WSEAS TRANSACTIONS on MATHEMATICS Hamid Shamloo and Bahareh Pirzadeh

Manuscript received Jan. 5, 2008; revised Apr. 6, 2008

Investigation of Characteristics of Separation Zones in

T-Junctions
HAMID SHAMLOO *, BAHAREH PIRZADEH**
Civil Engineering Department
K.N Toosi University of Technology
No.1346 Valiasr Street, Tehran
IRAN
*hshamloo@yahoo.com, ** b.pirzadeh@gmail.com

Abstract: The river diversion, for domestic, agricultural and industrial consumption, has a vital role to make
economic progress and to develop the human communities. There are different ways of river diversion which
are proportional to rivers' condition and the quantity of the diversion of water. Lateral river intake is one of
these ways. This paper provides detail application of FLUENT-2D software in simulation of lateral intake
flows. Numerical simulations undertaken in present two dimensional work use RSM turbulent model. Results of
velocity field measurement using K-ε Standard model were compared with Shettar & Murthy (1966). Then
using RSM turbulent model, dimensions of separation zone were measured and compared with Kasthuri &
Pundarikanthan (1987). In both cases good agreement are found between numerical and experimental results.

Key-Words: Open channel, Lateral Intake, Turbulence, Separation zone, Numerical modeling, Fluent

1 Introduction gradients in the vicinity of the intake induce region

In hydraulic and environmental engineering, one of mean-velocity gradients, depth-varying surface
commonly comes across branching channel flows. of flow division and separation, vortices, and zone
Some of distinctive characteristics of a dividing of flow reversal.
flow in an open channel are illustrated in Fig.1. A As the flow approaches the intake, it accelerates
zone of separation near the entrance of the branch laterally by the suction pressure at the end of branch
channel, a contracted flow region in the branch channel. This may cause the flow to divide into two
channel, and a stagnation point near the downstream portions, one entering the branched channel and the
corner of the junction can be observed. In the region other flowing downstream in the main channel. The
downstream of the junction, along the continuous diverted flow experiences an imbalance between the
far wall, separation due to flow expansion may transverse pressure gradient and shear and
occur (Ramamurthy et al. 2007). centrifugal forces indicating a clockwise secondary
motion cell (Neary et al. 1999).
A great number of experimental and analytical
studies are dealt with dividing flows. Taylor (1944)
conducted the first detailed experimental study in an
open channel and proposed a graphical solution,
which included a trial-and-error procedure. Grace
and Priest (1958) presented experimental results for
division of the flow with different width ratios of
the branch channel to the main channel. They also
classified division of the flow into two regimes,
Fig.1. Flow characteristics of a dividing flow in open with and without the appearance of local standing
channels waves near the branch. The regime without waves
corresponded to the case where the Froude numbers
Flows through lateral intakes adjoining rivers and were relatively small, and the regime with waves
canals are turbulent. The transverse pressure corresponded to the free over-fall conditions at

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 WSEAS TRANSACTIONS on MATHEMATICS Hamid Shamloo and Bahareh Pirzadeh

