A Versatile Sharp I nterface I mmersed A Versatile Sharp I nterface - - PowerPoint PPT Presentation

A Versatile Sharp I nterface I mmersed A Versatile Sharp I nterface I mmersed Boundary Method with Application to Boundary Method with Application to Complex Biological Flows Complex Biological Flows

Rajat Rajat Mittal Mittal Mechanical Engineering

Biological Flows Biological Flows

• Biomimetics

Biomimetics and and Bioinspired Bioinspired Engineering Engineering

– – What can we learn from Nature ? What can we learn from Nature ? – – How can we adapt Nature How can we adapt Nature’ ’s s solutions into engineered solutions into engineered devices/machines ? devices/machines ?

• Biomedical Engineering

Biomedical Engineering

– – Cardiovascular flows Cardiovascular flows – – Respiratory flows Respiratory flows – – Phonatory Phonatory/Speech Mechanisms /Speech Mechanisms – – Biomedical Devices Biomedical Devices

Flapping flight Flexible Propulsors Drafting Autorotation

Inspiration from Dragonflies Inspiration from Dragonflies

• Dragonflies

Dragonflies

– – Existed for 350 million years Existed for 350 million years – – Wingspan from 2 Wingspan from 2 – – 80 cm 80 cm – – Fast and agile Fast and agile

• Wing Design

Wing Design

– – Thin, lightweight Thin, lightweight – – Vein reinforced Vein reinforced – – Pleated along chord Pleated along chord – – Pterostigma Pterostigma – – Microstructure Microstructure

• Wing Configuration

Wing Configuration

– – Wing Wing-

• wing interaction?

wing interaction?

• Wing Flexion?

Wing Flexion?

Computational Modeling Computational Modeling

• Need to tackle

Need to tackle

– – Complex 3D geometries Complex 3D geometries – – Moving boundaries Moving boundaries – – Fluid Structure Interaction Fluid Structure Interaction – – Resolution of vortex dynamics Resolution of vortex dynamics – – Relatively low Reynolds numbers Relatively low Reynolds numbers

• Very challenging for conventional body

Very challenging for conventional body fitted methods. fitted methods.

• Immersed Boundary Methods

Immersed Boundary Methods

– – handle these problems in all their complexity. handle these problems in all their complexity.

ViCar3D ViCar3D

Vi Viscous scous Car Cartesian Grid Solver for tesian Grid Solver for 3D 3D Immersed Boundaries Immersed Boundaries

• Simulations on non

Simulations on non-

• conforming Cartesian Grids

conforming Cartesian Grids

– – Stationary/moving boundaries Stationary/moving boundaries – – Solids/membranes Solids/membranes

• Sharp Interface IBM method

Sharp Interface IBM method

– – No boundary forcing ( No boundary forcing (Peskin Peskin et al) et al) – – 3D ghost 3D ghost-

• cell methodology

cell methodology

• 2

2nd

nd Order Fractional Step Scheme

Order Fractional Step Scheme

• 2

2nd

nd Order non

Order non-

• dissipative central

dissipative central difference scheme difference scheme

– – IBM treatment also 2 IBM treatment also 2nd

nd order accurate

• rder accurate
• Non

Non-

• uniform meshes

uniform meshes

• Geometric

Geometric Multigrid Multigrid for Pressure Poisson for Pressure Poisson

• Global

Global Coeff Coeff Dynamic SGS Model Dynamic SGS Model (

(Vreman Vreman) )

Journal of Computational Physics Volume 227, I ssue 10, 1 May 2008, Pages 4825-4852

ViCar3D ViCar3D

• Parallelized

Parallelized

• Extensively validated

Extensively validated

T=1 T=1 T=3 T=3 T=5 T=5 Komoutsakos & Leonard VICAR3D VICAR3D

Impulsively Started Cylinder Re= 1000 Mittal et al 2008, JCP

2 M pts

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

Imaging Imaging

(MRI, CT, Laser Scan) (MRI, CT, Laser Scan) Geometric Models Geometric Models

Animation Animation

Of Geometric Models Of Geometric Models

CFD/FSI Solver CFD/FSI Solver

For Complex, Moving For Complex, Moving Organic Shapes Organic Shapes

Mimics Mimics Alias MAYA Alias MAYA VICAR3D VICAR3D

ViCar3D ViCar3D-

• Capabilities

Capabilities

• "Wake Topology and Hydrodynamic Performance of

Low-Aspect-Ratio Flapping airfoil", J. Fluid Mechanics (2006) Vol 566 pp 309-343 .

