Aeroelastic Wind Tunnel Testing of Very Flexible High-Aspect-Ratio Wings

Justin JaworskiWorkshop on Recent Advances in

Aeroelasticity, Experiment and TheoryJuly 2, 2010

Problem and Scope

• High altitude long endurance (HALE) aircraft– May operate at large deformations

• Aeroelastic phenomena can lead to catastrophic structural failure– Nonlinear structural and aerodynamic effects are important for very flexible aircraft

• We will address flutter and limit cycle oscillation (LCO) physics in low subsonic flow– Mach = 0.1-0.3– Reynolds ~ 106– “Leap frog” increments in the fidelity/sophistication of theory and experiment to better understand LCO

of HALE-type wings

Nonlinear Dynamic ResponseA

mpl

itude

Airspeed

X

Am

plitu

deAirspeed

X

“Good”nonlinearity

“Bad”nonlinearity

GOAL: Characterize dangerous sub-critical behavior with wind tunnel experiments and correlate with predictive models

Wind Tunnel Test

Mirror

Accelerometer

• Procedure– Increase air speed in small increments

past flutter point• Flutter leads to limit cycle oscillation• Frequency and amplitude at half-span

measured with an accelerometer• Pitch/plunge at wing tip measured

with laser/mirror system– Decrease air speed slowly in small

increments until static state is recovered

• Metrics for success– Flutter speed– Limit cycle oscillation (LCO)

amplitude– Hysteresis

• Tunnel specifications– Test section: 0.7 x 0.53 x 1.52 m3– Max speed: 90 m/s (200 mph)

ANSYS Model of HALE Wing

Dimensions in millimeters. Tip store placed at O

NACA0012

→ Use finite element modeling to validate the use of continuum beam models for representing the non-uniform experimental wing structure.

J.W. Jaworski and E.H. Dowell, J. Aircraft 26(2), 2009, 291-306

Aeroelastic Results for Wind-Tunnel-based Aerodynamics

θ0=1°

LCO Simulation

Bifurcation Diagram

D. Tang and E.H. Dowell, AIAA Journal 39(8), 2001, 291-306

Improvement of Aerodynamic Model

Research Question– How do the aeroelastic simulation results change if you use an

aerodynamic model based on CFD aerodynamic data instead of wind tunnel data?

• Flutter speed and limit cycle oscillations• Anticipate deviation of computational aeroelastic predictions and experiment

Approach– Identify a dynamic stall aerodynamic model based on CFD computations

• Modify existing time-marching aeroelastic model for CFD-based aerodynamics

Continuum Aeroelastic Model

∫ ′′′+=x

dxwv0

ˆ φφ

( )(2 =L2 x1) ( )IV vdFEI v EI E mv Mvd

Ix

wφ+ + +′′ ′′ =− && &&

( ) ( )( )1 x1 =2 L( )IV wdFEI w mEI EI w Mw Mg x Lx

vd

δφ ′′ ′′−+ + + − − =&& &&

φx, y, v

z, w

D. Tang and E.H. Dowell, J. Fluids and Structures 19(2004) 291-306

( )2 21 xmEI EdMGJ I v mKwdx

φ φ′′ ′′′− ′ + =−+ &&dxdMI xLx =+ =φφ &&

• Nonlinear stiffness from elastic coupling

• Modal expansions convert equations to ODEs in time

• Geometric twist angle depends on elastic interaction:

Aerodynamic Model

• “Strip theory” assumption– Wing treated as a series of

uniform panels– 3D fluid effects neglected– Approximation valid for

slender wings• ONERA semi-empirical

dynamic stall model used to compute aero loads on each panel

ONERA dynamic stall model

⎥⎦⎤

⎢⎣⎡

∂∆∂

+∆−=++

+++=+

++=

+=

αα

φσααφσαλλ

φα

γγ

γ

&&&&

&&&&&

&&&

LLLLL

LLLLLLLLL

LvLLL

LLL

CeCrrCCaC

aaCC

CksC

CCC

bbb

a

ba

)()( 00( )( )( )[ ]2220

220

220

0 ,,,,,

L

L

L

LLLvLLL

Crrr

Ceee

Caaa

ksa

∆+=

∆+=

∆+=

σαλ = const.

• Lift (or moment) divided into linear (CLa) and nonlinear (CLb) contributions• Requires both static and dynamic lift data to identify parameters• Distinguishes between pitch angle (φ) and effective angle of attack (α) that

includes quasi-steady effects• Easily solved in state-space form

Static Lift Deviation

• Nonlinear equation of the ONERA model is forced by the static lift deficit, ∆CL

• Better agreement between experiment and CFD values than for simplified static model

• The static lift deficit function, ∆CL, is the main difference between the nonlinear contributions of the CFD- and wind-tunnel-based ONERA dynamic stall models

Effect of Structural Nonlinearity

• Hysteresis disappears from LCO when nonlinear elastic coupling is removed– This effect is independent

of the ONERA model parameters

Bifurcation Diagram for ONERA Model Variants

Experiment

Original Simulation (Wind Tunnel Model)

Linear/Nonlinear Aero: Wind Tunnel/CFD

Linear/Nonlinear Aero: CFD/Wind Tunnel

Conclusions

• Accurate flutter prediction of HALE wing flutter requires nonlinearity in both the structure and aerodynamic models

• Correct higher-order flutter mode predicted• Good quantitative agreement between theory and experiment

– Flutter speed– LCO amplitude

• LCO hysteresis requires structural nonlinearity– Aerodynamic stall dynamics effect the hysteresis bandwidth when

structural nonlinearity is included in the model• Aerodynamic nonlinearity required in aeroelastic model for

stable LCO• Linear and nonlinear lift based on CFD data increase the

LCO amplitude and flutter speed relative to aerodynamic models based on wind tunnel data

Future Work

• Include rigid body modes in aeroelastic analysis– More realistic representation of

flight configuration• Experimental flow field

measurements about wing in LCO motion– Investigate roles of dynamic stall

and 3D flow• First-principles aeroelastic analysis

with CFD– Time domain vs. Frequency

domain

Acknowledgments

• Prof. Earl Dowell• Prof. Donald Bliss• Prof. Kenneth Hall• Prof. Laurens Howle• Prof. Lawrence Virgin

• Dr. Deman Tang• Dr. Jeffrey Thomas• Dr. Chad Custer• Dr. Howard Conyers

Aeroelastic Wind Tunnel Testing of Very Flexible High-Aspect-Ratio WingsProblem and ScopeNonlinear Dynamic ResponseWind Tunnel TestANSYS Model of HALE WingAeroelastic Results for Wind-Tunnel-based AerodynamicsImprovement of Aerodynamic ModelContinuum Aeroelastic ModelAerodynamic ModelONERA dynamic stall modelStatic Lift DeviationEffect of Structural NonlinearityBifurcation Diagram for ONERA Model VariantsConclusionsFuture WorkAcknowledgments