CFD simulation and experimental measurement of gas holdup and liquid interstitial velocity in

12 Pages·2011·0.8 MB·English

by  M. Šimčík

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ChemicalEngineeringScience66(2011)3268–3279
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Chemical Engineering Science
journal homepage: www.elsevier.com/locate/ces
CFD simulation and experimental measurement of gas holdup and liquid
interstitial velocity in internal loop airlift reactor
M. Sˇimcˇı´ka,n, A. Motab, M.C. Ruzickaa, A. Vicenteb, J. Teixeirab
aInstituteofChemicalProcessFundamentals,CzechAcademyofSciences,Rozvojova135,16502Prague6,CzechRepublic
bInstituteforBiotechnologyandBioengineering,CentreofBiologicalEngineering,UniversityofMinho,CampusdeGualtar,4710-057Braga,Portugal
a r t i c l e i n f o a b s t r a c t
Articlehistory: This paper documents experiments and CFD simulations of the hydrodynamics of our two-phase
Received30September2010 (water,air)laboratoryinternalloopairliftreactor(40l).Theexperimentsandsimulationswereaimed
Receivedinrevisedform atobtainingglobalflowcharacteristics(gasholdupandliquidinterstitialvelocityintheriserandinthe
28January2011 downcomer) inour particular airlift configurations. The experiments and simulations were donefor
Accepted31January2011
three different riser tubes with variable length and diameter. Gas (air) superficial velocities in riser
Availableonline5February2011
wereinrangefrom1to7.5cm/s.Uptothreecirculationregimeswereexperimentallyobserved(no
Keywords: bubblesindowncomer,bubblesindowncomerbutnotcirculating,andfinallythecirculatingregime).
Airlift The primary goal was to test our CFD simulation setup using only standard closures for interphase
CFD
forcesandturbulence,andassumingconstantbubblesizeisabletocaptureglobalcharacteristicsofthe
Hydrodynamics
flowforourexperimentalairliftconfigurationsforthethreecirculationregimes,andifthesimulation
Multiphaseflow
setupcouldbelaterusedforobtainingtheglobalcharacteristicformodifiedgeometriesofouroriginal
Multiphasereactors
Simulation airliftdesignorfordifferentfluids.TheCFDsimulationsweredoneincommercialcodeFluent6.3using
algebraic slip mixture multiphase model. The secondary goal was to test the sensitivity of the
simulationresultstodifferentclosuresforthedragcoefficientandtheresultingbubbleslipvelocity
and also for the turbulence. In addition to the simulations done in Fluent, simulation results using
differentcode(CFX12.1)anddifferentmodel(fullEuler–Euler)arealsopresentedinthispaper.The
experimentalmeasurementsofliquidinterstitialvelocityintheriserandinthedowncomerweredone
byevaluatingtheresponsetotheinjectionofasulphuricacidsolutionmeasuredwithpHprobes.The
gasholdupintheriseranddowncomerwasmeasuredwiththeU-tubemanometer.Theresultsshowed
thatthesimulationsetupworksquitewellwhentherearenobubblespresentinthedowncomer,and
thatthesensitivitytothedragclosureisratherlowinthiscase.Theagreementwasgettingworsewith
theincreaseofgasholdupinthedowncomer.Theuseofdifferentmultiphasemodelinthedifferent
code(CFX)gavealmostthesameresultsastheFluentsimulations.
&2011ElsevierLtd.Allrightsreserved.
1. Introduction whichare susceptibleto physicaldamageby fluid turbulence or
mechanicalagitation(Chisti,1998).
Airliftreactorsarepneumaticallyagitatedvessels,andareone The airlift reactor consists of two interconnected main parts,
amongdifferenttypesofmultiphasereactors.Theypossessgood theriserandthedowncomer.Gasisinjectedintotheriserandthe
mixing,massandheattransfercharacteristicsandtheyareused resultingdifferencebetweenaveragedensitiesintheriserandin
in a wide range of industrial applications such as waste water the downcomer provides a driving force for liquid circulation.
treatment, chemical (e.g. hydrogenations and oxidations) and Alsosolidparticlescanbepresent(catalyst,biomass,etc.).There
biochemical processes, and others. The other advantages are aretwomain groupsof airliftreactorsnamely,theinternalloop
simplicity of construction, absence of moving parts, and low airlift reactor and the external loop airlift reactor. The internal
power consumption. Their other advantageous features in case loopairliftreactorisabubblecolumndividedintothetwoparts
of biochemicalprocesses areease of long termsterile operation, byadrafttubeinsertedintothecolumn.Theexternalloopairlift
andahydrodynamicenvironmentsuitableforfragilebiocatalysts, consists of two separate columns connected with pipes. Other
important part, which may or may not be present, is the gas
separator.Itspurposeistopreventbubblesfrombeingentrained
nCorrespondingauthor. intothedowncomer,whichwoulddecreasethedrivingforcefor
E-mailaddress:[email protected](M.Sˇimcˇı´k). liquidcirculation.
0009-2509/$-seefrontmatter&2011ElsevierLtd.Allrightsreserved.
doi:10.1016/j.ces.2011.01.059
M.Sˇimcˇ´ıketal./ChemicalEngineeringScience66(2011)3268–3279 3269
The knowledge of the airlift hydrodynamics is needed for the Euler–Euler model) were used in the presented work, thus only
designoftheairliftreactor.Basicglobalquantitiessuchasgasholdup Euler–Eulermodelsareconsideredinthefollowingtext.Themain
and liquid velocities in the riser and in the downcomer, total advantageofCFDsimulationsifcomparedtoexperimentsisthatno
interfacial area, and others are needed to be known. The hydrody- experimentalapparatushastobebuilt;theequipmentdimensions
namicandotherrelevantparameterssuchastheairliftgeometryare and working fluids can be easily changed in simulations; etc.
