Engineering Applications of Computational Fluid ...

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Numerical Analysis and Prediction of the Velocity Field in Curved Open Channel Using Artificial Neural Network and Genetic Algorithm ba

ba

c

d

H. Bonakdari , S. Baghalian , F. Nazari & M. Fazli a

Department of Civil Engineering, Razi University, Kermanshah, Iran

b

Water and Wastewater Research Center, Razi University, Kermanshah, Iran

c

Department of Mechanical Engineering, Islamic Azad University, Hamedan Branch, Young Researchers Club, Hamedan, Iran d

Department of Civil Engineering, Bu-Ali Sina University, Hamedan, Iran Published online: 19 Nov 2014.

To cite this article: H. Bonakdari, S. Baghalian, F. Nazari & M. Fazli (2011) Numerical Analysis and Prediction of the Velocity Field in Curved Open Channel Using Artificial Neural Network and Genetic Algorithm, Engineering Applications of Computational Fluid Mechanics, 5:3, 384-396, DOI: 10.1080/19942060.2011.11015380 To link to this article: http://dx.doi.org/10.1080/19942060.2011.11015380

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Engineering Applications of Computational Fluid Mechanics Vol. 5, No. 3, pp. 384–396 (2011)

NUMERICAL ANALYSIS AND PREDICTION OF THE VELOCITY FIELD IN CURVED OPEN CHANNEL USING ARTIFICIAL NEURAL NETWORK AND GENETIC ALGORITHM H. Bonakdari*#+, S. Baghalian*#, F. Nazari** and M. Fazli

†

#

Downloaded by [Egerton University] at 16:16 26 August 2015

Department of Civil Engineering, Razi University, Kermanshah, Iran * Water and Wastewater Research Center, Razi University, Kermanshah, Iran + E-Mail: bonakdari @ yahoo.com(Corresponding Author) ** Department of Mechanical Engineering, Islamic Azad University, Hamedan Branch, Young Researchers Club, Hamedan, Iran † Department of Civil Engineering, Bu-Ali Sina University, Hamedan, Iran ABSTRACT: This paper presents numerical analysis and prediction of flow field in a 90o bend using Artificial Neural Networks (ANN) and Genetic Algorithm (GA). Firstly, a 3D Computational Fluid Dynamics (CFD) model is used to investigate the flow patterns and velocity profiles. Numerical simulation in two phases is done using the ANSYS-CFX software and k-ε turbulence model is used to solve turbulence equations. The results show secondary flow and centrifugal force influenced flow pattern and have good agreement with experimental data. Then two similar ANNs are trained based on GA and Back-Error Propagation (BEP) technique for velocity prediction in different sections of bend and their test results are compared with each other and with actual data. Since obtaining experimental data in every point of channel is not easy, ANN is used to obtain the velocity in some sections where experimental data are not available, and the results are compared with CFX’s result. Keywords:

artificial neural network, bend, genetic algorithm, numerical analysis, velocity field

to solve governing equations of flow for given geometry and boundary conditions. This provides the possibility of higher accuracy and simpler prediction of 3D flow behaviours. Wu et al. (2000), using a 3D numerical model, studied flow field and sediment transport in channel bends. Ruther and Olsen (2005) used a three-dimensional model for evaluation of velocity and bed level changes in a narrow 90o channel bend. Marchis and Napoli (2006), by a 3D numerical model, investigated flow fields in curved open channels. This model solved 3D Reynolds averaged NavierStocks equations and k–ε turbulence model had been used for solving turbulence equations. Bonakdari (2008) has studied effects of a bend on the velocity zone in a circular section by using CFD. Abhari et al. (2010) studied flow pattern in a channel with a 90o bend experimentally and numerically. They used CFD software for numerical analysis. In the last decade soft computing methods were the subject of many researches in engineering problems and especially water resources engineering (Cheng et al., 2002; Lin et al., 2006; Muttil and Chau, 2006; Muzzammil, 2008; Wu et al., 2008; Wang et al., 2009; Wu et al. 2009; Harter and Velho, 2010; Ghosh et al., 2010; Safikhani et al., 2011). Bhattacharya et al. (2007)

