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Pipeflows distorted by non-symmetric indentation or branching

Part of: Incompressible viscous fluids

Published online by Cambridge University Press:  26 February 2010

F. T. Smith
F. T. Smith
Affiliation:
Department of Mathematics, Imperial College, London, S. W. 7.
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Extract

The two inter-related aspects of this laminar flow study are, first, the effects of indentations of length O(a) and height O(aK-⅓) on an otherwise fully developed pipeflow and, second, the manner in which such a pipeflow adjusts ahead of any nonsymmetric distortion to the downstream conditions. Here K is the typical Reynolds number, assumed large, and a is the pipewidth. The flow structure produced by the particular slowly varying indentation, or by a suitable distribution of injection, comprises an inviscid core, effectively undisplaced, and a viscous wall-layer, where the swirl velocity attains values much greater than in the core and where the nonlinear governing equations involve the unknown pressure force. Linearized solutions for finite-length, unbounded or point indentations, and for finite blowing sections (which model the influence of a tube-branching), demonstrate the upstream influence inherent in the nonlinear problem, for steady or unsteady disturbances. It is suggested that the upstream interaction caused there provides the means for the upstream response in the general case where the indentation, say, produces a finite constriction of the tubewidth.

MSC classification

Secondary: 76D99: None of the above, but in this section
Type
Research Article
Information
Mathematika , Volume 23 , Issue 1 , June 1976 , pp. 62 - 83
Copyright
Copyright © University College London 1976

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