Hybrid RANS/LES Simulations of Supersonic base flow Franck SIMON, Sébastien DECK *, Philippe GUILLEN, Pierre SAGAUT Applied Aerodynamics Department, Châtillon, France * Speaker
Contents Context Test case Simulations overview (C DES,SGS model, numerical scheme) Results Conclusions
Context of the Study Many industrial configurations are concerned with base flows : missiles, projectiles, launchers Base drag and unsteady loads are of primary interest Difficulties : Poor knowledge of unsteady features of base flows Difficulty to have reliable experimental data RANS simulations failed to predict base flows accurately Objectives : Expansion waves recirculation Free shear layer Strong compressibility effects Better comprehension of supersonic base flow physics Unsteady wake Reattachment shock Capabilities evaluation of hybrid RANS/LES approaches for highly compressible flows
Experimental test case Data-base (Herrin & Dutton, AIAA J., vol 32,1994) : LDV data Static pressure sensors at the base M 2.46 p 5.04 10 5 i Pa T i Re D D U 321 K 2.85 10 6 m -1 63.5 mm 593.8 m s -1
Simulations Overview Assessment of hybrid RANS/LES methods : Influence of C DES (gray-area) Influence of the Subgrid Model and numerical scheme Influence of the inlet boundary layer thickness Mesh Method Scheme C DES M1 Zonal DES Roe (10-4 ) 0.65 M1 Zonal DES AUSM 0.65 M2 Zonal DES AUSM 0.65 M2 Zonal DES AUSM 0.55 M2 Zonal DES AUSM 0.4 M1 RANS/MILES Roe (10-1 ) M1 RANS/MILES Roe (10-4 ) M1 RANS/MILES AUSM M1 RANS/LES Roe (10-4 ) M1 LES Roe (10-4 ) Interest of hybrid methods RANS: BL or SA ~ 3 LES: Mixed Scale Model t = t. U / D 1.810 ( t = 0.2µ s) Velocity profile at 1 mm Upstream of the base
Computationnal Mesh M2 M1 : 5.10 6 points 4.15R (N θ =96, Φ=3.75 deg.) 8R 8R 10R O-H topology on the axis Y-Z Reattachement section (isotropic cells) M2 : 14.10 6 points (N θ =180, Φ=2 deg.)
Coherent Structures in Supersonic Base Flows Flow Initial development of the highly compressible mixing layer (M c > 1) Very weak azimutal coherence as predicted by studies on mixing layer at high M c Instability process differs from the subsonic case (KH 2D instability) Zonal DES - C DES =0.55 (M2-14.10 6 points) Recompression and reattachment zones Numerous turbulent scales at reattachment Realignment of the structures along the x-axis Q = Q U 50 D = 2
Influence of the Gray Area Zonal DES M2 L exp /R=2.67 C DES =0.4 C DES =0.55 C DES =0.65 C DES = 0.65 leads to the destruction of almost all coherent structures except in the reattachement region C DES =0.65 delays generation of instabilities Size of the separated bubble overestimated
Influence of the Numerical Scheme RANS/MILES M1 AUSM Roe ψ ROE =10-4 Roe ψ ROE =10-1 Turbulence resolving capabilities decreased with dissipative numerical schemes The azimutal coherence of the structures in the initial stage of the shear layer increases with the dissipation
Compressible Shear Layer Expansion Exp. Dutton 10% and 90% of the time-averaged longitudinal velocity RANS SA M2 RANS/MILES M1 RANS/LES M1 LES M1 Zonal DES CDES=0.40 M2 Zonal DES CDES=0.55 M2 Importance of the mean incoming boundary layer (thickness) Weak influence of the subgrid model No-converged statistics with C DES =0.65 in the «present calculations» Weak influence of the C DES value when instabilities exist in the mixing layer SGS modeling effect BL effect Influence of C DES
Time-averaged Base Pressure Cp = pb p 1 ρ U 2 2 Base pressure Resolved Reynolds Stresses difficulty to reproduce a flat base pressure profile due to an excessive backflow ability of ZDES to describe the compressible shear layer contradictory turbulence/base pressure agreement awaits explanations
Conclusions Investigation of Dutton s supersonic base flow (N xyz =5 10 6 and 14 10 6 ) High convective Mach number flow (compressibility effects) weak 3D instability modes (different from strong 2D KH instabilities) Assessment of a wide range of parameters relevant to hybrids RANS/LES importance of the incoming boundary layer profile => use of hybrid methods delay of instabilities generation with C DES =0.65 strong effect of the numerical scheme on the turbulence resolving capabilities weak effect of the SGS model in LES mode Contradictory agreement base pressure/turbulence field remains unclear deeper physical analysis will be a continuation of the present work