XXIX Congresso UIT sulla Trasmissione del Calore
Torino, 20-22 Giugno 2011
AIR-WATER TWO-PHASE FLOW IN A HORIZONTAL T-JUNCTION:
FLOW PATTERNS, PHASE SEPARATION AND PRESSURE DROPS.
Cristina Bertani, Daniele Grosso, Mario Malandrone, Bruno Panella
Dipartimento di Energetica, Politecnico di Torino
ABSTRACT
This paper reports further results of the experimental campaign on two-phase flow in horizontal T-junction that has being
carried out in the thermal-hydraulics laboratory of Dipartimento di Energetica of Politecnico di Torino since 2005. The test
facility is provided with a dividing T-junction, used in the branching configuration. The pipes forming the tee junction are
about 1 m long, their inner diameter is 10 mm and a mixture of air and water flows at pressures up to 1.5 barg.
The present work reports the results with water superficial velocities in the range 0.95-3.61 m/s and air superficial velocities in
the range 0.44-34.5 m/s. Flow patterns were also visualised systematically by filming the flow patterns across the three pipes in
each experimental run.
As far as the evaluation of pressure drops is concerned, experimental results are used to modify the Separated Flow Model: the
Zuber formulation for the void fraction is adopted and both the pressure drop correction factor and local pressure loss
coefficient are expressed as function not only of the extraction ratio but also of the flow pattern.
INTRODUCTION
Two-phase flow through T-junctions is frequent in
conventional power plants as well as in water nuclear reactors
and in chemical industries.
Since the 80’s several studies on this subject have been
carried out both theoretically and experimentally, for different
types of dividing T-junctions, i.e. branching tees and
impacting tees [1, 2]. Nevertheless, further experimental
studies are necessary in order to improve and validate models
able to predict the splitting of phases and the flow patterns in
the run and in the branch pipes of the branching-T and
pressure drops through the T-junction.
In branching tees one of the outlet pipes (named “run”) is
aligned with the inlet pipe and the other outlet (named
“branch”) is perpendicular to the inlet pipe.
The liquid and gaseous phases entering the T-junction can
be unevenly split at the junction, so that the flow rates in the
run and in the branch depend on the different momentum flux
of the two phases: the phase with higher momentum flux tends
to flow in the run pipe and the one with lower momentum flux
flows preferably into the branch. Also the flow quality can be
different in the run and branch pipe.
The pressure drop through the T-junction is strongly
influenced by the phase separation, as well as by the void
fraction and by the flow pattern in the pipes. On the other
hand the flow regime affects the pressure drops between the
inlet and the outlet pipes.
Phenomena are also affected by gravity effects and if the Tjunction lays on a horizontal plane, stratification phenomena
can occur.
An experimental research is being carried out at
Dipartimento di Energetica of Politecnico di Torino in order
to investigate pressure drops, phase splitting and flow patterns
in a horizontal T-junction with 10 mm inner diameter pipes.
In previous works experimental results on the effect of
extraction rate (ratio between total branch flow rate and total
inlet flow rate) and on phase separation have been performed.
In each test the flow patterns in the three pipes have been
observed.
In the first part of the experimental campaign [3, 4, 5, 6]
the superficial velocities of water and air reached maximum
values of 0.73 m/s and 63.3 m/s respectively, flow regimes
were bubbly, wavy, intermittent and annular.
In the second part of the experimental campaign [7] water
superficial velocities were raised to the range 1.53-3.61 m/s
(with air superficial velocity ranging up to 23.9 m/s) and the
flow patterns were bubbly or slug-plug flow. Experimental
results of flow patterns, phase separation and pressure drops
have been compared with data and correlations available in
the literature. In particular, the experimental results allowed to
develop a correction factor to be applied to the Separated
Flow Model.
The present work reports also the results of the third part of
the experimental campaign, covering an intermediate range of
water flow rate, with water superficial velocities in the range
0.95-1.36 m/s and air superficial velocities in the range 5.9834.5 m/s [8].
EXPERIMENTAL FACILITY
The experimental facility is schematically shown in fig. 1.
It mainly consists of the feeding lines for air and water, the
mixer, the T-junction, the outlet pipes and an air-water
separator having a volume of approximately 0.4 m3.
The water is sucked by a centrifugal pump from a tank
where the liquid level is maintained constant by feeding water
continuously.
