experimental aeroelasticity liege

7/25/2019 Experimental Aeroelasticity Liege

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AERO0032-1, Aeroelasticity and Experimental Aerodynamics, Lecture 2

Lecture 1:

Introduction Equations of

motion

G. Dimitriadis

Aeroelasticity and

Experimental Aerodynamics

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Introduction

Aereolasticity is the study of the interaction of inertial,structural and aerodynamic forces on aircraft, buildings,surface vehicles etc

Inertial Forces

Structural Forces Aerodynamic Forces

DynamicAeroelasticity

Structural dynamics Flight Dynamics

Static Aeroelasticity

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Why is it important?

The interaction between these threeforces can cause several undesirablephenomena: Divergence (static aeroelastic

phenomenon)

Flutter (dynamic aeroelastic phenomenon)

Vortex-induced vibration, buffeting(unsteady aerodynamic phenomena)

Limit Cycle Oscillations (nonlinearaeroelastic phenomenon)

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Static DivergenceNASA wind tunnel experiment on a forward swept wing

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Flutter

Flutter experiment: Winglet underfuselage of a F-16. Slow Mach

number increase.

The point of this experiment wasto predict the flutter Mach

number from subcritical test data

and to stop the test before flutteroccurs.

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Vortex-induced vibrations

Flow visualization of vortices shedbehind a cylinder

Vortex-induced vibrations

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Limit Cycle Oscillations

Stall flutter of a wing at an angle of

attack

Torsional LCO of a rectangle

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Even more LCOs

Galloping of a bridge deck

Torsional oscillations of a bridgedeck

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Many more LCOs

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These phenomena do not

occur only in the lab

Glider Limit CycleOscillations

Tacoma NarrowsBridge Flutter

Various phenomena

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Even on very expensive kit

Store-induced LCO on F-16

Fin buffeting on F-18

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How to avoid these

phenomena?

Aeroelastic Design (Divergence, Flutter,

Control Reversal)

Wind tunnel testing (Aeroelastic scaling)

Ground Vibration Testing (Complete

modal analysis of aircraft structure)

Flight Flutter Testing (Demonstrate thatflight envelope is flutter free)

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Wind Tunnel Testing

scale F-16 flutter model

F-22 buffetTest model

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Ground Vibration TestingGVT of F-35 aircraft

Space Shuttle horizontal GVT

GVT of A340

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Flight Flutter Testing

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So what is in the course?

Introduction to aeroelastic modeling

Modeling of static aeroelastic issues andphenomena:

Divergence

Modeling of dynamic aeroelastic phenomena: Flutter, vortex-induced vibration, stall flutter,

galloping

Practical aeroelasticity:Aeroelastic design

Ground Vibration Testing, Flight Flutter Testing

Non-aircraft aeroelasticity

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A bit of history

The first ever flutter incident occurred on theHandley Page O/400 bomber in 1916 in theUK.

A fuselage torsion mode coupled with an

antisymmetric elevator mode (the elevatorswere independently actuated)

The problem was solved by coupling theelevators

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More history

Control surface flutter became a frequentphenomenon during World War I and in theinterwar period.

It was solved in the mid-twenties by mass

balancing the control surface.

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Increasing airspeed

Aircraft flight speeds increased significantly during the 20sand 30s.

A number of high-speed racing aircraft suffered from flutterproblems

Supermarine S-4

Verville-Sperry R-3

Curtiss R-6

Loening R-4

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US flutter experiences in the

1930sGeneral Aviation YO-27: Wing-aileron andrudder-fuselage flutter

Fairchild F-24:Wing-aileron and

tail flutterBoeing YB-9A: Rudder-fuselage LCO

Curtiss YA-8: Rudder-fin flutter

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Other historic examples

Aircraft that experienced aeroelasticphenomena Handley Page O/400 (elevators-fuselage)

Junkers JU90 (fluttered during flight flutter test)

P80, F100, F14 (transonic aileron buzz)

T46A (servo tab flutter)

F16, F18 (external stores LCO, buffeting)

F111 (external stores LCO)

F117, E-6 (vertical fin flutter)

Read Historical Development of Aircraft Flutter, I.E.Garrick, W.H. Reed III, Journal of Aircraft, 18(11),897-912, 1981

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F-117 crash

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A F-117 crashed duringan airshow in Maryland inSeptember 1997

The inquest found thatfour fasteners thatconnected the elevonactuator to the wingstructure were missing.

This reduced theactuator-elevon stiffness,

leading to elevon-wingflutter


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Aeroelastic Modeling

Aircraft are very complex structures withmany modes of vibration and can exhibit verycomplex fluid-structure interactionphenomena

The exact modeling of the aeroelasticbehaviour of an aircraft necessitates thecoupled solution of: The full compressible Navier Stokes equations

The full structural vibrations equations

As this is very difficult, we begin withsomething simpler:

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Pitch Plunge AirfoilTwo-dimensional, two degree-offreedom airfoil, quite capable of

demonstrating most aeroelasticphenomena.

=pitch degree of freedom

h= plunge degree of freedomxf= position of flexural axis(pivot)

xc= position of centre of mass

Kh= plunge spring stiffnessK

= pitch spring stiffness

In fact, we will simplify evenfurther and consider a flat plate

airfoil (no thickness, no camber)

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Structural Model

There are two aspects to eachaeroelastic models

A structural model

An aerodynamic model

In some cases a control model is addedto represent the effects of actuators andother control elements

Develop the structural model

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Structural Model Details

Use total energy conservation

xf

xc

dx

dy

x

h

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Kinetic Energy

The total kinetic energy is given by

where

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Potential Energy

The potential energy is simply theenergy stored in the two springs, i.e.

