General Integral Formulation of Turbulent Buoyant Jets in Cross-Flow
Publication: Journal of Hydraulic Engineering
Volume 122, Issue 1
Abstract
The turbulent buoyant jet in a nonuniform cross-flow is formulated using a general integral method. The integral equations for the turbulent motion through the jet cross section are derived for a fixed control volume and expressed in vector form. In contrast to previous work, the new formulation does not require the a priori assumption of a velocity and concentration distribution. Coupled with a Lagrangian jet spreading hypothesis and the inclusion of added mass effect, the model is shown to predict correctly the properties of the asymptotic flow regimes in both the near field (straight jet and plume) and the far field (advected line puff and thermal). Predictions of the path-averaged jet properties are shown to be consistently supported by experimental data on visual trajectory and jet width, and centerline minimum dilution. The relation between the present formulation and previous Lagrangian/Eulerian models is also discussed.
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References
1.
Abraham, G. (1971). “The flow of round buoyant jets issuing vertically into ambient fluid flowing in a horizontal direction.”Publ. No. 81, Delft Hydr. Lab., Delft, The Netherlands.
2.
Auton, T. R., Hunt, J. C. R., and Prud'homme, M.(1988). “The force exerted on a body in inviscid unsteady non-uniform rotational flow.”J. Fluid Mech., 197, 241–257.
3.
Chan, T. L., and Kennedy, J. F. (1972). “Turbulent nonbuoyant or buoyant jets discharged into flowing or quiescent fluids.”Rep. No. 140, Iowa Inst. of Hydr. Res., Iowa City, Iowa.
4.
Cheung, V. (1991). “Mixing of a round buoyant jet in a current,” PhD thesis, Univ. of Hong Kong, Hong Kong.
5.
Chu, V. H., and Goldberg, M. B.(1974). “Buoyant forced plumes in crossflow.”J. Hydr. Div., ASCE, 100(9), 1203–1214.
6.
Chu, V. H. (1977). “A line-impulse model for buoyant jets in a crossflow.”Heat transfer and turbulent buoyant convection, Vol. 1, D. B. Spalding and N. Afgan, eds., Hemisphere Publishing Co., Washington, D.C., 325–337.
7.
Chu, V. H.(1979). “L. N. Fan's data on buoyant jets in crossflow.”J. Hydr. Div., ASCE, 105(5), 612–617.
8.
Chu, V. H.(1985). “Oblique turbulent jets in a crossflow.”J. Engrg. Mech., ASCE, 111(11), 1343–1360.
9.
Chu, V. H. (1994). “Lagrangian scalings of jets and plumes with dominant eddies.”Recent research advances in the fluid mechanics of turbulent jets and plumes, NATO ASI Series E: Applied Sciences, Vol. 255, P. A. Davies and M. J. Valente Neves, eds., Kluwer Academic Publishers, Dordrecht, The Netherlands, 45–72.
10.
Delvigne, G. A. L. (1980). “Round buoyant jet with three-dimensional trajectory in ambient flow.”Publ. No. 228, Delft Hydr. Lab., Delft, The Netherlands.
11.
Fan, L. N. (1967). “Turbulent buoyant jets into stratified or flowing ambient fluids.”Rep. No. KH-R-15, Calif. Inst. of Technol., Pasadena, Calif.
12.
Fischer, H. B., et al. (1979). Mixing in inland and coastal waters . Academic Press, New York, N.Y.
13.
Frick, W. E.(1984). “Non-empirical closure of the plume equations.”Atmos. Envir., 18(4), 653–662.
14.
Hirst, E. A.(1972). “Buoyant jets with three dimensional trajectories.”J. Hydr. Div., ASCE, 98(11), 1999–2014.
15.
Jirka, G. H., and Fong, H. L. M.(1981). “Vortex dynamics and bifurcation of buoyant jets in crossflow.”J. Engrg. Mech., ASCE, 107(3), 479–499.
16.
Knudsen, M. (1988). “Buoyant horizontal jets in an ambient flow,” PhD thesis, Univ. of Canterbury, Christchurch, New Zealand.