interrelated and their relationship can be quite complex and they However, the quality of the CFD simulation predictions, of course,
directly or indirectly influence each other in sometimes not so greatly depends on how well or how badly the employed CFD
obvious ways (Chisti, 1998), e.g. the driving force for the liquid models,submodelsandclosureequationsdescribeflowphenomena
circulationisthedifferenceingasholdupsbetweentheriserandthe occurring in the airlift reactor. Since the gas–liquid flows are very
downcomer. This driving force is balanced by friction losses in the complexwithflowphenomenaoccurringonawiderangeofspace
riser and the downcomer and in the bottom and top parts of the andtimescales,modelingofgas–liquidflowsisstillanopensubject
reactor(influenceofbottomandtopclearancesinthecaseofinternal and far from being complete. It is still necessary to validate
loopairliftsorlossesinconnectingpipesinthecaseofexternalairlifts simulation results against experiments. Euler–Euler models need
andoftheairliftgeometryingeneral).However,theresultingliquid closuresforallrelevantinterphaseforce(drag,lift,addedmass,etc.),
circulationinturnaffectstheriseranddowncomergasholdupand fortheturbulence(duetosinglephaseflowandduetobubbles)and
thus the driving force. The gas holdup depends also on bubble slip models for bubble coalescence and break-up, because the bubble
velocity,whichdependsonthebubblesize.Bubblesizeisinfluenced sizefiguresinmostoftheclosureequations.Sokolichinetal.(2004)
bythegasdistributor,coalescepropertiesoftheinvolvedfluidsand discussed the relevance of individual interphase forces for the
byturbulence.Turbulenceisinfluencedbyliquidcirculation,etc. simulation and also turbulence modeling issues in their review
The relevant hydrodynamic parameters need to be either paper.Theyobservedaweakdependencyofsimulationresults(in
obtainedexperimentallyorpredictedbymodelsofvarioustypes. partiallyaeratedrectangularbubblecolumn)ontheemployedvalue
A lot of experimental data have been published in the past on ofthebubbleslipvelocity.Theyexplainedthisweakdependenceby
globalquantities(holdup,liquidvelocities)inairliftreactorsand thefactthatthebubbletotalvelocitywasthesumofthebubbleslip
correlations based on these data. A large number of correlations velocityandtheliquidvelocity,whichcanberelativelyhigh,sothe
fortheseparametersarecompiledinChisti(1989),othercanbe, change in the bubble slip velocity had lower impact on the
e.g.,inChisti(1998). calculated gas holdup. It could be expected from the same reason
Many of the correlations presented in the literature are that the similar behavior (weak dependence of gas holdup on the
restrictedintheirvaliditytothesamereactorsize,typeandgas– bubbleslipvelocity)couldbefoundinairliftsimulations,ifbubbles
liquidsystemusedintheirdevelopment(Youngetal.,1991).Asa arepresentonlyintheriserandthedowncomerholdupiszero,and
rule, these correlations are system specific, being of little use in may be the dependence could be even weaker due to the more
designorscaleup,wheretheusualrequirementisforestimationof ordered flow in the airlift if compared to the bubble column.
expectedperformanceinlargerorgeometricallydifferentreactors However, if there is nonzero gas holdup in the downcomer, then
orfluids(Chisti,1998). Someauthorsemployedmodelsbasedon theeffectofthebubbleslipvelocitycouldbemuchstrongerdueto
mechanicalenergybalanceintheairliftreactor,e.g.Verlaanetal. countercurrentflowofbothphasesinthedowncomer.Itisthennot
(1986),Chisti(1989),andHeijnenetal.(1997).However,informa- surprisingthatsomeauthorsdidsimulationsofairliftsandobtained
tionaboutfrictionlosses(frictioncoefficients)mustbeprovidedas goodagreementwithexperimentsevenwheninappropriateclosure
an input parameter for these models. More recent experimental fordragforcewasused(e.g.Schiller–Naumanncorrelationforrigid
measurementsofairliftglobalhydrodynamiccharacteristics(riser spheredragusedfor5mmequivalentdiameterairbubbleinwater)
and downcomer holdup and velocities) can be found, e.g., in van incaseswithzerodowncomergasholdup.
Baten et al. (2003), Blazej et al. (2004), Merchuk et al. (1998) ThereareanumberofpapersdedicatedtotheEuler–EulerCFD
andvanBenthumetal.(1999)(internalloopairlifts)orinFreitas simulationsofairliftreactors.
et al. (2000) and Vial et al. (2002) (external loop airlifts). There External loop airlift simulation comparisons of radial profiles
werealsopaperspublishedonlocalgasholdupand/orlocalliquid of gas holdupand liquid velocity can be found, e.g. in Vial et al.
velocitymeasurements.LuoandAl-Dahhan(2008,2010)measured (2002),Royetal.(2006),orCaoetal.(2007).Thecomparisonof
liquid velocity profiles, turbulent quantities using the CARPT average gas holdup and liquid velocities with experiments for
technique and gas holdups profiles using computed tomography internalloop airlifts and for zero downcomer gas holdup can be
inaninternalloopairliftreactor.Theyobservedsignificanteffectof found, e.g. in Mudde and van den Akker (2001) (rectangular
topandbottomclearancesontheflow.Theyalsoobservedthatthe airlift), van Baten et al. (2003), or in Huang et al. (2008), who
bubbles are prone to concentrate in the riser center in radial also reported weak dependence of the simulation results on the
directionand the change frombubbly to churn-turbulent flow at bubblevelocityprescribedonthetopboundarycondition.Simu-
superficial gasvelocityof 2cm/s. Local gas holdups and/or liquid lationsforcaseswithnonzerodowncomerholdupweredone,e.g.
velocities in external loop airlift reactors were measured, e.g. byOeyetal.(2001),Huangetal.(2010),Talvyetal.(2007)orJia
byYoungetal.(1991), Vialetal.(2002), Wangetal.(2004), Cao etal.(2007).Talvyetal.(2007)comparedverticalandhorizontal
etal.(2007),Utigeretal.(1999),orLinetal.(2004). profiles of gas holdup in riser and downcomer, and horizontal
Apart from experiments, empirical correlations or theoretical liquid velocity profiles in downcomer with experiments in a
models such as the models based on mechanical energy balance, rectangular airlift. Jia et al. (2007) compared simulated and
CFDsimulationscanbeananothertool,whichcanbeusedtostudy experimental horizontal profiles of gas holdup and liquid in a
airlift hydrodynamics. There are two main groups of multiphase rectangularairliftandfoundagoodagreement.
flowmodelsusableforsimulationsonbubblecolumn/airliftscale.In
Euler–Euler models allphases are treated as interpenetratingcon-
tinua, while in Euler–Lagrange models the motion of individual 2. Goals
particles is tracked through the continuous fluid. The Euler–
Lagrange models, which track the motion of every single particle TheprimarygoalwastotesttheabilityofourCFDsimulation
(approximated as a mass point with closure equation for the setupto captureglobal characteristics of the flow in our experi-
interphase forces), can be used for smaller scale problems with mental 50l internal loop airlift with enlarged degassing zone
lowgasholdup.OnlyEuler–Eulermodels(mixturemodeland‘‘full’’ (riser and downcomer mean liquid interstitial velocities and gas
3270 M.Sˇimcˇ´ıketal./ChemicalEngineeringScience66(2011)3268–3279
holdup) in the three experimentally observed bubblecirculation Table1
regimes,andsoverifyifthesimulationsetupcouldbelaterused AirliftdimensionsforconfigurationscaseA,caseBandcaseC,and#ofgridcells
forobtainingtheglobalcharacteristicformodifiedgeometriesof perthesedimensionsinsimulations(SeeFig.1).
