STUDYOFTHEFARFIELDOFAPULSEDSPRAYFROMANAUTOMOTIVEFUE L INJECTOR By FaridRoshanghalb ADISSERTATION Submittedto MichiganStateUniversity inpartialfulllmentoftherequirements forthedegreeof MechanicalEngineering-DoctorofPhilosophy 2015 ABSTRACT STUDYOFTHEFARFIELDOFAPULSEDSPRAYFROMANAUTOMOTIVEFUE L INJECTOR By FaridRoshanghalb Pulsedliquidspraysfromautomotivefuelinjectorsareinh erentlycomplicatedandtheforma- tionanddevelopmentofspraysinvolvemultiplephysicalpr ocesseswhichtakeplacebothsimulta- neouslyandsequentially.Thepulsedspraycharacteristic sfarfromtheinjectororiceareaffected bycomplicatedmechanismsofprimaryandsecondarybreak-u patandclosetotheinjectortip. Thiscomplexityusuallyrequiresresearcherstomakeassum ptionsaboutbreak-upmechanisms.In addition,severaldropletcollisionmodelshavebeenpropo sedforsprays,butwhenusedincon- junctionwithbreak-upmechanismmodels,theaccuracyandl imitationofcollisionmodelshave beendifculttojudge.Thisstudyisintendedtoexplore,ex amineandcomparedifferentcolli- sionmodelsinapulsedfuelspray.Sincetrustworthylaserd iffractionmeasurementsofdroplet sizedistributioncanbeperformedfarfromtheinjectorori ce,thesedatacanbeusedasaccurate initialconditionsforsimulatingdownstreamspraydevelo pment.Sincethepulsedspraysfromau- tomotivefuelinjectorsarerelativelydenseones,thisstu dyeliminatesthecomplexityofsimulating two-phaseowequationsforbreak-upandinsteadsolvesthe simpleruidmechanicsproblemof theLagrangiantrajectoryofspraydroplets,togetherwith adropletcollisionmodel.Itwasfound thatforthesingle-holespraysofthisstudy,whenthedropl etsizedistributionisknownatsome planedownstreamofthebreak-upregion,thedevelopmentof thespraycanbemodeledaccu- ratelybyusingasimpleLagrangianmodelwhichcalculatest hedropletcollisionimpactparameter analyticallyateachcollision. Tomyparents,FarahnazandGholamreza,andmylovelywife, Dr.SoroorSoltani. iii ACKNOWLEDGMENTS Iwouldliketothankallthepeoplewhocontributedsomehowt othiswork.Firstandforemost IthankmyadvisorProfessorGilesBreretonwhohelpedmethr oughoutmyresearch.Heisnot justmythesisadvisor,butagoodfriendwhohaveledmethrou ghmygraduatestudyperiod.I wouldliketospeciallythankmybeautifulwife,Dr.SoroorS oltani,whoisalwayssupportive. Shehelpedmeincodingthesimulation.Iwouldliketothankm ycommitteemembersProfessors FarhadJeberi,HaroldSchockandDennisMillerfortheirint erestinmywork.Iwouldalsoliketo thankMr.EdTimmwhohelpedmealotinsettinguptheexperime nts. iv TABLEOFCONTENTS LISTOFTABLES ....................................... vii LISTOFFIGURES ...................................... viii Chapter1Introduction .................................. 1 1.1LiquidSprays.................................... .1 1.2TheImportanceofSprayResearch.................... ......2 Chapter2BackgroundandObjectives .......................... 4 2.1LiquidJetInstabilityandBreak-Up................. .........4 2.2SprayResearch................................... .5 2.3EvaporationinDropletsandSprays.................. ........10 2.4Micro-CharacterizationsofSprays................. .........11 2.5ObjectivesofthisStudy........................... .....14 Chapter3TheoreticalBackground ............................ 16 3.1DropletEvaporation.............................. ....16 3.1.1The d 2 Law..................................17 3.1.2TheSpaldingMass-NumberModel................... ..18 3.1.3CoupledODEModels............................20 3.1.4CoupledPDEDropletEvaporationModels............ .....22 3.2SprayDynamics................................... .24 3.2.1Break-Up...................................24 3.2.2CollisionModels............................... 26 3.3CoalescenceCriteriaCalculation.................. .........28 3.4TheO'RourkeCollisionModel....................... .....30 3.5ModelingtheGenerationofSatelliteDroplets........ ............32 3.5.1StretchingSeparationwithGeneratedSatelliteDrop lets...........32 3.5.2ReexiveSeparationandGenerationofSatelliteDrop lets..........37 3.6SingleDropletTrajectories....................... .......38 Chapter4ExperimentalMethods ............................ 41 4.1FuelDeliverySystem.............................. ...43 4.2FuelHeatingSystem............................... ..44 4.3InjectionControllerSystem....................... .......45 4.4MacroscopicandMicroscopicVisualizationSystems... .............45 4.4.1MacroscopicVisualizationSystem................ ......46 4.4.2Laplacian-GaussianEdgeDetection............... ......48 4.4.3MicroscopicMeasurementSystems................. ....52 4.4.4MalvernSpraytec............................... 53 v 4.4.5OpticalSupportBench(X-bar).................... ....55 4.4.6Transmitter..................................5 5 4.4.7Receiver....................................55 4.5ExperimentalPlan................................ ...56 Chapter5ExperimentalResults ............................. 58 5.1MeasurementErrorandMalvernInstrumentCalibration. ..............58 5.2DropletSizeDistributionwithinaPulsedn-HeptaneSpr ay.............63 5.3TheGeometryofaLowPressuren-HeptaneSprayatAmbient FuelTemperature.65 5.4TheEffectofFuelTemperatureontheGeometryofaLowPre ssuren-HeptaneSpray68 5.5TheMicroscopicCharacteristicsofann-HeptaneSpray. ..............68 5.6TheEffectofFuelTemperatureontheMicroscopicCharac teristicsofann-Heptane Spray.........................................74 Chapter6FuelSprayModeling ............................. 78 6.1Introduction.................................... ..78 6.2TestCalculationsandResults...................... .......80 6.2.1SimulationProcedure........................... ..80 6.2.2EffectofNumberofDropletsontheConvergenceofSize -Distribution Statistics....................................81 6.2.3EffectofMeanValueofInitialVelocitiesonDownstre amStatistics....85 6.2.4EffectofSyntheticTurbulenceinInitialVelocityon DownstreamStatistics87 6.2.5DropletCollision.............................. .89 6.2.5.1BinaryCollisionImpactParameter.............. ..89 6.2.6CollisionModelsComparison..................... ...91 6.2.6.1SimulationResultsusingtheO'RourkeModel...... ....92 6.2.6.2SimulationResultsusingtheKoCollisionModel... ......93 6.2.6.3SimulationResultsusingtheKoModelwiththeTaski ranImpact ParameterModel(ExtendedKoModel)..............95 6.2.6.4ComparingCollisionModels...................9 5 6.2.7EffectsofInstrumentationUncertainty........... .........98 6.2.8SimulationResultsAtElevatedTemperature........ .........99 Chapter7Summary,ConclusionsandRecommendationsforFut ureWork ..... 105 7.1SummaryandConclusions........................... ...105 7.2RecommendationsforFutureWork.................... ......108 BIBLIOGRAPHY ................................. 109 vi LISTOFTABLES Table2.1Meandiametersandapplications............... .......12 Table2.2MeandiametersinthesprayofFig.2.2........... ........13 Table4.1Waterheaterspecication.................... ......45 Table5.1StochasticvaluesofFig.5.15distribution..... ............70 Table5.2MeandropletsizesofFig.5.17................. ......71 Table5.3SpraymeandropletsizesofFig.5.22............ ........75 Table6.1Collisionmodelstestcases................... ......96 Table6.2n-heptanethermodynamicsproperties.......... .........102 vii LISTOFFIGURES Figure2.1Macroscopiccharacteristicsofasingle-jetDie selspray[1]........6 Figure2.2Arandomlygeneratedlog-normaldropletsdistri bution..........13 Figure3.1Temporalhistoryofdropletdiameterforevapora tionofamethanoldroplet [2]......................................18 Figure3.2Ohnesorgediagram.......................... ...26 Figure3.3Dieselinjection:primaryandsecondarybreak-u p.............27 Figure3.4Parametersusedtodescribedropletcollisions. ..............28 Figure3.5EffectofdropletdiameteroncoalescenceŒstret chingseparationinabi- narycollisionofthesamesizedroplets................. ..31 Figure3.6Thestretchingseparationprocess............ ..........35 Figure3.7Theprocessofreexiveseparation............ .........38 Figure3.8DragofasphericaldropletoverarangeofReynold snumbers[3].....40 Figure4.1Schematicofthepresentexperimentalsetup.... ............42 Figure4.2Schematicofacommonrailfuelinjector........ ..........44 Figure4.3Schematicofthemacroscopicvisualizationsyst em............46 Figure4.4BacklitimageofadirectDieselinjectionspray. .............47 Figure4.5Intensityandspatialintensityderivativefunc tionsneartheedges.....48 Figure4.6TheGaussiandistributionintwovariables..... ............49 Figure4.7TheLOGoperator............................ ..50 Figure4.8StepsofaLOGoperator....................... ...51 Figure4.9(a)n-heptanespraywithroughedgesbeforetheim ageprocessing.(b) Thesamesprayafterimplementingedgedetectionimageproc essing...51 viii Figure4.10Scatteringoflightfromsmallandlargeparticl es..............53 Figure4.11TheSpraytecspraymeasurement.............. ........54 Figure4.12KeycomponentsofaSpraytecsystem........... ........54 Figure4.13Asnapshotofascatteringpatternofthedetecto rarray...........56 Figure5.1Errorinmeasuringfuelsprayangleandpenetrati on............59 Figure5.2Flowvelocitymeasurementinvacuumsystem..... ..........60 Figure5.3Effectofthevacuumsystemoperationonmeasurem entresults(injection pressureandtemperatureare5 MPa ,25 C,respectively........61 Figure5.4Effectofusingaglasscontainerinmeasuringdro pletsizedistribution..62 Figure5.5Thepulsedspraydurationwhichwasusedbytheinj ectorinallexperiments62 Figure5.6CalibrationresultsofMalvernSpraytecwith37- 40 m microspheres...62 Figure5.7Percenterrorinmeasuredvolumemeandiameterve rsestransmissionfor SprayTech[4]................................64 Figure5.8Dropletsizedistributionvariationalongan-He ptanesinglesprayinjection64 Figure5.9n-Heptanesprayoverallshape................ .......65 Figure5.10Developmentofn-heptanesprayat10 MPa ,25 C ............66 Figure5.11Dependenceofsprayangleontimeandinjectionp ressureatafueltem- peratureof25 Cina25 Cambient.....................67 Figure5.12Effectofinjectionpressureonthespraytippen etrationatafueltemper- atureof25 Cina25 Cambient.......................67 Figure5.13Dependenceofsprayangleontimeandonfueltemp erature........68 Figure5.14Effectoffueltemperatureonspraytippenetrat ion.............69 Figure5.15Atypicalsizedistributionofdropletsinthefa reldofann-heptanespray ataninjectionpressureof5MPaandafuelandenvironmentte mperature of25 C...................................70 Figure5.16Variationofdropletsizemeanvaluesduringasi ngleinjection.......71 ix Figure5.17Effectofinjectionpressureonspraydropletss izedistribution.......72 Figure5.18Effectofinjectionpressureoncumulativespra ydropletsizecurve....72 Figure5.19Dropletsizedistributionatdifferentaxiallo cations,ataninjectorpressure of5MPaandfueltemperatureof25 C(here z istheaxialdistancefrom theinjectortip)...............................73 Figure5.20Axial SMD variationfortheinjectionconditionsofFig.5.19....... 73 Figure5.21Thevariationofdroplets SMD fordifferentoff-axiallocationsatambi- entfueltemperatureat25 C........................74 Figure5.22Effectoffueltemperatureonthespraydroplets izedistribution......75 Figure5.23Effectoffueltemperatureonthespraydroplets izecumulativedistribu- tioncurve..................................75 Figure5.24Dropletsizedistributionatdifferentaxiallo cations,ataninjectionpres- sureof5 MPa andafueltemperatureof75 C ,where z istheaxial distancefromtheinjectortip......................... 