fluid-structure-interaction for aero- and hydroelasticity
TRANSCRIPT
KIT – University of the State of Baden-Wuerttemberg and National Research Center of the Helmholtz Association
INSTITUTE OF FLUID MECHANICSFACULTY OF MECHANICAL ENGINEERING
www.kit.edu
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
Torsten SchenkelInstitute of Fluid Mechanics
Faculty of Mechanical Engineering
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.
Torsten SchenkelInstitute of Fluid Mechanics
Faculty of Mechanical Engineering
4 24.03.2010
are the governing equations for fluid and solid any different?
FSI for Aero- and Hydroelasticity -Application in Bio Fluid Mechanics
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):
Torsten SchenkelInstitute of Fluid Mechanics
Faculty of Mechanical Engineering
5 24.03.2010
fluids and solids share the same governing equations: continuum mechanics
FSI for Aero- and Hydroelasticity -Application in Bio Fluid Mechanics
Fluid:
Stokes
Solid:
Material Law (e.g. Hooke)
Torsten SchenkelInstitute of Fluid Mechanics
Faculty of Mechanical Engineering
6 24.03.2010
solution methods for coupled problems:
FSI for Aero- and Hydroelasticity -Application in Bio Fluid Mechanics
mononlithic partitioned elimination
X
Y
Torsten SchenkelInstitute of Fluid Mechanics
Faculty of Mechanical Engineering
7 24.03.2010 FSI for Aero- and Hydroelasticity -Application in Bio Fluid Mechanics
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:
Torsten SchenkelInstitute of Fluid Mechanics
Faculty of Mechanical Engineering
8 24.03.2010
schemes for partitioned coupling:
FSI for Aero- and Hydroelasticity -Application in Bio Fluid Mechanics
weakly coupled(explicit)
parallel
Solid
Fluid
Torsten SchenkelInstitute of Fluid Mechanics
Faculty of Mechanical Engineering
9 24.03.2010 FSI for Aero- and Hydroelasticity -Application in Bio Fluid Mechanics
weakly coupled(explicit)
serial parallel
load consistent
Solid
Fluid
schemes for partitioned coupling:
Torsten SchenkelInstitute of Fluid Mechanics
Faculty of Mechanical Engineering
10 24.03.2010 FSI for Aero- and Hydroelasticity -Application in Bio Fluid Mechanics
weakly coupled(explicit)
serial parallel
Solid
Fluid
space consistent load consistent
schemes for partitioned coupling:
Torsten SchenkelInstitute of Fluid Mechanics
Faculty of Mechanical Engineering
11 24.03.2010 FSI for Aero- and Hydroelasticity -Application in Bio Fluid Mechanics
weakly coupled(explicit)
serial, explicit parallel,explicit
space consistent
strongly coupled(implicit)
time step loops(iterative)
load consistent
schemes for partitioned coupling:
Torsten SchenkelInstitute of Fluid Mechanics
Faculty of Mechanical Engineering
12 24.03.2010
why not explicitly?
FSI for Aero- and Hydroelasticity -Application in Bio Fluid Mechanics
)()( tFE xK xxM =++&&
assumpt. : E = K
Fluid Solid
Torsten SchenkelInstitute of Fluid Mechanics
Faculty of Mechanical Engineering
13 24.03.2010 FSI for Aero- and Hydroelasticity -Application in Bio Fluid Mechanics
Fluid Solid
partitioninginterface
why not explicitly?
Torsten SchenkelInstitute of Fluid Mechanics
Faculty of Mechanical Engineering
14 24.03.2010 FSI for Aero- and Hydroelasticity -Application in Bio Fluid Mechanics
EtFx )(
=
Fluid Solid
)(tFE x=
why not explicitly?
Torsten SchenkelInstitute of Fluid Mechanics
Faculty of Mechanical Engineering
15 24.03.2010 FSI for Aero- and Hydroelasticity -Application in Bio Fluid Mechanics
)()( tFE xK xxMtR =>+= &&
xsolid
Rfluid
Fluid Solid
why not explicitly?
