Reynolds stress transport modelling of shock-induced separated flow

Abstract

Predicting the interaction process in transonic flow between the inviscid free stream and the turbulent boundary layer is a challenging task for numerical simulation, which involves complex physical phenomena. In order to capture the physics, a turbulence model capable of accounting for physical phenomena such as streamline curvature, strong non-local effects and history effects, and large irrotational strains should be used. In the present work a second-moment Reynolds Stress Transport Model (RSTM) is used for computing transonic flow in a plane channel with a bump. An explicit time-marching Runge-Kutta code is used for the mean flow equations. The convecting terms are discretized using a third-order scheme (QUICK), and no explicit dissipation is added. For solving the transport equations for the Reynolds stresses u 2 , v 2 , and uv as well as k and ϵ an implicit solver is used which—unlike the Runge-Kutta solver—proved to be very stable and reliable for solving source dominated equations. Second-order discretization schemes are used for the convective terms. As the RSTM is valid only for fully turbulent flow, a one-equation model is used near the wall. The two models are matched along a pre-selected grid line in the fully turbulent region. The agreement between predictions and measurements is, in general, good.