76 Figure5.25Thevariationofdroplets SMD fordifferentoff-axiallocationsatdiffer- entfueltemperaturesat5 MPa injectionpressure............77 Figure6.1SchematicoftheabilityoftheSpraytecinstrume nttomeasuresizedis- tributionsatdifferentlocations..................... ..80 Figure6.2Generatedrandomdropletsizedistributionford ifferentnumberofdroplets83 Figure6.3Dropletsinitialvelocity................... ........85 Figure6.4Simulateddropletsizedistributionat50 mm downstreamfordifferent initialmeanvelocities............................86 Figure6.5Simulateddropletsizedistributionat50 mm downstreamforsynthetic turbulencesininitialvelocities..................... ..88 Figure6.6Representationofabinaryimpactparameter.... ............90 Figure6.7Dropletsizedistributionforn-heptanesprayco llectedbyMalvernSpraytec at 25 C roomtemperatureand 5 MPa injectionpressure.........92 Figure6.8Dropletsizedistributionfromsimulationsatdi fferentaxiallocationsus- ingtheO'Rourkecollisionmodel.....................93 x Figure6.9Dropletsizedistributionfromsimulationatdif ferentaxiallocationsusing theKocollisionmodel...........................94 Figure6.10Obtaineddropletsizedistributionatdifferen taxiallocationusingKocol- lisionmodelandanalyticalimpactparameter(extendedKom odel)....95 Figure6.11Binarycollisionregimescriteriaforthesames izedroplets........97 Figure6.12Comparisonofdifferentcollisionmodelsresul ts..............98 Figure6.13Effectsofinstrumentationuncertaintyonpred icteddropletsizedistribu- tionusingextendedKocollisionmodel.................. .99 Figure6.14Evaporationofaliquiddropletinaquiescenten vironment........101 Figure6.15Simulationandlabdatacomparisonatn-heptane temperatureof 70 C ..104 Figure6.16LabdataandsimulationforextendedKocollisio nmodelatanelevated temperature.................................104 xi Chapter1 Introduction Thisthesisbeginswithintroducingsomebackgroundinform ationonliquidfuelsprays,onwhy theyareimportantandonwhatisandisnotknownaboutthem. 1.1LiquidSprays Liquidspraysaretwo-phaseowsinwhichtheliquidligamen tsordropletsarethediscretephase andthesurroundingvaporand/orgasisthecontinuousphase ,andareoftencontrastedwithbubbly owinwhichthediscreteandcontinuousphasestakeopposit eforms.Becauseliquiddensitiesare generallyhigherthangasdensities,bubblemotionsexperi encelowerkinematicinertiaandhigher dragforcesthandropletmotion.Theprocessofformingaspr ayiscalledatomizationandthe deviceusedtogeneratealiquidsprayiscalledaspraynozzl e,fuelinjectororatomizer.Sprays areusuallycharacterizedbytheirparticlesizedistribut ionandnumberdensity,andmeasurements ofthesequantitiesarecentraltodeningproductperforma nceoverarangeofapplications,from thedeliveryofdrugstothehumanrespiratorysystemtothea pplicationofcoatingsandagrochem- icals.Sprayspresentuniquechallengesintermsoftheirme asurementenvironmentandthespeed ofmeasurementrequired.Spraysaremainlyusedinindustry todistributematerialsoversome speciedarea,ortocreatealargeliquidsurfacearea.Some oftheindustriesinwhichspraysare usedwidelyinclude: 1 i )Thefoodindustry:spraysareusedtowashagriculturalfru itsandvegetables,andtodryfood productssuchasinstantcoffeeandpowdersoups. ii )Papermaking:spraysareusedtocleanpaperrolls. iii )Firesuppressionandmining:waterandsolutionsarespray edfromhosesandsprinklersfor recontrol,andwaterspraysareusedtoreducedustlevelsi nminingoperations. iv )Agriculture:pesticidesaresprayedovertargetsurfaces toprovideuniformdistributionsof chemicals. v )Fuelsprays:fuelinjectorsforgasolineanddieselengine sandatomizersforgasturbinesare usedtoprovideliquid-andvapor-phasefueldistributions forsubsequentcombustion. 1.2TheImportanceofSprayResearch Liquidspraysareinherentlycomplicatedandtheformation anddevelopmentofspraysinvolves multiplephysicalprocesseswhichtakeplacebothsimultan eouslyandsequentially.Therehave beenalargenumberofstudiesofliquidspraysthathaveledt oimproveunderstandingofspray break-up,geometricalsprayshape,andunderstandingofmi croscopicbehavior.However,these studieshaveledonlytopartialdescriptionsofsprayforma tionanddevelopment,andseveralother aspectsofspraysremainincompletelyunderstood,includi ngtheprocessesofprimaryandsec- ondarybreak-up.Somewell-understoodaspectsofspraymod elingrequiresignicantcomputa- tionalresourcesandsobothnewandsimplermodelsaredesir abletoprovideabetterpredictive capabilityforliquidsprays. Theobjectivesofthisdissertationaretocharacterize,ex plain,andprovidepredictivemodels forthesizedistributionofdropletsinthefareldofpulse dsprayfromautomotivefuelinjectors. 2 InChapter2,areviewofliteratureonspraysisgiven.InCha pter3,thetheoreticalbackground tospraysisintroducedandthedifcultiesinpredictingth eirbehaviorareexplained.InChapter 4,theexperimentalapparatusandthevisualizationandmea surementtechniquesofthepresent studyaredescribed.Experimentallymeasuredeffectsoffu eltemperatureandinjectionpressure onspraygeometricalshapeanddropletsizedistributional ongthesprayaxisarepresentedin Chapter5.InChapter6,thenumericalsimulationprocedure andnumericalresultsareintroduced. TheconclusionandproposedfutureworksaresummarizedinC hapter7. 3 Chapter2 BackgroundandObjectives Inthischapter,abriefsurveyisgivenofpreviousstudieso fliquidjets,sprays,instabilityand primaryjetbreak-up,secondarybreak-up,anddropletcoll isionandevaporation.Theterminology usedtodescribespraysisalsointroducedandexplained. 2.1LiquidJetInstabilityandBreak-Up Liquidjetshavebeenstudiedformorethanacentury.Savart 'sexperiment[5]wasoneofthe earlieststudiesofliquidjets,inwhichtheobservedeffec tsofsurfacetensiononjetinstabilityled himtoproposecapillaryinstabilityasapossiblemechanis mofjetbreak-up.Rayleighdeveloped arst-orderperturbationcalculationforthebreak-upofa liquidroundjetthatdidnotdependon ambienteffects[6].Heshowedthattheunstabledisturbanc esthatcausedjetbreak-upmustbe axisymmetricandthatthedisturbancewavelengthsmustbel ongerthanthecircumferenceofthe liquidjet. Donnellylaterconductedexperimentalstudiesofliquidje tbreak-upandshowedthatRayleigh's dropletmodeldidnotexplaintheobservationoflargemaind ropletsinterspersedwithsmallersatel- litedroplets[7].Furthermore,thesizeofthesedropletsw asfoundtovarywiththewavenumberof thedisturbances.Lafrancpresentedathird-orderperturb ationanalysisofthecapillaryinstability ofliquidjetsinwhichitwasshownthatthehigherorderterm saccountedquiteaccuratelyforthe 4 presenceofsatellitedroplets[8].Ranzproposedthatthes izesofdropletsinaliquidjetspraywere relatedtothewavelengthofthemostunstablewaves[ ? ].Thedelityofhisatomizationmodel wasquestionedbecauseaerodynamicallyinducedwavegrowt hrequiresanitetimetodevelop, inwhichcaseanunbrokenlengthshouldbeobservednearthen ozzleexit.Howevertheseun- stablewavesmayhavebeenmuchsmallerthanthejetdiameter andthereforedifculttoobserve experimentally[9]. 