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Buoyancy-driven unbalanced exchange flow through a horizontal opening

Published online by Cambridge University Press:  07 February 2020

N. H. Wise Open the ORCID record for N. H. Wise [Opens in a new window]  and
G. R. Hunt Open the ORCID record for G. R. Hunt [Opens in a new window]
N. H. Wise*
Affiliation:
Engineering Department, University of Cambridge, Trumpington Street, CambridgeCB2 1PZ, UK
G. R. Hunt
Affiliation:
Engineering Department, University of Cambridge, Trumpington Street, CambridgeCB2 1PZ, UK
*
†Email address for correspondence: [email protected]
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Abstract

Buoyancy-driven exchange flows occur in a variety of natural and industrial situations, including nuclear and hydraulic engineering, oceanography and building ventilation. Balanced exchange flows, whereby there is simultaneously an equal volume flux transferred vertically upwards and downwards through a horizontal opening, have previously been described theoretically. However, until now there has been no theoretical description of unbalanced exchange flows, whereby the volume flux in one direction through an opening exceeds that in the other. The model developed herein examines the growth of perturbations on the density interface at an opening made in a horizontal plane that connects buoyant fluid below with denser fluid above. By considering the interface as it is advected away from the plane of the opening by a bulk flow imposed in the vertical, we quantify the exchange for the unbalanced case. The model successfully predicts the Froude number criterion, which corresponds directly to the minimum dimensionless flow rate of the imposed flow, for the onset of unbalanced exchange across circular openings found experimentally. Additionally, comparisons made between the exchanges predicted and measured show excellent agreement across the entire range of possible flows, from unidirectional flow, through unbalanced exchange to balanced exchange. Consideration is given to applications of the model to ocean outfall design and to the prediction of building ventilation flows. For natural ventilation, the theoretical model we derive for unbalanced exchange bridges the gap in the prediction of air flow rates between displacement flows, where the flow is unidirectional, and balanced exchange flows.

JFM classification

Convection: Buoyancy-driven instability Geophysical and Geological Flows: Stratified flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 888 , 10 April 2020 , A22
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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