MeasurementofParticleVelocitiesinConicalSpoutedBedsUsinganOpticalFiberProbe
MartinOlazar,*Marı´aJ.SanJose´,SoniaAlvarez,AlbertoMorales,andJavierBilbao
DepartamentodeIngenierı´aQuı´mica,UniversidaddelPaı´sVasco,Apartado644,48080Bilbao,Spain
Theverticalcomponentsofparticlevelocitiesinthespoutandannularzonesofconicalspoutedbedshavebeenexperimentallydeterminedfordifferentvaluesbothofcontactorgeometricfactors(angleandairinletdiameter)andofoperatingconditions(particlediameter,stagnantbedheight,andairvelocity)bymeansofanopticalfiberprobe.Basedontheeffectoftheoperatingvariablesonthelongitudinalandradialprofilesoftheparticlevelocities,acorrelationhasbeendeterminedfortheircalculationatanypositioninthespoutzone.ThecorrelationproposedbyNe´methandPallaiforthecalculationoftheaverageparticlevelocityatthewallincylindricalspoutedbedshasbeenproventobevalidinconicalspoutedbeds.
Introduction
Recentstudiesonconicalspoutedbedshavefocusedonthedevelopmentoffundamentalhydrodynamicmodelstocharacterizetheirphysicalbehavior(Olazaretal.,1992,1993b,1995a;SanJose´etal.,1993,1995).However,muchofthisworkhasfocusedongas-phaseflow.Thepresentworkseekstoextendthepreviousstudiestoincludethesolidbehaviorintheseunits.Specifically,theverticalcomponentsoftheparticlevelocitiesareexperimentallydeterminedwiththeaidofanopticalfiberprobe.
Giventheirversatilityingasandsolidflow,conicalspoutedbedsareasuitablecontactmethodwhenshortgasresidencetimesarerequiredandwhenavigorousgas-solidcontactisneededduetothecharacteristicsofthesolid,suchaswideparticlesizedistribution(Olazaretal.,1993a;SanJose´etal.,1994),irregulartexture(Olazaretal.,1994a),orstickynature(Olazaretal.,1994b,1997).Asisevidentfromthesepapers,thesolidflowinconicalcontactorsisconsiderablydifferentfromthatincylindricalcontactors.Thistermisappliedtobothspoutedbedsmadeupofacylindricalcolumnwithaflatbottomandtoconventionalspoutedbeds,conical-cylindrical,inwhichmostofthebediswithinthecylindricalsection.Consequently,inthelattercase,thesolidflowinthecylindricalsection(mostofthebed)ishardlydependentonthedesignoftheconicalsection.Thespecificconicalcontactorused,withthegeometricfactorsthatinfluenceitshydrodynamics,isshowninFigure1.
Severalauthors(MathurandGishler,1955;Thorleyetal.,1959;MikhailikandAntanishin,1967;GorshteinandMukhlenov,1967;LefroyandDavidson,1969;MathurandEpstein,1974;VanVelzenetal.,1974;Kmiec,1980;SuciuandPatrascu,1978;Dayetal.,1987;KimandCho,1991;Royetal.,1994)studiedtheparticlevelocityincylindricalspoutedbedsanddeterminedthatthemaximumvelocityisreachedattheaxisofthespout,nearthebottomofthecontactor.Theseauthorsignoredtheradialcomponentoftheparticlevelocityin
*Towhomcorrespondenceshouldbeaddressed.Tele-phone:34-4-4647700,ext.2575.FAX:34-4-4648500.E-mail:iqpolaum@lg.ehu.es.
Figure1.Geometricfactorsofthecontactor.
thespout.VanVelzenetal.(1974)proposedthefollowingequationforthecalculationofparticlevelocityalongtheaxis:
υz(0))[υz(0)]max1-1-
[(zzm
)]2
(1)
wherethemaximumvelocityattheaxisiscalculatedfromtheoperatingconditionsusingtheempiricalrelationship(VanVelzenetal.,1974):
F0.5G1.09
[υz(0)]max)40
dpD00.5H00.35Dc0.25
(2)
Thelongitudinalpositionofthemaximumvelocityiscalculatedasfollows(VanVelzenetal.,1974):
F0.4G1.18
zm)1.60.67
dpDc
(3)
Theaforementionedauthorsacceptedaparabolicradialprofileforparticlevelocityatanylevelinthespout.EpsteinandGrace(1984)proposedthefollowingequation:
υz)υz(0)1-
[()]rrs
m
(4)
10.1021/ie9800243CCC:$15.00©1998AmericanChemicalSociety
PublishedonWeb10/07/1998
wheremvariesbetween1.3and2.2,dependingontheoperatingconditions(m)2.0forMathurandEpstein(1974)).
