Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-12-01T07:32:15.123Z Has data issue: false hasContentIssue false
  • English
  • Français

Dynamic interaction of multiple buoyant jets

Published online by Cambridge University Press:  10 August 2012

Adrian C. H. Lai  and
Joseph H. W. Lee
Adrian C. H. Lai
Affiliation:
The Center for Environmental Sensing and Modelling, Singapore–MIT Alliance for Research and Technology Centre, 1 CREATE Way, CREATE Tower, Singapore 138602, Republic of Singapore
Joseph H. W. Lee*
Affiliation:
Department of Civil and Environmental Engineering, The Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, People’s Republic of China
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

An array of closely spaced round buoyant jets interact dynamically due to the pressure field induced by jet entrainment. Mutual jet attraction can result in a significant change in jet trajectories. Jet merging also leads to overlapping of the passive scalar fields associated with the individual jets, resulting in mixing characteristics that are drastically different from those of an independent free jet. A general semi-analytical model for the dynamic interaction of multiple buoyant jets in stagnant ambient conditions is proposed. The external irrotational flow field induced by the buoyant jets is computed by a distribution of point sinks with strength equal to the entrainment per unit length along the unknown jet trajectories and accounting for boundary effects. The buoyant jet trajectories are then determined by an iterative solution of an integral buoyant jet model by tracking the changes in the external entrainment flow and dynamic pressure fields. The velocity and concentration fields of the jet group are obtained by momentum or kinetic energy superposition for merged jets and plumes, respectively. The modelling approach is supported by numerical solution of the Reynolds-averaged Navier–Stokes equations. The model shows that jet merging and mixing can be significantly affected by jet interactions. Model predictions of the multiple jet trajectories, merging height, as well as the centreline velocity and concentration of the buoyant jet group are in good agreement with experimental data for: (i) a clustered momentum jet group; (ii) a turbulent plume pair; and (iii) a rosette buoyant jet group. Dynamic interactions between a jet group are shown to decrease with the addition of an ambient cross-flow.

JFM classification

Wakes/Jets: Jets Convection: Plumes/thermals Mixing: Turbulent mixing
Type
Papers
Information
Journal of Fluid Mechanics , Volume 708 , 10 October 2012 , pp. 539 - 575
Copyright
Copyright © Cambridge University Press 2012

