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Several plume flows in pure and saline water at its density extremum

Published online by Cambridge University Press:  20 April 2006

J. C. Mollendorf ,
R. S. Johnson  and
B. Gebhart
J. C. Mollendorf
Affiliation:
Department of Mechanical Engineering, State University of New York at Buffalo, Amherst, New York 14260
R. S. Johnson
Affiliation:
Department of Mechanical Engineering, State University of New York at Buffalo, Amherst, New York 14260 Present address: Harrison Radiator Division, General Motors Corporation, Lockport, NY 14094.
B. Gebhart
Affiliation:
Department of Mechanical Engineering, State University of New York at Buffalo, Amherst, New York 14260 Present address: Department of Mechanical Engineering & Applied Mechanics, University of Pennsylvania, Philadelphia, PA 19104.
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Abstract

An accurate representation of the motion-causing buoyancy force, in the vicinity of the maximum-density condition in water at low temperatures, is determined by using a very accurate and quite simple equation of state for both pure and saline water. The resulting general laminar boundary-layer flow equations admit similarity solutions and, in the absence of salinity diffusion, require only one additional new dimensionless variable, called R. For flows of constant heat content in an unstratified ambient fluid, similarity is found only when the far-field temperature is at the temperature of maximum density. The three flow situations considered here are two above a horizontal line heat source and one above a point heat source. The first flow is a freely rising plane plume and the second is a wall plume (flow over a vertical, adiabatic surface with a horizontal line source imbedded in it). The third flow is the freely rising axisymmetric plume. These are the models in laminar theory of many processes which arise in cold water. A primary objective here is to calculate the effect of using a nonlinear density relation for water, which is much more accurate at low temperatures than the conventional linear one used in ‘classical’ analyses. The downstream variations of the temperature and velocity fields are found to be very different from those for flows where the effect of a density extremum is not included.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 113 , December 1981 , pp. 269 - 282
Copyright
© 1981 Cambridge University Press

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