TheradialprofiledeterminedbyHeetal.(1994)ismorecomplex,sincethemaximumparticlevelocityinthespoutisslightlydisplacedfromtheaxisintheuppersectionofthebed.ThisdisplacementofthemaximumvelocitywastheoreticallypredictedbyKrzywanskietal.(1992),whoattributedittoradialmovementoftheparticlesandinterparticlecollisionsinthespout.
Thefewpapersdealingwithparticlevelocitiesinconicalspoutedbedsrevealpeculiarcharacteristicsoftheparticlevelocityinthespout.Thus,Kmiec(1980)andBoulosandWaldie(1986)determinedthatthemaximumvelocitiesinthespoutsoftheconicalspoutedbedsarehigherthanthosecorrespondingtothecylin-dricalspoutedbedsandthattheyarereachedclosertothebase.RobinsonandWaldie(1978)andBoulosandWaldie(1986)provedthatneartheinterface,theparticlesdescendrelativelyquicklyjustpriortoentryinthespout.
Intheannularzoneofthecylindricalspoutedbeds,severalauthors(Thorleyetal.,1959;SuciuandPatras-cu,1978;Becker,1961;MathurandEpstein,1974;VanVelzenetal.,1974;Roveroetal.,1985;Dayetal.,1987;BenkridandCaram,1989;Royetal.,1994)determinedthatinthecylindricalsectionofthebed,theradialprofileoftheparticledownwardvelocityisalmostflat,withasmallvelocitydecreasenearthecontactorwallandattheinterfacebetweentheannularandspoutzones(BenkridandCaram,1989;KimandCho,1991;Heetal.,1994).Theparticlevelocityhasnoradialcomponentuntiltheparticlereachestheconicalsection,wheretheverticalcomponentincreasesandtheradialcomponentishigh.Mostoftheaforementionedauthorsassumealineardecreaseoftheparticlevelocityastheparticlesdescendalongthecylindricalsection.SuciuandPatrascu(1978)proposedthefollowingequationforthecalculationoftheaveragevelocityintheannularzone,asafunctionofthelongitudinalposition:
(υjz
a))0.043+0.16
(H
)(5)
Royetal.(1994)determinedthattheevolutionofvelocitywiththelongitudinalpositionisnotlinearbut,duetotheincreaseofbedvoidagewithlongitudinalposition(Heetal.,1994),isproportionaltoz0.65.ExperimentalSection
Theexperimentalunitwasdescribedinpreviouspapers(Olazaretal.,1992,1993b;SanJose´etal.,1993).Thestudyhasbeencarriedoutusingcontactorsmadeofpoly(methylmethacrylate).Thevaluesofthegeo-metricfactors)defined0.36m;inangle,Figureγ1)are33,as36,follows:and45°;columndiameter,Dctheircorrespondingheightoftheconicalsection,Hand0.36m;airinletdiameter,D0.03,c)0.50,0.45,0)0.04,and0.05m.Thedesignoftheairinletforsystemstabilitywasdescribedindetailinapreviouspaper(Olazaretal.,1992).Thestagnantbedheightwasvariedbetween0.05and0.30m.Thesolidsusedwereglass)3,4,spheresand5mm.
(density)2420kgm-3)ofdiametersdpTheprobeusedformeasurementoftheverticalcomponentofparticlevelocityatanypositioninthebedwasdescribedinapreviouspaper(Olazaretal.,1995b)
Ind.Eng.Chem.Res.,Vol.37,No.11,19984521
Figure2.Verticalcomponentoftheparticlevelocityinthespoutzone,atdifferentlongitudinalpositions.γ)33°,D3mm,H0)0.03m,d)p0)0.18m,u)ums.
andconsistsofanencasingofstainlesssteel,whosemaximumandminimumdimensionsare5.0and1.5mm,respectively,whichcontainsthreeopticalfibersarrangedinparallel.Whentheparticlepassesinfrontoftheprobehead,itreflectslightemittedbythecentralfiber.Thelightreflectediscollectedinsuccessionbythetwolateralfibersandissenttotwoanalogicalchannels.Fromastatisticalanalysis,bymeansofthecross-correlationfunction(incorporatedtotheMATLAB5.1program),thesignalswithastatisticallysignificantcorrelationcoefficient(indicatingthatthesameparticlespassinfrontofbothfibers)areaccepted.Thesecoef-ficientsarehigherthan90%inthespoutzoneandhigherthan60%intheannularzone.Fromtheeffectivedistancebetweenthetworeceivingfibersandthedelaytimebetweenthetwosignals,τ(timecorre-spondingtothemaximumvalueofthecross-correlationfunction),itcanbeascertainedwhetherthedisplace-mentisupwardordownward(positiveornegativetimedelay),andthevelocityoftheparticlealongthelongi-tudinaldirectioncanbecalculated:
υz)
deτ(6)
Theeffectivedistance,donarotarydiskofknownangulare)3.3mm,wasdeterminedvelocityfollowingtheproceduredescribedbyBenkridandCaram(1989).+12TheV).signalsA12-Vpasslightthroughsourceasendssignallightamplifiertotheemitting(-12tofiber,andafiltercontrolstheintensityofthebeam.Ananalogical/digitalinterfacesendsthedatatothecom-puterforprocessing.
