Incompressible Flow Between Finite Disks

Abstract

Solutions were developed and are shown here for the primary laminar steady flow field that occurs in an incompressible, isoviscous, Newtonian fluid which is contained between two finite parallel disks. One of the disks is made to rotate at constant velocity and the other is held stationary, and either a source or a sink is located concentric to the axis of rotation. The analysis is general, containing all terms of the Navier-Stokes equations for rotationally symmetric flows, and produces a four-parameter family of solutions. The high Reynolds number flow contains multiple cells, arranged along the radius, and the flow appears to be uniquely defined by the boundary condition and the Reynolds number.