trailing-edge curve closest to the leg's ray (a ray does not meet a polyline on a curved surface exactly), the curve being extended beyond its ends so that a leg leaving a skewed tip still ends on the trailing-edge line, and the control point moves with the legs so that it stays between the panel's own two legs (midway between parallel legs this is the paper's 3/4-chord point of the CP1 section; without this move the control points of a kinked wing land on neighbouring legs and the solve diverges). The curved bound-vortex regularisation of Section~\ref{sec:fix} and the AT force follow whichever legs are built. @@ -242,7 +242,7 @@ \subsection{Direction of the attached-trailed legs} The on-blade over Trefftz ratio is not a criterion between rib and streamwise legs (both are within 2\,\% except the streamwise arc at 1.035, where the climbing legs carry an attached-trailed force the flow-aligned legs of the other options do not); it does reject the perpendicular legs on the kinked wing (1.09, rising with $N$) and the singular earlier construction. The skewed-rib straight wing shows what the rib legs cost when the ribs are not aligned with the flow: the same wing, drawn with skewed ribs, gives 1.03 and 0.7\,\% less lift, whereas streamwise and perpendicular legs return the straight-wing result exactly. -\paragraph{Decision.} The perpendicular legs are rejected with evidence. Between rib and streamwise legs the referee does not decide sharply: each is within 1\,\% of the VLM lift on four of the five wings it can judge, the ribs win on the arc and the streamwise legs on the elliptic wing and against RANS on the V3. The streamwise legs are made the default: they depend only on the quarter-chord line, the trailing edge and the flow, not on how the input sections were drawn (the skewed-rib wing shows what that costs), they follow the inflow in sideslip, and on the real kite they give the closest polars to RANS. Their known cost is on wings with nearly vertical tips, where the climbing legs lower the lift: on the arc wing $-1.3$, $-2.1$ and $-3.0\,\%$ against the VLM at $4$, $8$ and $15^\circ$ (rib legs: $-0.2$, $+0.3$, $+1.6\,\%$), while in induced drag at the same angles the streamwise legs are the closer ones ($-1.3$, $-1.3$, $-1.0\,\%$ against $-2.4$, $-3.5$, $-4.8\,\%$); on the thesis curved-wing verification case the lift at high angle of attack drops by up to 7\,\%. On the V3 the streamwise lift slope ($0.065$ per degree) matches the RANS slope, the rib one ($0.078$) does not. An inflow without a mean direction (pure rotation) has no streamwise legs; the code then uses the rib legs for that inflow and logs a warning. Rib legs remain available (\texttt{leg\_direction="rib"}) and are what the tables of Sections~2--4 and Figures~\ref{fig:explain}--\ref{fig:polars} were made with; the quarter-chord regularisation itself is the same under either. The argument that chord and legs should follow the same direction has been tested in the one form the theory allows, the all-perpendicular CP1 construction, and it loses to the CP1 frame with flow-aligned legs; the paper itself separates the two choices. +\paragraph{Decision.} The perpendicular legs are rejected with evidence. Between rib and streamwise legs the referee does not decide sharply: each is within 1\,\% of the VLM lift on four of the five wings it can judge, the ribs win on the arc and the streamwise legs on the elliptic wing and against RANS on the V3. The rib legs stay the default. The streamwise legs have the conceptual advantages: they depend only on the quarter-chord line, the trailing edge and the flow, not on how the input sections were drawn (the skewed-rib wing shows what that costs), they follow the inflow in sideslip, and on the real kite they give the closest polars to RANS. But the code's main use is trim finding with an inflow that varies along the span, where the streamwise construction can only use the mean direction and therefore is an approximation of its own idea, rebuilt at every inflow; the rib legs give a fixed vortex system of the same accuracy. The streamwise legs' known cost is on wings with nearly vertical tips, where the climbing legs lower the lift: on the arc wing $-1.3$, $-2.1$ and $-3.0\,\%$ against the VLM at $4$, $8$ and $15^\circ$ (rib legs: $-0.2$, $+0.3$, $+1.6\,\%$), while in induced drag at the same angles the streamwise legs are the closer ones ($-1.3$, $-1.3$, $-1.0\,\%$ against $-2.4$, $-3.5$, $-4.8\,\%$); on the thesis curved-wing verification case the lift at high angle of attack drops by up to 7\,\%. On the V3 the streamwise lift slope ($0.065$ per degree) matches the RANS slope, the rib one ($0.078$) does not. An inflow without a mean direction (pure rotation) has no streamwise legs; the code then uses the rib legs for that inflow and logs a warning. The tables of Sections~2--4 and Figures~\ref{fig:explain}--\ref{fig:polars} were made with rib legs; the quarter-chord regularisation itself is the same under either. Use \texttt{leg\_direction="streamwise"} for uniform-inflow studies of wings whose sections are drawn obliquely to the flow, or in sideslip. The argument that chord and legs should follow the same direction has been tested in the one form the theory allows, the all-perpendicular CP1 construction, and it loses to the CP1 frame with flow-aligned legs; the paper itself separates the two choices. \paragraph{The authors' numbers.} For the swept--anhedral elliptic wing Table~2 of~\cite{gaunaa2026} gives $e_{\mathrm{Osw,Blade}}=1.101$ against $e_{\mathrm{Osw,Trefftz}}=1.080$ for LL-Gaunaa, i.e.\ on-blade induced drag 1.9\,\% \emph{below} the Trefftz plane, and their VLM reference is 2.8\,\% below (1.106 against 1.075); the appendix~\cite{appendix2026} gives 5\,\% and 1\,\% below for the 15\,\% and 25\,\% swept wings. The authors read this as a limitation of the Trefftz-plane analysis for curved wings. Here the near-field drag of the VLM is likewise below its own Trefftz drag on the non-planar wings (8\,\% on the elliptic wing), for the same reason: trailing legs that are not aligned with the wind carry a force that the near-field evaluation drops. @@ -279,7 +279,7 @@ \section{Assessment and open items} \begin{itemize}[nosep] \item The mechanism of the fix (straighten locally, regularise the legs, keep the far field) is that of Reid and Hunsaker~\cite{reid2020}; the difference-form goes back to Li et al.~\cite{li2018}. The contribution here is the replacement of the two empirical lengths by the thin-airfoil chordwise distribution, which fixes the cut-off at $0.15\,c$ from theory, and the demonstration that this yields Trefftz-consistent induced drag on curved kites. It should be presented as such, with~\cite{reid2020,li2020,guermond1990} cited. \item To be confirmed with the authors of~\cite{gaunaa2026,li2020}: how the curved bound-vortex influence is applied at the quarter chord in their code, and how it behaves when the number of sections is doubled. - \item Settled with a referee (Section~\ref{sec:legs}): the paper's perpendicular legs are rejected; streamwise legs are the default, rib legs remain available. Open: the attached-trailed force on legs that are not aligned with the flow (kinked wing 0.98, skewed ribs 1.03, streamwise legs on the arc 1.035), and a V3 referee with the exact skewed tips (AeroSandbox unskews them). Not quantified: the section polars are rib-section polars while CP1 applies them in the span-perpendicular plane. + \item Settled with a referee (Section~\ref{sec:legs}): the paper's perpendicular legs are rejected; rib legs stay the default, streamwise legs are available. A streamwise construction with the local inflow direction per node would remove the mean-direction limitation. Open: the attached-trailed force on legs that are not aligned with the flow (kinked wing 0.98, skewed ribs 1.03, streamwise legs on the arc 1.035), and a V3 referee with the exact skewed tips (AeroSandbox unskews them). Not quantified: the section polars are rib-section polars while CP1 applies them in the span-perpendicular plane. \end{itemize} \begin{thebibliography}{99}\small diff --git a/src/VSM/core/BodyAerodynamics.py b/src/VSM/core/BodyAerodynamics.py index 14f3fe8..3255ae0 100644 --- a/src/VSM/core/BodyAerodynamics.py +++ b/src/VSM/core/BodyAerodynamics.py @@ -61,7 +61,7 @@ def __init__( bridle_line_system: list = None, aerodynamic_center_location: float = 0.25, control_point_location: float = 0.75, - leg_direction: str = "streamwise", + leg_direction: str = "rib", ): """ Args: @@ -71,14 +71,16 @@ def __init__( control_point_location (float): chord fraction of the control point. leg_direction (str): direction of the attached-trailed legs, the chordwise vortex segments between the bound vortex and the - trailing edge. ``"streamwise"`` (default): along the apparent - velocity projected onto the local surface, up to the - trailing-edge curve, rebuilt whenever ``va`` is set; depends - only on the quarter-chord line, the trailing edge and the - flow, not on how the input sections were drawn, and follows - the inflow in sideslip. ``"rib"``: along the (interpolated) - input sections, ending at their trailing-edge points (the - behaviour before October 2026). ``"perpendicular"``: + trailing edge. ``"rib"`` (default): along the (interpolated) + input sections, ending at their trailing-edge points; a fixed + vortex system, independent of the inflow. ``"streamwise"``: + along the mean apparent velocity projected onto the local + surface, up to the trailing-edge curve, rebuilt whenever ``va`` + is set; depends only on the quarter-chord line, the trailing + edge and the flow, not on how the input sections were drawn, + and follows the inflow in sideslip, but with a spanwise-varying + inflow (body rates, distributed ``va``) it uses the mean + direction only. ``"perpendicular"``: perpendicular to the local quarter-chord line, up to the trailing-edge curve, as in Gaunaa, Li & Pirrung (TORQUE 2026, Sec. 3), with the control point between the panel's two legs; @@ -255,7 +257,7 @@ def instantiate( ml_models_dir=None, aerodynamic_center_location: float = 0.25, control_point_location: float = 0.75, - leg_direction: str = "streamwise", + leg_direction: str = "rib", ): """ Instantiate a BodyAerodynamics object from either a provided wing_instance or a YAML config file. @@ -270,7 +272,7 @@ def instantiate( center / bound vortex (default: 0.25). control_point_location (float): Chord fraction (from LE) of the control point (default: 0.75). - leg_direction (str): ``"streamwise"`` (default), ``"rib"`` or ``"perpendicular"``, see ``BodyAerodynamics.__init__``. + leg_direction (str): ``"rib"`` (default), ``"streamwise"`` or ``"perpendicular"``, see ``BodyAerodynamics.__init__``. Returns: BodyAerodynamics instance. diff --git a/tests/BodyAerodynamics/test_leg_direction.py b/tests/BodyAerodynamics/test_leg_direction.py index 702c3ae..95618fa 100644 --- a/tests/BodyAerodynamics/test_leg_direction.py +++ b/tests/BodyAerodynamics/test_leg_direction.py @@ -1,5 +1,5 @@ -"""Direction of the attached-trailed legs: along the flow (default), along -the ribs, or perpendicular to the quarter-chord line +"""Direction of the attached-trailed legs: along the ribs (default), along +the mean flow, or perpendicular to the quarter-chord line (``BodyAerodynamics(leg_direction=...)``). Perpendicular legs depend only on the quarter-chord line and the From a37ebabcafff48a65bf8a1d4beffb8c0338bf6a7 Mon Sep 17 00:00:00 2001 From: ocayon Date: Mon, 12 Oct 2026 21:36:07 +0200 Subject: [PATCH 18/37] docs: new aerodynamic model document with formulation, conventions and validation docs/Aerodynamic_model.pdf held chapter 4 of the 2022 MSc thesis, with no source in the repository and sections left empty. It is replaced by an 18-page document whose source is docs/aerodynamic_model/aerodynamic_model.tex (latexmk; the compiled file is copied to docs/Aerodynamic_model.pdf). Contents: scope and assumptions; geometry and the CP1 panel frame; the vortex system (filaments, Biot-Savart, cores, influence matrices, wake, the three attached-trailed leg constructions); the inner-outer coupling (TAT1-3, Gamma = 1/2 |V_inner| c Cl, quarter-chord directions, the curved bound-vortex regularisation, the attached-trailed force, the spanwise viscous correction, artificial viscosity, the LLT variant); solver, inflow, outputs, Trefftz drag and bridle lines; validation (horseshoe and elliptic analytical cases, Trefftz consistency, the AeroSandbox VLM referee on planar, swept, arc, elliptic and V3 wings, the V3 against RANS and the wind tunnel, mesh convergence, the regression cases); limits; a table of conventions. Every figure names the script that generates it. New figures 12 (classical wings against Prandtl and the VLM; the LLT loses its Trefftz consistency on a curved quarter-chord line, the VSM does not) and 13 (mesh convergence), from docs/validation/aerodynamic_model_figures.py. Co-Authored-By: Claude Fable 5.1 --- docs/Aerodynamic_model.pdf | Bin 383985 -> 2572013 bytes docs/README.md | 2 +- docs/aerodynamic_model/.gitignore | 9 + docs/aerodynamic_model/aerodynamic_model.tex | 348 ++++++++++++++++++ docs/figures/12_classical_wings.png | Bin 0 -> 133624 bytes docs/figures/13_mesh_convergence.png | Bin 0 -> 105264 bytes docs/figures/README.md | 17 + .../validation/aerodynamic_model_figures.json | 206 +++++++++++ docs/validation/aerodynamic_model_figures.py | 184 +++++++++ 9 files changed, 765 insertions(+), 1 deletion(-) create mode 100644 docs/aerodynamic_model/.gitignore create mode 100644 docs/aerodynamic_model/aerodynamic_model.tex create mode 100644 docs/figures/12_classical_wings.png create mode 100644 docs/figures/13_mesh_convergence.png create mode 100644 docs/validation/aerodynamic_model_figures.json create mode 100644 docs/validation/aerodynamic_model_figures.py diff --git a/docs/Aerodynamic_model.pdf b/docs/Aerodynamic_model.pdf index 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**[Aerodynamic_model.pdf](Aerodynamic_model.pdf)** - Theoretical background and mathematical formulations +12. **[Aerodynamic_model.pdf](Aerodynamic_model.pdf)** - The aerodynamic model: formulation, conventions and validation (source in `aerodynamic_model/aerodynamic_model.tex`; figures from `validation/` and `figures/`) ## Quick Start Examples diff --git a/docs/aerodynamic_model/.gitignore b/docs/aerodynamic_model/.gitignore new file mode 100644 index 0000000..5b4eb77 --- /dev/null +++ b/docs/aerodynamic_model/.gitignore @@ -0,0 +1,9 @@ +# build artefacts; the compiled document is installed as docs/Aerodynamic_model.pdf +*.aux +*.log +*.out +*.toc +*.fls +*.fdb_latexmk +*.synctex.gz +aerodynamic_model.pdf diff --git a/docs/aerodynamic_model/aerodynamic_model.tex b/docs/aerodynamic_model/aerodynamic_model.tex new file mode 100644 index 0000000..1ea0645 --- /dev/null +++ b/docs/aerodynamic_model/aerodynamic_model.tex @@ -0,0 +1,348 @@ +\documentclass[11pt,a4paper]{article} +\usepackage[margin=24mm]{geometry} +\usepackage{amsmath,amssymb,bm} +\usepackage{graphicx} +\usepackage{booktabs} +\usepackage{array} +\usepackage{enumitem} +\usepackage[hidelinks]{hyperref} +\usepackage{microtype} +\graphicspath{{../figures/}{../}} +\setlength{\parskip}{4pt} +\newcommand{\vect}[1]{\mathbf{#1}} +\newcommand{\code}[1]{\texttt{#1}} + +\title{The aerodynamic model of the Vortex Step Method code\\[4pt]\large formulation, conventions and validation} +\author{Vortex-Step-Method repository, \code{docs/aerodynamic\_model/aerodynamic\_model.tex}} +\date{October 2026} + +\begin{document} +\maketitle + +\begin{abstract} +\noindent This document describes the aerodynamic model implemented in the Vortex-Step-Method (VSM) code as it stands in October 2026: a nonlinear lifting-line method in which an outer three-dimensional vortex system (bound vortex, attached-trailed legs, frozen semi-infinite wake) is coupled to an inner two-dimensional airfoil model (polars) with the consistent coupling rules of Gaunaa, Li and Pirrung (TORQUE 2026). It states every convention the results depend on, gives the equations as they are coded, and collects the validation: analytical wings, the Trefftz-plane consistency of the induced drag, a vortex-lattice referee on planar, swept, curved and kite-like wings, and the TU~Delft V3 kite against RANS and wind-tunnel data. It replaces the thesis chapter that this file used to hold. Each section names the code that implements it and the script that reproduces its figures. +\end{abstract} + +\tableofcontents + +\section{Scope and how to read this document} +\label{sec:scope} +The code computes the steady aerodynamic forces and moments on one or more thin lifting surfaces in a prescribed inflow, including rigid-body rotation rates and an inflow that varies along the span, with optional bridle lines. It is used for kite design, trim and stability analysis and as the aerodynamic module of fluid--structure couplings, where it must be fast (a kite with 50 panels solves in well under a second), robust on unconventional planforms (curved, swept, low aspect ratio) and free of three-dimensional empirical data. Potential-flow vortex methods meet these requirements; among them the lifting line with sectional polars is the fastest, and its known weaknesses on curved and swept wings are what the coupling rules of Section~\ref{sec:coupling} address. + +Sections~\ref{sec:assumptions}--\ref{sec:solver} describe the model: assumptions, geometry and discretisation, the vortex system, the inner--outer coupling, and the solver with its outputs. Section~\ref{sec:validation} is the validation. Section~\ref{sec:conventions} is a table of conventions for people who read results. Every figure is generated by a script in \code{docs/validation} or \code{docs/figures}, named in its caption, and the numbers quoted in the text come from the JSON files those scripts write. The detailed derivation of the curved bound-vortex regularisation and the comparison with the literature are in a separate report, \code{docs/validation/curved\_bound\_vortex\_report.pdf}~\cite{report}; this document only summarises it. + +\section{Assumptions} +\label{sec:assumptions} +\begin{itemize}[nosep] + \item \textbf{Inner and outer region.} The flow is split into an inner region, where each wing section behaves as a two-dimensional airfoil described by its polar $C_l(\alpha)$, $C_d(\alpha)$, $C_m(\alpha)$, and an outer region of inviscid, irrotational, incompressible flow represented by vortex filaments. Viscosity enters only through the polars and the optional spanwise friction correction. + \item \textbf{Thin lifting surface.} The wing is represented by its sections' chord lines: a bound vortex on the quarter-chord line, the chordwise load distribution otherwise ignored. Thickness and camber act through the polars. + \item \textbf{Kutta--Joukowski in every section.} The sectional lift and the bound circulation are tied by $\Gamma=\tfrac12|\vect V_{\mathrm{inner}}|\,c\,C_l$ (Section~\ref{sec:gamma}); the no-penetration condition of the classical lifting line is replaced by this nonlinear relation, which admits any polar. + \item \textbf{Quasi-steady flow.} Every flow condition is solved as a steady problem; the starting vortex is at infinity, and rotation rates enter as a steady velocity distribution. Shed (time-varying) vorticity is not modelled. + \item \textbf{Frozen wake.} The trailed vorticity leaves the trailing edge along the local apparent velocity as straight semi-infinite filaments; wake roll-up and deformation are neglected. On a translating wing this is Prandtl's wake. + \item \textbf{Crossflow principle.} Only the component of the relative velocity perpendicular to the local quarter-chord line drives the inner airfoil model (CP1 of~\cite{gaunaa2026}); the spanwise component does not change the pressure forces. +\end{itemize} + +\section{Geometry and discretisation} +\label{sec:geometry} +\paragraph{Input.} A wing is a list of sections, each a leading-edge point $\vect{LE}$, a trailing-edge point $\vect{TE}$ and a polar (\code{Wing.add\_section}, or the YAML file read by \code{BodyAerodynamics.instantiate}). Coordinates are in a right-handed global frame; the examples and the kite data use $x$ downstream, $y$ to port (left tip), $z$ up. The sections are sorted along the span and need not be parallel: on a kite they are the ribs between inflatable struts, oblique to the flow near the tips. + +\paragraph{Mesh refinement} (\code{WingGeometry.refine\_aerodynamic\_mesh}). The quarter-chord points $\vect{LE}+\tfrac14(\vect{TE}-\vect{LE})$ form a polyline; $N+1$ new sections are placed along its arc length with uniform or cosine spacing (\code{spanwise\_panel\_distribution}), or the provided sections are split or kept. The chord vector of a new section interpolates the direction and the length of the two nearest input ribs, and its polar interpolates their coefficients on a common angle grid. The polars of the two bounding sections are averaged for each panel. + +\paragraph{Panel frame} (\code{BodyAerodynamics.compute\_panel\_properties}, Figure~\ref{fig:frame}). For panel $i$ between sections $j$ and $j+1$, the bound vortex runs between the quarter-chord points $\vect b_1$, $\vect b_2$ of the two sections. The frame is orthonormal and built on it: +\begin{align} +\vect e_{s}&=\frac{\vect b_1-\vect b_2}{|\vect b_1-\vect b_2|} &&\text{span, towards the left tip,}\notag\ +\vect e_{c}&=\frac{\vect t-(\vect t\cdot\vect e_s)\vect e_s}{|\vect t-(\vect t\cdot\vect e_s)\vect e_s|} &&\text{chord, leading to trailing edge,}\ +\vect e_{n}&=\vect e_c\times\vect e_s &&\text{normal, towards the suction side,}\notag +\end{align} +where $\vect t$ is the section chord direction. The chord $c$ of the panel is the length of the section chord vectors with their component along $\vect e_s$ removed, averaged over the two sections: chord and section plane are perpendicular to the local quarter-chord line (CP1). On a straight wing with ribs along the flow this is the plain chord; on the V3 kite tips, where the ribs are skewed by up to $0.77$ in chord-to-span dot product, it differs from the rib chord. In the code the three unit vectors are \code{z\_airf}, \code{y\_airf} and \code{x\_airf}. + +\paragraph{Reference points.} The aerodynamic centre $\vect P_i$ lies on the bound segment, at a spanwise position that weights the neighbouring panel widths (the \code{ncp} rule inherited from~\cite{damiani2019}), and is the point where the force directions are evaluated. The control point $\vect C_i$, where the inner velocity magnitude and angle of attack are evaluated, lies at the control-point chord fraction (default $3/4$) on the interpolated section; the bound vortex at the aerodynamic-centre fraction (default $1/4$). Both fractions are parameters of \code{BodyAerodynamics}. + +\begin{figure}[t]\centering +\includegraphics[width=\textwidth]{02_v3_frame_drag_direction_viscous_beta.png} +\caption{Panel frame on the V3 kite (\code{docs/figures/make\_pr\_figures.py}). Top left: the old frame built from the rib (blue) and the span-perpendicular frame of CP1 now used (red) at the left tip. Top right: the chord-to-span skew of the ribs and the angle by which a drag direction taken from the global span axis missed the local flow, up to $108^\circ$ at the tips. Bottom: the spanwise-flow angle $\beta$ of the viscous correction (Section~\ref{sec:viscous}) from the geometry alone (old) and from the relative velocity (new), at $0$ and $10^\circ$ sideslip.} +\label{fig:frame} +\end{figure} + +\section{The vortex system} +\label{sec:vortex} +\paragraph{Filaments} (\code{Panel}, \code{Filament}). Each panel carries a ring of five filaments of strength $\Gamma_i$ (Figure~\ref{fig:legs}): the bound segment $\vect b_2\to\vect b_1$ on the quarter-chord line, two attached-trailed legs from the bound points to the trailing-edge points $\vect T_1$, $\vect T_2$, and two semi-infinite wake filaments from $\vect T_1$ and $\vect T_2$ along the local apparent velocity, with opposite sense. Neighbouring panels share a section boundary, so the net trailed strength on boundary $j$ is $\Gamma_j-\Gamma_{j-1}$, as Helmholtz' theorems require. + +\paragraph{Induced velocities.} A straight segment $\vect A\to\vect B$ of strength $\Gamma$ induces at $\vect P$, with $\vect r_0=\vect B-\vect A$, $\vect r_1=\vect P-\vect A$, $\vect r_2=\vect P-\vect B$, +\begin{equation} +\vect u=\frac{\Gamma}{4\pi}\,\frac{\vect r_1\times\vect r_2}{|\vect r_1\times\vect r_2|^2}\;\vect r_0\cdot\Big(\frac{\vect r_1}{|\vect r_1|}-\frac{\vect r_2}{|\vect r_2|}\Big), +\label{eq:segment} +\end{equation} +and a semi-infinite filament from $\vect A$ along the unit direction $\vect e$, +\begin{equation} +\vect u=\frac{\Gamma}{4\pi}\,\frac{1+\vect r_1\cdot\vect e/|\vect r_1|}{|\vect r_1\times\vect e|^2}\;\vect r_1\times\vect e . +\label{eq:semiinf} +\end{equation} +Near a filament the velocity is regularised. The bound segments use a Vatistas core of radius $\epsilon_1=\delta\,|\vect r_0|$ with $\delta$ the \code{core\_radius\_fraction} (default $10^{-20}$, i.e.\ no core: the model never evaluates a bound segment on its own line, Section~\ref{sec:curved}); the legs and the wake use the viscous core of~\cite{damiani2019}, $\epsilon_2=\sqrt{4\alpha_0\nu\,r_\perp/U}$ with the Oseen parameter $\alpha_0=1.25643$, $\nu$ the kinematic viscosity and $r_\perp$ the distance along the filament to the foot of the evaluation point. Inside a core the velocity ramps linearly to zero; on the line it is zero. + +\paragraph{Influence matrices} (\code{BodyAerodynamics.compute\_AIC\_matrices}, \code{utils.assemble\_AIC\_matrices}). The velocity induced at every evaluation point by every ring of unit strength is assembled once per inflow into three $N\times N$ matrices, $\vect u=\mathrm{AIC}_x\boldsymbol\Gamma$ etc., evaluated with a numba kernel. For the VSM the evaluation points are the control points and the bound segment of the panel's own ring is included; for the LLT variant they are the aerodynamic centres and the own bound segment is excluded (it induces nothing on its own line). In the VSM the two-dimensional velocity of an infinite vortex of the panel's own strength along its bound direction is subtracted at its control point (TAT1 of~\cite{gaunaa2026}, Section~\ref{sec:coupling}), so that the inner model sees the three-dimensional disturbance only. + +\paragraph{Wake direction} (\code{Wake.frozen\_wake}). Each ring's wake follows that panel's own apparent velocity: the freestream plus the body-rate term, or the distributed inflow. In a uniform inflow this is the classical single straight wake; under yaw or roll rates it is locally aligned. On a translating wing the wake direction is a second-order effect (a per-panel wake changes the V3 lift by under 1\,\%). + +\paragraph{Direction of the attached-trailed legs} (\code{leg\_direction}, Figure~\ref{fig:legs}). Theory does not fix the path of the attached vorticity between the bound vortex and the trailing edge; \cite{gaunaa2026} calls it a modelling choice and takes the chordwise direction of CP1. The code offers three constructions. \code{"rib"} (default) runs the legs along the interpolated sections to their trailing-edge points, with the control point on the section: a fixed vortex system, independent of the inflow. \code{"streamwise"} runs them along the mean apparent velocity projected onto the surface, up to the trailing-edge curve, rebuilt whenever the inflow is set. \code{"perpendicular"} is the paper's construction, with the quarter-chord tangent averaged over one leg length so that the legs fan out instead of crossing at a planform kink. In the last two the control point moves with the legs so that it stays between the panel's own two legs. Section~\ref{sec:val-legs} compares the three against a vortex-lattice method; the rib legs are the default because the code's main use is trim finding with an inflow that varies along the span, where only the rib construction is unambiguous, and their accuracy is the same. + +\begin{figure}[p]\centering +\includegraphics[width=\textwidth]{10_leg_direction_geometry.png} +\caption{The vortex system seen from above (flow downwards) and from the side for the three leg constructions (\code{docs/validation/leg\_direction\_study.py --figures}): bound vortex (black), aerodynamic centres (dots), control points (crosses in the colour of their legs), rib legs (blue), streamwise legs (green), perpendicular legs (red), and the lattice of the vortex-lattice referee of Section~\ref{sec:val-legs} in grey. (a) A straight wing whose ribs are drawn skewed; (b) the root of a kinked swept wing; (c) a swept--anhedral elliptic wing; (d) the arc wing from the side, where streamwise legs climb along the nearly vertical tips; (e, f) the V3 kite and its tip.} +\label{fig:legs} +\end{figure} + +\section{The inner--outer coupling} +\label{sec:coupling} +This section follows the coupling rules of Gaunaa, Li and Pirrung~\cite{gaunaa2026}, which the code implements in full except for the direction of the legs (previous section) and the treatment of the curved bound vortex at the quarter chord (Section~\ref{sec:curved}). The rules are: CP1, only the span-perpendicular velocity drives the inner model; TAT1, that velocity excludes the section's own two-dimensional disturbance; TAT2, the magnitude of the sectional force follows from the flow at the three-quarter chord; TAT3, its direction from the flow at the quarter chord. + +\subsection{Inner velocity and circulation} +\label{sec:gamma} +At the control point $\vect C_i$ the three-dimensional relative velocity is the apparent velocity plus the induced velocity of the whole vortex system, $\vect V_{3D,i}=\vect V_{a,i}+\sum_j \mathrm{AIC}_{ij}\Gamma_j$. The inner velocity is its span-perpendicular part minus the two-dimensional disturbance of the section's own bound vortex (CP1 and TAT1): +\begin{equation} +\vect V_{\mathrm{inner},i}=\vect V_{3D,i}-(\vect V_{3D,i}\cdot\vect e_{s,i})\vect e_{s,i}-\vect V_{2D,\mathrm{bound},i},\qquad +\alpha_{3/4,i}=\operatorname{atan2}(\vect V_{\mathrm{inner},i}\cdot\vect e_{n,i},\ \vect V_{\mathrm{inner},i}\cdot\vect e_{c,i}), +\end{equation} +and the circulation follows from the sectional lift (eq.~4 of~\cite{gaunaa2026}, TAT2): +\begin{equation} +\Gamma_i=\tfrac12\,|\vect V_{\mathrm{inner},i}|\,c_i\,C_{l,i}(\alpha_{3/4,i}). +\label{eq:gamma} +\end{equation} +For a flat plate, $C_l=2\pi\alpha$, this is Weissinger's three-quarter-chord condition: on an infinite wing the bound vortex at $c/4$ induces at $3c/4$ exactly the downwash that makes the flow tangent there. On a swept infinite wing the perpendicular chord and velocity in~\eqref{eq:gamma} give the lift slope $2\pi\cos\Lambda$ of simple sweep theory; a streamwise chord would not. + +\subsection{Force magnitudes and directions} +\label{sec:forces} +The sectional lift, drag and moment per unit span use the inner velocity and the polar at $\alpha_{3/4}$: +\begin{equation} +L'_i=\tfrac12\rho|\vect V_{\mathrm{inner},i}|^2 c_i C_{l,i},\qquad D'_i=\tfrac12\rho|\vect V_{\mathrm{inner},i}|^2 c_i C_{d,i},\qquad M'_i=\tfrac12\rho|\vect V_{\mathrm{inner},i}|^2 c_i^2 C_{m,i}, +\end{equation} +multiplied by the panel width along the bound vortex. Their directions follow TAT3: the lift is perpendicular and the drag parallel to the undisturbed relative flow at the quarter chord, $\vect V_{1/4,i}$, within the span-normal plane (\code{is\_aoa\_corrected=True}, the default). $\vect V_{1/4,i}$ is the apparent velocity plus the induction of the trailed system (legs and wake of every ring) at $\vect P_i$, which for a straight wing is Prandtl's exact downwash, plus the influence of the curved or swept bound vortex of the next section. Taking the directions from the three-quarter-chord flow instead (\code{is\_aoa\_corrected=False}, the paper's LL-3/4) overestimates the induced drag by 20--40\,\%, Section~\ref{sec:val-trefftz}. The moment acts about the bound vortex, with the polar's $C_m$ referred to the quarter chord. + +\subsection{The curved bound vortex at the quarter chord} +\label{sec:curved} +On a curved or swept quarter-chord line the neighbouring bound segments induce a velocity at $\vect P_i$ that grows as the logarithm of the panel width: the lifting line evaluated on itself is singular (Li et al.~\cite{li2020}). The on-blade induced drag is $\rho\Gamma(w\cos\alpha+u\sin\alpha)$ with $w$ an induced angle of about one degree, so a chordwise velocity $u$ of 3\,\% of the freestream moves the drag by 12\,\%; evaluating the other panels' segments on the line made the V3 induced drag fall from 0.93 to 0.86 of the Trefftz value between 20 and 150 panels. The code regularises the term without a free parameter~\cite{report}: for each panel $i$ the wing is unrolled onto the tangent line of panel $i$, and the quarter-chord velocity is the classical downwash of the unrolled wing plus the difference between the actual and the unrolled vortex systems, both with the bound vorticity and the leg starting points spread along the chord with the thin-airfoil distribution $\gamma(x)\propto\sqrt{(c-x)/x}$ (24 strips, effective cut-off $0.15\,c$): +\begin{equation} +\vect V_{1/4,i}=\vect V_{a,i}+\sum_j\Gamma_j\Big[\vect K^{\mathrm{LL}}_{j,\mathrm{unrolled}(i)}(\vect P_i)+\vect K^{\mathrm{sheet}}_{j}(\vect P_i)-\vect K^{\mathrm{sheet}}_{j,\mathrm{unrolled}(i)}(\vect P_i)\Big]. +\label{eq:curved} +\end{equation} +The bracket is identically zero on a straight wing, finite everywhere, and the wake terms cancel between the two systems. Implementation: \code{utils.assemble\_curved\_bound\_correction\_AIC}, called once per solve. It shares its mechanism with the effective-lifting-line method of Reid and Hunsaker~\cite{reid2020}, whose two empirical lengths it replaces with the thin-airfoil distribution. Figure~\ref{fig:curved} shows the problem and the result; the full derivation, the literature and the rejected alternatives are in~\cite{report}. + +\begin{figure}[p]\centering +\includegraphics[width=\textwidth]{08_curved_bound_vortex_regularisation.png} +\caption{The curved bound vortex at the quarter chord (\code{docs/validation/curved\_bound\_vortex\_validation.py --figures}). (a) The log-singular self-induction of a curved line; (b) the chordwise velocity at mid-span of an arc wing from the polyline (grows with the panel count) and from the chordwise-spread sheet (finite); (c) why the drag is sensitive to it; (d) the thin-airfoil distribution; (e) the construction of eq.~\eqref{eq:curved}; (f) on-blade over Trefftz induced drag against panel count on the arc and the V3, before (dashed) and after (solid).} +\label{fig:curved} +\end{figure} + +\subsection{The attached-trailed force} +\label{sec:atforce} +The chordwise legs between the bound vortex and the trailing edge are attached to the wing and carry a Kutta--Joukowski force (Section~3 of~\cite{gaunaa2026}). On section boundary $j$, with net strength $\Delta\Gamma_j=\Gamma_j-\Gamma_{j-1}$ and leg vector $\vect l_j$, +\begin{equation} +\vect F_{\mathrm{AT},j}=\rho\,\Delta\Gamma_j\,\vect V_{3D}(\vect Q_j)\times\vect l_j, +\end{equation} +where $\vect V_{3D}(\vect Q_j)$ is the full relative velocity at the leg's three-quarter point, the point where the flow has no component through the wing. The force is spanwise and cancels on an unswept wing; on swept wings and on the curved outboard parts of a kite it changes lift and induced drag (Figure~\ref{fig:at}). It is on by default (\code{is\_with\_attached\_trailed\_vortex\_force}) and reported per boundary in \code{F\_attached\_trailed\_distribution}. + +\begin{figure}[t]\centering +\includegraphics[width=0.9\textwidth]{04_v3_attached_trailed_force.png} +\caption{Attached-trailed force on the inviscid V3 at $10^\circ$ (\code{make\_pr\_figures.py}). Left: force vectors per section boundary. Right: vertical and streamwise components, largest over the curved outboard region and zero at mid-span where the legs follow the flow. Total 18\,N of 760\,N lift.} +\label{fig:at} +\end{figure} + +\subsection{Spanwise-flow viscous correction} +\label{sec:viscous} +With \code{is\_with\_viscous\_drag\_correction} the friction force of each section is corrected for the spanwise flow following Gaunaa, Sørensen and Li~\cite{gaunaa2024}, eqs.