Journal of Fluid Mechanics

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The role of diffusion on the interface thickness in a ventilated filling box

N. B. KAYEa1, M. R. FLYNNa2 c1, M. J. COOKa3 and Y. JIa4

a1 Department of Civil Engineering, Clemson University, Clemson, SC 29634, USA

a2 Department of Mechanical Engineering, University of Alberta, Edmonton, AB, Canada T6G 2G8

a3 Department of Civil and Building Engineering, Loughborough University, Leicestershire LE11 3TU, UK

a4 Institute of Energy and Sustainable Development, De Montfort University, The Gateway, Leicester LE1 9BH, UK

Abstract

We examine the role of diffusivity, whether molecular or turbulent, on the steady-state stratification in a ventilated filling box. The buoyancy-driven displacement ventilation model of Linden et al. (J. Fluid Mech., vol. 212, 1990, p. 309) predicts the formation of a two-layer stratification when a single plume is introduced into an enclosure with vents at the top and bottom. The model assumes that diffusion plays no role in the development of the ambient buoyancy stratification: diffusion is a slow process and the entrainment of ambient fluid into the plume from the diffuse interface will act to thin the interface resulting in a near discontinuity of density between the upper and lower layers. This prediction has been corroborated by small-scale salt bath experiments; however, full-scale measurements in ventilated rooms and complementary numerical simulations suggest an interface that is not sharp but rather smeared out over a finite thickness. For a given plume buoyancy flux, as the cross-sectional area of the enclosure increases the volume of fluid that must be entrained by the plume to maintain a sharp interface also increases. Therefore the balance between the diffusive thickening of the interface and plume-driven thinning favours a thicker interface. Conversely, the interface thickness decreases with increasing source buoyancy flux, although the dependence is relatively weak. Our analysis presents two models for predicting the interface thickness as a function of the enclosure height, base area, composite vent area, plume buoyancy flux and buoyancy diffusivity. Model results are compared with interface thickness measurements based on previously reported data. Positive qualitative and quantitative agreement is observed.

(Received October 13 2009)

(Revised February 10 2010)

(Accepted February 11 2010)

(Online publication April 09 2010)

Correspondence:

c1 Email address for correspondence: mrflynn@ualberta.ca

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