The phase distribution and mechanical properties of annular flow have obvious, random characteristics because of the influence of turbulence. Thus, probability analysis is a suitable method for the study of annular flow. In the present work, the interchange rate and pressure gradient of fully developed annular flow are investigated in detail based on a probability model. The probability model tracks the atomization and deposition processes of a single particle to analyze the momentum and mass exchange between the gas and liquid phases. The interchange rate can be calculated by summing the generation or disappearance probability of droplets with different sizes. The pressure gradient can be obtained by solving the basic equations of the annular flow, which contains an improved relationship of interfacial shear stress. The predictions of the interchange rate and pressure gradient are well verified by comparison with experimental data available in the literature. Furthermore, the effects of the gas and liquid flow rates on the interchange rate and pressure gradient are discussed in detail.

References

1.
Schadel
,
S. A.
, and
Hanratty
,
T. J.
,
1989
, “
Interpretation of Atomization Rates of the Liquid Film in Gas-Liquid Annular Flow
,”
Int. J. Multiphase Flow
,
15
(
6
), pp.
893
900
.
2.
Sugawara
,
S.
,
1990
, “
Droplet Deposition and Entrainment Modeling Based on the Three-Fluid Model
,”
Nucl. Eng. Des.
,
122
(
1–3
), pp.
67
84
.
3.
Stevanovic
,
V.
, and
Studovic
,
M.
,
1995
, “
A Simple Model for Vertical Annular and Horizontal Stratified Two-Phase Flows With Liquid Entrainment and Phase Transitions: One-Dimensional Steady State Conditions
,”
Nucl. Eng. Des.
,
154
(
3
), pp.
357
379
.
4.
Holowach
,
M. J.
,
Hochreiter
,
L. E.
, and
Cheung
,
F. B.
,
2002
, “
A Model for Droplet Entrainment in Heated Annular Flow
,”
Int. J. Heat Fluid Flow
,
23
(
6
), pp.
807
822
.
5.
Okawa
,
T.
,
Kotani
,
A.
,
Kataoka
,
I.
, and
Naita
,
M.
,
2003
, “
Prediction of Critical Heat Flux in Annular Flow Using a Film Flow Model
,”
J. Nucl. Sci. Technol.
,
40
(
6
), pp.
388
396
.
6.
Anglart
,
H.
, and
Caraghiaur
,
D.
,
2011
, “
CFD Modeling of Boiling Annular-Mist Flow for Dryout Investigations
,”
Multiphase Sci. Technol.
,
23
(
2–4
), pp.
223
251
.
7.
Dallman
,
J. C.
,
Jones
,
B. G.
, and
Hanratty
,
T. J.
,
1979
, “
Interpretation of Entrainment Measurements in Annular Gas-Liquid Flow
,”
Two-Phase Momentum Heat and Mass Transfer
, Vol.
2, pp.
683
693
.
8.
Schadel
,
S. A.
,
Leman
,
G. W.
,
Binder
,
J. L.
, and
Hanratty
,
T. J.
,
1990
, “
Rates of Atomization and Deposition in Vertical Annular Flow
,”
Int. J. Multiphase Flow
,
16
(
3
), pp.
363
374
.
9.
Lopez de Bertodano
,
M. A.
,
Assad
,
A.
, and
Beus
,
S. G.
,
2001
, “
Experiments for Entrainment Rate of Droplets in the Annular Regime
,”
Int. J. Multiphase Flow
,
27
(
4
), pp.
685
699
.
10.
Baniamerian
,
Z.
, and
Aghanajafi
,
C.
,
2010
, “
Simulation of Entrainment Mass Transfer in Annular Two-Phase Flow Using the Physical Concept
,”
J. Mech.
,
26
(
3
), pp.
385
392
.
11.
Ishii
,
M.
, and
Mishima
,
K.
,
1989
, “
Droplet Entrainment Correlation in Annular Two-Phase Flow
,”
Int. J. Heat Mass Transfer
,
32
(
10
), pp.
1835
1846
.
12.
Utsuno
,
H.
, and
Kaminaga
,
F.
,
1998
, “
Prediction of Liquid Film Dryout in Two-Phase Annular-Mist Flow in a Uniformly Heated Narrow Tube Development of Analytical Method Under BWR Conditions
,”
J. Nucl. Sci. Technol.
,
35
(
9
), pp.
643
653
.
13.
Kataoka
,
I.
,
Ishii
,
M.
, and
Nakayama
,
A.
,
2000
, “
Entrainment and Deposition Rates of Droplets in Annular Two-Phase Flow
,”
Int. J. Heat Mass Transfer
,
43
(
9
), pp.
1573
1589
.
14.
Liu
,
Y.
