Aspect ratio and radius ratio dependence of flow pattern driven by differential rotation of a cylindrical pool and a disk on the free surface

Abstract

The aspect ratio and radius ratio dependence of the flow pattern driven by the differential rotation of a cylindrical pool and a disk on the free surface is investigated through a series of unsteady three-dimensional numerical simulations. The aspect ratio, which is defined as the height to the radius ratio of the pool, varies from 0.06 to 2.0 and the radius ratio of the disk to the cylindrical pool varies from 0.15 to 0.9. The rotation Reynolds numbers of the pool and disk range from 0 to 4730 and 0 to −5677, respectively, where the minus sign means the rotation direction of the disk is contrary to that of the cylindrical pool. The results show that the basic flow state is axisymmetric and steady but has rich structures at the meridian plane depending on the aspect and radius ratios. With the increase of the rotation Reynolds number, the flow transits to three-dimensional oscillatory flow, characterized by the velocity fluctuation waves traveling in the counter-clockwise or clockwise direction at different aspect ratios. The corresponding wave number and angular velocity of the fluctuation wave dependent on the aspect ratio are discussed. In addition, the flow characteristics also show an important dependence on the radius ratio. Various polygonal flow patterns are presented varying with the radius ratio and rotation Reynolds numbers. The fluctuation wave number decreases with the increase of the disk rotation Reynolds number, and the shear layer induced by the counter-rotation of the disk and pool is responsible for producing this flow instability.