EADS 2008 – All rights · PDF fileBaseline flutter analysis predictions ... AGARD 445.6 • FE-Model and Geometry 11x11 Grid points ... – Wing Buffet

EADS 2008 – All rights reserved

Recent Advances on Transonic Aeroelasticity

Wolfgang Luber

EADS – European Aeronautic Defence and Space Company

[email protected]

ICNPAA 2010 Sao Jose dos Campos, Brazil; June 29th – July 3rd 20 10

2EADS 2010 – All rights reserved ICNPAA-2010, Sao Jose dos Campos, Brazil - W. Luber -June/July 2010

Overview

• Introduction, Background

• Requirements on modern Aeroelastic Tools

• Correction Methods applied in Aeroelasticity

• Measurements of unsteady pressure Aerodynamic – PVDF Foils

• Aeroelastic Simulation Tool

• Small disturbance Euler method

• Conclusion


Application of classical aerodynamic and aeroelastic tools in the design, development and clearance of military aircraft projects by German Military Aircraft Industry

• EWR – Entwicklungsring (Heinkel, Junkers, Messerschmitt, Bölkow)

• MBB – Messerschmitt Bölow Blohm

• Dasa – Deutsche Aerospace, Daimler Benz Aerospace,

• EADS-MAS – European Aerospace, Defence and Space Company Military Air Systems

Background


VJ-101

F-104 Starfighter CCV

F-4 Phantom

AIRBUS A300 B

Tornado

Eurofighter

X-31

MIG-29

Application of classical Aeroelastic Tools

VAK 191


Steady aerodynamic requirementSteady aerodynamic loads of total rigid aircraft and components are required to be generated for sub-trans- and supersonic Mach number ranges, angle-of-attack ranges with/without control surface deflections.

Requirement for Static AeroelasticitySteady aerodynamic loads of total non-rigid aircraft and components are required to be generated for sub-trans- and supersonic Mach number ranges, angle-of-attack ranges with/without control surface deflections at several attitudes using the normal mode shapes or the flexibility matrix.

Requirement for unsteady rigid control surface aerodynamics and rigid body motionsUnsteady aerodynamic loads of total rigid aircraft and components are required to be generated for sub-trans- and supersonic Mach number ranges, angle-of-attack ranges with/without dynamic control surface deflections or rigid body motions.

Requirement for unsteady aerodynamics of flexible modesUnsteady aerodynamic loads of total flexible aircraft and components are required to be generated for sub-trans- and supersonic Mach number ranges, angle-of-attack ranges for dynamic modal mode deflections.

Aeroelastic Requirements


Requirement for classical Flutter predictionBaseline flutter analysis predictions (p-k method) are required based on the generalized unsteady aerodynamic forces extracted from the simulations and the generalized mass, damping and stiffness matrices.

Requirement for flutter simulationAllowance should be made for flutter simulation in the time-domain in the sub-trans- and supersonic Mach number range at moderate incidence for modal mode shapes, generalized masses and stiffnesses of the total aircraft .

Requirement for dynamic gust loadsGust loads from simulations for sub-trans- and supersonic Mach number at incidence for modal mode shapes, generalized masses and stiffnesses of total aircraft are required.

Requirement for Aero-servo-elasticityTransfer functions of rates and accelerations at the FCS sensor positions due to prescribed control surface inputs should be predicted in sub-trans- and supersonic flow at moderate incidence for the flexible total A/C (using normal mode shapes, generalized masses and stiffnesses).



Aero-servo-elastic StabilityFCS open loop transfer functions due to control surface inputs should be predicted for aero-servo-elastic stability investigation in sub-trans- and supersonic flow at moderate incidence for the flexible total A/C (using normal mode shapes, generalized mass and stiffness) including FCS feedback description. Closed loop flutter analysis to investigate flutter with effects of the flight control system shall be installed



Overview







• Conclusion


Correction Methods

ENHANCED A/C STABILISATION AN MANEUVRABILITY

• MULTIPLICATIVE CORRECTION METHOD

• ADDITIVE CORRECTION METHOD

( ) ( ) ( ) xxe

steadytheo

pp

theoppcorrpp icc

ciccic mod'''

exp,

''''''

0

αααα

α

⋅+⋅

∂∆∂

−

∂∆∂

+∆⋅+∆=∆⋅+∆

( ) ( ) ( )( )

steadytheop

p

theoppcorrpp c

cciccic

∂∆∂

∂∆∂⋅∆⋅+∆=∆⋅+∆

αα

/

/exp''''''