• Low-dimensional models and performance scaling of a

highly deformable fish pectoral fin; J. Fluid Mech. (2009),

• vol. 631, pp. 311–342.
• "Computational modelling and analysis of the

hydrodynamics of a highly deformable fish pectoral fin." (2010) , Journal of Fluid Mechanics , doi:10.1017/ S0022112009992941.

ViCar3D ViCar3D-

• Capabilities

Capabilities

CFD of the dolphin kick

• "Propulsive Efficiency of the Underwater Dolphin Kick

in Humans", Journal of Biomechanical Engineering, Vol. 131, May 2009

• "A computational method for analysis of underwater

dolphin kick hydrodynamics in human swimming", Sports Biomechanics, 8(1), pp. 60-77, March 2009.

• "A comparison of the kinematics of the dolphin kick in

humans and cetaceans", Human Movement Science, Vol.28, pp.99-112, 2009

High Re?? High Re??

• Rec = 105
• 512x256x32
• 128 CPUs
• Nonlinear dynamics and synthetic-jet-based control of

a canonical separated flow. J. Fluid Mech., doi:10.1017/ S002211201000042X

Flight Maneuvers in Insects Flight Maneuvers in Insects

Side View Top View Gravity

• Maneuver: change in heading and/or speed

Maneuver: change in heading and/or speed

• Insects display a large array of maneuvers

Insects display a large array of maneuvers

Flapping Frequency and Maneuvering Flapping Frequency and Maneuvering

~ /

turn

T I C I C

θθ θθ

θ θ τ = +

• High frequency flappers (f > 150 Hz)

High frequency flappers (f > 150 Hz)

– – Bees, Flies, wasps etc Bees, Flies, wasps etc – – τ

τturn

turn > 10

> 10τ

τflap

flap

– – Minute changes in kinematics Minute changes in kinematics required to execute turn. required to execute turn. (Dickinson et al) (Dickinson et al) – – Stroke plane/amplitude/pitch angle Stroke plane/amplitude/pitch angle

• Low frequency flappers (f < 50 Hz)

Low frequency flappers (f < 50 Hz)

– – Moths, butterflies, locusts etc. Moths, butterflies, locusts etc. – – τ

τturn

turn ~

~ τ

τflap

flap

– – Turns can be executed in O(1) flap if wings can produce Turns can be executed in O(1) flap if wings can produce sufficient turning moments. sufficient turning moments. – – Does this happen?? Does this happen??

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

+ + + + + + +

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

• Wings deform significantly

Wings deform significantly

• Greater repertoire of wing

Greater repertoire of wing kinematics. kinematics.

– – Large left Large left-

• right wing

right wing asymmetries asymmetries

• What causes deformation

What causes deformation

– – Flow and inertia induced Flow and inertia induced

• deformation. (
• deformation. (Daniels et al

Daniels et al) ) – – Also active deformation through Also active deformation through action of direct muscles on action of direct muscles on axillary axillary sclerites sclerites (wing joint). (wing joint).

• Perhaps even active control of

Perhaps even active control of deformability ?? deformability ??

Wing Flexion: Wing Flexion: Enabler of other Flight Modes Enabler of other Flight Modes

COBRE Insect Videogrammetry Lab Moth in Climbing Flight

Clap & peel enabled by wing flexion

Integrated Approach Integrated Approach

• High Speed

High Speed Videogrammetry Videogrammetry

– – JHU Laboratory for JHU Laboratory for Bioinspired Bioinspired Engineering Engineering – – Tyson Hedrick Lab (UNC) Tyson Hedrick Lab (UNC)

• Structural parameterization

Structural parameterization (

(Vallance Vallance Lab, GWU) Lab, GWU)

– – Wing Wing – – Body Body

• High Fidelity Computational Modeling of

High Fidelity Computational Modeling of Aerodynamics and Aero Aerodynamics and Aero-

• Structural Interaction

Structural Interaction

– – Sharp Interface Immersed Boundary Method Sharp Interface Immersed Boundary Method – – Direct and Large Direct and Large-

• Eddy Simulation

Eddy Simulation – – Wing deformation modeling using FEM Wing deformation modeling using FEM

Hawkmoth Hawkmoth in Hover in Hover

Hedrick Lab (UNC) Hedrick Lab (UNC)

Animated Model Rendered for CFD Animated Model Rendered for CFD

• Moth body based

Moth body based

• n high
• n 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 Dynamics Vortex Dynamics

• Strong spiral LEV on

Strong spiral LEV on downstroke downstroke. .

