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Numerical_1

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Numerical_1Numeri

    Numerical

JoURNALoFCoALSCIENCE&ENGINEERING

    ;(CHINA)ISSN1006-9097

    ;pp644_647Vo1.14No.4Dec.2008

    ;Numericalsimulationontileimpactingandcomminuting

    ;ofcoaibased01]liYNA

    ;LIFang.wei(李芳玮)’,LIYah.huan(李艳

    ),XUZhenliang(@~).,JINLong.zhe(金龙哲)’

    ;(1.SchoolofCivilandEnvironmentEngineering,UniversityofScienceandTechnologyBeijing,Beijing100083,China;

    ;2.CollegeofCivilEngineeringandArchitecture,LiaoningTechnologyUniversity,Fuxin123000,China;3.Instituteof

    ;VocationalandTechnical,LiaoningTechnologyUniversity,Fuxin123000,China) ;AbstractSimulatedcomminutionthatthecoaIimpactrigidwalIusingfiniteelementsoft- ;wareofexplicitformulationbasedondynamicsmodeIofelasticcollisionfHamiltonvaria- ;tionnalprinciple).thecriticaIvelocityofthecoaIimpactingcomminutionwasabout10m/s, ;andvalidatedthereleaseeffectofpressureinthecoaIimpactingcomminution.andthen ;extendappliedfieldofthefiniteelementsoftwareofexplicitfclrmulationLS-DYNAanalys-

    ;ingImpactcomminutionoftheelastic-plasticmaterial.Thesimulationresulthasgreat ;guidanceandreferencevalueforunderstandingtheimpactcomminutionmechanicsof ;coaIandothermaterialandmanufacturingcomminutionequipment.

    ;KeywordsLS-DYNA,FEM,impactandcomminute,contactimpact,numericalsimulat

    ion

    ;IntrOductiIj

    ;Thecoalpowderwhichisobtainedbyusingthe

    ;wateretultrafinecomminutiontechnologyisthe

    ;premiseformakingthehigh-poweredwatercoalslurry.

    ;Itsprincipleisasfollows.Itputsthecoalparticlepot

    ;inthehighpressuredreturnpassageandmakesthe

    ;coalpowderdirectlyinjectthroughthehighpressure

    ;waterbythepositivepressure.Andthenthecoalpar

    ;ticlewhichismixinguniformlywithwaterwillspurt

    ;outfromthenozzle.Theinternalcracksofthecoal

    ;particleswhichspurtoutfromthenozzlewillbeex

    ;pandedbytheimpactfunctionofthecoalparticleand

    ;tungstencarbidetarget,whichwillleadtothebreaking

    ;ofthecoalparticle.

    ;Itiswellknownthatthecoalisabrittlematerial

    ;whichisfu11ofthemicrocracks.Theintemalminute

;cracksofthecoalcanberegardedas”damage”.The

    ;coalmaterialcanbesimplifiedasanelasticplastic

    ;andsomedamagedmaterialwhenstudyingit.The ;maincomminutionofthewaterietultrafineistheim

    ;Tel:864186650626,Email:kyc2005@163.com

    ;pactfunctioncomminution.Andtheparenchymais ;thattheminutecracksexpandimmediately,whichwill ;lcadtothebreakingofthecoalwhentheimpactload ;exceedstheelasticplasticlimitofthecoalparticle. ;Thecontactimpactproblemistypicalinimpactdy

    ;namics.anditsnumericalsimulationisverydifficult ;inalotofimpactprojects.TheANSYS/LSDYNA

    ;softwarehaslotsofmeritsinautomaticcontact,con- ;cussion,impactandbigdistortion,bigdisplacement, ;bigstrain,multinonlinear-static,breakingcrack ;simulation,andsoon.Soithaswidespreadapplication ;intheimpactanalysisofcarcollision,metalmolding, ;andsoonfl_21.

    ;1Mathenlatjcalmodels

    ;1.1Thenumericalmethodofontact-impact’s

    ;InFig.1.twoobiectsAandBcontact.Theircur- ;rentconfigurationisand,theboundaryfaceis ;AAandAB,thecontactfacerecordsiscAnAB,the ;objectAisamasterbody,itscontactfaceisthemaster ;face,theobjectBisslavebody,itscontactfaceis ;L1Fangweiela1.Numel’icalsilnulationOlltheimpactingandcomminuting645

    ;slaveface.Eachtimestep,itsdisplacementcoordi- ;natedcondition:

    ;【一己=(甜一)0Ic,

    ;or=(vv.)0l,

    ;where,subscriptNshowscontactnorma1.

    ;AB

    ;Fig.1Contactbetweenobject

    ;IA+B=0,

    ;+=0,

    ;here,AandBarethenormalarecontactforceof ;theobjectsAandttAandttBarethetangential

    ;contactforceoftheobjectsAandB.Processingsym

    ;metricallypenaltyfunctionisusedinslidingcontact ;interface.

