Analysis of Compressibility Corrections for Turbulence Models in Hypersonic Boundary-Layer Applications

Abstract

To accurately predict the hypersonic turbulent boundary layer, the compressibility corrections for a two-equation turbulence model are investigated substantially. The two-equation shear-stress-transport model based on the assumption of an eddy-viscous coefficient is adopted. The closure approximations for pressure work, pressure dilatation, and dilatation dissipation are examined by a priori and a posteriori analyses. The direct numerical simulation (DNS) of a hypersonic boundary layer shows that the pressure work term has little influence on the turbulent energy transport, whereas the effect of pressure expansion and pressure diffusion terms can be counteracted. The individual closure assumptions are evaluated by using the DNS data. Furthermore, Reynolds-averaged Navier–Stokes simulations with compressibility corrections are conducted for the hypersonic boundary layers of a flat plate and a cone. Comparisons with the experimental data and engineering correlations show that the original turbulence model overestimates the heat flux, and the pressure dilation and dilation dissipation corrections lead to a decrease in heating transfer rates. The combination of a priori and a posteriori analyses comes to the conclusion that the Zeman correction of the dilation dissipation term is applicable in hypersonic boundary layers.