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ContentslistsavailableatScienceDirect

Particuology

jou rn al h om ep a g e :w w w . e l s e v i e r . c o m / l o c a t e / p a r t i c

Simulation of spray coating in a spouted bed using recurrence CFD

Paul Kieckhefen

a,∗

, Thomas Lichtenegger

b,c

, Swantje Pietsch

a

, Stefan Pirker

b

, Stefan Heinrich

a

aInstituteofSolidsProcessEngineeringandParticleTechnology,HamburgUniversityofTechnology,Hamburg,Germany

bDepartmentforParticulateFlowModelling,JohannesKeplerUniversity,Linz,Austria

cLinzInstituteofTechnology(LIT),JohannesKeplerUniversity,Linz,Austria

a r t i c l e i n f o

Articlehistory:

Received1November2017

Receivedinrevisedform5January2018 Accepted16January2018

Availableonline25June2018

Keywords:

CFD–DEM RecurrenceCFD Spraycoating Time-scaledecoupling Spoutedbed Draftplate

a b s t r a c t

Although numerical models such as the computational fluid dynamics–discrete element method (CFD–DEM)haveenabledtheaccuratesimulationoflaboratory-scaleapparatuses,theapplicationof thesemethodstolarge-scaleapparatuseswithmanyparticlesandtimescalesrangingfromminutesto hoursremainsachallenge.TherecentlydevelopedrecurrenceCFD(rCFD)methodseekstoovercome theseissuesinpseudo-periodicprocessesbyextrapolatinggloballyrecurringpatternsinaphysically meaningfulwayanddescribingthetransportandinteractionofpassivescalarsusingLagrangiantracers.

Spoutedbedsrepresentaninterestingtargetbecauseoftheassociatedvarietyofflowregimes.Theycan beeffectivelydescribedbyCFD–DEMonthetimescaleoftensofseconds,whereasindustriallyrelevant processestypicallytakehours.Inthiscontribution,weestablishedthevalidityofapplyingtheLagrangian rCFDmethodtospoutedbedsbydemonstratingtheaccuratereproductionoftheparticleresidencetime distributioninafictitioussprayzone.Thedepositionofspraydropletsontotracerparticleswassimulated for1h,andtheparticlesurfacecoveragedistributionwasestimatedusingastatisticalapproachforboth anunstabilizedprismaticspoutedbedandonestabilizedbydraftplates.

©2018ChineseSocietyofParticuologyandInstituteofProcessEngineering,ChineseAcademyof Sciences.PublishedbyElsevierB.V.Allrightsreserved.

Introduction

Spouted bed technology dates back to Mathur and Gishler (1955),whofirstappliedittotheproblemofdryingwheatgrains thatweretoocoarseandasphericaltobetreatedinregularfluidized beds.Today,thetechnologyhasexpandedtoregularuseindiverse areasincludingchemicalvapourdepositiononfinemetalpowders (Caussat,Juarez,&Vahlas,2006)andhigh-densitynuclearfuelpel- lets(Liuetal.,2017;Mollicketal.,2015;Marshall,2017), spray coatingofvariousmaterialssuchasfertilizers(daRosa&dosSantos Rocha,2010),coatingofaerogelparticles(Antonyuk,Heinrich,&

Smirnova,2012;Plawsky,Littman,&Paccione,2010),spraygranu- lationofcompositematerials(Wolff,Salikov,Antonyuk,Heinrich,

&Schneider,2014;Eichner,Salikov,Bassen,Heinrich,&Schneider, 2017),andcombustion/pyrolysis(Alvarez,Amutio,Lopez,Bilbao,

&Olazar,2015;Ochoaetal.,2017;Alvarezetal.,2017).

Althoughtheseprocessesarecommonlythedomainoffluidized beds,spoutedbedsofferhigherstabilitywhenusingdifficult-to-

Correspondingauthor.

E-mailaddress:paul.kieckhefen@tuhh.de(P.Kieckhefen).

fluidizematerialssuchasGeldartDparticlesorasphericalparticles suchasgrains.Thisrobustnessisattributedtotheuniquebeddistri- butionandcircularflowstructurewithintheapparatus.Thegasis introducedinthemiddleoftheapparatusandacceleratesparticles verticallyfromthesurroundingparticlebulk,creatingthetitular spout.Asthegasjetdiffusesabovethesurfaceoftheparticlebulk, entrainedparticlesdecelerateandfalldownontothebulk,whichis commonlycalledtheannulus.Theannulusrestsonslantedwalls, causingtheparticlestoflowtowardsthebulk.Thisexplanationis idealistic,astheflowpatternofrealapparatusesdeviatesfromthis patterndependingontheoperatingregime.Theapparatusescanbe constructedeitherasymmetrically,axisymmetrically/conically,or prismatically/slot-rectangularly(Piskova&Mörl,2008).Thefirst spoutedbedswereconical designsand weretypicallyoperated usinghighbedheights.Theprismatictypehasfoundcommercial adoption(Jacob,2009)becauseoftheadvantageofeasyscale-up byextrusionoftheprocesschamberandiscommonlyoperatedat shallowbedlevelstoensureintensemixingandphaseinteraction.

Fortheseprismaticspoutedbeds,researchistypicallyconducted usingpseudo-2Dreplicaofcommercialapparatusestoreducesys- temcomplexityandenablecomputationalmodelling.

https://doi.org/10.1016/j.partic.2018.01.008

1674-2001/©2018ChineseSocietyofParticuologyandInstituteofProcessEngineering,ChineseAcademyofSciences.PublishedbyElsevierB.V.Allrightsreserved.

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Nomenclature Greeksymbols

ı˛ Excessphasevolumefraction

˛ Phasevolumefraction

Efficiency

ε Poisson’sratio Arbitraryfield Filtercoefficient

Kinematicviscosity,m2/s ϕ Surfacefraction

Density,kg/m3 Residencetime,s

Deviatoricstresstensor,N/m2 ω Angularvelocity,s−1

Latinsymbols

A Modelparameter(Kolakalurimodel) d Diameter,m

D0 Diffusioncoefficient,m2/s

f Fractionofparticlesurfacecoatedbyasingledroplet F Force,N

g Gravitationalacceleration,m/s2 J Momentofinertia,kg/m2 m Masspervolumekg/m3

M Mass,kg

N Number

p Pressure,Pa n Normalvector

t Time,s

t Timestep,s Symbol

T Torque,Nm u Phasevelocity,m/s V Volume,m3 x Width/length,m x Coordinate,m Y Young’smodulus,Pa Dimensionlessnumbers Co Courantnumber Re Reynoldsnumber St Stokesnumber Subscripts/superscripts coll Collected dep Deposition

D Droplet/sprayphase eff Effective

fluc Fluctuation fr Friction

G Gasphase

min Minimum

n Normal

P Particlephase

rec Recurrencefield/quantity rfr Rollingfriction

t Tangential W Apparatuswall Abbreviations

CFD Computationalfluiddynamics DEM Discreteelementmethod rCFD RecurrenceCFD

Gryczkaet al.(2008)characterizedthepneumatic behaviour of one suchprismatic pseudo-2D apparatus, and Salikov et al.

