Fluid-Structure Interaction Problems using SU2 and ... · Fluid-Structure Interaction Problems...

Fluid-Structure Interaction Problems using SU2and External Finite-Element Solvers

R. Sanchez1, D. Thomas2, R. Palacios1, V. Terrapon2

1Department of Aeronautics, Imperial College London

2Department of Mechanical and Aerospace Engineering, University of Liege

First SU2 Annual Developers Meeting

TU Delft, 6 September 2016

Sanchez, Thomas, Palacios & Terrapon

Fluid-Structure Interaction Problems using SU2 and External Finite-Element Solvers

Outline

Objectives

Background and code structure

FSI solver and coupling techniques

Results

Conclusions

Objectives

I Development of FSI capabilities in SU2

I Target: static and dynamic aeroelastic simulation

I ALE solution from CFD solver needs:I Mesh deformationI Interface (interpolation)I Structural solver (FEA)

I Two approaches to the structural solverI Native implementation within SU2 source codeI Python wrapper to couple with third-party solvers

http://su2.stanford.edu

Native fluid solver1

Arbitrary Lagrangian-Eulerian (ALE) formulation:

+r · Fc(U, u⌦)�r · Fv(U)�Q = 0 in ⌦f

⇥ [0, t]

Space integration- Dual-grid, edge-based discretization- Vertex-based control volumes

Primalgrid

Dualgrid

Time integration- Dual time-stepping strategy

⇤(U) = 0

1Palacios, F. et al. (2013)

Native fluid solver: code structure

OutputInput

Space & Time Integration

Geometry: Dual Grid FV Mesh Euler / NS / RANS Solver

Variable: Node

CFD Numerical Methods

Flow Iteration

Single Physics Driver

Solid mechanics

Large deformationsComplex material behaviour

�! Finite deformation framework

For static problems:

S (x) = �W

int ��W

ext = 0

� : �d dv ��R

f · �v dv +R@v

t · �v da

�= 0

Linearising,@S (x)@x

�x = K�x = �S (x) where K = K

+K� �K

Integration using Finite Element MethodAfter inertia is added, time integration using Newmark and generalized-↵methods

Native structural solver: code structure

OutputInput

Space & Time Integrator

Geometry: FEM Mesh Solid Mechanics Solver

Variable: Node

FEM: Structural Analysis

Structural Iteration

Single Physics Driver

Element Geometrical model

Material modelGaussian Point

Native FSI solver⇤

⇢f ,v, E

Structure

Interface

p�, ⌧�,u�, u�

Fluid Mesh

u⌦, u⌦

p�, ⌧�

u�, u�

⇤Sanchez, R. et al. (SciTech, 2016)

Native FSI solver: Time coupling

InterfaceFluid Solver Structural Solver

(λ f,Γ )= u f,ΓF ,um.

Predictor uΓ = Pi(ut-1Γ )~

Interface

Equilibrium

λf,Γ λs,Γ+ = 0

Fluid Solver Structural Solver

Interface

Equilibrium

λf,Γ λs,Γ+ = 0

S (λ s,Γ )=us,Γ

Interface

Equilibrium

λf,Γ λs,Γ+ = 0

S (λ s,Γ )=us,ΓContinuity

uf,Γ us,Γ= =uΓ~~~

Relaxation = (1 ω) ωuΓ u f,Γ us,Γ~ ~

Interface

Equilibrium

λf,Γ λs,Γ+ = 0

Mesh Morpher

( )= u f,ΓMum.

Interface

Equilibrium

λf,Γ λs,Γ+ = 0

Mesh Morpher

( )= u f,ΓMum.

uΓn+1 un

Γ < εUpdate

uΓt+Δt

uΓ t+ΔttYES

Native FSI solver: Time coupling structure

OutputInput

Flow Iteration

Fluid-Structure Interaction Driver

MPI-Compliant Transfer Methods

Fluid Tractions

Structural Displacements

Native FSI solver: Spatial coupling

Fluid domain

Structural domain

Automaticdomain

decomposition

Automaticdomain

decomposition

Processor 1 Processor 2

Automaticdomain

decomposition

Automaticdomain

decomposition

Automaticdomain

decomposition

Automaticdomain

decomposition

Automaticdomain

decomposition

MPI-compliant

transfer routines

Automaticdomain

decomposition

MPI-compliant

transfer routines

Automaticdomain

decomposition

MPI-compliant

transfer routines

Automaticdomain

decomposition

MPI-compliant

transfer routines

Automaticdomain

decomposition

MPI-compliant

transfer routines

Interpolationuf = Hus

�s = HT�f

Native FSI solver: Spatial coupling structure

OutputInput

Flow Iteration

Fluid-Structure Interaction Driver

Structural

Mesh 0 Interface Vertex Mesh 1

Displacements Interpolation Mesh 1 - Mesh 0

Interface Vertex

Fluid Tractions

Interpolation Mesh 0 - Mesh 1

Python wrapper for external solvers

I Couple SU2 with a third-party solver: improved flexibility.

IPython wrapper: synchronizes the solvers within a single environment.

I Python wrapper calls all C++ functions in the new CDriver class.

I Additional compilation using SWIG: API ! importable python object.

I Communication between solver performed through memory.

I Examples of coupling in this work:

ICoupling with an in-house spring analogy solver.

ICoupling with a third-party structural solver: TACS (Kennedy & Martin, 2014).