• Vortex ring shed at the

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

• Weak LEV on upstroke

Weak LEV on upstroke

Lift Prediction Lift Prediction

• Wt. of insect ~ 13.6
• Wt. of insect ~ 13.6 mN

mN

• Average lift from CFD = 15.0

Average lift from CFD = 15.0 mN

• mN. Not bad!

. Not bad!

• How well does the time

How 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 parts Track 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 downstroke downstroke. .

• Some mismatch during upstroke

Some mismatch during upstroke

– – Larger cycle Larger cycle-

• to

to-

• cycle variations in upstroke

cycle 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)

• Hawkmoth

Hawkmoth in hover in hover

• Rigid wings

Rigid wings

• Kinematics based

Kinematics based

• n Ellington
• n Ellington’

’s data. s data.

• Average lift is comparable

Average 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 kinematics Discrepancy in kinematics – – Rigid versus deformable? Rigid versus deformable?

Current Liu et al.

Vortex Ring Impingement Experiments Vortex Ring Impingement Experiments

Vortex Ring Impingement: CFD Vortex Ring Impingement: CFD

Biophysics of Phonation Biophysics of Phonation

• NIH R01 grant focused

NIH R01 grant focused

• n flow
• n flow-
• structural

structural interaction in larynx interaction in larynx

• Understand the FSI

Understand the FSI mechanisms mechanisms

• Apply knowledge to

Apply knowledge to enhance laryngeal enhance laryngeal surgical procedures. surgical procedures.

Generator Generator

(Lungs (Lungs) )

Vibrator Vibrator

( (Larynx Larynx) )

Resonator Resonator

( (Pharynx, Pharynx, Nasal cavity, Nasal cavity, Sinuses) Sinuses)

Articulator Articulator

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

Modeling of Fluid Modeling of Fluid-

• Tissue

Tissue Interaction Interaction

• ViCar3D coupled to another solver that

ViCar3D coupled to another solver that computes deformation of elastic structures computes deformation of elastic structures

• Two approaches used for elastic structures

Two approaches used for elastic structures

– – Finite Finite-

• Element approach

Element approach – – Cartesian grid based approach (LECar3D) Cartesian grid based approach (LECar3D)

ViCar3D

(Glottal Aerodynamics)

LECar3D

(VF Deformation)

Aerodynamic Forces on VF VF Displacement & Velocity

• "An immersed-boundary

method for flow-structure interaction in biological systems with application to phonation", Journal of Computational Physics, 2008

Structural Dynamics of VF Structural Dynamics of VF

• Governing equations

Governing 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

Flow Flow-

• Induced Vibration (FEM)

Induced Vibration (FEM)

• Simulation Details

Simulation Details

– – 2D Simulation 2D Simulation – – Geometry based notionally on CT scan Geometry based notionally on CT scan

• f human larynx
• f human larynx

– – ViCar3D for air ViCar3D for air-

• flow

flow – – Finite Finite-

• Element for VF

Element for VF – – VF not fully adducted VF not fully adducted

• Observations

Observations

– – Kelvin Kelvin-

• Helmholtz

Helmholtz vortices vortices – – Bistable Bistable Jet Jet – – Sustained vibrations of vocal folds. Sustained vibrations of vocal folds.

