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Effects of reducing the reactor diameter on thedense
gas–solid fluidization of very heavyparticles: 3D
numerical simulations
Renaud Ansart, Florence Vanni, Brigitte Caussat, Carine Ablitzer, Méryl
Brothier
To cite this version:
Renaud Ansart, Florence Vanni, Brigitte Caussat, Carine Ablitzer, Méryl Brothier. Effects of
re-ducing the reactor diameter on thedense gas–solid fluidization of very heavyparticles: 3D numerical
simulations. Chemical Engineering Research and Design, Elsevier, 2016, vol. 117, pp. 575-583.
�10.1016/j.cherd.2016.11.008�. �hal-01413039�
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Eprints ID : 16724
To link to this article : DOI:10.1016/j.cherd.2016.11.008
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http://dx.doi.org/10.1016/j.cherd.2016.11.008
To cite this version : Ansart, Renaud and Vanni, Florence and
Caussat, Brigitte and Ablitzer, Carine and Brothier, Méryl Effects of
reducing the reactor diameter on thedense gas–solid fluidization of
very heavyparticles: 3D numerical simulations. (2016) Chemical
Engineering Research and Design, vol. 117. pp. 575-583. ISSN
0263-8762
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Effects
of
reducing
the
reactor
diameter
on
the
dense
gas–solid
fluidization
of
very
heavy
particles:
3D
numerical
simulations
Renaud
Ansart
a,∗,
Florence
Vanni
a,b,
Brigitte
Caussat
a,
Carine
Ablitzer
b,
Méryl
Brothier
caLaboratoiredeGénieChimique,UniversitédeToulouse,CNRS,INPT,UPS,Toulouse,France
bCEACadaracheDEN,DEC/SFER,LaboratoiredesCombustiblesUranium,F-13108Saint-PaulLezDurance,France cCEAMarcouleDEN,DTEC/SECAServiced’EtudedesCombustiblesetmatériauxàbased’Actinides,F-30207 BagnolssurCèze,France
Keywords:
Fluidization CFDsimulation
Verydenseparticlessuspension Euler–Eulermodeling
Microfluidizedbed
Inthisstudy,3DnumericalsimulationsusinganEuleriann-fluidapproachofagas–solid fluidizedbedcomposedofverydenseparticlesoftungsten(19,300kgm−3)werecarried outtoexaminethebehaviorofthissuspension,especiallytheeffectsofthereductionof thefluidizationcolumndiameteronthefluidizationquality.Tungstenwasselectedasa surrogatematerialofU(Mo)(Uraniummolybdene)whichisofinterestfornewnuclearfuels withlimitedenrichment.Comparisonsbetweenexperimentsandcomputationsfortheaxial pressureprofileofa5cmdiametercolumndemonstratethecapabilityofthemathematical modelsoftheNEPTUNECFDcodetosimulatethefluidizationofthispowderlocated out-sidetheclassificationofGeldart.Thenumericalresultsshowthatthemobilityintothebed oftheseverydenseparticlesisverylow.Thereductionofthefluidizationcolumn diam-eterfrom5cmto2cmdoesnothavesignificanteffectonthelocalsolidcirculationbut stronglydecreasestheaxialandradialmixingoftheparticlesduetowall-particlesfriction effects.Theseresultsconfirmandallowtobetterunderstandthewalleffectsexperimentally evidenced.
1.
Introduction
Gas–solidfluidized beds (FB) are widely used in industrial applicationssuchasdrying,coalcombustion(Basu,1999)and gasification (Hofbauer et al., 2002), oilrefining and nuclear application(KuniiandLevenspiel,1991).Thisisduetothefact thatFBreactorshaveexcellentheatandmasstransfer capa-bilities,highthroughputrates,andcanoperatecontinuously, thusreducingoperatingcosts(YdstieandDu,2011;Liuand Xiao,2014).
Inthe nuclearfield,newfuels,withlimited enrichment in235U,areunderdevelopmentforresearchreactors.U(Mo)
∗ Correspondingauthor.
E-mailaddress:renaud.ansart@ensiacet.fr(R.Ansart).