Clean and external Store A/C Normal Modes

Clean Aircraft Aircraft with I/B & O/B store Carriage


Damping vs Flutterspeed

Mach = 0.9 Clean Aircraft Mach = 0.95 External Store A/C


AGARD 445.6

• FE-Model and Geometry

11x11 Grid points

121 Plate elements

8 Elementes are fixed

NACA 64A004 Profil


AGARD 445.6

• Comparison with Reference Model two modes

Mode 1:

Lagrange: 9.629 Hz

AGARD Report: 9.599 Hz

Mode 2:

Lagrange: 38.12 Hz

AGARD Report: 38.17 Hz


AGARD 445.6

• CFD-Model

Grid system

64281 Grid points

5 Blocks

optimized for Euler-Calcs


Flutteranalysis AGARD 445.6

• Time Consumption– 1 Coupling step 200 to 360 Seconds (75% of CFD-Solution)– Generation of time series with 300 Steps – Average 4 time series are needed to enclose the dynamic pressure

of the flutter point with ±25 N/m2

– 7 points are required for each flutter slope

– Total Time of a flutter analysis (pure CPU time without pre and post processing):

10 Days


Flutter onset AGARD 445.6 (4)• Flutter Frequency Ratio

Machzahl

Flu

tterF

requ

ency

Rat

ioω

F/ω

α

0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.20.30

0.35

0.40

0.45

0.50

0.55

0.60

0.65

0.70

0.75

0.80

AGARD ReportLagrange/Doublet LatticeIterateLee-Rausch, Batina 1993Farhat, Lesoinne 1998


Flutter Case: M=0.901, αααα=0.0°


Flutter Case: M=0.901, αααα=0.0°


Overview




• Measurements of unsteady pressure Aerodynamic – PVDF Foil s



• Conclusion


Aircraft Components affected by Buffet

AIRBRAKE

EQUIPMENT

PILOT

FRONTFUSELAGE

EXTERNALSTORES

WINGS

FIN

ENGINE

REARFUSELAGE


Aerodynamic Loads on Airbrake


Application of Buffet Vibrations & Dynamic Loads

STRUCTURAL DESIGN• Predicted dynamic buffet loads are applied for the design of the following

components– Fin Structural Design – not covered by tuned gust analysis– Rear / Center Fuselage structural design– Wing Buffet – covered by tuned gust analysis

EQUIPMENT DESIGN AND QUALIFICATION

• Predicted and flight measured buffet vibrations are applied for the vibration qualification of equipment in front / center / rear fuselage and avionic bay

PILOT DISCOMFORTPredicted buffet vibrations are used to assess the pilot comfort


Prediction and Validation of Buffeting


PVDF Polyvenylidenfluorid


Location of unsteady pressure measuring


Polyvenyliden Fluorid Sensor Array Application

from Prof. W. Nitsche, TU Berlin


Trainer Model in NLR Transonic Windtunnel


Location unsteady pressure measuring points

Location of the port pressure pick ups

MP1 – MP12

Location of starboard pressure pick ups MP13 – MP24


PSD PS

Variance [Pa 2]

0

0

1.2x107

1000 2000

1000 20001000 20000Time History

Sp[Pa 2/Hz]

100

1000

104

105

106

t [sec]

[Pa2]]]]

f [Hz] f [Hz]

0.8x107

0.4x107

2.4x106

0.8x106

20000

-20000

Pa

PSD of pressure MP8 at 37.5 degrees

Power spectrum variance and time history


k = f l µ/U∞

0 0.5 1 1.5 20

0.002

0.004

0.006

0.008

0.01

α = 0°α = 5°α = 10°α = 12°α = 14°α = 15°α = 16°α = 18°α = 20°α = 21°α = 22°α = 23°α = 24°α = 25°α = 26°α = 27°α = 28°α = 29°α = 30°

PSD (amplitude of spectrum) of pressure coefficient P1 as function of angle of attack ; Sensor position P1 U

∞= 40 m/s, Relµ = 0.68 x 106.

