A direct numerical simulation study of the buoyant rise of bubbles at O(100) Reynolds number

Physics of Fluids

Volumn 17, Issue 9, 2005, Pages 1-19

  Esmaeeli, Asghar ^a   Tryggvason, Grétar ^b  

^a Southern Illinois University Carbondale   (United States)

^b Worcester Polytechnic Institute   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BUOYANCY; COMPUTER SIMULATION; CORRELATION METHODS; NUMERICAL METHODS; PROBABILITY DENSITY FUNCTION; REYNOLDS NUMBER;

BUOYANCY DRIVEN MOTION; DIRECT NUMERICAL SIMULATION;

BUBBLES (IN FLUIDS);

BUBBLY FLOW; FLUID MECHANICS; MATHEMATICAL ANALYSIS; REYNOLDS NUMBER;

EID: 27144503625     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.2056617     Document Type: Article

References (67)

1. B. Bunner and G. Tryggvason, "Dynamics of homogeneous bubbly flows. Part 1. Rise velocity and microstructure of the bubbles," J. Fluid Mech. JFLSA70022-112010.1017/S0022112002001179 466, 17 (2002).
2. B. Bunner and G. Tryggvason, "Dynamics of homogeneous bubbly flows. Part 2. Velocity fluctuations," J. Fluid Mech. JFLSA70022-112010.1017/S0022112002001180 466, 53 (2002).
3. B. Bunner and G. Tryggvason, "Effect of bubble deformation on the properties of bubbly flows," J. Fluid Mech. JFLSA70022-112010.1017/ S0022112003006293 495, 77 (2003).
4. M. Wu and M. Gharib, "Experimental studies on the shape and path of small air bubbles rising in clean water," Phys. Fluids PHFLE61070-663110.1063/1.1485767 14, L49 (2002).
5. K. Ellingsen and F. Risso, "On the rise of an ellipsoidal bubble in water: Oscillatory paths and liquid-induced velocity," J. Fluid Mech. JFLSA70022-112010.1017/S0022112001004761 440, 235 (2001).
6. C. Brücker, "Structure and dynamics of the wake of bubbles and its relevance for bubble interactions," Phys. Fluids PHFLE61070-663110.1063/1.870043 11, 1781 (1999).
7. K. Lunde and R. J. Perkins, "Shape oscillations of rising bubbles," Appl. Sci. Res. ASRHAU0003-699410.1023/A:1000864525753 58, 387 (1998).
8. A. Esmaeeli, E. A. Ervin, and G. Tryggvason, "Numerical simulations of rising bubbles," in Bubble Dynamics and Interface Phenomena, edited by J. R. Blake, J. M. Boulton-Stone, and N. H. Thomas (Kluwer, Dordrecht, 1994), pp. 247-255.
9. M. F. Göz, B. Bunner, M. Sommerfeld, and G. Tryggvason, "The unsteady dynamics of two-dimensional bubbles in a regular array," ASME FEDSM'00, ASME 2000 Fluids Engineering Division Summer Meeting, Boston, MA, 2000.
10. Y. Yurkovetsky and J. F. Brady, "Statistical mechanics of bubbly liquids," Phys. Fluids PHFLE61070-663110.1063/1.868869 8, 881 (1996).
11. P. Smereka, "On the motion of bubbles in a periodic box," J. Fluid Mech. JFLSA70022-1120 254, 79 (1993).
12. A. S. Sangani and A. K. Didwania, "Dynamic simulations of flows of bubbly liquids at large Reynolds numbers," J. Fluid Mech. JFLSA70022-1120 250, 307 (1993).
13. R. Zenit, D. L. Koch, and A. S. Sangani, "Measurements of the average properties of a suspension of bubbles rising in a vertical channel," J. Fluid Mech. JFLSA70022-112010.1017/S0022112000002743 429, 307 (2001).
14. R. E. G. Poorte and A. Biesheuvel, "Experiments on the motion of gas bubbles in turbulence generated by an active grid," J. Fluid Mech. JFLSA70022-112010.1017/S0022112002008273 461, 127 (2002).
15. M. Lance and J. Bataille, "Turbulence in the liquid phase of a uniform bubbly air-water flow," J. Fluid Mech. JFLSA70022-1120 222, 95 (1991).
16. C. W. Stewart, "Bubble interaction in low-viscosity liquids," Int. J. Multiphase Flow IJMFBP0301-932210.1016/0301-9322(95)00030-2 21, 1037 (1995).
17. V. I. Kushch, A. Sangani, P. D. Spelt, and D. Koch, "Finite-Weber number motion of bubbles through a nearly inviscid liquid," J. Fluid Mech. JFLSA70022-112010.1017/S0022112002008145 460, 241 (2002).
18. F. Risso and K. Ellingsen, "Velocity fluctuations in a homogeneous dilute dispersion of high-Reynolds-number rising bubbles," J. Fluid Mech. JFLSA70022-112010.1017/S0022112001006930 453, 395 (2002).
