A simple computational model for bubble plumes

Applied Mathematical Modelling

Volumn 24, Issue 3, 2000, Pages 215-233

  Bernard, Robert S ^a   Maier, Robert S ^b   Falvey, Henry T ^c  

^a US Army Engineer Res and Devmt C   (United States)

^b Army High Performance Computing Research Center   (United States)

^c Henry T Falvey and Associates Inc   (United States)

Author keywords

Bubble plumes; Bubbles; Ladles; Mixing; Models; Reservoirs; Turbulence

Indexed keywords

APPROXIMATION THEORY; BUBBLES (IN FLUIDS); LADLES; MATHEMATICAL MODELS; MIXING; RESERVOIRS (WATER); TURBULENCE; VELOCITY;

BUBBLE PLUMES; BUOYANT FORCE;

COMPUTATIONAL FLUID DYNAMICS;

BUBBLE DISTILLATION COLUMN; COMPUTATIONAL MODEL; PLUME;

EID: 0034162239     PISSN: 0307904X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0307-904X(99)00030-X     Document Type: Article

References (40)

1. H.E. Kobus, Analysis of the flow induced by air-bubble systems, in: Proc. Coastal Eng. Conf. London, ch. 65, vol. II, 1968, pp. 1016-1031.
2. K. Cederwall, J.D. Ditmars, Analysis of air-bubble plumes, Report KH-R-24, California Institute of Technology, Pasadena, CA, 1970.
3. Milgram J.H. Mean flow in round bubble plumes. J. Fluid Mech. 133:1983;345-376.
4. Mazumdar N.P., Islam N., Chanda A. A mathematical model for turbulent bubble plume. Physica Scripta. 53:1996;575-581.
5. Brevik I., Killie R. Phenomenological description of the axisymmetric air-bubble plume. Int. J. Multiphase Flow. 22(3):1996;535-549.
6. Deb Roy T., Majumdar A.K., Spalding D.B. Numerical prediction of recirculation flows with free convection encountered in gas-agitated reactors. App. Math. Modelling. 2:1978;146-150.
7. Grevet J.H., Szekely J., El-Kaddah N. An experimental and theoretical study of gas bubble driven circulation systems. Int. J. Heat Mass Transfer. 25(4):1982;487-497.
8. Mazumdar D., Guthrie R.I.L. Hydrodynamic modelling of some gas injection procedures in ladle metallurgy systems. Metall. Trans. B. 16B:1985;83-90.
9. Castillejos A.H., Salcudean M.E., Brimacobe J.K. Fluid flow and bath temperature destratification in gas-stirred ladles. Metall. Trans. B. 20B:1989;603-611.
10. Balaji D., Mazumdar D. Numerical computation of flow phenomena in gas-stirred ladle systems. Steel Res. 62(1):1991;16-23.
11. Millies M., Mewes D. Calculation of circulating flows in bubble columns. Chem. Engrg. Science. 50(13):1995;2093-2106.
12. Sheng Y.Y., Irons G.A. The impact of bubble dynamics on the flow in plumes of ladle water models. Metall. Mat. Trans. B. 26B:1995;625-635.
13. Pan S.-M., Ho Y.-H., Hwang W.-S. Three-dimensional fluid flow model for gas-stirred ladles. J. Mater. Engrg. Performance. 6(3):1997;311-318.
14. Delnoij E., Lammers F.A., Kuipers J.A.M., van Swaaij W.P.M. Dynamic simulation of dispersed gas-liquid two-phase flow using a discrete bubble model. Chem. Engrg. Science. 52(9):1997;1429-1458.
15. Park H.-J., Yang W.-J. Turbulent two-phase mixing in gas-stirred ladle systems for continuous casting applications. Num. Heat Transfer A. 31:1997;493-515.
16. Schwarz M.P., Turner W.J. Applicability of the standard k-. ε turbulence model to gas-stirred baths App. Math. Modelling. 12:1988;273-279.
17. Davidson M.R. Numerical calculations of two-phase flow in a liquid bath with bottom injection: The central plume. App. Math. Modelling. 14:1990;67-76.
18. Sokolichin A., Eigenberger G. Gas-liquid flow in bubble columns and loop reactors: Part I. Detailed modelling and numerical simulation. Chem. Engrg. Science. 49(24B):1994;5735-5746.
