Analysis of the equilibrium wall model for wall-bounded high-speed turbulent flows*

A priori and a posteriori analysis of the equilibrium wall model is performed for wall-bounded high-speed compressible turbulent flows. Available supersonic/hypersonic turbulent channel and boundary layer DNS databases are used for the a priori analysis. Two mixing-length models, and three damping function scalings are considered in this study. Sensitivity of the wall model results to different mixing-length models, damping function scalings, and model constants is assessed. While previous studies indicate that the semi-local scaling for the damping function is most accurate for compressible flows, our results suggest that this is true only for very cold thermal wall boundary conditions. For moderately cold to adiabatic wall conditions, a new mixed scaling appears to work better. Wall-modeled Large Eddy Simulations of a Mach 3 turbulent channel flow with cold wall boundary condition corresponding to the DNS of Coleman, Kim & Moser (JFM 1995), and an axisymmetric Mach 2.85 boundary layer at adiabatic wall conditions interacting with a shock corresponding to the experiments of Dunagan et al. (NASA TM 1986) are consistent with the trends obtained from the a priori analysis of DNS data.