(2015)createdaregimemapforGeldartDparticles.Theyobserved thatwithincreasinggasvelocity,thepressuredropincreaseswith bubblingoccurringatacertainpoint.Attheminimumspouting velocity,thepressuredropdecreasesandspoutingisinitiated.With increasinggasflowrate,thebedexpandsfurtherintotheprocess chamberandinstabilitiessuchaslateralspoutdeflectionsoccur.

Thepressuredroposcillatesregularlyinthedensespoutingregime and becomes moreirregular withincreasinggas velocitywhile the fluctuation intensity decreases and the primary frequency increases.Theseoscillationsarecausedbythespout–annulusinter- actions,astheannulusflowingintothespoutregioncausesparticle accelerationaswellasaninitialincreaseinthepressuredropfol- lowedbyasubsequentdecreaseastheparticlesareclearedfrom theregion. Instabilitiesarise because ofthe higher bedexpan- sions, astheseequatetoa lowerannulusheightwithlessbulk solidloadstabilizingthespout,preventingself-amplifyingdeflec- tionandlateralbeddistributionasymmetry.Atveryhighflowrates, thepressuredropfluctuationsdisappearbecauseofthehomoge- neousdistributionofthebedintheprocesschamberandthelack ofanannulustocausefluctuations.Thisflowregimeiscalleddilute spouting.

Spoutedbedsarewellsuitedforspraycoatingbecauseofthe intenseheatandmasstransferbetweenthegasandparticlephase (Kucharski&Kmiec,1983).DeOliveira,Freire,andCoury(1997) usedacylindrical–conicalspoutedbedtocoataluminaparticles withasucrosesolutionwithhighhomogeneityandobservedthat thehydrodynamic operatingregime had asubstantial effecton particlegrowth.

Most previous works have applied the fully Eulerian two- fluidmodel(TFM)ortheEulerian–Lagrangiancomputationalfluid dynamics–discreteelementmethod(CFD–DEM)tospoutedbeds.

Bothmethodshaveadvantagesanddisadvantagesdependingon thecontext.TheTFMusesthekinetictheoryofgranularflow,as describedbyLun,Savage,Jeffrey,andChepurniy(1984),andmodels granularmotioninanEulerianframeofreferenceusingthecon- ceptofgranulartemperatureandclosuresforfrictionalandnormal stresses.Thisapproachenablestheefficienttreatmentofsystems encompassingbillionsofveryfineparticles,asthecomputational demandscaleswiththenumberofgridcellsinsteadofthenum- berofindividualparticles.Thereareconstraintsonthecellsizeas coarsegridsmaynotresolveallrelevantflowstructuresandthus introduceinaccuracies (Schneiderbauer&Pirker,2014).Gryczka etal.(2009)andJacob(2009)conductedvariousTFMstudieson apseudo-2DspoutedbedusingFluentandwereunsuccessfulin reproducingthepressuredropfluctuations.

UnresolvedCFD–DEM,aselaboratedintheworkofZhu,Zhou, Yang,andYu(2007),usesanEuleriandescriptionofthefluidflow andtracksthesolidphaseusingcomputationalparcels,whichrep- resentthemotionofindividualphysicalparticles,ormultitudesfor coarse-graining(Bierwisch,Kraft,Riedel,andMoseler,2009).Par- celcontactsarecommonlyresolvedusingasoft-sphereapproach, inwhichparcelsareallowedtooverlapandtimestepsontheorder of106sarerequiredbythecontactmodel.Volumefractionsare mappedtoanEuleriangrid,wheretheflowissolved.Dragclo- suresplaceaconstraintonthecellsize,astheymodeltheeffectof unresolvedflowfeaturessuchasswarmingtoacertainextent.A comprehensivetreatmentofthegridsensitivityofCFD–DEMcan befoundintheworkofRadlandSundaresan(2014).Themaincom- putationaldemandliesintheresolutionofinterparticlecontacts.

Althoughthisapproachallowsfortheaccuratedepictionofbulk solidmotion, industrialandevenpilot-scalesystemscommonly containtoomanyparcelsforsimulationwithouttheapplicationof coarsegraining(Nasato,Goniva,Pirker,&Kloss,2015).Salikovetal.

(2015) conducted CFD–DEM simulations of pseudo-2Dspouted

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bedsinstableandunstableregimesandfoundexcellentagreement ofthepressuredropfluctuation.Pietschetal.(2017)extendedthis worktoGeldartBparticlesusingcoarse-grainingin3Dspouted beds.These worksonlysimulated tensofsecondsof operation, whereasspraycoatingrequiresontheorderoftensofminutesfor completionunderexperimentalconditions.

Inaseminalpaper(Lichtenegger&Pirker,2016),someofthe currentauthorsproposedthetimeextrapolationofrecurrentflows by first conductingfully resolved simulations, storing the flow fields,andsubsequentlyscoringthepairwisesimilarityofsystem statesintheformofa recurrenceplot(Eckmann,Kamphorst,&

Ruelle,1987).Fortheextrapolation,intervalsofcontiguousflow field states are alternated with random jumps to recreate the pseudo-periodicnatureofthesystemwhiledescribingthetrans- portofpassivescalars.Thistaskcanbeachievedbysolvingeither EuleriantransportequationsortransportingLagrangiantracers.

Theconceptwasfirsttestedonabubblecolumnsimulatedusing TFMand a steelmaking convertersimulated using thevolume- of-fluidapproach.Althoughthebubblecolumnshowedsuperior performancewhentheEulerianrCFDapproachwasapplied,the steelmakingconverterbenefitedfromLagrangiantreatment.Some ofthecurrentauthorsappliedtheLagrangianvarianttoafluidized bed(Lichtenegger&Pirker,2017;Lichtenegger,Peters,Kuipers,&

Pirker,2017)andextended themethodtopredictheattransfer;

theresults(extrapolatedfromafewsecondsofdata)showedexcel- lentagreementofthebeddistributionreproductionandglobalheat transfercharacteristicsonthescaleofminute,extrapolatedfrom fewsecondsofdata.

Inthiswork,weappliedtheLagrangianrCFDmethodtoathree- dimensionalspoutedbed simulatedusingCFD–DEM, paralleling theprevious works conducted by someof the current authors (Pietschetal.,2017).Wefirstvalidatedthemethodbyassessingthe reproductionofparticlevolumefractionsandthepredictionofpar- ticleholdupsandresidencetimesinafictitioussprayzone.Basedon thispreliminarywork,longer(1h≡3600s)spray-injectionsimula- tionswereusedtostudythecoatingqualityinathree-dimensional laboratory-scalespouted bed equipped withand without draft plates.