Torsten SchenkelInstitute of Fluid Mechanics
Faculty of Mechanical Engineering
16 24.03.2010 FSI for Aero- and Hydroelasticity -Application in Bio Fluid Mechanics
)()( tFE xK xxM =++&&
)()( tFK xxM =+&&
)(tFE x=
time [s]
disp
lacemen
t [-]
why not explicitly?
Torsten SchenkelInstitute of Fluid Mechanics
Faculty of Mechanical Engineering
17 24.03.2010
and yet it works!
FSI for Aero- and Hydroelasticity -Application in Bio Fluid Mechanics
Courtesy of FLUENT Inc.
for low fluid density!
Torsten SchenkelInstitute of Fluid Mechanics
Faculty of Mechanical Engineering
18 24.03.2010
characteristic numbers
FSI for Aero- and Hydroelasticity -Application in Bio Fluid Mechanics
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
Torsten SchenkelInstitute of Fluid Mechanics
Faculty of Mechanical Engineering
19 24.03.2010
implicit extension to serial explicit coupling scheme
FSI for Aero- and Hydroelasticity -Application in Bio Fluid Mechanics
F
Fluid Solid
Torsten SchenkelInstitute of Fluid Mechanics
Faculty of Mechanical Engineering
20 24.03.2010 FSI for Aero- and Hydroelasticity -Application in Bio Fluid Mechanics
EtFx )(
=
Fluid Solid
implicit extension to serial explicit coupling scheme
Torsten SchenkelInstitute of Fluid Mechanics
Faculty of Mechanical Engineering
21 24.03.2010 FSI for Aero- and Hydroelasticity -Application in Bio Fluid Mechanics
Fluid Solid
implicit extension to serial explicit coupling scheme
Torsten SchenkelInstitute of Fluid Mechanics
Faculty of Mechanical Engineering
22 24.03.2010 FSI for Aero- and Hydroelasticity -Application in Bio Fluid Mechanics
Fluid Solid
implicit extension to serial explicit coupling scheme
Torsten SchenkelInstitute of Fluid Mechanics
Faculty of Mechanical Engineering
23 24.03.2010 FSI for Aero- and Hydroelasticity -Application in Bio Fluid Mechanics
Fluid Solid
implicit extension to serial explicit coupling scheme
Torsten SchenkelInstitute of Fluid Mechanics
Faculty of Mechanical Engineering
24 24.03.2010 FSI for Aero- and Hydroelasticity -Application in Bio Fluid Mechanics
Fluid Solid
implicit extension to serial explicit coupling scheme
Torsten SchenkelInstitute of Fluid Mechanics
Faculty of Mechanical Engineering
25 24.03.2010
verification of coupling scheme
FSI for Aero- and Hydroelasticity -Application in Bio Fluid Mechanics
)()( tFE xK xxM =++&&
disp
lacemen
t [-]
time [s]
analyticalsimulation
Torsten SchenkelInstitute of Fluid Mechanics
Faculty of Mechanical Engineering
26 24.03.2010
proof of concept (standard test case)
FSI for Aero- and Hydroelasticity -Application in Bio Fluid Mechanics
smvinlet 5.0=
smkg
mkgPaE fluidfluidsolidsolid 01.0;1000;49.0;105 3
8 ====×= nrrn
Torsten SchenkelInstitute of Fluid Mechanics
Faculty of Mechanical Engineering
27 24.03.2010 FSI for Aero- and Hydroelasticity -Application in Bio Fluid Mechanics
explicit, serial coupling schemeload/position inconsistency
unstable
proof of concept (standard test case)
Torsten SchenkelInstitute of Fluid Mechanics
Faculty of Mechanical Engineering
28 24.03.2010 FSI for Aero- and Hydroelasticity -Application in Bio Fluid Mechanics
implicit, serial coupling schemeconsistent load/position
stable
proof of concept (standard test case)
Torsten SchenkelInstitute of Fluid Mechanics
Faculty of Mechanical Engineering
29 24.03.2010 FSI for Aero- and Hydroelasticity -Application in Bio Fluid Mechanics
