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AssociationoftheChemicalEngineersAChE

www.ache.org.rs/CICEQ

ChemicalIndustry&ChemicalEngineeringQuarterly16(4)295−308(2010) CI&CEQ

295

SANDIP KUMAR LAHIRI

K.C. GHANTA

Department Of Chemical

Engineering, Nit, Durgapur,

West Bengal, India

SCIENTIFIC PAPER

UDC 66:532.4

DOI 10.2298/CICEQ091030034L

SLURRY FLOW MODELLING BY CFD

Anattempthasbeenmadeinthepresentstudytodevelopageneralizedslurry

flowmodelusingCFDand utilize themodelto predict concentrationprofile.

ThepurposeoftheCFDmodelistogainbetterinsightintothesolidliquidslur-

ryflowinpipelines.Initiallyathree-dimensionalmodelproblemwasdeveloped

tounderstandtheinfluenceoftheparticledragcoefficientonthesolidconcen-

trationprofile.Thepreliminarysimulationshighlightedtheneedforcorrectmo-

dellingoftheinterphasedragforce.Thevariousdragcorrelationsavailablein

theliteraturewereincorporatedintoatwo-fluidmodel(Euler-Euler)alongwith

thestandardk- ε turbulencemodelwithmixturepropertiestosimulatethetur-

bulentsolid-liquidflowinapipeline.Thecomputationalmodelwasmappedon

toacommercialCFDsolverFLUENT6.2(ofFluentInc.,USA).Topushtheen- velopeofapplicabilityofthesimulation,recentdatafromKaushal(2005)(with

solidconcentrationupto50%)wasselectedtovalidatethethreedimensional

simulations.Theexperimentaldataconsistedofwater-glassbeadslurryat125

and440-micronparticlewithdifferentflowvelocity(from1to5m/s)andoverall

concentrationupto 10to 50%byvolume.Thepredicted pressuredropand

concentrationprofilewerevalidatedbyexperimentaldataandshowedexcel-

lentagreement.Interestingfindingscameoutfromtheparametricstudyofve-

locityandconcentrationprofiles.Thecomputationalmodelandresultsdiscus-

sedinthisworkwouldbeusefulforextendingtheapplicationsofCFDmodels

forsimulatinglargeslurrypipelines.

Keywords:CFD;slurryflow;dragcoefficient;concentrationprofile;velocityprofile.

Particletransportthroughpipesisanimportant

operationinmanyindustriesincludingfood,pharma-

ceutical,chemical,oil,mining,constructionandpower

generation industries. Inmany of theseapplications

thecarrierfluidmaybehighlyviscousandmayhave

aNewtonianor non-Newtonian rheologyand flow is

usually turbulent. It has been a serious concern of

researchers around the world to develop accurate

modelsforpressuredrop andconcentrationdistribu-

tioninslurrypipelinesovertheyears.

The need and benefits ofaccurately predictingvelocity profiles, concentration profiles andpressure

drop of slurry pipelines during the design phase is

enormousasitgivesbetterselectionofslurrypumps,

optimizationofpowerconsumptionandtherebyhelps

maximize theeconomicbenefit.Concentrationdistri-

butionmaybeused todeterminetheparametersof

direct importance (mixtureand solid flow rates) and

Correspondeningauthor: S.K.Lahiri, DepartmentOf Chemical

Engineering,Nit,Durgapur,WestBengal,India.E-mail:[email protected]:29November,2009

Paperrevised:20April,2010Paperaccepted:22June,2010

secondaryeffectssuchaswallabrasionandparticle

degradation.TherecentworksofKaushalandTomita

[1]andKumaretal .[2-4]areworthmentioninginthe

fieldofconcentrationdistributioninslurrypipelines.

Despitesignificantresearchefforts,predictionof

solidconcentrationprofileinslurrypipelinesisstillan

openproblemfordesignengineers.Designofslurry

pipelinesreliesonempiricalcorrelationsobtainedfrom

experimental data. These correlations are prone to

greatuncertaintyasonedepartsfromthelimitedda-

tabase that supports them.Moreover, forhigher va-luesofsolidconcentration,verylittleexperimentalda-

taonlocalsolidconcentrationisavailablebecauseof

thedifficultiesinthemeasurementtechniques.Consi-

deringthis,itwouldbemostusefultodevelopcom-

putationalmodels,whichwillallowapriori estimation

ofthesolidconcentrationprofile over the pipecross

section.

