A coupled level-set and volume-of-fluid method for the buoyant rise of gas bubbles in liquids

International Journal of Heat and Mass Transfer

Volumn 58, Issue 1-2, 2013, Pages 240-259

  Chakraborty, I ^a   Biswas, G ^a   Ghoshdastidar, P S ^a  

^a INDIAN INSTITUTE OF TECHNOLOGY KANPUR   (India)

Author keywords

Bubble bursting; Bubble formation; CLSVOF method; Coalescence; Interface thickness; Simulation; Single bubble dynamics; Two phase flows

Indexed keywords

BUBBLE BURSTING; CLSVOF METHOD; INTERFACE THICKNESS; SIMULATION; SINGLE BUBBLES;

BUBBLE FORMATION; BUBBLES (IN FLUIDS); COALESCENCE; REYNOLDS NUMBER;

LIQUIDS;

EID: 84870658339     PISSN: 00179310     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijheatmasstransfer.2012.11.027     Document Type: Article

References (75)

1. B. Ramaswamy Numerical simulation of unsteady viscous free surface flow J. Comput. Phys. 90 1990 396 430
2. J.M. Floryan, and H. Rasmussen Numerical methods for viscous flows with moving boundaries Appl. Mech. Rev. 42 1989 323 341
3. B.J. Daly Numerical study of two fluid Rayleigh-Taylor instability Phys. Fluids 10 1967 297 307
4. B.J. Daly A technique for including surface tension effects in hydrodynamics calculations J. Comput. Phys. 4 1969 97 117
5. J. Glimm, R. McBryan, and D.H. Menikoff Sharp, front tracking applied to Rayleigh-Taylor instability SIAM J. Sci. Statist. Comput. 7 1986 230 251
6. G. Tryggvason, B. Bunner, A. Esmaeeli, D. Juric, N. Al-Rawahi, W. Tauber, J. Han, S. Nas, and Y.J. Jan A front tracking method for the computations of multiphase flow J. Comput. Phys. 169 2001 708 759 (Pubitemid 33665464)
7. S.O. Univerdi, and G. Tryggvason A front-tracking method for viscous, incompressible, multi-fluid flows J. Comput. Phys. 100 1992 25 37
8. M. van Sint Annaland, W. Dijkhuizen, N.G. Deen, and J.A.M. Kuipers Numerical simulation of behavior of gas bubbles using 3-D front-tracking method AIChE J. 52 2006 99 110
9. S. Popinet, and S. Zaleski A front-tracking algorithm for accurate representation of surface tension Int. J. Numer. Methods Fluids 30 1999 775 793 (Pubitemid 29435293)
10. J. Hua, and J. Lou Numerical simulation of bubble rising in viscous liquids J. Comput. Phys. 222 2007 769 795
11. J. Hua, J.F. Stene, and P. Lin Numerical simulation of 3D bubbles rising in viscous liquids using front tracking method J. Comput. Phys. 227 2008 3358 3382
12. S. Shin, and D. Juric Modeling three-dimensional multiphase flow using a level contour reconstruction method for front tracking without connectivity J. Comput. Phys. 180 2002 427 470
13. G. Ryskin, and L.G. Leal Numerical solution of free-boundary problems in fluid mechanics. Part 2. Buoyancy driven motion of a gas bubble through a quiescent liquid J. Fluid Mech. 148 1984 19 35 (Pubitemid 15438186)
14. I.S. Kang, and L.G. Leal Numerical solution of axisymmetric unsteady free-boundary problems at finite Reynolds number. I. Finite difference scheme and its application to the deformation of a bubble in a uniaxial straining flow Phys. Fluids 30 1987 1929 1940
15. G.K. Youngren, and A. Acrivos On the shape of a gas bubble in a viscous extensional flow J. Fluid Mech. 76 1976 433 442
16. H.A. Stone, and L.G. Leal Relaxation and breakup of an initially extended drop in an otherwise quiescent liquid J. Fluid Mech. 198 1989 399 427
17. C. Pozrikidis The flow of liquid along a periodic wall J. Fluid Mech. 188 1988 275 300
18. J.M. Boulton-Stone, and J.R. Blake Gas bubble bursting at a free surface J. Fluid Mech. 254 1993 437 466
19. H.N. Oguz, and A. Prosperetti Bubble entrainment by the impact of drops on liquid surfaces J. Fluid Mech. 203 1990 143 179
20. C.W. Hirt, and B.D. Nichols Volume of fluid (VOF) method for the dynamics of free boundaries J. Comput. Phys. 39 1981 201 225
21. S.W.J. Welch, and J. Wilson A volume of fluid based method for fluid flows with phase change J. Comput. Phys. 160 2000 662 682
22. D.K. Agarwal, S.W.J. Welch, G. Biswas, and F. Durst Planar simulation of bubble growth in film boiling in near-critical water using a variant of the VOF method J. Heat Transfer (ASME) 126 2004 329 338 (Pubitemid 38958114)