Notice that gravity can be convenientlyignored

Total energy=kinetic energy+potentialenergy

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Equations of motion (1)

The equations of motion can be

obtained by inserting the expression for

the total energy into Lagrangesequation

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Equations of motion (2)

This should yield a set of two equations

of the form

or,

where Qis a vector of external forces

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Aerodynamic model

The possible aerodynamic models dependson flow regime and simplicity

In general, only four flow regimes are

considered by aeroelasticians: Incompressible

Subsonic

Transonic

Supersonic

For the moment we will deal only withincompressible modeling

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Incompressible, Unsteady

AerodynamicsOscillating airfoils leave behind them astrong vortex street. The vorticity in the wake

affects the flow over the airfoil:

The instantaneous aerodynamic forcesdepend not only on the instantaneous

position of the airfoil but also on the position

and strength of the wake vortices.

This means that instantaneous aerodynamicforces depend not only on the current motion

of the airfoil but on all its motion history fromthe beginning of the motion.

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Wake examples (Pitch)

Pitching airfoil-Low frequency

Pitching airfoil-High frequency

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Wake examples (Plunge)

Plunging airfoil-Low amplitude

Plunging airfoil-High amplitude

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Quasi-steady aerodynamics

The simplest possible modeling consists ofignoring the effect of the wake

Quasi-steady models assume that there are

only four contributions to the aerodynamicforces:

Horizontal airspeed U, at angle (t)to airfoil

Airfoil plunge speed,

Normal component of pitch speed,

Local velocity induced by the vorticity around theairfoil, vi(x,t)

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Lift and moment

xf

c/4

MxfL

h

The aerodynamicforce acting on

the wing is the liftand it is placed on

the quarter chord(aerodynamic

centre). There isalso anaerodynamic

moment acting

around theflexural axis.

NB: The lift is

defined positive

downwards

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Lift coefficient

The airfoil is uncambered but the

pitching motion causes an effective

camber with slope

From thin airfoil theory, cl=2(A0+A1/2),

where

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Lift coefficient (2)

Substituting all this into the equation for

the lift coefficient and carrying out the

integrations we get

This is the total circulatory lift acting on

the airfoil. There is another type of lift

acting on it, which will be presented in abit.

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Moment coefficient

The moment coefficient around theleading edge (according to thin airfoil)

theory is given by cm=-cl/4-(A1-A2)/4

Therefore, the moment coefficient

around the flexural axis is given by

cmxf=cm+xfcl/c

Substituting and integrating yields

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Added Mass

Apart from the circulatory lift and moment, theair exerts another force on the airfoil.

The wing is forcing a mass of air around it to

move. The air reacts and this force is knownas the added mass effect.

It can be seen as the effort required to movea cylinder of air with mass b2where b=c/2.

This force causes both lift and momentcontributions

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Full lift and moment

These are to be substituted into the structural equations of motion:

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Full aeroelastic equations of

motion The equations of motion are second order,

linear, ordinary differential equations.

Notice that the equations are of the form

And that there are mass, damping and

stiffness matrices both aerodynamic and

structural

A+ B( )!!q+ C+ UD( )!q+ E+ U2F( )q = 0

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Pitch-plunge equations of

motion

These are the full equations of motion for the pitch-plunge airfoil withquasi-steady aerodynamics. We will investigate them in more detail now.

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Static Aeroelasticity

First, we will study the static equilibrium

of the system.

Static means that all velocities andaccelerations are zero.

The equations of motion become

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Aerodynamic Coupling (1)

Let us apply an external moment Maroundthe flexural axis

The static equilibrium equations become

The second equation can only be satisfied if=M/(K

-U2ec2)

Then, the first equation can only be satisfied ifh= - U2cM/Kh(K-U

2ec2)

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This phenomenon is calledaerodynamic coupling. Changing thepitch angle causes a change in theplunge.

This is logical since increased pitchmeans increased lift.

However, if we apply a force Fon theflexural axis, the equations become

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The second equation can only be satisfied if=0

The first equation then gives h=F/Kh

In this case, there is no aerodynamiccoupling. Increasing the plunge does notaffect the pitch.

This is not the general case. The pitch-plungemodel ignores 3D aerodynamic effects

In real aircraft bending and torsion are bothcoupled.

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Static Divergence (1)

Look at the second static equilibrium equationwith an applied moment

If K>U2ec2then the spring and

aerodynamic stiffness constitute a restoring

force, which will balance the externalmoment.

However, if K


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Static divergence in pitch occurs when themoment caused by the lift around the flexuralaxis is higher than the structural restoringforce and of opposite sign.

For every pitch stiffness there is an airspeedabove which static divergence will occur.

If this airspeed is outside the flight envelopeof the aircraft, this is not a problem.

The pitch-plunge model does not allow for

static divergence in plunge. Again, this is because it ignores 3D effects.

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Remember that e=xf/c-1/4. If the flexural axis lies on the quarter-chord

(aerodynamic centre), then e=0.

Consequently, the moment of the lift aroundthe flexural axis also becomes zero.

It follows that static divergence is no longerpossible.

If xfis ahead of the aerodynamic centre, e


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Windmills

Upminster Windmill (1803) Bircham Windmill (1846)Pili windmill in Kos (1800)

The position of the flexural axis is very important for windmills

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experimental aeroelasticity liege

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