Computational Study of Disk Driven Rotating Flow in a Cylindrical Enclosure

Abstract

The problem of steady laminar flow in a stationary cylinder driven by a rotating disk at the top was studied numerically. Three governing equations in cylindrical coordinates were solved by the spatially second-order and temporally first-order accurate ADI method. The flow was characterized by three bulk quantities, namely the torque coefficient and the primary and secondary volumetric flow rates. Calculation of the torque coefficient presented a difficulty because the velocity gradient is singular where the rotating disk and the stationary cylinder meet. This problem was overcome by specifying a gap between the disk and cylinder in the boundary conditions. The results obtained compared favourably with previous experimental results. The relevant parameters for the problem were the rotational Reynolds number, the aspect ratio and the gap. The ranges investigated were as follows: Reynolds number from 1 to 105; aspect ratio from 0.02 to 3; and gap size from 0.1 to 10 percent of the cylinder radius. The results showed that the bulk quantities were dependent on the Reynolds number and the aspect ratio. The torque coefficient was also dependent on the gap, while the volumetric flow rates were only weakly dependent on the gap. For high aspect ratios, the bulk quantities approached constant values.