Slug flow is an essential flow pattern observed in microchannels where its transition boundaries in microchannels are characterized by two complex hydrodynamic phenomena, the bubble confinement and the bubble coalescence. Slug flow may be classified in terms of bubble size into two major zones: isolated bubble zone and coalescence bubble zone. In this paper, a semi-analytical model is developed for predicting the main characteristics of isolated bubble zone for flow boiling in a horizontal microchannel. The influences of surface tension, shear, and inertial forces have been taken into account. The model is developed on the basis of drift flux model, and a fully developed slug unit is chosen as a control volume for deriving the equations of motion. The effects of main operating conditions, mass and heat fluxes, on bubble length and bubble frequency have been investigated. The boundaries of slug flow regime have been identified based on the most proper diabatic flow pattern maps available in the literature for the chosen database. The model has been validated using the database available in the literature for flow boiling of R134a and R245fa in 0.509 mm and 3.0 mm inner diameter horizontal mini-tubes, respectively, and over wide range of mass fluxes (300G1000kg/m2s). This study has shown that the mass flux has a significant effect on the slug length and the bubble frequency. The model gave a good agreement with the experimental data of bubble length and bubble frequency with a mean absolute error (MAE) of 18.0% and 27.34%, respectively.

References

References
1.
Triplett
,
K. A.
,
Ghiaasiaan
,
S. M.
,
Abdel-Khalik
,
S. I.
, and
Sadowski
,
D. L.
,
1999
, “
Gas–Liquid Two-Phase Flow in Microchannels—Part I: Two-Phase Flow Patterns
,”
Int. J. Multiphase Flow
,
25
(
3
), pp.
377
394
.
2.
Garimella
,
S.
,
Killion
,
J. D.
, and
Coleman
,
J. W.
,
2002
, “
An Experimentally Validated Model for Two-Phase Pressure Drop in the Intermittent Flow Regime for Circular Microchannels
,”
ASME J. Fluids Eng.
,
124
(
1
), pp.
205
214
.
3.
Lee
,
P. C.
,
Tseng
,
F. G.
, and
Pan
,
C.
,
2004
, “
Bubble Dynamics in Microchannels—Part I: Single Microchannel
,”
Int. J. Heat Mass Transfer
,
47
(
25
), pp.
5575
5589
.
4.
Revellin
,
R.
,
Dupont
,
V.
,
Ursenbacher
,
T.
,
Thome
,
J. R.
, and
Zun
,
I.
,
2006
, “
Characterization of Diabatic Two-Phase Flows in Microchannels: Flow Parameter Results for R-134a in a 0.5 mm Channel
,”
Int. J. Multiphase Flow
,
32
(
7
), pp.
755
774
.
5.
Saisorn
,
S.
, and
Wongwises
,
S.
,
2008
, “
Flow Pattern, Void Fraction and Pressure Drop of Two-Phase Air–Water Flow in a Horizontal Circular Micro-Channel
,”
Exp. Therm. Fluid Sci.
,
32
(
3
), pp.
748
760
.
6.
Fu
,
X.
,
Zhang
,
P.
,
Huang
,
C. J.
, and
Wang
,
R. Z.
,
2010
, “
Bubble Growth, Departure and the Following Flow Pattern Evolution During Flow Boiling in a Mini-Tube
,”
Int. J. Heat Mass Transfer
,
53
(
21–22
), pp.
4819
4831
.
7.
Charnay
,
R.
,
Revellin
,
R.
, and
Bonjour
,
J.
,
2013
, “
Flow Pattern Characterization for R-245fa in Minichannels: Optical Measurement Technique and Experimental Results
,”
Int. J. Multiphase Flow
,
57
, pp.
169
181
.
8.
Qian
,
D.
, and
Lawal
,
A.
,
2006
, “
Numerical Study on Gas and Liquid Slugs for Taylor Flow in a T-Junction Microchannel
,”
Chem. Eng. Sci.
,
61
(
23
), pp.
7609
7625
.
9.
He
,
Q.
, and
Kasagi
,
N.
,
2008
, “
Numerical Investigation on Flow Pattern and Pressure Drop
,”
ASME
Paper No. ICNMM2008-62225.
10.
Zhuan
,
R.
, and
Wang
,
W.
,
2012
, “
Flow Pattern of Boiling in Micro-Channel by Numerical Simulation
,”
Int. J. Heat Mass Transfer
,
55
(
5–6
), pp.