~4, 10 and 11: with $\beta=\operatorname{atan2}(\vect V\cdot\vect e_s,\ |\vect V-(\vect V\cdot\vect e_s)\vect e_s|)$ the angle between the full relative velocity at the control point and the span-normal plane, and the Reynolds number and dynamic pressure referred to the span-normal velocity, the correction adds a drag increment along the inner flow direction and a spanwise friction force along $\vect e_s$. On the V3 it is below $0.002$ in $C_D$ even at $20^\circ$ sideslip; it is off by default. + +\subsection{Stall: artificial viscosity} +\label{sec:stall} +Past the stall onset the lift slope of a polar is negative and the fixed-point iteration of Section~\ref{sec:solver} loses stability. With \code{is\_with\_artificial\_viscosity} the spanwise artificial viscosity of Li, Gaunaa, Pirrung and Lønbæk~\cite{li2026} is applied implicitly to the circulation update once any panel is past its positive or negative stall onset, with the coefficient of their eq.~16 written for a non-uniform grid and the factor $k=0.035$; it is a no-op in attached flow. It is off by default; for post-stall solutions the \code{casadi\_newton} loop is the robust alternative. + +\subsection{The lifting-line variant} +\label{sec:llt} +With \code{aerodynamic\_model\_type="LLT"} the inner velocity is evaluated at the aerodynamic centre and the own bound segment is excluded; no two-dimensional subtraction and no quarter-chord correction are needed. This is Prandtl's lifting line with nonlinear polars, exact for straight wings of high aspect ratio and provided for comparison; the VSM is the model for curved, swept and low-aspect-ratio wings. + +\section{Solver, inflow and outputs} +\label{sec:solver} +\paragraph{Iteration} (\code{Solver.solve}). With the influence matrices assembled, the circulation is the fixed point of~\eqref{eq:gamma}. The base loop is an under-relaxed fixed-point iteration, $\boldsymbol\Gamma\leftarrow(1-\omega)\boldsymbol\Gamma+\omega\,\boldsymbol\Gamma_{\mathrm{new}}(\boldsymbol\Gamma)$, stopped when $\max|\Delta\Gamma|/\max|\Gamma|<$ \code{allowed\_error} ($10^{-6}$). The relaxation factor defaults to $0.8$ times the stability limit of~\cite{li2026}, eq.~11, evaluated on the actual panels and polars, +\begin{equation} +\omega_{\max}=\frac{2}{1+\tfrac14\max_i (c_i/\Delta s_i)\,C_{l,i}'}, +\end{equation} +exact for the LLT and halved for the VSM, whose three-quarter-chord control point sees about twice the trailed induction (measured 0.51--0.66, Figure~\ref{fig:relax}). Alternatives: Anderson acceleration (10--25 times fewer iterations in attached flow), a Newton loop with an exact CasADi Jacobian and pseudo-transient continuation (3--10 iterations, converges post-stall), and Broyden solvers. The initial circulation is elliptic, cosine, zero or a previous solution. + +\begin{figure}[t]\centering +\includegraphics[width=0.9\textwidth]{05_relaxation_factor.png} +\caption{Relaxation factor (\code{make\_pr\_figures.py}). Left: iterations on the V3 with the old fixed $0.01$ and with the default derived from the stability limit, for VSM and LLT. Right: the measured stability limit over the bound of~\cite{li2026} on rectangular wings: exact for the LLT, about half for the VSM.} +\label{fig:relax} +\end{figure} + +\paragraph{Inflow} (\code{BodyAerodynamics.va}, \code{va\_initialize}). The apparent velocity is a single vector (speed, angle of attack, sideslip), or one vector per panel, optionally with rigid-body rates about given axes through a reference point: $\vect V_{a,i}=\vect V_\infty-\boldsymbol\omega\times(\vect C_i-\vect r_0)$. The sign conventions are in Section~\ref{sec:conventions}. Each inflow rebuilds the wake (and, with streamwise legs, the legs). + +\paragraph{Forces, moments and coefficients} (\code{BodyAerodynamics.compute\_results}). Panel forces are summed in the global frame; lift, drag and side force are the components along the reference wind axes, built from a reference velocity $\vect V_{\mathrm{ref}}$ (the panel inflow when it is uniform, otherwise an area-weighted root-mean-square of the distribution without the rotational term) and the span direction: drag along $\vect V_{\mathrm{ref}}$, lift along $\vect V_{\mathrm{ref}}\times\vect e_{\mathrm{span}}$, side force completing the triad. Coefficients use $q_{\mathrm{ref}}=\tfrac12\rho|\vect V_{\mathrm{ref}}|^2$ and the projected area $S$ of the wing onto the $z$-plane; moment coefficients are further divided by the largest chord. The results dictionary also carries the spanwise distributions of $\Gamma$, $\alpha$, the sectional coefficients, the panel forces and moments, the centre of pressure, the Reynolds number on the largest chord, and the Trefftz-plane induced drag. + +\paragraph{Trefftz-plane induced drag} (\code{compute\_trefftz\_plane\_induced\_drag}, reported as \code{drag\_induced\_trefftz}). For a wing in one uniform inflow the far-wake induced drag of the converged circulation is computed in the plane perpendicular to the freestream from the trace of the frozen wake: each section boundary sheds a line vortex of strength $\Delta\Gamma_j$, and $D_i=\tfrac12\rho\sum_j\Gamma_j w_{n,j}\Delta s_j$ with $w_n$ the normal induced velocity on the trace. It depends only on the circulation and the wake, not on where the forces are evaluated on the blade, and is the referee of Section~\ref{sec:val-trefftz}. It is \code{None} with body rates or a distributed inflow. + +\paragraph{Bridle lines} (\code{compute\_line\_aerodynamic\_force}). Each line is a cylinder of length $\ell$ and diameter $d$ at angle $\theta$ to the local flow, with the cross-flow drag coefficient $C_{d,c}=1.1$ and the friction coefficient $C_f=0.01$: $C_{d,t}=C_{d,c}\sin^3\theta+\pi C_f\cos^3\theta$ along the flow and $C_{l,t}=C_{d,c}\sin^2\theta\cos\theta-\pi C_f\sin\theta\cos^2\theta$ normal to it, on the area $\ell d$. On the V3 the bridles add a constant $0.036$--$0.040$ to $C_D$; they matter for flight, not for the wind-tunnel model, which had none. + +\section{Validation} +\label{sec:validation} +The validation is layered: analytical results for what theory fixes exactly, an internal consistency check for the induced drag, an independent potential-flow referee (a vortex-lattice method) for lift and induced drag on wings where no analytical result exists, and RANS and wind-tunnel data for the real kite. Inviscid polars ($C_l=2\pi\alpha$, $C_d=0$) are used wherever the comparison is with potential-flow theory, so that the lifting line and the referee solve the same problem. + +\subsection{Analytical cases} +\label{sec:val-analytical} +\paragraph{Horseshoe vortices.} The induced velocity of three horseshoe vortices of prescribed strengths at a prescribed point is compared with the hand-computed Biot--Savart result (the \code{analytical\_horshoe\_vortices} case in \code{tests/verification\_cases}); it checks eqs.~\eqref{eq:segment} and~\eqref{eq:semiinf} and the sign conventions of the ring. + +\paragraph{Elliptic wings.} For an elliptic planform Prandtl's lifting line gives $C_L=2\pi\alpha/(1+2/\mathrm{AR})$ and $C_{D_i}=C_L^2/(\pi\mathrm{AR})$. Figure~\ref{fig:classical} compares the LLT and the VSM with these on wings of aspect ratio 20 and 4 with a straight quarter-chord line (cosine spacing, 60 panels), and with the vortex-lattice method of Section~\ref{sec:val-legs}; the numbers are in Table~\ref{tab:classical}. The LLT reproduces the theory it discretises: lift slope within $0.4$ and $1.4\,\%$, Oswald factor $0.997$ at both aspect ratios. The VSM, which does not assume a high aspect ratio, matches the theory at aspect ratio 20 (slope $-1.5\,\%$, Oswald $0.991$) and at aspect ratio 4 follows the lifting-surface solution instead of the line theory: its lift is within $1\,\%$ of the VLM at $4$, $8$ and $12^\circ$, where Prandtl's result is $11$--$12\,\%$ too high, with the Oswald factor $0.998$. The same elliptic planform drawn with a straight leading edge has a curved quarter-chord line; the LLT variant has no regularisation for that (Section~\ref{sec:curved}) and its on-blade induced drag then exceeds its own Trefftz value by $11\,\%$ at aspect ratio 20 and $36\,\%$ at aspect ratio 4, while the VSM stays within $2\,\%$. The regression test \code{tests/verification\_cases/elliptical\_wing} holds the LLT within $0.01$ in $C_L$ and $0.001$ in $C_{D_i}$ of the theory. + +\begin{figure}[t]\centering +\includegraphics[width=\textwidth]{12_classical_wings.png} +\caption{Classical wings (\code{docs/validation/aerodynamic\_model\_figures.py}). Left and middle: elliptic wings of aspect ratio 20 and 4, LLT and VSM against Prandtl's lifting line and the AeroSandbox vortex-lattice method (stars). Right: the rectangular AR 8 wing, VSM against the VLM at $5^\circ$ and the elliptic reference slope.} +\label{fig:classical} +\end{figure} + +\begin{table}[t]\centering\small +\caption{Classical wings: lift slope relative to Prandtl's $2\pi/(1+2/\mathrm{AR})$ and Oswald factor (inviscid polars, 60 panels, cosine spacing, straight quarter-chord line); rectangular AR 8 wing relative to the vortex-lattice method (80 panels, $5^\circ$, Table~\ref{tab:referee}).} +\label{tab:classical} +\begin{tabular}{lcc} +\toprule +case & lift slope / theory & Oswald factor\\ +\midrule +elliptic AR 20, LLT & 0.996 & 0.997\\ +elliptic AR 20, VSM & 0.985 & 0.991\\ +elliptic AR 4, LLT & 0.987 & 0.997\\ +elliptic AR 4, VSM & 0.886 & 0.998\\ +\midrule + & $C_L$ / VLM & $C_{D_i}$ / VLM\\ +rectangular AR 8, VSM & 0.998 & 0.991\\ +\bottomrule +\end{tabular} +\end{table} + +\subsection{Consistency of the induced drag: the Trefftz plane} +\label{sec:val-trefftz} +For a given circulation and frozen wake the Trefftz-plane drag is the far-field value; a force model that evaluates the forces on the blade with the correct local flow must reproduce it, independently of the panel count. Figure~\ref{fig:trefftz} shows the on-blade over Trefftz ratio on inviscid wings. With quarter-chord directions, the attached-trailed force and the curved bound-vortex regularisation it is $1.000$ on straight wings, within $2\,\%$ on the elliptic swept--anhedral wing and the $30^\circ$ swept wing, and within $2\,\%$ on the V3 at $5$, $10$ and $15^\circ$, at every resolution. Three-quarter-chord directions overshoot by 20--40\,\%. Before the regularisation the V3 ratio fell with the panel count (0.93, 0.90, 0.86 at 20, 50, 150 panels). The check is a consistency test of the force evaluation, not a validation of the circulation; that is what the next subsection does. + +\begin{figure}[t]\centering +\includegraphics[width=\textwidth]{03_trefftz_check.png} +\caption{On-blade over Trefftz-plane induced drag on inviscid wings against panel count (\code{make\_pr\_figures.py}); the ratio must be one for a consistent force model.} +\label{fig:trefftz} +\end{figure} + +\subsection{Vortex-lattice referee: lift and induced drag on planar, swept, curved and kite-like wings} +\label{sec:val-legs} +The Trefftz plane cannot judge the lift. For that the vortex-lattice method of AeroSandbox~\cite{aerosandbox} (horseshoe vortices, 16 chordwise by 80--160 spanwise panels, flat-plate sections, trailing legs along the body axis) was run on the same wings as the VSM with the three leg constructions of Section~\ref{sec:vortex}: a straight AR~8 wing, a yawed wing (uniform $30^\circ$ sweep, no kink) and a kinked $30^\circ$ swept wing at $5^\circ$, a circular-arc wing ($110^\circ$, radius four chords) at $8^\circ$, the swept--anhedral elliptic wing of~\cite{gaunaa2026} at $10^\circ$, and the inviscid V3 at $10^\circ$ (\code{docs/validation/vlm\_referee.py}). For the induced drag the Trefftz drag of the VLM's own circulation is used, because its near-field drag with trailing legs along the body axis is low on non-planar wings. For the V3 the referee is approximate: it takes its sections perpendicular to the local span, which unskews the tip ribs. Figure~\ref{fig:referee} and Table~\ref{tab:referee} give the result. + +\begin{figure}[p]\centering +\includegraphics[width=\textwidth]{11_leg_direction_referee.png} +\caption{Vortex-lattice referee (\code{leg\_direction\_study.py --figures}). Top: strip circulation of the VLM and of the VSM with the three leg constructions. Bottom: lift and on-blade induced drag relative to the VLM, and the V3 viscous drag against RANS for the three constructions.} +\label{fig:referee} +\end{figure} + +\begin{table}[t]\centering\small +\caption{VSM relative to the vortex-lattice referee: lift, and on-blade induced drag over the VLM's Trefftz drag (VSM at 80 panels, elliptic 160).} +\label{tab:referee} +\begin{tabular}{lcc|cc|cc|cc} +\toprule + & \multicolumn{2}{c|}{VLM} & \multicolumn{2}{c|}{rib legs} & \multicolumn{2}{c|}{streamwise} & \multicolumn{2}{c}{perpendicular}\\ +case & $C_L$ & $C_{D_i}$ & $C_L$ & $C_{D_i}$ & $C_L$ & $C_{D_i}$ & $C_L$ & $C_{D_i}$\\ +\midrule +straight AR 8, $5^\circ$ & 0.402 & 0.00654 & $-0.2\,\%$ & $-0.9\,\%$ & $-0.2\,\%$ & $-0.9\,\%$ & $-0.2\,\%$ & $-0.9\,\%$\\ +yawed $30^\circ$, $5^\circ$ & 0.360 & 0.00537 & $0.0\,\%$ & $-0.6\,\%$ & $0.0\,\%$ & $-0.6\,\%$ & $+1.4\,\%$ & $+2.0\,\%$\\ +kinked swept $30^\circ$, $5^\circ$ & 0.363 & 0.00568 & $-0.4\,\%$ & $-3.0\,\%$ & $-0.4\,\%$ & $-3.0\,\%$ & $-8.8\,\%$ & $+6.7\,\%$\\ +arc $110^\circ$, $8^\circ$ & 0.577 & 0.01481 & $+0.3\,\%$ & $-3.4\,\%$ & $-2.1\,\%$ & $-1.2\,\%$ & $+0.3\,\%$ & $-3.4\,\%$\\ +elliptic, swept--anhedral, $10^\circ$ & 0.807 & 0.02643 & $+0.9\,\%$ & $-0.1\,\%$ & $+0.1\,\%$ & $-4.4\,\%$ & $+0.8\,\%$ & $-0.3\,\%$\\ +V3, flat plate, $10^\circ$ (approx.) & 0.624 & 0.02961 & $+2.3\,\%$ & $-4.0\,\%$ & $-1.9\,\%$ & $-8.6\,\%$ & $-7.9\,\%$ & $-4.5\,\%$\\ +\bottomrule +\end{tabular} +\end{table} + +What the referee says: with rib legs the VSM reproduces the lifting-surface lift within $1\,\%$ on every wing except the V3 (2.3\,\%, where the referee itself is approximate) and the induced drag within 4\,\%; streamwise legs are equivalent on the planar wings and on the elliptic wing, 2\,\% low on the arc (the legs climb along the vertical tips) and closest to RANS on the V3; the paper's perpendicular legs lose 9\,\% of the lift on the kinked wing and 8\,\% on the V3, where they also cross at the tips above 80 panels, and are rejected. On the arc wing the rib legs stay within $+0.3$, $+1.6\,\%$ of the VLM lift at $8$ and $15^\circ$ while the streamwise legs drift to $-2.1$, $-3.0\,\%$. The lift distributions of the VLM and the VSM coincide along the span (Figure~\ref{fig:referee}, top), so the small differences in the totals are not local defects. + +\subsection{The TU Delft V3 kite against RANS and the wind tunnel} +\label{sec:val-v3} +The V3 is a 25\,m$^2$ leading-edge inflatable kite with a strongly curved, swept planform. The VSM uses its CAD geometry with two-dimensional RANS polars of the rib sections at Re\,$5\times10^5$ (optionally NeuralFoil polars with transition), 50 panels, and is compared with the three-dimensional RANS of Poland et al.~\cite{poland2026} (Re\,$10^6$, no bridles) and with the wind-tunnel measurements of the same authors on a 1:6.5 rigid model without bridles (Re\,$5\times10^5$, support tare subtracted, open-jet correction applied). Table~\ref{tab:v3} and Figures~\ref{fig:v3polars} and~\ref{fig:v3before} give the comparison. + +\begin{table}[t]\centering\small +\caption{V3 kite, zero sideslip, 50 panels, rib legs, 2D RANS polars: VSM against RANS (\code{leg\_direction\_study.py}) and the wind tunnel (\code{curved\_bound\_vortex\_validation.py}; the measured angles differ slightly from the nominal ones).} +\label{tab:v3} +\begin{tabular}{c|cc|cc|c} +\toprule + & \multicolumn{2}{c|}{VSM} & \multicolumn{2}{c|}{RANS} & wind tunnel\\ +$\alpha$ & $C_L$ & $C_D$ & $C_L$ & $C_D$ & $C_D$\\ +\midrule +$1^\circ$ & 0.207 & 0.0494 & 0.228 & 0.0491 & --\\ +$4^\circ$ & 0.461 & 0.0518 & 0.461 & 0.0517 & --\\ +$5^\circ$ & -- & 0.055 & -- & 0.052 ($4^\circ$) & 0.076 ($5.4^\circ$)\\ +$7^\circ$ & 0.697 & 0.0656 & 0.675 & 0.0644 & 0.090 ($7.3^\circ$)\\ +$9^\circ$ & -- & 0.079 & -- & 0.084 ($10^\circ$) & 0.107 ($9.4^\circ$)\\ +$10^\circ$ & 0.917 & 0.0866 & 0.869 & 0.0842 & --\\ +$13^\circ$ & 1.050 & 0.1206 & 1.043 & 0.1100 & 0.217 ($13.4^\circ$)\\ +\bottomrule +\end{tabular} +\end{table} + +Against RANS the drag is within 3\,\% up to $10^\circ$ and 10\,\% high at $13^\circ$, near the RANS stall; the lift is within $0.02$ on average, with a lift slope of $0.078$ per degree against $0.067$ in RANS and the wind tunnel. The wind tunnel measures more drag than any simulation, RANS included: the gap is lift-dependent, $\Delta C_D\approx0.003+0.037\,C_L^2$, while the zero-lift drag agrees (wind tunnel 0.041, VSM 0.038, RANS 0.043). Poland et al.\ attribute it to the 3--4\,mm model canopy, the flow behind the leading-edge tube and transition. It is not a lifting-line issue; the three-quarter-chord force directions of the old code appeared to close part of it only because they overestimate the induced drag by 20--40\,\% (Figure~\ref{fig:v3before}), a compensating error. The physically defensible levers for the wind tunnel are two-dimensional polars with transition at the test Reynolds number ($+0.009$ in $C_D$ at $9.4^\circ$) and, for flight, the bridles. + +\begin{figure}[p]\centering +\includegraphics[width=\textwidth]{09_v3_polars_curved_bound_vortex_fix.png} +\caption{V3 polars (\code{curved\_bound\_vortex\_validation.py --figures}): the solver before the consistent coupling (grey dashed), quarter-chord directions with the singular bound-on-line term (blue) and with the regularisation (red), against RANS and the wind tunnel.} +\label{fig:v3polars} +\end{figure} + +\begin{figure}[p]\centering +\includegraphics[width=\textwidth]{01_v3_polars_before_after.png} +\caption{V3 polars before and after the consistent coupling (\code{make\_pr\_figures.py}): the old solver (dashed black), the consistent implementation with three-quarter-chord directions (blue) and with quarter-chord directions (red, the default), dotted without the attached-trailed force, against RANS and wind-tunnel data, including sideslip.} +\label{fig:v3before} +\end{figure} + +\subsection{Mesh convergence} +\label{sec:val-mesh} +Figure~\ref{fig:mesh} shows lift, induced drag and the on-blade over Trefftz ratio of the inviscid V3 and of the straight wing against the number of panels, 10 to 160, uniform spacing. On the V3 the lift is within $0.4\,\%$ of its 160-panel value from 10 panels on and the induced drag within $3\,\%$ (within $0.5\,\%$ from 40 panels), with the on-blade over Trefftz ratio between 1.007 and 1.021. On the straight wing the lift converges from above ($5\,\%$ high at 10 panels, $1\,\%$ at 40), because the tip loading needs panels to be resolved, the induced drag is within $1.3\,\%$ throughout, and the ratio is 1.000 at every count. Fifty panels, the usual choice for the V3, put every integral quantity within $1\,\%$ of the converged value. + +\begin{figure}[t]\centering +\includegraphics[width=\textwidth]{13_mesh_convergence.png} +\caption{Mesh convergence (\code{aerodynamic\_model\_figures.py}): lift and induced drag relative to the 160-panel value, and the on-blade over Trefftz ratio, for the inviscid V3 at $10^\circ$ and the straight AR 8 wing at $5^\circ$.} +\label{fig:mesh} +\end{figure} + +\subsection{Regression cases in the test suite} +\label{sec:val-tests} +The test suite (\code{pytest tests}, 182 tests) holds, besides unit tests of every module: the analytical horseshoe case; the elliptic wing against Prandtl; a curved wing of aspect ratio 3.2 and a $30^\circ$ swept wing against the thesis implementation and, for the swept wing, XFLR5 and CFD polars; the V3 against the thesis implementation and the RANS polars; the Trefftz consistency of the regularisation on the arc wing at 20, 40 and 80 panels; the leg constructions (equality where they must coincide, the skewed-rib invariance, the kinked wing, the sideslip rebuild, the pure-rotation fallback); the relaxation-factor bound; body rates and distributed inflow; and the wake direction. The cases that verify the thesis vortex system pass \code{leg\_direction="rib"} explicitly. + +\subsection{Limits of the model} +\label{sec:limits} +The model is a steady, attached-flow, thin-surface method. It does not capture: stall and post-stall flow beyond what the sectional polars and the artificial viscosity provide; wake roll-up and the interaction of the wake with downstream surfaces; unsteady effects (shed vorticity, added mass); thickness effects on the induced flow; and the viscous drag sources that the V3 wind tunnel sees beyond RANS. On curved wings the on-blade induced drag carries a few per cent of uncertainty with respect to a lifting-surface solution, and the lift slope of the V3 is 15\,\% steeper than measured. The direction of the attached-trailed legs is a modelling choice; the rib construction is the default and the streamwise one the alternative for uniform inflow (Section~\ref{sec:val-legs}). + +\section{Conventions} +\label{sec:conventions} +\begin{table}[h]\centering\small +\begin{tabular}{>{\raggedright\arraybackslash}p{0.28\textwidth}>{\raggedright\arraybackslash}p{0.66\textwidth}} +\toprule +item & convention\\ +\midrule +global frame & right-handed; kite data and examples: $x$ downstream, $y$ to the left tip, $z$ up\\ +panel frame & $\vect e_s$ (\code{z\_airf}) along the bound vortex towards the left tip; $\vect e_c$ (\code{y\_airf}) leading to trailing edge, perpendicular to the span; $\vect e_n$ (\code{x\_airf}) $=\vect e_c\times\vect e_s$, suction side\\ +chord & perpendicular to the local quarter-chord line (CP1), averaged over the panel's two sections\\ +bound vortex, control point & at $1/4$ and $3/4$ of the chord by default (\code{aerodynamic\_center\_location}, \code{control\_point\_location})\\ +circulation & positive for positive lift in the panel frame; ring sense bound $\vect b_2\to\vect b_1$, leg $\vect b_1\to\vect T_1$, leg $\vect T_2\to\vect b_2$\\ +angle of attack, sideslip & degrees in \code{va\_initialize}; $\vect V_a=U(\cos\alpha\cos\beta,\ \sin\beta,\ \sin\alpha\cos\beta)$ in the global frame\\ +body rates & about given axes through \code{reference\_point}; $\vect V_{a,i}=\vect V_\infty-\boldsymbol\omega\times(\vect C_i-\vect r_0)$\\ +polars & $[\alpha\ \text{(rad)},\ C_l,\ C_d,\ C_m]$, $C_m$ about the quarter chord\\ +lift, drag, side & along $\vect V_{\mathrm{ref}}\times\vect e_{\mathrm{span}}$, $\vect V_{\mathrm{ref}}$ and their cross product; coefficients on $q_{\mathrm{ref}}$ and the projected area\\ +moments & about \code{reference\_point}, coefficients on projected area times largest chord\\ +units & SI throughout; $\rho=1.225$\,kg/m$^3$, $\mu=1.81\times10^{-5}$\,Pa\,s by default\\ +\bottomrule +\end{tabular} +\end{table} + +\begin{thebibliography}{99}\small +\bibitem{gaunaa2026} M.~Gaunaa, A.~Li, G.~R.~Pirrung, From thin airfoil theory to finite wings: consistent implementation of Lifting Line-based models, J.\ Phys.: Conf.\ Ser.\ 3224 (2026) 042030. +\bibitem{li2026} A.~Li, M.~Gaunaa, G.~R.~Pirrung, K.~L{\o}nb{\ae}k, Relaxation limits and artificial viscosity for lifting line methods, TORQUE 2026. +\bibitem{li2020} A.~Li, M.~Gaunaa, G.~R.~Pirrung, N.~Ramos-Garc\'ia, S.~G.~Horcas, The influence of the bound vortex on the aerodynamics of curved wind turbine blades, J.\ Phys.: Conf.\ Ser.\ 1618 (2020) 052038. +\bibitem{gaunaa2024} M.~Gaunaa, N.~N.~S{\o}rensen, A.~Li, Spanwise-flow correction of the viscous forces in lifting-line methods, J.\ Phys.: Conf.\ Ser.\ 2767 (2024) 022068. +\bibitem{reid2020} J.~T.~Reid, D.~F.~Hunsaker, A general approach to lifting-line theory, applied to wings with sweep, J.\ Aircraft 58 (2021), doi:10.2514/1.C035994. +\bibitem{damiani2019} R.~Damiani, F.~F.~Wendt, J.~M.~Jonkman, J.~Sicard, A vortex step method for nonlinear airfoil polar data as implemented in KiteAeroDyn, AIAA SciTech 2019, paper 2019-0804. +\bibitem{poland2026} J.~A.~W.~Poland, J.~M.~van Spronsen, M.~Gaunaa, R.~Schmehl, Wind tunnel load measurements of a leading-edge inflatable kite rigid-scale model, Wind Energ.\ Sci.\ 11 (2026) 911. +\bibitem{aerosandbox} P.~D.~Sharpe, AeroSandbox: a differentiable framework for aircraft design optimization, MIT (2021), \url{https://github.com/peterdsharpe/AeroSandbox}; version 4.2.8, \code{VortexLatticeMethod}. +\bibitem{report} Vortex-Step-Method repository, The curved bound vortex at the quarter chord of a lifting line: problem, regularisation, literature and the direction of the attached-trailed legs, \code{docs/validation/curved\_bound\_vortex\_report.pdf} (2026). +\bibitem{cayon2022} O.~Cayon, Fast aeroelastic model of a leading-edge inflatable kite, MSc thesis, TU Delft (2022); its chapter~4 was the previous content of this document. 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The bracket is the curvature, sweep and skew effect; it is identically zero on a straight wing with perpendicular legs, finite because both sheets regularise the near field at the chord scale, and convergent because no filament is evaluated on its own line. The semi-infinite wake filaments cancel identically between the actual and unrolled systems, so the wake model plays no role. Nothing else changes: the three-quarter-chord magnitude (which already contains the LL-mod term of~\cite{li2020}), the circulation map, the AT force and the wake are untouched. The single-filament limit of the bracket recovers the curved-minus-straight idea of~\cite{li2018}; the chordwise spreading is the discrete counterpart of the inner solution in~\cite{guermond1990}; the local straightening is the mechanism of~\cite{reid2020} without its two empirical lengths. The effective cut-off implied by the distribution is $\exp\langle\ln|x-c/4|\rangle_\gamma=0.1515\,c$; the number of strips does not matter beyond $M\approx 20$ (24 and 32 strips give the same arc self-induction to three digits). Implementation: \texttt{assemble\_curved\_bound\_correction\_AIC} in \texttt{src/VSM/core/utils.py}, called once per solve from \texttt{BodyAerodynamics.update\_effective\_angle\_of\_attack\_if\_VSM}; about 1\,s at 80 panels. +The first term is Prandtl's classical downwash of the straight wing with the actual $\Gamma(s)$, exact for straight wings (ratio 1.000). The bracket is the curvature, sweep and skew effect; it is identically zero on a straight wing with perpendicular legs, finite because both sheets regularise the near field at the chord scale, and convergent because no filament is evaluated on its own line. The semi-infinite wake filaments cancel identically between the actual and unrolled systems, so the wake model plays no role. Nothing else changes: the three-quarter-chord magnitude (which already contains the LL-mod term of~\cite{li2020}), the circulation map, the AT force and the wake are untouched. The single-filament limit of the bracket recovers the curved-minus-straight idea of~\cite{li2018}; the chordwise spreading is the discrete counterpart of the inner solution in~\cite{guermond1990}; the local straightening is the mechanism of~\cite{reid2020} without its two empirical lengths. The effective cut-off implied by the distribution is $\exp\langle\ln|x-c/4|\rangle_\gamma=0.1515\,c$; the number of strips does not matter beyond $M\approx 20$ (24 and 32 strips give the same arc self-induction to three digits). Implementation: \texttt{assemble\_curved\_bound\_correction\_AIC} in \texttt{src/VSM/core/utils.py}, called from \texttt{BodyAerodynamics.update\_effective\_angle\_of\_attack\_if\_VSM}; about 0.5\,s at 50 panels and 1\,s at 80. The matrix depends on the panel geometry only, so it is computed once per shape and reused for every inflow and circulation; a body that is the cached shape up to a rigid rotation and translation (a trim that rotates the kite for every residual evaluation) reuses the stored matrix rotated, and only a deformation recomputes it. \subsection{Verification against the Trefftz plane} From ba308781322f545a9099afb3e775b5f21be44e5e Mon Sep 17 00:00:00 2001 From: ocayon Date: Tue, 13 Oct 2026 09:48:04 +0200 Subject: [PATCH 23/37] docs: figure of the per-panel unrolled reference wing in the report and the model document docs/validation/unrolling_figure.py draws, for the arc wing, the kinked swept wing and the V3, the straight reference wing that the curved bound-vortex regularisation builds on each evaluation panel's own tangent (one per panel, nodes at their arc-length distances, legs along that panel's chord direction), and the distance between actual and unrolled nodes against the distance from the panel: the near field coincides and cancels in the difference, the far field is the curvature effect. Figure 14 in docs/figures, placed after eq. 6 of the regularisation report and in Section 5.3 of the aerodynamic model document; both PDFs rebuilt. 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zw4B7SHGwC^Ook9sfSs+e&+qkv49f@S@eJM%N#fXaz|8?pUsL>;e~4+YeR7O3nMT4~ zIc63Do*$g+0@N9M6Xpy&3hd;ZcoaO1h`ntS`%IO~BtVjWwncFo5QC99ms^k{&Mg(@ zF=&?@^PK`kaLNZZ-#PXJpoOKCFjN1-j#hYhqvrG)VlXVkg#!lf)Z~yE&~m7MwHR~= z&hDpxg7jxUn9~2C5DLIK3!zdtrxSJ_{;MUR8*p?h@MC~DaPR}|igQ6?!eNufp+tbj z3p)a5Wym0d970Hey$-wknlW^sLU6AAa8!cR0w*45nUtCOAEs)9KE#O#w47Z{W-vHT z9|Q`V7&%u=fWai=;0G^>fbgEFN>A#47%}ayv7_Lj4}T-F6%fE9{59VJ_SbR?u)l{6 zbYPByHG#qev8HjX)f5oxzbgZW`M+8M+V@`-B*Ie9S!v>oQ+{N)Ptbb*a3N!36+@;= z&{nwEqEf*7A}kC{@|cQ*T?^TUt_y=-AO-AS;4xur0S7#a^&{U6*GSy%u7 diff --git a/docs/validation/curved_bound_vortex_report.tex b/docs/validation/curved_bound_vortex_report.tex index 68f4e56..49f9766 100644 --- a/docs/validation/curved_bound_vortex_report.tex +++ b/docs/validation/curved_bound_vortex_report.tex @@ -150,7 +150,13 @@ \subsection{Formulation} +\mathbf K^{\mathrm{sheet}}_{j}(\mathbf P_i)-\mathbf K^{\mathrm{sheet}}_{j,\mathrm{unrolled}(i)}(\mathbf P_i)\Big].\;} \label{eq:fix} \end{equation} -The first term is Prandtl's classical downwash of the straight wing with the actual $\Gamma(s)$, exact for straight wings (ratio 1.000). The bracket is the curvature, sweep and skew effect; it is identically zero on a straight wing with perpendicular legs, finite because both sheets regularise the near field at the chord scale, and convergent because no filament is evaluated on its own line. The semi-infinite wake filaments cancel identically between the actual and unrolled systems, so the wake model plays no role. Nothing else changes: the three-quarter-chord magnitude (which already contains the LL-mod term of~\cite{li2020}), the circulation map, the AT force and the wake are untouched. The single-filament limit of the bracket recovers the curved-minus-straight idea of~\cite{li2018}; the chordwise spreading is the discrete counterpart of the inner solution in~\cite{guermond1990}; the local straightening is the mechanism of~\cite{reid2020} without its two empirical lengths. The effective cut-off implied by the distribution is $\exp\langle\ln|x-c/4|\rangle_\gamma=0.1515\,c$; the number of strips does not matter beyond $M\approx 20$ (24 and 32 strips give the same arc self-induction to three digits). Implementation: \texttt{assemble\_curved\_bound\_correction\_AIC} in \texttt{src/VSM/core/utils.py}, called from \texttt{BodyAerodynamics.update\_effective\_angle\_of\_attack\_if\_VSM}; about 0.5\,s at 50 panels and 1\,s at 80. The matrix depends on the panel geometry only, so it is computed once per shape and reused for every inflow and circulation; a body that is the cached shape up to a rigid rotation and translation (a trim that rotates the kite for every residual evaluation) reuses the stored matrix rotated, and only a deformation recomputes it. +Figure~\ref{fig:unroll} shows the construction. The first term is Prandtl's classical downwash of the straight wing with the actual $\Gamma(s)$, exact for straight wings (ratio 1.000). The bracket is the curvature, sweep and skew effect; it is identically zero on a straight wing with perpendicular legs, finite because both sheets regularise the near field at the chord scale, and convergent because no filament is evaluated on its own line. The semi-infinite wake filaments cancel identically between the actual and unrolled systems, so the wake model plays no role. Nothing else changes: the three-quarter-chord magnitude (which already contains the LL-mod term of~\cite{li2020}), the circulation map, the AT force and the wake are untouched. The single-filament limit of the bracket recovers the curved-minus-straight idea of~\cite{li2018}; the chordwise spreading is the discrete counterpart of the inner solution in~\cite{guermond1990}; the local straightening is the mechanism of~\cite{reid2020} without its two empirical lengths. The effective cut-off implied by the distribution is $\exp\langle\ln|x-c/4|\rangle_\gamma=0.1515\,c$; the number of strips does not matter beyond $M\approx 20$ (24 and 32 strips give the same arc self-induction to three digits). Implementation: \texttt{assemble\_curved\_bound\_correction\_AIC} in \texttt{src/VSM/core/utils.py}, called from \texttt{BodyAerodynamics.update\_effective\_angle\_of\_attack\_if\_VSM}; about 0.5\,s at 50 panels and 1\,s at 80. The matrix depends on the panel geometry only, so it is computed once per shape and reused for every inflow and circulation; a body that is the cached shape up to a rigid rotation and translation (a trim that rotates the kite for every residual evaluation) reuses the stored matrix rotated, and only a deformation recomputes it. + +\begin{figure}[p]\centering +\includegraphics[width=\textwidth]{14_unrolling_per_panel.png} +\caption{What ``unrolling'' means (\texttt{docs/validation/unrolling\_figure.py}). For an evaluation panel $i$ (star) the reference wing is built on panel $i$'s own tangent line through its aerodynamic centre: every node keeps its arc-length distance from the panel, the legs are perpendicular to the line in panel $i$'s chord direction with each panel's own chord, and the wake keeps its direction. There is one such reference wing per panel. (a, b) The arc wing with the references of a mid-span panel (blue) and a panel near the tip (red): the two straight wings are different, each tangent at its own panel. (c) The kinked swept wing seen from above, with the reference of a panel on the right half: the whole wing, including the other half, is laid along that panel's line, and the legs follow that panel's chord direction. (d) The distance between the actual and the unrolled nodes against their arc-length distance from the evaluation panel, for the arc wing and the V3: within a leg length the two systems coincide to second order, so the singular near field cancels in the difference of eq.~\eqref{eq:fix}; what remains is the far-field effect of the curvature, finite once both systems are spread over the chord.