Interaction of shock waves with turbulent boundary-layers can enhance the surface heat flux dramatically. Reynolds-averaged Navier-Stokes simulations based on constant turbulent Prandtl number often give grossly erroneous heat transfer predictions in SBLI flows. This is due to the fact that the underlying Morkovin's hypothesis breaks down in the presence of shock waves; thus, the turbulent Prandtl number can not be assumed to be a constant. In our recent work (Roy, Pathak and Sinha,AIAA 2017), we developed a new variable turbulent Prandtl number model based on linearized Rankine-Hugoniot conditions applied to shock-turbulence interaction. The turbulent Prandtl number is a function of the shock strength and we proposed a shock function to identify the location and strength of shock waves. The shock function also simulates the post-shock ralaxation of the turbulent heat flux, akin to that observed in canonical shock-turbulence interaction. In this work, we extend the variable turbulent Prandtl number model for hypersonic flows by considering the influence of upstream total temperature fluctuation on turbulent heat flux. The model is combined with the well-validated shock-unsteadiness k-ω model and is used to study eight test cases involving shock/boundary-layer interactions at Mach numbers ranging from 5 to 11. Comparison with experimental data shows significant improvement in the surface heat transfer rate in the interaction region. The shock function is also used to propose a robust form of the existing shock-unsteadiness k-ω model that simplifies the numerical implementation enormously.
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