the science of unmanned aerial vehicles with flexible

Nonlinear Fluid Structure Interaction

The Science Of Unmanned Aerial Vehicles WithFlexible Flying Surfaces

Casey St.Fleur and C. Nataraj

Dynamic Systems LabDepartment of Mechanical Engineering

Villanova University

April 10, 2013

Casey St.Fleur and C. Nataraj, Villanova Keystone AUVSI Symposium , April 2014 1/38


Outline

Motivation

Literature Review

Fluid Structure Interaction

Analytical Work

Experimental Setup

CFD

Acknowledgements



Motivation

Outline

1 Motivation

2 Literature Review

3 Fluid Structure Interaction

4 Analytical Work

5 Experimental Setup

6 CFD

7 Acknowledgements



Motivation

Flapping Flight



Motivation

Motivation

Performance Gap Between Nature and Engineering Platforms

Optimize Future Flapping Platforms

Poorly Understood Physics

Correlation Between Flexibility and EfficiencyRole of Geometric Nonlinearities and Anisotropy StructurePropertiesHow Leverage Unsteady Flow Features



Motivation

Flexible Wing Properties

Require Less Power

Good Performance Over a Range of Parameters

Lift Generation Over a Wide Range of Angle of Attacks

Too Much Flexibility Can Be A Negative



Literature Review

Outline

1 Motivation

2 Literature Review


4 Analytical Work


6 CFD

7 Acknowledgements



Literature Review

Current Research Areas

Experimental

Analytical

Computational



Literature Review

Experimental

Micro Fliers

Flapping Platform

Conn, et al. (2006) Zhang, et al. (2010)



Literature Review

Computational

Complicated Fluid Structure Equations

Computational Complex

Limited Insight



Literature Review

Analytical

Poorly Models Fluid Structure Interaction

None Capture the Nonlinear Elastic Properties of FlappingWings

Models Are Not Robust Enough to Model Different Wings

Toomey, et al. (2008) Zhang, et al. (2010)




Outline

1 Motivation

2 Literature Review


4 Analytical Work


6 CFD

7 Acknowledgements




Fluid Dynamics

Navier-Stokes

ρ∂ufluid

∂t +ρ(ufluid ·∇)ufluid = ∇·[−pI+µ(∇ufluid+(∇ufluid)T )]+F

Continuity

ρ∇ · ufluid = 0

Imperial College London




Solid Mechanics

Linear Equation of Motion

ρ∂2usolid

∂t2 −∇ · σ = Fv

Courtesy of Wikimedia Commons




Coupling

Courtesy of Comsol




Several Unsteady Mechanisms

Clap and Fling

Delayed Stall

Rotational Lift

Wing Wake Interaction

Sane, et al. (2003)

Miller, et al. (2004)



Analytical Work

Outline

1 Motivation

2 Literature Review


4 Analytical Work


6 CFD

7 Acknowledgements



Analytical Work

Proposed Models

Cantilever Beam Idealized Wing



Analytical Work

Derivation

u(X , t) = x(X , t)− X , v(X , t) = y(X , t)− Y , z = Z (1)

(∂x/∂X )2 + (∂y/∂Y )2 = 1 (2)

κ =∂2y/∂s2√

1− (∂y/∂s)2(3)

∫ t2

t1

δL dt +

∫ t2

t1

δW dt = 0 (4)



Analytical Work

Derivation Cont.

L = Tb − Vb (5)

Tb =1

2

∫ `

0mV 2

b dX , (6)

Vb =1

2

∫ `

0

(EI (X )κ2 + T (X )

∂2v

∂X 2

)dX (7)



Analytical Work

Derivation Cont.

FA(X , t) = −{∂

∂t+

[U

(1− ∂u

∂X

)−(∂u

∂t+ U

∂u

∂X

)]∂

∂X

}[V −

(∂u

∂t

∂v

∂X+ 2U

∂u

∂X

∂v

∂X

)− 1

2V

(∂v

∂X

)2]ρA

+1

2ρAV

∂v

∂X

∂V

∂X+ O(ε5)

(8)



Analytical Work

Derivation Cont.

Fpx = y ′2A∂p

∂x− y ′y ′′Ap + O(ε4)

Fpy = (y ′ − u′y ′ − y ′3)A∂p

∂x+

(y ′′ − u′′y ′ − u′y ′′ − 3

2y ′2y ′′

)Ap

+O(ε5) (9)

∂p

∂x=

1

2AρDU2CT

D

Dh(10)



Analytical Work

Derivation Cont.

FN =1

2ρDU2

{CN

[y ′ +

y

U+

yu′

U− u′y ′ +

x y

U2

− 1

2

(y ′3 +

y3

U3+

y ′2y

U+

y ′y2

U2

)+ CD

(y ′|y ′|+ y ′|y + |y ′|y

U+

y |y |U2

)}+ O(ε5)

FL =1

2ρDU2CT

[1− 1

2

(y ′2 + 2

y ′y

U+

y2

U2

)]+ O(ε4)



Analytical Work

Derivation Cont.

∫ t2

t1

δWdt =

∫ t2

t1

∫ `

0{[−Fpx + FL cos θ+(FA + FN) sin θ] δx

+ [Fpy + FL sin θ − (FA + FN) cos θ] δy} dXdt (11)

where, from geometry of deformation, we obtain θ = y ′ − u′y ′ − (1/3)y ′3 + O(ε5).

y(s, t) =N∑i=1

φi (s)ηi (t) (12)



Experimental Setup

Outline

1 Motivation

2 Literature Review


4 Analytical Work


6 CFD

7 Acknowledgements



Experimental Setup

Experiment Outline

Controlled Input

Flapping FrequentFlapping AmplitudeWing Profile and ElasticityWind Velocity

Measured Outputs

Wing DeflectionNet Lift and Drag ForcesFluid Induced Pressure on the WingsMotor Voltage and Current



Experimental Setup

Pressure Sensor

Courtesy of PPS



Experimental Setup

H-Bridge Circuit



Experimental Setup

Proposed Flapping Test Bed

Front View Side View



Experimental Setup

Flapping Test Bed Version 1



Experimental Setup

Flapping Test Bed Clip 1



Experimental Setup

Flapping Test Bed Clip 2



CFD

Outline

1 Motivation

2 Literature Review


4 Analytical Work


6 CFD

7 Acknowledgements



CFD

CFD Model



CFD

CFD Results



Acknowledgements

Outline

1 Motivation

2 Literature Review


4 Analytical Work


6 CFD

7 Acknowledgements



Acknowledgements

Acknowledgements

Many aspects of this project were supported by Office ofNaval Research Grant No. N000-14-09-1-119

Moritz Endowed Chair Professorship, Villanova University



Acknowledgements

Thanks!


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