Research Article Eulerian-Eulerian Simulation of Particle ...

Research ArticleEulerian-Eulerian Simulation of Particle-Liquid Slurry Flow inHorizontal Pipe

Titus Ntow Ofei and Aidil Yunus Ismail

Petroleum Engineering Department Universiti Teknologi PETRONAS 32610 Bandar Seri Iskandar Malaysia

Correspondence should be addressed to Titus Ntow Ofei titusofeihotmailcom

Received 25 July 2016 Accepted 14 August 2016

Academic Editor Alireza Bahadori

Copyright copy 2016 T N Ofei and A Y Ismail This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

In this study a computational fluid dynamics (CFD) simulation which adopts the inhomogeneous Eulerian-Eulerian two-fluidmodel in ANSYS CFX-15 was used to examine the influence of particle size (90 120583m to 270 120583m) and in situ particle volume fraction(10 to 40) on the radial distribution of particle concentration and velocity and frictional pressure lossThe robustness of variousturbulence models such as the 119896-epsilon (119896-120576) 119896-omega (119896-120596) SSG Reynolds stress shear stress transport and eddy viscositytransport was tested in predicting experimental data of particle concentration profiles The 119896-epsilon model closely matched theexperimental data better than the other turbulence models Results showed a decrease in frictional pressure loss as particle sizeincreased at constant particle volume fraction Furthermore for a constant particle volume fraction the radial distribution ofparticle concentration increased with increasing particle size where high concentration of particles occurred at the bottom of thepipe Particles of size 90 120583m were nearly buoyant especially for high particle volume fraction of 40 The CFD study shows thatknowledge of the variation of these parameters with pipe position is very crucial if the understanding of pipeline wear particleattrition or agglomeration is to be advanced

1 Introduction

Conveyance of slurries through pipelines is commonthroughout the worlds Over the decades the flow of slurriesthrough pipelines had been a common practice for variousindustries such as the oil and gas food pharmaceuticalsolid handling tailing and even power generation Manyfactors affect slurry flow behaviour in pipelines Theseinclude particle size velocity profile frictional pressure lossand concentration profile [1ndash4] Past studies have suggestedmany empirical correlations to predict slurry flow behaviournonetheless the capability of these correlations is limited tosome data range and experimental setup

In the oil and gas industry applications of horizontalwell have increased especially in cementing operations andhydraulic fracturing treatment Furthermore in unconsoli-dated formations oil is usually produced along with sandparticles and transported through horizontal pipes To havean efficient design accurate prediction of the transport ofslurry properties in horizontal pipe is required Recently

CFD has become an effective tool for modelling complexmultiphase flow behaviours as it has the capability to tackleunlimited number of physical and operation conditions

Ekambara et al [3] used CFD simulation to investigatethe effect of in situ solids volume concentration particlesize mixture velocity and particle diameter on local time-averaged solids concentration profiles particle and liquidvelocity profiles and frictional pressure loss The simulatedresults were compared to experimental data from publishedliterature with good agreement The study revealed thatparticles were asymmetrically distributed in the vertical planewith the degree of asymmetry increasing with increasingparticle size

Nabil et al [4] examined the effect of particle size onfrictional pressure loss in a horizontal pipeline using bothexperimental setup and CFD technique They observed thatfine particle size recorded the least pressure loss whereascoarse particle size recorded the highest pressure loss foreach constant particle volume fraction (5 to 30) CFDprediction of pressure loss was in agreement with measured

Hindawi Publishing CorporationJournal of Petroleum EngineeringVolume 2016 Article ID 5743471 10 pageshttpdxdoiorg10115520165743471

2 Journal of Petroleum Engineering

experimental data especially at low particle volume fractionand fine particle size Furthermore the study revealed thatthe particle velocity profiles were asymmetric in nature anddependent on particle size The degree of asymmetry wasobserved to be directly proportional to the particle size dueto the gravitational effect and inversely proportional to themixture velocity at constant volume fraction

An approach related to slurry flow modelling startedwhere one-dimensional (1D) Schmidt-Rouse equation [5] orequivalent to Hunt [6] was developed to relate the particlesedimentation rate to the turbulence exchange rate as rep-resented by solid eddy diffusivity Based on this formulationKarabelas [7] built an empirical model to predict the profileof particle concentration Work done by him was thencontinued by Kaushal and coworkers [8ndash12] in developing adiffusionmodelThemodel proposed amodification for soliddiffusivity for coarse slurry flows and their functions showthat the increase in solid concentration is due to the increasein the solid diffusivity However the model was formulatedwithout taking into consideration solid diffusivity on bothparticle size and pipe Reynold number [13] By comparingtheir pressure loss data with modified Wasp model theyfound a match at higher fluid velocity however significantdeviation shows at flow velocities near the deposition velocity[14]

A 1D two-layer model considering coarse particle slurrywas developed by Wilson [15] The author considered eachlayer with a uniform velocity and particle concentrationbecause he assumes the particles to be very coarse Doron etal [16] developed a 2D model to predict flow patterns andpressure loss which is similar to Wilsonrsquos model where theauthors assumed the lower layer as stationary Wilson andPugh [17] expanded the dispersive forcemodel by accountingfor particles suspended by fluid turbulence and contact-load (Columbic) friction Their model prediction of particleconcentration and velocity profile was in a good agreementwith measured experimental data

Doron and Barnea [18] extended their study to a three-layer model of slurry fluid flow in horizontal pipeline whichconsists of a suspended layer a bed layer and a dispersivelayer which lies in between the suspended and bed layersThey assumed the dispersive layer to be high in concentrationgradient where a no-slip condition was imposed betweenfluid and solid particles The model prediction successfullyshowed assent with experimental data Ramadan et al [19]also proposed a three-layer model The model predictionswere then compared with experimental data where satisfac-tory agreement was achieved

Messa andMalavasi [20] proposed a new two-fluidmodelfor the simulation of fully suspended liquid-solid slurry flowsin horizontal pipes The model is claimed to address wallboundary conditions for solid phase viscosity of the slurrymixture which incorporates particle shape and a solutionalgorithm which reduces computational burdenThe authorsemphasised that the new model increased the accuracyof the pressure gradient predictions without affecting themodelrsquos capability in reproducing other engineering featuressuch as solid volume fraction and velocity distributions Maet al [21] conducted a CFD study for calculating erodent

particle trajectories in slurry flow It involves the capturingof the movement of erodent particles using the discretephase method (DPM) and calculating the interfaces betweenfluid phase and gas phase using the volume of fluid (VOF)method The authors revealed that their model results werein reasonable agreement with experimental observations interms of normal impact velocity on the specimen surfaceRecentlyMiedema [22] proposed a framework for predictinghead loss and limit deposit velocity in slurry flowThe frame-work is based on constant spatial volumetric concentrationcurves and uniform sand or gravels for five flow regimesin Newtonian fluid namely the stationary or fixed bedregime the sliding bed regime the heterogeneous regime thehomogeneous regime and the sliding flow regimeTheauthorconcluded that the new framework explained the behaviourof very small particles in terms of the mobilisation of thelubrication effect of the particle poor viscous sublayer

In this study the effects of particle size (90 120583m to 270 120583m)and volume fraction (10 to 40) which are typical ofslurry conditions in the oil and gas industry are analysedon the radial distribution of particle concentration andvelocity and frictional pressure loss in horizontal pipe usingCFD method The findings are helpful to understand slurrytransport behaviour on pipeline wear particle attrition oragglomeration

2 Materials and Method

A commercial CFD software ANSYS-CFX 150 is imple-mented in this study The inhomogeneous Eulerian-Eulerianmodel sometimes called the two-fluid model which regardsboth continuous (liquid) and dispersed (solid) phases asinterpenetrating continuum is used to model the slurry flowThe Eulerian-Eulerian model is best suited for high volumefractions of the dispersed phase which is averaged over eachcontrol volume Each phase is governed by similar conser-vation equations and modelling is needed for interactionbetween the phases turbulent dispersion of particles andcollision of particle with walls A drawback of this modelis however that complex closure relations are required Thefollowing continuity and momentum equations representingthe two-phase flow model are described for the sake ofbrevity