sections downstream of the junction. Without the 2 Importance of Study

appearance of standing waves, the downstream-to- Appropriate sediment control at water intakes is one
upstream depth ratio and the branch-to-downstream of the primary goals of their design. The storage
depth ratio were nearly equal to unity and ratios volume of any sedimentation chamber downstream
mildly decreased while the branch-to-main channel has to last as long as possible and, in the case of a
upstream discharge ratio increased. hydro power plant, the turbines must be protected
Law and Reynolds (1966) investigated the problem from the incoming sediments. The design of an
of dividing flows using analytical and experimental intake has traditionally been refined by carrying out
methods. They concluded that for a dividing flow at physical model studies. It has recently become more
low Froude numbers in a right-angled dividing popular to improve the design process using the
flow, the momentum and energy principles can both result from a numerical model study. Applying
be applied to describe the flow in the main channel computational fluid dynamics (CFD) in this field of
extension. engineering can improve the final design and
Existing results (Krishnappa and Seetharamiah accelerate the design process. Also it is importance
1963; Law 1965; Sridharan 1966; Ramamurthy and lies in the fact that the analysis of the junctions is of
Satish 1988) indicate that the flow condition at the considerable use to engineers engaged on the design
entrance to the branch is generally unsubmerged of irrigation systems, storm sewers, channel in
when the Froude number Fr in the branch is greater sewerage treatment works, power installations and
than a threshold value (0.3 or 0.35). This feature other similar projects.
becomes important in correlating discharge The topic of the present study is the use of 2-D
distribution with other flow parameters. When the numerical model to predict the velocity profile and
flow at the section of maximum contraction is un- dimension of separation zone in the flow
submerged, division of the flow at the junction is approaching a water intake.
relatively unaffected by changes in the downstream
section of the branch channel.
For branching channels or intakes, result obtained 3 Experimental Results
from different researchers (Kasthuri and Dimension of separation zone obtained from the
Pundarikhathan 1987; Best and Reid (1984); Neary current numerical model were compared with
et al 1999) indicate that both length and width of the laboratory experiment results performed by
separation zone decrease with increasing the Kasthuri and Pundarikanthan (1987) and Velocity
discharge ratio. profiles obtained from the current numerical model
Shettar and Murthy (1996) deployed depth-averaged were compared with laboratory experiment results
mean flow equations associated by the standard k- performed by Shettar and Murthy (1996).
In both experimental set-up, the main channel was
ε model. Results obtained from their model for an
6m long and the intake was 3m long, fitted at its
open channel T-junction showed that for discharge
ratio 0.52, a good agreement between measurements midpoint. The width of both channels (b) was 0.3m,
and model results can be obtained. the bed slope was zero and channels were 0.25m
Ramamurthy et al. (2007) presented experimental deep, as illustrated in Fig.2. The channel bed was
finished with smooth cement plaster and walls were
data related to 3D mean velocity components and
built from Perspex sheets.
water surface profiles for dividing flows in open
channels. The data set presented in their paper was In Kasthuri and Pundarikanthan’s experimentsl
composed of water surface mappings and 3D (1987) flows were subcritical during all runs and the
velocity distributions in the vicinity of the channel Froude number in inlet varying from 0.1 to 0.4.
They have presented relationships between the
junction region.
maximum non-dimensional length (SL/b) and non-
Dimensions of separation zone obtained from the
current 2D-numerical model were compared with dimensional width (SW/b) of the separation zone,
those of Kasthuri and Pundarikanthan’s experiments and R=Qb/Q (Q is the total discharge in the
(1987). Velocity field measurements were upstream boundary of the main channel, Qb is the
intake discharge).
compared with measured velocities of Shettar and
In Shettar and Murthy’s experiments (1996) the
Murthy (1996).
discharge ration was 0.52 and the Froude number at
inlet was 0.54 so the velocity at inlet was 0.85m/s.

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They presented depth-averaged mean velocity

profiles in different sections across the main and
intake channel.

Z
Y X
Fig3. Scaled Residuals

5 Governing equations
Fig2. Layout of main channel and intake
The governing equations of fluid flow in rivers and
channels are generally based on three-dimensional
Reynoldes averaged equations for incompressible
4 Numerical Model Description free surface unsteady turbulent flows as follows [2]:
FLUENT is the CFD solver of choice for complex
flow ranging from incompressible (transonic) to ∂U i ∂U i 1 ∂ 2 ∂U i ∂U j (1)
highly compressible (supersonic and hypersonic) +U j = − P + k δ ij + ν T +
∂t ∂x j ρ ∂x j 3 ∂x J ∂xi
flows. It Provide multiple solver options, combined
with a convergence-enhancing multi-grid method,
FLUENT delivers optimum solution efficiency and There are basically five terms: a transient term and a
accuracy for a wide range of speed regimes (Fluent convective term on the left side of the equation. On
user guide 2003). the right side of the equation there is a
FLUENT solves governing equations sequentially pressure/kinetic term, a diffusive term and a stress
using the control volume method. The governing term.
equations are integrated over each control volume to In the current study, it is assumed that the density of
construct discrete algebraic equations for dependent water is constant through the computational domain.
variables. These discrete equations are linearized The governing differential equations of mass and
using an implicit method. momentum balance for unsteady free surface flow
Turbulent flows can be simulated in FLUENT using can be expressed as [8,9]:
the standard K-ε, LES, RNG, or the Reynolds-stress
∂u i (2)
(RSM) closure schemes. The model optimizes =0
computational efficiency by allowing the user to ∂xi
choose between various spatial (Second-order ∂u i ∂u 1 ∂P (3)
+uj i = − + g xi + υ∇ 2 u i
upwind, first-order, QUICK) discritization scheme. ∂t ∂x j ρ ∂xi
We used second order upwind discritization scheme
for Pressure, Momentum, Turbulent kinetic energy Where t=time; ui is the velocity in the xi direction; P
and turbulent dissipation rate and used SIMPLE is the pressure; ν is the molecular viscosity; gxi is
algorithm for Pressure-Velocity Coupling Method. the gravitational acceleration in the xi direction, and
For these problems, the conversions creations ρ is the density of flow.
in Fluent (Scaled Residuals) decreases to 10-6 As in the current study, only the steady state
for all equations (Fig.3). condition has been considered, therefore equation
(2) to (3) incorporate appropriate initial and