Simulations CFD–DEMsimulation

Aswe will only provide a short overview of theCFD–DEM method,thereaderisreferredtotheworkofZhou,Kuang,Chu,and Yu(2010)foranin-depththeoreticaltreatmentandtotheworkof Kloss,Goniva,Hager,Amberger,andPirker(2012)forimplemen- tationofthismethodintheCFDEMcouplingsoftware.

Gas-phasegoverningequations

Thegasphasewasassumedtobehaveasanincompressiblefluid atthelowvelocitiesinvolved.Itstimeevolutionwasmodelledin anEulerianframeofreferenceusingthecontinuumEq.(1) and momentumtransportEq.(2)

∂˛G

∂t +∇·(˛GuG)=0, (1)

∂(˛GuG)

∂t +∇·˛GuGuG=−˛G∇p

GG∇·G

GG

iFi,drag GV ,

(2) whereuGG,andGarethevelocity,volumefraction,andden- sityofthegasphase,respectively;pisthepressure;andVisthe volumeofthecorrespondingmeshcell.Undertheassumptionof Newtonianfluidbehaviour,thedeviatoricstresstensorisgivenby

G=GvG

uG+(∇uG)

.Thenetinterphaseforceactingupona particleiisgivenbyFi,interphase=Fi,drag+Fi,p,whereFi,p=Vipisthe pressuregradientforce.ThedragforceFi,dragwascalculatedusing thecorrelationdevelopedbyBeetstra,vanderHoef,andKuipers (2007).

Becauseofthefinemeshintheinletregion,thesolidphasevol- umefractionwascalculatedbydividingeachparticleinto29points andmappingthesepointstothemesh.Detailsofthisprocedurecan befoundinRadl,Gonzales,Goniva,andPirker(2014).Thevolume fractionfield and momentumexchange field weresmoothened usinganapproachdevelopedbyPirker,Kahrimanovic,andGoniva (2011)toensurestabilityandenabletheuseofhighertimesteps.

Fora field that istobesmoothened,a conservativediffusion equation

∂t =L2smooth

tCFD2, (3)

issolved(Radletal.,2014),whereLsmoothisthesmoothinglength, whichiscommonlyselectedtobeontheorderofthreeparticle diameters.

Particleequationsofmotion

InDEM,asproposedbyCundallandStrack(1979)andimple- mentedinLIGGGHTS(Klossetal.,2012),particlemotionisresolved bysolvingtheNewtonianequationsofmotion

x¨i= 1 Mi

j

Fj→i+Fi,interphase

+g, (4)

ω˙i= 1 Ji

j

Tj→i, (5)

wherexiandMiarethepositionandmassofaparticlei,respec- tively;gisthegravitationalaccelerationvector;ωistheangular velocity;Jithemomentofinertia;andTj→iisthetorqueacting oniduetoj.TheinterparticlecontactforceFj→i=Fnj→i+Ftj→iof particlejactinguponanotherparticleiiscomposedofanormal componentFnj→iandatangentialcomponentFtj→i.Thesoft-sphere model,asimplementedinLIGGGHTS,usesaglobaltimestepand integratesoverallforcesactingupontheparticles.Contactforces areresolvedbyallowingtheparticlestooverlapandbyapplying overlap-dependentforcemodelssuchastheHertz–Mindlin–Tsuji model(Tsuji,Tanaka,&Ishida,1992).Thesemodelsaccountfor thesingle-particlemechanicalpropertiessuchasthecoefficientof restitution,modulusofelasticity,andPoisson’sratio.Themaximum particleoverlapshouldbekeptunder0.3%oftheparticleradius (Lommen,Schott,&Lodewijks,2014)foraccuratereproductionof bulkbehaviour,whichputsrestraintsonthevalueoftheglobal timestep.Rollingfrictionwasmodelledusingtheconstantdirec- tionaltorquemodelasdescribedintheworkofAi,Chen,Rotter, andOoi(2011),inwhichatorqueproportionaltothedifferencein angularvelocityoftwointeractingparticleswasapplied.

RecurrenceCFDsimulations

As previously proposed by some of the current authors (Lichtenegger&Pirker,2016),therecurrentnatureofcertainflows canbeusedtotime-extrapolatetheseprocessesusingtoolsfrom recurrencestatistics, namelyrecurrence plotsand signalrecon- struction.Wewillonlyprovideabriefsummaryoftheaspectsof themethodthatpertaintothecurrentcase.

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Recurrencestatistics

AsdescribedinLichteneggeretal.(2017),thecontinuousrecur- renceplotR˛Gisconstructedusingthegasphasevolumefraction

˛G:

R˛G(ti,tj)=1− 1 N˛G

V

G(ti)−˛G(tj))

2

dV, (6)

N˛G=max

ti,tj

V

G(ti)−˛G(tj))

2

dV, (7)

wheretiandtjaretwotimeswithcorrespondingflowstates,Vis theentiretyoftheflowdomain,andN˛Gisanormalizationfactor.

Becauseofthenormalization,themaindiagonalcontainsvaluesof 1andthemostdissimilarstateshavevaluesof0.

Thetemporalresolution neededforrecurrentpattern recon- structionislimitedbythetemporalrequirement

trec<

2

˙2, (8)

foragivenfieldquantity,where·denotestimeaveraging.The field-samplingintervaltrecwasselectedtosatisfytheserequire- ments.

PreviousexperimentalworkonspoutedbedsbyWang,Zhong, and Jiaqiang(2012)appliedtheoriginal,binaryrecurrenceplot method(Eckmannetal.,1987)toattractorsreconstructedfrom thetimedelayembeddedfromthepressuredroptimeandsuccess- fullydetectedrecurrentpatternsspecifictocertainflowregimesin spoutedbeds.

Recurrentprocesses

Based onthe recurrenceplot and underlying field data,the recurrent flow patterns can be extrapolated by constructing a sequenceoftimeindicesthatcorrespondtofieldsinthesampled database.Practically,thistaskisrealizedbyseparatingthesampled fielddatabaseintotwohalves.Ifthecurrentsequenceofconsec- utivefieldsendsinthesecondhalfofthedatabase,asearchfor themaximuminsimilarityisperformedinthefirsthalf,orvice versa,andthismaximumisusedasastartingpointforthenext sequence.Intheremainderofthispaper,wewillrefertosuchfields as“recurrencefields”.

