Unsteadiness in a Spanwise Homogeneous Shock Train Interaction

Mechanisms of unsteadiness within a Mach 2.0 shock train in a constant area channel are studied numerically using large eddy simulations. The streamwise sequence of shock wave/turbulent boundary layer interactions (STBLIs) displays both eddying motions in the near-wall regions and shock oscillations in regions away from the wall. The main goal of this work is to describe both of these phenomena independently, with a secondary effort dedicated to identifying the degree to which the two processes are coupled. To this end, time traces of wall pressure fluctuations and shock wave oscillations are subjected to rigorous statistical, time-domain, and frequency-domain analyses. Time-mean separation is observed underneath the first (and strongest) STBLI in the shock train, inducing a more than three decade shift in the most energetic frequencies of the flow and displaying low-frequency dynamics akin to strongly separated external flow interactions. Beneath subsequent STBLIs, spectral content and two-point correlations indicate that wall pressure perturbations are only weakly influenced by outer shock motion, suggesting shocks beyond the first separated interaction leave only a minimal imprint at the wall. In this region, fluctuating wall loads are instead induced by large-scale structures in the outer turbulent flow, with wall pressure disturbances in the vicinity of given individual STBLI having the ability to propagate and impact adjacent interactions. Despite the varied wall pressure behavior between the first and subsequent interactions, descriptions of shock motion across various individual interactions display largely similar frequency and amplitude distributions, indicating the oscillatory behavior of the shocks is generally similar between successive STBLIs. Through application of band-pass filtering, the frequency dependent behavior of both the entire shock train and shocks in individual STBLIs are observed. Most notably, at low frequencies shock oscillations through the entire system are coherent, with motion of the leading separation shock in the first STBLI inducing an orderly and coherent response in downstream waves after an appropriate time delay.