Application of Linear and Nonlinear Two-Equation Turbulence Models in Hypersonic Flows

Abstract

A nonlinear two-equation model has been implemented in the OpenFOAM framework and has been assessed for the computation of hypersonic flows with shock-wave boundary-layer interactions (SWBLIs), together with two other linear, low-Reynolds number models, namely the Launder–Sharma model and the shear stress transport model. Supersonic and hypersonic flow computations resulting from the use of these three models have been compared with experimental benchmark cases over a range of conditions. The three original models tested do generally return reasonable predictions of wall pressure in most cases, with the nonlinear model resulting in the best capability among the three in predicting flow separation. The wall heat flux in the interaction region, however, is overpredicted, in most cases by all three models (sometimes showing quite a dramatic overprediction). While the overall wall heat flux predictions of the nonlinear model are closer to the measured values, it is nevertheless evident that there is a need for further improvement. To address this need, the inclusion of a new source term in the dissipation rate equation is proposed, which aims to restrict the turbulent length scales in the shock-wave boundary-layer interaction region. This is inactive in incompressible flows and exerts only a minor influence in supersonic SWBLI cases. Computations of a range of supersonic and hypersonic flows with SWBLI show that this inclusion of the proposed source term in the dissipation rate equation, of both the nonlinear and the linear models, has significant effects only in hypersonic flows. These effects are mainly confined to the thermal predictions of these models. In the nonlinear model predictions, the overestimation of the wall heat flux in the SWBLI region is largely eliminated, while, in the corresponding predictions of the linear model, the overestimation is substantially reduced. The cubic nonlinear model tested, with the proposed new source term to the dissipation rate equation, is thus shown to be a very reliable and cost-effective tool for the Reynolds-averaged Navier–Stokes modeling of supersonic and hypersonic flows.