2.2SprayResearch Liquidsprayshavebeenstudiedformanyyearsbecauseofthe irpracticalimportanceandthe difcultyinpredictingtheirbehaviorfromrstprinciple s.Whilesomespraysarecontinuousand steady,atleastaftersomeinitialstart-uptransient,oth ersconsistofmultipleshortpulsesmaynever reachasteadystate.Thespraysconsideredinthisthesisar ethosethatarisefromasingle-pulse injection,suchasinanautomobileengine.Inthesesprays, liquidistypicallyinjectedforseveral millisecondsintoasurroundinggasthatmaymoveatsomelow relativevelocity,sothatthetipof thesprayhastodisplaceonlyalightgas. Beforedescribingresearchintospraycharacteristics,so meterminologyusedtodescribelarge- scalesprayfeatureswillbeintroduced.Themacroscopicch aracteristicsofadieselsprayare usuallydescribedbytheirshapeaccordingtothreemainpar ameters:spraypenetrationdistance; sprayangle;andspraybreak-uplength.Theseparametersar eoftenusedtocomparetheresults ofdifferentspraypredictionmodelswithmeasuredcharact eristicstoassesstheutilityofsuch modelsfordescribingspraydevelopment.Theyarealsoused tomodelcombustioninburnersand inenginecylinders,andtopredictwhetherornotsprayeddr opletswillcollidewithwalls. Thespraytippenetrationisdenedasthetime-dependentdi stancecoveredbythesprayinthe 5 Figure2.1Macroscopiccharacteristicsofasingle-jetDie selspray[1] surroundinggasphase.Thetippenetrationlengthisdeterm inedbytheeffectsofthemomentumof theinjecteduidandtheresistiveforceexertedbythegasp hase.Severalmodelsweredevelopedto predictthepropagationofthespraytipasafunctionoftime ,fordifferentinjectionconditionsand werecomparedwithexperimentaldata[10].Spraypenetrati onlengthsandsprayconeangleswere measuredexperimentallyusingphotographictechniques.S uchtechniqueswereusedbyMiller andBeardsley[11]whostudiedtheeffectoftheambientgasd ensityonthepenetrationlengthof anenginespray. Severalattemptshavebeenmadetondcorrelationsthatcan predictthefuel-spraytippenetra- tionespeciallyforDieselfuelsprays.Dent(1971)propose dfromexperimentaldataacorrelation applicabletopulsedDieselsprays,describedbythefollow ingequation[12]: S ( t )=3 :07 P ˆ g 1 = 4 294 T g 1 = 4 p d 0 t; (2.1) 6 where t isthetimeafterthestartofinjection, P isthepressuredifferenceatthenozzlehole, d 0 is thenozzleholediameter,and T g and ˆ g aretheambientgastemperatureanddensity,respectively. Thiscorrelationpredictsthatspraytippenetrationincre asesinproportiontothesquarerootof timeandisindependentoftheinjecteduidcharacteristic s.AccordingtoCorreas(1988),thetip penetrationofaDieselfuelsprayisproportionaltothesqu arerootoftimeandthemeanvelocity atthebeginningoftheinjection.Hisproposedcorrelation is[13]: S ( t )= C 1 U 0 :5 0 q d eq t;d eq = d 0 r ˆ l ˆ g ;(2.2) where d eq isanequivalentdiameter, ˆ l istheliquiddensityand C 1 isanexperimentalconstant. Jawardetal.proposedasanalternativecorrelation[14]: S ( t )= C 2 P 0 :25 q tˆ 0 :25 l ˆ 0 :14 g ;(2.3) where C 2 isanexperimentallydeterminedconstant.Anempiricalequ ationwasproposedby Jimenezetal.whichstatesthatthetippenetrationispropo rtionaltotimeraisedtothepowerof 0.9[15]: S ( t )=0 :6 3 U 0 t 0 :9 ˆ g ˆ l 0 :163 ;(2.4) where U 0 isthemeanliquidvelocityatthebeginningoftheinjection . Animportantparameteroffuelspraysistheangleoftheedge ofthesprayasitemergesfrom theoriceoftheinjector.Whiledifferentwaystomeasuret heconeanglehavebeenproposed, acommondenitionisthatitistheanglethatisformedbytwo straightlinesincontactwiththe spray'soutlineatadistanceequivalentto 60 timesthediameteratexitfromtheinjector[1].When aspecicamountoffuelisinjectedintoachamberusinginje ctorsofdifferentdesigns,theeffect 7 ofchangingtheconeanglehasareciprocaleffectonthepene trationlengthofthespray.Thatisto say,alargerconeanglereducesthepenetrationlengthandc ancauseinterferencebetweensprays inamulti-oricenozzle,whichcanpromotemergingofdropl etsthroughcollision.Ontheother hand,alargerpenetrationlengthresultswhenthereisasma llerconeangle,whichcancausethe spraytocollidewiththecombustion-chamberwall,whichis undesirable. Therehavebeenseveralattemptstoproposeformulastodete rminetheconeangle.Oneofthe mostwidelyused,whichcanbeusedforgasphaseswithdensit ieslowerthan15kg/m 3 ,is[1]: tan 2 =0 :13 1+ ˆ g ˆ l ;(2.5) where istheconeangle, ˆ g and ˆ l arethegasandliquidphasedensity,respectively.Intheab ove equation,theaspectratiooftheinjectorisnotincluded,a lthoughReitzandBracoconsidereditin theirinvestigations[16].AccordingtoHiroyasuetal.the coneanglecanbedeterminedas[17]: =0 :05 d 2 ˆ a ( ˆ l ˆ a ) 2 a ! 1 = 4 ;(2.6) where d istheoricediameter, a isthegasphaseviscosity, ˆ a and ˆ l arethegasandliquidphase density,respectively. Reitzetal.conductedexperimentsusingnozzleswithwider angeofdiameters,andovera widerangeofliquid-andgas-phasepressures[9].Usingahi gh-speedcamera,theywereableto calculatesprayanglesunderdifferentoperatingconditio ns.Theyshowedthatthesprayanglein- creasedwithincreasinginjectionvelocity.Williamsprop osedastatisticalformalismfordescribing thebehaviorofsprayswhichincludedtheeffectsofdroplet growth,theformationofnewdroplets, collisionsandaerodynamicforces[18].Thisstudywasasig nicantsteptowardsmodelingthe 8 spray'sbreak-upstatisticallyandaccountingforcollisi onsbetweendroplets.Williamsusedthe Liouvilletheoremtodescribethesingle-particleprobabi litydensity.Reitzetal.[19]implemented threecoupledmodelstosimulateDiesel-fuelsprays.Theyu sedowcavitationandevaporation modelsfortheEulerianliquidphasealongwithanatomizati onmodelforhigh-pressureDiesel sprays.Luretetal.usedadirectnumericalsimulationtoim provetheEuleriumLagrangianSpray Atomization(ELSA)model[20],whichwasoriginallypropos edbyValletetal.[21]. Arcoumanisetal.[22]developedacavitation-inducedatom izationmodel,whichusedthetotal areaattheexitoftheinjectionholeoccupiedbycavitation bubblestocalculatetheradiusof anequivalentbubblehavingthesameareaastheentirecavit ation-bubblepopulation.Huhand Gosman[23]publishedaphenomenologicalsprayatomizatio nmodelbasedontheassumption thatcavitationandturbulenceinsidethenozzleholeareat tributedtoturbulentuctuationsinthe exitow,asthedominantsourceofperturbationsatthefree surfaceoftheliquidjet.Baumgarten etal.developedamodelforcavitationandturbulenceinduc edprimarybreak-upwhichwasableto imposetheinuenceofthecavitationnozzleowontheirspr aybreak-up.Theirmodeldescribed thetransitionfromthecavitatingowinsidetheinjection holetothedensespraynearthenozzle [24]. WanandPeters[25],Sazhinetal.