In spite of the inadequate fundamental know-

ledge required for the formulation and modelling of

multiphaseturbulentflows,theneedtopredictslurry

behaviourhandledinvariousindustrieshasmotivated

work,aimingatobtainingapproximate solutions. Ef-



S.K.LAHIRI,K.C.GHANTA:SLURRYFLOWMODELLINGBYCFD CI&CEQ16(4)295−308 (2010)

296

fortsarestillontodevelopmorereasonablecorrela-

tionbasedmodelsforthepredictionofconcentration

profileinpipesandinthisdirection,theworkofRoco

and Shook [5,6],Gillieset al . [7,8], Mukhtar [9] and

Kaushal et al . [10] isworthmentioning.Most of the

equationsavailableintheliteratureforpredictingver-

ticalsolidsconcentrationprofilesinslurrypipelineare

empirical innatureandhavebeen developedbased

onlimiteddataformaterialshavingequi-sizedornar-

rowsize-rangeparticleswithverylowconcentrations.

Mostoftheearlierstudiesonslurrypipelinesystems

arebasedon moderatevolumetricconcentrationsof

solids (say up to 20%). Much larger concentrations

now coming into common use show more compli-

cated behaviour. Also in any practical situation, the

solidsarecoarserinsizewithbroadparticlegrading

beingtransportedatlargeflowvelocities.

Anattempthasbeenmadeinthepresentstudy

todevelopageneralizedslurryflowmodelusingCFD

andutilizethemodeltopredicttheconcentrationpro-

file. A comprehensive computational fluid dynamics

(CFD)modelwasdeveloped inthepresentstudyto

gain insight into the solid-liquid slurry flow in pipe-

lines.

In recent years, CFD becomesa powerful tool

beingusedinareaslikefluidflow,heat/masstransfer,

chemicalreactionsandrelatedphenomenabysolving

mathematicalequationsthatgoverntheseprocesses

usinganumericalalgorithmonacomputer. A brief review of recent literature shows little

progress in simulating flow in slurry pipelines using

CFD.Forsolid–liquidmultiphaseflows,thecomplexity

ofmodellingincreasesconsiderablyandthisremains

anareaforfurtherresearchanddevelopment.Dueto

the inherent complexity of multiphase flows, from a

physicalaswellasanumericalpointofview,“gene-

ral”applicableCFDcodesarenon-existent.Therea-

sonsforthelackoffundamentalknowledgeonmul-

tiphaseflowsarethree-fold:

1) Multiphase flow is a very complex physical

phenomenonwheremanyflowtypescanoccur(solid– –liquid, gas–solid, gas–liquid, liquid–liquid, etc.) and

withineach flow type several possible flow regimes

can exist (e.g . inslurry flow four regimes exist, na-

mely homogeneous flow, heterogeneous flow, flow

withmovingbedandsaltation).

2)Thecomplexphysicallawsandmathematical

treatmentofphenomenaoccurringinthepresenceof

the two phases (interface dynamics, coalescence,

break-up,drag,solid–liquidinteraction,...)arestilllar-

gely underdeveloped.For example, to date there is

stillnoagreementonthegoverningequations.Inad-

dition,proposedconstitutivemodelsareempiricalbut

often lack experimental validation for the conditions

theyareappliedunder.

3)Thenumericsforsolvingthegoverningequa-

tions and closure laws of multiphase flows are ex-

tremely complex. Very often multiphase flows show

inherent oscillatory behaviour, requiring costly tran-

sientsolutionalgorithms.AlmostallCFDcodesapply

extensionsofsingle-phasesolvingprocedures,lead-

ingtodiffusiveorunstablesolutions,andrequirevery

shorttime-steps.

Inspiteofthemajordifficultiesmentionedabove,

attemptshavebeenmadetosimulatesolid-liquidflow

inpipelines.Asmallnumberofstudiesisfocusedon

predicting the solid concentration distribution in the

experimentalslurrypipelines.Althoughsomedegree

of success is reported, a number of limitations are

apparent.Consideringthelimitationsinthepublished

studies, the present work has been undertaken to

systematicallydevelopaCFDbasedmodeltopredict

the solidconcentration profile inslurrypipeline.The

aimistoexplorethecapabilityofCFDtomodelsuch

complexflow.

Inthiswork,asolidsuspensioninafullydeve-

loped pipe flow was simulated. The two-fluidmodel

basedontheEulerian-Eulerianapproachalongwitha

standardk -ε turbulencemodelwithmixtureproperties

wasused.Thecomputationalmodeldevelopedinthis

workwasusedtosimulatesolid-liquidflowintheex-

perimental setup used by Kaushal et al . [11]. Themodelpredictionswereevaluatedbycomparingpre-

dictionswiththeexperimentaldata.

BACKGROUND WORKS

CFD studies onsolid-liquid slurry flow inpipe-

lines have not been widely performed as observed

from the literature and majority of the documented

data focuses onempirical correlationsofconcentra-

tion profile of water-based slurries of fine particles.

Thereis,therefore,aclearneedforexperimentaldata

and CFD models to describe the flow of large par-

ticles in Newtonian fluids as they are relevant to a

number of industrial applications such as the con-

veyingof particulate foodmixtures,gravel, and coal

lumps.

