Effect of back-pressure forcing on shock train structures in rectangular channels

The deceleration of a supersonic flow to the subsonic regime inside a high-speed engine occurs through a series of shock waves, known as a shock train. The generation of such a flow structure is due to the interaction between the shock waves and the boundary layer inside a long and narrow duct. The understanding of the physics governing the shock train is vital for the improvement of the design of high-speed engines and the development of flow control strategies. The present paper analyses the sensitivity of the shock train configuration to a back-pressure variation. The complex characteristics of the shock train at an inflow Mach number M = 2 in a channel of constant height are investigated with two-dimensional RANS equations closed by the Wilcox k-omega turbulence model. Under a sinusoidal back-pressure variation, the simulated results indicate that the shock train executes a motion around its mean position that deviates from a perfect sinusoidal profile with variation in oscillation amplitude, frequency, and whether the pressure is first increased or decreased.