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Determination of appropriate configuration ofsubmerged vanes using fuzzy TOPSIS optimizationSeyed Hessam Seyed Mirzaeia & Seyed Ali Ayyoubzadehb

a Department of Civil Engineering, Queen's University, Kingston, Ontario, Canada K7L3N6b Department of Water Structures Engineering, Tarbiat Modares University, Tehran, IranPublished online: 05 Feb 2014.

To cite this article: Seyed Hessam Seyed Mirzaei & Seyed Ali Ayyoubzadeh (2013) Determination of appropriate configurationof submerged vanes using fuzzy TOPSIS optimization, Journal of Applied Water Engineering and Research, 1:2, 102-117, DOI:10.1080/23249676.2013.873164

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Journal of Applied Water Engineering and Research, 2013Vol. 1, No. 2, 102–117, http://dx.doi.org/10.1080/23249676.2013.873164

Determination of appropriate configuration of submerged vanes using fuzzy TOPSISoptimization

Seyed Hessam Seyed Mirzaeia and Seyed Ali Ayyoubzadehb∗

aDepartment of Civil Engineering, Queen’s University, Kingston, Ontario, Canada K7L3N6; bDepartment of Water StructuresEngineering, Tarbiat Modares University, Tehran, Iran

(Received 25 June 2013; accepted 3 December 2013 )

Submerged vanes are river-training structures installed vertically in front of intake ports to exclude sediment at water intakes.The performance of submerged vanes depends on their dimensions, configuration and shape. This study was aimed atnumerically investigating the effect of vane configuration on sedimentation in a 90◦ intake from a straight channel, anddetermine an appropriate configuration for installing the vanes. Simulations were done using the FLUENT mathematicalmodel, and the fuzzy technique order performance by similarity to ideal solution multi-objective optimization method wasused for choosing the appropriate configuration. All simulations were done for the three discharge ratios of 0.11, 0.16 and0.21. The results showed that a longitudinal distance of nine times the vane height, a transverse distance of three timesthe vane height and 25◦ angle of attack are the appropriate parameters for the configuration of submerged vanes to controlsediment in front of intake ports.

Keywords: appropriate configuration; FLUENT mathematical model; fuzzy TOPSIS method; multi-objective optimization;submerged vanes sediment control sediment management

1. IntroductionSediment management, in particular the control of sedi-ment movement, scour and deposition is one of the mostdifficult problems encountered by river engineers. Depo-sition of sediment is also a recurring problem at manywater intakes and diversions. The submerged-vane tech-nique is a new approach for solving the sedimentationproblem in intake channels. Submerged vanes are lowaspect ratio flow-training structures mounted vertically onthe river bed at an angle with respect to the flow direc-tion. The vanes aim is to generate a secondary circulationin the main flow and are designed to modify near-bed flowpattern and to re-distribute flow and sediment transportwithin the channel cross-section. Due to the pressure changearound the vanes, the pressure increases from bottom to topon the low-pressure side, decreases from bottom to top onthe high-pressure side. These pressure changes cause thefluid flowing along the high-pressure side to develop anupward velocity component, while on the low-pressure sidethere is a downward velocity component (Barkdoll 1997).

Much research in the field of submerged vanes hasbeen undertaken in the last decades. Odgaard and Kennedy(1983) attempted to design a system of vanes to stop orreduce bank erosion in river curves. Odgaard and Spoljaric(1986), through laboratory tests, suggested that vanes werelaid out to change the cross-sectional profile of the bed in a

∗Corresponding author. Email: ayyoub@modares.ac.ir

straight channel; significant changes in depth were achievedwithout causing significant changes in cross-sectional area,energy slope and downstream sediment transport. Odgaardand Wang (1991) investigated scour and deposition controlwith submerged vanes and reported that the vanes functionby generating secondary circulation in the flow. The circu-lation alters magnitude and direction of the bed shear stressand causes a change in the distribution of velocity, depthand sediment transport in the area affected by the vanes.Marelius and Sinha (1998) investigated the physics of flowpassing the vanes with a large angle of attack. The mainobjective of their study was to find an optimal angle ofattack, which produces a strong secondary current. Ouyanget al. (2009) investigated the effects of a vane’s dimensionsand shape on its performance in a sediment control capacity.His study showed that for a rectangular vane, the optimalvane height is related to the length of the vane and is within0.58–0.70 water depths.

In this research, a numerical investigation was per-formed to determine the appropriate configuration of sub-merged vanes, considering a combination of the effectsof several parameters in the optimization process usinga computational fluid dynamics solver. The simulationswere done for various configurations of submerged vanes.Three simulations for the different longitudinal distancesbetween vanes (δs) with 1Hv increments in the range of

© 2014 IAHR and WCCE

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(8–10)Hv, two simulations for the different transverse dis-tances between vanes (δn) in the range of (2–3)Hv with 1Hvincrements and three simulations for angle of attack (α) inthe range of 15◦–25◦ with 5◦ increments were conducted.Appropriate dimensions of submerged vanes have beenconsidered (Omidbeigi 2010; Seyed Mirzaei 2011). Finally,by using the fuzzy technique order performance by similar-ity to ideal solution (TOPSIS) multi-objective optimizationmethod, the appropriate configuration for submerged vaneswas determined.

