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Availableonlineat
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;ve- locityprofile.
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-
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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
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[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
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“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:
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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
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Figure1.Comparisonofexperimentalandcalculatedverticalconcentrationprofileforflowof125 μ mglassbeadsin
54.9mmdiameterpipeatdifferenteffluxconcentrationandflowvelocity.
Figure2.Comparisonofexperimentalandcalculatedverticalconcentrationprofileforflowof125 μ mglassbeadsin54.9mmdiameter
pipeatdifferenteffluxconcentrationandflowvelocity
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Figure3.Experimentalandcalculatedverticalconcentrationprofileforflowof440 μ mglassbeadsin54.9mmdiameterpipe.
Figure4.Experimentalandcalculatedverticalconcentrationprofileforflowof440 μ mglassbeadsin54.9mmdiameterpipe.
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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%.
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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%.
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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
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Figure9.Comparisonofverticalvelocityprofileata)1,b)3andc)5m/sfordifferenteffluxconcentration.
Figure10.Parityplotofpredictedvs.experimentalpressuredropforslurryflowatdifferent
overallarea-averageconcentrationsandflowvelocities.
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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)
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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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