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

Omid Seyedashraf et al. / International Journal of Engineering and Technology Sciences (IJETS) 3 (3): 262-274, 2015.

263 | P a g e

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).

Omid Seyedashraf et al. / International Journal of Engineering and Technology Sciences (IJETS) 3 (3): 262-274,

2015.

270 | P a g e

(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

)


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

)


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

)


Experimental

FLOW3D

FLUENT

0

10

20

30

40

50

60

-22 -17 -12 -7 -2 3 8 13 18

Vel

oci

ty (

cm/s

)


Experimental

FLOW3D

FLUENT

0

10

20

30

40

50

60

-22 -17 -12 -7 -2 3 8 13 18

Vel

oci

ty (

cm/s

)


Experimental

FLOW3D

FLUENT


272 | P a g e

(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

)


Experimental

FLOW3D

FLUENT

0

10

20

30

40

50

60

-22 -12 -2 8 18

Vel

oci

ty (

cm/s

)


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.

References

[1] Seyedashraf O, Akhtari AA, Khatib Shahidi M.

Numerical Study of Channel Convergence Effects

on Flow Pattern in 90 Degree Bends. 9th

International Congress on Civil Engineering,

Civilica, Isfahan, 2012.

[2] Termini D, Piraino M. Experimental analysis of

cross-sectional flow motion in a large amplitude

meandering bend. Earth Surface Processes and

Landforms 2011; 36 (2): 244-256.

[3] Morvan H, Pender G, Wright N, Ervine D.

Three-Dimensional Hydrodynamics of Meandering

Compound Channels. Journal of Hydraulic

Engineering 2002; 128 (6): 674-682.

[4] Kang S, Sotiropoulos F. Flow phenomena and

mechanisms in a field-scale experimental

meandering channel with a pool-riffle sequence:

Insights gained via numerical simulation. Journal

of Geophysical Research: Earth Surface 2011;

116(F03011).

[5] Constantinescu G, Koken M, Zeng J. The

structure of turbulent flow in an open channel bend

of strong curvature with deformed bed: Insight

provided by detached eddy simulation Water

Resources Research 2011; 47 (5).

[6] Thompson J. On the origin of the windings of

rivers in alluvial plains, with remarks on flow of

water in pipes. Proceedings of the Royal Society of

London, London, 1876.

[7] De Vriend HJ. A Mathematical Model Of

Steady Flow In Curved Shallow Channels. Journal

of Hydraulic Research 1977; 15 (1): 37-54.

[8] Damaskinidou‐Georgiadou, A., Smith, K., Flow

in Curved Converging Channel, Journal of

Hydraulic Engineering. 112 (1986) 476-495.

[9] Ghamry HK. Two Dimensional Vertically

Averaged and Moment Equations for Shallow Free

Surface Flows, Department of Civil and

Environmental Engineering, Alberta, Edmonton,

1999.

[10] Ahmadi MM, Ayyoubzadeh SA, Montazeri

Namin M, Samani JMV. A 2D Numerical Depth-

averaged Model for Unsteady Flow in Open

Channel Bends, Journal of Agriculture Science

Technology 2009; 11:457-468.


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[11] Akhtari AA. Surveying flow in strongly-

curved open channel and evaluation of the effect of

internal non submerged vanes on flow pattern

through the bends, Ph.D. thesis, Ferdowsi

University of Mashhad, 2010.

[12] Abhari MN, Ghodsian M, Vaghefi M,

Panahpur N. Experimental and numerical

simulation of flow in a 90° bend. Flow

Measurement and Instrumentation 2010; 21 (3)

292-298.

[13] Ghobadian R, Mohammadi K. Simulation of

subcritical flow pattern in 180° uniform and

convergent open-channel bends using SSIIM 3-D

model. Journal of Water Science and Engineering

2011; 4 (3).

[14] Vietz GJ, Rutherfurd ID, Stewardson MJ,

Finlayson BL. Hydrodynamics and sedimentology

of concave benches in a lowland river.

Geomorphology 2012; 147(0): 86-101.

[15] Ramamurthy A, Han S, Biron P. Three-

Dimensional Simulation Parameters for 90° Open

Channel Bend Flows. Journal of Computing in

Civil Engineering 2012; 27 (3): 282-291.

[16] Fluent, I., FLUENT 6.3 User's Guide,

Lebanon, New Hampshire, 2006.

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