AAE556 Lecture 15 Finite element subsonic aeroelastic models

Everything you wanted to know about aerodynamics but were afraid to ask• Lift per unit length ly changes along the span of a 3-D wing • The 2-D lift curve slope is not the same as the

AAE 556 Aeroelasticity

Lecture 15 Finite element subsonic aeroelastic

models

I like algebra Algebra is my friend.

Purdue Aeroelasticity 15-2

Lift computation

idealizations

Everything you wanted to know about aerodynamics but were afraid to ask

• Lift per unit length l(y) changes along

the span of a 3-D wing

• The 2-D lift curve slope is not the same

as the 3-D lift curve slope

• Lift curve slope in degrees

• e = Oswald’s efficiency factor

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Aerodynamic strip theory

• Wing is sub-divided into

a set of small spanwise

strips

• The lift and pitching

moment on each strip is

modeled as if the strip

had infinite span

Paneling methods

• The wing is replaced by a thin

surface

• This surface is replaced by a

finite number of elements or

panels with aerodynamic

features such as singularities

• There is an aerodynamic

influence coefficient matrix with

interactive elements

Strip theory gives different

results

Source: G Dimitriadis, University of Liege

Paneling - idealization

requirements and limitations

Purdue Aeroelasticity 15-10

Panel aero model finding the lift distribution

p i =VG i

Lifting line wing model

trailing vortices extending to infinity

Downwash matching points at 3/4 chord

The wing can be unswept or have non-constant chord

Horseshoe vortices with varying strength

bound at 1/4 chord points

Purdue Aeroelasticity 15-12

Panel aerodynamics interacts because

of downwash (angle of attack) matching

Each horseshoe vortex creates a flow field

around it The 3/4 chord downwash is affected by every other vortex on

the wing The vortex strengths must be

adjusted so that all conditions are satisfied.

Vortex influence decays

with distance

Aerodynamic relationship

wing

Solving for vortex strengths allow us to

approximate the lift distribution

Relationship between local

angle of attack and segment

lift values.

2D lift curve slope

Matrix elements are functions of wing planform geometry

Matrix is square, but not symmetrical

 i = rigid + q structural +  control

Structural idealization

Purdue Aeroelasticity 15-16

Each panel has its own FBD and

panel geometry

Put them all together to get the static equilibrium

equations – this is where the aeroelastic

interaction occurs

        i r s c 1 A ij   p j

q

local angles dynamic pressure

lift on each element

  q s      Cp i j  j

Wing Geometry

15-18

Purdue Aeroelasticity

Flexible and Rigid lift distributions

(M=0.5) areas under each curve are equal

4.87 13.85

Purdue Aeroelasticity 15-20

Flexible and Rigid lift

distribution (M=0.6)

Rigid and flexible roll

effectiveness (pb/2V)

MRev= 0.55

Purdue Aeroelasticity 15-22

Rigid wing and flexible wing C L 

Divergence Mach number

Divergence Mach No = 0.590

Purdue Aeroelasticity 15-24

Summary

• Use of bound vortices creates a math model that can predict subsonic high aspect ratio

wing lift distribution.

• This model has been incorporated into a

MATLAB code that you will use to do some homework exercises to calculate divergence, lift effectiveness and control effectiveness.

• You will compare the trends previously

derived