19. S. O. Unverdi and G. Tryggvason, "A front-tracking method for viscous, incompressible, multi-fluid flows," J. Comput. hys. JCTPAH0021-999110.1016/0021-9991(92)90307-K 100, 25 (1992).
20. A. Esmaeeli and G. Tryggvason, "Direct numerical simulations of bubbly flows. Part I-Low Reynolds number arrays," J. Fluid Mech. JFLSA70022-112010.1017/S0022112098003176 377, 313 (1998).
21. K. Sankaranarayanan, I. G. Kevrekidis, S. Sundaresan, J. Lu, and G. Tryggvason, "A comparative study of lattice Boltzmann and front-tracking finite-difference methods for bubble simulations," Int. J. Multiphase Flow IJMFBP0301-932210.1016/S0301-9322(02)00120-9 29, 109 (2003).
22. B. Bunner and G. Tryggvason, "Direct numerical simulation of three-dimensional bubbly flows," Phys. Fluids PHFLE61070-6631 11, 1167 (1999).
23. B. P. Leonard, "A stable and accurate convective modeling procedure based on quadratic upstream interpolation," Comput. Methods Appl. Mech. Eng. CMMECC0045-782510.1016/S0045-7825(99)00431-4 19, 59 (1979).
24. M. Ishii, T. C. Chawla, and N. Zuber, "Constitutive equation for vapor drift velocity in two-phase annular flow," AIChE J. AICEAC0001-1541 22, 283 (1976).
25. M. Ishii and N. Zuber, "Drag coefficient and rise velocity in bubbly, droplet or particulate flows," AIChE J. AICEAC0001-154110.1002/aic.690250513 25, 843 (1979).
26. A. Esmaeeli, "Numerical simulation of bubbly flows," Ph.D. thesis, University of Michigan, 1995.
27. H. Oka and K. Ishii, "Numerical analysis on the motion of gas bubbles using level set method," J. Phys. Soc. Jpn. JUPSAU0031-901510.1143/JPSJ.68.823 68, 823 (1999).
28. R. Clift, J. R. Grace, and M. E. Weber, Bubbles, Drops, and Particles (Academic, New York, 1978).
29. A. F. Fortes, D. D. Joseph, and T. S. Lundgren, "Nonlinear mechanics of fluidization of beds of spherical particles," J. Fluid Mech. JFLSA70022-1120 177, 467 (1987).
30. D. W. Moore, "The boundary layer on a spherical gas bubble," J. Fluid Mech. JFLSA70022-1120 16, 161 (1963).
31. A. Blanco and J. Magnaudet, "The structure of the axisymmetric high-Reynolds number flow around an ellipsoidal bubble of fixed shape," Phys. Fluids PHFLE61070-663110.1063/1.868515 7, 1265 (1995).
32. D. W. Moore, "The rise velocity of distorted gas bubbles in a liquid of small viscosity," J. Fluid Mech. JFLSA70022-1120 23, 749 (1965).
33. A. S. Sangani, D. Z. Zhang, and A. Prosperetti, "The added mass, Basset, and viscous drag coefficients in nondilute bubbly liquids undergoing small-amplitude oscillatory motion," Phys. Fluids A PFADEB0899-821310.1063/1.857838 3, 2955 (1991).
34. P. N. Segré, E. Herbolzheimer, and P. M. Chaikin, "Long-range correlations in sedimentation," Phys. Rev. Lett. PRLTAO0031-900710.1103/PhysRevLett.79.2574 79, 2574 (1997).
35. E. Guazzelli, "Evolution of particle-velocity correlations in sedimentation," Phys. Fluids PHFLE61070-6631 13, 1437 (2001).
36. A. Esmaeeli and G. Tryggvason, "Direct numerical simulations of bubbly flows. Part II-Moderate Reynolds number arrays," J. Fluid Mech. JFLSA70022-112010.1017/S0022112099004310 385, 325 (1999).
37. D. A. Drew, "Mathematical modeling of two phase flow," Annu. Rev. Fluid Mech. ARVFA30066-418910.1146/annurev.fl.15.010183.001401 15, 261 (1983).
38. M. Ishii, Thermo-Fluid Dynamic Theory of Two-Phase Flows (Eyrolles, Paris, 1975).
39. J. M. Delhaye, "Jump conditions and entropy sources in two-phase systems. Local instant formulation," Int. J. Multiphase Flow IJMFBP0301-9322 1, 393 (1974).
40. H. Nicolai, B. Herzhaft, E. J. Hinch, L. Oger, and E. Guazzelli, "Particle velocity fluctuations and hydrodynamic self-diffusion of sedimenting non-Brownian spheres," Phys. Fluids PHFLE61070-663110.1063/1.868733 7, 12 (1995).
41. L. van Wijngaarden, "Hydrodynamic interaction in liquid gas flow," Appl. Sci. Res. ASRHAU0003-6994 38, 331 (1982).
