Assessment of RANS Turbulence Models for Hypersonic Flat Plates

Abstract

Many hypersonic flow applications have cold walls, where the wall temperature is significantly less than the recovery, or adiabatic, temperature. Current Reynolds-Averaged Navier-Stokes and Favre-Averaged Navier-Stokes approaches using linear eddy viscosity models for turbulence were not designed and optimized with hypersonic flow problems in mind, and thus have weaknesses that are continuously being studied and addressed. This study evaluates the performance of the Menter Shear Stress Transport (SST) and Spalart–Allmaras (SA) models on a group of hypersonic flat plate cases from a recent direct numerical simulation (DNS) database. Quantities of interest examined include velocity, temperature, turbulent kinetic energy, modeled turbulent kinetic energy budget terms, eddy viscosity, Reynolds stresses, heat fluxes, wall skin friction, wall heat transfer, and Reynolds analogy factor. Generally, the SA model performs better than the SST model in capturing the quantities of interest, but higher Mach number can occasionally reduce the accuracy of SA. Both models generally have increased errors in the quantities of interest with lower temperature ratio, with the SST model having a considerable sensitivity to lower temperature ratio. SST significantly underpredicts turbulent kinetic energy, fails at predicting key turbulent kinetic energy budget terms, and the Boussinesq approximation fails in capturing Reynolds normal stresses. For wall quantities, both models generally have increased errors at the lowest and highest Reynolds numbers studied, with the skin friction having increased errors with lower temperature ratio.