Precomputed Panel Solver for Aerodynamics Simulation Haoran Xie The University of Tokyo / JAIST H.XIE@JAIST 0
Aerodynamics Simulation for Graphics and Fabrication T . Martin, et al., SIGGRAPH15 J. Wejchert. SIGGRAPH91 E. Ju, et al., SIGGRAPH14 H.XIE@JAIST 1
Aerodynamics in Graphics Data- Heuristic Coupling Driven Method Based @N.Umetani, et al, TOG2014 @P.Yang, et al, SCA2014 @X.Wei, et al, SCA2013 @T.Martin, et al, TOG2015 @E.Ju, et al, TOG2013 @J.Tan, et al, TOG2011 Low Accuracy Simplified Model Heavy Computation H.XIE@JAIST 2
Aerodynamics in Engineering Grid-Based Singularity-Based @Chen et al., Sci. China-Phys. Mech. Astron., 2013. @D. Willis, Journal of Aircraft, 2014 Heavy Computation Low Cost and Good Accuracy H.XIE@JAIST 3
Aerodynamics in Engineering Grid-Based Singularity-Based We extend panel method ! @Chen et al., Sci. China-Phys. Mech. Astron., 2013. @D. Willis, Journal of Aircraft, 2014 Heavy Computation Low Cost and Good Accuracy H.XIE@JAIST 4
Motivation Our goal is to create a fast aerodynamic simulation algorithm, enabling designers to design gliders with interactive feedbacks. @ANSYS Fluent CFD Tutorial our work CFD tools H.XIE@JAIST 5
Computational Framework Aerodynamics Simulation Algorithm Precomputed panel method (x10,000~) Interactive simulation pipeline Interactive Glider Design System Assembly-based user interface Glider design and fabrication H.XIE@JAIST 6
Computational Framework Aerodynamics Simulation Algorithm Precomputed panel method (x10,000~) Interactive simulation pipeline Interactive Glider Design System Assembly-based user interface Glider design and fabrication H.XIE@JAIST 7
Flow Assumption airflow Real Flow: turbulent, unsteady leading edge Potential Flow: inviscid, incompressible trailing edge wake panels H.XIE@JAIST 8 @Marine Hydrodynamics, MIT Lectures
Flow Elements Uniform Source Sink Basic Elements H.XIE@JAIST 9
Flow Elements Streamline Doublet Uniform stagnation point Source flow around cylinder Sink Superposition Basic Elements H.XIE@JAIST 10
Flow Elements Streamline Doublet Uniform stagnation point Source flow around cylinder Sink Superposition Basic Elements @cfd2012.com/aircraft-design H.XIE@JAIST 11
Panel Method [Hess and Smith, 1967] 𝑗 : element index 𝑗 Doublet Body Panel Wake Panel doublet strength H.XIE@JAIST 12
Panel Method [Hess and Smith, 1967] 𝑗 : element index 𝑗 Doublet Body Panel Wake Panel doublet strength Green’s Identity: velocity potential fixed (~ doublet strengths U) (~ body state) H.XIE@JAIST 13
Panel Method Why we still need panel solver nowadays Fast, Robust, Accurate in aircraft design Suitable for many applications [AIAA conference, 2010] [Journal of Aircraft, 2014] [AIAA conference, 2013] [AIAA Journal, 2013] H.XIE@JAIST 14
Computation Issue for each frame: 6,000 ? ※ mesh size: N= 6000 6 Matrix 6,000 6 Operation Interactive design: 0.01 seconds Standard Panel Method: 400 seconds H.XIE@JAIST 15
Body State Doublet N 6 1 1 N 𝒀 6 N U 𝑻 × 𝑬 𝓞 × × Precomputed Precomputed Doublets Body ※ N: mesh size State Linear !! (6D velocities) 16 H.XIE@JAIST
Doublet Force doublet body state 6 force x = f ( U , X ) = 6 1 𝑫 𝒚 𝒀 6 𝒀 6 Precomputed ( ※ we compute torque in similar way) H.XIE@JAIST 17
Precomputed Process Precomputation:480.0s Precomputation: 120.0s Runtime: 360.0s Runtime:0.007s Surface Surface Compute D,S O(N) O(N 2 ) Discretization Discretization matrices O(N) O(N 2 ) Compute D,S Compute O(N 3 ) matrices Strength Compute Compute O(N 3 ) O(N 2 ) Local Strength Velocity Compute O(1) Compute O(N 2 ) Compute Local O(N 2 ) force&moment force&moment Velocity O(1) Compute C Compute Compute O(N 2 ) matrices Body State Body State O(1) Precomputed Panel Method O(1) Standard Panel Method O(N 3 ) (N = mesh size) H.XIE@JAIST 18
Computation Cost Panel Method Ours 600 500 400 300 200 100 (seconds) 0 (x2,160) (x50,252) (x27,205) (x41,809) (x68,053) H.XIE@JAIST 19
Computational Framework Aerodynamics Simulation Algorithm Precomputed panel method (x10,000~) Interactive simulation pipeline Interactive Glider Design System Assembly-based user interface Glider design and fabrication H.XIE@JAIST 20
Full Simulation pipeline Geometry Preprocessing Aerodynamics Precomputation pre-computation runtime H.XIE@JAIST 21
