J. Fluid Meeh. zyxwvutsr (1985), zyxwvutsrq vol. 153, pp. zyxwvuts 339-380 Prided in zyxwvutsrq cleat Britain 339 Computation of convective laminar flow in rotating cavities By JOHN W. CHEW Theoretical Science Group, Rolls-Royce Limited, Derby (Received 16 December 1983 and in revised form 10 October 1984) zyx Numerical predictions are presented for the centrifugally driven free convection in a sealed rotating cavity and for the buoyancy-affected flow through a cavity with an inner cylindrical source and an outer cylindrical sink. Results for a sealed cavity filled with a high-viscosity siliconeoil are in good agreement with previously published experimental measurements of the mean Nusselt number. When the heat transfer is conduction-dominated the results away from the cylindrical surface agree with Dorfman’s (1968) similarity solution,’ but as convection becomes important they depart from this solution. In an air-filled cavity, for both the free convection and radial outflow cases, the results away from the cylindrical surface are generally in reasonable agreement with Chew’s (1982) similarity solution, although property variations and radial heat conduction do cause some departure from this solution. The extent of the region in which the heat transfer was influenced by the presence of the cylindrical surface, and the Nusselt number distribution in this region are shown to be sensitive to the thermal boundary conditions imposed on this surface. 1. Introduction In two earlier papers (Chew 1984; Chew, Owen zyxw & Pincombe 1984) a finite- difference program for prediction of steady sourcesink flow in a rotating cylindrical cavity was described and results for a cavity having a net radial outflow of fluid were presented. This program has now been extended to solve the energy equation in addition to the mass and momentum conservation equations, and to allow for property variations of the fluid. In the present paper numerical results are given for flows which are induced or strongly affected by buoyancy in the centrifugal force field. Three classes of flow are considered: ‘free convection’ in a sealed cavity filled with a high-viscosity silicone oil; free convection in an air-filled cavity; and the flow in a cavity having a radial outflow of air. Motivation for this work comes from the gas-turbine industry where an understanding of the flow between co-rotating disks is important for estimating disk cooling rates. Insight into the flow in a finite cavity can be gained from the closely related, but somewhat simpler, case of the flow between two infinite co-rotating disks at different uniform temperatures. Similari ty solutions for centrifugally driven flow have been given by several workers. Dorfman’s (1968) solution, which assumes a linear temperature profile across the cavity in the solution for the flow field, is valid both for the Ekman-layer regime where separate boundary layers on each disk are separated by a central core and in a merged boundary-layer regime in which there is no central core. Barcilon & Pedlosky (1967) and Hudson (1968) have derived solutions for Ekman-layer flow assuming the temperature in each Ekman layer is equal to that on the adjacent disk. These solutions are valid for air in convection-