2. Numerical model description and governingequations

In this research the FLUENT mathematical model has beenutilized for simulating the flow pattern. This model pro-vides multiple choices of solver option, combined witha convergence-enhancing multi-grid method, and deliv-ers optimum solution efficiency and accuracy for a widerange of speed regimes. Accurate prediction of laminar andturbulent flows, various modes of heat transfer, chemicalreactions, multiphase flows and other phenomena with com-plete mesh flexibility and solution-based mesh adoption isone of the main features of FLUENT (2006).

In this study, we used the second-order upwind dis-cretization scheme for momentum, turbulent kinetic energy,turbulent dissipation rate and Reynolds stresses, and thestandard discretization scheme for pressure. Also, the SIM-PLE algorithm for the pressure–velocity coupling methodwas used. Since in the intersection of lateral intakes andrivers the flow is turbulent and very complex, we usedthe Reynolds stress model (RSM) turbulence model in thispaper.

The governing equations of fluid flow in riversand channels are generally based on three-dimensionalReynolds averaged equations for incompressible free sur-face unsteady turbulent flows as follows (Neary & Odgaard1993):

∂Ui

∂t+ Uj

∂Ui

∂xj

= 1ρ

∂

∂xj

[(−p + 2

3k)

δij + νT

(∂Ui

∂xj+ ∂Uj

∂xi

)], (1)

where t = time; Ui (i = 1, 2, 3) and ui (i = 1, 2, 3) arethe mean and fluctuating velocity components in the x(lateral), y (streamwise) and z (vertical) direction, respec-tively; P = total pressure; k = turbulently kinetic energy;δij = Kronecker delta; vT = turbulent viscosity; and j = 1,2, 3. There are basically five terms: a transient term and aconvective term on the left side of the equation. On the rightside of the equation there is a pressure/kinetic term, a diffu-sive term and a stress term. In the current study, it is assumedthat the density of water is constant through the computa-tional domain. The governing differential equations of mass

and momentum balance for unsteady free surface flow canbe expressed as (Chen & Lian 1992)

∂ui

∂xi= 0, (2)

∂ui

∂t+ uj

∂ui

∂xj= − 1

ρ

∂P∂xi

+ gxi + ν∇2ui, (3)

where v is the molecular viscosity; gxi is the gravitationalacceleration in the xi direction. As in the current study,only the steady-state condition has been considered, there-fore Equations (2) and (3) incorporate appropriate initialand boundary conditions deployed to achieve equilibriumconditions.

3. Optimization method descriptionSince several criteria were considered for choosing theappropriate configuration of the vanes, and for each cri-terion a specific configuration had the best performance,choosing the appropriate configuration by considering theeffects of all criteria was not possible. Therefore, a multi-objective optimization method was utilized to choose theappropriate configuration of the vanes.

One of the most classical methods for solving the multi-criteria decision-making problem is TOPSIS. This tech-nique is based on the principle that the chosen alternativeshould have the shortest distance from the fuzzy positiveideal solution (FPIS), i.e. the solution that minimizes thecost criteria and maximizes the benefit criteria; and thelongest distance from the fuzzy negative ideal solution(FNIS), i.e. the solution that maximizes the cost criteria andminimizes the benefits criteria (Saghafian & Hejazi 2005).

In this research the distance of dividing streamline fromintake port in near surface level, the secondary flow strengthand the amount of shear stress imposed on the bed in frontof the intake port and the volume of the flow entering intothe intake from two middle depth and surface levels wereconsidered as benefit criteria, and the distance of dividingstreamline from intake port in near-bed level and the volumeof the flow entering into the intake from near-bed level wereconsidered as the cost criteria.

Considering the above-mentioned criteria, we haveadapted the relevant steps of fuzzy TOPSIS as presentedbelow:

(1) Computing the fuzzy decision matrixThe fuzzy decision matrix for the alternatives

and the criteria was constructed. The columns andthe rows of this matrix represent the consideredcriteria and alternatives, respectively.

D =

⎡⎢⎢⎢⎣

x11 x12 . . . x1nx21 x22 . . . x2n...

.... . .

...xm1 xm2 . . . xmn

⎤⎥⎥⎥⎦ (4)

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104 S.H. Seyed Mirzaei and S.A. Ayyoubzadeh

where xij , i = 1, 2, . . . , m; j = 1, 2, . . . , n are lin-guistic variables which are described by triangularfuzzy numbers.

(2) Normalizing the fuzzy decision matrixBy using linear scale transformation to bring the

various criteria scales into a comparable scale, theraw data were normalized. The normalized fuzzydecision matrix R is given by (Saghafian & Hejazi2005)

R = [rij]m×n, i = 1, 2, . . . , m, j = 1, 2, . . . , n(5)

where⎧⎪⎪⎨⎪⎪⎩

rij =(

aij

c∗j

,bij

c∗j

,cij

c∗j

)and

c∗j = maxi cij (benefit criteria)

(6)

⎧⎪⎪⎨⎪⎪⎩

rij =(

a−j

c∗j

,a−

j

c∗j

,a−

j

c∗j

)and

a−j = mini aij (cost criteria)

(7)

(3) Computing the distance of each alternative fromFPIS and FNIS

The distance of each weighted alternative i =1, . . . , m from the FPIS (d∗

i ) and the FNIS (d−i ) was

computed as follows (Saghafian & Hejazi 2005):

d∗i =

n∑j=1

d(vij , v∗j ), i = 1, 2, . . . , m,

v∗j = (1, 1, 1), (8)

d−i =

n∑j=1

d(vij , v−j ), i = 1, 2, . . . , m,

v−j = (0, 0, 0). (9)

The distance between two triangular fuzzy num-bers of m = (m1, m2, m3) and n = (n1, n2, n3) wascalculated using the following equation:

d(m, n)

=√

13[(m1 − n1)2 + (m2 − n2)2 + (m3 − n3)2]

(10)

(4) Computing the closeness coefficient (CC) of eachalternative

The CC of each alternative was calculated as(Saghafian & Hejazi 2005)

cci = d−i

d∗i + d−

i, i = 1, 2, . . . , m (11)

(5) Ranking the alternatives

In this step, according to the calculated CCthe different alternatives were ranked in decreas-ing order. The best alternative was farthest fromthe FNIS, and closest to the FPIS.