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

1. Baines, W. D. & Keffer, K. F. 1974 Entrainment by a multiple source turbulent jet. Adv. Geophys. 18B, 289–298.Google Scholar
2. Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.Google Scholar
3. Craft, T. J. & Launder, B. E. 2001 On the spreading mechanism of the three-dimensional turbulent wall jet. J. Fluid Mech. 435, 305–326.CrossRefGoogle Scholar
4. Davidson, M. J. 1989 The behaviour of single and multiple horizontally discharged buoyant jets in a non-turbulent ambient fluid. PhD thesis, University of Canterbury, New Zealand.Google Scholar
5. Davidson, M. J., Gaskin, S. & Wood, I. R. 2002 A study of a buoyant axisymmetric jet in a small co-flow. J. Hydraul. Res. 40 (4), 477–489.CrossRefGoogle Scholar
6. Davidson, M. J., Papps, D. A. & Wood, I. R. 1994 The behaviour of merging buoyant jets. In Recent Research Advances in the Fluid Mechanics of Turbulent Jets and Plumes (ed. Davies, P. A. & Valente Neves, M. J. ), pp. 465–478. Dordrecht.CrossRefGoogle Scholar
7. 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
8. Fox, D. G. 1970 Forced plume in a stably stratified fluid. J. Geophys. Res. 75, 6818–6835.CrossRefGoogle Scholar
9. Gaskin, S. J. 1995 Single buoyant jet in a crossflow and the advected line thermal. PhD thesis, University of Canterbury, New Zealand.Google Scholar
10. Hinze, J. O. 1975 Turbulence. McGraw-Hill.Google Scholar
11. Hodgson, J. E., Moawad, A. K. & Rajaratnam, N. 1999 Concentration field of multiple circular turbulent jets. J. Hydraul. Res. 37 (2), 249–256.Google Scholar
12. Kaminski, E., Tait, S. & Carazzo, G. 2005 Turbulent entrainment in jets with arbitrary buoyancy. J. Fluid Mech. 526, 361–376.CrossRefGoogle Scholar
13. Kaye, N. B. & Linden, P. F. 2004 Coalescing axisymmetric turbulent plumes. J. Fluid Mech. 502, 41–63.CrossRefGoogle Scholar
14. Knystautas, R. 1964 The turbulent jet from a series of holes in line. Aeronaut. Q. 15, 1–28.CrossRefGoogle Scholar
15. Kuang, C. P., Lee, J. H. W., Liu, S. G. & Gu, J. 2006 Numerical study on plume interaction above an alternating diffuser in stagnant water. China Ocean Engng 20 (2), 289–302.Google Scholar
16. Kwon, S. J. 2005 Behavior of buoyant discharges from a rosette-type diffuser. PhD thesis, Seoul National University.Google Scholar
17. Lai, A. C. H. 2009 Mixing of a rosette buoyant jet group. PhD thesis, The University of Hong Kong.Google Scholar
18. Lai, A. C. H. & Lee, J. H. W. 2010 Multiple tandem jet interaction in a crossflow. J. Hydrodyn. B 22 (5/suppl. 1), 639–643.Google Scholar
19. Lai, C. K. C. & Lee, J. H. W. 2012 Mixing of inclined dense jets in stationary ambient. J. Hydro-environ. Res. 6 (1), 9–28.CrossRefGoogle Scholar
20. Lai, A. C. H., Yu, D. & Lee, J. H. W. 2011 Mixing of a rosette jet group in a crossflow. J. Hydraul. Engng ASCE 137 (8), 787–803.CrossRefGoogle Scholar
21. Lamb, H. 1932 Hydrodynamics, 6th edn. Dover.Google Scholar
22. Lee, J. H. W. & Chu, V. H. 2003 Turbulent Jets and Plumes – a Lagrangian Approach. Kluwer.CrossRefGoogle Scholar
23. Lee, A. W. T. & Lee, J. H. W. 1998 Effect of lateral confinement on initial dilution of vertical round buoyant jet. J. Hydraul. Engng ASCE 124 (3), 263–279.CrossRefGoogle Scholar
24. Lee, J. H. W. & Greenberg, M. D. 1984 Line momentum source in shallow inviscid fluid. J. Fluid Mech. 145, 287–304.CrossRefGoogle Scholar
25. Lee, J. H. W. & Jirka, G. H. 1980 Multiport diffuser as line source of momentum in shallow water. Water Resour. Res. 16 (4), 695–708.CrossRefGoogle Scholar
26. Lee, J. H. W. & Jirka, G. H. 1981 Vertical round buoyant jet in shallow water. J. Hydraul. Div. ASCE 107 (HY12), 1651–1675.CrossRefGoogle Scholar
27. Linden, P. F. 1999 The fluid mechanics of natural ventilation. Annu. Rev. Fluid Mech. 31, 201–238.CrossRefGoogle Scholar
28. Liseth, P. 1970 Mixing of merging buoyant jets from a manifold in stagnant receiving water of uniform density. PhD thesis, University of California.Google Scholar
29. Liseth, P. 1976 Wastewater disposal by submerged manifolds. J. Hydraul. Div. ASCE 102 (1), 1–14.Google Scholar
30. Marsters, G. F. 1977 Interaction of two plane, parallel jets. AIAA J. 15 (12), 1756–1762.CrossRefGoogle Scholar
31. Miller, D. R. & Comings, E. W. 1960 Force–momentum fields in a dual jet flow. J. Fluid Mech. 7, 237–256.CrossRefGoogle Scholar
32. Milne-Thomson, L. M. 1968 Theoretical Hydrodynamics. Macmillan.CrossRefGoogle Scholar
33. Monismith, S. G., Koseff, J. R., Thompson, J. K., O’Riordan, C. A. & Nepf, H. M. 1990 A study of model bivalve siphon currents. Limnol. Oceanogr. 35 (3), 680–696.CrossRefGoogle Scholar
34. Morton, B. R., Taylor, G. I. & Turner, J. S. 1956 Turbulent gravitational convection from maintained and instantaneous sources. Proc. R. Soc. Lond. A 234, 1–23.Google Scholar
35. Pani, B. S. & Dash, R. 1983 Three-dimensional single and multiple free jets. J. Hydraul. Engng ASCE 109 (2), 254–269.CrossRefGoogle Scholar
36. Pani, B. S., Lai, A. C. H. & Lee, J. H. W. 2009 Application of Reichardt’s hypothesis for multiple coflowing jets. J. Hydro-environ. Res. 3 (3), 121–128.CrossRefGoogle Scholar
37. Pera, L. & Gebhart, B. 1975 Laminar plume interactions. J. Fluid Mech. 68, 259–271.CrossRefGoogle Scholar
38. Pratte, B. D. & Keffer, J. F. 1972 The swirling turbulent jet. Trans. ASME: J. Basic Engrg 94 (4), 739–748.CrossRefGoogle Scholar
39. Priestley, C. H. B. & Ball, F. K. 1955 Continuous convection from an isolated source of heat. Q. J. R. Meteorol. Soc. 81 (348), 144–157.CrossRefGoogle Scholar
40. Roberts, P. J. W. & Snyder, W. H. 1993a Hydraulic model study for Boston outfall I. Riser configuration. J. Hydraul. Engng ASCE 119 (9), 970–987.CrossRefGoogle Scholar
41. Roberts, P. J. W. & Snyder, W. H. 1993b Hydraulic model study for Boston outfall II. Environmental performance. J. Hydraul. Engng ASCE 119 (9), 988–1002.CrossRefGoogle Scholar
42. Rouse, H., Yih, C. S. & Humphreys, H. W. 1952 Gravitational convection from a boundary source. Tellus 4, 201–210.Google Scholar
43. Seo, I. W., Kwon, S. J. & Yeo, H. K. 2004 Merging characteristics of buoyant discharges from rosette-type diffusers in shallow water. J. Civil Engng KSCE 8 (6), 679–688.CrossRefGoogle Scholar
44. Shih, T. H., Liou, W. W., Shabbir, A., Yang, Y. & Zhu, J. 1995 A new k– eddy viscosity model for high Reynolds number turbulent flows. Comput. Fluids 24 (3), 227–238.CrossRefGoogle Scholar
45. Sorrell, F. Y. & Smith, B. W. 1982 Discharge jet interaction with multiple port diffusers. J. Fluids Engng 104, 40–45.CrossRefGoogle Scholar
46. Squire, H. B. 1951 The round laminar jet. Q. J. Mech. Appl. Maths 4, 321–329.CrossRefGoogle Scholar
47. Taylor, G. I. 1958 Flow induced by jets. J. Aerosp. Sci. 25, 464–465.Google Scholar
48. 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
49. Wood, I. R., Bell, R. G. & Wilkinson, D. L. 1993 Ocean Disposal of Wastewater. World Scientific.CrossRefGoogle Scholar
50. Yannopoulos, P. C. & Noutsopoulos, G. C. 2006 Interaction of vertical round turbulent buoyant jets. Part II: superposition method. J. Hydraul. Res. 44 (2), 233–248.CrossRefGoogle Scholar