Incoming parameters and backpressure.

This study numerically investigates the low-frequency oscillations of shock trains within a two-stage divergent isolator equipped with four vortex generator jets, operating at Mach 3.034 under a constant backpressure of 0.25 MPa. Detailed flow field analysis and spectral examination of pressure signals provide a comprehensive quantitative and qualitative understanding of the unsteady behavior and its underlying mechanisms. The results reveal that the shock train undergoes low-frequency streamwise oscillations at 102 Hz, with displacement amplitudes reaching up to 2.5 times the isolator inlet height. This oscillatory behavior is characterized by a spring-like effect within the shock train and a wave-like breathing effect in the separation region. Two distinct driving mechanisms govern the oscillatory behavior of the shock train, resulting in characteristic path independence for its upstream and downstream motions. The dominant mechanism is attributed to the inherent instability of the separation region (downstream mechanism), while spatial non-uniformities introduced by the upstream vortex generator jets and the duct geometry act as secondary amplifying factors, collectively contributing to the oscillatory behavior.