Simulating FSI Problems via the Curvilinear …wim/academy/...HbidNHybrid Non-itilF /I dB dinertial Frame/Immersed Boundary Borazjani, PhD Thesis, 2008 Bd ki ti tilb tfBody kinematics,

Simulating FSI Problems via the Curvilinear gImmersed Boundary Method

From Biofluids to Wind TurbinesFrom Biofluids to Wind Turbines

Iman Borazjani, Trung Le, SeokKoo Kang, Suresh

B h d F ti S ti lBehara, and Fotis Sotiropoulos

Computational Hydrodynamics & Biofluids GroupSaint Anthony Falls Laboratory

University of MinnesotaMinneapolis, MN

Immersed boundary Colloquium, AmsterdamJune 16, 2009

Sharp-Interface Cartesian/Immersed Boundary Approach

Gilmanov and Sotiropoulos, JCP, 2005

Arbitrarily complex 3D bodies are discretized with unstructured triangular mesh immersed in a gCartesian mesh

Immersed boundary treated as a h i t fFluid

Cartesian fluid mesh

sharp interface

Efficient node classification Borazjani et al JCP 2008

Fluid

Boundary

Solid

Unstructured

fluid mesh Borazjani et al., JCP, 2008

Velocities at the boundary are reconstructed via quadratic

Solid

body mesh interpolation in the normal direction2nd-order accurate - Gilmanov & Sotiropoulos, JCP, 2005

St. Anthony Falls LaboratoryUNIVERSITY OF MINNESOTA

p , ,

Curvilinear Immersed Boundary FSI yMethod (CURVIB-FSI)

Moving immeresed boundaries over Body-fitted background mesh

Sharp interface treatment via 2nd

For details see:

Gilmanov and Sotiropoulos, A Hybrid Cartesian/Immersed Boundary Sharp interface treatment via 2nd-order accurate reconstruction

Fully-curvilinear, Cristoffel-symbol-free

p , y yMethod for Simulating Flows with 3D Geometrically Complex Moving Bodies J. Comp. Physics, 207 (2): 457-492, 2005

y , ynon-staggered grid fractional step method

Effi i t K l b d l

Ge and Sotiropoulos, A Numerical method for Solving the 3D Unsteady Incompressible Navier-Stokes Equations in Curvilinear Domains with Complex Immersed Boundaries, J. Comp. Physics, Efficient Krylov-based solvers

MPI implementation

p , p y ,225(2), 1782-1809, 2007

Borazjani, Ge, and Sotiropoulos, Curvilinear Immersed Boundary Partitioned FSI approach: Strong coupling with dynamic under-relaxation

Convergence rate for discrete divergence of the velocity field (107

grid nodes)

j yMethod for Simulating Fluid Structure Interaction with Complex 3D Rigid Bodies, forthcoming, J. Comp. Physics, 2008


Bi-leaflet Mechanical Heart Valves

Physiologic upstream flow waveform

Peak systole Re = 6000y

Plug inflow conditions

10×106 grid nodes, 2500 time steps per cyclecycle

PIV measurements obtained at the Georgia Tech CFM laboratory

FSI simulation

2 θ

θmin

Mdtdc

dtdI =+

θθ2

2 θ

θmax

I = 0.001 and c = 0


Stability and Robustness of FSI SolveryBorazjani, PhD Thesis, 2008; Borazjani, Ge & Sotiropoulos, JCP, 2008

Due to small inertia even the strong-coupling might not converge.

Under-relaxation to stabilize:11 ~)1( ++ +−= lll QQQ αα

α = 0.7

Aitken acceleration to find stR+

<<1

20 α

α = 0.5I

Rs

fst ρ

ρ H=

under-relaxation coefficient:Aitken

1

11 ~

+

++

Δ

−=Δl

lll

QQQQ

1

1

11

1

)1(

+

+

++

−=

Δ−ΔΔ

−+=

l

ll

llll

QQQ

λα

λλλ


FSI Simulations Borazjani, PhD Thesis, 2008; Borazjani, Ge & Sotiropoulos, JCP, 2008

Q Criteria: ½(||Ω||2-||S||2) (H t 1988)

Out of plane vorticity


(Hunt 1988)

Out of Plane Vorticity Comparisons:Out of Plane Vorticity Comparisons:FSI vs. PIV

t=240 msect=240 msec

Borazjani, PhD ThesisPhD Thesis, 2008











t 300t=300 msecBorazjani, PhD ThesisPhD Thesis, 2008








FSI Validation with In Vitro MeasurementsBorazjani PhD Thesis 2008; Borazjani et al JCP 2008Borazjani, PhD Thesis, 2008; Borazjani et al, JCP, 2008

Comparison of calculated leaflet kinematics with measurement in a straight aorta


measurement in a straight aorta

Anatomic AortaBorazjani et al, Ann. of Biomed Eng, Tentatively AcceptedSotiropoulos & Borazjani, Med. & Bio. Eng & Comp, 2009, review article


Overset-CURVIB method

Overset gridOverset grid

Body-fitted grid for aorta and branches

Cartesian grid toCartesian grid to contain left ventricle

Left ventricle and the valve asthe valve as immersed boundary


BMHV Driven by the Ventricle MotionBMHV Driven by the Ventricle Motion


Aquatic Swimming:Aquatic Swimming:Tethered Virtual Swimmers

Tethered LampreyBorazjani I and Sotiropoulos F

Tethered MackerelBorazjani I and Sotiropoulos F (2008) Borazjani, I. and Sotiropoulos, F.

