Precomputed Panel Solver for Aerodynamics Simulation Haoran Xie - - PowerPoint PPT Presentation

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Precomputed Panel Solver for Aerodynamics Simulation Haoran Xie - - PowerPoint PPT Presentation

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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.,

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Precomputed Panel Solver for Aerodynamics Simulation

Haoran Xie The University of Tokyo / JAIST

H.XIE@JAIST

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H.XIE@JAIST 1

Aerodynamics Simulation

for Graphics and Fabrication

  • J. Wejchert. SIGGRAPH91
  • E. Ju, et al., SIGGRAPH14

T . Martin, et al., SIGGRAPH15

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H.XIE@JAIST 2

Aerodynamics in Graphics

@E.Ju, et al, TOG2013 @N.Umetani, et al, TOG2014 @X.Wei, et al, SCA2013 @T.Martin, et al, TOG2015 @P.Yang, et al, SCA2014

Data- Driven Heuristic Method Coupling Based

@J.Tan, et al, TOG2011

Simplified Model Heavy Computation Low Accuracy

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H.XIE@JAIST 3

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

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H.XIE@JAIST 4

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

We extend panel method !

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H.XIE@JAIST 5

Motivation

CFD tools

@ANSYS Fluent CFD Tutorial

  • ur work

Our goal is to create a fast aerodynamic simulation algorithm, enabling designers to design gliders with interactive feedbacks.

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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

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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

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H.XIE@JAIST 8

Flow Assumption

airflow

trailing edge leading edge wake panels

Real Flow:

turbulent, unsteady

@Marine Hydrodynamics, MIT Lectures

Potential Flow:

inviscid, incompressible

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H.XIE@JAIST 9

Flow Elements

Source Sink Uniform Basic Elements

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H.XIE@JAIST 10

Flow Elements

Source

Streamline

Sink Uniform Basic Elements

Superposition

Doublet

stagnation point flow around cylinder

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H.XIE@JAIST 11

Flow Elements

Source

Streamline

Sink Uniform Basic Elements

Superposition

Doublet

@cfd2012.com/aircraft-design

stagnation point flow around cylinder

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Panel Method

Body Panel Wake Panel

Doublet doublet strength

𝑗 𝑗 : element index

H.XIE@JAIST 12

[Hess and Smith, 1967]

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Panel Method [Hess and Smith, 1967]

Body Panel Wake Panel

Doublet doublet strength

𝑗 𝑗 : element index

H.XIE@JAIST 13

Green’s Identity:

(~ doublet strengths U) fixed velocity potential (~ body state)

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Panel Method

 Why we still need panel solver nowadays

 Fast, Robust, Accurate in aircraft design  Suitable for many applications

H.XIE@JAIST 14

[Journal of Aircraft, 2014] [AIAA conference, 2010] [AIAA conference, 2013] [AIAA Journal, 2013]

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15

Computation Issue

※ mesh size: N= 6000 6,000

Matrix Operation

6,000 for each frame:

Standard Panel Method: 400 seconds Interactive design: 0.01 seconds

6 6

?

H.XIE@JAIST

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H.XIE@JAIST 16

Body State  Doublet

Body State Doublets

𝓞

N N N 6 6 1 1

𝑬 𝑻 U

𝒀

※ N: mesh size

Precomputed Precomputed

(6D velocities)

Linear !!

× × ×

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H.XIE@JAIST 17

Doublet  Force

1

𝒀

𝑫𝒚

6 6

body state

6

forcex = f( U , X ) = 𝒀

6

doublet Precomputed

(※ we compute torque in similar way)

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H.XIE@JAIST 18

Precomputed Process

Surface Discretization Compute D,S matrices Compute Strength Compute Local Velocity Compute force&moment Compute Body State

O(N) O(N2) O(N3) O(N2) O(N2) O(1)

Surface Discretization Compute D,S matrices Compute Strength Compute Local Velocity Compute C matrices Compute Body State

O(N) O(N2) O(N3) O(N2) O(N2) O(1)

Compute force&moment

O(1) Standard Panel Method O(N3) Precomputed Panel Method O(1)

(N = mesh size)

Precomputation: 120.0s Precomputation:480.0s Runtime: 360.0s Runtime:0.007s

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H.XIE@JAIST 19

Computation Cost

100 200 300 400 500 600 Panel Method Ours

(x2,160) (x50,252) (x27,205) (x41,809) (x68,053)

(seconds)

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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

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H.XIE@JAIST 21

Full Simulation pipeline

Geometry Preprocessing Aerodynamics Precomputation

pre-computation runtime

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H.XIE@JAIST 22

Geometry Preprocessing

mesh segmentation wing recognition wake-panel generation input

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H.XIE@JAIST 23

Wing Recognition

0.05 0.18 0.21 0.04 0.29 0.46 0.47

?

