Shock Train Response to High-Frequency Backpressure Forcing

Abstract

Numerical simulations are performed to study the effect of backpressure disturbances on a shock train. The basic problem consists of a shock train within a constant-area channel with an inflow and backpressure applied to the outlet. By subjecting the shock train to different fixed backpressures, it is shown that the shock train length varies linearly with backpressure, while the shock spacing is conserved. Through backpressure step forcing, it is shown that the response of the shocks, after an initial lag, is largely determined by the magnitude of the step change. Step increases in backpressure cause upstream shock movements with higher shock pressures. The opposite response occurs with backpressure decreases. With sinusoidal backpressure forcing, the shock train oscillates at the applied forcing frequency. The forcing propagates disturbances upstream, and therefore there is a noticeable forcing-response lag. Higher frequency disturbances are filtered as they travel upstream through the shock train while lower frequencies induce larger shock oscillations and produce upstream offsets in the shock positions. Further examination of the flow reveals a region of low-frequency motion below the leading shock, which becomes strongly amplified by the lowest backpressure forcing frequency.