Flow Structures in Sharply-Curved Open Channel Bends … … · · 2015-08-12Flow Structures in...
Transcript of Flow Structures in Sharply-Curved Open Channel Bends … … · · 2015-08-12Flow Structures in...
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International Journal of Engineering & Technology Sciences
Volume 03, Issue 03, Pages 262-274, 2015
ISSN: 2289-4152
Flow Structures in Sharply-Curved Open Channel Bends-Numerical
Comparison of Two CFD Models
Omid Seyedashraf a, Somaye Elyasi b, Ali Akbar Akhtari b,*
a Department of Civil Engineering, Kermanshah University of Technology, P.O. Box: 67178-63766, Kermanshah, Iran b Department of Civil Engineering, Razi University, P.O. Box: 67149-67346, Kermanshah, Iran
* Corresponding author. Tel.: +98-9188583216
E-mail address: [email protected]
A b s t r a c t
Keywords:
Sharply-Curved Open
Channel Bend, FLUENT,
FLOW3D,
Volume Of Fluid,
RNG k-ε.
There is a lack of insight in the application and comparison of CFD models on numerical
simulation of water flow in sharp open channel bends. In this paper, we report on successful
numerical experiments in curved bends, which are conducted using two commercial finite-
volume and finite-difference models (FLUENT and FLOW3D). A comparison of numerical
results was carried out based on a collation with experimental data. The models are
validated against experimental results. All salient features of the water flow which can be
found in the experimental measurements can be identified in the numerical results of both
CFD packages. Consequently, FLUENT has the advantage of employing irregular meshing
forms, thus being less CPU-intensive than FLOW3D. However, FLOW3D benefits user-
friendly pre-processing tools. According to the results, it is evident that FLOW3D shows
better performance over FLUENT. Slight discrepancies were noted, which can be credited
to the different numerical techniques used to conduct the simulations. The calculated
RMSEs for FLUENT and FLOW3D are 7.9 and 4.5 for the velocity results, and 0.9 and
0.29 for the water level results, respectively. Since, it is evident that the accuracy of the
obtained results significantly depends on the grid form; more precise numerical results can
be obtained by conducting a mesh analysis study.
Accepted:03May2015 © Academic Research Online Publisher. All rights reserved.
1. Introduction
The analysis of the flow pattern in open channel
bends must be taken into account in the design and
construction of channels. This is key in studying
the morphology of rivers since it is very unlikely to
see a straight stream in a length longer than ten
channel section width in a river reach. The helical
motion of fluid particles is of the major
distinguishing characteristics in an open channel
bend flow. This motion is induced by the secondary
currents in conjunction with the existing
momentum along the channels. The phenomenon is
known as the main reason of the winding river
morphology and the trend to produce shoals and
deeps along river reaches. These currents are
shaped because of the disequilibrium in pressure
gradient and centrifugal force at arbitrary sections.
Many researchers so far employed three-
dimensional numerical models to study flow
characteristics and mechanism of helical motions
around open channel bends [1-5]. Thompson [6] is
among the pioneering researchers, presented data
and analyzed the flow behavior in open channel
bends. He defined the development of a helicoidal
flow in curved channels and described the event as
being the consequence of the changes in velocity of
fluid segments alongside the water depth. De
Vriend [7], applied a three-dimensional numerical
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model to simulate the flow features in open channel
bends. However, the model seems not to behave
well in sharp curvatures. Excluding the studies
carried out by Damaskinidou‐Georgiadou and
Smith [8], not many inclusive surveys on a
converging bend can be found in the literature.
They investigated the flow pattern in converging
bends in both experimental and numerical
approaches. The research involved three-
dimensional velocity measurements and a flow
visualization method for the surface and bottom
flow fields. Ghamry [9], developed a two-
dimensional vertically averaged and moment
equations to account for problems where more
vertical details are significant and essential. They
have employed an implicit Petrov-Galerkin finite-
element scheme. Ahmadi et al. [10], described two-
dimensional depth-averaged calculations of flow in
open channel flow bends. Employing a finite-
volume projection method approach for solving the
governing equations. They validated the numerical
results and concluded that the inclusion of the
dispersion terms improved the simulation results.