our original airlift design or for different fluids. The comparison
CaseA CaseB CaseC
wasdoneforthreedifferentrisertubes.TheCFDsimulationswere
doneincommercialcodeFluent6.3usingalgebraicslipmixture (mm) #of (mm) #of (mm) #of
multiphasemodel.Simulationsresultsusingdifferentmodel(full gridcells gridcells gridcells
Euler–Euler)indifferentcode(CFX12.1)arealsopresentedinthe
D1 100 12 100 12 100 12
paper. The experimental and simulation setups are described D2 62 12 87 12 62 12
inSections3and4,respectively. D3 70 14 92 14 70 14
The secondary goal was to test the sensitivity of the simula- D4 142 28 142 28 142 28
tions to the different bubble slip velocity, and to the different D5 420 28 420 28 420 28
H1 23 5 23 5 23 5
turbulenceclosure models (variants of k–e, k–o). This wasdone
H2 1200 60 1200 60 1400 70
usingthemixturemodelinFluent6.3code. H3 200 16 200 20 0 0
H4 170 14 170 12 170 14
H5 120 6 120 6 120 6
3. Experimentalsetup
The experiments were done in an internal loop airlift reactor was50l.Thedowncomerinnerdiameterwas14.2cm.Measure-
withenlargeddegassingzone.Thetotalvolumeoftheapparatus ments were done for three different riser tubes: 120(cid:2)6.2cm
(case A), 120(cid:2)8.7cm (case B) and 140(cid:2)6.2cm (case C)
(height(cid:2)inner diameter). The airlift geometry is depicted in
Fig. 1 and the relevant dimensions are summarized in Table 1.
The gas was entering the airlift through the 10cm diameter
porous plate sparger. The diameter of the ‘‘active’’ zone of the
sparger,throughwhichthegasflowwaspassing,was (cid:3)8cm.Air
and tap water were used as the gas and liquid phase. Gas
superficialvelocitiesintheriserwereinrangefrom1to7.5cm/s.
Thenetwaterflowthroughtheairliftwaszero.
The liquid interstitial velocity in the riser and in the down-
comerweremeasuredwithfourpHprobes(twoMethrommodel
620probesintheriserandtwomodel691probesinthedown-
comer) and evaluated from the probe signal response to a
sulphuricacidsolutioninjection.Theprobesignalwasmonitored
andthedatastoredusingLabviewprogram.Thesignalsampling
rate was 10Hz. The mean liquid interstitial velocity (V ¼U/a),
L L L
was estimated as V ¼(x (cid:4)x )/(t (cid:4)t ), where x are probe
L 2 1 2 1 1,2
verticalpositionsandt areprobesignalpeaktimes.Theprobes
1,2
wereplacedatx¼8.4and117.5cmintheriser,andatx¼9.0and
117.5cm in the downcomer (x¼0 being the sparger level). The
reported values of interstitial liquid velocity are four measure-
ments averages. The interstitial liquid velocity was measured in
the downcomer in cases A and C, and the riser velocity was
calculated from a continuity equation. It was done the opposite
wayincaseB.
Thetracerwasinjectedintothedowncomer18.4cmabovethe
gas distributor(10ml of 4.5M H SO solution).Initial pHinside
2 4
the airlift was 10 and was set by the addition of NaOH solution
priortothestartofthemeasurement.
The gas holdups in the riser and downcomer were estimated
using U-tube manometers. The agreement of this estimate with
therealgasholdupintheapparatusmaybeaffectedbyapressure
dropduetoflow.
4. Simulationsetup
ThemainpartofthesimulationswasdoneinCFDcodeFluent
6.3 using the algebraic slip mixture model and the simulation
setup is described in detail in Section 4.1. A part of the Fluent
simulationswaslaterrecalculatedintheCFX12.1codeusingthe
fullEuler–Eulermodelandtheirresultsarealsopresentedinthis
paper,althoughthecaseBCFXsimulationswerenotfinisheddue
toconvergenceproblemsandtheresultsarenotshown.TheCFX
setup is described in Section 5.2. The airlift geometry is shown
Fig.1. Airliftgeometry(notinscale). inFig.1. Thegasdistributorinthesimulationdomaingeometry
M.Sˇimcˇ´ıketal./ChemicalEngineeringScience66(2011)3268–3279 3271
turbulent viscosity and m is the molecular viscosity of phase k.
k
The k-th phase drift velocity is calculated as v ¼v –v ¼v –
dr,k k m kc
(1/r )Pn arv , where v ¼v –v is the slip velocity of the
m i¼1 i i ic kc k c
phasek(cindexisforthecontinuousphase).
Equationforthek-thphaseslipvelocity
The k-th phase slip velocity is calculated from the following
algebraicequation:
v ¼t ðr (cid:4)r Þa=ðfr Þ(cid:4)ðZ=sÞðra =a (cid:4)ra =a Þ ð3Þ
kc k k c k t t k k c c
The first term on the right hand side of Eq. (3) is due to the
drag force, where t ¼r d2/(18m) is k-phase particle relaxation
k k k c
time,f¼C Re/24isadragfunction,Re¼d 9v 9r/m,acceleration
D k kc c c
a¼g–(v (cid:6)r)v –@v /@t and C is drag coefficient. The drag
Fig.2. ComputationalgridforcasesAandC(left),andcaseB(right)attheairlift m m m D
coefficient C was calculated from Tomiayama0s correlation
cross-section. D
(Tomiyamaetal.,2002)forasinglebubble:
had the same diameter asthe riser.The computationalgridwas h n o i
C ¼max min 24=Reð1þ0:15Re0:687Þ,72=Re ,ð8=3ÞEo=ðEoþ4Þ
the same for both Fluent and CFX simulations and contained D
48,100(caseA),49,100(caseB)and44,700(caseC)gridcells.The ð4aÞ
computationalgrid(attheairliftcross-section)isshowninFig.2
where Eo¼(r (cid:4)r )gd2/s. The bubble equivalent diameter d in
andnumberofgridcellspereachairliftdimensioncanbefound L G
simulationswassetto5mm.Previouslydonevisualobservations
in Table 1. The grid was sufficient to obtain grid independent
of the bubbly flow using a high speed camera, suggest that this
results(seeSection5.1forthegridindependencetestresult).The
bubble diameter could reasonably well represent the typical
timestepinallsimulationswas0.005s.
bubble size in our airlift, at least for lower gas flow rates.
