PowderTechnology,63(1990)45-5345 Gas-solidflowandcollectionofsolidsinacycloneseparator L.X.Zhou* DepartmentofEngineeringMechanics,TsinghuaUniversity,Beg&g100084 (China) s.L.soo** DepartmentofMechanicalandIndustrialEngineering,UniversityofIllinoisatUrbana-Chumpaign, 1206 WestGreenStreet,Urbana,IL61801 (U.S.A.) (Received August 21,1989; in revised form April 25,1990) Abstract LDVmeasurementsweremadetocompareandtovalidatecomputationsofflowandpressure dropinacycloneseparatorbyananalyticalsolutionwithapproximationofconstantviscosity anda solutionbasedonthe/C--Eturbulencemodel. Results explain the significance of the solid- bodycoreofthevortexandthedifficultyofthek--Emethodwhenappliedtovortexmotion. Amethodofimprovingtheperformanceofthecycloneseparatorwithacentralbodywas illustrated. Introduction Thecycloneprinciplehasbeenappliedto dust separationformorethan a hundred years. Mostattentionhasbeenpaidtofindingnew techniquestoreducethepressuredropand toincreasethecollectionefficiency[l-3]. However,muchremainstobedone.Funda- mentalstudiesforunderstandingthebasic processesinacycloneareofparticularim- portance.Due tothecomplexityofverystron- glyswirlingturbulentgas-solidflowsina cyclone,ithasbeenchallengingtocarryout theoretical,numericalandexperimentalstu- dies.Atheoreticalanalysis wasperformedby Soo[4]onthegasflowfield,dustdispersion anddust collectionin acyclone,basedonthe fundamentalsofmultiphasefluiddynamics. Recently,Zhouetal.[5]developednumerical modelingand LDV measurementsofgas-solid flows,and also proposedan innovativecyclone separatorwithaspecialcentralbodytore- markably reducethe pressuredrop.The results *PartofthisresearchwasperformedasaVisiting ProfessorattheUniversityofIllinoisatUrbana-Cham- paign. **Towhomcorrespondenceshouldbeaddressed. 0032-5910/90/$3.50 reportedarethoseobtainedthroughthe US-Chinaco-operativeresearchsponsoredby theNational ScienceFoundation.Thedetailed measurementsofthe gas flow field in a cyclone separatorbylaserDopplervelocimetry(LDV) andthenumericalsimulationofthis flowfield byusingthek--Eturbulencemodelandthe SIMPLE(Semi-ImplicitMethodforPressure- LinkedEquations)algorithmgivearelatively completepictureofthewholeflowfield[6]. ThenumericalpredictionsandLDVmeasu- rementsarecomparedwiththeanalyticalso- lution.Thisfurtherstheunderstandingofthe mechanismofthe vortexflowin a cycloneand indicates that, in spite ofseveral simplifications modein thetheoreticalanalysis,theclassical analyticalsolutionfurnishesavalidapproxi- mationofthebasicphysicalfeaturesofthe vortexflow. Analyticalsolution Basedontheconceptofa vortexpipeflow, Soosolvedthecontinuityequationforthe cylindrical co-ordinatesystemr,4, z and conju- gatevelocitycomponents,u,v,wasshown inFig.1.Otherparametersarethestatic 0ElsevierSequoia/PrintedinTheNetherlands 46 Fig.1.Dimensions,co-ordinatesandconjugatevelocities forflowinacycloneseparator.Thecut-outshowsthe centralbodywhenused. pressure pand the effectivekinematic viscosity ye. Thesolutiongivestheradialdistribution ofaxialvelocityinacyclone w*=w w = z*f(r*) (1) whereti= Q/(71-Ro2),Z* =1 -z/z,,and f(r*)is givenbyapolynomial J(r*>= a,+ a,@+ C&r*4+ C&r*6 (2) wherer* =r/R(z)and *2 a,=q (1 l-Y*,a2=-~cz,T~*~ (3) with Theradialdistributionoftangentialvelocity isgivenby v=P[l-exp($)I (4) whereC is themaximumvorticity.Theradius ofthecoreofsolidbodyrotationisgivenby R,=(5) Inaddition,wehave v,=v+y. (6) wherevisthekinematicviscosity,r+isthe eddy viscosityand (G/C%)= A/L.The pressure dropthroughacyclonewithasteepconeof lengthListhus Ap= AP*P&~=02 LwRv35 =CJ60--2 0 R,CC W02(7) wherepa isthedensityofthegasphase,and forinletarea A,andexitarea AlvhAh 0 W=x- (8) Foragivencyclone,wherethefollowingas- sumptionsarevalid: wc& -=const c and V, -=const c (10) thepressuredropwiII taketheform Ap = Kpavi n2 (11) whereKwi l l bedeterminedasanempirical constant. Numericalsimulation Thegeometricalconfigurationandsizesof thecycloneseparatortobestudiedare shown inFig.1,where R,=0.15m,D,=0.3m rl= 0.085m,&=0.17m, A,=rRo2 = 0.0227m2 2,= 