4. Numerical model validationIn order to validate the model, the flow pattern was simu-lated in a flume with the dimensions and other specificationsconsistent with that of the flume used in the hydraulic lab-oratory of Tarbiat Modares University, and in the presenceof the submerged vanes with dimensions and configura-tions consistent with that of the vanes used in Omidbeigi’sexperimental research (2010); The velocity data obtainedfrom the simulations were then validated against the Omid-beigi’s measured velocity data. He utilized Vectrino – ahigh-resolution acoustic velocimeter used to measure 3Dwater velocity in a wide variety of applications from thelaboratory to the ocean – to measure water velocity. Thisdevice is a newer version of the acoustic Doppler velocime-ter. The measured velocity data were 3D water velocities indifferent sections of the main and intake channels with theaccuracy of ±0.5%.

Figure 1 shows the numerical and experimental trans-verse profiles of velocity in Z = 0.09 m level for 11 sectionsof the main channel and 4 sections of intake channel, respec-tively, for the intake flow rate of 0.21. Comparison of theresults shows that the accuracy of the RSM turbulencemodel in prediction of the flow field both along the main andintake channels is appropriate, and the results from the tur-bulence model have suitable consistency with experimentalresults and no considerable difference is seen among them.

In Figure 2, the in-depth velocity profiles for Qr = 0.21the intake channel has been represented. The under studysection is in the section of y = 1.37 m in the intake channel,where the flow turbulence is high. Considering Figure 8,it can be said that in the intake channel, the results fromthe RSM turbulence model have good consistency withthe experimental results. The average percentage of relativeerror is 7% approximately.

5. Numerical modeling5.1. Computational domain propertiesA rectangular channel of 18 m length, by 1 m wide has beenconsidered for simulations that at the distance of 11.43 mfrom its upstream inlet, a branch channel of 2.5 m long and0.4 m wide intersects it with an angle of 90, and forms aT -shaped conjunction (Figure 3). All of the walls are con-sidered rigid. As can be seen from Figure 1, two rowsof submerged vanes, each row consisting of five vanes,are installed in the main channel, in front of the intakeentrance. The vane dimensions and configurations are givenin Table 1. Hv and d in this table represent the submergedvanes’ height and the flow depth, respectively. Also, thehydraulic properties of the computational domain are given

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Figure 1. Numerical and experimental transverse velocity profiles in Z = 0.09 m (Qr = 0.21).

Figure 2. Numerical and experimental depth velocity profiles in y = 1.37 m (Qr = 0.21).

Figure 3. Layout of the computaional domain.

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Table 1. The submerged vanes’ dimensions and configuration.

The first vane row Angle of Transverse Longitudinaldistance from the intake attack (α) distance (δn) distance (δs) Length Height

3Hv 25◦–15◦ (2–3)Hv (8–10)Hv 4Hv 0.2d

Table 2. Hydraulic properties of the computational domain.

Water depthQ1 (l/s) Q2 (l/s) Qr = (Q2/Q1) (d) (m) Re Fr

58 6.38 0.11 0.15 57,607 0.329.28 0.16

12.18 0.21

in Table 2. Qr in this table represents the discharge ratio.Considering the values of the Froude and Reynolds num-ber, it can be said that the flow is in a turbulent state and issub-critical.

5.2. Boundary and initial conditionsDepending on the nature of the flow, appropriate conditionsmust be specified at the domain boundaries. As shown inFigure 4, for the two outlets, the outflow boundary conditionis used. To ensure that the flow returns to the undisturbedpattern before reaching the outlets, the length of the mainand intake channels was chosen properly, and sufficient dis-tance was provided between the junction and two outlets.For setting the velocity to be zero at the solid boundaries, theno-slip boundary condition is specified. In the main chan-nel inlet, the velocity inlet boundary condition was used.The uniform velocity of 0.39 m/s (resulting from divisionof the inlet flow to the area of the flow section (A/Q1)) wasapplied to the domain. Also for the turbulence parametersof the domain input, the values 0.462 and 3% were consid-ered for the hydraulic diameter and the turbulence intensity,respectively. Since the flow depth was less than 10% of thechannel depth, therefore a symmetry boundary condition isapplied for the free surface (Rodi 1979). Finally, for wallsand the submerged vanes, the wall boundary condition hasbeen considered.

Figure 4. The specified boundary conditions.

5.3. Grid adjustmentThe standard wall function is used in the RSM, to connectthe areas affected by the molecular viscosity and the innerareas of the field. Considering this, the adjustment of firstnodes’ distance in the direction perpendicular to the wall(y1) was calculated as follows:

cf

2≈ 0.0359Re−0.2 = 0.004, (12)

uτ =√

τw

ρ= Ue

√cf

2= 0.024 m/s, (13)

y1 = 50v

uτ

= 0.002 m, (14)

where the cf /2 is the shell friction coefficient and uτ is theshear velocity.