TheuseofCFD,however,hasbeenhampered

by lack of understanding of the complex solid–liquid

flows and thatresulthas onlybeen addressed in a

handfulofstudies[12-21].

Detailed measurements of the flow field and

pressure drop in these systems are scarce. Some

limitedstudiesexperimentedwithmagneticresonan-

ce imaging [22] and ultrasound Doppler velocimetry




297

[23]. Barigou et al . used positron emission particle

tracking(PEPT)tostudytheflowofcoarse(d=5or

10mm)nearlyneutrally-buoyantalginateparticlesin

shear-thinning carboxymethyl cellulose (CMC) fluids

andreportedinformationonflowregimes,solidphase

velocity profiles, and particle passage time distribu-

tions [21]. Computational modelling in this specific

areahasbeenevenmorelimited.Inarareattempt,

Krampa-Morluetal .usedCFDtostudytheflowfea-

turesofcoarseaqueoussolid–liquidslurriesinturbu-

lent upward flow includingvelocity profiles [24].The

model,implementedusingthecommercialCFDsoft-

ware CFX4.4 (Ansys Inc.), was tested usingexperi-

mentaldatafromSumneretal.[25].Theparticleshad

adensityof2650kg/m3andadiameterof0.47or1.7

mmandweresimulatedatconcentrationsupto30%

by volume. The authors concluded that, using the

defaultsettings,thecodefailedtoaccuratelypredict

important features of the flow. Recently, Eesa and

BarigouinvestigatedthecapabilitiesofCFDtomodel

theflowofcoarsenearly-neutralbuoyantparticlesin

shear-thinning CMC fluids ina horizontal pipe for a

limitednumberofflowcases[21].CFDresultsofpar-

ticlevelocityprofileswerevalidatedwithexperimental

data obtained by PEPT, while pressure drop pre-

dictions were compared with a number of selected

correlationsfromtheliterature.Inarecentpaper[26],

aCFDmodelbasedonthecommercialcodeANSYS

CFX 10.0, is used to conduct a detailed parametricstudy of the transport of nearly neutral-buoyant

coarseparticlesinlaminarnonNewtonianbothhori-

zontalandverticalflow.

FORMULATION OF MULTIPHASE CFD MODEL

TheEulerian–Euleriantwo-fluidmodelwasadop-

ted here, whereby both the liquid and solid phases

areconsideredascontinua.Treatingthesolidphase

as an Eulerian phase is possible provided that the

inter-phase interactionsareadequatelymodelled. In

fact,theEulerianapproachhasbeenreportedtobe

efficientfor simulatingmultiphaseflowsonce the in-

teraction terms are included [27]. The Eulerian–La-

grangian model,however,whichsimulates the solid

phase asa discrete phaseand thus allowsparticle

tracking,isinprinciplemorerealistic.However,after

evaluatingthe relevant literature aswell asconduc-

ting a number of simulation trials, it was concluded

that the number of dispersed particles that can be

trackedwithinall thedifferentcommercialCFD soft-

wareavailableiscurrentlyverylimited,thusrestricting

theapplicabilityof theEulerian–Lagrangianmodel to

onlydilutemixtureswellbelow5%byvolume[28].

Eulerian Model

In the Eulerian-Eulerianapproach, two phases

are considered to be interpenetrating continua. For

the present CFD simulations, the Eulerian-Eulerian

multiphase model implemented in the commercialcode Fluent 6.2 was used. With this approach, the

continuity and the momentum equations are solved

for each phase and therefore, the determination of

separateflowfieldsolutionsisallowed.TheEulerian

modelisthemostcomplexandcomputationallyinten-

siveamongthemultiphasemodels.Itsolvesasetof

“n ”momentumandcontinuityequationsforeachpha-

se. Coupling is achieved through the pressure and

interphaseexchangecoefficients.Forgranularflows,

thepropertiesareobtainedfromapplicationofkinetic

theory.

ContinuityEquation

Thecontinuityequationforagenericphaseqis

givenby:

q q q q q( ) ( ) 0t

∂+ ∇ =

∂α ρ α ρ ν (1)

Thesolutionofthisequationforeachsecondary

phase,alongwiththeconditionthatthevolumefrac-

tions sum to one, allows for the calculation of the

primary-phasevolumefraction.

MomentumEquations

Fluid-fluidmomentumequations. Theconserva-tionofmomentumforafluidphaseqis:

q q qq q q q q q q

q lift,q vm,qq q

p q pqpq pq1

( ) ( )

( )

( )

q

n

p

p g t

F F F

K m

α ρ ν α ρ ν ν α τ α ρ

α ρ

υ υ υ

=

∂+ ∇ = − ∇ + ∇ + +

∂+ + + +

+ − +

(2)

qF

is an external body force, lift,qF

is a lift

force, vm,qF

isa virtual mass force,K pq is an inter-

actionforcebetweenphases, andp is the pressure

sharedbyallphases.

