  The interaction between the self-excited shock train flow and the cavity
shear layer in a scramjet isolator is investigated numerically using
detached-eddy simulations (DES). The effect of changing the position of the
shock train by controlling the back pressure ratio and the effect of changing
the cavity front wall angle are analyzed using unsteady statistics and modal
analysis. The propagation mechanism of the pressure disturbance was
investigated by spatiotemporal cross-correlation coefficient analysis. In the
present numerical study, a constant isolator section with a cavity front wall
was considered, followed by a diffuser section simulated at Mach number 2.2
with three different back pressure ratios. The change in back pressure provides
three different conditions. To understand the unsteady dynamics of the
interaction of the shear layer with the shock train, the spatiotemporal
trajectory of the wall pressure and the centerline pressure distribution, the
spatiotemporal cross-correlation coefficient, and the modal analysis by dynamic
mode decomposition are obtained. The results show that the low-frequency shock
train oscillation dominates the cavity oscillation. The spatiotemporal
cross-correlation between the wall surface and the cavity bottom wall indicates
the propagation of local disturbances originating from the separated boundary
layer caused by the shock and the recirculation zone in the corners of the
cavity. Dynamic mode decomposition analysis shows the shear layer at the
leading edge of the cavity and the downstream propagation of large eddies from
the cavity. It also shows the pairing of coherent structures between the shock
train and the recirculation zone of the cavity.