PSD of pressure coefficient vs AoA


0 5 10 15 20 25 30

0.02

0.05

0.1

αcP rms of buffet pressures35 40 45

0.2

0.3

[·]

cP rms

[−]

MP2

MP9

MP1

P2

P1

MP8MP12

MP6

MP11

M = 0.5

Comparisons of c prms values of signals at P1 and P2 (TUM TEST) TO MP1, MP2 , MP6, MP9 , MP8 , MP11 , MP12 (NLR TEST)Mach = 0.5

Comparison of pressure pick ups: NLR and TUM


0.02

0.05

0.1

0.02

0.05

0.1

P1

MP9

MP8

Comparison rms values P1 and MP9/MP8rms M0.5

0 5 10 15 20 25 30α

Comparison of c p rms from TUM test signal P1 with NLR test signals MP8 a nd MP9Mach = 0.5

Comparison of MP8 and MP9: NLR and TUM


From the result of the comparison of the two differ ent measurements it can be concluded that the PVDF foil technique is adequa te for the application of the buffet prediction. This could be demonstrated t hrough the validation of PVDF measured unsteady buffet pressures.

Furthermore it is concluded that the application of PVDF buffet pressure measurement technique leads to strong cost reductio ns compared to the classical approach during the design and certificat ion of military aircraft structures including buffet dynamic loads.

This is due to the fact that for the PVDF measureme nt the existing aerodynamic wind tunnel model for the derivation of stationary aerodynamic coefficients can be applied and it is n ot necessary to built an additional wind tunnel model for buffet as in case of the classical method.

Conclusion


Overview







• Conclusion


Aeroelastic Simulation System

Fundamental equations:

� Nonlinear potential theory

� Isentropy assumption Clebsch Potential Correction (prediction of weak shocks)

�No friction and rotation

�Application:

�Analysis of flutter in time and frequency domain

• prediction of deformations

• prediction of steady/unsteady pressure distributions

• Dynamic Response, dynamic loads, gust loads

( ) ( ) ( ) ( ) 0=⋅+⋅+⋅+ zzyyxxt φρφρφρρ


X

Y

Z

cpt0.300.210.130.04

-0.04-0.13-0.21-0.30-0.39-0.47-0.56-0.64-0.73-0.81-0.90

Ma = 0.93α = 2.2°δiB = 0.0°δoB = -5.0°ε = 0.0°η´FP = 0.0°


x/c [-]

CP

[-]

0 0.25 0.5 0.75 1

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

AESIM lo sideAESIM up sideEXP Data lo sideEXP Data up sideCP*

WING SECTION 04 y/(b/2) = 36.7 %

x/c [-]

CP

[-]

0 0.25 0.5 0.75 1

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

AESIM lo sideAESIM up sideEXP Data lo sideEXP Data up sideCP*

WING SECTION 06 y/(b/2) = 49.8 %

Ma = 0.93α = 2.2°δiB = 0.0°δoB = -5.0°ε = 0.0°η´FP = 0.0°


x/c [-]

CP

[-]

0 0.25 0.5 0.75 1

-1

-0.9

-0.8

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

flex lo sideflex up siderigid lo siderigid up sideCP*

WING SECTION 43 y/(b/2) = 84 %

x/c [-]

CP

[-]

0 0.25 0.5 0.75 1

-0.9

-0.8

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4



Ma = 0.80α = 2.20°δiB = 1.85°δoB = 1.85°ε = -5.0°η´FP = -3.0°

H = sea level


x/c [-]

CP

[-]

0 0.25 0.5 0.75 1

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4


CANARD SECTION 30 y/(b/2) = 43 %

x/c [-]

CP

[-]

0 0.25 0.5 0.75 1

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3


CANARD SECTION 34 y/(b/2) = 95 %

Ma = 0.80α = 2.20°δiB = 1.85°δoB = 1.85°ε = -5.0°η´FP = -3.0°

H = sea level


X

Y

Z

cp0.400.340.270.210.140.080.01

-0.05-0.11-0.18-0.24-0.31-0.37-0.44-0.50

Ma = 1.2α = 4.1°δiB = 0.95°δoB = 0.95°ε = 0.0°η´FP = 0.0°


x/c [-]

CP

[-]

0 0.25 0.5 0.75 1

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

AESIM lo sideAESIM up sideexp. data (oB pyl) lo sideexp. data (oB pyl) up side

WING SECTION 06 y/b = 49.8 %

x/c [-]

CP

[-]

0 0.25 0.5 0.75 1

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

AESIM lo sideAESIM up sideexp. data (oB pyl) lo sideexp. data (oB pyl) up side

WING SECTION 08 y/b = 60.8 %

Ma = 1.2α = 4.1°δiB = 0.95°δoB = 0.95°ε = 0.0°η´FP = 0.0°


x/c [-]

CP

[-]

0 0.25 0.5 0.75 1

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

flex lo sideflex up siderigid lo siderigid up side


x/c [-]

