Swirling Inflow Within the Narrow Gap of Two Disks

Abstract

The results of an analytical study dealing with the asymptotic swirling inflow, generated within the gap of two closely placed parallel disks, are presented. It is shown that the radial velocity component can be expressedby a single parameter, which combines the reduced Reynolds number and radial position. The latter velocity is found to flatten at the midgap position with the Reynolds number producing a plateau that progressively expands toward the walls. Under the action of viscous diffusion, the axial distribution of the tangential velocity is found to exhibit a similar property. The radial profile of the static pressure is shown to depend on the relative vortex strength and the Reynolds number. As inertia begins to dominate the viscous forces, the mid-channel tangential velocity curvature in the axial direction is found to tend asymptotically to zero, thus, encouraging the centerline velocity to approach the free-vortex profile. The results of the analytical study compare favorably with previous and present experimental evidence.