Significant Supersonic Modes and the Wall Temperature Effect in Hypersonic Boundary Layers

Abstract

There has been renewed interest in studying supersonic modes in hypersonic boundary layers. Recent computational results have shown supersonic modes in hot-wall flows, upending the notion that they exist only in cold-wall flows. Furthermore, supersonic modes with larger peak growth rates than the second mode have been encountered in a very blunt cone geometry. Therefore, conditions leading to supersonic modes and their dominant amplification must be thoroughly and systematically investigated. Specifically, the impact of wall temperature in high-enthalpy environments is of immediate interest. This work uses thermochemical nonequilibrium direct numerical simulation (DNS) and linear stability theory (LST) to simulate Mach 10 flow over a 1 mm nose radius axisymmetric cone. Despite LST results indicating no supersonic modes in either the hot- or cold-wall flow, DNS results indicate their presence in both cases, with the cold wall exciting the supersonic mode comparably to the second mode. Further fast Fourier transform analyses suggest that this was a result of the nonlinear interaction between an unstable subsonic mode S, stable supersonic mode F1, and the slow acoustic spectrum. Because the supersonic mode in the cold-wall case had a comparable growth rate to the second mode, the supersonic mode could impact transition unexpectedly if not accounted for.