The domain grid has been adjusted so that in zones nearto the wall and in the regions with intense changes of param-eters (the submerged vanes range) a fine mesh grid is usedand in other regions a coarser mesh grid has been provided.Figure 5 shows an example of the grid.

Also, it is important to establish that grid-independentresults are obtained. The grid structure must be fine enoughespecially near the wall boundaries, the junction and thesubmerged vanes, which is the region of rapid variation. Asample of the grid is shown in Figure 4. Three simulationswere done for fine, medium and coarse grids with differentnumbers of nodes in the x, y and z directions. The numberof nodes in different directions in both the main and lateralchannels is presented in Table 3.

In order to test the accuracy of the grids, and choosinga grid type with the least number of nodes to mini-mize the time of simulation, as in the previous section,the flow pattern was simulated in a flume and in the

Figure 5. Computational grid.

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Table 3. Number of nodes in different grid types.

Number of nodes in length, Number of nodes in length,Grid width and depth of the width and depth of the Total number oftype main channel (x, y, z) intake channel (x, y, z) the nodes

Coarse 14 × 85 × 269 14 × 38 × 35 360,675Medium 20 × 85 × 269 20 × 38 × 35 504,945Fine 20 × 96 × 310 20 × 46 × 40 672,987

Figure 6. Numerical and experimental transverse velocity profiles for different grid types in Z = 0.09 m (Qr = 0.21).

presence of submerged vanes with specifications consis-tent with those used in Omidbeigi’s experimental research(2010).

In Figure 6, the numerical depth-averaged velocity pro-files for three fine, medium and coarse grids were comparedwith experimental results in Z = 0.09 m when Qr = 0.21.From this figure, it can be concluded that numerical resultsgenerally have a reasonable agreement with measured ones.Although at some sections computed results did not agreevery well with those measured, which might be partly dueto the three-dimensional effects, but the results obtainedfrom different grids have suitable consistency, and noconsiderable difference was seen among them.

Figure 7 represents the depth velocity profiles for dif-ferent grid types y = 2.115 m in the intake channel whenQr = 0.21. Considering this figure, it can be concluded thatthe numerical velocity data obtained from different gridtypes did not have a remarkable difference, and had a goodconsistency with the measured velocity.

In conclusion, the results were independent of the gridsize, if at least 360,375 nodes are used. Therefore, inorder to do the simulations in the least time and witha good accuracy, the coarse grid was considered in thecomputational domain.

6. Modeling results6.1. Investigating the dividing streamline6.1.1. The effect of inter-vane longitudinal distance on

dividing streamlineFigure 8 represents the distance between the dividingstreamline from intake port, in-depth change for differentlongitudinal distances between the vanes, and for threeintake ratios of 11%, 16% and 21% when α = 25◦. Z∗ on thevertical axis represents the dimensionless depth parameter,which is the ratio of the certain elevation to the flow depth(z/d) and W ∗ on the horizontal axis represents dimension-less width of the dividing streamline, which is the ratio ofthe distance of the dividing streamline from the intake portto the main channel width. Comparison between Figure 8(a)and 8(c) shows that when the intake ratio is low, the increasein the longitudinal distance between the vanes negativelyaffects the intake conditions, causing an increase in theflow volume from the near-bed levels, which conveys alarge amount of bed load, into the intake, while the flowvolume entering from the middle depth and surface levelsinto the intake channel, and containing less suspended loaddecreases. But in higher intake ratios, the distance of divid-ing streamline from intake entrance is almost independent

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Figure 7. Numerical and experimental depth velocity profiles for different grid types in y = 2.115 m (Qr = 0.21).

Figure 8. The dividing streamlines changes in depth level with changes in the longitudinal distance between the vanes(δn = 3Hv, α = 25◦).

of the longitudinal distances between the vanes, and the lon-gitudinal inter-vane distance does not significantly affect thedividing streamline.

6.1.2. The effect of inter-vane transverse distance on thedividing streamline

In Figure 9, the dividing streamline in-depth changes withdifferent transverse distances between the vanes for threeintake ratios of 11%, 16% and 21% when α = 25◦ is shown.Considering this figure, it can be concluded that with lowand medium intake ratios, the less the transverse distancebetween the vanes, the better the intake conditions and more

flow from the middle and near-surface depths that containless sediment enters into the intake. But when the intakeratio is increased to 0.21 of the total flow, increasing thetransverse distance between the vanes will contribute tobetter intake conditions, and more flow enters the intakefrom the middle depth level.

6.1.3. Investigation of the submerged van angle withrespect to the flow direction effect on the dividingstreamline

Figure 10 represents the dividing streamlines in-depthchange corresponding to the submerged-vane installation

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Figure 9. The in-depth dividing streamlines change trends corresponding to the intake flow (δs = 10Hv, α = 25◦).

Figure 10. The in-depth dividing streamlines change trends corresponding to the vanes’ angles with respect to the flow direction(δn = 3Hv, δs = 10Hv).

angle when δs = 10 Hv and δn = 3 Hv. According to thisfigure the near-bed flow entering the intake entrance isalmost independent of the installation angle of the vanes.But with low intake ratios, when the vane angle withrespect to the flow direction is 15◦ more flow from the mid-dle depths and surface levels diverges toward the intake

entrance. However when the rate of intake is 0.16 times ofthe total flow, the dividing streamlines in-depth change isalmost identical for all three installation angles, but whenQr = 0.21, the change trend corresponding to the Qr = 0.11is reversed and the 25◦ installation angle would providebetter conditions for the intake.

