Effects of inflow Mach numbers on shock train dynamics and turbulence features in a backpressured supersonic channel flow

Abstract

Investigations on shock train dynamics and relevant turbulence features in a backpressured supersonic channel flow are carried out using direct numerical simulation for three inflow Mach numbers of Ma0= 1.61, 2.0, and 2.45. As Ma0 increases, the shock train undergoes a structural change characterized by the leading shock which changes from the symmetric “λ” (Ma0=1.61) to the symmetric “X” (Ma0=2.00) and then to the asymmetric “X” pattern (Ma0=2.45). The symmetry breaking of shock structures induces asymmetric separation, which significantly alters the distribution characteristics of wall variables such as wall pressure and friction. To examine the unsteady behaviors of the shock train, a mode decomposition technique, namely, reduced-order variational mode decomposition [Liao et al., J. Fluid Mech. 966, A7 (2023)], is adopted taking its merit of adaptively extracting time-frequency features of dynamic systems. The modal analysis reveals that the shock train system exhibits significant centralization of low-frequency energy. Specifically, two basic types of low-frequency oscillation modes dominate the unsteady motion of the shock train: one depicts overall translating oscillation while another represents accordion-like oscillation. The analysis of turbulent kinetic energy shows that turbulence amplification is mainly dominated by the interaction of the decelerating mean flow with streamwise velocity fluctuations in the vicinity of the leading shock for all three cases, which is unaffected by the symmetry breaking of shock structures.