Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-23T14:06:57.336Z Has data issue: false hasContentIssue false

Source and boundary condition effects on unconfined and confined vertically distributed turbulent plumes

Published online by Cambridge University Press:  12 July 2018

N. B. Kaye*
Affiliation:
Glenn Department of Civil Engineering, Clemson University, Clemson, SC 29634, USA
P. Cooper
Affiliation:
Sustainable Buildings Research Centre, University of Wollongong, Wollongong, NSW 2522, Australia
*
Email address for correspondence: [email protected]

Abstract

Plumes generated by vertically distributed sources of buoyancy have been observed to have substantially lower entrainment coefficients than their equivalent-geometry constant buoyancy flux plumes. Two differences between distributed and localized sources of buoyancy are the presence of a wall shear stress at the source and that non-ideal source conditions are distributed over the whole height of the enclosure for a vertically distributed source. Herein the impact of non-ideal source and boundary conditions on vertically distributed plumes is analysed. It is shown that, at small heights, the plume volume flow rate is significantly influenced by the wall-source volume flux. At larger heights the wall-source buoyancy is greater than the mean plume buoyancy, creating a non-self-similar horizontal buoyancy distribution within the plume. Recent experiments into the behaviour of a vertically distributed source of buoyancy in a confined region have also shown that the plume partially detrains in the stratified region of the enclosure. This detrainment has not been observed for constant buoyancy flux plumes in a confined region. Although models have been proposed to quantify the detrainment process, it is still unclear why vertically distributed buoyancy sources detrain while constant buoyancy flux plumes do not in the same physical geometry. The impact of source and boundary effects on previously published experiments on vertically distributed plumes are reviewed and the possible implications for plume entrainment and detrainment are discussed.

Type
JFM Papers
Copyright
© 2018 Cambridge University Press 

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

Baines, W. D. 1983 A technique for the direct measurement of volume flux of a plume. J. Fluid Mech. 132, 247256.Google Scholar
Baines, P. G. 2005 Mixing regimes for the flow of dense fluid down slopes into stratified environments. J. Fluid Mech. 538, 245267.Google Scholar
Baines, W. D. & Turner, J. S. 1969 Turbulent buoyant convection from a source in a confined region. J. Fluid Mech. 37, 5180.Google Scholar
Bonnebaigt, R., Caulfield, C. P. & Linden, P. F. 2018 Detrainment of plumes from vertically distributed sources. Environ. Fluid Mech. 18 (1), 323.Google Scholar
Caudwell, T., Flór, J. & Negretti, M. 2016 Convection at an isothermal wall in an enclosure and establishment of stratification. J. Fluid Mech. 799, 448475.Google Scholar
Cengel, Y. A. & Ghajar, A. J. 2015 Heat and Mass Transfer: Fundamentals and Applications, 5th edn. McGraw-Hill Education.Google Scholar
Chen, M. H. & Cardoso, S. S. 2000 The mixing of liquids by a plume of low-Reynolds number bubbles. Chem. Engng Sci. 55 (14), 25852594.Google Scholar
Chen, Z. D., Li, Y. & Mahoney, J. 2001 Natural ventilation in an enclosure induced by a heat source distributed uniformly over a vertical wall. Build. Environ. 36 (4), 493501.Google Scholar
Cooper, P. & Hunt, G. R. 2010 The ventilated filling box containing a vertically distributed source of buoyancy. J. Fluid Mech. 646, 3958.Google Scholar
Cortes, A., Rueda, F. J. & Wells, M. G. 2014 Experimental observations of the splitting of a gravity current at a density step in a stratified water body. J. Geophys. Res. 119, 10381053.Google Scholar
Craven, B. A. & Settles, G. S. 2006 A computational and experimental investigation of the human thermal plume. Trans. ASME J. Fluids Engng 128 (6), 12511258.Google Scholar
Fischer, H. B., List, E. J., Koh, R. C. Y., Imberger, J. & Brooks, N. H. 1979 Mixing in Inland and Coastal Waters. Academic Press.Google Scholar
Gayen, B., Griffiths, R. & Kerr, R. 2016 Simulation of convection at a vertical ice face dissolving into saline water. J. Fluid Mech. 798, 284298.Google Scholar
Germeles, A. E. 1975 A model for LNG tank rollover. Adv. Cryog. Engng 21, 326336.Google Scholar
Gladstone, C. & Woods, A. W. 2014 Detrainment from a turbulent plume produced by a vertical line source of buoyancy in a confined, ventilated space. J. Fluid Mech. 742, 3549.Google Scholar
Hogg, C., Dalziel, S., Huppert, H. & Imberger, J. 2017 Inclined gravity currents filling basins: the impact of peeling detrainment on transport and vertical structure. J. Fluid Mech. 820, 400423.Google Scholar
Hubner, J.2004 Buoyant plumes in a turbulent environment. PhD thesis, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, UK.Google Scholar
Hunt, G. R. & Kaye, N. 2001 Virtual origin correction for lazy turbulent plumes. J. Fluid Mech. 435, 377396.Google Scholar
Huppert, H. E., Sparks, R. S. J., Whitehead, J. A. & Hallworth, M. A. 1986 Replenishment of magma chambers by light inputs. J. Geophys. Res. 91 (B6), 61136122.Google Scholar
Kaye, N.1998 Interaction of turbulent plumes. PhD thesis, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, UK.Google Scholar
Kaye, N. B. 2008 Turbulent plumes in stratified environments: a review of recent work. Atmos.-Ocean 46 (4), 433441.Google Scholar
Kaye, N. B. & Linden, P. F. 2004 Coalescing axisymmetric turbulent plumes. J. Fluid Mech. 502, 4163.Google Scholar
Kaye, N. & Scase, M. 2011 Straight-sided solutions to classical and modified plume flux equations. J. Fluid Mech. 680, 564573.Google Scholar
Kerr, R. & McConnochie, C. 2015 Dissolution of a vertical solid surface by turbulent compositional convection. J. Fluid Mech. 765, 211228.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, 309335.Google Scholar
Ma, Y., Flynn, M. & Sutherland, B. 2017 Convection from a line-source into a two-layer stratified ambient fluid. J. Fluid Mech. 818, 4667.Google Scholar
McConnochie, C. D. & Kerr, R. C. 2016 The turbulent wall plume from a vertically distributed source of buoyancy. J. Fluid Mech. 787, 237253.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, 123.Google Scholar
Paillat, S. & Kaminski, E. 2014 Entrainment in plane turbulent pure plumes. J. Fluid Mech. 755, R2.Google Scholar
Wells, A. J. & Worster, M. G. 2008 A geophysical-scale model of vertical natural convection boundary layers. J. Fluid Mech. 609, 111137.Google Scholar
Wells, A. J. & Worster, M. G. 2011 Melting and dissolving of a vertical solid surface with laminar compositional convection. J. Fluid Mech. 687, 118140.Google Scholar