The two-phase mixture develops in a T-mixer that is
located at the inlet of the test section.
The test section is shown in fig. 2. It consists of three
plexiglas pipes (10 mm in diameter, about 1 m long) named
inlet, run and branch. Four pressure taps are placed on each of
them.
A system of valves allows to obtain different values of the
total flow rate in the run and in the branch pipe.
compressed
air line
air discharge
air inlet
flowmeter
air outlet
flowmeters
separation tank
by-pass line
water
tank
pump diaphragm air-water
mixer
for water
flow rate
measurement
branch
tee-junction
inlet
run
Table 1: Test matrix
Water inlet flow rate [g/s]: 77295 (six groups of flow rates
with average values of 83 g/s, 105 g/s, 132 g/s, 180 g/s, 230
g/s, 283 g/s)
Water temperature [°C]: 12.213.5
Inlet pressure at pressure tap I1 [barg]: 0.611.51
Air inlet flow rate [Nm3/h]: 0.2215.9
Inlet flow quality [%]: 0.036.26
Branch flow rate/inlet flow rate: 01
Water superficial velocity at the inlet [m/s]: 0.953.61
Air superficial velocity at the inlet [m/s]: 0.4434.5
Flow pattern in the inlet pipe: annular, intermittent and
bubbly
EXPERIMENTAL RESULTS
water discharge
tank
Figure 1. Experimental facility.
As far as instrumentation is concerned, a resistance
temperature detector measures the inlet water temperature,
while a pressure transducer (full-scale 5 bar) and a differential
pressure transducer (full-scale 0.37 bar) are respectively used
to measure the inlet pressure at tap I1 and the pressure drops
between the different pressure taps in the test section.
Flow meters with full-scale 1050 and 5000 Nl/h measure
the air flow rate at the inlet of the test section. The inlet water
flow rate is evaluated as function of the pressure drop through
a diaphragm, which is measured by a differential pressure
transducer (full-scale 0.37 bar).
The experimental results on phase separation between run
and branch, the pressure drops and the flow patterns are here
presented.
Phase separation
The phase separation is described by the ratio between the
flow rates in the branch and the ones in the inlet
FBG  WG3 WG1 , FBL  WL3 WL1 , whose values are
reported in fig. 3. In the tested range of conditions, FBG is
always much higher than FBL; it reaches a value of
approximately 0.9 and remains constant when FBL is higher
than 0.3.
Therefore air flows preferably into the branch pipe in all
the tests, as already shown in [3], [4], [5], [6] and [7];
moreover there is a slight influence of the water flow rate on
FBG , which decreases at increasing water flow rates.
1.00
FBG
0.80
0.60
0.40
Figure 2. Test section, with the pressure taps I1I4, R1R4,
B1B4.
0.20
Water and air flowing through one of the exit pipes are sent
to the separator tank and the separator exit valves are
regulated so that the water level in the separator is kept
constant. The air flow rate exiting the separator tank is
measured by flow meters with full-scale of 340 Nl/h, 1050
N/l and 6000 Nl/h. The flow rate of water through one of the
outlet pipes is measured by means of the weighting technique.
The data acquisition system makes use of Field Points by
National Instruments and works in Labview environment.
A Panasonic video camera Model AG-DVC30E was used
in order to visualise the flow patterns.
Table 1 summarizes the test conditions of the third part of
the experimental campaign and also the test matrix of the
experiments already reported in [7].
0.00
0.00
Group 1 - Wl 83 g/s
Group 2 - Wl 105 g/s
Group 3 - Wl 132 g/s
Group 4 - Wl 180 g/s
Group 5 - Wl 230 g/s
Group 6 - Wl 283 g/s
0.20
0.40
0.60
0.80
1.00
FBL
Figure 3. Phase separation between run and branch.
Flow patterns
The prevailing flow patterns in the three pipes were
intermittent-slug (with slugs of different lengths) and bubbly
at higher water flow rates.
At low water flow rate annular flow regime was also
observed; it most often occurs in the transition region with
2
water flow rate 105 g/s
air flow rate 9471 Nl/h
FBL 0.31
1.9
Pressure / (bar)
intermittent flow; pulsated perturbations are observed to be
more consistent near the transition zone.
Transition regimes are also observed between intermittent
flow and bubbly flow. Sometimes both intermittent and
bubbly or intermittent and annular flow patterns occurred
simultaneously.