} +\label{fig:unroll} +\end{figure} \subsection{Verification against the Trefftz plane} diff --git a/docs/validation/unrolling_figure.py b/docs/validation/unrolling_figure.py new file mode 100644 index 0000000..da7ec7c --- /dev/null +++ b/docs/validation/unrolling_figure.py @@ -0,0 +1,147 @@ +"""Figure 14 of docs/figures: what "unrolling the wing onto a panel's tangent" +means in the curved bound-vortex regularisation (report Section 4, eq. 6). + +For an evaluation panel i the reference wing is built on panel i's own +tangent line through its aerodynamic centre: every node keeps its arc-length +coordinate along the bound line, the legs are perpendicular to the line in +panel i's chord direction with each panel's own chord, and the wake keeps its +direction. The reference is different for every panel. The figure shows it +for two panels of the arc wing (3-D and front view), for a panel of the +kinked swept wing (top view), and how far the unrolled nodes move from the +actual ones as a function of the distance from the evaluation panel (the +near field cancels in the difference, the far field is the curvature effect). + +Usage (from the repository root, seconds):: + + python docs/validation/unrolling_figure.py +""" + +from __future__ import annotations + +import logging +from pathlib import Path + +import numpy as np + +import curved_bound_vortex_validation as cbv + +logging.disable(logging.CRITICAL) +FIG = Path(__file__).resolve().parents[1] / "figures" + + +def geometry(body): + P = body.panels + bound = np.array([p.bound_point_1 for p in P] + [P[-1].bound_point_2]) + te = np.array([p.TE_point_1 for p in P] + [P[-1].TE_point_2]) + ac = np.array([p.aerodynamic_center for p in P]) + chord_dir = np.array([p.y_airf for p in P]) + chords = np.array([p.chord for p in P]) + return bound, te, ac, chord_dir, chords + + +def unrolled(bound, te, ac, chord_dir, chords, i, ac_fraction=0.25): + """Nodes and leg ends of the reference wing of panel i (as the kernel builds it).""" + seg = bound[1:] - bound[:-1] + L = np.linalg.norm(seg, axis=1) + s = np.concatenate(([0.0], np.cumsum(L))) + t = seg[i] / L[i] + s_P = 0.5 * (s[i] + s[i + 1]) + nodes = ac[i][None, :] + (s - s_P)[:, None] * t[None, :] + # leg of node k: panel i's chord direction, the adjacent panel's chord + c_node = np.concatenate(([chords[0]], 0.5 * (chords[1:] + chords[:-1]), [chords[-1]])) + ends = nodes + (1.0 - ac_fraction) * c_node[:, None] * chord_dir[i][None, :] + return nodes, ends, s - s_P + + +def draw_wing(ax, bound, te, ij=None, color="k", lw=1.2, alpha=1.0, label=None, legs=True): + if ij is None: + ax.plot(bound[:, 0], bound[:, 1], bound[:, 2], color=color, lw=lw, alpha=alpha, label=label) + if legs: + for a, b in zip(bound, te): + ax.plot([a[0], b[0]], [a[1], b[1]], [a[2], b[2]], color=color, lw=0.6, alpha=alpha) + ax.plot(te[:, 0], te[:, 1], te[:, 2], color=color, lw=0.6, alpha=alpha, ls=":") + else: + u, v = ij + ax.plot(bound[:, u], bound[:, v], color=color, lw=lw, alpha=alpha, label=label) + if legs: + for a, b in zip(bound, te): + ax.plot([a[u], b[u]], [a[v], b[v]], color=color, lw=0.6, alpha=alpha) + ax.plot(te[:, u], te[:, v], color=color, lw=0.6, alpha=alpha, ls=":") + + +def main(): + import matplotlib + + matplotlib.use("Agg") + import matplotlib.pyplot as plt + + plt.rcParams.update({"font.size": 9}) + fig = plt.figure(figsize=(15, 9.5)) + ax3 = fig.add_subplot(2, 2, 1, projection="3d") + axf = fig.add_subplot(2, 2, 2) + axt = fig.add_subplot(2, 2, 3) + axd = fig.add_subplot(2, 2, 4) + + # ---- arc wing, two evaluation panels ---- + body = cbv.arc(20) + bound, te, ac, cdir, chords = geometry(body) + picks = [(10, "tab:blue", "panel 10 (mid-span)"), (2, "tab:red", "panel 2 (near the tip)")] + draw_wing(ax3, bound, te, color="k", label="actual wing (bound line, legs, trailing edge)") + draw_wing(axf, bound, te, ij=(1, 2), color="k", label="actual wing") + for i, col, lab in picks: + nodes, ends, _ = unrolled(bound, te, ac, cdir, chords, i) + draw_wing(ax3, nodes, ends, color=col, lw=1.4, alpha=0.9, label=f"unrolled reference of {lab}") + draw_wing(axf, nodes, ends, ij=(1, 2), color=col, lw=1.4, alpha=0.9, label=f"unrolled reference of {lab}") + ax3.plot([ac[i, 0]], [ac[i, 1]], [ac[i, 2]], "*", color=col, ms=12) + axf.plot([ac[i, 1]], [ac[i, 2]], "*", color=col, ms=12) + axf.plot(nodes[:, 1], nodes[:, 2], "o", color=col, ms=2.5) + ax3.set_xlabel("x"); ax3.set_ylabel("y"); ax3.set_zlabel("z") + ax3.set_title("(a) arc wing: the reference wing is straight, tangent at the evaluation panel") + ax3.view_init(elev=22, azim=-60) + ax3.set_box_aspect((1.0, 3.0, 1.6)) + ax3.legend(fontsize=7, loc="upper left", frameon=False) + axf.set_aspect("equal"); axf.set_xlabel("y"); axf.set_ylabel("z") + axf.set_title("(b) front view: nodes keep their arc-length distance from the evaluation panel") + axf.legend(fontsize=7, frameon=False, loc="lower center") + + # ---- kinked swept wing, one evaluation panel on the right half ---- + body = cbv.swept(20) + bound, te, ac, cdir, chords = geometry(body) + i = 5 + nodes, ends, _ = unrolled(bound, te, ac, cdir, chords, i) + draw_wing(axt, bound, te, ij=(1, 0), color="k", label="actual wing (ribs along the flow)") + draw_wing(axt, nodes, ends, ij=(1, 0), color="tab:red", lw=1.4, label=f"unrolled reference of panel {i}: legs along its chord direction") + axt.plot([ac[i, 1]], [ac[i, 0]], "*", color="tab:red", ms=12) + axt.plot(nodes[:, 1], nodes[:, 0], "o", color="tab:red", ms=2.5) + axt.invert_yaxis(); axt.set_aspect("equal") + axt.set_xlabel("y"); axt.set_ylabel("x (flow downwards)") + axt.set_title("(c) kinked swept wing, top view: the other half is laid along the panel's own line") + axt.legend(fontsize=7, frameon=False, loc="lower left") + + # ---- how far the unrolled nodes sit from the actual ones ---- + body = cbv.arc(40) + bound, te, ac, cdir, chords = geometry(body) + for i, col, lab in ((20, "tab:blue", "panel 20 (mid-span)"), (4, "tab:red", "panel 4 (near the tip)")): + nodes, ends, ds = unrolled(bound, te, ac, cdir, chords, i) + gap = np.linalg.norm(nodes - bound, axis=1) + axd.plot(np.abs(ds), gap, "o-", color=col, ms=3, label=f"arc wing, {lab}") + body = cbv.v3_inviscid(40) + bound, te, ac, cdir, chords = geometry(body) + for i, col, lab in ((20, "tab:green", "V3, panel 20 (mid-span)"), (3, "tab:orange", "V3, panel 3 (tip)")): + nodes, ends, ds = unrolled(bound, te, ac, cdir, chords, i) + gap = np.linalg.norm(nodes - bound, axis=1) + axd.plot(np.abs(ds), gap, "s--", color=col, ms=3, label=lab) + axd.axvspan(0, 0.75, color="0.9", label="within one leg length (0.75 c)") + axd.set_xlabel("arc-length distance of node from the evaluation panel") + axd.set_ylabel("distance between actual and unrolled node") + axd.set_title("(d) the near field coincides and cancels; the far field is the curvature effect") + axd.legend(fontsize=7, frameon=False) + fig.suptitle("Unrolling the wing onto the evaluation panel's tangent: one reference wing per panel", y=0.995) + fig.tight_layout(rect=(0, 0, 1, 0.97)) + out = FIG / "14_unrolling_per_panel.png" + fig.savefig(out, dpi=150) + print("figure 14 written to", out) + + +if __name__ == "__main__": + main() From 66f50134ba6b3540c7646c171cceedd6ed174f8c Mon Sep 17 00:00:00 2001 From: ocayon Date: Tue, 13 Oct 2026 13:09:18 +0200 Subject: [PATCH 24/37] docs: figure of the chordwise spreading of the bound vorticity docs/validation/chord_spread_figure.py draws the 24 thin-airfoil strips on real and unrolled panels of the arc wing, the chordwise velocity one neighbouring segment induces at the quarter-chord point as a filament and as a sheet (equal beyond a chord, finite within it only for the sheet, levelling at the 0.15 c cut-off), and the running sum of the neighbours from far to near at 40 to 320 panels (filaments keep rising, sheets settle). Figure 15 in docs/figures, placed after the spreading paragraph of the regularisation report and in Section 5.3 of the aerodynamic model document; both PDFs rebuilt. Co-Authored-By: Claude Fable 5.1 --- docs/Aerodynamic_model.pdf | Bin 2899463 -> 3179524 bytes docs/aerodynamic_model/aerodynamic_model.tex | 8 +- docs/figures/15_chord_spread.png | Bin 0 -> 315917 bytes docs/figures/README.md | 12 + docs/validation/chord_spread_figure.py | 225 ++++++++++++++++++ .../validation/curved_bound_vortex_report.pdf | Bin 1887895 -> 2168050 bytes .../validation/curved_bound_vortex_report.tex | 8 +- 7 files changed, 251 insertions(+), 2 deletions(-) create mode 100644 docs/figures/15_chord_spread.png create mode 100644 docs/validation/chord_spread_figure.py diff --git a/docs/Aerodynamic_model.pdf b/docs/Aerodynamic_model.pdf index 198bcd440f7bc2ba14acaf02e8ffa80637005725..e2383d557a25ef43a5864599374f4d1856d9d62c 100644 GIT binary patch delta 353212 zcmZU319W6v({3H*{u{D32n$5sML?HWiG=~|nfEa3#v={N|n>p>7_;Aq#adV`J>x|L04<|izsg# zKLOjvc@K#W7}X|(e$Svppw?iqf+nv}r6N7I-fHkVu8aR%>L{;&3Lx#Oyx+tDV`Ap_ 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above with the reference of a panel on the right half; (d) the distance between actual and unrolled nodes against the distance from the evaluation panel: the near field coincides (the singular part cancels in the difference), the far field is the curvature effect. + +## 15 Chordwise spreading of the bound vorticity +Generated by `docs/validation/chord_spread_figure.py`. (a) Three panels of +the arc wing from above with the bound vortex replaced by the 24 +thin-airfoil strips, weights as line shade, each strip with its own legs; +(b) the same strips on the real curved panels and on the unrolled straight +reference, nearly coincident in the neighbourhood; (c) the chordwise +velocity one neighbouring segment induces at the quarter-chord point +against its distance, filament against sheet: equal beyond a chord, the +filament grows and the sheet levels off at the 0.15 c cut-off within it; +(d) the running sum of the neighbours from far to near at 40 to 320 panels: +filaments keep rising with refinement (the logarithm), sheets settle. diff --git a/docs/validation/chord_spread_figure.py b/docs/validation/chord_spread_figure.py new file mode 100644 index 0000000..ef65e66 --- /dev/null +++ b/docs/validation/chord_spread_figure.py @@ -0,0 +1,225 @@ +"""Figure 15 of docs/figures: the chordwise spreading of the bound vorticity in +the curved bound-vortex regularisation (report Section 4, eqs. 4-6). + +(a) Three neighbouring panels of the arc wing with their bound segments + replaced by the 24 thin-airfoil strips along the chord (line weight and + shade proportional to the strip weight), each strip with its own legs on + the node's leg line. +(b) The same panels on the unrolled (straight) reference line of the middle + panel, with the same strips. +(c) Chordwise velocity induced at the quarter-chord point of the middle panel + by ONE neighbouring bound segment of unit strength, against its arc-length + distance, for the single filament and for the spread sheet: far away the + two coincide, within a chord the sheet stays finite where the filament + grows. +(d) The running sum of those contributions from the far field inwards, for + several panel counts: the filament sum keeps rising as the nearest + neighbours get closer (the logarithm), the sheet sum settles. + +Usage (from the repository root, seconds):: + + python docs/validation/chord_spread_figure.py +""" + +from __future__ import annotations + +import logging +from pathlib import Path + +import numpy as np + +import curved_bound_vortex_validation as cbv +from VSM.core.utils import thin_airfoil_strips + +logging.disable(logging.CRITICAL) +FIG = Path(__file__).resolve().parents[1] / "figures" +AC = 0.25 + + +def seg_velocity(a, b, p): + """Unit-strength straight segment a->b at p (Biot-Savart), zero on the line.""" + r1, r2 = p - a, p - b + cr = np.cross(r1, r2) + n = np.dot(cr, cr) + if n < 1e-20: + return np.zeros(3) + return cr / (4 * np.pi * n) * np.dot(b - a, r1 / np.linalg.norm(r1) - r2 / np.linalg.norm(r2)) + + +def geometry(body): + P = body.panels + bound = np.array([p.bound_point_1 for p in P] + [P[-1].bound_point_2]) + te = np.array([p.TE_point_1 for p in P] + [P[-1].TE_point_2]) + ac = np.array([p.aerodynamic_center for p in P]) + chord_dir = np.array([p.y_airf for p in P]) + chords = np.array([p.chord for p in P]) + return bound, te, ac, chord_dir, chords + + +def strips_of_panel(b1, b2, t1, t2, x, w): + """Strip segments of one panel: stations along each node's leg line.""" + f = (x - AC) / (1.0 - AC) + a = b1[None, :] + f[:, None] * (t1 - b1)[None, :] + b = b2[None, :] + f[:, None] * (t2 - b2)[None, :] + return a, b, w + + +def unrolled(bound, te, ac, chord_dir, chords, i): + seg = bound[1:] - bound[:-1] + L = np.linalg.norm(seg, axis=1) + s = np.concatenate(([0.0], np.cumsum(L))) + t = seg[i] / L[i] + s_P = 0.5 * (s[i] + s[i + 1]) + nodes = ac[i][None, :] + (s - s_P)[:, None] * t[None, :] + c_node = np.concatenate(([chords[0]], 0.5 * (chords[1:] + chords[:-1]), [chords[-1]])) + ends = nodes + (1.0 - AC) * c_node[:, None] * chord_dir[i][None, :] + return nodes, ends, s - s_P + + +def draw_strips(ax, bound, te, panels, x, w, ij, color, show_legs=True): + u, v = ij + for j in panels: + a, b, ww = strips_of_panel(bound[j], bound[j + 1], te[j], te[j + 1], x, w) + for k in range(len(ww)): + lw = 0.3 + 6.0 * ww[k] + ax.plot([a[k, u], b[k, u]], [a[k, v], b[k, v]], color=color, lw=lw, alpha=0.35 + 0.65 * ww[k] / ww.max(), solid_capstyle="butt") + if show_legs: + for k in range(0, len(ww), 6): + ax.plot([a[k, u], te[j, u]], [a[k, v], te[j, v]], color=color, lw=0.4, alpha=0.5) + ax.plot([b[k, u], te[j + 1, u]], [b[k, v], te[j + 1, v]], color=color, lw=0.4, alpha=0.5) + + +def main(): + import matplotlib + + matplotlib.use("Agg") + import matplotlib.pyplot as plt + from matplotlib.lines import Line2D + + plt.rcParams.update({"font.size": 9}) + fig = plt.figure(figsize=(14, 10)) + ax = np.empty((2, 2), dtype=object) + ax[0, 0] = fig.add_subplot(2, 2, 1) + ax[0, 1] = fig.add_subplot(2, 2, 2, projection="3d") + ax[1, 0] = fig.add_subplot(2, 2, 3) + ax[1, 1] = fig.add_subplot(2, 2, 4) + x, w = thin_airfoil_strips(24) + + # ---- (a) real panels near the tip of the arc wing, front-ish view (y, z) with the chord along x shown by projection + body = cbv.arc(16) + bound, te, ac, cdir, chords = geometry(body) + i = 3 + panels = [i - 1, i, i + 1] + A = ax[0, 0] + # top view (x along the page downwards, y across): shows the chordwise strips + for j in range(len(bound) - 1): + A.plot([bound[j, 1], bound[j + 1, 1]], [bound[j, 0], bound[j + 1, 0]], color="0.6", lw=1) + for j in panels: + A.plot([bound[j, 1], bound[j + 1, 1]], [bound[j, 0], bound[j + 1, 0]], color="k", lw=2.2) + for k in (j, j + 1): + A.plot([bound[k, 1], te[k, 1]], [bound[k, 0], te[k, 0]], color="k", lw=0.8) + draw_strips(A, bound, te, panels, x, w, (1, 0), "tab:red") + A.plot([ac[i, 1]], [ac[i, 0]], "*", color="tab:blue", ms=13, zorder=5) + A.annotate("P_i (quarter chord of panel i)", (ac[i, 1], ac[i, 0]), textcoords="offset points", xytext=(10, -12), fontsize=8, color="tab:blue") + A.set_xlim(bound[i - 1, 1] - 0.15, bound[i + 2, 1] + 0.15) + A.set_ylim(1.08, -0.08) + A.set_aspect("equal") + A.set_xlabel("y"); A.set_ylabel("x (chordwise, flow downwards)") + A.set_title("(a) three real panels of the arc wing, top view: the bound vortex spread into 24 strips") + + # ---- (b) 3-D view: the real strips (red) and the unrolled copies (green) of the same panels + B = ax[0, 1] + nodes, ends, _ = unrolled(bound, te, ac, cdir, chords, i) + B.plot(bound[:, 0], bound[:, 1], bound[:, 2], color="0.6", lw=1) + B.plot(nodes[:, 0], nodes[:, 1], nodes[:, 2], color="0.6", lw=1, ls=":") + for pts, tes, col in ((bound, te, "tab:red"), (nodes, ends, "tab:green")): + for j in panels: + B.plot([pts[j, 0], pts[j + 1, 0]], [pts[j, 1], pts[j + 1, 1]], [pts[j, 2], pts[j + 1, 2]], color="k", lw=2) + a, b, ww = strips_of_panel(pts[j], pts[j + 1], tes[j], tes[j + 1], x, w) + for k in range(len(ww)): + B.plot([a[k, 0], b[k, 0]], [a[k, 1], b[k, 1]], [a[k, 2], b[k, 2]], color=col, lw=0.3 + 5.0 * ww[k], alpha=0.35 + 0.65 * ww[k] / ww.max()) + for k in (j, j + 1): + B.plot([pts[k, 0], tes[k, 0]], [pts[k, 1], tes[k, 1]], [pts[k, 2], tes[k, 2]], color="k", lw=0.6) + B.plot([ac[i, 0]], [ac[i, 1]], [ac[i, 2]], "*", color="tab:blue", ms=12) + B.set_xlabel("x"); B.set_ylabel("y"); B.set_zlabel("z") + pts_all = np.vstack([bound[i - 1:i + 3], te[i - 1:i + 3], nodes[i - 1:i + 3], ends[i - 1:i + 3]]) + lo, hi = pts_all.min(axis=0) - 0.1, pts_all.max(axis=0) + 0.1 + B.set_xlim(lo[0], hi[0]); B.set_ylim(lo[1], hi[1]); B.set_zlim(lo[2], hi[2]) + B.set_box_aspect(tuple(hi - lo)) + B.view_init(elev=25, azim=-50) + B.set_title("(b) the same strips on the real (red, curved) and on the unrolled (green, straight) panels") + + # ---- (c) one neighbouring segment's chordwise velocity at P_i against distance: filament vs sheet + C = ax[1, 0] + body = cbv.arc(320) + bound, te, ac, cdir, chords = geometry(body) + i = 160 + p = ac[i] + seg = bound[1:] - bound[:-1] + s = np.concatenate(([0.0], np.cumsum(np.linalg.norm(seg, axis=1)))) + s_mid = 0.5 * (s[:-1] + s[1:]) + d = np.abs(s_mid - s_mid[i]) + v_fil, v_sheet = np.zeros(len(seg)), np.zeros(len(seg)) + for j in range(len(seg)): + if j == i: + continue + v_fil[j] = seg_velocity(bound[j], bound[j + 1], p)[0] + a, b, ww = strips_of_panel(bound[j], bound[j + 1], te[j], te[j + 1], x, w) + v_sheet[j] = sum(ww[k] * seg_velocity(a[k], b[k], p)[0] for k in range(len(ww))) + o = np.argsort(d) + m = (d > 0) + C.loglog(d[m], np.abs(v_fil[m]), ".", color="tab:red", ms=4, label="single filament at the quarter chord") + C.loglog(d[m], np.abs(v_sheet[m]), ".", color="tab:green", ms=4, label="chord-spread sheet (24 strips)") + C.axvline(0.15, color="0.5", ls="--", lw=0.8) + C.text(0.16, np.abs(v_fil[m]).max() * 0.5, "effective cut-off 0.15 c", fontsize=8, color="0.3") + C.axvline(1.0, color="0.8", ls=":", lw=0.8); C.text(1.05, np.abs(v_fil[m]).max() * 0.5, "one chord", fontsize=8, color="0.5") + C.set_xlabel("arc-length distance of the neighbouring segment from P_i (chord = 1)") + C.set_ylabel("|chordwise velocity at P_i| per unit circulation, one segment") + C.set_title("(c) what one neighbour induces: the sheet is the filament beyond a chord, finite within it") + C.legend(fontsize=8, frameon=False) + + # ---- (d) running sum from the far field inwards, for several panel counts + D = ax[1, 1] + for N, col in ((40, "0.75"), (80, "0.55"), (160, "0.35"), (320, "0.1")): + body = cbv.arc(N) + bound, te, ac, cdir, chords = geometry(body) + i = N // 2 + p = ac[i] + seg = bound[1:] - bound[:-1] + s = np.concatenate(([0.0], np.cumsum(np.linalg.norm(seg, axis=1)))) + s_mid = 0.5 * (s[:-1] + s[1:]) + d = np.abs(s_mid - s_mid[i]) + vf, vs = np.zeros(N), np.zeros(N) + for j in range(N): + if j == i: + continue + vf[j] = seg_velocity(bound[j], bound[j + 1], p)[0] + a, b, ww = strips_of_panel(bound[j], bound[j + 1], te[j], te[j + 1], x, w) + vs[j] = sum(ww[k] * seg_velocity(a[k], b[k], p)[0] for k in range(len(ww))) + o = np.argsort(-d) # far to near + dd = d[o][d[o] > 0] + D.semilogx(dd, np.cumsum(vf[o][d[o] > 0]), "-", color=col, lw=1.2, label=f"filaments, {N} panels") + D.semilogx(dd, np.cumsum(vs[o][d[o] > 0]), "--", color="tab:green", lw=1.2, alpha=min(1.0, 0.35 + 0.08 * (N // 40)), label=f"sheets, {N} panels") + D.invert_xaxis() + D.set_xlabel("distance from P_i of the segments summed so far (far field on the left)") + D.set_ylabel("running sum of the chordwise velocity at P_i") + D.set_title("(d) summing the neighbours from far to near: filaments keep growing, sheets settle") + D.legend(fontsize=7, frameon=False, ncol=2) + + handles = [ + Line2D([], [], color="k", lw=2.2, label="bound vortex (quarter-chord line)"), + Line2D([], [], color="k", lw=0.8, label="legs to the trailing edge"), + Line2D([], [], color="tab:red", lw=2, label="strips of the real panels (shade = weight)"), + Line2D([], [], color="tab:green", lw=2, label="strips of the unrolled panels"), + Line2D([], [], color="tab:blue", marker="*", ls="", ms=10, label="evaluation point P_i"), + ] + fig.legend(handles=handles, loc="lower center", ncol=5, frameon=False, bbox_to_anchor=(0.5, 0.0)) + fig.suptitle("Chordwise spreading of the bound vorticity: the sheet that replaces the line", y=0.995) + fig.tight_layout(rect=(0, 0.04, 1, 0.98)) + out = FIG / "15_chord_spread.png" + fig.savefig(out, dpi=150) + print("figure 15 written to", out) + + +if __name__ == "__main__": + main() diff --git a/docs/validation/curved_bound_vortex_report.pdf b/docs/validation/curved_bound_vortex_report.pdf index f56d2d03eef6967de56eec6013ca29e13febce8b..94e2d300ecec7b56f56b532956726f93b80ae99e 100644 GIT binary patch delta 301284 zcmZs?1yEJd8b4|Q(k&vA3eufYQqrB$(s2ms-h_a3hop3OcXxwyi*$FxTi$#BZ{B>qX6TemFhWxSb$4l(?qow+JuTSUA|@(uUtqLPMI1wrlK> zP-=_drFE5(VJB&GoA{7Wxoh6s;$LdjT?q?iX7slK)m#z6{+WM{AI_&k;3>Uh$;VlS z4}wIzg)_!X&U(!>?4QGv<9a@L?$DQ z!i(^ZoT1{*-FYLTE{}V^)zB29kW+RRsc&?9M@b0w6(pbVy4#<22vz^fl zMDl%!4-s}cUkA+uAL7wOAekTgBTzk@mUAjl;rt-FVU|qxaHYNJf<|c4q8tZDWV*%` zA}Xc&-yd~NXo{0LK@rGN>eXsY@nxY-wT${|ZbfnmpIr!RlYf~~8zPCWQ4O4M%~8Cw zps}Jj?tT68*}2k7qRI~g*`;-AUta$%Xni2_e^X3`f6}ApKUKm{ui8%pmlP5|LbhR% zVA}K=7^rS(qQOw0?0D;( 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b/docs/validation/curved_bound_vortex_report.tex @@ -141,7 +141,13 @@ \subsection{Formulation} \begin{equation} \mathbf n_{k,jq} = \mathbf b_{k,j} + \frac{x_q - x_{ac}}{1-x_{ac}}\,(\mathbf T_{k,j}-\mathbf b_{k,j}),\qquad x_{ac}=\tfrac14, \end{equation} -so that the strip legs are collinear with the actual legs, and the chordwise stations and weights follow the thin-airfoil distribution $\gamma(x)\propto\sqrt{(c-x)/x}$ through $x_q=\sin^2\phi_q$, $w_q\propto\cos^2\phi_q$, $\phi_q=(q-\tfrac12)\pi/(2M)$, $M=24$ (\texttt{thin\_airfoil\_strips}). The distribution has its centroid at $c/4$, so the far field of the sheet equals that of the single filament. +so that the strip legs are collinear with the actual legs, and the chordwise stations and weights follow the thin-airfoil distribution $\gamma(x)\propto\sqrt{(c-x)/x}$ through $x_q=\sin^2\phi_q$, $w_q\propto\cos^2\phi_q$, $\phi_q=(q-\tfrac12)\pi/(2M)$, $M=24$ (\texttt{thin\_airfoil\_strips}). The distribution has its centroid at $c/4$, so the far field of the sheet equals that of the single filament. Figure~\ref{fig:spread} shows the strips on real and unrolled panels and what the spreading does to the induction of a neighbouring segment: nothing beyond a chord, a finite value instead of a growing one within it. + +\begin{figure}[p]\centering +\includegraphics[width=\textwidth]{15_chord_spread.png} +\caption{The chordwise spreading (\texttt{docs/validation/chord\_spread\_figure.py}). (a) Three panels of the arc wing from above: the bound vortex of each panel replaced by 24 strips at the thin-airfoil stations, line weight and shade proportional to the strip weight, each strip with its own legs on the node's leg line. (b) The same strips on the real, curved panels (red) and on the unrolled, straight panels of the middle panel's reference (green): in the panel's neighbourhood the two sheets nearly coincide, which is why their difference is small there. (c) The chordwise velocity that one neighbouring bound segment of unit strength induces at the quarter-chord point $\mathbf P_i$ against its arc-length distance, as a single filament and as the spread sheet: beyond a chord the two are the same, within a chord the filament grows without bound and the sheet levels off at the cut-off $0.15\,c$ that the distribution fixes. (d) The running sum of those contributions from the far field inwards for 40 to 320 panels: with filaments every refinement adds a new nearest neighbour and the sum keeps rising, the logarithm of Li et al.; with sheets the sum settles to the same value at every panel count.} +\label{fig:spread} +\end{figure} For each evaluation panel $i$, the \emph{unrolled} reference wing is built on the tangent line $\mathbf t_i$ of panel $i$ through $\mathbf P_i$: every node keeps its arc-length coordinate along the bound line, the legs are perpendicular to the line in panel $i$'s chord direction with the panel's own chord length, and the wake keeps its direction. The quarter-chord velocity is then \begin{equation} From 5667520495009481746864880259947753be3b5b Mon Sep 17 00:00:00 2001 From: ocayon Date: Tue, 13 Oct 2026 14:35:08 +0200 Subject: [PATCH 25/37] docs(validation): review pass on the curved bound-vortex report before printing New Section 4.2 'Reading of the formulation': the quarter-chord construction is the same handover rule as TAT1 at the three-quarter chord (3D minus what the 2D section already contains, with the unrolled wing as the section's straight continuation); the chordwise sheet is the vorticity the inner model is made of, with a table showing that the three-quarter chord sums converge and need no sheet while the quarter-chord sums do not; the two sheet terms are the same panel in two positions. 'Other approaches' gains the per-panel segment-minus-infinite-line subtraction, tested and divergent like one over the panel width squared. Table 4's perpendicular-leg rows now use the current construction (the earlier rows were the superseded fixed-length legs). Open items gain the body-rate direction velocity (effective torsional rate, Li, Gaunaa and Pirrung 2026 preprint). Abstract mentions the leg referee; title block and date updated; 17 pages. 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z2l6$F!UbeGARKQ^*T@+Xf#Q%Gz<{Oy&py`kKL7+CgpzBJkZ)5V7Ss_G0S2U3l!ps| z9&uX&0$|(UL10P5Z7CN(+^&8c&`n`n*>k(9*O)z){K{@E%;v76TAZ#Q!;Y81U{F; z;+d2T-QB&wZvYQ`^Qxrn=I9Ro0_?8;r7m`IKLU7E4FsB~jz+6vv4=Dc9t5u!z!?#c t9*t2$;Z?-eQTG0SaV*8a>+$nmww_)-o(_&oWQIXS$s{eUp?{d^{{cj#@<;#x diff --git a/docs/aerodynamic_model/aerodynamic_model.tex b/docs/aerodynamic_model/aerodynamic_model.tex index 4775adb..81c9974 100644 --- a/docs/aerodynamic_model/aerodynamic_model.tex +++ b/docs/aerodynamic_model/aerodynamic_model.tex @@ -125,7 +125,7 @@ \subsection{The curved bound vortex at the quarter chord} \vect V_{1/4,i}=\vect V_{a,i}+\sum_j\Gamma_j\Big[\vect K^{\mathrm{LL}}_{j,\mathrm{unrolled}(i)}(\vect P_i)+\vect K^{\mathrm{sheet}}_{j}(\vect P_i)-\vect K^{\mathrm{sheet}}_{j,\mathrm{unrolled}(i)}(\vect P_i)\Big]. \label{eq:curved} \end{equation} -The bracket is identically zero on a straight wing, finite everywhere, and the wake terms cancel between the two systems. Implementation: \code{utils.assemble\_curved\_bound\_correction\_AIC}, about 0.5\,s at 50 panels. The matrix depends on the panel geometry only, so it is computed once per shape and reused for every inflow and circulation; a body that is the cached shape up to a rigid rotation and translation reuses the stored matrix rotated, which keeps a trim that rotates the kite for every residual evaluation at the cost of one evaluation per deformed shape. It shares its mechanism with the effective-lifting-line method of Reid and Hunsaker~\cite{reid2020}, whose two empirical lengths it replaces with the thin-airfoil distribution. Figure~\ref{fig:curved} shows the problem and the result; the full derivation, the literature and the rejected alternatives are in~\cite{report}. +The bracket is identically zero on a straight wing, finite everywhere, and the wake terms cancel between the two systems. Figure~\ref{fig:unroll} shows the unrolled reference wing for two panels of an arc wing and one of a kinked swept wing: it is a different straight wing for every panel, tangent at that panel, and it coincides with the real wing in the panel's neighbourhood, which is why the singular near field cancels in the difference and only the far-field effect of the curvature remains. Implementation: \code{utils.assemble\_curved\_bound\_correction\_AIC}, about 0.5\,s at 50 panels. The matrix depends on the panel geometry only, so it is computed once per shape and reused for every inflow and circulation; a body that is the cached shape up to a rigid rotation and translation reuses the stored matrix rotated, which keeps a trim that rotates the kite for every residual evaluation at the cost of one evaluation per deformed shape. It shares its mechanism with the effective-lifting-line method of Reid and Hunsaker~\cite{reid2020}, whose two empirical lengths it replaces with the thin-airfoil distribution. Figure~\ref{fig:curved} shows the problem and the result; the full derivation, the literature and the rejected alternatives are in~\cite{report}. \begin{figure}[p]\centering \includegraphics[width=\textwidth]{08_curved_bound_vortex_regularisation.png} @@ -133,6 +133,12 @@ \subsection{The curved bound vortex at the quarter chord} \label{fig:curved} \end{figure} +\begin{figure}[p]\centering +\includegraphics[width=\textwidth]{14_unrolling_per_panel.png} +\caption{Unrolling the wing onto the evaluation panel's tangent (\code{docs/validation/unrolling\_figure.py}). (a, b) Arc wing: the reference wings of a mid-span panel (blue) and a near-tip panel (red), each straight and tangent at its own panel (star), nodes at their arc-length distances. (c) Kinked swept wing from above: the reference of a panel on the right half lays the other half along that panel's line, legs along that panel's chord direction. (d) Distance between actual and unrolled nodes against their distance from the evaluation panel: the near field coincides and cancels, the far field is the curvature effect.} +\label{fig:unroll} +\end{figure} + \subsection{The attached-trailed force} \label{sec:atforce} The chordwise legs between the bound vortex and the trailing edge are attached to the wing and carry a Kutta--Joukowski force (Section~3 of~\cite{gaunaa2026}). 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at 40 to 320 panels: filaments keep rising with refinement (the logarithm), sheets settle. + +## 16 Two vortices meeting at a kink: line against sheet +Generated by `docs/validation/kink_figure.py`. The chordwise velocity that a +vortex of unit strength, starting where another ends and turned by 2, 5 or +10 deg, induces at a point of the first one at distance r from the kink: +as a single filament it goes like theta / r without limit, as the +chord-spread sheet it equals the filament beyond a third of a chord, is +bounded within, and vanishes at the kink. 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In~\cite{li2020} (Section~2.2) that influence is the induction of the 3D bound vortex minus that of an infinitely long 2D vortex of the section's own strength, evaluated at the \emph{three-quarter} chord, assumed constant along the chord, and added to the quarter-chord velocity. \texttt{develop} instead evaluated the other panels' bound segments \emph{on the quarter-chord line itself} (commit \texttt{9c43c1a}), which~\cite{li2020} calls LL-P\&S and shows to be log-singular and non-convergent. This is the cause of the problem treated here (Section~\ref{sec:problem}). A literal implementation of the~\cite{li2020} recipe in this code was also tested and fails on straight wings (Section~\ref{sec:lit}); the 2026 paper and its online appendix~\cite{appendix2026} do not specify the quarter-chord term further, so the form used in the authors' code needs clarification with them. The branch replaces the term by the regularisation of Section~\ref{sec:fix}. + \item \emph{The curved bound-vortex influence on the direction velocity.} Reference~\cite{gaunaa2026} states that LL-Gaunaa includes ``the influence of the curved bound vortex'' according to~\cite{li2020}. In~\cite{li2020} (Section~2.2) that influence is the induction of the 3D bound vortex minus that of an infinitely long 2D vortex of the section's own strength, evaluated at the \emph{three-quarter} chord, assumed constant along the chord, and added to the quarter-chord velocity. \texttt{develop} instead evaluated the other panels' bound segments \emph{on the quarter-chord line itself} (commit \texttt{9c43c1a}), which~\cite{li2020} calls LL-P\&S and shows to be log-singular and non-convergent. This is the cause of the problem treated here (Section~\ref{sec:problem}). A literal implementation of the~\cite{li2020} recipe in this code was also tested and fails on straight wings (Section~\ref{sec:lit}); the form that reproduces the authors' published behaviour, curved-minus-straight bound segments at the control point, works with their perpendicular legs and not with rib legs (Table~\ref{tab:hyp}), and needs confirmation with them. The branch replaces the term by the regularisation of Section~\ref{sec:fix}. \item \emph{The direction of the attached-trailed legs.} Reference~\cite{gaunaa2026} (Section~3) states that the framework ``does not indicate how the trailed vorticity should connect from the 1/4 chord junctions to the trailing edge'', that this ``is not specified by theoretical results'' and ``is effectively a modeling choice'', and aligns the legs ``with the local chordwise direction up to the trailing edge'', i.e.\ perpendicular to the quarter-chord line (CP1). The code kept the legs along the input ribs; the paper's construction and a streamwise one were implemented (\texttt{leg\_direction}) and the three were compared against a vortex-lattice referee (Section~\ref{sec:legs}, Figures~\ref{fig:legs} and~\ref{fig:referee}). The perpendicular legs lose 9\,\% of the lift on a kinked swept wing and 8\,\% on the V3, where they also cross at the tips above 80 panels; rib and streamwise legs reproduce the lifting-surface lift within 1\,\% on straight, yawed, kinked, arc and swept--anhedral elliptic wings (streamwise: 2\,\% low on the arc). The rib legs remain the default (Section~\ref{sec:legs}, Decision); the streamwise construction is available as an option. This is now a documented choice backed by a referee rather than an untested deviation. \end{enumerate} @@ -99,6 +99,27 @@ \subsection{Li, Gaunaa, Pirrung, Ramos-Garc\'ia, Horcas (2020): evaluate at the \emph{Test in the VSM framework.} The recipe was implemented literally: for every panel $j$, the finite bound segment at the control point $\mathbf C_i$ minus (for $j=i$) the infinite line, reused at $\mathbf P_i$. Results (on-blade/Trefftz): straight AR\,8 wing 0.848, straight AR\,4 wing 0.815, arc 0.84, swept--anhedral elliptic wing with perpendicular legs 0.865, swept $30^\circ$ wing $0.50\to0.35$. The straight-wing failure is decisive: for a finite wing with spanwise-varying $\Gamma$ the ``3D minus 2D'' difference at the three-quarter chord is not zero (it contains the finite-span tails and the $\Gamma$-variation of the bound vortex; $+0.02$\,m/s at mid-span and $+0.11$\,m/s near the tips at $U=20$\,m/s on the AR\,8 wing), and eq.~\eqref{eq:drag} amplifies it. The same quantity used for the three-quarter-chord angle of attack, which the VSM has always done, is correct and untouched; only its reuse as a quarter-chord velocity fails. Since~\cite{gaunaa2026} reports LL-Gaunaa within 0.6\,\% of a VLM on straight wings, the authors' implementation must differ from this literal reading, most plausibly by taking ``curved minus straight'' (as first described in~\cite{li2018}) rather than ``3D minus 2D''. This should be confirmed with the authors. In their appendix the on-blade Oswald factor sits 5.6\,\% and 1.1\,\% above the Trefftz one for the 15\,\% and 25\,\% swept wings, within 0.6\,\% for the dihedral, anhedral and combined wings. +\emph{The hypothesised form, tested.} The reading that fits all their published numbers is: the bound segments of the real wing minus those of the wing unrolled onto the section's tangent, single filaments, evaluated at the three-quarter-chord control point where every distance is at least half a chord, and reused at the quarter chord (\texttt{\_curved\_minus\_straight\_cp} in the validation script, \texttt{--hypothesis}). It is zero on straight wings by construction and finite everywhere. Table~\ref{tab:hyp} shows what it does here. With the paper's perpendicular legs it is mesh-independent and within 1--2\,\% of the Trefftz plane on the elliptic wing and the V3, i.e.\ it is a working regularisation of the bound vortex, with the half-chord distance to the control point as its cut-off (on the arc it gives 0.993 against 0.999 for the sheet's $0.15\,c$). With the legs along the ribs it fails on the V3, 0.81 falling to 0.74, because legs that are not perpendicular to the bound line carry a logarithm of their own at the quarter-chord point (the same one that makes the swept wing with streamwise legs diverge in Table~\ref{tab:conv} without the bound term), and a bound-only difference at the control point cannot see it. The authors never meet that case because CP1 makes their legs perpendicular; a kite with ribs does. This is the most likely reason their code converges where the literal reading of~\cite{li2020} does not, and the reason the construction of Section~\ref{sec:fix} differences the whole vortex system, legs included, rather than the bound segments alone. + +\begin{table}[h]\centering\small +\caption{The hypothesised LL-Gaunaa quarter-chord term (curved minus straight bound segments, single filaments, at the control point, reused at the quarter chord): on-blade over Trefftz induced drag, inviscid polars, with rib legs and with the paper's perpendicular legs.} +\label{tab:hyp} +\begin{tabular}{llcccc} +\toprule +case & legs & $N=20$/40 & 80 & 160 & trend\\ +\midrule +straight AR 8 & either & 1.000 & 1.000 & -- & exact\\ +circular arc, $110^\circ$, $R=4c$ & either & 0.992 / 0.993 & 0.993 & 0.993 & converged, 0.7\,\% low\\ +elliptic, swept--anhedral & rib & 0.993 & 0.986 & 0.979 & drifting\\ +elliptic, swept--anhedral & perpendicular & 1.020 & 1.017 & 1.012 & converging\\ +V3 kite & rib & 0.809 & 0.772 & 0.735 & diverging\\ +V3 kite & perpendicular & 1.006 & 1.015 & -- & converged\\ +swept $30^\circ$, kinked & rib & 0.908 & 0.840 & -- & diverging\\ +swept $30^\circ$, kinked & perpendicular & 1.129 & 1.138 & -- & fan of legs at the kink\\ +\bottomrule +\end{tabular} +\end{table} + \subsection{Reid and Hunsaker (2020), Goates and Hunsaker (2021, 2023): effective lifting line and jointed legs} References~\cite{reid2020,goates2021,goates2023} (open-source implementation MachUpX) prove that the induced velocity on a lifting line is finite only where the line's second derivative vanishes and the trailing vortices leave it perpendicularly. Their construction: each control point sees an \emph{effective} lifting line, straight (tangent) near the point and blended into the true curve with a Gaussian of prescribed width (``blending distance'', recommended $\gtrsim 25\,\%$ of the span, MachUpX default one semispan); each trailing vortex has a finite \emph{joint} of length $\delta c$ perpendicular to the effective line before turning along the freestream (recommended $\delta\gtrsim0.15$, MachUpX default 0.15). Bound segments of the other sections are kept. Validation is on circulation distributions and $C_L$ of planar swept wings against panel methods and experiment; induced drag and non-planar wings are not examined. @@ -167,6 +188,23 @@ \subsection{Reading of the formulation} \emph{The sheet is what the profile is made of, not a numerical device.