0.686m,2,=0.394m L=2,+2,=1.08m Inletnozzlecross-sectionalareaA,,, =0.0126 m2 InFig.1,thedimensionSoftheexitpipe waschosenatthesameheight(0.11m)as theinletnozzleandthediameteroftheexit pipewas0.95m,givinganexitflowareaof 0.007m(smallerthantheinletarea A,)and hencelargeexitflowvelocity.Theaim wasto minimizetheobstructionsintheopticalpath of LDV at a sacritlce of the collectionefficiency. The flowparametersare:air volumetricflow rateQ=0.266m3/s;inlettangentialvelocity 21, = 21m/s;meanaxialvelocityinthecylin- dricalpartofthecycloneZZ= Q/(71-Ro2)= 3.75 m/s;mean axial velocityin the exit tube (vortex finder)w,= Ql(&r2)=11.7m/s;and the swirl numberoftheflowis s=&,D,l(4A~=3.18. Therefore,thevortexflowinthiscycloneis a swirling turbulentflow.Thedesignandope- rating parameters were chosento facilitate LDV measurementsandnumericalmodeling.The collectionefficiencyofthecyclonehastobe sacrificedalsobecausethevalidityofthek--~ approximationdoesnotfavorverylargevor- ticity. As a starting point,consideran axisymmetric turbulentflow,neglecting:(i)theeffectof particlesonthegasflowfield;(ii)thenon- isothermaleffect;(iii)thethree-dimensional effectcausedbytheinletnozzle.Item(iii)is expectedtooccuronlywithinashortaxial distance.Theequationsofconservationbased onthewell-knownk-eturbulencemodelare as follows(with w,uand vdenotingtheaxial, radialandtangentialcomponentsofgasve- locity,respectively): Continuityequation Axialmomentumequation la&.u ;$r/AZ- () & (13) Radialmomentumequationofthegasphase (12) ofthegasphase Tangentialmomentumequationofthegas phase Peh3.J -p$+_- r&r Turbulentkineticenergyequation (15) (16) Turbulent kineticenergydissipation rate equa- tion +;(G&c-~2~4 where c&&=0.09, cr =1.44,c2 =1.92, a,=1,a,=1.33 (17) Theseequationsaresimultaneousnonlinear partial differential equations,and theyare sol- vedbya finite differencenumericalprocedure developedbyPatankarandSpalding[ 61,the SIMPLE algorithm.Thedifferentialequations arefirstintegratedinthecomputationalcell toobtainthefinitedifferenceequationsby 48 usinga hybriddifferencescheme.Thesefinite differenceequationsarethensolvedbythe P- V correctiontechnique,thatis,pre- ssure-velocitycorrectionswithline-by-line TDMA(TriDiagonal-MatrixAlgorithm)itera- tionsandunder-relaxations. Theboundaryconditionsare:uniformdis- tributionsofinlettangentialvelocityandtur- bulencecharacteristicsat the nozzleinlet, fully developedflowconditionsat the outlet, noslip conditionsat thewall,andconditionsofsym- metryattheaxis.Forregionsimmediately adjacenttothewall,thewallfunctionap- proximationsare usedfornear-wall grid nodes tomodifythelowReynoldsnumber(C/V,) effect. ThegridarrangementisshowninFig.2. Bothcoarseandfinegridsareadoptedalter- nativelytofacilitatetheconvergence.Inthe two-dimensionalmodeling,theactualtangen- tial inlet is simulated as an annular inlet which isalineinthecomputeddomain.So,atiny radial inlet velocitymustbegiveninorderto start thecomputations.Besides,theswirl ve- locitymustbeintroducedgraduallyduring several tens of iterations to improve the conver- gence.Thecomputationsweremadeonthe ELEXImachineandtheCPUtimeisnearly 1h. Experiments Theexperimentshavebeencarriedouton aset-upreportedin[ 51.Thetestsectionis acyclonemodelmadeofPlexiglaswiththe samegeometricalconfigurationandsizesas abovedescribedinnumericalsimulation.The airissuppliedbyacentrifugalblowerand glassparticlesofdifferentsizesaresupplied byapowderfeederdrivenbyanelectroma- gneticvibrationtypeSKQ-4.Theparticleand gasvelocityaremeasuredbyalaserDoppler velocimetermadeinthePeoplesRepublicof China withsmokeas tracerparticlesformea- suring gas velocity.The static and total pressure distributionsaremeasuredbystaticpressure tapsandPitottubes,andthecollectioneffi- ciencyismeasuredsimplybyweighingthe collecteddust.Somepreliminarydatahave beenobtainedforparticlevelocity,andthe completeresult will bereportedat a later date. Somedifficulty wasencounteredin measuring the gasand particle velocityin the regionnear thewall,butinmostregionsthedatahave