Mesh Segmentation: → convex shape decomposition Extracting wing parts:

→ bottom-up clustering process

Oriented Bounding Box

[O. Kaick et al, TOG2014]

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H.XIE@JAIST 24

Wake Panel

wake panels trailing edge positive surface trailing edge negative surface

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H.XIE@JAIST 25

Full Simulation Pipeline

Geometry Preprocessing Aerodynamics Precomputation pre-computation runtime

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H.XIE@JAIST 26

Aerodynamics Precomputation

precomputed doublet strength precomputed body state precomputed

body state

force + torque

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H.XIE@JAIST 27

Full Simulation Pipeline

Geometry Preprocessing Aerodynamics Precomputation pre-computation runtime

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H.XIE@JAIST 28

RIGD BODY Simulation

Kinematic Equations: Dynamics Equations: [Kobilarov et al, TOG2009] Quadratic to body state!

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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

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H.XIE@JAIST 30

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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

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H.XIE@JAIST 32

Glider Design

assembling&editing

Precomputed

rotation scaling translation

𝑉 = 𝑸𝟐𝑆 𝑙𝑸𝟑𝑆 + 𝑸𝟐 ෠ 𝑈 𝑌

Doublet Matrix Body State

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H.XIE@JAIST 33

Glider Fabrication

launching device launching hook added mass Fabricated Gliders

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H.XIE@JAIST 34

launching

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Results

Aerodynamics validation and glider design.

H.XIE@JAIST 35

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Results

Aerodynamics Simulation Algorithm

 Aerodynamics validation  Simulation comparison

Interactive Glider Design System

 Glider design (stable & unstable)  Bird glider design

H.XIE@JAIST 36

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H.XIE@JAIST

Validation: Sphere

theoretical value 105 meshes 440 meshes 956 meshes

Pressure Distribution: Flow around a sphere 1m

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H.XIE@JAIST 38

Validation: Airfoil

Pressure Distribution: Flow around an airfoil

NACA0012 Airfoil wind tunnel data Location section A section B section C

A B C

1m 4m

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H.XIE@JAIST 39

Validation: Glider

Pressure Distribution: Flow around a glider Lift Force Coefficients Drag Force Coefficients

  • ur model

wind tunnel data

Angle of Attack (degree)

  • 5 0 5 10 15

1 0.5 Coefficients

77.6 cm 137.0 cm

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H.XIE@JAIST 40

Influence of AoA

Wind Tunnel Visualization

Boundary layer separation @UAF Physics 211

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H.XIE@JAIST 41

Validation: Glider

Pressure Distribution: Flow around a glider Lift Force Coefficients Drag Force Coefficients

  • ur model

wind tunnel data

Angle of Attack (degree)

  • 5 0 5 10 15

1 0.5 Coefficients

77.6 cm 137.0 cm

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H.XIE@JAIST 42

Validation: Comparison

@wikipedia

no tail design small tail design big tail design

not stable, tumbling a lot not stable, tumbling few stable, no tumbling

Source distribution | Pressure Distribution | Fabrication Results

Saqqara Bird: about 2,200 years old, excavated in 1898 from a tomb in Saqqara, Egypt.

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H.XIE@JAIST 43

Comparison

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Results

Aerodynamics Simulation Algorithm

 Aerodynamics validation  Simulation comparison

Interactive Glider Design System

 Glider design (stable & unstable)  Bird glider design

H.XIE@JAIST 44

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H.XIE@JAIST 45

Glider Design

Single-wing gliders Tandem-wing gliders

✔ ✔

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H.XIE@JAIST 46

Glider Design

45° 30° 0°

  • ur simulation

captured trajectory

unstable

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H.XIE@JAIST 47

experiments

unstable

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H.XIE@JAIST 48

Glider Design

45° 30° 0°

  • ur simulation

captured trajectory

stable

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H.XIE@JAIST 49

experiments

stable

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H.XIE@JAIST 50

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Bird Glider

assembly parts

A normal glider fuselage with bird wings

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H.XIE@JAIST 52

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H.XIE@JAIST

Conclusion

Interactive Glider Design Precomputed Panel Solver

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H.XIE@JAIST

Limitations

We assume forward flight. It cannot handle flying in other directions. We assume potential flow, so cannot handle unstable turbulences Mesh segmentation can be wrong, leading to inaccurate simulation.

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H.XIE@JAIST 55

Future Work

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Thank You! Q&A