Thedownwardvelocityoftheparticlesalongthewallhasbeenmeasuredbyatechniquebasedonvideorecordingandimagetreatment,whichwasdescribedinapreviouspaper(Olazaretal.,1996).Results
ParticleVelocitiesintheSpout.Asanexampleoftheresultsobtainedinthespoutzonebymeansoftheopticalfiber,theverticalcomponentsoftheparticlevelocityinthespoutareschematicallyoutlinedinFigure2foroneoftheexperimentalsystemsstudied.Thedelimitationoftheinterfacebetweenthespoutandannularzones,whichisdrawninFigure2,wascarried
4522Ind.Eng.Chem.Res.,Vol.37,No.11,1998
Figure3.Longitudinalprofilesoftheverticalcomponentofparticlevelocityinthespoutzone.γ)33°,Du)u0)0.03m,dp)3mm,H0)0.18m,ms.Points,experimentalresults.Lines,calculatedwitheqs7-9.
Figure4.Radialprofilesoftheverticalcomponentoftheparticlevelocityinthespoutzone.γ)33°,D0)0.03m,dp)3mm,H0)0.18m,u)ums.Points,experimentalresults.Lines,calculatedwitheqs7-9.
outinapreviouspaper(Olazaretal.,1995b)bymeansoftheopticalprobe.Thespoutshapeisqualitativelysimilarforalltheexperimentalsystemsstudied.Atfirst,itwidensinaverypronouncedwaynearthecontactorinletandthenthereisaneck,andfinallythespoutwidensagainuptothebedsurface.Itisnote-worthythattheaveragediameterofthespoutismuchgreaterthanthecontactorinletdiameter.
ThevaluesoftheverticalcomponentoftheparticlevelocityplottedinFigure2areshowninmoredetailinFigures3and4,wherethelongitudinalandradialprofiles,respectively,areplotted.Inthesefigures,pointsareexperimentalresultsandlinesarecalculatedwiththecorrelationsproposedfurtheron.
InFigure3,itisobservedthatatagivenradialposition,theverticalcomponentoftheparticlevelocityreachesamaximumvalueatagivenlongitudinalpositionnearthebottom.Astheradialpositionishigher,thismaximumbecomeslesspronouncedandislocatedatahigherlongitudinalposition.
InFigure4,itisobservedthattheverticalcomponentoftheparticlevelocityhasamaximumvalueattheaxisforallthelongitudinalpositions.Besides,thehigherthelongitudinalpositionalongthespout,thelesspronouncedthismaximum.
Theradialandlongitudinalprofilesofvelocityinthespoutchangewiththegeometryofthespoutand,consequently,withtheoperatingconditionsthatinflu-
encethisgeometry.Withtheaimofanalyzingindetailtheeffectoftheoperatingconditionsontheparticlevelocity,thevelocityresultsobtainedforseveralradialpositionsalongtheaxisandnearthebottomwillbesubsequentlystudied.Theseresultsarerepresentativeoftheshapeofthevelocityprofilesinthespout.
InFigure5,theeffectbothofthegeometricfactorsofthecontactor(angleandinletdiameter)andoftheoperatingconditions(particlediameter,stagnantbedheight,andairvelocity)onthelongitudinalprofileoftheverticalcomponentoftheparticlevelocityalongthespoutaxisisanalyzed.
Theseresultsshowthatthemaximumparticleveloc-ityisreachedatapositionbetween0.02and0.03mfromtheairinlet,andthispositionisnotsignificantlyaffectedbytheoperatingvariables.However,athigheraxiallocations,theparticlevelocitydecreaseslinearlywithdistance.
Ofthevariablesstudied,Figure5,thestagnantbedheightappearstohavethemostsignificanteffectonthemaximumparticlevelocity.Particlesizealsohasagreatinfluence(althoughsmallerthanthatofthestagnantbedheight).Theothervariableshaveasmallerinfluence.
Whentheeffectoftheoperatingvariablesisanalyzed,stagnantbedheightistheoneofgreaterinfluence,Figure5d.Thus,thehigherthestagnantbedheight,thehighertheparticlevelocityalongthespoutaxis.Thisisfollowedbyparticlesize,whichalsohasagreatinfluence,Figure5c.Astheparticlesizeissmaller,theparticlevelocityalongthespoutaxisincreasesnotice-ably.Theinfluenceoftheremainingvariablesissmaller.Whenthecontactorangle,Figure5a,andtheairvelocity(overthatcorrespondingtotheminimumforspouting)areincreased,Figure5e,theparticlevelocityalongthespoutaxisincreasesslightly,whereasastheairinletdiameterisincreased,theparticlevelocitydecreases,Figure5b.
