Assessment of Reynolds Averaged Navier-Stokes Models for a Hypersonic Cold-Wall Turbulent Boundary Layer

Abstract

Turbulent heating of hypersonic vehicles is a first-order design consideration that remains a challenge to model accurately. High Mach number, as well as strong heat transfer to the vehicle surface, introduce significant uncertainties into the prediction of aerodynamic heating and drag by modern Computational Fluid Dynamics (CFD) codes. In the present study, three widely-used Boussinesq based Reynolds Averaged Navier Stokes (RANS) turbulence models are assessed using recently published Direct Numerical Simulation (DNS) data for a hypersonic zero-pressure gradient turbulent boundary layer at wind-tunnel relevant conditions. Simulations are performed at Mach 2, 6, 8, 11, and 14, with wall to recovery temperature ratios ranging from 0.18 to 1.0. Velocity and temperature profiles are compared between the two modeling approaches, as are wall heat transfer and skin friction. The Spalart-Allmaras (SA) turbulence model achieves better agreement with the DNS profiles than the Menter Baseline (BSL) and Shear Stress Transport (SST) models for all cases presented here. Errors in the temperature profile show a clear dependence on wall cooling when the SST model is used, ranging from 5\% when the wall is adiabatic to 25\% when the wall is strongly cooled. SA profile predictions yielded errors that were a factor of 2-3 times smaller than those of the SST model, and which showed no obvious trend with respect to Mach number or wall cooling. Wall heat transfer and skin friction results follow the opposite trend, with the SA model yielding roughly twice the error as the BSL and SST models for the Mach 11 and 14 cases. For these most extreme cases, none of the RANS models are able to accurately predict skin friction and heat transfer, with errors reaching 30\% for the Mach 11 case. Errors also increase with Reynolds number based on comparison with the DNS results for the M11Tw020 case, which covers Re$_{\tau}$ up to 1200. This indicates that errors in RANS predictions at flight-relevant flow conditions may exceed those of the present study. The Zeman compressibility correction yields promising improvements to heat transfer and skin friction predictions for the strongly cooled high Mach number cases, however, temperature profile errors are increased significantly when this correction is used.