(Uraniummolybdene)fuelpowdersdispersedinanaluminum matrix are among the most promising materials. But the coating ofU(Mo)byabarriermaterialisnecessarytolimit interfacialinteractionsbetweenthefuelanditsmatrixunder irradiation(Mazaudieretal.,2008).Siliconseemstobeagood candidate (Zweifel et al., 2013). Amongother technics, the FluidizedBedChemicalVaporDepositionprocess(FB-CVD)is understudytodeposituniformsiliconlayersonU(Mo) parti-cles(Vannietal.,2015a).FB-CVDisanefficienttechnologyto uniformlycoatpowdersbyagreatvarietyofmaterials(Vahlas etal.,2006).Thereisaninterestinbeingabletotreatweights ofU(Mo)aslowaspossiblebytheFB-CVDprocess.Itisto
Nomenclature
Romansymbols
Ar Archimedenumber(−)
dp particlediameter(m)
ec particle–particlenormalrestitutioncoefficient
(–)
g gravitationalconstant(ms−2)
mp particlemass(kgm−3)
P meangaspressure(Nm−2) q2
p randomkineticenergy(m2s−2) Uk,i meanvelocityofphasek(ms−1) Umf minimumfluidizationvelocity(ms−1)
uk,i fluctuatingvelocityofphasek(ms−1)
Vf superficialgasvelocity(ms−1) Greeksymbols
˛k volumefractionofphasek(–)
g gasviscosity(kgm−1s−1) k densityofphasek(kgm−3) p granulartemperature(kgm−2s−2) Subscripts g gas p particle
benotedthatforpreliminaryexperimentsatungstenpowder (19,300kgm−3,75mofmediandiameter)whoseproperties areveryclosetothoseofU(Mo)(17,500kgm−3,50mmedian diameter)hasbeenusedasasurrogatepowder.Both pow-dersareofveryhighdensity.Themaximumdimensionless densityis10,000intheGeldart’sclassification,butthe dimen-sionlessdensityofthetungstenparticlesclearlyexceedsthe upperlimit(Fig.1).Firstexperimentshavedemonstratedthat theFB-CVDtechnologycanuniformlycoat1,500goftungsten powderwithsiliconinareactorof3.8cmindiameter.Other experimentshaveshownthatthisweightcannotbedecreased inthereactorof3.8cmbecausethetargetdeposition temper-ature(650◦C)cannotbereachedsinceheatexchangebetween thereactorwallsand thebed ofparticles becomestoolow (Vannietal.,2015a).
Anexperimentalstudyhasbeenconductedinglassand steelcolumnstospecificallyanalyzetheimpactofdecreasing
Fig.1–Representationofthetungstenparticleswitha diameterof75minGeldart’sclassificationmodifiedby
Yang(2007).
thereactordiameterfrom5to2cmonthefluidization hydro-dynamicsofthetungstenpowder(Vannietal.,2015b).Itwas foundthatuniformsilicondepositioncouldonlybeachieved ifthefluidizedbedhydrodynamicswasofgoodquality,i.e.if itinvolveshighthermalandmasstransferratesbetweenthe gasandthesolidphases.Thisexperimentalstudyhasshown thatwalleffectsdecreasingthequalityofbedhydrodynamics appearinthereactorof2cmfor100gand 180gofpowder. Thiswasevidencedbyanincreaseofthehystereticbehavior ofthepressuredropcurves,anincreaseoftheminimum flu-idizationvelocityandadecreaseofthebedvoidage.Thiswas especiallyevidentinaglasscolumnwheretheelectrostatic effectscannotbeneglected(Vannietal.,2015b).
Theaimofthepresentstudyistocomplementthe exper-imentalworkbyusing3Dnumericalsimulationstoanalyze more precisely the influence of a decrease of the reactor diameteronsomekeylocalparametersofthefluidizedbed hydrodynamics.Theresultsareexpectedtobehelpfulinthe FB-CVDprocessdesignandinthechoiceofitsoptimalgas flowparameters.
Very few studies are available in the literature about the numerical simulation of fluidized beds involving such denseparticles.For UO2 particles of2mmindiameter,Liu
et al. (2015a) studied the impact of particle density up to 10,800kgm−3 on the fluidization behavior of particles in spoutingbedusing2DCFD-DEMcoupling.Theparticlecycle time,spoutbehavior,dominantspoutfrequencyandgas–solid contact efficiency was discussed and a flow pattern map under different densities and different gas velocities was obtained.Pannalaet al.(2007)alsostudiedconicalspouted bedwithheavyparticles(upto6,050kgm−3zirconiaparticles fornuclearfuelcoaters)by2-DEulerian–Euleriannumerical simulations.
