aeroelastic stability analysis using modal...

Aeroelastic Stability Analysis Using Modal Approach

Hassan Kassem

City University London

4th OpenFOAM User Meeting UK & Éire

Hassan Kassem (City University London) Flutter, OpenFOAM OFUM2016 1 / 26

Outline

1 Introduction

2 Numerical Model

3 Results and Discussion


Introduction

Outline

1 IntroductionAeroelasticityTransonic FlutterComputational Aeroelasticity (CAE)

2 Numerical Model



Introduction Aeroelasticity

AeroelasticityOverview

Aerodynamic forces

Inertial forces Elastic forces


Introduction Aeroelasticity

AeroelasticityOverview

FlutterSelf-excitedoscillation of elasticbody in fluid stream

Aerodynamic forces

Inertial forces Elastic forces


Introduction Transonic Flutter

AeroelasticityDefinitions

Transonic FlutterThe transonic flutter limitappears to be low in anyflight range. Transonic Dip


Introduction Computational Aeroelasticity (CAE)

Computational Aeroelasticity (CAE)

CAE

CFD CSD


Introduction Computational Aeroelasticity (CAE)

Computational Aeroelasticity (CAE)

Fluid-Structure CouplingForces depend on displacement.Displacement depends on forces.

CAE

CFD CSD

Coupling


Numerical Model

Outline

1 Introduction

2 Numerical ModelOverviewAerodynamic ModelAeroelastic ModelFluid Structure Coupling



Numerical Model Overview


Initial ConditionsMode Shapes




Initial ConditionsMode Shapes CSD

Initial Forces





Initial ForcesCFD

Displacement





Initial ForcesCFD

Displacement

Forces


Numerical Model Aerodynamic Model

Aerodynamic ModelOpenFOAM

Conservation of mass:

∂ρ

∂t+∇ · [uρ] = 0

Conservation of momentum:

∂(ρu)∂t

+∇ · [u(ρu)] +∇p = 0

Conservation of total energy:

∂(ρE)

∂t+∇ · [u(ρE)] +∇ · [up] = 0

where ∇ is the nabla vector operator , ∇ ≡ ∂i ≡ ∂∂xi≡ ( ∂

∂x1, ∂∂x2

, ∂∂x3

).


Numerical Model Aeroelastic Model

Equation of Motion

Bending-Torsion coupled beam

EIh′′′′ + mh −mxαα = 0

GJα′′ + mxαh − Iαα = 0

Generalized Coordinates

[M]{q}+ [K ]{q} = {F}{q} = [φ]{η}

ηi + ω2i ηi = Qi ; i = 1,2, . . . ,N

Qi = {φ}Ti {F}

ω2i = {φ}T

i [K ]{φ}i

1 = {φ}Ti [M]{φ}i

[φ] is the modal matrix.

{η} is the generalized coordinates.


Numerical Model Fluid Structure Coupling

Displacement Coupling

{P1} = [R]{P0}+ {h}

[R] =

cosα −sinα 0sinα cosα 0

0 0 1



WHY?



Implementation

srcelasticBodyDynamics

elasticBodyelasticBodyMeshelasticBodyForceelasticBodyMotionFileelasticBodyMotion

elasticBodyMotionCSDODECSDInputelasticBodyMotionState

pointPatchFields/derived/elasticBodyDisplacement


Results and Discussion

Outline

1 Introduction

2 Numerical Model

3 Results and DiscussionTypical wing sectionGoland Wing ModesPitching Goland WingFlutter Analysis


Results and Discussion Typical wing section

NACA 64A010 Aerofoil

Lift Coefficient

-0.1

-0.05

0

0.05

0.1

-1.5 -1 -0.5 0 0.5 1 1.5

Cl

Angle of Attack α

Experimental, DavisOpenFOAM

Typical Wing Section

eac.g

kh

kα

h

α

U∞



Damped Response

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0 10 20 30 40 50

Non

-Dim

ensi

onal

Dis

plac

emen

t

Non-Dimensional Structural Time τ

hbα

(a) Displacements.

-0.12

-0.08

-0.04

0

0.04

0.08

0.12

0 10 20 30 40 50

Forc

esC

oeffi

cien

ts


clcm

(b) Forces Coefficients.