CP

[-]

0 0.25 0.5 0.75 1

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

flex lo sideflex up siderigid lo siderigid up side


Ma = 1.20α = 5.00°δiB = 3.33°δoB = 3.33°ε = 0°η´FP = 0°

H = 7783 ft


y/(b/2) [-]

CA

(y)

[-]

0.2 0.4 0.6 0.8 1

0.1

0.2

0.3

0.4

0.5

0.6

Ca (y) rigidCa (y) elastic

LIFT DISTRIBUTION CANARD

fuselage

y/(b/2) [-]

CA

(y)

[-]

0 0.25 0.5 0.75 10

0.1

0.2

0.3

0.4

0.5

0.6

Ca (y) rigidCa (y) elastic

LIFT DISTRIBUTION WING

inboard flap outboard flap

fuselage

Ma = 1.20α = 5.00°δiB = 3.33°δoB = 3.33°ε = 0°η´FP = 0°

H = 7783 ft


Mode 3

Demonstration of AESIM Code - Validation


Stability and Control Derivatives



Real Amp

ImagPhs

Unsteady pressuresMode 8, Ma=0.8,57Hz

LIFTING SURFACE

LOWER PART FULL POTENTIAL

UPPER PART LIFTING SURFACE

FULL POTENTIAL


Frequency [Hz]

VE

AS

[KT

S]

0 5 10 15 20 25 300

200

400

600

800

1000

1200

1400

1600

1800

Damping [%]

VE

AS

[KT

S]

-25 -20 -15 -10 -5 0 50

200

400

600

800

1000

1200

1400

1600

1800

Mode 1Mode 2Mode 3Mode 4Mode 5Mode 6Mode 7Mode 8Mode 9Mode 10Zero Damping Line

AESIM Full Potential, new grid, Ma∞=0.8, α=0°

Validation of flutter analysis

1552 KTS EAS


AESIM-BASIC

Aerodynamic and Elastic Loading in Selected Cuts due to Gust

1-cos gust

Gust Example



Conclusions – Actual Status

•The industrial validation process for improved aeroelastic tool AESIM based on industrial requirements as proposed with the present contribution has been performed for the example of a modern fighter aircraft configuration

• Almost all industrial minimum and partly nominal general and validation requirements could be demonstrated to be met for the present simulations using AESIM with full potential code in the subsonic, transonic and supersonic region at low to medium incidences

• In detail the validation of steady aerodynamic and steady aeroelasticsimulations of a rigid and flexible wing and of complete rigid and flexible aircraft has been carried out successfully. Validations of unsteady aerodynamic simulations of wing and total aircraft with oscillating control surfaces and simulations of unsteady aerodynamics of normal modes have been performed. Flutter and gust simulations had been validated using results from classical tools.


• Additional effort is needed for the improvement of flutter and gust simulations. Improvements of MIMO technique , reduced order models have to be investigated. • Improved aerodynamic prediction capability (AESIM FP) includingcorrection methods from wind tunnel experiments is needed in subsonic, transonic and supersonic region for medium incidence for static aeroelasticity, dynamic load and classical flutter prediction and aeroservoelasticity combined with affordable turn around times for high number of configuration

Conclusions – Actual Status


Overview







• Conclusion


Overview

• Introduction


• Calculation of Generalized Aerodynamic Forces (GAFs)

• CFD Models and steady state results

• Linear flutter analysis: theory

• Structural dynamics, GAFs and flutter results

• Conclusion


Introduction

• Industrial flutter analysis process is mainly based on aerodynamic forces computed by classical potential methods

• Nonlinear aerodynamics requested, but with an acceptable computing time

• Development of the small disturbance Euler method AER-SDEu at the Institute of Aerodynamics of the TUM

• Direct computation of the unsteady flow quantities for harmonic oscillations

→ Computation of the GAF matrices: Integration in flutter analysis process


Small Disturbance Euler Method

• AER-SDEu based on the full nonlinear Euler solver AE R-Eu

• For small disturbances of the flow the unsteady flow quantities can be decomposed into a time invariant mean part and a time dependent part

→ Time linearization of the Euler equations about a mean state

• Harmonic oscillation of the considered structure

→ Flow quantities respond harmonically with amplitude and phase shift

→ Cell centered Finite Volume Method

→ Flux-difference scheme (Roe) with 2nd order spatial accuracy

→ Implicit time integration (LU-SSOR)

→ Pseudo time marching procedure for steady and formal steady computations

→ Dual-time stepping for time-accurate computations

• Assumptions for AER-SDEu :


