A theoretical and computational study of the vibration excitation on the transition criteria of shock wave reflections

In this paper, we study the vibration excitation on the reflection of shock waves in hypersonic flows by using analytical and computational approaches. First, a theoretical approach is established to solve the shock relations which are further applied to develop the shock polar analytical method for high-temperature air. Then, a comparative investigation using calorically perfect gas model and thermally perfect gas model considering vibration excitation indicates an obvious change to the overall profile of the shock polar. The post-shock pressure increases within the strong branch of the shock polar while decreases within the weak branch due to vibration excitation of air molecules. A more notable phenomenon is the increase in the maximum deflection angle of the shock polar which can significantly influence the detachment criterion of shock reflection transition in high-temperature air flows. The shock polar analysis of shock reflection shows that the vibration excitation result in an obvious increase to the detachment criterion while a slight increase to the von Neumann criterion. A series of computations are conducted to confirm the above analytical findings on the shock reflection considering the vibration excitation. A slight difference of transition criterion between the theory and computations is found to be caused by the existence of the expansion fan which is an inherent flow structure. The proposed shock polar analytical method is proved to be an effective but simple approach for the study of shock wave reflections in hypersonic flows.