Hysteresis of the dynamic oblique shock wave induced by an oscillating ramp in supersonic flow

The hysteresis of dynamic oblique shock induced by an oscillating ramp at three different motion scenarios is demonstrated by two-dimensional numerical simulations. The angle of the oscillating ramp varies between 7° and 9° in a supersonic flow with an incoming Mach number of 2.5, in which no separation flow occurs in the boundary layer around the compression corner. It is found that the dynamic flow downstream of the oblique shock exhibits a partition hysteresis phenomenon with two distinct hysteresis regions: one is in the vicinity of the ramp wall, and the other is adjacent to the oblique shock wave. The effects of centrifugal force, Coriolis force, viscous force, and the lag in dynamic shock position on these two hysteresis phenomena regions are discussed and elucidated based on a comparative analysis of viscous and inviscid results. Additionally, a method for accurately predicting the dynamic shock wave angle is proposed for the inviscid flow, with the verified error less than 0.5%.