Wall-cooling effects on secondary instabilities of Mack mode disturbances at Mach 6

In hypersonic boundary layers, Mack modes play a crucial role in flow instability, whose secondary instability is a hot research topic. Since hypersonic flight vehicles will probably work under high-stagnation temperature conditions, which significantly affect the aerodynamic heating calculation and aero-thermal protection design of hypersonic vehicles, it is necessary to compare the primary and secondary instabilities in high-stagnation temperature boundary layers and that in the Boeing/AFOSR Mach 6 quiet tunnel (BAM6QT). Herein, wall-cooling is adopted in order not to consider chemical reactions. With the same freestream temperature of 100 K, two Mach 6 boundary layers with the wall temperature of 20 and 600 K, corresponding to the cooled wall condition and the quiet wind tunnel condition, respectively, are chosen to conduct the linear/non-linear stability and the secondary instability analysis. Our results show that the most dangerous Mack mode originates from a fast discrete mode in the present cooled-wall flow and the most dangerous Mack mode is born from the slow discrete modes in BAM6QT boundary layers. Furthermore, when the primary amplitude of Mack mode disturbances is large, the fundamental resonance always dominates the secondary instability, resulting in steady streaky structures that have the largest amplitude in the spectrum. In addition, the present results point out that the distribution of the eigenfunctions of the fundamental modes and subharmonic modes are significantly different under various wall-temperatures. What is more, different ratios of wall temperature to incoming flow temperature have changed the spanwise wave-angle of the secondary disturbances.