1. INTRODUCTION The study of flow patterns in curved channels is a subject of interest to researchers and engineers of the hydraulic science. Investigating of flow patterns in channel bends is much more complex than straight reaches. Dietrich et al. (1979) investigated topography of river bed using a mathematical model. They showed that a spiral current caused transfer of maximum shear stress toward outer bend, so the maximum scour would occur in that place. One important feature of flows in curved channels is the presence of secondary flow caused by centrifugal force. This type of flow influences sedimentation and erosion and creates irregular topography in bend (Blanckaert and Graf, 2001; Kassem and Chaudhry, 2002). However, due to the complicated flow properties, precise prediction of the structure of the flow at open channel bends is difficult. 3D computational method based on a non-linear Reynolds averaged Navier-Stockes model is an effective tool for simulating open channel flows with a bend (Kimura et al., 2008). During the twentieth century, with the advent of high-speed digital computer applications, the computational fluid dynamic (CFD) software was developed. The latter uses numerical techniques

Received: 18 Jan. 2011; Revised: 22 Mar. 2011; Accepted: 30 Mar. 2011 384


Engineering Applications of Computational Fluid Mechanics Vol. 5, No. 3 (2011)

points of the channel with good accuracy. In the second part, an ANN using experiment data is trained based on the GA for prediction of velocity field in different sections of the bend. In addition, the same ANN is trained based on BEP technique and its test results are compared with results of the GA. Test results of trained ANN based on both GA and BEP show that predicted data are in good agreement with actual data. Then the velocities in some sections where experimental data are not available are calculated using ANN and compared with results of CFX.

used ANN in sedimentation modeling for the approach channel of the port area of Rotterdam. Also the influence of some factors on the sedimentation process such as waves, wind, tides, surge and river discharge were studied. Bilgil and Altun (2008) studied the flow resistance in smooth open channels by using ANN. They presented an approach to estimate the friction coefficient via an ANN. The obtained value of the friction coefficient was used to predict the open channel flows in order to carry out a comparison between the proposed ANN based approach and the conventional ones. Kocabas et al. (2008) presented an ANN approach for the prediction of critical submergence of an intake in still water and open channel flow for permeable and impermeable bottom. Then they compared the experimental, ANN and Multiple Linear Regression approaches results. Yuhong and Wenxin (2009) studied the application of ANN for prediction of friction factor of open channel flows. They applied the Lvenberg-Marquardt learning algorithm to train the model using laboratory experimental data, and the trained network was tested by a single set separated from the rest of the data. Emiroglu et al. (2011) estimated the discharge capacity of triangular labyrinth side-weirs using ANN. In the mentioned study, laboratory test results were used to determine the discharge coefficient of triangular labyrinth side-weirs. Also they compared the performance of the ANN model with multinonlinear regression models. In this paper numerical analysis and prediction of flow field in a 90o bend using ANN and GA are presented. In the first part of the paper, by 3D numerical simulation of flow field with ANSYSCFX software, variation of velocity profiles in different sections of bend is investigated in two phases (water+air). In order to solve turbulence equations, the k-ε model is used. Numerical results are verified using experimental data obtained in an experimental analysis in Tarbiat Modares University of Tehran. This study shows that the numerical model results have good agreement with experimental ones. There are always some limitations in experimental studies and obtaining experimental data in every point of a channel is not easy. Also after doing an experimental test and obtaining the velocity in the desired point, measuring the velocity in other points needs to do the experimental test again. Artificial intelligence solves this problem. By training an ANN based on experimental data of the points that are available, the ANN help investigators to calculate the velocity in other

2. EXPERIMENTAL AND NUMERICAL MODEL 2.1

Experimental model

Experiments were done at the hydraulics laboratory of Tarbiat Modares University of Tehran. The tested channel consisted of a 90o bend and two straight reaches upstream and downstream of the bend. The lengths of upstream and downstream reaches were 7.1 m and 5.2 m long, respectively. The channel consisted of rectangular cross section with 0.6 m width, 0.6 m height and 0.11 m height of water with 1.8 m radius of bend to centreline. The ratio of bend radius to channel width was 3. Fig. 1 and Fig. 2 show a schematic view of the channel and experimental set up, respectively.