LagrangianrCFD

Foreachstepwithinasequence,thecorrespondinggasphase velocity urecG , particle phase velocity urecP , and particle volume fraction˛recP fieldsareloadedfromthedatabase.Basedonthese velocities,tracersareevolvedbyintegrating

˙

xi=urecP +ufluc, (9)

whereurecP istheparticlephasevelocityinterpolatedontherecur- rencefield and ufluc is the fluctuationvelocity. This additional velocitycomponentisintroducedtomodeltheeffectofinterpar- ticlecollisionsand toeffectivelypreventoverpackingof tracers relativetotherecurrencephasefractions.Anexpressionforthis componentwasderivedbyLichteneggerandPirker(2016)from firstprinciplesinspiredbyclassicalBrowniandiffusion:

ufluc=nrand

D0 ı˛P

6t˛P, (10)

wherenrand is arandomunit vectorwithnrand=1,D0 isthe diffusioncoefficient,ı˛P=max(0,˛P−˛recP )istheexcessvolume fraction,andtisthelocaltimestep.TheselectionofD0ishighly dependentontheflowsituationbecauseofitspurposeinmod- ellinggranulartemperature/collisions, andas such, D0 mustbe calibratedwithrespecttotheunderlyingCFD–DEMsimulation.For tracersinregionswithnorecurrenceinformation,asqualifiedby

˛recP <0.02,thetrajectorywascalculatedaccordingtotheeffectof single-spheredragforceandgravity.

Spraymodelling

TheinjectedspraywasmodelledasLagrangiandropletparcels withmassMDND withND dropletsin aparcel.Because oftheir smalldiameterandlowrelaxationtimetrelax,D=Dd2D/(18vGG)<

5ms, thedroplets wereassumed tomoveat thefluidvelocity, whichavoidstheneedforcalculationofthedragforce.Thedroplets wereinjectedatthenozzleinletpatch,whichwasangledtorepro- ducetheexperimentallymeasuredspraycone,asoutlinedinour previouswork(Pietschetal.,2018).Inaddition,weassumedno dropletevaporation,anddropletparcelswereremovedfromthe systemwhentheycontactedtheapparatuswallsoroutlet.

The droplet deposition was modelled using a filtercorrela- tionproposedbyKolakaluri(2013)toavoidnumericallyexpensive directcontactdetection.Thetargetquantitywasthedeposition efficiency

dep=1.5trCFDuG,recuP,rec˛P/dP, (11) withinasingletimestep,accordingtowhichmassisstrippedfrom thedropletparcels.AsimilarapproachwasusedbyAskarishahi, Salehi,andRadl(2017),albeitusinganEuleriandropletphase.The filtercoefficient,

= St3.2eff

St3.2eff+4.3, (12)

dependsontheeffectiveStokesnumber Steff= St

2(A+1.14Re1/5m ˛−3/2G ), (13) andthemodelparameter

A= 6−6˛5/3P

6−9˛1/3P +9˛5/3P −6˛2P, (14) where Rem=(1−˛P)uG,recuP,recdP/vG is the superficial Reynolds number andSt=uGuPd2DP/(9dPvG)is theStokes number.

Ineverytimestep,themassstrippedfromeachdropletparcel iscalculated,mappedontoanEulerianfield,andthendistributed amongthetracersinthecells.Thisprocessstripsdropletsfromthe dropletparceluntiltheyareremovedwhenND<ND,min=1.

Droplet impacts coat the particlesurface. Kariuki, Freireich, Smith,Rhodes,and Hapgood(2013)proposedusingastatistical approachtocalculatethepercentageofaparticlesurfacecoated byimpactingdroplets.Thekeyparametersinthisapproacharethe areacoatedbyasingledropletAD,projandtheratioofthisareato thetotalparticlesurfacef=ADA,projP =(dD

2dP)2.Thedegreeofcoating canthusbeapproximatedas

ϕcoverage=1−(1−f)Ncoll, (15)

where Ncoll is the number of droplets collected by a particle.

Althoughthisapproachdoesnotconsiderspreadingduetosurface wetting,porosity,fluidflow,andparticlerotation,itiseffectivein representingthegeneralcharacterofcoatingqualityestimation, namelyasymptoticbehaviourregardinginjectionofmorecoating liquid.

Furthermore,weassumethatthecoatingprocesshasaneg- ligibleeffectonthegranulardynamicsbecauseofthelowmass injectedandgeneralresistanceofspoutedbedstochangingbed loads.Theevaporationofthecoatingliquidisassumedtobeinstan- taneous and to have noeffect onthefluid dynamics, which is reasonablegiventhelowinjectionrateandhighgasflowrates,

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Table1

Processconditionsandgas(subscriptG)anddroplet(subscriptD)phasematerial properties.

Processconditions

Processairflowrate, ˙VG(m3/h) 230

Atomizationairflowrate, ˙VG,nozzle(m3/h) 5

Particlebed,MP(kg) 1.5

Sprayflowrate, ˙Mspray(kg/h) 0.3

Gasphaseproperties

Density,G(kg/m3) 1.225

Kinematicviscosity,vG(m2/s) 1.5×10−5

Dropletphaseproperties

Dropletdiameter,dD(␮m) 40

Dropletdensity,D(kg/m3) 1000

Dropletinjectionrate, ˙ND(s−1) 1×105

Table2

Meshandnumericalsetup.

CFDmesh

Numberofmeshcells,Ncells 73,647

Cellsizes

Inletregion,xcells,in 2.5mm1.4dP

Processchamber,xcells,pc 5mm2.8dP

Freeboard,xcells,fb 10mm5.6dP

CFD–DEMsimulation

CFDtimestep,tCFD(s) 2.5×10−5

MaximumCourantnumber,Comax,CFD 0.8

CFDwriteinterval,tW,CFD(s) 5×10−3

DEMtimestep,tDEM(s) 1×10−6

Numberofparticles,NP,DEM 472,850

RecurrenceCFDsimulation

Globaltimestep,trCFD(s) 5×10−3

ParticleCourantnumber,Comax,P,rCFD 1 Numberofparticletracers,NP,rCFD 472,850 Dropletparcelinjectionrate, ˙ND,rCFD(s−1) 1×105

equatingtoamaximumincreaseintheairhumidityofapproxi- mately1g/kg.

Simulationsetup

Theprocessconditionsandgasphasepropertiesarelistedin Table1.Theoverallsetupofthecasewasselectedtobeascale-up ofcase3discussedbySalikovetal.(2015).

Geometryandmeshgeneration

Thegeometryoftheapparatusisidenticaltothatofthecommer- cialProCell5(GlattGmbH,Germany)lab-scalespoutedbedwith aprismaticangleof60,widthof250mm,anddepthof200mm, similartothoseusedbySalikovetal.(2015),Gryczkaetal.(2009), andPietschetal.(2017).Theprecisedimensionsoftheinletgeom- etrycanbefoundinGryczkaetal.(2009).Thelowerregionofthe inletgeometrywassimplifiedbyremovingthecurvedregionand mergingthetwoinletslits.

Thesprayconehalf-anglewasexperimentallydeterminedtobe approximately17.Toreproducethesprayconeanditsflowveloc- ityprofile,theboundaryofthenozzlewascurvedtoreproducethe complementaryangleof73.Meshingwasperformedusingthe OpenFOAMhexahedralcut-cellmeshersnappyHexMesh.Thecell sidelengthsarelistedinTable2,andtheresultingmeshisshownin Fig.1.Theparticle(subscriptP)andapparatus(subscriptW)mate- rialandcontactpropertiesarelistedinTable3,whichareadapted fromSalikovetal.(2015).

