computational aeroelasticity - metu | aerospace …yyaman/avt086/kolonay/ray_kolo… · ·...

Kolonay 1

CRD

Computational Aeroelasticity

The Cultural and Convention CenterMETU

Inonu bulvariAnkara, Turkey

Sponsored by:RTA-NATO

The Applied Vehicle Technology Panel

presented byR.M. Kolonay Ph.D.

General Electric Corporate Research & Development CenterAnkara, Turkey Oct.. 1-5, 2001

Kolonay 2

CRD

• Introduction- Fluid-Structure Interactions

•Aeroelasticity- Aeroelastic analysis/design in an MDA/MDO Environment

• Static Aeroelasticity

• Dynamic Aeroelasticity

• Commercial Programs with Aeroelastic Analysis/DesignCapabilities

Presentation Outline

Kolonay 3

CRD

Dynamic Aeroelastic Phenomena

• Dynamic Response

• Limit Cycle Oscillations (LCO)

• Buffet

• Flutter

Dynamic Aeroelasticity

Solutions found in time, frequency, and Laplace domain usuallywith generalized coordinates

Kolonay 4

CRD Dynamic Aeroelasticity

Dynamic Response

Transient response due to a rapidly applied load.

• Atmospheric Turbulence- Continuous random- Discrete random (gust)

• Landing loads

• “Snap” maneuvers

• Store Separation

Kolonay 5


Limit Cycle Oscillations

Typically caused by shock induced oscillations on a surface or flow/shocks attaching/detaching from a surface trailing edge.

• Panel Flutter

• Control Surface “Buzz”

• Store/Wing configurations

Reduces structural life

Usually requires nonlinear flow conditions and possibly nonlinearstructures (cs hinge stiffness)

Kolonay 6


Buffet

Response due to time-dependentseparated flows (usually vortical)impinging on structural surfaces.

• Bluffed bodies on horizontal and vertical surfaces

• Wings, strakes etc.. on vertical tails (often a twin tail prob-lem)

Reduces structural life

Requires nonlinear aerodynamics to capture phenomena

Kolonay 7


Flutter

Dynamic instability where-by the system extracts energy from thefree stream flow producing a divergent response.

• Usually resultant of coupling of 2 or more structural modes- Wing bending and torsion- Wing bending control surface hinge torsion- Wing torsion fuselage bending- Horizontal or vertical tail and fuselage

Divergent behavior can occur within a few cycles and be cata-strophic

Theodore Von Karman is said to have remarked that

“some men fear flutter because they do not understand it, whileothers fear it because they do”[8]

Kolonay 8

CRD

Mot

ion

Mot

ion

Mot

ion

Stable (A)

Neutral (B)

Unstable (C)F

requ

ency

A

BC

Torsion Mode

Bending Mode


FlutterTime Histories

Modal Coupling

Dynamic Pressure

Ko 9

D Dynamic Aeroelasticity

ro(20)

t

(21)

h forcesq.

(22)

or me initial state.(23)

t( )

3 igenvalue problem

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F

le

WE

F

(2

Flutterm the aeroelastic EOM

ere represents motion independent external (20) can be written as

stability solve the homogenous equation from so

Mu̇̇ Ku+ F u u̇ u̇̇ t, , ,( )=

F u u̇ u̇̇ t, , ,( ) F u u̇ u̇̇, ,( ) F t( )+=

F t( )

Mu̇̇ Bu̇ Ku+ + Q1[ ] u̇̇ Q2[ ]u̇ Q3[ ]u F+ + +=

Mu̇̇ Bu̇ Ku+ + Q1[ ] u̇̇ Q2[ ]u̇ Q3[ ]u+ +=

) can be solved by time integration or as an e

Ko 10

D

ra ssume that the

ns ments

(24)

ss and synchronous

(25)

it ubstituting into

4

(26)

0

0


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T

u

A

W

(2

Eigenvalue Solutionsnsform (23) to modal coordinates and a

teady aerodynamics depend only on displace

ume that the structural response is separable

h independent of time and .S

) gives

uh{ }

Mhhuh˙̇ Buh

˙ Khhuh12---ρV

2Qhh[ ]uh–+ + =

uh{ } qh{ }est

=

qh{ } s σ iω+=

Mhhs2

Bhhs Khh12---ρV

2Qhh–+ + q h{ } =

Ko 11

D

n

aeroelastic stiff-

causing roots

es

h amplitude and


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CR

• Eq. (26) is the basic flutter eigenvalue equatio

• All matrices can be expressed as real but the

ness matrix is unsymmetric

to be complex conjugate pairs.