Fig. 1

Fig. 2

385

Schematic of 90o Channel.

Experimental set up.



The bed and sidewalls of the channel were made of glass supported by metal frames. It should be mentioned that the initial flow turbulence was reduced using a netted metal plate placed before the straight channel. The discharge was measured by a calibrated orifice set in the supply pipe. A gate was located at the end of the system and before the outlet tank for changing and fixing the depth of water. Experiments were conducted for discharges of 25 litres/s. For measuring components of velocity (longitudinal and lateral components) the P-EMS velocimeter was used. With regard to the effect of banks and channel bed on velocity components, 14 transverse points along the channel width and 5 different layers of water were selected for determining the actual flow pattern. The water levels were located at 1 cm, 2 cm, 7.5 cm and 11 cm from the bed. Fig. 3 shows the grid points used for the velocity measurement at each cross section of the bend. Measurements were done at two sections before the bend (20 cm and 40 cm, respectively), two sections after the bend (20 cm and 60 cm, respectively) and eleven sections in the bend (0o, 10o, 20o, 30o, 40o, 45o, 50o, 60o, 70o, 80o and 90o respectively (Fig. 4)).

2.2

Numerical model

2.2.1 Governing equations The motion of fluids is expressed by conservation laws for mass, momentum and energy. The equation for mass is known as the continuity equation while the equation for momentum is called equation of motion that is an expression of Newton’s law. If viscous fluid and inviscid fluid are considered in these equations, they are known as the Navier-Stockes and Euler equations, respectively. In the general form, the set of governing equations for homogeneous mixture of multiphase flows in the Cartesian coordinates are as follows:

  m   .(  mU m )  0 t      (  mU m )   m (U m . )U m t     ( pm )  .(   t )  f

(1)

(2)

where p is pressure,  is viscous stress tensor,

 t is turbulence viscous stress tensor and f is buoyancy force. For multiphase flows a volume fraction transport equation is added to the governing equations as follows:

  ( l l )   .( l lU m )  0 t

Fig. 3

(3)

where  l represents the liquid phase volume fraction. Turbulence equations for homogeneous multiphase flows are the same as the single phase equation when the mixture density and viscosity are used. For the k   model, the turbulence equations are as follows:

Grid points for velocity measurement.

 ( m k )   .(  mUk ) t (4)    mt   )k   Pk   m  . (  m  k     (  m )   .(  mU  ) t (5)    m ,t     .  (  m  )   (C 1 Pk  C 2  m )    k Fig. 4

where k is the turbulence kinetic energy,  is the turbulence eddy dissipation. C 1 , C 2 ,  k and

Locations of selected sections in bend.

386


  are turbulence constants, and Pk is the turbulence production due to viscous force which is expressed as follows:

     Pk   m ,t U .(U  U T )   2   .U (3 m ,t .U   m k )  Pkb 3

where Pkb

(6)

is buoyancy production term.

 m ,  m and  m ,t are mixture density, mixture viscosity and mixture respectively as follows:

turbulent

viscosity,

2

m    n n

(7)

n 1

Fig. 5


2

m    n n

(8)

 m c k 2  

(9)

as powerful algorithms and discretization techniques, and is also flexible in implementation of boundary conditions via user defined FORTRAN subroutines (Morvan et al., 2001).

n 1

 m ,t

Flow chart of solution process of flow equations.

2.2.2 Introducing ANSYS-CFX

2.2.3 Simulation of flow field

Computational fluid dynamic (CFD) is a tool based on computer for simulating the behavior of systems involving fluid flow, heat transfer, and other related physical processes. The accurate predictions of flow and contaminant transport in bends offer numerous applications to protect the environment. 3D numerical software is used to solve governing equations of flow and hydraulic problems. This has been made possible by advances in computer technology and numerical algorithm development. On the modeling side, CFD seems more and more important in general process applications. One of computational fluid dynamics codes is ANSYS-CFX software. ANSYS-CFX is a code that uses thefinite volume approach for solving the complete incompressible Reynolds-averaged Navier-Stokes equations. In ANSYS-CFX, the hydrodynamic equations (u, v, w, and p) are solved in a single system and the solver is fully coupled. The solver solves the discrete system of linearized equations using a multi-grid accelerated Incomplete Lower Upper (ILU) factorization technique. The multi-grid process is carried out on a fine mesh in early iterations and on progressively coarser ones in later iterations. Then the results are returned from the coarsest virtual mesh to the original fine mesh. The flow chart of solution process of flow equations has been shown in Fig. 5. The advantage of using this code to other codes is that it offers multiple validated solutions as well