} The three-quarter-chord sums converge (Table~\ref{tab:cpconv}): the control point is half a chord from every filament, the lumped vortex at the quarter chord with the control point at the three-quarter chord reproduces thin-airfoil lift exactly (Pistolesi), and a sheet there would change that equivalence without regularising anything. The quarter-chord point lies on the line, and there the neighbours sit at a fraction of a chord. What is there, in the inner model's own terms, is the neighbour's chordwise sheet, bent slightly out of the section's plane; two sheets at a small angle induce a finite velocity on each other, two lines do not. Spreading the bound vorticity with the thin-airfoil distribution therefore uses, for the neighbours, the vorticity the inner model already uses for the section itself; the cut-off $0.15\,c$ is that distribution's, not a choice. The unrolled system is spread with the same strips so that collinear neighbours, which are the own 2D vortex, cancel exactly. The first term of eq.~\eqref{eq:fix} is left as single filaments because it is Prandtl's exact downwash of the straight wing, which spreading the leg starts would alter; the spreading enters only through the difference, which is zero wherever the wing is straight. +\emph{Why two lines diverge and two sheets do not} (Figure~\ref{fig:kink}). Let line 2 start where line 1 ends, turned by an angle $\theta$ out of their common plane, and let $\mathbf P$ sit on line 1 at distance $r$ from the kink. The velocity line 2 induces at $\mathbf P$, perpendicular to the plane of the two lines and hence along the chord, is +\begin{equation} +v=\frac{\Gamma\,(1-\cos\theta)}{4\pi\, r\sin\theta}\;\approx\;\frac{\Gamma\theta}{8\pi r}, +\label{eq:kink} +\end{equation} +unbounded as $\mathbf P$ approaches the kink for any $\theta\neq0$. A smooth line of curvature $\kappa$ is a continuum of such kinks: the element at arc distance $d$ is seen under the angle $\kappa d/2$ and contributes $\mathrm{d}v=\Gamma\kappa\,\mathrm{d}s/(8\pi d)$, and the sum from the nearest element at the panel width $\Delta s$ to the span $L$ is $(\Gamma\kappa/8\pi)\ln(L/\Delta s)$ per side: the logarithm, one constant per doubling, no limit because the nearest element is always at the panel width. Give each line its chordwise sheet and let $\mathbf P$ sit at chord station $x_P$: the element of sheet 2 at station $x$ and arc distance $d$ is at distance $\sqrt{d^2+\Delta x^2}$, $\Delta x=x-x_P$, and the same geometry gives +\begin{equation} +\mathrm{d}v=\frac{\Gamma\gamma(x)\,\mathrm{d}x}{4\pi}\;\frac{\kappa d^2/2}{(d^2+\Delta x^2)^{3/2}}\,\mathrm{d}s, +\end{equation} +which is the line's $\Gamma\kappa\,\mathrm{d}s/(8\pi d)$ for $d\gg|\Delta x|$ and vanishes like $d^2$ for $d\ll|\Delta x|$: seen from more than a chord away the sheet is the line, seen from within the chord the chordwise offset keeps the element away from $\mathbf P$ (at the kink itself the induced velocity is perpendicular to the purely chordwise vector from the element to $\mathbf P$ and has no chordwise component at all). Integrated over $d$ the element gives $(\Gamma\kappa\gamma\,\mathrm{d}x/8\pi)[\ln(2L/|\Delta x|)-1]$, finite, with the chordwise offset in the place of the panel width; averaged over the chord with the thin-airfoil weight, $\langle\ln|x-x_P|\rangle_\gamma$ is finite because the logarithm is integrable, and the result is $(\Gamma\kappa/8\pi)\ln(L/c_{\mathrm{eff}})$ with $c_{\mathrm{eff}}=\exp\langle\ln|x-c/4|\rangle_\gamma=0.15\,c$. The mesh has dropped out. In physical terms a line vortex is a singularity and two singularities touching at an angle have no finite mutual velocity; a sheet is a regular distribution, the 2D airfoil induces the finite, uniform $\Gamma/(\pi c)$ on its own chord, and two sheets touching along a rib see a finite velocity. The neighbouring sections of a curved wing are sheets touching along their common rib. + +\begin{figure}[t]\centering +\includegraphics[width=\textwidth]{16_kink_line_vs_sheet.png} +\caption{Two vortices meeting at a kink of angle $\theta$ (\texttt{docs/validation/kink\_figure.py}): the chordwise velocity that line 2, of unit strength, induces at a point of line 1 at distance $r$ from the kink, as a single filament and as the chord-spread sheet. (a) Kinks of 2, 5 and $10^\circ$: the filament follows eq.~\eqref{eq:kink}, a line of slope $-1$ without limit; the sheet coincides with it beyond about a third of a chord, is bounded within, and vanishes at the kink. (b) The $5^\circ$ case with the small-angle formula.} +\label{fig:kink} +\end{figure} + \emph{The two sheet terms are the same panel in two positions.} $\mathbf K^{\mathrm{sheet}}_j$ is panel $j$ where it is, on the curved line, with its legs along its rib; $\mathbf K^{\mathrm{sheet}}_{j,\mathrm{unrolled}(i)}$ is the same panel with the same strips laid on panel $i$'s tangent at the same arc-length distance, with its leg in panel $i$'s chord direction. Biot--Savart depends on where a segment is and how it is oriented with respect to $\mathbf P_i$, so the two differ wherever the wing is curved: by little for the neighbours, whose two positions almost coincide (Figure~\ref{fig:unroll}d), and by the whole curvature effect for the far panels. Nothing singular is ever subtracted from anything singular. \begin{table}[h]\centering\small @@ -315,7 +353,7 @@ \subsection{Effect on the V3 kite polars} \section{Assessment and open items} \begin{itemize}[nosep] \item The mechanism of the fix (straighten locally, regularise the legs, keep the far field) is that of Reid and Hunsaker~\cite{reid2020}; the difference-form goes back to Li et al.~\cite{li2018}. The contribution here is the replacement of the two empirical lengths by the thin-airfoil chordwise distribution, which fixes the cut-off at $0.15\,c$ from theory, and the demonstration that this yields Trefftz-consistent induced drag on curved kites. It should be presented as such, with~\cite{reid2020,li2020,guermond1990} cited. - \item To be confirmed with the authors of~\cite{gaunaa2026,li2020}: how the curved bound-vortex influence is applied at the quarter chord in their code, and how it behaves when the number of sections is doubled. + \item To be confirmed with the authors of~\cite{gaunaa2026,li2020}: whether their quarter-chord term is the curved-minus-straight bound-segment difference evaluated at the control point (Table~\ref{tab:hyp}), which reproduces their behaviour here with perpendicular legs, and how it behaves when the number of sections is doubled. \item With body rates the apparent velocity is built at the control points and the same array feeds the quarter-chord direction and the attached-trailed force; the rotational term's variation along the chord, $\omega\times(\mathbf r_{1/4}-\mathbf r_{3/4})$, is the effective torsional rate $T_0\dot\theta$ of Li, Gaunaa and Pirrung~\cite{li2026wes}, whose coned-blade benchmark shows it worth 4\,\% of power at $10^\circ$ cone. On the V3 at 20\,m/s and a yaw rate of 0.3\,rad/s the local angle error reaches $0.8^\circ$ at the tips while the total drag changes 0.6\,\%, the error being antisymmetric across the span; the yawing moment is affected. To fix: evaluate the apparent velocity at the aerodynamic centre for the direction and at the leg points for the attached-trailed force. \item Settled with a referee (Section~\ref{sec:legs}): the paper's perpendicular legs are rejected; rib legs stay the default, streamwise legs are available. A streamwise construction with the local inflow direction per node would remove the mean-direction limitation. Open: the attached-trailed force on legs that are not aligned with the flow (kinked wing 0.98, skewed ribs 1.03, streamwise legs on the arc 1.035), and a V3 referee with the exact skewed tips (AeroSandbox unskews them). Not quantified: the section polars are rib-section polars while CP1 applies them in the span-perpendicular plane. \end{itemize} diff --git a/docs/validation/curved_bound_vortex_validation.json b/docs/validation/curved_bound_vortex_validation.json index 2749e8d..016c95e 100644 --- a/docs/validation/curved_bound_vortex_validation.json +++ b/docs/validation/curved_bound_vortex_validation.json @@ -967,5 +967,139 @@ ] ] } + }, + "hypothesis": { + "straight AR 8 | rib": [ + [ + 40, + 1.000024161341956 + ], + [ + 80, + 0.9999993387640974 + ] + ], + "straight AR 8 | perpendicular": [ + [ + 40, + 1.0000241613419563 + ], + [ + 80, + 0.9999993387640969 + ] + ], + "arc 110 deg, R = 4c | rib": [ + [ + 20, + 0.9919889241351971 + ], + [ + 40, + 0.9929117510746198 + ], + [ + 80, + 0.9932188147962667 + ], + [ + 160, + 0.9933325347824923 + ] + ], + "arc 110 deg, R = 4c | perpendicular": [ + [ + 20, + 0.9919889241351972 + ], + [ + 40, + 0.9929117510746205 + ], + [ + 80, + 0.9932188147962674 + ], + [ + 160, + 0.993332534782493 + ] + ], + "elliptic, 10% sweep, 25% anhedral | rib": [ + [ + 40, + 0.9932342067650138 + ], + [ + 80, + 0.9858651181185718 + ], + [ + 160, + 0.9785889361575972 + ] + ], + "elliptic, 10% sweep, 25% anhedral | perpendicular": [ + [ + 40, + 1.0199567023879592 + ], + [ + 80, + 1.0168719114436031 + ], + [ + 160, + 1.0119122471412831 + ] + ], + "V3 kite, inviscid, 10 deg | rib": [ + [ + 40, + 0.8091027651645845 + ], + [ + 80, + 0.7720494570082395 + ], + [ + 160, + 0.7353715823776639 + ] + ], + "V3 kite, inviscid, 10 deg | perpendicular": [ + [ + 40, + 1.0062872487784804 + ], + [ + 80, + 1.014504918905616 + ], + [ + 160, + NaN + ] + ], + "swept 30 deg (kinked) | rib": [ + [ + 40, + 0.9077132879044357 + ], + [ + 80, + 0.8395483504523779 + ] + ], + "swept 30 deg (kinked) | perpendicular": [ + [ + 40, + 1.128765146083736 + ], + [ + 80, + 1.138138258123495 + ] + ] } } \ No newline at end of file diff --git a/docs/validation/curved_bound_vortex_validation.py b/docs/validation/curved_bound_vortex_validation.py index f247195..9f7e3c2 100644 --- a/docs/validation/curved_bound_vortex_validation.py +++ b/docs/validation/curved_bound_vortex_validation.py @@ -211,6 +211,31 @@ def _ring_trailed(bp1, bp2, te1, te2, ep, wake, U): ) +def _curved_minus_straight_cp(eval_points, bp1, bp2, te1, te2, cdir, chords, va_norm, ac, core, sx, sw): + """Hypothesised form of the authors' LL-Gaunaa quarter-chord term: the bound + segments of the real wing minus those of the wing unrolled onto panel i's + tangent, single filaments, evaluated at the 3/4-chord control point of + panel i and reused at the quarter chord (constant along the chord). Zero + on straight wings by construction; finite because the control point is + half a chord off every line; no treatment of the legs.""" + n = len(chords) + out = np.zeros((3, n, n)) + fwd = np.linalg.norm(bp1[0] - bp2[1]) < np.linalg.norm(bp2[0] - bp1[1]) if n > 1 else True + L = np.linalg.norm(bp2 - bp1, axis=1) + s = np.concatenate(([0.0], np.cumsum(L))) + sgn = 1.0 if fwd else -1.0 + for i in range(n): + C = eval_points[i] + (0.75 - ac) * chords[i] * cdir[i] # 3/4-chord control point + t = (bp2[i] - bp1[i]) / L[i] + sP = 0.5 * (s[i] + s[i + 1]) + for j in range(n): + ra = eval_points[i] + sgn * (s[j] - sP) * t + rb = eval_points[i] + sgn * (s[j + 1] - sP) * t + ub1, ub2 = (ra, rb) if fwd else (rb, ra) + out[:, i, j] = _seg(bp2[j], bp1[j], C) - _seg(ub2, ub1, C) + return out + + def _reid_hunsaker(eval_points, bp1, bp2, te1, te2, cdir, chords, va_norm, ac, core, sx, sw): """Reid & Hunsaker (2020): for each control point the lifting line is straightened near the point (Gaussian blend of width STATE['blend'] times @@ -345,6 +370,32 @@ def table_reid_hunsaker(): return rows +def table_hypothesis(quick): + """The hypothesised Li/Gaunaa form with rib legs and with the paper's + perpendicular legs, against the sheet regularisation.""" + print("\non-blade / Trefftz, curved-minus-straight bound segments at the 3/4 chord reused at the 1/4 chord (single filaments)") + cases = [ + ("straight AR 8", straight, (40, 80)), + ("arc 110 deg, R = 4c", arc, (20, 40, 80) if quick else (20, 40, 80, 160)), + ("elliptic, 10% sweep, 25% anhedral", elliptic_swept_anhedral, (40, 80) if quick else (40, 80, 160)), + ("V3 kite, inviscid, 10 deg", v3_inviscid, (40, 80) if quick else (40, 80, 160)), + ("swept 30 deg (kinked)", swept, (40, 80)), + ] + out = {} + for name, mk, Ns in cases: + for legs in ("rib", "perpendicular"): + vals = [] + for N in Ns: + try: + r, cl = ratio(mk(N, leg_direction=legs), _curved_minus_straight_cp) + except ValueError: + r = float("nan") + vals.append((N, r)) + out[f"{name} | {legs}"] = vals + print(f" {name:34s} {legs:13s} " + " ".join(f"N={N}: {r:.3f}" for N, r in vals), flush=True) + return out + + def arc_self_induction(): """Chordwise induced velocity at the arc mid-span quarter-chord point from the other panels' bound vortices: polyline (log-divergent) and chordwise- @@ -556,14 +607,23 @@ def figure_09(pol): def main(argv=None): ap = argparse.ArgumentParser(description=__doc__, formatter_class=argparse.RawDescriptionHelpFormatter) ap.add_argument("--quick", action="store_true", help="only the regularised, on-line and trailed-only variants") + ap.add_argument("--hypothesis", action="store_true", help="only the table of the hypothesised Li/Gaunaa form") ap.add_argument("--figures", action="store_true", help="also regenerate docs/figures/08 and 09") args = ap.parse_args(argv) out = {} t0 = time.time() + if args.hypothesis: + path = OUT / "curved_bound_vortex_validation.json" + out = json.load(open(path)) if path.exists() else {} + out["hypothesis"] = table_hypothesis(args.quick) + json.dump(out, open(path, "w"), indent=1) + print(f"\nresults written to {path} ({time.time() - t0:.0f} s)") + return out["variants"] = table_variants(args.quick) out["arc_self_induction"] = arc_self_induction() if not args.quick: out["reid_hunsaker"] = table_reid_hunsaker() + out["hypothesis"] = table_hypothesis(args.quick) if args.figures: print("\nV3 viscous polars for figure 09") out["v3_polars"] = v3_polars() diff --git a/docs/validation/kink_figure.py b/docs/validation/kink_figure.py new file mode 100644 index 0000000..9e1931f --- /dev/null +++ b/docs/validation/kink_figure.py @@ -0,0 +1,78 @@ +"""Figure 16 of docs/figures: why two line vortices meeting at an angle have +no finite mutual velocity and two chordwise sheets do (report Section 4.2). + +Line 1 runs along -y from the kink, line 2 starts at the kink turned by the +angle theta out of the plane. P sits on line 1 (at its quarter chord) at +distance r from the kink. Plotted: the chordwise velocity at P induced by a +unit-strength line 2 (single filament at the quarter chord) and by the same +circulation spread over the chord with the thin-airfoil strips, against r. + +Usage (from the repository root, seconds):: + + python docs/validation/kink_figure.py +""" + +from __future__ import annotations + +from pathlib import Path + +import numpy as np + +from VSM.core.utils import thin_airfoil_strips + +FIG = Path(__file__).resolve().parents[1] / "figures" + + +def seg(a, b, p): + r1, r2 = p - a, p - b + cr = np.cross(r1, r2) + n = np.dot(cr, cr) + if n < 1e-24: + return np.zeros(3) + return cr / (4 * np.pi * n) * np.dot(b - a, r1 / np.linalg.norm(r1) - r2 / np.linalg.norm(r2)) + + +def main(): + import matplotlib + + matplotlib.use("Agg") + import matplotlib.pyplot as plt + + plt.rcParams.update({"font.size": 9}) + x, w = thin_airfoil_strips(24) + L = 50.0 + rs = np.logspace(-3, 1, 80) + fig, ax = plt.subplots(1, 2, figsize=(13, 5)) + for theta_deg, col in ((2.0, "tab:blue"), (5.0, "tab:red"), (10.0, "tab:green")): + t = np.radians(theta_deg) + e2 = np.array([0.0, np.cos(t), np.sin(t)]) + vf, vs = [], [] + for r in rs: + P = np.array([0.25, -r, 0.0]) + a0 = np.array([0.25, 0.0, 0.0]) + vf.append(abs(seg(a0, a0 + L * e2, P)[0])) + vs.append(abs(sum(w[q] * seg(np.array([x[q], 0, 0]), np.array([x[q], 0, 0]) + L * e2, P)[0] for q in range(24)))) + ax[0].loglog(rs, vf, "-", color=col, label=f"line, kink {theta_deg:.0f} deg") + ax[0].loglog(rs, vs, "--", color=col, label=f"sheet, kink {theta_deg:.0f} deg") + if theta_deg == 5.0: + ax[1].loglog(rs, vf, "r-", label="line, computed") + ax[1].loglog(rs, (1 - np.cos(t)) / (4 * np.pi * rs * np.sin(t)), "k:", label="line, (1 - cos theta) / (4 pi r sin theta)") + ax[1].loglog(rs, vs, "r--", label="sheet, computed") + ax[0].axvline(0.15, color="0.6", ls=":") + ax[0].text(0.16, 2.0, "0.15 c", color="0.4") + ax[0].set_xlabel("distance r of P from the kink, along line 1 (chord = 1)") + ax[0].set_ylabel("|chordwise velocity at P| per unit circulation of line 2") + ax[0].set_title("(a) two vortices meeting at a kink: line 2 seen from a point on line 1") + ax[0].legend(fontsize=8, frameon=False) + ax[1].set_xlabel("r (chord = 1), kink 5 deg") + ax[1].set_ylabel("|chordwise velocity at P|") + ax[1].set_title("(b) kink 5 deg: line, small-angle formula, sheet") + ax[1].legend(fontsize=8, frameon=False) + fig.tight_layout() + out = FIG / "16_kink_line_vs_sheet.png" + fig.savefig(out, dpi=150) + print("figure 16 written to", out) + + +if __name__ == "__main__": + main() From 0c3567920e5f0eb708a331fbc79118901968de51 Mon Sep 17 00:00:00 2001 From: ocayon Date: Tue, 13 Oct 2026 20:07:25 +0200 Subject: [PATCH 27/37] docs(validation): sensitivity of the correction to the chordwise strip loading Replace the flat-plate thin-airfoil strip weights by the NeuralFoil loading (gamma = ue_upper - ue_lower) of the V3 centre section at 5, 10 and 15 deg and of a NACA 4412. The effective cut-off moves from 0.16 c to 0.13 c and the centroid aft of the quarter chord; the arc wing changes by at most 0.3 % and the V3 induced drag by 0.5-1.5 %, within the referee's own uncertainty. The flat-plate weights are kept (solution-independent, cached per shape). Script docs/validation/strip_weight_sensitivity.py, report Section 4.2 (Table tab:strips). Co-Authored-By: Claude Fable 5.1 --- .../validation/curved_bound_vortex_report.tex | 18 ++++ docs/validation/strip_weight_sensitivity.py | 96 +++++++++++++++++++ 2 files changed, 114 insertions(+) create mode 100644 docs/validation/strip_weight_sensitivity.py diff --git a/docs/validation/curved_bound_vortex_report.tex b/docs/validation/curved_bound_vortex_report.tex index 97b51c1..09cba4d 100644 --- a/docs/validation/curved_bound_vortex_report.tex +++ b/docs/validation/curved_bound_vortex_report.tex @@ -207,6 +207,24 @@ \subsection{Reading of the formulation} \emph{The two sheet terms are the same panel in two positions.} $\mathbf K^{\mathrm{sheet}}_j$ is panel $j$ where it is, on the curved line, with its legs along its rib; $\mathbf K^{\mathrm{sheet}}_{j,\mathrm{unrolled}(i)}$ is the same panel with the same strips laid on panel $i$'s tangent at the same arc-length distance, with its leg in panel $i$'s chord direction. Biot--Savart depends on where a segment is and how it is oriented with respect to $\mathbf P_i$, so the two differ wherever the wing is curved: by little for the neighbours, whose two positions almost coincide (Figure~\ref{fig:unroll}d), and by the whole curvature effect for the far panels. Nothing singular is ever subtracted from anything singular. +\emph{The distribution is not a sensitive choice.} The flat-plate loading is the one the lumped-vortex model assumes, but a real section loads differently, and in thin-airfoil terms its bound vorticity is its pressure jump, $\gamma(x)\propto\Delta C_p(x)$. Table~\ref{tab:strips} replaces the strip weights by the NeuralFoil loading of the V3 centre section and of a NACA~4412 (\texttt{strip\_weight\_sensitivity.py}). The LEI profile is nose-heavier than the flat plate, its cut-off $c_{\mathrm{eff}}$ falls from $0.16\,c$ to $0.13\,c$, and its centroid sits aft of the quarter chord because of the camber. The arc wing moves by at most 0.3\,\%, the V3 by 0.5--1.5\,\% of the induced drag ($\Delta C_D\le0.0005$ at $10^\circ$), the same order as the referee's own uncertainty. Since the loading depends on the angle of attack, using it would make the correction depend on the solution and cost the per-shape cache; the flat-plate weights are kept. + +\begin{table}[h]\centering\small +\caption{Strip weights from real section loadings instead of the flat plate: effective cut-off, centroid, and on-blade over Trefftz induced drag (inviscid polars). NeuralFoil samples the chord from $x/c=0.016$, so the leading-edge peak is partly missed and the centroids are a few percent of chord too far aft.} +\label{tab:strips} +\begin{tabular}{lcccccc} +\toprule +strip loading & $c_{\mathrm{eff}}/c$ & centroid & arc 40 & arc 80 & V3 40 & V3 80\\ +\midrule +flat plate, thin airfoil (implemented) & 0.158 & 0.250 & 0.999 & 0.999 & 1.007 & 1.008\\ +V3 centre section, $5^\circ$ & 0.138 & 0.311 & 1.003 & 1.002 & 1.020 & 1.022\\ +V3 centre section, $10^\circ$ & 0.127 & 0.287 & 0.999 & 0.998 & 1.013 & 1.015\\ +V3 centre section, $15^\circ$ & 0.133 & 0.288 & 1.000 & 0.999 & 1.013 & 1.014\\ +NACA 4412, $10^\circ$ & 0.141 & 0.300 & 1.003 & 1.002 & 1.022 & 1.024\\ +\bottomrule +\end{tabular} +\end{table} + \begin{table}[h]\centering\small \caption{Why the three-quarter chord needs no sheet. Arc wing, mid-span panel, unit circulation on every other panel, bound segments as single filaments: the normal component at the control point converges (the neighbours build up the infinite-line value $1/(2\pi\cdot c/2)=0.318$ that TAT1 subtracts); the chordwise component at the quarter-chord point adds a constant per doubling.} \label{tab:cpconv} diff --git a/docs/validation/strip_weight_sensitivity.py b/docs/validation/strip_weight_sensitivity.py new file mode 100644 index 0000000..9d1add4 --- /dev/null +++ b/docs/validation/strip_weight_sensitivity.py @@ -0,0 +1,96 @@ +"""Sensitivity of the curved bound-vortex correction to the chordwise +distribution of the strips (report Section 4.2). + +The implemented strips carry the flat-plate thin-airfoil loading +gamma(x) ~ sqrt((c - x)/x). Here they are replaced by the loading of real +sections from NeuralFoil, gamma(x) = ue_upper - ue_lower at its 32 +boundary-layer stations (the leading-edge peak below x/c = 0.016 is not +sampled, which biases the centroid aft by a few percent of chord): a NACA +0012 as a check, the V3 centre section (LEI profile, data/TUDELFT_V3_KITE) +at 5, 10 and 15 deg, and a NACA 4412. For each distribution the effective +cut-off c_eff = exp and the centroid are printed, then the +on-blade / Trefftz ratio and CD of the arc wing and the V3 (inviscid polars). + +Usage (from the repository root, about two minutes):: + + PYTHONPATH=docs/validation python docs/validation/strip_weight_sensitivity.py +""" +import warnings +import numpy as np + +warnings.filterwarnings("ignore") +import aerosandbox as asb +import neuralfoil as nf +import yaml + +import VSM.core.BodyAerodynamics as BA +import curved_bound_vortex_validation as cbv +from curved_bound_vortex_validation import ratio, arc, v3_inviscid, solve, DATA +from VSM.core.utils import thin_airfoil_strips + +XB = np.asarray(nf.bl_x_points) + + +def nf_weights(airfoil, alpha, Re=5.6e5, **kw): + out = airfoil.get_aero_from_neuralfoil(alpha=alpha, Re=Re, model_size="xxxlarge", **kw) + ue_u = np.array([out[f"upper_bl_ue/vinf_{k}"] for k in range(32)]).ravel() + ue_l = np.array([out[f"lower_bl_ue/vinf_{k}"] for k in range(32)]).ravel() + g = ue_u + ue_l # NeuralFoil lower-surface ue is signed negative; the jump is ue_u - (-ue_l) + dx = np.gradient(XB) + w = g * dx + circ = w.sum() # integral gamma dx / (U c) ~ CL / 2 + return XB.copy(), w / w.sum(), float(out["CL"]), circ + + +def stats(x, w): + return float(np.exp(np.sum(w * np.log(np.abs(x - 0.25))))), float(np.sum(w * x)) + + +def main(): + x0, w0 = thin_airfoil_strips() + dists = {"flat plate, thin airfoil (implemented)": (x0, w0)} + print(f"{'distribution':48s} {'c_eff':>6s} {'centroid':>9s} {'CL_nf':>6s} {'2*int(gamma)':>12s}") + print(f"{'flat plate, thin airfoil (implemented)':48s} {stats(x0, w0)[0]:6.3f} {stats(x0, w0)[1]:9.3f}") + + # flat plate through NeuralFoil, as a check of the pipeline + plate = asb.Airfoil("naca0012") + x, w, cl, circ = nf_weights(plate, 5.0) + print(f"{'naca0012 at 5 deg, NeuralFoil':48s} {stats(x, w)[0]:6.3f} {stats(x, w)[1]:9.3f} {cl:6.3f} {2 * circ:12.3f}") + + d = yaml.safe_load(open(DATA / "CAD_derived_geometry" / "aero_geometry_CAD_neuralfoil.yaml")) + rows = d["wing_sections"]["data"] + ids = [r[0] for r in rows] + print("airfoil ids along the span:", ids) + mid = rows[len(rows) // 2][0] + af_info = {r[0]: r[2] for r in d["wing_airfoils"]["data"]}[mid] + dat = DATA / "CAD_derived_geometry" / af_info["dat_file_path"] + coords = np.loadtxt(dat, delimiter=",") + lei = asb.Airfoil(name=f"V3 section {mid}", coordinates=coords) + nf_kw = dict(xtr_lower=af_info.get("xtr_lower", 1.0), xtr_upper=af_info.get("xtr_upper", 1.0), n_crit=af_info.get("n_crit", 9.0)) + for a in (5.0, 10.0, 15.0): + x, w, cl, circ = nf_weights(lei, a, **nf_kw) + name = f"V3 mid section {mid} at {a:.0f} deg, NeuralFoil" + print(f"{name:48s} {stats(x, w)[0]:6.3f} {stats(x, w)[1]:9.3f} {cl:6.3f} {2 * circ:12.3f}") + dists[name] = (x, w) + x, w, cl, circ = nf_weights(asb.Airfoil("naca4412"), 10.0) + print(f"{'naca4412 at 10 deg, NeuralFoil':48s} {stats(x, w)[0]:6.3f} {stats(x, w)[1]:9.3f} {cl:6.3f} {2 * circ:12.3f}") + dists["naca4412 at 10 deg, NeuralFoil"] = (x, w) + + print("\non-blade / Trefftz (CD) with each distribution as strip weights") + cases = [("arc 110 deg, R = 4c", arc, (40, 80)), ("V3 kite, inviscid, 10 deg", v3_inviscid, (40, 80))] + for name, (x, w) in dists.items(): + xx = np.ascontiguousarray(x, dtype=float) + ww = np.ascontiguousarray(w, dtype=float) + BA.thin_airfoil_strips = lambda n_strips=24, xx=xx, ww=ww: (xx, ww) + line = f" {name:48s}" + for cname, mk, Ns in cases: + for N in Ns: + r = solve(mk(N), cbv.REGULARISED) + rt = float(r["drag"] / r["drag_induced_trefftz"]) + line += f" {cname[:3]} N={N}: {rt:.3f} ({float(r['cd']):.4f})" + print(line, flush=True) + BA.thin_airfoil_strips = thin_airfoil_strips + + +if __name__ == "__main__": + main() From b5fb374eb5c64c6ad76849339ff1a794d08d1c09 Mon Sep 17 00:00:00 2001 From: ocayon Date: Tue, 13 Oct 2026 20:08:10 +0200 Subject: [PATCH 28/37] docs(validation): rebuild the report PDF with the strip-loading table 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z-r=_(V6Xt@PB19|gm~Eehh{Sj6R+hP6g&xL3t$}vUR6PRu@qRTMFYYL6bOcc2O1QP z0B$6hP6yTzK*zNLMue#ttb<18v~~Zr=rkZK!9XxjJHrtI*)U56tOErUv%!H@9(1;h zqNYh2e8x8ui~@-tl-SJrgl2E>`VfMFk{HGe7-PX_2w*%21}E@!K*LOg0bM)>ToEv* zSpWoS2X+zwgOBboC;}+n;8Gv}wZl~cNciqJhS^u*wMZ@xbC>2*Klm zc-U+Jlq?`0!z2g_Mo6aU&7;uQsC%nIITE^+LXlh1&vv zt*|3-9{>_4vpO+gmin)Irq_Sa+>iFq5fd|{m6y|?yn?4_P;!Af6K23*pbSsZU>!7h zf-yq@1_Hau1Pj6NZUsUxME`3v^nwzs0~3uEFwm;OPfP{}fdwS+Xa`7@%=I6rc)<-6 z3?aBF0rOO5t^oj8HXH^TE11ndp$u+>0LFOnMZcl}cc3`fFbYs5!l#-Lj08_u;P#1m z>J8#NfWb%l5DWxnIMWmo=tSW_s3C;IKoz#)#9(F%Qxmv@qdhjlXh#4>fG0Kp19dQ< z0ong@0Rmlzqu_}Mz%Xzf0~q~&hj}j!R<1$#z@P|r5KuZYmh&P22egp5LNsXb3 Date: Tue, 3 Nov 2026 13:47:20 +0100 Subject: [PATCH 30/37] perf(utils): allocation-free numba filament kernels (~70x faster AIC) The induced-velocity kernels carried vectors as length-3 arrays; in numba every temporary (np.cross, r1 - r0, np.zeros(3)) is a heap allocation, and those allocations were ~95% of the cost: ~1.1 us per filament evaluation. They now carry 3-tuples, which numba keeps on the stack (~15-19 ns). Formulas, branch structure and summation order are unchanged, so the matrices still match the Filament.py reference to round-off (the equivalence tests at rtol 1e-12 pass). error_model="numpy" keeps NumPy's inf/nan semantics for zero denominators instead of numba's scalar ZeroDivisionError, so degenerate geometry behaves as before. V3 kite, 36 panels: AIC 7.3 -> 0.10 ms; casadi_newton solve 44 -> 24 ms. Affects assemble_AIC_matrices, assemble_curved_bound_correction_AIC and induced_velocity_at_points. Numerical, not physical; outputs unchanged. Generated with Claude Code --- src/VSM/core/utils.py | 363 ++++++++++++++++++++++++------------------ 1 file changed, 207 insertions(+), 156 deletions(-) diff --git a/src/VSM/core/utils.py b/src/VSM/core/utils.py index d4c4643..10c3630 100644 --- a/src/VSM/core/utils.py +++ b/src/VSM/core/utils.py @@ -30,156 +30,210 @@ def jit_dot(a, b): # round-off; Filament.py remains the readable reference implementation. # The only intentional difference: the bound-vortex in-core branch cannot # emit the logging.info diagnostic from compiled code. +# +# Vectors are carried as 3-tuples of floats, not length-3 arrays: numba +# keeps tuples on the stack, whereas every small-array temporary (np.cross, +# r1 - r0, np.zeros(3)) is a heap allocation, and those allocations were +# ~95% of the kernel cost (~1.1 us -> ~25 ns per filament evaluation). +# error_model="numpy" keeps NumPy's inf/nan semantics for a zero +# denominator (numba's default would raise ZeroDivisionError on scalars), +# so degenerate geometry behaves as it did with the array kernels. # ===================================================================== _ALPHA0_OSEEN = 1.25643 # Oseen parameter (Filament._alpha0) _NU_AIR = 1.48e-5 # kinematic viscosity of air [m^2/s] (Filament._nu) +_ZERO3 = (0.0, 0.0, 0.0) + + +@jit(nopython=True, cache=True, error_model="numpy") +def _row(a, i): + """Row ``i`` of an (n, 3) array as a 3-tuple.""" + return (a[i, 0], a[i, 1], a[i, 2]) + + +@jit(nopython=True, cache=True, error_model="numpy") +def _add(a, b): + return (a[0] + b[0], a[1] + b[1], a[2] + b[2]) + + +@jit(nopython=True, cache=True, error_model="numpy") +def _sub(a, b): + return (a[0] - b[0], a[1] - b[1], a[2] - b[2]) + + +@jit(nopython=True, cache=True, error_model="numpy") +def _scale(s, a): + return (s * a[0], s * a[1], s * a[2]) + + +@jit(nopython=True, cache=True, error_model="numpy") +def _div(a, s): + return (a[0] / s, a[1] / s, a[2] / s) + + +@jit(nopython=True, cache=True, error_model="numpy") +def _dot(a, b): + return a[0] * b[0] + a[1] * b[1] + a[2] * b[2] -@jit(nopython=True, cache=True) + +@jit(nopython=True, cache=True, error_model="numpy") +def _cross(a, b): + return ( + a[1] * b[2] - a[2] * b[1], + a[2] * b[0] - a[0] * b[2], + a[0] * b[1] - a[1] * b[0], + ) + + +@jit(nopython=True, cache=True, error_model="numpy") +def _norm(a): + return np.sqrt(a[0] * a[0] + a[1] * a[1] + a[2] * a[2]) + + +@jit(nopython=True, cache=True, error_model="numpy") def _vel_bound_vortex(XV1, XV2, XVP, gamma, core_radius_fraction): """Bound-filament induced velocity (Vatistas core), as in Filament.velocity_3D_bound_vortex.""" - r0 = XV2 - XV1 - r1 = XVP - XV1 - r2 = XVP - XV2 + r0 = _sub(XV2, XV1) + r1 = _sub(XVP, XV1) + r2 = _sub(XVP, XV2) - r1Xr0 = np.cross(r1, r0) - epsilon = core_radius_fraction * np.linalg.norm(r0) - dist = np.linalg.norm(r1Xr0) / np.linalg.norm(r0) + r1Xr0 = _cross(r1, r0) + epsilon = core_radius_fraction * _norm(r0) + dist = _norm(r1Xr0) / _norm(r0) if dist > epsilon: - r1Xr2 = np.cross(r1, r2) - return ( + r1Xr2 = _cross(r1, r2) + return _scale( gamma / (4 * np.pi) - * r1Xr2 - / (np.linalg.norm(r1Xr2) ** 2) - * np.dot(r0, r1 / np.linalg.norm(r1) - r2 / np.linalg.norm(r2)) + / (_norm(r1Xr2) ** 2) + * _dot(r0, _sub(_div(r1, _norm(r1)), _div(r2, _norm(r2)))), + r1Xr2, ) elif dist < 1e-12 * epsilon: - return np.zeros(3) + return _ZERO3 else: - r1_radial = r1 - np.dot(r1, r0) * r0 / (np.linalg.norm(r0) ** 2) - r2_radial = r2 - np.dot(r2, r0) * r0 / (np.linalg.norm(r0) ** 2) - r1_proj = np.dot(r1, r0) * r0 / ( - np.linalg.norm(r0) ** 2 - ) + epsilon * r1_radial / np.linalg.norm(r1_radial) - r2_proj = np.dot(r2, r0) * r0 / ( - np.linalg.norm(r0) ** 2 - ) + epsilon * r2_radial / np.linalg.norm(r2_radial) - r1Xr2_proj = np.cross(r1_proj, r2_proj) - vel_ind_proj = ( + r0_sq = _norm(r0) ** 2 + r1_axial = _div(_scale(_dot(r1, r0), r0), r0_sq) + r2_axial = _div(_scale(_dot(r2, r0), r0), r0_sq) + r1_radial = _sub(r1, r1_axial) + r2_radial = _sub(r2, r2_axial) + r1_proj = _add(r1_axial, _div(_scale(epsilon, r1_radial), _norm(r1_radial))) + r2_proj = _add(r2_axial, _div(_scale(epsilon, r2_radial), _norm(r2_radial))) + r1Xr2_proj = _cross(r1_proj, r2_proj) + vel_ind_proj = _scale( gamma / (4 * np.pi) - * r1Xr2_proj - / (np.linalg.norm(r1Xr2_proj) ** 2) - * np.dot( + / (_norm(r1Xr2_proj) ** 2) + * _dot( r0, - r1_proj / np.linalg.norm(r1_proj) - r2_proj / np.linalg.norm(r2_proj), - ) + _sub(_div(r1_proj, _norm(r1_proj)), _div(r2_proj, _norm(r2_proj))), + ), + r1Xr2_proj, ) - return dist / epsilon * vel_ind_proj + return _scale(dist / epsilon, vel_ind_proj) -@jit(nopython=True, cache=True) +@jit(nopython=True, cache=True, error_model="numpy") def _vel_trailing_vortex(XV1, XV2, XVP, gamma, Uinf): """Finite trailing-leg induced velocity (viscous core), as in Filament.velocity_3D_trailing_vortex.""" - r0 = XV2 - XV1 - r1 = XVP - XV1 - r2 = XVP - XV2 + r0 = _sub(XV2, XV1) + r1 = _sub(XVP, XV1) + r2 = _sub(XVP, XV2) - r_perp = r1 - np.dot(r1, r0) * r0 / (np.linalg.norm(r0) ** 2) - epsilon = np.sqrt(4 * _ALPHA0_OSEEN * _NU_AIR * np.linalg.norm(r_perp) / Uinf) + r0_sq = _norm(r0) ** 2 + r_perp = _sub(r1, _div(_scale(_dot(r1, r0), r0), r0_sq)) + epsilon = np.sqrt(4 * _ALPHA0_OSEEN * _NU_AIR * _norm(r_perp) / Uinf) - r1Xr0 = np.cross(r1, r0) - dist = np.linalg.norm(r1Xr0) / np.linalg.norm(r0) + r1Xr0 = _cross(r1, r0) + dist = _norm(r1Xr0) / _norm(r0) if dist > epsilon: - r1Xr2 = np.cross(r1, r2) - return ( + r1Xr2 = _cross(r1, r2) + return _scale( gamma / (4 * np.pi) - * r1Xr2 - / (np.linalg.norm(r1Xr2) ** 2) - * np.dot(r0, r1 / np.linalg.norm(r1) - r2 / np.linalg.norm(r2)) + / (_norm(r1Xr2) ** 2) + * _dot(r0, _sub(_div(r1, _norm(r1)), _div(r2, _norm(r2)))), + r1Xr2, ) elif dist < 1e-12 * epsilon: - return np.zeros(3) + return _ZERO3 else: - r1_radial = r1 - np.dot(r1, r0) * r0 / (np.linalg.norm(r0) ** 2) - r2_radial = r2 - np.dot(r2, r0) * r0 / (np.linalg.norm(r0) ** 2) - r1_proj = np.dot(r1, r0) * r0 / ( - np.linalg.norm(r0) ** 2 - ) + epsilon * r1_radial / np.linalg.norm(r1_radial) - r2_proj = np.dot(r2, r0) * r0 / ( - np.linalg.norm(r0) ** 2 - ) + epsilon * r2_radial / np.linalg.norm(r2_radial) - r1Xr2_proj = np.cross(r1_proj, r2_proj) - vel_ind_proj = ( + r1_axial = _div(_scale(_dot(r1, r0), r0), r0_sq) + r2_axial = _div(_scale(_dot(r2, r0), r0), r0_sq) + r1_radial = _sub(r1, r1_axial) + r2_radial = _sub(r2, r2_axial) + r1_proj = _add(r1_axial, _div(_scale(epsilon, r1_radial), _norm(r1_radial))) + r2_proj = _add(r2_axial, _div(_scale(epsilon, r2_radial), _norm(r2_radial))) + r1Xr2_proj = _cross(r1_proj, r2_proj) + vel_ind_proj = _scale( gamma / (4 * np.pi) - * r1Xr2_proj - / (np.linalg.norm(r1Xr2_proj) ** 2) - * np.dot( + / (_norm(r1Xr2_proj) ** 2) + * _dot( r0, - r1_proj / np.linalg.norm(r1_proj) - r2_proj / np.linalg.norm(r2_proj), - ) + _sub(_div(r1_proj, _norm(r1_proj)), _div(r2_proj, _norm(r2_proj))), + ), + r1Xr2_proj, ) - return dist / epsilon * vel_ind_proj + return _scale(dist / epsilon, vel_ind_proj) -@jit(nopython=True, cache=True) +@jit(nopython=True, cache=True, error_model="numpy") def _vel_semiinfinite(XV1, Vf, XVP, gamma, Uinf, filament_direction): """Semi-infinite trailing-vortex induced velocity, as in Filament.velocity_3D_trailing_vortex_semiinfinite.""" GAMMA = -gamma * filament_direction - r1 = XVP - XV1 - r1XVf = np.cross(r1, Vf) - r_perp = r1 - np.dot(r1, Vf) * Vf + r1 = _sub(XVP, XV1) + r1XVf = _cross(r1, Vf) + r1_axial = _scale(_dot(r1, Vf), Vf) + r_perp = _sub(r1, r1_axial) - if np.linalg.norm(r_perp) < 1e-16: - return np.zeros(3) + if _norm(r_perp) < 1e-16: + return _ZERO3 - epsilon = np.sqrt(4 * _ALPHA0_OSEEN * _NU_AIR * np.linalg.norm(r_perp) / Uinf) + epsilon = np.sqrt(4 * _ALPHA0_OSEEN * _NU_AIR * _norm(r_perp) / Uinf) - dist = np.linalg.norm(r1XVf) / np.linalg.norm(Vf) + dist = _norm(r1XVf) / _norm(Vf) if dist > epsilon: K = ( GAMMA / 4 / np.pi - / np.linalg.norm(r1XVf) ** 2 - * (1 + np.dot(r1, Vf) / np.linalg.norm(r1)) + / _norm(r1XVf) ** 2 + * (1 + _dot(r1, Vf) / _norm(r1)) ) - return K * r1XVf + return _scale(K, r1XVf) elif dist < 1e-12 * epsilon: - return np.zeros(3) + return _ZERO3 else: - r1_radial = r1 - np.dot(r1, Vf) * Vf - r1_proj = np.dot(r1, Vf) * Vf + epsilon * r1_radial / np.linalg.norm(r1_radial) - r1XVf_proj = np.cross(r1_proj, Vf) + r1_radial = r_perp + r1_proj = _add(r1_axial, _div(_scale(epsilon, r1_radial), _norm(r1_radial))) + r1XVf_proj = _cross(r1_proj, Vf) K = ( GAMMA / 4 / np.pi - / np.linalg.norm(r1XVf_proj) ** 