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Figure 11. Secondary flow strength changes along with changes in longitudinal distances among the vanes (δn = 3Hv, α = 25◦,Qr = 0.21).

6.2. Investigating the secondary flow strengthMost of the studies undertaken during the recent years haveused the vorticity criterion for calculation of the vortexpower. But this criterion is not accurate in estimating thevortex power because the effect of the wall roughness onthe vortex is not removed (Haller 2005). The wall rough-ness and also the width of the section from which the flowwill pass are among the wall-related factors that cause theformation of vortex estate and the mentioned criterion cal-culates the vortex power more than the actual power (Haller2005).

In this study, a criterion called the Q-criterion was usedfor calculating the vortex strength which is by far moreaccurate in calculation of the vortex strength compared withthe vorticity criterion. This criterion is defined using thefollowing equation (Haller 2005):

Qij = 12

(�2

ij − S2ij

), (15)

where �ij is the vorticity value and its equation is as follows:

�ij = 12

(∂ui

∂xj− ∂uj

∂xi

), (16)

where u indicates velocity.Sij is the tension rate resulting from the wall which is

defined using the following equation:

Sij = 12

(∂ui

∂xj+ ∂uj

∂xi

), (17)

6.2.1. Investigation of the inter-vane longitudinal andtransverse distance on the secondary flow strength

In Figures 11 and 12, the secondary flow strength changesalong with changes in longitudinal and transverse distances

between the vanes when α = 25◦ and Qr = 0.21 have beenpresented, respectively. Considering Figure 11, it can beobserved that increasing the longitudinal distance betweenthe vanes does not greatly affect the secondary flow strengthformed around the vanes. However, Figure 12 shows thatby increasing the transverse distance between the vanes, thesecondary flow strength of the vanes that have been locatedin the first column is increased and by reaching the flow tothe vanes in the second column, the secondary flow strengthis decreased. But within the width of the intake channel, thesecondary flow strength changes are not considerable.

6.2.2. Investigating the effect of the van angle with theflow direction changes on the secondary flowstrength

In order to better investigate the secondary flow strengthchanges along with the change in installation angle of thevanes, in Figure 13(a)–(c), the secondary flow strengthchanges have been shown just in front of the intake entrance(from x = 11.43 to x = 11.83) for different intake ratios.These figures show that in all intake ratios in front ofthe intake entrance, up to the zone close to the middlesection of the intake entrance (x = 11.63 m), the secondaryflow strength around the vanes with 15◦ and 25◦ angles ishigher in comparison with the angle 20◦. But simultane-ously by reaching the flow to the middle of the submergedvane located in the middle of the intake entrance, it can beseen that the increase in the secondary flow strength whenα = 25◦ is lesser than the other angles. On the other hand,the maximum secondary flow strength around the vanes infront of the intake entrance is dependent on the intake flowand is at a maximum with an intake ratio of 0.11 around thevanes with the angle of 15◦, and intake ratios of 0.16 and0.21 around the vanes with 20◦ angle. But after the middlesection of the intake entrance, the secondary flow strength

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Figure 12. Secondary flow strength changes along with changes in transverse distances among the vanes (δs = 10Hv, α = 25◦,Qr = 0.21).

Figure 13. Secondary flow strength changes along with changes in the vanes angle in front of the intake port in intake ratios of (a) 0.11,(b) 0.16, (c) 0.21.

difference around the vanes with different installation anglesis not remarkable.

6.3. Investigating the bed shear stress6.3.1. Investigating the effect of changes in the

inter-vane longitudinal and transverse distanceson the bed shear stress

In Figure 14, the shear stress imposed on the bed when δn =3Hv, α = 25◦ and Qr = 0.21 is represented. As can be seenfrom this figure, by the increase in the longitudinal distance

between the vanes, no considerable changes occur in the bedshear stress inside the intake channel, and only by increasingthe longitudinal distance from 9 to 10 times the vane height,the high-shear stress zone dimensions, which are locatedclose to the right side of the intake channel, are a littledecreased and the low-shear stress zone dimensions, whichare located opposite to it, are a little increased. But whenδs is increased from 9Hv to 10Hv, the zone with mediumshear stress, which is located after the intake entrance andclose to the inner wall of the intake channel, is considerablyincreased.

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Figure 14. Bed shear stress contours for different longitudinal distances between the vanes (δn = 3Hv, Qr = 0.21).

Figure 15. Bed shear stress contours for different transversel distances between the vanes (δs = 10Hv, Qr = 0.21).

Considering Figure 15, it can be said that the increasein the transverse distance between the vanes will not havea considerable effect on the shear stress imposed on thebottom and causes only an increase in the area with mediumshear stress which is located close to the inside wall of themain channel and after the intake entrance.

6.3.2. Investigating the effect of the vane angle with theflow direction on the shear stress

Figure 16 shows the shear stress on the bottom when δs =10Hv, δn = 3Hv and Qr = 0.21 with different intake angles.Considering this figure, it can be concluded that by increas-ing the vane angle with respect to the flow direction, the

dimension of the low-shear stress zone in the intake channelhas an increasing–decreasing trend, while the dimensionsof the high-shear stress zone have an increasing–decreasingtrend. Also, the zone with medium shear stress after theintake entrance and close to the inner wall of the intakechannel will initially increase with the increase in the intakeangle and subsequently will decrease.