As achieving a good grid in numerical model is important, in this paper, for plotting physical model of channel ICEM software is used. Since higher accuracy is needed, grids have been made finer near the water surface and the walls than other parts. In this model, in the upstream straight reach of bend, the number of nodes, maximum spacing and minimum spacing are 65, 1 and 0.001, respectively, and in the downstream straight reach of the bend, they are 110, 1 and 0.001, respectively. Details of gridding, in other parts of the model are illustrated in Fig. 6. To achieve fully developed flow in the numerical model, the lengths of straight reaches in the experimental model were increased to 15 m in upstream bend and 37 m in downstream bend. The solution of flow field was carried out using ANSYS-CFX software. The solution of flow field was continued until achieving 1e-6 in residuals. kε is the considered turbulence model for solving turbulence equations. Boundary conditions around the computational domain are required in order to determine the solution. Common boundary conditions encountered in the open channel flow problems include inlet, outlet, noslip wall and free surface conditions. The boundary conditions are: (1) uniform distribution of velocity and water level at the inlet (upstream), (2) pressure condition at the outlet (downstream), (3) solid wall with no slip condition without roughness on the solid walls and (4) free surface 387



Fig. 6

Gridding in plane and section, (a) gridding in plane and (b) gridding in section, in two-phase model.

condition based on a volume of fluid method on the free surface. After solution processing by the ANSYS-CFX, the results of the numerical model were validated by the experimental model.

technique. In each network, transfer functions for neurons of hidden and output layers are Tansig and are defined in equation (10).

f (n) 

3. PREDICTION USING ANN 3.1

Artificial neural network

3.2

Artificial neural networks offer an alternative procedure to tackle complex problems, and are applied in different applications. The most popular type of neural network is Multi-Layer Feed Forward (MLFF). A schematic diagram of typical MLFF neural-network architecture is shown in Fig. 7. The network usually includes an input layer, some hidden layers and an output layer. Usually knowledge is stored as a set of connection weights. Training is the process of modifying the connection weights, in some orderly fashion, using a suitable learning method. In this study, an ANN was trained based on the GA for the prediction of velocity field in different sections of the bend. The inputs of the mentioned ANN were depth, radius and angle of different points of bend, and target outputs were corresponding velocities obtained in the experiment. Also the same ANN was trained based on the Back-Error Propagation (BEP)

2 (1  exp(-2n)) -1

(10)

Back-error propagation technique

One of the most powerful learning algorithms in neural networks is BEP that was presented by Rumelhart and Mcclelland (1986). The structure of the back-propagation is shown in Fig. 7. In this study the structure of neural network consists of input layer, hidden layer, and output layer. The variables M , N and L are the total neuron numbers in the input layer, hidden layer and output layer, respectively. Values wMN are the weights between the input and the hidden layer. Values wLN are the weights between the hidden and the output layer. The operation of BEP consists of three steps: 1- Feed-forward step:

v j  wLN (n).u j 1 (n) o j (n)   (v j (n)) 

388

2 1  exp(v j (2n))

(11) (12)


recombination procedure. Mutation is the main operator for protecting the algorithm from permanently losing genetic material through the evolution of generations, which changes parts of the individuals periodically. Also crossover is used for the recombination of genetic exchange among individuals. Migration is the movement of individuals among sub-populations of existing individuals, with the best individuals from one sub-population replacing the worst individuals in another sub-population. The best individual is proposed as the solution to the problem by GA. Fig. 8 shows the flowchart of basic GA.

where, o j is output, u j is input, u j 1 is output of hidden layer and  is transfer function. 2- Back-propagation step:

 j (n)  e j (n). ' (v j (n))  (d j (n) - o j (n))o j (n)(1- o j (n))

