UNSTEADY TAU AND ROM FOR FLUTTER COMPUTATIONS OF TRANSPORT AIRCRAFT. Reik Thormann, Ralph Voß. Folie 1

Transcription

1 UNSTEADY TAU AND ROM FOR FLUTTER COMPUTATIONS OF TRANSPORT AIRCRAFT Reik Thormann, Ralph Voß Folie 1 Standardfoliensatz >

2 Outline Motivation Synthetic Mode Correction (SMC) Linearized CFD Method Pulse Excitation 2D Test case NACA64A010 (unsteady aerodynamics) Application to FERMAT reference aircraft (transonic flutter) Outlook Folie 2

3 Unsteady Aerodynamic for Flutter in Transonic and separated flow regime for industrial applications For a flutter analysis of a new aircraft a huge number of simulations are necessary Mach number: 1-7, Frequencies: 5-12, Symmetry: 2, Mode shapes: , Loading: > 1 Mio Cases! Reduction of computational complexity is necessary Use of different CFD Methods for different flight conditions Correction of the classic DLM with CFD Linearized CFD Methods Pulse Excitation POD Methods Folie 3

4 Synthetic mode shapes Pitch & torsion N SM so-called synthetic mode shapes s,n, with: s = 1,,N SM N RM mode shapes from the structural model r,n, with: r = 1,,N RM Unsteady CFD computations are performed for a small number N SM of synthetic modes p CFD s,m interpolated from the CFD grid to the DLM grid, pressure jumps between lower and upper lifting surfaces p CFD s,n CFD Synthetic Mode Corrected result (SMC), is generated by multiplying the corresponding DLM result with a complex number. This number is composed as the weighted sum of the single factors p N SM SMC DLM r, n pr, n s s 1 F s, n Heave & bending CFD DLM F s, n ps, n / ps, n Folie 4

5 Synthetic mode approximation for real large transport AC r, n N SM s s 1 r s, n minimize s r Mode 7 Mode 22 Real Mode Approximation with 10 Modes Mode 40 MAC( r, s) 2 T r s T T r r s s Folie 5

6 Linearised Frequency Domain Solver (LFD) Cooperation with DLR-AS Unsteady RANS Equation (1): Fourier series expansion of u(t) and x(t) analysis of small periodic motions Linearisation of (1) about steady equilibrium condition: Fourier expansion yields a complex valued linear system of equations Folie 6

7 Pulse Method Unsteady 1. Harmonic extracted from pulse excitation of airfoil. Effort for all necessary frequencies with the cost of 1 monofrequent simulation Linearity of transonic and separated flow wrt small disturbances! No Implementation in the TAU-Code necessary, only a TAU-Python-Script T = (2*pi*cref)/ (Uinf*kmin) dt = (2*pi*cref)/ (Uinf*kmax*N) Ntime = T/dt = N*kmax/kmin Folie 7

8 2D Test case NACA64A grid points Ma=0.8, Re=12.5e6 rigid pitch motion Folie 8

9 Linear TAU for unsteady attached flow, frozen viscosity AoA = 0 k = Folie 9

10 Linear TAU for unsteady separated flow, frozen viscosity AoA = 2 k = Folie 10

11 LFD - Turbulent flow - full linearisation AoA=2.0, amp = 0.5, red. f = 0.2, Petsc Folie Folie 11 Standardfoliensarz Kick-off > IMPULSE

12 NACA64A010: Computational Time Method Computational time Time saving factor URANS s 1 LFD FACEMAT 5.434s 12 LFD FACEMAT with GMRES 1.235s 53 LFD PETSC GMRES 96s 680 Only for small configurations! PULSE Method s 50 (50 frequencies!!) Time saving factors depends on the parameters of the time integration in URANS (number of periods, time steps per period, number of inner iterations) Folie 12

13 New Reference Model for Flutter Analysis: Research Model from drag prediction workshop DPW4: FERMAT Grid: ~4.1e6 points, 100e3 surface points 80h on 64 CPUs (AMD Opteron 1.9GHz) for 1480 time steps (kmin=0.05, kmax=1.0 with 64 samples, initial 200 timesteps ) R. Voss, L. Tichy, R. Thormann. A ROM Based Flutter Prediction Process and its Validation with a new Reference Model. 15th International Forum of Aeroelasticity and Structural Dyn. IFASD, Paris, France, June 26-30, 2011 Folie 13

14 Modal properties of the reference model No Eigenmode Frequency [Hz] Damping [-] Gen. mass [kg m 2 ] 1 1 st bending st torsion In-plane bending nd bending rd bending th bending Folie 14

15 Fermat correction factor F Mach dependence Magnitude correction factor, 1st synthetic mode, * = 0.15 Imag CFD DLM F s, n ps, n / ps, n Cp(DLM) Real Cp(TAU) Folie 15

16 Fermat correction factor F FREQUENCY dependence M= Magnitude of correction factor, 1st synthetic mode, * = 0.15 and 1.00 Phase angle of correction factor, 1st synthetic mode, * = 0.15 and 1.00 Folie 16

17 Comparison PULSE vs. monofrequent excitation y = 0.6m (50% span) k=0.25 k=0.4 Folie 17

18 Steady and quasisteady characteristics of FERMAT (DPW4 model) C L / C M / AoA and quasi-steady lift and moment coefficients of the reference model for CL(mean)=0.50 Folie 18

19 RANS-based transonic dip flutter boundary adopting SMC method FERMAT aircraft CL = 0.50 Re = 4 mio Ma= (attached) Ma= (detached) SMC with rigid pitch and heave mode (40 snapshots) Windtunnel total pressure Ptot 0,85 0,8 0,75 0,7 0,65 0,6 0,55 0,5 0,45 0,4 0,75 0,8 0,85 0,9 0,95 Mach DLM synth. mode synth.modes Folie 19

20 Conclusion Couple of methods developed to reduce the computational effort on 2 sides: efficient calculation of snapshots (LFD, pulse response) ROM for interpolating between the snapshots with SMC for the mode-axis First complex test case presented for flutter analysis with rigid-pitch and heave correction Outlook improve the LFD especially for separated flow Improve the capabilities of the ROM (additional parameters: Ma, AoA) Further validation of the ROM on the FERMAT configuration Folie 20