L2_Static Aeroelasticity of 2D Wing Segment
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Transcript of L2_Static Aeroelasticity of 2D Wing Segment
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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=
Static Aeroelastic Load and Divergence
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
Static Aeroelastic Load and Divergence
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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?
Static Aeroelastic Load and Divergence
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