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 WSEAS TRANSACTIONS on MATHEMATICS Hamid Shamloo and Bahareh Pirzadeh

boundary conditions deployed to achieve

equilibrium conditions.
∂
∂t
( ρ ui'u 'j ) +
∂
∂xk
( )
ρuk ui'u 'j = −
∂
∂xk
[ ( )]
ρ ui'u 'j uk' + p δ kj ui' + δ ik u 'j +

Under-relaxation factors are chosen between 0.2

and 0.5. The small value of under-relaxation factors
∂
∂xk
µ
∂ ' '
∂xk
( )
uiu j − ρ ui'uk'
∂u j
∂xk
∂u
(
+ u 'j uk' i − ρβ g i u 'jθ + g j ui'θ
∂xk
)
is required for the stability of the solution of ' '
interpolation scheme. +p
∂ui' ∂u j
+
∂x j ∂xi
∂u ' ∂u j
− 2µ i
∂xk ∂xk
(
− 2 ρΩ k u 'j um' ε ikm + ui'um' ε jkm + suser)
The simplest and most widely used two-equation (8)
turbulence model is the k-ε model that solves two
separate equations to allow the turbulent kinetic
energy and dissipation rate to be independently
determined. 6 Boundary conditions
The turbulence kinetic energy, k, is modeled as: Appropriate conditions must be specified at domain
boundaries depending on the nature of the flow.
∂k ∂k ∂ ν T ∂k (4) Outflow boundary condition used for two outlets at
+U j = + Pk − ε
∂t ∂x j ∂x j σ k ∂x j all of runs. The length of the main and branch
channels were chosen properly; therefore sufficient
Where Pk is given by: distance is provided between the junction and two
outlets to ensure that the flow returned to the
∂U j ∂U j ∂U i undisturbed pattern. The no-slip boundary condition
Pk = ν T + (5)
∂xi ∂xi ∂x j is specified to set the velocity to be zero at the solid
boundaries and assumed to be smooth.
k
ν T = cµ (6) In simulation performed in the first case of present
ε2 study, velocity inlet boundary condition is specified,
The dissipation of k is denoted ε, and modeled as: and set to 0.85 m/s for comparing velocity across
∂ε ∂ε ∂ ν T ∂ε ε ε2 the main channel and branch corresponding to the
+U j = + Cε 1 Pk + Cε 2 (7)
∂t ∂x j ∂x j σ k ∂x j k k Shettar & Murthy experiments. In this case
Discharge ratios R=Qb/Q equal to 0.52 (as used by
Shettar and Murthy-1996) was used.
The constants in the k-ε model have the following In the second case, velocity inlet boundary
values: cµ=0.09, cε1=1.44, cε2=1.92, σk=1.0 and condition set to 0.5m/s to provide similar
σε=1.30 Experimental Froude number with Kasthuri and
The Reynolds stress model (RSM) provides closure Pundarikanthan experiments. In this case Seven
of the Reynolds-averaged Navier-Stokes equations discharge ratios R=Qb/Q equal to 0.2, 0.35, 0.45,
by solving transport equations for Reynoldes 0.52, 0.65, 0.80 and 0.90 were used.
stresses and an equation for energy dissipation rate It is also important to establish that grid-
(four-equation for 2D flows and seven-equation for independent results have been obtained. The grid
3D flows). Since the RSM accounts for the effects structure must be fine enough especially near the
of streamline curvature, swirl, rotation, and rapid wall boundaries and the junction, which is the
changes in strain rate in a more rigorous manner region of rapid variation. Various flow
than one-equation and two-equation models, it has computational trials have been carried out with
greater potential to give accurate predictions for different number of grids in x and y directions. It
complex flows. was found that results are independent of grid size,
The exact transport equations for the transport of if at least 3550 nodes are used (Pirzadeh 2007).
the Reynolds stresses, ρ u i' u 'j , may be written as Computational mesh is shown in Fig.4.
follows:

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 WSEAS TRANSACTIONS on MATHEMATICS Hamid Shamloo and Bahareh Pirzadeh

-0.5

Y/b
Fig.4. Computational geometry and grid -1
0 0.25 0.5 0.75 1
Present Study Shettar&Murthy(1996)

