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

Published online by Cambridge University Press:  09 April 2010

N. B. KAYE ,
M. R. FLYNN ,
M. J. COOK  and
Y. JI
N. B. KAYE
Affiliation:
Department of Civil Engineering, Clemson University, Clemson, SC 29634, USA
M. R. FLYNN*
Affiliation:
Department of Mechanical Engineering, University of Alberta, Edmonton, AB, CanadaT6G 2G8
M. J. COOK
Affiliation:
Department of Civil and Building Engineering, Loughborough University, Leicestershire LE11 3TU, UK
Y. JI
Affiliation:
Institute of Energy and Sustainable Development, De Montfort University, The Gateway, Leicester LE1 9BH, UK
*
†Email address for correspondence: [email protected]
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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.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 652 , 10 June 2010 , pp. 195 - 205
Copyright
Copyright © Cambridge University Press 2010

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References

REFERENCES

Baines, W. D. 1983 Direct measurement of volume flux of a plume. J. Fluid Mech. 132, 247–256.CrossRefGoogle Scholar
Baines, W. D. & Turner, J. S. 1969 Turbulent buoyant convection from a source in a confined region. J. Fluid Mech. 37, 51–80.CrossRefGoogle Scholar
Germeles, A. E. 1975 Forced plumes and mixing of liquids in tanks. J. Fluid Mech. 71, 601–623.CrossRefGoogle Scholar
Howell, S. A. & Potts, I. 2002 On the natural displacement flow through a full-scale enclosure and the importance of the radiative participation of the water vapour content of the ambient air. Build. Environ. 37, 817–823.CrossRefGoogle Scholar
Huppert, H. E., Sparks, R. S. J., Whitehead, J. A. & Hallworth, M. A. 1986 Replenishment of magma chambers by light inputs. J. Geophys. Res. 91, 6113–6122.CrossRefGoogle Scholar
Kaye, N. B. & Hunt, G. R. 2004 Time-dependent flows in an emptying filling box. J. Fluid Mech. 520, 135–156.CrossRefGoogle Scholar
Kaye, N. B., Ji, Y. & Cook, M. J. 2009 Numerical simulation of transient flow development in a naturally ventilated room. Build. Environ. 44, 889–897.CrossRefGoogle Scholar
Lin, Y. J. P. & Linden, P. F. 2002 Buoyancy-driven ventilation between two chambers. J. Fluid Mech. 463, 293–312.CrossRefGoogle Scholar
Linden, P. F., Lane-Serff, G. F. & Smeed, D. A. 1990 Emptying filling boxes: the fluid mechanics of natural ventilation. J. Fluid Mech. 212, 309–335.CrossRefGoogle Scholar
Manins, P. C. 1979 Turbulent buoyant convection from a source in a confined region. J. Fluid Mech. 91, 765–781.CrossRefGoogle Scholar
Morton, B. R., Taylor, G. I. & Turner, J. S. 1956 Turbulent gravitational convection from maintained and instantaneous sources. Proc. R. Soc. A 234, 1–23.Google Scholar
Woods, A. W., Caulfield, C. P. & Phillips, J. C. 2003 Blocked natural ventilation: the effect of a source mass flux. J. Fluid Mech. 495, 119–133.CrossRefGoogle Scholar