21 Continuity Equations The volume-averaged incom-pressible isothermal and transient Navier-Stokes continuityequations for both liquid and solid phases are respectivelygiven by [23 24]

120597120597119905 (h119897) + nabla (h119897119880119897) = 0120597120597119905 (h119904) + nabla (h119904119880119904) = 0

(1)

where h119897 and h119904 are the volume fraction of liquid and solidrespectively and119880119897 and119880119904 are the velocity vector of liquid andsolid respectivelyThemass exchange between the liquid andsolid phases due to reaction or combustion is not considered

Journal of Petroleum Engineering 3

22 Momentum Equations The momentum balance for theliquid and solid phases which includes the interphase mo-mentum transfer term that models the interaction betweeneach phase is given by the Navier-Stokes equations as [23 24]

120588119897k119897 [120597119880119897120597119905 + 119880119897 sdot nabla119880119897]= minusk119897nabla119901 + k119897nabla sdot 120591119897 + k119897120588119897119892 minus119872

120588119904h119904 [120597119880119904120597119905 + 119880119904 sdot nabla119880119904]= minush119904nabla119901 +h119904nabla sdot 120591119897 + nabla sdot 120591119904 minus nabla119875119904 +h119904120588119904119892 +119872

(2)

where 119892 is the gravity term 119901 is the thermodynamic pressure120588119897 and 120588119904 are density of liquid and solid respectively119872 is thesum of interfacial forces including drag force and lift forceand 120591119897 and 120591119904 are the shear stress tensor for both liquid andsolid respectively

The liquid phase and solid phase stress tensors can berepresented respectively as

120591119897 = 120583119897 [nabla119880119897 + (nabla119880119897)119879] minus 23120583119897 (nabla sdot 119880119897) 119868120591119904 = (minus119875119904 + 120577119904119880119904) 119868

+ 120583119904 [nabla119880119904 + (nabla119880119904)119879] minus 23 (nabla sdot 119880119904) 119868 (3)

where 120583119897 and 120583119904 are the shear liquid and solid viscosityrespectively and 120577119904 is the bulk solid viscosity which accountsfor the resistance of the granular particles to compress andexpand and has the form [25]

120577119904 = 43h21199041205881199041198891199011198920 (1 + 119890)radicΘ120587 (4)

Similarly 119875119904 is the solid pressure that represents the solidsphase normal forces caused by particle-particle interactionsand takes the form [26]

119875119904 = 120588119904h119904Θs + 2120588119904h2119904Θs (1 + 119890) 1198920 (5)

The first term represents the particle velocity fluctuations andthe second term represents the particle collisions

The shear solid viscosity can be represented as the sum ofthe kinetic and collisional contributions as

120583119904 = 120583119904kin + 120583119904col (6)

The kinetic and collisional component of the solids viscosityare modelled respectively as [26]

120583119904kin = 5radic12058748120588119904119889119901(1 + 119890) 1198920 (1 +

45120578 (1 + 119890) 1198920h119904)2radicΘ

120583119904col = 45h21199041205881199041198891199011198920 (1 + 119890)radicΘ120587 (7)

23 Interphase Models

231 Drag Force For spherical particles the drag force perunit volume is given as

119872119889 = 31198621198634119889119904 k1199041205881198971003816100381610038161003816119880119904 minus 1198801198971003816100381610038161003816 (119880119904 minus 119880119897) (8)

For densely distributed solid particles where the solid volumefraction k119904 lt 02 the Wen and Yu [27] drag coefficient119862119863 model may be utilised This model is modified andimplemented in ANSYS-CFX to ensure the correct limitingbehaviour in the inertial regime as

119862119863 = kminus165119897 max[ 241198731015840Re119901 (1 + 015119873

10158400687Re119901 ) 044] (9)

where1198731015840Re119901 = k119897119873Re119901 and119873Re119901 = 120588119897|119880119897 minus 119880119904|119889119904120583119897For large solid volume fraction k119904 gt 02 the Gidaspow

drag model may be used with the interphase drag force perunit volume defined as [26]

119872119863 = 150 (1 minus k119897)2 120583119897

k1198971198892119904 + 74(1 minus k119897) 120588119897 1003816100381610038161003816119880119897 minus 1198801199041003816100381610038161003816119889119904 (10)

In this study both Wen and Yu and Gidaspow drag modelswere employed depending on the computed solid volumefraction

232 Lift Force Model For spherical solid particles ANSYS-CFX employs the Saffman and Mei lift force model as

119872119871= 32120587 radic]119897

119889119904radic1003816100381610038161003816nabla times 11988011989710038161003816100381610038161198621015840119871h119904120588119897 (119880119904 minus 119880119897) (nabla times 119880119897 + 2Ω) (11)

Saffman [28 29] correlated the lift force for low Reynoldsnumber past a spherical solid particle where 1198621015840119871 = 646 and0 le 119873Re119901 le 119873Re120596 le 1 For higher range of solid particleReynolds number Saffmanrsquos correlation was generalised byLun et al [25] as follows

1198621015840119871=

646 sdot 119891 (119873Re119901 119873Re120596) for 119873Re119901 lt 40646 sdot 00524 sdot (120573119873Re119901)12 for 40 lt 119873Re119901 lt 100

(12)

where

120573 = 05(119873Re120596119873Re119901)

119891 (119873Re119901 119873Re120596) = (1 minus 0331412057305) sdot 119890minus01119873Re119901+ 0331412057305

119873Re120596 = 1205881198971205961198971198892119904120583119897

120596119897 = 1003816100381610038161003816nabla times 1198801198971003816100381610038161003816

(13)


Figure 1 2D and 3D meshed geometry

233 Turbulence 119896-120576Model The 119896-120576 turbulence model offersa good compromise in terms of accuracy and robustnessfor general purpose simulations It is a semiempirical modelbased on transport equation for the estimation of turbulentlength scale and velocity scale from the turbulent kineticenergy (119896) and dissipation rate (120576) [30] In multiphase flowthe transport equations for 119896 and 120576 are phase dependentand assume a similar form to the single-phase transportequations respectively as

120597120597119905 (119862120572120588120572119896120572) + nablasdot (119862120572 (120588120572119880120572119896120572 minus (120583 + 120583119905120572120590119896 )nabla119896120572))= 119862120572 (119875120572 minus 120588120572120576120572) + 119879(119896)120572120573

120597120597119905 (119862120572120588120572120576120572) + nabla sdot (119862120572120588120572119880120572120576120572 minus (120583 + 120583119905120572120590120576 )nabla120576120572)= 119862120572 120576120572119896120572 (1198621205761119875120572 minus 1198621205762120588120572120576120572) + 119879

(120576)120572120573

(14)

where 1198621205761 = 144 1198621205762 = 192 119862120583 = 009 120590119896 = 10 and 120590120576 =13 are standard constants 119879(120576)120572120573

and 119879(119896)120572120573

are the interphasetransfer for 120576 and 119896 respectively

Diffusion of momentum in phase 120572 is governed by aneffective viscosity as

120583eff = 120583 + 120583119905120572 (15)

The 119896-120576model assumes that the turbulence viscosity is linkedto the turbulence kinetic energy and dissipation by therelation

120583119905120572 = 119862120583120588120572 1198962120572120576120572 (16)

The governing sets of partial differential equations werediscretised using finite volume technique The discretisedequations together with initial and boundary conditions aresolved iteratively for each control volume of pressure dropand cuttings concentration using ANSYS-CFX 150 solver