Miniaturizationofchemicalreactors,whichisoneofthe most popular research areas inchemical engineering, has led to the concept of micro-fluidized bed reactors (Wang et al., 2011). Wang et al. (2011) haveshown byCFD simu-lations that for Geldart A particles, the onset of turbulent fluidizationisadvancedsignificantlyinmicrofluidizedbeds.
ZivkovicandBiggs(2015)pointedouttheimportanceofwall surfaceforcesrelativetovolumetricforces,suchasgravity, onmicro-scalefluidizedbeds(thecross-sectionaldimensions ofthemicrochannelswere 400×175m2). Liuetal.(2015b)
performed several 2D Eulerian–Eulerian numerical simula-tionsforagas–solidmicro-fluidizedbed(channelwidth3mm) for Geldart A particles (53m and 1,400kgm−3) and com-pared the predicted minimum bubbling velocity and bed voidagetoexperimentalmeasurements.Theyusedveryfine meshes(ofapproximately oneparticlediameter).Using the Gidaspow drag model, their simulations have shown that thepredictedminimumbubblingvelocitiesweresignificantly lowerthan theirexperimentaldata(Liuetal.,2015b).Wang and Fan (2011) have established a flow regime map from experimental results obtained in column diameters start-ing from 0.7mm to 5mm in size for FCC particles. Their results revealed an increase in the minimum fluidization andbubblingvelocitiescomparedtothoseinlarge-scale flu-idized beds. To the best of our knowledge, no numerical work has been reported concerning reduced diameter flu-idizedbedsofheavyparticles,whicharestudiedinthepresent article.
Theexperimentalfluidizationset-upwillbefirstpresented beforedetailingthenumericalmodelandpresentingand dis-cussingtheresultsofthesimulation.
Table1–Particlepropertiesandparticlesizedistribution characteristicsofthetungstenparticlesobtainedwitha MalvernMasterSizerSirocco2000indrymode.
Meandiameter Value(m)
d3/2 70 d10 50 d50 75 d90 105 Density Value(kgm−3) Particle 19,300 Bulk 9,600 Umf(Thonglimpetal.,1984) 3.2cms−1
Fig.2–Schematicoftheexperimentalsetup.
2.
Experimental
set
up
Theexperimentalsetupiscomposedofthreesteelcolumns of1mheightand5,3and2cmofinnerdiameter(Vannietal., 2015b).AllareequippedwithasimilarInoxporousplate dis-tributor(PoralTM40).Thetungstenpowderused(CERAC,Inc.
T-1220)issuppliedbyNeyco.Itsgraindensity isclaimedto be19,300kgm−3.TheParticleSizeDistributioncharacteristics ofthepowderaresummarizedinTable1withitsbulk den-sity.Theexperimentswereconductedatambienttemperature usingargonasthefluidizinggas.Itsflowratewascontrolled byamassflowcontroller(AeraFC-7710C0,0-20slm).A dif-ferentialfastresponsepressuresensor(GEDruckLPX5380), withtapsunder the distributor andon top ofthecolumn, wasusedtomeasurethetotalpressuredropacrossthebed anddeterminetheminimumfluidizationvelocity.Threeother pressuresensorsweresetonthe5cmcolumnat0cm,3cm and4.5cmabovethedistributortomeasuretheaxialpressure profile(Fig.2).Thesamplingrateforpressuremeasurementis 2Hzandthetime-averagesarerealizedduring2min.
3.
Numerical
simulation
description:
Euler
n-fluid
approach
Three-dimensional numerical simulations are carried out using the code NEPTUNECFD. This Eulerian n-fluid
unstructuredparallelizedmultiphaseflowsoftwarehasbeen developedintheframeworkoftheNEPTUNEproject finan-ciallysupportedbyCEA(Commissariatàl’EnergieAtomique et aux énergies alternatives), EDF (Electricite de France), IRSN(InstitutdeRadioprotectionetdeSuretéNucléaire),and AREVA-NP (Méchitouaet al., 2003). Themodeling approach forpoly-dispersedfluid-particleflowsisimplementedbythe InstitutdeMécaniquedesFluidesdeToulouse(IMFT)inthe NEPTUNE CFDV1.08version.Thenumericalsolverhasbeen developedforHighPerformanceComputing(Neauetal.,2010, 2013).
