Skip to main content
×
Home
    • Aa
    • Aa

Universal solutions for Boussinesq and non-Boussinesq plumes

  • T. S. VAN DEN BREMER (a1) and G. R. HUNT (a1)
Abstract

Closed-form solutions describing the behaviour of buoyant axisymmetric turbulent rising plumes and fountains, emitted vertically from area sources in unconfined quiescent environments of uniform density, are proposed in a form that is universally applicable to Boussinesq and non-Boussinesq plumes. This paper, thereby, generalizes the results obtained separately for steady Boussinesq and non-Boussinesq plumes, including asymptotic virtual source corrections. The flux balance parameter Γ = Γ(z), a local Richardson number, is instrumental in describing the behaviour of steady plumes and the initial rise behaviour of fountains with height z. Non-dimensional graphs (cf. the ‘scale diagrams’ of Morton & Middleton, J. Fluid Mech., vol. 58, 1973, pp. 165–176) are plotted, showing certain characteristic heights for different source conditions, characterized by one single source flux balance parameter, giving a unique representation of the behaviour of Boussinesq fountains and both Boussinesq and non-Boussinesq plumes. Finally, a length scale has been identified that characterizes the height over which non-Boussinesq effects are important for lazy plumes rising from area sources.

Copyright
Corresponding author
Email address for correspondence: gary.hunt@imperial.ac.uk
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

W. D. Baines 1983 A technique for the direct measurement of volume flux of a plume. J. Fluid Mech. 132, 247256.

L. J. Bloomfield & R. C. Kerr 2000 A theoretical model of a turbulent fountain. J. Fluid Mech. 424, 197216.

G. Carazzo , E. Kaminski & S. Tait 2006 The route to self-similarity in turbulent jets and plumes. J. Fluid Mech. 547, 137148.

S. S. S. Cardoso & A. W. Woods 1993 Mixing by a turbulent plume in a confined stratified region. J. Fluid Mech. 250, 277305.

P. Carlotti & G. R. Hunt 2005 Analytical solutions for turbulent non-Boussinesq plumes. J. Fluid Mech. 538, 343359.

C. P. Caulfield & A. W. Woods 1998 Turbulent gravitational convection from a point source in a non-uniformly stratified environment. J. Fluid Mech. 360, 229248.

B. M. Cetegen , E. E. Zukoski & T. Kubota 1984 Entrainment in the near field and far field of fire plumes. Combust. Sci. Technol. 39, 305331.

D. T. Conroy & S. G. Llewellyn Smith 2008 Endothermic and exothermic chemically reacting plumes. J. Fluid Mech. 612, 291310.

T. K. Fannelop & D. M. Webber 2003 On buoyant plumes rising from area sources in a calm environment. J. Fluid Mech. 497, 319334.

G. R. Hunt & N. G. Kaye 2001 Virtual origin correction for lazy turbulent plumes. J. Fluid Mech. 435, 377396.

G. R. Hunt & N. B. Kaye 2005 Lazy plumes. J. Fluid Mech. 533, 329338.

E. Kaminski , S. Tait & G. Carazzo 2005 Turbulent entrainment in jets with arbitrary buoyancy. J. Fluid Mech. 526, 361376.

N. B. Kaye & G. R. Hunt 2006 Weak fountains. J. Fluid Mech. 558, 319328.

N. B. Kaye 2008 Turbulent plumes in stratified environments: a review of recent work. Atmos.-Ocean 46, 433441.

P. F. Linden 1999 The fluid mechanics of natural ventilation. Annu. Rev. Fluid Mech. 31, 201238.

B. R. Morton 1959 Forced plumes. J. Fluid Mech. 5, 151163.

B. R. Morton & J. Middleton 1973 Scale diagrams for forced plumes. J. Fluid Mech. 58, 165176.

B. R. Morton , G. Taylor & J. S. Turner 1956 Turbulent gravitational convection from maintained and instantaneous sources. Proc. R. Soc. Lond. A 234, 123.

P. N. Papanicolaou , I. G. Papakonstantis & G. C. Christodoulou 2008 On the entrainment coefficient in negatively buoyant jets. J. Fluid Mech. 614, 447470.

C. H. B. Priestley & F. K. Ball 1955 Continuous convection from an isolated source of heat. Quart. J. R. Meteorol. Soc. 81, 144157.

F. P. Ricou & D. B. Spalding 1961 Measurements of entrainment by axisymmetrical turbulent jets. J. Fluid Mech. 11, 2132.

G. G. Rooney & P. F. Linden 1996 Similarity considerations for non-Boussinesq plumes in an unstratified environment. J. Fluid Mech. 318, 237250.

M. M. Scase , C. P. Caulfield & S. B. Dalziel 2006 a Boussinesq plumes and jets with decreasing source strengths in stratified environments. J. Fluid Mech. 563, 463472.

M. M. Scase , C. P. Caulfield & S. B. Dalziel 2008 Temporal variation of non-ideal plumes with sudden reductions in buoyancy flux. J. Fluid Mech. 600, 181199.

M. M. Scase , C. P. Caulfield , S. B. Dalziel & J. C. R. Hunt 2006 b Time-dependent plumes and jets with decreasing source strengths. J. Fluid Mech. 563, 443461.

M. M. Scase , C. P. Caulfield , P. F. Linden & S. B. Dalziel 2007 Local implications for self-similar turbulent plume models. J. Fluid Mech. 575, 257265.

A. Shabbir & W. K. George 1994 Experiments on a round turbulent buoyant plume. J. Fluid Mech. 275, 132.

J. S. Turner 1966 Jets and plumes with negative or reversing buoyancy. J. Fluid Mech. 26, 779792.

J. S. Turner 1986 Turbulent entrainment: the development of the entrainment assumption, and its application to geophysical flows. J. Fluid Mech. 173, 431471.

H. Wang & A. W-K. Law 2002 Second-order integral model for a round turbulent buoyant jet. J. Fluid Mech. 459, 397428.

A. W. Woods 1997 A note on non-Boussinesq plumes in an incompressible stratified environment. J. Fluid Mech. 345, 347356.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

Metrics

Full text views

Total number of HTML views: 1
Total number of PDF views: 53 *
Loading metrics...

Abstract views

Total abstract views: 121 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 23rd September 2017. This data will be updated every 24 hours.