42. P. D. M. Spelt and A. Biesheuvel, "On the motion of gas bubbles in homogeneous isotropic turbulence," J. Fluid Mech. JFLSA70022-112010.1017/S0022112096004739 336, 221 (1997).
43. P. D. M. Spelt and A. Biesheuvel, "Dispersion of gas bubbles in large-scale homogeneous isotropic turbulence," Appl. Sci. Res. ASRHAU0003-699410.1023/A:1000820810732 58, 463 (1998).
44. C. T. Crowe, T. R. Troutt, and J. N. Chung, "Numerical models for two-phase turbulent flows," Annu. Rev. Fluid Mech. ARVFA30066-4189 26, 11 (1996).
45. A. Sokolichin, G. Eigenberger, A. Lapin, and A. Lübbert, "Dynamic numerical simulation of gas-liquid two-phase flows: Euler-Euler versus Euler-Lagrange," Chem. Eng. Sci. CESCAC0009-2509 52, 611 (1997).
46. G. K. Batchelor and A. A. Townsend, "Turbulent diffusion," Survey in Mechanics (Cambridge University Press, Cambridge, 1956).
47. H. Nicolai and E. Guazzelli, "Effect of vessel size on the ydrodynamics diffusion of sedimenting spheres," Phys. Fluids PHFLE61070-663110.1063/1.868727 7, 3 (1995).
48. A. J. C. Ladd, "Dynamic simulations of sedimenting spheres," Phys. Fluids A PFADEB0899-821310.1063/1.858695 5, 299 (1993).
49. G. Bossis and J. F. Brady, "Dynamic simulation of sheared suspension. I. General method," J. Chem. Phys. JCPSA60021-960610.1063/1.446585 80, 5141 (1984).
50. H. Zhou and C. Pozrikidis, "Pressure-driven flow of suspensions of liquid drops," Phys. Fluids PHFLE61070-663110.1063/1.868048 6, 80 (1994).
51. J. F. Brady and G. Bossis, "The rheology of concentrated suspensions of spheres in simple shear flow by numerical simulation," J. Fluid Mech. JFLSA70022-1120 155, 105 (1985).
52. H. Lamb, Hydrodynamics (Dover, New York, 1932).
53. J. Happel and H. Brenner, Low Reynolds Number Hydrodynamics (Prentice-Hall, Englewood Cliffs, NJ, 1965).
54. S. Kim and S. J. Karrila, Microhydrodynamics: Principles and Selected Applications (Butterworth, Washington DC/Heinemann, London, 1991).
55. J. B. W. Kok, "Dynamics of pair of gas bubbles moving through liquid. Part I. Theory," Eur. J. Mech. B/Fluids EJBFEV0997-7546 12, 515 (1993).
56. L. van Wijngaarden, "The mean rise velocity of pairwise-interacting bubbles in liquid," J. Fluid Mech. JFLSA70022-1120 251, 55 (1993).
57. D. Legendre, J. Magnaudet, and G. Mougin, "Hydrodynamic interactions between two spherical bubbles rising side by side in a viscous liquid," J. Fluid Mech. JFLSA70022-112010.1017/ S0022112003006463 497, 133 (2003).
58. T. M. Reed and K. E. Gubbins, Applied Statistical Mechanics (McGraw-Hill, New York, 1973).
59. J. Hoshen and R. Kopelman, "Percolation and cluster distribution. I. Cluster multiple labeling technique and critical concentration algorithm," Phys. Rev. B PLRBAQ0556-280510.1103/PhysRevB.14.3438 14, 3438 (1976).
60. C. Chang and R. L. Powell, "Dynamic simulation of bimodal suspensions of hydrodynamically interacting spherical particles," J. Fluid Mech. JFLSA70022-1120 253, 1 (1993).
61. C. Chang and R. L. Powell, "Self-diffusion of bimodal suspensions of hydrodynamically interacting spherical particles in shearing flow," J. Fluid Mech. JFLSA70022-1120 281, 51 (1994).
62. X. Li, R. Charles, and C. Pozrikidis, "Simple shear flow of suspensions of liquid drops," J. Fluid Mech. JFLSA70022-1120 320, 395 (1996).
63. G. I. Taylor, "The formation of emulsions in definable fields of flow," Proc. R. Soc. London, Ser. A PRLAAZ0950-1207 146, 501 (1932).
64. D. I. Meiron, "On the stability of gas bubbles rising in an inviscid fluid," J. Fluid Mech. JFLSA70022-1120 198, 101 (1989).
65. L. S. Fan and K. Tsuchiya, Bubble Wake Dynamics in Liquids and Liquid-Solid Suspensions (Butterworth, Boston, 1990).
66. G. K. Batchelor, An Introduction of Fluid Dynamics (Cambridge University Press, Cambridge, 1967).
67. E. Steinthorsson and G. Tryggvason, "A front tracking scheme for high density ratio multifluid flows," AIAA 99-3326 14th Computational Fluid Dynamics Conference, 28 June-1 July 1999, Norfolk, VA, AIAA Paper No. 99-3326.