Theradialprofileoftheverticalcomponentofparticlevelocityatthebaseofthespout,atz)0.025m,isanalyzedinFigure6.Pointsareexperimentalresults,andlinesarecalculatedwiththecorrelationsproposedfurtheron.Thevariablesofgreaterinfluenceare,inorderofinfluence,stagnantbedheight,Figure6d,particlesize,Figure6c,andairinletdiameter,Figure6b(inthiscaseduetothemodificationofthespoutgeometryinducedbyachangeininletdiameter).Theinfluenceofthecontactorangle,Figure6a,andofairvelocity,Figure6e,aresmall.
Withtheaimofhavinganequationvalidforcalcula-tionoftheparticlelocalvelocities,severalmathematicalexpressionsweretried.ThebestfitwasobtainedwithanexpressionsimilartothatproposedbyEpsteinandGrace(1984),i.e.,eq4,buttakingintoaccountthat,inconicalspoutedbeds,theradialprofileoftheverticalcomponentofvelocitychangeswiththelongitudinalpositionand,consequently,theexponent(namedmwillalsochangewithbedlevel.Theproposedexpres-z)sionis
υz)υz(0)[1-
(rmz
r)](7)
s
Bynonlinearregressionfittingoftheexperimentalresults(Box,1965)toeq7,theparameterm3.0.Intheuppersectionztakesvaluesbetween1.0andofthespout,mztakesthevalue1.0foralltheexperimental
Ind.Eng.Chem.Res.,Vol.37,No.11,19984523
Figure5.Effectofthegeometricfactorsofthecontactor(a,contactorangle;b,inletdiameter)andoftheoperatingconditions(c,particlediameter;d,stagnantbedheight;e,airvelocity)onthelongitudinalprofilesoftheverticalcomponentoftheparticlevelocityalongthespoutaxis.
systemsstudied,whilethemaximumvalueofmz(mz)m0)isreachedatadistancebetweenz)0.020andz)0.030mfromthecontactorinlet.Ithasbeenproventhatmzdecreasesfromitsmaximumvalue,m0,withthelongitudinalposition,inalltheexperimentalsys-tems,accordingtothefollowingexpression:
mz)1+(m0-1)exp[-100(z-0.025)2]
(8)
Ineq8,m0isafunctionofboththegeometricfactorsofthecontactorandoftheoperatingvariables.Bystudyingthesevariables,groupedintotheconventionaldimensionlessmoduliusedinthehydrodynamicstudyofconicalspoutedbeds(Olazaretal.,1992),thefollow-ingexpressionisobtained:
dp
m0)1.41
Di
()()()-0.31
H0Di
0.77
uums
0.80
γ0.50exp
(-1.87D0
Di
(9)
)Thefittingoftheexperimentalresultsoftheverticalcomponentofthevelocity,υz,toeqs7-9wascarried
outbythecomplexmethodofnonlinearregression(Box,1965)andgaveaglobalregressioncoefficientofr2)0.90,withamaximumrelativeerrorof12%.TheadequacyofthefittingisshowninFigures4and6,wherepointsareexperimentalresultsandlinesarecalculatedwitheqs7-9.
Thevalidityofeq7forthepredictionofthescarceexperimentaldatapublishedintheliteratureforconicalspoutedbedswasanalyzed.Itisnoteworthythatthesedatacorrespondtoparticularexperimentalsystems.Thus,Kmiec(1978)usedshallowbeds,andconse-quently,onlyaqualitativeassessmentmaybemadeaboutthevalidityofeq7,whichprovidesvaluesofthesameorder,althoughslightlysmallerthantheexperi-mentalonesofKmiec(1980).TheresultsofWaldieandWilkinson(1986)areaveragevaluesforthespoutsectionatseverallevels,andtheyarelowerthanthosecalculatedbymeansofeq7.
ParticleVelocityintheAnnularZone.TheresultsofFigures7and8,whichcorrespondtooneoftheexperimentalsystemsstudied,areanexampleofthegeneralshapeofthelongitudinalprofiles,Figure
4524Ind.Eng.Chem.Res.,Vol.37,No.11,1998
Figure6.Effectofthegeometricfactorsofthecontactor(a,contactorangle;b,inletdiameter)andoftheoperatingconditions(c,particlediameter;d,stagnantbedheight;e,airvelocity)ontheradialprofilesoftheverticalcomponentoftheparticlevelocityatthebaseofthespout,atz)0.025m.Points,experimentalresults.Lines,calculatedwitheqs7-9.
