Numerical studies of mixed recirculatory flow in annuli of stationary and rotating horizontal cylinders with different radius ratios

Abstract

Mixed recirculatory flow in the annuli of stationary and rotating horizontal cylinders were studied numerically. A set of distorted ‘false transient’ parameters were introduced to speed up the steady state solution of the unsteady vorticity, energy and stream function—vorticity equations. The inner cylinder of the annuli is assumed heated and rotating at Reynolds numbers that exclude the effects of centrifugal acceleration and three‐dimensional Taylor vortices. The Prandtl number considered is in the range of 0.01 to 1.0 and Rayleigh number in the range of 102 to 106. Radius ratios of the cylinders considered are 1.25, 2.5 and 5.0. For a radius ratio of 2.5, inner cylinder rotation in the Reynolds number range of 0 to 1120 was considered. Vertical eccentricities in the range of ±2/3 were studied for cases of the rotating inner cylinder. Numerical experiments show that the mean Nusselt number increases with Rayleigh number for both cases of concentric and eccentric stationary inner cylinder. At a Prandtl number of order 1.0 with a fixed Rayleigh number, when the inner cylinder is made to rotate, the mean Nusselt number decreases throughout the flow. At lower Prandtl number of the order 0.1 to 0.01, the mean Nusselt number remained fairly constant with respect to the rotational Reynolds number.