Source–sink flow inside a rotating cylindrical cavity

Abstract

The axisymmetric flow inside a rotating cavity with radial outflow or inflow of fluid is discussed. The basic theoretical model of Hide (1968) is extended, using the integralmomentum techniques of von Kármán (1921), to include laminar and turbulent flows; both linear and nonlinear equations are considered. The size of the source region is estimated using a ‘free disk’ model for the outflow case and a free vortex for the inflow case. In both cases, the estimates are in good agreement with available experimental data. Theoretical values of the tangential component of the velocity outside the Ekman layers on the disks, obtained from solutions of the laminar and turbulent integral equations, are compared with experimental values. The experiments were conducted in a number of rotating-cavity rigs, with a radial outflow or inflow of air, and laser-Doppler anemometry was used to measure the velocity in the ‘interior core’ between the Ekman layers. The measurements provide good support for the theoretical models over a wide range of flow rates, rotational speeds and radial locations. Although only isothermal flow is considered in this paper, the methods can be readily extended to non-isothermal flow and heat transfer.