19. Becker S., Sokolichin A., Eigenberger G. Gas-liquid flow in bubble columns and loop reactors: Part II. Comparison of detailed experiments and flow simulations. Chem. Engrg. Science. 49(24B):1994;5747-5762.
20. Schwarz M.P. Simulation of gas injection into liquid melts. App. Math. Modelling. 20:1996;41-51.
21. Mazumdar D., Guthrie R.I.L. The physical and mathematical modelling of gas stirred ladle systems. ISIJ International. 35(1):1995;1-20.
22. Jakobsen H.A., Sannaes B.H., Grevskott S., Svendsen H.F. Modelling of vertical bubble-driven flows. Ind. Engrg. Chem. Res. 36:1997;4052-4074.
23. Mazumdar D., Guthrie R.I.L. A comparison of three mathematical modelling procedures for simulating fluid flow phenomena in bubble-stirred ladles. Metall. Mat. Trans. B. 25B:1994;308-312.
24. Launder B.E., Spaulding D.B. The numerical computation of turbulent flows. Comp. Meth. App. Mech. Engrg. 3:1974;269-289.
25. R.S. Bernard, Preliminary development of a three-dimensional numerical model for reservoir hydrodynamics, Technical report HL-95-9, Waterways Experiment Station, US Army Corps of Engineers, Vicksburg, MS, 1995.
26. R.S. Bernard, MAC3D: numerical model for reservoir hydrodynamics with application to bubble diffusers, Technical report CHL-98-23, Waterways Experiment Station, US Army Corps of Engineers, Vicksburg, MS, 1998.
27. R. Clift, J.R. Grace, M.E. Weber, Bubbles, Drops and Particles Academic Press, New York, 1978.
28. A. Müller, E. Grass, A. Wüest, A. Gyr, Modelling of bubble plumes, in: Proc. Tech. Session B: Topics in Hydraulic Modelling, 23rd IAHR Congress, 1987, pp. 348-353.
29. Johansen S.T., Boysan F. Fluid dynamics in bubble stirred ladles: Part II. Mathematical modeling. Metall. Trans. B. 19B:1998;755-764.
30. Bernard R.S., Kapitza H. How to discretize the pressure gradient for curvilinear MAC grids. J. Comp. Phys. 99:1992;288-298.
31. B.K. Soni, J.F. Thompson, M. Stokes, M.H. Shih, GENIE++, EAGLEVIEW, and TIGER: General and special purpose graphically interactive grid systems, AIAA-92-0071, AIAA 30th Aerospace Sciences Meeting and Exhibit, Reno, NV, 1992.
32. P.J. Roache, Computational Fluid Dynamics, Hermosa, Albuquerque, NM, 1982.
33. Kapitza H., Eppel D. A 3-D poisson solver based on conjugate gradients compared to standard iterative methods and its performance on vector computers. J. Comp. Phys. 68:1987;474-484.
34. W. Rodi, Turbulence Models and their Applications in Hydraulics - A State of the Art Review, International Association for Hydraulic Research, Delft, The Netherlands, 1980.
35. Mazumdar D., Guthrie R.I.L. Mixing models for gas stirred metallurgical reactors. Metall. Trans. B. 17B:1986;725-733.
36. Castello-Branco M., Schwerdtfeger K. Large-scale measurements of the physical characteristics of round vertical bubble plumes in liquids. Metall. Mat. Trans. B. 25B:1994;359-371.
37. N.J. Hornewer, G.P. Johnson, D.M. Robertson, M. Hondzo, Field-scale tests for determining mixing patterns associated with coarse-bubble air diffuser configurations, Egan Quarry, Illinois, in: Proc. Theme B: Environmental and Coastal Hydraulics: Protecting the Aquatic Habitat, 27th IAHR Congress, 1997, pp. 57-63.
38. Nakanishi K., Fujii T., Szekely J. Possible relationship between energy dissipation and agitation in steel processing operations. Ironmaking and steelmaking. 3:1975;193-197.
39. Asai S., Okamoto T., He J., Muchi I. Mixing time of refining vessels stirred by gas injection. Trans. ISIJ. 23:1983;43-50.
40. Leitch A.M., Baines W.D. Liquid volume flux in a weak plume. J. Fluid Mech. 205:1989;77-98.