The liquid droplet size distribution in gas-liquid vertical upward annular flow is investigated through a CFD (computational fluid dynamics)-PBM (population balance model) coupled model in this paper. Two-fluid Eulerian scheme is employed as the framework of this model and a population balance equation is used to obtain the dispersed liquid droplet diameter distribution, where three different coalescence and breakup kernels are investigated. The Sauter mean diameter d32 is used as a bridge between a two-fluid model and a PBM. The simulation results suggest that the original Luo–Luo kernel and the mixed kernel A (Luo’s coalescence kernel incorporated with Prince and Blanch’s breakup kernel) can only give reasonable predictions for large diameter droplets. Mixed kernel B (Saffman and Turner’s coalescence kernel incorporated with Lehr’s breakup kernel) can accurately capture the particle size distribution (PSD) of liquid droplets covering all droplet sizes, and is appropriate for the description of liquid droplet size distribution in gas-liquid annular flow.

1.
Hay
,
K. J.
,
Liu
,
Z. -C.
, and
Hanratty
,
T. J.
, 1996, “
Relation of Deposition to Drop Size When the Rate Law is Nonlinear
,”
Int. J. Multiphase Flow
0301-9322,
22
(
5
), pp.
829
848
.
2.
Trabold
,
T. A.
, and
Kumar
,
R.
, 2000, “
High Pressure Annular Two-Phase Flow in a Narrow Duct: Part I—Local Measurements in the Droplet Field
,”
ASME J. Fluids Eng.
0098-2202,
122
(
2
), pp.
364
374
.
3.
Andreussi
,
P.
,
Romano
,
G.
, and
Zanelli
,
S.
, 1978, “
Drop Size Distribution in Annular Mist Flow
,”
Proceedings of the First Conference on Liquid Atomisation in Spray Systems
, Tokyo.
4.
Swithenbank
,
J.
,
Beer
,
J. M.
,
Taylor
,
D. S.
,
Abbot
,
D.
, and
McCreath
,
G. C.
, 1976, “
A Laser Diagnostic Technique for the Measurement of Droplet and Particle Size Distribution
,”
Experimental Diagnostics in Gas Phase Combustion Systems: AIAA Progress in Astroautics and Aeronautics
,
B. T.
Zinn
, ed.,
AIAA
,
New York
.
5.
Azzopardi
,
B. J.
, 1985, “
Drop Sizes in Annular Two-Phase Flow
,”
Exp. Fluids
0723-4864,
3
(
1
), pp.
53
59
.
6.
Combellack
,
J. H.
, and
Matthews
,
G. A.
, 1981, “
Droplet Spectra Measurements of Fan and Cone Atomisers Using a Laser Diffraction Technique
,”
J. Aerosol Sci.
0021-8502,
12
(
6
), pp.
529
540
.
7.
Watanabe
,
T.
, and
Ebihara
,
K.
, 2002, “
Numerical Simulation of Droplet Flows and Evaluation of Interfacial Area
,”
ASME J. Fluids Eng.
0098-2202,
124
(
3
), pp.
576
583
.
8.
Yu
,
Z.
,
Hemminger
,
O.
, and
Fan
,
L. S.
, 2007, “
Experiment and Lattice Boltzmann Simulation of Two-Phase Gas-Liquid Flows in Microchannels
,”
Chem. Eng. Sci.
0009-2509,
62
(
24
), pp.
7172
7183
.
9.
Hao
,
L.
, and
Cheng
,
P.
, 2009, “
Lattice Boltzmann Simulations of Liquid Droplet Dynamic Behavior on a Hydrophobic Surface of a Gas Flow Channel
,”
J. Power Sources
0378-7753,
190
(
2
), pp.
435
446
.
10.
Kim
,
L. S.
,
Jeong
,
H. K.
,
Ha
,
M. Y.
, and
Kim
,
K. C.
, 2008, “
Numerical Simulation of Droplet Formation in a Micro-Channel Using the Lattice Boltzmann Method
,”
J. Mech. Sci. Technol.
1738-494X,
22
(
4
), pp.
770
779
.
11.
Consolini
,
L.
,
Aggarwal
,
S. K.
, and
Murad
,
S.
