Numerical Benchmarking of Fluid-Structure Interaction ... · 5 Boundary and initial conditions Numerical benchmarking of fluid-structure interaction between elastic object and laminar

Universität DortmundFakultät für Mathematik

IAMtechnische universität dortmund

Numerical Benchmarking of Fluid-Structure Interaction between elastic object and laminar incompressible flow

S. Turek, J. Hron, M. Razzaq, H. WobkerTU Dortmund

with support by

M.Schäfer, M. Heck, M. Krafczyk, J. Tölke, S. Geller, H.-J. Bungartz, M. Brenk, R. Rannacher, T. Dunne, W. Wall, A. Gerstenberger, E. Rank, A. Düster, S. Kollmannsberger

K.-U. Bletzinger, R. Wüchner, A.Kupzok, T. Gallinger, U. Israel

2

Key questionAccurate and robust description of the interaction mechanisms w.r.t. highly dynamical and nonlinear behaviour and significant geometry changes?

That includes: Quality of different discretization techniques (FEM, FV, FD, LBM, resp., beam, shell, volume elements) for FSI?Robustness and numerical efficiency of the integrated solvercomponents?Coupling mechnisms?

1st step: Identification of appropriate FSI setting for numerical benchmarking

2nd step: FSI benchmark setting due to experimental studies3rd step: Extension to FSI-Optimisation benchmark

Numerical benchmarking of fluid-structure interaction between elastic object and laminar incompressible flow

Requirements for numerical FSI benchmarking

3Numerical benchmarking of fluid-structure interaction between elastic object and laminar incompressible flow

Mainly based on the successful DFG flow around cylinder benchmarkRealistic materials

Incompressible Newtonian fluid, laminar flow regimeElastic solid, large deformations

Comparative evaluationSetup with periodical oscillationsNon-graphically based quantities

Computable configurationsLaminar flowReasonable aspect ratiosSimple geometry (2D)

4

Computational domainDomain dimensions

Detail of the submerged structure


( ) ( ) ( ) ( )0.20.2,,0.2 0.15, ,0.20.6,0 ==== CBtA

5

Boundary and initial conditions


Inflow Parabolic velocity profile is prescribed at the left end of the channelOutflow Condition can be chosen by the user, assuming zero reference pressure

(stress free or do nothing) otherwise The no-slip condition is prescribed for the fluid on the other boundary parts. i.e.

top and bottom wall and cylinderInitial Zero velocity in the fluid and no deformation of the structure + smooth increase

of the inflow profile

6

Fluid and structure propertiesIncompressible fluid with density

Elastic material with density : St. Venant –Kirchhoff material


( ) fffff

f

tσρρ div vv v

=∇+∂∂

0 vdiv =f

fρ

( ) vv I Tffffff p ∇+∇+−= νρσ

Fdet ,u I F , =∇+= Jssρ

( )T2

2

Fdiv u −=∂∂ s

ss

tσρ

( )( ) TFE2 ItrEF1 sss

Jμλσ +=

( )I FF21 E T −=

ftΩin

sΩin

7

Suggested material parameterssolid fluid

density densityPoisson ratio kinematic viscosityshear modulus


Parameter polybutadiene & glycerine polypropylene & glycerine

0.910.500.53

1.10.42317

1.26

1.13

1.26

1.13

Parameter FSI1 FSI2 FSI31

0.40.5

10.40.5

10.42.0

11

11

11

0.2 1 2

Parameter FSI1 FSI2 FSI310.4

10.4

10.4

20

0.2

100

1

200

2

sρ fρsν fνsμ

]kg/ms10[ 26sμ

sν]kg/m10[ 33sρ

]kg/m10[ 33fρ]/m10[ 23 sf −ν

]kg/ms10[ 26sμ

sν]kg/m10[ 33sρ

]kg/m10[ 33fρ]/m10[ 23 sf −ν

]m/[ sU

f

s

ρρβ =

2

E AeUf

s

ρ=

sν

]m/s[U

f

dUν

Re =

4105.3 × 3104.1 × 3104.1 ×

8

Quantities of interestThe position of the end of the structure\item pressure difference between the points A(t) and B

Forces exerted by the fluid on the whole body, i.e. lift and drag forces acting on the cylinder and the structure together

Frequency and maximum amplitudeCompare results for one full period and 3 different levels of spatial discretization h and 3 time step sizes


( ) ( ) ( )( )tytxtA ,=

( ) ( ) ( )( )tptptp tABAB −=Δ

( ) ∫ ∫=∫ +=∫=2 01

, |

S S

Sf

S

f

SLD dSnndSndSdSnFF σσσσ

tΔ

9

1.Step: CFD tests for validation


CFD1 CFD2 CFD31

1

1

1

1

10.2 1 220

0.2

100

1

200

2

Test Drag LiftCFD1 14.29 1.119

CFD2 136.7 10.53

CFD3[4.395] [4.395]

]kg/m10[ 33fρ

]s/m10[ 23−fν]s/m[U

]s/m[Uf

dUν

=Re

618.54.439 ± 8.43789.11 ±−

2.Step: CSM tests for validationCSM1 CSM2 CSM310.40.5

10.42.0

10.40.5

2 2 210.41.4

10.45.6

10.41.4

2 2 2

test ux of A [ m] uy of A [ m]

CSM1CSM2CSM3

[1.0995] [1.0995]