[26]andNaberandSiebers[ 27]modeledspraypenetration bysolvingthecrosssectionalaveragedequationsofthelqu id-phaseow,describingthemass andmomentumbalanceinthespray.Sjoberg[18]attemptedto incorporateconditionsatthetip regionofthespraybyassumingthatdropletswerecollected inaregionnearthespraytip;the shapeofthenear-tipregionwasapproximatedbyaballofgro wingradius.Roismanetal.[28] studiedahighspeedfuelspraypenetrationatdistancesmuc hlongerthanthebreak-uplengthina pressurechamber.Intheirproposedspraypropagationmode l,inertiaoftheliquid-airmixtureand theformationofthevortex-ring-likestructuresnearthel eadingedgeofthespraywereconsidered. 9 Theirpropagationpredictionagreedwellwithexperimenta ldatareportedbyKamimotoetal.[28]. PanchagnulaandSojka[29]carriedoutatheoreticalstudyo fdropletSMD(SauterMeanDiam- eter)andreportedthatSMDincreasedwithincreasingaxial distanceforaneffervescentatomizer spray.TheyattributedthisSMDincreasetobothcoalescenc eoflarge-andmedium-sizedroplets andevaporationofsmalldroplets.Acontrastingconclusio nwasreachedbyGhaemietal.[30], whoshowedthattheincreaseofdropletsSMDwithincreasing downstreamaxialdistancefroman atomizerwasprimarilytheresultofevaporationofsmalldr opletsandtoamuchlesserextentthe resultofcoalescence.Kastengrenetal.studiedtheeffect ofambientgasdensityonthestructureof dieselspraysnearnozzlesusingx-rayradiography.Theiro bservationsshowedthatthespraywidth becamemuchlargerastheambientdensityincreased[31].Kl ein-Douweletal.usedtheshadow- graphtechniquetodeterminemacroscopiccharacterizatio nsofaDieselfuelinjectionspray.Their workrevealedthatnotallfuelspraysbehaveidentically,e venwhenexternalconditionsarekept theesame[32];thisobservationsuggestedastochasticnat ureinspraybehavior.Taskiranand Ergenemanperformedanexperimenttondthetemporalandsp atialevolutionofDieselsprays. Theyinvestigatedthespraypenetrationandconeangleandf oundthattheconeanglewastime dependentintheirpulsedsprays[33]. 2.3EvaporationinDropletsandSprays Dropletevaporationhasbeenmodeledwithvaryingdegreeso fcomplexity,accordingtotheaccu- racydesired.Somedropletmodelshavebeendevelopedbased ontheassumptionthatthedroplet surfacetemperatureisuniformanddoesnotchangewithtime .Thissimplicationreducesthe dimensionalityoftheproblembyeliminatingtheneedtosol veanenergyequationfordroplet temperature[34]andcanbedesirableinsimpliedanalytic alstudiesofdropletevaporationand 10 thermalignitionoffuelvapor/airmixture[35Œ39].Oneoft hemostcommonlyusedassump- tionsinmodelingdropletevaporationisthatthedropletre tainsitssphericalform,evenwhen moving[40Œ42].Generally,thefueldropletevaporationpr ocessincludestwomainphases:the transportoffuelmoleculesfromthesurfaceofthedropleti ntogasthroughevaporationandsur- facerecession;anddiffusionoffuelvaporfromthedroplet surfaceofthedropletsintotheambient gas.Empiricalcorrelationshavebeenproposedfortheevap orationofdroplets[43,44].Sazhinet al.proposednumericalmodelingofdropletheatingandevap orationbyconvectionandradiation fromthesurroundinggas.Theirworkwasbasedonananalytic alsolutionoftheheatconduc- tionequationinsidethedroplet,withtheassumptionofaco nstantconvectiveheattransfercoef- cient[45].Wooetal.developedananalyticalmasstransfer expressiontodescribetheevaporation ofpuredropletsintheconvectiveregime[46].Brereton[47 ]developedasphericalmodelwith temperature-dependentpropertiesforevaporationofmult icomponentliquiddropletsbysimplify- ingthepartialdifferentialequationsofdropletheattran sferandmassdiffusionbyapproximating themasordinarydifferentialequations.Torresetal.[48] usedthePeng-Robinsonequationof statetoextendtheircoupledPDEmodelofthecontinuity,th ermalenergyandspeciesdiffusion equationstohighpressuresandimplementedtheirmulticom ponentfuelmodelintoKIVA-3V. 2.4Micro-CharacterizationsofSprays Dropletsproducedbyatomizersarenotusuallyofuniformdi ameterandsocanmoreusefullybe describedbyadistribution.Onewayofdescribingasprayis byspecifyingthemeandiameter ofthedropletsatcertainlocations.Therearemultiplede nitionsofmeandropletdiameterand eachonemaybeusefulforinterpretingparticularsprayphe nomena.Ageneralrelationshipfor 11 calculatingthemeandiameteris: d ab = P N i =0 N i d a i P N i =0 N i d b i ! 1 =a b ;(2.7) where i representsthedifferentclassesofdropletswhichhavethe samediameter d i ,and N isthe totalnumberofdroplets,and a and b areintegers.Table2.1showsthedifferentmeandiameter denitionsandtheirapplications. Table2.1Meandiametersandapplications a b Name Symbol Application 1 0 ArithmeticDiameter(AMD) d 10 Comparison 2 0 SurfaceArea d 2 20 Surfaceareacontrolling 3 0 Volume d 2 30 Volumecontrolling 2 1 SurfaceAreaLength d 21 Absorption 3 1 VolumeLength d 31 Evaporation 3 2 SauterMeanDiameter(SMD) d 32 Vaporization 4 3 DeBrouckere d 43 Combustionequilibrium ThemostcommonlyusedmeandiameteristheSMD,whichrepres entsthediameterofanimagi- narydropletthathasthesameratioofthetotalliquidvolum einaspraytothetotaldropletsurface areainaspray.Itcanbeinterpretedasavaluethatshowsthe atomizationquality.Thesmallerthe SMD,thenerthedropletsandthebettertheatomizationoft hespray.Theaerodynamicforces onadropletandthetimeittakestovaporizedependonitssiz e,withsmallerdropletshavingmore rapidaccelerationordecelerationandshortervaporizati ontimesthanlargerones.Fig.2.2shows alog-normaldropletdistributionwhichisgeneratedrando mlyforatotalnumberof 1000 droplets. MeandiametersofthisdistributionarepresentedinTable2 .2. 