Unsteady Viscous Flow Between Parallel Disks With a Time-Varying Gap Width and a Central Fluid Source

Abstract

A theoretical analysis is presented for the unsteady laminar flow of an incompressible fluid between parallel disks with a time-varying gap width and a central fluid source of constant flow rate. New series solutions to the Navier-Stokes equations are obtained, on the basis of asymptotic series expansion in the radial direction and a new theory of “multifold series expansion” with respect to the time variable. The solutions cover the general case of arbitrarily time-varying gap width. Moreover, it can describe precisely the complicated non-linear interaction between the two coexisting flows due to the gap-width variation and to the central fluid source. Experiments were carried out for the case of sinusoidally oscillating gap-width variation, and it has been confirmed that the present solutions agree well with the experiments, even in severe cases that an approximate superposition theory neglecting the aforementioned interaction effect produces a remarkable error.