Table1.EquationsProposedintheLiteratureforCalculationoftheParticleVelocityattheWall
authors
Thorleyetal.(1959)Becker(1961)
Shigeo(1965)Matsen(1968)Abdelrazek(1969)Ne´methandPallai(1970)
equation
W)υjwAa(1-a)F)K(D0/Dc)-0.25(Us/Ums)1.23(H0/Dc)1.0
2[(υjw)/gH0]0.4[Ua/(Ums)M]2)B(z/HM)b
whereatz/HM<0.25,B)0.055,andb)1;atz/HM>0.25,B)0.21,andb)2υjw/Ums)7.6×10-3(gDc/Ums2)-0.4(D0/Dc)-0.7(Us/Ums)1.7υjw/(υjw)ms)Us/Umslog(υjw/Ums))(3.42×10-4)Re(H0/Dc)-1.543υjw)(υjw)M(H0/HM)1/3υjw)(υjw)ms(Us/Ums)3/2
(10)
(11)(12)(13)(14)(15)(16)
7,andoftheradialprofiles,Figure8,oftheverticalcomponentoftheparticlevelocityalongtheannularzone.Inthesefigures,pointsareexperimentalresultsandlinesaretracedalongthepointsinordertofollowthetendencyoftheresults.
InFigure7,itisobservedthatgiventheconicalgeometryofthecontactor,theclosertheparticlestothebottomofthecontactor,thehighertheiraccelerationand,consequently,themaximumcomponentofthedownwardvelocityisreachednearthebottomandclosetotheinterfacebetweenthespoutandannularzone.Atthebottomofthecontactor,themaincomponentoftheparticlevelocityistheradialone.Theradialprofilesoftheverticalcomponentoftheparticlevelocity,Figure8,showtheexistenceofamaximumvalueataradialposition,whichshiftstowardhigherradialpositionsasthelongitudinalpositioninthebedishigher.
TheaveragevaluesoftheparticlevelocityinthespoutandannularzonesareplottedinFigure9againstthelongitudinalposition.Asisobserved,theaverageupwardparticlevelocityinthespoutdecreasesalmostlinearlywiththelongitudinalposition.Theaveragedownwardvelocityalongtheannularzonehasaslightaccelerationintheuppersectionofthebedandin-creaseslinearlytowardthebottomofthebed.
Figure7.Longitudinalprofilesoftheverticalcomponentoftheparticlevelocityintheannularzone.γ)33°,H0)0.18m,dp)4mm,D0)0.03m,u)ums.
Figure8.Radialprofilesoftheverticalcomponentoftheparticlevelocityintheannularzone.γ)33°,H)0.03m,u)u0)0.18m,dp)4mm,D0ms.
Figure9.Longitudinalprofilesofaverageparticlevelocitiesinthespoutandannularzones.γ)33°,D)u0)0.03m,dp)4mm,H0)0.18m,ums.
ParticleVelocityattheWall.Thedifferentcor-relationsproposedintheliteratureforcalculationoftheparticledownwardvelocityalongthewallincylindricalspoutedbedsaresetoutinTable1.MathurandEpstein(1974)drewattentiontothelimitationsontheapplicationofthesecorrelations,astheirvaliditywasrestrictedtotherangeofexperimentalconditionsinwhichtheyweredetermined.Severalauthors(Roveroetal.,1985;BoulosandWaldie,1986;Randelmanetal.,1987;Dayetal.,1987;BenkridandCaram,1989;Royetal.,1994;Heetal.,1994)provedthattheparticlevelocityatthewallisseverelyaffectedbywallfriction
Ind.Eng.Chem.Res.,Vol.37,No.11,19984525
Table2.ComparisonoftheExperimentalValuesoftheParticleVelocityattheWallwithThoseCalculated
UsingEquation16ProposedbyNemethandPallai(1970)γ,D0,dp,H0,υjw,ms-1
degmmmu/umsexptleq1633
0.03
0.0040.181.02
3.1×10-21.203.8×10-24.1×10-21.304.2×10-24.6×10-20.005
0.181.023.7×10-21.204.1×10-24.9×10-21.305.0×10-25.5×10-20.040.0040.181.022.8×10-21.203.4×10-23.7×10-21.304.0×10-24.2×10-20.05
0.0040.181.022.2×10-21.202.7×10-23.0×10-21.303.0×10-23.3×10-2360.030.0040.181.023.7×10-21.203.9×10-24.9×10-21.305.2×10-25.5×10-245
0.03
0.004
0.18
1.024.5×10-21.205.2×10-25.9×10-21.30
5.8×10-2
6.6×10-2
andthatitisconsequentlyapoorrepresentationoftheparticlevelocityintheannularzone.