There is a good agreement between the flow patterns
occurring in our experiments and the prediction of TaitelDuckler’s map [9], as shown in fig. 4a and 4b.
1.8
Inlet
Run
Branch
1.7
1.6
1.5
1.4
10
1.3
Intermittent + Bubbly
Annular
0
1
Fr
1.7
Pressure / (bar)
Stratified + Wavy
0.01
Intermittent + Bubbly
Intermittent / Annular
Annular / Intermittent
Annular
0.001
0.01
0.1
1
10
100
1000
Branch
1.3
T
Slug / Plug
Slug / Plug
Bubbly / Intermittent
Intermittent / Bubbly
Bubbly
0.01
1
10
0.5
1
1.5
2
Distance from I1 pressure tap / (m)
2.5
Figure 5. Examples of pressure behaviour at different air and
water flow rates.
PRESSURE
DROPS
IN
THE
As far as the evaluation of the pressure drops in the teejunction is concerned, the models already reported in [3], [4],
[5], [6] and [7] have been used. The differential pressure
between inlet and run Δp 12  p1  p 2 is evaluated by a
momentum flux balance with a correction factor k12 which is
determined experimentally:
1
0.1
Run
ANALYSIS OF
T-JUNCTION
Bubbly
2.5
Inlet
0
10
2
1.5
X
Figure 4a. Comparison between observed flow patterns and
Taitel-Duckler’s map.
1.5
1.6
1.4
0.001
1
Distance from I1 pressure tap / (m)
water flow rate 283 g/s
air flow rate 222 Nl/h
FBL 0.62
1.8
0.1
0.5
100
1000
10000
X
Figure 4b. Comparison between observed flow patterns and
Taitel-Duckler’s map for bubbly and plug-slug regimes.
Pressure distributions along inlet, run and branch
Pressures along inlet, run and branch pipes have been
measured. The pressure difference between inlet and run and
between inlet and branch have been determined by
extrapolating the values measured at the pressure taps to the
centre of the junction (a second order polynomial has been
used). The extrapolated values of p1-p3 and p1-p2 are
respectively in the ranges 14÷126 mbar and (-10)÷(-128)
mbar, with an uncertainty of 4 mbar, which correspond to a
relative uncertainty of 3÷40 %.
Typical pressure values in tests with low water flow rate
are shown in fig. 5. As already reported in [7], both linear and
non linear pressure distributions have been found: greater
nonlinearity occurs at increasing air flow rate, while profiles
tend to be more linear at high water flow rate.
 G2 G2 
p12  k12   2  1 


 2 1 
(1)
The differential pressure between inlet and branch
p13  p1  p 3 is evaluated as the sum of a reversible
pressure change due to kinetic energy variation and an
irreversible pressure drop that depends on the local pressure
drop coefficient k13 referred to the inlet mass velocity:
p13 
 H3
2
 G2 G2 
G2
  23  21   k13  1  


2  L
 3 1 
(2)
In the Homogeneous Flow Model (HFM) and in the
Separated Flow Model (SFM) the pressure drops are
evaluated by means of Eq. (1) and (2) using two-phase
multiplier and density calculated in different ways, and the
Rouhani void fraction correlation [10].
Instead, in the Reimann & Seeger model (RSM) the
pressure drop p12 is given by the sum of the pressure drop
through the vena contracta and the one through the successive
enlargement, and the pressure difference p13 is evaluated by
Eq. (2) using the homogeneous density [11].
In the present work the experimental values for Δp12 and
Δp13 are compared with HFM, SFM and RSM.
Figure 6 shows a fairly good agreement between
experimental data and SFM (as already reported in [7]); on the
other hand, the prediction of HFM is less accurate in the tests
with low water flow rates and therefore low pressure drops.
relatively well with the experimental data for Δp13 , while its
accuracy is much lower for the Δp12.
