Droplet flows with coalescence and breakup are simulated numerically using the lattice Boltzmann method. It is shown that the rising velocities are in good agreement with those obtained by the force balance and the empirical correlation. The breakup of droplets after coalescence is simulated well in terms of the critical Weber number. A numerical method to evaluate the interfacial area and the volume fraction in two-phase flows is proposed. It is shown that the interfacial area corresponds to the shape, the number and the size of droplets, and the proposed method is effective for numerical evaluation of interfacial area even if the interface changes dynamically.

1.
The RELAP5 Development Team, 1995, “RELAP5/MOD3 Code Manual,” NUREG/CR-5535.
2.
Safety Code Development Group, 1986, “TRAC-PF1/MOD1: An Advanced Best Estimate Computer Program for Pressurized Water Reactor Thermal-Hydraulic Analysis,” NUREG/CR-3858.
3.
Sato
,
T.
,
Jung
,
R.-T.
, and
Abe
,
S.
,
2000
, “
Direct Simulation of Droplet Flow With Mass Transfer at Interface
,”
ASME J. Fluids Eng.
,
122
, pp.
510
516
.
4.
Lee, W. J., 1998, “State-of-the-Art Report on the Theoretical Modeling of Interfacial Area Concentration,” KAERI/AR-497/98.
5.
Delhaye
,
J. M.
, and
Bricard
,
P.
,
1994
, “
Interfacial Area in Bubbly Flow: Experimental Data and Correlations
,”
Nucl. Eng. Des.
,
151
, pp.
65
77
.
6.
Kocamustafaogullari
,
G.
,
Huang
,
W. D.
, and
Razi
,
J.
,
1994
, “
Measurement and Modeling of Average Void Fraction, Bubble Size and Interfacial Area
,”
Nucl. Eng. Des.
,
148
, pp.
437
453
.
7.
Zeitoun
,
O.
,
Shoukri
,
M.
, and
Chatoorgoon
,
V.
,
1994
, “
Measurement of Interfacial Area Concentration in Subcooled Liquid-Vapor Flow
,”
Nucl. Eng. Des.
,
152
, pp.
243
255
.
8.
Frisch
,
U.
,
Hasslacher
,
B.
, and
Pomeau
,
Y.
,
1986
, “
Lattice-Gas Automata for the Navier-Stokes Equation
,”
Phys. Rev. Lett.
,
56
, pp.
1505
1508
.
9.
Rothman
,
D. H.
, and
Zaleski
,
S.
,
1994
, “
Lattice-Gas Models of Phase Separation: Interfaces, Phase Transitions, and Multiphase Flow
,”
Rev. Mod. Phys.
,
66
, pp.
1417
1479
.
10.
Chen
,
H.
, and
Doolen
,
G. D.
,
1998
, “
Lattice Boltzmann Method for Fluid Flows
,”
Annu. Rev. Fluid Mech.
,
30
, pp.
329
364
.
11.
McNamara
,
G. G.
, and
Zanetti
,
G.
,
1988
, “
Use of the Boltzmann Equation to Simulate Lattice-Gas Automata
,”
Phys. Rev. Lett.
,
61
, pp.
2332
2335
.
12.
Bhatnagar
,
P. L.
,
Gross
,
E. P.
, and
Krook
,
M.
,
1954
, “
A Model for Collision Processes in Gases. I: Small Amplitude Processes in Charged and Neutral One-Component System
,”
Phys. Rev.
,
94
, pp.
511
525
.
13.
Chen
,
H.
,
Chen
,
S.
, and
Matthaeus
,
W. H.
,
1992
, “
Recovery of the Navier-Stokes Equations using a Lattice-Gas Boltzmann Method
,”
Phys. Rev. A
,
45
, pp.
R5339–R5342
R5339–R5342
.
14.
Benzi
,
R.
,
Succi
,
S.
, and
Vergassola
,
M.
,
1992
, “
The Lattice Boltzmann-Equation—Theory and Applications
,”
Phys. Rep.
,
222
, pp.
145
197
.
15.
Takada
,
N.
,
Misawa
,
M.
,
Tomiyama
,
A.
, and
Fujiwara
,
S.
,
2000
, “
Numerical Simulation of Two- and Three-Dimensional Two-Phase Fluid Motion by Lattice Boltzmann Method
,”
Comput. Phys. Commun.