Akhtari [11], has carried out experiments on 30,
60 and 90 strongly-curved open channel bends
with a central radius of 60cm. With a 1.5 ratio of
curvature radius to channel width considering five
different discharge values, Akhtari collected
extensive data, like velocity and water depth
profiles and noticed that at a distance equal to
channel width from the bend entry and bend exit,
the water surface was not being affected by the
curvature. Abhari, Ghodsian, Vaghefi and
Panahpur [12], implemented the finite element
code (SSIIM) and numerically studied the flow
pattern in an open channel bend. Despite their
numerical model was not successful to capture the
minimum secondary flow, however it was able to
predict the main secondary flow and the affected
flow pattern after the bend. Similar research were
carried out making use of the SSIIM software for
numerical simulation of the identical hydraulic
phenomenon by many other researchers [13].
Termini and Piraino [2], investigated the flow field
in a sharply-curved laboratory flume with smooth
vertical banks and mobile bed. The study was
carried out through gathering data from three mean
velocity components.
Vietz, Rutherfurd, Stewardson and Finlayson [14],
studied the flow separation zone in a sharply
curved natural bend with the outer bank widening,
recirculation zone and depositional environment.
They noticed that the benches are maintained at all
flow stages from benchfull to bankfull.
Ramamurthy, Han and Biron [15] compared two
commercial CFD software (PHOENICS and
FLUENT) for numerical simulation of fluid flow in
a 90 open channel bend. Accordingly, they
employed different turbulent and free surface
models. They concluded that the best agreements
with experimental results were obtained by
FLUENT making use of RSM turbulent model
imparting the salient features of the volume of fluid
(VOF) free surface model.
The objective of this paper is to compare the
performance of two regularly used CFD packages
(FLUENT and FLOW3D) in numerical simulation
of flow in a sharp open channel bend, which was
previously investigated by Akhtari [11].
Accordingly, the complete numerical approach to
simulate the flow fields were described. The main
configurations, e.g. the turbulence and the free-
surface models, were kept identical. However,
since FLOW3D uses the Cartesian coordinates, the
employed pre-processing grid forms for two
simulations were dissimilar.
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2. Governing equations
The utilized governing equations are based on
conservation of mass, momentum, and energy.
FLOW3D and FLUENT were employed in order to
solve the respective governing equations.
FLOW3D is based on the finite-difference method
(FDM) while FLUENT employs the finite-volume
method (FVM) to approximately solve the
equations on the discretized computational domain.
The FVM involves discretization and integration of
the governing equations over the control volumes.
However, the FDM estimates the derivatives in
differential form of the equations by difference
statements formulated at discrete points. Since the
compressibility and the heat transfer are ignored
here, the energy equation is crossed out from the
equation system. The governing equations
(Reynolds Averaged Navier-Stokes equations) are
stated as follows:
im
i
uS
t x
(1)
i ji
j i
i jji
j j i j
u uu p
t x x
u uuu
x x x x
(2)
where t is time, ui is the i-th component of the
Reynolds-averaged-velocity, xi the i-th axis (with
the axis x3 vertical and oriented upward), is the
water density, p is the Reynolds averaged pressure,
g is the acceleration due to the gravity, is the
viscosity that is equal to zero in this study, and Sm
is the mass exchange between the two phases
(water and air). Moreover, the term ( jiuu ) has
to be approximated in order to close the equation
system. Consequently, the mean rate of
deformation must be linked to the Reynolds-
stresses as follows:
i
j
j
itji
x
u
x
uuu (3)
here t is the turbulent viscosity.
The rotating nature of the turbulent flow indicates
that the Renormalization Group (RNG) k-ε
turbulence model included in both CFD packages
should work fairly well in this investigation [1].
