Kinetic Energy Approach to Dissolving Axisymmetric Multiphase Plumes
Publication: Journal of Hydraulic Engineering
Volume 135, Issue 12
Abstract
A phenomenological kinetic energy theory of buoyant axisymmetric multiphase plumes is constructed, with particular attention to the modeling of the dispersed phase. The dissolution is treated by means of the Ranz-Marshall equation involving a mass-transfer coefficient dependent on the plume properties. The model is compared with various experiments, yielding satisfactory agreement. A central ingredient in the model is the turbulent correlation parameter , playing a role analogous to the conventional entrainment coefficient . We use experimental data to suggest a relationship between , the initial gas flux at the source, and the depth of the gas release.
Get full access to this article
View all available purchase options and get full access to this article.
References
Asaeda, T., and Imberger, J. (1993). “Structure of bubble plumes in linearly stratified environments.” J. Fluid Mech., 249, 35–57.
Bhaumik, T. (2005) “Numerical modeling of multiphase plumes: a comparative study between two-fluid and mixed-fluid integral models.” MS thesis, Texas A&M Univ.
Bombardelli, F. A., Buscaglia, G. C., Rehmann, C. R., Rincon, L. E., and Garcia, M. H. (2007). “Modeling and scaling of aeration bubble plumes: A two-phase flow analysis.” J. Hydraul. Res., 45, 617–630.
Bravo, H. R., Gulliver, J. S., and Hondzo, M. (2007). “Development of a commercial code-based two-fluid model for bubble plumes.” Environ. Modell. Software, 22, 536–547.
Brevik, I. (1977). “Two-dimensional air-bubble plume.” J. Wtrwy., Port, Coast. and Oc. Div., 103(1), 101–115.
Brevik, I., and Killie, R. (1996). “Phenomenological description of the axisymmetric air-bubble plume.” Int. J. Multiphase Flow, 22, 535–549.
Brevik, I., and Kluge, R. (1999). “On the role of turbulence in the phenomenological theory of plane and axisymmetric air-bubble plumes.” Int. J. Multiphase Flow, 25, 87–108.
Brevik, I., and Kristiansen, Ø. (2002). “The flow in and around air-bubble plumes.” Int. J. Multiphase Flow, 28, 617–634.
Buscaglia, G. C., Bombardelli, F. A., and Garcia, M. H. (2002). “Numerical modeling of large-scale bubble plumes accounting for mass transfer effects.” Int. J. Multiphase Flow, 28, 1763–1785.
Chen, F., and Yapa, P. D. (2004). “Modeling gas separation from a bent deepwater oil and gas jet/plume.” J. Mar. Syst., 45, 189–203.
Chen, F., and Yapa, P. D. (2007). “Estimating the oil droplet size distributions in deepwater oil spills.” J. Hydraul. Eng., 133(2), 197–207.
Clift, R., Grace, J. R., and Weber, M. E. (2005). Bubbles, drops and particles, Dover, New York.
Crounse, B. C., Wannamaker, E. J., and Adams, E. E. (2007). “Integral model of a multiphase plume in quiescent stratification.” J. Hydraul. Eng., 133, 70–76.
Ditmars, J. D., and Cederwall, K. (1974) “Analysis of air-bubble plumes.” Proc., 14th Conf. on Coastal Engineering, ASCE, Reston, Va., 2209–2226.
Esmaeeli, A., and Tryggvason, G. (1999). “Direct numerical simulations of bubbly flows. Part 2. Moderate Reynolds number arrays.” J. Fluid Mech., 385, 325–358.
Fanneløp, T. K., and Sjøen, K. (1980) “Hydrodynamics of underwater blowouts.” Proc., AIAA 18th Aerospace Science Meeting, AIAA, Reston, Va.
George, W. K. (1989). “The self-preservation of turbulent flows and its relation to initial conditions and coherent structures.” Advances in turbulence, Hemisphere, New York, 39–73.
Johansen, Ø. (2000). “Deepblow—a Lagrangian plume model for deep water blowouts.” Spill Sci. Technol. Bull., 6, 103–111.
Kubasch, J. H. (2001) “Bubble hydrodynamics in large pools.” Ph.D. thesis, Swiss Federal Institute of Technology, Zürich.
Lee, J. H. W., and Cheung, V. (1990). “Generalized Lagrangian model for bouyant jets in current.” J. Environ. Eng., 116(6), 1085–1106.