1741
1753
.
11.
Magnini
,
M.
,
Pulvirenti
,
B.
, and
Thome
,
J. R.
,
2013
, “
Numerical Investigation of Hydrodynamics and Heat Transfer of Elongated Bubbles During Flow Boiling in a Microchannel
,”
Int. J. Heat Mass Transfer
,
59
(
1
), pp.
451
471
.
12.
Moriyama
,
K.
, and
Inoue
,
A.
, and
Ohira
,
H.
,
1992
, “
The Thermo Hydraulic Characteristics of Two-Phase Flow in Extremely Narrow Channels
,”
J. Heat Transfer-Jpn. Res.
,
21
(
8
), pp.
838
856
.
13.
Abiev
,
R. S.
,
2008
, “
Simulation of the Slug Flow of a Gas–Liquid System in Capillaries
,”
Theor. Found. Chem. Eng.
,
42
(
2
), pp.
105
117
.
14.
Consolini
,
L.
, and
Thome
,
J. R.
,
2010
, “
A Heat Transfer Model for Evaporation of Coalescing Bubbles in Micro-Channel Flow
,”
Int. J. Heat Fluid Flow
,
31
(
1
), pp.
115
125
.
15.
Cooper
,
M.
,
1969
, “
The Microlayer and Bubble Growth in Nucleate Pool Boiling
,”
Int. J. Heat Mass Transfer
,
12
(
8
), pp.
915
933
.
16.
Mikic
,
B. B.
,
Rohsenow
,
W. M.
, and
Griffith
,
P.
,
1970
, “
On Bubble Growth Rates
,”
Int. J. Heat Mass Transfer
,
13
(
4
), pp.
657
666
.
17.
Jacobi
,
A. M.
, and
Thome
,
J. R.
,
2002
, “
Heat Transfer Model for Evaporation of Elongated Bubble Flows in Micro Channels
,”
ASME J. Heat Transfer
,
124
(
6
), pp.
1131
1136
.
18.
Mehta
,
B.
, and
Khandekar
,
S.
,
2014
, “
Measurement of Local Heat Transfer Coefficient During Gas–Liquid Taylor Bubble Train Flow by Infra-Red Thermography
,”
Int. J. Heat Fluid Flow
,
45
(
1
), pp.
41
52
.
19.
Patil
,
C. M.
, and
Kandlikar
,
S. G.
,
2014
, “
Pool Boiling Enhancement Through Microporous Coatings Selectively Electrodeposited on Fin Tops of Open Microchannels
,”
Int. J. Heat Mass Transfer
,
79
, pp.
816
828
.
20.
Tibiriçá
,
C.
, and
Ribatski
,
G.
,
2014
, “
Flow Patterns and Bubble Departure Fundamental Characteristics During Flow Boiling in Microscale Channels
,”
Exp. Therm. Fluid Sci.
,
59
, pp.
152
165
.
21.
Houshmand
,
F.
, and
Peles
,
Y.
,
2014
, “
Transient Wall Temperature Measurements of Two-Phase Slug Flow in a Microchannel
,”
Thermomechanical Phenomena in Electronic Systems, Intersociety Conference
, New York, pp.
1215
1221
.
22.
Yan
,
C.
,
Yan
,
C.
,
Sun
,
L.
,
Wang
,
Y.
, and
Zhang
,
X.
,
2014
, “
Slug Behavior and Pressure Drop of Adiabatic Slug Flow in a Narrow Rectangular Duct Under Inclined Conditions
,”
Ann. Nucl. Energy
,
64
, pp.
21
31
.
23.
Bretherton
,
F. P.
,
1961
, “
The Motion of Long Bubbles in Tubes
,”
J. Fluid Mech.
,
10
(
2
), pp.
166
188
.
24.
Fukano
,
T.
,
Kariyasaki
,
A.
, and
Kagawa
,
M.
,
1989
, “
Flow Patterns and Pressure Drop in Isothermal Gas–Liquid Concurrent Flow in a Horizontal Capillary Tube
,”
ANS Proceedings 1989 National Heat Transfer Conference
, Philadelphia, PA, Aug. 6–9, pp.
153
161
.
25.
Abiev
,
R.
,
2010
, “
Method for Calculating the Void Fraction and Relative Length of Bubbles Under Slug Flow Conditions in Capillaries
,”
Theor. Found. Chem. Eng.
,
44
(
1
), pp.
86
101
.
26.