explicit, serial coupling schemeload/position inconsistency
unstable
implicit, serial coupling schemeconsistent load/position
stable
proof of concept (standard test case)
Torsten SchenkelInstitute of Fluid Mechanics
Faculty of Mechanical Engineering
30 24.03.2010
validation and benchmarking
FSI for Aero- and Hydroelasticity -Application in Bio Fluid Mechanics
inlet: pressure inlet (udf)
outlet: pressure outlet (p=0)
wall: no slip
Symmetry: 2D axisymmetric
inner surface:
Pulse Wave Velocity (Moens-Korteweg):
Torsten SchenkelInstitute of Fluid Mechanics
Faculty of Mechanical Engineering
31 24.03.2010 FSI for Aero- and Hydroelasticity -Application in Bio Fluid Mechanics
Pulse Wave Velocity:
12tD
23tD
validation and benchmarking
Torsten SchenkelInstitute of Fluid Mechanics
Faculty of Mechanical Engineering
32 24.03.2010 FSI for Aero- and Hydroelasticity -Application in Bio Fluid Mechanics
¥u
validation and benchmarking
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
Torsten SchenkelInstitute of Fluid Mechanics
Faculty of Mechanical Engineering
33 24.03.2010
summary FSI methodology
FSI for Aero- and Hydroelasticity -Application in Bio Fluid Mechanics
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.
Torsten SchenkelInstitute of Fluid Mechanics
Faculty of Mechanical Engineering
34 24.03.2010 FSI for Aero- and Hydroelasticity -Application in Bio Fluid Mechanics
Part 2: Application in Bio Fluid Mechanics
Ventricular Flow
Abdominal Aortic Aneurysm (AAA)
Torsten SchenkelInstitute of Fluid Mechanics
Faculty of Mechanical Engineering
35 24.03.2010
accord.: Dössel et.al.
heart function (crudely simplified)
FSI for Aero- and Hydroelasticity -Application in Bio Fluid Mechanics
Torsten SchenkelInstitute of Fluid Mechanics
Faculty of Mechanical Engineering
37 24.03.2010
fibre orientation
Leonid Zhukov, Alan H. BarrDepartment of Computer ScienceCalifornia Institute of Technology
DT MRI (post mortem)
FSI for Aero- and Hydroelasticity -Application in Bio Fluid Mechanics
Torsten SchenkelInstitute of Fluid Mechanics
Faculty of Mechanical Engineering
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
Torsten SchenkelInstitute of Fluid Mechanics
Faculty of Mechanical Engineering
39 24.03.2010
myocardium motion - heart twist
S. WulfinghoffDiploma thesisKIT 2007
KaHMo – Karlsruhe Heart ModelFSI for Aero- and Hydroelasticity -Application in Bio Fluid Mechanics
Torsten SchenkelInstitute of Fluid Mechanics
Faculty of Mechanical Engineering
40 24.03.2010
myocardium motion
S. KrittianPh.D. thesisKIT 2009
KaHMo – Karlsruhe Heart ModelFSI for Aero- and Hydroelasticity -Application in Bio Fluid Mechanics
Torsten SchenkelInstitute of Fluid Mechanics
Faculty of Mechanical Engineering
41 24.03.2010
ventricular flow
3 dim. streamlines λ2 structures
S. KrittianPh.D. thesisKIT 2009
KaHMo – Karlsruhe Heart ModelFSI for Aero- and Hydroelasticity -Application in Bio Fluid Mechanics
Torsten SchenkelInstitute of Fluid Mechanics
Faculty of Mechanical Engineering
42 24.03.2010
abdominal aortic aneurysm AAA
U. Janoske,DHBW Mosbach, Univ. Wuppertal
FSI for Aero- and Hydroelasticity -Application in Bio Fluid Mechanics
Torsten SchenkelInstitute of Fluid Mechanics
Faculty of Mechanical Engineering
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
KaHMo – Karlsruhe Heart ModelFSI for Aero- and Hydroelasticity -Application in Bio Fluid Mechanics