0.20
+50%
0.15
0.20
0.10
Δp predicted / (bar)
+50%
0.15
Δp predicted / (bar)
0.10
-50%
0.05
-50%
0.05
0.00
-0.05
0.00
-0.10
-0.05
-0.15
-0.10
-0.20
-0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20
-0.15
Δp measured / (bar)
-0.20
Δp12 SFMZF - Wl 83 g/s
Δp12 SFMZF - Wl 105 g/s
Δp12 SFMZF - Wl 132 g/s
Δp12 SFMZF - Wl 180 g/s
Δp12 SFMZF - Wl 230 g/s
Δp12 SFMZF - Wl 283 g/s
-0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20
Δp measured / (bar)
Δp13 SFM - Wl 83 g/s
Δp13 SFM - Wl 105 g/s
Δp13 SFM - Wl 132 g/s
Δp13 SFM - Wl 180 g/s
Δp13 SFM - Wl 230 g/s
Δp13 SFM - Wl 283 g/s
Δp13 HFM - Wl 83 g/s
Δp13 HFM - Wl 105 g/s
Δp13 HFM - Wl 132 g/s
Δp13 HFM - Wl 180 g/s
Δp13 HFM - Wl 230 g/s
Δp13 HFM - Wl 283 g/s
Figure 6. Comparison of experimental pressure drops and the
predictions of HFM e SFM.
As in [7], a new correlation has been developed in order to
improve the agreement with the experimental data; the
following correction factor has been applied to the loss
coefficient k13 of SFM:
Firr  0.534  0.946 W3 W1 
(3)
A better agreement with SFM can be achieved by
substituting the Rouhani correlation with the Zuber
formulation and using the drift velocity ugj = 0 and C0 = 1.2,
i.e. the values for slug flow in horizontal pipes. The
comparison between the modified separated flow model
(hereafter indicated as SFMZ) and experimental data is shown
in fig. 7. No satisfying correction factor has been found to
improve the prediction of Δp12.
Finally, the accuracy of the Reimann & Seeger model has
been evaluated. In order to evaluate Δp13 , the correlation
originally suggested by Reimann & Seeger for k13 has been
substituted with the correlation more recently proposed by
Buell [10], as this latter allows a slightly better prediction of
the experimental data. As shown in fig. 8, the RSM agrees
Figure 7. Comparison of experimental pressure differences
and the value predicted by SFMZ.
0.2
+50%
0.15
0.1
Δp calcolata (bar)
Δp12 SFM - Wl 83 g/s
Δp12 SFM - Wl 105 g/s
Δp12 SFM - Wl 132 g/s
Δp12 SFM - Wl 180 g/s
Δp12 SFM - Wl 230 g/s
Δp12 SFM - Wl 283 g/s
Δp12 HFM - Wl 83 g/s
Δp12 HFM - Wl 105 g/s
Δp12 HFM - Wl 132 g/s
Δp12 HFM - Wl 180 g/s
Δp12 HFM - Wl 230 g/s
Δp12 HFM - Wl 283 g/s
Δp13 SFMZF - Wl 83 g/s
Δp13 SFMZF - Wl 105 g/s
Δp13 SFMZF - Wl 132 g/s
Δp13 SFMZF - Wl 180 g/s
Δp13 SFMZf - Wl 230 g/s
Δp13 SFMZf - Wl 283 g/s
-50%
0.05
0
-0.05
-0.1
-0.15
-0.2
-0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20
Δp measured / (bar)
Δp12 RSM - Wl 83 g/s
Δp12 RSM - Wl 105 g/s
Δp12 RSM - Wl 132 g/s
Δp12 RSM - Wl 180 g/s
Δp12 RSM - Wl 230 g/s
Δp12 RSM - Wl 283 g/s
Δp13 RSM - Wl 83 g/s
Δp13 RSM - Wl 105 g/s
Δp13 RSM - Wl 132 g/s
Δp13 RSM - Wl 180 g/s
Δp13 RSM - Wl 230 g/s
Δp13 RSM - Wl 283 g/s
Figure 8. Comparison of experimental pressure drops with the
prediction of the Riemann & Seeger model.
Finally, as far as the evaluation of pressure drops is
concerned, we attempted to develop a new model (hereafter
indicated as PM) that takes into account the different flow
patterns occurring in the experimental tests. As a basis, the
typical correlations of the SFMZ have been used, but we
introduced coefficients k12 e k13 that also depend on flow
pattern and extraction ratio.
The structure chosen for the above mentioned coefficients
is the one proposed by El-Shaboury, Soliman and Sims [12]:
Figure 9 shows that, by the use of the above mentioned
coefficients, the data dispersion is reduced and the most part
of points are within ±25%. Almost all the points for Δp13 lay
within ±20%.