Fig.1. Surfacemeshoftheapparatus.

Table3

Particle(subscriptP)andapparatus(subscriptW)materialandcontactproperties, adaptedfromSalikovetal.(2015).

Diameter,dP(mm) 1.8

Particledensity,P(kg/m3) 1040

Young’smodulus,YP=YW(Pa) 1×109

Poisson’sratio,εP=εW 0.25

Coefficientof restitution

eP–P 0.9

eP–W 0.75

Coefficientoffriction kfr,P–P 0.5

kfr,P–W 0.24

Coefficientofrolling friction

krfr,P–P 0.06

krfr,P–W 0.05

CFD–DEMsimulations

Thefullsimulationswereconductedusinganextendedversion oftheCFDEMcoupling(Klossetal.,2012)softwarepackage.

AnoverviewofthenumericalsetupisprovidedinTable2.The CFDtimesteptCFDwassettosatisfyCo=ut/x<1anddid not exceedmax(Co)≈0.8 duringtheentire simulation. Forthe DEMpart,thetimestepwassettobeapproximately20%ofthe Rayleightime.InterphasecouplingwasperformedonceperCFD timestep,orevery25DEMtimesteps.Thesmoothinglengthwas setto5×103mm.Theinletwasprescribedafixedvelocitybound- arycondition.Forturbulencemodelling,thek–εmodelwasused withaninletturbulenceintensityof5%.

First,1.5kgof1.8mm␥-Al2O3particleswereinsertedataheight of0.2m<y<0.3mwithinthefreeboard regionoftheapparatus.

Thesimulationwasstoppedafter3sandresumedusinga field samplingfrequencyof200Hzfor10s,resultinginafielddatabase comprising2000entriesandrequiring16GBofmemory.Thedata generatedinthisrunwasnotusedforresidencetimecomputation toavoidbiases.Thesimulationwascontinuedforanother10s,and theresidencetimewithinthecone,showninFig.2,wascalculated.

AnotherCFD–DEM simulationwasperformedusingidentical settingsandgeometrybutfeaturingdraftplates,asproposedby Pietschetal.(2017).Thesedraftplateswere60-mmhigh,located 10mmabovethemidprofile,anddistanced45-mmapart.

rCFDsimulations

ThetracerequationsofmotiondescribedinEq.(9)wereimple- mented based on the hard-sphere Lagrangian particle tracking (LPT)algorithm presentin OpenFOAM5.x(Weller,Tabor,Jasak,

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Fig.2.ShapeanddimensionsofthesprayconeusedinbothfullCFD–DEMandrCFD simulations.

Fig.3. SchematicofinterprocesscommunicationinCFDEMcouplingandOpen- FOAMLagrangianparticletracking(LPT).

& Fureby, 1998), which is described in detail in Macpherson, Nordin, and Weller (2010). This implementation enabled effi- cient treatmentof thecomplex walls present in thegeometry.

For thewalls,simple elasticrestitutionwasassumed, unlikein ourfirstimplementationofthismethodinCFDEMcouplingusing CFDEM/LIGGGHTS.There,simplereflectivewallboundarycondi- tionswereappliedtoavoidcostlycontactdetection.

Anothernotabledifferenceis themodeofparallelization, as illustratedinFig.3.CFDEMcouplingusesdifferentdomainsubdivi- sionsfortheCFDandDEMsides,whichenablesefficientdynamic loadbalancingontheDEMsidebutintroducesabottleneck:during coupling,theDEMinformationisdistributedtoallCFDprocesses, whichiscommonlycalled“all-to-all”communicationandwhich canbeverycostlydependingonthenumberofpartitionsandpar- ticles.Additionally,datamustbecopiedbetweentheconstituent codesOpenFOAMandLIGGGHTS.Incontrast,OpenFOAMLPTuses thesamegeometricsubdivisionsforbothparticlesandthefluid domain, meaning that no furtherinter-process communication

Fig.4. OptimaldomaindecompositionsusingCFDEMcouplingemploying“all-to- all”communicationandOpenFOAMLagrangianparticletracking(LPT).

needstooccurwhileevolvingtheparticlecloud,exceptforinter- processboundarycrossingofparticles.Thisprocessrequirescareful selectionofthedomaindecompositiongeometrytoensureoptimal performanceforcasesinwhichbothCFDandDEMaresimilarly demanding;however,theLagrangianphaseisnothomogeneously distributed, asillustratedfor asimple case inFig.4. Thisprob- lemdoes notappear for mostLagrangian rCFDapplications,as thedecompositioncanbeselectedtorepresenta homogeneous distributionofparticlesamongdomains.Themaincomputational demandhereliesintheEuler–Lagrangemappingandsolvingthe underlyingphysicssuchastransportprocessesandintegrationof equationsofmotion.Thesetwostepsbenefitthemostfromaco- locationofCFDfielddataandparticleinformationwithinthesame process,makingOpenFOAMLPTthesuperiorchoice.

ShortrecurrenceCFDsimulationsof35swereperformedfor thediffusion coefficientcalibrationusing a samplingfrequency of200Hzfortheprobesand1Hzforthefields.Thefluctuation velocitieswerelimitedto1m/stopreventtracersfromdiffusing fartherthanapproximatelyonecelldiameterintheprocesscham- berwithinonetimestep.Thefirst5swerenotusedforresidence timecalculation.

Resultsanddiscussion CFD–DEMsimulation

Theverticalparticlevelocityasa functionoftime inpromi- nentprobinglocationsinthespoutandannulusisshowninFig.5.

Theparticlesinthespoutexperiencedmostlyupwardsmotion,as expected.Themaximumvelocitiesheredidnotexceed3m/swith arootmeansquare(RMS)velocityof1.2m/sandaRMStemporal derivativeof28.2m/s2,givinganupperboundofthefieldsampling intervaloftw,CFD<0.04s.Theparticlesintheannulusunderwent alternatingperiodsofupwardanddownwardmotion,indicating lateralspoutejectionsthatarethedefiningfeatureoftheinsta- bleoperatingregime.Notably,thelowresultingRMSvelocityand relativelyhightemporalvariabilityresultedinastrictercriterion forthefieldsamplingintervaloftw,CFD<0.02s.Therefore,afield samplingintervaloftw,CFD=0.005swasselectedtoensureappro- priatereproductionofthesystemdynamics.Thisintervalwasalso assumedtobesufficientforthecasecontainingdraftplates,asthese stabilizeflowpatternsinboththespoutandannulus.

TheresultingrecurrenceplotinFig.6hasmanylaminardiago- nals,especiallyintheregion4s≤trec≤8s,indicatingthepresence ofa highdegreeofrecurrentsystemstateswithinthesampled databaseaswellas aninterval withlowrecurrence withinthe sampledtimespanattrec≈3sandtrec≈9s.

