Ray Kolonay 2

Kolonay 1

CRD

Computational AeroelasticityThe Cultural and Convention Center

METUInonu bulvari

Ankara, 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


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


BuffetResponse due to time-dependent separated 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)


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-strophicTheodore 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

M

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n

M

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M

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Stable (A)

Neutral (B)

Unstable (C)F

r

e

q

u

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n

c

y

A

BC

Torsion Mode

Bending Mode


FlutterTime Histories

Modal Coupling

Dynamic Pressure

Kolonay 9


From ro(20)

let(21)

Whe rEq. ( b

(22)For s so

(23)

)

B+

u

(23) s lem the ae

re20) can

tability

F t(

Mu

M

can beFlutterelastic EOM

epresents motion independent external forcese written as

lve the homogenous equation from some initial state.

Mu Ku+ F u u u t, , ,( )=

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

u Ku+ Q1[ ] u Q2[ ]u Q3[ ]u F t( )+ + +=

Bu Ku+ + Q1[ ] u Q2[ ]u Q3[ ]u+ +=

olved by time integration or as an eigenvalue prob

Kolonay 10

CRD

Tran (2unst ero

(24)Assu at us

(25)With in nto(24)

(26)

hh

hh

Dynamic Aeroelasticitysformeady a

me th

gives

M

qh{ }

MEigenvalue Solutions3) to modal coordinates and assume that thedynamics depend only on displacements

the structural response is separable and synchrono

dependent of time and .Substituting i

uh{ }

uh Buh

Khhuh12---V

2 Qhh[ ]uh+ + 0=

uh{ } qh{ }est

=

s i+=

s2 Bhhs Khh

12---V

2Qhh+ + qh{ } 0=

Kolonay 11

CRD

6 a ff-

ma ts

co

- GOft

Do

al

Sta

KKPP

Dynamic AeroelasticityEq. (2 All m

ness

to be

-

phase-

Sever-

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Qhh) is the basic flutter eigenvalue equationtrices can be expressed as real but the aeroelastic sti

trix is unsymmetric causing roo

mplex conjugate pairs.eneralized unsteady aerodynamic forces

en assumed harmonic cast in frequency domain with amplitude and

ublet Lattice, CPM, Mach Box, Strip Theory

solutions exist for solving (26)Method

Method Method

Methodte space

Khh12---V

2Qhh

EK

Kolonay 12

CRD

can pr

7)

- sel trea

- ref i-chplex

, gene

-

- free sity

- redu ncy

- eig f m

- dam

s

2

V

bp k (Mhh B

QhhI ]=

k

qhi 1

Dynamic Aeroelasticity be ex

ected frees

erence sem - com

,

stream den

ced freque

envector o

ping factor

Vb----

2p

i+ )hh Khh

QR iQ+[P-K Flutter Solutionessed as . (26) becomes

(2

m speed

ord response frequency and eigenvalueralized mass, damping, stiffness matrices

generalized aerodynamic matrix

,

odal coordinates

sVkb------ i+( )

Vb---- p= =

MhhVb---- pBhh Khh

V2

2----------Q k( )hh+ + qh 0=

k bV-------=

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

0=

Qhh Qhh M k,( )

Qhh kQhh

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, = 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, = 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, = 50.50 Hz.Mode 1, = 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)

G

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a

l

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p

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m

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t

1= 13.06821= 88.352(Hz)2= 5.94082= 52.285(Hz)3= 24.10023= 30.268(Hz)4= .16874= 15.574(Hz)

DATAFITERROR

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)

G

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t

1= -.03661= 15.561(Hz)2= 32.09162= 30.286(Hz)3= 445.60373= .612(Hz)4= 4.77384= 52.054(Hz)

DATAFITERROR

0.0 0.1 0.2 0.3 0.4

-0.0020

-0.0010

0.0000

0.0010

0.0020

0.0030

Time (sec)

G

e

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e

r

a

l

i

z

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d

D

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p

l

a

c

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m

e

n

t

1= 5.76351= 52.269(Hz)2= 25.91592= 30.188(Hz)3= .03963= 15.564(Hz)4= 12.46104= 88.338(Hz)

DATAFITERROR

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)

