A Phenomenological Model for Turbulent Heat Flux in High-Speed Flows With Shock-Induced Flow Separation

High-speed flows with shock waves impinging on turbulent boundary layers pose severe challenge to current computational methods and models. Specifically, the peak wall heat flux is grossly overpredicted by Reynolds-averaged Navier-Stokes (RANS) simulations using conventional turbulence models. This is because of the constant Prandtl number assumption, which fails in the presence of strong adverse pressure gradient (APG) of the shock waves. Experimental data suggest a reduction of the turbulent Prandtl number in boundary layers subjected to APG. We use a phenomenological approach to develop an algebraic model based on the available data and cast it in a form that can be used in high-speed flows with shock-induced flow separation. The shock-unsteadiness (SU) k-omega model is used as the baseline, since it gives good prediction of flow separation and the regions of APG. The new model gives marked improvement in the peak heat flux prediction near the reattachment point. The formulation is applicable to both attached and separated flows. Additionally, the simplicity of the formulation makes it easily implementable in existing numerical codes.