,
Li
,
W. Z.
, and
Quan
,
S. L.
,
2011
, “
A Self-Standing Two-Fluid CFD Model for Vertical Upward Two-Phase Annular Flow
,”
Nucl. Eng. Des.
,
241
(
5
), pp.
1636
1642
.
15.
Hughmark
,
G. A.
,
1973
, “
Film Thickness, Entrainment, and Pressure Drop in Upward Annular and Dispersed Flow
,”
AIChE J.
,
19
(
5
), pp.
1062
1065
.
16.
Kulov
,
N. N.
,
Maksimov
,
V. V.
,
Maljusov
,
V. A.
, and
Zhavoronkov
,
N. M.
,
1979
, “
Pressure Drop, Mean Film Thickness and Entrainment in Downward Two-Phase Flow
,”
Chem. Eng. J.
,
18
(
2
), pp.
183
188
.
17.
Asali
,
J. C.
,
Leman
,
G. W.
, and
Hanratty
,
T. J.
,
1985
, “
Entrainment Measurements and Their Use in Design Equations
,” PhysicoChem.
Hydrodyn.
,
6
(1–2), pp.
207
221
.
18.
Fukano
,
T.
, and
Furukawa
,
T.
,
1998
, “
Prediction of the Effects of Liquid Viscosity on Interfacial Shear Stress and Fricational Pressure Drop in Vertical Upward Gas Liquid Annular Flow
,”
Int. J. Multiphase Flow
,
24
(
4
), pp.
587
603
.
19.
Saito
,
T.
,
Hughes
,
E. D.
, and
Carbon
,
M. W.
,
1978
, “
Multi-Fluid Modeling of Annular Two-Phase Flow
,”
Nucl. Eng. Des.
,
50
(
2
), pp.
225
271
.
20.
Kishore
,
B. N.
, and
Jayanti
,
S.
,
2004
, “
A Multidimensional Model for Annular Gas-Liquid Flow
,”
Chem. Eng. Sci.
,
59
(
17
), pp.
3577
3589
.
21.
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
,
47
(
24
), pp.
5323
5338
.
22.
Schubring
,
D.
, and
Shedd
,
T. A.
,
2011
, “
A Model for Pressure Loss, Film Thickness, and Entrained Fraction for Gas-Liquid Annular Flow
,”
Int. J. Heat Fluid Flow
,
32
(
3
), pp.
730
739
.
23.
Li
,
H. W.
,
Wong
,
T. N.
,
Skote
,
M.
, and
Duan
,
F.
,
2013
, “
A Simple Model for Predicting the Pressure Drop and Film Thickness of Non-Newtonian Annular Flows in Horizontal Pipes
,”
Chem. Eng. Sci.
,
102
, pp.
121
128
.
24.
Zhang
,
R.
,
Liu
,
H. X.
, and
Liu
,
M. Y.
,
2015
, “
A Probability Model for Fully Developed Annular Flow in Vertical Pipes: Prediction of the Droplet Entrainment
,”
Int. J. Heat Mass Transfer
,
84
, pp.
225
236
.
25.
Zhang
,
R.
,
Liu
,
H. X.
,
Dong
,
S.
, and
Liu
,
M. Y.
,
2017
, “
A Probability Model for Fully Developed Annular Flow in Vertical Pipes: Film Thickness, Interfacial Shear Stress, and Droplet Size Distribution
,”
ASME J. Heat Transfer
,
139
(
3
), p. 032001.
26.
Cousins
,
L. B.
,
Denton
,
W. H.
, and
Hewitt
,
G. F.
,
1965
, “
Liquid Mass Transfer in Annular Two-Phase Flow
,” Harwell, Exeter, UK, UKAEA Report, AERE Report No. 4926.
27.
Cousins
,
L. B.
, and
Hewitt
,
G. F.
,
1968
, “
Liquid Phase Mass Transfer in Annular Two-Phase Flow: Droplet Deposition and Liquid Entrainment
,” Harwell, Exeter, UK, UKAEA Report, AERE Report No. 5657.
28.
Asali
,
J. C.
,
1984
, “
Entrainment in Vertical Gas-Liquid Annular Flows
,” Ph.D. thesis, University of Illinois at Urbana-Champaign, Urbana, IL.
29.
Fore
,
L. B.
, and
Dukler
,
A. E.
,
1995
, “
Droplet Deposition and Momentum Transfer in Annular Flow
,”
AIChE J.
,
41
(
9
), pp.
2040
2046
.
30.
Alamu
,
M. B.
, and
Azzopardi
,
B. J.
,
2011
, “
Simultaneous Investigation of Entrained Liquid Fraction, Liquid Film Thickness and Pressure Drop in Vertical Annular Flow
,”
ASME J. Energy Resour. Technol.
,
133
(
2
), p.
023103
.
You do not currently have access to this content.