Small disturbance Euler method

• Only first harmonic is considered (neglecting of higher harmonics)

• Introducing these assumptions into the Euler equations yields the small disturbance Euler equations

→ An unsteady problem is reduced to a formal steady problem for the perturbation part

τςηξςηξςηξ iket ⋅+= ),,(ˆ),,(),,,( xxx

• Coordinate vector of deformed grid

• Arbitrary flow quantity (complex amplitude)

τζηξφζηξφτζηξφ ike⋅+= ),,(ˆ),,(),,,(


Steadystatesolution

Time Domain

AER-Eu

AER-SDEu

AER-Eu

FourierAnalysis

Frequency Domain

Unsteady flowquantities

(several cycles):cp(τ)

• Reduction of computational time (at least by an order of magnitude) with AER-SDEu

• Nonlinearities of a steady state solution are introduced into the AER-SDEucomputation

Small disturbance Euler method

1st Harmonic ofperturbedflow quantities: Re , Impc pc

1st Harmonic ofperturbedflow quantities: Re , Impc pc


→ Computational grid in reference position

→ Computational grid in the deflected position

→ Steady state solution generated by the nonlinear method AER-Eu:

Computation of the GAF matrices

ij

S

pj

Sipij dcdcGAF SuSu ˆˆ ⋅⋅+⋅⋅= ∫∫

pc

pc

• The AER-SDEu method requires as input:

• The AER-SDEu method provides as output (e.g.):

• The GAF matrix can now be computed as (for fixed kred and Ma∞):

ipcju

SdidS

Steady state pressure coefficient

Surface vector of reference position

Disturbance part due to eigenmode i

Vector of deflection of eigenmode j

Disturbed surface vector of eigenmode i

pc


CFD-Models and steady state results

• The integration of AER-SDEu into the aeroelastic analysis process is demonstrated for two models:

→ AGARD-Wing 445.6 (weakened model 3)

→ Fuselage-Cropped-Delta-Wing (FCDW)


AGARD-Wing 445.6

NACA 65A004airfoil:

φ0.25 = 45°Sweep (1/4-Line):

Λ = 1.65Aspect ratio:

λ = 0.66Taper ratio:

10cr /10cr /11cr

Farfield distance (x/y/z)

1.0×10-3crOff-Body-Distance:

6144Surface cells (wing):

450560Block dimension (cells):

1-Block C-HGrid topology:

• Computations performed for 4 Mach numbers (Ma∞

= 0.499, 0.678, 0.901, 0.954), 6 reduced frequencies and 5 eigenmodes

• CFD-mesh properties:

• Geometric properties:

cr - root chord


• Steady state result at Ma∞

= 0.954 (transonic case), AoA = 0°

• Weak shock on wing inner section (e.g. at η = 0.25)

AGARD-Wing 445.6


FCDW

2 × 6720Surface cells (fuselage):

10cr /10cr /10cr

Farfield distance (x/y/z)

5.0×10-3crOff-Body-Distance:

2 × 3072Surface cells (wing):

2 × 215040Block dimension (cells):

2-Block H-OGrid topology:

• Generic aeroelastic model built by EADS DS - MAS, DLR, Dassault Aviation, ONERA, Alenia

• Computations performed for 5 Mach numbers (Ma∞

= 0.5, 0.7, 0.852, 0.875, 0.921), 6 reduced frequencies and 4 eigenmodes

• CFD-mesh properties:


FCDW

Ma∞

= 0.852Ma∞

= 0.875Ma∞

= 0.921

• Steady state results for various Mach numbers at AoA = 2°

FCDW upper sideSonic isosurface (Ma = 1.0)

U∞


• Steady pressure distribution at Ma∞

= 0.852, AoA = 2°

• Strong shock on wing upper side

• Experiment shows also strong shock on wing lower side in contrast to the computation

FCDW

Contour plot wing upper side


Linear flutter analysis: theory

• Computation of the normal modes with the dynamic equation

• Eigenvectors X1, X2,… written as columns in the modal matrix Φ

• Displacements‘ vector X written in the modal basis

• Generalization of the mass- and stiffness matrix

• Linear flutter equation in the modal basis

0XKXM =⋅+⋅ &&

qΦX ⋅=

MΦΦM Tgen =

0qGAFKM gengen =⋅

⋅−+⋅

⋅ ∞∞ )(),(

2

ppMaqV

Lp ref

[ ]K21 XXΦ =

KΦΦK Tgen =


Linear flutter analysis: theory

Flutter point (zero damping):

