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Two-dimensional planar plumes: non-Boussinesq effects

Published online by Cambridge University Press:  04 June 2014

T. S. van den Bremer*
Affiliation:
Department of Engineering Science, University of Oxford, Parks Road, Oxford OX1 3PJ, UK
G. R. Hunt*
Affiliation:
Department of Engineering, University of Cambridge, Trumpington Street, Cambridge CB2 1PZ, UK
*
Email addresses for correspondence: ton.vandenbremer@eng.ox.ac.uk, gary.hunt@eng.cam.ac.uk
Email addresses for correspondence: ton.vandenbremer@eng.ox.ac.uk, gary.hunt@eng.cam.ac.uk

Abstract

In an accompanying paper (van den Bremer & Hunt, J. Fluid Mech., vol. 750, 2014, pp. 210–244) closed-form solutions, describing the behaviour of two-dimensional planar turbulent rising plumes from horizontal planar area and line sources in unconfined quiescent environments of uniform density, that are universally applicable to Boussinesq and non-Boussinesq plumes, are proposed. This universality relies on an entrainment velocity unmodified by non-Boussinesq effects, an assumption that is derived in the literature based on similarity arguments and is, in fact, in contradiction with the axisymmetric case, in which entrainment is modified by non-Boussinesq effects. Exploring these solutions, we show that a non-Boussinesq plume model predicts exactly the same behaviour with height for a pure plume as would a Boussinesq model, whereas the effects on forced and lazy plumes are opposing. Non-intuitively, the non-Boussinesq model predicts larger fluxes of volume and mass for lazy plumes, but smaller fluxes for forced plumes at any given height compared to the Boussinesq model. This raises significant questions regarding the validity of the unmodified entrainment model for planar non-Boussinesq plumes based on similarity arguments and calls for detailed experiments to resolve this debate.

Type
Papers
Copyright
© 2014 Cambridge University Press 

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References

van den Bremer, T. S. & Hunt, G. R. 2010 Universal solutions for Boussinesq and non-Boussinesq plumes. J. Fluid Mech. 644, 165192.CrossRefGoogle Scholar
van den Bremer, T. S. & Hunt, G. R. 2014 Two-dimensional planar plumes and fountains. J. Fluid Mech. 750, 210244.CrossRefGoogle Scholar
Carlotti, P. & Hunt, G. R. 2005 Analytical solutions for turbulent non-Boussinesq plumes. J. Fluid Mech. 538, 343359.CrossRefGoogle Scholar
Delichatsios, M. A. 1988 On the similarity of velocity and temperature profiles in strong (variable density) turbulent buoyant plumes. Combust. Sci. Technol. 60, 253266.CrossRefGoogle Scholar
Ezzamel, A.2011 Free and confined buoyant flows. PhD Thesis, Imperial College London, UK.Google Scholar
Fanneløp, T. K. & Webber, D. M. 2003 On buoyant plumes rising from area sources in a calm environment. J. Fluid Mech. 497, 319334.CrossRefGoogle Scholar
Hunt, G. R. & van den Bremer, T. S. 2011 Classical plume theory: 1937–2010 and beyond. IMA J. Appl. Math. 76 (3), 424448.CrossRefGoogle Scholar
Ricou, F. P. & Spalding, D. B. 1961 Measurements of entrainment by axisymmetrical turbulent jets. J. Fluid Mech. 11, 2132.CrossRefGoogle Scholar
Rooney, G. G.1997 Buoyant flows from fires in enclosures. PhD Thesis, University of Cambridge, UK.Google Scholar
Rooney, G. G. & Linden, P. F. 1996 Similarity considerations for non-Boussinesq plumes in an unstratified environment. J. Fluid Mech. 318, 237250.CrossRefGoogle Scholar
Thomas, P. J. & Delichatsios, M. A. 2007 Notes on the similarity of turbulent buoyant fire plumes with large density variations. Fire Safety J. 42, 4350.CrossRefGoogle Scholar
Woods, A. W. 1997 A note on non-Boussinesq plumes in an incompressible stratified environment. J. Fluid Mech. 345, 347356.CrossRefGoogle Scholar