Reynolds‐stress modelling of M = 2.25 shock‐wave/turbulent boundary‐layer interaction

Abstract

SUMMARY M = 2.25 shock-wave/turbulent-boundary-layer interactions over a compression ramp for several angles (8, 13 and 18 • ) at Reynolds-number Re 0 = 7 × 10 3 were simulated with three low-Reynolds secondmoment closures and a linear low-Reynolds standard k-ε model. A detailed assessment of the turbulence closures by comparison with both mean-flow and turbulent experimental quantities is presented. The Reynolds-stress model which is wall-topology free and which uses an optimized redistribution closure, is in good agreement with experimental data both for wall-pressure and mean-velocity profiles. Detailed analysis of three components of the Reynolds-stress tensor (comparison with measurements and transport-equation budgets) provides a critical evaluation of full Reynolds-stress models for the separated supersonic compression ramp. The discrepancy observed in the shock-wave foot region, between computations and measurements for the Reynolds-stresses profiles, could be explained by considering the experimental shock-wave oscillation and directions for future modelling work are indicated.

Implicit meanflow–multigrid algorithms for Reynolds stress model computation of 3‐D anisotropy‐driven and compressible flows

“…Notice that the model predicts a marked pressure plateau between the first and the second oblique shock waves of the -structure (Figure 4), while the measurements show a more gradual increase ofp w . This is indicative of 3-D effects in the measurements [81].…”

“…The restriction (transfer) and prolongation (interpolation) operators are based on the characteristic MG approach of Leclercq and Stoufflet [78], which maintains the upwind character of the scheme and ensures stability of the multigrid algorithm. The method [17] has been applied to several 2-D and 3-D flows, including shock wave/turbulent boundary layer interactions (SWTBLI) [17,18,[79][80][81], flows with large separation [17,82], and multistage transonic turbomachinery flows [18], and has consistently given CPU-speed-ups in the range r CPUSUP ∈ [3,4].…”

Reynolds-Stress Model Prediction of 3-D Duct Flows

“…Obviously in all of the previous cases, density fluctuations have negligible influence [5], so that Favre (used in §2.1) or Reynolds averages are, for practical purposes, equivalent. The flow is modelled by the Reynolds-averaged Navier-Stokes (RANS) equations [32,70], coupled with the appropriate modelled turbulence-transport equations ( §2.1, §2.2). All computations were performed for air thermodynamics [70].…”

“…The flow is modelled by the Reynolds-averaged Navier-Stokes (RANS) equations [32,70], coupled with the appropriate modelled turbulence-transport equations ( §2.1, §2.2). All computations were performed for air thermodynamics [70].…”

Near-wall second moment closure based on DNS analysis of pressure correlations

“…Experience with a previously developed second-moment closure 1 in complex flows around or inside complex geometries [2][3][4][5][6] has shown satisfactory prediction of separation, with a slightly slower than experiment reattachment behavior. Furthermore the Reynolds-stress model developed by Gerolymos and Vallet (GV RSM 1 ) follows Lumley's 7 suggestion to model together redistribution and the anisotropy of dissipation (φ ij − ε ij + 2 3 εδ ij ).…”