G

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p

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1= .02821= 15.569(Hz)2= 25.87332= 30.095(Hz)3= 5.76883= 52.242(Hz)4= 12.07914= 88.547(Hz)

DATAFITERROR

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)

G

e

n

e

r

a

l

i

z

e

d

D

i

s

p

l

a

c

e

m

e

n

t

1= 5.76351= 52.269(Hz)2= 25.91592= 30.188(Hz)3= .03963= 15.564(Hz)4= 12.46104= 88.338(Hz)

DATAFITERROR

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)

G

e

n

e

r

a

l

i

z

e

d

D

i

s

p

l

a

c

e

m

e

n

t

1= 13.06821= 88.352(Hz)2= 5.94082= 52.285(Hz)3= 24.10023= 30.268(Hz)4= .16874= 15.574(Hz)

DATAFITERROR

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)

G

e

n

e

r

a

l

i

z

e

d

D

i

s

p

l

a

c

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m

e

n

t

1= .02821= 15.569(Hz)2= 25.87332= 30.095(Hz)3= 5.76883= 52.242(Hz)4= 12.07914= 88.547(Hz)

DATAFITERROR

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)

G

e

n

e

r

a

l

i

z

e

d

D

i

s

p

l

a

c

e

m

e

n

t

1= -.03661= 15.561(Hz)2= 32.09162= 30.286(Hz)3= 445.60373= .612(Hz)4= 4.77384= 52.054(Hz)

DATAFITERROR

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

Mode 1

Mode 4Mode 2

Mode 3Vf = 11,971 in/sec

rad 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


D

a

m

p

i

n

g

r

a

t

i

o

(

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, = 0.00, = 9.307E-09 slugs/ in )


F

r

e

q

u

e

n

c

y

(

r

a

d

i

a

n

s

)

Damping ratio (g)

Velocity Root Locus

rad f 96=

Kolonay 19



6000 8000 10000 12000 14000

100

200

300

400

500


Velocity vs. FrequencyF

r

e

q

u

e

n

c

y

(

r

a

d

i

a

n

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)

Kolonay 21


y Sub

Sup

adSub

SupStead-

-

Unste-

- MSC/NASTRANAerodynamicssonicDoublet Lattice (k=0)3-D panel Method (available in the near future)Bypass option for any AICersonicZONA51Bypass option for any AICAerodynamic databaseImport/export loads data

y AerodynamicsonicDoublet Lattice with body interferenceStrip TheoryersonicMach Box

Kolonay 22

CRD

turVer

A5 DFleCom esAbDivSleMuAerImpStruc-

Static-

-

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-

-

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al Modelingy rich selection of FE

eroelastic AnalysisOF trim (no drag/thrust trim)xible increment analysis

putes rigid, restrained and unrestrained flexible stability derivativle to add experimental load correction factors to AICergence of restrained vehiclender body modelsltiple set selectable aerodynamic modelsoelastic databaseort/export loads data

Aeroelastic Software

Kolonay 23

CRD

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nsient analysisst (random and discrete 1-d)tter P-K, K, K-E (K-E allows k=0)

curve fits cubic through all points

rfacenite plate splinen plate splineite plate splinem splineid load Transfer

t Processingensive Flight Loads pre/post processing functionality in PATRAN

M k,( )


Kolonay 24


/A y A

ub

up

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upUAIStead

- S

- S

Unste- S

- SSTROS Aeroelastic Capabilitieserodynamics

sonicUSSAERO (Woodward Aerodynamics, flat panel)QUADPAN (Lockheed Martin, 3-D panel)Bypass option for any AICMultiple set selectable aerodynamic models

ersonicUSSAERO (flat panel)QUADPAN (3-D panel)Bypass option for any AIC

y AerodynamicsonicDoublet LatticeersonicConstant Pressure Method (Apa, Northrop)

Kolonay 25

CRD

turMe s,

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putes rigid and four types of flexible stability derivativesr defined loads Optimization

ic Aeroelasticityst Responsetter P-K (computes flutter velocity)eral choices for curve fits

rfacenite Plate spline

Q M k,( )


Kolonay 26

CRD

3-DBeaRig

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-

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sy to add user defined functionality and tailor the


Kolonay 27

CRD

1. Bis f, A -Wes-ley Pu Co2. We Fu sitySchoo ona3. Sm nd ry toAircra ture4. Nei HeASTR ore5. Ben Od ateAeroe mu Flow-Induc tio6. Far Sp ber1995.7. Ma . H il,1971.8. I.E. an nal ofAircra 18,

Referencesshley and Halfman Aeroelasticity, Dover Publications, Addisonmpany, Inc., 1995.ndamentals of Static and Dynamic Aeroelasticity, Purdue Univerutics and Astronautics, West Lafayette, IN 1992.

