A theoretical analysis was carried out to predict the influences of wall inclination angles of large reservoirs on the onset of gas entrainment during single and dual discharges from a stratified two-phase region. The findings reveal that when the wall inclination angle differs from zero, along with low values of Froude number, two distinct flow regimes occur: the gas-entrainment and no gas-entrainment regimes. A new criterion has been developed to predict the critical Froude number at the transition from the gas-entrainment to the no-gas-entrainment regime. The critical Froude number is defined as a function of the wall inclination angle for a single discharge. For dual discharge, the critical Froude number is found to be dependent on the wall inclination angle, the separating distance between the centerlines of the two branches, as well as the Froude number of the second branch. Furthermore, four different flow regions are mapped, representing the flow regime, as well as the two-phase flow for each branch. These maps serve to predict the flow regions, mass flow rates, and quality during single and dual two-phase discharges. For the gas-entrainment regime, the predicted values of the critical height at the onset of gas entrainment are compared with the experimental data reported in literatures. Comparisons showed good concurrence between the measured and predicted results. Furthermore, the influence of the wall inclination angle on the flow regions, the predicted critical height, and the location of the gas entrainment are presented and discussed at different values of independent variables.

1.
Zuber
,
N.
, 1980, “
Problems in Modeling of Small Breaks LOCA
,” Nuclear Regulatory Commission, Report No. NUREG–0724.
2.
Smoglie
,
C.
, and
Reimann
,
J.
, 1986, “
Two-Phase Flow Through Small Breaks in a Horizontal Pipe With Stratified Flow
,”
Int. J. Multiphase Flow
0301-9322,
12
, pp.
609
625
.
3.
Schrock
,
V. E.
,
Revankar
,
S. T.
,
Mannheimer
,
R.
,
Wang
,
C. H.
, and
Jia
,
D.
, 1986, “
Steam-Water Critical Flow Through Small Pipes From Stratified Upstream Regions
,”
Proceeding of the Eighth International Heat Transfer Conference
,
San Francisco, CA
, Vol.
5
, pp.
2307
2311
.
4.
Yonomoto
,
T.
, and
Tasaka
,
K.
, 1988, “
New Theoretical Model for Two-Phase Flow Discharged From Stratified Two-Phase Region Through Small Break
,”
J. Nucl. Sci. Technol.
0022-3131,
25
, pp.
441
455
.
5.
Yonomoto
,
T.
, and
Tasaka
,
K.
, 1991, “
Liquid and Gas-Entrainment to a Small Break Hole From a Stratified Two-Phase Region
,”
Int. J. Multiphase Flow
0301-9322,
17
, pp.
745
765
.
6.
Micaelli
,
J. C.
, and
Memponteil
,
A.
, 1989, “
Two-Phase Flow Behavior in a Tee-Junction—The Cathare Model
,”
Proceedings of the Fourth International Topical Meeting on Nuclear Reactor Thermal-Hydraulics
,
Karlsruhe, Germany
, Oct. 10–13, Vol.
2
, pp.
1024
1030
.
7.
Hassan
,
I. G.
,
Soliman
,
H. M.
,
Sims
,
G. E.
, and
Kowalski
,
J. E.
, 1998, “
Two-Phase Flow From a Stratified Region Through a Small Side Branch
,”
J. Fluids Eng.
0098-2202,
120
, pp.
605
612
.
8.
Xue
,
M.
, and
Yue
,
D. P.
, 1998, “
Nonlinear Free Surface Flow Due to an Impulsively Started Submerged Point Sink
,”
J. Fluid Mech.
0022-1120,
364
, pp.
325
347
.
9.
Miloh
,
T.
, and
Tyvand
,
P. A.
, 1993, “
Nonlinear Transient Free Surface Flow and Dip Formation Due to Point Sink
,”
Phys. Fluids A
0899-8213,
5
(
6
), pp.
1368
1375
.
10.
Lubin
,
B. T.
, and
Springer
,
G. S.
, 1966, “
The Formation of a Dip on the Surface of a Liquid Draining From a Tank
,”
J. Fluid Mech.
0022-1120,
29
, pp.
385
390
.
11.
Zhou
,
Q. N.
, and
Graebel
,
W. P.
, 1990, “
Axisymmetric Draining of a Cylindrical Tank With a Free Surface
,”
J. Fluid Mech.
0022-1120,
221
, pp.
511
532
.
12.
Haugen
,
K. B.
, and
Tyvand
,
P. A.
, 2003, “
Free Surface Evolution Due to an Impulsive Bottom Sink at Uniform Depth
,”
Phys. Fluids
1070-6631,
15
(
3
), pp.
742
751
.
13.
Forbes
,
L. K.
, and
Hocking
,
G. C.
, 2005, “
Flow Due to a Sink Near a Vertical Wall in Infinitely Deep Fluid
,”
Comput. Fluids
0045-7930,
34
, pp.
684
704
.
14.
Forbes
,
L. K.
, and
Hocking
,
G. C.
, 2003, “
On the Computation of Steady Axisymmetric Withdrawal From a Two-Layer Fluid
,”
Comput. Fluids
0045-7930,
32
, pp.
385
401
.
15.
Forbes
,
L. K.
, and
Hocking
,
G. C.
, 1998, “
Withdrawal From a Two-Layer Inviscid Fluid in a Duct
,”
J. Fluid Mech.
0022-1120,
361
, pp.
275
296
.
16.
Vanden Broeck
,
J.-M.