InFigure10,theeffectoftheoperatingvariablesonthelongitudinalprofileoftheparticlevelocityalongthewall(velocitymeasuredinthewalldirection)isana-lyzed.Itisobservedthattheparticlevelocityatthewallincreasesastheparticlesdescend.Atfirst,theincreaseisexponentialandthenthevelocityincreaseslinearlytoamaximumvaluenearthebottomofthebed.Theparticlevelocityatthewallishigherasthevalueofthefollowingvariablesisincreased:contactorangle,Figure10a;particlesize,Figure10c;stagnantbedheight,Figure10d;andairvelocity,Figure10e.Ontheotherhand,theparticlevelocityatthewalldecreasesasthecontactorinletdiameterisincreased,Figure10b.TheadequacyoftheequationsofTable1forpredict-ingtheexperimentalvaluesofthisstudyhasbeenanalyzed.Itmustbepointedoutthateq11(Becker,1961)andeq15(Ne´methandPallai,1970)arenotapplicabletoconicalspoutedbeds,astheseequationstakeintoaccountthemaximumspoutablebedheight,HM.Inconicalspoutedbeds,thereisnomaximumspoutablebedheight(Olazaretal.,1993a,b).Ontheotherhand,inconicalspoutedbeds,thevariationoftheparticlevelocityatthewallwiththelongitudinalpositionisgreat,Figure10,andforthisreason,thevaluesfittedtotheequationinTable1areaveragevaluesbetweenthesurfaceandthebottomofthebed.Ithasbeenproventhateq16proposedbyNe´methandPallai(1970)suitablyfitstheexperimentalresults,Table2,witharegressioncoefficientr2)0.98andarelativeerrorlowerthan3%.Thefittingofeq12proposedbyShigeo(1965)isalsoacceptable,witharegressioncoefficientr2)0.87andarelativeerrorlowerthan14%.Thefittingoftheothercorrelationsispoor.Inthesecalculations,thevalueofDhasbeentakenasthearithmeticmeancforconicalbedsbetweenthebasediameter,Dbedheight,i,andtheupperdiameterofthestagnantDb.Conclusions
Astrongdependencyofthegeometricfactorsofthecontactorandoftheoperatingconditionshasbeenfoundontheverticalcomponentofparticlevelocityinthespoutandannularzonesofconicalspoutedbeds.The
4526Ind.Eng.Chem.Res.,Vol.37,No.11,1998
Figure10.Effectofthegeometricfactorsofthecontactor(a,contactorangle;b,inletdiameter)andoftheoperatingconditions(c,particlediameter;d,stagnantbedheight;e,airvelocity)onthelongitudinalprofilesofparticlevelocityatthewall.
stagnantbedheightandparticlessizehaveagreatinfluenceonthevelocityprofileinthespout.
Themaximumvalueoftheupwardvelocityinthespoutzoneisreachedattheaxisofthespoutandnearthecontactorinlet(atzbetween0.02and0.03m).Forlongitudinalpositionsfurtherawayfromthebottom,themaximumvelocityalsocorrespondstothespoutaxis.Forthemathematicalmodelingofthesolidflowpatterninthespoutzone,theadequacyofeqs7-9hasbeenproveninawiderangeofexperimentalconditions.Theseequations,togetherwithothersdeterminedinapreviouspaper(SanJose´etal.,1998)forcalculationoflocalbedvoidagesinthespoutandannularzones,willbeusedinsubsequentpapersformodelingthesolidflowpatternanddefiningsolidtrajectoriesthroughouttheentirebed.
Thedownwardvelocityoftheparticlesintheannularzonehasamaximumvaluenearthebottomofthecontactorandataradialpositionclosetotheinterfacebetweenthespoutandannularzone.Asthebedlevelishigher,themaximumvelocitycorrespondstoaradialpositionfurtherawayfromtheinterface.Equation16,proposedbyNe´methandPallai(1970),hasbeenproventobesuitableforcalculationoftheaverageparticlevelocityalongthecontactorwall.Acknowledgment
ThisworkwascarriedoutwiththefinancialbackingoftheDepartmentofEducation,UniversityandRe-searchoftheGovernmentoftheBasqueCountry(ProjectNo.PI94/33),andoftheMinisteryofEducationandCultureoftheSpanishGovernment(ProjectDGICYTNo.PB94-1359).Nomenclature
Aa)crosssectionoftheannularzone,m2B,b)parametersineq11