23. W.J. Rider, and D.B. Kothe Reconstructing volume tracking methods J. Comput. Phys. 141 1998 112 152
24. M. Rudman Volume tracking methods for interfacial flow calculations Int. J. Numer. Methods Fluids 24 1997 671 691
25. L. Chen, S.V. Garimella, J.A. Reizes, and E. Leonardi The development of a bubble rising in a viscous liquid J. Fluid Mech. 387 1999 61 96
26. M. van Sint Annaland, N.G. Deen, and J.A.M. Kuipers Numerical simulation of gas bubbles behavior using a three-dimensional volume of fluid method Chem. Eng. Sci. 60 2005 2999 3011 (Pubitemid 40436044)
27. S. Osher, and J.A. Sethian Fronts propagating with curvature-dependent speed: algorithm based on Hamilton-Jacobi formulations J. Comput. Phys. 79 1988 12 49
28. M. Sussman, P. Smereka, and S. Osher A level set approach for computing solutions to incompressible two-phase flow J. Comput. Phys. 114 1994 146 159 (Pubitemid 124013478)
29. J.A. Sethian Level Set Methods and Fast Marching Methods 1999 Cambridge University Press Cambridge, UK
30. D. Jacqmin Calculation of two-phase Navier-Stokes flows using phase-field modeling J. Comput. Phys. 155 1999 96 127
31. A. Bourlioux, Coupled level set volume of fluid algorithm for tracking material interfaces, in: Proceedings of the 6th International Symposium on Computational Fluid Dynamics, Lake Tahoe, vol. 15, 1995.
32. M. Sussman, and E.G. Puckett A coupled level set and volume of fluid method for computing 3D and axisymmetric incompressible two-phase flows J. Comput. Phys. 162 2000 301 337
33. G. Son, and N. Hur A coupled level-set and volume-of-fluid method for the buoyancy-driven motion of fluid particles Num. Heat Transfer B 42 2002 523 542
34. G. Son Efficient implementation of a coupled level-set and volume-of-fluid method for three-dimensional incompressible two-phase flows Num. Heat Transfer B 43 2003 549 565
35. G. Pianet, S. Vincent, J. Leboi, J.-P. Caltagirone, and M. Anderhuber Simulating compressible gas bubbles with a smooth volume tracking 1-fluid method Int. J. Multiphase Flow 36 2010 273 283
36. M.W. Williams, D.B. Kothe, E.G. Puckett, W. Shyy, and R. Narayan Fluid Dynamics at Interface 1999 Cambridge University Press Cambridge 294
37. S.J. Cumins, M.M. Francois, and D.B. Kothe Estimating curvature from volume fractions Comput. Struct. 83 2005 425 434 (Pubitemid 40219663)
38. M.M. Francois, S.J. Cumins, E.D. Dendy, D.B. Kothe, J.M. Sicilian, and M.W. Williams A balance-force algorithm for continuous and sharp interfacial surface tension models within a volume tracking framework J. Comput. Phys. 213 2006 141 173 (Pubitemid 43179835)
39. S. Popinet An accurate adaptive solver for surface-tension-driven interfacial flows J. Comput. Phys. 228 2009 5838 5866
40. Y. Renardy, and M. Renardy PROST: A parabolic reconstruction of surface tension for the volume-of-fluid method J. Comput. Phys. 183 2002 400 421 (Pubitemid 36100562)
41. D. Gerlach, G. Tomar, G. Biswas, and F. Durst Comparison of volume-of-fluid methods for computing surface tension-dominant two-phase flows Int. J. Heat Mass Transfer 49 2006 740 754 (Pubitemid 43177720)
42. I. Chakraborty, B. Ray, G. Biswas, F. Durst, A. Sharma, and P.S. Ghoshdastidar Computational investigation on bubble detachment from submerged orifice in quiescent liquid under normal and reduced gravity Phys. Fluids 21 2009 062103-01 062103-17
43. M. Ohta, T. Imura, Y. Yoshida, and M. Sussman A computational study of the effect of initial bubble conditions on the motion of a gas bubble rising in viscous liquids Int. J. Multiphase Flow 31 2005 223 237 (Pubitemid 40180740)
44. A.K. Das, and P.K. Das Bubble evolution through submerged orifice using smoothed particle hydrodynamics: basic formulation and model validation Chem. Eng. Sci. 64 2009 2281 2290
45. K. Sankaranarayanan, X. Shan, K. Kevrekidis, and I.G. Sundaresan Bubble flow simulations with the lattice Boltzmann method Chem. Eng. Sci. 54 1999 4817 4823 (Pubitemid 29466745)
46. X. Frank, D. Funfschilling, N. Midoux, and H.Z. Li Bubble in a viscous liquid: lattice Boltzmann simulation and experimental validation J. Fluid Mech. 546 2006 113 122 (Pubitemid 43124741)
