Effects of the sidewall thermal conditions on the gas flows in a rapidly rotating cylinder

Abstract

Numerical studies are presented of the flows of a gas in a rapidly rotating cylindrical container. The reference Ekman number is small, and the peripheral Mach number is O(1). Fluid motions are induced by small differences in the boundary temperatures. In order to assess the effects of thermal boundary conditions at the sidewall on the flow structure and temperature field, three types of conditions at the sidewall are adopted, i.e. a linearly varying, an insulated, and an isothermal temperature condition. Analyses are made of comprehensive and systematically organized numerical results, which have been acquired by solving the complete, compressible Navier-Stokes equations. Contour maps of the temperature and stream function are constructed. In the short-bowl regime, the closed circulation near the sidewall is strongly affected by the thermal conditions; the importance of the work done by compression produced in the radial motions is emphasized. However, the axial flow in the inner inviscid region is found to be mainly controlled by the Ekman suction. In the long-bowl regime, the global flow structure is considerably influenced by the sidewall thermal condition. This is due principally to the significant diffusion of momentum in the radial direction.