Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-23T19:23:25.679Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Brown, S. N. and Daniels, P. G.. J. Fluid Mech., 67 (1975), 743.CrossRefGoogle Scholar
Fraenkel, L. E.. Proc. Roy. Soc. Lond., A272 (1963), 406.Google Scholar
Gill, A. E.. J. Fluid Mech., 21 (1965), 145.CrossRefGoogle Scholar
Gillis, J. and Brandt, A.. Weizmann Inst., AF EOAR, 63–73 (1964), SR-1.Google Scholar
Goldstein, S.. Qu. J. Mech. & Appl. Math., 1 (1948), 43.CrossRefGoogle Scholar
Hall, P.. J. Fluid Mech., 64 (1974), 209.CrossRefGoogle Scholar
Knopp, K.. Theory and Applic. of Inf. Series, (Hafner, N.Y., 1947).Google Scholar
Lee, J. S. and Fung, Y. C.. Microvasc. Res., 3 (1971), 272.CrossRefGoogle Scholar
Manton, M. J.. J. Fluid Mech., 49 (1971), 451.CrossRefGoogle Scholar
Smith, F. T.. J. Fluid Mech., 57 (1973), 803.CrossRefGoogle Scholar
Smith, F. T.. To appear in Qu. J. Mech. Appl. Math. (1975a).Google Scholar
Smith, F. T.. To appear in Qu. J. Mech. Appl. Math. (1975b).Google Scholar
Smith, F. T.. To appear in J. Fluid Mech. (1976a).Google Scholar
Smith, F. T.. To appear in Proc. Roy. Soc. Lond., A. (1976b).Google Scholar
Smith, F. T.. To appear in Proc. Roy. Soc. Lond., A. (1976c).Google Scholar
Smith, F. T.. To appear in J. Fluid Mech. (1976d).Google Scholar
Smith, F. T. and Stewartson, K.. Proc. Roy. Soc. Lond., A332 (1973), 1.Google Scholar
Stewartson, K.. Proc. Roy. Soc. Lond., A319 (1970), 289.Google Scholar
Stewartson, K.. In Advs. in Appl. Mechs., 14 (1974), 145 (Academic Press,, 1974).Google Scholar
Tillett, J. P. K.. J. Fluid Mech., 32 (1968), 273.CrossRefGoogle Scholar
Wilson, S. D. R.. J. Fluid Mech., 38 (1969), 793.Google Scholar