24 GeometryModelling andMeshing The three-dimension-al (3D) horizontal pipe geometry wasmodelled using ANSYS150 Workbench Design Modeller The dimensions of thegeometry were taken from literature [31] In order to ensurea fully developed flow a hydrodynamic entrance length wascomputed using the following expression

119871ℎ = 44 times 11987316Re times 119863ℎ (17)

where 119873Re is the Reynolds number of the liquids and 119863ℎ isthe hydraulic diameter

The geometry was meshed into small grid cell usingunstructured tetrahedral mesh type with inflation layerscreated at the boundary of the pipe to accurately capture theflow effect in that region [32] Figure 1 presents themeshed 3Dgeometry The number of elements were optimised until theresults were no longer affected In this study the optimisednumber of elements used was 801848

25 Boundary and Initial Conditions At the inlet of thepipe mixture velocity and volume fraction of both liquidand particles phases were specified At the outlet staticpressure was specified At the wall no-slip condition wasimposed on the liquid while free-slip condition was imposedon the particles To initiate the numerical solution averagevolume fractions andmixture velocitywere specified as initialconditions

26 Numerical Solution In this transient simulation particle-water slurry study the Navier-Stokes governing equationstogether with their closure terms were solved using ANSYS-CFX-150 solver The mass and momentum equations werediscretised using the control volume technique The first-order implicit method was adopted for time discretisationwhereas the second-order implicit method was also adoptedfor space in solving the conservation law equations TheSIMPLE algorithm was utilised to solve the pressure-velocitycoupling in the momentum equations while the high resolu-tion discretisation scheme was employed for the convectiveterms A constant time-step of 0001 s and a total time of20 s were used to perform the entire simulationThe solutionwas assumed to be converged when the root mean square(RMS) of the normalised residual error reached 10minus4 for allsimulations

27 Model Validation The simulation model setup wasvalidated against experimental data available in literature[31] The particles properties employed were as follows size119889119901 = 270 120583m specific gravity SG = 265 and in situparticle volume fraction k119904 = 010 The mixture velocityused is 54ms Several simulation runs were carried outto investigate the accuracy of various turbulence models inpredicting the experimental particle concentration profiledata The 119896-epsilon (119896-120576) 119896-omega (119896-120596) SSG Reynoldsstress shear stress transport and eddy viscosity transportwere among the testedmodelsThe 119896-120576model was very robustin predicting the particle concentration profile as comparedto the othermodels as shown in Figure 2 thus confirming the


0 01 02 03 04 05

08

06

04

02

00

10

SSG Reynold stressEddy viscosity transport

Experimental

Shear stress transport

rR

Particle concentration (mdash)

k-epsilonk-omega

Figure 2 Comparison of predicted and experimental particle concentration profile

Table 1 Simulation matrix

Simulation parameter ValuesPipe diameter119863 103mmPipe length 44 times 119863Size of particle 90 120583mndash270 120583mParticle volume fraction 010ndash045Specific gravity of particle 265Specific gravity of water 100Velocity of mixture 54msTurbulence equation 119896-120576model

validity of the simulation model The simulation matrix usedin performing sensitivity study is shown in Table 1 where the119896-120576model was employed in all simulation run

3 Results and Discussion

This section shows the effects of particle size and in situparticle volume fraction on the radial distribution of particleconcentration and velocity and frictional pressure loss

31 Effect of Particle Size on Particle Concentration Contourplots of particle concentration as a function varying particlesize at the outlet of the pipe are shown in Figures 3(a)ndash3(d) With a constant in situ particle volume fraction ofk119904 = 010 there are significant differences in the particleconcentration as the particle size increases It is observed thatthe smallest particles (119889119901 = 90 120583m) were more buoyant andhomogeneously dispersed in the liquid phase As the particlesize increases from 119889119901 = 90 120583m to 270120583m the particleconcentration becomes high at the bottom of the pipe dueto gravitational effect which prevents the large particles fromtravelling farther and exiting out of the pipe The maximumrecorded particle concentrations deposited at the bottom ofthe horizontal pipe are 151 215 258 and 307 forparticle size of 119889119901 = 90 120583m 150 120583m 210 120583m and 270120583mrespectively These results show that in the transportation

of oil in addition to sand particles larger particles mayaccumulate at the bottom of the pipe thereby blocking theeffective flow area and reducing productivity

Figures 4(a)ndash4(c) also show the predicted concentrationprofiles in the radial direction of the horizontal pipe for threedifferent in situ particle volume fractions k119904 = 10 25and 40 with varying particle sizes The results representa broad spectrum of fluid turbulence effect on particle sus-pension from neutrally buoyant to sluggish especially at thebottom of the pipe as particle size increases for each constantin situ particle volume fraction This phenomenon was alsoobserved by Ekambara et al [3] It is noteworthy that particleconcentration increased as in situ particle volume fractionalso increased For particle size of 119889119901 = 90 120583m there wasno noticeable change in the particle concentration profile forall in situ particle volume fractions (see Figures 4(a)ndash4(c))This is because the particles are relatively fine and themixturevelocity is significantly greater than the deposition velocityNonetheless for particle size of 119889119901 = 270 120583m and k119904 = 10the particle concentration profile collapses rapidly due to theweak particle-particle interactions which is further overcomeby the particle depositional velocity (see Figure 4(a)) Whenthe in situ particle volume fraction increases to k119904 = 40a strong particle-particle bond is formed thereby suspendingthe particle concentration in almost the entire pipe as shownin Figure 4(c) A further description can be viewed in thecontour plots in Figures 5(a)ndash5(c)

32 Effect of In Situ Particle Volume Fraction on ParticleVelocity Figures 6(a) and 6(b) show the effect of in situparticle volume fraction on particle velocity for constant par-ticle size of 90120583m and 270120583m which represent the fine andcoarse particles respectively Generally it is observed fromboth results that particle velocity profiles were asymmetricalabout the central axis however the degree of asymmetry isinfluenced by particle size For particle size of 270120583m theparticle velocity profile plots are more skewed to the bottomof the pipe as shown in Figure 6(b) This is due to particlesettling of the coarse particles as a result of gravity effectThis


Cutti

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n

0142

0133

0124

0114

0105

0096

0087

0077

0068

0059

0151

0 20000 4000 6000 8000

(ＧＧ)

(a)

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ngs v

olum

e fra

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n

0 20000 4000 6000 8000

(ＧＧ)

0196

0177

0157

0138

0119

0099

0080

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0041

0022

0215

(b)Cu

tting

s vol

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ract

ion

0 20000 4000 6000 8000

(ＧＧ)

0232

0207

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0107

0082

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0006

0258

(c)Cu

tting

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ume f

ract

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0 20000 4000 6000 8000

(ＧＧ)

0277

0246

0216

0185

0155

0124

0093

0063

0032

0002

0307

(d)

Figure 3 Contour plots of particle concentration at k119904 = 10 (a) 119889119901 = 90 120583m (b) 119889119901 = 150 120583m (c) 119889119901 = 210 120583m and (d) 119889119901 = 270 120583m

phenomenon has also been demonstrated experimentallyby Gillies and Shook [33] Furthermore for each constantparticle size particle velocity increased with decreasing insitu particle volume fraction This is due to fluid turbulenceeffect on the weak particle-particle interaction of the low insitu particle volume fraction of k119904 = 10 The increase inparticle velocity for varying in situ particle volume fractionsis howevermore pronounced for fine particle size of 90120583masshown in Figure 6(a)

33 Effect of Particle Size on Frictional Pressure Loss InFigure 7 the effect of particle size on frictional pressure lossfor constant in situ particle volume fraction is presented It

is observed that frictional pressure loss in the pipe decreasedwith increasing particle size for each constant in situ particlevolume fraction It is noteworthy that turbulent flowwill keepfine particles (119889119901 = 90 120583m) in suspension This will increasethe effective viscosity of the suspension and hence decreaseits Reynolds number Since friction factor is inversely pro-portional to the Reynolds number a decrease in Reynoldsnumber will increase friction factor The frictional pressureloss will ultimately increase since it is directly proportional tothe friction factor On the contrary coarse particle sizes (119889119901 gt90 120583m) will settle easily at the bottom of the horizontal pipethus blocking part of the effective flow areaThis will increasethe fluid velocity in the effective flow area and as a result


