Fluid-Structure-Interaction for Aero- and Hydroelasticity ...

KIT – University of the State of Baden-Wuerttemberg and National Research Center of the Helmholtz Association

INSTITUTE OF FLUID MECHANICSFACULTY OF MECHANICAL ENGINEERING

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Fluid-Structure-Interaction for Aero- and Hydroelasticity:Application in Bio Fluid MechanicsTorsten Schenkel

Torsten SchenkelInstitute of Fluid Mechanics

Faculty of Mechanical Engineering

2 24.03.2010 FSI for Aero- and Hydroelasticity -Application in Bio Fluid Mechanics

Part 1: FSI methodology



3 24.03.2010

fluid-structure interaction?

FSI for Aero- and Hydroelasticity -Application in Bio Fluid Mechanics

Traditionally problems of

fluid mechanics, heat transfer, structuralmechanics, magneto dynamics, electrodynamics etc.

are treated independently from each other.

Initially

fluid mechanics and heat transfer

were treated in a combined way, since thegoverning equations are the same.

Recently

„multiphysics”

seems to be the call of the day.

FSI: Fluid Structure Interaction is just one part of this.



4 24.03.2010

are the governing equations for fluid and solid any different?


For Fluid Mechanics:Euler formulation of momentum balance in a continuum:

For Structural Mechanics:Lagrange formulation of momentum balance in a continuum:

Arbitrary Lagrange Euler (ALE):



5 24.03.2010

fluids and solids share the same governing equations: continuum mechanics


Fluid:

Stokes

Solid:

Material Law (e.g. Hooke)



6 24.03.2010

solution methods for coupled problems:


mononlithic partitioned elimination

X

Y




partitioned: exchange of loads and position between dedicated solvers

Boundary conditions at common interface:

kinematics: dynamics:

both boundary conditions have to be fulfilled to reach equilibrium

solution methods for coupled problems:



8 24.03.2010

schemes for partitioned coupling:


weakly coupled(explicit)

parallel

Solid

Fluid





serial parallel

load consistent

Solid

Fluid






serial parallel

Solid

Fluid

space consistent load consistent






serial, explicit parallel,explicit

space consistent

strongly coupled(implicit)

time step loops(iterative)

load consistent




12 24.03.2010

why not explicitly?


)()( tFE xK xxM =++&&

assumpt. : E = K

Fluid Solid




Fluid Solid

partitioninginterface

why not explicitly?




EtFx )(

=

Fluid Solid

)(tFE x=

why not explicitly?




)()( tFE xK xxMtR =>+= &&

xsolid

Rfluid

Fluid Solid

why not explicitly?




)()( tFE xK xxM =++&&

)()( tFK xxM =+&&

)(tFE x=

time [s]

disp

lacemen

t [-]

why not explicitly?



17 24.03.2010

and yet it works!


Courtesy of FLUENT Inc.

for low fluid density!



18 24.03.2010

characteristic numbers


Reynolds Number:

WomersleyNumber:

Ratio of mean inertial forcesand viscous forces

Ratio of pulsatile inertial forcesand viscous forces

Density Ratio:Ratio of solid and fluid densities

proposed FSI Numbers:

Ratio of elastic andviscous forces

Ratio of elastic andinertial forces



19 24.03.2010

implicit extension to serial explicit coupling scheme


F

Fluid Solid




EtFx )(

=

Fluid Solid





Fluid Solid





Fluid Solid





Fluid Solid





Fluid Solid




25 24.03.2010

verification of coupling scheme


)()( tFE xK xxM =++&&

disp

lacemen

t [-]

time [s]

analyticalsimulation



26 24.03.2010

proof of concept (standard test case)


smvinlet 5.0=

smkg

mkgPaE fluidfluidsolidsolid 01.0;1000;49.0;105 3

8 ====×= nrrn




explicit, serial coupling schemeload/position inconsistency

unstable





implicit, serial coupling schemeconsistent load/position

stable





explicit, serial coupling schemeload/position inconsistency

unstable

implicit, serial coupling schemeconsistent load/position

stable




30 24.03.2010

validation and benchmarking


inlet: pressure inlet (udf)

outlet: pressure outlet (p=0)

wall: no slip

Symmetry: 2D axisymmetric

inner surface:

Pulse Wave Velocity (Moens-Korteweg):




Pulse Wave Velocity:

12tD

23tD





¥u


FSI benchmark case, Turek, Hron

D = 0,10m Ū = 1m/sH = 0,41m ≈ 4D f ≈ 2HzL = 0,35m = 3,5 D λtheo ≈ 0,5 mT = 0,02m = 1/5 D



33 24.03.2010

summary FSI methodology


l Continua of Fluid and Solid are governed by the same equations.

l Yet, different frames of reference lead to different approaches to the numerical treatment(FVM vs. FEM).

l Special requirements on either side often prohibit monolithic codes.

l Typical explicit coupling schemes cannot achieve equilibrium for each time step.

l Explicit coupling schemes are conditionally stable, when e.g. the inertial forces in the fluidare small compared to the elastic forces.

l In aeroelastic applications the inertial forces in the fluid are negligible and explicit couplingschemes can be employed.

l Iterative looping over serial, explicit coupling scheme leads to strongly coupled implicitscheme.

l Implicit coupling scheme is unconditionally stable.




Part 2: Application in Bio Fluid Mechanics

Ventricular Flow

Abdominal Aortic Aneurysm (AAA)



35 24.03.2010

accord.: Dössel et.al.

heart function (crudely simplified)




37 24.03.2010

fibre orientation

Leonid Zhukov, Alan H. BarrDepartment of Computer ScienceCalifornia Institute of Technology

DT MRI (post mortem)




38 24.03.2010

myocardium composite tissue model

Krittian, Ph.D. thesisKIT 2009

endocardium matrix epicardium

KaHMo – Karlsruhe Heart ModelFSI for Aero- and Hydroelasticity -Application in Bio Fluid Mechanics



39 24.03.2010

myocardium motion - heart twist

S. WulfinghoffDiploma thesisKIT 2007




40 24.03.2010

myocardium motion

S. KrittianPh.D. thesisKIT 2009




41 24.03.2010

ventricular flow

3 dim. streamlines λ2 structures

S. KrittianPh.D. thesisKIT 2009




42 24.03.2010

abdominal aortic aneurysm AAA

U. Janoske,DHBW Mosbach, Univ. Wuppertal




43 24.03.2010

thank you for your attention

Can we predict the hemodynamics in the human heart? WSEAS Medical Physiology 2010, Cambridge, UK

questions and answers


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