(However these experiments were done for a bubble column
4.1. Fluentsimulations
and not the airlift configuration of our experimental unit, and
were done only for low gas flow rates due to the opaqueness of
The mixture model was employed for simulations done in
the bubbly layer.) The drag coefficient calculated from (4a) is
Fluent6.3code.Themodelassumesthattwoormorephasesare
C ¼1.215 for a single 5mm bubble, with a corresponding slip
D
interpenetrating. It can solve cases, where two or more phases
velocity (cid:3)0.23m/s.Allbubbleswereassumedtobeofthesame
moveatdifferentvelocitiesanditassumeslocalequilibriumover
size,therewasnobubblebreak-up/coalescencemodelemployed
short spatial length scales, i.e. dispersed phases move at their
inoursimulations.
terminal velocities. This model is simpler than full Euler–Euler
Anotherclosure,Schiller–Naumann,wasemployedjustfortest
multiphasemodel.The mixturemodelsolvesthecontinuityand
purposes to examine an effect of bubble slip velocity on the
the momentum equation for a mixture with averaged mixture
simulationresults(seeSection5.1)
properties(density,velocity,andviscosity),analgebraicequation
for the dispersed phase(s) slip velocity and a volume fraction CD¼24=Reð1þ0:15Re0:687ÞforReo1000
equation for the secondary phase(s). The mixture model should
C ¼0:44forRe41000 ð4bÞ
requirelesscomputationalresourcesthantheEuler–Eulermodel, D
since it solves fewer equations. However, it can be sometimes However, all other presented simulations used the previous
more difficult to converge with more iterations required to be Eq.(4a)forcalculatingthedragcoefficient.
done,thusdiminishingthementionedadvantageovertheEuler– ThesecondtermontherighthandsideofEq.(3)appearsdue
Euler model. Model equations, boundary conditions and other to a dispersion of secondary phase by turbulence. The st is the
solverparametersaredescribedinfollowingparagraphs. turbulent Prandtl number and Zt is the turbulent diffusivity
The algebraic slip mixture model solves the continuity and calculatedfrom
momentum equation for the mixture, the algebraic equation for
dispersedphaseslipvelocityandvolumefractionequationforthe Zt¼Cmk2=eðgg=ð1þggÞð1þCbz2gÞ(cid:4)1=2
secondaryphasetoupdatethecompositionofthemixturedueto zg¼9vkc9=ð2=3kÞ1=2
flow(Manninenetal.1996),andfinallytheturbulencemodelis
C ¼1:8(cid:4)1:35cos2y
solved to provide the closure for the turbulent viscosity, which b
y¼v v =ð9v 99v 9Þ
appearsinthemomentumequationforthemixture. kc k kc k
Continuityequation Cm¼0:09
Themixturecontinuityequationis Theggisatimeratiobetweenthetimescaleoftheenergetic
@r =@tþrUðr v Þ¼0 ð1Þ turbulent eddies affected by the crossing-trajectories effect, see
m m m
Fluent user’s guide. The value of s was set to 0.01. The default
where v ¼(1/r )Pn a r v is the mixture mass averaged t
m m k¼1 k k k value was 0.75. The lower value, which was used in our Fluent
velocity, and r ¼Pn a r is the mixture density, a is the
m k¼1 k k k simulations, enhances a turbulent dispersion. The lower value
k-thphasevolumefraction.Thesumsareoverall(n)phases(k).
waschosen,becauseforcaseBbubblesflowingintotheriserdid
Momentumequation
notdispersefastenoughacrossthewholerisercrosssectionasit
Themixturemomentumequationis
wasvisuallyobservedinexperiments.
@ðr v Þ=@tþrU(cid:2)r v v (cid:3)¼(cid:4)rpþrU½m ðrv þrvTÞ(cid:5)þr g Phasevolumefractionequationforthesecondaryphase
m m m m m m m m m
þrU Xn a r v v ! ð2Þ equTahtieonmifxotrutrheecodmisppeorssiteidonphisasuepsd(aotnedlyboynseodlviisnpgertsheedtprahnasspeoirnt
k k dr,k dr,k
k¼1 ourcase)
where n is the number of phases (2 in our case),
mm¼(Pkn¼1akmk)+mt is the mixture effective viscosity, mt is the @ðakrkÞ=@tþrUðakrkvmÞ¼(cid:4)rUðakrkvdr,kÞ ð5Þ
3272 M.Sˇimcˇ´ıketal./ChemicalEngineeringScience66(2011)3268–3279
Turbulencemodel The continuity equations of continuous (c) and dispersed (d)
The standard k–e model was used to model turbulence. This phaseare
model belongs to a group of Reynolds averaged Navier–Stokes @a r =@tþrUð@a r v Þ¼0 ð10Þ
equation models. The instantaneous velocity in the momentum c c c c c
equation is divided into the average and fluctuating part @a r =@tþrUð@a r v Þ¼0 ð11Þ
d d d d d
u¼v +v0. Then the momentum equation is ensemble averaged
m
and the resulting term (cid:4)r(cid:6)(rv0v0) is modeled as Themomentumequationsofphasecanddare
r(cid:6)[mt(rvm+rvmT)], where mt is the turbulence viscosity, which @ðacrcvcÞ=@tþrUðacrcvcvcÞ¼(cid:4)acrpþrU½acmc,effðrvcþrvTcÞ(cid:5)
againrequiresaclosureequation.Theclosureis þa r gþM ð12Þ
c c cd
mt¼rmCmk2=e ð6Þ @ða r v Þ=@tþrUða r v v Þ¼(cid:4)a rpþrU½a m ðrv þrvTÞ(cid:5)
Theturbulentkineticenergykandturbulentdissipationratee d d d d d d d þadr gþM d d,eff d d ð13Þ
areobtainedbysolvingtheirtransportequations d d dc
whereM ¼(cid:4)M isaforceactingonthephasecduetophasesd
@ðr kÞ=@tþrUðr v kÞ¼rU½m =s ðrkÞ(cid:5)þG (cid:4)r e ð7Þ cd dc
m m m t,m k k,m m (drag, lift, etc.), and m and m are effective viscosities
c,eff d,eff
consistingofamolecularandaturbulentviscosity
@ðrmeÞ=@tþrUðrmvmeÞ¼rU½mt,m=seðreÞ(cid:5)þe=kðC1eGk,m(cid:4)C2ermeÞ
ð8Þ mc,eff¼mcþmtcandmd,eff ¼mdþmtd
Thusunlikethemolecularviscosity,theturbulentviscosityis Onlydragandturbulencedispersionforcewereconsideredin
not a constant, but it depends on the local flow field. The term oursimulations
Gk,misaturbulenceproductionduetomeanvelocityshear. Mcd¼Mcd,DþMcd,TD ð14Þ
G ¼m½rv þðrv ÞT(cid:5): rv ð9Þ
k,m t m m m M ¼K ðv (cid:4)v Þ¼ð3=4ÞðC =dÞa r 9v (cid:4)v 9ðv (cid:4)v Þ ð15Þ
cd,D cd d c D d c d c d c
TheturbulentmodelconstantswereCm¼0.09,sk¼1,se¼1.3,
wheredisdispersedphaseparticle(bubble)equivalentdiameter.
