Thermally-driven gas flows in a rapidly-rotatingcylinder

Abstract

Numerical studies are made of flows of a gas in a rapidly-rotating cylindrical container. The reference Ekman number is small, and the peripheral Mach number is O(1). The internal flows are generated by applying a small temperature gradient on the boundaries of the cylinder. Analyses are made of comprehensive and systematically-organized numerical results, which have been acquired by solving the complete, compressible Navier-Stokes equations. The results are examined to reveal the effects of the Ekman number and of the cylinder aspect ratio. The existence of the short-bowl flow regime is verified by cross-checking the numerical data with the previous analytical predictions. The characteristic details of this flow regime are described. The diagnostic studies by using the numerical results exhibit the predominant dynamic balance in the flow field. The changeover in the character of the flow is scrutinized by varying the aspect ratio ∧. For large values of ∧, the long-bowl approach solution is shown to be consistent with the numerical results. The demarcation between these two regimes is assessed by reviewing the numerical data. The flow details in a shallow cylinder are also presented. On the basis of the foregoing results, the effect of sidewall thermal boundary conditions are also considered. Steady-state linear motions that occur due to a small change in the boundary temperature are analyzed. In order to examine the flow structure and temperature distribution under various thermal boundary conditions, three types of conditions are assumed at the sidewall i.e., linearly-varying, insulated and isothermal temperature condition. Contour maps of the temperature and stream function are constructed for these three cases. In the short-bowl regime, the closed circulation near the sidewall is strongly affected by the thermal conditions owing to the work done by compression produced during the radial motion. On the other hand, the axial flow in the inner inviscid region...