(400K points)

3D Vocal Fold Model 3D Vocal Fold Model

• Analysis of flow-structure interaction in the larynx

during phonation using an immersed-boundary method;

• J. Acoust. Soc. Am. 126 2 , August 2009.
• Computational Study of the Effect of False Vocal Folds
• n Glottal Flow and Vocal Fold Vibration During

Phonation," Annals of Biomedical Engineering, Vol. 37,

• No. 3 pp. 625-642 March 2009

Towards Patient Towards Patient-

• Specific Models

Specific Models

Sagittal View Axial View

30

Direct Computation of Low Direct Computation of Low-

• Mach Number Sound

Mach Number Sound Linearized Linearized Perturbed Compressible Equations (LPCE) Perturbed Compressible Equations (LPCE)

( , ) '( , ) ( , ) ( , ) '( , ) ( , ) ( , ) '( , ) x t x t u x t U x t u x t p x t P x t p x t ρ ρ ρ = + = + = +

• LPCE (Seo & Moon, JCP, 2006)

Subtracting INS from CNS Linearization and suppressing the generation and evolution of vortical component

• n the acoustic field.

Need to use high (6th) order schemes to accurately model sound propagation ' ( ) ' ( ') U u t ρ ρ ρ ∂ + ⋅∇ + ∇⋅ = ∂

• '

1 ( ' ) ' u u p t U ρ ∂ +∇ ⋅ + ∇ = ∂

• '

( ) ' ( ') ( ' ) p p u u D t U P P Dt P γ ∂ + ⋅∇ + ∇⋅ + ⋅∇ = − ∂

• St

PSD (dB)

0.2 0.4 0.6 0.8 1 1.2 20 40 60 80 100 120

Noise generated by turbulent flow over a circular cylinder at ReD = 46000 , M = 0.21

Immersed Boundary Method for Immersed Boundary Method for LPCE LPCE ( Approximating Polynomial Method)

( Approximating Polynomial Method)

R

Body point (x0,y0,z0) Ghost point (x’ 1,y’ 1,z’ 1) Data points (x’ m,y’ m,z’ m)

( ', ', ') ( ', ', ') ( ') ( ') ( ') ,

N N N i j k ijk i j k

x y z x y z c x y z i j k N φ

= = =

Φ = + + ≤

∑∑∑

• N

N Number of Number of coefficients coefficients 2D 2D 3D 3D 1 1 3 3 4 4 2 2 6 6 10 10 3 3 10 10 20 20 4 4 15 15 35 35

[ ]

2 2 1

( ' , ' , ' ) ( ' , ' , ' )

M m m m m m m m m

w x y z x y z ε φ

=

= Φ −

∑

(H. Luo et al.)

32

t p'

2 4 6 8 10

• 4.0E-05

0.0E+00 4.0E-05 8.0E-05 c

Benchmark: Sound scattering by Benchmark: Sound scattering by a Circular Cylinder a Circular Cylinder

p'rms

30 60 90 120 150 180 10

• 6

10

• 5

Directivity at r=5

Acoustic Scattering from Complex Geometries Acoustic Scattering from Complex Geometries

y/D ∆p'

20 40 60 80

• 0.001
• 0.0005

0.0005 0.001

34

DNS

Comparison with DNS

DNS : full compressible N-S

• Eqs. on a body-fitted O-grid

ViCar3D carLPCE

Phonation and Speech

Sound in Complex Configurations

Sound in Complex Configurations

Acknowledgements Acknowledgements

• Postdocs

Postdocs and Students and Students

– – Xudong Xudong Zheng Zheng, Jung , Jung-

• Hee

Hee Seo Seo, , Qian Qian Xue Xue, , Lingxiao Lingxiao Zheng Zheng, , Ehsan Ehsan Aram, Aram, Haoxiang Haoxiang Luo Luo, , Haibo Haibo Dong Dong

• Collaborators

Collaborators

– – Dr.

• Dr. Fady

Fady Najjar Najjar (LLNL), (LLNL), Prof. George Lauder

• Prof. George Lauder (Harvard

(Harvard U.), Prof. James U.), Prof. James Tangorra Tangorra (Drexel U.), Prof. Ian Hunter (Drexel U.), Prof. Ian Hunter (MIT), (MIT), Prof. Frank Fish

• Prof. Frank Fish (Westchester University), Prof.

(Westchester University), Prof. Ryan Ryan Vallance Vallance (GWU), Prof. James Hahn (GWU), Dr. (GWU), Prof. James Hahn (GWU), Dr. Steve Steve Bielamowicz Bielamowicz, , Prof. Tyson Hedrick (UNC)

• Prof. Tyson Hedrick (UNC)
• Sponsors

Sponsors

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

Questions? Questions?