3.1. Mathematicalmodels
The Eulerian n-fluid approach used is a hybrid method (MoriokaandNakajima,1987)inwhichthetransport equa-tions are derived by phase ensemble averaging for the continuousphaseandbyuseofthekinetictheoryofgranular flowssupplementedbyfluideffectsforthedispersedphase. Themomentumtransferbetweengasandparticlephasesis modeled using the draglaw ofWenand Yu (Wenand Yu, 1965),limitedbytheErgun(Ergun,1952)equationfordense flows (Gobinet al., 2003;Fede et al., 2016). The collisional particle stresstensor isderivedinthe frameofthe kinetic theoryofgranularmedia(Boëlleetal.,1995).Inthepresent studythegasflowequationsaretreatedaslaminarbecause thegasReynoldsstresstensorinthemomentumequationis negligiblecomparedtothedragterm.Forthesolidphase,a transportequationforthe particlefluctuantkineticenergy, q2
p,issolved. Accordingtothe largeinertiaoftheparticles
and to thelow inelasticityofparticles (ec=0.9), the spatial
correlationbetweenneighboringparticlefluctuantvelocities willremainnegligible(Fox,2014;Fevrieretal.,2005;Simonin etal.,2002).Theparticlefluctuatingmotionmaybeassumed spatiallyuncorrelatedobeyingthesocalledmolecularchaos assumptionsothattheproductoftheparticlemassand par-ticle fluctuantkinetic energympq2p canbe identifiedto the
granulartemperaturepdefinedinspatialgranularflow
the-ories(LunandSavage,1986).
The gas–particle turbulent correlation is negligible.The effectsoftheparticle–particlecontactforceintheverydense zoneoftheflowaretakenintoaccountintheparticlestress tensor by the additionalfrictionalstress tensor (Srivastava and Sundaresan,2003).AlltheequationsoftheEuler–Euler approacharedetailedinFotovatetal.(2015).
3.2. Numericalparameters
3.2.1. Geometry
Thereferencefluidizedbedisacolumnof5cmindiameter and40cminheightwithaconicalportionatitstopend.The influenceofthe columndiameterreductionisanalyzedby comparisonwithcolumnsof3and2cmindiameterandof similarheight.
3.2.2. Mesh
The3Dreferencemesh(Fig.3)iscomposedof277,635 hexa-hedra,basedonO-gridtechniquewith50cellsonthecolumn diameterandapproximatelyx=y≈1mmandz=1.9mm.
Itisnoteworthythatafinermesh,refinedof1.5ineachspace direction,hasbeentestedbutnomeshrefinementeffectwas observedonthebedheightandonthetime-averagedradial profilesofsolidvolumefraction,solidvelocityandsolidtime variancevelocity.
Fig.3–3Dmeshforthenumericalsimulationwith277,635 cells.
Table2–Phases’propertiesusedforthesimulation.
Parameters Value
Gasdensity(Argon) 1.6kgm−3 Gasviscosity 2.23×10−5Pas Particlediameter 70m Particledensity 19,300kgm−3
The meshes for the 3 and 2cm column diameter have exactlythesamenumberofcellsandwereobtainedby apply-inghomothetictransformation.
3.2.3. Phaseproperties
Theflowiscomposedoftwophases:gas(argon)andtungsten particles.Thephases’propertiesaresummarizedinTable2. The particles are assumed to be spherical with a mono-dispersediameterequaltotheSauterdiameter.Theauthors havetestedsimulationswiththemediandiameterbut dis-crepancywithexperimentalresultswereobservedespecially forthepredictionoftheminimumfluidizationvelocity.
3.2.4. Boundaryconditions
Atthebottom(z=0),thefluidizationgridisaninletforthegas withanimposeduniformsuperficialvelocity(Vf)
correspond-ingtothefluidizationvelocityandawallfortheparticles.At thetopofthefluidizedbed,afreeoutletforbothgasand par-ticlesisdefined.Thewall-typeboundaryconditionisno-slip forthegasandfortheparticles(Fedeetal.,2016).
3.2.5. Initialconditions
ThesolidmassesusedineachcolumnaredetailedinTable3. Theycorrespondtoaratiobetweenthefixedbedheightand thecolumndiameterH0/Dcloseto3.
3.2.6. Simulationprogress
Thenumericalsimulationshavebeenperformedonparallel computerswith20cores.Anumericalsimulationisdivided
Table3–Solidmasses.
