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Detrainment from a turbulent plume produced by a vertical line source of buoyancy in a confined, ventilated space

Published online by Cambridge University Press:  21 February 2014

Charlotte Gladstone  and
Andrew W. Woods
Charlotte Gladstone*
Affiliation:
BP Institute, University of Cambridge, Madingley Road, Cambridge CB3 0EZ, UK
Andrew W. Woods
Affiliation:
BP Institute, University of Cambridge, Madingley Road, Cambridge CB3 0EZ, UK
*
†Email address for correspondence: lotty@bpi.cam.ac.uk
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Abstract

New experiments are presented which explore the dynamics of a turbulent buoyant plume produced by a vertically distributed linear source of buoyancy of strength $f$ per unit height. In a uniform environment, the plume volume flux increases with height from the base of the source, $z$, as $q(z) = {2^{-1/3}} {\pi }^{2/3} \alpha ^{4/3} f^{1/3} z^2$ where the entrainment coefficient, $\alpha = 0.09\pm 0.01$. In an enclosed space, with a net upward vertical ventilation flow $Q_V$, the buoyant plume generates a steady ambient stratification. The lowest part of the space, $z<h_i$, where $q(h_i)=Q_V$, is filled with fluid supplied by the ventilation flow and there is a net upflow in the ambient. Above this, $z>h_i$, the ambient fluid is linearly stratified with a reduced gravity gradient $f/Q_V$, and has no net vertical motion. Instead, for $z>h_i$, the time-averaged volume flux in the plume equals the ventilation flow. The intermittent entrainment of ambient fluid into the plume is now matched by intermittent detrainment from the plume, and the mean buoyancy in the plume relative to the ambient remains constant. The supply of fresh ventilation fluid to the ambient in the linearly stratified zone only occurs through the local detrainment and consequent horizontal intrusion of fluid from the plume. This has key implications for design of ventilation systems, in which there may be vertically distributed sources of buoyancy.

JFM classification

Convection: Convection Geophysical and Geological Flows: Geophysical and Geological Flows Convection: Plumes/thermals
Type
Papers
Information
Journal of Fluid Mechanics , Volume 742 , 10 March 2014 , pp. 35 - 49
Copyright
© 2014 Cambridge University Press 

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References

Baines, P. G. 2001 Mixing in flows down gentle slopes into stratified environments. J. Fluid Mech. 443, 237–270.Google Scholar
Baines, W. D. 1983 A technique for the direct measurement of volume flux of a plume. J. Fluid Mech. 132, 247–256.Google Scholar
Baines, W. D. & Turner, J. S. 1969 Turbulent buoyant convection from a source in a confined region. J. Fluid Mech. 37, 51–80.Google Scholar
Campbell, A. N. & Cardoso, S. S. S. 2010 Turbulent plumes with internal generation of buoyancy by chemical reaction. J. Fluid Mech. 655, 122–151.Google Scholar
Chen, Z. D., Li, Y. & Mahoney, J. 2001 Natural ventilation of an enclosure induced by a heat source distributed uniformly over a vertical wall. Build. Environ. 36, 493–501.Google Scholar
Conroy, D. T., Smith, S. G. Llewellyn & Caulfield, C. P. 2005 Evolution of a chemically reacting plume in a ventilated room. J. Fluid Mech. 537, 221–253.Google Scholar
Cooper, P. & Hunt, G. R. 2010 The ventilated filling box containing a vertically distributed source of buoyancy. J. Fluid Mech. 646, 39–58.Google Scholar
Cooper, P., Mayo, G. A. & Sorenson, P. 1998 Natural ventilation of an enclosure with a distributed buoyancy source applied to one vertical wall. In Proceedings of the 6th International Conference on Air Distribution in Rooms, Stockholm, Sweden.Google Scholar
Etheridge, D. W. & Sandberg, M. 1996 Building Ventilation: Theory and Measurement. John Wiley & Sons.Google Scholar
Gifford, F. A. 1967 The rise of strongly radiactive plumes. J. Appl. Meteorol. 6, 644–649.Google Scholar
Gladstone, C. & Woods, A. W. 2001 On buoyancy-driven natural ventilation of a room with a heated floor. J. Fluid Mech. 441, 293–314.Google Scholar
Heiselberg, P. K. & Sandberg, M. 1990 Convection from a slender cylender in a ventilated rooml. In ROOMVENT ’90, International Conference on Engineering Aero- and Thermodynamics of Ventilated Rooms, Oslo.Google Scholar
Hunt, G. R. & Kaye, N. B. 2005 Lazy plumes. J. Fluid Mech. 533, 329–338.Google Scholar
Lane-Serff, G. F., Linden, P. F. & Hillel, M. 1993 Forced, angled plumes. J. Hazard. Mater. 33, 75–99.Google Scholar
Linden, P. F. 1999 The fluid mechanics of natural ventilation. Annu. Rev. Fluid Mech. 31, 201–238.Google 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.Google 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
Mott, R. W. & Woods, A. W. 2009 On the mixing of a confined stratified fluid by a turbulent buoyant plume. J. Fluid Mech. 623, 149–165.Google Scholar
Pantin, H. M. 1979 Interaction between velocity and effective density in turbidity flow: phase-plane analysis, with criteria for autosuspension. Mar. Geol. 31, 59–99.CrossRefGoogle Scholar
Sparks, R. S. J., Bursik, M. I., Carey, S. N., Gilbert, J. S., Glase, L. S., Sigurdsson, H. & Woods, A. W. 1997 Volcanic Plumes. Wiley-Blackwell.Google Scholar
Wong, A. B. D., Griffiths, R. W. & Hughes, G. O. 2001 Shear layers driven by turbulent plumes. J. Fluid Mech. 434, 209–241.Google Scholar
Woods, A. W. 2010 Turbulent plumes in nature. Annu. Rev. Fluid Mech. 42, 391–412.CrossRefGoogle Scholar