12 1001011020102030405060708090Droplet diameter (mm)Number of dropletsFigure2.2Arandomlygeneratedlog-normaldropletsdistri bution In1981,O'Rourkeproposedacollisionmodelbasedonastati sticalapproach[49].Thismodel Table2.2MeandiametersinthesprayofFig.2.2 MeanDiameterName MeanValue( m ) ArithmeticDiameter(AMD) 32.0 SurfaceArea 39.8 Volume 48.6 SurfaceAreaLength 49.6 VolumeLength 59.9 SauterMeanDiameter(SMD) 72.3 DeBrouckere 96.9 13 didnotrequireknowledgeoftheexactlocationsofanytwoco llidingdropletsastheprobability ofcollisionwascomputedstatisticallybasedonthelocald istributionofthedropletspresent.The modelincludedonlycoalescenceandgrazingseparationofd ropletsandsocouldnotmimicother processesobservedinbinarycollisions.AshgrisandPoo(1 990)observedthatdropletseparation producedsatellitedropletsfromtheinteractingregionbe tweentwocollidingdroplets.Ashgriz andPooextendedtheO'Rourkemodelanddividedtheseparati onprocessintothetwoclassesof stretchingandreexiveseparationtoaccountforthecreat ionofsatellitedroplets[50].Otherre- searcherssuchasQianandLaw(1997),Estradeetal.(1999)a ndBrennatal.(2001)alsoshowed thatsatellitedropletsareformedinthesecollisionproce ssesandthattheaveragesizeofdroplets decreasesaftercollision[51Œ53]. 2.5ObjectivesofthisStudy Fromtheliteraturereview,itappearsthatmuchempiricali nformationisavailableaboutmacro- scopicfeaturesofsprays,suchastheirpenetrationlength sandspreadingangles.Phenomenasuch asdropletevaporationalsoappeartobewellunderstoodfor isolatedsphericaldroplets.Lessis knownaboutmicroscopicfeaturesofsprayssuchasdroplets izeandvelocitydistributions,and fewmeasurementsofthesequantitieshavebeenreported.Wh ilemechanismsofinstabilitythat promotethebreak-upofliquidjetsintodropletshavebeeni dentied,andmodelsforthecolli- sionoftwoisolateddropletshavebeendeveloped,itisnotc learhowwellthesemodelscanbe adaptedtopredictdetailsofrealsprayswithmanyinteract ing,evaporatingdroplets.Norisitclear howanunstableliquidjetdevelopsintoaspraywithapartic ularspreadingangleanddropletsize distribution. Theobjectivesofthisstudyaretomakenewexperimentalmea surementsinanimpulsively 14 startedfuelspraytoaddresssomeoftheseunresolvedissue sandtotesttheabilitiesofproposed modelstoexplainthebehaviorofrealjets.Inparticular,i tisplannedto: i )makenewmeasurementsoftheeffectsoffueldeliverypress ureonmacroscopicspraychar- acteristics; ii )makenewmeasurementsofthedependenceofdropletsizedis tributionondistancefromthe spraynozzle; iii )makenewmeasurementsoftheeffectsoffueltemperatureon spraycharacteristicsand dropletsizedistribution; iv )evaluatetheadequacyofdropletevaporationmodelsinexp lainingtemperature-dependent effectsondropletsizedistribution v )evaluatetheutilityofdropletcollisionmodelsforexpla iningthedependenceofdropletsize distributionondownstreamdistance. Inaddressingtheseobjectives,theutilityofsingle-drop letevaporationmodelsandtwo-dropletcol- lisionmodelsfordescribingentiresprayscanbeassessed. Inthefollowingchapters,thetheoretical backgroundandexperimentalsetuparedescribedandthedro pletsizedistributionmeasurement techniquesareexplainedindetail.Experimentalmeasurem entsoffuelspraysarethenreported andcomparedwithnumericalcalculationsofthedevelopmen tofn-heptanesprays. 15 Chapter3 TheoreticalBackground Inthischapter,thetheoreticalbackgroundispresentedfo rthebasicphysicalprocessesthattake placewithinliquidsprays.Theprocessesincludebreak-up ,droplettransport,dropletcollisionand dropletevaporation. 3.1DropletEvaporation Dropletevaporationisatwo-phaseowphenomenonthatcan, inprinciple,besolvedbyusingthe three-dimensionalcontinuity,Navier-Stokes,thermalen ergyandspeciesconservationequationsto describeboththeliquidtransportwithineachdropletandt heowofgassurroundingeachdroplet. Thesetwoequationsystemscanthenbecoupledbycontrol-vo lumeapplicationsofthesameprin- ciplestoathinregionattheboundaryofeachdroplet.Howev erthisapproachisimpracticalasit wouldneedenormouscomputationalresourcesandisnotcurr entlyusedinspraystudies.Instead, modelshavebeenintroducedtomakeevaporationcalculatio nsmorepractical,thoughthesimpli- cationstheyintroducelimittheirvaliditytoparticularc lassesofevaporationproblems.Severalof thesemodelsaredescribedbelow,andintroducedinorderof increasinggeneralityandcomplexity. Adropletisasmall,oftenspherical,volumeofliquidbound edalmostcompletelybyafree surface.Boththesizeandtheshapeareinuencedbythedrop let'ssurfacetension,whichacts tominimizethedropletsurfacearea,tendingtoproduceasp hericalshapeforagivenvolumeof 16 liquid.Theprocessofdropletevaporationcomprisestwoma inphases[34]: i )transportoffuelmoleculesfromthesurfaceofthedroplet togasintheimmediatevicinity ofdroplets,throughevaporationwithsurfacerecession;a nd ii )diffusionandadvectionoffuelvaporfromthesurfaceofth edropletintotheambientgas. Inthecaseofdropletsofmixturesofliquids,athirdphasei spresent:thediffusionofliquidwithin thedropletasthesurfaceconcentrationsofevaporatingsp ecieschange.Therstphaseisusually describedbyequilibriumthermodynamicrelationsrelatin gthemomentaryconcentrationsinthe liquidandvaporphase,suchasthegasphasebeingsaturated forpuredroplets,orRaoult'slaw fordropletsofliquidmixtures.Thesecondphaseisconcern edwithconvectiveheatandmass transfer,usuallywiththeassumptionthatthedropletreta insitssphericalshape,evenwhenin motion[40,41,54]onaccountofthedominanceofsurfaceten sionoverinertia.Itisalsousually assumedthatthetemperatureisuniformoverthedropletsur facethoughitcanvarywithtime.It hasbeenshownfromthree-dimensionalinternalowcalcula tionsthatisothermsoftencoincide withstreamlines[55]inbothstationaryandfast-movingdr oplets,whichjustiesthisassumption. 