Fluid-solidmomentumequations

FLUENT uses a multi-fluid granular model to

describetheflowbehaviorofafluid-solidmixture.The

solid-phase stresses are derived by making an

analogy between the random particlemotionarising

from particle-particle collisions and the thermal mo-

tion of molecules in a gas, taking into account the

inelasticity of the granular phase. As the case for a

gas, the intensityof the particlevelocity fluctuations

determines the stresses, viscosity, and pressure of

the solid phase. The kinetic energy associated with

the particle velocity fluctuations is representedbya




298

“pseudo-thermal” or granular temperature which is

proportionaltothemeansquareoftherandommotion

ofparticles.

Theconservationofmomentumforthe8thsolid

phaseis:

s s s ss s s s s s s

s lift,s vm,ss s

l s lsls ls1

( ) ( )

( )

( )n

p

p g t

F F F

K m

α ρ ν α ρ ν ν α τ α ρ

α ρ

υ υ υ

=

∂+ ∇ = − ∇ + ∇ + +

∂+ + + +

+ − +

(3)

where p s is the sth solid’s pressure, K ls = K sl is the

momentumexchangecoefficientbetweenfluidphase

landsolidphases,n isthetotalnumberofphases.

Theliftforce lift,sF

andthevirtualmassforce vm,sF

have been neglected in the calculations, because

theygiveaminorcontributiontothesolutionwithres-

pecttotheotherterms.

Interphaseexchangecoefficient

ItcanbeseeninEqs.(2)and(3)thatmomen-

tum exchangebetween the phases isbasedon the

valueof the fluid-fluidexchange coefficientK pq and,

for granular flows, the fluid-solid and solid-solid ex-

changecoefficientsKls.

Fluid-solid exchange coefficient . The fluid-solid

exchange coefficient K ls is in the following general

form:

s sls

s

f K

α ρ

τ = (4)

where f is defined differently for the different ex-

changecoefficientmodels(asdescribedbelow),and

τ s,the“particulaterelaxationtime”,isdefinedas:

2s s

s

l18

d ρτ

μ= (5)

whered s isthediameterofparticlesofphases.

All definitions of f includea drag function (C D)

thatisbasedontherelativeReynoldsnumber(Re s).

Itisthedragfunctionthatdiffersamongtheexchangecoefficientmodels. The following threemodels were

foundintheliteraturewhicharepromisingandwidely

used for calculating solid liquid interaction in slurry

flow.

Syamlal-O’Brienmodel[29]:

Forthismodel,f isdefinedas:

D s l

2l r,s24

C Re f

v

α

μ= (6)

wherethedragfunctionhasaformderivedbyDalla

Valle[30]:

2D

s

r,s

4.8(0.63 )C

Re

v

= + (7)

This model is based on measurements of the

terminal velocitiesof particles in fluidizedorsettling

beds,withcorrelationswhicharefunctionsofthevo-

lumefractionandtherelativeReynoldsnumber:

s ll s

s

l

d v v Re

ρ

μ

−=

(8)

wherethesubscriptlisforthelthfluidphase,sisfor

thesth solidphase, andd sisthediameterofthes

th

solidphaseparticles.

The fluid-solid exchange coefficient has theform:

s l l ss lls D2

r,s s l r,s

3

4

Re K C v v

v d v

α α ρ

μ= −

(9)

where v r,s is the terminal velocity correlation for the

solidphase:

r,s s

2 2s s

0.5( 0.06

(0.06 ) 0.12 (2 ) )

v A Re

Re Re B A A

= − +

+ + − + (10)

with

4.14l A α= (11)

and

1.28l l0.8 for 0.85B α α= ≤ (12)

or

2.65l l0.8 for 0.85B α α= > (13)

Thismodelisappropriatewhenthesolidsshear

stressesaredefinedaccordingtoSyamlaletal .[31].

WenandYumodel[32]:

ForthemodelofWenandYu,thefluid-solidex-

changecoefficientisofthefollowingform:

s l l -2.65s lls D l

s

3

4K C v v d

α α ρα= −

(14)

where:

0.687D l s

l s

24(1 0.15( ) )C Re

Re α

α= + (15)

Thismodelisappropriatefordilutesystems.

Gidaspowmodel[33]:

The Gidaspow model is a combination of the

WenandYumodelandtheErgunequation[34].

Thefluid-solidexchangecoefficient,K ls,isofthe

formgivenbyEq.(14).Whenα l≤0.8:




299

s l l s ls lls D2

l s s

(1 )150 1.75K C v v

d d

α α μ α ρ

α

−= + −

(16)

Thismodelisrecommendedfordensefluidized

beds.

