Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-12-01T02:46:14.491Z Has data issue: false hasContentIssue false
  • English
  • Français

Large-eddy simulation of a buoyant plume in uniform and stably stratified environments

Published online by Cambridge University Press:  09 April 2010

B. J. DEVENISH ,
G. G. ROONEY  and
D. J. THOMSON
B. J. DEVENISH*
Affiliation:
Met Office, FitzRoy Road, Exeter EX1 3PB, UK
G. G. ROONEY
Affiliation:
Met Office, FitzRoy Road, Exeter EX1 3PB, UK
D. J. THOMSON
Affiliation:
Met Office, FitzRoy Road, Exeter EX1 3PB, UK
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We consider large-eddy simulation (LES) of buoyant plumes in uniform and stably stratified environments. We show that in the former case the results agree well with the simple plume model of Morton, Taylor & Turner (Proc. R. Soc. Lond. A, vol. 234, 1956, p. 1). In particular, we calculate an entrainment constant which is consistent with laboratory and field measurements and find no significant difference between the radial spreading rates of vertical velocity and buoyancy. In a stably stratified environment, the LES plume shows better agreement with Morton et al. (1956) below the level at which the buoyancy first vanishes than above this level. Above the level of neutral buoyancy, the LES plume is characterized by an ascending core of negative buoyancy surrounded by a descending annulus of positive buoyancy. We compare the LES data with the model of Bloomfield & Kerr (J. Fluid Mech., vol. 424, 2000, p. 197), which explicitly accounts for these coherent motions. The model exhibits many qualitative aspects of the LES plume and quantitative agreement can be improved by adjusting the downward volume flux relative to the upward volume flux in a manner consistent with the LES plume. This simple adjustment, along with revised values of the entrainment constants, represents the combined effects of an overturning region at the top of the plume (where a fluid element reverses direction), ‘plume-top’ entrainment (whereby the plume entrains ambient fluid above the plume) as well as lateral entrainment and detrainment processes (both external and internal) occurring above the top of the model plume.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 652 , 10 June 2010 , pp. 75 - 103
Copyright
Copyright © Cambridge University Press 2010

