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Kumnit Nong and Padmanabhan Seshaiyer Department of Mathematical Sciences George Mason University Eugenio Aulisa Department of Mathematics and Statistics Texas Tech University Sonia Garcia Department of Mathematics United States Naval Academy Edward Swim Department of Mathematics Sam Houston State University COMSOL 2010 Boston, USA (October 8, 2010) Computational Methods for Multi-physics Applications with Fluid-structure Interaction COMSOL Conference 2010 Boston Presented at the
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Computational Methods for Multi-physics Applications with Fluid-structure Interaction · 2011-03-08 · Computational Methods for Multi-physics Applications with Fluid-structure Interaction

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Page 1: Computational Methods for Multi-physics Applications with Fluid-structure Interaction · 2011-03-08 · Computational Methods for Multi-physics Applications with Fluid-structure Interaction

Kumnit Nong and Padmanabhan Seshaiyer

Department of Mathematical Sciences George Mason University

Eugenio Aulisa

Department of Mathematics and Statistics Texas Tech University

Sonia Garcia

Department of Mathematics United States Naval Academy

Edward Swim

Department of Mathematics Sam Houston State University

COMSOL 2010

Boston, USA

(October 8, 2010)

Computational Methods for Multi-physics Applications

with Fluid-structure Interaction

COMSOL Conference 2010 Boston Presented at the

Page 2: Computational Methods for Multi-physics Applications with Fluid-structure Interaction · 2011-03-08 · Computational Methods for Multi-physics Applications with Fluid-structure Interaction

Fluid

Flow-structure interaction (FSI)

0.

).(

),0(:

u

fpuuut

u

TFluid

f

f

Solid Fluid Solid

])([5.0~~2)~(~

~.

),0(:

2

2

T

s

s

ww

tr

bt

w

TSolid

Page 3: Computational Methods for Multi-physics Applications with Fluid-structure Interaction · 2011-03-08 · Computational Methods for Multi-physics Applications with Fluid-structure Interaction

Fluid-Structure Interaction (1D)

)(t0 1 2

Fluid Structure Fluid Structure

0 2

)1,())(,(

)1,())(,(

0)1,(1)(

)2,1(),(

)1,0(),(23

2

2

2

2

2

2

tx

dtt

x

u

tt

dttu

ttdt

xxtgx

d

t

d

xxtfx

uu

x

u

t

u

sf

ss

fff

Page 4: Computational Methods for Multi-physics Applications with Fluid-structure Interaction · 2011-03-08 · Computational Methods for Multi-physics Applications with Fluid-structure Interaction

ALE Formulation

)),(,()),(,(5.1)),(,(),(

)()(),(

),(

)),(,(),(

:))(,0( allFor

))(,0()()(

),(

2

2

txtftxtx

uwutxt

x

ut

t

v

s

ttx

sx

txtwtdt

dx

s

txtt

xxtw

sssf

s

s

ss

Page 5: Computational Methods for Multi-physics Applications with Fluid-structure Interaction · 2011-03-08 · Computational Methods for Multi-physics Applications with Fluid-structure Interaction
Page 6: Computational Methods for Multi-physics Applications with Fluid-structure Interaction · 2011-03-08 · Computational Methods for Multi-physics Applications with Fluid-structure Interaction
Page 7: Computational Methods for Multi-physics Applications with Fluid-structure Interaction · 2011-03-08 · Computational Methods for Multi-physics Applications with Fluid-structure Interaction
Page 8: Computational Methods for Multi-physics Applications with Fluid-structure Interaction · 2011-03-08 · Computational Methods for Multi-physics Applications with Fluid-structure Interaction
Page 9: Computational Methods for Multi-physics Applications with Fluid-structure Interaction · 2011-03-08 · Computational Methods for Multi-physics Applications with Fluid-structure Interaction

Coupled FSI with Control

T

sxxstts

T t

fxxxftf

T

ss

T t

ff

fddg

fuuuul

fdd

fuuM

0

0

1

0

)(

1

0

0

1

22

0

)(

1

22

)(

)5.1(

21ˆ

21

21ˆ

21

Page 10: Computational Methods for Multi-physics Applications with Fluid-structure Interaction · 2011-03-08 · Computational Methods for Multi-physics Applications with Fluid-structure Interaction

Auxiliary system of PDEs

• In the fluid domain:

• In the solid domain:

0ˆ5.1

05.1

uuullu

luuuu

xxxftf

f

xxxftf

0

ddgg

gdu

xxstts

s

xxsts

Page 11: Computational Methods for Multi-physics Applications with Fluid-structure Interaction · 2011-03-08 · Computational Methods for Multi-physics Applications with Fluid-structure Interaction

Fluid-velocity Profile

Page 12: Computational Methods for Multi-physics Applications with Fluid-structure Interaction · 2011-03-08 · Computational Methods for Multi-physics Applications with Fluid-structure Interaction

Displacement Profile

Page 13: Computational Methods for Multi-physics Applications with Fluid-structure Interaction · 2011-03-08 · Computational Methods for Multi-physics Applications with Fluid-structure Interaction

MAV: Membrane Wing Deflection

Computational modeling of highly flexible membrane wings for MAVs

Ferguson, L., Aulisa, E., Seshaiyer P. and Gordnier R., (AIAA 2006-1661) Computational modeling of coupled membrane-beam flexible wings for MAVs

L. Ferguson, P. Seshaiyer, R. Gordnier, P. Attar (AIAA 2007-1787) Nonlinear Models for Biologically- Inspired Elastic Membrane Wings

E. Swim and P. Seshaiyer (AIAA-2008-2008)

Page 14: Computational Methods for Multi-physics Applications with Fluid-structure Interaction · 2011-03-08 · Computational Methods for Multi-physics Applications with Fluid-structure Interaction

Experimental Challenges in MAV Design

• Small size • High surface-to-volume ratio • Constrained weight and volume limitations • Low Reynolds number regime • Low aspect ratio fixed to rotary to flapping

wings • Longer flight time • Better range-payload performance

Page 15: Computational Methods for Multi-physics Applications with Fluid-structure Interaction · 2011-03-08 · Computational Methods for Multi-physics Applications with Fluid-structure Interaction

Computational Challenges in MAV Design

Structural Dynamics

Fluid Dynamics

Guidance & Control

Propulsion & Power

FSI

Page 16: Computational Methods for Multi-physics Applications with Fluid-structure Interaction · 2011-03-08 · Computational Methods for Multi-physics Applications with Fluid-structure Interaction

Model of a flexible MAV wing

Page 17: Computational Methods for Multi-physics Applications with Fluid-structure Interaction · 2011-03-08 · Computational Methods for Multi-physics Applications with Fluid-structure Interaction

Computational Model for MAV

O

ft onan

I

fontn )2sin(025.01.0

Inflow Outflow

21

21010

100

)(

invwv

invEwEw

infwEw

yy

tfyytt

tt

1 onwn t

N

fonn

in

0

0 3

Page 18: Computational Methods for Multi-physics Applications with Fluid-structure Interaction · 2011-03-08 · Computational Methods for Multi-physics Applications with Fluid-structure Interaction

Membrane Wing Deflection

Page 19: Computational Methods for Multi-physics Applications with Fluid-structure Interaction · 2011-03-08 · Computational Methods for Multi-physics Applications with Fluid-structure Interaction

Membrane Wing Deflection