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Simulation of Turbulent Combustion Flame Feature Based on Fractal Theory for SI Engines

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Simulation of Turbulent Combustion Flame Feature Based on Fractal Theory for SI Enginesof,on,Flame,Based,for,flame,based

    Simulation of Turbulent Combustion Flame Feature Based on Fractal Theory for SI

    Engines

    Trans.TianjinUniv.2010.16:256261

    DOl10.1007/s1220901013808

    SimulationofTurbulentCombustionFlame

    BasedonFractalTheoryforSIEn

    Feature

    

    gmes

    ZHANGJun(张军),DUQing(杜青)',SONGDongxian(宋东先)2,

    YANGYanxiang(杨延相)'

    (1.InternalCombustionEngineResearchInstitute,TianjinUniversity,Tianjin300072,China;

    2.StateKeyLaboratoryofEngines,TianjinUniversity,Tianjin300072,China) TianjinUniversityandSpringerVerlagBerlinHeidelberg2010

    Abstract:Theflamestructureofgasolineengineiscomplicatedandhasthecharacteristicoffracta1geometry.A

    fractalcombustionmodelwasusedtosimulatetheengineworkingcycle.Basedonthismodel,thefractaldimension

    andlaminarflamesurfaceareaofturbulentpremixedflameswerestudiedunderdifferentworkingconditions.The

    experimentalsystemmainlyincludesanopticalengineandasetofphotographyequipmentusedtoshoottheimagesof

    turbulentflameofspark.ignitionengine.Thedifferencebox

    countingmethodwasusedtoprocess2Dcombustion

images.Incontrasttotheexperimentalresults,thecomputationalresultsshowthatthefractalc

    ombustionmodelisan

    effectivemethodofsimulatingtheenginecombustionprocess.Thestudyprovidesabetterun

    derstandingforflame

    structureanditspropagation.

    Keywords:turbulentcombustiomfractalsimulation:opticalengine

    CombustionmodelsforSIenginesareimportant andhavebeenwelldeveloped.Accordingtodimensions involvedinmodels,theycanbeclassifiedasthreetypes, iezero..quasi.andmultidimensiona1models'J.Due

    toIessthanmulti.dimensionaImodelsatcostandmore accuratethanzerodimensionalmodels.thequasi

    dimensionalmodelshavebeenwidelyusedtosimulate sparkignition(SI)enginecombustion.Becausethe flameseparatesthecylinderchargeintoaburnedzone andanunburnedzone,thequasidimensionalmodels

    reasonablyrepresenttheactualphysicalcombustion process.Thefractalcombustionmodelisatypeofquasi

    dimensionalmodel,whichpredictsthechargeburning rateonthebasisoftheturbulentflamepropagationand characterizesthesurfaceareaoftheturbulentflameby thetheoryoffractalgeometryo_.Duetoitsself-

    similarityandbeingabletoconsidertheinfluenceof flowparameters.residualgascontentandcombustion chambershapeoncombustion,thefractalcombustion modelhasbecomeoneofthedominantquasi

    dimensionalmodelsrecently[0.13].

    InthisPaper,thefractalandstructuralparametersof turbulentflameareanalyzed,simulatedandcompared betweenexperimentalandcomputationalresults.The

    experimentalstudywascarriedoutonanopticalsingle- cylinderengineequippedwithaquartzwindowonthe cylinderhead.Theimagesofincylinderturbulentcorn

    bustionflamewereacquiredthroughahigh-speeddigital CCDcamera.ThefractaIcombustionmodeIisbasedon theturbulentflamestructure,itspropagationspeedand therelatedcombustionregimesoccurringintheinternal combustionengine.

    1Experimentalsystem

    Theexperimentalsystemmainlyincludesanoptical engine,ahighspeedCCDcamera,asetofinjectionsys

    ternandsomecontrolelements.Fig.1showsthelayoutof theexperimentalsystem.

    1.1Opticalengine

    Arealsinglecylinderfour-strokeenginewasredes

    ignedtoanopticalengineandthepistonandcylinder blockwereregenerated.Atransparentquartzwindow waslocatedonthetopofthepistonandareflectingmir- rorwaslocatedatthebottomofenginetogivetheim

    agesofcombustionflame.Theopticalengineisequipped withanFAIelectronicfuelinjection(EFI)systemto controltheignitiontime,injectiontimingandinjection Accepteddate:20100325.

    *SuppoSedbvNationalNaturalScienceFoundationofChina(No.50876072)andTianjinM

    unicipalScienceandTechnologyCommission

    (No.07JCYBJC03900).

    ZHANGJun,bornin1982,male,doctoratestudent. CorrespondencetoDUQing,E-mail:duqing@tju.edu.cn. ZHANGJunetnl:SimulationofTurbulentCombustionFlameFeatureBasedonFractalTheo

    ryforSIEngines

pulseaccurately.Moreover,theengine'Slubricationsys

    temandchaintransmissionmechanismwerealsoredes

    ignedtomaketheperformanceoftheredesignedengine thesameastheprimaryengine.Themainparametersof theopticalenginearelistedinTab.1.