• - Generalized unsteady aerodynamic forc

- Often assumed harmonic cast in frequency domain witphase

- Doublet Lattice, CPM, Mach Box, Strip Theory

• Several solutions exist for solving (26)- Method

- Method

- Method

- Method- State space

Khh12---ρV

2Qhh–

Qhh

KK E–P K–P

Ko 12

D

ca ecomes

(27)

- s

- re

,

- fre

- re

- e

- da

0=

k(≡

hh

h =

–


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CR

s

V

b

p

M

Qh

ρ

k

qh

γ

i ≡

P-K Flutter Solution

n be expressed as . (26) b

elected freestream speed

ference semi-chord

- complex response frequency and eigenvalue

, generalized mass, damping, stiffness matrices

- generalized aerodynamic matrix

estream density

duced frequency,

igenvector of modal coordinates

mping factor

sVkb

------ γ i+( ) Vb---- p= =

Vb----

2p

2Mhh

Vb---- pBhh Khh

ρV2

2----------Q k( )hh–+ + qh

γ i+ )Bhh Khh

QR

iQI

+[ ]

kωbV

-------=

1

Kolonay 13

CRD

P-K Method Comments

• Matrices are real but non-symmetric yielding complex roots.

• Flutter equation only “true” when , an estimate elsewhere

• Mode switching often occurs making results interpretation difficult

• depends on Mach number and reduced frequency

• Solution requires to be a continuous function of .

- Results in curve fitting which can cause errors

• Above formulation does not allow

• User responsible for determining “match point solutions”

γ 0=

Qhh Qhh M k,( )

Qhh k

Qhh

k 0=


Kolonay 14

CRD

AGARD 445.6 Flutter Calculations

X

Y

Z

31.38

27.48

23.57

19.67

15.77

11.86

7.958

4.055

.1511

-3.753

-7.656

-11.56

-15.46

-19.37

-23.27

-27.17

X

Y

ZX

YZ

X

YZ


X

Y

Z

71.52

65.25

58.97

52.69

46.42

40.14

33.87

27.59

21.31

15.04

8.761

2.485

-3.791

-10.07

-16.34

-22.62

X

Y

ZX

YZ

X

YZ

Mode 4,ω = 89.94 Hz.

X

Y

Z

25.09

20.38

15.68

10.97

6.269

1.565

-3.139

-7.843

-12.55

-17.25

-21.96

-26.66

-31.36

-36.07

-40.77

-45.48

X

Y

ZX

YZ

X

YZ

Mode 2,ω = 37.12 Hz.

X

Y

Z

27.92

26.05

24.19

22.32

20.45

18.59

16.72

14.85

12.98

11.12

9.250

7.383

5.516

3.649

1.782

-.08551

X

Y

ZX

YZ

X

YZ

Mode Shapes and frequencies

Mode 3,ω = 50.50 Hz.Mode 1,ω = 9.63 Hz.

Kolonay 15


AGARD 445.6 Time Integration Response

0.0 0.1 0.2 0.3 0.4

-0.0015

-0.0010

-0.0005

0.0000

0.0005

0.0010

0.0015

Time (sec)

Gen

eral

ized

Dis

plac

emen

t

γ1= 13.0682ω1= 88.352(Hz)

γ2= 5.9408ω2= 52.285(Hz)

γ3= 24.1002ω3= 30.268(Hz)

γ4= .1687ω4= 15.574(Hz)

DATA

FIT

ERROR

0.0 0.1 0.2 0.3 0.4

-0.015

-0.010

-0.005

0.000

0.005

0.010

0.015

Time (sec)

Gen

eral

ized

Dis

plac

emen

t

γ1= -.0366ω1= 15.561(Hz)

γ2= 32.0916ω2= 30.286(Hz)

γ3= 445.6037ω3= .612(Hz)

γ4= 4.7738ω4= 52.054(Hz)

DATA

FIT

ERROR

0.0 0.1 0.2 0.3 0.4

-0.0020

-0.0010

0.0000

0.0010

0.0020

0.0030

Time (sec)

Gen

eral

ized

Dis

plac

emen

t

γ1= 5.7635ω1= 52.269(Hz)

γ2= 25.9159ω2= 30.188(Hz)

γ3= .0396ω3= 15.564(Hz)

γ4= 12.4610ω4= 88.338(Hz)