Wasserman, L. S., Application of Three Dimensional Flutter Theos, USAAF TR 4798, 1942.

rendeen, D.L., Venkayya, V.B., ASTROS Enhancements, Vol III-tical Manual, WL-TR-95-3006.dvar O., Fluid-Structure Coupling Requirements for Time-Accurlations, AD-Vol.53-3, Fluid-Structure Interaction, Aeroelasticity,n and Noise, Volume III ASME, 1997.ecial course on Parallel Computing in CFD, AGARD-R807, Octo

., The NASTRAN Theoretical Manual, NASA-SP-221(01), Apr

d W.H. Reed, III Historical Development of Aircraft Flutter, Jour No. 11, November 1981.plinghofblishingisshaar, l of Aerilg, B. aft Strucll, D.J., OS Thediksen, lastic Sied Vibrahat, C.,

cNeal, R

Garrickft, Vol.

Kolonay 28

CRD

9. Gru er ngthAnaly pt n,,AFFD 5-110. Ha J., byDeterm tera -889.11. Ne , M ndlerCorpo 15mman Asis and OL-TR-7ssig, H.inant I

ill, D.J.ration, 8ospace Corporation, An Automated Procedure for Flutter and Streimization of Aerospace Vehicles Volume I. Theory and Applicatio37.An Approximate True Damping Solution of the Flutter Equation tion, Journal of Aircraft, Vol. 8, No. 11, November 1971, pp. 885SC/Flight Loads and Dynamics Training,, The MacNeal-Schwe

Colorado Boulevard, Los Angeles, CA, August 1999.

References

Computational AeroelasticityThe Cultural and Convention CenterMETUInonu bulvariAnkara, TurkeySponsored by:RTA-NATOThe Applied Vehicle Technology Panelpresented byR.M. Kolonay Ph.D.General Electric Corporate Research & Development CenterAnkara, Turkey Oct.. 1-5, 2001 Introduction- Fluid-Structure Interactions Aeroelasticity- Aeroelastic analysis/design in an MDA/MDO Environment

Static Aeroelasticity Dynamic Aeroelasticity Commercial Programs with Aeroelastic Analysis/Design Capabilities

Presentation OutlineReferences1. Bisplinghoff, Ashley and Halfman Aeroelasticity, Dover Publications, Addison-Wesley Publishi...2. Weisshaar, Fundamentals of Static and Dynamic Aeroelasticity, Purdue University School of Ae...3. Smilg, B. and Wasserman, L. S., Application of Three Dimensional Flutter Theory to Aircraft S...4. Neill, D.J., Herendeen, D.L., Venkayya, V.B., ASTROS Enhancements, Vol III- ASTROS Theoretica...5. Bendiksen, Oddvar O., Fluid-Structure Coupling Requirements for Time-Accurate Aeroelastic Sim...6. Farhat, C., Special course on Parallel Computing in CFD, AGARD-R807, October 1995.7. MacNeal, R. H., The NASTRAN Theoretical Manual, NASA-SP-221(01), April, 1971.8. I.E. Garrick and W.H. Reed, III Historical Development of Aircraft Flutter, Journal of Aircr...9. Grumman Aerospace Corporation, An Automated Procedure for Flutter and Strength Analysis and O...10. Hassig, H.J., An Approximate True Damping Solution of the Flutter Equation by Determinant It...11. Neill, D.J., MSC/Flight Loads and Dynamics Training,, The MacNeal-Schwendler Corporation, 8...