C1e¼1.44,C2e¼1.92.
Drag coefficient was set to C ¼1.215 resulting in a bubble slip
The boundary conditions were no-slip condition on all airlift D
velocity (cid:3)0.23m/s((cid:3)5mmbubbleinwater).
walls.Standardwallfunctionwasusedtomodelavelocityprofile
in the walls vicinity and to provide inner ‘‘boundary’’ condition M ¼C K n =s ðra =a (cid:4)ra =a Þ ð16Þ
cd,TD TD cd tc tc d d c c
for Reynolds averaged velocity field. Zero liquid velocity and
whereC ¼1,K ismomentumtransfercoefficientfordragforce,
0.25m/s gas vertical velocitywere prescribed at the inlet for all TD cd
n is turbulent kinematic viscosity of the continuous phase,
phases. Gas volume fraction was then set to a constant value to tc
s ¼0.9.
obtain the desired gas flow rate into the airlift. Zero liquid tc
Twoequationk–emodelwasusedtomodelturbulenceandto
velocitywasset at theoutletboundary and zerogradients were
obtain a closure for turbulent viscosity in the continuous phase
setforgasvelocityandgasvolumefraction(userdefinedfunction
m :
wasusedtodothis).Theinitialconditionwaszeroliquidvelocity tc
and gas volume fraction, initial turbulence kinetic energy was mtc¼Cmrck2c=ec ð17Þ
k¼0.001m2/s2, and dissipation rate e¼0.0001m2/s3. The time
intervalof30swasthensimulatedtolettheflowreachasteady @ðacrckcÞ=@tþrUðacrcvckcÞ¼rU½acðmcþmtc=skÞðrkcÞ(cid:5)þacGc(cid:4)acrcec
orpseudosteadystate.Thenanother120sormoreofaflowtime ð18Þ
wassimulatedtoobtaintime-averagedquantitiesforevaluation.
The segregated pressure-based solver in Fluent was used to @ðacrcecÞ=@tþrUðacrcvcecÞ¼rU½acðmcþmtc=seÞðrecÞ(cid:5)
solvethemodelequations,nodebasedgradientoptionwasused þacec=kcðC1eGc(cid:4)C2ercecÞ ð19Þ
to evaluate variables’ gradients. PISO scheme was used as a
whereG ¼m [rv +(rv )T]:rv
pressure–velocitycouplingalgorithm,PRESTO!schemewasused c tc c c c
forpressurediscretizationandtheQUICKschemeforvelocity,gas The turbulentmodel constantswereCm¼0.09, sk¼1,se¼1.3,
volumefraction,turbulencekineticenergy,anddissipationrate.A C1e¼1.44,C2e¼1.92.
Turbulenceviscosityinthedispersedphasem wascalculated
first order implicit scheme was employed for the time td
as
discretization.
m ¼ðr =r Þm =s ð20Þ
td d c tc
4.2. CFXsimulations wheres¼1.
Theboundaryconditionswereno-slipconditionforliquidand
In addition to the simulations run in Fluent code (setup free-slipconditionforgasphaseonwalls.Zerovelocityforliquid
described in Section 4.1), some simulations were later recalcu- and0.25m/sforgasphasewereused.Thevolumefractionofgas
latedinCFX12.1usingEuler–Eulertwo-fluidmodel.Theirsetup phase was set to obtain the desired value of gas flow rate. The
isdescribedinthissection.Unlikethemixturemodel,thismodel ‘‘degassing’’conditionwasusedattheoutlet—liquidvelocityisto
solves continuityand momentumequation for eachphase. Thus zero,whilethegasphaseisallowedtoescape.
for a two phase flow there are two continuity and two momen-
tumequations,onesetforcontinuousphasecandonefordispersed
phased.Thetwomomentumequationsarecoupledtogethervia 5. Results
pressure (pressure field is shared by both phases), and via
interphase force terms, which accounts for various forces (drag, The results section has two main parts. Auxiliary simulation
lift, added mass, turbulent dispersion force, and others) and resultsarepresentedinSection5.1.Thefirstpartconsistsofgrid
cancel each other out when momentum equations of individual independence test result, brief comparison of few simulations
phasesareaddedtogether.Dragforceandturbulencedispersion with different turbulence models for a selected airlift configura-
force were accounted for in our CFX simulations. Other forces tion, and finally a comparison of two different closures for the
werenotconsidered. drag force. All of the simulation results discussed in Section 5.1
M.Sˇimcˇ´ıketal./ChemicalEngineeringScience66(2011)3268–3279 3273
0.9 0.08
0.8 0.07
0.7
0.06
0.6
0.05
s) 0.5
L (m/ 0.4 α (-) 0.04
V
0.03
0.3
0.02
0.2
0.1 Tomiyama drag 0.01 Tomiyama drag
Schiller-Naumann drag Schiller-Naumann drag
0 0
0 0.02 0.04 0.06 0.08 0 0.02 0.04 0.06 0.08
UG (m/s) UG (m/s)
0.007
Tomiyama drag
0.006
Schiller-Naumann drag
0.005
0.004
α (-)
0.003
0.002
0.001
0
0 0.02 0.04 0.06 0.08
UG (m/s)
Fig.3. CaseAsimulationresults(Section5.1).Comparisonoftwodragclosuresfor5mmbubbles:Tomiyama(blackmarks,Eq.(4a))andSchiller–Naumann(whitemarks,
Eq.(4b)).(a)RiserliquidinterstitialvelocityVL,(b)risergasholdupa,and(c)downcomergasholdupavs.risergassuperficialvelocityUG.
