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Stability and mixing of a vertical plane buoyant jet in confined depth

Published online by Cambridge University Press:  19 April 2006

Gerhard H. Jirka  and
Donald R. F. Harleman
Gerhard H. Jirka
Affiliation:
School of Civil and Environmental Engineering, Cornell University, Ithaca, New York
Donald R. F. Harleman
Affiliation:
Department of Civil Engineering, Massachusetts Institute of Technology, Cambridge
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Abstract

A plane turbulent buoyant jet discharging vertically into a two-dimensional channel of confined depth is considered. The channel opens at both ends into a large outside reservoir, thus defining a steady symmetrical flow field within the channel. The analysis is aimed at two aspects, the stability and the bulk mixing characteristics of the discharge. A stable discharge configuration is defined as one in which a buoyant surface layer is formed which spreads horizontally and does not communicate with the initial buoyant jet region. On the other hand, the discharge configuration is unstable when a recirculating cell exists on both sides of the jet efflux.

It is shown that discharge stability is only dependent on the dynamic interaction of three near-field regions, a buoyant jet region, a surface impingement region and an internal hydraulic jump region. The buoyant jet region is analysed with the assumption of a variable entrainment coefficient in a form corresponding to an approximately constant jet-spreading angle as confirmed by different experimental sources. The properties of surface impingement and internal jump regions are determined on the basis of control volume analyses. Under the Boussinesq approximation, only two dimensionless parameters govern the near-field interaction; these are a discharge densimetric Froude number and a relative depth. For certain parameter combinations, namely those implying low buoyancy and shallow depth, there is no solution to the conjugate downstream condition in the hydraulic jump which would satisfy both momentum and energy conservation principles. Arguments are given which interpret this condition as one which leads to the establishment of a near-field recirculation cell and, thus, discharge instability.

The far-field boundary conditions, while having no influence on discharge stability, determine the bulk mixing characteristics of the jet discharge. The governing equations for the two-layered counterflow system in the far field are solved. The strength of the convective transport, and hence the related dilution ratio, is governed by another non-dimensional parameter, the product of the relative channel length and the boundary friction coefficient.

Experiments in a laboratory flume, covering a range of the governing parameters, are in excellent agreement with the theoretical predictions, both the stability criterion and the bulk mixing characteristics.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 94 , Issue 2 , 25 September 1979 , pp. 275 - 304
Copyright
© 1979 Cambridge University Press

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