Cross-flow vortices and their secondary instabilities in hypersonic and high-enthalpy boundary layers

Abstract

Compared to the streamwise instability, the cross-flow instability in high-enthalpy flows has received relatively less attention, but the latter is of vital importance in the flow transition for practical configurations. This work aims to investigate the cross-flow primary and secondary instabilities in hypersonic and high-enthalpy boundary layers, considering thermochemical non-equilibrium (TCNE) effects. The numerical tools adopted include a high-order shock-fitting solver, nonlinear parabolized stability equations and secondary instability theory (SIT). The flow over a swept parabola is calculated at a free-stream Mach number of 16. It is found that TCNE has a destabilizing effect on the cross-flow mode with a non-catalytic wall. Two important non-dimensional parameters are summarized to explain this effect. One is the ratio between the wall and boundary-layer edge temperatures, and the other is the cross-flow Mach number. Due to nonlinear effects, the stationary cross-flow vortices evolve and exhibit the classic rollover structures as in lower-speed flows. Two different disturbance energy norms are used in the energy budget analysis to classify the secondary cross-flow instability modes. The results from SIT highlight the importance of type-IV modes in TCNE flows at the downwash region of the vortex. The type-IV modes arise with the combined contribution from the wall-normal (on top and trough of the vortex) and spanwise (in the downwash region) production terms. The type-I mode is dominant in the calorically perfect gas case with an adiabatic wall, whereas the type-IV mode has the largest growth rate in the TCNE cases irrespective of wall temperature variation.