Solid-solidexchangecoefficient .Thesolid-solid

exchangecoefficient,K ss,hasthefollowingform(Sy-

amlal[35]):

ss2

2ls fr,ls s s l l l s 0,ls

l s3 3

l s s

3(1 )( ) ( )2 8

2 ( )l

K

e C d d g v v

d d

π π α ρ α ρ

π ρ ρ

=

+ + += −

+

(17)

where:e ls-coefficientofrestitution,C fr,ls-coefficient

offrictionbetweenthelthands

thsolid-phaseparticles

(C fr,ls=0),d l-thediameteroftheparticlesofsolidand

g 0,ls-theradialdistributioncoefficient.

Implementation of CFD model

The geometryusedconsistedof apipe ofdia-

meterD = 105 mm. The pipe length, L,was much

greater than the maximum entrance length, Le, re-

quiredforfullydevelopedflow.Insingle-phaseNew-

tonianlaminarflow,Lecanbeestimatedfrom[36]:

et0.062

LRe

D =

where

f mt

f

u D Re

ρ

μ=

isthetubeReynoldsnumberandu misthemeanflow

velocity. There is no correlation available for esti-

matingLeintwo-phasesolid–liquidflow.However,for

almostalltheparticlesusedhere,theaboveequation

shouldgiveareasonableestimateofLe.Whilstsuch

estimateswereusedasaguide,aseriesofnumerical

trialswereconductedusingdifferentpipelengths.For

allofthecasessimulatedhere,apipelengthof3m

was sufficient to give a fully developed solid–liquid

flow through most of the pipe lengthwhilstkeeping

computational cost low. Usinga longerpipe didnot

affecttheresults.Thegeometrywasmeshedintoap-

proximately1.8×105tetrahedralcells.

For Eulerian multiphase calculations, we used

thePhaseCoupledSIMPLE (PC-SIMPLE)algorithm

[37]forthepressure-velocitycoupling.PC-SIMPLEis

anextensionoftheSIMPLEalgorithmtomultiphase

flows.The velocitiesare solved coupled byphases,

but in a segregated fashion. The geometry was

meshed intoapproximately 50000quadrilateralcells

inGAMBIT2.2pre-processor.Adensecomputational

gridwasusedbecauseofthepilot-scalepipedimen-

sions.Theinitialconditionswere:a)uniformfullyde-

veloped velocityprofile atpipeinletandb)thesolid

particlesuniformlydistributedatpipe inlet.The first-

-orderupwinddiscretizationschemewasusedforthe

volumefraction,momentumequations,turbulenceki-

neticenergy (k ),and turbulencedissipation rate (ε ).

All the simulations were performed in double pre-

cision.

Simulationsofthecarrierfluidflowingalonewere

performedfirsttoservebothasaninitialvalidationof

the code and the numerical grid, and to reveal the

effectsofsolidparticlesontheliquidvelocity(byde-

selectingthevolumefractionequations).Oncetheini-

tial solution for theprimaryphasewasobtained,the

volume fraction equationswere turned back onand

thecalculationcontinuedwithallphases.Aninletflow

rate boundary condition was used at the pipe inlet,

whilestaticpressurewasspecifiedattheoutlet.The

homogeneousvolumetricfractionofeachphasewas

specifiedat the inlet.Usingflowrateas aboundary

conditionisthecommonwayofformulatingpipeflow

problems,i.e.onedesignsasystemtodeliveragiven

flow rate.It isnotedhoweverthatusinga pressure-

specifiedinletboundaryconditionisastricterwayof

testingtheCFDcodeasaflowrateboundarycondi-

tionmaybeperceivedasawayofhelpingtosteerthe

simulation towards the right solution. This pressure

optionwastestedbutitdidnotaffecttheresultsofthe

CFDcomputations.Theusualno-slipboundarycondi-tion was adopted at the pipe wall. Simulation was

steady state. Theconcentrationdistributionwas uni-

forminz direction.

The solution was assumed tohave converged

whenthemassandmomentumresidualsreached10 –4

for all of the equations solved. Also the slopes of

residuals approach to zero. This typically required

150iterations.

Due to the complexity of the solid–liquid flows

considered here, the simulations initially required a

greatdealofexperimentationandoptimization.Ofpri-

mary importance was the appropriate modelling offorcesandinteractionsbetweenthetwophases.The

drag forcewasmodelled using the Syamlal-O’Brien

model(1993),WenandYu(1966)modelandGidas-

powmodel(1992).

RESULTS AND DISCUSSION OF 3D SIMULATION

Concentration profile

Figures 1–4 show the experimental and CFD

predictedverticalconcentrationprofileofslurryof125

and440μmglassbeadsin54.9mmdiameterpipeat

differenteffluxconcentrationsandflowvelocity.The




300

Figure1.Comparisonofexperimentalandcalculatedverticalconcentrationprofileforflowof125 μ mglassbeadsin

54.9mmdiameterpipeatdifferenteffluxconcentrationandflowvelocity.

