Powder Technology 284 (2015) 336–343

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Powder Technology

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Performance investigation of micro- and nano-sized particle erosion in a90° elbow using an ANFIS model

Shahaboddin Shamshirband a,⁎, Amir Malvandi b, Arash Karimipour c, Marjan Goodarzi d,⁎⁎, Masoud Afrand c,Dalibor Petković e, Mahidzal Dahari f, Naghmeh Mahmoodian d,g

a Department of Computer System and Information Technology, Faculty of Computer Science and Information Technology, University of Malaya, 50603 Kuala Lumpur, Malaysiab Department of Mechanical Engineering, Neyshabur Branch, Islamic Azad University, Neyshabur, Iranc Department of Mechanical Engineering, Faculty of Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Isfahan, Irand Young Researchers and Elite Club, Mashhad Branch, Islamic Azad University, Mashhad, Irane University of Niš, Faculty of Mechanical Engineering, Deparment for Mechatronics and Control, Aleksandra Medvedeva 14, 18000 Niš, Serbiaf Department of Mechanical Engineering, Faculty of Engineering, University of Malaya, 50603 Kuala Lumpur, Malaysiag Medical Engineering Department, Hakim Sabzevari University, Sabzevar, Iran

dG

g!m

v!PRtk

V!

GαρAε

⁎ Corresponding author. Tel.: +60 146266763; fax: +6⁎⁎ Corresponding author. Tel.: +60 1114354102; fax: +

E-mail addresses: shamshirband@um.edu.my (S. ShamMarjan_g_2003@yahoo.com (M. Goodarzi).

http://dx.doi.org/10.1016/j.powtec.2015.06.0730032-5910/© 2015 Elsevier B.V. All rights reserved.

a b s t r a c t

a r t i c l e i n f o

Article history:Received 20 December 2014Received in revised form 11 June 2015Accepted 30 June 2015Available online 8 July 2015

Keywords:ANFISEstimationErosion corrosionCFD

The accuracy of soft computing technique was employed to predict the performance of micro- and nano-sizedparticle erosion in a 3-D 90° elbow. The process, capable of simulating the total and maximum erosion ratewith adaptive neuro-fuzzy inference system (ANFIS), was constructed. The developed ANFIS network waswith three neurons in the input layer, and one neuron in the output layer. The inputs included particle velocity,particle diameter, and volume fraction of the copper particles. The size of these particleswas selected in the rangeof 10 nm to 100 μm.Numerical simulations have been performedwith velocities ranging from 5 to 20m/s and forvolume fractions of up to 4%. The governing differential equations have been discretized by the finite volumemethod for ANFIS training data extraction. The ANFIS results were compared with the CFD results using root-mean-square error (RMSE) and coefficient of determination (R2). The CFD results show that an improvementin predictive accuracy and capability of generalization can be achieved by the ANFIS approach. The followingcharacteristics were obtained: ANFIS model can be used to forecast the maximum and total erosion rate withhigh reliability and therefore can be applied for practical purposes.

© 2015 Elsevier B.V. All rights reserved.

μ

Nomenclature σσ Diameter

0 122639654.60 122 639654.shirband),

(m)

f(

k Generation of turbulent kinetic energy (m2 s−2)

C

Gravitational acceleration (m s−2)

b

p Particle mass (Kg)

v

p Particle velocity (m s−1)

υ

Pressure (N m−2) u e Reynolds number (V D υ−1)

Time

(s) Su Turbulence kinetic energy (m2 s−2) D Velocities vector (m s−1) p

reek symbols

Angle between the particle trajectory and wall Density (Kg m−3)

f

Cell face area at the wall Dissipation rate of turbulent kinetic energy (m2 s−3)

Dynamic viscosity

(Pa s) k Effective Prandtl Number for k ε Effective Prandtl number for ε a) Function of impact angle (dp) Function of particle diameter (v) Function of relative velocity among particles

Relative velocity among particles

t Turbulence eddy viscosity (m2 s−1)

Volume Fraction of particle

bscripts

Drag Particle Turbulent t

1. Introduction

It is acknowledged that erosion–corrosion (E–C) is one of thecommonest failure modes of pipelines. E–C could cause significantdegradation of pipelines in oil and gas fields and result in prematurefailure and necessary replacement of the line. Massive costs are directedannually to alleviating the erosion–corrosion of pipelines. Elbow is animportant component of most practical pipe configurations in oil and

Table 1Point values for impact angle function [11].

