The effects of compressibility on the instability of two-dimensional flow past a rotating cylinder executing high rotation rates are investigated, in detail, using a novel analysis based on compressible enstrophy transport equation (CETE). Accurate analysis of instability necessitates the generation of high fidelity numerical solutions and this is achieved by employing optimized numerical methods which enable high accuracy direct numerical simulation (DNS) 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 is reported in the literature. Results demonstrate single-sided vortex shedding, presence of significant compressibility in the flow field confirmed by local Mach number, 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 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.
The paper discusses the combined implementation of overset grid and patched grid methodologies and it's testing for transonic and supersonic flows. The motivation is to make the grid generation process easier and less time consuming as well as having optimum resolution as per the requirement of local flow gradients, with no effect on the accuracy of simulation. In the near-body region body fitted curvilinear structured grid and in the off-body region Cartesian grid layers with gradual coarser resolution away from the body were used. Curvilinear and Cartesian blocks were coupled with overset grid technique, where as different Cartesian layers were coupled through grid patching. In the overset grid module, barycentric coordinates were used to search the donor cells of each fringe cell. Area weighted averaging was utilised for fringe cell conservative variable interpolation from their corresponding donor cells and it preserved the conservation at shocks without generating spurious oscillations. The area fractions required for area weighted averaging were found by using polygon clipping algorithm in efficient manner. Steady state inviscid & viscous flows and unsteady state moving shock simulations were carried out to test with patched grid and overset grid combination and shocks passed through these block boundaries without getting distorted.
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