Recent Advances on Transonic Aeroelasticity

Transcription

1 Recent Advances on Transonic Aeroelasticity Wolfgang Luber EADS European Aeronautic Defence and Space Company ICNPAA 2010 Sao Jose dos Campos, Brazil; June 29th July 3rd 2010 EADS 2008 All rights reserved

2 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 ICNPAA-2010, Sao Jose dos Campos, Brazil - W. Luber - 2

3 Background 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 ICNPAA-2010, Sao Jose dos Campos, Brazil - W. Luber - 3

4 Application of classical Aeroelastic Tools VJ-101 VAK 191 AIRBUS A300 B F-104 Starfighter CCV Tornado X-31 Eurofighter F-4 Phantom EADS 2010 All rights reserved June/July 2010 MIG-29 ICNPAA-2010, Sao Jose dos Campos, Brazil - W. Luber - 4

5 Aeroelastic Requirements Steady aerodynamic requirement Steady 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 Aeroelasticity Steady 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 motions Unsteady aerodynamic loads of total rigid aircraft and components are required to be generated for subtrans- 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 modes Unsteady 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. ICNPAA-2010, Sao Jose dos Campos, Brazil - W. Luber - 5

6 Aeroelastic Requirements Requirement for classical Flutter prediction Baseline 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 simulation Allowance 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 loads Gust 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-elasticity Transfer 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). ICNPAA-2010, Sao Jose dos Campos, Brazil - W. Luber - 6

7 Aeroelastic Requirements Aero-servo-elastic Stability FCS open loop transfer functions due to control surface inputs should be predicted for aero-servoelastic 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 ICNPAA-2010, Sao Jose dos Campos, Brazil - W. Luber - 7

8 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 ICNPAA-2010, Sao Jose dos Campos, Brazil - W. Luber - 8

9 Correction Methods MULTIPLICATIVE CORRECTION METHOD ' '' ' '' ( c + i c ) = ( c + i c ) p p corr p p theo ( c p / α ) exp ( c p / α ) theo steady ENHANCED A/C STABILISATION AN MANEUVRABILITY ADDITIVE CORRECTION METHOD ' '' ' '' p p ( cp i cp ) ( cp i cp ) ' '' + = + + ( α + i α ) mode xx corr theo c α exp, α 0 c α theo steady ICNPAA-2010, Sao Jose dos Campos, Brazil - W. Luber - 9

10 Clean and external Store A/C Normal Modes Clean Aircraft Aircraft with I/B & O/B store Carriage ICNPAA-2010, Sao Jose dos Campos, Brazil - W. Luber - 10

11 Damping vs Flutterspeed Mach = 0.9 Clean Aircraft Mach = 0.95 External Store A/C ICNPAA-2010, Sao Jose dos Campos, Brazil - W. Luber - 11

12 AGARD FE-Model and Geometry NACA 64A004 Profil 11x11 Grid points 121 Plate elements 8 Elementes are fixed ICNPAA-2010, Sao Jose dos Campos, Brazil - W. Luber - 12

13 AGARD Comparison with Reference Model two modes Mode 1: Lagrange: Hz AGARD Report: Hz Mode 2: Lagrange: Hz AGARD Report: Hz ICNPAA-2010, Sao Jose dos Campos, Brazil - W. Luber - 13

14 AGARD CFD-Model Grid system Grid points 5 Blocks optimized for Euler-Calcs ICNPAA-2010, Sao Jose dos Campos, Brazil - W. Luber - 14

15 Flutteranalysis AGARD 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/m 2 7 points are required for each flutter slope Total Time of a flutter analysis (pure CPU time without pre and post processing): 10 Days ICNPAA-2010, Sao Jose dos Campos, Brazil - W. Luber - 15

16 Flutter onset AGARD (4) Flutter Frequency Ratio 0.80 Flutter Frequency Ratio ω F / ω α AGARD Report Lagrange/Doublet Lattice Iterate Lee-Rausch, Batina 1993 Farhat, Lesoinne Machzahl ICNPAA-2010, Sao Jose dos Campos, Brazil - W. Luber - 16

17 Flutter Case: M=0.901, α=0.0 ICNPAA-2010, Sao Jose dos Campos, Brazil - W. Luber - 17

18 Flutter Case: M=0.901, α=0.0 ICNPAA-2010, Sao Jose dos Campos, Brazil - W. Luber - 18

19 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 ICNPAA-2010, Sao Jose dos Campos, Brazil - W. Luber - 19

