Abstract
The present paper deals with the axisymmetrical flow field around a circular disk moving slowly along the axis of a circular cylinder vessel containing a viscous liquid. It is solved numerically by the finite difference method. The effects of Reynolds number of the disk motion and the side-wall of the cylinder vessel on the flow field around the disk were discussed on the basis of numerical calculations. The expansion phenomenon of stream lines in the vicinity of the disk is suppressed by the approach of the side-wall of the cylinder vessel and the length of the vortex region in the rear of disk decreases with an increase of the diameter ratio of disk to cylinder. By applying the energy dissipation method to the flow field, the drag on a circular disk was calculated in the ranges of 0.01-50 of Reynolds number and 0.1-0.67 of the diameter ratio. The drag on a circular disk at the same Reynolds number increases with an increase of the diameter ratio. Breach's formula about the drag on a disk of infinitesimal thickness in the unbounded viscous liquid is extended to the formula in the bounded viscous liquid on the assumption that three coefficients in his formula are dependent on the diameter ratio. And, the new formula for the drag on a disk of infinitesimal thickness considering the side-wall effect of a circular cylinder vessel was proposed on the basis of the present calculations.