7. ResultsDue to the importance of the amount of the flow enteringinto the intake channel from different levels, the near-bed,middle-depth, and surface levels of the water column, threeother parameters have been considered in addition to the

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Figure 16. Bed shear stress contours for different vanes’ angles (δn = 3Hv, δs = 10Hv, Qr = 0.21).

above-mentioned parameters to calculate the CC. Theseparameters are:

• Intake flow volume from the near-bed level in thewater column: this parameter is defined as the volumesurrounded by dividing streamline, bed, and 0.1d infront of the intake channel.

• Intake flow volume from the middle depth level inthe water column: the volume surrounded by divid-ing streamline, 0.1d and 0.6d in front of the intakechannel.

• Intake flow volume from the near-surface depth: thevolume surrounded by dividing streamline, 0.6d, andwater surface in front of the intake channel.

For optimization, a decision matrix must first be formed.Initially in any of the intake flows, the calculated values foreach of the parameters under study were divided into sevencategories. For this purpose, the minimum and maximumvalues for each parameter concerning the desired intakeflow were determined and their difference was divided bythe integer 7 so that the category ranges were obtained andthen the categorization was effected. In the next step, therectangular fuzzy number of the option was written depend-ing on the category to which the option number belonged;thus, the decision matrix was formed. In Table 4, a sampleof the decision matrix for Qr = 0.11 is shown.

The decision matrix is normalized considering whetherthe studied criterion was a cost or benefit criterion.Table 5 shows a sample of normalized decision matrix for

Qr = 0.11. Then the distance between the options and thepositive ideal (1,1,1) and the negative ideal (0,0,0) was cal-culated. For example, the distance between the intake flowvolume and near-bed level criterion is calculated as follows:

d−i =

√13[(0 − 0.3)2 + (0 − 0.5)2 + (0 − 0.7)2] = 0.526

(18)

d∗i =

√13[(0.3 − 1)2 + (0.5 − 1)2 + (0.7 − 1)2] = 0.526

(19)

In Table 6, the d−i and d∗

i for each of the criterion in Qr =0.11 and α = 15◦ are shown.

Finally for each of the alternatives, the CC is calculated,as an example the CC for alternative no. 1 in Table 6 is asfollows:

cci = d−i

d∗i + d−

i, = 3.97

6.61 + 3.97= 0.375 (20)

In this research, 54 simulations were performed, and10 criteria were considered for optimization. Therefore adecision matrix with 10 columns and 54 rows was con-structed. The calculated CC changes with the longitudinaldistance and the vane angle with respect to the flow direc-tion for two transverse distances of 2Hv and 3Hv is shown inthree-dimensional graphs. The horizontal axis of the graphsshows the longitudinal distance between the vanes and theirvertical axes represent the CC and the axis perpendicular

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Table 4. A sample of the decision matrix (Qr = 0.11).

Distance of Distance of Max bedIntake flow Intake flow Intake flow dividing streamline dividing streamline shear stress in

volume from the volume from the volume from from intake port from intake port front of the Area of Width of Length ofα δs/Hv δn/Hv near-bed level middle depth level the near surface in surface level in near-bed level intake entrance Q-criterion the vortex the vortex the vortex

15◦ 8 2 (0,1,3) (0,0,1) (9,10,10) (1,3,5) (7,9,10) (9,10,10) (3,5,7) (9,10,10) (1,3,5) (9,10,10)3 (0,1,3) (0,0,1) (0,0,1) (0,1,3) (3,5,7) (9,10,10) (9,10,10) (9,10,10) (1,3,5) (9,10,10)

9 2 (3,5,7) (0,0,1) (0,0,1) (3,5,7) (5,7,9) (9,10,10) (1,3,5) (9,10,10) (1,3,5) (9,10,10)3 (0,1,3) (0,0,1) (0,0,1) (1,3,5) (1,3,5) (9,10,10) (3,5,7) (9,10,10) (1,3,5) (9,10,10)

10 2 (5,7,9) (0,1,3) (9,10,10) (5,7,9) (5,7,9) (9,10,10) (1,3,5) (9,10,10) (3,5,7) (9,10,10)3 (3,5,7) (0,1,3) (0,1,3) (5,7,9) (1,3,5) (9,10,10) (1,3,5) (9,10,10) (1,3,5) (9,10,10)

20◦ 8 2 (0,1,3) (0,0,1) (0,0,1) (0,1,3) (9,10,10) (9,10,10) (3,5,7) (9,10,10) (0,1,3) (9,10,10)3 (1,3,5) (0,0,1) (0,0,1) (1,3,5) (0,1,3) (7,9,10) (3,5,7) (9,10,10) (0,0,1) (9,10,10)

9 2 (3,5,7) (0,0,1) (1,3,5) (3,5,7) (9,10,10) (9,10,10) (5,7,9) (9,10,10) (0,0,1) (9,10,10)3 (5,7,9) (0,0,1) (3,5,7) (5,7,9) (3,5,7) (7,9,10) (5,7,9) (7,9,10) (0,1,3) (7,9,10)

10 2 (9,10,10) (9,10,10) (9,10,10) (9,10,10) (3,5,7) (0,0,1) (0,0,1) (3,5,7) (7,9,10) (3,5,7)3 (5,7,9) (0,0,1) (0,0,1) (7,9,10) (1,3,5) (7,9,10) (1,3,5) (7,9,10) (0,0,1) (7,9,10)

25◦ 8 2 (0,0,1) (0,0,1) (0,0,1) (0,0,1) (9,10,10) (9,10,10) (7,9,10) (9,10,10) (9,10,10) (9,10,10)3 (1,3,5) (0,0,1) (0,0,1) (1,3,5) 1,3,5)) (7,9,10) (3,5,7) (7,9,10) (3,5,7) (7,9,10)

