Role of turbulent Prandtl numbers on heat flux at hypersonic Mach numbers

A new turbulence model suited for calculating the turbulent Prandtl number as part of the solution is presented. Because of the high Reynolds numbers involved, a formulation based on the Reynolds-averaged Navier-Stokes equations is developed. The model is based on a set of two equations: one governing the variance of the enthalpy and the other governing its dissipation rate. These equations were derived from the exact energy equation and thus take into consideration compressibility and dissipation terms. The model is used to study three cases involving shock-wave/boundary-layer interaction at Mach numbers of 9.22, 8.18, and 5.0. In general, heat transfer prediction for separated flows showed improvement over traditional turbulence models in which the turbulent Prandtl number is assumed constant. It is concluded that using a model that calculates the turbulent Prandtl number as part of the solution is a key to bridging the gap between theory and experiment for hypersonic flows dominated by strong shock-wave/boundary-layer interactions.