20 Aircraft Components affected by Buffet AIRBRAKE FIN EQUIPMENT ENGINE PILOT REAR FUSELAGE FRONT FUSELAGE EXTERNAL STORES WINGS ICNPAA-2010, Sao Jose dos Campos, Brazil - W. Luber - 20

21 Aerodynamic Loads on Airbrake ICNPAA-2010, Sao Jose dos Campos, Brazil - W. Luber - 21

22 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 DISCOMFORT Predicted buffet vibrations are used to assess the pilot comfort ICNPAA-2010, Sao Jose dos Campos, Brazil - W. Luber - 22

23 Prediction and Validation of Buffeting ICNPAA-2010, Sao Jose dos Campos, Brazil - W. Luber - 23

24 PVDF Polyvenylidenfluorid ICNPAA-2010, Sao Jose dos Campos, Brazil - W. Luber - 24

25 Location of unsteady pressure measuring ICNPAA-2010, Sao Jose dos Campos, Brazil - W. Luber - 25

26 Polyvenyliden Fluorid Sensor Array Application from Prof. W. Nitsche, TU Berlin ICNPAA-2010, Sao Jose dos Campos, Brazil - W. Luber - 26

27 Trainer Model in NLR Transonic Windtunnel ICNPAA-2010, Sao Jose dos Campos, Brazil - W. Luber - 27

28 Location unsteady pressure measuring points Location of the port pressure pick ups MP1 MP12 Location of starboard pressure pick ups MP13 MP24 ICNPAA-2010, Sao Jose dos Campos, Brazil - W. Luber - 28

29 PSD of pressure MP8 at 37.5 degrees 10 6 PSD Sp[Pa 2 / Hz ] PS [Pa 2 ] 2.4x x x x x Variance [Pa 2 ] f [Hz] Time History f [Hz] Pa t [sec] Power spectrum variance and time history ICNPAA-2010, Sao Jose dos Campos, Brazil - W. Luber - 29

30 PSD of pressure coefficient vs AoA 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 = k = f l µ /U PSD (amplitude of spectrum) of pressure coefficient P1 as function of angle of attack ; Sensor position P1 U = 40 m/s, Re lµ = 0.68 x ICNPAA-2010, Sao Jose dos Campos, Brazil - W. Luber - 30

31 Comparison of pressure pick ups: NLR and TUM 0.3 [ ] c P rms MP12 MP6 MP8 MP1 MP11 MP2 MP M = 0.5 P2 P c P rms of buffet pressures α [ ] 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 ICNPAA-2010, Sao Jose dos Campos, Brazil - W. Luber - 31

32 Comparison of MP8 and MP9: NLR and TUM P1 MP9 MP Comparison rms values P1 and MP9/MP8 α rms M0.5 Comparison of c p rms from TUM test signal P1 with NLR test signals MP8 and MP9 Mach = 0.5 ICNPAA-2010, Sao Jose dos Campos, Brazil - W. Luber - 32

33 Conclusion From the result of the comparison of the two different measurements it can be concluded that the PVDF foil technique is adequate for the application of the buffet prediction. This could be demonstrated through 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 reductions compared to the classical approach during the design and certification of military aircraft structures including buffet dynamic loads. This is due to the fact that for the PVDF measurement the existing aerodynamic wind tunnel model for the derivation of stationary aerodynamic coefficients can be applied and it is not necessary to built an additional wind tunnel model for buffet as in case of the classical method. ICNPAA-2010, Sao Jose dos Campos, Brazil - W. Luber - 33

34 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 ICNPAA-2010, Sao Jose dos Campos, Brazil - W. Luber - 34

35 Aeroelastic Simulation System Fundamental equations: ( ρ) ( ρ φ ) + ( ρ φ ) + ( ρ φ ) = 0 t + x x y y z z 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 ICNPAA-2010, Sao Jose dos Campos, Brazil - W. Luber - 35

36 X Z Y cpt Ma = 0.93 α = 2.2 δ ib = 0.0 δ ob = -5.0 ε = 0.0 η FP = 0.0 ICNPAA-2010, Sao Jose dos Campos, Brazil - W. Luber - 36

