Reynolds-Averaged Numerical Simulations of Conical Shock-Wave/Boundary-Layer Interactions

Abstract

We carry out a parametric study of conical shock-wave/turbulent boundary-layer interactions by means of numerical simulation of the Reynolds-averaged Navier–Stokes (RANS) equations, with the eventual goal of establishing the predictive capabilities of standard turbulence models. Preliminary assessment of several linear-eddy-viscosity models for the case of planar interactions shows that the $k-\epsilon$ model and its variants as well as the Spalart–Allmaras model yield accurate prediction of the typical interaction length scale. Numerical simulations of conical interactions at high Reynolds numbers under attached and separated flow conditions generally support good capability of RANS to predict the gross flow features, including conditions of incipiently and fully separated flow. Comparison with direct numerical simulation data at low Reynolds numbers suggests that caution should be made because certain turbulence models may yield unrealistic incoming velocity profiles. With this caveat, we again find that RANS models yield satisfactory prediction of the three-dimensional flow organization and associated length scales. The $N$ -wave mean wall pressure signature is quantitatively predicted, and accurate information about the fluctuating pressure variance can be obtained from RANS data in a postprocessing stage by extension of correlations developed for low-speed separation bubbles.