Numerical Investigation of Transonic Shock Oscillations on Stationary Aerofoils A. Soda, T. Knopp, K. Weinman German Aerospace Center DLR, Göttingen/Germany Symposium on Hybrid RANS-LES Methods Stockholm/Sweden, 07/2005 1
Outline 1 Shock-buffet : relevance & physical background 2 Numerical tool (DLR-Tau solver) 3 Two approaches : URANS vs. DES 4 URANS results 5 DES results 6 Conclusions & future work 2
1.1 Transonic Flow Features Aerodynamic limit (lift stall, drag rise, unsteady vortex shedding) Aeroelastic limit (aero-excitation: flutter, buffet, buffeting, LCO) Transonic Flutter Dip (a) Shock/BL interactions typical for aeronautical applications (b) Aeroelastic flutter curve typical for transonic flight regime 3
1.2 Shock/BL Interaction Pressure increase accross the normal shock BL thickening & shock-induced BL separation Flow deflection Normal shock transforms into oblique shock Conservation of momentum Shock-fanning (multiple weak compression waves) Supersonic tongue Separation bubble reaches TE Large TE pressure fluctuation (unsteady wake) 4
1.3 Self-Sustained Shock Oscillation Unsteady wake Propagation of pressure perturbations from TE through the flow field Modifying pressure field around the shock Self-sustained shock oscillation (SHOCK-BUFFET) even on stationary structures! Interplay between shock, BL and TE pressure field Buffet feeding mechanism Relevance of shock-buffet : Large transient loads in a narrow Ma-α window! Shock frequency can be close to flutter frequency! 5
2 DLR-Tau Code Time-accurate URANS solver on unstructured/hybrid grids Spatial discretisation Finite volumes, cell-centered on dual grid Central differencing for convective and viscous fluxes Reconstruction of gradients : Green-Gauss-MUSCL (URANS) and Least_Square (DES) Temporal discretization Inner iterations : explicit Runge-Kutta scheme Acceleration to steady state : multigridding, Res-smoothing Time-accurate computations : implicit dual-time stepping with 2nd order BDF scheme Parallel computations via MPI 6
3.1 URANS Computations 2-D calculations NLR 7301 supercritical aerofoil Linear-µ t -based turbulence modelling 1-eq. S-A Edwards 2-eq. LEA k-ω (Rung et al. 1999) Full multigrid (Full Approx. Scheme) MG cycle : 3v Temporal resolution t = 1e-04 s NTPER 500 NINNER = 100 7
3.2 DES Computations DES : URANS for attached flow & LES (SGS model) in separated regions 3-D calculations with NLR 7301 2-D grid extended in span-wise 2 different grids (Ny = 32/64) DES modelling SA-DES Low-Re modification (Strelets et al.) Temporal resolution t = 1e-05 s NTPER 5000 NINNER = 50 8
3.3 Influence of Modelling Parameters Ma = 0.87 Re = 40 mio alpha = 2.8 deg Sensitivity of CFD results for a transport aircraft close to the buffet boundary (steady RANS results by Rumsey et al. 2001) 9
4.1 NLR 7301 RANS Results Validation (a) Steady RANS results (b) Time-accurate URANS results, shock-buffet 10
4.2 NLR 7301 URANS - Two Isolated Buffet Regions 2-eq. LEA turbulence Central solver Temporal discretisation :: NTPER = 500, NINNER = 100 11
4.3 NLR 7301 URANS - Influence of Incidence Angle Ma = 0.77 Re = 2.3 mio 2-eq. LEA turbulence Central solver Temporal discretisation :: NTPER = 500, NINNER = 100 12
4.4 NLR 7301 URANS Detachment of Eddies Ma = 0.77, Re = 2.3 mio Alpha = -6 deg Alpha = -3 deg Alpha = 6 deg Alpha = 12 deg Massive separation & eddy detachment are the URANS result still plausible? 13
5.1 NLR 7301 Shock-Buffet DES vs. URANS Ma = 0.70 alpha = 5 deg Re = 2.3 mio URANS (1 CPU P4 2.0 GHz) : 1 NINNER / 0.7 s 1 period / 13 hrs DES (16 CPUs P4 2.0 GHz) : 1 NINNER / 2.5 s 1 period / 142 hrs (6 days) 14
5.2 NLR 7301 Shock-Buffet DES vs. URANS Ma = 0.70 alpha = 5 deg Re = 2.3 mio 15
5.3 NLR 7301 Shock-Buffet DES vs. URANS Ma = 0.70 alpha = 5 deg Re = 2.3 mio 16
5.3 NLR 7301 Shock-Buffet DES Results Ma = 0.70 alpha = 5 deg Re = 2.3 mio 17
5.4 Acoustic Apect of Shock-Buffet Ma = 0.70 alpha = 5 deg Re = 2.3 mio 18
5.5 Comprehensive Acoustic Theory Theories derived from experimental data Finke (1977), Lee (1990), Deck (2004) Propagation of pressure waves in the flow field Main shock-buffet driving force T = x*u DOWNSTR + x*u UPSTR x = x SHOCK -x T.E. 1 Main pressure propagation in a laminar BL 2 Main pressure popagation in case of turb. BL 3 Pressure waves travelling around the shock? 4 Propagation of pressure waves along the the lower surface x 19
6.1 Conclusions URANS methods can successfully predict unsteady flows with shock/bl interaction and strong separation URANS methods mature for engineering use in aerospace industry Choice of URANS modelling parameters is important! For detailed analysis and better understanding of shock-buffet physics Step beyond URANS necessary DES/LES/DNS 6.2 Future Work DES modelling Making DES accessible to engineers (efficiency, robustness) Moving closer to DNS? Making DES fit for thin-layer (shock-induced) separation Physics : validation of comprehensive acoustic mechanism in 2-D and 3-D 20