The Split of Horizontal Two-Phase Flow at a T- Junction – CFD Study
Amir T. Al-Wazzan,
Department of Mechanical Engineering, University of Malaya, 50603 KL, Malaysia
ABSTRACT
A procedure for simulation the split of
horizontal two-phase flow at a T-junction was
presented using the CFD aspects. Water was
used as the liquid phase while the air was used
as the gas phase. The values of the superficial
velocities were ranging (2.0-10.0 m/sec) for the
air and (0.2-1.0 m/sec) for the water.
PHOENICS was used as the CFD code. The
results were compared with experimental
results obtained by some investigators and
with theoretical models prepared by some
investigators previously.
reported that when annular flow approaches a
tee, a sudden increase in the amount of liquid
extracted for a small increase in the gas takeoff occurred. The film reacting to the pressure
increase along the main pipe and slowing
down explained this trend. Shoham et al.(10)
and Hwang et al.(5) adopted a similar concept,
but argued that more accurate predictions can
be obtained if the dividing streamlines are
different for each phase. This difference was
proposed by Shoham to be the result of
centrifugal separation of the phases produced
by the fluids following a circular path into the
side arm, whereas Hwang determined ‘zones
of influence’ from a balance between the
dominated forces acting on each phase,
Azzopardi(2) improved the model of Azzopardi
and Whalley (1) by predicting the critical gas
take-off value at which film-stop occurred and
the extra amount of liquid taken off. A’selfstanding’ model which has been rigorously
compared with data is currently not available
for implementation into the flow split model of
Azzopardi(2). Hart et al.(4) proposed a model for
separated flows with liquid hold-up values less
than 0.06. This is based on the Bernoulli
equations for each phase along the main pipe
and from the main pipe to the side arm. Loss
coefficients for the liquid were assumed equal
to those for the gas phase, which were
described by single-phase correlations. Ottens
et al(6)
extended the models range of
applicability to all values of hold-up by
developing correlations for the liquid-phase
loss coefficients, however predictions were
only compared with stratified-wavy air-water
flow split data. A detailed discussion of these
models and the inherent assumptions is
presented by Roberts et al.(8).
No universal agreement exists on the main
parameters controlling the film thickness
distribution. As explained by Flores et al.(3) and
Sutharshan et al.(11), the physical mechanisms
which have been proposed are the
circumferential secondary gas flow, wave
INTRODUCTION
Junctions are an often-necessary feature of
many pipelines or pipework systems. For
single-phase flows, there are equations, which
though empirical, enable engineers to carry out
designs. In the case of two-phase flow,
however, the number of variables is much
larger; in addition there are complicating
factors in the partition and mixing of the
phases.
When a two-phase mixture flows through a
dividing T-junction, there is an almost
inevitable, maldistribution of the phases
between the outlets. The unequal splitting of
gas and liquid at T-junction was observed to
create problems in the industry where it may
be found. For example, in gas distribution
networks, condensate can be formed in
pipelines in winter due to low temperature. It
was found that the condensate appears at
some delivery stations while the other stations
receive only dry gas. This kind of uneven
splitting may result in creating operational and
separation problems.
Large amounts of data have been acquired
and a number of models have been developed
so far, on two-phase flow splitting at Tjunctions. Azzopardi and Whalley (1) proposed
that the fluids emerging through the branch
outlet were extracted from a segment of the
main pipe nearest the side arm. They also
1
spreading and transfer of liquid entrainment
and deposition of droplets. Penmatcha et al(7)
investigated two-phase splitting under stratified
wavy flow conditions at a regular horizontal Tjunction with an inclined branch arm. They
developed a mechanistic model for the
prediction of the splitting phenomenon for both
the horizontal and the downward orientations
of the side arm. This model based on the
momentum equations applied for the
separation streamlines of the gas phase and
the liquid phase. Roberts et al.(9) presented a
model for predicting the flow split of horizontal
air-water annular flow at a T-junction with a
side arm at an arbitrary inclination to the
horizontal. They stated that under certain
conditions, an abrupt increase in the amount of
liquid extracted into the side arm was observed
due to liquid coming to rest in the main pipe.
Where:
 i : phase density
COMPUTATIONAL FLUID DYNAMICS
CFD codes are structured around the
numerical algorithms that can tackle fluid flow
problems. In order to provide easy access to
their solving power, all numerical CFD
packages include sophisticated user interfaces
to input problem parameters and to examine
the results. There are three distinct streams of
numerical solution techniques: finite difference,
finite element and spectral methods. The main
differences between the three separate
streams are associated with the way in which
the flow variables are approximated and with
the discretisation processes. In this study,
PHOENICS was used as the CFD code. The
finite volume method that was originally
developed as a special finite difference
formulation was implemented in this package.
Considering the time average, the equation will
be:
vel : phase velocity vector
W : mass flow rate of the entering phase
t : time
As the result base on above equation it
becomes Cartesian form as follows:
W
................ (2)
Where:
x , y , z : distances in three directions at right
angle
u i , v i , wi : phase velocity components
W
d ri  i 
 div ri   i  vel  J i diff 
dt
................ (3)
Where:
J i diff 
: turbulent diffusion flux,
representing transport by randommotion mechanisms.