Figure2.Comparisonofexperimentalandcalculatedverticalconcentrationprofileforflowof125 μ mglassbeadsin54.9mmdiameter

pipeatdifferenteffluxconcentrationandflowvelocity




301

Figure3.Experimentalandcalculatedverticalconcentrationprofileforflowof440 μ mglassbeadsin54.9mmdiameterpipe.

Figure4.Experimentalandcalculatedverticalconcentrationprofileforflowof440 μ mglassbeadsin54.9mmdiameterpipe.




302

agreementbetweencalculatedandexperimentalcon-

centrationprofilesisquitegoodasevidentfromthese

curves.Howeverthediscrepancyfoundbetweenthe

experimental results and the calculated results in

caseoflowsolidconcentrationandlowvelocity( C vf =

=9.4%v m=1m/s)indicatethat thedevelopedCFD

modelisnotfullycapabletocapturethephenomena

atverylowvelocitywherethegradientofsolidprofile

ismoreinverticalplane.

Figures 5and 6 showconcentrationprofilesin

theverticalplaneforslurryof125and440μm,res-

pectively,byC v/C vf vs . y /D ,whereC visthevolumetric

concentration at y = y /D , y being distance from the

pipebottomandD thepipediameter.It isobserved

thattheparticlesareasymmetricallydistributedinthe

vertical plane with the degree of asymmetry in-

creasingwithincreaseinparticlesizebecauseofthe

gravitationaleffect.Itisalsoobservedthatthedegree

of asymmetry for the same overall concentration of

slurryincreaseswithdecreasingflowvelocity.Thisis

expectedbecausewithdecreaseinflowvelocitythere

will bea decreasein turbulent energy,which isres-

ponsible for keeping the solidsin suspension.From

thesefigures,itisalsoobservedthatforagivenvelo-

city,increasingconcentrationreducestheasymmetry

becauseofenhancedinterferenceeffectbetweenso-

lidparticles.Theeffectofthisinterferenceissostrong

that the asymmetry even at lower velocities is very

muchreduced at higherconcentrations.Therefore it

canbeconcludedthatthedegreeofasymmetryinthe

concentration profiles in the vertical plane depends

upon particle size, flowvelocity and overall concen-

trationofslurry.

Measuredconcentrationprofilesshowadistinct

change in the shape for slurries of coarser particle

size(i.e .,440µm)withhigherconcentrationsatlower

velocities (Figures 3 and 4). It isobserved that the

maximumconcentrationatthebottomdoesnotchan-

geandextendsuptocentreofthepipeline,thusmak-

inga sudden drop inthe concentrationin the upper

half of the pipeline. The reason for such a distinct

changeinshapeofconcentrationprofilesmaybeat-

tributedtotheslidingbedregimeforcoarserparticles

atlowervelocitiesandhigherconcentrations.

Figure5.Concentrationprofilesintheverticalplaneforslurryof125 μ mparticlesize.a)Case-a:Feedconc.=10%;b)case-b:Feedconc.=30%;c)case-c:Feedconc.=50%.




303

Velocity profile

Figures7–9showthecorrespondingverticalve-

locityprofileacrossthepipecrosssectionatpipeout-

let.Duetotheunavailabilityofexperimentaldata,the

agreementbetweenexperimentalandpredictedvelo-

cityprofilecouldnotbejudged.However,thevelocity

profilepatternsinthosefiguresmatchthetheoretical

understanding.Therefore, itmay beconcluded indi-

rectlythattheCFDmodeliscapableofvalidatingthe

velocityprofileforslurryflow.Thesolidphasevelocity

profile is generally asymmetrical about the central

axisatlowvelocity(say1m/s).Theasymmetryinthe

solidphasevelocityprofileisaresultofparticleset-

tling due to the density difference between the two

phases.Theasymmetricalnatureofvelocityprofileis

reduced at higher velocity range (say 3-5 m/s) and

velocityprofilebecomessymmetrical.

Figure10showsthecomparisonofvelocitypro-

file atdifferentefflux concentration for different flow

velocityfor125 μmparticles.Fromthisfigure,it can

beconcludedthatthevelocityprofiledoesnotchange

muchduetoincreaseinconcentrationfrom10to50%.

Pressure drop

The parity plot of predicted and experimental

pressuredropisshowninFigure11.Fromthisfigure,

it isevident that the agreement between the calcul-

ated and experimental pressuredrop is quite good.