Column 5cm 3cm 2cm Massofsolid(g) 2,827 741 181
Table4–Experimentalandpredictedminimum fluidizationvelocities.
Umf(cms−1) D=5cm D=3cm D=2cm
Exp.glasscolumn 2.92 3.82 4.11 Exp.steelcolumn 3.14 3.02 3.19 Simulation 3.41 3.50 3.82
intotwosteps:atransitorystepof10scorrespondingtothe establishmentofthehydrodynamicsofthefluidizedbedand anestablishedregimeduringwhichthe statisticsare com-putedfor100s.Thenumericalradialprofilespresentedinthis studyarefromtheO–xdirectionbuttheyaresymmetricalwith theprofilesoftheO–ydirection.Theauthorshavecheckedthat alltime-averagedbedvaluesareaxisymmetric.
4.
Results
and
discussion
Asshown inFig.4,Vanniet al.(2015b)haveobservedwall effectsfora2cmglasscolumn,consistinginanincreaseofthe hystereticbehaviorbetweenincreasinganddecreasing pres-suredropcurvesandoftheminimumfluidizationvelocityin theglasscolumn.Thisobservationislessmarkedinthesteel columnduetothereductionofelectrostaticforces.
Defluidization curves in Fig. 5 present a comparison betweennumericalresultsandexperimentalmeasurements carriedoutofthetotalbedpressure dropatdecreasinggas velocityinthesteelcolumnVannietal.(2015b).The horizon-tal dashedlines correspondtothetheoreticalbed pressure drop(equaltothebedweightpercolumnsurfacearea).A rela-tivegoodagreementcanbeobserved.However,thenumerical resultsslightlyunderestimatethepressureinthefixedbed part.Thisleadstoanoverestimationoftheminimum fluidiza-tionvelocityasdetailedinTable4.Thisslightoverestimation oftheminimumfluidizationvelocitycanbeattributedtothe nonregular shapeofparticles (Fig.6).Itisnoteworthythat thenumericalresultspredictanincreaseoftheminimum flu-idizationvelocityforthecolumnof2cmastheexperimental ones,confirmingtheexistenceofwalleffects.TheThonglimp etal.(1984)correlationwasusedtocalculateUmf.Thevalue
of3.2cms−1wasfoundlogicallyclosetotheexperimentalUmf
valueinthesteel5cmcolumnwheretheelectrostaticandwall effectsareminimum.
Forthefollowingsimulations,thegasfluidizationvelocity hasbeenfixedat12cms−1.Thefluidizationratioisthenclose to3forthecolumnsof5and3cmandto2.8forthecolumn of2cm.Theminimumfluidizationvelocitiesusedto calcu-latethefluidizationratioaretheexperimentalones.Theyare extractedfromFig.5usingtheDavidsonandHarrisonmethod (Davidsonetal.,1963).
Thepredictedtime-averaged gaspressure atthe wallas afunctionofheightforthethreesteelcolumnsispresented inFig.7.Thenumericaldatawere extractedfromthe cells directlyatthewalltoplotthesecurves.Forallcases,thegas pressuredropislinearinsidethebedwithalmostthesame slope. Thepressure gradient isthen constant and isnota functionofthecolumndiameter.Moreover,the experimen-talmeasurementsforthecolumnof5cmshowaverygood agreementwiththenumericalvalues.
Table 5shows the time-averagedpressure gradient pre-dictedatthewall.Thevaluesofthepressuregradientinside thebedforthedifferentcolumnsarealmostthesameas pre-viouslyobserved.Usingthispressuregradientatthewall,the voidfractionoftheoverallfluidizedbedhasbeenestimated
Fig.4–ExperimentalbedpressuredropcurvesintheglassandsteelcolumnsforH0/D=3.
Fig.5–Comparisonbetweenexperimentalmeasurements forsteelcolumnandnumericalresultsofthebedpressure dropcurvesobtainedatdecreasinggasflowrate.
Fig.6–SEMviewoftungstenparticles.
Table5–Time-averagedgaspressuredrop,bedheight andsolidvolumefraction,Vf=12cms−1.