(13)

where,  j represents the local gradient function,

e j shows the error function, o j means the actual output and d j is desired output. 3- Adjust weighted value:

wNM (n  1)  wNM ( n)  wNM (n)


 wNM ( n)   j ( n).o j ( n)

3.4

(14)

The first prediction procedure of the present study consists of three main stages. In the first stage, two MLFF neural networks were created with an input, a hidden and an output layer with 3, 5 and 1 neuron, respectively. The inputs of the ANNs were depth, radius and angle of different points of the bend, and the target output was corresponding velocities. In the second stage, ANN trainings were done based on experimental data of 642 different points. For training ANNs, GA and BEP techniques were applied and layer weights of ANN were obtained. In the third stage, some experimental data not used in the training process were used to test the trained ANNs. For this propose, coordinates of these data were applied as inputs to trained ANNs and corresponding outputs were obtained. Then, the outputs of the trained ANN based on GA and BEP were compared with corresponding velocities from experimental data. In this procedure, the GA generation, population size and BEP iterations were assumed as 1000, 20 and 1000, respectively. The second prediction procedure of this study was similar to one mentioned above though there were some differences. In the second procedure, an MLFF neural network was trained based on BEP and was used to predict the velocity fields in some sections where experimental data were not available. This ANN had an input, a hidden and an output layer with 3, 40 and 1 neuron, respectively, and BEP iterations were assumed as 1000. In the training process of this ANN the inputs were depth, radius and angle of 713 different points of bend, and the target output was corresponding experimental velocities. Test results of this ANN were compared with results of CFX. It should be mentioned that the data were applied to all ANNs of this article in normalized form.

where,  is the learning rate. Repeating these three steps results in the value of the error function being zero or a constant value.

Fig. 7

3.3

Prediction procedure

Schematic diagram of multilayer feed forward neural network.

Genetic algorithm

GA is a common optimization method in engineering applications popularized by Holland (1975). This method in all iterations generates a population of points that uses stochastic instead of deterministic operators to approach the optimal solution. The first population is formed by initializing a set of individuals and is submitted to genetic operators, resulting in the evolution of populations through generations. GA in each generation investigates the individuals according to an objective function and selects the best individuals. The individuals that are evaluated as better, according to the objective function, have a higher possibility of participation in the 389


Start

Initial Population Fitness Evaluation for All of Individuals

Reproduction

Crossover

Mutation


Best Individual

Update Population

Stopping Criteria

End Fig. 8

Flowchart of basic GA.

component of velocity are more obvious. After this section, the secondary flow is expanded. The existence of centrifugal force in bend causes a lateral slope in water level in the bend so that water level at the outer wall increases and in inner wall decreases. As a result lateral pressure gradient is formed. Distributions of the lateral velocity component obtained from the numerical model were compared with experimental data at sections 30o, 45o, 60o and 90o in Fig. 10. In Fig. 10d, the effect of secondary flow on velocity changes is obvious. The negative and positive values corroborate the strength of secondary flow in the bend, and especially toward the end of the bend. As is visible from Figs. 9 and 10, according to experimental results maximum values of velocity occurr near the free surface, but numerical results show that the maximum values of velocity occur on the free surface. It should be mentioned that the numerical and experimental results do not have large differences in most sections.

4. RESULTS 4.1 4.1.1

Results of CFX Verifying

The values of longitudinal and lateral velocity distributions achieved from the numerical model were compared with experimental data in Figs. 9 and 10. As illustrated in Figs.9 and 10, the model was in good agreement with experimental results. But in some sections, the results of the numerical model have some differences with experimental results. In this study effects on sediment in flow pattern have been omitted because effects of sediment on velocity are not sizable. So simulation has been done in 2 phases instead of 3phases (i.e. air, water and sediment). It should be mentioned that sediment changes level of water and reduce velocity in regions where sedimentation occurs. Fig. 9 shows that the maximum values of longitudinal component of velocity occurr near the water surface. So it is clear that at these sections the effect of secondary flow is negligible. Fig. 9d shows that the influence of secondary flow on the longitudinal velocity component at secton 60o is considerable. The secondary flows toward the inner wall on bed and toward the outer wall on the surface result in the displacement of the maximum velocity location. This location of maximum longitudinal velocity moves from the inner wall toward the outer wall of the channel bend. At section 90o (Fig. 9e) the effect of the secondary flow and variations of longitudinal