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Fig.5. VerticalparticlevelocitiesUP,y(straightline)atprobelocations1(spout) and8(annulus)aswellasthecorrespondingrootmeansquarevelocities

UP,y2 (dashedline)andtemporalderivatives

dUP,y/dt

2

(dottedline).Thesignals werelow-passfilteredusingacut-offfrequencyof50Hztoremovenumericalnoise.

Fig.6. Recurrencematrixderivedfromthevolumefractionfield˛Psampledfor10s at200Hz.

ReproductionofbeddistributionanddynamicsinrCFD

ToensurethevalidityoftherCFDsimulationsandavoidover- packingof thetracer particles relative to thevolume fractions presentintherecurrencefields,theintensityofthevelocityfluc- tuationswascalibrated.Forthis process,35-ssimulationsusing diffusioncoefficientsin therangeof0≤D0≤1×102m2/swere conducted.Toeliminatetheeffectofrandomrecurrencepathcal- culation,apre-calculatedpathwasusedforthesesimulations.

Thesuccessof thesimulation canbejudgedbyitsabilityto reproducetheinstantaneousvolumefractionsatprobelocations relativetotherecurrencefieldsandthetime-averagedvolumefrac- tion,aswellastopredicttheresidencetimewithinthepreviously describedsprayzone.

Reproductionofdynamicvolumefraction

Theresultingtracervolumefractionsandcorrespondingrecur- renceparticlevolumefractionsatasamplelocationinthespout regionareplottedas afunctionof timeinFig.7. Agreementof therecurrenceparticlevolumefractionsandtracervolumefrac- tionsimpliesaccuratereproductionofboththebeddistribution andgranularfluxes,asforD0≥5×10−4m2/s,whereanincreaseof thediffusioncoefficientD0 doesnotimprovetheagreement.For D0<1×104m2/s,thetracervolumefractionfrequentlyexceeded therecurrencevolumefraction,whichindicatesinaccuraterepro- ductionofthebeddistribution.Here,thetracervolumefraction evenexceededtheclose-packedvolumefractionlimitof˛P>0.67.

Without the relaxation model (D0=0m2/s), the tracer volume fractionattheprobinglocationwasconsistentlylowerthanthe recurrencevolumefraction.Thismismatchindicatesthatthebed distributionwasseverelymisrepresentedduetoparticlesaccumu- latingelsewhereinthesystem.

Fig.7.RecurrenceCFDtracervolumefractionsfordifferentdiffusioncoefficientsD0andcorrespondingparticlevolumefractionsattheprobelocationinthespoutregionat x=0m,y=0.075m,z=0.05m,whichisapproximatelythesameheightandlateralpositionsasthefictitioussprayzone.

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Fig.8.Penaltyscoresfordifferentdiffusioncoefficients.

Toremovesubjectivityfromtheselectionofthediffusioncoef- ficient,apenaltyfunction1/Ndatapoints˛P−˛P,rec2 wasapplied to all 10 sampling locations in the apparatus. The locations were in prominent regions within the annulus and spout to enable theaccuracy of thebed distributionreproduction tobe gauged.Thetime-averagedpenaltyscoresaveragedoverallloca- tionsfordifferentdiffusioncoefficients areshown inFig.8.The penaltyscoredecreasedwithincreasingdiffusioncoefficientupto D0=1×104m2/s,atwhichpointaminimumoccurred.Forhigher diffusioncoefficients,thescoreincreasedagain,possiblydueto artefactsinducedbythestrongdiffusion.Thisbehaviorisgener- allyinaccordancewiththequalitativeobservationsmadewhen comparingthetracerandrecurrencevolumefractionsatasingle samplingpoint.

Time-averagedvolumefractionreproduction

Reproducing the time-averaged recurrence volume fraction determinedbythetracersisarequirementforusingtheLagrangian rCFDapproach, as a failuretoreproduce this parameterwould

invalidatealltheresultsoffurthersimulations.Theresultingtime- averaged tracer and recurrence volume fractions in a planeat z=0.1marepresentedinFig.9.Applyingnovelocityfluctuations (D0=0)resultedinveryhigh,unphysicaltracervolumefractions closeto thewalls and, consequently,lowerbed concentrations andexpansionsinthespoutregions.Thisproblempersistedfor low diffusion coefficients, e.g., D0=1×105m2/s. Starting with D0=5×10−4m2/s, the significantly overpacked regions in the annulusdisappearedandtheappropriatemeanshapeofthebulk wasaccuratelyreproduced.Ashigherdiffusioncoefficientsintro- duceerrorssuchasunphysicalmixinginbulkregions,thelowest viablediffusioncoefficientD0=5×10−4m2/swasselectedforfur- therinvestigations.

Influenceonholdupandresidencetimedistributionwithina fictitioussprayzone

Togaugetheaccuracyofthesimulationsrelativetoareal-world targetvalue,asprayzonewasdefined.Thisstepwasvaluable,as unlikethe previousexamples,thefateof singleparticles could beassessed,enabling clarificationoftheeffectofrandom-walk- inducedunphysicalmixing.

Examplesoftheinstantaneoussprayzoneholdupfordifferent diffusioncoefficientsand thefullCFD–DEM simulationarepre- sentedin Fig.10.Thesignals haveverysimilarpseudo-periodic patterns.Exceptforthesimulationwithoutthediffusionmodel, wherepoordistributionofsolidsledtoanoverallholdupunderes- timation,thepeaksintherCFDsimulationswerehigherregardless ofthediffusioncoefficient.Themeanholdupwasgenerallyonly slightlyoverestimatedrelativetothatofthefullCFD–DEMsimu- lation.Theseminordeviationsmaybeexplainedbyoverpacking, indicatinganinsufficiencyofthediffusion-basedrelaxationmodel.

Thesprayzoneresidencetimedistributionsforvariousdiffu- sioncoefficientsandforthefullsimulationaregiveninFig.11.As inthepreviouscases,alackofdiffusiverelaxationleadstopoor agreementwiththeCFD–DEMsimulation.Theuseofhigherdif- fusioncoefficientsresultedingoodagreementwiththeCFD–DEM

Fig.9.Time-averagedparticlevolumefractionsatz=0.1m.Theplotstitled“D0presenttheaveragedtracervolumefractionsforvariousdiffusioncoefficientsandthattitled

“Recurrence”presentsthetime-averagedrecurrencevolumefractionfield.

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Fig.10.DependenceofinstantaneoussprayconeholdupondiffusioncoefficientforrCFDsimulationsandfullCFD–DEMsimulation.Thedottedlinesindicatethetime- averagedholdups.