Column 5cm 3cm 2cm P/L(mbarm−1) 1,006 1,012 1,017 Bedheight(cm) 13.79 10.05 5.55 ¯ ˛g 0.468 0.465 0.462 ˛g 0.497 0.512 0.517 error(˛¯g,˛g) 6.1% 10.1% 11.9%
byneglectingthefrictionforcesoftheparticlesatthewalland assuminganequilibriumbetweenthebuoyancyandthedrag forces: ¯ ˛g=1− 1 (p−g)g P L (1)
Thisestimationofthebedvoidfractioncanbecompared to the mean volume fraction obtained by integrating the localvoidfractionovertheentirecellsofthecomputational domain:
˛g=
Vbed
˛gdV (2)
Thiscomparison(lastline,Table5)showsthattherelative errorincreaseswiththereductionofcolumndiameter.Hence, fortheconditionstested, thefrictionforcesatthewallcan notbeneglectedanymorefora2cmcolumnoffluidization. Thesmallerthecolumndiameteris,thehigherarethe wall-particlefrictionforces.Whenthecolumndiameterdecreases, theratiobetweenthewallsurfaceandtheparticlesvolume increaseswhichgeneratesaliftingeffectofthebed.Thus,the reductionofthecolumndiameterincreasesthevoidfraction causingthebedexpansion.Noexperimentalmeasurements
P-P
ref(mbar)
0 50 100 150Height (cm)
0 5 10 15 20 Simulations column D=5cm Simulations column D=3cm Simulations column D=2cm Experiments column D=5cmFig.7–Time-averagedaxialprofilesofgaspressureatthe wallfromnumericalsimulationsandexperimental measurements(Prefisavalueabovethedensefluidized
Table6–Phasespropertiesusedforthesimulationof sandparticle.
Parameters Value
Gasdensity(Argon) 1.6kgm−3 Gasviscosity 2.23×10−5Pas Sandparticlediameter 206m Sandparticledensity 2,600kgm−3
Umf(Thonglimpetal.,1984) 3.2cms−1
havebeenperformedinthesteelcolumntobecomparedwith thesepredictedvalues.
Sometime-averagedradialprofileshavebeencalculated at2/3ofthebedheight.Thebedheighthasbeendetermined (Table5)fromthechangingslopeoftheaxialprofilesofthe time-averagedgaspressure(Fig.7).Consequently,theprofiles wereextractedononecellatthepositionofz=9.1cm,6.6cm and3.6cmrespectivelyforthecolumnsof5cm,3cmand2cm.
Fig.8(a)showsthetime-averagedradialprofileofthesolids volumefraction.Numericalpredictionspresentaminimum at the center of the tube and a maximum near the wall. Thistrendisthesameasthatnormallyobservedfor classi-calGeldartgroupBparticles.However,byperformingspecific simulationswithsandparticles(Table6)ofsimilarminimum fluidizationvelocity,wehaveverifiedthatthefluidizationof tungstenpowdershowshighsolidvolumefractionin compar-isontoresultsobtainedformoreconventionalsandparticles. Thus,theexpansionofthispowderislowerthanforsand par-ticles.Moreover,itisnoteworthythatthereductionofcolumn
diameter inducesa reduction ofthe extremaof the time-averagedradialprofileofthesolidsvolumefractionandsoan increaseofthemeanbedvoidfraction.Thiseffectconfirms thepreviousobservationsontheincreaseofthevoidfraction.
Fig.8(b)and(c)showsrespectivelythetime-averaged verti-calcomponentofsolidphasevelocityandtheassociatedsolid massflux.Theradialprofilesaresimilarwithapositive maxi-mumvalueatthecenterandanegativeminimumonecloseto thewallduetobubbleriseinthecenterofthetube.Because thesizeandthenthevelocityofthebubblesare limitedby thereductionofthecolumndiameter,themaximumofthe particlevelocitydecreases.
Theparticlesriseatthecenterofthecolumnisobserved inFig.9whichshowsthesolidvelocityvectorsforthethree columns.Anupwardsolidflowinthecenterofthetubeand adownwardmoreconcentratedsolidflownearthewallare clearlyobservedwiththeformationoftwo2Dloops(resulting intorusin3Dcylindricalgeometry)atthebottomandatthe topofthefluidizedbed.Ascanbenoticed,thereductionofthe columndiameterdoesnotinfluencethelocalbehaviorofthe particlesinthefluidizedbed.Suchaconicalcirculation pat-ternhasalreadybeenobservedindensefluidizedbed(Fotovat etal.,2015;WertherandMolerus,1973).