,
129
, pp.
233
246
.
16.
Wagner
,
A. J.
,
Giraud
,
L.
, and
Scott
,
C. E.
,
2000
, “
Simulation of a Cusped Bubble Rising in a Viscoelastic Fluid with a New Numerical Method
,”
Comput. Phys. Commun.
,
129
, pp.
227
232
.
17.
Nie
,
X.
,
Qian
,
Y.-H.
,
Doolen
,
G. D.
, and
Chen
,
S.
,
1998
, “
Lattice Boltzmann Simulation of the Two-Dimensional Rayleigh-Taylor Instability
,”
Phys. Rev. E
,
58
, pp.
6861
6864
.
18.
He
,
X.
,
Zhang
,
R.
,
Chen
,
S
, and
Doolen
,
G. D.
,
1999
, “
On the Three-Dimensional Rayleigh-Taylor Instability
,”
Phys. Fluids
,
11
, pp.
1143
1152
.
19.
He
,
X.
,
Chen
,
S.
, and
Zhang
,
R.
,
1999
, “
A Lattice Boltzmann Scheme for Incompressible Multiphase Flow and Its Application in Simulation of Rayleigh-Taylor Instability
,”
J. Comput. Phys.
,
152
, pp.
642
663
.
20.
Sehgal
,
B. R.
,
Nourgaliev
,
R. R.
, and
Dinh
,
T. N.
,
1999
, “
Numerical Simulation of Droplet Deformation and Bread-Up by Lattice-Boltzmann Method
,”
Prog. Nucl. Energy
,
34
, pp.
471
488
.
21.
Xi
,
H.
, and
Duncan
,
C.
,
1999
, “
Lattice Boltzmann Simulations of Three-Dimensional Single Droplet Deformation and Breakup Under Simple Shear Flow
,”
Phys. Rev.
,
59
, pp.
3022
3026
.
22.
Gunstensen
,
A. K.
, and
Rothman
,
D. H.
,
1991
, “
Lattice Boltzmann Model of Immiscible Fluids
,”
Phys. Rev. A
,
43
, pp.
4320
4327
.
23.
Rothman
,
D. H.
, and
Keller
,
J. M.
,
1988
, “
Immiscible Cellular-Automaton Fluids
,”
J. Stat. Phys.
,
52
, pp.
1119
1127
.
24.
Grunau
,
D.
,
Chen
,
S.
, and
Eggert
,
K.
,
1993
, “
A Lattice Boltzmann Model for Multiphase Fluid Flows
,”
Phys. Rev. A
,
5
, pp.
2557
2562
.
25.
Hou
,
S.
,
Shan
,
X.
,
Zou
,
Q.
,
Doolen
,
G. D.
, and
Soll
,
W. E.
,
1997
, “
Evaluation of Two Lattice Boltzmann Models for Multiphase Flows
,”
J. Comput. Phys.
,
138
, pp.
695
713
.
26.
Landau, L. D., and Lifshitz, E. M., 1959, Fluid Mechanics, Pergamon, New York.
27.
Kandhai
,
D.
,
Koponen
,
A.
,
Hoekstra
,
A.
,
Kataja
,
M.
,
Timonen
,
J.
, and
Sloot
,
P. M. A.
,
1999
, “
Implementation Aspects of 3D Lattice-BGK: Boundaries, Accuracy, and a New Fast Relaxation Method
,”
J. Comput. Phys.
,
150
, pp.
482
501
.
28.
Watanabe, T., Ebihara, K., Ito, G., and Kohno, K., 2000, “Development of a Two-Phase Flow Simulation Code using the Lattice Boltzmann Method and Its Parallelization,” JAERI-Data/Code 2000-029.
29.
Levich, V. G., 1962, Physicochemical Hydrodynamics, Prentice Hall, N.J.
30.
Clift, R., Grace, J. R., and Weber, M. E., 1978, Bubbles, Drops, and Particles, Academic Press, New York.
31.
Crabtree
,
J. R.
, and
Bridgwater
,
J.
,
1971
, “
Bubble Coalescence in Viscous Liquids
,”
Chem. Eng. Sci.
,
26
, pp.
839
851
.
32.
Wallis, G. B., 1969, One-Dimensional Two-Phase Flow, McGraw-Hill, New York.
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