Db,Dc,Di,D0)upperdiameterofthestagnantbedanddiametersofthecolumn,ofthebedbottom,andoftheinlet,respectively,m
de)effectivedistancebetweenthetworeceivingfibers,mm
dp)particlediameter,mm
G)gasmassflowrateperunitofcolumncrosssection,kgm-2s-1
H,Hc,H0)heightsofthedevelopedbed,oftheconicalsection,andofthestagnantbed,respectively,mHM)maximumspoutablebedheight,mm)exponentineq4
m0)parameterdefinedbyeq9
mz)exponentineq7,definedbyeq8
r)radialdistancefromtheaxisoftheconicalcontactor,m
Re)superficialparticleReynoldsnumberrs)spoutradiusatlevelz,m
u,ums)velocityandminimumspoutingvelocityofthegas,ms-1
Ua,Ums,(Ums)M)superficialgasvelocityintheannularzone,minimumspoutingvelocity,andminimumspout-ingvelocityatthe-1
maximumspoutablebedheight,respectively,msW)solidscirculationrate,kgs-1
z)longitudinaldistancefromthebottomoftheconicalcontactor,m
zm)longitudinalpositionofthemaximumparticlevelocity,m
GreekLetters
a)bedvoidageintheannularzoneγF))contactordensityofangle,thesolid,rad
kgm-3
τυ),υjdelayυtimebetweentwosignals,sww,(w)M,(υw)ms)particlevelocityparalleltothewall,averageparticlevelocity,andparticlevelocitiescorre-spondingtothemaximumspoutablebedheightandminimumspoutingvelocity,respectively,ms-1υz,υjz)componentofparticlevelocityinthezdirectionanditsaveragevalueatagivenlevel,ms-1
υz(0),[υz(0)]max)componentofparticlevelocityinthezdirectionattheaxisanditsmaximumvalue,zone,ms-1υja)averageparticlevelocityintheannularms-1
LiteratureCited
Abdelrazek,I.D.AnalysisofThermo-ChemicalDepositioninSpoutedBeds.Ph.D.Thesis,UniversityofTennessee,Knoxville,1969.
Becker,H.A.AnInvestigationofLawsGoverningtheSpoutingofCoarseParticles.Chem.Eng.Sci.1961,13,245.
Benkrid,A.;Caram,H.S.SolidFlowintheAnnularRegionofaSpoutedBed.AIChEJ.1989,35,1328.
Boulos,M.I.;Waldie,B.High-ResolutionMeasurementofPar-ticlesVelocitiesinaSpoutedBedUsingLaser-DopplerAn-emometry.Can.J.Chem.Eng.1986,64,939.
Box,M.J.ANewMethodofConstrainedOptimizationandaComparisonwithotherMethods.Comput.J.1965,1,42.
Day,J.Y.;Morgan,M.H.,III;Littman,H.MeasurementsofSpoutVoidageDistributions,ParticleVelocitiesandParticleCircula-tionRatesinSpoutedBedsofCoarseParticles.II.ExperimentalVerification.Chem.Eng.Sci.1987,42,1461.
Epstein,N.;Grace,J.R.SpoutingofParticulateSolids.InHandbookofPowderScienceandTechnology;Otten,L.,Fayed,M.E.,Eds.;VanNostrandReinhold:NewYork,1984;Chapter11.
Gorshtein,A.E.;Mukhlenov,I.P.TheMovementofSolidMaterialintheSpoutingBed.Zh.Prikl.Khim.(Leningrad)1967,40,2469.
He,Y.L.;Qin,S.Z.;Lim,C.J.;Grace,J.R.ParticleVelocityProfilesandSolidFlowPatternsinSpoutedBeds.Can.J.Chem.Eng.1994,72,561.
Kim,S.J.;Cho,S.Y.ParticleVelocityandCirculationRateinLiquidSpoutedBeds.Korean.J.Chem.Eng.1991,8,131.Kmiec,A.HydrodynamicsofFlowsandHeatTransferinSpoutedBeds.Chem.Eng.J.1980,19,189.
Krzywanski,R.S.;Epstein,N.;Bowen,B.D.Multi-DimensionalModelofaSpoutedBed.Can.J.Chem.Eng.1992,70,858.Lefroy,G.A.;Davidson,J.F.TheMechanicsofSpoutedBeds.Trans.1nst.Chem.Eng.1969,47,120.
Mathur,K.B.;Epstein,N.SpoutedBeds;Academic:NewYork,1974.
Mathur,K.B.;Gishler,P.E.ATechniqueforContactingGaseswithCoarseSolidParticles.AIChEJ.1955,1,157.
Matsen,J.M.VoidFractionVariationintheSpoutedBedAnnulus.Ind.Eng.Chem.ProcessDes.Dev.1968,7,159.Mikhailik,V.D.;Antanishin,M.V.ThespeedofParticlesandVoidageintheCoreoftheSpoutingBed.VestiAkad.Nauk.BSSRMinskSer.Fiz.Takln.Nauk1967,3,81.Ne´meth,J.;Pallai,I.SpoutedBedTechniqueanditsApplication.Magy.Kem.Lapja.1970,25,74.Olazar,M.;SanJose´,M.J.;Aguayo,A.T.;Arandes,J.M.;Bilbao,J.StableOperationConditionsforGas-SolidContactRegimesinConicalSpoutedBeds.Ind.Eng.Chem.Res.1992,31,1784.