0 005 01 015 02 025 03 035

05

0

minus 05

minus1

1


Nor

mal

ised

radi

al p

ositi

onr

R

90 Ｇ

150 Ｇ

210 Ｇ

270 Ｇ

(a)

0 005 01 015 02 025 03 035 04 045

05

minus 05

minus1Particle concentration (mdash)

Nor

mal

ised

radi

al p

ositi

onr

R

90 Ｇ

150 Ｇ

210 Ｇ

270 Ｇ

1

0

(b)

0 01 02 03 04 05 06


05

0

minus 05

minus1

1

Nor

mal

ised

radi

al p

ositi

onr

R

90 Ｇ

150 Ｇ

210 Ｇ

270 Ｇ

(c)

Figure 4 Effect of particle size on particle concentration profile (a) k119904 = 10 (b) k119904 = 25 and (c) k119904 = 40

increase the Reynolds number The friction factor decreasesthereby resulting in an increase in the pressure loss It wasobserved that as particle size increased from 119889119901 = 90 120583m to270120583m the frictional pressure loss decreased by 279 476and 381 for constant particle volume fraction k119904 of 1025 and 40 respectively

34 Effect of In Situ Particle Volume Fraction on FrictionalPressure Loss The presence of solid particles in the liquidphase increases the frictional pressure loss due tomomentuminteraction between the solids and the liquid It is shown inFigure 8 that high particle volume fraction resulted in highfrictional pressure loss as compared to low particle volumefractionThis is mainly due to high friction between particle-particle particle-liquid and particle-wall interactions Forinstance a percentage increase in frictional pressure lossesof 1064 558 593 and 773 occurred as the in situparticle volume fraction increased fromk119904 = 10 to 40 at aconstant particle size of 90 120583m 150 120583m 210 120583m and 270 120583mrespectively

4 Conclusion

The Eulerian-Eulerian two-fluid model was adopted in athree-dimensional transient simulation of slurry flow in ahorizontal pipe The particle concentration particle velocityand frictional pressure loss were some of the output resultsobserved as functions of particle size and in situ particlevolume fraction The 119896-120576 turbulence model was found to sat-isfactorily predict the concentration profile of experimentaldata as compared to other turbulence models The particleconcentration profiles for fine particles were neutrally buoy-ant as the fluid turbulence kept the particles in suspensionThe particle concentration profiles for coarse particle wereprimarily dependent on the in situ particle volume fractionParticle velocity profiles for high particle volume fractionwere asymmetric nonetheless fine particle size travelledfaster than coarse particle size Frictional pressure loss wasincreased for fine particle-sized slurry and decreased forcoarse particle-sized slurry Moreover high particle volumefraction resulted in high frictional pressure loss The studyhas shown that the available CFD models are capable of


0 20000 4000 6000 8000

(ＧＧ)

0277

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(ＧＧ)

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0370

0330

0290

0250

0210

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0090

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(b)

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(ＧＧ)

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ctio

n

0445

0402

0358

0314

0270

0227

0183

0139

0096

0052

0489

(c)

Figure 5 Contour plots of particle concentration at 119889119901 = 270 120583m (a) k119904 = 10 (b) k119904 = 25 and (c) k119904 = 40

250 350 450 550 650

10

25

40

05

00

minus 05

minus10

10

Particle velocity (ms)

Nor

mal

radi

al p

ositi

onr

R

(a)

10

25

40

220 320 420 520 620

05

00

minus 05

minus10

10


Nor

mal

radi

al p

ositi

onr

R

(b)

Figure 6 Effect of in situ particle volume fraction on particle velocity profile (a) 119889119901 = 90 120583m and (b) 119889119901 = 270 120583m


Particle size (Ｇ)

Fric

tiona

l pre

ssur

e los

s (Pa

m)

90 150 210 270

10

25

40

4500

3500

2500

1500

5500

Figure 7 Effect of particle size on frictional pressure loss for con-stant in situ particle volume fraction

Fric

tiona

l pre

ssur

e los

s (Pa

m)

10 15 20 25 30 35 40

In situ particle volume fraction ()

90 Ｇ150 Ｇ

210 Ｇ

270 Ｇ

0

4000

3000

2000

1000

5000

6000

Figure 8 Effect of in situ particle volume fraction on frictionalpressure loss for constant particle size

satisfactorily predicting slurry flows and other hydrodynamicflows

Competing Interests

The authors declare that there are no competing interestsregarding the publication of this paper

References

[1] C Y Wong C B Solnordal and J Wu ldquoCFD modelling andexperimental observations of changing surface profiles causedby solid particle erosionrdquo Society of PetroleumEngineers Journalvol 29 no 1 pp 61ndash74 2013

[2] S K Lahiri and K C Ghanta ldquoSlurry flow modelling by CFDrdquoChemical Industry amp Chemical Engineering Quarterly vol 16no 4 pp 295ndash308 2010

[3] A Ekambara R S Sanders K Nandakumar and J HMasliyah ldquoHydrodynamic simulation of horizontal slurry

pipeline flow using ANSYS-CFXrdquo Industrial amp EngineeringChemistry Research vol 48 no 17 pp 8159ndash8171 2009

[4] T Nabil I El-Sawaf and K El-Nahhas ldquoComputationalfluid dynamics simulation of the solid-liquid slurry flow ina pipelinerdquo in Proceedings of the 17th International WaterTechnology Conference Istanbul Turkey November 2013

[5] R G Gillies C A Shook and K C Wilson ldquoAn improvedtwo layer model for horizontal slurry pipeline flowrdquo CanadianJournal of Chemical Engineering vol 69 no 1 pp 173ndash178 1991

[6] J N Hunt ldquoThe turbulent transport of suspended sediment inopen channelsrdquo Proceedings of the Royal Society of London AMathematical Physical and Engineering Sciences vol 224 no1158 pp 322ndash335 1954

[7] A J Karabelas ldquoVertical distribution of dilute suspensions inturbulent pipe flowrdquo AIChE Journal vol 23 no 4 pp 426ndash4341977

[8] D R Kaushal Y Tomita and R R Dighade ldquoConcentrationat the pipe bottom at deposition velocity for transportation ofcommercial slurries through pipelinerdquo Powder Technology vol125 no 1 pp 89ndash101 2002

[9] D R Kaushal and Y Tomita ldquoComparative study of pressuredrop in multisized particulate slurry flow through pipe andrectangular ductrdquo International Journal of Multiphase Flow vol29 no 9 pp 1473ndash1487 2003

[10] D R Kaushal K Sato T Toyota K Funatsu and Y TomitaldquoEffect of particle size distribution on pressure drop andconcentration profile in pipeline flow of highly concentratedslurryrdquo International Journal of Multiphase Flow vol 31 no 7pp 809ndash823 2005

[11] V Seshadri S N Singh and D R Kaushal ldquoA model for theprediction of concentration and particle size distribution for theflow of multisized particulate suspensions through closed ductsand open channelsrdquo Particulate Science amp Technology vol 24no 2 pp 239ndash258 2006

[12] D R Kaushal and Y Tomita ldquoExperimental investigation fornear-wall lift of coarser particles in slurry pipeline using 120574-raydensitometerrdquo Powder Technology vol 172 no 3 pp 177ndash1872007

[13] I C Walton ldquoEddy diffusivity of solid particles in a turbulentliquid flow in a horizontal piperdquo AIChE Journal vol 41 no 7pp 1815ndash1820 1995