wereobtainedfrommixturemodelsimulationsdoneinFluent6.3 Fouradditionalturbulencemodelsinadditiontostandardk–e
(seeSection4.1forsimulationsetup).Themainsimulationresults modelweretestedforthecaseC,withgasflowrate3.6l/minprior
andtheircomparisonwithexperimentallymeasureddata(liquid to the main simulation campaign. These four models were RNG
interfacialvelocityandgasholdupintheriserandinthedown- k–emodel,RNGk–emodelwithswirlmodificationforturbulence
comer)arepresentedinSection5.2.Theresultsforbothsimula- viscosity,realizablek–emodelandstandard(notSST)k–omodel.
tion setups (Fluent, CFX) are presented. In experiments, there Themodelsarenotdescribedinthispaperandreaderisreferred
were higher liquid velocities in the downcomer for the larger to Fluent’s 6.3 User Guide (Fluent Inc. 2006) for details about
diameterriser(caseB)(lowerdowncomercrosssectionarea)and thesemodels(simulationswererunwithdefaultsolversettings).
thus gas phase was entrained into the downcomer. If cases A Thechoiceofthementionedturbulencemodelshadonlyaminor
(shorterdrafttube)andC(longerdrafttube)arecompared,then impact on results of the simulations. The largest difference
forthelongertubethegasseparationwasbetterresultinginno betweenstandardk–emodelresultsandtheothermodelresults
gas in the downcomer, while for the shorter draft tube (case A) was1.4%forinterstitialliquidvelocityand4.9%forgasholdupin
bubbles were entrained into the downcomer for the highest gas riser on ‘‘coarse grid’’ and 1.7% and 4.9% on the coarse grid,
flowrate. respectively.Standardk–emodelwasthenkeptforallsubsequent
simulations.Thisturbulencemodeltestwasdonebecauseofour
previous experience with the simulation of a partially aerated
5.1. Auxiliarysimulationresults rectangular bubble column, where a strong influence of these
turbulence models was observed (qualitatively different flow
The grid independence test was done for the case C fields,3(cid:2) lowerturbulentviscositypredictedbytheRNGmodel
(1400(cid:2)62cm riser) with riser air superficial velocity 2cm/s if compared to standard k–e). However, the choice of the turbu-
(3.6l/min). One simulation (Fluent) was run on a refined ‘‘fine’’ lence model had only a minor impact on the airlift simulation
grid with8(cid:2) more grid cells than in the standard ‘‘coarse’’ grid resultspresentedinthispaper.
case (357,600 vs. 44,700 cells). The difference in the liquid Different closures for drag coefficient were tested on cases A
interstitial velocity and gas holdup in the riser was within 1%. and C to test the effect of changing the bubble slip velocity on
Thusitcouldbeconcludedthatthestandardgridwassufficientto simulation results. Tomiyama closure for drag (4) for a single
obtaingridindependentresults. bubble (5mm equivalent diameter) and Schiller–Naumann
3274 M.Sˇimcˇ´ıketal./ChemicalEngineeringScience66(2011)3268–3279
closure for 5mm bubble were compared for case A, and 1
Tomiyama closure for 3 and 5mm bubble were compared for
case C. Simulations were done for five gas flow rates in range 0.9
1.9–13.6l/minforbothcaseAandcaseC.
Case A comparison between the drag closures is shown in 0.8
Fig.3a–c(riserliquidinterstitialvelocityandriseranddowncomer
0.7
gas holdup vs. gas flow rate). We are aware that the Schiller–
Naumannclosureisvalidonlyforrigidspheres,whichiscertainly
0.6
notthecaseof5mmairbubbleinwater.However,theaimofthis s)
m/
comparison was only to examine an influence of changing a slip 0.5
velocity of bubbles on simulation results. The Tomiyama closures L (
V
resulted in bubble slip velocities (riser volume average) in range 0.4
22.2 to 22.9cm/s depending on the gas flow rate (was lower for
0.3
highergasflowrates).TheSchiller–Naumannslipvelocitywasfrom
37.6to38.6cm/s,thus (cid:3)70%higher.Nevertheless,eventhisrather
0.2
bigdifferenceinslipvelocitiesdidnotcauseverysignificantchanges Tomiyama drag, 5mm bubbles
in simulation outputs. The relative difference between the gas 0.1 Tomiyama drag, 3mm bubbles
holdupsinriserwasfrom11.2%to15.8%andwasdecreasingwith
increasing gas flow rate (maximum absolute holdup difference 0
between the two closures was 0.8%). The reason for this is the 0 0.02 0.04 0.06 0.08
UG (m/s)
co-currentflowofliquidandgasphasesintheriser.Thegasholdup
in the riser is given by a ¼U /V , where U is gas superficial
G G G G
velocitygivenbyairflowrateintotheairliftandV isgasinterstitial
G
velocityintheriser,whichisV ¼V +V .Theeffectofchangingthe 0.08
G L slip
bubble slip velocity V on the holdup in the airlift riser is then
slip
smaller then it would be in a case of bubbles rising through a 0.07
stagnantliquid(V ¼0),becausetheliquidvelocityV intheriseris
L L
relativelyhighifcomparedtobubbleslipvelocityV .Thesituation
slip 0.06
would be different in the downcomer, where the phases flow
countercurrently and the slip velocity value could have significant
0.05
impactonthedowncomerandalsothewholeairlifthydrodynamics.
Therewaseffectivelyzerogasholdupinthedowncomerforallcase
A gas flow rates except for the highest one with Tomiyama drag α (-) 0.04
correlation, when the gas just started to be entrained into the
downcomer, and the downcomer holdup was (cid:3)8% of the riser 0.03
holdup.The difference betweenliquidinterstitialvelocitiesforthe
two drag coefficient correlations was from 1.6% to 8.5% and was
0.02
decreasingwithincreasingofthegasflowratewithasharperdrop
of this difference for the highest gas flow rate, where the driving Tomiyama drag, 5mm bubbles
0.01
force for liquid circulation was decreased by the small amount of
Tomiyama drag, 3mm bubbles
gasentrainedintothedowncomer(Tomiayamacorrelationcase).
Case C comparison between simulations assuming 3 and 5mm 0
diameter bubbles is shown in Fig. 4a and b. Tomiyama drag 0 0.02 0.04 0.06 0.08
correlationwasusedforboth.Theresultingvolumeaveragedbubble UG (m/s)
slipvelocitiesintheriserwerefrom19.4to20.0cm/s(3mmbubble)
Fig.4. CaseCsimulationresults(Section5.1).Tomiyamadragclosure(Eq.(4a))
and from 22.3 to 23.0cm/s (5mm bubble). There was only a very
resultsfor3mm(whitemarks)and5mmbubble(blackmarks).(a)Riserliquid
small difference between 3 and 5mm bubble simulations. The
interstitialvelocityVL,(b)risergasholdupvs.risergassuperficialvelocityUG.
reasonsforthisarethesameasdescribedinthepreviousparagraph.