2 - * (1 + np.dot(r1_proj, Vf) / np.linalg.norm(r1_proj)) + / _norm(r1XVf_proj) ** 2 + * (1 + _dot(r1_proj, Vf) / _norm(r1_proj)) ) - return K * r1XVf_proj + return _scale(K, r1XVf_proj) -@jit(nopython=True, cache=True) +@jit(nopython=True, cache=True, error_model="numpy") def _vel_bound_2D(XVP, bound_point_1, bound_point_2): """2D bound-vortex correction at the evaluation point, as in Panel.compute_velocity_induced_bound_2D (gamma = 1).""" - r3 = XVP - (bound_point_1 + bound_point_2) / 2 - r0 = bound_point_1 - bound_point_2 - r0_unit_X_r3 = np.cross(r0 / np.linalg.norm(r0), r3) - return (1 / (2 * np.pi)) * (r0_unit_X_r3 / (np.linalg.norm(r0_unit_X_r3) ** 2)) + r3 = _sub(XVP, _div(_add(bound_point_1, bound_point_2), 2.0)) + r0 = _sub(bound_point_1, bound_point_2) + r0_unit_X_r3 = _cross(_div(r0, _norm(r0)), r3) + return _scale(1 / (2 * np.pi), _div(r0_unit_X_r3, _norm(r0_unit_X_r3) ** 2)) -@jit(nopython=True, cache=True) +@jit(nopython=True, cache=True, error_model="numpy") def assemble_AIC_matrices( eval_points, bound_point_1, @@ -212,43 +266,43 @@ def assemble_AIC_matrices( n = eval_points.shape[0] AIC = np.empty((3, n, n)) for icp in range(n): - ep = eval_points[icp] + ep = _row(eval_points, icp) for jring in range(n): + bp1 = _row(bound_point_1, jring) + bp2 = _row(bound_point_2, jring) + te1 = _row(TE_point_1, jring) + te2 = _row(TE_point_2, jring) if evaluation_point_on_bound: - velocity_induced = np.zeros(3) + velocity_induced = _ZERO3 else: velocity_induced = _vel_bound_vortex( - bound_point_2[jring], - bound_point_1[jring], - ep, - 1.0, - core_radius_fraction, + bp2, bp1, ep, 1.0, core_radius_fraction ) - wake_unit = wake_units[jring] + wake_unit = _row(wake_units, jring) wake_speed = wake_speeds[jring] - velocity_induced = velocity_induced + _vel_trailing_vortex( - bound_point_1[jring], TE_point_1[jring], ep, 1.0, wake_speed + velocity_induced = _add( + velocity_induced, _vel_trailing_vortex(bp1, te1, ep, 1.0, wake_speed) ) - velocity_induced = velocity_induced + _vel_trailing_vortex( - TE_point_2[jring], bound_point_2[jring], ep, 1.0, wake_speed + velocity_induced = _add( + velocity_induced, _vel_trailing_vortex(te2, bp2, ep, 1.0, wake_speed) ) - velocity_induced = velocity_induced + _vel_semiinfinite( - TE_point_1[jring], wake_unit, ep, 1.0, wake_speed, 1.0 + velocity_induced = _add( + velocity_induced, + _vel_semiinfinite(te1, wake_unit, ep, 1.0, wake_speed, 1.0), ) - velocity_induced = velocity_induced + _vel_semiinfinite( - TE_point_2[jring], wake_unit, ep, 1.0, wake_speed, -1.0 + velocity_induced = _add( + velocity_induced, + _vel_semiinfinite(te2, wake_unit, ep, 1.0, wake_speed, -1.0), ) if subtract_bound_2D and icp == jring: - velocity_induced = velocity_induced - _vel_bound_2D( - ep, bound_point_1[jring], bound_point_2[jring] - ) + velocity_induced = _sub(velocity_induced, _vel_bound_2D(ep, bp1, bp2)) AIC[0, icp, jring] = velocity_induced[0] AIC[1, icp, jring] = velocity_induced[1] AIC[2, icp, jring] = velocity_induced[2] return AIC -@jit(nopython=True, cache=True) +@jit(nopython=True, cache=True, error_model="numpy") def assemble_curved_bound_correction_AIC( eval_points, bound_point_1, @@ -315,50 +369,53 @@ def assemble_curved_bound_correction_AIC( for j in range(n): s_node[j + 1] = s_node[j] + L[j] for i in range(n): - ep = eval_points[i] - t = seg[i] / L[i] - c_i = chord_dir[i] + ep = _row(eval_points, i) + t = _div(_row(seg, i), L[i]) + c_i = _row(chord_dir, i) s_P = 0.5 * (s_node[i] + s_node[i + 1]) U = va_norm[i] for j in range(n): - ra = ep + sgn * (s_node[j] - s_P) * t - rb = ep + sgn * (s_node[j + 1] - s_P) * t + ra = _add(ep, _scale(sgn * (s_node[j] - s_P), t)) + rb = _add(ep, _scale(sgn * (s_node[j + 1] - s_P), t)) if fwd: rb2 = ra rb1 = rb else: rb2 = rb rb1 = ra - leg = (1.0 - ac_fraction) * chords[j] * c_i - rte1 = rb1 + leg - rte2 = rb2 + leg - bp1 = bound_point_1[j] - bp2 = bound_point_2[j] - te1 = TE_point_1[j] - te2 = TE_point_2[j] + leg = _scale((1.0 - ac_fraction) * chords[j], c_i) + rte1 = _add(rb1, leg) + rte2 = _add(rb2, leg) + bp1 = _row(bound_point_1, j) + bp2 = _row(bound_point_2, j) + te1 = _row(TE_point_1, j) + te2 = _row(TE_point_2, j) # unrolled legs (single filaments) minus actual legs (single filaments) - v = _vel_trailing_vortex(rb1, rte1, ep, 1.0, U) + _vel_trailing_vortex( - rte2, rb2, ep, 1.0, U + v = _add( + _vel_trailing_vortex(rb1, rte1, ep, 1.0, U), + _vel_trailing_vortex(rte2, rb2, ep, 1.0, U), ) - v = v - _vel_trailing_vortex(bp1, te1, ep, 1.0, U) - _vel_trailing_vortex( - te2, bp2, ep, 1.0, U + v = _sub( + _sub(v, _vel_trailing_vortex(bp1, te1, ep, 1.0, U)), + _vel_trailing_vortex(te2, bp2, ep, 1.0, U), ) # chordwise-spread actual system minus chordwise-spread unrolled system for q in range(n_strips): f = (strip_x[q] - ac_fraction) / (1.0 - ac_fraction) w = strip_w[q] - n1 = bp1 + f * (te1 - bp1) - n2 = bp2 + f * (te2 - bp2) - u1 = rb1 + f * (rte1 - rb1) - u2 = rb2 + f * (rte2 - rb2) - v = v + w * ( - _vel_bound_vortex(n2, n1, ep, 1.0, core_radius_fraction) - - _vel_bound_vortex(u2, u1, ep, 1.0, core_radius_fraction) - + _vel_trailing_vortex(n1, te1, ep, 1.0, U) - + _vel_trailing_vortex(te2, n2, ep, 1.0, U) - - _vel_trailing_vortex(u1, rte1, ep, 1.0, U) - - _vel_trailing_vortex(rte2, u2, ep, 1.0, U) + n1 = _add(bp1, _scale(f, _sub(te1, bp1))) + n2 = _add(bp2, _scale(f, _sub(te2, bp2))) + u1 = _add(rb1, _scale(f, _sub(rte1, rb1))) + u2 = _add(rb2, _scale(f, _sub(rte2, rb2))) + strip = _sub( + _vel_bound_vortex(n2, n1, ep, 1.0, core_radius_fraction), + _vel_bound_vortex(u2, u1, ep, 1.0, core_radius_fraction), ) + strip = _add(strip, _vel_trailing_vortex(n1, te1, ep, 1.0, U)) + strip = _add(strip, _vel_trailing_vortex(te2, n2, ep, 1.0, U)) + strip = _sub(strip, _vel_trailing_vortex(u1, rte1, ep, 1.0, U)) + strip = _sub(strip, _vel_trailing_vortex(rte2, u2, ep, 1.0, U)) + v = _add(v, _scale(w, strip)) A[0, i, j] = v[0] A[1, i, j] = v[1] A[2, i, j] = v[2] @@ -378,18 +435,18 @@ def thin_airfoil_strips(n_strips=24): return np.ascontiguousarray(x, dtype=float), np.ascontiguousarray(w / w.sum(), dtype=float) -@jit(nopython=True, cache=True) +@jit(nopython=True, cache=True, error_model="numpy") def _on_segment_line(XV1, XV2, XVP): """True if XVP lies on the line through XV1 and XV2 (to round-off).""" - r0 = XV2 - XV1 - r1 = XVP - XV1 - len0 = np.linalg.norm(r0) + r0 = _sub(XV2, XV1) + r1 = _sub(XVP, XV1) + len0 = _norm(r0) if len0 == 0.0: return True - return np.linalg.norm(np.cross(r1, r0)) <= 1e-10 * len0 * max(np.linalg.norm(r1), len0) + return _norm(_cross(r1, r0)) <= 1e-10 * len0 * max(_norm(r1), len0) -@jit(nopython=True, cache=True) +@jit(nopython=True, cache=True, error_model="numpy") def induced_velocity_at_points( points, bound_point_1, @@ -413,31 +470,25 @@ def induced_velocity_at_points( n = bound_point_1.shape[0] out = np.zeros((m, 3)) for ip in range(m): - ep = points[ip] - vel = np.zeros(3) + ep = _row(points, ip) + vel = _ZERO3 for j in range(n): g = gamma[j] - wake_unit = wake_units[j] + bp1 = _row(bound_point_1, j) + bp2 = _row(bound_point_2, j) + te1 = _row(TE_point_1, j) + te2 = _row(TE_point_2, j) + wake_unit = _row(wake_units, j) wake_speed = wake_speeds[j] - vel = vel + _vel_bound_vortex( - bound_point_2[j], bound_point_1[j], ep, g, core_radius_fraction - ) + vel = _add(vel, _vel_bound_vortex(bp2, bp1, ep, g, core_radius_fraction)) # a straight filament induces nothing on its own line; skip the # legs the point lies on (the kernel would divide by zero there) - if not _on_segment_line(bound_point_1[j], TE_point_1[j], ep): - vel = vel + _vel_trailing_vortex( - bound_point_1[j], TE_point_1[j], ep, g, wake_speed - ) - if not _on_segment_line(TE_point_2[j], bound_point_2[j], ep): - vel = vel + _vel_trailing_vortex( - TE_point_2[j], bound_point_2[j], ep, g, wake_speed - ) - vel = vel + _vel_semiinfinite( - TE_point_1[j], wake_unit, ep, g, wake_speed, 1.0 - ) - vel = vel + _vel_semiinfinite( - TE_point_2[j], wake_unit, ep, g, wake_speed, -1.0 - ) + if not _on_segment_line(bp1, te1, ep): + vel = _add(vel, _vel_trailing_vortex(bp1, te1, ep, g, wake_speed)) + if not _on_segment_line(te2, bp2, ep): + vel = _add(vel, _vel_trailing_vortex(te2, bp2, ep, g, wake_speed)) + vel = _add(vel, _vel_semiinfinite(te1, wake_unit, ep, g, wake_speed, 1.0)) + vel = _add(vel, _vel_semiinfinite(te2, wake_unit, ep, g, wake_speed, -1.0)) out[ip, 0] = vel[0] out[ip, 1] = vel[1] out[ip, 2] = vel[2] From 424d15d813794bf95ca13936c39f1b2ecbc6ce3d Mon Sep 17 00:00:00 2001 From: ocayon Date: Tue, 3 Nov 2026 14:00:52 +0100 Subject: [PATCH 31/37] feat(core): quarter-chord force law as xp kernels with a public API The section force law moves into VSM.core.panel_kernels, pure functions over an xp namespace (numpy or casadi), so CasADi callers (AWETrim's CasADi trim) use VSM's formula instead of restating it. compute_results calls the same kernels for its per-panel force, so the formula lives once. - BodyAerodynamics.compute_quarter_chord_AIC_matrices(core_radius_fraction, va_norm_array, va_unit_array): public quarter-chord induction, AIC_LLT + the cached curved bound-vortex correction. update_effective_angle_of_ attack_if_VSM now uses it (one source). - panel_kernels: relative_flow, quarter_chord_velocity, direction_angle, section_force_directions, section_force_magnitudes, section_force_vectors, panel_forces, panel_moment_local, attached_trailed_forces, row helpers. compute_results and compute_attached_trailed_vortex_forces call them. - Solver.casadi_panel_force_function(): CasADi function (v_rel, v_qc, axes, chord, width, rho) -> per-panel force, local moment, alpha, alpha_dir, umag, cl, cd, cm, on the same polar lookups as the casadi_newton residual (factored into _casadi_polar_lookups; the residual function is unchanged). Refactor plus API: no physics change. Every numeric solve output matches VSM 1201f6f to <= 1.5e-14 relative for is_aoa_corrected True and False on a straight, a swept, an arc wing and the LEI V3 kite (frozen reference in tests/BodyAerodynamics/data, written with 1201f6f). CasADi kernels equal the NumPy ones to 1e-12; a CasADi graph with the induction matrices as parameters reproduces compute_results panel forces to 2e-16. Generated with Claude Code --- src/VSM/core/BodyAerodynamics.py | 194 ++++++----- src/VSM/core/Solver.py | 215 +++++++++---- src/VSM/core/panel_kernels.py | 236 ++++++++++++++ .../data/panel_kernel_reference.npz | Bin 0 -> 215246 bytes tests/BodyAerodynamics/panel_kernel_cases.py | 115 +++++++ tests/BodyAerodynamics/test_panel_kernels.py | 303 ++++++++++++++++++ 6 files changed, 904 insertions(+), 159 deletions(-) create mode 100644 src/VSM/core/panel_kernels.py create mode 100644 tests/BodyAerodynamics/data/panel_kernel_reference.npz create mode 100644 tests/BodyAerodynamics/panel_kernel_cases.py create mode 100644 tests/BodyAerodynamics/test_panel_kernels.py diff --git a/src/VSM/core/BodyAerodynamics.py b/src/VSM/core/BodyAerodynamics.py index 4eaf8ac..467cc95 100644 --- a/src/VSM/core/BodyAerodynamics.py +++ b/src/VSM/core/BodyAerodynamics.py @@ -17,6 +17,7 @@ thin_airfoil_strips, ) from . import jit_cross, jit_norm, jit_dot +from VSM.core import panel_kernels def _rigid_rotation_between(points_0, points_1, dirs_0, dirs_1, rel_tol=1e-9): @@ -1331,11 +1332,7 @@ def compute_attached_trailed_vortex_forces( (forces, points): ``(n+1, 3)`` force vectors and the points they act at. """ panels = self.panels - n = len(panels) gamma = np.asarray(gamma, dtype=float).ravel() - gamma_net = np.zeros(n + 1) - gamma_net[:n] += gamma # leg bound_1 -> TE_1 of panel j sits on boundary j - gamma_net[1:] -= gamma # leg TE_2 -> bound_2 of panel j sits on boundary j+1 bound_point_1 = np.ascontiguousarray( [p.bound_point_1 for p in panels], dtype=float @@ -1355,13 +1352,7 @@ def compute_attached_trailed_vortex_forces( t = (cp - ac) / (1.0 - ac) points = np.ascontiguousarray(bound + t * legs) - # inflow at a boundary: mean of the neighbouring panels' inflow va_array = np.asarray(va_array, dtype=float) - va_boundary = np.zeros((n + 1, 3)) - va_boundary[:n] += va_array - va_boundary[1:] += va_array - va_boundary[1:n] *= 0.5 - va_speeds = np.linalg.norm(va_array, axis=1) wake_units, wake_speeds = self._wake_directions( va_speeds, va_array / va_speeds[:, None] @@ -1377,8 +1368,9 @@ def compute_attached_trailed_vortex_forces( wake_speeds, float(core_radius_fraction), ) - v_rel = va_boundary + v_ind - forces = rho * gamma_net[:, None] * np.cross(v_rel, legs) + # net leg circulation and boundary inflow (mean of the neighbouring + # panels') are formed in the kernel + forces = panel_kernels.attached_trailed_forces(gamma, va_array, v_ind, legs, rho) return forces, points def compute_results( @@ -1416,10 +1408,6 @@ def compute_results( cl_array[icp] = panel_i.compute_cl(alpha_array[icp]) cd_array[icp], cm_array[icp] = panel_i.compute_cd_cm(alpha_array[icp]) panel_width_array[icp] = panel_i.width - lift = (cl_array * 0.5 * rho * Umag_array**2 * chord_array)[:, np.newaxis] - drag = (cd_array * 0.5 * rho * Umag_array**2 * chord_array)[:, np.newaxis] - moment = (cm_array * 0.5 * rho * Umag_array**2 * chord_array**2)[:, np.newaxis] - # Quarter-chord force directions (TAT3) apply to the VSM model, whose # circulation loop evaluates at 3/4 chord. The LLT model already # evaluates on the quarter chord without any bound-vortex influence @@ -1440,6 +1428,28 @@ def compute_results( alpha_corrected = alpha_array[:, np.newaxis] alpha_uncorrected = alpha_array[:, np.newaxis] + # Section force law (VSM.core.panel_kernels): magnitudes from the polar + # at the 3/4-chord angle and section speed, directions from + # alpha_corrected (the quarter-chord angle, or the 3/4-chord one). + lift_2D_array, drag_2D_array, moment_2D_array, dir_flow_array = ( + panel_kernels.section_force_vectors( + alpha_array, + Umag_array, + cl_array, + cd_array, + cm_array, + chord_array, + x_airf_array, + y_airf_array, + z_airf_array, + rho, + alpha_dir=np.ravel(alpha_corrected), + ) + ) + moment_local_3D_array = panel_kernels.panel_moment_local( + moment_2D_array, panel_width_array, z_airf_array + ) + # Initializing variables cl_prescribed_va_list = [] cd_prescribed_va_list = [] @@ -1496,45 +1506,19 @@ def compute_results( ### Defining panel_variables # Defining directions of airfoil that defines current panel_i z_airf_span = panel_i.z_airf # along the span - y_airf_chord = panel_i.y_airf # along the chord - x_airf_normal_to_chord = panel_i.x_airf # normal to the chord - # TODO: implement these - alpha_corrected_i = alpha_corrected[i] panel_chord = panel_i.chord panel_width = panel_i.width panel_area = panel_chord * panel_width area_all_panels += panel_area - ### Calculate the direction of the induced apparent wind speed to the airfoil orientation - # this is done using the CORRECTED CALCULATED (comes from gamma distribution) angle of attack - # For VSM the correction is applied, and it is the angle of attack, from calculating induced velocities at the 1/4c aerodynamic center location - # For LTT the correction is NOT applied, and it is the angle of attack, from calculating induced velocities at the 3/4c control point - induced_va_airfoil = ( - np.cos(alpha_corrected_i) * y_airf_chord - + np.sin(alpha_corrected_i) * x_airf_normal_to_chord - ) - dir_induced_va_airfoil = induced_va_airfoil / jit_norm(induced_va_airfoil) - - ### Calculate the direction of the lift and drag vectors - # lift is perpendical/normal to induced apparent wind speed - dir_lift_induced_va = jit_cross(dir_induced_va_airfoil, z_airf_span) - dir_lift_induced_va = dir_lift_induced_va / jit_norm(dir_lift_induced_va) - # drag is parallel/tangential to induced apparent wind speed - # (TAT3: the local inner flow direction, which lies in the panel's - # span-perpendicular plane; the global span axis is NOT used here) - dir_drag_induced_va = dir_induced_va_airfoil - - ### Calculating the MAGNITUDE of the lift and drag - # The VSM and LTT methods do NOT differ here, both use the uncorrected angle of attack - # i.e. evaluate the magnitude at the (3/4c) control point - # 2D AIRFOIL aerodynamic forces, so multiplied by chord - lift_induced_va_mag = lift[i] - drag_induced_va_mag = drag[i] - - # panel force VECTOR NORMAL to CALCULATED induced velocity - lift_induced_va = lift_induced_va_mag * dir_lift_induced_va - # panel force VECTOR TANGENTIAL to CALCULATED induced velocity - drag_induced_va = drag_induced_va_mag * dir_drag_induced_va + ### Section force vectors (per unit span) from the force law above: + # lift normal and drag along the direction-defining flow + # dir_induced_va_airfoil (TAT3: the local inner flow direction, in + # the panel's span-perpendicular plane; the global span axis is NOT + # used), magnitudes at the 3/4c control point for VSM and LLT alike. + dir_induced_va_airfoil = dir_flow_array[i] + lift_induced_va = lift_2D_array[i] + drag_induced_va = drag_2D_array[i] ftotal_induced_va = lift_induced_va + drag_induced_va ### Converting forces to prescribed wing va @@ -1689,13 +1673,10 @@ def compute_results( # (1) Panel aerodynamic center in global frame: panel_ac_global = panel_i.aerodynamic_center # 3D [x, y, z] - # (2) Convert local (2D) pitching moment to a 3D vector in global coords. - # Use the axis around which the moment is defined, - # which is the z-axis pointing "spanwise" - moment_axis_global = panel_i.z_airf - - # Scale by panel width if your 'moment[i]' is 2D moment-per-unit-span: - M_local_3D = moment[i] * moment_axis_global * panel_i.width + # (2) Local (2D) pitching moment as a 3D vector in global coords: + # along the z-axis pointing "spanwise", times the width + # (panel_kernels.panel_moment_local). + M_local_3D = moment_local_3D_array[i] # (3) Force application point used for r x F: # use aerodynamic center (1/4c) for all models. @@ -1937,7 +1918,7 @@ def compute_results( ( "cm_panel_dist", np.divide( - moment[:, 0], + moment_2D_array, 0.5 * rho * Umag_array**2 * chord_array**2, out=np.zeros_like(chord_array), where=(Umag_array > 0.0) & (chord_array > 0.0), @@ -2144,39 +2125,39 @@ def _curved_bound_correction_cached( } return AIC_corr - def update_effective_angle_of_attack_if_VSM( - self, - gamma, - core_radius_fraction, - x_airf_array, - y_airf_array, - va_array, - va_norm_array, - va_unit_array, + def compute_quarter_chord_AIC_matrices( + self, core_radius_fraction, va_norm_array, va_unit_array ): - """Updates the angle of attack at the aerodynamic center of each panel, - Calculated at the AERODYNAMIC CENTER, which needs an update for VSM - And can just use the old value for the LLT + """Induction matrices of the force-direction flow at the panel + quarter chords (aerodynamic centres): ``v_qc = va + AIC_qc gamma``. + + The direction-defining flow is the undisturbed relative flow at the + quarter chord (TAT3 in Gaunaa, Li & Pirrung, TORQUE 2026). The LLT + AIC holds the freestream-independent trailed system (legs + wake) + evaluated on the quarter chord, which is Prandtl's exact downwash for + a straight line but misses the influence of a curved or swept bound + vortex. Evaluating the other panels' bound segments on the line itself + is logarithmically singular (Li et al. 2020, "LL-P&S"), so the + curvature/sweep/skew influence is added as the chord-regularised + difference between the actual and the locally unrolled vortex + systems; see assemble_curved_bound_correction_AIC. + + The matrices depend on the geometry and the wake (``va_norm_array``, + ``va_unit_array``, as in :meth:`compute_AIC_matrices`), not on the + circulation, so a caller can freeze them numerically, e.g. as + parameters of a CasADi graph (see ``VSM.core.panel_kernels``). Args: - None + core_radius_fraction (float): Vortex core radius fraction. + va_norm_array (np.ndarray): (n,) panel inflow speeds [m/s]. + va_unit_array (np.ndarray): (n, 3) panel inflow directions. Returns: - None + Tuple[np.ndarray, np.ndarray, np.ndarray]: the x, y and z + components, each (n, n): ``AIC_LLT + AIC_curved_correction``. """ - # The direction-defining flow is the undisturbed relative flow at the - # quarter chord (TAT3 in Gaunaa, Li & Pirrung, TORQUE 2026). The LLT - # AIC holds the freestream-independent trailed system (legs + wake) - # evaluated on the quarter chord, which is Prandtl's exact downwash for - # a straight line but misses the influence of a curved or swept bound - # vortex. Evaluating the other panels' bound segments on the line itself - # is logarithmically singular (Li et al. 2020, "LL-P&S"), so the - # curvature/sweep/skew influence is added as the chord-regularised - # difference between the actual and the locally unrolled vortex - # systems; see assemble_curved_bound_correction_AIC. - aerodynamic_model_type = "LLT" AIC_x, AIC_y, AIC_z = self.compute_AIC_matrices( - aerodynamic_model_type, core_radius_fraction, va_norm_array, va_unit_array + "LLT", core_radius_fraction, va_norm_array, va_unit_array ) eval_points = np.ascontiguousarray( [panel.aerodynamic_center for panel in self.panels], dtype=float @@ -2194,7 +2175,9 @@ def update_effective_angle_of_attack_if_VSM( [panel.TE_point_2 for panel in self.panels], dtype=float ) chords = np.ascontiguousarray([panel.chord for panel in self.panels], dtype=float) - chord_dir = np.ascontiguousarray(y_airf_array, dtype=float) + chord_dir = np.ascontiguousarray( + [panel.y_airf for panel in self.panels], dtype=float + ) # The correction depends on the panel geometry only (the wake terms # cancel between the actual and the unrolled systems, and the leg core # radius has no measurable effect), so it is computed once per shape @@ -2209,21 +2192,34 @@ def update_effective_angle_of_attack_if_VSM( chord_dir, chords, np.ascontiguousarray(va_norm_array, dtype=float).ravel(), float(core_radius_fraction), ) - AIC_x = AIC_x + AIC_corr[0] - AIC_y = AIC_y + AIC_corr[1] - AIC_z = AIC_z + AIC_corr[2] - induced_velocity_all = np.array( - [ - np.matmul(AIC_x, gamma), - np.matmul(AIC_y, gamma), - np.matmul(AIC_z, gamma), - ] - ).T - relative_velocity_array = va_array + induced_velocity_all - v_normal_array = np.sum(x_airf_array * relative_velocity_array, axis=1) - v_tangential_array = np.sum(y_airf_array * relative_velocity_array, axis=1) - alpha_array = np.arctan2(v_normal_array, v_tangential_array) + return AIC_x + AIC_corr[0], AIC_y + AIC_corr[1], AIC_z + AIC_corr[2] + def update_effective_angle_of_attack_if_VSM( + self, + gamma, + core_radius_fraction, + x_airf_array, + y_airf_array, + va_array, + va_norm_array, + va_unit_array, + ): + """Force-direction angle of each panel: the angle of the relative flow + at the quarter chord, ``va + AIC_qc gamma`` with the matrices of + :meth:`compute_quarter_chord_AIC_matrices`. + + Returns: + np.ndarray: (n, 1) angles [rad]. + """ + AIC_x, AIC_y, AIC_z = self.compute_quarter_chord_AIC_matrices( + core_radius_fraction, va_norm_array, va_unit_array + ) + relative_velocity_array = panel_kernels.quarter_chord_velocity( + va_array, gamma, AIC_x, AIC_y, AIC_z + ) + alpha_array = panel_kernels.direction_angle( + relative_velocity_array, x_airf_array, y_airf_array + ) return alpha_array[:, np.newaxis] def compute_line_aerodynamic_force( diff --git a/src/VSM/core/Solver.py b/src/VSM/core/Solver.py index 576f3ba..42d4342 100644 --- a/src/VSM/core/Solver.py +++ b/src/VSM/core/Solver.py @@ -3,6 +3,7 @@ import logging from scipy.linalg import solve_banded from . import jit_cross +from VSM.core import panel_kernels class Solver: @@ -1028,56 +1029,12 @@ def _casadi_newton_key(self, alpha_tables, cl_tables, cd_tables, cm_tables) -> t digest.hexdigest(), ) - def _build_casadi_newton_function(self, alpha_tables, cl_tables, cd_tables=None, cm_tables=None): - """Build the CasADi function of the PER-PANEL section physics that - :meth:`gamma_loop_casadi_newton` assembles its residual and exact - Jacobian from. - - The circulation residual whose root the Newton loop finds is - - R(gamma) = (I - diag(mu(alpha)) L) gamma - G_raw(gamma), - - exactly the fixed point the ``base`` and ``anderson`` loops iterate - towards (``gamma = (I - diag(mu) L)^-1 G_raw(gamma)``, see - :meth:`_regularize_gamma_target`), including the Li/Gaunaa viscosity - ``mu_i = max(0, -k S Cl'_i / dz_i^2)`` gated on any panel being past - its stall onset (``mu = 0`` without artificial viscosity). Everything - that is not the dense induction ``v_ind = AIC gamma`` is local to a - panel: ``G_raw_i``, ``mu_i`` and ``alpha_i`` depend on ``gamma`` only - through the panel's own relative velocity ``v_rel_i``. So the symbolic - function takes ``v_rel`` (and ``L gamma``) as INPUTS and returns - - h_i = G_raw_i + mu_i (L gamma)_i, c_i = dh_i / dv_rel_i (3 values) - - plus ``mu``, ``alpha`` and ``|v_rel x z|``; the Newton loop then forms - ``R = gamma - h`` and, by the chain rule through ``v_rel = va + AIC - gamma`` (with ``dh_i/d(L gamma)_i = mu_i``), - - J = I - diag(mu) L - sum_k diag(c_k) AIC_k - - in NumPy. This keeps the CasADi graph O(n) -- independent of the - n x n induction matrices -- so it costs ~0.1 ms per evaluation and - builds in tens of milliseconds, while the dense algebra runs in BLAS. - - The 2-D polars are ``ca.interpolant`` tables. Queries are clamped to - the table range first, so the lookup reproduces ``np.interp`` (constant - beyond both ends) and the lift slope is the same central difference of - the same piecewise-linear table that :meth:`_lift_slope_from_ctx` - evaluates. When every panel shares one alpha grid (the normal outcome - of batch polar generation) the lookup is a single 2-D interpolant over - (alpha, panel index) evaluated exactly at the integer panel nodes; - otherwise one 1-D interpolant per panel. ``polar_interpolation = - "bspline"`` swaps the piecewise-linear table for a cubic spline - through the same nodes (degree 1 along the panel-index axis, so panel - rows never mix). - - Outputs, in order: ``h``, ``dh/dv_rel`` (n x 3, from the corner- - averaged polar), ``mu``, ``alpha``, ``umag``, ``gate``, then for - callers that build FORCES from the same lookups: ``h_avg`` (h with the - corner-averaged Cl -- differentiate this for a kink-tolerant - Jacobian), ``cl``, ``cd``, ``cm`` at ``alpha`` and their corner- - averaged counterparts ``cl_avg``, ``cd_avg``, ``cm_avg``. With - "bspline" polars the averaged outputs equal the exact ones. + def _casadi_polar_lookups(self, alpha_tables, cl_tables, cd_tables=None, cm_tables=None): + """Clamped CasADi lookups ``alpha (n) -> cl, cd, cm (n)`` of the + per-panel polars, shared by :meth:`_build_casadi_newton_function` and + :meth:`_build_casadi_panel_force_function` (see the former for the + interpolation). Returns ``(cl_of, cd_of, cm_of, smooth)``, ``smooth`` + True for "bspline" polars. """ import casadi as ca @@ -1089,16 +1046,6 @@ def _build_casadi_newton_function(self, alpha_tables, cl_tables, cd_tables=None, f"(panel {i} violates this)." ) - v_rel = ca.MX.sym("v_rel", n, 3) - x_airf = ca.MX.sym("x_airf", n, 3) - y_airf = ca.MX.sym("y_airf", n, 3) - z_airf = ca.MX.sym("z_airf", n, 3) - chord = ca.MX.sym("chord", n) - width = ca.MX.sym("width", n) - stall_angles = ca.MX.sym("stall_angles", n) - stall_angles_neg = ca.MX.sym("stall_angles_neg", n) - l_gamma = ca.MX.sym("l_gamma", n) # (L gamma), a parameter here - shared_grid = all( table.shape == alpha_tables[0].shape and np.array_equal(table, alpha_tables[0]) @@ -1154,6 +1101,75 @@ def lookup(alpha_vec): cl_of = make_lookup("cl", cl_tables) cd_of = make_lookup("cd", cd_tables) cm_of = make_lookup("cm", cm_tables) + return cl_of, cd_of, cm_of, smooth + + def _build_casadi_newton_function(self, alpha_tables, cl_tables, cd_tables=None, cm_tables=None): + """Build the CasADi function of the PER-PANEL section physics that + :meth:`gamma_loop_casadi_newton` assembles its residual and exact + Jacobian from. + + The circulation residual whose root the Newton loop finds is + + R(gamma) = (I - diag(mu(alpha)) L) gamma - G_raw(gamma), + + exactly the fixed point the ``base`` and ``anderson`` loops iterate + towards (``gamma = (I - diag(mu) L)^-1 G_raw(gamma)``, see + :meth:`_regularize_gamma_target`), including the Li/Gaunaa viscosity + ``mu_i = max(0, -k S Cl'_i / dz_i^2)`` gated on any panel being past + its stall onset (``mu = 0`` without artificial viscosity). Everything + that is not the dense induction ``v_ind = AIC gamma`` is local to a + panel: ``G_raw_i``, ``mu_i`` and ``alpha_i`` depend on ``gamma`` only + through the panel's own relative velocity ``v_rel_i``. So the symbolic + function takes ``v_rel`` (and ``L gamma``) as INPUTS and returns + + h_i = G_raw_i + mu_i (L gamma)_i, c_i = dh_i / dv_rel_i (3 values) + + plus ``mu``, ``alpha`` and ``|v_rel x z|``; the Newton loop then forms + ``R = gamma - h`` and, by the chain rule through ``v_rel = va + AIC + gamma`` (with ``dh_i/d(L gamma)_i = mu_i``), + + J = I - diag(mu) L - sum_k diag(c_k) AIC_k + + in NumPy. This keeps the CasADi graph O(n) -- independent of the + n x n induction matrices -- so it costs ~0.1 ms per evaluation and + builds in tens of milliseconds, while the dense algebra runs in BLAS. + + The 2-D polars are ``ca.interpolant`` tables. Queries are clamped to + the table range first, so the lookup reproduces ``np.interp`` (constant + beyond both ends) and the lift slope is the same central difference of + the same piecewise-linear table that :meth:`_lift_slope_from_ctx` + evaluates. When every panel shares one alpha grid (the normal outcome + of batch polar generation) the lookup is a single 2-D interpolant over + (alpha, panel index) evaluated exactly at the integer panel nodes; + otherwise one 1-D interpolant per panel. ``polar_interpolation = + "bspline"`` swaps the piecewise-linear table for a cubic spline + through the same nodes (degree 1 along the panel-index axis, so panel + rows never mix). + + Outputs, in order: ``h``, ``dh/dv_rel`` (n x 3, from the corner- + averaged polar), ``mu``, ``alpha``, ``umag``, ``gate``, then for + callers that build FORCES from the same lookups: ``h_avg`` (h with the + corner-averaged Cl -- differentiate this for a kink-tolerant + Jacobian), ``cl``, ``cd``, ``cm`` at ``alpha`` and their corner- + averaged counterparts ``cl_avg``, ``cd_avg``, ``cm_avg``. With + "bspline" polars the averaged outputs equal the exact ones. + """ + import casadi as ca + + n = self.n_panels + cl_of, cd_of, cm_of, smooth = self._casadi_polar_lookups( + alpha_tables, cl_tables, cd_tables, cm_tables + ) + + v_rel = ca.MX.sym("v_rel", n, 3) + x_airf = ca.MX.sym("x_airf", n, 3) + y_airf = ca.MX.sym("y_airf", n, 3) + z_airf = ca.MX.sym("z_airf", n, 3) + chord = ca.MX.sym("chord", n) + width = ca.MX.sym("width", n) + stall_angles = ca.MX.sym("stall_angles", n) + stall_angles_neg = ca.MX.sym("stall_angles_neg", n) + l_gamma = ca.MX.sym("l_gamma", n) # (L gamma), a parameter here def cross_rows(a, b): return ca.horzcat( @@ -1264,6 +1280,85 @@ def _casadi_newton_function(self): self._casadi_newton_cache[key] = fn return fn + def _build_casadi_panel_force_function( + self, alpha_tables, cl_tables, cd_tables=None, cm_tables=None + ): + """CasADi function of the per-panel section forces, the force law of + ``compute_results`` (``VSM.core.panel_kernels.panel_forces``) on the + polar lookups of the circulation solve. See + :meth:`casadi_panel_force_function`.""" + import casadi as ca + + n = self.n_panels + cl_of, cd_of, cm_of, _ = self._casadi_polar_lookups( + alpha_tables, cl_tables, cd_tables, cm_tables + ) + v_rel = ca.MX.sym("v_rel", n, 3) + v_qc = ca.MX.sym("v_qc", n, 3) + x_airf = ca.MX.sym("x_airf", n, 3) + y_airf = ca.MX.sym("y_airf", n, 3) + z_airf = ca.MX.sym("z_airf", n, 3) + chord = ca.MX.sym("chord", n) + width = ca.MX.sym("width", n) + rho = ca.MX.sym("rho") + + alpha, umag = panel_kernels.relative_flow(v_rel, x_airf, y_airf, z_airf, xp=ca) + alpha_dir = panel_kernels.direction_angle(v_qc, x_airf, y_airf, xp=ca) + cl, cd, cm = cl_of(alpha), cd_of(alpha), cm_of(alpha) + force, moment_local = panel_kernels.panel_forces( + alpha, umag, cl, cd, cm, chord, width, x_airf, y_airf, z_airf, rho, + alpha_dir=alpha_dir, xp=ca, + ) + return ca.Function( + "vsm_panel_forces", + [v_rel, v_qc, x_airf, y_airf, z_airf, chord, width, rho], + [force, moment_local, alpha, alpha_dir, umag, cl, cd, cm], + ["v_rel", "v_qc", "x_airf", "y_airf", "z_airf", "chord", "width", "rho"], + ["force", "moment_local", "alpha", "alpha_dir", "umag", "cl", "cd", "cm"], + ) + + def casadi_panel_force_function(self): + """CasADi function of the per-panel section forces of the current + panels (the ones of the last :meth:`solve`), cached per polar set like + the ``casadi_newton`` residual function. + + Inputs (numeric or symbolic), ``n = n_panels``: + + * ``v_rel`` (n, 3): relative velocity at the 3/4-chord control points, + ``va + AIC gamma`` -- sets ``alpha``, ``umag`` and so the polar + magnitudes ``cl, cd, cm``; + * ``v_qc`` (n, 3): the force-direction flow. For the quarter-chord law + (``is_aoa_corrected=True``) ``va + AIC_qc gamma`` with + ``BodyAerodynamics.compute_quarter_chord_AIC_matrices`` (or + ``panel_kernels.quarter_chord_velocity``); for ``False`` pass + ``v_rel`` again; + * ``x_airf, y_airf, z_airf`` (n, 3), ``chord, width`` (n), ``rho``. + + Outputs: ``force`` (n, 3) [N], ``moment_local`` (n, 3) [Nm] (the + quarter-chord pitching moment along ``z_airf``), ``alpha``, + ``alpha_dir`` [rad], ``umag`` [m/s], ``cl, cd, cm`` (n). + + Same as ``compute_results`` per panel WITHOUT the attached-trailed + vortex force (``panel_kernels.attached_trailed_forces``) and the + viscous drag correction. Taking ``v_qc`` rather than the matrices keeps + the graph O(n); the caller forms the dense product. + """ + import casadi # noqa: F401 (clear error when the optional dep is missing) + + alpha_tables, cl_tables, cd_tables, cm_tables = self._polar_tables() + key = ("panel_forces",) + self._casadi_newton_key( + alpha_tables, cl_tables, cd_tables, cm_tables + ) + fn = self._casadi_newton_cache.get(key) + if fn is None: + fn = self._build_casadi_panel_force_function( + alpha_tables, cl_tables, cd_tables, cm_tables + ) + if len(self._casadi_newton_cache) >= 32: + self._casadi_newton_cache.pop(next(iter(self._casadi_newton_cache))) + self._casadi_newton_cache[key] = fn + return fn + def gamma_loop_casadi_newton(self, gamma_initial: np.ndarray) -> tuple: """Newton solve of the circulation residual with an exact CasADi Jacobian, globalised by pseudo-transient continuation diff --git a/src/VSM/core/panel_kernels.py b/src/VSM/core/panel_kernels.py new file mode 100644 index 0000000..f074f61 --- /dev/null +++ b/src/VSM/core/panel_kernels.py @@ -0,0 +1,236 @@ +"""Section force law of the VSM as ``xp`` kernels. + +Pure functions over a math namespace ``xp``, either ``numpy`` (the default) +or ``casadi``, so the same formula serves ``BodyAerodynamics.compute_results`` +and a CasADi graph (``Solver.casadi_panel_force_function``, or a caller's own +graph such as AWETrim's CasADi trim). The formula lives here only; callers do +not restate it. + +Conventions: + +* Per-panel vectors are rows of an ``(n, 3)`` array; per-panel scalars are + ``(n,)`` arrays in NumPy and ``(n, 1)`` columns in CasADi. +* ``x_airf`` is the chord normal, ``y_airf`` the chord (leading to trailing + edge), ``z_airf`` the span direction of each panel (``Panel`` axes). +* Angles are in radians. ``alpha = atan2(v . x_airf, v . y_airf)``. +* ``umag = |v_rel x z_airf|`` is the speed the 2-D section sees; the dynamic + pressure of the section force is ``0.5 rho umag^2``, not the freestream one. + +The force law (Gaunaa, Li & Pirrung, TORQUE 2026): the MAGNITUDES of lift, +drag and moment come from the polar at the 3/4-chord control-point angle +``alpha``; the DIRECTIONS come from the direction angle ``alpha_dir``. With +``is_aoa_corrected=True`` (TAT3, VSM model) ``alpha_dir`` is the angle of the +flow at the quarter chord, ``va + AIC_qc gamma`` with the matrices of +``BodyAerodynamics.compute_quarter_chord_AIC_matrices``; with ``False`` it is +``alpha`` itself. +""" + +from __future__ import annotations + +from typing import Any + +import numpy as np + + +# --------------------------------------------------------------------- xp rows +def _is_casadi(xp: Any) -> bool: + return hasattr(xp, "horzcat") + + +def hstack_columns(xp: Any, *cols): + """``(n, k)`` from ``k`` per-row columns.""" + if _is_casadi(xp): + return xp.horzcat(*cols) + return np.column_stack(cols) + + +def cross_rows(a, b, xp=np): + """Row-wise cross product of two ``(n, 3)`` arrays.""" + return hstack_columns( + xp, + a[:, 1] * b[:, 2] - a[:, 2] * b[:, 1], + a[:, 2] * b[:, 0] - a[:, 0] * b[:, 2], + a[:, 0] * b[:, 1] - a[:, 1] * b[:, 0], + ) + + +def dot_rows(a, b, xp=np): + """Row-wise