The RNG k-ε equations are derived from an
accurate and statistical method. It is comparable to
the standard k-ε equations; however, there is an
extra term in the ε equation for turbulence
dissipation and mean shear. Its suitable effect of
swirl on turbulence makes the model appropriate
for swirling secondary flows. Neglecting the body
forces, the turbulent kinetic energy and dissipation
equations would be as follows:
2
eff
i ti
ki i
kU S
x
k
x x
(4)
21
2
eff 2
i ti
i i
U C Sx k
C Rx x k
(5)
where R is an additional term related to mean strain
and turbulence quantities, which is the main
difference between RNG and standard k-ε model. S
is calculated from velocity gradients, αε, αk, C1εand
C2ε are derived through RNG theory [16].The
equation for k contains additional turbulent
fluctuation terms, which are unknown.
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Furthermore, the VOF model was employed in both
CFD software packages as the preferred free
surface model. The value of the volume fraction of
water, F, was calculated in all computational cells
through solving the advection equation defined:
1
0
xF
y z
FFuA
t V x
FvA FwAy z
(6)
here F is equal to 1 when the cell is full of the
secondary phase (water). This parameter varies
between 0 and 1.
3. Numerical Modeling
Table (1) depicts the overall numerical procedure
used for carrying out the simulations.
Table 1: Numerical schemes used in FLUENT and FLOW3D
Numerical scheme FLUENT FLOW3D
Numerical model FVM FDM
Solver Pressure based Pressure based (GMRES)
Scheme Implicit Implicit
Pressure-velocity coupling PISO SOR implicit
Under relaxation factors Pressure:0.3, Momentum: 0.7, volume fraction: 0.5 Over-relaxation factor OMEGA: 1.7
Convective/Advection terms MUSCL IMPADV
Free surface model VOF TruVOF
Turbulence model RNG k-ε RNG k-ε
Boundary conditions:
Inlet Velocity inlet Volume Flow Rate
Outlet Outflow Specified Pressure
Walls Non-equilibrium wall functions Wall
3.1 Numerical Simulation Using FLUENT
Griding is the first step to conduct numerical
simulations. GAMBIT, which is a commonly used
pre-processor in CFD simulations, was employed
to create the geometry. Accordingly, the flow
region was discretized into 386,400 non-
overlapping structured finite elements. A grid-
independence study was carried out and it was
concluded that the structured curvilinear mesh was
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the appropriate grid form for the meandering
sections [11]. Accordingly, 175 longitudinal, 50
latitudinal and 28 altitudinal segments were created
in the computational domain. To provide ideal
conditions for having a fully developed flow, the
identical open channel created in the laboratory
was numerically simulated. Figure 1 depicts the
geometric layout of the benchmark.
Fig. 1: Schematic of the open channel bend.
Figure 2 shows the employed grid form prepared in GAMBIT.
(a)
(b)
Fig. 2: Grid form used for numerical simulations using FLUENT: (a) section view (b) plan view.
The hydraulic parameters for the fluid flow used in the laboratory are depicted in Table 2.
Table 2: Experimental characteristics
Radius of curvature (m) Depth of flow (m) Channel width (m) Mean velocity (m/s) Reynolds number
0.6 0.12 0.403 0.394 36765
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The-state-of-art CFD code, FLUENT, was used for
numerical simulation presented in this section. The
code employs the FVM in conjunction with a
coupling method, which concurrently solves the
governing equations in the computational domain.
The third order monotone upstream centered
scheme for conservation law (MUSCL) was
employed to discretize the convection terms.
Moreover, in order to couple the velocity and
pressure parameters, the pressure-implicit with
splitting of operators (PISO) method was
implemented in this work. PISO merges pressure
effect using momentum and continuity equations to
acquire correction terms for pressure. The VOF
method was also implemented in order to deal with
the air-water interactions. The VOF method is
formulated based on the fact that two or more
phases will not interpenetrate. Accordingly, for
each extra phase added to the flow region, a new
variable must be presented in the volume fraction
of the respective phase in each control volume.
