Non-isothermal laminar flow and heat transfer between disks corotating in a fixed enclosure

Abstract

This is a numerical investigation of the coupled laminar flow and heat transfer in the space between a pair of disks attached to a hub rotating about a vertical axis in a fixed cylindrical enclosure. A temperature variation is imposed in the fluid by setting the disks at different uniform temperatures, the temperature of the bottom disk being higher than that of the top disk. The Boussinesq approximation is used to characterize buoyancy forces in the momentum conservation equations. The different types of interdisk flow that arise as a function of angular velocity are described. At low Reynolds numbers the flow is primarily driven by gravity-induced buoyancy. As the Reynolds number increases, free convection yields to centrifugally-induced buoyancy. At sufficiently high Reynolds numbers, convection patterns induced by the strong shear at the enclosure wall dominate the interdisk flow and heat transfer but centrifugal buoyancy continues to influence the 3-D flow structure with respect to the isothermal case. One of the effects of buoyancy is the appearance of a new transition in the bifurcation diagram previously investigated by the authors for the isothermal flow case. Here, centrifugal buoyancy favors the generation of a 3-D flow which features a strong breaking of its symmetry properties with respect to the interdisk midplane, as in the isothermal case. Heat transfer rates are calculated for a range of Reynolds numbers and interdisk spacings. Special attention is paid to the high Reynolds number forced convection regime which is of practical interest. It is shown that the scales derived from heat and mass transfer analyses of the freely rotating disk apply to the present problem. In many of the present cases, 2-D (axisymmetric) and 3-D calculations yield very similar values for the overall heat transfer rates. This is especially the case for those flows with a wavy 3-D structure, meaning flows which, on average, are symmetrical with respect to the interdisk midplane. However, examples are also provided where the flow is strongly 3-D, requiring computationally intensive calculations to obtain accurate predictions of the corresponding heat transfer rates.