Reynolds Stress Models for Shock - Turbulence lnteraction

Abstract

A systematic deficiency of current turbulence models which are based on the Reynolds averaged Navier-Stokes equations (RANS) is their inability to correctly predict the interaction of turbulence with shocks. This is because RANS models do not account for the unsteady motion or fragmentation of the shock wave within the interaction zone. Typically, significant over-prediction of the turbulent energy amplification occurs without dedicated adjustment of the applied turbulence model. An empirical shock correction for Reynolds-Stress models (RSM) is proposed. This corrective model is based on rescaling of the production and re-distribution terms in the Reynolds stress and length scale equations. The method is tested for two common RSM models and enables them to correctly predict the turbulence amplification, anisotropy and dissipation downstream of the interaction with a normal shock wave.