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Emptying filling boxes: the fluid mechanics of natural ventilation

Published online by Cambridge University Press:  26 April 2006

P. F. Linden
Department of Applied Mathematics and Theoretical Physics. University of Cambridge, Silver Street, Cambridge CB3 9EW, UK
G. F. Lane-Serff
Department of Applied Mathematics and Theoretical Physics. University of Cambridge, Silver Street, Cambridge CB3 9EW, UK
D. A. Smeed
Department of Applied Mathematics and Theoretical Physics. University of Cambridge, Silver Street, Cambridge CB3 9EW, UK


This paper describes the fluid mechanics of the natural ventilation of a space connected to a large body of stationary ambient fluid. The flows are driven by buoyancy differences between the interior and exterior fluids. Connections with the ambient fluid are high level and low level openings. Two main forms of ventilation are identified: mixing ventilation and displacement ventilation. Mixing ventilation occurs when the incoming ambient fluid mixes with the fluid within the space, as is, the case if dense fluid enters through a high level inlet. In this case vertical stratification is weak. Displacement ventilation occurs when dense fluid enters at low levels and displaces the lighter fluid within the space out through high level openings. A strong stable stratification develops in this case, and there is little mixing between the incoming fluid and that in the interior. Both of these modes of ventilation are studied theoretically and the results are compared with laboratory experiments. Transient draining flows which occur when a space initially contains fluid of a density different from the ambient are examined.

The presence of internal sources of buoyancy allows steady states to be established, and the effects of point, line and vertically distributed sources are studied. These steady states are extensions of filling box models, with the addition of continuous exchange of fluid with the environment outside the space. A major result of this work is that the form of the stratification within the space depends on the entrainment caused by the convective elements (plumes) produced by the buoyancy sources, but is independent of the strength of the sources. The strength of the stratification and the magnitudes of the velocities do, however, depend on the source strength. The effects of opening size(s) and configurations are determined, and criteria for producing a particular stratification within the space are established. Applications of this work to the ventilation of buildings are presented.

Research Article
© 1990 Cambridge University Press

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Baines, W. D. & Turner, J. S., 1969 Turbulent buoyant convection from a source in a confined region. J. Fluid Mech. 37, 5180.Google Scholar
Baines, W. D., Turner, J. S. & Campbell, I. H., 1990 Turbulent fountains in an open chamber. J. Fluid Mech. 212, 557592.Google Scholar
Batchelor, G. K.: 1967 An Introduction to Fluid Dynamics. Cambridge University Press.
Brown, W. G., Wilson, A. G. & Selvason, K. R., 1963 Heat and moisture flow through openings by convection. J. Am. Soc. Heating Ventilation Air Conditioning Engng 5, 4954.Google Scholar
Dalziel, S. B.: 1988 Two-layer hydraulics – maximal exchange flows. Ph.D. thesis, University of Cambridge.
Epstein, M.: 1988 Buoyancy-driven exchange flow through openings in horizontal partitions. Intl Conf. on Cloud Vapor Modelling. Nov. 1987, Cambridge, MA.Google Scholar
Lane-Serff, G. F.: 1989 Heat flow and air movements in buildings. Ph.D. thesis, University of Cambridge.
Linden, P. F. & Simpson, J. E., 1985 Buoyancy driven flows through an open door. Air Infiltration Rev. 6, 45.Google Scholar
Morton, B. R., Taylor, G. I. & Turner, J. S., 1956 Turbulent gravitational convection from maintained and instantaneous sources. Proc. R. Soc. Lond. A A234, 123.Google Scholar
Penz, F. A.: 1983 Passive solar heating in existing dwellings. ETSU publication ETSU-5–1056a.Google Scholar
Penz, F. A.: 1986 A monitoring exercise in a school atrium. Appl. Energy 22, 113.Google Scholar
Worster, M. G. & Huppert, H. E., 1983 Time-dependent profiles in a filling box. J. Fluid Mech. 132, 457466.Google Scholar