Simulations of compressibility effects in centrifugal buoyancy-induced flow in a closed rotating cavity

Abstract

In this study, we investigate centrifugal buoyancy-induced flow by conducting numerical experiments for Rayleigh numbers in the range of 105 to 108. The primary focus of the study is to understand the fluid flow and heat transfer induced by centrifugal buoyancy in a rapidly rotating system with direct relevance to the internal air system of a gas-turbine engine. We solve the compressible Navier–Stokes equations in an inertial frame of reference. Flow visualization shows the formation of counter-rotating convection cells in the domain analogous to Rayleigh–Bénard convection. The prediction of wall heat transfer shows good agreement with experimental data for low Rayleigh number but deviates for the high Rayleigh number cases. Further, the effect of compressibility or Mach number is studied by running additional simulations with varying flow Mach numbers at fixed Rayleigh and Rossby numbers. A strong dependence of flow structure and induced wall heat transfer rate on the flow Mach number is observed. The increase in flow Mach number causes density stratification, which suppresses the formation of convection rollers and reduces the wall heat transfer rate. Furthermore, a guideline is provided on how to reduce the computational cost for the high Rayleigh number cases.