A computational study of torque and volumetric flow rates in a confined rotating fluid and optimum iteration parameters in cavity flow.

摘要

The problem of laminar steady flow in a stationary cylinder with a rotating top disk was studied numerically. Three governing equations in cylindrical coordinates were solved by the alternating-direction implicit (ADI) method. To characterize the flow, three bulk quantities were selected, namely, the torque coefficient and the primary and secondary volumetric flow rates. Determination of the torque coefficient presented a difficulty because a singularity exists in the velocity gradient at the corner where the rotating disk and the stationary cylinder meet. This problem was overcome by specifying a gap between the disk and cylinder and incorporating this into the boundary conditions. The results obtained using these boundary conditions compared favourably with previous experimental, analytical and computational studies. The relevant parameters for the problem were the rotational Reynolds number, the aspect ratio (the ratio of the height of the cylinder to its radius) and the gap. The ranges of parameters investigated were as follows: Reynolds number from 1 to 10$sp5$; aspect ratio from 0.02 to 3; and gap size from 0.1% to 10% of the cylinder radius. The results indicated 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. In addition, the effect of iteration parameters on convergence of the cavity problem was studied. The stream function equation was solved by the SOR (successive over-relaxation) method and the vorticity equation by the ADI method. The results obtained were contour plots of the number of iterations required for convergence in the iteration parameter space and graphs of the optimum iteration parameters as functions of Reynolds number and grid spacing. The range of values examined were from Re = 10 on a 21 x 21 grid to Re = 1000 on a 101 x 101 grid. It was found that the iteration parameter space contained four regions: a converging region, an overflow region (associated with numerical instability), an underflow region and a nonconverging region. The optimum iteration parameters were dependent on the Reynolds number and the grid spacing, and a strong coupling between iteration parameters was shown.Dept. of Mechanical, Automotive, and Materials Engineering. Paper copy at Leddy Library: Theses u26 Major Papers - Basement, West Bldg. / Call Number: Thesis1992 .L354. Source: Dissertation Abstracts International, Volume: 54-05, Section: B, page: 2710. Thesis (Ph.D.)--University of Windsor (Canada), 1992.