Representation of Stokes Flow Through a Planar Contraction by Papkovich-Fadle Eigenfunctions

Abstract

Stokes flow through a planar contraction is represented by matching together two series of Papkovich-Fadle eigenfunctions. Each series represents the solution in one of the unbounded rectangular regions upstream and downstream of the contraction plane. The coefficients of the series are obtained by weakly enforcing C3 matching conditions at the contraction plane using the Galerkin method. A post-processing technique is used to improve the appearance of the streamline plots near the singularity in the solution at the re-entrant corner of the channel. The pressure variation along the channel, as well as the excess pressure drop due to the contraction and the size of the upstream recirculating zone versus the contraction ratio, are presented. Channel contraction ratios of between two and six are considered.