37 WING SECTION 04 y/(b/2) = 36.7 % C P [-] WING SECTION 06 y/(b/2) = 49.8 % AESIM lo side AESIM up side EXP Data lo side EXP Data up side C P * x/c [-] Ma = 0.93 α = 2.2 δ ib = 0.0 δ ob = -5.0 ε = 0.0 η FP = 0.0 C P [-] AESIM lo side AESIM up side EXP Data lo side EXP Data up side C P * x/c [-] ICNPAA-2010, Sao Jose dos Campos, Brazil - W. Luber - 37

38 WING SECTION 38 y/(b/2) = 54 % flex lo side flex up side rigid lo side rigid up side C P * -0.4 C P [-] H = sea level x/c [-] Ma = 0.80 α = 2.20 δ ib = 1.85 δ ob = 1.85 ε = -5.0 η FP = -3.0 C P [-] WING SECTION 43 y/(b/2) = 84 % x/c [-] flex lo side flex up side rigid lo side rigid up side C P * ICNPAA-2010, Sao Jose dos Campos, Brazil - W. Luber - 38

39 CANARD SECTION 30 y/(b/2) = 43 % flex lo side flex up side rigid lo side rigid up side C P * -0.2 C P [-] CANARD SECTION 34 y/(b/2) = 95 % x/c [-] flex lo side flex up side rigid lo side rigid up side C P * H = sea level Ma = 0.80 α = 2.20 δ ib = 1.85 δ ob = 1.85 ε = -5.0 η FP = -3.0 C P [-] x/c [-] ICNPAA-2010, Sao Jose dos Campos, Brazil - W. Luber - 39

40 X Z Y cp Ma = 1.2 α = 4.1 δ ib = 0.95 δ ob = 0.95 ε = 0.0 η FP = 0.0 ICNPAA-2010, Sao Jose dos Campos, Brazil - W. Luber - 40

41 WING SECTION 06 y/b = 49.8 % C P [-] AESIM lo side AESIM up side exp. data (ob pyl) lo side exp. data (ob pyl) up side x/c [-] Ma = 1.2 α = 4.1 δ ib = 0.95 δ ob = 0.95 ε = 0.0 η FP = 0.0 C P [-] WING SECTION 08 y/b = 60.8 % AESIM lo side AESIM up side exp. data (ob pyl) lo side exp. data (ob pyl) up side x/c [-] ICNPAA-2010, Sao Jose dos Campos, Brazil - W. Luber - 41

42 WING SECTION 38 y/(b/2) = 54 % flex lo side flex up side rigid lo side rigid up side -0.3 C P [-] WING SECTION 40 y/(b/2) = 68 % x/c [-] flex lo side flex up side rigid lo side rigid up side H = 7783 ft Ma = 1.20 α = 5.00 δ ib = 3.33 δ ob = 3.33 ε = 0 η FP = 0 C P [-] x/c [-] ICNPAA-2010, Sao Jose dos Campos, Brazil - W. Luber - 42

43 0.6 LIFT DISTRIBUTION WING C A (y) [-] Ca (y) rigid Ca (y) elastic 0.1 fuselage 0.6 LIFT DISTRIBUTION CANARD inboard flap outboard flap y/(b/2) [-] Ca (y) rigid Ca (y) elastic H = 7783 ft Ma = 1.20 α = 5.00 δ ib = 3.33 δ ob = 3.33 ε = 0 η FP = 0 C A (y) [-] fuselage y/(b/2) [-] ICNPAA-2010, Sao Jose dos Campos, Brazil - W. Luber - 43

44 Demonstration of AESIM Code - Validation Mode 3 ICNPAA-2010, Sao Jose dos Campos, Brazil - W. Luber - 44

45 Demonstration of AESIM Code - Validation Stability and Control Derivatives ICNPAA-2010, Sao Jose dos Campos, Brazil - W. Luber - 45

46 UPPER PART LIFTING SURFACE LOWER PART FULL POTENTIAL LIFTING SURFACE Real Imag Amp Phs FULL POTENTIAL Unsteady pressures Mode 8, Ma=0.8,57Hz ICNPAA-2010, Sao Jose dos Campos, Brazil - W. Luber - 46