Fig.11.Sprayzoneresidencetimedistributionsafter10-ssimulationtimeforvar- iousdiffusioncoefficients.NotethatthegraphsforD0=5×10−4m2/s(dotted)and D0=1×10−2m2/s(dash-dot)practicallyoverlap.

simulation,withsomeunderpredictionofthefractionofparticles withhighresidencetimes.Asevenexcessivediffusioncoefficients donotsubstantiallyaffecttheresidencetimedistribution,itcan beassumedthatunphysicalmixingdoesnotoccurtoadegreethat wouldadverselyaffecttheoutcome.Thelimitofthefluctuation velocityof1m/smight alsoplaya role inpreventingexcessive diffusion.

Spraycoating

Thesimulationpredictedoversprayof2.3%fortheunstabilised spoutedbedand0.8%forthestabilizedone,which,whilesomewhat optimistic,qualitativelyindicatesthattheprocessmightbenefit

Fig.12.Fractionalsurfacecoveragedistributionsafter1hofsprayinjection.

fromthedenserand lessvariableflow patterninthestabilized apparatus.

Thefractionalsurfacecoveragedistributionscalculatedusing Eq.(15)fortheunstabilisedspoutedbedandthatequippedwith draftplatesafter1hofsprayinjectionareshowninFig.12.Surpris- ingly,themedianfractionalcoveragewasidenticalat90%,withan overallnarrowerdistributionobservedfortheunstabilisedsystem.

Thisresultcanbeattributedtoinhibitedmixingalongtheappara- tusdepthaxis(z),astheprimarycomponentofparticlemotionis withinthex−yplane.Withtheejectionssuppressedbythedraft plates,thismodeofmixingisgreatlyreduced.

Basedonthesefindings,characterizationoftheregionsinwhich dropletdepositionoccurswasperformed,asshowninFig.13.Inthe unstabilisedapparatus,mostdepositionoccurreddirectlyabove

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Fig.13.Time-averageddepositionratedensitydistributionsattheapparatusmidplanes(z=0.1mintheupperplotsandx=0minthelowerplots).

thenozzlewithinadiffusecloud,whichisinclearcontrasttothe apparatuswithdraftplates,forwhichthemaindepositionzone wasmoresharplydefinedandshiftedapproximately2-cmhigher totheupperendoftheplates,possiblyduetohigherbackground gasvelocities withinthechannelpresentedbytheplates.Com- parisonofthelateralprofilesindicatedthatthedepositionarea wasverycompactinitslongitudinalexpansioninthestabilized case,signifyinglesslongitudinalgasflow,whichcouldmoveeither dropletsorparticlesalongthisdirection.

Overall,these findings provideinsight intotheoptimization potentialofthespoutedbedapparatus.Althoughtheevaluated design(Pietschetal.,2017)didnotimprovethecoatingquality, it mightbe interestingfor otherapplications. Processesrequir- ingintensivecontactwithagranularcatalystshouldbenefitfrom theincreasedstability,resultinginanarrowgasphaseresidence timedistributionandlowbypass;however,furtherinvestigation isrequired.

ToreducethecalculationtimewithoutapplyingrCFD,onemay betempted touse time-averaged velocity and volume fraction fieldstomovetracersforbothparticlesanddropletswhilemod- ellingdropletdepositioninthesamewayperformedinthisstudy.

Althoughthisapproachmaybeviableforthestabilizedapparatus, itwouldintroducegreatinaccuraciesfortheunstabilizedvariant, asanygivenstateoftheflowfieldswoulddiffergreatlyfromthe averagebecauseofthelateraldeflectionsandirregularejections.

Performanceconsiderations

TheCFD–DEMsimulationsrequiredwalltimesof13daysfor 13-ssimulationson2×12coresofIntelE5-2680v3processors.The residencetimecalculationsusingrCFDwereperformedon12cores ofthesamehardwareandrequired36minofwalltimefor35s, with12minspentloadingtheapproximately16GBofrecurrence fieldsfromstorageintomemoryandcalculating therecurrence matrix.Theseparameterscorrespondtoa2100-foldnetspeedup whenexcludingtheloadingtimes,whichbecomenegligiblewhen consideringtheoveralldurationofthesimulationsforwhichthe applicationofrCFDisappropriateanddesirable.

Thespraysimulationsaddedtheburdenofanother(negligible) setofrecurrencetracers(sprayparcels)andthedropletdeposition calculations,whichreducedtheperformanceto≈1500s/daywith aspeedupof1500times.Asthedepositionalgorithmonlyinvolves

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oneEulerianfieldcalculationandtwonon-nestedloopsoverall tracers,thisfindingprovidedfurtherevidenceoftheleannessand efficiencyoftheparticletrackingalgorithmpresentinOpenFOAM.

Discussionofmodellimitations

Aspromisingasthefindingsandperformanceappear,thepro- posedmethodinitscurrentstateisonlyapplicabletoaspecificclass ofprocesses.Recurrentflowpatternscanbefoundonanyscale inturbulentflowbutareinpracticemodelledusinga sub-grid- scalemodel.Morecomplexphysicalmodelssuchasheattransfer orchemistryareusuallysolvedusingasteady-statesolutionofthe systemathandortransientsimulationsforflowswithstrongly coupledphysicsforsubsequentextrapolationinpost-processing.

AlthoughrCFDcaneliminatetheneedtoextrapolatephysicsin post-processingbyinsteadextrapolatingthedynamicsanddirectly solvingthephysics,itisonlyappropriatewhennegligibleback- propagationfromthesolvedphysicstothefluiddynamicsoccurs.

Acentralweakpointofthemethodinitscurrentformisthe relaxationmechanism. Althoughdiffusion byrandom walkis a simple,inexpensive,andelegantsolutiontotheoverpackingprob- lem,italsointroducesartificialmixing.Here,amoresophisticated approachisneededthataccountsforadditionalinformationabout thestateofthesystemduringtherecurrencedatabasegeneration.

Forgranularsystems,appropriatequantitiesmaybethegranular temperatureorstatisticalmomentsofthegranularfluxacrosscell faces.

Becausethemethodtradestimecomplexityforspacecomplex- ity,memoryusagewillbeoneofthebottlenecksforapplicationof themethodtolargerapparatuses.Usingthemethodisonlyviable whenrecurrentpatternsoccurontimescaleswithinafeworders ofmagnitudeofthetemporalresolutioncriterion(Eq.(8)),asoth- erwise,thememoryrequirementswouldbeincreased.Thesizeof therecurrencedatabasemustbecarefullybalancedbetweenthe lowerboundofcontainingall prominentflow patternsandthe upperboundoftheavailablememorysize.

A case that would greatly benefit from therCFD method is oneexhibiting ideallystrongly periodicpatterns,which deviate strongly from the mean, as this would inhibit convergence of steady-statemodelsandthusrequirecomputationallyexpensive transientsimulations.