9 2 (3,5,7) (0,0,1) (0,0,1) 1,3,5)) (9,10,10) (9,10,10) (9,10,10) (9,10,10) (7,9,10) (9,10,10)3 (7,9,10) (0,0,1) (0,0,1) (7,9,10) (0,0,1) (7,9,10) (3,5,7) (0,0,1) (5,7,9) (0,0,1)

10 2 (5,7,9) (0,0,1) (0,0,1) (7,9,10) (5,7,9) (9,10,10) (9,10,10) (9,10,10) (3,5,7) (9,10,10)3 (9,10,10) (0,0,1) (0,0,1) (9,10,10) (0,0,1) (7,9,10) (3,5,7) (0,0,1) (3,5,7) (0,0,1)

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Table 5. A sample of the normalized decision matrix (Qr = 0.11).

Intake flow Intake flow Distance of Distance of Max bed shearIntake flow volume from volume from dividing streamline dividing streamline stress in front Area Width Length

volume from the the middle the near from intake port from intake port in of the intake of the of the of theα δs/H v δn/Hv near-bed level depth level surface in surface level near-bed level entrance Q-criterion vortex the vortex vortex

15◦ 8 2 (1,0,0) (0,0,0.1) (0.9,1,1) (0,0,0) (0.7,0.9,1) (0.9,1,1) (0.3,0.5,0.7) (0,0,0) (0,0,0) (0,0,0)3 (1,0,0) (0,0,0.1) (0,0,0.1) (1,0,0) (0.3,0.5,0.7) (0.9,1,1) (0.9,1,1) (0,0,0) (0,0,0) (0,0,0)

9 2 (0,0,0) (0,0,0.1) (0,0,0.1) (0,0,0) (0.5,0.7,0.9) (0.9,1,1) (0.1,0.3,0.5) (0,0,0) (0,0,0) (0,0,0)3 (1,0,0) (0,0,0.1) (0,0,0.1) (0,0,0) (0.1,0.3,0.5) (0.9,1,1) (0.3,0.5,0.7) (0,0,0) (0,0,0) (0,0,0)

10 2 (0,0,0) (0,0.1,0.3) (0.9,1,1) (0,0,0) (0.5,0.7,0.9) (0.9,1,1) (0.1,0.3,0.5) (0,0,0) (0,0,0) (0,0,0)3 (0,0,0) (0,0.1,0.3) (0,0.1,0.3) (0,0,0) (0.1,0.3,0.5) (0.9,1,1) (0.1,0.3,0.5) (0,0,0) (0,0,0) (0,0,0)

20◦ 8 2 (1,0,0) (0,0,0.1) (0,0,0.1) (1,0,0) (0.9,1,1) (0.9,1,1) (0.3,0.5,0.7) (0,0,0) (1,0,0) (0,0,0)3 (0,0,0) (0,0,0.1) (0,0,0.1) (0,0,0) (0,0.1,0.3) (0.7,0.9,1) (0.3,0.5,0.7) (0,0,0) (1,0,0) (0,0,0)

9 2 (0,0,0) (0,0,0.1) (0.1,0.3,0.5) (0,0,0) (0.9,1,1) (0.9,1,1) (0.5,0.7,0.9) (0,0,0) (1,1,0) (0,0,0)3 (0,0,0) (0,0,0.1) (0.3,0.5,0.7) (0,0,0) (0.3,0.5,0.7) (0.7,0.9,1) (0.5,0.7,0.9) (0,0,0) (0,0,0) (0,0,0)

10 2 (0,0,0) (0.9,1,1) (0.9,1,1) (0,0,0) (0.3,0.5,0.7) (0,0,0.1) (0,0,0.1) (0,0,0) (0,0,0) (0,0,0)3 (0,0,0) (0,0,0.1) (0,0,0.1) (0,0,0) (0.1,0.3,0.5) (0.7,0.9,1) (0.1,0.3,0.5) (0,0,0) (1,0,0) (0,0,0)

25◦ 8 2 (1,1,0) (0,0,0.1) (0,0,0.1) (1,1,0) (0.9,1,1) (0.9,1,1) (0.7,0.9,1) (0,0,0) (0,0,0) (0,0,0)3 (0,0,0) (0,0,0.1) (0,0,0.1) (0,0,0) (0.1,0.3,0.5) (0.7,0.9,1) (0.3,0.5,0.7) (0,0,0) (0,0,0) (0,0,0)

9 2 (0,0,0) (0,0,0.1) (0,0,0.1) (0,0,0) (0.9,1,1) (0.9,1,1) (0.9,1,1) (0,0,0) (0,0,0) (0,0,0)3 (0,0,0) (0,0,0.1) (0,0,0.1) (0,0,0) (0,0,0.1) (0.7,0.9,1) (0.3,0.5,0.7) (1,1,0) (0,0,0) (1,1,0)

10 2 (0,0,0) (0,0,0.1) (0,0,0.1) (0,0,0) (0.5,0.7,0.9) (0.9,1,1) (0.9,1,1) (0,0,0) (0,0,0) (0,0,0)3 (0,0,0) (0,0,0.1) (0,0,0.1) (0,0,0) (0,0,0.1) (0.7,0.9,1) (0.3,0.5,0.7) (1,1,0) (0,0,0) (1,1,0)

Table 6. A sample of the calculated d−i and d∗

i (Qr = 0.11, α = 15◦).

