Interaction between Mack second mode and radiation mode in high-enthalpy boundary layers

Abstract

Instabilities of high-enthalpy flat-plate boundary layers in thermochemical equilibrium conditions are studied using a linear stability theory (LST) and parabolized stability equations. A supersonic radiation mode is found to be unstable at the downstream location of the second mode. This mode synchronizes with the second mode as its phase velocity approaches cr=1−1/Ma. The amplification rate is expected to be comparable to the second mode when Ma>14 and Tw<14Te. The results of disturbance evolution indicate that the radiation mode is generated by the second mode through a synchronization process. The coefficient for the amplitude response of the radiation mode to the forcing second mode is around 1. After the radiation mode is excited, the second mode itself still exists in the boundary layer, leading to a co-existence of dual unstable modes. Owing to the competition between the two modes, the disturbance amplitudes exhibit significant oscillations. A two-mode amplitude prediction model based on the LST is proposed by properly superposing the two modes' amplitudes. The accurate prediction of the N-factor demonstrates that the proposed model can be used to predict a high-enthalpy boundary layer transition involving these two modes.