(2009). Journal of Experimental Biology, 212, 576-592.

Borazjani, I. and Sotiropoulos, F. (2008). Journal of Experimental Biology 211, 1541-1558.


Major Conclusions of Numerical Experiments with Tethered Swimmers

For each Reynolds number there is unique Strouhal number (St*) that self-propelled swimming is possible

fASTail-beat frequency f

St* is decreasing as Re increases

Lamprey (anguilliform) has higher efficiency in the transitional regime

UfSt = Tail-beat Amplitude A

Lamprey (anguilliform) has higher efficiency in the transitional regime (Re=4000) while mackerel (carangiform) in the inertial regime (Re=∞)

Lamprey (anguilliform) requires less power than mackerel (carangiform)Lamprey (anguilliform) requires less power than mackerel (carangiform) across all flow regimes!

Body shape or kinematics?


How to study effects of body shape and kinematics?kinematics?


Body Shape and Kinematics Effects

KinematicsAnguilliform Carangiform

Mac

kere

l

pe

M

M k E l Mackerel

ody

Sha

p Macker-Eel Mackerel

Bo

yLa

mpr

ey

Lamprey Lamp-Rel


Self-propelled Swimming H b id N i ti l F /I d B dHybrid Non-inertial Frame/Immersed Boundary

Borazjani, PhD Thesis, 2008

B d ki ti t il b t f d i it fBody kinematics, tail beat frequency f and viscosity of fluid are fixed

Th i i l it i d t i d b d th f th

ν

The swimming velocity is determined based on the forces on the fish body

Fdt

dumcm

=

Non-inertial frame of reference Conservative formulation -Developed by Beddhu et al (1996) and used by Kim & Choi (2006):

u 1⎞⎛ ∂ Ω

dt

uuwuvuu 2

Re1])[( ∇+−∇=+−⋅∇+⎟

⎠⎞

⎜⎝⎛∂∂ p

t r

kT tt uQuvu =+= )()(rr

Ω

r

rcm

ar tt

rw

ruv

uQuvu

×Ω=

×Ω+=

=+= )()(

Inertial frame

Non-inertial frame


r Inertial frame

Effect of Kinematics on Swimming Velocity (Re 4000)Effect of Kinematics on Swimming Velocity (Re~4000)

Borazjani & Sotiropoulos, Gallery of Fluid Motion winner, Phys. Fluids, 2009

The Camera move with the slower swimmerAnguilliform kinematics vs. carangiform kinematicsThe dots show the swimming speed of each swimmerThe dots show the swimming speed of each swimmer

Lamprey Body Mackerel Body


Effect of Kinematics on Swimming Velocity (Inviscid)Effect of Kinematics on Swimming Velocity (Inviscid)

Borazjani & Sotiropoulos, Gallery of Fluid Motion winner, Phys. Fluids, 2009

The Camera move with the slower swimmerAnguilliform kinematics vs. carangiform kinematicsThe dots show the swimming speed of each swimmerThe dots show the swimming speed of each swimmer

Lamprey Body Mackerel Body


The Next Challenge: Swimming in Turbulent Flows


Aquatic Plankton like PropulsionAquatic Plankton-like Propulsion


Is the antenna deformation important?Is the antenna deformation important? Speed effect vs. Orientation effect

Rigid AntennaDeformable AntennaSt. Anthony Falls LaboratoryUNIVERSITY OF MINNESOTA

Rigid AntennaDeformable Antenna

Antenna Force ContributionBorazjani, PhD Thesis, 2008

Borazjani, Sotiropouols, Malkeil & Katz, J Exp Bio, under review

Th t

Drag

Phase Phase Ph PhaseThrust Phase 1

Phase 2

Phase3

Phase4

(CF)Rigid= -0.182 (CF)Deformable = -0.342St. Anthony Falls LaboratoryUNIVERSITY OF MINNESOTA

( F)Rigid ( F)Deformable

Stream Restoration

Cross vane Stone deflectors

Pictures from “Habitat improvement for trout streams”, Fish & boat commission PA 2007

Purpose: control of sedimentation and aquatic environments


Fish & boat commission, PA, 2007

LES of Natural Meandering Streams g(Seokkoo Kang, PhD student, SAFL)

with in-stream structures no structures


AcknowledgementsAcknowledgements

Funding from NIH NCED NSF and resources formFunding from NIH, NCED, NSF and resources form Minnesota Supercomputing InstitutePofessor Sotiropoulos Trung Le SeokKoo KangPofessor Sotiropoulos, Trung Le, SeokKoo Kang, and Suresh BeharaExperimental data of BMHV flows provided by DrExperimental data of BMHV flows provided by Dr. Yoganathan at CFM lab Georgia TechExperimental data for Copepods provided by Dr. Yen p p p p yfrom Georgia Tech and Dr. Katz from Johns HopkinsLamprey CT scan was Dr. Fish, and Dr. Smits from p yPrinceton university


Thank you!Thank you!

Documents

Simulating FSI Problems via the Curvilinear …wim/academy/...HbidNHybrid Non-itilF /I dB dinertial Frame/Immersed Boundary Borazjani, PhD Thesis, 2008 Bd ki ti tilb tfBody kinematics,