Therefore, the volume fractions of all phases sum
to unity.
The employed boundary conditions were:
1. Two separate inlets as water and air inlets
with identical group IDs were defined as
‘Velocity-inlet’ while the ‘Open Channel’
option activated for it. The option is useful to
have a fixed water level for inlet boundaries.
2. The ‘Outflow’ boundary condition was
selected as the outflow basin along with two
separate outlets having the same group ID.
3. ‘Symmetry’ boundary condition was chosen
as the upper surface boundary section.
Choosing the symmetry boundary type the
normal components and gradients’ quantity
will be null.
4. ‘Wall’ boundary condition was used for
defining side walls and bottom surfaces.
Since walls are key sources of turbulence, the non-
equilibrium wall function, which are manageable
with the k-ε models that are suitable for complex
flows, have been implemented to deal with fast
fluctuations of unknown parameters such as
velocities [5].
Completing the iterations, the numerical
convergence was attained after 3,500 iterations.
3.2 Numerical Simulation Using FLOW3D
FLOW-3D is one of the most powerful software in
the field of fluid dynamics. This software has been
used extensively for research on the behavior of
one-, two-and three-dimensional fluid dynamics.
Making use of the FDM it solves the governing
equations. FLOW-3D is based on the Cartesian
grid, thus uses rectangular grid forms. The software
benefits fast numerical simulations since
rectangular grids require less memory to discretize
the flow region. The flow region was discretized
into 1,250,000 non-overlapping and structured
finite elements. This program can model free
surface flow benefiting the VOF model. One of the
main features of this program is the ability to
model different physical models, which include
shallow water, viscosity, cavitation, turbulence,
surface tension and porous particles.
FLOW-3D employs the fractional area/volume
obstacle representation (FAVOR) scheme to model
complex geometries and obstacles in computational
domain. The flow geometry was constructed using
the AutoCAD software and imported into the
model as a stereo lithography (STL) file, which is
shown in Figure 3.
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Block #1
Block #2
Block #3
STL
file
Fig. 3: The STL file imported in FLOW3D.
Figure 4 also depicts the grid form used for the numerical simulation procedures.
Fig.4: Grid form used for numerical simulations using FLOW3D: (A) section view (B) plan view of the bend.
It is of great consequence to create equal conditions
between the experimental and numerical case
studies. The employed boundary conditions were as
follows:
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1. The “Volume Flow Rate” with a constant
discharge of 25 lit/s has been chosen as
the input boundary condition.
2. The “Wall” boundary condition was
employed for all solid boundaries.
3. The “Specified Pressure” boundary
condition was selected as the outflow
basin along with two separate outlets
having the same group ID.
4. Validation and Comparison
The obtained numerical results from both CFD
software were put side by side Akhtari’s
experimental data and the reliability of the
employed numerical procedures were questioned
[11]. To assess the performance of numerical
models, a regularly used criteria were used, which
is the root mean square error (RMSE).
Accordingly, the best fit between experimental and
numerical values will give RMSE values close to
0. This measure is defined as follows:
2
1
1 ˆ( )n
i iiRMSE U U
n (7)
Where iU is the observed velocity; ˆiU is the
simulated velocity and n is the number of observed
data. RMSE of the numerical velocity data and
water level results were calculated and listed in
Table 3 and Table 4, respectively.
Table 3: Root mean square errors of velocity results
0o section 45o section 90 section 40cm section 80cm section
FLUENT 7.30 5.36 11.45 6.10 9.30
FLOW3D 3.28 3.5 4.34 7.92 3.93
Table 4: Root mean square errors of water level
0o section 45o section 90 section
FLUENT 0.93 0.83 0.94
FLOW3D 0.65 0.17 0.05
As seen, FLOW3D shows better performance since
the cells employed in its grid form were smaller in
comparing with the ones utilized in the mesh file
used by FLUENT. The numerical and experimental
analogy of the water levels in different sections of
the channel bend is shown in Figure 5 (a-c).