Lide, D. R., and Frederikse, H. P. R. (1995). CRC handbook of chemistry and physics, 76th Ed., CRC, Boca Raton, Fla.
Lima Neto, I. E., Zhu, D. Z., and Rajaratnam, N. (2008a). “Air injection in water with different nozzles.” J. Environ. Eng., 134(4), 283–294.
Lima Neto, I. E., Zhu, D. Z., and Rajaratnam, N. (2008b). “Bubbly jets in stagnant water.” Int. J. Multiphase Flow, 34, 1130–1141.
McDougall, T. J. (1978). “Bubble plumes in stratified environments.” J. Fluid Mech., 85, 655–672.
McGinnis, D. F., Lorke, A., Wüest, A., Stöckli, A., and Little, J. C. (2004). “Interaction between a bubble plume and the near field in a stratified lake.” Water Resour. Res., 40, W10206.
Milgram, J. H. (1983). “Mean flow in round bubble plumes.” J. Fluid Mech., 133, 345–376.
Milgram, J. H., and Van Houten, R. J. (1980) “Plumes from sub-sea well blowouts.” Proc., 3rd Int. Conf., BOSS, Vol. I, MIT, Cambridge, Ma., 659–684.
Morton, B. R., Taylor, G. I., and Turner, J. S. (1956). “Turbulent gravitational convection from maintained and instantaneous sources.” Proc. R. Soc. London, Ser. A, 234, 1–23.
Motarjemi, M., and Jameson, G. J. (1978). “Mass transfer from very small bubbles—The optimum bubble size for aeration.” Chem. Eng. Sci., 33, 1415–1423.
Perry, R. H., and Green, D. W. (1997). Perry’s chemical engineers’ handbook, 7th Ed., McGraw-Hill, New York.
Ranz, W. E., and Marshall, W. R., Jr. (1952). “Evaporation from droplets, parts I & II.” Chem. Eng. Prog., 48, 173–180.
Seol, D. G., and Socolofsky, S. A. (2008). “Vector post-processing algorithm for phase discrimination of two-phase PIV.” Exp. Fluids, 45(2), 223–239.
Simonnet, M., Gentric, C., Olmos, E., and Midoux, N. (2007). “Experimental determination of the drag coefficient in a swarm of bubbles.” Chem. Eng. Sci., 62, 858–866.
Socolofsky, S. A. (2001) “Laboratory experiments of multi-phase plumes in stratification and crossflow.” Ph.D. thesis, Massachusetts Institute of Technology.
Socolofsky, S. A., Bhaumik, T., and Seol, D. G. (2008). “Double-plume integral models for near-field mixing in multiphase plumes.” J. Hydraul. Eng., 134(6), 772–783.
Socolofsky, S. A., Crounse, B. C., and Adams, E. (2002). “Multiphase plumes in uniform, stratisfied and flowing environments.” Environmental fluid mechanics—Theories and applications, ASCE, Reston, Va.
Topham D. R. (1975) “Hydrodynamics of an oil well blowout.” Beufort Sea Technical Rep. No. 33, Institution of Ocean Sciences, Sidney, British Columbia.
Wüest, A., Brooks, N. H., and Imboden, D. M. (1992). “Bubble plume modeling for lake restoration.” Water Resour. Res., 28, 3235–3250.
Yapa, P. D., and Zheng, L. (1997). “Simulation of oil spills from underwater accidents. I: Model development.” J. Hydraul. Res., 35(5), 673–688.
Zheng, L., and Yapa, P. D. (1998). “Simulation of oil spills from underwater accidents. II: Model verification.” J. Hydraul. Res., 36(1), 117–134.
Zheng, L., and Yapa, P. D. (2002). “Modeling of gas dissolution in deepwater oil/gas spills.” J. Mar. Syst., 31, 299–309.
Zheng, L., Yapa, P. D., and Chen, F. H. (2003). “A model for simulating deepwater oil and gas blowouts—Part I: Theory and model formulation.” J. Hydraul. Res., 41(4), 339–351.
Information & Authors
Information
Published In
Journal of Hydraulic Engineering
Volume 135 • Issue 12 • December 2009
Pages: 1041 - 1051
Copyright
© 2009 ASCE.
History
Received: Sep 23, 2008
Accepted: Jun 29, 2009
Published online: Jul 1, 2009
Published in print: Dec 2009
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.