0.20
+25%
0.15
+50%
-25%
0.10
k12  C1  W3 W1   C 2  W3 W1   C3
k13  C 4  W3 W1 2  C5  W3 W1   C 6
(4)
where:
C1  A  logRe 1   B  logRe1   C
2
C2  D  logRe 1   E  logRe 1   F
Δp predicted / (bar)
2
-50%
0.05
0.00
-0.05
-0.10
2
C3  G  logRe 1 2  H  logRe 1   I
C4  J  logRe 1 2  K  logRe 1   L
-0.15
-0.20
-0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20
Δp measured / (bar)
C5  M  logRe1 2  N  logRe1   O
C6  P  logRe1 2  Q  logRe1   R
Re 1  4  Wl   D   G 
The Reynolds number is relative to the total inlet flow rate
considered as gaseous.
The values of the constants A, B, C, D, E, F, G, H, I, J, K,
L, M, N, O, P, Q, R have been evaluated as function of flow
patterns by Ordinary Least Squares method.
Depending on the flow regime, the experimental data have
been divided in 3 categories: groups 1 and 2 (prevailing
annular flow), groups 3, 4 and 5 (prevailing intermittent flow)
and group 6 (prevailing bubbly flow).
The values of the coefficients are reported in table 2.
Table 2. Coefficients of C1, C2, C3, C4, C5, C6
Groups
Coefficients
1, 2
3, 4, 5
6
A
-4.60269
-1.78736
-0.9042
B
18.94891 9.432442
5.289937
C
6.935419 3.449248
2.134877
D
-2.46753
0.39601
-0.84824
E
18.03551 -1.45399
5.058304
F
6.605532 -0.19884
2.062545
G
1.331346 0.231864
-0.02306
H
-8.38945
-1.88181
-0.36177
I
-0.8198
2.144975
3.836273
J
-0.8876
-0.13973
-1.21451
K
4.459246 0.824035
7.206477
L
1.572819 0.284914
2.383148
M
-0.49942
-0.10123
-1.14079
N
3.670348 0.796002
7.06621
O
1.295305 0.275062
2.346834
P
0.317543 0.016217
0.795197
Q
-1.88525
-0.05564
-4.73273
R
-0.6322
-0.00984
-1.46615
Δp12 PM - Wl 83 g/s
Δp12 PM - Wl 105 g/s
Δp12 PM - Wl 132 g/s
Δp12 PM - Wl 180 g/s
Δp12 PM - Wl 230 g/s
Δp12 PM - Wl 283 g/s
Δp13 PM - Wl 83 g/s
Δp13 PM - Wl 105 g/s
Δp13 PM - Wl 132 g/s
Δp13 PM - Wl 180 g/s
Δp13 PM - Wl 230 g/s
Δp13 PM - Wl 283 g/s
Figure 9. Experimental pressure drops versus the prediction of
the PM.
Table 3 summarizes the accordance between PM and the
experimental data of respectively Δp12 and Δp13 in terms of
percentage of data that fall into ±20%, ±30% and ±50%.
It is evident the very good agreement between experimental
data and the predictions of the PM.
Table 3. Prediction of Δp12 and Δp13
SFM HFM SFMZF RSM
p12
±50%
63
39
76
44
±30%
52
33
61
30
±20%
30
28
37
24
SFM HFM SFMZF RSM
p13
±50%
68
42
99
79
±30%
40
31
92
53
±20%
24
18
78
36
PM
94
89
78
PM
97
97
93
CONCLUSIONS
The present experimental results on two-phase flow
through a T-junction extend the analysis of ref. [7] to an
intermediate range of water flow rates. The flow patterns
observed in the junction were predominantly annular flow (at
lower liquid flow rates), intermittent-slug and bubbly flow (at
higher liquid flow rates), and are substantially in good
agreement with Taitel-Duckler map.
The phenomena of phase separation reported in references
[4], [5], [6] and [7] have been confirmed, and a bigger part of
the air flow rate flows through the branch pipe.
The pressure has been measured along the inlet, the branch
and the run pipes and pressure drops in the junction from inlet
to run and from inlet to branch have been evaluated by
extrapolation and compared with homogeneous and separated
phase models and Reimann & Seeger model. Especially for
the pressure difference between inlet and run the SFM
resulted to be more accurate, in particular in the modified
version SFMZ, than HFM and RSM.
