NATURAL CONVECTION IN AN ANNULAR FLUID LAYER ROTATING AT WEAK ANGULAR VELOCITY

Abstract

A study is made by numerical methods of natural convection in an annular fluid layer confined between two horizontal cylindrical boundaries rotating at the same angular velocity. The problem is examined for two-dimensional flow with isothermal boundaries, the outer boundary being warmer. The weak rotation regime only is considered, for which the centrifugal acceleration is neglected. Governing equations for the flow field are solved in a non-inertial coordinate system rotating with the boundaries, in order to remove uniform solid-body rotation effects from the pure natural convection flow. Results indicate that a significant mass of fluid far from the boundaries remains tied up to the gravity vector at first, when the angular velocity is small, and thus does not take part to the solid body rotation. At high Rayleigh numbers, a critical Ekman number exists beyond which this flow pattern disappears abruptly and solid body rotation takes over, in contrast with the smooth transition observed at lower Rayleigh numbers. Multiple solutions are possible over a certain range of Ekman numbers, showing one type of flow or another in the cavity, depending on the initial conditions.