Assessment of Turbulence Models for Transonic / Supersonic Smooth Surface Separation

A systematic comparison of the principle modern turbulence prediction methods for the solution of the Navier-Stokes equations for the calculation of high speed flows about slender forebodies at low to moderate angle of attack is presented. This class of flow involves smooth surface turbulent boundary layer separation resulting in steady symmetric leeside vortices, and also the formation of embedded shock waves from the displacement effect of the large vortices in supersonic flow. As such this flow is both complex and highly sensitive to the state of the boundary layers on the body. This study revealed that the method which most consistently provides accurate predictions of the overall forces and moments on the body, the most accurate distribution of surface pressure and can most accurately resolve the flow features, including leeside vortices and embedded shock wave features, is the Solution Adaptive Simulation method. Detached Eddy Simulation and the Reynold Stress Model, which would be expected to provide superior accuracy over the RANS based linear eddy viscosity models, on the whole, failed to provide better predictions. In fact, the k-omega Realizable and k-omega SST turbulence models provided data which was almost as consistently accurate as the Solution Adaptive Simulation method. The standard k-omega turbulence model appears to be completely unsuitable for the computation of this class of high speed flow problem, and this may be associated with the poor initial / default prescription of the value of omega at the far-field boundary.