A Sharp Interface Immersed Boundary Method A Sharp Interface Immersed Boundary Method for Flow, FSI & for Flow, FSI & AeroacousticsAeroacoustics II: II: Application to Biological FlowsApplication to Biological Flows

RajatRajat MittalMittalMechanical Engineering

OutlineOutline

Insect FlightInsect Flight

Dolphin kick in Olympic swimmersDolphin kick in Olympic swimmers

FSI of Phonation: Towards a CFD based FSI of Phonation: Towards a CFD based surgery planning toolsurgery planning tool

Cardiovascular Cardiovascular HemodynamicsHemodynamics

• Turning in a Monarch Butterfly• Sequence shows 1.5 flaps• >90o change in heading !• Turning distance < body size• Turn on a dime!

+

+

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+

+

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How does the Butterfly do this ? How does the Butterfly do this ? Deformable WingsDeformable Wings

Wings deform significantlyWings deform significantly

Greater repertoire of wing Greater repertoire of wing kinematics.kinematics.

–– Large leftLarge left--right wing right wing asymmetriesasymmetries

What causes deformationWhat causes deformation

–– Flow and inertia induced Flow and inertia induced deformation. (deformation. (Daniels et alDaniels et al))

–– Also active deformation through Also active deformation through action of direct muscles on action of direct muscles on axillaryaxillary scleritessclerites (wing joint).(wing joint).

Perhaps even active control of Perhaps even active control of deformability ??deformability ??

Flight Stabilization ??Flight Stabilization ??

Consider a Flapping Wing MAV in an Urban Consider a Flapping Wing MAV in an Urban Environment:Environment:–– Shear layers, wakes, corner flows Shear layers, wakes, corner flows ……

–– Understand flight stabilization in insectsUnderstand flight stabilization in insects

What can we learn from insects?What can we learn from insects?

Integrated ApproachIntegrated ApproachHigh Speed High Speed VideogrammetryVideogrammetry–– Tyson Hedrick LabTyson Hedrick Lab (UNC Chapel(UNC Chapel--Hill)Hill)

Structural parameterization Structural parameterization ((VallanceVallance Lab, GWU)Lab, GWU)–– WingWing–– BodyBody

High Fidelity Computational Modeling of High Fidelity Computational Modeling of Aerodynamics and AeroAerodynamics and Aero--Structural InteractionStructural Interaction–– Sharp Interface Immersed Boundary MethodSharp Interface Immersed Boundary Method–– Direct and LargeDirect and Large--Eddy Simulation Eddy Simulation –– Wing deformation modeling using FEM Wing deformation modeling using FEM

HighHigh--Speed HighSpeed High--Resolution Resolution VideogrammetryVideogrammetry

X Y

Z

X Y

Z

X Y

Z

X Y

Z

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Z

YX

Z

Y X Y

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X Y

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110

5075

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20 4060

80100

120

1

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4 3

0.00 0.04 0.08 0.12 0.16-40

-20

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20

A

ccel

erat

ion

(m/s

2 )

Time (s)

X-direction Y-direction Z-direction

Trajectory

Body Acceleration Painted Lady

COBRE Insect VideogrammetryLab

Rendering for CFD

Closing the Loop for Closing the Loop for CFD in Biology/Biomedical EngineeringCFD in Biology/Biomedical Engineering

Imaging Imaging (MRI, CT, Laser Scan)(MRI, CT, Laser Scan)

Geometric ModelsGeometric Models

AnimationAnimationOf Geometric ModelsOf Geometric Models

CFD/FSI SolverCFD/FSI SolverFor Complex, Moving For Complex, Moving

Organic ShapesOrganic Shapes

MimicsMimics Alias MAYAAlias MAYA

VICAR3DVICAR3D

HawkmothHawkmoth in Hoverin Hover

Hedrick Lab (UNC)Hedrick Lab (UNC)

Animated Model Rendered for CFDAnimated Model Rendered for CFD

Moth body based Moth body based on highon high--res laser res laser scan.scan.

Animation created Animation created in MAYA by in MAYA by matching high matching high speed video.speed video.

Vortex DynamicsVortex Dynamics

Strong spiral LEV on Strong spiral LEV on downstrokedownstroke..

Vortex ring shed at the Vortex ring shed at the end of end of downstrokedownstroke from from each wing.each wing.

Weak LEV on upstrokeWeak LEV on upstroke

Lift PredictionLift PredictionWt. of insect ~ 13.6 Wt. of insect ~ 13.6 mNmN

Average lift from CFD =15.0 Average lift from CFD =15.0 mNmN. Not bad!. Not bad!

