On the origin and propagation of perturbations that cause shock train inherent unsteadiness

Abstract

In constant area back pressured ducts, shock trains exhibit inherent unsteadiness where the shock system fluctuates about its time-averaged position despite constant bulk inflow and outflow conditions. In this work, the underlying causes of inherent unsteadiness are identified and the flow dynamics of the system is studied for a shock train in a Mach 2.0 ducted flow that is mechanically back pressured. High-speed schlieren movies and pressure measurements are collected to quantify the shock system fluctuations. Cross-spectral analysis of this data is used to identify specific perturbations, i.e. the fluid phenomena that impact the shock train motion. Key information about each perturbation is also obtained, including where it originates, what direction it travels and how it impacts each shock. Oil flow visualization and particle image velocimetry are then used to gain insight into the physical structure of perturbations and the flow phenomena that generate them. The results identify a complex, frequency-dependent dynamical system that is influenced by (i) upstream propagating acoustic waves that emanate from separation bubbles, (ii) vortices that shed from separation bubbles and convect downstream and (iii) upstream propagating acoustic waves generated in the diffuser. With this information, a scaling argument for the shock train inherent unsteadiness is presented.