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Abdalla, I. E., Cook, M. J., Rees, S. J. & Yang, Z. 2007 Large-eddy simulation of buoyancy-driven natural ventilation in an enclosure with a point heat source. Intl J. Comput. Fluid Dyn. 21, 231–245.CrossRefGoogle Scholar
Akselvoll, K. & Moin, P. 1996 Large-eddy simulation of turbulent-confined coannular jets. J. Fluid Mech. 315, 387–411.CrossRefGoogle Scholar
Baines, W. D. & Turner, J. S. 1969 Turbulent buoyant convection from a source in a confined region. J. Fluid Mech. 37, 51–80.CrossRefGoogle Scholar
Bastiaans, R. J. M., Rindt, C. C. M., Nieuwstadt, F. T. M. & van Steenhoven, A. A. 2000 Direct and large-eddy simulation of the transition of two- and three-dimensional plane plumes in a confined enclosure. Intl J. Heat Mass Transfer 43, 2375–2393.CrossRefGoogle Scholar
Bloomfield, L. J. & Kerr, R. C. 2000 A theoretical model of a turbulent fountain. J. Fluid Mech. 424, 197–216.CrossRefGoogle Scholar
Briggs, G. A. 1975 Plume rise predictions. In Lectures on Air Pollution and Environmental Impact Analyses (ed. Haugen, D. A.), pp. 59–111. American Meteorological Society.Google Scholar
Briggs, G. A. 1984 Plume rise and buoyancy effects. In Atmospheric Science and Power Production (ed. Randerson, D.), pp. 327–366. Office of Research, US Department of Energy.Google Scholar
Cardoso, S. S. S. & Woods, A. W. 1993 Mixing by a turbulent plume in a confined stratified region. J. Fluid Mech. 250, 277–305.CrossRefGoogle Scholar
Devenish, B. J. & Edwards, J. M. 2009 Large-eddy simulation of the plume generated by the fire at the Buncefield oil depot in December 2005. Proc. R. Soc. Lond. A 465, 397–419.Google Scholar
George, W. K., Alpert, R. L. & Tamanini, F. 1977 Turbulence measurements in an axisymmetric buoyant plume. Intl J. Heat Mass Transfer 20, 1145–1154.CrossRefGoogle Scholar
Gupta, A. K. 1993 Fire plume: theories and their analysis. J. Appl. Fire Sci. 2, 269–298.CrossRefGoogle Scholar
Hunt, G. R. & Kaye, N. G. 2001 Virtual origin correction for lazy turbulent plumes. J. Fluid Mech. 435, 377–396.CrossRefGoogle Scholar
Kantha, L. H. & Clayson, C. A. 2000 Numerical Models of Oceans and Oceanic Processes. Academic Press.Google Scholar
Leonard, B. P., Lock, A. P. & MacVean, M. K. 1996 Conservative explicit unrestricted-time-step multidimensional constancy-preserving advection schemes. Mon. Weather Rev. 124, 2588–2606.2.0.CO;2>CrossRefGoogle Scholar
Lin, Y. J. P. & Linden, P. F. 2005 The entrainment due to a turbulent fountain at a density interface. J. Fluid Mech. 542, 25–52.CrossRefGoogle Scholar
Linden, P. F. 2000 Convection in the environment. In Perspectives in Fluid Dynamics (ed. Batchelor, G. K., Moffat, H. K. & Worster, M. G.), pp. 289–345. Cambridge University Press.Google Scholar
List, E. J. 1982 Turbulent jets and plumes. Annu. Rev. Fluid Mech. 14, 189–212.CrossRefGoogle Scholar
Manins, P. C. 1973 Confined convective plumes. PhD thesis, University of Cambridge, Cambridge.Google Scholar
Manins, P. C. 1979 Turbulent buoyant convection from a source in a confined region. J. Fluid Mech. 91, 765–781.CrossRefGoogle Scholar
Mason, P. 1989 Large-eddy simulation of the convective atmospheric boundary layer. J. Atmos. Sci. 46, 1492–1516.2.0.CO;2>CrossRefGoogle Scholar
McDougall, T. J. 1981 Negatively buoyant vertical jets. Tellus 33, 313–320.CrossRefGoogle Scholar
Morton, B. R. 1959 Forced plumes. J. Fluid Mech. 5, 151–163.CrossRefGoogle Scholar
Morton, B. R., Taylor, G. & Turner, J. S. 1956 Turbulent gravitational convection from maintained and instantaneous sources. Proc. R. Soc. Lond. A 234, 1–23.Google Scholar
Nieuwstadt, F. T. M. & de Valk, J. P. J. M. M. 1987 A large eddy simulation of buoyant and non-buoyant plume dispersion in the atmospheric boundary layer. Atmos. Env. 21, 2573–2587.CrossRefGoogle Scholar
Pasquill, F. & Smith, F. B. 1983 Atmospheric Diffusion. Ellis Horwood.Google Scholar
Pham, M. V., Plourde, F. & Doan, K. S. 2007 Direct and large-eddy simulations of a pure thermal plume. Phys. Fluids 19, 125103.CrossRefGoogle Scholar
Piacsek, S. A. & Williams, G. P. 1970 Conservation properties of convection difference schemes. J. Comput. Phys. 6, 392–405.CrossRefGoogle Scholar
Plourde, F., Pham, M. V., Kim, S. D. & Balanchandar, S. 2008 Direct numerical simulations of a rapidly expanding thermal plume: structure and entrainment interaction. J. Fluid Mech. 604, 99–123.CrossRefGoogle Scholar
Le Ribault, C., Sarkar, S. & Stanley, S. A. 1999 Large eddy simulation of a plane jet. Phys. Fluids 11, 3069–3083.CrossRefGoogle Scholar
Rooney, G. G. & Linden, P. F. 1996 Similarity considerations for non-Boussinesq plumes in an unstratified environment. J. Fluid Mech. 318, 237–250.CrossRefGoogle Scholar
Scase, M. M., Caulfield, C. P. & Dalziel, S. B. 2006 Boussinesq plumes and jets with decreasing source strengths in stratified environments. J. Fluid Mech. 563, 463–472.CrossRefGoogle Scholar
Turner, J. S. 1973 Buoyancy Effects in Fluids. Cambridge University Press.CrossRefGoogle Scholar
Turner, J. S. 1986 Turbulent entrainment: the development of the entrainment assumption, and its application to geophysical flows. J. Fluid Mech. 173, 431–471.CrossRefGoogle Scholar
Yan, Z. H. 2007 Large-eddy simulations of a turbulent thermal plume. Heat Mass Transfer 43, 503–514.CrossRefGoogle Scholar
Zhou, X., Luo, K. H. & Williams, J. J. R. 2001 Large-eddy simulation of a turbulent forced plume. Eur. J. Mech. B. Fluids 20, 233–254.CrossRefGoogle Scholar