How well does the timeHow well does the time--variation of lift compare to experiment?variation of lift compare to experiment?

Experimental determination?Experimental determination?–– Track acceleration of CM of wing, body partsTrack acceleration of CM of wing, body parts

–– Use simple dynamical model of insect to back out lift on wing.Use simple dynamical model of insect to back out lift on wing.

Fairly good prediction of peak thrust during Fairly good prediction of peak thrust during downstrokedownstroke..

Some mismatch during upstrokeSome mismatch during upstroke–– Larger cycleLarger cycle--toto--cycle variations in upstrokecycle variations in upstroke

Interestingly, upstroke is found to be quite ineffective!Interestingly, upstroke is found to be quite ineffective!

down up

Comparison with Past Models Comparison with Past Models Liu et al (Chiba University)Liu et al (Chiba University)HawkmothHawkmoth in hoverin hoverRigid wingsRigid wingsKinematics based Kinematics based on Ellingtonon Ellington’’s data.s data.Average lift is comparableAverage lift is comparable

However simulations show However simulations show significant lift generation significant lift generation during up (back) stroke.during up (back) stroke.

Possibilities?Possibilities?–– Discrepancy in kinematicsDiscrepancy in kinematics–– Rigid versus deformable?Rigid versus deformable?

Current

Liu et al.

Insect Flight Stability in Unsteady Insect Flight Stability in Unsteady EnvironmentsEnvironments

Conventional View:Conventional View: Stabilization achieved by changes inStabilization achieved by changes in

Many large insects seem to Many large insects seem to also changealso change

––

––

Role of ?Role of ?

{ } { } { } { } { }{ }

body wing wing wing body bodycp cp

body wing

I I r F r F

I I

ω

ω

⎡ ⎤+ = × + ×⎣ ⎦⎡ ⎤− +⎣ ⎦

{ }wingF

bodyI⎡ ⎤⎣ ⎦

wingI⎡ ⎤⎣ ⎦

+X

+Z+Zb

+Xb

abdominalflexion

pitch

proboscis

A. B.

C. D.

{ }bodyF

How to study gust response in How to study gust response in insects?insects?

Controlled experiments with freely flying Controlled experiments with freely flying insects are challenging!insects are challenging!

Need experimental assays that areNeed experimental assays that are–– For For untethereduntethered free flightfree flight

–– Predictable (to enable highPredictable (to enable high--speedspeed--rezrez videographyvideography))

–– RepeatableRepeatable

–– Provide a variety of (and calibrated) gust perturbations.Provide a variety of (and calibrated) gust perturbations.

ApproachApproachWork with Work with HawkmothsHawkmoths ((ManducaManduca SextaSexta) ) –– Large insect (~4Large insect (~4”” span)span)

–– Easy to culture/maintain.Easy to culture/maintain.

–– Excellent hoverer.Excellent hoverer.

–– Can be conditioned to approach and hover in front of nectar Can be conditioned to approach and hover in front of nectar source.source.

Hovering flight perturbed by incident vortex ringsHovering flight perturbed by incident vortex rings

–– Can control magnitude of impulse, energy and Can control magnitude of impulse, energy and vorticityvorticity of of the incident vortex ring.the incident vortex ring.

Small/large/massive perturbation.Small/large/massive perturbation.

–– Control size of ring and location/orientation of impactControl size of ring and location/orientation of impact

Pitch, roll, yawPitch, roll, yaw moments can be generated.moments can be generated.

Vortex Ring Impingement: Vortex Ring Impingement: Low Impulse ImpactLow Impulse Impact

High Impulse ImpactHigh Impulse Impact

Also track• Head-thorax- abdomen• Multiple points on wing• Body/Wing CoM

Vortex Ring Impingement: CFDVortex Ring Impingement: CFD

• Introduced in 1980, no regulation

• David Berkoff and Daichi Suzuki swim half the race using the dolphin kick, prompting FINA regulation

• Subsequently allowed for 15 meters after the start and every turn

• Undulatory wave travels down the length of the body, smallest amplitude at the fingertips, largest amplitude at the toes

Hydrodynamics of the Dolphin KickHydrodynamics of the Dolphin Kick

L

AU

f: frequency

UCslip

LA

UAfStLU :;;;Re ==

νRe: Reynolds numberRe: Reynolds numberSt : St : StrouhalStrouhal NumberNumber

The Dolphin Kick: The Dolphin Kick: Key ParametersKey Parameters

Issues that we hoped to address:Issues that we hoped to address:

What is the mechanism of thrust production in the What is the mechanism of thrust production in the human dolphin kick?human dolphin kick?–– No specific adaptation for swimmingNo specific adaptation for swimming–– Significant anatomical asymmetry Significant anatomical asymmetry stroke asymmetrystroke asymmetry–– What part of the body contribute thrust/drag etcWhat part of the body contribute thrust/drag etc–– ““active dragactive drag”” versus passive dragversus passive drag

How does thrust and power consumption scale with How does thrust and power consumption scale with StStand and A/LA/L–– Optimality?Optimality?–– Wake vortex topology?Wake vortex topology?