Intake flow Intake flow Intake flow Distance of Distance of Max bedvolume from volume from volume from dividing streamline dividing streamline shear stress Area Width Lengththe near-bed the middle the near from intake port from intake port in front of the of the of the of the

level depth level surface in surface level in near-bed level intake entrance Q-criterion vortex vortex vortex Sum

δs/Hv δn/Hv d−i d∗

i d−i d∗

i d−i d∗

i d−i d∗

i d−i d∗

i d−i d∗

i d−i d∗

i d−i d∗

i d−i d∗

i d−i d∗

i∑10

i=1 d−i

∑10i=1 d∗

i

8 2 0.58 0.82 0.06 0.97 0.97 0.06 0 1 0.88 0.18 0.97 0.06 0.53 0.53 0 1 0 1 0 1 3.97 6.613 0.58 0.82 0.06 0.97 0.06 0.97 0.58 0.82 0.53 0.53 0.97 0.06 0.97 0.06 0 1 0 1 0 1 3.73 7.21

9 2 0 1 0.06 0.97 0.06 0.97 0 1 0.72 0.34 0.97 0.06 0.34 0.72 0 1 0 1 0 1 2.14 8.053 0.58 0.82 0.06 0.97 0.06 0.97 0 1 0.34 0.72 0.97 0.06 0.53 0.53 0 1 0 1 0 1 2.53 8.05

10 2 0 1 0.18 0.88 0.97 0.06 0 1 0.72 0.34 0.97 0.06 0.34 0.72 0 1 0 1 0 1 3.18 7.053 0 1 0.18 0.88 0.18 0.88 0 1 0.34 0.72 0.97 0.06 0.34 0.72 0 1 0 1 0 1 2.02 8.25

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(a)

(b)

(c)

Figure 17. The calculated closing coefficients changes based on the parameters effective in preventing the entry of sediments into theintake entrance for three intake ratios of (a) 11%, (b) 16% and (c) 21%.

to the plain shows the vane angle with respect to the flowdirection.

Figure 17(a)–(c) shows the variation of calculated CCbased on the parameters effective in preventing the sed-iments from entering into the intake entrance for threeintake ratios of 11%, 16% and 21%, respectively. Con-sidering Figure 17(a), it can be said that with an intakeratio of 0.11 if the vanes are installed in front of theintake entrance with δn = 2Hv, δδs = 8Hv and α = 25◦,they can prevent more of the sediments from entering intothe intake entrance compared with other configurations.But with increase in the intake flow, as has been shown

in Figure 17(b) and 17(c), the δn = 3Hv, δs = 9Hv andα = 25◦ is the optimized configuration.

8. ConclusionIn this research the appropriate configuration of submergedvanes was determined considering seven optimizationcriteria. The fuzzy TOPSIS multi-objective optimizationmethod was utilized for the optimization process. The dis-tance of the dividing streamline from the intake wall in thesurface and near-bed levels, the amount of the inflow tothe intake from near-bed, middle-depth and surface levels,

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secondary flow strength and the shear stress imposed on thebed were parameters considered in the optimization process.Three discharge ratios of 0.11, 0.16 and 0.21 were con-sidered for the simulations. In determining the appropriatesubmerged-vane configuration, three cases for simulatingthe inter-vane longitudinal distance, two cases for simulat-ing the inter-vane transverse distance and three cases forsimulating the angle of the vanes with respect to the flowdirection were considered. Appropriate dimensions of sub-merged vanes were considered. The results of the studyshow that for controlling sediment in front of intake ports,a longitudinal distance of 9Hv, a transverse distance of 3Hvand a 25◦ angle of attack are the appropriate parameters forconfiguration for submerged vanes.

NotationA area of the flow sectioncf

2shell friction coefficient

d flow depthgxi gravitational acceleration in the xi directionHv height of the vaneP pressureQ1 inlet flowQ2 intake dischargeQr discharge ratioSij tension rateT Timeui velocity in the xi directionuτ shear velocityy1 first node’s distance from the wallα angle between the vanes and the flow directionδn transverse distance between the vanesδs longitudinal distance between the vanesP density of flowN molecular viscosity�ij vorticity value

Notes on contributorsSeyed Hessam Seyed Mirzaei was born on 16 September 1986,obtained his BSc degree in water Engineering from Universityof Tehran in 2008. He got his MSc degree in Water StructuresEngineering at Tarbiat Modares University in 2011. Now, he is aPhD student at Queen’s University in Canada, and is cooperatingwith this university both as a research and teacher assistant.

Seyed Ali Ayyoubzadeh was born in 19 April 1960. He receivedhis BSc, MSc and PhD educations at Shahid Chamran (Ahvaz,Iran), Tehran (Iran) and Birmingham (England) Universities,

respectively. He started his academic life at the Tabiat ModaresUniversity in 1997 after finishing his PhD study. Now, he is Vice-Dean for Academic Affairs of Faculty of Agriculture and associateprofessor of Water Structures Engineering Department, TMU. Heteaches courses and supervised several researches in sediment,river engineering and hydraulic modelling for the MSc and PhDstudents. He has written over 140 publications including papers injournals, national and international conference proceedings, bookchapters. He is also a director of the Water Sciences and Engineer-ing committee of the Ministry of Culture and Higher Education ofI.R. of Iran, which is responsible for planning and revising of thewater and sciences majors in BSc, MSc and PhD programs in thenational universities. You can reach him at ayyoub (@) modares(.) ac (.) ir.

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