Python wrapper: code structure

SU2C++ Source Code

CDriver class

Third-party SolverSource Code

C++ API Object

*.so/*.a

Wrapped_SU2_Solver.py Wrapped_External_Solver.py

FSI Python Script

SWIGlink

Py import Py import

FSI solver for rigid body applications

xfxCG cc/2

h t(�)

α t(�)

mh+ S↵+ C

h = �L

Sh+ If ↵+ C

↵ = M

xfxCG cc/2

h t(�)

α t(�)

mh + S↵ + Chh + Khh = �L

Sh + If ↵ + C↵↵ + K↵↵ = M

NACA 0012 using the Python wrapper

I Two-dimensional aeroelastic problem

Ik � ! SST turbulence model

I Sub- and post-critical conditions

I Re = 4 · 106 for c = 1 m

I Initial pitch angle 5�

= 45 rad/s

I Strongly-coupled scheme

xfxCG cc/2

h t(�)

α t(�)

Sh + If ↵ + C↵↵ + K↵↵ = M

- NACA 0012 (Python wrapper)

0 20 40 60 80 100 120τ

Wagner modelCoupled computation

0 20 40 60 80 100 120τ

Mach = 0.1

xfxCG cc/2

h t(�)

α t(�)

Sh + If ↵ + C↵↵ + K↵↵ = M

0 20 40 60 80 100 120τ

Mach = 0.1

0 10 20 30 40 50 60 70τ

M∞ = 0.3

0 10 20 30 40 50 60 70τ

α[rad]

xfxCG cc/2

h t(�)

α t(�)

Sh + If ↵ + C↵↵ + K↵↵ = M

0 20 40 60 80 100 120τ

Mach = 0.1

0 10 20 30 40 50 60 70τ

M∞ = 0.3M∞ = 0.357

0 10 20 30 40 50 60 70τ

α[rad]

xfxCG cc/2

h t(�)

α t(�)

Sh + If ↵ + C↵↵ + K↵↵ = M

0 20 40 60 80 100 120τ

Mach = 0.1

0 10 20 30 40 50 60 70τ

M∞ = 0.3M∞ = 0.357M∞ = 0.364

0 10 20 30 40 50 60 70τ

α[rad]

xfxCG cc/2

h t(�)

α t(�)

Sh + If ↵ + C↵↵ + K↵↵ = M

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45M∞

Flutter point

Plunge mode WagnerPitch mode WagnerPlunge mode computedPitch mode computed

xfxCG cc/2

h t(�)

α t(�)

Sh + If ↵ + C↵↵ + K↵↵ = M

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45M∞

Flutter point

Plunge mode WagnerPitch mode WagnerPlunge mode computedPitch mode computed

0 50 100 150 200 250τ

h/b,α[rad

plunge modepitch mode

xfxCG cc/2

h t(�)

α t(�)

Sh + If ↵ + C↵↵ + K↵↵ = M

τ = 85.95 τ = 86.40 τ = 86.85

τ = 87.30 τ = 87.75 τ = 88.20

(a) (b) (c)

(e)(d) (f)

xfxCG cc/2

h t(�)

α t(�)

Sh + If ↵ + C↵↵ + K↵↵ = M

Isogai Wing Section using the Python wrapper

I Two-dimensional aeroelastic problem

I Swept back wing: elastic axis xf

= �b

I Transonic regime: M1 = 0.7 - 0.9

= 100 rad/s

I Strongly-coupled scheme

I Speed index:

⇤ =U1

3 NACA 0012 (Python wrapper)

xfxCG cc/2

h t(�)

α t(�)

Sh + If ↵ + C↵↵ + K↵↵ = M

0.7 0.75 0.8 0.85 0.9 0.95M∞

V∗ f

Stable

Unstable

Current calculationsSpline interpolationLiu et al.Alonso & JamesonBiao et al.Thomas et al.

3 NACA 0012 (Python wrapper)

- Isogai Wing Section (Python wrapper)

Native FSI solver with deformable solids

14 .5 H

slip-wall

outlet

Geometry:==

Fluid properties==

0.5131.18

m/skg/mkg/m s

1.82 10. 5

Structural properties==

ν =100s

Pakg/m

.2.50 105

Re = 332

slip-wall

14 .5 H

slip-wall

outlet

slip-wall

Wall and Ramm (1998) 3.08 1.31

f dmax(cm)(Hz)

14 .5 H

slip-wall

outlet

slip-wall

Wall and Ramm (1998)

Matthies and Steindorf (2003)

Dettmer and Peric (2006)

Wood et al. (2008)

Kassiotis et al. (2011)

Habchi et al. (2013)

Froehle and Persson (2014)

3.08 1.31

2.99 1.34

2.96 1.13.31 1.4

2.78 1.13.13 1.2

3.17 1.0

3.25 1.02

3.18 1.12

f dmax(cm)(Hz)

Flow-drivenvibrations

Transition

Structuralresonance

Transition

Structuralresonance

Transition

Beam-drivenvibrations

Transition

T = 0.317 s f = 3.15 Hz

Transition

T = 0.317 s f = 3.15 Hz

Transition

T = 0.317 s f = 3.15 Hz

d = 1.15 cm max

Transition

Complex vortical

structures

Large dis-

placements

Strong FSIcouplings

Complex vortical

structures

Large dis-

placements

Strong FSIcouplings

Conclusions

1. Open-source FSI solvers tailored to computational aeroelasticity.

2. Two approaches adoptedI Natively embedded solverI Python code wrapper for improved flexibility

3. Software architecture ready and demonstrated on first applications.Modularity has been preserved.

4. Source code already merged. Some first tutorials are available (more tocome).

Fluid-Structure Interaction Problems using SU2 and ... · Fluid-Structure Interaction Problems...

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