    Fig.1Schematicofexperimentalsystem

    Tab.1Specificationsoftheopticalengine 1.2Experimentalsetupforcollectingopticalimages Ahigh.speeddigita1CCDcamera(MotionCorder Analyzer,SR.Ultra,madebyKODAKCompanyin USA).isthecoreofthesystemforobtainingtheflame images.Fig.2showsthesketchmapofopticalimagecol

    lectingsetup.Thelightemittedduringflamepropagation wascollectedbyaquartzwindowandreflectedbya45. inclinedmirrorlocatedatthebottomoftheengine. Quartz

    Reflecting

    mirror(45.)

    Fig.2Sketchofimagecollectingsetup

    10000frames/s.Inthisexperiment,thecollectingspeed wassettobe1000frames/sandeachimagehadadis. playsize(resolution)of256×240pixels.Also,inorder

    tomeasuremetimeofeachimageaccurately.themag. netoignitionsignalwassetasthesynchronizationsignal oftheCCDcameraandthepulseshotbythephoto. electricencoderwassetasthetimingbenchmarksigna1. 2Computationalmethod

    2.1Fractalcombustionmodel

    Themassburningratedmb/dtisoftendefinedas

=4SL=Pu(1)

    wherePuistheunburnedgasdensity;ATandALarethe surfaceareaOfturbulentflameandlaminarflame.respec. tively;SListhelaminarflamespeed.

    Thefracta1combustionmodelassumesthatthetur- bulentpremixedflameofSIenginesisawrinkledlami

    narflame,andthewrinkledsurfaceareaoftheflameis characterizedbyfractalgeometryl2_.Thenitsflame

    surfaceareacanbeeasilycomputedas

    =

    2

    whereD3isthefractaldimension;Zmandlmarethe outerandinnercutoffscale,respectively.Thevaluefor fractaIdimensionvarieswiththeleveloftheflame. Thecameracancollect2048imagesoncebyusingsurface

    areawrinkling.Thefractaldimensionisex

    high.speedRAManditsmaximumcollectingspeedispressedas[]

    257

    TransactionsofTianjinUniversityVo1.16No.42010 =

    /S1+

    S/1(3)T+T"

    2.2Incylinderturbulentmodel

    Inthefractalcombustionmodel,thein-cylindertur- bulenceischaracterizedbyaK-kmodel4].whichcanbe

    describedasfollows.

    Kineticenergyofthemeanflowfield:

    dK

    ?P?

    Kineticenergyoftheturbulentflow:

    dt

    P+后一

    ?一(5)lJ"

    wheremisthemassofthechargeincylinder;rniand rh.

    aretheintakeandexhaustmassflowrate,respec- tively;istherateofkineticenergydissipation;andP representstheturbulentproductionterm. 2.3Heattransfermodel

    Theheattransfertothewallsofcombustioncham

    ber,i.e.,thecylinderhead,thepistonandthecylinder liner,iscalculatedfrom

    Qwi=4aw()(6)

    whereand4arewallheatflowandsurfacearea (includingcylinderhead,piston,liner),respectively;aw

    isheattransfercoefficient,whichiscalculatedaccord. ingtoWoschniheattransfermodel[asfollows:

    aw=130D.p

    .

    0-.?

    [CIcm"}-(Pc-Pc0)0

    whereC1andC2areempiricalconstants; tureinthecylinderatintakevalveclosing

    258

    istempera.

    (IVC):and

P.1ispressureinthecylinderatIVC.

    2.4Simulationprocess

    Inthesimulationprocess,thereareseveralcontrol- lingparameters,includingignitiondelay,thebeginning andendingofturbulentflame,theturbulenceproduction anddissipation,theeffectofresidualgascontenton combustion.Alltheseparametersareeitherconstantor expressedasafunctionofenginespeedandthephase angleofintakecam.Forfullload,allthefractalparame

    tersareeithertreatedasconstantorcorrelatedasafunc

    tionofenginespeedandintakecamshift.Forpartload, allthecombustionparameters,exceptforignitiondelay, canbeeithertreatedasconstantorcorrelatedasafunc

    tionofenginespeed,loadandintakecamshift.Ignition delayisinfluencedconsiderablybytheresidualgascon

    tentanditcannotbetreatedasconstantasin1oad.

    3Resultsanddiscussion

    3.1Combustionflameimages

    Theexperimentalstudywascarriedoutunderdif- ferentengineworkingconditions.Consideringtheinten. sitVofquartzwindowonthetopofcylinderandthe compressionratioofopticalengine,theenginespeed shouldnotbetoohighanditshouldbekeptatl000 r/minapproximately.Fig.3showsagroupofcombustion flameimagesunderstandardworkingcondition:93 gasoline;enginespeed950r/min;theignitiontimeO.