The agreement of the SFM predictions with experimental
pressures drops through the T-junction, as proposed in the
PM, strongly improves by using corrective factors of the
pressure drop coefficients that are dependent on the extraction
ratio and flow patterns.
ACKNOWLEDGMENT
The authors wish to thank Gladis Di Giusto e Rocco
Costantino for their support in the facility setup and the
development of the experimental campaign.
NOMENCLATURE
Symbol
Quantity
C0
D
ER
FBG, FBL
Distribution parameter (Zuber model)
Inlet diameter
Extraction ratio ER=W3/W1
FBG = WG3/WG1, FBL = WL3/WL1
Froude number
Fr
SI Unit
 

Fr  G g  g   l   g  d  g
g
G
p
Gravity acceleration
Mass velocity
Pressure
T
T  dp dzL
ugj
V
W
x
Drift velocity (Zuber)
Superficial velocity
Mass flow rate
Flow quality WGi/Wi
Martinelli’s parameter
X
z






 12
g   L   G 
X  dp dzL dp dzG 
m/s2
kg/(s m2)
Pa
1
2
m/s
m/s
kg/s
1
2
Axial coordinate
Void fraction
Two-phase multiplier
Dynamic viscosity
Density
Superficial tension
Subscripts
E
G
H
L
M
1, 2, 3
m
Referred to energy conservation
Gas
Referred to homogeneous model
Liquid
Referred to momentum flux
Inlet,run, branch pipes
m
kg/(m s)
kg/m3
N/m
REFERENCES
[1] B. J. Azzopardi, P. B. Whalley, The effect of flow
patterns on two-phase flow in a T junction, Int. J.
Multiphase Flow, vol. 8, pp. 491-507, 1982.
[2] L. Oranje, Handling two-phase condensate flow in
offshore pipeline systems, Oil and Gas J., vol. 81, pp.
128-138 C, 1983.
[3] A. Quaranta, Fluidodinamica bifase in giunzioni a T,
Thesis, Facoltà di Ingegneria I, Politecnico di Torino,
Torino, 2005.
[4] C. Bertani, M. Malandrone, B. Panella, A. Quaranta, P.
Squillari, Pressure drop and phase separation in a
horizontal T-junction, Procs. XXIV UIT Heat Transfer
Congress, pp. 267-274, Napoli, 2006.
[5] C. Bertani, M. Malandrone, B. Panella, Two-Phase Flow
in an horizontal T-Junction: Pressure drop and phase
separation, Procs. HEFAT2007, 5th International
Conference on Heat Transfer, Fluid Mechanics and
Thermodynamics, Sun City, South Africa, Paper number:
BCI, 2007.
[6] C. Bertani, M. Malandrone, B. Panella, Regimi di
deflusso e separazione delle fasi in una giunzione a T
orizzontale con deflusso di miscele aria-acqua, Procs.
XXVI UIT Heat Transfer Congress, CD Rom, Paper n°
B51, Palermo, 2008.
[7] C. Bertani, D. Grosso, M. Malandrone, B. Panella,
Deflusso bifase di miscele aria-acqua in una giunzione a
T orizzontale per elevate velocità superficiali della fase
liquida, Procs. XXVIII UIT Heat Transfer Congress, pp.
127-132, Brescia, 2010.
[8] D. Grosso, Fluidodinamica bifase in una giunzione a T
orizzontale, Thesis, Facoltà di Ingegneria I, Politecnico
di Torino, Torino, 2010.
[9] Y. Taitel, A.E. Dukler, A model for predicting flow
regime transitions in horizontal and near horizontal gasliquid flow, AJChE J., vol. 22, pp. 47-55, 1976.
[10] J.R. Buell, H.M. Soliman, G.E. Sims, Two phase
pressure drop and phase separation at a horizontal tee
junction, Int. J. Multiphase Flow, vol. 20, pp. 819-836,
1994.
[11] J. Reimann, W. Seeger, Two-phase flow in a T-junction
with a horizontal inlet-Part II: pressure differences, Int. J.
Multiphase Flow, vol. 12, pp. 587-608, 1986.
[12] A. M. F. El-Shaboury, H. M. Soliman, G. E. Sims, TwoPhase flow in a horizontal equal-sided impacting tee
junction, Int. J. Multiphase Flow, vol. 33, pp. 411-431,
2007.