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Powder Technology 284 (2015) 336343
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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 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: firstname.lastname@example.org (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 ta 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
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),
f(k Generation of turbulent kinetic energy (m2 s2)
CGravitational acceleration (m s2)
bp Particle mass (Kg)
vp Particle velocity (m s1)
ue Reynolds number (V D 1)
Turbulence kinetic energy
Angle between the particle trajectory and wall
Cell face area at the wall
Dissipation rate of turbulent kinetic energy(m2 s3)
Effective Prandtl Number for k
Effective Prandtl number for
Function of impact angle
Function of particle diameter
(v)Function of relative velocity among particles
Relative velocity among particles
tTurbulence eddy viscosity (m2 s1)
Volume Fraction of particle
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 .
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 .
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 , Gulden , and Saravanan,Surappa and Pramila Bai . 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 . 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  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  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 . 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 . 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 . 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 . 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 . 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 NavierStokes (RANS) equations,the commercially available finite volume based software, FLUENT, hasbeen selected, as previously employed in the studies done by .
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 .
In the present study,DPMwasused to solve themultiphaseflowcom-prising diluted fluidsolid, as the loading ratio of particles were less than10 vol.% (between 0 and 4%) . 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 model.
All the equation terms were discretized by the method of secondorder upwind [30,31] and the pressurevelocity 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 , thevelocity exponent and diameter functions were set to 2.6 and1.8 109, respectively. The convergence of solution was achievedwhen the residuals in all the equations fell below 106 [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:
V! : V!V! P : V! V!T g!: 2
Standard k turbulence model:
Turbulent kinetic energy transport equation:
Dissipation of turbulent kinetic energy transport equation:
C1GkC2 : 4
Table 2Coefficients for Standard k turbulent model.
C k C1 C2
0.09 1 1.3 1.44 1.92
338 S. Shamshirband et al. / Powder Technology 284 (2015) 336343
The turbulent eddy viscosity obtained fromPrandtlKolomogorovrelation:
The turbulence kinetic energy production of the mean velocitygradients, Gk, is given as:
Gk tV!: V
The constants for the Standard k turbulence model in the aboveformula are represented in Table 2 [33,36].
is an external force acting on the particles which for fineparticleswith high density ratio (more than one) are drag and buoyancyforces .
Therefore, the equation of motion can be simplified to the followingform:
FD v! v!p
wherein, Rep is the particle Reynolds number and is given as :
Rep dp v
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 24Re 1 11:2355Re0:653
8:8798 Re 11
The solid particle erosion rates are defined as [44,45]:
f a b Af
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].
Fig. 2.Maximum erosion rate versus particle size.
339S. Shamshirband et al. / Powder Technology 284 (2015) 336343
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
Fig. 4. Pressure (a) and erosion (b) contours on the wall of the bend.
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 IfThen rules with an appropriatemembership function to generate the stipulated inputoutput pairs.In this study, the ANFIS system that is functionally equivalent to the
Table 3Statistical parameters for data sets.
Variable Statistical parameters
Particle size 10 nm 100 mParticle 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) 336343
first-order Sugeno fuzzy model was used. A typical rule set with a fuzzyIfThen rule can be expressed as
if x is A; then f1 p1x t: 13
The ANFIS architecture for three inputs x, y, and z is shown in Fig....