[14] E JWasp J P Kenny and R L Gandhi Solid Liquid Flow SlurryPipeline Transportation Trans Tech Publications Clausthal-Zellerfeld Germany 1st edition 1977

[15] K C Wilson ldquoA unified physical-based analysis of solid-liquidpipeline flowrdquo in Proceedings of the 4th International Conferenceof Hydraulic Transport of Solids in Pipes (Hydrotransport 4 rsquo76)Paper A1 pp 1ndash16 BHRA Fluid Engineering Cranfield UK1976

[16] P Doron D Granica and D Barnea ldquoSlurry flow in horizontalpipes-experimental and modelingrdquo International Journal ofMultiphase Flow vol 13 no 4 pp 535ndash547 1987

[17] K C Wilson and F J Pugh ldquoDispersive-force modelling ofturbulent suspension in heterogeneous slurry flowrdquo CanadianJournal of Chemical Engineering vol 66 no 5 pp 721ndash727 1988

[18] P Doron and D Barnea ldquoA three-layer model for solid-liquidflow in horizontal pipesrdquo International Journal of MultiphaseFlow vol 19 no 6 pp 1029ndash1043 1993

[19] A Ramadan P Skalle and A Saasen ldquoApplication of a three-layer modeling approach for solids transport in horizontal andinclined channelsrdquoChemical Engineering Science vol 60 no 10pp 2557ndash2570 2005


[20] G V Messa and S Malavasi ldquoImprovements in the numericalprediction of fully-suspended slurry flow in horizontal pipesrdquoPowder Technology pp 358ndash367 2015

[21] L Ma C Huang Y Xie et al ldquoModeling of erodent particletrajectories in slurry flowrdquoWear vol 334-335 pp 49ndash55 2015

[22] S A Miedema ldquoThe heterogeneous to homogeneous transitionfor slurry flow in pipesrdquo Ocean Engineering vol 123 pp 422ndash431 2016

[23] B G M Van Wachem and A E Almstedt ldquoMethods for mul-tiphase computational fluid dynamicsrdquo Chemical EngineeringJournal vol 96 no 1ndash3 pp 81ndash98 2003

[24] M Eesa and M Barigou ldquoHorizontal laminar flow of coarsenearly-neutrally buoyant particles in non-Newtonian convey-ing fluids CFD and PEPT experiments comparedrdquo Interna-tional Journal of Multiphase Flow vol 34 no 11 pp 997ndash10072008

[25] C K K Lun S B Savage D J Jeffrey and N ChepurniyldquoKinetic theories for granular flow inelastic particles in Couetteflow and slightly inelastic particles in a general flowfieldrdquoJournal of Fluid Mechanics vol 140 pp 223ndash256 1984

[26] DGidaspowMultiphase Flow and Fluidization ContinuumandKinetic Theory Descriptions Academic Press New York NYUSA 1994

[27] C Y Wen and Y H Yu ldquoMechanics of fluidizationrdquo ChemicalEngineering Progress Symposium Series vol 62 no 62 pp 100ndash111 1966

[28] P G Saffman ldquoThe lift on a small sphere in a slow shear flowrdquoJournal of Fluid Mechanics vol 22 no 2 pp 385ndash400 1965

[29] P G Saffman ldquoThe lift on a small sphere in a slow shear flowmdashcorrigendumrdquo Journal of Fluid Mechanics vol 31 no 3 p 6241968

[30] B E Launder and D B Spalding ldquoThe numerical computationof turbulent flowsrdquoComputerMethods inAppliedMechanics andEngineering vol 3 no 2 pp 269ndash289 1974

[31] R G Gillies C A Shook and J Xu ldquoModelling heterogeneousslurry flows at high velocitiesrdquo Canadian Journal of ChemicalEngineering vol 82 no 5 pp 1060ndash1065 2004

[32] T N Ofei S Irawan and W Pao ldquoCFD method for predictingannular pressure losses and cuttings concentration in eccentrichorizontal wellsrdquo Journal of Petroleum Engineering vol 2014Article ID 486423 16 pages 2014

[33] R G Gillies and C A Shook ldquoConcentration distributionsof sand slurries in horizontal pipe flowrdquo Particulate Science ampTechnology vol 12 no 1 pp 45ndash69 1994

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



experimental data especially at low particle volume fractionand fine particle size Furthermore the study revealed thatthe particle velocity profiles were asymmetric in nature anddependent on particle size The degree of asymmetry wasobserved to be directly proportional to the particle size dueto the gravitational effect and inversely proportional to themixture velocity at constant volume fraction

An approach related to slurry flow modelling startedwhere one-dimensional (1D) Schmidt-Rouse equation [5] orequivalent to Hunt [6] was developed to relate the particlesedimentation rate to the turbulence exchange rate as rep-resented by solid eddy diffusivity Based on this formulationKarabelas [7] built an empirical model to predict the profileof particle concentration Work done by him was thencontinued by Kaushal and coworkers [8ndash12] in developing adiffusionmodelThemodel proposed amodification for soliddiffusivity for coarse slurry flows and their functions showthat the increase in solid concentration is due to the increasein the solid diffusivity However the model was formulatedwithout taking into consideration solid diffusivity on bothparticle size and pipe Reynold number [13] By comparingtheir pressure loss data with modified Wasp model theyfound a match at higher fluid velocity however significantdeviation shows at flow velocities near the deposition velocity[14]

A 1D two-layer model considering coarse particle slurrywas developed by Wilson [15] The author considered eachlayer with a uniform velocity and particle concentrationbecause he assumes the particles to be very coarse Doron etal [16] developed a 2D model to predict flow patterns andpressure loss which is similar to Wilsonrsquos model where theauthors assumed the lower layer as stationary Wilson andPugh [17] expanded the dispersive forcemodel by accountingfor particles suspended by fluid turbulence and contact-load (Columbic) friction Their model prediction of particleconcentration and velocity profile was in a good agreementwith measured experimental data

Doron and Barnea [18] extended their study to a three-layer model of slurry fluid flow in horizontal pipeline whichconsists of a suspended layer a bed layer and a dispersivelayer which lies in between the suspended and bed layersThey assumed the dispersive layer to be high in concentrationgradient where a no-slip condition was imposed betweenfluid and solid particles The model prediction successfullyshowed assent with experimental data Ramadan et al [19]also proposed a three-layer model The model predictionswere then compared with experimental data where satisfac-tory agreement was achieved

Messa andMalavasi [20] proposed a new two-fluidmodelfor the simulation of fully suspended liquid-solid slurry flowsin horizontal pipes The model is claimed to address wallboundary conditions for solid phase viscosity of the slurrymixture which incorporates particle shape and a solutionalgorithm which reduces computational burdenThe authorsemphasised that the new model increased the accuracyof the pressure gradient predictions without affecting themodelrsquos capability in reproducing other engineering featuressuch as solid volume fraction and velocity distributions Maet al [21] conducted a CFD study for calculating erodent

particle trajectories in slurry flow It involves the capturingof the movement of erodent particles using the discretephase method (DPM) and calculating the interfaces betweenfluid phase and gas phase using the volume of fluid (VOF)method The authors revealed that their model results werein reasonable agreement with experimental observations interms of normal impact velocity on the specimen surfaceRecentlyMiedema [22] proposed a framework for predictinghead loss and limit deposit velocity in slurry flowThe frame-work is based on constant spatial volumetric concentrationcurves and uniform sand or gravels for five flow regimesin Newtonian fluid namely the stationary or fixed bedregime the sliding bed regime the heterogeneous regime thehomogeneous regime and the sliding flow regimeTheauthorconcluded that the new framework explained the behaviourof very small particles in terms of the mobilisation of thelubrication effect of the particle poor viscous sublayer

In this study the effects of particle size (90 120583m to 270 120583m)and volume fraction (10 to 40) which are typical ofslurry conditions in the oil and gas industry are analysedon the radial distribution of particle concentration andvelocity and frictional pressure loss in horizontal pipe usingCFD method The findings are helpful to understand slurrytransport behaviour on pipeline wear particle attrition oragglomeration