47. L. Amaya-Bower, and T. Lee Single bubble rising dynamics for moderate Reynolds number using Lattice Boltzmann method Comput. Fluids 39 2010 1191 1207
48. D. Bhaga, and M.E. Weber Bubbles in viscous liquids: shapes, wakes, and velocities J. Fluid Mech. 105 1981 61 85 (Pubitemid 13529401)
49. J.G. Hnat, and J.D. Buckmaster Spherical cap bubbles and skirt formation Phys. Fluids 19 1976 182 194
50. G. Brereton, and D. Korotney Coaxial and oblique coalescence of two rising bubbles I. Sahin, G. Tryggvason, Dynamics of Bubbles and Vortices Near a Free Surface vol. 119 1991 ASME New York, AMD
51. J.U. Brackbill, D.B. Kothe, and C. Zemach A continuum method for modeling surface tension J. Comput. Phys. 100 1992 335 354
52. F.H. Harlow, and J.E. Welch Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface Phys. Fluids 8 1965 2182 2189
53. Y.C. Chang, T.Y. Hou, B. Merriman, and S. Osher A level set formulation of Eulerian interface capturing methods for incompressible fluid flows J. Comput. Phys. 124 1996 449 464 (Pubitemid 126170327)
54. H.A. Van der Vorst BI-CGSTAB: a fast and smoothly converging variant of BI-CG for the solution of nonsymmetric linear systems SIAM J. Sci. Stat. Comput. 13 1992 631 644
55. E.G. Puckett, A.S. Almgren, J.B. Bell, D.L. Marcus, and W.J. Rider A high-order projection method for tracking fluid interfaces in variable density incompressible flows J. Comput. Phys. 130 1997 269 282 (Pubitemid 127170574)
56. K. Mukundakrishnan, S. Quan, D.M. Eckmann, and P.S. Ayyaswamy Numerical study of wall effects on buoyant gas-bubble rise in a liquid-filled finite cylinder Phys. Rev. E. 76 2007 036308-01 036308-15
57. J.R. Grace Shapes and velocities of bubbles rising in infinite liquids Trans. Inst. Chem. Eng. 51 1973 116 120
58. R. Clift, J.R. Grace, and M.E. Weber Bubbles, Drops, and Particles 1978 Academic New York
59. J.R. Grace The viscosity of fluidized beds Can. J. Chem. Eng. 1970 30 33
60. T. Bonometti, and J. Magnaudet Transition from spherical cap to toroidal bubbles Phys. Fluids 18 2006 052102-01 052102-12
61. Z. Yu, and L.-S. Fan Direct simulation of the buoyant rise of bubbles in infinite liquid using level set method Can. J. Chem. Eng. 86 2008 267 275
62. T. Bonometti, and J. Magnaudet An interface-capturing method for incompressible two-phase flows. Validation and application to bubble dynamics Int. J. Multiphase Flow 33 2007 109 133 (Pubitemid 46138022)
63. M. Sussman, and P. Smereka Axisymmetric free boundary problems J. Fluid Mech. 341 1997 269 294
64. D. Bhaga, and M.E. Weber In-line interaction of a pair of bubbles in a viscous liquid Chem. Eng. Sci. 35 1980 2467 2474 (Pubitemid 11463983)
65. L. Duchemin, S. Popinet, C. Josserand, and S. Zaleski Jet formation in bubbles bursting at a free surface Phys. Fluids 14 2002 3000 3008
66. M.S. Longuet-Higgins, B.R. Kerman, and K. Lunde The release of air bubbles from an underwater nozzle J. Fluid Mech. 230 1991 365 390 (Pubitemid 21711819)
67. R. Kumar, and N.R. Kuloor The formation of bubbles and drops Adv. Chem. Eng. 8 1970 255 368
68. E. Gaddis, and A. Vogelpohl Bubble formation in quiescent liquids under constant flow conditions Chem. Eng. Sci. 41 1986 97 105 (Pubitemid 16489140)
69. M. Jamialahmadi, M.R. Zehtaban, H. Muller-Steinhagen, A. Sarrafi, and J.M. Smith Study of bubble formation under constant flow condition Chem. Eng. Res. Des. 79 2001 523 532
70. S.C. Chuang, and V.W. Goldschmidt Bubble formation due to a submerged capillary tube in quiescent and co-flowing systems Trans. ASME, J. Basic Eng. 92 1970 705 711
71. H.N. Oguz, and A. Prosperetti Dynamics of bubble growth and detachment from a needle J. Fluid Mech. 257 1993 111 145
72. I. Chakraborty, G. Biswas, and P.S. Ghoshdastidar Bubble generation in quiescent and co-flowing liquids Int. J. Heat Mass Transfer 54 2011 4673 4688
73. A. Sevilla, J.M. Gordillo, and C. Martinez-Bazan Transition from bubbling to jetting in a coaxial air-water jet Phys. Fluids 17 2005 018105-01 018105-04
74. A.G. Marin, F. Campro-Cortes, and J.M. Gordillo Generation of micron-sized drops and bubbles through viscous coflows Colloid Surf. A 344 2009 2 7
75. C. Clanet, and J.C. Lasheras Transition from dripping to jetting J. Fluid Mech. 383 1999 307 326