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The discharge plume parameter $\unicode[STIX]{x1D6E4}_{d}$ and its implications for an emptying–filling box

Published online by Cambridge University Press:  16 March 2017

O. Vauquelin Open the ORCID record for O. Vauquelin [Opens in a new window] ,
E. M. Koutaiba ,
E. Blanchard  and
P. Fromy
O. Vauquelin*
Affiliation:
Aix-Marseille Université, Laboratoire IUSTI, UMR CNRS 7343, 5 rue Enrico Fermi, 13 453 Marseille CEDEX 13, France
E. M. Koutaiba
Affiliation:
Aix-Marseille Université, Laboratoire IUSTI, UMR CNRS 7343, 5 rue Enrico Fermi, 13 453 Marseille CEDEX 13, France Centre Scientifique et Technique du Bâtiment, 84 avenue Jean Jaurès, 77 447 Marne-la-Vallée, France
E. Blanchard
Affiliation:
Centre Scientifique et Technique du Bâtiment, 84 avenue Jean Jaurès, 77 447 Marne-la-Vallée, France
P. Fromy
Affiliation:
Centre Scientifique et Technique du Bâtiment, 84 avenue Jean Jaurès, 77 447 Marne-la-Vallée, France
*
†Email address for correspondence: [email protected]
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Abstract

The natural ventilation flow driven by an internal buoyant plume in a box involving an upper opening (vent) located at the ceiling (for the outflow) and a large lower opening at the floor (for the inflow) is examined theoretically in a general non-Boussinesq case. Analytical solutions of this emptying–filling box problem allow the characteristics of the flow at the vent to be determined. From these characteristics, a non-dimensional parameter $\unicode[STIX]{x1D6E4}_{d}$ (called the discharge plume parameter) is expressed. This parameter characterizes the initial balance of volume, buoyancy and momentum fluxes in the plume-like flow that forms above the vent. We then note that the value of $\unicode[STIX]{x1D6E4}_{d}$ allows the buoyant fluid layer depth in the box to be estimated, which is a new and interesting result for natural ventilation problems. Following previous experimental results, the decrease of the vent discharge coefficient $C_{d}$ when $\unicode[STIX]{x1D6E4}_{d}$ increases is discussed and a theoretical model based on plume necking is proposed. The emptying–filling box model is then extended for a variable $C_{d}$ (depending on $\unicode[STIX]{x1D6E4}_{d}$ ). Even though the discharge coefficient may be markedly reduced at high values of $\unicode[STIX]{x1D6E4}_{d}$ , our results show that this only affects transients and the steady state of an emptying–filling box for relatively thin buoyant fluid layers.

JFM classification

Convection: Convection Mixing: Mixing Convection: Plumes/thermals
Type
Papers
Information
Journal of Fluid Mechanics , Volume 817 , 25 April 2017 , pp. 171 - 182
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Copyright
© 2017 Cambridge University Press 

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