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Oscillatory behaviour in an emptying–filling box

Published online by Cambridge University Press:  28 September 2015

O. Vauquelin
O. Vauquelin*
Affiliation:
Aix-Marseille Université, Laboratoire IUSTI, UMR CNRS 7343, 5 rue Enrico Fermi, 13 453 Marseille, CEDEX 13, France
*
†Email address for correspondence: olivier.vauquelin@univ-amu.fr
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Abstract

The emptying–filling box problem is examined theoretically in a general non-Boussinesq case. The steady solutions are first reviewed and expressed both as a function of a pure geometrical parameter and as a function of a dimensionless number ${\it\Theta}$ that characterizes the strength of the buoyant source relative to the box height. A linearization of the conservation equations is performed around the steady state and a second-order differential equation is derived that facilitates consideration of the existence of underdamped oscillations in the emptying–filling process. These oscillations are quantified in terms of frequency, damping ratio and phase shift, which constitutes the major outcome of this study. It is shown that oscillations can exist whatever the strength of the buoyancy source, even if their amplitude remains extremely weak for ‘small plumes’.

JFM classification

Mathematical Foundations: General fluid mechanics Convection: Plumes/thermals Mixing: Turbulent mixing
Type
Papers
Information
Journal of Fluid Mechanics , Volume 781 , 25 October 2015 , pp. 712 - 726
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Copyright
© 2015 Cambridge University Press 

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References

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
van den Bremer, T. S. & Hunt, G. R. 2014 Two-dimensional planar plumes: non-Boussinesq effects. J. Fluid Mech. 750, 245–258.Google Scholar
Candelier, F. & Vauquelin, O. 2012 Matched asymptotic solutions for turbulent plumes. J. Fluid Mech. 699, 489–499.Google Scholar
Coffey, C. J. & Hunt, G. R. 2010 The unidirectional emptying box. J. Fluid Mech. 660, 456–474.Google Scholar
Holford, J. M. & Hunt, G. R. 2001 The dependence of the discharge coefficients on density contrast – experimental measurements. In Proceedings of 14th Australasian Fluid Mechanics Conference, Adelaide University, Adelaide, NSW, Australia (ed. Dally, B. B.), pp. 123–126.Google Scholar
Hunt, G. R. & Coffey, C. J. 2010 Emptying boxes – classifying transient natural ventilation flows. J. Fluid Mech. 646, 137–168.CrossRefGoogle Scholar
Hunt, G. R. & Kaye, N. B. 2001 Virtual origin correction for lazy turbulent plumes. J. Fluid Mech. 435, 377–396.Google Scholar
Hunt, G. R. & Kaye, N. B. 2005 Lazy plumes. J. Fluid Mech. 533, 329–338.Google Scholar
Hunt, G. R. & Linden, P. F. 1998 Time-dependent displacement ventilation caused by variations in internal heat gains: application to a lecture theatre. In Proceedings of ROOMVENT 1998, the 6th International Conference on Air Distribution in Rooms, KTH Stockholm, Stockholm, Sweden (ed. Mundt, E. & Malmstrom, T. G.), vol. 2, pp. 203–210.Google Scholar
Hunt, G. R. & Linden, P. F. 2001 Steady-state flows in an enclosure ventilated by buoyant forces assisted by wind. J. Fluid Mech. 426, 355–386.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. & Hunt, G. R. 2007 Overturning in a filling box. J. Fluid Mech. 576, 297–323.Google Scholar
Lane-Serff, G. F. & Sandbach, S. D. 2012 Emptying non-adiabatic filling box: the effects of heat transfers on the fluid dynamics of natural ventilation. J. Fluid Mech. 701, 386–406.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.CrossRefGoogle Scholar
Michaux, G. & Vauquelin, O. 2008 Solutions for turbulent buoyant plumes rising from circular sources. Phys. Fluids 20, 066601.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 234, 1–23.Google Scholar
Mott, R. W. & Woods, A. W. 2012 Quasi-steady states in natural displacement ventilation driven by periodic gusting of wind. J. Fluid Mech. 707, 1–23.Google Scholar
Roes, M. A., Bolster, D. T. & Flynn, M. R. 2014 Buoyant convection from a discrete source in a leaky porous medium. J. Fluid Mech. 755, 204–229.Google Scholar
Rooney, G. G. & Linden, P. F. 1996 Similarity considerations for non-Boussinesq plumes in an unstratified environment. J. Fluid Mech. 318, 237–250.Google Scholar
Rooney, G. G. & Linden, P. F. 1997 Strongly buoyant plume similarity and small-fire ventilation. Fire Safety J. 29, 235–258.Google Scholar
Shrinivas, A. B. & Hunt, G. R. 2014 Transient ventilation dynamics induced by heat sources of unequal strength. J. Fluid Mech. 738, 34–64.Google Scholar
Worster, M. G. & Huppert, H. E. 1983 Time-dependent density profiles in a filling box. J. Fluid Mech. 132, 457–466.Google Scholar