Wall Cooling Effect on High-Enthalpy Supersonic Modes over a Cone

Abstract

High-enthalpy hypersonic boundary-layer transition plays an important role in many entry/descent vehicles. The aerothermodynamic performance of these vehicles strongly depends on the transition location on the surface. However, detailed transition flow physics in these chemically reacting boundary layers are poorly understood and transition estimates during the design phase rely heavily on empirically derived transition criteria such as . One of the most intriguing characteristics in hypersonic boundary layers is the presence of unstable supersonic modes, first identified in the 1990s. Due to a recent surge in hypersonic applications, there has been renewed interest in studying the flow physics of supersonic modes using either theory or direct numerical simulations. This paper investigates the rise of supersonic modes in a high-enthalpy hypersonic flow over a 5 deg half-angle cone at various wall temperatures using both quasi-parallel linear stability theory and linear parabolized stability equations (PSEs). It was found that supersonic modes exist in all wall temperature conditions, including the adiabatic wall case. A cooler wall temperature causes the second Mack mode to become an unstable supersonic mode naturally downstream of the upper-branch neutral location when the wall is sufficiently cooled. In terms of the integrated growth, the second mode is still the dominant mode. Nonetheless, supersonic modes can cause additional series of relatively weaker growth than that of the second mode beyond the peak amplitude location. According to the present linear PSE results, the formation of unstable supersonic modes is mainly associated with the synchronization of phase speed between the instability and acoustic waves in a nonparallel boundary layer, and not due to nonlinear modal interaction as suggested in the literature.