Flow near a slowly rotating disk in a finite cylinder

Abstract

Numerical soilutons for the steady flow of a viscous fluid driven by a slowly rotating disk in a cylinder of finite aspect ratio are presented. Based on the comprehensive flow data acquired, the torque exerted on the disk is computed. The radial and axial structures of both the azimuthal and meridional flow details are exhibited. The effect of small, but non-zero, Reynolds number is discussed. The torque increases rapidly as the disk-cylinder radius ratio approaches unity because of the concentrated flow gradients near the tip of the disk. As the cylinder aspect ratio increases, the torque decreases. The flow can be approximated by the infinite cylinder model if the aspect ratio is greater than about 2.0. The theoretical torque estimate by using the infinite cylinder configuration is shown to be in reasonable agreement with the numerical results for large aspect ratios.