4.1.2. Investigation of variation of longitudinal velocity

Using the Tecplot software, velocity contours at different sections along the bend are plotted in Fig. 11. Fig. 11 (b) shows that at the start of the bend, the zone of maximum velocity is near the inner wall. When the flow approaches the bend, the secondary flow is generated via the interaction of the centrifugal force and the pressure gradient, and subsequently, it influences the flow behavior 390



Fig. 9

Distributions of longitudinal component of velocity at sections: (a) 20 cm before the bend, (b) 0o, (c) 30o, (d) 60o, (e) 90o and (f) 20 cm after the bend.

Fig. 10 Distributions lateral component of velocity at sections: (a) 30o, (b) 45o, (c) 60o and (d) 90o of bend.

391



and lateral momentum transport, so the lateral momentum is transferred toward the outer wall of the channel bend (Figs. 11d and e). As is shown in Figs. 11, the increasing trend of longitudinal velocity in the inner wall has continued until before the section 90o and in this section longitudinal velocity is approximately constant. The velocity decreases after section 90o. In the outer wall, variation of velocity is contrary to that at the inner wall. At a section 20 cm after the bend, strong reduction of velocity in the inner wall is visible and it occurs because of separation of flow (Fig. 12) from the wall. Based upon the mechanism of spiral motion in bends, it is clear that the influence of this stream is not limited to the bend. It influences straight reaches before and after the bend. Influences of the secondary flow on velocity components are illustrated in Fig. 11. 4.2

(a)

(b)

Results of ANN

Results of the comparison of GA and BEP for 10 different points were tabulated in Table 1. As was mentioned in section 3.4, the ANNs of the first prediction procedure have an input, a hidden and an output layer with 3, 5 and 1 neuron, respectively. Also ANN trainings were done using experimental data of 642 different points. In the procedure, the GA generation, population size and BEP iteration were assumed as 1000, 20 and 1000 respectively. As indicated in Table 1, the average errors of GA and BEP results are 5.18% and 5.91%, respectively. Therefore, it can be concluded that, for assumed condition, GA is a little better than BEP technique for velocity predictions in this state. Another ANN was created for predicting velocity fields in different sections using BEP. As was mentioned before, in the second procedure ANN has an input, a hidden and an output layer with 3, 40 and 1 neuron, respectively. The ANN trainings were done using experimental data of 713 different points and the number of BEP iterations was 1000. The main advantage of the proposed prediction procedure is approximating the velocity field for points where experimental data are not available. For example, in this study the experimental data have been obtained only in 11 sections in the bend, ANN helps investigators to study the velocity fields in other sections. In Figs. 13, the longitudinal velocity profile has been plotted using results of ANN and CFX in sections 15o, 25o, 35o, 55o, 65o and 75o. It can be concluded from above figures that at the front end of the bend (section 35o) the maximum velocity occurred in the inner wall. The maximum

(c)

(d)

(e)

Fig. 11 Contours of longitudinal velocity at sections: (a) 20 cm before the bend, (b) 0o, (c) 45o, (d) 90o and (e) 20 cm after the bend.

Fig. 12 Separation Region.

392


Table 1 Velocities from ANN and experiment for different points on bend.


No

Coordinates of Point

Velocity

Angle

Radius

Depth

EXP

ANN

(deg)

(m)

(m)

(m/s)

GA (m/s)

GA Error(%)

BEP(m/s)

BEP Error(%)

1

10

1.85

0.075

0.356

0.341

5.958

0.341

5.836

2

10

1.95

0.045

0.314

0.328

6.470

0.297

8.014

3

20

1.85

0.045

0.301

0.310

4.620

0.290

5.626

4

30

1.95

0.045

0.301

0.310

4.620

0.290

5.626

5

30

1.95

0.045

0.319

0.312

3.402

0.329

4.310

6

45

1.85

0.075

0.308

0.305

1.271

0.289

8.993

7

45

1.95

0.045

0.331

0.309

9.698

0.342

4.781

8

60

1.85

0.075

0.311

0.323

5.732

0.296

7.230

9

70

2.025

0.11

0.320

0.308

5.325

0.304

7.050

10

90

2.05

0.075

0.318

0.307

4.676

0.321

1.597

(a)

(b)

(c)

(d)

(e)

(f)

Fig. 13 Longitudinal velocity profiles in sections: (a) 15o, (b) 25o, (c) 35o, (d) 55o, (e) 65o and (f) 75o.

