l2_static aeroelasticity of 2d wing segment

8/10/2019 L2_Static Aeroelasticity of 2D Wing Segment

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Xie Changchuan

2014 Autumn

2nd Static Aeroelasticityof 2D Wing Segment


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Content1The model of 2D wing segment

2Solution of aeroelastic load and divergency

3The model of the 2D wing with control surface

4Control efficiency and reversal

Main AimsUnderstand the basic phenomena, concepts,

math principles, corresponding analysis

methods and the mechanism of staticaeroelasticity of the aircraft from the simplest

models of 2D wing segment.


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The static aeroelasticity

The success of Wright

brothers and the failure

of Longley

Slowly deform, ignore the inertial forces

The problems:

Load RedistributionStatic aeroelastic divergence

Control efficiency

Control reversal


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Airfoilsymmetry thin Spanunity(1)

Chordc Air force center1/4 chord

Elastic centere behind air force center

Coefficient of torsion spring

Slope of lifting curve Initial AOA

Elastic angle Speed of flowV

KyC

0

The model of 2D wing segment


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Forces on the wing segment

The change of the plunging

would not produce air force

Direct analysis

2

0 0

1( ) ( )

2e y yF V C c qcC

= + = +

0( )e e yM F ec qecC = = +

s K=

Lift

Moment

Elastic torque


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2D segment equilibrium equation

0( )yK qecC

= +

0 01

y

y

qecC qR

K qecC qR

= =

0( )

y yK qecC qecC

=

s aM=Equality of air forceand elastic force

Obtain the elastic angle

Aeroelastic load0 0 0

1

( )

1e

qRqRK

q

qRM K

qRR = +

=

0 0r yM qecC qRK

= =

/ /y meC K C K

= =

01 1e rq

MKqR qR

qR

=

=Elastic incremental load

Rigid load


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Static Aeroelastic Load and Divergence

Aeroelastic load0

1e

qRM K

qR

=

/mC K

=

1 0 ?qR =

01

qRq

=elastic angle

1/divm

Kq R

C

= =

eM

0

/

1 /

div

div

q q

q q =

divq qWhen


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0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

0

1

2

3

4

5

6

7

8

9

10

M1

M0

1

0

M

+0

k K

=

2

a yqec C=

The force lines

are parallel

div yK q ecC

=

div Kq ecC=


Iteration analysis

Process of iteration


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0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00

2

4

6

8

10

12

14

16

18

20

/

0

q/qdiv

The relationship of twist angle and dynamic pressure



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The energy analysis

Consider the quilibrium

state of the system *

The little disturbance of

twist angle

Virtual work of air force*

a yW M qecC

= =

*U K =

aW U >

The critical case = divy

aW U K

q

ecC

=

Work of outer force is larger than the incrementalof elastic potential energy, the system is unstable.

Static Aeroelastic Divergence

Virtual work of elastic force

When


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Analysis by equation theory

The equation of

static aeroelasticity

Look as a linear

algebra equation0A

0( )yK qecC

= +

0( )y yK qecC qecC

=

x b=

=0A

all Eig( ) 0A >

any Eig( ) 0A =

0div yK q ecC

= div

y

Kq

ecC

=

Static Aeroelastic Divergence

When1x A b=

Unique solution

Infinite many solutions

The critical case


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Summary

The static aeroelastic

divergence div

y m

K Kq

ecC C

= =

0

/

1 /

div

div

q q

q q =

0

/

1 /

dive

div

q qK

q q =

Four solutionmethods

Force equilibriumof Newton

Iteration method

Energy principle Theory of linear

equation

How to promote the divergence speed/dynamic pressure?


The static aeroelastic

response

When divq q

Lifting coefficient = y m yy y yy

qcC C K C C C CK qecC

+

= +

When the numrator equals to 0 =0y mrev ycC C K C q

+

( / )=ev

y

m

r

yK C Cq

cC

When

Usually is positiveyC

is negativemC


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Control efficiency

Rigid lifting coefficient r

y yC C

=

revq q< Define the elastic control efficiency

( )

y y m y

r

y y y

C qcC C K C

C K qecC C

+

= =

1 / 1 /

1 / 1 ( / )( / )

rev rev

div rev div rev

q q q q

q q q q q q = =

0 0 =

When

y

div

K

Cq

ec

=

( / )=ev

y

m

r

yK C Cq

cC

Divergence

D. P.

Reversal

D. P.


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Control efficiency and reversal of wing segment

with control surface

Homework

1

Please draw the curve of the control efficiencyvarying with dynamic pressure

Consider the case of , the horizontal axis using the

dimensionless number . Further, determine the curve

shape when and .

2The control efficiency and reversal of wing

segment with leading edge control surface

The model and the parameters are same with the model inclass, but with the leading edge control surface. Please deduct

the expressions of the control reversal dynamic pressure and

the control efficiency. Comparing with the case of trailing edge

control, give out necessary discussion.

/ divq qdivq q

l2_static aeroelasticity of 2d wing segment

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