Are certain Are certain ““gaitsgaits”” more effective than others?more effective than others?

Optimal Optimal StrouhalStrouhal Number in Mammals that Number in Mammals that Swim Using Dolphin KickSwim Using Dolphin Kick

Courtesy: Dr. Frank FishCourtesy: Dr. Frank FishWestchester UniversityWestchester University

Olympic Swimmers Versus Dolphins?Olympic Swimmers Versus Dolphins?

Strouhal Number vs. Velocity

0.10

0.30

0.50

0.70

0.90

1.10

1.30

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50

Length Specicfic Velocity (U/L)

Stro

uhal N

umbe

rMaleFemaleCetaceanLinear (Male)Linear (Female)Linear (Cetacean)

{{Range for Range for most efficient most efficient swimmingswimming

UAfSt =

Laser Body ScanLaser Body Scan

Lenny Krayzelburg Gabrielle Rose

The CFD ProcessThe CFD Process

Courtesy USA SwimmingCourtesy USA Swimming

Static Geometric BodyStatic Geometric Body ModelModel

Typical Joint StructureAnimation SetupAutodesk MAYA

Model Animation Model Animation

Match Dolphin KickMatch Dolphin Kick KinematicsKinematics

Interface with CFDInterface with CFD……ViCar3DViCar3D

Strokes ModeledStrokes Modeled

Strouhal Number vs. Velocity

0.10

0.30

0.50

0.70

0.90

1.10

1.30

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50

Length Specicfic Velocity (U/L)

Stro

uhal N

umbe

r

MaleFemaleCetaceanLinear (Male)Linear (Female)Linear (Cetacean)

Vortex Structures and ThrustVortex Structures and Thrust-- Dolphin KickDolphin Kick

Slow kickSlow kick Fast kickFast kick

Vortex Ring Formation

The Ultimate Olympic Swimmer !The Ultimate Olympic Swimmer !

Active Drag and Thrust

Female 1

Female 2

Female 3

Male 1

Male 2

Useful

Total

WW

η=

0

0

( )

( )

Usefull

n nXn

nnn

T U U dt

F U U dt

τ

τη∞

∞

−

=

⋅ −

∑∫

∑∫

2Fc U

cη ∞+

=Ideal Froude Efficiency(Lighthill Slender Body Theory)

Work, Power & EfficiencyWork, Power & Efficiency

Froude Propulsive Efficiency

Actual Froude Efficiency

204.22261.4

59.91262.4

482.73426.4

141.71912.7

Male 2Cetacean

332.337.3639.071.8Male 1

187.434.9416.377.6Female 3

109.332.1289.885.1Female 2

159.723.4290.442.5Female 1

Total Work [J]Useful Work [J]Mean Total Power [Watts]

Mean Useful Power [Watts]

62.975.3

29.455.8

Male 2Cetacean

70.511.2Male 1

60.918.7Female 3

59.929.4Female 2

62.214.6Female 1

Ideal Efficiency ηF [%]Actual Efficiency η [%]

Work, Power & EfficiencyWork, Power & Efficiency

What have we learnt?What have we learnt?Propulsive efficiency of dolphin kick in humans Propulsive efficiency of dolphin kick in humans varies from about 10varies from about 10--30% . 30% . (>55% for dolphins).(>55% for dolphins).

Human dolphin kick constrained by anatomyHuman dolphin kick constrained by anatomy–– Small Small ““flukefluke””

–– Discrete joints that preclude smooth wave Discrete joints that preclude smooth wave (active drag)(active drag)

–– AnteriorAnterior--posterior asymmetry (up and down stroke)posterior asymmetry (up and down stroke)

Almost all the thrust comes from foot Almost all the thrust comes from foot (beyond ankle)(beyond ankle)

Down stroke produces most of the thrustDown stroke produces most of the thrust

Upstroke effectiveness can be improved by Upstroke effectiveness can be improved by increasing ankle flexibilityincreasing ankle flexibility–– ““FloppyFloppy”” ankles are the best for the dolphin kick ankles are the best for the dolphin kick

Biophysics of Phonation Biophysics of Phonation

NIH R01 grant focused NIH R01 grant focused on flowon flow--structural structural interaction in larynxinteraction in larynxUnderstand the FSI Understand the FSI mechanismsmechanismsApply knowledge to Apply knowledge to enhance laryngeal enhance laryngeal surgical procedures.surgical procedures.

