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

[+] Author and Article Information
M. A. Rogerson, Y. L. Yeow

Department of Chemical Engineering, The University of Melbourne, Parkville 3052, Australia

J. Appl. Mech 66(4), 940-944 (Dec 01, 1999) (5 pages) doi:10.1115/1.2791802 History: Received August 27, 1997; Revised May 03, 1999; Online October 25, 2007


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.

Copyright © 1999 by The American Society of Mechanical Engineers
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