, 2003, “
A Molecular Dynamics Simulation of Droplet Evaporation
,”
Int. J. Heat Mass Transfer
0017-9310,
46
(
17
), pp.
3179
3188
.
12.
Benson
,
C. M.
,
Zhong
,
J.
,
Gimelshein
,
S. F.
,
Levin
,
D. A.
, and
Montaser
,
A.
, 2003, “
Simulation of Droplet Heating and Desolvation in Inductively Coupled Plasma—Part II: Coalescence in the Plasma
,”
Spectrochim. Acta, Part B
0584-8547,
58
(
8
), pp.
1453
1471
.
13.
Chen
,
P.
,
Sanyal
,
J.
, and
Dudukovi
,
M. P.
, 2005, “
Numerical Simulation of Bubble Columns Flows: Effect of Different Breakup and Coalescence Closures
,”
Chem. Eng. Sci.
0009-2509,
60
(
4
), pp.
1085
1101
.
14.
Sanyal
,
J.
,
Marchisio
,
D. L.
,
Fox
,
R. O.
, and
Dhanasekharan
,
K.
, 2005, “
On the Comparison Between Population Balance Models for CFD Simulation of Bubble Columns
,”
Ind. Eng. Chem. Res.
0888-5885,
44
(
14
), pp.
5063
5072
.
15.
Wang
,
T.
, and
Wang
,
J.
, 2007, “
Numerical Simulations of Gas–Liquid Mass Transfer in Bubble Columns With a CFD–PBM Coupled Model
,”
Chem. Eng. Sci.
0009-2509,
62
(
24
), pp.
7107
7118
.
16.
Bhole
,
M. R.
,
Joshi
,
J. B.
, and
Ramkrishna
,
D.
, 2008, “
CFD Simulation of Bubble Columns Incorporating Population Balance Modeling
,”
Chem. Eng. Sci.
0009-2509,
63
(
8
), pp.
2267
2282
.
17.
Drumm
,
C.
,
Attarakih
,
M. M.
, and
Bart
,
H. -J.
, 2009, “
Coupling of CFD With DPBM for an RDC Extractor
,”
Chem. Eng. Sci.
0009-2509,
64
(
4
), pp.
721
732
.
18.
McCoy
,
B. J.
, 2001, “
A New Population Balance Model for Crystal Size Distributions: Reversible, Size-Dependent Growth and Dissolution
,”
J. Colloid Interface Sci.
0021-9797,
240
(
1
), pp.
139
149
.
19.
Wang
,
Q.
,
Luo
,
Z.
,
Ni
,
M.
, and
Cen
,
K.
, 2003, “
Particle Population Balance Model for a Circulating Fluidized Bed Boiler
,”
Chem. Eng. J.
0300-9467,
93
(
2
), pp.
121
133
.
20.
Liao
,
Y.
, and
Lucas
,
D.
, 2009, “
A Literature Review of Theoretical Models for Drop and Bubble Breakup in Turbulent Dispersions
,”
Chem. Eng. Sci.
0009-2509,
64
, pp.
3389
3406
.
21.
Coulaloglou
,
C. A.
, and
Tavlarides
,
L. L.
, 1977, “
Description of Interaction Processes in Agitated Liquid-Liquid Dispersions
,”
Chem. Eng. Sci.
0009-2509,
32
(
11
), pp.
1289
1297
.
22.
Prince
,
M. J.
, and
Blanch
,
H. W.
, 1990, “
Bubble Coalescence and Break-Up in Air-Sparged Bubble Columns
,”
AIChE J.
0001-1541,
36
(
10
), pp.
1485
1499
.
23.
Luo
,
H.
, and
Svendsen
,
H. F.
, 1996, “
Theoretical Model for Drop and Bubble Breakup in Turbulent Dispersions
,”
AIChE J.
0001-1541,
42
(
5
), pp.
1225
1233
.
24.
Lehr
,
F.
,
Millies
,
M.
, and
Mewes
,
D.
, 2002, “
Bubble-Size Distributions and Flow Fields in Bubble Columns
,”
AIChE J.
0001-1541,
48
(
11
), pp.
2426
2443
.
25.
