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Contaminant dispersion in some time-dependent laminar flows

Published online by Cambridge University Press:  20 April 2006

C. Jimenez  and
P. J. Sullivan
C. Jimenez
Affiliation:
Department of Applied Mathematics, University of Western Ontario, London, Canada
P. J. Sullivan
Affiliation:
Department of Applied Mathematics, University of Western Ontario, London, Canada
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Abstract

Time-dependent flows occur naturally as in pulsatile blood flow and in tidal estuaries and comprise many of the man-made flows of practical importance. A knowledge of the rate of mixing of a contaminant substance in such time-dependent flows is of paramount interest in, for example, the injection of a chemical substance in blood flow, the discharge of outfalls in estuaries, and the mutual contamination length of two feed fluids when switching from one feed line to another as part of a manufacturing process. This paper presents a study of contaminant spread in two specific and well-defined flows and provides a basis for the interpretation of contaminant mixing in the more complex flow situations that normally prevail.

An extension of the probabilistic formulation of the streamwise dispersion of contaminant molecules given in Dewey & Sullivan (1982) is used to study time-dependent laminar flows between parallel plates and in tubes wherein the flows are homogeneous in the streamwise direction. The two flows considered in detail are oscillating flows and impulsively started flows. In impulsively started flows it is shown that, although the basic dispersive mechanism acts in much the same way as described by Taylor (1953), the start-up effects on the dispersion can be quite prolonged and very significantly reduce the streamwise spread of contaminant over that which is observed in the fully developed flow. In oscillatory flows, unlike the situation presented by Taylor (1953) in which a diminished value of molecular diffusivity κ increases the contaminant cloud axial growth rate in a tube of radius a, it is found that optimal streamwise contaminant spread results from a value of κ that depends upon kinematic viscosity v and frequency ω. The streamwise cloud-variance growth rate is explored over the full range of the two parameters γ2 = ωa2/κ and λ2 = ωa2/2v for all time, and it is shown that a global maximum results when γ ≈ 2π and λ ≈ 2.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 142 , May 1984 , pp. 57 - 77
Copyright
© 1984 Cambridge University Press

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