    CABTDC:thepulsewidthofiniection0.096ms:andthe widthofthrottleopening30%.

    ?一一一口一

8.CA2.CA35.CA9.2.CAl4.9.CA

    20.6.CA26.3.CA377.CA433.CA

    490.CA54.7.CA60.4.CA66.1.CA7l_8.CA

    Fig.3Flameimagesunderstandardworkingcondition ZHANGJunetal:SimulationofTurbulentCombustionFlameFeatureBasedonFractalTheo

    ryfo,SIEngines

    Fig.4(a)showstheeffectsofenginespeedoncom' bustion.Whentheenginespeedrises,thecombustion becomesmoreviolentandtheflamehasamoreserious fragmentation.AndasimilarcaseappearsinFig.4(b) andFig.4(c).respectively.Theignitionadvanceangle andinjectionpulsewidthhaveadirectinfluenceonthe wrinkleofturbulentflame.Theearlierignitionangleand thewiderinjectionpulsebothcanstrengthentheintensity ofenginecombustionprocess.

    650r/min750r/rain850r/min950r/min1050r/min (a)Flameimagesunderdifferentenginespeeds 12_3.CA130.CA137.CA14.4.CA15.1.CA

    (b)Flameimagesunderdifferentignitionadvanceangles OO.016ms0.048msO.080ms0.096ms

    (C)Flameimagesunderdifferentinjectionpulsewidths Fig.4Flameimagesunderdifferentworkingconditions 3.2Experimentalresultsandsimulation

    Thepreprocessingoffractalimages,whichmainly includeseliminatingthenoiseofflameimagesandad

    justingthegrayofimages,isused.Thenoiseofcombus. tionimagemostlycomesfromthecombustionofoptical engineandCCDcameraitself.Onlyaftereliminating noisebyusingthemedianfilteringmethod,themore

    distinctflameimagescanbeacquired.Thepurposeof

    adjustingthegrayofimagesistoobtain2Dgrayimages ofcombustionflames.Basedontheimagesofbinariza

    tion,theflameedgescanbeextracted,andfinallythe fractaldimensionwillbecalculated.Itshouldbenoticed thatexperimentalresultsaredependentonmethodsof imagepostprocessing,whichincludesareacaliper method,boxes.counting,differencebox.counting.Inthis paperfractaldimensionsareobtainedbyusingdifference

    countingmethod.inwhichnoneofflameedgesneed box

    tObepickedup.Underthiscondition.thefractaldimen

    sionsaretheclosesttorealvalues.Thefollowingex

    perimentaldataarebasedontheflameimagesshownin Fig.3.

    3.2.1Comparisonbetweenexperimentalandcomputa

    tionalresults

    Fig.5givesacomparisonoffractaldimensionbe

    tweenexperimentalandcomputationalresults.Fig.5 showsthatthefractaldimensionincreasesatthestagesof turbulentflamedevelopmentandpropagationandde

    creasesatthelatecombustionstage.Thereisanagree

    mentbetweenexperimentalandcomputationalresults, exceptthatthecomputationalmaximumffactaldimension Crankangle/(.CA)

    Fig.5Comparisonoffractaldimension

    

    259

    TransactionsofTianjinUniversityVo1.16No.42010 arrivesalittleearlierthanthatoftheexperiment.which canbeattributedtotime.delayingOfCCDcameraandthe errorsgeneratedfromflameimagesprocessing.

    Fig.6showstherelationshipbetweenthelaminar flamesurfaceareaandcrankangle.Thelaminarflame surfaceareaincreaseswiththeincreaseofcrankangleto someextent,andthenstartstodecreaseatsomecrank angle,whichisconfirmedbyexperimentalandcomputa- tionalresults.Therealsoexistsafewdiscrepancies. whichisattributedtotheinfluenceofexperimentalappa- ratusandmethodofimageprocessing.Butbothofthe trendswithcrankanglearealmostconsistent,exceptthat thecomputationalmaximumvalueappearsalittleearlier thanthatoftheexperiment.

    Crankangle/(.CA)

    Fig.6Relationshipbetweenlaminarflamesurfaceareaand crankangle

    3.2.2Resuitsofcomputationalmode1underdifferent workingconditions

    Theef.fect0fenginespeedonfractaldimensionand laminarflamesurfaceareaisshowninFig.7(a)and(b) undertheconditionoftheoretica1mixtureratioforpart lpad.Whentheenginespeedrises.theturbulenceinten. sityincombustionchamberisstrengthened.whichis helpfultoquickenthespeedofchemicalreactions,gen

    cratethehigherrateofflamewrinklingandenlargethe surfaceareaofcombustionflame.Asaresult.thein. cylindercombustionprocessbecomesmuchmorevio. 1ent,andthefracta1dimensionandlaminarflamesurface areabothincrease.

    Theeffectofignitionadvanceangleonfractaldi. mensionandlaminarflamesurfaceareaisshownjnFig.8 (a)and(b)undertheworkingconditionsthatengine

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