A theoretical analysis has been developed to predict the critical height and the location of the onset of gas entrainment during discharge from a stratified two-phase region through two oriented-side branches mounted on a vertical wall. In this analysis, a point sink model was first developed, followed by a more accurate three-dimensional finite branch model. The models are based on a new modified criterion for the onset of gas entrainment. The theoretically predicted critical height and the location of the onset of gas entrainment are found to be a function of the mass rate of each branch ($Fr1$ and $Fr2$), the distance between the centerlines of the two branches $(L∕d)$, and the inclination angle $(θ)$. The effects of these variables on the predicted critical height and the onset location were investigated. Furthermore, comparison between the theoretically predicted results and the available experimental data was carried out to verify the developed models. The comparison shows that the predicted results are very close to the measured data within a deviation percentage of 12% at $Fr1>10$. This small deviation percentage reflects a good agreement between the measured and predicted results.

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.
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
.
4.
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
.
5.
Micaelli
,
J. C.
, and
Memponteil
,
A.
, 1989, “
Two-Phase Flow Behaviour in a Tee-Junction—The Cathare Model
,”
Proceedings of the Fourth International Topical Meeting on Nuclear Reactor Thermal-Hydraulics
, Karlsruhe, Germany, Vol.
2
, pp.
1024
1030
, October 10–13.
6.
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
,”
ASME J. Fluids Eng.
0098-2202,
120
, pp.
605
612
.
7.
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.
8.
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
.
9.
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
.
10.
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
.
11.
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
(
2
), pp.
385
390
.
12.
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
.
13.
Zhou
,
Q. N.
, 1989, “
Numerical Solution of Nonlinear Interaction of Density Interface with a Drain
,” Ph.D. thesis, Department of Mechanical Engineering and Applied Science, The University of Michigan, Ann Arbor.
14.
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
.
15.
Parrott
,
S. D.
, 1993, “
Experiments on The Onsets of Gas Pull-Through and Liquid Entrainment During Dual Discharge From a Large Reservoir
,” M.Sc. thesis, University of Manitoba, Winnipeg, MB, Canada.
16.
Hassan
,
I. G.
,
Soliman
,
H. M.
,
Sims
,
G. E.
, and
Kowalski
,
J. E.
, 1996, “
Experimental Investigation of the Two-Phase Discharge From A Stratified Region Through Two Side Branches
,”
Exp. Therm. Fluid Sci.
0894-1777,
13
, pp.
117
128
.
17.
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
,” M.Sc. thesis, University of Manitoba, Winnipeg, MB.
18.
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 I—Analysis of Liquid Entrainment
,”
Int. J. Multiphase Flow
0301-9322,
27
, pp.
1011
1028
.
19.
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
.
20.
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
.
21.
Schetz
,
J. A.
, and
Fuhs
,
A. E.
, 1996,
Handbook of Fluid Dynamics and Fluid Machinery
,
Fundamentals of Fluid Mechanics
, Vol.
1
,
Wiley
,
New York
.
22.
Craya
,
A.
, 1949, “
Theoretical Research on the Flow of Non-Homogeneous Fluids
,”
Houille Blanche
0018-6368,
4
, pp.
44
55
.
23.
Soliman
,
H. M.
, and
Sims
,
G. E.
, 1991, “
Theoretical Analysis of the Onset of Liquid Entrainment for Slots of Finite Width
,”
Int. J. Heat Fluid Flow
0142-727X,
12
, pp.
360
364
.
24.
Soliman
,
H. M.
, and
Sims
,
G. E.
, 1992, “
Theoretical Analysis of the Onset of Liquid Entrainment for Orifices of Finite Width
,”
Int. J. Multiphase Flow
0301-9322,
18
, pp.
229
235
.
25.
Stroud
,
A. H.
, 1971,
Approximate Calculation of Multiple Integrals
,
Prentice-Hall
,
Englewood Cliffs, NJ
.