dot product of two ``(n, 3)`` arrays -> per-row scalar.""" + if _is_casadi(xp): + return xp.sum2(a * b) + return np.sum(a * b, axis=1) + + +def norm_rows(a, xp=np): + return xp.sqrt(dot_rows(a, a, xp)) + + +def scale_rows(s, a, xp=np): + """Per-row scalar ``s`` times the ``(n, 3)`` rows of ``a``.""" + if _is_casadi(xp): + return xp.repmat(s, 1, a.shape[1]) * a + return np.asarray(s)[:, None] * a + + +def unit_rows(a, xp=np): + """Rows of ``a`` divided by their norms.""" + norms = norm_rows(a, xp) + if _is_casadi(xp): + return a / xp.repmat(norms, 1, a.shape[1]) + return a / norms[:, None] + + +def _atan2(y, x, xp): + return xp.atan2(y, x) if _is_casadi(xp) else np.arctan2(y, x) + + +def _matvec(matrix, vector, xp): + if _is_casadi(xp): + return xp.mtimes(matrix, vector) + return matrix @ vector + + +# ------------------------------------------------------------------ section flow +def relative_flow(v_rel, x_airf, y_airf, z_airf, xp=np): + """Angle of attack and section speed of the relative velocity ``v_rel`` + (``Solver.compute_aerodynamic_quantities``): + ``alpha = atan2(v_rel . x_airf, v_rel . y_airf)``, ``umag = |v_rel x z_airf|``.""" + alpha = direction_angle(v_rel, x_airf, y_airf, xp) + umag = norm_rows(cross_rows(v_rel, z_airf, xp), xp) + return alpha, umag + + +def quarter_chord_velocity(va, gamma, AIC_x, AIC_y, AIC_z, xp=np): + """Relative flow at the panel quarter chords, ``va + AIC_qc gamma``. + + ``AIC_*`` are the ``(n, n)`` quarter-chord induction matrices of + ``BodyAerodynamics.compute_quarter_chord_AIC_matrices`` (trailed system on + the quarter chord plus the curved bound-vortex correction), ``va`` the + ``(n, 3)`` panel inflow and ``gamma`` the ``(n,)`` circulation. + """ + induced = hstack_columns( + xp, + _matvec(AIC_x, gamma, xp), + _matvec(AIC_y, gamma, xp), + _matvec(AIC_z, gamma, xp), + ) + return va + induced + + +def direction_angle(v, x_airf, y_airf, xp=np): + """Angle of the flow ``v`` (``(n, 3)``) in each panel's section plane, + ``atan2(v . x_airf, v . y_airf)``. Applied to the quarter-chord flow it is + the TAT3 direction angle of the force law.""" + return _atan2(dot_rows(x_airf, v, xp), dot_rows(y_airf, v, xp), xp) + + +# ------------------------------------------------------------------- force law +def section_force_directions(alpha_dir, x_airf, y_airf, z_airf, xp=np): + """Unit flow and lift directions of each section at direction angle + ``alpha_dir``: ``dir_flow = unit(cos(a) y_airf + sin(a) x_airf)`` (in the + plane normal to ``z_airf``; drag acts along it, TAT3's local inner flow, + not the global span axis) and ``dir_lift = unit(dir_flow x z_airf)``.""" + dir_flow = scale_rows(xp.cos(alpha_dir), y_airf, xp) + scale_rows( + xp.sin(alpha_dir), x_airf, xp + ) + dir_flow = unit_rows(dir_flow, xp) + dir_lift = unit_rows(cross_rows(dir_flow, z_airf, xp), xp) + return dir_flow, dir_lift + + +def section_force_magnitudes(umag, cl, cd, cm, chord, rho): + """2-D lift, drag [N/m] and pitching moment [Nm/m] about the quarter + chord, ``c_x 0.5 rho umag^2 chord`` (``chord^2`` for the moment). The + coefficients are the polar values at the 3/4-chord angle.""" + lift = cl * 0.5 * rho * umag**2 * chord + drag = cd * 0.5 * rho * umag**2 * chord + moment = cm * 0.5 * rho * umag**2 * chord**2 + return lift, drag, moment + + +def section_force_vectors( + alpha, umag, cl, cd, cm, chord, x_airf, y_airf, z_airf, rho, alpha_dir=None, xp=np +): + """2-D (per unit span) lift and drag vectors and the flow direction. + + ``alpha_dir`` None uses ``alpha`` (the ``is_aoa_corrected=False`` law). + Returns ``(lift_2d (n, 3), drag_2d (n, 3), moment (n,), dir_flow (n, 3))``. + """ + if alpha_dir is None: + alpha_dir = alpha + lift, drag, moment = section_force_magnitudes(umag, cl, cd, cm, chord, rho) + dir_flow, dir_lift = section_force_directions(alpha_dir, x_airf, y_airf, z_airf, xp) + return scale_rows(lift, dir_lift, xp), scale_rows(drag, dir_flow, xp), moment, dir_flow + + +def panel_forces( + alpha, + umag, + cl, + cd, + cm, + chord, + width, + x_airf, + y_airf, + z_airf, + rho, + alpha_dir=None, + xp=np, +): + """Per-panel 3-D force [N] and local pitching moment [Nm]. + + ``force = width (lift_2d + drag_2d)`` (see :func:`section_force_vectors`); + ``moment_local = width (cm q chord^2) z_airf``, the quarter-chord moment as + a vector along the span axis. ``alpha_dir`` None gives the 3/4-chord + directions (``is_aoa_corrected=False``); pass :func:`direction_angle` of + :func:`quarter_chord_velocity` for the quarter-chord law (``True``). + + Not included: the attached-trailed vortex force + (:func:`attached_trailed_forces`) and the viscous drag correction + (``BodyAerodynamics.viscous_drag_correction``, NumPy only). + + Returns ``(force (n, 3), moment_local (n, 3))``. + """ + lift_2d, drag_2d, moment, _ = section_force_vectors( + alpha, umag, cl, cd, cm, chord, x_airf, y_airf, z_airf, rho, alpha_dir, xp + ) + force = scale_rows(width, lift_2d + drag_2d, xp) + return force, panel_moment_local(moment, width, z_airf, xp) + + +def panel_moment_local(moment, width, z_airf, xp=np): + """3-D local pitching moment [Nm] of each panel: the 2-D quarter-chord + moment [Nm/m] (:func:`section_force_magnitudes`) as a vector along the + span axis ``z_airf``, times the panel width. ``(n, 3)``.""" + return scale_rows(width, scale_rows(moment, z_airf, xp), xp) + + +# ---------------------------------------------------- attached trailed vortices +def attached_trailed_forces(gamma, va_panels, v_induced, legs, rho, xp=np): + """Kutta-Joukowski force on the attached trailed (AT) legs (Gaunaa, Li & + Pirrung 2026, Sec. 3), ``rho (gamma_j - gamma_{j-1}) (v_rel_j x l_j)`` on + boundary ``j = 0..n`` with ``gamma_{-1} = gamma_n = 0``. + + ``v_rel_j`` is the mean of the neighbouring panels' inflow ``va_panels`` + (the tip boundaries take their one panel's) plus ``v_induced``, the full + vortex system's induction at the AT force points, ``(n+1, 3)``. ``legs`` + are the ``(n+1, 3)`` leg vectors, bound vortex to trailing edge. Returns + the ``(n+1, 3)`` boundary forces. + """ + n = va_panels.shape[0] + to_boundary = np.zeros((n + 1, n)) # gamma_net = to_boundary @ gamma + to_boundary[np.arange(n), np.arange(n)] += 1.0 + to_boundary[np.arange(1, n + 1), np.arange(n)] -= 1.0 + # boundary inflow = mean of the neighbouring panels (halving is exact) + mean = np.abs(to_boundary) + mean[1:n] *= 0.5 + if _is_casadi(xp): + gamma_net = xp.mtimes(xp.DM(to_boundary), gamma) + va_boundary = xp.mtimes(xp.DM(mean), va_panels) + if isinstance(legs, np.ndarray): + legs = xp.DM(legs) + else: + gamma_net = to_boundary @ np.asarray(gamma, dtype=float).ravel() + va_boundary = mean @ va_panels + return scale_rows(rho * gamma_net, cross_rows(va_boundary + v_induced, legs, xp), xp) diff --git a/tests/BodyAerodynamics/data/panel_kernel_reference.npz b/tests/BodyAerodynamics/data/panel_kernel_reference.npz new file mode 100644 index 0000000000000000000000000000000000000000..897a218e9f7388822722217b06d42415f251e143 GIT binary patch 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        C{asHSd-MMXCeBC>j zy4|z_OU=9TY*=ABZV9MyitJRuK3-?ro+fzm!8O?qBTUHQwsU7CHmYzVhl{QTb@-60 zRq_`@j>J*}1S(EBE1Zv$H~lb>i+ za=Em;IOeexo@}8SJCxhY^{$F);apb@b}qM=&px1d4Cmgj&(7uUT>3^b{JKcz25ejb zY7Q5?*Be%k6yWCY8I@h*>cPC_+ziZZ>5^}kVs1A5n23LLflxb#Q$&gu8~wNR9L{X3 zo3g=$`#J3EMmlU{fr1Y2PM=t@!VDcI`#_g1S%HcUcb-@3vtfBVIvi=!4cLIcC+To~ z=hB>w&co87S$Ax~hT^5^`r!JiYsdy;_w;X9CWTVl-*Cu(V5RXB^`ocf_n{Uako?k! zEl=U54#(&2R%~P*s;-mN^gFe5hUF45t^dK!9v9%|KW>I+bvxuW^m3#Hj1c1127{mq zduvUY4W5ZvTMU9O-_LuwF2y18?GOmAv@fmFl>Ryed^@jKM+|~X z_7bI)ER=?wPzpMhAM2fx{#FOfbLVgQT3r6!L2Z(2MQEy&})kP zLvkmmFAW0xTF#oFYe7 zCT{_T!hU!tD^aNX!pnS}69VR~y**Oxk5eZJ&PgG|5Uz0Jh5h=`8G#CvU3mMrGaMmu zd+vsJ^NXp;9j1721OgPOxNyhFdo)7iZMSe3S&u+ ztCOinom#8IQ)=k}iPh~et66UDhf`EMQ3|?34w+pjeTx_7@(`z>D`ZbH@HU=H$^*EEgCuzrJyb9G$n|ja)B3&kvB$RGuRwCk1sgq6UyPE zu<&kjeG-;W6^D<*cDK9if#GR9?-*ow0A(vof1>kFq~9Nc2JybFt>vVoN0Q&9@4 zu~E~vJi{rieNYPOvHO~ADyJyW?!Vv^Tx1>O1Eibb5Oc#9O$Og7o}N_bhi9{88jeAS z_0{9MXH$y@xU`+&hhn&0_FlAIJskPMA4PJ@?8cgxZsW-DGf*VA%?^<}n@8Om;4Gdq z6GIBq*-k)bVlxms76y (body factory, solver kwargs) +CASES = { + "straight": (straight_body, {}), + "swept": (swept_body, {}), + "arc": (arc_body, {}), + "v3": (v3_body, {}), + "v3_viscous_noAT": ( + v3_body, + {"is_with_viscous_drag_correction": True, "is_with_attached_trailed_vortex_force": False}, + ), + "v3_yaw_rate": (lambda: v3_body(yaw_rate=0.4), {"reference_point": [0.1, 0.0, 0.5]}), +} + + +def numeric_outputs(results: dict) -> dict: + """Every numeric entry of a ``solve`` result, as float arrays.""" + out = {} + for key, value in results.items(): + try: + array = np.asarray(value, dtype=float) + except (TypeError, ValueError): + continue + out[key] = array + return out + + +def run_case(name: str, is_aoa_corrected: bool) -> dict: + factory, kwargs = CASES[name] + solver = Solver(allowed_error=1e-10, is_aoa_corrected=is_aoa_corrected, **kwargs) + results = solver.solve(factory()) + assert results["gamma_converged"] + return numeric_outputs(results) + + +def all_outputs() -> dict: + flat = {} + for name in CASES: + for corrected in (True, False): + for key, value in run_case(name, corrected).items(): + flat[f"{name}|{corrected}|{key}"] = value + return flat + + +if __name__ == "__main__": + np.savez(sys.argv[1], **all_outputs()) diff --git a/tests/BodyAerodynamics/test_panel_kernels.py b/tests/BodyAerodynamics/test_panel_kernels.py new file mode 100644 index 0000000..cc20943 --- /dev/null +++ b/tests/BodyAerodynamics/test_panel_kernels.py @@ -0,0 +1,303 @@ +"""The section force law as ``xp`` kernels (``VSM.core.panel_kernels``). + +Contract: + +* moving the force law into the kernels changed no output: every numeric + result of ``Solver.solve`` equals the one of VSM ``1201f6f`` (the commit + before the move) to round-off, for ``is_aoa_corrected`` True and False, on + a straight, a swept, a curved (arc) wing and the LEI V3 kite; +* the public quarter-chord induction matrices are the ones the force + directions are computed from; +* every kernel gives the same numbers with ``xp=casadi`` as with + ``xp=numpy``; +* a CasADi graph with the induction matrices as parameters reproduces the + per-panel forces of ``compute_results``. +""" + +import sys +from pathlib import Path + +import numpy as np +import pytest + +sys.path.insert(0, str(Path(__file__).resolve().parent)) + +from panel_kernel_cases import CASES, REFERENCE_FILE, run_case, v3_body, arc_body # noqa: E402 +from VSM.core import panel_kernels # noqa: E402 +from VSM.core.Solver import Solver # noqa: E402 +from VSM.core.utils import thin_airfoil_strips, assemble_curved_bound_correction_AIC # noqa: E402 + +RTOL = 1e-12 + +_FORCE_KEYS = ("Fx", "Fy", "Fz") +_MOMENT_KEYS = ("Mx", "My", "Mz") + + +# ----------------------------------------------------------- no-change regression +@pytest.fixture(scope="module") +def reference(): + return np.load(REFERENCE_FILE) + + +@pytest.mark.parametrize("is_aoa_corrected", [True, False]) +@pytest.mark.parametrize("case", list(CASES)) +def test_solve_outputs_match_reference_commit(reference, case, is_aoa_corrected): + """Every numeric output equals VSM 1201f6f to round-off. Entries that + vanish by symmetry (side force of a symmetric wing, ...) are compared + against the case's force or moment scale instead of their own.""" + outputs = run_case(case, is_aoa_corrected) + prefix = f"{case}|{is_aoa_corrected}|" + expected_keys = {k[len(prefix):] for k in reference.files if k.startswith(prefix)} + assert set(outputs) == expected_keys + family_scale = { + "force": max(abs(float(reference[prefix + k])) for k in _FORCE_KEYS), + "moment": max(abs(float(reference[prefix + k])) for k in _MOMENT_KEYS), + "other": max(abs(float(reference[prefix + k])) for k in ("cl", "cd")), + } + for key, value in outputs.items(): + ref = reference[prefix + key] + assert value.shape == ref.shape, key + if not ref.size: + continue + if key[0] == "F" or key in ("lift", "drag", "side", "drag_induced_trefftz", "bridle_line_forces"): + family = "force" + elif key[0] == "M": + family = "moment" + else: + family = "other" + scale = max(np.max(np.abs(ref)), 1e-3 * family_scale[family]) + np.testing.assert_allclose(value, ref, rtol=0.0, atol=RTOL * scale, err_msg=key) + + +# ------------------------------------------------------ quarter-chord induction +@pytest.mark.parametrize("factory", [arc_body, v3_body]) +def test_quarter_chord_matrices_are_llt_plus_curved_correction(factory): + """The public matrices equal the trailed system on the quarter chord plus + the curved bound-vortex correction, assembled independently here.""" + body = factory() + va = np.array([p.va for p in body.panels]) + va_norm = np.linalg.norm(va, axis=1) + va_unit = va / va_norm[:, None] + core = 0.05 + public = body.compute_quarter_chord_AIC_matrices(core, va_norm, va_unit) + + llt = body.compute_AIC_matrices("LLT", core, va_norm, va_unit) + rows = lambda name: np.ascontiguousarray([getattr(p, name) for p in body.panels], dtype=float) # noqa: E731 + strip_x, strip_w = thin_airfoil_strips() + correction = assemble_curved_bound_correction_AIC( + rows("aerodynamic_center"), rows("bound_point_1"), rows("bound_point_2"), + rows("TE_point_1"), rows("TE_point_2"), rows("y_airf"), + np.array([p.chord for p in body.panels]), va_norm, + float(body._aerodynamic_center_location), core, strip_x, strip_w, + ) + for k in range(3): + assert public[k].shape == (body.n_panels, body.n_panels) + np.testing.assert_allclose(public[k], llt[k] + correction[k], rtol=1e-13, atol=1e-15) + if factory is arc_body: # curved: the correction is not negligible + assert np.max(np.abs(correction)) > 1e-3 * np.max(np.abs(llt)) + + +def test_quarter_chord_direction_angle_uses_the_public_matrices(): + body = v3_body() + solver = Solver(allowed_error=1e-10) + results = solver.solve(body) + va_norm = np.linalg.norm(solver.va_array, axis=1) + AIC_qc = body.compute_quarter_chord_AIC_matrices( + solver.core_radius_fraction, va_norm, solver.va_array / va_norm[:, None] + ) + gamma = results["gamma_distribution"] + v_qc = solver.va_array + np.column_stack([A @ gamma for A in AIC_qc]) + alpha_qc = np.arctan2( + np.sum(solver.x_airf_array * v_qc, axis=1), np.sum(solver.y_airf_array * v_qc, axis=1) + ) + np.testing.assert_allclose(np.ravel(results["alpha_at_ac"]), alpha_qc, rtol=0, atol=1e-14) + + +# --------------------------------------------------------- casadi == numpy +@pytest.fixture(scope="module") +def solved_v3(): + """A converged V3 solve and the arrays a force-law caller needs.""" + body = v3_body() + solver = Solver( + allowed_error=1e-10, + is_aoa_corrected=True, + is_with_attached_trailed_vortex_force=True, + ) + results = solver.solve(body) + va_norm = np.linalg.norm(solver.va_array, axis=1) + AIC_qc = body.compute_quarter_chord_AIC_matrices( + solver.core_radius_fraction, va_norm, solver.va_array / va_norm[:, None] + ) + return body, solver, results, AIC_qc + + +def _numpy_inputs(solver, results, AIC_qc): + gamma = np.asarray(results["gamma_distribution"], dtype=float) + aic = (solver.AIC_x, solver.AIC_y, solver.AIC_z) + v_rel = panel_kernels.quarter_chord_velocity(solver.va_array, gamma, *aic) + alpha, umag = panel_kernels.relative_flow( + v_rel, solver.x_airf_array, solver.y_airf_array, solver.z_airf_array + ) + panels = solver.panels + return { + "gamma": gamma, + "v_rel": v_rel, + "alpha": alpha, + "umag": umag, + "cl": np.array([p.compute_cl(a) for p, a in zip(panels, alpha)]), + "cd": np.array([p.compute_cd_cm(a)[0] for p, a in zip(panels, alpha)]), + "cm": np.array([p.compute_cd_cm(a)[1] for p, a in zip(panels, alpha)]), + "AIC_qc": AIC_qc, + } + + +def test_kernels_casadi_equals_numpy(solved_v3): + ca = pytest.importorskip("casadi") + body, solver, results, AIC_qc = solved_v3 + d = _numpy_inputs(solver, results, AIC_qc) + x, y, z = solver.x_airf_array, solver.y_airf_array, solver.z_airf_array + chord, width, rho = solver.chord_array, solver.width_array, solver.rho + + col = lambda v: ca.DM(np.asarray(v, dtype=float).reshape(-1, 1)) # noqa: E731 + mat = lambda a: ca.DM(np.asarray(a, dtype=float)) # noqa: E731 + + def same(ca_value, np_value): + ca_array = np.array(ca_value, dtype=float).reshape(np.shape(np_value)) + scale = max(np.max(np.abs(np_value)), 1e-300) + np.testing.assert_allclose(ca_array, np_value, rtol=0, atol=RTOL * scale) + + # flow + same(panel_kernels.relative_flow(mat(d["v_rel"]), mat(x), mat(y), mat(z), xp=ca)[0], d["alpha"]) + same(panel_kernels.relative_flow(mat(d["v_rel"]), mat(x), mat(y), mat(z), xp=ca)[1], d["umag"]) + v_qc_np = panel_kernels.quarter_chord_velocity(solver.va_array, d["gamma"], *AIC_qc) + v_qc_ca = panel_kernels.quarter_chord_velocity( + mat(solver.va_array), col(d["gamma"]), *[mat(A) for A in AIC_qc], xp=ca + ) + same(v_qc_ca, v_qc_np) + alpha_dir_np = panel_kernels.direction_angle(v_qc_np, x, y) + same(panel_kernels.direction_angle(v_qc_ca, mat(x), mat(y), xp=ca), alpha_dir_np) + + # force law, both direction laws + for alpha_dir in (None, alpha_dir_np): + np_out = panel_kernels.panel_forces( + d["alpha"], d["umag"], d["cl"], d["cd"], d["cm"], chord, width, x, y, z, rho, + alpha_dir=alpha_dir, + ) + ca_out = panel_kernels.panel_forces( + col(d["alpha"]), col(d["umag"]), col(d["cl"]), col(d["cd"]), col(d["cm"]), + col(chord), col(width), mat(x), mat(y), mat(z), rho, + alpha_dir=None if alpha_dir is None else col(alpha_dir), xp=ca, + ) + for ca_value, np_value in zip(ca_out, np_out): + same(ca_value, np_value) + np_vec = panel_kernels.section_force_vectors( + d["alpha"], d["umag"], d["cl"], d["cd"], d["cm"], chord, x, y, z, rho, + alpha_dir=alpha_dir, + ) + ca_vec = panel_kernels.section_force_vectors( + col(d["alpha"]), col(d["umag"]), col(d["cl"]), col(d["cd"]), col(d["cm"]), + col(chord), mat(x), mat(y), mat(z), rho, + alpha_dir=None if alpha_dir is None else col(alpha_dir), xp=ca, + ) + for ca_value, np_value in zip(ca_vec, np_vec): + same(ca_value, np_value) + + # attached trailed vortex force + legs = np.random.default_rng(0).normal(size=(body.n_panels + 1, 3)) + v_ind = np.random.default_rng(1).normal(size=(body.n_panels + 1, 3)) + same( + panel_kernels.attached_trailed_forces( + col(d["gamma"]), mat(solver.va_array), mat(v_ind), legs, rho, xp=ca + ), + panel_kernels.attached_trailed_forces(d["gamma"], solver.va_array, v_ind, legs, rho), + ) + + +# ------------------------------------------- casadi graph == compute_results +def _boundary_shares(n): + """(n, n+1) split of boundary loads onto panels, compute_results' rule.""" + shares = np.zeros((n, n + 1)) + shares[0, 0] = 1.0 + shares[n - 1, n] = 1.0 + for j in range(1, n): + shares[j - 1, j] = shares[j, j] = 0.5 + return shares + + +def _compute_results_at(body, solver, gamma): + """compute_results for this ``gamma`` with ``alpha``/``umag`` evaluated at + the same ``gamma``. (``solve`` passes the loop's last alpha, which lags the + returned gamma by one iteration, i.e. agrees with it only to the + convergence tolerance.)""" + alpha, umag, _ = solver.compute_aerodynamic_quantities(gamma) + va_norm = np.linalg.norm(solver.va_array, axis=1) + return body.compute_results( + gamma, solver.rho, solver.aerodynamic_model_type, solver.core_radius_fraction, + solver.mu, alpha, umag, solver.chord_array, solver.x_airf_array, + solver.y_airf_array, solver.z_airf_array, solver.va_array, va_norm, + solver.va_array / va_norm[:, None], solver.panels, False, + solver.is_with_viscous_drag_correction, solver.reference_point, + solver.is_aoa_corrected, + relative_velocity_array=solver.compute_relative_velocity(gamma), + is_with_attached_trailed_vortex_force=solver.is_with_attached_trailed_vortex_force, + ) + + +@pytest.mark.parametrize("is_aoa_corrected", [True, False]) +def test_casadi_graph_reproduces_compute_results_forces(is_aoa_corrected): + """Graph: gamma, va and the 3/4-chord and quarter-chord matrices are MX + parameters; ``v_rel`` and ``v_qc`` come from ``quarter_chord_velocity``, + the section forces from ``Solver.casadi_panel_force_function``. Evaluated + at a converged gamma it reproduces compute_results' panel forces and + moments (the attached-trailed part removed, as it is not in the + function).""" + ca = pytest.importorskip("casadi") + body = v3_body() + solver = Solver(allowed_error=1e-10, is_aoa_corrected=is_aoa_corrected) + gamma_converged = solver.solve(body)["gamma_distribution"] + results = _compute_results_at(body, solver, gamma_converged) + n = solver.n_panels + va_norm = np.linalg.norm(solver.va_array, axis=1) + AIC_qc = body.compute_quarter_chord_AIC_matrices( + solver.core_radius_fraction, va_norm, solver.va_array / va_norm[:, None] + ) + + gamma = ca.MX.sym("gamma", n) + va = ca.MX.sym("va", n, 3) + A_cp = [ca.MX.sym(f"A_cp_{k}", n, n) for k in range(3)] + A_qc = [ca.MX.sym(f"A_qc_{k}", n, n) for k in range(3)] + v_rel = panel_kernels.quarter_chord_velocity(va, gamma, *A_cp, xp=ca) + v_qc = panel_kernels.quarter_chord_velocity(va, gamma, *A_qc, xp=ca) if is_aoa_corrected else v_rel + forces_fn = solver.casadi_panel_force_function() + force, moment_local = forces_fn( + v_rel, v_qc, solver.x_airf_array, solver.y_airf_array, solver.z_airf_array, + solver.chord_array, solver.width_array, solver.rho, + )[:2] + graph = ca.Function("forces", [gamma, va, *A_cp, *A_qc], [force, moment_local]) + + force_num, moment_num = graph( + gamma_converged, solver.va_array, + solver.AIC_x, solver.AIC_y, solver.AIC_z, *AIC_qc, + ) + force_num = np.array(force_num) + moment_num = np.array(moment_num) + + shares = _boundary_shares(n) + f_at = np.array(results["F_attached_trailed_distribution"]) + assert f_at.shape == (n + 1, 3) # AT force on (the default) + expected_force = np.array(results["F_distribution"]) - shares @ f_at + reference_point = np.zeros(3) + ac = np.array([p.aerodynamic_center for p in solver.panels]) + at_points = body.compute_attached_trailed_vortex_forces( + gamma_converged, solver.rho, solver.core_radius_fraction, solver.va_array + )[1] + expected_moment = ( + np.array(results["M_distribution"]) + - shares @ np.cross(at_points - reference_point, f_at) + - np.cross(ac - reference_point, expected_force) + ) + f_scale = np.max(np.abs(expected_force)) + np.testing.assert_allclose(force_num, expected_force, rtol=0, atol=RTOL * f_scale) + np.testing.assert_allclose( + moment_num, expected_moment, rtol=0, atol=RTOL * np.max(np.abs(expected_moment)) + ) From a801b5ba31e2d53fa167118df04c008912d027dd Mon Sep 17 00:00:00 2001 From: ocayon Date: Tue, 3 Nov 2026 14:12:26 +0100 Subject: [PATCH 32/37] perf: vectorised Trefftz drag and projected area, cheaper Newton residual calls - compute_trefftz_plane_induced_drag: the O(n^2) per-panel Python loop with np.cross becomes one vectorised evaluation (1.3 -> 0.2 ms at 36 panels). It is a far-wake diagnostic computed on every solve; output unchanged. - Wing.compute_projected_area: vectorised over the strips (1.3 -> 0.1 ms). Also stops normalising the caller's z_plane_vector in place. - gamma_loop_casadi_newton: the inputs that are constant within a solve are converted to CasADi matrices once, and the loop calls a cached variant of the residual function with only the six outputs it reads (same graph). ~185 -> ~77 us per residual evaluation. Numerical, not physical. Sums are reordered, so outputs move at round-off only: every solve output still matches 1201f6f to <= 1.5e-14 relative. V3, 36 panels, casadi_newton: ~24 -> ~17 ms per solve. Generated with Claude Code --- src/VSM/core/BodyAerodynamics.py | 22 ++++++------- src/VSM/core/Solver.py | 53 ++++++++++++++++++++++++++------ src/VSM/core/WingGeometry.py | 28 ++++++++--------- 3 files changed, 66 insertions(+), 37 deletions(-) diff --git a/src/VSM/core/BodyAerodynamics.py b/src/VSM/core/BodyAerodynamics.py index 467cc95..a4d190e 100644 --- a/src/VSM/core/BodyAerodynamics.py +++ b/src/VSM/core/BodyAerodynamics.py @@ -1299,17 +1299,17 @@ def compute_trefftz_plane_induced_drag(self, gamma, rho): ).astype(float) d_gamma = np.concatenate(([gamma[0]], gamma[1:] - gamma[:-1], [-gamma[-1]])) q = origins - np.outer(origins @ e_inf, e_inf) # projected onto the plane - drag = 0.0 - for i in range(n): - mid = 0.5 * (q[i] + q[i + 1]) - d = mid - q - r2 = np.sum(d * d, axis=1) - v_t = np.sum( - (d_gamma / (2.0 * np.pi * r2))[:, None] * np.cross(e_inf, d), axis=0 - ) - # trace segment in the sense of the bound vortex (section i+1 -> i) - drag += gamma[i] * np.dot(np.cross(v_t, q[i] - q[i + 1]), e_inf) - return 0.5 * rho * drag + # velocity of all wake vortices k at every trace-segment midpoint i + mid = 0.5 * (q[:-1] + q[1:]) # (n, 3) + d = mid[:, None, :] - q[None, :, :] # (n, n+1, 3) + r2 = np.sum(d * d, axis=2) + v_t = np.sum( + (d_gamma[None, :] / (2.0 * np.pi * r2))[:, :, None] * np.cross(e_inf, d), + axis=1, + ) + # trace segment in the sense of the bound vortex (section i+1 -> i) + drag = np.sum(gamma[:n] * (np.cross(v_t, q[:-1] - q[1:]) @ e_inf)) + return 0.5 * rho * float(drag) def compute_attached_trailed_vortex_forces( self, gamma, rho, core_radius_fraction, va_array diff --git a/src/VSM/core/Solver.py b/src/VSM/core/Solver.py index 42d4342..96d3766 100644 --- a/src/VSM/core/Solver.py +++ b/src/VSM/core/Solver.py @@ -202,6 +202,7 @@ def __init__( # rejected and the step quartered (0.5 = residual may at most double). self._newton_reject_ratio = 0.5 self._casadi_newton_cache: dict = {} + self._casadi_newton_loop_cache: dict = {} #: Diagnostic: did the last casadi_newton solve fall back to base? self.last_fallback = False #: Diagnostic: residual evaluations used by the last casadi_newton solve. @@ -1359,6 +1360,31 @@ def casadi_panel_force_function(self): self._casadi_newton_cache[key] = fn return fn + def _casadi_newton_loop_function(self): + """The residual function restricted to the six outputs the Newton loop + reads (``h, dh_dvrel, mu, alpha, umag, gate``): the same graph, minus + the force-side lookups it would otherwise evaluate on every call. + Cached per polar set alongside the full function.""" + import casadi as ca + + alpha_tables, cl_tables, cd_tables, cm_tables = self._polar_tables() + key = self._casadi_newton_key(alpha_tables, cl_tables, cd_tables, cm_tables) + loop_fn = self._casadi_newton_loop_cache.get(key) + if loop_fn is None: + fn = self._casadi_newton_function() + inputs = fn.mx_in() + loop_fn = ca.Function( + "vsm_panel_residual_loop", + inputs, + fn.call(inputs)[:6], + fn.name_in(), + fn.name_out()[:6], + ) + if len(self._casadi_newton_loop_cache) >= 32: + self._casadi_newton_loop_cache.pop(next(iter(self._casadi_newton_loop_cache))) + self._casadi_newton_loop_cache[key] = loop_fn + return loop_fn + def gamma_loop_casadi_newton(self, gamma_initial: np.ndarray) -> tuple: """Newton solve of the circulation residual with an exact CasADi Jacobian, globalised by pseudo-transient continuation @@ -1407,7 +1433,9 @@ def gamma_loop_casadi_newton(self, gamma_initial: np.ndarray) -> tuple: fallback to decide. """ try: - fn = self._casadi_newton_function() + import casadi as ca + + fn = self._casadi_newton_loop_function() except ImportError as exc: # pragma: no cover - depends on optional dep raise ImportError( "gamma_loop_type='casadi_newton' requires the optional 'casadi' " @@ -1424,14 +1452,19 @@ def gamma_loop_casadi_newton(self, gamma_initial: np.ndarray) -> tuple: stall_angles = np.full(n, np.inf) stall_angles_neg = np.full(n, -np.inf) laplacian = np.zeros((n, n)) - params = ( - self.x_airf_array, - self.y_airf_array, - self.z_airf_array, - self.chord_array, - self.width_array, - stall_angles, - stall_angles_neg, + # Constant within the solve: converted to CasADi matrices once, which + # halves the cost of each residual evaluation. + params = tuple( + ca.DM(np.asarray(value, dtype=float)) + for value in ( + self.x_airf_array, + self.y_airf_array, + self.z_airf_array, + self.chord_array, + self.width_array, + stall_angles, + stall_angles_neg, + ) ) aic = (self.AIC_x, self.AIC_y, self.AIC_z) @@ -1440,7 +1473,7 @@ def evaluate(x): # v_rel = va + AIC gamma (see _build_casadi_newton_function). v_rel = self.va_array + np.column_stack([a @ x for a in aic]) l_gamma = laplacian @ x - h, dh_dvrel, mu, alpha, umag, gate = fn(v_rel, *params, l_gamma)[:6] + h, dh_dvrel, mu, alpha, umag, gate = fn(v_rel, *params, l_gamma) h = np.asarray(h, dtype=float).ravel() dh_dvrel = np.asarray(dh_dvrel, dtype=float) mu = np.asarray(mu, dtype=float).ravel() diff --git a/src/VSM/core/WingGeometry.py b/src/VSM/core/WingGeometry.py index ecc56c4..81fb1fd 100644 --- a/src/VSM/core/WingGeometry.py +++ b/src/VSM/core/WingGeometry.py @@ -627,22 +627,18 @@ def compute_projected_area(self, z_plane_vector=np.array([0.0, 0.0, 1.0])): """ sections = self.sections n = np.asarray(z_plane_vector, dtype=float) - n /= np.linalg.norm(n) - - def proj(P): - # orthogonal projection onto plane with normal n - return P - np.dot(P, n) * n - - S = 0.0 - for i in range(len(sections) - 1): - A = proj(sections[i].LE_point) - B = proj(sections[i].TE_point) - C = proj(sections[i + 1].TE_point) - D = proj(sections[i + 1].LE_point) - # two triangles: (A,B,C) and (A,C,D) - S += 0.5 * np.linalg.norm(np.cross(B - A, C - A)) - S += 0.5 * np.linalg.norm(np.cross(C - A, D - A)) - return S + n = n / np.linalg.norm(n) # not in place: never modify the caller's array + + LE = np.array([section.LE_point for section in sections], dtype=float) + TE = np.array([section.TE_point for section in sections], dtype=float) + # orthogonal projection onto the plane with normal n + LE = LE - np.outer(LE @ n, n) + TE = TE - np.outer(TE @ n, n) + A, B, C, D = LE[:-1], TE[:-1], TE[1:], LE[1:] + # two triangles per strip: (A,B,C) and (A,C,D) + area_ABC = 0.5 * np.linalg.norm(np.cross(B - A, C - A), axis=1) + area_ACD = 0.5 * np.linalg.norm(np.cross(C - A, D - A), axis=1) + return float(np.sum(np.column_stack([area_ABC, area_ACD]))) def compute_flat_area(self) -> float: """Calculate the total flat (undeformed) wing area in 3D space. From 3cb7bd0c377f3bb6badc47a359914a779ac97804 Mon Sep 17 00:00:00 2001 From: ocayon Date: Tue, 3 Nov 2026 14:54:08 +0100 Subject: [PATCH 33/37] feat(solver): polar tables as inputs of the CasADi panel functions On a deforming wing each panel's blended polar changes slightly every coupled iteration. The CasADi residual and panel-force functions embedded the tables as constants and were cached per table set, so a caller that re-trims deformed shapes (AWETrim's CasadiTrim) rebuilt its graph every iteration and could not afford to SX-expand it. - _casadi_newton_function(table_inputs=False) and casadi_panel_force_function(table_inputs=False): with True the functions take cl_table, cd_table, cm_table, each (n_panels, n_alpha), as extra inputs and are cached per (panel count, alpha grid, settings), not per table values. The lookup is one 1-D parametric linear interpolant on the shared grid, mapped over panels: same nodes and clamping, so the outputs equal the embedded-table ones to round-off. Omitted tables default to NaN, never to a silently zero polar. - Solver.casadi_polar_table_inputs() and casadi_stall_angle_inputs(): the current tables and stall-gate angles in the input layout. - Linear polars on one shared alpha grid only (a parametric cubic spline refits per call, ~0.1 s); other cases raise a clear ValueError. VSM's own loops keep the embedded-table functions and are unchanged: all solve outputs are bit-identical to a801b5b (4 loop types, both is_aoa_corrected settings, viscosity on/off). Expanded to SX, the table function evaluates as fast as the embedded one (+2% at 135 panels). Generated with Claude Code --- src/VSM/core/Solver.py | 210 ++++++++++++++++-- .../Solver/test_casadi_polar_table_inputs.py | 168 ++++++++++++++ 2 files changed, 365 insertions(+), 13 deletions(-) create mode 100644 tests/Solver/test_casadi_polar_table_inputs.py diff --git a/src/VSM/core/Solver.py b/src/VSM/core/Solver.py index 96d3766..bb03468 100644 --- a/src/VSM/core/Solver.py +++ b/src/VSM/core/Solver.py @@ -6,6 +6,26 @@ from VSM.core import panel_kernels + +def _table_symbols(n_panels: int, alpha_tables) -> dict: + """Symbolic ``(n_panels, n_alpha)`` polar tables for ``table_inputs``.""" + import casadi as ca + + n_alpha = int(np.asarray(alpha_tables[0]).size) + return {name: ca.MX.sym(f"{name}_table", n_panels, n_alpha) for name in ("cl", "cd", "cm")} + + +def _with_table_inputs(inputs: list, input_names: list, table_syms): + """Append the table inputs (if any) and default them to NaN, so a call + that omits them (CasADi fills omitted inputs with 0 by default) gives NaN + rather than a silently zero polar.""" + if table_syms is None: + return inputs, input_names, {} + inputs = inputs + [table_syms[k] for k in ("cl", "cd", "cm")] + input_names = input_names + ["cl_table", "cd_table", "cm_table"] + defaults = [0.0] * (len(inputs) - 3) + [float("nan")] * 3 + return inputs, input_names, {"default_in": defaults} + class Solver: """Solver for aerodynamic circulation distribution and force computation. @@ -203,6 +223,7 @@ def __init__( self._newton_reject_ratio = 0.5 self._casadi_newton_cache: dict = {} self._casadi_newton_loop_cache: dict = {} + self._casadi_table_input_cache: dict = {} # polar tables as inputs #: Diagnostic: did the last casadi_newton solve fall back to base? self.last_fallback = False #: Diagnostic: residual evaluations used by the last casadi_newton solve. @@ -1030,12 +1051,91 @@ def _casadi_newton_key(self, alpha_tables, cl_tables, cd_tables, cm_tables) -> t digest.hexdigest(), ) - def _casadi_polar_lookups(self, alpha_tables, cl_tables, cd_tables=None, cm_tables=None): + def _casadi_table_input_key(self, alpha_tables) -> tuple: + """Cache key of the functions that take the polar tables as INPUTS + (``table_inputs=True``): the graph depends on the panel count, the + shared alpha grid, the interpolation and the regularization settings, + not on the table values, so one function serves every shape whose + blended polars change but keep the grid.""" + self._check_table_inputs_supported(alpha_tables) + grid = np.ascontiguousarray(alpha_tables[0], dtype=float) + return ( + "table_inputs", + self.n_panels, + bool(self.is_with_artificial_viscosity), + float(self.artificial_viscosity_factor), + self.polar_interpolation, + hashlib.blake2b(grid.tobytes(), digest_size=16).hexdigest(), + ) + + def _check_table_inputs_supported(self, alpha_tables) -> None: + if self.polar_interpolation != "linear": + # A parametric cubic spline refits its coefficients on every call + # (~0.1 s per evaluation), which defeats the purpose. + raise ValueError( + "Polar tables as CasADi inputs need polar_interpolation='linear' " + f"(got {self.polar_interpolation!r})." + ) + if not all( + table.shape == alpha_tables[0].shape and np.array_equal(table, alpha_tables[0]) + for table in alpha_tables[1:] + ): + raise ValueError( + "Polar tables as CasADi inputs need every panel polar on one " + "shared alpha grid." + ) + + def casadi_polar_table_inputs(self) -> dict: + """The current panels' polar tables in the layout of the ``table_inputs`` + CasADi functions (:meth:`_casadi_newton_function` and + :meth:`casadi_panel_force_function` with ``table_inputs=True``): + ``{"cl_table", "cd_table", "cm_table"}``, each ``(n_panels, n_alpha)``, + row ``i`` = panel ``i``'s coefficients on the shared alpha grid + (``panel.panel_polar_data[:, 0]``, radians). + + Pass them on every call, next to the geometry: a deformed shape blends + its section polars with new weights, so the values change while the + grid, and with it the function, stays the same. + """ + alpha_tables, cl_tables, cd_tables, cm_tables = self._polar_tables() + self._check_table_inputs_supported(alpha_tables) + return { + "cl_table": np.vstack(cl_tables), + "cd_table": np.vstack(cd_tables), + "cm_table": np.vstack(cm_tables), + } + + def casadi_stall_angle_inputs(self) -> dict: + """``{"stall_angles", "stall_angles_neg"}`` [rad] of the current panel + polars, the gate inputs of the residual function as + :meth:`gamma_loop_casadi_newton` passes them (plus / minus infinity + without artificial viscosity). They are derived from the tables, so a + caller passing new tables passes these new values with them.""" + if self.is_with_artificial_viscosity: + return { + "stall_angles": self._panel_stall_angles(), + "stall_angles_neg": self._panel_negative_stall_angles(), + } + return { + "stall_angles": np.full(self.n_panels, np.inf), + "stall_angles_neg": np.full(self.n_panels, -np.inf), + } + + def _casadi_polar_lookups( + self, alpha_tables, cl_tables, cd_tables=None, cm_tables=None, table_symbols=None + ): """Clamped CasADi lookups ``alpha (n) -> cl, cd, cm (n)`` of the per-panel polars, shared by :meth:`_build_casadi_newton_function` and :meth:`_build_casadi_panel_force_function` (see the former for the interpolation). Returns ``(cl_of, cd_of, cm_of, smooth)``, ``smooth`` True for "bspline" polars. + + ``table_symbols`` (``{"cl": MX, "cd": MX, "cm": MX}``, each + ``(n, n_alpha)``) makes the table VALUES symbolic inputs instead of + constants: one 1-D parametric linear interpolant on the shared grid, + mapped over the panels. It reproduces the constant table exactly + (same nodes, same clamping); only the shared-grid linear case is + supported (see :meth:`_check_table_inputs_supported`). """ import casadi as ca @@ -1059,6 +1159,33 @@ def _casadi_polar_lookups(self, alpha_tables, cl_tables, cd_tables=None, cm_tabl kind = self.polar_interpolation smooth = kind == "bspline" + if table_symbols is not None: + self._check_table_inputs_supported(alpha_tables) + grid = np.asarray(alpha_tables[0], dtype=float) + lo, hi = float(grid[0]), float(grid[-1]) + row_interpolant = ca.interpolant("polar_row", "linear", [grid], 1) + alpha_row = ca.MX.sym("alpha_row") + values_row = ca.MX.sym("values_row", grid.size) + # One panel's lookup; .map(n) evaluates it column-wise over panels. + row_lookup = ca.Function( + "polar_row_lookup", + [alpha_row, values_row], + [row_interpolant(ca.fmin(ca.fmax(alpha_row, lo), hi), values_row)], + ).map(n) + + def make_parametric_lookup(table): + def lookup(alpha_vec): + return row_lookup(alpha_vec.T, table.T).T + + return lookup + + return ( + make_parametric_lookup(table_symbols["cl"]), + make_parametric_lookup(table_symbols["cd"]), + make_parametric_lookup(table_symbols["cm"]), + smooth, + ) + def make_lookup(name, value_tables): """Clamped lookup ``alpha_vec (n) -> values (n)`` of one polar column.""" if shared_grid: @@ -1104,7 +1231,9 @@ def lookup(alpha_vec): cm_of = make_lookup("cm", cm_tables) return cl_of, cd_of, cm_of, smooth - def _build_casadi_newton_function(self, alpha_tables, cl_tables, cd_tables=None, cm_tables=None): + def _build_casadi_newton_function( + self, alpha_tables, cl_tables, cd_tables=None, cm_tables=None, table_inputs=False + ): """Build the CasADi function of the PER-PANEL section physics that :meth:`gamma_loop_casadi_newton` assembles its residual and exact Jacobian from. @@ -1154,12 +1283,18 @@ def _build_casadi_newton_function(self, alpha_tables, cl_tables, cd_tables=None, Jacobian), ``cl``, ``cd``, ``cm`` at ``alpha`` and their corner- averaged counterparts ``cl_avg``, ``cd_avg``, ``cm_avg``. With "bspline" polars the averaged outputs equal the exact ones. + + ``table_inputs=True`` appends the inputs ``cl_table``, ``cd_table``, + ``cm_table`` (each ``(n, n_alpha)``, :meth:`casadi_polar_table_inputs`) + and takes the table values from them instead of embedding them; see + :meth:`_casadi_newton_function`. """ import casadi as ca n = self.n_panels + table_syms = _table_symbols(n, alpha_tables) if table_inputs else None cl_of, cd_of, cm_of, smooth = self._casadi_polar_lookups( - alpha_tables, cl_tables, cd_tables, cm_tables + alpha_tables, cl_tables, cd_tables, cm_tables, table_symbols=table_syms ) v_rel = ca.MX.sym("v_rel", n, 3) @@ -1244,9 +1379,12 @@ def averaged(lookup): seeds = [ca.DM(np.eye(3)[k][None, :].repeat(n, axis=0)) for k in range(3)] dh_dvrel = ca.horzcat(*[ca.jtimes(h_for_jacobian, v_rel, seed) for seed in seeds]) + inputs = [v_rel, x_airf, y_airf, z_airf, chord, width, stall_angles, stall_angles_neg, l_gamma] + input_names = ["v_rel", "x_airf", "y_airf", "z_airf", "chord", "width", "stall_angles", "stall_angles_neg", "l_gamma"] + inputs, input_names, options = _with_table_inputs(inputs, input_names, table_syms) return ca.Function( - "vsm_panel_residual", - [v_rel, x_airf, y_airf, z_airf, chord, width, stall_angles, stall_angles_neg, l_gamma], + "vsm_panel_residual_tables" if table_inputs else "vsm_panel_residual", + inputs, [ h, dh_dvrel, @@ -1262,11 +1400,29 @@ def averaged(lookup): averaged(cd_of), averaged(cm_of), ], - ["v_rel", "x_airf", "y_airf", "z_airf", "chord", "width", "stall_angles", "stall_angles_neg", "l_gamma"], + input_names, ["h", "dh_dvrel", "mu", "alpha", "umag", "gate", "h_avg", "cl", "cd", "cm", "cl_avg", "cd_avg", "cm_avg"], + options, ) - def _casadi_newton_function(self): + def _casadi_newton_function(self, table_inputs: bool = False): + """The per-panel residual function (:meth:`_build_casadi_newton_function`) + of the current panels, cached. + + ``table_inputs=False`` (default, what :meth:`gamma_loop_casadi_newton` + uses): the polar tables are constants of the graph, cached per table + set. ``table_inputs=True``: the tables are the extra inputs + ``cl_table, cd_table, cm_table``, cached per alpha grid, so a caller + that re-trims deformed shapes builds the function once and passes + :meth:`casadi_polar_table_inputs` (and :meth:`casadi_stall_angle_inputs`) + per shape. Same outputs to round-off; needs ``polar_interpolation= + "linear"`` and one shared alpha grid. Omitted table inputs default to + NaN, so a call that forgets them fails loudly instead of using zeros. + """ + if table_inputs: + return self._cached_table_input_function( + "newton", self._build_casadi_newton_function + ) alpha_tables, cl_tables, cd_tables, cm_tables = self._polar_tables() key = self._casadi_newton_key(alpha_tables, cl_tables, cd_tables, cm_tables) fn = self._casadi_newton_cache.get(key) @@ -1282,7 +1438,7 @@ def _casadi_newton_function(self): return fn def _build_casadi_panel_force_function( - self, alpha_tables, cl_tables, cd_tables=None, cm_tables=None + self, alpha_tables, cl_tables, cd_tables=None, cm_tables=None, table_inputs=False ): """CasADi function of the per-panel section forces, the force law of ``compute_results`` (``VSM.core.panel_kernels.panel_forces``) on the @@ -1291,8 +1447,9 @@ def _build_casadi_panel_force_function( import casadi as ca n = self.n_panels + table_syms = _table_symbols(n, alpha_tables) if table_inputs else None cl_of, cd_of, cm_of, _ = self._casadi_polar_lookups( - alpha_tables, cl_tables, cd_tables, cm_tables + alpha_tables, cl_tables, cd_tables, cm_tables, table_symbols=table_syms ) v_rel = ca.MX.sym("v_rel", n, 3) v_qc = ca.MX.sym("v_qc", n, 3) @@ -1310,15 +1467,21 @@ def _build_casadi_panel_force_function( alpha, umag, cl, cd, cm, chord, width, x_airf, y_airf, z_airf, rho, alpha_dir=alpha_dir, xp=ca, ) - return ca.Function( - "vsm_panel_forces", + inputs, input_names, options = _with_table_inputs( [v_rel, v_qc, x_airf, y_airf, z_airf, chord, width, rho], - [force, moment_local, alpha, alpha_dir, umag, cl, cd, cm], ["v_rel", "v_qc", "x_airf", "y_airf", "z_airf", "chord", "width", "rho"], + table_syms, + ) + return ca.Function( + "vsm_panel_forces_tables" if table_inputs else "vsm_panel_forces", + inputs, + [force, moment_local, alpha, alpha_dir, umag, cl, cd, cm], + input_names, ["force", "moment_local", "alpha", "alpha_dir", "umag", "cl", "cd", "cm"], + options, ) - def casadi_panel_force_function(self): + def casadi_panel_force_function(self, table_inputs: bool = False): """CasADi function of the per-panel section forces of the current panels (the ones of the last :meth:`solve`), cached per polar set like the ``casadi_newton`` residual function. @@ -1343,9 +1506,16 @@ def casadi_panel_force_function(self): vortex force (``panel_kernels.attached_trailed_forces``) and the viscous drag correction. Taking ``v_qc`` rather than the matrices keeps the graph O(n); the caller forms the dense product. + + ``table_inputs=True`` appends ``cl_table, cd_table, cm_table`` as + inputs (see :meth:`_casadi_newton_function`). """ import casadi # noqa: F401 (clear error when the optional dep is missing) + if table_inputs: + return self._cached_table_input_function( + "panel_forces", self._build_casadi_panel_force_function + ) alpha_tables, cl_tables, cd_tables, cm_tables = self._polar_tables() key = ("panel_forces",) + self._casadi_newton_key( alpha_tables, cl_tables, cd_tables, cm_tables @@ -1360,6 +1530,20 @@ def casadi_panel_force_function(self): self._casadi_newton_cache[key] = fn return fn + def _cached_table_input_function(self, kind: str, builder): + """Function of ``kind`` with the polar tables as inputs, built once + per (panel count, alpha grid, settings) and then reused for any + table values.""" + alpha_tables, cl_tables, cd_tables, cm_tables = self._polar_tables() + key = (kind,) + self._casadi_table_input_key(alpha_tables) + fn = self._casadi_table_input_cache.get(key) + if fn is None: + fn = builder(alpha_tables, cl_tables, cd_tables, cm_tables, table_inputs=True) + if len(self._casadi_table_input_cache) >= 32: + self._casadi_table_input_cache.pop(next(iter(self._casadi_table_input_cache))) + self._casadi_table_input_cache[key] = fn + return fn + def _casadi_newton_loop_function(self): """The residual function restricted to the six outputs the Newton loop reads (``h, dh_dvrel, mu, alpha, umag, gate``): the same graph, minus diff --git a/tests/Solver/test_casadi_polar_table_inputs.py b/tests/Solver/test_casadi_polar_table_inputs.py new file mode 100644 index 0000000..34ed806 --- /dev/null +++ b/tests/Solver/test_casadi_polar_table_inputs.py @@ -0,0 +1,168 @@ +"""Polar tables as inputs of the CasADi panel functions (``table_inputs=True``). + +Contract: with the tables passed as inputs, the residual and panel-force +functions give the same outputs as the functions with the tables embedded; +one function, built once, serves a second shape whose blended polars differ +(no rebuild); omitted tables give NaN, not a silently zero polar; and the +function still expands to SX. +""" + +import sys +from pathlib import Path + +import numpy as np +import pytest + +ca = pytest.importorskip("casadi") + +REPO = Path(__file__).resolve().parents[2] +sys.path.insert(0, str(REPO / "tests" / "BodyAerodynamics")) + +from panel_kernel_cases import V3_FILE # noqa: E402 +from VSM.core.BodyAerodynamics import BodyAerodynamics # noqa: E402 +from VSM.core.Solver import Solver # noqa: E402 + +RTOL = 1e-12 + + +def _v3(distribution): + body = BodyAerodynamics.instantiate( + n_panels=20, file_path=V3_FILE, spanwise_panel_distribution=distribution + ) + body.va_initialize(10.0, 8.0, 3.0) + return body + + +def _solved(body, **solver_kwargs): + solver = Solver(gamma_loop_type="casadi_newton", allowed_error=1e-10, **solver_kwargs) + results = solver.solve(body) + return solver, np.asarray(results["gamma_distribution"], dtype=float) + + +def _newton_inputs(solver, gamma): + v_rel = solver.compute_relative_velocity(gamma) + n = solver.n_panels + laplacian = ( + solver._build_spanwise_laplacian() + if solver.is_with_artificial_viscosity + else np.zeros((n, n)) + ) + return { + "v_rel": v_rel, + "x_airf": solver.x_airf_array, + "y_airf": solver.y_airf_array, + "z_airf": solver.z_airf_array, + "chord": solver.chord_array, + "width": solver.width_array, + "l_gamma": laplacian @ gamma, + **solver.casadi_stall_angle_inputs(), + } + + +def _force_inputs(solver, gamma): + v_rel = solver.compute_relative_velocity(gamma) + return { + "v_rel": v_rel, + "v_qc": v_rel, + "x_airf": solver.x_airf_array, + "y_airf": solver.y_airf_array, + "z_airf": solver.z_airf_array, + "chord": solver.chord_array, + "width": solver.width_array, + "rho": solver.rho, + } + + +def _assert_outputs_equal(out_tables, out_const): + assert set(out_tables) == set(out_const) + for key, value in out_const.items(): + expected = np.array(value, dtype=float) + actual = np.array(out_tables[key], dtype=float) + scale = max(np.max(np.abs(expected)), 1e-300) + np.testing.assert_allclose(actual, expected, rtol=0, atol=RTOL * scale, err_msg=key) + + +@pytest.mark.parametrize("viscosity", [False, True]) +def test_table_inputs_reproduce_embedded_tables(viscosity): + """Residual function (all 13 outputs, incl. the corner-averaged ones and + the viscosity lift slope) and panel-force function, against the + embedded-table functions of the same shape.""" + solver, gamma = _solved(_v3("uniform"), is_with_artificial_viscosity=viscosity) + tables = solver.casadi_polar_table_inputs() + assert tables["cl_table"].shape == (solver.n_panels, solver.panels[0].panel_polar_data.shape[0]) + + args = _newton_inputs(solver, gamma) + if viscosity: # put a panel past stall so the gate and mu are exercised + args["stall_angles"] = args["stall_angles"] - 0.3 + _assert_outputs_equal( + solver._casadi_newton_function(table_inputs=True)(**args, **tables), + solver._casadi_newton_function()(**args), + ) + f_args = _force_inputs(solver, gamma) + _assert_outputs_equal( + solver.casadi_panel_force_function(table_inputs=True)(**f_args, **tables), + solver.casadi_panel_force_function()(**f_args), + ) + + +def test_one_function_serves_a_second_shape_without_rebuild(): + """Shapes A and B have the same panel count and alpha grid but differently + blended polars. The table-input function built for A, given B's tables and + geometry, equals a fresh embedded-table build for B, and no new + table-input function is built.""" + solver_a, gamma_a = _solved(_v3("uniform")) + fn = solver_a._casadi_newton_function(table_inputs=True) + force_fn = solver_a.casadi_panel_force_function(table_inputs=True) + cache_size = len(solver_a._casadi_table_input_cache) + + body_b = _v3("cosine") + tables_a = solver_a.casadi_polar_table_inputs() + solver_a.solve(body_b) # same solver object, now on shape B + gamma_b = solver_a.solve(body_b)["gamma_distribution"] + tables_b = solver_a.casadi_polar_table_inputs() + assert np.max(np.abs(tables_b["cl_table"] - tables_a["cl_table"])) > 1e-3 # the polars differ + + assert solver_a._casadi_newton_function(table_inputs=True) is fn + assert solver_a.casadi_panel_force_function(table_inputs=True) is force_fn + assert len(solver_a._casadi_table_input_cache) == cache_size + + fresh_b, _ = _solved(_v3("cosine")) + _assert_outputs_equal( + fn(**_newton_inputs(solver_a, gamma_b), **tables_b), + fresh_b._casadi_newton_function()(**_newton_inputs(solver_a, gamma_b)), + ) + _assert_outputs_equal( + force_fn(**_force_inputs(solver_a, gamma_b), **tables_b), + fresh_b.casadi_panel_force_function()(**_force_inputs(solver_a, gamma_b)), + ) + + +def test_omitted_tables_give_nan_not_zero(): + solver, gamma = _solved(_v3("uniform")) + out = solver._casadi_newton_function(table_inputs=True)(**_newton_inputs(solver, gamma)) + assert np.all(np.isnan(np.array(out["h"], dtype=float))) + out = solver.casadi_panel_force_function(table_inputs=True)(**_force_inputs(solver, gamma)) + assert np.all(np.isnan(np.array(out["force"], dtype=float))) + + +def test_table_input_functions_expand_to_sx(): + solver, gamma = _solved(_v3("uniform"), is_with_artificial_viscosity=True) + tables = solver.casadi_polar_table_inputs() + for fn, args in ( + (solver._casadi_newton_function(table_inputs=True), _newton_inputs(solver, gamma)), + (solver.casadi_panel_force_function(table_inputs=True), _force_inputs(solver, gamma)), + ): + _assert_outputs_equal(fn.expand()(**args, **tables), fn(**args, **tables)) + + +def test_newton_loop_is_unchanged_and_does_not_build_table_functions(): + solver, _ = _solved(_v3("uniform")) + assert solver._casadi_table_input_cache == {} + + +def test_unsupported_cases_raise_clearly(): + solver, _ = _solved(_v3("uniform"), polar_interpolation="bspline") + with pytest.raises(ValueError, match="polar_interpolation='linear'"): + solver._casadi_newton_function(table_inputs=True) + with pytest.raises(ValueError, match="polar_interpolation='linear'"): + solver.casadi_polar_table_inputs() From 0a051a76a68ff233c75fc4ae06c0a5892af0c873 Mon Sep 17 00:00:00 2001 From: ocayon Date: Tue, 3 Nov 2026 16:29:00 +0100 Subject: [PATCH 34/37] docs(changelog): 2.3.0 entry Lists the default-result changes of the consistent lifting-line coupling (each with the option that restores the old behaviour where one exists), the removed options, the new CasADi APIs, fixes and speedups, and notes that the release includes the 2.2.0 content that had not been merged. Generated with Claude Code --- changelog.md | 104 +++++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 104 insertions(+) diff --git a/changelog.md b/changelog.md index 3daddb9..707ff01 100644 --- a/changelog.md +++ b/changelog.md @@ -4,6 +4,110 @@ All notable changes to this project will be documented in this file. The format is based on [Keep a Changelog](http://keepachangelog.com/) and this project adheres to [Semantic Versioning](http://semver.org/). +## [2.3.0] - 03/11/2026 + +**Default results change.** The lifting-line coupling now follows the consistent +formulation of Gaunaa, Li & Pirrung (TORQUE 2026): circulation from the inner +velocity, span-perpendicular sections, quarter-chord force directions, +attached-trailed-vortex forces and a chord-regularised curved bound vortex. +Forces, moments and coefficients computed with the defaults differ from 2.2.0, +most on swept and curved wings (kites). Each new default can be switched back +individually where an option exists (listed below). See +`docs/aerodynamic_model` for the formulation and its validation. + +This release also contains everything shipped in 2.2.0. `v2.2.0` was tagged on +the `improve_plotting` branch, which had not been merged into `develop`/`main`. + +### Changed (results) +- Circulation target is `Gamma = 0.5 |V_inner| c Cl` with the inner + (span-perpendicular, own-2D-induction-removed) velocity, instead of + `0.5 Umag^2 / Umagw c Cl`. On the V3 kite the old map put the circulation + 2-6 % low. +- Panel frame and chord follow the Crossflow Principle: the chord direction is + perpendicular to the bound vortex, the normal is chord x span, and the panel + chord is the perpendicular one. Unswept panels are unchanged; on swept panels + the chord shrinks (V3 tip panels by 56 % and 19 %). +- `is_aoa_corrected=True` by default: lift and drag directions come from the + flow at the quarter chord (TAT3), with magnitudes from the 3/4-chord angle. + `is_aoa_corrected=False` restores the 3/4-chord directions. +- The quarter-chord flow includes the influence of a curved or swept bound + vortex through a chord-regularised correction (the actual minus a locally + unrolled vortex system). On-blade induced drag matches the Trefftz plane + within about 1 % on arc, swept and kite geometries, independently of the + panel count. It is computed once per shape and rotated under rigid motion. +- Drag acts along the local inner flow, not the global span axis. +- `is_with_attached_trailed_vortex_force=True` by default: Kutta-Joukowski force + on the chordwise attached trailed vortex segments (`F_attached_trailed_distribution` + in the results). +- `relaxation_factor=None` by default: 0.8 x the fixed-point stability limit of + Li et al. (2026), evaluated per solve (`Solver.compute_relaxation_factor_limit`). + 2.2.0 used a fixed 0.01; pass a number to keep a fixed value. +- Each wake ring follows its own panel's apparent velocity. Results in uniform + translating inflow are unchanged to round-off; they change under body rates or + distributed inflow. +- Bridle line segments are charged at their own inflow, not the wing's mean. +- With `is_with_viscous_drag_correction=True`, the Gaunaa 2024 correction receives + the full 3D relative velocity (the spanwise flow it models). +- With `is_with_artificial_viscosity=True`, the regularization is also gated on + negative stall. +- `Wing.preserve_section_order` (default False): skip the section re-sorting; + `update_wing_from_points` sets it, since its arrays already define the arc order. + +### Removed / breaking +- `Solver` options `is_smooth_circulation`, `smoothness_factor`, + `is_artificial_damping`, `artificial_damping`, + `is_with_simonet_artificial_viscosity`, `simonet_artificial_viscosity_fva` + (stored, never read) and the `gamma_loop_type` values `simonet_stall`, + `non_linear_simonet_stall`, `non_linear_simonet_stall_newton_raphson` (they + raised `ImportError`). An unknown `gamma_loop_type` now raises `ValueError`. +- `Solver.compute_aerodynamic_quantities` no longer returns `Umagw`; the relative + velocity is available from `Solver.compute_relative_velocity(gamma)`. +- The Anderson loop no longer falls back to the base loop by default + (`anderson_fallback_to_base=True` restores it). + +### Added +- `gamma_loop_type="casadi_newton"`: Newton solve of the circulation residual + with an exact CasADi Jacobian, globalised by pseudo-transient continuation, + with fallback to the base loop (`newton_max_iterations`, + `newton_pseudo_time_step`, `newton_fallback_to_base`, `polar_interpolation`). + Requires the optional `casadi` package. +- `stagnation_patience` / `stagnation_rtol`: optional early stop of stagnating + circulation loops. +- `BodyAerodynamics(..., leg_direction="rib" | "streamwise" | "perpendicular")` + for the attached-trailed legs (default `"rib"`, unchanged). +- `results["drag_induced_trefftz"]`: Trefftz-plane induced drag as a far-wake + reference (uniform inflow only). +- `VSM.core.panel_kernels`: the section force law as functions over an `xp` + namespace (`numpy` or `casadi`): `relative_flow`, `quarter_chord_velocity`, + `direction_angle`, `panel_forces`, `attached_trailed_forces` and row helpers. + `compute_results` uses them itself. +- `BodyAerodynamics.compute_quarter_chord_AIC_matrices`: the induction of the + force-direction flow at the quarter chords, for callers that freeze it. +- `Solver.casadi_panel_force_function()`: per-panel forces as a CasADi function. + With `table_inputs=True` (also on the residual function) the polar tables are + inputs, so one graph serves every deformed shape; + `Solver.casadi_polar_table_inputs()` and `casadi_stall_angle_inputs()` return + them in the input layout. +- Documentation: aerodynamic model document (formulation, conventions, + validation) and the curved bound-vortex validation report. + +### Fixed +- Circulation loops stop on non-finite circulation instead of running on. +- `Solver`: SyntaxError in the pseudo-transient reject condition (hotfix on `main` + after 2.2.0, now also here). +- `Wing.compute_projected_area` no longer normalises the caller's + `z_plane_vector` in place. + +### Performance +- AIC assembly JIT-compiled with numba, then made allocation-free (vectors as + tuples): about 1 us -> 20 ns per filament evaluation, 7.3 -> 0.1 ms for a + 36-panel AIC. +- Curved bound-vortex correction computed once per shape and rotated under + rigid motion. +- Faster Li/Gaunaa artificial viscosity, vectorised force law, Trefftz drag and + projected area, cheaper `casadi_newton` residual calls. A 36-panel V3 + `casadi_newton` solve takes about 17 ms (about 50 ms before these changes). + ## [2.2.0] - 02/09/2026 Release cut from the `improve_plotting` branch. This is the version used to From b7debded311fd54bb268c1e15d283a5ff7259a5c Mon Sep 17 00:00:00 2001 From: ocayon Date: Wed, 4 Nov 2026 12:24:03 +0100 Subject: [PATCH 35/37] test(masure): skip the regression tests when the model files are absent The models in data/ml_models are git-ignored, so these six tests failed on every clean checkout, including CI. Skip the module when they are missing. test_masure_regression_requires_model_files checked data/models, a path that does not exist, so it was always skipped. The module-level check replaces it and that test now runs when the files are present. No source change. Test bug, no effect on results. Generated with Claude Code --- tests/AirfoilAerodynamics/test_masure.py | 14 ++++++++------ 1 file changed, 8 insertions(+), 6 deletions(-) diff --git a/tests/AirfoilAerodynamics/test_masure.py b/tests/AirfoilAerodynamics/test_masure.py index 76abfc7..f4e9148 100644 --- a/tests/AirfoilAerodynamics/test_masure.py +++ b/tests/AirfoilAerodynamics/test_masure.py @@ -6,6 +6,14 @@ from pathlib import Path from VSM.core.AirfoilAerodynamics import AirfoilAerodynamics +# The regression models are git-ignored, so they are absent on a clean checkout (CI). +pytestmark = pytest.mark.skipif( + not Path(__file__) + .parent.parent.parent.joinpath("data", "ml_models", "ET_re1e6.pkl") + .exists(), + reason="Real model files not available", +) + class TestMasureRegressionReal: """Test cases for masure_regression with real model file integration.""" @@ -196,12 +204,6 @@ def test_masure_regression_different_parameters( assert airfoil.CD is not None, f"CD should not be None for param set {i}" assert airfoil.CM is not None, f"CM should not be None for param set {i}" - @pytest.mark.skipif( - not Path(__file__) - .parent.parent.parent.joinpath("data", "models", "ET_re1e6.pkl") - .exists(), - reason="Real model files not available", - ) def test_masure_regression_requires_model_files( self, masure_params, small_alpha_range, test_reynolds, masure_config_path ): From f90a2da630a5232b4b3c6af9513eac7889c3a88b Mon Sep 17 00:00:00 2001 From: ocayon Date: Wed, 4 Nov 2026 12:40:05 +0100 Subject: [PATCH 36/37] docs(changelog): complete the 2.3.0 entry Name the chordwise thin-airfoil loading of the curved bound-vortex correction, a new modelling assumption. Add the anderson_max_iterations default, the new Panel leg methods and the SurfplanAdapter dependency, and set the release date. Documentation only, no effect on results. Generated with Claude Code --- changelog.md | 17 ++++++++++++----- 1 file changed, 12 insertions(+), 5 deletions(-) diff --git a/changelog.md b/changelog.md index 707ff01..18ccb51 100644 --- a/changelog.md +++ b/changelog.md @@ -4,7 +4,7 @@ All notable changes to this project will be documented in this file. The format is based on [Keep a Changelog](http://keepachangelog.com/) and this project adheres to [Semantic Versioning](http://semver.org/). -## [2.3.0] - 03/11/2026 +## [2.3.0] - 04/11/2026 **Default results change.** The lifting-line coupling now follows the consistent formulation of Gaunaa, Li & Pirrung (TORQUE 2026): circulation from the inner @@ -31,10 +31,14 @@ the `improve_plotting` branch, which had not been merged into `develop`/`main`. flow at the quarter chord (TAT3), with magnitudes from the 3/4-chord angle. `is_aoa_corrected=False` restores the 3/4-chord directions. - The quarter-chord flow includes the influence of a curved or swept bound - vortex through a chord-regularised correction (the actual minus a locally - unrolled vortex system). On-blade induced drag matches the Trefftz plane - within about 1 % on arc, swept and kite geometries, independently of the - panel count. It is computed once per shape and rotated under rigid motion. + vortex through a correction: the actual minus a locally unrolled vortex + system, with the bound vorticity and the leg starting points spread over the + chord using the flat-plate thin-airfoil loading `gamma(x) ~ sqrt((c - x)/x)` + (24 strips, effective cut-off 0.15 c, not a tuning parameter). This is a new + modelling assumption. The correction is zero on a straight wing with + perpendicular legs. On-blade induced drag matches the Trefftz plane within + about 1 % on arc, swept and kite geometries, independently of the panel + count. It is computed once per shape and rotated under rigid motion. - Drag acts along the local inner flow, not the global span axis. - `is_with_attached_trailed_vortex_force=True` by default: Kutta-Joukowski force on the chordwise attached trailed vortex segments (`F_attached_trailed_distribution` @@ -50,6 +54,7 @@ the `improve_plotting` branch, which had not been merged into `develop`/`main`. the full 3D relative velocity (the spanwise flow it models). - With `is_with_artificial_viscosity=True`, the regularization is also gated on negative stall. +- `anderson_max_iterations` default raised from 100 to 1000. - `Wing.preserve_section_order` (default False): skip the section re-sorting; `update_wing_from_points` sets it, since its arrays already define the arc order. @@ -64,6 +69,7 @@ the `improve_plotting` branch, which had not been merged into `develop`/`main`. velocity is available from `Solver.compute_relative_velocity(gamma)`. - The Anderson loop no longer falls back to the base loop by default (`anderson_fallback_to_base=True` restores it). +- `SurfplanAdapter` is now a required dependency. ### Added - `gamma_loop_type="casadi_newton"`: Newton solve of the circulation residual @@ -75,6 +81,7 @@ the `improve_plotting` branch, which had not been merged into `develop`/`main`. circulation loops. - `BodyAerodynamics(..., leg_direction="rib" | "streamwise" | "perpendicular")` for the attached-trailed legs (default `"rib"`, unchanged). +- `Panel.set_leg_end_points` and `Panel.reset_legs_to_ribs`. - `results["drag_induced_trefftz"]`: Trefftz-plane induced drag as a far-wake reference (uniform inflow only). - `VSM.core.panel_kernels`: the section force law as functions over an `xp` From a1322677247d154171777e4d6888dd8370da5a03 Mon Sep 17 00:00:00 2001 From: ocayon Date: Wed, 4 Nov 2026 12:56:25 +0100 Subject: [PATCH 37/37] docs(changelog): describe the circulation velocity as the effective velocity Say that the circulation uses the span-perpendicular effective velocity, including induction, and state the old formula in the same terms. Documentation only, no effect on results. Generated with Claude Code --- changelog.md | 14 ++++++++------ 1 file changed, 8 insertions(+), 6 deletions(-) diff --git a/changelog.md b/changelog.md index 18ccb51..cd1244e 100644 --- a/changelog.md +++ b/changelog.md @@ -7,8 +7,9 @@ and this project adheres to [Semantic Versioning](http://semver.org/). ## [2.3.0] - 04/11/2026 **Default results change.** The lifting-line coupling now follows the consistent -formulation of Gaunaa, Li & Pirrung (TORQUE 2026): circulation from the inner -velocity, span-perpendicular sections, quarter-chord force directions, +formulation of Gaunaa, Li & Pirrung (TORQUE 2026): circulation from the +effective velocity including induction, span-perpendicular sections, +quarter-chord force directions, attached-trailed-vortex forces and a chord-regularised curved bound vortex. Forces, moments and coefficients computed with the defaults differ from 2.2.0, most on swept and curved wings (kites). Each new default can be switched back @@ -19,10 +20,11 @@ This release also contains everything shipped in 2.2.0. `v2.2.0` was tagged on the `improve_plotting` branch, which had not been merged into `develop`/`main`. ### Changed (results) -- Circulation target is `Gamma = 0.5 |V_inner| c Cl` with the inner - (span-perpendicular, own-2D-induction-removed) velocity, instead of - `0.5 Umag^2 / Umagw c Cl`. On the V3 kite the old map put the circulation - 2-6 % low. +- Circulation target is `Gamma = 0.5 |V_eff| c Cl`, instead of + `0.5 |V_eff|^2 / |V_a| c Cl`. `V_eff` is the span-perpendicular effective + velocity: inflow plus induction, without the section's own 2D induction (the + inner velocity of Gaunaa et al.). `V_a` is the span-perpendicular inflow + without induction. On the V3 kite the old map put the circulation 2-6 % low. - Panel frame and chord follow the Crossflow Principle: the chord direction is perpendicular to the bound vortex, the normal is chord x span, and the panel chord is the perpendicular one. Unswept panels are unchanged; on swept panels

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From ee92398a56bc0596f4f2206be28ab5b395cbf3df Mon Sep 17 00:00:00 2001 From: ocayon Date: Tue, 13 Oct 2026 20:30:05 +0200 Subject: [PATCH 29/37] docs(validation): rewrite the curved bound-vortex report around the physics Narrative: Prandtl's straight wing as the exact baseline and why; curvature makes two line vortices at an angle induce an unbounded velocity on each other, hence the logarithm and the mesh drift; Li and Gaunaa avoid the quarter-chord point and assume the velocity constant along the chord and the legs perpendicular; a section is a chordwise sheet and two sheets at an angle see a finite velocity; the correction is the real wing as sheets minus the wing straightened at the section as sheets, added to Prandtl, so that curvature is isolated and the section's own field never enters; results against the Trefftz plane, a vortex lattice and RANS. Alternatives tested, strip-loading sensitivity, the leg study in detail and the implementation status move to appendices. 16 pages (was 19). Co-Authored-By: Claude Fable 5.1 --- .../validation/curved_bound_vortex_report.pdf | Bin 2320004 -> 2294879 bytes .../validation/curved_bound_vortex_report.tex | 438 +++++++++--------- 2 files changed, 211 insertions(+), 227 deletions(-) diff --git a/docs/validation/curved_bound_vortex_report.pdf b/docs/validation/curved_bound_vortex_report.pdf index 6495eac25416e1d938a8d921c72e3d5f282a4071..4488902b397d28cb10dce86a938ac6b7c4a77d62 100644 GIT binary patch delta 259055 zcmagGbzD?i`#vlw-HpHi(lx~}L$?wlUDDklt-t`%APOT4-O?Z+AR#4^Dxic&Nr%!U zDCj$k&pDp+JiqVf{bM$JuYIq(Ryo&okCE>l;(U%x#CfcPY9?lsvM~b!f!3E7pUaE= z<;Cst;(U4W_`6N=^3Dth#e9H3?aRwuR5u|loA2c@Xr|A zqNqseP>;#U5PvNFWds}EUl0GMMeNWavBt3;V}tqs?e(w0`<=&sI*4t-&bq%e{b|8Y zBLg%L`m2+}rA};MSY6mVtfzl^Vg#^bk8Qzf#Rg!D62zCrgNlMt z&iGs?Bn1H>R=p?cGbs~ForngtP04uuzen`a+Mif{&mq(tg$Qbdn1mMl0&Cze?=Gi4 zE2;Y*ACs*aP`h}HIM^3B*k!}Iuwc! zK!tsWbp>nN7u8Dy#uFC>p}rGc#ziTNeTR(%s~bCc|MC#~fL$M0?;TMwWN4HxF$-!G 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zr3Sb_6O;pkQ5VP!C`Cv(#(m}`<|pCl=*kL?KH$iUayW442Detx1i`5lZGLd>TqZP_ zexZ^S;PH3H2K4`DelXHs<}@S8AE5(gwTqpG;WJ>uMj*hmG>jA- zxeKSgF*Fo>!3CLWK^wWX%|m=c!C$}$7=IZ_Yjz~4a8e&N#W1=CL=7Hbf s(1kN180$g*{}Oiyd_5;3(lb1ASGbQaHy(U@2an~XaD#vBwK3)XKioUy4FCWD diff --git a/docs/validation/curved_bound_vortex_report.tex b/docs/validation/curved_bound_vortex_report.tex index 5d35793..14a8446 100644 --- a/docs/validation/curved_bound_vortex_report.tex +++ b/docs/validation/curved_bound_vortex_report.tex @@ -13,20 +13,20 @@ \setlength{\parindent}{0pt} \title{On-blade induced drag of curved lifting lines in the Vortex Step Method:\\ problem statement, literature, and a parameter-free regularisation} -\author{Working document, awegroup/Vortex-Step-Method, branch \texttt{feature/curved-bound-vortex-regularisation}} -\date{17 September 2026 (rebuilt 12 October 2026)} +\author{Working document, awegroup/Vortex-Step-Method, \texttt{develop}} +\date{17 September 2026, revised 13 October 2026} \begin{document} \maketitle \begin{abstract} -The \texttt{develop} branch of the Python Vortex Step Method (VSM) was aligned with the coupling rules of Gaunaa, Li and Pirrung (TORQUE 2026): force magnitudes from the three-quarter-chord flow, force directions from the quarter-chord flow, and a Kutta--Joukowski force on the attached-trailed vortex legs. With these rules the on-blade induced drag equals the Trefftz-plane value exactly on straight wings, but on the TU~Delft V3 kite it is 7--15\,\% low and decreases without bound as the number of spanwise panels increases. This document states the problem, identifies its cause (the logarithmically singular self-induction of the curved bound vortex, evaluated on its own line to set the force direction, entering the drag through $\rho\Gamma\,u\sin\alpha$), reviews how the literature treats the singularity, tests the two published remedies inside the VSM framework, and describes the parameter-free regularisation now implemented: the quarter-chord velocity is built from the classical lifting-line downwash of the wing unrolled onto the local tangent line, plus the difference between the actual and the unrolled vortex systems with the bound vorticity and the leg starting points spread chordwise with the thin-airfoil distribution. The result is identically zero on straight wings, mesh-independent, and within 1\,\% of the Trefftz-plane induced drag on an arc wing, a swept wing, the swept--anhedral elliptic wing of Gaunaa et al., and the V3 kite. All tables are reproduced by \texttt{docs/validation/curved\_bound\_vortex\_validation.py}. +The \texttt{develop} branch of the Python Vortex Step Method (VSM) was aligned with the coupling rules of Gaunaa, Li and Pirrung (TORQUE 2026): force magnitudes from the three-quarter-chord flow, force directions from the quarter-chord flow, and a Kutta--Joukowski force on the attached-trailed vortex legs. With these rules the on-blade induced drag equals the Trefftz-plane value exactly on straight wings, but on the TU~Delft V3 kite it is 7--15\,\% low and decreases without bound as the number of spanwise panels increases. This document states the problem, identifies its cause (the logarithmically singular self-induction of the curved bound vortex, evaluated on its own line to set the force direction, entering the drag through $\rho\Gamma\,u\sin\alpha$), reviews how the literature treats the singularity, tests the two published remedies inside the VSM framework, and describes the parameter-free regularisation now implemented: the quarter-chord velocity is built from the classical lifting-line downwash of the wing unrolled onto the local tangent line, plus the difference between the actual and the unrolled vortex systems with the bound vorticity and the leg starting points spread chordwise with the thin-airfoil distribution. The result is identically zero on straight wings, mesh-independent, and within 1\,\% of the Trefftz-plane induced drag on an arc wing, a swept wing, the swept--anhedral elliptic wing of Gaunaa et al., and the V3 kite. A second part settles the direction of the attached-trailed legs, which the theory leaves open, against a vortex-lattice referee: the paper's perpendicular legs lose 8--9\,\% of the lift on kinked and kite-like wings, legs along the ribs or along the flow reproduce the lifting-surface lift within 1\,\%. All tables are reproduced by the scripts in \texttt{docs/validation}. \end{abstract} \section{Status of the implementation with respect to Li and Gaunaa} \label{sec:status} -The \texttt{develop} branch (commits \texttt{233a238}\ldots\texttt{62c53af}) implements the following elements of Gaunaa, Li and Pirrung~\cite{gaunaa2026} and Li, Gaunaa, Pirrung and L{\o}nb{\ae}k~\cite{li2026}: +Since the September 2026 commits (\texttt{233a238}\ldots\texttt{62c53af}) the code implements the following elements of Gaunaa, Li and Pirrung~\cite{gaunaa2026} and Li, Gaunaa, Pirrung and L{\o}nb{\ae}k~\cite{li2026}: \begin{itemize}[nosep] \item CP1: the inner 2D velocity is the component perpendicular to the local quarter-chord line, and the chord is measured perpendicular to that line; \item TAT1: the section's own 2D bound-vortex induction is subtracted at the three-quarter-chord point (the VSM \texttt{subtract\_bound\_2D} term, which the code has had since its inception); @@ -124,6 +124,7 @@ \subsection{Other approaches} \begin{itemize}[nosep] \item \emph{Li et al.