Self-similar unstart characteristics of supersonic contraction duct with an expansion corner

Inlet unstart is detrimental to hypersonic airbreathing flights. By unstart, we mean the separation-induced collapse of a supersonic duct flow. The unstart characteristics of a two-dimensional contraction duct with an expansion corner are numerically investigated to develop a universal prediction method and to determine the unstart mechanism. The unstart boundaries under varying contraction angles, entrance heights, and Reynolds numbers are obtained by translating the cowl plate. A self-similar empirical equation of unstart boundary that unifies multiple variables is proposed through similarity analysis. To estimate the unstart boundaries of large-angle ducts, the alternative area ratio is presented. Three types of unstarts are identified according to the distribution of the unstart boundaries and the evolution mechanism of separation region: the long-cowl, transitional, and short-cowl unstart. The long-cowl unstart stems from the mass flow limit at the throat, while the other two unstarts stem from the separation region growth. The wall pressure criteria for unstart are correlated with the dimensionless cowl length and the characteristic separation scale in the critical state to facilitate unstart detection. Moreover, the self-similar compression intensity is proposed to characterize the maximum pressure increase induced by the unit effective area contraction in the started state.