Ind.Eng.Chem.Res.,Vol.37,No.11,19984527
Olazar,M.;SanJose´,M.J.;Pen˜as,F.J.;Aguayo,A.T.;Bilbao,J.
TheStabilityandHydrodynamicsofConicalSpoutedBedswithBinaryMixtures.Ind.Eng.Chem.Res.1993a,32,2826.Olazar,M.;SanJose´,M.J.;Aguayo,A.T.;Arandes,J.M.;Bilbao,J.PressureDropinConicalSpoutedBeds.Chem.Eng.J.1993b,51,53.
Olazar,M.;SanJose´,M.J.;LLamosas,R.;Bilbao,J.Hydrody-namicsofSawdustandMixturesofWoodResiduesinConicalSpoutedBeds.Ind.Eng.Chem.Res.1994a,33,993.Olazar,M.;SanJose´,M.J.;Zabala,G.;Bilbao,J.ANewReactorinJetSpoutedBedRegimeforCatalyticPolymerizations.Chem.Eng.Sci.1994b,49,4579.Olazar,M.;SanJose´,M.J.;Pen˜as,F.J.;Aguayo,A.T.;Arandes,J.M.;Bilbao,J.ASimplifiedModelforGasFlowinConicalSpoutedBeds.Chem.Eng.J.1995a,56,19.Olazar,M.;SanJose´,M.J.;LLamosas,R.;Alvarez,S.;Bilbao,J.StudyofLocalPropertiesinConicalSpoutedBedsUsinganOpticalFiberProbe.Ind.Eng.Chem.Res.1995b,34,4033.Olazar,M.;SanJose´,M.J.;Aguado,R.;Bilbao,J.SolidFlowinJetSpoutedBeds.Ind.Eng.Chem.Res.1996,35,2716.
Olazar,M.;Arandes,J.M.;Zabala,G.;Aguayo,A.T.;Bilbao,J.DesignandSimulationofaCatalyticPolymerizationReactorinDiluteSpoutedBedRegime.Ind.Eng.Chem.Res.1997,36,1637.
Randelman,R.;Benkrid,A.;Caram,H.S.InvestigationoftheSolidFlowPatterninaSpoutedBed.AIChESymp.Ser.1987,83,23.
Robinson,T.;Waldie,B.ParticleCycleTimesinaSpoutedBedofPolydisperseParticles.Can.J.Chem.Eng.1978,56,632.Rovero,G.;Piccinini,N.;Lupo,A.SolidVelocitiesinFullandHalf-SectionalSpoutedBeds.Entropie1985,124,43.
Roy,D.;Larachi,F.;Legros,R.;Chaouki,J.AStudyofSolidBehaviourinSpoutedBedsUsing3-DParticleTracking.Can.J.Chem.Eng.1994,72,2945.SanJose´,M.J.;Olazar,M.;Aguayo,A.T.;Arandes,J.M.;Bilbao,J.ExpansionofSpoutedBedsinConicalContactors.Chem.Eng.J.1993,51,45.SanJose´,M.J.;Olazar,M.;Pen˜as,F.J.;Bilbao,J.SegregationinConicalSpoutedBedswithBinaryandTertiaryMixturesofEquidensitySphericalParticles.Ind.Eng.Chem.Res.1994,33,1838.SanJose´,M.J.;Olazar,M.;Pen˜as,F.J.;Arandes,J.M.;Bilbao,J.CorrelationforCalculationoftheGasDispersionCoefficientinConicalSpoutedBeds.Chem.Eng.Sci.1995,50,2161.SanJose´,M.J.;Olazar,M.;Alvarez,S.;Bilbao,J.LocalBedVoidageinConicalSpoutedBeds.Ind.Eng.Chem.Res.1998,submitted.
Shigeo,N.ParticleBehaviourinSpoutedBeds.Bachelor’sThesis,HokkaidoUniversity,Saporo,Japan,1965.
Suciu,G.C.;Patrascu,M.ParticleCirculationinaSpoutedBed.PowderTechnol.1978,19,109.
Thorley,B.;Saunby,J.B.;Mathur,K.B.;Osberg,G.L.AnAnalysisofAirandSolidsFlowinaSpoutedWheatBed.Can.J.Chem.Eng.1959,37,184.
VanVelzen,D.;Flamn,H.J.;Langenkamp,H.;Casile,A.MotionofSolidsinSpoutedBeds.CanJ.Chem.Eng.1974,52,156.Waldie,B.;Wilkinson,D.MeasurementofParticleMovementinaSpoutedBedUsingaNewMacroprocessorBasedTechnique.Can.J.Chem.Eng.1986,64,944.
ReceivedforreviewJanuary14,1998
RevisedmanuscriptreceivedAugust10,1998
AcceptedAugust11,1998
IE9800243
因篇幅问题不能全部显示，请点此查看更多更全内容