The calculated pressure drops for slurry of 125 μm

particlesarepresented inFigure12at overall area-

-average concentrations around 10, 20, 30, 40 and

50%. It is observed that the pressure drop at any

givenflowvelocityincreaseswithincreaseinconcen-

tration.Thistrendisseenforallconcentrationsatall

velocities.Therateofincreaseinpressurewithcon-

centrationissmallatlowvelocitiesbutitincreasesra-

pidlyathighervelocities.

The pressure drops for slurry of 440 μm par-

ticlesarepresentedinFigure13atoverallarea-ave-

rage concentrations around 10, 20, 30 and 40%.

Fromthisfigure,itisobservedthatthepressuredrop

atanygiven flowvelocity increases with increasein

concentration, but the rate of increase is compara-

tivelysmallerathigherflowvelocities.Furthermore,at

lowervelocities,the pressuredropremainsconstantatlowerconcentrationsanddecreaseswithflowvelo-

Figure6.Concentrationprofilesintheverticalplaneforslurryof440 μ mparticlesize.a)Case-a:Feedconc.=10%;

b)case-b:Feedconc.=30%;c)case-c:Feedconc.=40%.




304

Figure7.CFDpredictedsolidphaseverticalvelocityprofileforflowof125 μ mglassbeadsin54.9mmdiameterpipe

atdifferenteffluxconcentrationandflowvelocity.

Figure8.CFDpredictedsolidphaseverticalvelocityprofileforflowof440 μ mglassbeadsin54.9mmdiameterpipe

cityathigherconcentrations.FromFigures12and13,

itisobservedthatfiner-sizedparticleshavelesspres-

suredropatlowerflowvelocitiesandmorepressure

dropathigher flow velocitiesthancoarser particles.

Such an increase in pressuredrop for coarser par-

ticlesatlowervelocityisduetotheincreasedamount

ofparticlesmovinginthebedduetothegravitational

effect,while,inthecaseoffinerparticlesizeathigher

velocities, the pressuredrop ismore due togreater

surface area causing more frictional losses in sus-

pension.

Contours of solid concentration and velocity

Figures13to43(Supplementarymaterial)show

contoursofvolume fractionofsolidand contoursof

solidvelocityat thepipeoutletatdifferent flowvelo-

cities and efflux concentration. These pictures help

visualizethesolidsdistributionacrossthepipecross

section.OneofthebiggestadvantagesofCFDisthe

ability to generate such types of concentration and

velocitycontours.Figure14showshowsolidsettled

atthebottomof thepipe (indicatedbyredcolourat

thebottom).Solidconcentrationatthetopofthepipe




305

Figure9.Comparisonofverticalvelocityprofileata)1,b)3andc)5m/sfordifferenteffluxconcentration.

Figure10.Parityplotofpredictedvs.experimentalpressuredropforslurryflowatdifferent

overallarea-averageconcentrationsandflowvelocities.




306

Figure11.Pressuredropforslurryof125µmparticlesizeatdifferentoverallarea-averageconcentrationsandflowvelocities.

Figure12.Pressuredropforslurryof440µmparticlesizeatdifferentoverallarea-averageconcentrationsandflowvelocities.

is very low and at the top most points are virtually

absent(indicatedbythebluecolouratthetopofthe

pipe). In the large area at the centre portion of the

pipe, the solid concentration remains uniform (indi-

catedbygreencolour).Figure15showsthevelocity

contoursacrossthepipecrosssectionattheoutletof

the pipe. From this picture it is clear thatmaximum

velocity is not at the centre of the pipe but slightlylowerthanthepipeaxis.Thisisduetosolidstending

tosettleatthebottomofthepipeduetolowvelocity

(1 m/s) of slurry which makes the velocity profile

asymmetrical.AcomparisonofvelocityprofilesinFi-

gures15and19revealsthefactthatatahighervelo-

city(5m/s),thevelocityprofilebecomessymmetrical

and maximumvelocity occurs at the pipe axis.This

maybeduetotheflatconcentrationprofileforhigher

turbulence at higher velocity. Another marked diffe-

renceofvelocityprofilesinFigures15and26shows

thatwiththeincreaseofsolidconcentration(from9.4

to30.3%)atsameslurryvelocity(1m/s),theasym-

metrical nature of velocity profile increasesand the

maximum velocity locationmovesmore towards the

bottomofthepipe.Comparisonofconcentrationpro-

filecontourinfigures18,23,29and33revealsthatat

afixedflowvelocity(say5m/s),whensolidconcen-

trationincreasesfrom10to50%,theasymmetryna-

tureofconcentration profile reducesbecauseofen-

hancedinterferenceeffectbetweensolidparticles.The measured concentration profiles show a

distinct change in the shape for slurries of coarser

particlesize(i.e .,440µm)atlowervelocities(Figures

42–44).Itwasobservedthatmostofthesolidsettled

down at the bottom of the pipe for coarser particle

resultinginsteepconcentrationgradient.

