Secondary subharmonic instability of hypersonic boundary layer in thermochemical equilibrium over a flat plate

Abstract

The transition from laminar to turbulent flow is a complex phenomenon and difficult to predict. There have been significant contributions over the years, enhancing the understanding of mechanisms that cause transition. The effect of chemical reactions on boundary-layer instability becomes significant for high-temperature flow. The existence of the secondary instability before the transition in a low-disturbance environment has been proved in earlier studies, although none of these studies considered high-temperature effects. The real gas (identified as a gas undergoing high-temperature phenomena) effects on the secondary subharmonic instability for a two-dimensional hypersonic boundary layer over a flat plate are studied using the Floquet model. The real gas is assumed to be in thermochemical equilibrium, where air is considered as a mixture of perfect gases in local thermal and chemical equilibrium. A five-species air model is used to compute the air mixture's thermal and transport properties. The stability of the primary disturbance is analyzed using linear stability theory, whereas a mean flow superposed with a second mode primary disturbance has been considered for the secondary instability analysis. The local and global methods have been used to solve the eigenvalue problem based on the finite difference method. The real gas effect on the secondary instability is destabilizing since the maximum secondary amplification rate is higher and appears at a lower Reynolds number for the real gas than that of the perfect gas. The increase in the primary wave amplitude increases the secondary amplification rate significantly. Furthermore, secondary disturbances decay faster into the freestream compared to primary disturbances. The eN method is employed to compute the amplification factor for the secondary amplification rate for the real and perfect gas. Based on the growth rate and N-factor for the secondary disturbances, it is found that the real gas flow is more unstable and susceptible to transitioning earlier than the perfect gas.