Geometry Preprocessing mesh wing wake-panel input segmentation recognition generation H.XIE@JAIST 22
Wing Recognition Mesh Segmentation: → convex shape decomposition Oriented Bounding Box [O. Kaick et al, TOG2014] Extracting wing parts: → bottom-up clustering process 0.18 0.21 0.05 0.04 ? 0.47 0.29 0.46 H.XIE@JAIST 23
Wake Panel positive surface trailing edge negative surface trailing edge wake panels H.XIE@JAIST 24
Full Simulation Pipeline Geometry Preprocessing Aerodynamics Precomputation pre-computation runtime H.XIE@JAIST 25
Aerodynamics Precomputation precomputed precomputed body state doublet strength body state force + torque precomputed H.XIE@JAIST 26
Full Simulation Pipeline Geometry Preprocessing Aerodynamics Precomputation pre-computation runtime H.XIE@JAIST 27
RIGD BODY Simulation [Kobilarov et al, TOG2009] Kinematic Equations: Quadratic to body state! Dynamics Equations: H.XIE@JAIST 28
Computational Framework Aerodynamics Simulation Algorithm Precomputed panel method (x10,000~) Interactive simulation pipeline Interactive Glider Design System Assembly-based user interface Glider design and fabrication H.XIE@JAIST 29
H.XIE@JAIST 30
Computational Framework Aerodynamics Simulation Algorithm Precomputed panel method (x10,000~) Interactive simulation pipeline Interactive Glider Design System Assembly-based user interface Glider design and fabrication H.XIE@JAIST 31
Glider Design scaling translation rotation 𝑉 = 𝑸 𝟐 𝑆 𝑙𝑸 𝟑 𝑆 + 𝑸 𝟐 𝑈 𝑌 Doublet Matrix Body State Precomputed assembling&editing H.XIE@JAIST 32
Glider Fabrication added mass launching device Fabricated Gliders launching hook H.XIE@JAIST 33
launching H.XIE@JAIST 34
Results Aerodynamics validation and glider design. 35 H.XIE@JAIST
Results Aerodynamics Simulation Algorithm Aerodynamics validation Simulation comparison Interactive Glider Design System Glider design (stable & unstable) Bird glider design H.XIE@JAIST 36
Validation: Sphere Pressure Distribution: Flow around a sphere theoretical value 956 1m meshes 440 meshes 105 meshes H.XIE@JAIST 37
Validation: Airfoil Pressure Distribution: Flow around an airfoil wind tunnel data section A A 4m B section B section C C 1m NACA0012 Airfoil Location H.XIE@JAIST 38
Validation: Glider Pressure Distribution: 1 Lift Force Flow around a glider Coefficients wind tunnel data Coefficients our model 0.5 137.0 cm 0 77.6 cm Drag Force Coefficients -5 0 5 10 15 Angle of Attack (degree) H.XIE@JAIST 39
Influence of AoA Wind Tunnel Visualization Boundary layer separation @UAF Physics 211 H.XIE@JAIST 40
Validation: Glider Pressure Distribution: 1 Lift Force Flow around a glider Coefficients wind tunnel data Coefficients our model 0.5 137.0 cm 0 77.6 cm Drag Force Coefficients -5 0 5 10 15 Angle of Attack (degree) H.XIE@JAIST 41
Validation: Comparison Saqqara Bird: about 2,200 years old, excavated in 1898 from a tomb in Saqqara, Egypt . Source distribution | Pressure Distribution | Fabrication Results not stable, tumbling a lot no tail design not stable, tumbling few small tail design @wikipedia stable, no tumbling big tail design H.XIE@JAIST 42
Comparison H.XIE@JAIST 43
Results Aerodynamics Simulation Algorithm Aerodynamics validation Simulation comparison Interactive Glider Design System Glider design (stable & unstable) Bird glider design H.XIE@JAIST 44
Glider Design Single-wing gliders Tandem-wing gliders ✔ ✔ H.XIE@JAIST 45
Glider Design unstable our simulation captured trajectory 45 ° 30 ° 0 ° H.XIE@JAIST 46
experiments unstable H.XIE@JAIST 47
Glider Design stable our simulation captured trajectory 45 ° 30 ° 0 ° H.XIE@JAIST 48
experiments stable H.XIE@JAIST 49
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Bird Glider A normal glider fuselage with bird wings assembly parts H.XIE@JAIST 51
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Conclusion Precomputed Panel Solver Interactive Glider Design H.XIE@JAIST 53
Limitations We assume potential flow, so cannot handle unstable turbulences Mesh segmentation can be wrong, leading to inaccurate simulation. We assume forward flight. It cannot handle flying in other directions. H.XIE@JAIST 54
Future Work H.XIE@JAIST 55
Thank You! Q&A H.XIE@JAIST 56
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