47 Validation of flutter analysis AESIM Full Potential, new grid, Ma =0.8, α= KTS EAS VEAS [KTS] VEAS [KTS] Mode 1 Mode 2 Mode 3 Mode 4 Mode 5 Mode 6 Mode 7 Mode 8 Mode 9 Mode 10 Zero Damping Line Damping [%] Frequency [Hz] ICNPAA-2010, Sao Jose dos Campos, Brazil - W. Luber - 47

48 Demonstration of AESIM Code - Validation AESIM-BASIC Gust Example 1-cos gust Aerodynamic and Elastic Loading in Selected Cuts due to Gust ICNPAA-2010, Sao Jose dos Campos, Brazil - W. Luber - 48

49 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 aeroelastic simulations 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. ICNPAA-2010, Sao Jose dos Campos, Brazil - W. Luber - 49

50 Conclusions Actual Status 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) including correction 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 ICNPAA-2010, Sao Jose dos Campos, Brazil - W. Luber - 50

51 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 ICNPAA-2010, Sao Jose dos Campos, Brazil - W. Luber - 51

52 Overview Introduction Small disturbance Euler method Calculation of Generalized Aerodynamic Forces (GAFs) CFD Models and steady state results Linear flutter analysis: theory Structural dynamics, GAFs and flutter results Conclusion ICNPAA-2010, Sao Jose dos Campos, Brazil - W. Luber - 52

53 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 ICNPAA-2010, Sao Jose dos Campos, Brazil - W. Luber - 53

54 Small Disturbance Euler Method AER-SDEu based on the full nonlinear Euler solver AER-Eu 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: 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 ICNPAA-2010, Sao Jose dos Campos, Brazil - W. Luber - 54

55 Small disturbance Euler method Coordinate vector of deformed grid x( ξ, η, ς, t) = x( ξ, η, ς ) + xˆ( ξ, η, ς ) e ikτ Arbitrary flow quantity (complex amplitude) φ( ξ, η, ζ, τ) = φ( ξ, η, ζ ) + φˆ( ξ, η, ζ ) e ikτ 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 ICNPAA-2010, Sao Jose dos Campos, Brazil - W. Luber - 55

56 Small disturbance Euler method Time Domain AER-Eu Steady state solution AER-Eu AER-SDEu Unsteady flow quantities (several cycles): c p (τ) Frequency Domain Fourier Analysis 1 st Harmonic of perturbed flow quantities: Re ĉp, Im ĉp 1 st Harmonic of perturbed flow quantities: Re ĉp, Im ĉ p 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-SDEu computation ICNPAA-2010, Sao Jose dos Campos, Brazil - W. Luber - 56

57 Computation of the GAF matrices The AER-SDEu method requires as input: Computational grid in reference position Computational grid in the deflected position Steady state solution generated by the nonlinear method AER-Eu: c p The AER-SDEu method provides as output (e.g.): ĉ p The GAF matrix can now be computed as (for fixed k red and Ma ): GAF ˆ ij = cp i uj ds + S S c p u j ds ˆ i c p ds Steady state pressure coefficient Surface vector of reference position u j ĉ pi dŝi Disturbance part due to eigenmode i Vector of deflection of eigenmode j Disturbed surface vector of eigenmode i ICNPAA-2010, Sao Jose dos Campos, Brazil - W. Luber - 57

58 CFD-Models and steady state results The integration of AER-SDEu into the aeroelastic analysis process is demonstrated for two models: AGARD-Wing (weakened model 3) Fuselage-Cropped-Delta-Wing (FCDW) ICNPAA-2010, Sao Jose dos Campos, Brazil - W. Luber - 58

59 AGARD-Wing Computations performed for 4 Mach numbers (Ma = 0.499, 0.678, 0.901, 0.954), 6 reduced frequencies and 5 eigenmodes Geometric properties: Taper ratio: Aspect ratio: Sweep (1/4-Line): airfoil: λ = 0.66 Λ = 1.65 φ 0.25 = 45 NACA 65A004 CFD-mesh properties: Grid topology: Block dimension (cells): Surface cells (wing): Off-Body-Distance: Farfield distance (x/y/z) 1-Block C-H c r 10c r /10c r /11c r c r - root chord ICNPAA-2010, Sao Jose dos Campos, Brazil - W. Luber - 59

60 AGARD-Wing Steady state result at Ma = (transonic case), AoA = 0 Weak shock on wing inner section (e.g. at η = 0.25) ICNPAA-2010, Sao Jose dos Campos, Brazil - W. Luber - 60

