Insights in Turbulence Modeling for Crossing-Shock-Wave/Boundary-Layer Interactions

Abstract

The impact of turbulence modeling on the numerical simulation of the crossing-shock-wave/boundary-layer interactionsoccuringinaMach4e owon7 ££ 7deg,7 ££ 11deg,and15 £ 15degdouble-sharpe nplatesisanalyzed. The full Reynolds-averaged Navier ‐Stokes equations are solved with linear and weakly nonlinear formulations of the k‐! turbulence model, on grids up to 4 ££ 10 6 cells. The overpredicted heat transfer on the bottom plate is shown to be closely related to the main three-dimensional features developing in these e ows. The stronger the interaction, the more the numerical solutions violate the realizability principles. By introducing a dependence of cµ on the velocity gradients, realizable solutions are obtained and analyzed. The heat-transfer coefe cients are effectively lowered but not sufe ciently to meet the experimental data. The expected impact of other corrections, based on a limitation of the turbulent length scale or some compressibility effects, is evaluated and shown to be insufe cienttoe llthegapbetweencomputedandmeasuredheat-transfercoefe cients.Thestreamlinesarriving near the wall in the regions of overpredicted heat transfer are shown to originate from the very narrow regions close to the e n leading edges, in the upper part of the incoming boundary layer, and to be associated with an increase of turbulent kinetic energy when approaching the bottom wall, rather than when crossing the shock waves.