beentakensuccessfully. Resultsanddiscussions Axialvelocity Figure3(a)givesacomparisonofaxial velocitydistributionsobtainedbymeasure- ments(circles),numericalpredictions(solid lines)andanalyticalsolution(dashedlines). Thecalculationsbasedontheanalyticalso- lution are given in AppendixA. All these results appeartobein goodagreementexceptin the near-axisregion.Surprisingly goodagreement isobtainedforthepositionofzerovelocity line,whichisalmostthesameforallthese threemethodsofstudy.Alltheresultsshow thesametrend.Astheairflowentersthe cyclonetangentially, it movestowards the wall, forminganouterdownwardvortexflowdue tothestrongactionofthecentrifugalforce. (4 (a)CoarseGrid(16x7) @I (b)FineGrid(50x20) Fig.2.Gridsystemfornumericalcomputations. idAx10 Velocity -NumerPred ---AnolytSolu .l .Experiment (b)Tangent&al Velocity Fig. 3.Comparisonofmeasurements with computeddata. Aftertheflowreachesthebottom,itturns upward and formsan inner upward vortexflow. Themagnitudeofthemaximumupwardve- locityis muchlarger than the maximumdown- wardvelocity.Thevortexmotioncausesvery lowpressurein the regionnear the axis, where solidbodyrotationhasaneffect.Therefore, the maximum upward axial velocityis not right at the center line, but is locatedat somedistance fromthe axis.Experimentsand numericalpre- dictionshaveshownthatincaseofastrong swirleventheaxialvelocityinthenear-axis regioncanbedownward,thusformingtwo recirculatingflowregionsinthez-rplaneof the cyclone,i.e.,the axial velocityprofiles take theformofs-shapedcurves.Inthenear-axis region,boththeanalyticalsolutionandnu- mericalpredictionsgivemuchhighervalues thanthoseobtainedfrommeasurements.For analyticalsolution,thediscrepancymaybe causedbythe simplificationsmadein the axial momentumequation(e.g.,neglectingthevis- cousterm).Fornumericalsimulation,thedis- crepancyisaresultofthedefectofthek-e model,whichcannotaccountforthenon- isotropiceffectandhencegiveshighervalues oftheturbulentviscosity,leadingtoahigh axialvelocityneartheaxis.Clearly,it would bebettertousethealgebraicstressmodel 49 insteadoftheIGE modeltosimulatestrongly swirlingturbulentflowsneartheaxis. Tangenti alvel oci ty Figure3(b)givesthecomparisonoftan- gential velocitydistributionsobtainedbymea- surements (circles),numericalpredictions(so- lid lines)and analytical solution(dashedlines). Thecalculationsbasedontheanalyticalso- lution are given in AppendixB. All these results showasimilartrend:thetangentialflowof the vortexmotionconsistsof two parts, a near- axis coreofforcedvortex(solidbodyrotation) wherevincreaseswithincreasingr,andan outerfreevortex(h-rotationalflow),wherev decreaseswithincreasingr.Itisinteresting tonotethatalltheseresultsgivealmostun- changedmaximumtangentialvelocityandits radialpositionatdifferentaxialdistancesex- ceptinthenear-bottomregion.Thisisthe resultofconservationofangularmomentum, and the analytical solutioncan reflect the main featureofthe vortexmotion,althoughactually theflowisnonuniformlyturbulent.Obviously goodagreementisobtainedin thefreevortex region(forr>0.05m).On theotherhand,in thesolidbodyrotationregiontheagreement ispoorforthemaximumtangentialvelocity anditsradialposition.Thenumericalpredic- tionsgivebetterresults,butthepredicted maximumtangential velocityv,islowerthan thatmeasured.Theanalyticalsolutiongives amuchhigherv,andamuchsmallercore radius than thosemeasured and simulated. The discrepancyispossiblycausedbythesimpli- ficationsmadein theanalyticalsolution(e.g., constant viscosityin the tangential momentum equation),andonceagain,thedefectofthe ,%--Emodelinoverpredictingtheturbulent vis- cosityhas led tostrongermixingthan actually occurred. Pressuredropand pressuredi stri buti on Fi gure4 gives the comparisonof the pressure drop as a functionof the inlet tangential velocity obtainedbymeasurements(circles),numerical predictions(solidlines)and analytical solution (dashedlines).Alltheseresultsaregenerally in goodagreement.However,the results show that the pressuredropis proportionaltopvdr, andnshouldbesomewhathigherthan2, possibly2