17.
Knudsen, M., and Wood, I. R. (1985). “An axisymmetric jet in a moving fluid.”Proc., 9th Australasian Fluid Mech. Conf., 484–487.
18.
Knudsen, M., and Wood, I. R.(1989). “Discussion of `Initial dilution of horizontal jet in crossflow,' by J. H. W. Lee, and P. Neville-Jones.”J. Hydr. Engrg., ASCE, 115(2), 279–282.
19.
Lee, J. H. W., and Cheung, V.(1990). “Generalized Lagrangian model for buoyant jets in current.”J. Envir. Engrg., ASCE, 116(6), 1085–1106.
20.
Lee, J. H. W., Cheung, Y. K., and Cheung, V. (1987). “Mathematical modelling of a round buoyant jet in a current: an assessment.”Proc., Int. Symp. on River Pollution Control and Mgmt., S62–S82.
21.
Lee, J. H. W., and Rodi, W. (1994). “Numerical simulation of line puffs.”Recent research advances in the fluid mechanics of turbulent jets and plumes, NATO ASI Series E: Applied Sciences, Vol. 255, P. A. Davies and M. J. Valente Neves, eds., Kluwer Academic Publishers, Dordrecht, The Netherlands, 73–88.
22.
Lee, J. H. W., and Wong, C. F.(1993). “Experiments on advected line momentum puffs.”Proc., 25th IAHR Congr., Int. Assoc. for Hydr. Res. (IAHR), 5, 250–257.
23.
Muellenhoff, W. P., et al. (1985). “Initial mixing characteristics of municipal ocean discharges.”Rep. EPA-600/3-85-073, U.S. Envir. Protection Agency (EPA), Newport, Oreg.
24.
Ricou, F. P., and Spalding, D. B.(1961). “Measurements of entrainment by axisymmetric turbulent jets.”J. Fluid Mech., 11, 21–32.
25.
Schatzmann, M. (1978). “The integral equations for round buoyant jets in stratified flows.”J. Appl. Math. and Phys. ( ZAMP ), 29, 608–630.
26.
Schatzmann, M.(1979a). “An integral model of plume rise.”Atmos. Envir., 13, 721–731.
27.
Schatzmann, M. (1979b). “Derivation of the integral conservation equations for buoyant jets with three-dimensional trajectories.”Rep. No. SFB 80/T/150, Ausbreitungs- und tansportortvorgänge in strömungen, Universität Karlsruhe, Germany.
28.
Schatzmann, M. (1981). “Mathematical modeling of submerged discharges into coastal waters.”Proc., 19th IAHR Congr., Int. Assoc. for Hydr. Res. (IAHR), Vol. 3, 239–246.
29.
Scorer, R. S. (1978). Environmental aerodynamics . Ellis Horwood, Chichester, U.K.
30.
Wong, C. F. (1991). “Advected line thermals and puffs,”M. Phil. thesis, Dept. of Civ. and Struct. Engrg., Univ. of Hong Kong, Hong Kong.
31.
Wood, I. R.(1993). “Asymptotic solutions and behavior of outfall plumes.”J. Hydr. Engrg., ASCE, 119(5), 555–580.
32.
Wright, S. J. (1977). “Effects of ambient crossflow and density stratification on the characteristic behavior of round turbulent buoyant jets.”Rep. No. KH-R-36, W. M. Keck Lab. of Hydr. and Water Resour., California Inst. of Technol., Pasadena, Calif.
33.
Wright, S. J. (1994). “The effect of ambient turbulence on jet mixing.”Recent research advances in the fluid mechanics of turbulent jets and plumes, NATO ASI Series E: Applied Sciences, Vol. 255, P. A. Davies and M. J. Valente Neves, eds., Kluwer Academic Publishers, Dordrecht, The Netherlands, 13–27.
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Published In
Journal of Hydraulic Engineering
Volume 122 • Issue 1 • January 1996
Pages: 27 - 34
Copyright
Copyright © 1996 American Society of Civil Engineers.
History
Published online: Jan 1, 1996
Published in print: Jan 1996
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