A Numerical Study of the Flow Due to a Rotating Disk With a Center Sink

Abstract

The flow due to a rotating disk in an infinite fluid with a sink located at the center of the disk is studied numerically. The problem is solved as an unsteady flow problem by an implicit alternating-direction technique and the method of successive over-relaxation. Solutions are computed for various values of a single parameter, β = Q02πων3, which contains the sink strength (Q0 ) and the disk speed (ω). The solutions converge to steady state values, and the values obtained for large radii are compared with an earlier solution for the case of the disk without the sink, with good agreement. It is found that a dividing stream surface is present which separates the sink flow from the centrifugal flow. The numerical results were limited to values of β below 12 in order to keep the computation time within reasonable limits.