GeneratorGenerator(Lungs(Lungs))

VibratorVibrator((LarynxLarynx))

ResonatorResonator((Pharynx,Pharynx,

Nasal cavity,Nasal cavity,Sinuses)Sinuses)

ArticulatorArticulator((Cheek, Cheek, tongue, tongue, Teeth,Teeth,lips)lips)

Medialization LaryngoplastyMedialization LaryngoplastySurgical procedure of choice for unilateral VF Surgical procedure of choice for unilateral VF paralysisparalysis–– Cord injectionCord injection–– Synthetic implant inserted to Synthetic implant inserted to medializemedialize

paretic VFparetic VF

Surgical outcome highly sensitive to implant Surgical outcome highly sensitive to implant shape and placementshape and placement–– Requires mm level precisionRequires mm level precision–– IntraIntra--operative trialoperative trial--andand--error procedureerror procedure

Relatively high revision rate for this surgery Relatively high revision rate for this surgery in the USA.in the USA.

Surgeons have no means of predicting the Surgeons have no means of predicting the effects of the implant on the vibratory effects of the implant on the vibratory characteristics of the paralyzed vocal foldcharacteristics of the paralyzed vocal fold

Can a surgical planning tool based on a Can a surgical planning tool based on a computational biomechanical model of the computational biomechanical model of the larynx improve the surgical outcome ??larynx improve the surgical outcome ?? Current Thyroplasty Procedure

Thyroplasty Implant

Thyroplasty Window

Paretic Vocal Fold

Structural Dynamics of VFStructural Dynamics of VF

Governing equationsGoverning equations

Model assumed in current study

Schematic showing VF substructure

cover

ligament

body

•The tissue materials are assumed to be transversely isotropic.

•Material properties are obtained from experiments (e.g., Titze et al 2000).

•Multi-property, non-homogeneous structure

3D Vocal Fold Model3D Vocal Fold Model

Effects of Tension Imbalance on PhonationSmaller VF vibration amplitude

Lack of full glottal closure leads to leakage flow

“Breathy” voice

Multiple incommensurate frequenciesChaotic vibration

Period Doubling

Bifurcation

Towards PatientTowards Patient--Specific ModelsSpecific Models

Sagittal View

Axial View

Computation of Voiced Sound Computation of Voiced Sound GenerationGeneration

45

Flow field in Vocal tractFlow field in Vocal tract

46

t/T

dQ/d

t

0 1 2 3 4 5-10

0

10

t/T0

P10 12 14 16 18

-1

-0.5

0

0.5

Hydrodynamic pressure near the vocal tract inlet

Time derivative of glottal flow rate

Frequency [Hz]

SP

L[d

B]

0 500 1000 1500 2000 2500 30000

20

40

60

80

100

120

Acoustic fieldAcoustic field

47

t/T0

∆p'

10 12 14 16 18 20

-1

0

1

X 10-4

Acoustic pressure at 60 cm from the mouth

New Initiative in Cardiovascular New Initiative in Cardiovascular FlowsFlows

Forty years after the seminal work of Peskin!

Simulation of LeftSimulation of Left--Ventricle FlowVentricle Flow

AcknowledgementsAcknowledgements

PostdocsPostdocs and Studentsand Students–– XudongXudong ZhengZheng, Jung, Jung--HeeHee SeoSeo, , QianQian XueXue, , LingxiaoLingxiao

ZhengZheng, , EhsanEhsan Aram, Rajneesh Aram, Rajneesh BhardwajBhardwaj

CollaboratorsCollaborators–– Dr. Dr. FadyFady NajjarNajjar (LLNL), Prof. Frank Fish (Westchester (LLNL), Prof. Frank Fish (Westchester

University), Prof. Ryan University), Prof. Ryan VallanceVallance (GWU), Prof. James (GWU), Prof. James Hahn (GWU), Dr. Steve Hahn (GWU), Dr. Steve BielamowiczBielamowicz, Prof. Tyson , Prof. Tyson Hedrick (UNC)Hedrick (UNC)

SponsorsSponsors–– AFOSR, NIH, NSF, USA Swimming, NASAAFOSR, NIH, NSF, USA Swimming, NASA

Questions?Questions?

Looking for a postdoc to work on cardiovascular flow modeling !