Therelativedifferencebetweengasholdupsintheriserwasfrom2.2%
to3.5%,anditwasfrom0.6%to1.8%fortheriserliquidinterstitial shownforcaseAandcaseC,simulationsofcaseBweredoneonlyin
velocity.Again,thedifferencewasdecreasingwithincreasingofgas Fluent.Bothsetups(Fluent,CFX)gaveverysimilarresults.Although
flowrate.Therewasnogasinthedowncomer. there was a difference in their results in the radial gas holdup
It could be concluded that if the gas phase is present only in profile,ithadonlyaminorimpactontheglobalholdupandvelocity
theriserandnotinthedowncomer,thentheimpactofabubble values. In Fluent simulations the gas holdup radial profile was
slipvelocitychangeisnotsosignificantduetoco-currentflowof almostcompletelyflat,whileinCFXsimulationstherewasarelative
both phases. However, if the gas phase is rising through a difference of 13% between the riser axis and the riser wall value.
stagnantliquidorevenifthephasesareflowingcountercurrently Thiswasduetothestrongerturbulentdispersionprescribedinthe
(downcomer), then, of course, this impact can be much more Fluentsimulationsetup (s,Eq. (3)). Theliquid velocity profilesin
t
significant. CFXandFluentsimulationsweresimilar,withrelativedifferencein
themaximalvelocity o3%(caseA,UG¼7.5cm/s).Nevertheless,as
alreadypointedout,theglobalvaluespredictedbyCFXandFluent
5.2. Mainsimulationresults—comparisonwithexperiments simulationswerealmostthesame.
Gasflowratesinthesimulationswerefrom1.9to13.6l/min
Simulationresultsforthethreeairliftconfigurations(casesA,B (1.05–7.51cm/s gas superficial velocity based on riser cross
andC)andtheircomparisonwithexperimentallymeasureddataare section) for case A and C, and from 1.9 to 26.8l/min (0.53–
presentedinthissection.BothFluentandCFXsimulationresultsare 7.51cm/s)forcaseB.
M.Sˇimcˇ´ıketal./ChemicalEngineeringScience66(2011)3268–3279 3275
1.0 0.25
0.9
0.8 0.20
0.7
s) 0.6 s) 0.15
m/ 0.5 m/
L ( L (
V 0.4 V 0.10
0.3
0.2 simulation Fluent 0.05 simulation Fluent
simulation CFX simulation CFX
0.1
experiment experiment
0.0 0.00
0 0.02 0.04 0.06 0.08 0 0.02 0.04 0.06 0.08
UG (m/s) UG (m/s)
0.12 0.07
simulation Fluent
0.10 0.06 simulation CFX
experiment
0.05
0.08
0.04
α (-) 0.06 α (-)
0.03
0.04
0.02
simulation Fluent
0.02
simulation CFX 0.01
experiment
0.00 0.00
0 0.02 0.04 0.06 0.08 0 0.02 0.04 0.06 0.08
UG (m/s) UG (m/s)
Fig.5. CaseAsimulationsvs.experiments(Section5.2).Fluentsimulations(blackmarks),CFXsimulations(stars),experiments(whitemarks).(a)Riserliquidinterstitial
velocityVL,(b)downcomerliquidinterstitialvelocityVL,(c)risergasholdupa,and(d)downcomergasholdupavs.risergassuperficialvelocityUG.
from experiments as a function of gas flow rate are shown in
Fig. 5a–d. Gas holdup fields for different gas flow rates can be
seen in Fig. 6. A very good agreement was obtained for liquid
interstitial velocity. The relative difference between simulations
(Fluent) and experiments was from 0.7% to 4.4% and it was
increasing with gas flow rate. The Fluent and CFX simulations
alsoagreedverywellwitheachotherwithCFXpredictingslightly
lowervalues.Thesituationwasworseinthecaseofgasholdup.
Simulations strongly underpredicted gas holdup in the riser
(30% relative difference for the highest gas flow rate), and also
inthedowncomer,wherethemoment,whenbubblesarestarting
to be entrained into the downcomer was shifted to higher gas
flowratesinsimulations.Thegasholdupfromsimulationsinthe
downcomerforthehighestgasflowratewaslessthan1/10ofthe
experimentally obtained value. If a gas interstitial velocity is
estimatedfromV ¼U /a ,whereU isthegassuperficialvelocity
G G G G
givenbygasflowrate,anda istheexperimentallymeasuredgas
G
holdup, then for the highest gas flow rate the V would be
G
(cid:3)74cm/s, which is actually lower than the measured and
simulated liquid velocity and would result in a negative bubble
Fig. 6. Case A simulations (Section 5.2): Gas holdup fields for gas flow rates
1.9, 3.6, 4.5, 9.1 and 13.6l/min (riser gas superficial velocity (cid:3)1.0, 2.0, 2.5, 5.0, slip velocity, which is of course not possible. The reason of the
7.5cm/s). discrepancybetweensimulationandexperimentisthenprobably
duetotheexperimentalmethodusedtoobtainestimatesofgas
5.2.1. CaseA holdups. Holdup estimates measured with U-tube manometers
Liquidinterstitialvelocitiesandgasholdupsintheriserandin canbenegativelyinfluencedbyapressuredropduetoflow.This
thedowncomerobtainedfromsimulations(FluentandCFX)and willbediscussedattheendofSection5.2.
3276 M.Sˇimcˇ´ıketal./ChemicalEngineeringScience66(2011)3268–3279
0.8 0.50
0.7 0.45
0.40
0.6
0.35
0.5
VL (m/s) 00..34 VL (m/s) 000...223050
0.15
0.2
0.10
simulation
0.1 simulation
experiment 0.05 experiment
0.0 0.00
0 0.02 0.04 0.06 0.08 0 0.02 0.04 0.06 0.08
UG (m/s) UG (m/s)
0.16 0.14
0.14 0.12
0.12
0.10
0.10
0.08
α (-) 0.08 α (-)
0.06
0.06
0.04
0.04
0.02 simulation 0.02 simulation
experiment experiment
0.00 0.00
0 0.02 0.04 0.06 0.08 0 0.02 0.04 0.06 0.08
UG (m/s) UG (m/s)
Fig. 7. Case B simulations vs. experiments (Section 5.2): fluent simulations (black marks), experiments (white marks). (a) Riser liquid interstitial velocity VL,
(b)downcomerliquidinterstitialvelocityVL,(c)risergasholdupa,and(d)downcomergasholdupavs.risergassuperficialvelocityUG.