Wallis
,
B. G.
,
1969
,
One-Dimensional Two-Phase Flow
,
McGraw-Hill
,
New York
.
27.
Warnier
,
M. J. F.
,
De Croon
,
M. H. J. M.
,
Rebrov
,
E. V.
, and
Schouten
,
J. C.
,
2010
, “
Pressure Drop of Gas–Liquid Taylor Flow in Round Micro-Capillaries for Low to Intermediate Reynolds Numbers
,”
Microfluid. Nanofluid.
,
8
(
1
), pp.
33
45
.
28.
Suo
,
M.
, and
Griffith
,
P.
,
1963
,
Two-Phase Flow in Capillary Tubes
,
Air Force Office of Scientific Research (OAR)
,
Cambridge, MA
.
29.
Zhang
,
P.
, and
Fu
,
X.
,
2009
, “
Two-Phase Flow Characteristics of Liquid Nitrogen in Vertically Upward 0.5 and 1.0 mm Micro-Tubes: Visualization Studies
,”
Cryogenics
,
49
(
10
), pp.
565
575
.
30.
Kandlikar
,
S.
,
2010
, “
Scale Effects on Flow Boiling Heat Transfer in Microchannels: A Fundamental Perspective
,”
Int. J. Therm. Sci.
,
49
(
7
), pp.
1073
1085
.
31.
Ong
,
C. L.
, and
Thome
,
J. R.
,
2011
, “
Macro-to-Microchannel Transition in Two-Phase Flow—Part 1: Two-Phase Flow Patterns and Film Thickness Measurements
,”
Exp. Therm. Fluid Sci.
,
35
(
1
), pp.
37
47
.
32.
Chung
,
P. M.-Y.
, and
Kawaji
,
M.
,
2004
, “
The Effect of Channel Diameter on Adiabatic Two-Phase Flow Characteristics in Microchannels
,”
Int. J. Multiphase Flow
, 30(7–8), pp.
735
761
.
33.
Bonnecaze
,
R. H.
,
Erskine
,
W.
, Jr.
, and
Greskovich
,
E. J.
,
1971
, “
Holdup and Pressure Drop for Two-Phase Slug Flow in Inclined Pipelines
,”
AIChE J.
,
17
(
5
), pp.
1109
1113
.
34.
Liu
,
H.
,
Vandu
,
C. O.
, and
Krishna
,
R.
,
2005
, “
Hydrodynamics of Taylor Flow in Vertical Capillaries: Flow Regimes, Bubble Rise Velocity, Liquid Slug Length, and Pressure Drop
,”
Ind. Eng. Chem. Res.
,
44
(
14
), pp.
4884
4897
.
35.
Kreutzer
,
M. T.
,
Kapteijn
,
F.
,
Moulijn
,
J. A.
, and
Heiszwolf
,
J. J.
,
2005
, “
Multiphase Monolith Reactors: Chemical Reaction Engineering of Segmented Flow in Microchannels
,”
Chem. Eng. Sci.
,
60
(
22
), pp.
5895
5916
.
36.
Walsh
,
E.
,
Muzychka
,
Yu.
,
Walsh
,
P.
,
Egan
,
V.
, and
Punch
,
J.
,
2009
, “
Pressure Drop in Two Phase Slug/Bubble Flows in Mini Scale Capillaries
,”
Int. J. Multiphase Flow
,
35
(
10
), pp.
879
884
.
37.
Abiev
,
R. S.
,
2011
, “
Modeling of Pressure Losses for the Slug Flow of a Gas–Liquid Mixture in Mini- and Microchannels
,”
Theor. Found. Chem. Eng.
,
45
(
2
), pp.
156
163
.
38.
Mac Giolla Eain
,
M.
,
Egan
,
V.
,
Howard
,
J.
,
Walsh
,
P.
,
Walsh
,
E.
, and
Punch
,
J.
,
2015
, “
Review and Extension of Pressure Drop Models Applied to Taylor Flow Regimes
,”
Int. J. Multiphase Flow
,
68
, pp.
1
9
.
39.
Gaakeer
,
W. A.
,
de Croon
,
M. H. J. M.
,
van der Schaaf
,
J.
, and
Schouten
,
J. C.
,
2012
, “
Liquid–Liquid Slug Flow Separation in a Slit Shaped Micro Device
,”
Chem. Eng. J.
,
207–208
, pp.
440
444
.
40.
Fowkes
,
F.
