Evaluation of novel wall function approach for supersonic flow problems involving separations induced by geometry and shocks

Abstract

Supersonic combustion ramjet engine involves complex flow physics including shock-turbulent boundary layer interaction (STBLI) and shock-induced separations. The general approach while using an averaged Navier-Stokes equations to capture these flow separation, due to the flow physics and/or geometry accurately, is to use a low-Reynolds turbulence model. This requires the placement of first grid point in the viscous sublayer ( y + ≃ 1 ), which implies a need of finer mesh near the wall leading to an overall increase in number of cells in the computational domain and thus an increase in overall computational time. The wall-function method is a substitute to this approach which allows for the use of a coarser mesh in the region near to the wall. However, the standard wall-function methods are generally not very successful in capturing flow separations. In this work, we have employed a generalized wall function approach which incorporates the effect of both pressure gradient and compressibility in its formulation and have evaluated its performance for complex supersonic flow cases involving shock-turbulence boundary layer interactions (STBLI) and shock induced separations, which have not been done previously. We have shown that this method captures the flow physics accurately even with much coarser meshes near the wall. Further, insensitivity of the method to the placement of first grid point has also been demonstrated.