• V∞FP, ρ ∞FP → q∞FP

• ωFP

ref

FP

q

q∞

ref

FP

ωω

Flutter Speed Index

Flutter Frequency Ratio

V-g curve

-0,4

-0,2

0,0

0,2

0 20 40 60 80

Velocity [m/s]

Dam

ping

[-]

V-f curve

0

20

40

60

80

100

120

140

0 20 40 60 80

Velocity [m/s]

Fre

quen

cy [H

z]


AGARD-Wing 445.6: normal modes


AGARD-Wing 445.6: GAFs

GAF-Matrix at Ma∞

= 0.901 (high subsonic) for bending (mode 1) and torsion (mode 2)

GAF-Matrix at Ma∞

= 0.954 (transonic) forbending (mode 1) and torsion (mode 2)


AGARD-Wing 445.6: flutter results

• As expected, good correlation in Flutter Speed Index between AER-SDEu and Potential Theory in the subsonic domain

• Transonic dip detected for AER-SDEu

• Excellent correlation between AER-SDEu and experiment in Flutter Speed Index for all Ma∞

• Satisfying correlation in Flutter Frequency Ratio between AER-SDEu and experiment for all Ma∞

→ AER-SDEu GAFs‘ integration validated

* D.E. Raveh, Y. Levy and M. Karpel, “Efficient Aeroelastic Analysis Using Computational Unsteady Aerodynamics”, Journal of Aircraft, Vol. 38, No. 3, 2001, pp. 547-556.

** X. Chen, G.-C. Zha, M.-T. Xang, “ Numerical Simulation of 3D-Wing Flutter With Fully Coupled Fluid-Structural Interaction”, 44th AIAA Aerospace Science Meeting And Exhibit, 9-12 Jan. 2006, Reno, NV.


FCDW: normal modes

The measurement showed strong nonlinearities at this mode!

→ Only theoretical comparison of the flutter results possible


FCDW: GAFs

GAF-Matrix at Ma∞

= 0.7 (high subsonic) for bending (mode 1) and torsion (mode 3)

GAF-Matrix at Ma∞

= 0.852 (transonic) for bending (mode 1) and torsion (mode 3)


FCDW: flutter results

• Up to Ma∞=0.7, good correlation between AER-SDEu and Potential Theory

• Strong transonic dip observed by AER-SDEu

• Strong discrepancy to the experimental results for Ma∞=0.875 and Ma∞=0.921 (nonlinearities in the structure not reproduced in the FE-model)


Conclusion

• GAFs successfully and robustly extracted from a small disturbance Euler method (AER-SDEu)

• Same matrix-format for GAFs out of Potential Theory as for small disturbance GAFs → direct integration in the linear flutter analysis without loss of quality

• Good correlation with linear flutter predictions out of the Potential Theory in the subsonic domain

• High quality of linear flutter predictions in the transonic domain, because of the consideration of an aerodynamic nonlinear steady-state (AGARD-Wing 445.6)

• AER-SDEu: reduction of computational time by an order of magnitude (with respect to a fully nonlinear time-matching computation)

→→→→ Successful integration of AER-SDEu in the linear flu tter analysis


Thank You

Acknowledgements:

I wish to acknowledge the contribution of Technical University of Munich, DLR, the NLR and the Colleagues of EADS MAS.


FFAST

• FFAST � Future Fast Aeroelastic Simulation Technologies

• European Research Project, Running time 3 years

• Kick off meeting in January 2010

F S TFUTURE FAST AEROELASTIC SIMULATION TECHNOLOGIES

F S TFUTURE FAST AEROELASTIC SIMULATION TECHNOLOGIES


• Goal: produce a much lower dimensional system having the same input/output characteristics as the original full order model

– far less evaluation time and storage– can be used as an efficient surrogate to the original, – replace the aerodynamics in coupled aeroelastic simulations, or – develop a simpler & faster controller suitable for real time applications

Physics and geometry CFD ROMSystem of n ODEs

Reduced system of r << n ODEs

Reduced basis: POD modes

Large-scale model,high-fidelity CFD data

Low-dim. description of large-scale system dynamics

Wide range of validity Restricted range of validity

Wind-tunnel experiment

input output

Background: Reduced-Order ModellingFFAST


End of presentation

Documents

EADS 2008 – All rights · PDF fileBaseline flutter analysis predictions ... AGARD 445.6 • FE-Model and Geometry 11x11 Grid points ... – Wing Buffet