3.1.1The d 2 Law Asimplemodelfordescribingtherateofevaporationofadro pletisthe d 2 `law'.Thismodel relationshipcanbethoughtofasdescribingasphericaldro pletofapureliquidinastationarygas environmentofconstanttemperatureintimeandspace,equa ltotheliquid'swet-bulbtemperature. Undertheseassumptions,itcanbeshownthattherateofdecr easeofthedroplet'ssurfaceareais proportionaltotime[56],as d 2 = d 2 0 t; (3.1) 17 where d isthedropletdiameterattime t , d 0 istheinitialdropletdiameterand isanexperimentally determinedevaporationconstant.Thismodelisincomplete asitdoesnotpredictavalueof and, evenwhenavalueof isprovidedfromempiricalsources,itistoosimplistictop redictthesize ofdropletsaccuratelyunderforcedconvectionorinthena lstagesofevaporation,whensurface tensionbecomesimportant.Fig.3.1showsexperimentalmea surementsofthenon-dimensional dropletratiovaluewithtimeforpuremethanolfornearquie scentconditionsatanambientpressure of 1 atmosphereandatemperatureof 300 K,togetherwithatofthe d 2 model. Figure3.1Temporalhistoryofdropletdiameterforevapora tionofamethanoldroplet[2] 3.1.2TheSpaldingMass-NumberModel Anotherwayofmodelingdropletevaporationistodeneamas stransfercoefcient( h m )such that _m 00 = h m ( ˆ v s ˆ v 1 ) ;(3.2) 18 where _m 00 isthemassuxofvaporatthedropletsurfaceand ˆ v s and ˆ v 1 aredensitiesofvapor adjacenttoandfarfromthedroplet.Forstationarydroplet sinaquiescentatmosphere,evaporation iscontrolledbytherateofdiffusionofvaporand h m is: h m = 2 Dg d d ;(3.3) where Dg isthebinarydiffusioncoefcientoffuelvaporingasand d d isthedropletdiameter.For thegeneralcaseofevaporationcontrolledbybothdiffusio nandconvection,adimensionlessmass transfercoefcientcanbespeciedbyaSherwoodnumber,de nedas[57]: Sh = d d h m Dg ;(3.4) Sh =2 whendropletevaporationisdrivenonlybymoleculardiffus ion.Forthemoregeneralcase ofevaporationdrivenbybothconvectionanddiffusion,cor relationsfor Sh areusuallydeveloped fromexperimentalorsimulationdata.Onesuchcorrelation for Sh formovingevaporatingdroplets is[58]: Sh = 2+0 :87 Re 1 = 2 f Sc 1 = 3 f 1+ B M 0 :7 ;(3.5) where Re f = U d d d f ;(3.6) Sc f = f Dg ;(3.7) B M = ˆ v s ˆ v 1 ˆ g s = Y s Y 1 1 Y s (3.8) 19 where Re f istheReynoldsnumberatthelmsurroundingeachdroplet( 20 Re f 2000 ), Sc f istheSchmidtnumberinthelmregion, B M istheSpaldingmassnumberand Y v s isthemass fractionatthedropletsurface.Itcanbeshownfrom[59]tha t: Y s = 1 [1+ M 1 M f (1 P 1 P f )] ;(3.9) where M 1 , M f , P 1 and P v f aretheambientgasandliquidmolecularweights,andtheamb ient andliquidvaporpressureatthedropletsurfacerespective ly.Themassevaporationrateuxfora singledropletis _m 00 = d dt ˇ 6 ˆ d d 3 d ˇd 2 d ! = 1 6 ˆ d d dt ( d d ) :(3.10) FromEqs.3.2,3.4and3.5,therateofthedropletdiameterde creasecanbedeterminedas: d d d dt ( d d )=6 ˆ d 2+0 :87 Re 1 = 2 f Sc 1 = 3 f 1+ B M 0 :7 Dg ( ˆ v s ˆ v 1 ) :(3.11) Thisordinarydifferentialequationcanbeintegratedtoyi eld d d ( t ) usingstandardnumericalmeth- ods. 3.1.3CoupledODEModels Simplemodelsforheatingandevaporatingofnon-isotherma ldropletshavealsobeendeveloped. Somemodelsarebasedonapproximationsofthetemperaturea ndconcentrationprolesinside dropletsastheirsteady-stateforms,whichresultsinODEs fordropletdiameter,andaveragetem- peratureandspeciesconcentration.Forasphericallysymm etricdropletofapureliquid,theun- 20 steadyonedimensionalheatconductionequationinsidethe dropletcanbewrittenas: ˆ l c l @T @t = k l r 2 @ @r ( r 2 @T @r ) ;(3.12) where ˆ l , c l and k l aretheliquiddropletdensity,heatcapacityandthermalco nductivityrespec- tively(assumedtobeconstant). r isthedistancefromthecenterofdroplet, t istimeand T isthe droplettemperature.Ifthedropletisheatedbyconvection fromthesurroundinggas,andhasa constantsurfacetemperature T s equaltothesaturationtemperature T sat ,theboundarycondition atthedropletsurfacecanbewrittenas: h T g T sat = ˆ l L _R + k l @T @r r = R ;(3.13) where h istheconvectionheattransfercoefcient, L isthespecicheatofevaporationand T g is theambientgastemperature.Ifaquasi-steady(parabolic) formofthetemperatureproleinside thedropletisassumed[60]: T = T c +( T sat T c ) r R 2 ;(3.14) where T c isthetemperatureatthecenterofdropletand R isthedropletradius.Integratingboth sidesofEq.3.12withrespectto r yields ˆ l c l Z R r =0 @T @t r 2 dr = k l R 2 @T @r r = R :(3.15) TakingthederivativeofEq.3.14withrespectto t and r respectivelyyields _T = _T c _T c r R 2 +( T sat T c ) 2 r 2 _R R 3 ;(3.16) 21 @T @r = 2 r R 2 ( T sat T c ) :(3.17) AftersubstitutingEqs.3.16and3.17intoEq.3.15andsimpl ifying: _R = k l Rˆ l L hR k l T g T sat 2( T sat T c ) :(3.18) Givenaninitialvalueofthedropletdiameter,Eq.3.18canb eintegratednumericallytoobtainthe dropletdiameteratanytime. 3.1.4CoupledPDEDropletEvaporationModels Themostsophisticatedandexpensiveapproachestocalcula tingdropletevaporationtypicallyin- volvesphericallysymmetrictreatmentsofmulticomponent dropletsinagaseousenvironment.In thiscasethebulkcontinuityequationis: @ˆ @t + r :( ˆv )=0 ;(3.19) @ˆ l @t + 1 r 2 @ @r r 2 ˆ l v l =0 ;(3.20) where ˆ and v arethegasphasedensityandvelocity,respectively.Subsc ript l representsthe propertiesofthedroplet,while r isthedropletradius.Thecontinuityequationforspecies i , assumingFickiandiffusion,canbewrittenas @ ( ˆy i ) @t + r : ˆy i v = r : ˆD i r y i (3.21) @ ( ˆ l y l;i ) @t + 1 r 2 @ @r r 2 ˆ l v l y l;i = 1 r 2 @ @r r 2 ˆ l Dl @y l;i @r ! (3.22) 22 Thethermalenergyequationiswrittenas @ ( ˆI ) @t + r :( ˆIv )= r : r T + ˆ X h i Di r y i p r :v (3.23) @ ( ˆ l T l ) @t + 1 r 2 @ @r r 2 T l ˆ l v l = 1 c p r 2 @ @r r 2 l @T l @r + ˆ l Dl c p r 2 P i fuel @ @r r 2 h l;i @y l;i @r h l;i @ @r r 2 @y l;i @r (3.24) ByintegratingEq.3.21overaninnitesimallythincontrol volumeatthedropletsurface,the interfaceconditionformassfractionofspecies i canbederivedas: h ˆ ls v ls v s y gs;i y l;i + ˆ ls Dl;i r y ls;i ˆ gs Dg;i r y gs;i i :^ n =0 (3.25) ˆ ls v ls _r s y gs;i y l;i + ˆ ls Dl @y i @r ls ˆ gs Dg;i Sh g;i y g 1 ;i y gs;i 2 r s =0 (3.26) Sincethetotalmassfractionisequalto 1 ,thefollowingconstraintcanbeapplied: X i fuel y l;i =1 (3.27) togetherwith[48]: X i fuel Dl;i r y l;i =0 (3.28) Asummationoverallspecies i ofEq.3.25yields: 2 6 4 ˆ ls v ls v s y gs;F 1 ˆ gs X i fuel Dg;i r y gs;i 3 7 5 :^ n =0 (3.29) 23 BymanipulatingEqs.3.23and3.25,theenergyconservation attheinterfacecanbeexpressedas: 8 < : X i L is ˆ ls h v ls v s y ls;i + Dl r y ls;i i + gs r T gs ls r T ls 9 = ; :^ n =0 (3.30) Forasphericallysymmetricdroplet,Eq.3.29isanequation forthesurfaceregressionrate: _r s v ls = ˆ gs P i fuel Dg;i Sh g;i y g 1 ;i y gs;i 2 ˆ ls r s y gs;F (3.31) AninterfaceconditionontemperaturecanbederivedfromEq .3.30asfollows[48]: 8 < : X i L is ˆ ls _r s v ls y ls;i + Dl @y i @r ls l @T @r ls + g Nu g T g 1 ;i T s 2 r s 9 = ; =0 (3.32) Thissystemofequationscanthenbesolved,togetherwithat emperature-dependentlibraryof liquidproperties,usingaPDEsolverforthegoverningequa tionsinsidethedroplet,andaroot- ndingproceduresuchasBroyden'smethodformatchingtheP DEandcontrol-volume-obtained surfaceconditionstoobtainedetailedsolutionsoftherat eofrecessionofthedropletsurfaceand thechangesintemperatureandspeciesproleswithinthedr opletasafunctionoftime. 