Analysis of the unsteady shock wave motion in inlet unstart processes

This paper is focused on the shock wave motion during inlet starting and unstarting phenomena (swallowing and expelling of shock waves) on supersonic and hypersonic diffusers, which are critical for the efficient operation of both ramjets and scramjets. The motion speed of a normal shock wave along the inlet duct during these processes is analyzed to better understand the influence of design parameters, such as the Mach number (M infinity) and contraction ratio (CR), on the speed and stability behavior of the shock wave position. A one-dimensional (1D) quasi-steady mathematical model is presented here, labeled DS2M (Duct Shock Speed Model), which allows for fast approximate calculations. This simple approach is useful for analyzing how the shock wave motion speed changes along the duct as a function of the duct geometry and operating parameters. It also allows for shock wave position stability assessment around equilibrium positions. This model is also suitable for hypersonic configurations, where the set of shock waves that appears, so-called pseudo-shock, could be appropriately replaced by an equivalent normal shock, subjected to a corrected Mach number, lower than that of the original system. In the presentation of results, both stable and unstable cases are discussed, showing how the shock wave can be swallowed or expelled depending on the evolution of the flow and duct geometry. Finally, the results obtained from the DS2M model developed here are compared with relevant published experimental data (including shock unstart experiments on two-dimensional and three-dimensional inlets with and without combustion, as well as buzz analysis in a scramjet), showing a good agreement. Difficulties concerning the comparison exercises are outlined.