Flow in an Open Tank With a Free Surface Driven by the Spinning Bottom

Abstract

An investigation is made of flows of a viscous incompressible fluid inside a circular cylindrical tank. The flow is driven by the spinning bottom endwall disk of the tank. Numerical solutions of the Navier-Stokes equations were obtained over a range of rotational Reynolds number and of aspect ratio (cylinder height/radius) using two kinds of boundary condition at the top: a closed tank with a rigid lid and an open tank with a free surface. We provide descriptions of flow details for these two boundary conditions at the top. For small aspect ratios, the nature of the azimuthal flow is distinctly different depending on the type of the top boundary condition, i.e., a Couette flow under a rigid lid and a solid-body rotation under a free surface. These qualitative flow patterns are insensitive to the Reynolds number. For flows with a finite aspect ratio and at small Reynolds numbers, the change in the top boundary condition has little impact on the flow. For flows with a finite aspect ratio and at large Reynolds numbers, the prevailing flow patterns are of boundary layer-type. At a given vertical level, the angular velocity attains a larger value under a free surface than under a rigid lid.