\ 2018}~\cite{li2018}: correct a straight-blade model by the difference between the curved and an imaginary straight bound vortex. Same subtraction idea as below, but with single filaments, hence mesh dependent; abandoned in~\cite{li2020}. \item \emph{Guermond 1990}~\cite{guermond1990}: matched-asymptotic lifting-line theory for curved and swept wings. Shows analytically that the curvature term is finite once the inner (airfoil-scale) problem is accounted for, using Hadamard finite-part integrals. It is the theoretical basis for a chord-scale cut-off but is not a numerical scheme with horseshoes and polars. + \item \emph{Each segment minus its own infinite line, at the quarter chord.} The natural extension of TAT1 to the neighbours: for every panel $j$ subtract from its finite bound segment the infinite line through it. It works for the own section at the three-quarter chord, where the point is half a chord from the line, and fails at the quarter-chord point, which lies at a distance from a neighbour's line that shrinks with the square of the arc-length separation: the infinite-line term then grows like one over the panel width squared. On the arc wing the mid-span sum goes $-27$, $-110$, $-448$, $-1805$ at 20, 40, 80, 160 panels, against $+0.075$ to $+0.117$ for the segments alone. Tested here, not usable. \item \emph{Vortex core on the bound vortex} (e.g.\ QBlade~\cite{qblade}, core radius a fraction of chord): Reid and Hunsaker note these are ``very sensitive to the cutoff/core distance''. Tested here with the code's Vatistas kernel: the projection of an on-line point to the core boundary produces spurious velocities of order $\Gamma/(4\pi\epsilon)$ and unusable results. \item \emph{Three-quarter-chord directions} (Weissinger, Ranneberg~\cite{ranneberg2015}, the VSM default before the \texttt{develop} branch): no singularity, but the induced drag is overestimated by 20--40\,\% on the V3~\cite{gaunaa2026}. \item \emph{Trefftz-plane drag only} (Ranneberg): exact for the total in steady uniform inflow, unavailable with body rates or distributed inflow, no spanwise distribution. @@ -149,7 +150,7 @@ \subsection{Formulation} \label{fig:spread} \end{figure} -For each evaluation panel $i$, the \emph{unrolled} reference wing is built on the tangent line $\mathbf t_i$ of panel $i$ through $\mathbf P_i$: every node keeps its arc-length coordinate along the bound line, the legs are perpendicular to the line in panel $i$'s chord direction with the panel's own chord length, and the wake keeps its direction. The quarter-chord velocity is then +For each evaluation panel $i$, the \emph{unrolled} reference wing is built on the tangent line $\mathbf t_i$ of panel $i$ through $\mathbf P_i$: every node keeps its arc-length coordinate along the bound line, the legs are perpendicular to the line in panel $i$'s chord direction, each with its own panel's chord length, and the wake keeps its direction. There is one such reference wing per evaluation panel. The quarter-chord velocity is then \begin{equation} \boxed{\; \mathbf V_{1/4,i}=\mathbf V_\infty+\sum_j\Gamma_j\Big[\mathbf K^{\mathrm{LL}}_{j,\mathrm{unrolled}(i)}(\mathbf P_i) @@ -158,6 +159,29 @@ \subsection{Formulation} \end{equation} Figure~\ref{fig:unroll} shows the construction. The first term is Prandtl's classical downwash of the straight wing with the actual $\Gamma(s)$, exact for straight wings (ratio 1.000). The bracket is the curvature, sweep and skew effect; it is identically zero on a straight wing with perpendicular legs, finite because both sheets regularise the near field at the chord scale, and convergent because no filament is evaluated on its own line. The semi-infinite wake filaments cancel identically between the actual and unrolled systems, so the wake model plays no role. Nothing else changes: the three-quarter-chord magnitude (which already contains the LL-mod term of~\cite{li2020}), the circulation map, the AT force and the wake are untouched. The single-filament limit of the bracket recovers the curved-minus-straight idea of~\cite{li2018}; the chordwise spreading is the discrete counterpart of the inner solution in~\cite{guermond1990}; the local straightening is the mechanism of~\cite{reid2020} without its two empirical lengths. The effective cut-off implied by the distribution is $\exp\langle\ln|x-c/4|\rangle_\gamma=0.1515\,c$; the number of strips does not matter beyond $M\approx 20$ (24 and 32 strips give the same arc self-induction to three digits). Implementation: \texttt{assemble\_curved\_bound\_correction\_AIC} in \texttt{src/VSM/core/utils.py}, called from \texttt{BodyAerodynamics.update\_effective\_angle\_of\_attack\_if\_VSM}; about 0.5\,s at 50 panels and 1\,s at 80. The matrix depends on the panel geometry only, so it is computed once per shape and reused for every inflow and circulation; a body that is the cached shape up to a rigid rotation and translation (a trim that rotates the kite for every residual evaluation) reuses the stored matrix rotated, and only a deformation recomputes it. +\subsection{Reading of the formulation} +\label{sec:reading} +Three remarks make eq.~\eqref{eq:fix} less opaque than it looks. + +\emph{The rule is the one the VSM already uses at the three-quarter chord.} The outer problem is the inviscid vortex system, the inner problem the 2D section with its polar, and the coupling hands the inner model the flow it does not already contain. A 2D section is an infinite straight wing: an infinitely long straight bound sheet along the chord with a straight wake. At the three-quarter chord the own infinite bound vortex is subtracted (TAT1) because the polar has it; on a straight wing the neighbours are collinear with that infinite vortex and add nothing, and the whole trailed system stays in because the 2D model has none of it. At the quarter chord the same subtraction is made: the own straight continuation is the unrolled wing, the section's tangent line with the neighbours laid on it, so ``real minus unrolled'' is ``3D minus what the profile already knows about itself and its straight continuation'', applied to the whole system. On a straight wing the two coincide and nothing is handed over beyond Prandtl's downwash. + +\emph{The sheet is what the profile is made of, not a numerical device.} The three-quarter-chord sums converge (Table~\ref{tab:cpconv}): the control point is half a chord from every filament, the lumped vortex at the quarter chord with the control point at the three-quarter chord reproduces thin-airfoil lift exactly (Pistolesi), and a sheet there would change that equivalence without regularising anything. The quarter-chord point lies on the line, and there the neighbours sit at a fraction of a chord. What is there, in the inner model's own terms, is the neighbour's chordwise sheet, bent slightly out of the section's plane; two sheets at a small angle induce a finite velocity on each other, two lines do not. Spreading the bound vorticity with the thin-airfoil distribution therefore uses, for the neighbours, the vorticity the inner model already uses for the section itself; the cut-off $0.15\,c$ is that distribution's, not a choice. The unrolled system is spread with the same strips so that collinear neighbours, which are the own 2D vortex, cancel exactly. The first term of eq.~\eqref{eq:fix} is left as single filaments because it is Prandtl's exact downwash of the straight wing, which spreading the leg starts would alter; the spreading enters only through the difference, which is zero wherever the wing is straight. + +\emph{The two sheet terms are the same panel in two positions.} $\mathbf K^{\mathrm{sheet}}_j$ is panel $j$ where it is, on the curved line, with its legs along its rib; $\mathbf K^{\mathrm{sheet}}_{j,\mathrm{unrolled}(i)}$ is the same panel with the same strips laid on panel $i$'s tangent at the same arc-length distance, with its leg in panel $i$'s chord direction. Biot--Savart depends on where a segment is and how it is oriented with respect to $\mathbf P_i$, so the two differ wherever the wing is curved: by little for the neighbours, whose two positions almost coincide (Figure~\ref{fig:unroll}d), and by the whole curvature effect for the far panels. Nothing singular is ever subtracted from anything singular. + +\begin{table}[h]\centering\small +\caption{Why the three-quarter chord needs no sheet. Arc wing, mid-span panel, unit circulation on every other panel, bound segments as single filaments: the normal component at the control point converges (the neighbours build up the infinite-line value $1/(2\pi\cdot c/2)=0.318$ that TAT1 subtracts); the chordwise component at the quarter-chord point adds a constant per doubling.} +\label{tab:cpconv} +\begin{tabular}{lccccc} +\toprule +panels & 20 & 40 & 80 & 160 & 320\\ +\midrule +at the 3/4-chord control point, normal & 0.198 & 0.252 & 0.282 & 0.297 & 0.305\\ +at the 1/4-chord point, chordwise & 0.075 & 0.089 & 0.103 & 0.117 & 0.130\\ +\bottomrule +\end{tabular} +\end{table} + \begin{figure}[p]\centering \includegraphics[width=\textwidth]{14_unrolling_per_panel.png} \caption{What ``unrolling'' means (\texttt{docs/validation/unrolling\_figure.py}). For an evaluation panel $i$ (star) the reference wing is built on panel $i$'s own tangent line through its aerodynamic centre: every node keeps its arc-length distance from the panel, the legs are perpendicular to the line in panel $i$'s chord direction with each panel's own chord, and the wake keeps its direction. There is one such reference wing per panel. (a, b) The arc wing with the references of a mid-span panel (blue) and a panel near the tip (red): the two straight wings are different, each tangent at its own panel. (c) The kinked swept wing seen from above, with the reference of a panel on the right half: the whole wing, including the other half, is laid along that panel's line, and the legs follow that panel's chord direction. (d) The distance between the actual and the unrolled nodes against their arc-length distance from the evaluation panel, for the arc wing and the V3: within a leg length the two systems coincide to second order, so the singular near field cancels in the difference of eq.~\eqref{eq:fix}; what remains is the far-field effect of the curvature, finite once both systems are spread over the chord.} @@ -165,6 +189,7 @@ \subsection{Formulation} \end{figure} \subsection{Verification against the Trefftz plane} +Table~\ref{tab:fix} repeats Table~\ref{tab:conv} with eq.~\eqref{eq:fix} in place: the ratio is 1.000 on the straight wing, within 1\,\% on the arc and the V3 at every panel count, and no longer drifts. \begin{table}[h]\centering\small \caption{On-blade over Trefftz-plane induced drag with eq.~\eqref{eq:fix}, inviscid polars (\texttt{curved\_bound\_vortex\_validation.py}).} @@ -178,14 +203,14 @@ \subsection{Verification against the Trefftz plane} swept $30^\circ$, streamwise ribs & -- & -- & 0.971 & 0.982 & 0.988\\ circular arc, $110^\circ$, $R=4c$ & 1.008 & 1.001 & 0.999 & 0.999 & 0.999\\ elliptic, 10\,\% sweep, 25\,\% anhedral, rib legs & -- & -- & 1.014 & 1.015 & 1.017\\ -elliptic, same, perpendicular legs & -- & -- & 1.024 & 1.024 & --\\ +elliptic, same, perpendicular legs & -- & -- & 1.025 & 1.024 & 1.020\\ V3 kite, rib legs & -- & 1.011 & 1.007 & 1.008 & 1.010\\ -V3 kite, perpendicular legs & -- & -- & 1.042 & 1.038 & --\\ +V3 kite, perpendicular legs & -- & -- & 1.015 & 1.018 & crosses\\ \bottomrule \end{tabular} \end{table} -Two residuals remain and are unrelated to the bound vortex: the swept wing converges to 0.99 rather than 1.00, and the straight wing with skewed ribs sits at 1.03 with or without the fix. Both point to the attached-trailed force on non-perpendicular legs and are a separate, smaller item. The 4\,\% excess with perpendicular legs on the V3 is likewise not caused by the bound-vortex term (it is the same with the bound segments on the line). +Two residuals remain and are unrelated to the bound vortex: the swept wing converges to 0.99 rather than 1.00, and the straight wing with skewed ribs sits at 1.03 with or without the fix. Both point to the attached-trailed force on legs that are not aligned with the flow and are a separate, smaller item, taken up in Section~\ref{sec:legs}. The perpendicular-leg rows use the construction of Section~\ref{sec:legs}; on the V3 it cannot be built above 80 panels. \subsection{Direction of the attached-trailed legs} \label{sec:legs} @@ -291,6 +316,7 @@ \section{Assessment and open items} \begin{itemize}[nosep] \item The mechanism of the fix (straighten locally, regularise the legs, keep the far field) is that of Reid and Hunsaker~\cite{reid2020}; the difference-form goes back to Li et al.~\cite{li2018}. The contribution here is the replacement of the two empirical lengths by the thin-airfoil chordwise distribution, which fixes the cut-off at $0.15\,c$ from theory, and the demonstration that this yields Trefftz-consistent induced drag on curved kites. It should be presented as such, with~\cite{reid2020,li2020,guermond1990} cited. \item To be confirmed with the authors of~\cite{gaunaa2026,li2020}: how the curved bound-vortex influence is applied at the quarter chord in their code, and how it behaves when the number of sections is doubled. + \item With body rates the apparent velocity is built at the control points and the same array feeds the quarter-chord direction and the attached-trailed force; the rotational term's variation along the chord, $\omega\times(\mathbf r_{1/4}-\mathbf r_{3/4})$, is the effective torsional rate $T_0\dot\theta$ of Li, Gaunaa and Pirrung~\cite{li2026wes}, whose coned-blade benchmark shows it worth 4\,\% of power at $10^\circ$ cone. On the V3 at 20\,m/s and a yaw rate of 0.3\,rad/s the local angle error reaches $0.8^\circ$ at the tips while the total drag changes 0.6\,\%, the error being antisymmetric across the span; the yawing moment is affected. To fix: evaluate the apparent velocity at the aerodynamic centre for the direction and at the leg points for the attached-trailed force. \item Settled with a referee (Section~\ref{sec:legs}): the paper's perpendicular legs are rejected; rib legs stay the default, streamwise legs are available. A streamwise construction with the local inflow direction per node would remove the mean-direction limitation. Open: the attached-trailed force on legs that are not aligned with the flow (kinked wing 0.98, skewed ribs 1.03, streamwise legs on the arc 1.035), and a V3 referee with the exact skewed tips (AeroSandbox unskews them). Not quantified: the section polars are rib-section polars while CP1 applies them in the span-perpendicular plane. \end{itemize} @@ -298,6 +324,7 @@ \section{Assessment and open items} \bibitem{gaunaa2026} M.~Gaunaa, A.~Li, G.~R.~Pirrung, From thin airfoil theory to finite wings: consistent implementation of Lifting Line-based models, J.\ Phys.: Conf.\ Ser.\ 3224 (2026) 042030. \bibitem{appendix2026} M.~Gaunaa, A.~Li, G.~R.~Pirrung, Internet appendix for ``From thin airfoil theory to finite wings'', Zenodo, doi:10.5281/zenodo.18222326 (2026). \bibitem{li2026} A.~Li, M.~Gaunaa, G.~R.~Pirrung, K.~L{\o}nb{\ae}k, Relaxation limits and artificial viscosity for lifting line methods, TORQUE 2026. +\bibitem{li2026wes} A.~Li, M.~Gaunaa, G.~R.~Pirrung, Unsteady airfoil aerodynamics in attached flow: from unsteady thin-airfoil theory to wind turbine implementation, Wind Energ.\ Sci.\ Discuss., doi:10.5194/wes-2026-168 (2026). Reference implementation: doi:10.5281/zenodo.22793702. \bibitem{li2020} A.~Li, M.~Gaunaa, G.~R.~Pirrung, N.~Ramos-Garc\'ia, S.~G.~Horcas, The influence of the bound vortex on the aerodynamics of curved wind turbine blades, J.\ Phys.: Conf.\ Ser.\ 1618 (2020) 052038. \bibitem{li2018} A.~Li, G.~Pirrung, H.~Aa.~Madsen, M.~Gaunaa, F.~Zahle, Fast trailed and bound vorticity modeling of swept wind turbine blades, J.\ Phys.: Conf.\ Ser.\ 1037 (2018) 062012. \bibitem{reid2020} J.~T.~Reid, D.~F.~Hunsaker, A general approach to lifting-line theory, applied to wings with sweep, J.\ Aircraft 58 (2021), doi:10.2514/1.C035994. From 3130ba2bb2bc968c650a9c2c09daf489fb663245 Mon Sep 17 00:00:00 2001 From: ocayon Date: Tue, 13 Oct 2026 15:59:59 +0200 Subject: [PATCH 26/37] docs(validation): why sheets converge where lines do not, and the hypothesised LL-Gaunaa term Report Section 4.2: derivation of the velocity two line vortices meeting at a kink induce on each other (Gamma (1 - cos theta) / (4 pi r sin theta), unbounded at the kink), its sum over a curved line (the logarithm of the span over the panel width) and the same sum for chord-spread sheets (the logarithm of the span over 0.15 c, mesh-independent), with figure 16 from docs/validation/kink_figure.py. Report Section 3.1: the form that reproduces the published behaviour of LL-Gaunaa, curved-minus-straight bound segments as single filaments at the three-quarter-chord control point reused at the quarter chord, is now implemented in the validation script (--hypothesis) and tabulated: it is mesh-independent and within 1-2 % of the Trefftz plane with the paper's perpendicular legs, and fails with rib legs on the V3 (0.81 -> 0.74) and the kinked wing, because skewed legs carry their own logarithm that a bound-only difference cannot see. Open item and status updated accordingly. Co-Authored-By: Claude Fable 5.1 --- docs/figures/16_kink_line_vs_sheet.png | Bin 0 -> 166504 bytes docs/figures/README.md | 9 ++ .../validation/curved_bound_vortex_report.pdf | Bin 2177691 -> 2315629 bytes .../validation/curved_bound_vortex_report.tex | 42 +++++- .../curved_bound_vortex_validation.json | 134 ++++++++++++++++++ .../curved_bound_vortex_validation.py | 60 ++++++++ docs/validation/kink_figure.py | 78 ++++++++++ 7 files changed, 321 insertions(+), 2 deletions(-) create mode 100644 docs/figures/16_kink_line_vs_sheet.png create mode 100644 docs/validation/kink_figure.py diff --git a/docs/figures/16_kink_line_vs_sheet.png b/docs/figures/16_kink_line_vs_sheet.png new file mode 100644 index 0000000000000000000000000000000000000000..e58cd05e373ab2f08dc620cd0a23d0e2c123086b GIT binary patch literal 166504 zcmeFZcQ~Bw*DkC@7bQd|NJ5ITKwy5nQ(;pyP&BFMwf$0PXo zj=h(co2LXXFXVq;!Q<*-$NTDDT@1Jjk(-L4Cl(eh73KrmE_+lP3mXgTnSz|IU&i+Q 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zM3Iiwk-$a#_DFeOKBaZ4jV0zBEAU+8Oe525m$#*S31O@co|QIf$UITv`DRPOp@QlA3mhN0qdw~Epz6B%q-4loypjAe3291RYG-h%u}gsZ_dvH-Uv&(p_I#g zB^eT;=7u#mXsS^`%c|U(fcVZ?+Db+WqM-yZmlfC8ekbVQYX-UIvw{NeRU`n`*Kt4L zA)H2cV_bpMoiU!y{n>H_WG(vCVrnH%5w%so54}3PLFdzAd-4ALy$<$+1RESpy;}-x zMlO?<6$Ws8qKB_DZx-KKoNsuQtt~KA3J;Euq~Zwzwb!TGrDvnviR4VQmZ`};Cqh}? z1Tkae9SmG~cMX$tcU-vdY4Y__9aW@HzP^tQU6N5e&EWLpPt9nW1gGvM3SsBAXAW*jr;eRfn{*}V#|M>=vEFX(YjtT8I UpUWg8N(QX;Th Date: Thu, 8 Oct 2026 14:49:51 +0200 Subject: [PATCH 19/37] fix(solver): restore the reject condition broken by 1105122 (SyntaxError) 1105122 (Copilot Autofix, "Refactor ratio and gate condition") replaced five lines with one: it kept the new ratio expression but deleted the crossed_gate assignment and the opening `if not finite(trial) or (` with its condition, leaving a bare `):` at Solver.py:1447. Every `import VSM` on main raised SyntaxError: unmatched ')', so every fresh install of a package that depends on VSM@main (AWETrim) failed. Restores the condition and keeps the autofix's intended change: a trial with exactly zero residual now has ratio = inf (accepted) instead of 0 (rejected). (cherry picked from commit beb0a4fee9686a6519f328b6ceac57d3fec50fc9) --- src/VSM/core/Solver.py | 4 ++++ 1 file changed, 4 insertions(+) diff --git a/src/VSM/core/Solver.py b/src/VSM/core/Solver.py index 8b7457e..576f3ba 100644 --- a/src/VSM/core/Solver.py +++ b/src/VSM/core/Solver.py @@ -1444,6 +1444,10 @@ def finite(state): trial = evaluate(current["x"] + direction) evaluations += 1 ratio = np.inf if finite(trial) and norm(trial) == 0 else (norm(current) / norm(trial) if finite(trial) else 0.0) + crossed_gate = finite(trial) and trial["gate"] != current["gate"] + if not finite(trial) or ( + ratio < self._newton_reject_ratio + and not (crossed_gate and dt <= dt_restart) ): # Residual grew too much: reject and shrink. EXCEPT across # the viscosity gate, the residual's one discontinuity: From 2644b5cae82638484ec2ed9ccc5f191be619c4ff Mon Sep 17 00:00:00 2001 From: ocayon Date: Mon, 12 Oct 2026 22:10:20 +0200 Subject: [PATCH 20/37] perf(solver): compute the curved bound-vortex correction once per geometry The quarter-chord correction (assemble_curved_bound_correction_AIC) depends on the panel geometry only: the wake terms cancel between the actual and the unrolled systems and the inflow speed does not change the result (bit identical on the V3 at 10, 20 and 40 m/s). It costs about 0.5 s at 50 panels and was rebuilt on every solve, which multiplied in a coupled aerostructural trim that solves one deformed geometry hundreds of times (231 s against 60 s for one LEI-V3 wireframe case with the old force directions). It is now cached on a hash of the arrays the kernel reads (evaluation and bound points, leg ends, chord directions, chords) plus the chord fractions, so a rebuild, a rotation, a moved point or a changed leg construction invalidates it; a solve on an unchanged geometry takes about 0.1 s at 54 panels. Results are unchanged. Test: one kernel evaluation for two inflows on the same panels, identical results to a fresh body, and a recomputation after a rotation. Suite: 183 passed, 5 skipped. Co-Authored-By: Claude Fable 5.1 --- docs/Solver.md | 6 ++- src/VSM/core/BodyAerodynamics.py | 48 ++++++++++++++----- .../test_curved_bound_vortex.py | 36 ++++++++++++++ 3 files changed, 77 insertions(+), 13 deletions(-) diff --git a/docs/Solver.md b/docs/Solver.md index 489788f..4007ede 100644 --- a/docs/Solver.md +++ b/docs/Solver.md @@ -264,7 +264,11 @@ non-uniform grid (the paper derives it for uniform rectangular wings). identically zero on straight wings, has no tunable length (the distribution fixes the cut-off at 0.15 c), and brings the on-blade induced drag within 1% of the Trefftz plane on an arc wing, the V3 and the paper's swept-anhedral - elliptic wing at every resolution (figure 08). It shares its mechanism with + elliptic wing at every resolution (figure 08). The correction depends on + the panel geometry only, so it is computed once per geometry (about 0.5 s at + 50 panels) and reused for every inflow and circulation until the panels are + rebuilt or moved; a coupled trim that solves one deformed shape hundreds of + times pays for it once. It shares its mechanism with the effective-lifting-line method of Reid & Hunsaker (2020), whose two empirical lengths it replaces. On the V3 it raises the drag by about 5% of the induced drag at 10 deg, onto the RANS value (figure 09). diff --git a/src/VSM/core/BodyAerodynamics.py b/src/VSM/core/BodyAerodynamics.py index 3255ae0..cf199ee 100644 --- a/src/VSM/core/BodyAerodynamics.py +++ b/src/VSM/core/BodyAerodynamics.py @@ -1,3 +1,4 @@ +import hashlib import numpy as np import logging import pandas as pd @@ -2139,21 +2140,44 @@ def update_effective_angle_of_attack_if_VSM( [panel.TE_point_2 for panel in self.panels], dtype=float ) chords = np.ascontiguousarray([panel.chord for panel in self.panels], dtype=float) - strip_x, strip_w = thin_airfoil_strips() - AIC_corr = assemble_curved_bound_correction_AIC( - eval_points, - bound_point_1, - bound_point_2, - TE_point_1, - TE_point_2, - np.ascontiguousarray(y_airf_array, dtype=float), - chords, - np.ascontiguousarray(va_norm_array, dtype=float).ravel(), + chord_dir = np.ascontiguousarray(y_airf_array, dtype=float) + # The correction depends on the panel geometry only (the wake terms + # cancel between the actual and the unrolled systems, and the leg core + # radius has no measurable effect), so it is computed once per + # geometry and reused for every inflow and circulation. A coupled + # trim solves the same deformed geometry hundreds of times; the + # kernel costs about 0.5 s at 50 panels. The key hashes the arrays + # the kernel reads, so any rebuild or moved point invalidates it. + key = ( float(self._aerodynamic_center_location), float(core_radius_fraction), - strip_x, - strip_w, + hashlib.sha1( + b"".join( + a.tobytes() + for a in (eval_points, bound_point_1, bound_point_2, TE_point_1, TE_point_2, chord_dir, chords) + ) + ).hexdigest(), ) + cache = getattr(self, "_curved_bound_cache", None) + if cache is not None and cache[0] == key: + AIC_corr = cache[1] + else: + strip_x, strip_w = thin_airfoil_strips() + AIC_corr = assemble_curved_bound_correction_AIC( + eval_points, + bound_point_1, + bound_point_2, + TE_point_1, + TE_point_2, + chord_dir, + chords, + np.ascontiguousarray(va_norm_array, dtype=float).ravel(), + float(self._aerodynamic_center_location), + float(core_radius_fraction), + strip_x, + strip_w, + ) + self._curved_bound_cache = (key, AIC_corr) AIC_x = AIC_x + AIC_corr[0] AIC_y = AIC_y + AIC_corr[1] AIC_z = AIC_z + AIC_corr[2] diff --git a/tests/BodyAerodynamics/test_curved_bound_vortex.py b/tests/BodyAerodynamics/test_curved_bound_vortex.py index d84b44a..6e399e8 100644 --- a/tests/BodyAerodynamics/test_curved_bound_vortex.py +++ b/tests/BodyAerodynamics/test_curved_bound_vortex.py @@ -86,3 +86,39 @@ def test_arc_wing_ratio_is_mesh_independent(): r40 = _ratio(_arc(40)) r80 = _ratio(_arc(80)) assert abs(r80 - r40) < 3e-3 + + +def test_curved_bound_correction_is_cached_per_geometry(): + """The quarter-chord correction depends on the geometry only: a second + inflow on the same panels reuses it, a moved geometry recomputes it.""" + import VSM.core.BodyAerodynamics as BA + + calls = [] + original = BA.assemble_curved_bound_correction_AIC + + def counting(*args, **kwargs): + calls.append(1) + return original(*args, **kwargs) + + BA.assemble_curved_bound_correction_AIC = counting + try: + body = _arc(16) + solver = Solver(allowed_error=1e-7, max_iterations=4000) + body.va_initialize(10.0, 8.0, 0.0) + r1 = solver.solve(body) + body.va_initialize(20.0, 4.0, 5.0) + r2 = solver.solve(body) + assert len(calls) == 1, "same geometry, different inflow: one kernel evaluation" + # a fresh body with the same geometry gives the same answer as the cached one + body_ref = _arc(16) + body_ref.va_initialize(20.0, 4.0, 5.0) + r_ref = solver.solve(body_ref) + assert np.isclose(r2["cl"], r_ref["cl"], rtol=1e-12) + assert np.isclose(r2["cd"], r_ref["cd"], rtol=1e-12) + # moving the geometry invalidates the cache + body.rotate(angle_deg=5.0, axis=[0.0, 1.0, 0.0]) + body.va_initialize(20.0, 4.0, 5.0) + solver.solve(body) + assert len(calls) == 3 + finally: + BA.assemble_curved_bound_correction_AIC = original From 0e5a67f0a8a4353d08f37cfc1c54c1385c7b617a Mon Sep 17 00:00:00 2001 From: ocayon Date: Mon, 12 Oct 2026 22:23:43 +0200 Subject: [PATCH 21/37] perf(solver): reuse the curved bound-vortex correction under rigid motion A trim that rotates the body for every residual evaluation (AWETrim's quasi-steady trim) rebuilds the panels each time, so the per-geometry cache of 2644b5c never hit: profiling one LEI-V3 coupled case showed the kernel on all 280 solves, 135 s of 222 s. The cache now stores the evaluation, bound and leg-end points, the chord directions and chords of the computed geometry; when the current panels are that geometry up to a rigid rotation and translation (Kabsch fit, residual below 1e-9 of the size), the stored matrix is rotated instead of rebuilt, since its entries are velocity vectors that rotate with the body. A different shape recomputes. Test: one kernel evaluation for a rotated body, the same lift and drag as a body built in the rotated position, and a recomputation after a trailing-edge point is moved. Suite: 183 passed, 5 skipped. Co-Authored-By: Claude Fable 5.1 --- src/VSM/core/BodyAerodynamics.py | 99 ++++++++++++------- .../test_curved_bound_vortex.py | 21 +++- 2 files changed, 84 insertions(+), 36 deletions(-) diff --git a/src/VSM/core/BodyAerodynamics.py b/src/VSM/core/BodyAerodynamics.py index cf199ee..4eaf8ac 100644 --- a/src/VSM/core/BodyAerodynamics.py +++ b/src/VSM/core/BodyAerodynamics.py @@ -1,4 +1,3 @@ -import hashlib import numpy as np import logging import pandas as pd @@ -20,6 +19,25 @@ from . import jit_cross, jit_norm, jit_dot +def _rigid_rotation_between(points_0, points_1, dirs_0, dirs_1, rel_tol=1e-9): + """Rotation matrix R with points_1 = R points_0 + t and dirs_1 = R dirs_0 + (Kabsch), or None when the two point sets are not the same rigid body + to within ``rel_tol`` of the geometry's size.""" + c0 = points_0.mean(axis=0) + c1 = points_1.mean(axis=0) + q0 = points_0 - c0 + q1 = points_1 - c1 + scale = max(float(np.abs(q0).max()), 1e-300) + u, _, vt = np.linalg.svd(q0.T @ q1) + d = np.sign(np.linalg.det(vt.T @ u.T)) + R = vt.T @ np.diag([1.0, 1.0, d]) @ u.T + if np.abs(q0 @ R.T - q1).max() > rel_tol * scale: + return None + if np.abs(dirs_0 @ R.T - dirs_1).max() > rel_tol: + return None + return R + + class BodyAerodynamics: """BodyAerodynamics class @@ -2090,6 +2108,42 @@ def va_initialize( rates_in_body_frame=rates_in_body_frame, ) + def _curved_bound_correction_cached( + self, eval_points, bp1, bp2, te1, te2, chord_dir, chords, va_norm, core_radius_fraction + ): + """The curved bound-vortex correction (3, N, N) for the current panels, + from the cache when the panels are the cached ones up to a rigid + rotation and translation, otherwise recomputed and stored.""" + ac = float(self._aerodynamic_center_location) + points = np.vstack([eval_points, bp1, bp2, te1, te2]) + cache = getattr(self, "_curved_bound_cache", None) + if ( + cache is not None + and cache["ac"] == ac + and cache["core"] == float(core_radius_fraction) + and cache["points"].shape == points.shape + and np.allclose(cache["chords"], chords, rtol=0.0, atol=1e-12) + ): + R = _rigid_rotation_between(cache["points"], points, cache["chord_dir"], chord_dir) + if R is not None: + if np.allclose(R, np.eye(3), atol=1e-14): + return cache["AIC"] + return np.ascontiguousarray(np.einsum("ab,bij->aij", R, cache["AIC"])) + strip_x, strip_w = thin_airfoil_strips() + AIC_corr = assemble_curved_bound_correction_AIC( + eval_points, bp1, bp2, te1, te2, chord_dir, chords, va_norm, + ac, float(core_radius_fraction), strip_x, strip_w, + ) + self._curved_bound_cache = { + "ac": ac, + "core": float(core_radius_fraction), + "points": points.copy(), + "chord_dir": np.array(chord_dir, dtype=float), + "chords": np.array(chords, dtype=float), + "AIC": AIC_corr, + } + return AIC_corr + def update_effective_angle_of_attack_if_VSM( self, gamma, @@ -2143,41 +2197,18 @@ def update_effective_angle_of_attack_if_VSM( chord_dir = np.ascontiguousarray(y_airf_array, dtype=float) # The correction depends on the panel geometry only (the wake terms # cancel between the actual and the unrolled systems, and the leg core - # radius has no measurable effect), so it is computed once per - # geometry and reused for every inflow and circulation. A coupled - # trim solves the same deformed geometry hundreds of times; the - # kernel costs about 0.5 s at 50 panels. The key hashes the arrays - # the kernel reads, so any rebuild or moved point invalidates it. - key = ( - float(self._aerodynamic_center_location), + # radius has no measurable effect), so it is computed once per shape + # and reused for every inflow and circulation. A trim that rotates + # the body for each residual evaluation keeps the shape: the stored + # matrix is then rotated instead of rebuilt (its entries are velocity + # vectors, so they rotate with the geometry and ignore translations). + # The kernel costs about 0.5 s at 50 panels; a coupled trim solves + # one deformed shape hundreds of times. + AIC_corr = self._curved_bound_correction_cached( + eval_points, bound_point_1, bound_point_2, TE_point_1, TE_point_2, + chord_dir, chords, np.ascontiguousarray(va_norm_array, dtype=float).ravel(), float(core_radius_fraction), - hashlib.sha1( - b"".join( - a.tobytes() - for a in (eval_points, bound_point_1, bound_point_2, TE_point_1, TE_point_2, chord_dir, chords) - ) - ).hexdigest(), ) - cache = getattr(self, "_curved_bound_cache", None) - if cache is not None and cache[0] == key: - AIC_corr = cache[1] - else: - strip_x, strip_w = thin_airfoil_strips() - AIC_corr = assemble_curved_bound_correction_AIC( - eval_points, - bound_point_1, - bound_point_2, - TE_point_1, - TE_point_2, - chord_dir, - chords, - np.ascontiguousarray(va_norm_array, dtype=float).ravel(), - float(self._aerodynamic_center_location), - float(core_radius_fraction), - strip_x, - strip_w, - ) - self._curved_bound_cache = (key, AIC_corr) AIC_x = AIC_x + AIC_corr[0] AIC_y = AIC_y + AIC_corr[1] AIC_z = AIC_z + AIC_corr[2] diff --git a/tests/BodyAerodynamics/test_curved_bound_vortex.py b/tests/BodyAerodynamics/test_curved_bound_vortex.py index 6e399e8..574682c 100644 --- a/tests/BodyAerodynamics/test_curved_bound_vortex.py +++ b/tests/BodyAerodynamics/test_curved_bound_vortex.py @@ -115,10 +115,27 @@ def counting(*args, **kwargs): r_ref = solver.solve(body_ref) assert np.isclose(r2["cl"], r_ref["cl"], rtol=1e-12) assert np.isclose(r2["cd"], r_ref["cd"], rtol=1e-12) - # moving the geometry invalidates the cache + # a rigid rotation keeps the shape: the stored matrix is rotated, not rebuilt, + # and the result equals that of a body built in the rotated position body.rotate(angle_deg=5.0, axis=[0.0, 1.0, 0.0]) body.va_initialize(20.0, 4.0, 5.0) - solver.solve(body) + r_rot = solver.solve(body) + assert len(calls) == 2 + body_rot = _arc(16) + body_rot.rotate(angle_deg=5.0, axis=[0.0, 1.0, 0.0]) + body_rot.va_initialize(20.0, 4.0, 5.0) + r_rot_ref = solver.solve(body_rot) assert len(calls) == 3 + assert np.isclose(r_rot["cl"], r_rot_ref["cl"], rtol=1e-10) + assert np.isclose(r_rot["cd"], r_rot_ref["cd"], rtol=1e-10) + # a deformation (different shape) recomputes + wing = body.wings[0] + le = np.array([sec.LE_point for sec in wing.sections]) + te = np.array([sec.TE_point for sec in wing.sections]) + te[len(te) // 2] += np.array([0.1, 0.0, 0.0]) + body.update_from_points(le, te, "reuse_initial_polar_data", [sec.polar_data for sec in wing.sections]) + body.va_initialize(20.0, 4.0, 5.0) + solver.solve(body) + assert len(calls) == 4 finally: BA.assemble_curved_bound_correction_AIC = original From 7f44bfae89b42faa745273d6f28df3d7773629c3 Mon Sep 17 00:00:00 2001 From: ocayon Date: Tue, 13 Oct 2026 08:52:26 +0200 Subject: [PATCH 22/37] docs: the curved bound-vortex correction is computed once per shape, not once per solve Both the regularisation report and the aerodynamic model document said the kernel is called once per solve; since 2644b5c and 0e5a67f it is computed once per deformed shape and reused under rigid motion. PDFs rebuilt. 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