CONCLUSION

Inthisstudy,thecapabilityofCFDwasexplored

tomodelcomplexsolidliquidslurryflowinpipeline.It

wasfoundthatthecommercialCFDsoftware(FLUENT)




307

iscapabletosuccessfullymodelthesolid–liquidinter-

actionsinslurryflowandthepredictedconcentration

profilesresultsshowreasonablygoodagreementwith

theexperimentaldata.Thefollowingconclusionshave

beendrawnonthebasisofpresentstudy:

1.Theparticleconcentrationprofilewasmodel-

ledfor high concentration slurry transport where the

maximumoverallarea-averageconcentrationis50%

byvolumeemployingcoarseparticlesandhigherflow

velocitiesupto5m/s.

2.Itwasobservedthattheparticleswereasym-

metricallydistributedintheverticalplanewiththede-

greeofasymmetryincreasingwithincreaseinparticle

size because of the gravitational effect. It was also

observedthatthedegreeofasymmetryforthesame

overall concentration of slurry increased with de-

creasingflowvelocity.

3.Foragivenvelocity,increasingconcentration

reduced the asymmetry because ofenhanced inter-

ferenceeffectbetweenthesolidparticles.Theeffect

ofthisinterferencewassostrongthattheasymmetry

evenatlowervelocitiesisverymuchreducedathigh-

erconcentrations.

4. A distinct change in the shape of concen-

trationprofileswasobservedindicatingtheslidingbed

regimeforcoarserparticlesatlowerflowvelocities.

5. The solid phase velocity profile is generally

asymmetrical about the central axis at low velocity

(say1 m/s).Theasymmetryin thesolidphasevelo-city profile is a result of particle settling due to the

densitydifferencebetweenthetwophases.Theasym-

metricalnatureofvelocityprofileisreducedathigher

velocity range(say3-5 m/s) andvelocityprofile be-

comessymmetrical.

6.Pressuredrop atany given flow velocity in-

creaseswithincreaseinconcentration.Thistrendis

seenforallconcentrationsatallvelocities.Therateof

increaseinpressurewithconcentrationissmallatlow

velocitiesbutitincreasesrapidlyathighervelocities.

Thecomputationalmodelandresultsdiscussed

in this work would be useful for extending the ap-plicationsofCFD models for simulating large slurry

pipelines.

Supplementary material

Figures 13–43can be foundasSupplementary

material to this article at the CI&CEQ website, http:

//www.ache.org.rs/CICEQ/,orbegivenbycorres-

pondingauthoronrequest.

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SANDIP KUMAR LAHIRI

K.C. GHANTA

Department Of Chemical

Engineering, Nit, Durgapur,

West Bengal, India

NAUČNI RAD

MODELOVANJE STRUJANJA SUSPENZIJE POMOĆU

RAČUNARSKE TEHNIKE SIMULACIJE STRUJANJA

FLUIDA (CFD)

Uovojstudijijerazvijenopštimodeltokasuspenzijepomo ć ura č unarsketehnikesimula-

cijastrujanjafluida(CFD)uciljupredvi đ anjaprofilakoncentracije.PrimenomCFDmo-

delasesti č eboljiuvidufenomenevezanezaproticanjesuspenzijekrozcevi.Razvijen

etrodimenzionimodelradi ispitivanjauticajakoeficijentatrenjanaprofilkoncentracije.

Preliminarnasimulacijaukazujenapotrebuproširenjamodelazaopisivanjeme đ ufazne

siletrenja.Razli č itekorelacijezaodre đ ivanjekoeficijentatrenja,kojesudostupneulite- raturi,suuklju č eneudvofaznimodel(Euler-Euler).Ovajmodeljeprikazanporedstan-

dardnogk- ε modelakojiopisujeturbulentnitoksmešekrozcev.Zaizra č unavanjaprime-

nommodelakoriš ć enjekomercijalniCFDprogramFluent6.2(FluentInc.,USA).Radi

ilustracijeprimenljivosti trodimenzionesimulacijekoriš ć enisupodaciKaushal-a(2005)

(zakoncentracijuč vrstefaze50%).Modeljeprimenjennasuspenziju č esticastakladi-

menzija125i440μ muvodiprirazli č itimprotocima(od1-5m/s)iukupnukoncentraciju

č vrstefazeod10do50vol.%.Izra č unatevrednostipadapritiskaikoncentracioniprofili

dobijeniprimenommodelaieksperimentalnipodacipokazalisuodli č noslaganje.Intere-

santni fenomenisuprime ć enipri korelisanju brzine i profila koncentraciječ vrstefaze.

Primenamodelamožebitikorisnaprisimulacijitokauvelikimproto č nimsistemima.

Klju č ne re č i:CFD; tok suspenzije;koeficijent trenja; profil koncentracije; profil

brzine.

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