A novel compressible enstrophy transport equation-based analysis of instability during Magnus–Robins effects for high rotation rates

Abstract

The effects of compressibility on the instability of a two-dimensional flow past a rotating cylinder executing high rotation rates are investigated, in detail, using a novel analysis based on the compressible enstrophy transport equation (CETE). Accurate analysis of the instability necessitates the generation of high fidelity numerical solutions, and this is achieved by employing optimized numerical methods that enable high accuracy direct numerical simulation of compressible flows. To study the effects of compressibility induced by rotation alone, a low free stream Mach number and two high rotation rates are considered, as compared to that reported in the literature. Results demonstrate single-sided vortex shedding, the presence of significant compressibility in the flow field confirmed by local Mach number, and temperature and density gradient fields with transient formation of supersonic pockets noted for the higher rotation speed cases. The temporal instability is studied by analyzing the relative contributions of different terms in the CETE to the growth of enstrophy. As per the authors' knowledge, this is the first such research effort demonstrating an application of the CETE for instabilities. Analysis shows that viscous diffusion is the dominant mechanism in creating the flow instability with a secondary role played by the baroclinic mechanism.