    ;1.2Basicgoverningequationofcoalparticleim- ;pacttarget

    ;Massconservation:

    ;p(x,t)J(X,t)=pax).(1)

;Momentumconservation:

    ;+:.(2)

    ;Ui

    ;Energyconservation:

    ;

    ;=

    ;.

    ;(3)

    ;wnere,=

    ;(+avj)J-.smeaeroionorthecoalparticle. ;Theconstitutiverelationofthecoalparticle: ;o-=(,…).(4)

    ;1.3Otherconditions

    ;Boundarycondition:

    ;ui(,t)1tar=ui(,f).

    ;Initialcondition:

    ;(,o)=()I.,u(X,o)=u0()ItaIg.

    ;No-interpenetrationconditionbetweencoalparti

    ;cleandtarget0aln===0.

    ;Thecontactfacestrengthconstraint: ;+targ=0,+=0.

    ;Meaningofthemarkconcreteisshowninthe ;Reference3].

    ;2Movementdifferentialequationofthe ;discretefiniteelement

    ;UsingtheFEMofLagrangian’smesh,making

    ;thestructurespaceofthecoalparticleandthetarget

    ;discrete,spacecoordinatesxi(x,0ofc0a1,etofany

    ;particleontheelementanytimeis: ;,f)=xu(t),(5)

    ;here,N/istheshapefunctionofthenodeI.There

    ;dundantsubscriptexpressesthatsumsinitsvalue ;scope?

    ;SodisplacementofanypointXintheelementis: ;ui,f)=xi(X,f)=?,()(f),(6)

    ;where,xjt)-X~isthedisplacementofthenodeIin ;theelement.Inlikemanner,velocity,theacceleration,

    ;thedeformationrateandthevirtualvelocityofany ;pointintheelementis:

    ;zii,t)=?,)(),(7)

    ;//,(X,t)=()(f),(8)

    ;=

    ;(+]=+

    ;()=(),

;f=JBWcrdV,f”=』?pbdV+I4NTdA,

    ;=

    ;pNNdV+IPoNNdVoisthesystemmass

    ;matrix,nothingtodowiththetime,onlyneedscom

    ;putationintheinitialtime.

    ;3Resultsandanalysises

    ;Inthenumericalsolution.thematerialnon.1inea~ ;thestructurenon.1inearandthecontactconditionnon

    ;1inearareincluded.thetwo.dimensionalaxialsymme

    ;tryentityelement.thevelocityinitialconditionandthe ;displacementboundaryconditionaswellasthemesh ;breaksimulationisinvolved.

    ;3.1Modelingandmeshdevelopment

    ;3.1.1Basicpremise

    ;IkingtheexperimentaldataofShanxiXishan ;Coa1sampleasthesimulateddata.assumptingthecoal ;particleisthebal1.thecoalparticle’sandtarget’sma—

    ;terialparametersareshowninTables1and2,MAT ;PLASTICK?MATICmateria1mode1ischoosedas

    ;thecoalparticle.Accordingtothestudyobject, ;rIUGIDmateria1modelischoosedasthetarget. ;646JournalofCoalScience&Engineering(China, ;Table2Materialparameteroftarget

    ;3.1.2Modelingandmeshdevelopment

    ;Accordingtotheassumpting,coalparticleand ;thetargetissimplifiedtothetwodimensionalaxial

    ;symmetrymodel,thegeometricmodelandthefinite ;elementmodelareshowninFigs.2and3.Thecoal ;particleandthetargetareallchoosed2Dsolid162 ;elements.Thecoalparticleisdividedinto3668three ;nodeelements,simplepointintegralpattemischoosed; ;thetargetisdividedinto3000quadranglemeshele

    ;ments.

    ;Fig.2Geometricmodelofcoalandtarget

    ;Fig.3Finiteelementmodelofcoal

    ;3.2Initialconditionandboundarycondition ;Coalparticle:impactingfixedrigidtargetverti

    ;callyby1.0,2.5.5.0,7.5m/sandtheradiusis ;0.15mm;

    ;Target:aroundoftargetisfixed.

    ;Thecontroltimeisthatthemovementtimebe. ;forethecontactaddstothecontactingtime.thetrue ;contactingtimein10Bs,anditjustrightmatchthe ;Referencef451,thecontroltimeis25gs.

;3.3Numericalsimulationresultanalysis

    ;FromFig.4(a),wecanseetheimpactvelocityis ;biggerandthemissesstressisbigger,thisconformsto ;actual;Fig.4(b)showsimpactvelocityisbigger,its ;contacttimeisshorter,thenthecoa1particlereceives ;theformidablestressfunctioninsuchashorttimeis ;obtained,subsequentlybreakOCCllrS.

