Analysis and modelling of unsteady oblique shock trains under asymmetric incoming boundary layers

An experimental study was conducted to investigate the characteristics of unsteady oblique shock trains in a constant-area rectangular duct under an asymmetric incoming boundary layer. High-speed schlieren techniques and high-frequency pressure measurements were utilised in this study. The results indicate that the oblique shock train mainstream leans significantly towards the thin-boundary-layer side. Under downstream periodic excitation, the shock train moves periodically, and its shape changes during the movement. This phenomenon occurs to match the downstream pressure by altering the relative Mach number in front of the shock train, with the average pressure rise slope along the thick-boundary-layer side changing periodically. Additionally, unlike a normal shock train, the pressure rise distribution along the thick-boundary-layer side is nearly linear, and the correlation coefficients between the transducers on this side and the most downstream transducer are higher than those on the thin-boundary-layer side. Due to differences in flow structure and pressure rise distribution, the existing amplitude prediction model proposed by Xiong et al. ( J. Fluid Mech. vol. 846, 2018, pp. 240–262) for the unsteady normal shock train is no longer applicable to the unsteady oblique shock train. Therefore, a new prediction model is derived and verified by experiments. Moreover, it is found that using only the downstream pressure transducer information on the thick-boundary-layer side can effectively predict the amplitude of the shock-train motion. Combined with the prediction model, a novel method is proposed to estimate the amplitude of the shock-train motion conveniently.