Momentum General Equation:


 B  dpi 

Wi  (ui )   Wi  ui   Fi  ri  i

 dx 
d ri  i  ui   div ri i  vel ui  Vi ...............................(4)
MATHEMATICAL FORMULATION
The equations that have been implemented
in PHOENICS for simulating the two-phase
flow are as follow:

d ri i  d ri  i  ui  d ri  i  vi  d ri  i  wi 



dt
dx
dy
dz
Where:
Vi : momentum transport by viscous action
with phase i
Fi : friction factor of all other phases present
Phase-Mass General Equation:
Bi : body force per unit volume of i
p i : pressure of phase i
d ri  i 
W
 div ri   i  vel  .............. (1)
dt
(ui )  : ui of inflow mass
2
The following relevant laws of physics were
implemented as well:
 Conservation laws:
1. Newton’s second law of motion.
2. 1st law of thermodynamics.
3. Chemical-element balances.
 Transport laws:
1. Newton’s law of viscosity.
2. Fourier’s heat conduction law.
3. Fick’s diffusion law.
phase maldistribution. Also, from the directions
of flow shown in figure 1(*), we can predict
confidentially how the phases would be
distributed to the side arms.
SIMULATION
In this study, the simulation of the horizontal
T-junction was done with the following details:
1. 3D turbulent two-phase air-water flow in
1.5 inches horizontal T-junction.
2. Cartesian computational grid was used for
the domain setting (2.0, 0.15, 0.0381 m).
3. Turbulence represeted via the k-e EP
turbulence model with additional setting on
ENUT=GRND3 ‘ON’.
4. The following notes were considered:
 Air and water enter uniformly at inlet of
various velocities.
 The inlet void fraction is taken
according to the various velocities.
 Both phases are allowed to leave at the
outlet of the pipe.
 The expected flow pattern is a logical
two-phase flow pattern and logical
pressure and velocity profiles.
 The pipe body is employed uses
imported STL file from the AutoCad
drawing.
Figure (1): Mixture velocity vector (Vsl=0.2 m/sec)
(Vsg=2.0 m/sec)
From the pressure drop contour results, it is
clear that the pressure drop can be predicted
depending on the phase distribution. The
maximum amount of pressure drop will be in
the opposite part of the inlet section due to the
impact effect and the minimum value will be in
at the side corners due to the secondary flow.
Figure 2 below shows this phenomenon:
RESULTS
The first step of simulation was with low
liquid loading (Vsl=0.2 m/sec & Vsg=2.0 m/sec)
in a T-junction of 0.038m diameter for the inlet
and the side arms. The simulation gave the
fact that the mixing will change slowly to an air
predominant flow pattern. When it reaches the
T-junction, the water will spread in the lower
corner due to secondary flow. For the same
reason, the velocity of the mixture will increase
significantly at the inlet of the junction. It will
reach its minimum value at the corners where
the secondary flow occurs. This phenomenon
can be justified logically by the turbulence and
Figure (2): Pressure
drop
contour (Vsl=0.2 m/sec)
Figure
5.4.2
(Vsg=2.0 m/sec)
Pressure drop
contour
The contour of the void fraction will give a clear
view about the maldistribution of the phases in
the inlet section and in the side arms as well.
This is shown in figure 3:
(*): all the figures were generated with the top view
3
Figuredrop
5.4.5
Figure(5): Pressure
contour (Vsl=Vsg=2m/sec)
Figure (3): Void fraction contour (Vsl=0.2 m/sec)
(Vsg=2 m/sec)
Pressure drop
contour
Figure 6 below
gives a clear view about the
contour of the void fraction. The gradual
decreasing in the void fraction before the
connection point refers to the geometry of the
slug flow such that the minimum concentration
will be at the connection point and the
maximum impacted the front of the pipe
causing the highest pressure drop shown in
figure 5 above.
With equalizing the velocities of both air and
water to 2m/sec, the slug flow pattern would be
generated. This flow pattern is well known with
its high degree of complication and
disturbance.
Figure
4
shows
the
concentrations of the insitu velocities on the
neck of the junction.
Figure (4): Mixture
velocity
Figure
5.4.4vector
Air &(Vsl=Vsg=2 m/sec)
water velocity vector
Also, from figure 4 above, the phenomenon of
the secondary gas flow is quite clear and the
location of its occurrence can be determined
confidentially.
The irregularity of the velocity distribution will
cause differences in the pressure drop profile.
The liquid slug generates a high pressure drop
at the internal face of the pipe close to the
connection point as it is shown in figure 5 :
Figure (6): Void
fraction
contour
Figure
5.4.6
Void (Vsl=Vsg=2 m/sec)
fraction contour
Within further increments in gas phase
velocity to 10 m/sec and decreasing the water
velocity to1 m/sec, the same criterion would
appear with more significant and noticeable
features. This would change the velocity
distribution and pressure drop profiles.
The maximum velocity would be in the center
of the main pipe at the area that produces the
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highest amount of pressure drop due to the
high degree of turbulence. At the connection
point, a small amount of pressure drop will
occur because of an immediate change in the
phase distribution. These phenomena are
obvious in figures 7 & 8:
The void fraction simulation shown in figure 9
reflects the spatial distribution caused by the
turbulence.
Figure (9): Void
fraction
contour
Figure
5.4.9
Void(Vsl=1 m/sec)
fraction contour (Vsg=10 m/sec)
The gradual decrement towards the
connection point refers to the nature of slug
flow that has been generated within these flow
conditions.
For determination the mixture velocity along
the section, PHOENICS produced the velocitydistance graph (figure 10) below. For the
second and third cases of simulation, the
mixture velocities are almost the same. There
is a wide gap between them and the velocity
profile of the first case because within low
liquid loading, the liquid would occupy the
bottom of the pipe and the high velocity comes
from the high gas velocity.
Air
water
Figure (7):Figure
Mixture 5.4.7
velocity
vector
(V&
sl= 1m/sec)
velocity vector
(Vsg=10 m/sec)
From figure 7 above, the secondary flow
phenomenon is clear as well.
18
10 air & 1 water velocity inlet
Vel. Vs Dist. T-junction Pipe
2 air & 0.2 water velocity inlet
2 air & 2 water velocity inlet
16
14
Velocity (m/s)
12
Figure (8): Pressure drop contour (Vsl=1 m/sec)
(Vsg=10 m/sec)
10
8
6
The unsteady state of the flow can be
determined from the pressure drop profile
above.
4
2
0
0
0.02
0.04
0.06
0.08
0.1
Distance (m)
0.12
0.14
Figure (10): Velocities plot
5
0.16
0.18
0.2