Point Angle Value

1 0 02 20 0.83 30 14 45 0.55 90 0.4

337S. Shamshirband et al. / Powder Technology 284 (2015) 336–343

gas transportation. However, abrupt diversion in the flow direction in a90-degree elbowwould cause great change in the motion and distribu-tion of solid particles, thus leading to considerable difference in E–C be-havior at different locations of the elbow [1].

A large number of experimental investigations have been performedregarding the topic of erosion–corrosion in the past years such as stud-ies done by Lonsdale and Southard [2], Gulden [3], and Saravanan,Surappa and Pramila Bai [4]. However, numerical techniques, with allthe recent advances, were not successful in producing results withreasonable accuracy. Many reasons are involved in this slow-movingdevelopment. The most important reason is related to the modeling ofmass transfer next to the solid boundaries, which requires solvingthe pertaining governing equations. In this sense, boundary layer inaqueous flows is sometimes located beneath the viscous sub-layer,necessitating the use of fine near-wall grids. Applying thesefinemeshesin the near-wall region, together with the proper turbulence model —which needs huge number of computations, it is possible to evaluatethe data of mass transfer for corrosive species [5,6]. Thus, in CFDmodeling, a Lagrangian description (DPM model) has a considerableexcellence compared to an Eulerian description (DEM) because exactwall interaction information can be obtained without any additionalmodeling which means less calculation time [7]. Utilizing this informa-tion, an erosion model can be applied to specify erosion rates.

The erosion prediction method in three dimensional elbows wasstudied by Chen, McLaury, and Shirazi [8] using Fluent 6.3. The k–εturbulence model together with DPM model was employed to solvethe problem. Their results showed that increasing the particle concen-tration decreases the corrosion-dominated regime at the pipe bend.Their comparison of erosion rate also showed a good agreementbetween the numerical and experimental results.

A novel method by combining array electrode technique withcomputational fluid dynamics (CFD) simulation has been proposed byZhang, Zeng, Huang, and Guo [9] to determine the correlation betweenthe corrosion behavior at the elbow of pipeline and the hydrodynamicsof fluid flow. They noted that the distribution of themeasured corrosionrates is in good accordance with the distributions of flow velocity andshear stress at the elbow. However, in the case of liquid–solid condition,it is not clear how the addition of solid particles affect the E–C atdifferent locations of an elbow.

A prediction model to specify erosion wear profiles in a two dimen-sional jet impingement test has been proposed by Gnanavelu, Kapur,Neville, Flores, and Ghorbani [10]. Their model was developed basedon experimental and numerical data for the material wear. They notedthat the predicted results are in a sensible relation with the experimen-tal data. However, a few basic errors were always found in the modeldue to some simplifications made for material hardening, and particlesize and shape in addition to the simulation errors.

A two dimensional solution of sand erosion in pipe, which is of prac-tical importance in oil and gas industry, was developed by Mohyaldin,Elkhatib, and Ismail [11]. Three different methods including empirical,semi-empirical, and computational fluid dynamics (CFD) were utilizedin their solution. The results showed that the data from CFD techniqueof Discrete Phase Model (DPM)was in good agreement with the resultsof semi-empirical method of direct impingement model. However, theCFD model greatly underpredicted the results taken from empiricalmethod.

In this study, the influences of particle velocity, particle diameter andparticle volume fractions on total and maximum erosion rate areinvestigated. Since for such an uncertain and nonlinear process,analyzing could be very challenging and time consuming, soft comput-ing techniques are preferred. It is attempted to estimate the effect of dif-ferent parameters onmicro- and nano-sized copper particle erosion in a3-D 90° elbow (pipe bend) by soft computingmethodology i.e. adaptiveneuro-fuzzy inference system (ANFIS).

ANFIS is a type of neural networks which is very powerful [12]. ANFIShas high learning and prediction capabilities, which makes it a very

efficient tool for encountered uncertainties in any system. ANFIS hasbeen used by researchers in various engineering systems [13–17]. FuzzyInference System (FIS) is the main part of ANFIS. FIS is based on ‘If–Then’ rules and thus can be employed to predict the behavior of manynonlinear systems. FIS does not require knowledge of the physical processas a precondition for application [18–20]. A CFD simulation is also carriedout to extract the training and check the data for the ANFIS network.

2. Numerical method

To solve the Reynolds Averaged Navier–Stokes (RANS) equations,the commercially available finite volume based software, FLUENT, hasbeen selected, as previously employed in the studies done by [21–25].

The finite volume method on the basis of a certain kind of residualweighting technique, divides the computational domain into finitecontrol volumes. The differential equation is finally integrated on eachof these control volumes which contains just a node [26–28].

In the present study,DPMwasused to solve themultiphaseflowcom-prising diluted fluid–solid, as the loading ratio of particles were less than10 vol.% (between 0 and 4%) [29]. Here, the simulation of fluid,representing the continuous phase, was carried out using the Eulerianmethod, while particle phase was modeled by the Lagrangian approach.

Standard wall functions were used together with the previouslydiscussed Standard k–ε model.

All the equation terms were discretized by the method of secondorder upwind [30,31] and the pressure–velocity equation were coupledby the SIMPLE algorithm [32,33]. A piece-wise linear profile was used tospecify the impact angle function (see Table 1). Based on [10], thevelocity exponent and diameter functions were set to 2.6 and1.8 × 10−9, respectively. The convergence of solution was achievedwhen the residuals in all the equations fell below 10−6 [27,34].

3. Governing equations of turbulent micro- and nano-fluid erosion

Continuity, momentum, DPM, and turbulent equations are used toanalyze the flow [21,22,35]. The governing equations are:

Continuity equation:

∂∂t

ρð Þ þ ∇: ρV!� �

¼ 0: ð1Þ

Momentum equation:

∂∂t

ρV!� �

þ ∇: ρV!

V!� �

¼ −∇P þ ∇: μ ∇V!þ ∇V

!T� �� �

þ ρ g!: ð2Þ

Standard k–ε turbulence model:

Turbulent kinetic energy transport equation:

∂ ρkð Þ∂t

þ ∇: ρV!k

� �¼ ∇: μ þ μ t

σk

� �∇k

� �þ Gk−ρε: ð3Þ

Dissipation of turbulent kinetic energy transport equation:

∂ ρεð Þ∂t

þ ∇: ρV!ε

� �¼ ∇: μ þ μ t

σε

� �∇ε

� �þ εk

Cε1Gk−ρεCε2ð Þ: ð4Þ

(a) =2%ϕ

Table 2Coefficients for Standard k–ε turbulent model.

Cμ σk σε Cε1 Cε2

0.09 1 1.3 1.44 1.92

338 S. Shamshirband et al. / Powder Technology 284 (2015) 336–343

The turbulent eddy viscosity obtained fromPrandtl–Kolomogorovrelation:

μ t ¼ Cμρk2

ε: ð5Þ

The turbulence kinetic energy production of the mean velocitygradients, Gk, is given as:

Gk ¼ μ t∇V!: ∇V

!þ ∇V!T

� �−

23∇:V!

3μt∇:V!þ ρk

� �: ð6Þ

The constants for the Standard k–ε turbulence model in the aboveformula are represented in Table 2 [33,36].

DPM:

mpd v!p

dt¼ ∑ F

! ð7Þ

where F!

is an external force acting on the particles which for fineparticleswith high density ratio (more than one) are drag and buoyancyforces [37].

Therefore, the equation of motion can be simplified to the followingform:

d v!p

dt¼ FD v!− v!p

� �þg ρp−ρ� �

ρgð8Þ

where [38]

FD ¼ 18μ

ρpd2p

!CDRep24

� �ð9Þ

wherein, Rep is the particle Reynolds number and is given as [39–41]:

Rep ¼ ρdp v!p− v!�� ��μ

!: ð10Þ

Fig. 1. ANFIS structure with two inputs, one output and two rules.

The Drag coefficient, CD, as a function of the particle Reynoldsnumber is defined by [42,43]:

CD ¼ 24Re

1þ 11:2355Re0:653� �

þ −0:8271ð ÞRe8:8798þ Re

ð11Þ

The solid particle erosion rates are defined as [44,45]:

Rerosion ¼XNp¼1

m�

pC dp

f að Þνb νð Þ

Af

!ð12Þ

where C(dp) is particle diameter function, f(a) is impingement anglefunction, v is the relative velocity among particles, b is velocityexponent, and Af is the cell face area at the wall [37,44].

(b) =4%ϕ

Fig. 2.Maximum erosion rate versus particle size.

339S. Shamshirband et al. / Powder Technology 284 (2015) 336–343

4. Neuro-fuzzy computing

Soft computing is an innovative approach in the construction ofsystems that are computationally intelligent which possess humanlikeexpertise within a specific domain. These systems are supposed toadapt in changing environments, learn to dobetter and explain their de-cision making process. It is usually more beneficial to employ severalcomputing methods in a synergistic way rather than building a systembased exclusively on one technique only. This is useful in confrontingreal-world computing problems. The result of such synergistic use ofcomputing techniques is the construction of complementary hybrid in-telligent systems. The epitome of designing and constructing intelligentsystems of this kind is neuro-fuzzy computing: firstly, neural networksrecognizing patterns and adapting to copewith evolving environments;and secondly, fuzzy inference systemswhich include human knowledge

(a)

(b)

Fig. 4. Pressure (a) and erosion (b) contours on the wall of the bend.

(a) =2%

(b) =4%

ϕ

ϕ

Fig. 3. Total erosion rate versus particle size.

and implement decision making and differentiation. The combinationand integration of these two complementary methodologies producesa novel discipline called neuro-fuzzy computing.

4.1. Adaptive neuro-fuzzy application

The adaptive neuro-fuzzy inference system (ANFIS) can serve as abasis to construct a set of fuzzy ‘If–Then’ rules with an appropriatemembership function to generate the stipulated input–output pairs.In this study, the ANFIS system that is functionally equivalent to the

Table 3Statistical parameters for data sets.

Variable Statistical parameters

Min Max

Particle size 10 nm 100 μmParticle velocity 5 m/s 20 m/sVolume fraction of particles 0.02 0.04

Fig. 5. ANFIS decision surfaces for the effect of total andmaximum erosion rate of the elbow.

Fig. 5 (continued).

340 S. Shamshirband et al. / Powder Technology 284 (2015) 336–343

first-order Sugeno fuzzy model was used. A typical rule set with a fuzzy‘If–Then’ rule can be expressed as

if x is A; then f1 ¼ p1xþ t: ð13Þ

The ANFIS architecture for three inputs x, y, and z is shown in Fig. 1.Nodes at the same layer have similar functions. The output of the ithnode in layer l is denoted as Ol,i.

The first layer consists of input variables membership functions(MFs) and supplies the input values to the next layer. Every node i isan adaptive node with a node function

O1;i ¼ μ x; y; zð Þi for i ¼ 1;2 ð14Þ

where x, y= input to the ith node; μ(x, y, z)i =membership functions.The MFs can be described by bell-shaped function

f x; a; b; cð Þ ¼ 1

1þ x−ca

2b ð15Þ

where {a, b, c} is the parameter set. These parameters are updatedduring training procedure of the ANFIS network. The neural networkbranch of the ANFIS network did selection procedure of the member-ship parameters.

The second layer (membership layer) multiplies incoming signalsfrom the first layer and sends the product out. Each node outputrepresents the firing strength of a rule or weight like

O2;i ¼ wi ¼ μ xð Þi � μ xð Þiþ1; i ¼ 1;2: ð16Þ

(a)

(b)

Fig. 6. Scatter plots of predicted values of (a) total erosion rate and (b) maximum erosionrate by ANFIS model.

341S. Shamshirband et al. / Powder Technology 284 (2015) 336–343

The third layer (i.e. the rule layer) is non-adaptivewhere every nodei calculates the ratio of the rule's firing strength to the sum of all rules'firing strengths like:

O3;i ¼ w�i ¼

wi

w1 þw2; i ¼ 1;2: ð17Þ

The outputs of this layer are called normalized firing strengths ornormalized weights.

The fourth layer (i.e. the defuzzification layer) provides the outputvalues resulting from the inference of rules, where every node i is anadaptive node with node function

O4;i ¼ w�i � f i ¼ w�

i pixþ qiyþ rið Þ ð18Þ

where {pi, qi, ri} is consequent parameters. These parameters present theoptimal ANFIS parameters.

The fifth layer sums up all the inputs from the fourth layer and con-verts the fuzzy classification results into a crisp output. The node in thefifth layer is not adaptive and this node computes the overall output ofall incoming signals

O5;i ¼Xi

w�i � f i ¼

Xi

wi � f iXi

wi: ð19Þ

The outputs of the fifth layer represent the ANFIS prediction results.

5. Evaluation of model performances

To analyze the performance of the ANFIS model and measurementvalues, the following statistical indicators were selected:

1) Root-mean-square error (RMSE)

RMSE ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiXni¼1

Oi−Pið Þ2

n

vuuut: ð20Þ

2) Coefficient of determination (R2)

R2 ¼

Xni¼1

Oi−Oi

� �� Pi−Pi " #2

Xni¼1

Oi−Oi

� ��Xni¼1

Pi−Pi : ð21Þ

where Oi = ANFIS value, Pi = measurement values, and n = the totalnumber of test data.

6. Results

6.1. Initial numerical modeling

In the present work, the fluid flows in a 90 degree elbow wasinvestigated in turbulent regime to get the initial results. The fluid wascomprised of suspensions of micron- and nano-sized copper particlesin water. The elbow was made of Aluminium (3003 Alloy), having adiameter of 0.0032 m (18 inches), with 1.5 being the ratio of the bendradius to the inside diameter of the pipe. The attached pieces of pipeat two sides of the elbow were 0.016 m (58 inches) long, being 5 timesbigger than the pipe diameter. Velocities of water flowing through thepipe were considered equal to 5 m/s, 10 m/s and 20 m/s, assuming thesame for the solid particles. Solid particles were assumed to be sphericaland have diameters equal to 10, 50, and 100 μmand 10, 50, and 100 nm,suspended in volume concentrations of 2% and 4%. To investigate the

effect of particle size and velocity on the total and maximum erosionrates, the FLUENT software was utilized.

Fig. 2a and b demonstrate the effect of solid particles size on themaximum erosion rate. It can be understood that themaximumerosionrate is dependent on the fluid velocities. A threshold value for thevelocity and particle size can be established, below which the erosioncan be neglected. It is also found that the erosion rate increases withthe particle diameter in a linear manner. Setting all the parametersfixed, it can be noted that the value of maximum erosion rate increasesby the rise in particle volume fraction. This increment is about 4.5 timesin average. Results are in agreement with the findings of Zhu, Lin, Feng,Deng, Kong, Wang, and Zeng [42].

Total erosion rate depicted in Fig. 3a and b, showing the similartrend, was found to be higher by increase in the particle diameterand inlet fluid velocity. The reason is that the particle impact velocityrises as the inlet flow velocity and particle size increases. Thisincrement can be quantified by the present proposed numericalmethod. It was observed that the total erosion rate grows by about8.5 times, when flow experiences a shift of velocity from 10 m/s to20 m/s at volume concentrations equals to 2%. This rise is approxi-mately 9.5 times at volume concentration of 4%. Increasing thevolume concentration from 2% to 4% resulted in a lift in totalerosion to 8 times which is similar to findings by Habib, Badr, Said,Ben‐Mansour, and Al‐Anizi [43].

Fig. 4a and b illustrates the pressure and erosion contours inside theelbow for V= 10 m/s, particle size = 100 μm and the volume fractionsof (Cu) 4%. As seen, the maximum erosion is observed near themidpoint, along the symmetry plane of the pipe bend, which is the loca-tion that the pressure is maximum.

Table 4Performance statistics of the ANFIS model in total and maximum erosion rate estimation.

RMSE R2

Total erosion rate 0.0022677 0.9934Maximum erosion rate 1.8629E-05 0.9842

342 S. Shamshirband et al. / Powder Technology 284 (2015) 336–343

6.2. Input variables

In this study, the particle size, particle velocity, and copper volumefraction (φ) was used to generate the ANFIS model. To get a morereliable evaluation and comparison, ANFISmodel is tested by evaluatinga data set that was not used during the training process. The statisticalparameters (particle size, particle velocity and particle's volumefraction) for data sets are calculated and given in Table 3. Matlabsoftware was used for ANFIS simulations. The two outputs of theANFIS network are total erosion rate and maximal erosion rate.

6.3. ANFIS model analysis

The ANFIS network was initially trained with measured data by theabove presented CFD procedure. Three bell-shaped membershipfunctions were used to fuzzify the ANFIS inputs. After training process,the ANFIS networks were tested to determine the total and maximumerosion rate of the elbow. The ANFIS decision surfaces for estimationof total and maximum erosion rate of the elbow are shown in Fig. 4for the four input parameters.

The CFD total erosion rate and predicted values using ANFIS modelare shown in Fig. 5(a). Fig. 5(b) presents the numerical maximumerosion rate and predicted values using ANFIS model. As noted, the R2

correlation coefficient is very high for total erosion rate prediction byANFIS. Therefore ANFIS has a notable correlation with the total erosionrate. Fig. 6(a) and (b) show the forecasting of total and maximumerosion rates by ANFIS model, respectively. According to coefficient ofdetermination in Fig. 6 the better prediction was achieved for totalerosion rate than for maximum erosion rate. This can be seen in Fig. 7

(a)

(b)

Fig. 7. ANFIS forecasting of (a) total erosion rate and (b) maximum erosion rate.

also where the ANFIS forecasting is presented according to differentdata samples.

The performance of ANFISmodel that estimated total andmaximumerosion rate was evaluated according to a statistical criteria such asRMSE and coefficient of determination R2 for different particlediameters and volume fraction as well as various velocities. Thisconfirms the RMSE statistics evaluated in Table 4. It can be concludedthat the proposed ANFIS model can be used to forecast the total andmaximum erosion rate with high reliability for total erosion rate.

7. Conclusions and future work

The accuracy of an adaptive neuro-fuzzy technique in estimation oftotal and maximum erosion rate of copper particles flow through anelbowwas investigated in this study. The study indicated that modelingof the erosion rates is possible through the use of ANFIS technique. TheANFIS model used particle velocity, particle diameter and particle'svolume fraction as the input parameters. It can be outlined that ANFISmodel can be used for forecasting maximum and total erosion rateswith a high reliability.

Themain advantages of the ANFISmodel are computational efficiencyand adaptability. The proposed ANFIS model can be embedded as amodule to estimate the solar radiation data as well. In this work weanalyzed dilute flow conditions. For the future investigations we willextend it to dense flow conditions.

Acknowledgment

The authors gratefully acknowledge High Impact Research GrantUM.C/HIR/MOHE/ENG/23, UMRG Grant RP012C-13AET and Faculty ofEngineering, University of Malaya, Malaysia for support in conductingthis research work.

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