Damped Response. M∞ = 0.85, V ∗ = 0.439



Near Flutter Point

-0.02

-0.01

0

0.01

0.02

0 10 20 30 40 50

Non

-Dim

ensi

onal

Dis

plac

emen

t


hbα

(a) Displacements.

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0 10 20 30 40 50

Forc

esC

oeffi

cien

ts


clcm


Damped Response. M∞ = 0.825, V ∗ = 0.612



Divergent Response

-0.4

-0.2

0

0.2

0.4

0 10 20 30 40

Non

-Dim

ensi

onal

Dis

plac

emen

t


hbα

(a) Displacements.

-1

-0.5

0

0.5

1

0 10 20 30 40

Forc

esC

oeffi

cien

ts


clcm


Divergent Response. M∞ = 0.875, V ∗ = 1.420


Results and Discussion Goland Wing Modes

Goland Wing

Goland Wing Properties

Property Value

Chord, c 1.829 mSemispan, s 6.096 mThickness to chord ratio, 0.04Mass, M 534.7 kg/mBending stiffness, EI 9.789× 106 Nm2

Torsional stiffness, GJ 0.989× 106 Nm2

Mass moment of inertia, Iα 129.5 kgm

Surface Mesh


Results and Discussion Pitching Goland Wing

Pitching Goland wing

Mach = 0.92 with 0.5◦ amplitude and 3.0 Hz frequency

-0.02

-0.01

0

0.01

0.02

-0.04 -0.02 0 0.02 0.04

CM

Cl

OpenFOAMENS3DAE, Beran

CAPTSD, BeranFluent, Parker

Moment Coefficient verses Lift Moment


Results and Discussion Pitching Goland Wing

Free Vibration Modes for Goland Wing

Frequency Results (Hz)

CALFUN-B Beran NASTRAN Chung

1st Mode 2.01 1.97 1.95 1.932ndMode 3.73 4.05 4.08 3.923rd Mode 10.36 9.65 - -4th Mode 13.53 13.4 - -

Mode Shapes

0

ω1 = 12.6 rad/s

ω2 = 23.4 rad/s

0

0 0.25 0.5 0.75 1Normalized Spanwise Distance

ω3 = 65.1 rad/s

0 0.25 0.5 0.75 1Normalized Spanwise Distance

ω4 = 85.0 rad/s

Bending Torsion


Results and Discussion Flutter Analysis

Flutter Boundary

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0 50 100 150 200 250 300

Hea

veD

ispl

acem

ent,

h

Non-Dimensional Time, τ

80 m/s100 m/s110 m/s120 m/s

Heave Response of the tip, M∞ = 0.8

100

150

200

250

0.75 0.8 0.85 0.9 0.95

Flut

terS

peed

,Uf(

m/s)

Mach Number, M∞

Theodorsen, EastepDoublet Lattice, Eastep

MSC/NASTRAN(FE), BeranCAPTSDv-NLS(Beam), Beran

CAPTSDv-NLS(FE), BeranZONA6, Kurdi

OpenFOAM

Flutter boundary for Goland Wing



Generalized Coordinates

-0.01

-0.005

0

0.005

0.01

0 50 100 150 200 250 300 350

Gen

eral

ized

Dis

plac

emen

t,q


Mode1Mode2Mode3Mode4

Damped Response. M∞ = 0.8, V∞ = 80m/s

-0.02

-0.01

0

0.01

0.02

0 50 100 150 200 250 300 350

Gen

eral

ized

Dis

plac

emen

t,q


Mode1Mode2Mode3Mode4

Near flutter point Response. M∞ = 0.8, V∞ = 110m/s



Goland wing


Summary

Summary

The developed model for coupling the fluid-structure interactionbased on free vibration natural modes of elastic wing ishighlighted.Two case studies have been investigated and the predicted resultsare compared with numerical data from the literature.

OutlookThis model will be used for predicting the transonic speed ofcomposite wings.The model will be extended for three-dimensional wings based onplate theory.This model could be coupled directly with different solvers!


Summary

Thank you for your [email protected]

Twitter: @HIKASSEMResearchGate/Hassan_Kassem10


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