    ;Inthenumericalsimulationprocesswecanob. ;tainthatwhentheimpactvelocityis2.5m/s.thecoal ;graintoseparatewiththetargetfromthecontactdoes ;notstave(i.e.elementnotstave),asshowninFig.5(a). ;Impactvelocity(m/s)

    ;(a)

    ;(b)

    ;Fig.4Therelationofmaximalstress,contacttime ;withimpactvelocity

    ;Whenthecoalparticleimpactsthetargetbv ;5.0m/sandachievesthebiggestdisplacement.itdoes ;notbreak,butthecoalparticleOccurstobreakinthe ;ejectprocess.whichexplainedthatwhenthecoa1par

    ;ticleandthetargetfromthecontacttothebiggest ;compression,thecompressedstressdoesnotachieve ;thecompressivestrengthlimitofthecoalparticle,be. ;causethecommonmaterialtensilestrengthisfar ;smallerthanthecompressionstrength,thecoalparti. ;cleoccurrstobreakintheejectprocessbecausethe ;mechanismofreleaseofhydraulictensilestress,it ;achievesthetensilestrengthlimit.asshownin ;Fig.5(1)).

    ;,?henthecoalparticleimpactvelocityisbigger ;than10rn/s,thecoalparticleisnoteject,buthasoc. ;curredintensebreakinthecompressionprocess,as ;showninFig.6,explainedthatcompressionstresshas ;achievedthecompressionstrengthextremeofthecoal ;particlewhenthecompressionprocessismaximizing, ;italsofurtherObtainscausesthecoalparticleimpact ;breakinadvance.theminimumcritica1velocityis ;aboutl0rn/s.

    ;(_爵白三)s?2.叽一目fs.uJ=.一日II,.

    ;y

    ;LIFangwei.eta1.Numericalsimulationontheimpactingandcomminuting647

    ;Thestationwh

    ;.

    ;enthecoalandnel2.

;.898x10-4

    ;3181targethaVethemimaltouchl2.×0

    ;(13.5s)

    ;Thestationaftercoaland

    ;targetrebound(21.5s)

    ;(a)

    ;O

    ;8.

    ;232×106

    ;i?174x104116x10

    ;嚣譬

    ;2.058x10

    ;10

    ;Thestationwhenthecoa1andthe ;targethavethemaximaltouch ;(7.5as)

    ;Thebrokenstationaftercoal ;andtargetapaa(11s)

    ;(b)

    ;Fig.5Impactstationofcoalwhenvelocityis2.5and5.0m/s

    ;Thebrokenstationwhenthecoa1 ;beginstoimpactthetarget(3.5gs) ;Thefatiguecrackstationduring ;thecoalimpact(10gs)

    ;6.175×l05

    ;4.940x10-5

    ;3.705xl05

    ;2.470~l05

    ;1.235×105

    ;O

    ;1.7l8×l

    ;1.374×1O

    ;1.O31×10.4

    ;6-87I×lo_

    ;3.435×lO

    ;O

    ;Fig.6Thebrokenstationofcoalwhenvelocityis10m/s

    ;4Conclusions

    ;ThePaDerhasusedtheANSYS/LSDYNAsoft

    ;waretosimulatethecoalparticleofimpacttarget

    ;comminution,theresultsareasfollows. ;f11Ithasbuilttheconstitutiverelationofthe

    ;elastic.plasticmodel,whichassumingthecoalparticle

    ;asbal1.Andthenithasobtainedthecriticalvelocityof

    ;thecoalparticlecomminutionbychoosingappropriate ;computationalmethodsandtheboundaryconditions, ;anditsvalueisabout10rn/s.

    ;f21Whenthecoalparticlesareimpactingthetar- ;3.884×1O

    ;2330×1O

    ;1554x1O

    ;7.768x10

    ;0

    ;3.450x1O

    ;2760xl0

    ;2.070~105

    ;1.380x10

    ;6900xlO

    ;O

    ;getat5m/s.itcanbeseenthatthebreakingoccuron ;theprocessofejecting,whichhasapprovedthepres

    ;surereleasemechanismofthecoalparticles’impact

    ;comminution.Butthecoalparticlecannotbecom

    ;minutedatthisvelocity.Thecoalparticleswillbe ;comminutedbycompressedstresswhenthevelocity ;getto10m/s,andthemechanismofreleaseofhy

    ;draulicpressureisnotobvious.

    ;f3Itcanbeseenthatwhentheimpactvelocity ;ofisincreasing.andthecollisionpressureisincreas

    ;ingaccordingl~butthetimeoftheimpactandcontact ;isgettingshorterintherangeofelasticity. ;References

    ;徐之纶.弹性力学[M].北京:人民教育出版社,1982:

    ;291293.

    ;XuZhilun.Elasticmechanics[M].Beijing:PeopleEduca

    ;tionPress,1982:291293

    ;JohnsonKL.Contactmechanics[M].Beijing:Higher ;EducationPress,1992:399400.

    ;靳钟铭,弓培林,靳文学.煤体压裂特性研究[J].岩石

    ;力学与工程学报,2002,2l(1):7072.

    ;JinZhongming,GongPeilin,JinWenxue.Studyonthe ;characteristicofcoalmassfracture[J].ChineseJournalof ;RockMechanicsandEngineering,2002,2l(1):7072.

    ;JohnO.Hallquist,LSDYNATheorymanual2006.Liv

    ;ermoreSoftwareTechnologyCorporation,2006. ;LivermoreSoftwareTechnologyCorporation.Keyword ;Manual970,2003

    ;

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