Unique Superposition Solution of Multiple Plane or Round Buoyant Jets for Tracer and Buoyancy Fluxes
Publication: Journal of Environmental Engineering
Volume 138, Issue 9
Abstract
The present paper proves the uniqueness of the superposition solution regarding tracer or buoyancy for parallel multiple (plane or round) turbulent buoyant jets with positive buoyancy in general, which are discharged vertically upwards into a still environment from sources of relatively short spacing. The multiple plane buoyant jets are of infinite length, whereas the multiple round buoyant jets may form groups of any arrangement shape. The proof is based on the observation that the partial differential equation of tracer or buoyancy conservation becomes linear with respect to the mean tracer or buoyancy fluxes of single plane or round turbulent buoyant jets, which simultaneously satisfy the aforementioned equation. Alternatively, the validity of similar assumptions to the Reichardt’s hypothesis, for either plane or round turbulent buoyant jets, has been verified. Findings denote that the solution of a group of interacting buoyant jets with respect to the tracer or buoyancy fluxes can be uniquely obtained by superimposing the particular solutions corresponding to each single buoyant jet of the group. In addition, the superposition method is suitably applied to predict the profiles of the tracer or buoyancy flux above a finite two-dimensional or three-dimensional source.
Get full access to this article
View all available purchase options and get full access to this article.
References
Alexander, L. G., Baron, T., and Comings, E. W. (1953). “Transportation of momentum, mass and heat in turbulent jets.”, Univ. of Illinois.
Chu, P. C. K. (1996). “Mixing of turbulent advected line puffs.” Ph.D. thesis, Dept. of Civil and Structural Engineering, Univ. of Hong Kong, Hong Kong.
Hodgson, J. E., Moawad, A. K., and Rajaratnam, N. (1999). “Concentration field of multiple circular turbulent jets.” J. Hydraul. Res., 37(2), 249–256.
Kaye, N. B., and Linden, P. F. (2004). “Coalescing axisymmetric turbulent plumes.” J. Fluid Mech., 502, 41–63.
Knystautas, R. (1964). “The turbulent jet from a series of holes in a line.” Aeronaut. Q., 15, 1–28.
Maxwell, W. H. C. (1970). “Flux development region in submerged jets.” J. Engrg. Mech. Div., 96(EM6), 1061–1079.
Maxwell, W. H. C., and Chang, K.-C. (1971). “Methodology for synthesis and optimization of diffusion patterns in flow systems.”, Water Resources Center, Dept. of Civil Engineering, Univ. of Illinois, Urbana-Champaign IL.
Pani, B., and Dash, R. (1983). “Three-dimensional single and multiple free jets.” J. Hydraul. Eng., 109(2), 254–269.
Pani, B. S., Lee, J. H. W., and Lai, A. C. H. (2009). “Application of Reichardt’s hypothesis for multiple coflowing jets.” J. Hydro-environ. Res., 3(3), 121–128.
Papps, D. A., and Wood, I. R. (1997). “The effect of an intermittant flapping motion on the properties of merging plumes.” J. Hydraul. Res., 35(4), 455–472.
Ramaprian, B. R., and Chandrasekhara, M. S. (1983). “Study of vertical plane turbulent jets and plumes.”, Iowa Institute of Hydraulic Research, Univ. of Iowa, Iowa City, IA.
Ramaprian, B. R., and Chandrasekhara, M. S. (1985). “LDA measurements in plane turbulent jets.” J. Fluids Eng., 107(2), 264–271.
Ramaprian, B. R., and Chandrasekhara, M. S. (1989). “Measurements in vertical plane turbulent plumes.” J. Fluids Eng., 111(1), 69–77.
Reichardt, H. (1943). “On a new theory of free turbulence (translation of the original paper published in ZAMM in 1941).” J. R. Aeronaut. Soc., 47(1), 167–176.
Wang, H., and Law, A. W.-K. (2002). “Second-order integral model for a round turbulent buoyant jet.” J. Fluid Mech., 459, 397–428.
Yannopoulos, P. C. (1984). “Interaction of vertical round turbulent buoyant jets.” Ph.D. dissertation, Dept. of Civil Engineering, National Technical Univ. of Athens, Athens, Greece (in Greek).
Yannopoulos, P. C. (1996). “Superposition model for multiple plumes and jets predicting end effects.” J. Geophys. Res., 101(D10), 15153–15167.
Yannopoulos, P. C. (2006). “An improved integral model for plane and round turbulent buoyant jets.” J. Fluid Mech., 547, 267–296.
Yannopoulos, P. C. (2010). “Advanced integral model for groups of interacting round buoyant jets.” Environ. Fluid Mech., 10(4), 415–450.
Yannopoulos, P., and Noutsopoulos, G. (2006). “Interaction of vertical round turbulent buoyant jets—Part II: Superposition method.” J. Hydraul. Res., 44(2), 233–248.
Information & Authors
Information
Published In
Journal of Environmental Engineering
Volume 138 • Issue 9 • September 2012
Pages: 985 - 989
Copyright
© 2012 American Society of Civil Engineers.
History
Received: Sep 18, 2011
Accepted: Feb 17, 2012
Published online: Feb 21, 2012
Published in print: Sep 1, 2012
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.