Self-sustained oscillations in high-speed cylinder wake flows

Abstract

Flow in the wake generated by a solid body presents an important class of problems in fluid dynamics, with wide ranging scientific implications and engineering applications. The present work investigates the structure and dynamics of flow in the near-wake of a high-speed 2D circular cylinder, treating it as a canonical problem. In the low-speed flow regime, wake regions are typically characterized by vortex shedding and vorticity growth due to convective instabilities. Whereas in the high-speed regime the general wake structure differs significantly with the formation of shock waves and strong shear layers, and coupled dynamics between them. While a large body of literature exists on flow unsteadiness in low-speed cylinder wakes, the unsteady high-speed wake problem has received surprisingly little attention. Most of the existing literature on high-speed cylinder wakes explains only the mean (time-averaged) flow structure, leaving unsteady flow features largely unexplored. A recent study of a 2D cylinder wake at Mach 4 revealed coherent oscillations in the near-wake region, and the oscillation frequency showed universal behavior with respect to the flow Reynolds number. The present work was aimed at obtaining a detailed understanding of the unsteady flow dynamics of a 2D cylinder wake at high speeds. To that end, flow experiments were performed at Mach 6 in the Roddam Narasimha Hypersonic Wind Tunnel at IISc. As a precursor to the cylinder wake experiments, a detailed characterization of free-stream disturbances in the wind tunnel at Mach 6 was carried out using a combined experimental and numerical approach. In the cylinder wake experiments, high-speed schlieren visualization of the near-wake region and time-resolved measurements of wall pressure in the aft-region were performed. Spectral proper orthogonal decomposition (SPOD) of schlieren data revealed coherent flow oscillations with a dominant timescale. The universal behaviour with respect to Reynolds number reported earlier, where the near-wake shear layer length and freestream velocity were used as length and velocity scales to construct a non-dimensional frequency (Strouhal number), was also observed in the present Mach 6 flow. Notably, the universal Strouhal number value was found to be nearly the same between Mach 4 and Mach 6, indicating a strong form of universality, one which also holds with respect to Mach number. A hypothesis for the cause of near-wake flow emerged from the earlier study at Mach 4. The self-sustaining nature of oscillations was qualitatively explained through an acoustic feedback mechanism at play in the near-wake region. Building on that hypothesis, a simple quantitative aeroacoustic model is developed in the present work to explain flow oscillations. The model draws inspiration from high-speed cavity flow studies, where downstream propagating vortical disturbances in the shear layer impinge on the cavity shoulder and generate acoustic disturbances, which in turn propagate upstream through the subsonic separated flow region and excite the shear layer disturbances. Strouhal number predictions from the aeroacoustic model are found to match well with experimental measurements, thereby lending support to the physical understanding of flow oscillations in the near-wake region.