,
1964
, “
Attractive Forces at the Interaces
,”
Ind. Eng. Chem.
,
56
(
12
), pp.
40
52
.
41.
Kandlikar
,
S.
,
2006
, “
Effect of Liquid–Vapor Phase Distribution on the Heat Transfer Mechanisms During Flow Boiling in Minichannels and Microchannels
,”
Heat Transfer Eng.
,
27
(
1
), pp.
4
13
.
42.
Marchand
,
A.
,
Weijs
,
J. H.
,
Snoeijer
,
J. H.
, and
Andreotti
,
B.
,
2011
, “
Why is Surface Tension a Force Parallel to the Interface?
Am. J. Phys.
,
79
(
10
), pp.
999
1008
.
43.
Singh
,
J. K.
, and
Kwak
,
S. K.
,
2007
, “
Surface Tension and Vapor–Liquid Phase Coexistence of Confined Square-Well Fluid
,”
J. Chem. Phys.
,
126
(
2
), p.
24702
.
44.
Ashbaugh
,
H.
,
2009
, “
Blowing Bubbles in Lennard–Jonesium Along the Saturation Curve
,”
J. Chem. Phys.
,
130
(
20
), p.
204517
.
45.
Bratland
,
O.
,
2010
, “Pipe Flow2 Multi-Phase Flow Assurance,”
Dr. Ove Brantland Flow Assurance Consulting
, Norway.
46.
Gelb
,
L. D.
,
Gubbins
,
K. E.
,
Radhakrishnan
,
R.
, and
Sliwinska-Bartkowiak
,
M.
,
1999
, “
Phase Separation in Confined Systems
,”
Rep. Prog. Phys.
,
62
(
12
), pp.
1573
1659
.
47.
Santos
,
R. M.
, and
Kawaji
,
M.
,
2012
, “
Developments on Wetting Effects in Microfluidic Slug Flow
,”
Chem. Eng. Commun.
,
199
(
12
), pp.
1626
1641
.
48.
Alam
,
T.
,
Li
,
W.
,
Yang
,
F.
,
Chang
,
W.
,
Li
,
J.
,
Wang
,
Z.
,
Khan
,
J.
, and
Li
,
C.
,
2016
, “
Force Analysis and Bubble Dynamics During Flow Boiling in Silicon Nanowire Microchannels
,”
Int. J. Heat Mass Transfer
,
101
, pp.
915
926
.
49.
Li
,
W.
, and
Wu
,
Z.
,
2010
, “
A General Correlation for Adiabatic Two-Phase Pressure Drop in Micro/Mini-Channels
,”
Int. J Heat Mass Transfer
,
53
(
13–14
), pp.
2732
2739
.
50.
Churchil
,
S. W.
,
1977
, “
Friction-Factor Equation Spans All Fluid-Flow Regimes
,”
Chem. Eng.
,
84
(
24
), pp.
91
92
.
51.
Gregory
,
G. A.
,
Nicholson
,
M. K.
, and
Aziz
,
K.
,
1978
, “
Correlation of the Liquid Volume Fraction in the Slug for Horizontal Gas-Liquid Slug Flow
,”
Int. J. Multiphase Flow
,
4
(
1
), pp.
33
39
.
52.
Orell
,
A.
, and
Rembrand
,
R.
,
1986
, “
A Model for Gas–Liquid Slug Flow in a Vertical Tube
,”
Ind. Eng. Chem., Fundam.
,
25
(
2
), pp.
196
206
.
53.
McAdams
,
W. H.
,
Woods
,
W. K.
, and
Heroman
,
L. C.
, Jr.
,
1942
, “
Vaporization Inside Horizontal Tubes—II: Benzene-Oil Mixtures
,”
Trans. ASME
,
64
(
3
), pp.
193
200
.
54.
Akers
,
W. W.
,
Deans
,
H. A.
, and
Crosser
,
O. K.
,
1959
, “
Condensing Heat Transfer Within Horizontal Tubes
,”
Chem. Eng. Prog. Symp. Ser.
,
55
(
29
), pp.
171
176
.
55.
Cicchitti
,
A.
,
Lombardi
,
C.
,
Silvestri
,
M.
,
Soldaini
,
G.
, and
Zavattarelli
,
R.
,
1959
,
Two-Phase Cooling Experiments: Pressure Drop, Heat Transfer and Burnout Measurements
,
Centro Informazioni Studi Esperienze
,
Milan, Italy
.
56.