2 Materials and Method

A commercial CFD software ANSYS-CFX 150 is imple-mented in this study The inhomogeneous Eulerian-Eulerianmodel sometimes called the two-fluid model which regardsboth continuous (liquid) and dispersed (solid) phases asinterpenetrating continuum is used to model the slurry flowThe Eulerian-Eulerian model is best suited for high volumefractions of the dispersed phase which is averaged over eachcontrol volume Each phase is governed by similar conser-vation equations and modelling is needed for interactionbetween the phases turbulent dispersion of particles andcollision of particle with walls A drawback of this modelis however that complex closure relations are required Thefollowing continuity and momentum equations representingthe two-phase flow model are described for the sake ofbrevity

21 Continuity Equations The volume-averaged incom-pressible isothermal and transient Navier-Stokes continuityequations for both liquid and solid phases are respectivelygiven by [23 24]

120597120597119905 (h119897) + nabla (h119897119880119897) = 0120597120597119905 (h119904) + nabla (h119904119880119904) = 0

(1)

where h119897 and h119904 are the volume fraction of liquid and solidrespectively and119880119897 and119880119904 are the velocity vector of liquid andsolid respectivelyThemass exchange between the liquid andsolid phases due to reaction or combustion is not considered





(2)






120577119904 = 43h21199041205881199041198891199011198920 (1 + 119890)radicΘ120587 (4)


119875119904 = 120588119904h119904Θs + 2120588119904h2119904Θs (1 + 119890) 1198920 (5)



120583119904 = 120583119904kin + 120583119904col (6)


120583119904kin = 5radic12058748120588119904119889119901(1 + 119890) 1198920 (1 +

45120578 (1 + 119890) 1198920h119904)2radicΘ

120583119904col = 45h21199041205881199041198891199011198920 (1 + 119890)radicΘ120587 (7)



119872119889 = 31198621198634119889119904 k1199041205881198971003816100381610038161003816119880119904 minus 1198801198971003816100381610038161003816 (119880119904 minus 119880119897) (8)


119862119863 = kminus165119897 max[ 241198731015840Re119901 (1 + 015119873

10158400687Re119901 ) 044] (9)



119872119863 = 150 (1 minus k119897)2 120583119897

k1198971198892119904 + 74(1 minus k119897) 120588119897 1003816100381610038161003816119880119897 minus 1198801199041003816100381610038161003816119889119904 (10)



119872119871= 32120587 radic]119897



1198621015840119871=


(12)

where

120573 = 05(119873Re120596119873Re119901)


119873Re120596 = 1205881198971205961198971198892119904120583119897

120596119897 = 1003816100381610038161003816nabla times 1198801198971003816100381610038161003816

(13)






(120576)120572120573

(14)


and 119879(119896)120572120573



120583eff = 120583 + 120583119905120572 (15)


120583119905120572 = 119862120583120588120572 1198962120572120576120572 (16)



119871ℎ = 44 times 11987316Re times 119863ℎ (17)







0 01 02 03 04 05

08

06

04

02

00

10


Experimental


rR


k-epsilonk-omega












Cutti

ngs v

olum

e fra

ctio

n

0142

0133

0124

0114

0105

0096

0087

0077

0068

0059

0151

0 20000 4000 6000 8000

(ＧＧ)

(a)

Cutti

ngs v

olum

e fra

ctio

n

0 20000 4000 6000 8000

(ＧＧ)

0196

0177

0157

0138

0119

0099

0080

0061

0041

0022

0215

(b)Cu

tting

s vol

ume f

ract

ion

0 20000 4000 6000 8000

(ＧＧ)

0232

0207

0182

0157

0132

0107

0082

0057

0032

0006

0258

(c)Cu

tting

s vol

ume f

ract

ion

0 20000 4000 6000 8000

(ＧＧ)

0277

0246

0216

0185

0155

0124

0093

0063

0032

0002

0307

(d)






0 005 01 015 02 025 03 035

05

0

minus 05

minus1

1


Nor

mal

ised

radi

al p

ositi

onr

R

90 Ｇ

150 Ｇ

210 Ｇ

270 Ｇ

(a)

0 005 01 015 02 025 03 035 04 045

05

minus 05


Nor

mal

ised

radi

al p

ositi

onr

R

90 Ｇ

150 Ｇ

210 Ｇ

270 Ｇ

1

0

(b)

0 01 02 03 04 05 06


05

0

minus 05

minus1

1

Nor

mal

ised

radi

al p

ositi

onr

R

90 Ｇ

150 Ｇ

210 Ｇ

270 Ｇ

(c)




4 Conclusion



0 20000 4000 6000 8000

(ＧＧ)

0277

0307

0246

0216

0185

0155

0124

0093

0063

0032

0002

Cutti

ngs v

olum

e fra

ctio

n(a)

0 20000 4000 6000 8000

(ＧＧ)

Cutti

ngs v

olum

e fra

ctio

n

0370

0330

0290

0250

0210

0170

0130

0090

0050

0010

0410

(b)

0 20000 4000 6000 8000

(ＧＧ)

Cutti

ngs v

olum

e fra

ctio

n

0445

0402

0358

0314

0270

0227

0183

0139

0096

0052

0489

(c)


250 350 450 550 650

10

25

40

05

00

minus 05

minus10

10


Nor

mal

radi

al p

ositi

onr

R

(a)

10

25

40

220 320 420 520 620

05

00

minus 05

minus10

10


Nor

mal

radi

al p

ositi

onr

R

(b)



Particle size (Ｇ)

Fric

tiona

l pre

ssur

e los

s (Pa

m)

90 150 210 270

10

25

40

4500

3500

2500

1500

5500


Fric

tiona

l pre

ssur

e los

s (Pa

m)

10 15 20 25 30 35 40


90 Ｇ150 Ｇ

210 Ｇ

270 Ｇ

0

4000

3000

2000

1000

5000

6000



Competing Interests


References






































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













(2)






120577119904 = 43h21199041205881199041198891199011198920 (1 + 119890)radicΘ120587 (4)


119875119904 = 120588119904h119904Θs + 2120588119904h2119904Θs (1 + 119890) 1198920 (5)



120583119904 = 120583119904kin + 120583119904col (6)


120583119904kin = 5radic12058748120588119904119889119901(1 + 119890) 1198920 (1 +

45120578 (1 + 119890) 1198920h119904)2radicΘ

120583119904col = 45h21199041205881199041198891199011198920 (1 + 119890)radicΘ120587 (7)



119872119889 = 31198621198634119889119904 k1199041205881198971003816100381610038161003816119880119904 minus 1198801198971003816100381610038161003816 (119880119904 minus 119880119897) (8)


119862119863 = kminus165119897 max[ 241198731015840Re119901 (1 + 015119873

10158400687Re119901 ) 044] (9)



119872119863 = 150 (1 minus k119897)2 120583119897

k1198971198892119904 + 74(1 minus k119897) 120588119897 1003816100381610038161003816119880119897 minus 1198801199041003816100381610038161003816119889119904 (10)



119872119871= 32120587 radic]119897



1198621015840119871=


(12)

where

120573 = 05(119873Re120596119873Re119901)


119873Re120596 = 1205881198971205961198971198892119904120583119897

120596119897 = 1003816100381610038161003816nabla times 1198801198971003816100381610038161003816

(13)






(120576)120572120573

(14)


and 119879(119896)120572120573



120583eff = 120583 + 120583119905120572 (15)


120583119905120572 = 119862120583120588120572 1198962120572120576120572 (16)



119871ℎ = 44 times 11987316Re times 119863ℎ (17)







