Numerical study of swirling flows in a cylindrical container with co-/counter-rotating end disks under stable temperature difference

Abstract

A numerical study was conducted to investigate swirling flows of a Boussinesq fluid confined in a cylindrical container with co-/counter-rotating end disks. A vertically stable temperature gradient is imposed, with the stationary sidewall assumed as adiabatic. Flows are studied for a range of parameters: the Reynolds number, Re, 100 ⩽ Re ⩽ 2000; the Richardson number, Ri, 0 ⩽ Ri ⩽ 1.0; and the Prandtl number, Pr, Pr = 1.0. The ratio of the angular velocity of the top disk to the bottom disk, s, −1.0 ⩽ s ⩽ 1.0. The cylinder aspect ratio: h = 2.0. For the case of negligibly small temperature difference ( Ri ∼ 0) and high Re, interior fluid rotates with an intermediate angular velocity of both end disks when they are co-rotating ( s > 0). When end disks are counter-rotating ( s < 0), shearing flow with meridional recirculation is created. For the case of large temperature difference ( Pr · Ri ∼ O(1)), the Ekman suction is suppressed and the sidewall boundary layer disappears at mid-height of the cylinder. For all the values of s considered in the present study, the bulk of the fluid is brought close to rest with the fluid in the vicinity of both end disks rotating in each direction. The secondary flow in the meridional section of the cylindrical container exhibits various types of vortices as the governing parameters are varied. These flow patterns are presented in the form of diagrams on the ( s, Re) plane and ( s, Ri) plane. The average Nusselt number is computed and presented as functions of Ri, Re and s.