6. Ottens et al. (1994) “ Gas-liquid flow
splitting in regular, reduced and impacting
T-junctions” 14th Int. Congress on
Fluidodinamica Multifase nell’Impiantistica
Industriale, Acona Italy.
7. Penmatch et al. (1996) “ Two-phase
stratified flow splitting at a T-junction with
an inclined branch arm” Int. J. Multiphase
Flow 22, 6, 1105-1122.
8. Roberts et al. (1994) “Two-phase flow at Tjunctions” PhD thesis, University of
Nottingham, UK.
9. Roberts et al. (1995) “ The split of
horizontal semi-annular flow at a large
diameter T-junction” Int. J. Multiphase Flow
21, 455-466.
10. Shoham et al. (1989) “Two-phase flow
splitting in a horizontal reduced pipe tee”
Chemical Engineering Science 44, 23882391.
11. Sutharshan et al. (1995) “Measurements of
circumferential and axial film velocities in
horizontal annular flow” Int. J. Multiphase
Flow 21, 193-206.
CONCLUSIONS
In order to avoid the slug flow that is
unfavorable from both an operational and a
safety point of view, the velocities of both
phases should be controlled. This will help
also in reducing the pressure drop
especially at the junction.
The sudden change in the velocity profile
represents a significant change in the flow
patterns which requires more attention
during the time of operation.
PHOENICS can provide the main
objectives of the two-phase flow simulation
and can predict the maldistribution of the
phases in the pipe during the flow.
The capabilities of PHOENICS include the
ability to predict all the important factors in
the two-phase flow phenomenon like the
pressure drop, void fraction and phase
distribution.
The simulation results acquired from
PHOENICS are quite close to the results
acquired from experiments and the
theoretical models.
PHOENICS can be used for designing a
two-phase flow system.
REFERENCES
1. Azzopardi,B.J. & Walley,P.B. (1982) “The
effect of flow pattern on two-phase flow in a
T-junction” Int. J. Multiphase Flow 8, 481507.
2. Azzopardi,B.J. (1989) “The split of annularmist flows at vertical and horizontal Ts”
Proc.8th Int. Conference on Offshore
Mechanics and Arctic Engineering.
3. Flores,A.G. et al. (1995) “Gs-phase
secondary flow in horizontal stratified and
annular two-phase flow” Int. J. Multiphase
Flow 21, 207-221.
4. Hart,J. et al. (1991) “ A model for predicting
liquid route preference during gas-liquid
flow through horizontal branched pipelines”
Chemical Engineering Science 46, 16091622.
5. Hwang et al. (1988) “ Phase separation in
dividing two-phase flow” Int. J. Multiphase
Flow 14, 439-458.
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