0 01 02 03 04 05

08

06

04

02

00

10


Experimental


rR


k-epsilonk-omega












Cutti

ngs v

olum

e fra

ctio

n

0142

0133

0124

0114

0105

0096

0087

0077

0068

0059

0151

0 20000 4000 6000 8000

(ＧＧ)

(a)

Cutti

ngs v

olum

e fra

ctio

n

0 20000 4000 6000 8000

(ＧＧ)

0196

0177

0157

0138

0119

0099

0080

0061

0041

0022

0215

(b)Cu

tting

s vol

ume f

ract

ion

0 20000 4000 6000 8000

(ＧＧ)

0232

0207

0182

0157

0132

0107

0082

0057

0032

0006

0258

(c)Cu

tting

s vol

ume f

ract

ion

0 20000 4000 6000 8000

(ＧＧ)

0277

0246

0216

0185

0155

0124

0093

0063

0032

0002

0307

(d)






0 005 01 015 02 025 03 035

05

0

minus 05

minus1

1


Nor

mal

ised

radi

al p

ositi

onr

R

90 Ｇ

150 Ｇ

210 Ｇ

270 Ｇ

(a)

0 005 01 015 02 025 03 035 04 045

05

minus 05


Nor

mal

ised

radi

al p

ositi

onr

R

90 Ｇ

150 Ｇ

210 Ｇ

270 Ｇ

1

0

(b)

0 01 02 03 04 05 06


05

0

minus 05

minus1

1

Nor

mal

ised

radi

al p

ositi

onr

R

90 Ｇ

150 Ｇ

210 Ｇ

270 Ｇ

(c)




4 Conclusion



0 20000 4000 6000 8000

(ＧＧ)

0277

0307

0246

0216

0185

0155

0124

0093

0063

0032

0002

Cutti

ngs v

olum

e fra

ctio

n(a)

0 20000 4000 6000 8000

(ＧＧ)

Cutti

ngs v

olum

e fra

ctio

n

0370

0330

0290

0250

0210

0170

0130

0090

0050

0010

0410

(b)

0 20000 4000 6000 8000

(ＧＧ)

Cutti

ngs v

olum

e fra

ctio

n

0445

0402

0358

0314

0270

0227

0183

0139

0096

0052

0489

(c)


250 350 450 550 650

10

25

40

05

00

minus 05

minus10

10


Nor

mal

radi

al p

ositi

onr

R

(a)

10

25

40

220 320 420 520 620

05

00

minus 05

minus10

10


Nor

mal

radi

al p

ositi

onr

R

(b)



Particle size (Ｇ)

Fric

tiona

l pre

ssur

e los

s (Pa

m)

90 150 210 270

10

25

40

4500

3500

2500

1500

5500


Fric

tiona

l pre

ssur

e los

s (Pa

m)

10 15 20 25 30 35 40


90 Ｇ150 Ｇ

210 Ｇ

270 Ｇ

0

4000

3000

2000

1000

5000

6000



Competing Interests


References






































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation














(120576)120572120573

(14)


and 119879(119896)120572120573



120583eff = 120583 + 120583119905120572 (15)


120583119905120572 = 119862120583120588120572 1198962120572120576120572 (16)



119871ℎ = 44 times 11987316Re times 119863ℎ (17)







0 01 02 03 04 05

08

06

04

02

00

10


Experimental


rR


k-epsilonk-omega












Cutti

ngs v

olum

e fra

ctio

n

0142

0133

0124

0114

0105

0096

0087

0077

0068

0059

0151

0 20000 4000 6000 8000

(ＧＧ)

(a)

Cutti

ngs v

olum

e fra

ctio

n

0 20000 4000 6000 8000

(ＧＧ)

0196

0177

0157

0138

0119

0099

0080

0061

0041

0022

0215

(b)Cu

tting

s vol

ume f

ract

ion

0 20000 4000 6000 8000

(ＧＧ)

0232

0207

0182

0157

0132

0107

0082

0057

0032

0006

0258

(c)Cu

tting

s vol

ume f

ract

ion

0 20000 4000 6000 8000

(ＧＧ)

0277

0246

0216

0185

0155

0124

0093

0063

0032

0002

0307

(d)






0 005 01 015 02 025 03 035

05

0

minus 05

minus1

1


Nor

mal

ised

radi

al p

ositi

onr

R

90 Ｇ

150 Ｇ

210 Ｇ

270 Ｇ

(a)

0 005 01 015 02 025 03 035 04 045

05

minus 05


Nor

mal

ised

radi

al p

ositi

onr

R

90 Ｇ

150 Ｇ

210 Ｇ

270 Ｇ

1

0

(b)

0 01 02 03 04 05 06


05

0

minus 05

minus1

1

Nor

mal

ised

radi

al p

ositi

onr

R

90 Ｇ

150 Ｇ

210 Ｇ

270 Ｇ

(c)




4 Conclusion



0 20000 4000 6000 8000

(ＧＧ)

0277

0307

0246

0216

0185

0155

0124

0093

0063

0032

0002

Cutti

ngs v

olum

e fra

ctio

n(a)

0 20000 4000 6000 8000

(ＧＧ)

Cutti

ngs v

olum

e fra

ctio

n

0370

0330

0290

0250

0210

0170

0130

0090

0050

0010

0410

(b)

0 20000 4000 6000 8000

(ＧＧ)

Cutti

ngs v

olum

e fra

ctio

n

0445

0402

0358

0314

0270

0227

0183

0139

0096

0052

0489

(c)


250 350 450 550 650

10

25

40

05

00

minus 05

minus10

10


Nor

mal

radi

al p

ositi

onr

R

(a)

10

25

40

220 320 420 520 620

05

00

minus 05

minus10

10


Nor

mal

radi

al p

ositi

onr

R

(b)



Particle size (Ｇ)

Fric

tiona

l pre

ssur

e los

s (Pa

m)

90 150 210 270

10

25

40

4500

3500

2500

1500

5500


Fric

tiona

l pre

ssur

e los

s (Pa

m)

10 15 20 25 30 35 40


90 Ｇ150 Ｇ

210 Ｇ

270 Ｇ

0

4000

3000

2000

1000

5000

6000



Competing Interests


References






































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 01 02 03 04 05

08

06

04

02

00

10


Experimental


rR


k-epsilonk-omega












Cutti

ngs v

olum

e fra

ctio

n

0142

0133

0124

0114

0105

0096

0087

0077

0068

0059

0151

0 20000 4000 6000 8000

(ＧＧ)

(a)

Cutti

ngs v

olum

e fra

ctio

n

0 20000 4000 6000 8000

(ＧＧ)

0196

0177

0157

0138

0119

0099

0080

0061

0041

0022

0215

(b)Cu

tting

s vol

ume f

ract

ion

0 20000 4000 6000 8000

(ＧＧ)

0232

0207

0182

0157

0132

0107

0082

0057

0032

0006

0258

(c)Cu

tting

s vol

ume f

ract

ion

0 20000 4000 6000 8000

(ＧＧ)

0277

0246

0216

0185

0155

0124

0093

0063

0032

0002

0307

(d)






0 005 01 015 02 025 03 035

05

0

minus 05

minus1

1


Nor

mal

ised

radi

al p

ositi

onr

R

90 Ｇ

150 Ｇ

210 Ｇ

270 Ｇ

(a)

0 005 01 015 02 025 03 035 04 045

05

minus 05


Nor

mal

ised

radi

al p

ositi

onr

R

90 Ｇ

150 Ｇ

210 Ｇ

270 Ｇ

1

0

(b)

0 01 02 03 04 05 06


05

0

minus 05

minus1

1

Nor

mal

ised

radi

al p

ositi

onr

R

90 Ｇ

150 Ｇ

210 Ｇ

270 Ｇ

(c)




4 Conclusion



0 20000 4000 6000 8000

(ＧＧ)

0277

0307

0246

0216

0185

0155

0124

0093

0063

0032

0002

Cutti

ngs v

olum

e fra

ctio

n(a)

