VISCOUS FLOW BETWEEN PARALLEL DISKS WITH A TIME-VARYING GAP WIDTH AND A CENTRAL FLUID SOURCE

The present paper concerns the unsteady laminar incompressible flow between two parallel disks with a fluid source at the center of the disk (s). Both the flow rate of the source and the gap width between the disks are varied arbitrarily with time and independently of each other. Such a flow often appears in a nozzle-flapper valve or in a statical pressure bearing such as the piston shoes of a swash type axial piston pump. Series solutions to the Navier-Stokes equations are obtained, on the basis of an asymptotic expansion in the radial direction and a new theory of “multifold series expansion” for the time variable. The solutions describe precisely the non-linear interaction between the two coexisting flows. Experiments were carried out for the case where both the gap width and source flow were varied sinusoidally. The solutions agree well with the experimental results over a wide range of the flow conditions.