DATA

FIT

ERROR

0.0 0.1 0.2 0.3 0.4

-0.0040

-0.0030

-0.0020

-0.0010

0.0000

0.0010

0.0020

0.0030

0.0040

Time (sec)

Gen

eral

ized

Dis

plac

emen

t

γ1= .0282ω1= 15.569(Hz)

γ2= 25.8733ω2= 30.095(Hz)

γ3= 5.7688ω3= 52.242(Hz)

γ4= 12.0791ω4= 88.547(Hz)

DATA

FIT

ERROR

Mode 1 Mode 3

Mode 2 Mode 4

M 0.901 q, 0.66psi U, 11908 in/sec= = =

Kolonay 16


AGARD 445.6 Time Response Integration

0.0 0.1 0.2 0.3 0.4

-0.0020

-0.0010

0.0000

0.0010

0.0020

0.0030

Time (sec)

Gen

eral

ized

Dis

plac

emen

t

γ1= 5.7635ω1= 52.269(Hz)

γ2= 25.9159ω2= 30.188(Hz)

γ3= .0396ω3= 15.564(Hz)

γ4= 12.4610ω4= 88.338(Hz)

DATA

FIT

ERROR

0.0 0.1 0.2 0.3 0.4

-0.0015

-0.0010

-0.0005

0.0000

0.0005

0.0010

0.0015

Time (sec)

Gen

eral

ized

Dis

plac

emen

t

γ1= 13.0682ω1= 88.352(Hz)

γ2= 5.9408ω2= 52.285(Hz)

γ3= 24.1002ω3= 30.268(Hz)

γ4= .1687ω4= 15.574(Hz)

DATA

FIT

ERROR

0.0 0.1 0.2 0.3 0.4

-0.0040

-0.0030

-0.0020

-0.0010

0.0000

0.0010

0.0020

0.0030

0.0040

Time (sec)

Gen

eral

ized

Dis

plac

emen

t

γ1= .0282ω1= 15.569(Hz)

γ2= 25.8733ω2= 30.095(Hz)

γ3= 5.7688ω3= 52.242(Hz)

γ4= 12.0791ω4= 88.547(Hz)

DATA

FIT

ERROR

0.0 0.1 0.2 0.3 0.4

-0.015

-0.010

-0.005

0.000

0.005

0.010

0.015

Time (sec)

Gen

eral

ized

Dis

plac

emen

t

γ1= -.0366ω1= 15.561(Hz)

γ2= 32.0916ω2= 30.286(Hz)

γ3= 445.6037ω3= .612(Hz)

γ4= 4.7738ω4= 52.054(Hz)

DATA

FIT

ERROR

M 0.901 q, 0.67psi U, 11998 in/sec= = =

Mode 1

Mode 4Mode 2

Mode 3Vf = 11,971 in/sec

radω f 90=

Kolonay 17

CRD

AGARD 445.6 P-K Flutter Solution

6000 8000 10000 12000 14000

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

MODE 1MODE 2MODE 3MODE 4


Dam

ping

rat

io (g

)

Velocity (V in/sec)

Velocity vs. Damping

Vf =1181 in/sec

Kolonay 18

CRD


-0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2

100

200

300

400

500


445.6 Wing Damping Ratio versus Frequency

(M= .901, α = 0.00°, ρ∞ = 9.307E-09 slugs/ in )


Fre

quen

cy (

radi

ans)

Damping ratio (g)

Velocity Root Locus

radω f 96=

Kolonay 19



6000 8000 10000 12000 14000

100

200

300

400

500


Velocity vs. FrequencyF

requ

ency

(ra

dian

s)

Velocity (V in/sec)

Kolonay 20

CRD Aeroelastic Software

Global Aeroelastic Software Developments• MSC/NASTRAN (U.S.)

• UAI/ASTROS (recently bought by MSC) (U.S.)

• UAI/NASTRAN (U.S.)