7 Results and Discussions Fig5. X-Velocity Profile in the Main channel (X*=-5.50)
7-1- velocity field
In the first case of this paper numerical 0
investigations are performed for evolution of the
ability of an available 2D flow solver to cop with
the fully turbulent flow in a T-junction.
In the Fig.(5) to (14) results of the numerical model -0.5
are compared with experimental depth averaged
Y/b
velocity profiles in the main and the branch channel
at 10 no dimensional locations at x and y direction.
-1
From these figures, it can be concluded that results
0 0.25 0.5 0.75 1
generally have reasonable agreement with measured
ones, but at some sections (especially in branch Present Study Shettar&Murthy(1996)

channel) computed results do not agree very well

Fig6. X-Velocity Profile in the Main channel (X*=-0.50)
with those measured, which might be partly due to
the three dimensional effects. Further, Shettar and 0
Murthy (1996) presented depth-averaged mean flow
velocities but in the current 2D-study surface
velocities have been used.
As the flow approaches the branch inlet, the -0.5
building up of transverse slop implies a negative
Y/b

pressure gradient accompanied by fluid acceleration

near the inner wall and positive pressure gradient
accompanied by fluid deceleration near the outer -1
0 0.25 0.5 0.75 1
wall (Fig.15). The forward velocity maximum shift
towards the inner banks as the flow inters the inlet Present Study Shettar&Murthy(1996)

region. As the flow starts entering into the branch,

the resultant velocity along the inlet reduces and Fig7. X-Velocity Profile in the Main channel (X*=0.0)
hence, at the downstream edge of the inlet, forward
0
velocity maximum shift away from the inner wall.
The flow remaining in the main channel expand to
the full width of the main channel and due to the
curvature already attained by it at the junction -0.5
region, flow is directed towards the inner wall and
Y/b

again the velocity maximum shift towards

it(Fig.16).
-1
0 0.25 0.5 0.75

Present Study Shettar&Murthy(1996)

Fig8. X-Velocity Profile in the Main channel (X*=0.50)

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0 0.5

-0.5
0
Y/b

-0.25 0.25 0.75

X/b
-1
0 0.25 0.5 0.75 -0.5

Present Study Shettar&Murthy(1996) Present Study Shettar&Murthy (1996)

Fig9. X-Velocity Profile in the Main channel (X*=1.50) Fig13. Y-Velocity Profile in the Branch channel (Y*=2.65)

0 0.5

-0.5
0
Y/b

0.0 0.3 0.5 0.8

X/b

-1
0 0.25 0.5
-0.5
Present Study Shettar&Murthy(1996) Present Study Shettar&Murthy (1996)

Fig10. X-Velocity Profile in the Main channel (X*=7.0) Fig14. Y-Velocity Profile in the Branch channel (Y*=3.65)

0.5
7-2- dimension of separation zone in the intake
In the second step at this study, numerical
approaches were used to understand flow structure
0
and separation zone at the water intake.
-0.2 0.3 0.8 It was found that the size and location of separation
zone is very much dependent on the discharge ratio.
X/b

The result showed that for high discharge ratio the

-0.5
separation occurs in the downstream side of water
intake whereas in low discharge ratio, it occurs in
Present Study Shettar&Murthy (1996) the upstream side.
Figs. (17) to (23) show 2D streamline plots. These
Fig11. Y-Velocity Profile in the Branch channel (Y*=0.65)
plots elucidate the structure of the dividing stream
0.5 surface and the zone of flow separation in intake.
The flow at the junction can be divided into two
regions; the region from which the branch channel
abstracts the water and the region where the flow
0
continues in the main channel. The streamline
-0.5 0 0.5 1 which divides these two regions is known as
dividing streamline. However, the dividing
X/b

streamline obtained in the present two-dimensional

-0.5
analysis should be viewed caution.
By comparing these figures, it is seen that an
Present Study Shettar&Murthy (1996)
increase in discharge ratio causes shortening and
narrowing of the separation zone.
Fig12. Y-Velocity Profile in the Branch channel (Y*=1.65)

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A second separation zone may occur in the section

of the main channel downstream of the junction
because of flow expansion in this region. The width
and length of the separation zone increase when R
increases. When R is very small, the separation
zone would not exist.