393


3. For adopted training procedures, GA was a little better than BEP technique for velocity prediction of the channel.

velocity gradually moves to the outer wall. Both methods (i.e. ANN and CFX) can predict the flow pattern well and there are good agreements between results of ANN and CFX, but each method has advantages and disadvantages as follows:

4. The main advantage of the procedure is the prediction of the approximate velocity at points where experimental data are not available.

1. Compared to the ANN method, the CFX is time-consuming since it uses numerical methods, and the accuracy of these methods depends on the number of nodes and elements in the mesh. The finer the mesh, the longer the solution time and the more accurate the results.

It is suggested that as a continuation to this study, the prediction can be done using some other artificial intelligence techniques such as Fuzzy Logic (FL), SVM etc. Also the ANN can be trained by some other methods and some other optimization techniques, such as Particle Swarm Optimization (PSO) and Artificial Bees Colony (ABC). Also the presented procedure can be used in predicting some other properties of flow besides velocity, such as shear stresses, depth of water or variations of channel bed. In addition, the presented procedure can be applied to prediction and analysis of the properties of other types of channels and other structures across the flow.


2. The ANN needs data at points in some sections, but CFX needs data for boundary conditions only. 3. When there are not enough data from considered model to training it, the ANN model can not be used for a suitable prediction. 5. CONCLUSIONS

NOMENCLATURE

In this study numerical analysis and prediction of flow field in a 90o bend using ANN and GA were presented. In the first part of the paper, a 3D model of turbulence stream pattern in a 90o bend was simulated using a numerical and model. Using experimental and numerical analysis, variation of velocity components in the 90o bend was studied. The other part of this paper dealt with the prediction of the velocity field using ANN. In the prediction part, at first, two similar MLFF neural networks were created. Then coordinates of different points were applied as input values and corresponding velocity as target outputs to create ANNs. Some experimental data were used to train the ANNs. Some experimental data that had not been used in the training process were used to test the trained ANNs based on GA and BEP techniques. Finally, the results of ANN and CFX methods were compared in sections where experimental data were not available. The main conclusions of this study are as follows:

B(m) Cε1 Cε2 CU dj ej f k L M m N Oj Pk Pkb Ri Ro t U ui uj+1 WLN

1. Results of numerical model showed that they were in good agreement with experimental results. Also there were good agreement between results of ANN and CFX. 2. Results of ANNs that had been trained using GA and BEP indicated that the velocity field was predicted with good approximation in both training methods and it was concluded that the proposed procedures were useful for velocity prediction in channel bends.

WMN y(m) 394

Width of channel k   Turbulence model constant k   Turbulence model constant k   Turbulence model constant Desired output of ann Error function of ann Buoyancy force Turbulence kinetic energy per units mass(m2/s2) Total neuron number in output layer of ann Total neuron number in input layer of ann Subscript to indicate mixture quantities Total neuron number in hidden layer of ann Output of ann Shear production of turbulence (Pa/S) Buoyancy production Inner radius of bend(m) Reynolds number(m) Time (s) Vector of velocity (m/s) Input of ANN Output of hidden layer of ANN Weights between the hidden and the output layer of ANN Weights between the input and the hidden layer of ANN Height from channel bottom




j   u

t

 k


  t 

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Used as subscript to indicate the volume fraction for each phase Local gradient function of ANN Turbulence dissipation rate (m2/s3) Learning rate of ANN Molecular viscosity (Pa.s) Turbulence viscosity (Pa.s) Density (kg/m3) Turbulence model constant for the k equation k   Turbulence model constant Viscose stress tensor Turbulence viscose stress tensor Transfer function of ANN’s layers

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