Conclusions

In this work,we successfully appliedtherCFD methodto a laboratory-scale3Dspoutedbedapparatus.Thiseffortpresented aparticularchallenge,astheentiresetofflowregimes,ranging frombulkflowintheannulustodenseanddiluteflowinthespout andfountain,wererepresented.Themethodwasshowntoaccu- ratelyreproduceflowpatterns,asevidentbyacomparisonofthe resultingaveragedvolumefractionsandresidencetimedistribu- tionwithinasprayconewiththoseobtainedfromafullCFD–DEM simulation,whilerequiringonly0.05%ofthecalculationtimeafter generatingtherecurrencedatabase.

Thisperformancegainallowedforthedirectinvestigationof sprayinjectiononthetimescaleof1hinlessthanthreedaysof walltime,whichwouldhaverequiredatotalof3600daysusing fullCFD–DEM.Theaddition ofdraftplatesledtoworsemixing performance,whichcanbeattributedtothestabilizedspouting pattern,andproducedawidersurfacecoveragedistributionamong theparticles.Thisworkisonlyafirststepinexploringthepoten- tialoftheapparatusanditsmodificationsforpracticalapplications.

Thereducedmixingalongtheapparatusdepthmayalsointroduce opportunitiesforcontinuousdryinginapparatusesscaledupby

increasingtheapparatusdepthorinchemicalreactorswherethe granularphaseactsasacatalyst.

Infutureworks, rCFDwillbeappliedtoadditionalproblems withdiversephysicalchallenges,and,inparticular,itslimitsmust besystematicallydetermined.Newrelaxationmodelsshouldbe developedusingsimplerdensegranularandbulkflowsituations becauseinmorecomplexsystems,inaccuraciesmaybemaskedby theinterplayofdifferentfactors.Furtherdevelopmentsregarding algorithmicreductionofsampleddatawillpavethewaytobroad applicationforindustrial-scaleproblems.Asforspoutedbeds,new approachesformeasuring,orideallymonitoring,coatingquality areneededandwouldprovideachancetovalidatetheassumptions madeandconclusionsdrawninthiswork.

Acknowledgements

T.LichteneggeracknowledgesfundingfromtheLinzInstitute ofTechnology(LIT),JohannesKeplerUniversity(projectLIT-2016- 1-YOU-007).S.PietschacknowledgesfinancialsupportfromBASF SE.

References

Ai,J.,Chen,J.F.,Rotter,J.M.,&Ooi,J.Y.(2011).Assessmentofrollingresistance modelsindiscreteelementsimulations.PowderTechnology,206(3),269–282.

Alvarez,J.,Amutio,M.,Lopez,G.,Bilbao,J.,&Olazar,M.(2015).Fastco-pyrolysis ofsewagesludgeandlignocellulosicbiomassinaconicalspoutedbedreactor.

Fuel,159,810–818.

Alvarez,J.,Lopez,G.,Amutio,M.,Mkhize,N.M.,Danon,B.,vanderGryp,P.,etal.

(2017).Evaluationofthepropertiesoftyrepyrolysisoilsobtainedinaconical spoutedbedreactor.Energy,128,463–474.

Antonyuk,S.,Heinrich,S.,&Smirnova,I.(2012).Discreteelementstudyofaerogel particledynamicsinaspoutedbedapparatus.ChemicalEngineering&Technol- ogy,35(8),1427–1434.

Askarishahi,M.,Salehi,M.S.,&Radl,S.(2017).Full-physicssimulationsofspray- particleinteractioninabubblingfluidizedbed.AIChEJournal,63(7),2569–2587.

Beetstra,R.,vanderHoef,M.A.,&Kuipers,J.A.M.(2007).Dragforceofinterme- diateReynoldsnumberflowpastmono-andbidispersearraysofspheres.AIChE Journal,53(2),489–501.

Bierwisch,C.,Kraft,T.,Riedel,H.,&Moseler,M.(2009).Three-dimensionaldiscrete elementmodelsforthegranularstaticsanddynamicsofpowdersincavity filling.JournaloftheMechanicsandPhysicsofSolids,57(1),10–31.

Caussat,B.,Juarez,F.L.,&Vahlas,C.(2006).Hydrodynamicstudyoffinemetal- licpowdersinanoriginalspoutedbedcontactorinviewofchemicalvapor depositiontreatments.PowderTechnology,165(2),65–72.

Cundall,P.A.,&Strack,O.D.L.(1979).Adiscretenumericalmodelforgranular assemblies.Géotechnique,29(1),47–65.

daRosa,G.S.,&dosSantosRocha,S.C.(2010).Effectofprocessconditionsonparticle growthforspoutedbedcoatingofurea.ChemicalEngineeringandProcessing:

ProcessIntensification,49(8),836–842.

DeOliveira,W.P.,Freire,J.T.,&Coury,J.R.(1997).Analysisofparticlecoatingby spoutedbedprocess.InternationalJournalofPharmaceutics,158(1),1–9.

Eckmann,J.P.,Kamphorst,S.O.,&Ruelle,D.(1987).Recurrenceplotsofdynamical systems.EurophysicsLetters,4(9),973–977.

Eichner,E.,Salikov,V.,Bassen,P.,Heinrich,S.,&Schneider,G.A.(2017).Usingdilute spoutingforfabricationofhighlyfilledmetal–polymercompositematerials.

PowderTechnology,316,426–433.

Gryczka,O.,Heinrich,S.,Deen,N.G.,vanSintAnnaland,M.,Kuipers,J.A.M.,Jacob,M., etal.(2009).CharacterizationandCFD-modelingofthehydrodynamicsofapris- maticspoutedbedapparatus.ChemicalEngineeringScience,64(14),3352–3375.

Gryczka,O.,Heinrich,S.,Miteva,V.,Deen,N.G.,Kuipers,J.A.M.,Jacob,M.,etal.

(2008).Characterizationofthepneumaticbehaviorofanovelspoutedbed apparatuswithtwoadjustablegasinlets.ChemicalEngineeringScience,63(3), 791–814.

Jacob,M.(2009).ProCelltechnology:Modellingandapplication.PowderTechnology, 189(2),332–342.

Kariuki,W.I.,Freireich,B.,Smith,R.M.,Rhodes,M.,&Hapgood,K.P.(2013).Distri- butionnucleation:Quantifyingliquiddistributionontheparticlesurfaceusing thedimensionlessparticlecoatingnumber.ChemicalEngineeringScience,92, 134–145.

Kloss,C.,Goniva,C.,Hager,A.,Amberger,S.,&Pirker,S.(2012).Models,algorithms andvalidationforopensourceDEMandCFD–DEM.ProgressinComputational FluidDynamics,AnInternationalJournal,12(2–3),140–152.

Kolakaluri,R.(2013).Directnumericalsimulationsandanalyticalmodelingofgranular filtration.Doctoraldissertation.USA:IowaStateUniversity.

Kucharski,J.,&Kmiec,A.(1983).Hydrodynamics,heatandmasstransferduring coatingoftabletsinaspoutedbed.TheCanadianJournalofChemicalEngineering, 61(3),435–439.

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