Dukler
,
A. E.
,
Moye
,
Wicks
, III
, and
Cleveland
,
R. G.
,
1964
, “
Frictional Pressure Drop in Two-Phase Flow—B: An Approach Through Similarity Analysis
,”
AIChE J.
,
10
(
1
), pp.
44
51
.
57.
Beattie
,
D. R. H.
, and
Whalley
,
P. B.
,
1982
, “
A Simple Two-Phase Frictional Pressure Drop Calculation Method
,”
Int. J. Multiphase Flow
,
8
(
1
), pp.
83
87
.
58.
Lin
,
S.
,
Kwok
,
C. C. K.
,
Li
,
R.-Y.
,
Chen
,
Z.-H.
, and
Chen
,
Z.-Y.
,
1991
, “
Local Frictional Pressure Drop During Vaporization of R-12 Through Capillary Tubes
,”
Int. J. Multiphase Flow
,
17
(
1
), pp.
95
102
.
59.
Fukano
,
T.
, and
Kariyasaki
,
A.
,
1993
, “
Characteristics of Gas–Liquid Two-Phase Flow in a Capillary Tube
,”
Nucl. Eng. Des.
,
141
(
1–2
), pp.
59
68
.
60.
Mishima
,
K.
, and
Hibiki
,
T.
,
1996
, “
Some Characteristics of Air–Water Two-Phase Flow in Small Diameter Vertical Tubes
,”
Int. J. Multiphase Flow
,
22
(
4
), pp.
703
712
.
61.
Chen
,
W. L.
,
Twu
,
M. C.
, and
Pan
,
C.
,
2002
, “
Gas–Liquid Two-Phase Flow in Micro-Channels
,”
Int. J. Multiphase Flow
,
28
(
7
), pp.
1235
1247
.
62.
Nicklin
,
D. J.
,
Wilkes
,
J. O.
, and
Davidson
,
J. F.
,
1962
, “
Two-Phase Flow in Vertical Tubes
,”
Inst. Chem. Eng. Trans.
,
40
(
1
), pp.
61
68
.
63.
Mattar
,
L.
, and
Greygory
,
G. A.
,
1974
, “
Air–Oil Slug Flow In an Upward-Inclined Pipe—I: Slug Velocity, Holdup And Pressure Gradient
,”
J. Can. Pet. Technol.
,
13
(
1
), pp.
1
8
.
64.
Ishii
,
M.
,
1977
, “
One-Dimensional Drift-Flux Model and Constitutive Equations for Relative Motion Between Phases in Various Two-Phase Flow Regimes
,”
Argonne National Laboratory, Argonne, Illinois
.
65.
Mishima
,
K.
, and
Hibiki
,
T.
,
1996
, “
Some Characteristics of Air–Water Two-Phase Flow in Small Diameter Vertical Tubes
,”
Int. J. Multiphase Flow
,
22
(
4
), pp.
703
712
.
66.
Barnea
,
D.
, and
Brauner
,
N.
,
1985
, “
Holdup of the Liquid Slug in Two Phase Intermittent Flow
,”
Int. J. Multiphase Flow
,
11
(
1
), pp.
43
49
.
67.
Taitel
,
Y.
,
Saricab
,
C.
, and
Bril
,
J. P.
,
2000
, “
Slug Flow Modeling for Downward Inclined Pipe Flow: Theoretical Considerations
,”
Int. J. Multiphase Flow
,
26
(
5
), pp.
833
844
.
68.
Hetsroni
,
G.
,
Mosyak
,
A.
,
Pogrebnyak
,
E.
, and
Segal
,
Z.
,
2006
, “
Periodic Boiling in Parallel Micro-Channels at Low Vapor Quality
,”
Int. J. Multiphase Flow
,
32
(
10
), pp.
1141
1159
.
69.
Shen, V. K., Siderius, D. W., Krekelberg, W. P., and Hatch, H. W., eds.
,
2011
, “
NIST Standard Reference Simulation Website, NIST Standard Reference Database Number 173
,” National Institute of Standards and Technology, Gaithersburg, MD, accessed Jan. 7, 2015, http://webbook.nist.gov/chemistry/fluid
70.
Revellin
,
R.
, and
Thome
,
J. R.
,
2007
, “
A New Type of Diabatic Flow Pattern Map for Boiling Heat Transfer in Microchannels
,”
J. Micromech. Microeng.
,
17
(
4
), pp.
788
796
.
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