ReferencesDynamic Aeroelastic Phenomena Dynamic Response Limit Cycle Oscillations (LCO) Buffet Flutter

Dynamic AeroelasticityFlutter

Dynamic AeroelasticityDynamic AeroelasticityDynamic ResponseTransient response due to a rapidly applied load. Atmospheric Turbulence- Continuous random- Discrete random (gust)

Landing loads Snap maneuvers Store Separation

Dynamic AeroelasticityLimit Cycle OscillationsTypically caused by shock induced oscillations on a surface or flow/ shocks attaching/detaching f... Panel Flutter Control Surface Buzz Store/Wing configurationsReduces structural lifeSolutions found in time, frequency, and Laplace domain usually with generalized coordinatesUsually requires nonlinear flow conditions and possibly nonlinear structures (cs hinge stiffness)

Dynamic AeroelasticityBuffetResponse due to time-dependent separated flows (usually vortical) impinging on structural surfaces. Bluffed bodies on horizontal and vertical surfaces Wings, strakes etc.. on vertical tails (often a twin tail problem)


Dynamic AeroelasticityFlutterDynamic instability where-by the system extracts energy from the free stream flow producing a div... 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 catastrophicsome men fear flutter because they do not understand it, while others fear it because they do[8]

Dynamic AeroelasticityFlutterFrom the aeroelastic EOM(20)let

(21)Where represents motion independent external forcesEq. (20) can be written as

(22)For stability solve the homogenous equation from some initial state.

(23)

Eigenvalue SolutionsTransform (23) to modal coordinates and assume that the unsteady aerodynamics depend only on disp...(24)Assume that the structural response is separable and synchronous

(25)With independent of time and .Substituting into (24) gives

(26) Eq. (26) is the basic flutter eigenvalue equation All matrices can be expressed as real but the aeroelastic stiffness matrix is unsymmetric causi... - Generalized unsteady aerodynamic forces- Often assumed harmonic cast in frequency domain with amplitude and phase- Doublet Lattice, CPM, Mach Box, Strip Theory

Several solutions exist for solving (26)- Method- Method- Method- Method- State space

P-K Flutter Solutioncan be expressed as . (26) becomes(27)- selected freestream speed- reference semi-chord- complex response frequency and eigenvalue, , generalized mass, damping, stiffness matrices- generalized aerodynamic matrix- freestream density- reduced frequency,- eigenvector of modal coordinates- damping factor

Dynamic AeroelasticityDynamic AeroelasticityP-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

Dynamic AeroelasticityAGARD 445.6 Flutter CalculationsMode Shapes and frequencies

Dynamic AeroelasticityAGARD 445.6 Time Integration Response

Dynamic AeroelasticityAGARD 445.6 Time Response Integration

Dynamic AeroelasticityAGARD 445.6 P-K Flutter Solution

Dynamic AeroelasticityAGARD 445.6 P-K Flutter Solutionradrad

Dynamic AeroelasticityAGARD 445.6 P-K Flutter Solution

Aeroelastic SoftwareGlobal 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)

Aeroelastic SoftwareMSC/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 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 stability derivatives- Able to add experimental load correction factors to AIC- Divergence of restrained vehicle- Slender body models- Multiple set selectable aerodynamic models- Aeroelastic database- Import/export loads data

Dynamic Aeroelasticity- Frequency response analysis- Random analysis- Transient analysis- Gust (random and discrete 1-d)- Flutter P-K, K, K-E (K-E allows k=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 functionality in PATRAN environment

Aeroelastic SoftwareUAI/ASTROS Aeroelastic Capabilities 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)

Structural Modeling- Membrane type FEM (Rods, Beams, Shear panels, Quadrilateral Plates, Composites)

Static Aeroelastic Analysis- Full 6 DOF Trim- Computes rigid and four types of flexible stability derivatives- 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- 3-D surface spline- Beam spline- Rigid load Transfer

Very easy to add user defined functionality and tailor the system

Dynamic AeroelasticityDynamic Aeroelasticity(23) can be solved by time integration or as an eigenvalue problem

Aeroelastic SoftwareAeroelastic SoftwareAeroelastic SoftwareAeroelastic Software

Ray Kolonay 2

Documents

mu ku f u u u t

u ku q1 u q2 u q3 u

bu ku q1 u q2 u q3 u

structural surfaces

crd introduction fluid

structural modes wing

divergent response

synchronodependent of