Fig. 8(d) presents the time-averaged granular temper-ature of particles, which represents the frequency of particle–particlecollisions.Forthethreecolumns,itpresents amaximumatthecenterofthetubeandaminimumnear the wall.Itisnoteworthythatthe granulartemperatureof tungstenparticlesismorethanfifteentimeslowerthanfor the sand particles fora fluidization ratio of4.This means
Fig.9–Crosssectionalviewatthecenterofthecolumnofthetime-averagedvolumefractionsandofthestreamlinesofthe tungstenparticlesvelocity,Vf=12cms−1.
Fig.10–Effectofcolumndiameteronthetime-averagedflowvariablesradialprofilesatz=2/3×bedheight,Vf=12cms−1.
thatthehighdensityofthetungstenparticlestendsto drasti-callyreducethefrequencyofparticle–particlecollisions.The granulartemperatureincreaseswiththereductionofthe col-umndiameterdue toanincrease ofthe solidshearstress atthewall.Themeangranulartemperatureforthecolumn of2cmistwicehigherthanforthecolumnof5cm.So,the reductionofthecolumndiameterincreasesthefrequencyof particle–particlecollisionsbutthisremainsnotablylowerthan forconventionalpowders.
Fig.10(a)and(b)presentsthetime-varianceofthe verti-calandhorizontalsolidphasevelocities.Thetime-variance oftheverticalcomponentofsolidvelocityismaximumatthe centerandminimumnearthewallandthestandard devia-tionisapproximativelyofthesameorderasthetime-averaged velocity.Thetime-varianceofverticalvelocityoftungsten par-ticlesisofthesameorderasthatofsandparticles butthe time-varianceofhorizontalvelocityisthreetimeslower.The time-varianceoftheverticalandthehorizontalcomponents ofsolidvelocitiesdecreaseswiththereductionofthecolumn
diameterduetotheconfinementeffect.Thismeansthatthe solidmixinginthefluidizedbeddecreasesconfirmingthewall effectsexperimentallyobserved.Thisresultcanalsoexplain that the heat transfer ratesbetween the particles and the reactorwallsdecreasewiththecolumndiameter,asobserved experimentally(Vannietal.,2015b).
FirstCVDexperimentshaveshownthattheconversionrate ofsilaneislowerthanforconventionalpowders.Thiscanbe explainedbythesimulationresults,indicatingalower parti-clemobilityandalowerparticlemixingfortheseverydense tungstenparticles(Vannietal.,2015a).
5.
Conclusion
3Dnumericalsimulations,usinganEulerian2-fluidmethod, wereperformedinthisworktoanalyzethehydrodynamicsof veryheavyparticlesoftungsten,locatedoutsidetheclassical classificationofGeldart,inadensegas–solidfluidizedbed.
Theaimwastostudytheinfluenceofthereductionofcolumn diameter.
Thesimulationsaresuccessfulinreproducingthe exper-imentalmeasurements ofaxial gas pressure drop and the increaseofminimumfluidizationvelocitybydecreasingthe columndiameterfrom 5cm to2cm. Thenumericalresults pointedoutthatthereductionofcolumndiameterincreases thevoidfractioninthedensefluidizedbedduetowall-particle frictioneffects.From 5cmto2cm ofcolumndiameter,the particleshaveaconventionallocalcirculationwiththesolids risinginanannularzoneofincreasedbubbledevelopmentin thecolumncenterandthendescendingnearthewall.
However,theveryhighdensityoftungstenparticlestends todrasticallyreducetheirmobilityinsidethebed.Moreover, thereductionofcolumndiameterdecreasesthesolidmixing, confirmingthewalleffectsexperimentallyobserved.
As the measurements have shown that the tungsten particlescaneasilybecomeelectrostaticallycharged,future numericalsimulationswilltakethisfactintoaccount,inorder to improve the predictive capability of the model. Finally, futureexperimentalresearchopportunitieswouldbetocarry outexperimentsonthelocalbehaviorofdensegas–tungsten particle suspension. It would be interesting to access to thebubbles sizeand velocityusingappropriateprobesand accordingtotheparticlestrajectoryfromRadioactiveParticle Tracking(RPT)ortoPositronEmissionParticleTracking(PEPT) measurementstodeterminetheparticlevelocity.
Acknowledgements
ThisworkwasgrantedaccesstotheHPCresourcesofCALMIP undertheallocationP11032andCINESundertheallocation gct6938 made byGENCI.The authors acknowledge helpful commentsprovidedbyProfessorOlivierSimonin.
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