• ELFINI (France, Dessault)

• LAGRANGE (Germany, formerly MBB)

• STARS (Great Britain, RAE)

• OPTSYS (Sweden, SAAB)

• COMPASS (China)

• ARGON (Russia, Central Aerohydrodynamic Institute)

Ko 21

D Aeroelastic Software

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CR

MSC/NASTRAN• Steady Aerodynamics

- Subsonic•Doublet Lattice (k=0)•3-D panel Method (available in the near future)•Bypass option for any AIC

- Supersonic•ZONA51•Bypass option for any AIC•Aerodynamic database•Import/export loads data

• Unsteady Aerodynamic- Subsonic

•Doublet Lattice with body interference•Strip Theory

- Supersonic•Mach Box

Ko 22

D

stability derivativesIC

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•Piston Theory•ZONA51

• Structural Modeling- Very rich selection of FE

• Static Aeroelastic Analysis- 5 DOF trim (no drag/thrust trim)- Flexible increment analysis- Computes rigid, restrained and unrestrained flexible- Able to add experimental load correction factors to A- Divergence of restrained vehicle- Slender body models- Multiple set selectable aerodynamic models- Aeroelastic database- Import/export loads data

Aeroelastic Software

Ko 23

D

ality in PATRAN envi-

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CR

• Dynamic Aeroelasticity- Frequency response analysis- Random analysis- Transient analysis- Gust (random and discrete 1-d)- Flutter P-K, K, K-E (K-E allowsk=0)

- curve fits cubic through all points

• F-S Interface- Infinite plate spline- Thin plate spline- Finite plate spline- Beam spline- Rigid load Transfer

• Pre-Post Processing- Extensive Flight Loads pre/post processing function

ronment

Q M k,( )


Ko 24

D Aeroelastic Software

bilities

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CR

UAI/ASTROS Aeroelastic Capa• Steady Aerodynamics

- Subsonic•USSAERO (Woodward Aerodynamics, flat panel)•QUADPAN (Lockheed Martin, 3-D panel)•Bypass option for any AIC•Multiple set selectable aerodynamic models

- Supersonic•USSAERO (flat panel)•QUADPAN (3-D panel)•Bypass option for any AIC

• Unsteady Aerodynamic- Subsonic

•Doublet Lattice- Supersonic

•Constant Pressure Method (Apa, Northrop)

Ko 25

D

Quadrilateral Plates,

rivatives

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• Structural Modeling- Membrane type FEM (Rods, Beams, Shear panels,

Composites)

• Static Aeroelastic Analysis- Full 6 DOF Trim- Computes rigid and four types of flexible stability de- User defined loads- Trim Optimization

• Dynamic Aeroelasticity- Gust Response- Flutter P-K (computes flutter velocity)

- Several choices for curve fits

• F-S Interface- Infinite Plate spline

Q M k,( )


Ko 26

D

nd tailor the sys-

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- 3-D surface spline- Beam spline- Rigid load Transfer

• Very easy to add user defined functionality atem


Ko 27

D

. B ations, Addison-Wes-y P

. W ty”, Purdue Universitycho .

. S ional Flutter Theory toircr

. N cements, Vol III-ST

. B ts for Time-Accurateero , Aeroelasticity, Flow-du

. Fa ARD-R807, October995

. M P-221(01), April,971

. I.E aft Flutter,” Journal ofircr

References

isplinghoff, Ashley and Halfman “Aeroelasticity”, Dover Publicublishing Company, Inc., 1995.

eisshaar, “Fundamentals of Static and Dynamic Aeroelasticiol of Aeronautics and Astronautics, West Lafayette, IN 1992

milg, B. and Wasserman, L. S., “Application of Three Dimensaft Structures”, USAAF TR 4798, 1942.

eill, D.J., Herendeen, D.L., Venkayya, V.B., “ASTROS EnhanROS Theoretical Manual”, WL-TR-95-3006.

endiksen, Oddvar O., “Fluid-Structure Coupling Requiremenelastic Simulations”, AD-Vol.53-3, Fluid-Structure Interactionced Vibration and Noise, Volume III ASME, 1997.

rhat, C., “Special course on Parallel Computing in CFD”, AG.

acNeal, R. H., “The NASTRAN Theoretical Manual,” NASA-S.

. Garrick and W.H. Reed, III “Historical Development of Aircraft, Vol. 18, No. 11, November 1981.

lonay

CR

1le

2S

3A

4A

5AIn

61

71

8A

Ko 28

D

. G for Flutter and Strengthna ry and Application,”,FF

0. H Flutter Equation byete er 1971, pp. 885-889.

1. N MacNeal-Schwendlerorp 1999.

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CR

9AA

1D

1C

rumman Aerospace Corporation, “An Automated Procedure lysis and Optimization of Aerospace Vehicles Volume I. TheoDL-TR-75-137.

assig, H.J., “An Approximate True Damping Solution of the rminant Iteration,” Journal of Aircraft, Vol. 8, No. 11, Novemb

eill, D.J., “MSC/Flight Loads and Dynamics Training,”, The oration, 815 Colorado Boulevard, Los Angeles, CA, August

References

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