0 20000 4000 6000 8000

(ＧＧ)

Cutti

ngs v

olum

e fra

ctio

n

0370

0330

0290

0250

0210

0170

0130

0090

0050

0010

0410

(b)

0 20000 4000 6000 8000

(ＧＧ)

Cutti

ngs v

olum

e fra

ctio

n

0445

0402

0358

0314

0270

0227

0183

0139

0096

0052

0489

(c)


250 350 450 550 650

10

25

40

05

00

minus 05

minus10

10


Nor

mal

radi

al p

ositi

onr

R

(a)

10

25

40

220 320 420 520 620

05

00

minus 05

minus10

10


Nor

mal

radi

al p

ositi

onr

R

(b)



Particle size (Ｇ)

Fric

tiona

l pre

ssur

e los

s (Pa

m)

90 150 210 270

10

25

40

4500

3500

2500

1500

5500


Fric

tiona

l pre

ssur

e los

s (Pa

m)

10 15 20 25 30 35 40


90 Ｇ150 Ｇ

210 Ｇ

270 Ｇ

0

4000

3000

2000

1000

5000

6000



Competing Interests


References






































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Cutti

ngs v

olum

e fra

ctio

n

0142

0133

0124

0114

0105

0096

0087

0077

0068

0059

0151

0 20000 4000 6000 8000

(ＧＧ)

(a)

Cutti

ngs v

olum

e fra

ctio

n

0 20000 4000 6000 8000

(ＧＧ)

0196

0177

0157

0138

0119

0099

0080

0061

0041

0022

0215

(b)Cu

tting

s vol

ume f

ract

ion

0 20000 4000 6000 8000

(ＧＧ)

0232

0207

0182

0157

0132

0107

0082

0057

0032

0006

0258

(c)Cu

tting

s vol

ume f

ract

ion

0 20000 4000 6000 8000

(ＧＧ)

0277

0246

0216

0185

0155

0124

0093

0063

0032

0002

0307

(d)






0 005 01 015 02 025 03 035

05

0

minus 05

minus1

1


Nor

mal

ised

radi

al p

ositi

onr

R

90 Ｇ

150 Ｇ

210 Ｇ

270 Ｇ

(a)

0 005 01 015 02 025 03 035 04 045

05

minus 05


Nor

mal

ised

radi

al p

ositi

onr

R

90 Ｇ

150 Ｇ

210 Ｇ

270 Ｇ

1

0

(b)

0 01 02 03 04 05 06


05

0

minus 05

minus1

1

Nor

mal

ised

radi

al p

ositi

onr

R

90 Ｇ

150 Ｇ

210 Ｇ

270 Ｇ

(c)




4 Conclusion



0 20000 4000 6000 8000

(ＧＧ)

0277

0307

0246

0216

0185

0155

0124

0093

0063

0032

0002

Cutti

ngs v

olum

e fra

ctio

n(a)

0 20000 4000 6000 8000

(ＧＧ)

Cutti

ngs v

olum

e fra

ctio

n

0370

0330

0290

0250

0210

0170

0130

0090

0050

0010

0410

(b)

0 20000 4000 6000 8000

(ＧＧ)

Cutti

ngs v

olum

e fra

ctio

n

0445

0402

0358

0314

0270

0227

0183

0139

0096

0052

0489

(c)


250 350 450 550 650

10

25

40

05

00

minus 05

minus10

10


Nor

mal

radi

al p

ositi

onr

R

(a)

10

25

40

220 320 420 520 620

05

00

minus 05

minus10

10


Nor

mal

radi

al p

ositi

onr

R

(b)



Particle size (Ｇ)

Fric

tiona

l pre

ssur

e los

s (Pa

m)

90 150 210 270

10

25

40

4500

3500

2500

1500

5500


Fric

tiona

l pre

ssur

e los

s (Pa

m)

10 15 20 25 30 35 40


90 Ｇ150 Ｇ

210 Ｇ

270 Ｇ

0

4000

3000

2000

1000

5000

6000



Competing Interests


References






































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 005 01 015 02 025 03 035

05

0

minus 05

minus1

1


Nor

mal

ised

radi

al p

ositi

onr

R

90 Ｇ

150 Ｇ

210 Ｇ

270 Ｇ

(a)

0 005 01 015 02 025 03 035 04 045

05

minus 05


Nor

mal

ised

radi

al p

ositi

onr

R

90 Ｇ

150 Ｇ

210 Ｇ

270 Ｇ

1

0

(b)

0 01 02 03 04 05 06


05

0

minus 05

minus1

1

Nor

mal

ised

radi

al p

ositi

onr

R

90 Ｇ

150 Ｇ

210 Ｇ

270 Ｇ

(c)




4 Conclusion



0 20000 4000 6000 8000

(ＧＧ)

0277

0307

0246

0216

0185

0155

0124

0093

0063

0032

0002

Cutti

ngs v

olum

e fra

ctio

n(a)

0 20000 4000 6000 8000

(ＧＧ)

Cutti

ngs v

olum

e fra

ctio

n

0370

0330

0290

0250

0210

0170

0130

0090

0050

0010

0410

(b)

0 20000 4000 6000 8000

(ＧＧ)

Cutti

ngs v

olum

e fra

ctio

n

0445

0402

0358

0314

0270

0227

0183

0139

0096

0052

0489

(c)


250 350 450 550 650

10

25

40

05

00

minus 05

minus10

10


Nor

mal

radi

al p

ositi

onr

R

(a)

10

25

40

220 320 420 520 620

05

00

minus 05

minus10

10


Nor

mal

radi

al p

ositi

onr

R

(b)



Particle size (Ｇ)

Fric

tiona

l pre

ssur

e los

s (Pa

m)

90 150 210 270

10

25

40

4500

3500

2500

1500

5500


Fric

tiona

l pre

ssur

e los

s (Pa

m)

10 15 20 25 30 35 40


90 Ｇ150 Ｇ

210 Ｇ

270 Ｇ

0

4000

3000

2000

1000

5000

6000



Competing Interests


References






































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 20000 4000 6000 8000

(ＧＧ)

0277

0307

0246

0216

0185

0155

0124

0093

0063

0032

0002

Cutti

ngs v

olum

e fra

ctio

n(a)

0 20000 4000 6000 8000

(ＧＧ)

Cutti

ngs v

olum

e fra

ctio

n

0370

0330

0290

0250

0210

0170

0130

0090

0050

0010

0410

(b)

0 20000 4000 6000 8000

(ＧＧ)

Cutti

ngs v

olum

e fra

ctio

n

0445

0402

0358

0314

0270

0227

0183

0139

0096

0052

0489

(c)


250 350 450 550 650

10

25

40

05

00

minus 05

minus10

10


Nor

mal

radi

al p

ositi

onr

R

(a)

10

25

40

220 320 420 520 620

05

00

minus 05

minus10

10


Nor

mal

radi

al p

ositi

onr

R

(b)



Particle size (Ｇ)

Fric

tiona

l pre

ssur

e los

s (Pa

m)

90 150 210 270

10

25

40

4500

3500

2500

1500

5500


Fric

tiona

l pre

ssur

e los

s (Pa

m)

10 15 20 25 30 35 40


90 Ｇ150 Ｇ

210 Ｇ

270 Ｇ

0

4000

3000

2000

1000

5000

6000



Competing Interests


References






































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Particle size (Ｇ)

Fric

tiona

l pre

ssur

e los

s (Pa

m)

90 150 210 270

10

25

40

4500

3500

2500

1500

5500


Fric

tiona

l pre

ssur

e los

s (Pa

m)

10 15 20 25 30 35 40


90 Ｇ150 Ｇ

210 Ｇ

270 Ｇ

0

4000

3000

2000

1000

5000

6000



Competing Interests


References






































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation


























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









Research Article Eulerian-Eulerian Simulation of Particle ...

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