5.2.2. CaseB
The results are shown in Fig. 7a–d (gas holdups and liquid
interstitialvelocities)andinFig.8(simulatedgasholdupfields).
ThiscaseBisinteresting,because threedifferentbubblecircula-
tion regimes were experimentally observed with the change of
thegasflowrate.Atfirst,forthelowestgasflowrate,therewere
no gas bubbles inside thedowncomer.Then for higherrates the
bubbles started to be entrained into the downcomer, but the
bubble front did not reach the downcomer bottom yet. And
finally,forthehighestgasflowrate,thefrontreachedtheairlift
bottom and bubbles started to circulate with a corresponding
change of interstitial liquid velocity and gas holdup vs. gas flow
rate curve trends. Now the question was if our simulations are
able to capture this behavior. The answer is that they can, but
only partially. There was an initially good agreement in liquid
Fig.8. CaseBsimulations(Section5.2):instantaneousgasholdupfieldsforgas
interstitialvelocities.Thedifferencebetweenthesimulationand
flowrates1.9,3.6,4.5,9.1,13.6,17.9and26.8l/min(risergassuperficialvelocity
theexperimentforthelowestexperimentallymeasuredgasflow (cid:3)0.5,1.0,1.3,2.6,3.8,5.0,7.5cm/s).
ratewas o3.5% and it wascontinuallyincreasing withgas flow
rate.Itwas8.5%forthesecondhighestflowrate,whichisstillok.
Butforthehighestflowrate,wheretherewasasteeperriseofthe simulations and there appeared no bubble circulation regime
experimentally measured liquid velocity due to the regime evenforthemaximalgasflowrate.Theliquidinterstitialvelocity
change, the experiment/simulation difference was 46%. Gas didnotchangemuchwithanincreaseinthegasflowrateinthe
holdup in the riser and in the downcomer and also the point at simulations, except for the lower rates (only 6.2% increase from
which bubbles start to enter the downcomer was captured very gas flow rate 4.5–26.8l/min). The liquid superficial velocity in
well. However, the agreement for the highest gas flow rate was simulations (and thus a total circulating liquid flow rate), was
badagain.Thebubblefrontdidnotreachtheairliftbottominthe even decreasing with gas flow rate. The reason was that the
M.Sˇimcˇ´ıketal./ChemicalEngineeringScience66(2011)3268–3279 3277
driving force for the liquid circulation, the difference between governing equations of the flow. In our simulations the bubble
average holdups in the riser and in the downcomer, was slowly sizewasprescribeddirectly(5mmforallflowrates,allbubbles
decreasingwithgasflowratefromacertainpoint(Q ¼4.5l/min, assumedtohaveasamesize).Theweakpointofoursimulations
G
U ¼1.26cm/s),whilethegasholdupsintheriserandthedown- and the cause of disagreement between simulations and experi-
G
comerwererisinglinearly.Theabsolutedifferencebetweenthem ments can be any of the above mentioned issues, probably the
(riser/downcomer)was1.7%atQ ¼4.5l/min(U ¼1.26cm/s)and specificationofbubblesizeand/ortheslipvelocityadjustmenton
G G
1.2%at26.8l/min(U ¼7.51cm/s).Theliquidsuperficialvelocity thelocalgasholdup.Althoughmeasurementsofbubblesizewere
G
in theriserdropped from34.6 to 32.3cm/s inthis gasflow rate donewithahighspeedcamera,theycouldbedoneonlyforvery
rangeinsimulations. lowgasflowrates.Thebubblylayersoonbecameopaqueasthe
ForcaseBsimulations,therewasaverygoodagreementwith holdupincreased.Nevertheless,ifextrapolatedforthehigherflow
experiments for low gas flow rates. The deviation from experi- rates,andtakingintoaccounttheweakdependencyofthebubble
mentsthenstartedtoincreaseslowlywithgasflowrateandthen risevelocityonthebubblediameterinrangeofbubbleequivalent
itrosesuddenlyforthehighestgasflowratewiththeonsetofa diameters cca 4–10mm (see e.g. Jamialahmadi et al., 1994), our
bubble circulation regime, which was not captured by the assumptionwasthatthe5mmfixedbubblesizecanreasonably
simulations. As it was pointed out earlier, flow in a downcomer well represent the typical bubble slip velocities encountered in
(countercurrentflow)isinfluencedbyabubbleslipvelocitymuch theairlift.Whenthebubbleswereentrainedintothedowncomer,
morethanaflowinariser(co-current).Demandsontheaccuracy thisassumptionwasprobablytoocrude.
ofdragforceclosurearethenquitehighifbubblesarepresentin
the downcomer. Drag coefficient and bubble slip velocity for
givenfluidsdependonbubblesize,shapeandonlocalgasholdup 5.2.3. CaseC
(andotherfactorssuchasapresenceofsurfactants).Toobtaina Simulations (Fluent and CFX) and experiments of case C are
correctbubbleslipvelocity(a)areliableclosureequationforitis compared in Fig. 9a–c. Gas holdup fields for different gas flow
neededand(b)correctinputsintothisclosurearerequired.Our rates can be seen in Fig. 10. A good simulation/experiment
closurewasEq.(3).Abubblesizecanbeeitherprescribeddirectly agreement was obtained for liquid interstitial velocity. The
or it can be a result from a bubble coalescence/break-up model relativedifferencebetweensimulations(Fluent)andexperiments
solution. The local gas holdup is then provided by solving variedfrom4.6%to8.3%.Andagain,asforthecaseA,theFluent
1.0 0.25
0.9
0.8 0.20
0.7
s) 0.6 s) 0.15
m/ 0.5 m/
L ( L (
V 0.4 V 0.10
0.3
0.2 simulation Fluent 0.05 simulation Fluent
simulation CFX simulation CFX
0.1
experiment experiment
0.0 0.00
0 0.02 0.04 0.06 0.08 0 0.02 0.04 0.06 0.08
UG (m/s) UG (m/s)
0.08
0.07
0.06
0.05
α (-) 0.04
0.03
0.02
simulation Fluent
0.01 simulation CFX
experiment
0.00
0 0.02 0.04 0.06 0.08
UG (m/s)
Fig.9. CaseCsimulationsvs.experiments(Section5.2):fluentsimulations(blackmarks),CFXsimulations(stars),experiments(whitemarks).(a)Riserliquidinterstitial
velocityVL,(b)downcomerliquidinterstitialvelocityVL,and(c)risergasholdupavs.risergassuperficialvelocityUG.