310−× 310−×]kg/m10[ 33sρ

sν187.7−

4690.0−

305.14305.14 ±−

10.66−

97.16−

160.65607.63 ±−

]kg/ms10[ 26sμ

sνf

s

ρρβ =

]m/s[ 2g

]m/s[ 2g

]kg/ms10[E 26s

Numerical benchmarking of fluid-structure interaction between elastic object and laminar incompressible flow10

FSI1: steady, small deformations

11Numerical benchmarking of fluid-structure interaction between elastic object and laminar incompressible flow

parameter FSI1 FSI2 FSI3

10.40.5

10.40.5

10.42.0

11

11

11

0.2 1 2

parameter FSI1 FSI2 FSI3

10.4

10.4

10.4

200.2

1001

2002

ux of A [ m] uy of A [ m] drag lift310−×310−×

]kg/m10[ 33sρsν

]kg/ms10[ 26sμ

]kg/m10[ 33sρ]s/m10[ 23−sν

]s/m[U

f

s

ρρβ =

sν2

E AeUf

s

ρ=

f

dUν

Re =

]s/m[U

4105.3 × 3104.1 × 3104.1 ×

0.02270493 0.8208773 14.29426 0.763746FSI1

12

FSI2: large deformations, periodical oscillations

Test ux of A [ m] uy of A [ m] drag lift

FSI2


310 −× 310−×]86.3[70.1285.14 ±− ]93.1[7.8130.1 ± ]86.3[65.7706.215 ± ]93.1[8.23761.0 ±

13

FSI3: large deformations, complex oscillations

Test ux of A [ m] ux of A [ m] drag lift

FSI3


310−×310 −×

]93.10[72.288.2 ±− ]46.5[99.3447.1 ± ]93.10[74.275.460 ± ]46.5[91.15350.2 ±

14

Status of numerical benchmarkingSubtests for validating CFD and CSM components are available:

CSM1-3: "OK"CFD1: "easy" → Re=20CFD2: (also) "easy" → Re=100CFD3: "non-trivial" → Re=200

FSI settings with desired properties: FSI1: "simple" → for validation onlyFSI3: "hard" → due to CFD3 FSI2: fully oscillating while CFD2 (≈same Re number!) is steady

Excellent check for interaction mechanismsEvaluation and comparison of mathematical and algorithmiccomponents - everybody is invited to participate.


⇒


FSI4: Benchmarking of experimental data

15

Flustruc experiment, Erlangen, http://www.lstm.uni-erlangen.de/flustruc/

fluid parameters

density of the fluidkinematic viscosity

1.05e-6 [kg/mm^3]164.0

solid parameters

density of the beam (steel)density of the rear massshear moduluspoisson ratio

7.85e-6[kg/mm^3]7.8e-6 [kg/mm^3]7.58e130.3

geometry parameter value [mm]

channel lengthchannel widthcylinder center positioncylinder radiuselastic structure lengthelastic structure thicknessrear mass lengthrear mass thicknessreference point (at t=0)reference point

LWCRlw

w‘h‘

AB

338.0240.0(0.0, 0.0)11.0500.0410.04.0(71.0, 0.0)(11.0, 0.0)

Numerical benchmarking of fluid-structure interaction between elastic object and laminar incompressible flow 16

FSI4: New configuration+ Laminar Flow (glycerine)+ “2D‘‘ flow and deformation- Rotational degree of freedom- Large aspect ratio (thin structure),- Corners

Flustruc experiment, Erlangen Computation

Laminar: Velocity=1.07 m/s, Re=140

Zoomed


FSI4: PlotsFront body angle

Period of motion

Trailing edge displacement


FSI4: Experiment and numerical simulations

Experiment Numerical



FSI4: Experiment and numerical simulations

19

Experiment Numerical



FSI OptimizationThe main design aims could beI) Drag/Lift minimizationII) Minimal pressure lossIII) Minimal nonstationary oscillations

To reach these aims, we might allow1. Boundary control of inflow section2. Change of geometry: elastic channel walls or length/thickness of

elastic beam3. Optimal control of volume forces

Optimal control of nonstationary flow might be hard for the starting

Results for the moment are combination of I)-III) with 1)-3)


FSI OPT 1Uncontrolled flow

Lift 0 Aim:

w.r.t V1, V2. V1 velocity from topV2 velocity from below

≠( )22 minimize Vlift α+

ux of A [ m] uy of A [ m] drag lift310−×310−×

FSI1 0.0227 0.8209 14.295 0.7638

h=0.04


TESTS for FSI 1 (Boundary control)Level 1 Level 2

FSI OPT 1

Itersteps

extreme point drag Lift

1e0 57 (3.74e-1,3.88e-1) 1.5471e+01 8.1904e-1

1e-2 60 (1.04e0,1.06e0) 1.5474e+01 2.2684e-2

1e-4 73 (1.06e0,1.08e0) 1.5474e+01 2.3092e-4

1e-6 81 (1.06e0,1.08e0) 1.5474e+01 2.3096e-6

Itersteps

extreme point drag Lift

59 (3.66e-1,3.79e-1) 1.5550e+01 7.8497e-1

59 (1.02e0,1.04e0) 1.5553e+01 2.1755e-2

71 (1.04e0,1.05e0) 1.5553e+01 2.2147e-4

86 (1.04e0,1.05e0) 1.5553e+01 2.2151e-6

α

Level 1 Level 2


Outlook

( )22 minimize Vlift α+( )outin pp - minimize

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Numerical Benchmarking of Fluid-Structure Interaction ... · 5 Boundary and initial conditions Numerical benchmarking of fluid-structure interaction between elastic object and laminar