, and
Keller
,
J. B.
, 1997, “
An Axisymmetric Free Surface With a 120Degree Angle Along a Circle
,”
J. Fluid Mech.
0022-1120,
342
, pp.
403
409
.
17.
Vanden Broeck
,
J.-M.
, and
Keller
,
J. B.
, 1987, “
Free Surface Flow Due to a Sink
,”
J. Fluid Mech.
0022-1120,
175
, pp.
109
117
.
18.
Ahmed
,
M.
,
Hassan
,
I.
, and
Esmail
,
N.
, 2003, “
Modeling of the Onset of Gas Entrainment Through a Finite-Side Branch
,”
ASME J. Fluids Eng.
0098-2202,
125
, pp.
902
909
.
19.
Ahmed
,
M.
,
Hassan
,
I.
, and
Esmail
,
N.
, 2004, “
Theoretical Analysis of the Onset of Gas Entrainment From a Stratified Region Through a Single-Oriented Branch at Moderate Froude Numbers
,”
Can. J. Chem. Eng.
0008-4034,
82
(
6
), pp.
1175
1182
.
20.
Parrott
,
S. D.
,
Soliman
,
H. M.
,
Sims
,
G. E.
, and
Krishnan
,
V. S.
, 1991, “
Experiments on the Onset of Gas Pull-Through During Dual Discharge From a Reservoir
,”
Int. J. Multiphase Flow
0301-9322,
17
, pp.
119
129
.
21.
Parrott
,
S. D.
, 1993, “
Experiments on the Onsets of Gas Pull-Through and Liquid Entrainment During Dual Discharge From a Large Reservoir
,” MS thesis, University of Manitoba, Winnipeg, MB, Canada.
22.
Hassan
,
I. G.
, 1995, “
Single, Dual and Triple Discharge From a Large Stratified, Two Phase Region Through Small Branches
,” Ph.D. thesis, University of Manitoba, Winnipeg, MB, Canada.
23.
Maier
,
M. R.
,
Soliman
,
H. M.
,
Sims
,
G. E.
, and
Armstrong
,
K. F.
, 2001, “
Onsets of Entrainment During Dual Discharge From a Stratified Two-Phase Region Through Horizontal Branches With Centerlines Falling in an Inclined Plane: Part 1. Analysis of Liquid Entrainment
,”
Int. J. Multiphase Flow
0301-9322,
27
, pp.
1011
1028
.
24.
Maier
,
M. R.
,
Soliman
,
H. M.
,
Sims
,
G. E.
, and
Armstrong
,
K. F.
, 2001, “
Onsets of Entrainment During Dual Discharge From a Stratified Two-Phase Region Through Horizontal Branches With Centerlines Falling in an Inclined Plane: Part 2. Experiments on Gas and Liquid Entrainment
,”
Int. J. Multiphase Flow
0301-9322,
27
, pp.
1029
1049
.
25.
Maier
,
M. R.
, 1998, “
Onsets of Entrainment During Dual Discharge From a Stratified Two-Phase Region Through Horizontal Branches With Centerlines Falling in an Inclined Plane
,” MS thesis, University of Manitoba, Winnipeg, MB, Canada.
26.
Ahmed
,
M.
,
Hassan
,
I.
, and
Esmail
,
N.
, 2004, “
The Onset of Gas Pull-Through During Dual Discharge From Stratified Two-Phase Region-Theoretical Analysis
,”
Phys. Fluids
1070-6631,
16
(
9
), pp.
3385
3392
.
27.
Ahmed
,
M.
, 2006, “
Theoretical Analysis of the Onset of Gas-Entrainment From a Stratified Two-Phase Region Through Two Side Oriented Branches Mounted on a Vertical Wall
,”
ASME J. Fluids Eng.
0098-2202,
128
, pp.
131
141
.
28.
Yildirim
,
N.
,
Kocabas
,
F.
, and
Gulcan
,
S.
, 2000, “
Flow-Boundary Effects on Critical Submergence of Intake
,”
J. Hydraul. Eng.
0733-9429,
126
(
4
), pp.
288
297
.
29.
Daves
,
J. T.
, and
Rideal
,
E. K.
, 1963,
Interfacial Phenomena
,
Academic
,
London
.
30.
Croxton
,
C. A.
, 1986,
Fluid Interfacial Phenomena
,
Wiley
,
New York
.
31.
Hite
,
J.
, and
Mih
,
W.
, 1994, “
Velocity of Air-Core Vortices at Hydraulic Intakes
,”
J. Hydraul. Eng.
0733-9429,
120
(
3
), pp.
284
297
.
32.
Jain
,
A.
, and
Raju
,
K.
, 1978, “
Air Entrainment in Radial Flow Towards Intakes
,”
J. Hydr. Div.
0044-796X,
104
(
HY9
), pp.
1323
1329
.
33.
Schetz
,
J. A.
, and
Fuhs
,
A. E.
, 1996, “
Handbook of Fluid Dynamics and Fluid Machinery
,”
Fundamentals of Fluid Mechanics
,
Wiley
,
New York
, Vol.
1
.
34.
Stroud
,
A. H.
, 1971,
Approximate Calculation of Multiple Integrals
,
Prentice-Hall
,
Englewood Cliffs, NJ
.
35.
Taylor
,
G. I.
, 1950, “
The Instability of Liquid Surfaces When Accelerated in a Direction Perpendicular to their Planes,”-I
,
Proc. R. Soc. London, Ser. A
1364-5021,
201
, pp.
192
196
.
You do not currently have access to this content.