Alipchenkov
,
V. M.
,
Nigmatulin
,
R. I.
,
Soloviev
,
S. L.
,
Stonik
,
O. G.
,
Zaichik
,
L. I.
, and
Zeigarnik
,
Y. A.
, 2004, “
A Three-Fluid Model of Two-Phase Dispersed-Annular Flow
,”
Int. J. Heat Mass Transfer
0017-9310,
47
(
24
), pp.
5323
5338
.
26.
Dorao
,
C. A.
,
Fernandino
,
M.
,
Patruno
,
L. E.
,
Dupuy
,
P. M.
,
Jakobsen
,
H. A.
, and
Svendsen
,
H. F.
, 2009, “
Macroscopic Description of Droplet–Film Interaction for Gas–Liquid Systems
,”
Appl. Math. Model.
0307-904X,
33
(
8
), pp.
3309
3318
.
27.
Ishii
,
M.
, and
Mishima
,
K.
, 1990, “
Droplet Entrainment Correlation in Annular Two-Phase Flow
,” Technical Report No. ANL/PPRNT-90-211, Argonne National Laboratory, IL.
28.
Pan
,
L.
, and
Hanratty
,
T. J.
, 2002, “
Correlation of Entrainment for Annular Flow in Horizontal Pipes
,”
Int. J. Multiphase Flow
0301-9322,
28
(
3
), pp.
385
408
.
29.
Sawant
,
P.
,
Ishii
,
M.
, and
Mori
,
M.
, 2008, “
Droplet Entrainment Correlation in Vertical Upward Co-Current Annular Two-Phase Flow
,”
Nucl. Eng. Des.
0029-5493,
238
(
6
), pp.
1342
1352
.
30.
Hancox
,
W. T.
,
Ferch
,
R. L.
,
Liu
,
W. S.
, and
Nieman
,
R. E.
, 1980, “
One-Dimensional Models for Transient Gas-Liquid Flows in Ducts
,”
Int. J. Multiphase Flow
0301-9322,
6
(
1–2
), pp.
25
40
.
31.
Kishore
,
B. N.
, and
Jayanti
,
S.
, 2004, “
A Multidimensional Model for Annular Gas–Liquid Flow
,”
Chem. Eng. Sci.
0009-2509,
59
(
17
), pp.
3577
3589
.
32.
Schiller
,
L.
, and
Naumann
,
Z.
, 1935, “
A Drag Coefficient Correlation
,”
Z. Ver. Dtsch. Ing.
0341-7255,
77
(
318
), pp.
318
320
.
33.
Fluent
, 2006, Fluent 6.3 User’s Guide, Fluent Inc., Lebanon.
34.
Hulburt
,
H. M.
, and
Katz
,
S.
, 1964, “
Some Problems in Particle Technology: A Statistical Mechanical Formulation
,”
Chem. Eng. Sci.
0009-2509,
19
(
8
), pp.
555
574
.
35.
Hounslow
,
M. J.
,
Ryall
,
R. L.
, and
Marshall
,
V. R.
, 1988, “
A Discretized Population Balance for Nucleation, Growth, and Aggregation
,”
AIChE J.
0001-1541,
34
(
11
), pp.
1821
1832
.
36.
Saffman
,
P. G.
, and
Turner
,
J. S.
, 1956, “
On the Collision of Drops in Turbulent Clouds
,”
J. Fluid Mech.
0022-1120,
1
(
1
), pp.
16
30
.
37.
Fore
,
L. B.
,
Ibrahim
,
B. B.
, and
Beus
,
S. G.
, 2002, “
Visual Measurements of Droplet Size in Gas–Liquid Annular Flow
,”
Int. J. Multiphase Flow
0301-9322,
28
(
12
), pp.
1895
1910
.
38.
Kocamustafaogullari
,
G.
,
Smits
,
S. R.
, and
Razi
,
J.
, 1994, “
Maximum and Mean Droplet Sizes in Annular Two-Phase Flow
,”
Int. J. Heat Mass Transfer
0017-9310,
37
(
6
), pp.
955
965
.
39.
Fore
,
L. B.
, and
Dukler
,
A. E.
, 1995, “
The Distribution of Drop Size and Velocity in Gas-Liquid Annular Flow
,”
Int. J. Multiphase Flow
0301-9322,
21
(
2
), pp.
137
149
.
You do not currently have access to this content.