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2015.
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(a)
(b)
(c)
Fig. 5: Experimental and numerical results of water levels in different sections: A- 0, B- 45, C- 90.
10
10.5
11
11.5
12
12.5
13
-22 -17 -12 -7 -2 3 8 13 18
Wat
er l
evel
(cm
)
Distance from middle of the channel (cm)
Experimental
FLOW3D
FLUENT
10
10.5
11
11.5
12
12.5
13
-22 -17 -12 -7 -2 3 8 13 18
Wat
er l
evel
(cm
)
Distance from middle of the channel (cm)
Experimental
FLOW3D
FLUENT
10
10.5
11
11.5
12
12.5
13
-22 -17 -12 -7 -2 3 8 13 18
Wat
er l
evel
(cm
)
Distance from middle of the channel (cm)
Experimental
FLOW3D
FLUENT
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Moreover, the comparisons between the experimental and the predicted flow velocities are shown in the Figure 6(a-e).
(a)
(b)
(c)
0
10
20
30
40
50
60
-22 -17 -12 -7 -2 3 8 13 18
Vel
oci
ty (
cm/s
)
Distance from middle of the channel (cm)
Experimental
FLOW3D
FLUENT
0
10
20
30
40
50
60
-22 -17 -12 -7 -2 3 8 13 18
Vel
oci
ty (
cm/s
)
Distance from middle of the channel (cm)
Experimental
FLOW3D
FLUENT
0
10
20
30
40
50
60
-22 -17 -12 -7 -2 3 8 13 18
Vel
oci
ty (
cm/s
)
Distance from middle of the channel (cm)
Experimental
FLOW3D
FLUENT
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(d)
(e)
Fig. 6: Comparison of cross-sectional velocity profiles: (a) 0; (b) 45; (c) 90, and (d) 40cm; (e) 80cm after the bend.
From the trends mentioned in Figures (5) and (6) it
is obvious that both CFD software were able to
catch the salient characteristics of the water flow in
sharply-curved open channel bends. It can be seen
that along the curved sections, the distribution of
the velocity is not symmetric and the max velocity
was shifted towards the outer bank of the bend.
This happens because of the existence of helicoidal
flow and pressure changes in meanderings. The
average velocities obtained experimentally and
numerically in the 45 section are 44.60 cm/s,
43.90 cm/s and 46.44 cm/s obtained by FLOW3D
and FLUENT, respectively. The value reaches zero
near the side-walls from the highest velocity
underneath the water level and nearby the outer
0
10
20
30
40
50
60
-22 -17 -12 -7 -2 3 8 13 18
Vel
oci
ty (
cm/s
)
Distance from middle of the channel (cm)
Experimental
FLOW3D
FLUENT
0
10
20
30
40
50
60
-22 -12 -2 8 18
Vel
oci
ty (
cm/s
)
Distance from middle of the channel (cm)
Experimental
FLOW3D
FLUENT
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bank. This happens because of the boundary layer
development.
5. Conclusions
Comparing the results obtained by two CFD
models (FLUENT and FLOW3D) for the
numerical simulation of water flow in sharp open
channel bends, it was found that FLOW3D had a
more successful performance. However, this
conclusion cannot be extended to all similar
simulations since not all of the numerical
techniques used in both models were similar.
Although, the same turbulence and free surface
models were employed nevertheless some
numerical procedures were different (e.g. the
convection/advection terms were discretized using
different approaches). Moreover, the employed
grid form and the size of computational cells were
dissimilar. This was due to the limitations in
choosing identical mathematical approaches and
pre-processing tools. Accordingly, comparing the
number of computational cells used for both
simulations, FLOW3D’s better performance was
an expected result. Concerning how the pre-
processing tools can affect the results; the issue can
be an attention-getting topic in numerical studies of
hydraulic phenomena. More studies are being
conducted presently to further investigate the effect
of grid forms on numerical predictions to improve
the simulation and their efficiency.
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