Fig.18. 2D Streamlines plot for R=0.35

Fig15. Contours of predicted static pressure (Pascal)

Fig.19. 2D Streamlines plot for R=0.45

Fig16. Contours of predicted velocity magnitude (m/s)

Fig.20. 2D Streamlines plot for R=0.52

Fig.17. 2D Streamlines plot for R=0.20

Fig.21. 2D Streamlines plot for R=0.65

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0.9
Present Study
Kasthuri,Pundarikanthan(1984)

0.7

SW/b
0.5

0.3
0.0 0.5 1.0
R

Fig.22. 2D Streamlines plot for R=0.80 Fig.24. Dimensionless width separation zone vs. Ratio of
discharge

4
Present Study
Kasthuri,Pundarikanthan(1984)

SL/b
2

1
0.0 0.5 1.0
R
Fig.23. 2D Streamlines plot for R=0.90
Fig.25. Dimensionless Length separation zone vs. Ratio
of discharge
Figs.(24) to (25) present the predicted variation of
non-dimensional width and length of separation
Fig.26. shows that the contraction coefficient Cc,
zone in the intake for different discharge ratios.
Measurement of Kasthuri and Pundarikanthan (Cc=effective width of lateral intake/width of
(1987) is included for comparison. A good intake), increases linearly as discharge ratio
agreement is found between the experimental data increases. This indicates that a smaller branch
and the present numerical results. discharge Qb results in a small effective width in the
Results indicate that both length and width of the recirculation region of the branch channel.
separation zone decrease with increasing discharge
ratio. Separation zone reduces the effective width of 0.75
the channel. Separation zone can be defined as the Numerical Results(FLUENT)
area of reduced pressure and re-circulating fluid
with low velocities; therefore it has a strong
sediment deposition potential in which sediment
Cc

0.5
particles enter the branch channel. It can be seen
that for a lower discharge ratio, more than 60% of
the branch channel width is occupied by the re-
circulating zone. Numerically, it is found that the 0.25
recirculation region ends before the end of the 0 0.25 0.5 0.75 1
branch channel. R
Fig26. Contraction coefficient in branch channel

8 Summary and Conclusions

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 WSEAS TRANSACTIONS on MATHEMATICS Hamid Shamloo and Bahareh Pirzadeh

Using lateral intake is a method of floodwater total discharge in main channel

Q =
driving. In arid and semi-arid areas, floodwater upstream
contain large amount of sediment that will be R = Q b/Q, discharge ratio
carried into the intakes and decreases channel ε = dissipation rate
conveyance. Sediment conveys into the intake and distance in main channel,
settles in the separation zone beside the upstream X = downstream from branch channel
side of lateral channel. Sedimentation in separation centerline
zone reduces the conveyance of lateral channel, thus distance in branch channel from
Y =
it is important to determine the length and width of opposite main channel wall
separation zone. X* = X normalized by channel width
In this study the velocity components and Y* = Y normalized by channel width
dimensions of separation zone at the intake for Maximum width of separation
SW =
dividing flows in a 90°, sharp-edged, rectangular zone in intake
open channel junction formed by channels of equal Maximum width of separation
SL =
width are obtained on the basis of numerical studies. zone in intake
It was found the size and location of separation zone Effective width of lateral
Cc =
is very much dependent on the discharge ratio. In all intake / b
cases, the results showed an increase in discharge
ratio causes shorting and narrowing of the
separation zone. References
The largest Y-Velocities appear to occur just [1] BEST J.L., REID., “Separation zone at
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discharge ratios simulated, where the maximum Hydraulic Engineering, Vol.110, No.11,
flow contraction occurs. 1984,pp.1588-1594
A separation zone may also occur in the main [2] FLUENT user’s guide manual-version 6.1.,
channel downstream of the junction, because of the Fluent Incorporated, N.H., 2003
flow expansion. The width and length of this [3] GRACE J. L., and PRIEST, M. S,” Division
separation zone increase with the increase in the of flow in open channel junctions”, Bulletin
discharge ratio zone increase with the increase in No. 31, Engineering Experimental Station,
the discharge ratio R. Alabama Polytechnic Institute, 1958.
[4] KASTHURI B. and
PUNDARIKHANTHAN N.V, “Discussion
Notation on separation zone at open channel
The following symbols are used in this paper: junction.”, Journal of Hydraulic
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No.2, 1999,pp.126-140
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[9] NEARY V.S. and ODGAARD A.J.,

“Three-dimensional flow structure at open-
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Intakes”, M.S.C thesis, K.N.Toosi
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[11] RAMAMURTHY A.S, SATISH M.G,
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of Characteristics of Separation Zones in T-
Junctions”, Proceedings of the 12th
WSEAS International Conference on
APPLIED MATHEMATICS”, Cairo,
Egypt, Desember29-31, 2007, PP.189-193
[15] Shamloo H., Pirzadeh B., “Numerical
investigation of Velocity Field in Dividing
Open-Channel Flow”, Proceedings of the
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[17] TAYLOR, E.H. “Flow characteristics at
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