Skip to main content Accessibility help
×
Home

On the entrainment coefficient in negatively buoyant jets

  • PANOS N. PAPANICOLAOU (a1), ILIAS G. PAPAKONSTANTIS (a2) and GEORGE C. CHRISTODOULOU (a2)

Abstract

Integral models proposed to simulate positively buoyant jets are used to model jets with negative or reversing buoyancy issuing into a calm, homogeneous or density-stratified environment. On the basis of the self-similarity assumption, ‘top hat’ and Gaussian cross-sectional distributions are employed for concentration and velocity. The entrainment coefficient is considered to vary with the local Richardson number, between the asymptotic values for simple jets and plumes, estimated from earlier experiments in positively buoyant jets. Top-hat and Gaussian distribution models are employed in a wide range of experimental data on negatively buoyant jets, issuing vertically or at an angle into a calm homogeneous ambient, and on jets with reversing buoyancy, discharging into a calm, density-stratified fluid. It is found that geometrical characteristics such as the terminal (steady state) height of rise, the spreading elevation in stratified ambient and the distance to the point of impingement are considerably underestimated, resulting in lower dilution rates at the point of impingement, especially when the Gaussian formulation is applied. Reduction of the entrainment coefficient in the jet-like flow regime improves model predictions, indicating that the negative buoyancy reduces the entrainment in momentum-driven, negatively buoyant jets.

Copyright

References

Hide All
Abraham, G. 1967 Jets with negative buoyancy in homogeneous fluid. J. Hydraul. Res. 5, 235248.
Baines, W. D., Turner, J. S. & Campbell, I. H. 1990 Turbulent fountains in an open chamber. J. Fluid Mech. 212, 557592.
Bloomfield, L. J. & Kerr, R. C. 1998 Turbulent fountains in a stratified fluid. J. Fluid Mech. 358, 335356.
Bloomfield, L. J. & Kerr, R. C. 2000 A theoretical model of a turbulent fountain. J. Fluid Mech. 424, 197216.
Bloomfield, L. J. & Kerr, R. C. 2002 Inclined turbulent fountains. J. Fluid Mech. 451, 283294.
Carazzo, G., Kaminski, E. & Tait, S. 2006 The route to self-similarity in turbulent jets and plumes. J. Fluid Mech. 547, 137148.
Fan, L. N. 1967 Turbulent buoyant jets into stratified or flowing ambient fluids. Tech. Rep. KH-R-15, W. M. Keck Laboratory of Hydraulics and Water Resources, California Institute of Technology, Pasadena, CA, USA.
Fischer, H. B., List, E. J., Koh, R. C. Y., Imberger, J. & Brooks, N. H. 1979 Mixing in Inland and Coastal Waters. Academic.
Hutter, K. & Hofer, K. 1978 Freistrahlen im homogenen und stratifizierten Medium—ihre Theorie und deren Vergleich mit dem Experiment. Mitteilungen der Versuchsanstalt für Wasserbau, Hydrologie und Glaziologie, ETH Zürich, Nr. 27.
Jirka, G. H. 2004 Integral model for turbulent buoyant jets in unbounded stratified flows: part I; single round jet. Env. Fluid Mech. 4, 156.
Kaminski, E., Tait, S. & Carazzo, G. 2005 Turbulent entrainment in jets with arbitrary buoyancy. J. Fluid Mech. 526, 361376.
Konstantinidou, K. & Papanicolaou, P. N. 2003 Vertical round and orthogonal buoyant jets in a linear density-stratified fluid. In Proc. 30th IAHR Congress on Water Engineering and Research in a Learning Society: Modern Developments and Traditional Concepts; Inland Waters—Research, Engineering and Management Theme (ed. Ganoulis, J. & Prinos, P.; theme ed. Nezu, I. & Kotsovinos, N.), vol. 1, pp. 293–300.
Lindberg, W. R. 1994 Experiments on negatively buoyant jets, with or without cross-flow. In Recent Research Advances in the Fluid Mechanics of Turbulent Jets and Plumes (ed. Davies, P. A. & Neves, M. J. Valente), pp. 131145. Kluwer.
List, E. J. 1982 Mechanics of turbulent buoyant jets and plumes. In Turbulent Buoyant Jets and Plumes (ed. Rodi, W.), pp. 168. Pergamon.
List, E. J. & Imberger, J. 1973 Turbulent entrainment in buoyant jets and plumes. J. Hydraul. Div. ASCE 99, 14611474.
Papakonstantis, I., Kampourelli, M. & Christodoulou, G. 2007 Height of rise of inclined and vertical negatively buoyant jets. In Proc. 32nd IAHR Congress: Harmonizing the Demands of Art and Nature in Hydraulics; Fluid Mechanics and Hydraulics Theme (ed. Di Silvio, G. & Lanzoni, S.; theme ed. Cenedese, A.), CD-ROM.
Papanicolaou, P. N. & Kokkalis, T. J. 2008 Vertical buoyancy preserving and non-preserving fountains, in a homogeneous calm ambient. Intl J. Heat Mass Transfer 51, 41094120.
Papanicolaou, P. N. & List, E. J. 1988 Investigations of round vertical turbulent buoyant jets. J. Fluid Mech. 195, 341391.
Priestley, C. H. B. & Ball, F. K. 1955 Continuous convection from an isolated source of heat. Q. J. R. Met. Soc. 81, 144157.
Roberts, P. J. W., Ferrier, A. & Daviero, G. 1997 Mixing in inclined dense jets. ASCE J. Hydraul. Engng 123, 693699.
Roberts, P. J. W. & Toms, G. 1987 Inclined dense jets in flowing current. ASCE J. Hydraul. Engng ASCE 113, 323341.
Rouse, H., Yih, C. S. & Humphreys, H. W. 1952 Gravitational convection from a boundary source. Tellus 4, 201210.
Turner, J. S. 1966 Jets and plumes with negative or reversing buoyancy. J. Fluid Mech. 26, 779792.
Turner, J. S. 1986 Turbulent entrainment: the development of the entrainment assumption, and its application to geophysical flows. J. Fluid Mech. 173, 431471.
Wang, H. & Law, A. W.-K. 2002 Second-order integral model for a round turbulent buoyant jet. J. Fluid Mech. 459, 397428.
Wong, D. R. & Wright, S. J. 1988 Submerged turbulent buoyant jets in stagnant linearly stratified fluids. J. Hydraul. Res. 26, 199223.
Woods, A. W. & Caulfield, C. P. 1992 A laboratory study of explosive volcanic eruptions. J. Geophys. Res. 97, 66996712.
Yannopoulos, P. C. 2006 An improved integral model for plane and round turbulent buoyant jets. J. Fluid Mech. 547, 267296.
Zeitoun, M. A., McIlhenny, W. F. & Reid, R. O. 1970 Conceptual designs of outfall systems for desalting plants. R & D Progress Report No. 550, Office of Saline Water, US Dept. of Interior, Washington, DC, USA, p. 139.
Zhang, H. & Baddour, R. E. 1998 Maximum penetration of vertical round dense jets at small and large Froude numbers. ASCE J. Hydraul. Engng. 124, 550553.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

On the entrainment coefficient in negatively buoyant jets

  • PANOS N. PAPANICOLAOU (a1), ILIAS G. PAPAKONSTANTIS (a2) and GEORGE C. CHRISTODOULOU (a2)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed