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  • Powder Technology 284 (2015) 336343

    Contents lists available at ScienceDirect

    Powder Technology

    j ourna l homepage: www.e lsev ie r .com/ locate /powtec

    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 Petkovi e, Mahidzal Dahari f, Naghmeh Mahmoodian d,ga 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 Ni, Faculty of Mechanical Engineering, Deparment for Mechatronics and Control, Aleksandra Medvedeva 14, 18000 Ni, Serbiaf Department of Mechanical Engineering, Faculty of Engineering, University of Malaya, 50603 Kuala Lumpur, Malaysiag Medical Engineering Department, Hakim Sabzevari University, Sabzevar, Iran






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

    E-mail addresses: (S. (M. Goodarzi). 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 m.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.



    0 122639654.60 122 639654.shirband),



    k Generation of turbulent kinetic energy (m2 s2)


    Gravitational acceleration (m s2)


    p Particle mass (Kg)


    p Particle velocity (m s1)


    (N m2)


    e Reynolds number (V D 1)




    Turbulence kinetic energy

    (m2 s2)


    Velocities vector

    (m s1)


    reek symbols

    Angle between the particle trajectory and wall


    (Kg m3)


    Cell face area at the wall

    Dissipation rate of turbulent kinetic energy

    (m2 s3)

    Dynamic viscosity

    (Pa s)


    Effective Prandtl Number for k

    Effective Prandtl number for


    Function of impact angle


    Function of particle diameter


    Function of relative velocity among particles

    Relative velocity among particles


    Turbulence eddy viscosity (m2 s1)

    Volume Fraction of particle






    1. Introduction

    It is acknowledged that erosioncorrosion (EC) is one of thecommonest failure modes of pipelines. EC 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 erosioncorrosion 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) 336343

    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 EC be-havior at different locations of the elbow [1].

    A large number of experimental investigations have been performedregarding the topic of erosioncorrosion 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 kturbulence 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 liquidsolid condition,it is not clear how the addition of solid particles affect the EC 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 [1317]. FuzzyInference System (FIS) is the main part of ANFIS. FIS is based on IfThen 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 [1820]. A CFD simulation is also carriedout to extract the training and check the data for the


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