61 FCDW 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: Grid topology: Block dimension (cells): Surface cells (fuselage): Surface cells (wing): Off-Body-Distance: Farfield distance (x/y/z) 2-Block H-O c r 10c r /10c r /10c r ICNPAA-2010, Sao Jose dos Campos, Brazil - W. Luber - 61

62 FCDW Steady state results for various Mach numbers at AoA = 2 Sonic isosurface (Ma = 1.0) Ma = FCDW upper side U ICNPAA-2010, Sao Jose dos Campos, Brazil - W. Luber - 62

63 FCDW 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 Contour plot wing upper side ICNPAA-2010, Sao Jose dos Campos, Brazil - W. Luber - 63

64 Linear flutter analysis: theory Computation of the normal modes with the dynamic equation Eigenvectors X 1, X 2, written as columns in the modal matrix Φ M X & + K X = Displacements vector X written in the modal basis Φ = Generalization of the mass- and stiffness matrix X = Φ q Linear flutter equation in the modal basis M gen = Φ T MΦ 0 [ K] X 1 X 2 K gen = Φ T KΦ p L ref V 2 Mgen + K gen q GAF( Ma, p) q( p) = 0 ICNPAA-2010, Sao Jose dos Campos, Brazil - W. Luber - 64

65 Linear flutter analysis: theory 0,2 V-g curve Flutter point (zero damping): Damping [-] 0,0-0, V FP, ρ FP q FP ω FP -0,4 Velocity [m/s] Frequency [Hz] V-f curve Flutter Speed Index Flutter Frequency Ratio q FP q ω ω ref FP ref Velocity [m/s] ICNPAA-2010, Sao Jose dos Campos, Brazil - W. Luber - 65

66 AGARD-Wing 445.6: normal modes ICNPAA-2010, Sao Jose dos Campos, Brazil - W. Luber - 66

67 AGARD-Wing 445.6: GAFs GAF-Matrix at Ma = (high subsonic) for bending (mode 1) and torsion (mode 2) GAF-Matrix at Ma = (transonic) for bending (mode 1) and torsion (mode 2) ICNPAA-2010, Sao Jose dos Campos, Brazil - W. Luber - 67

68 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 ** 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. ICNPAA-2010, Sao Jose dos Campos, Brazil - W. Luber - 68

69 FCDW: normal modes The measurement showed strong nonlinearities at this mode! Only theoretical comparison of the flutter results possible ICNPAA-2010, Sao Jose dos Campos, Brazil - W. Luber - 69

70 FCDW: GAFs GAF-Matrix at Ma = 0.7 (high subsonic) for bending (mode 1) and torsion (mode 3) GAF-Matrix at Ma = (transonic) for bending (mode 1) and torsion (mode 3) ICNPAA-2010, Sao Jose dos Campos, Brazil - W. Luber - 70

71 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) ICNPAA-2010, Sao Jose dos Campos, Brazil - W. Luber - 71

72 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 flutter analysis ICNPAA-2010, Sao Jose dos Campos, Brazil - W. Luber - 72

73 Thank You Acknowledgements: I wish to acknowledge the contribution of Technical University of Munich, DLR, the NLR and the Colleagues of EADS MAS. ICNPAA-2010, Sao Jose dos Campos, Brazil - W. Luber - 73

74 F S T FFAST FUTURE FAST AEROELASTIC SIMULATION TECHNOLOGIES FUTURE FAST AEROELASTIC SIMULATION TECHNOLOGIES FFAST Future Fast Aeroelastic Simulation Technologies European Research Project, Running time 3 years Kick off meeting in January 2010 ICNPAA-2010, Sao Jose dos Campos, Brazil - W. Luber - 74

75 FFAST Background: Reduced-Order Modelling 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 input Physics and geometry CFD System of n ODEs ROM Reduced system of r << n ODEs output Wide range of validity Restricted range of validity Reduced basis: POD modes Wind-tunnel experiment Large-scale model, high-fidelity CFD data Low-dim. description of largescale system dynamics ICNPAA-2010, Sao Jose dos Campos, Brazil - W. Luber - 75

76 End of presentation ICNPAA-2010, Sao Jose dos Campos, Brazil - W. Luber - 76