3.2SprayDynamics 3.2.1Break-Up Intheatomizationofaroundliquidjet,adivergingsprayfo rmsatthenozzleexit.Itisalso thelocationofbreak-upoftheliquidjet.Theinjectedliqu idstreambecomesunstabletosmall disturbancesoverawiderangeofconditions.Whiletheprec isemechanismsofbreak-uparestilla 24 topicofresearch,liquidjetbreak-upisusuallydividedin todifferentregimesthatreectdifferences intheshapeofjetsastheoperatingconditionsarechanged. Fourmainbreak-upregimeshave beenidentiedforaroundliquidjetinjectedintoastagnan tgas:theRayleighregime;therst wind-inducedregime;thesecond-windinducedregimeandth eatomizationregime[61].Rayleigh break-uptakesplaceatlowliquid-streamvelocitywhensma ll-amplitudedisturbancesontheliquid surfacepromoteamplicationinteractionsbetweentheliq uidandgasphasesandinitiatebreak- upoftheliquidstreamintodroplets.Inthisregime,thedro pletdiametersarelargerthanthejet diameterandthebreak-upoccursseveralnozzlediametersd ownstreamofthenozzle.Therst wind-inducedregimeissimilartotheRayleighregimeexcep tthedropletdiametersareofthe orderofthejetdiameter.Forhighspeedliquidjets,itisbe lievedthatthegrowthofunstable short-wavelengthsurfacewavesresultsinbreak-upofthes econdwind-inducedandatomization regimes.Inthesecondwind-inducedregime,dropletdiamet ersaresmallerthanthejetdiameter andevensmallerintheatomizationregime.Intheatomizati onregime,break-upstartsatthenozzle exit.Inordertomakeaquantitativeclassicationofthebr eak-upregimes,theOhnesorgenumber isintroducedastheratiooftheinertiaandsurfacetension forces: Oh = We l Re l ;(3.33) wheretheWeberandReynoldsnumbersaredenedas We l = U 2 dˆ l ˙ ;(3.34) Re l = Udˆ l l ;(3.35) 25 where ˆ l istheliquiddensity, ˙ istheliquidsurfacetension, l istheliquiddynamicviscosity, U is theliquidjetvelocityand d isthenozzlediameter.Theso-calledOhnesorgediagramrep resentsthe differentbreak-upregimes,whichareshowntogetherwitht hezoneofDieselinjectionapplications inthefollowinggure. Figure3.2Ohnesorgediagram InDieselsprays,theprimarybreak-upistherstdisintegr ationofthecoherentliquidintolarge dropletsneartheholeoftheinjector,andthesecondarybre ak-uptakesplacefartherdownstream. Fig.3.3isaschematicoftheprimaryandsecondarybreak-up inatypicalDieselspray.Thephysics ofprimaryandsecondarybreak-uparebelievedtobeverycom plicated,andstochasticbreak-up modelshavebeendevelopedtogeneratearangeofdropletsiz esathighWebernumbers[62,63]. 3.2.2CollisionModels Inregionsofsprayswheredropletdistributionissparse,d ropletsizedistributionisaffectedmainly byevaporation.However,athighWebernumbersandwherethe dropletdistributionwithinthe 26 Figure3.3Dieselinjection:primaryandsecondarybreak-u p sprayisdense,collisionprocessescanplayanimportantro leintheformationofthedropletsize distribution.Althoughdropletbreak-upcanbeinducedbyi nteractionsbetweensprayandgasmo- tion,dropletcollisionisthemutualimpactoftwodroplets ,causedbytheirdifferencesinvelocity anddirectionwithinaspray.Astwodropletsimpinge,there gionofgasseparatingthemcanbe trappedastheycollide,raisingthegaspressure.Whenther elativevelocityofdropletsisnotlarge enoughtoovercomethepressureforcesbetweenthedroplets ,theydonotimpingebutbounce apart.Iftherelativevelocityishigher,dropletscancoll ideandtemporarilyorpermanentlycoa- lescence.AtrelativelylowWebernumbers,thecoalescence ispermanentandthecharacteristics ofthenewbiggerdropletcanbeobtainedfromtheinitialsiz esandvelocitiesofthedroplets.At higherWebernumbers,temporarycoalescenceoccursandthe excesskineticenergyofthedroplets leadstotheirseparation.Dropletsthatcoalescetemporar ilytendtoundergoreexiveorstretching separationatlowandhighimpactparametersrespectively[ 50,51]. Oneoftheearliestworkindropletcollisionhasbeendoneby Rayleigh[64]whoobservedthat smallraindropletsbounceuponcollision. Severalexperimentalstudieshavebeenperformedonthedif ferentmechanismsofbinarydroplet collision.AshgrizandPooobservedthatboththereexivea ndstretchingseparationsproduce satellitedropletsfromtheinteractingpartsbetweentwoc ollidingdroplets,andresultinasizere- ductionindroplets[50].Theafter-collisioncharacteris ticsusuallyaredescribedbythefollowing 27 non-dimensionalparameters[65]: We = ˆd 1 U 2 rel ˙ ;(3.36) = d 1 d 2 ;(3.37) b = 2 B d 1 + d 2 ;(3.38) where We istheWebernumberbasedondropletdiameter, isthedropletsizeratio, b isthe impactparameter, ˆ and ˙ arethedensityandsurfacetensionoftheliquidphase,andt hesubscripts 1 and 2 representsmallerandlargerdropletsrespectively. B isthedistancefromthecenterofone droplettotherelativevelocityvector( U rel )placedonthecenteroftheotherdroplet,asshownin Fig.3.4.Forahead-oncollision,thevalueof b iszero; i.e. theinteractionheightofthecollision regionisequaltothesummationoftheradiiofthetwodrople ts(seeEq.3.38). Figure3.4Parametersusedtodescribedropletcollisions 3.3CoalescenceCriteriaCalculation Inanattempttopredictthereasonablecriteriaforcoalesc ence,itisassumedthattheinteraction oftwosphericaldropletsofdiameters d 1 , d 2 producesasphericaldropletofdiameter d 0 rotating withanangularmomentum aboutitscenterofgravity. 28 d 0 =( d 3 1 + d 3 2 ) 1 3 ;(3.39) Thecriterionadoptedisthatseparationoccursiftherotat ionalenergyexceedsthesurfaceen- ergyrequiredtoreformthetwodropletsfromthecoalescedd ropletsofdiameter d 0 .Themoment ofinertia I ofasphererotatingaboutitsaxisthroughitscentercanbew rittenas I = Z r = r 0 r =0 r 2 dm = 8 ˇ 15 ˆr 0 5 = ˇ 60 ˆd 0 5 ;(3.40) Therotationalkineticenergycanbeexpressedby[66] RE = 2 2 I = 10 ˇˆU rel 2 B 2 d 6 1 d 6 2 3 d 11 0 ;(3.41) where, RE istherotationalkineticenergy.Thesurfaceenergyrequir edtoformtwodroplets ofdiameters d 1 and d 2 fromalargerdropletofdiameter d 0 andsurfacetension ˙ isgivenby[66] SE = ˇd 2 1 ˙ 2 6 4 1+ d 2 d 1 2 + ( 1+ d 2 d 1 3 ) 2 3 3 7 5 ;(3.42) where, SE isthesurfaceenergy.Followingthecriterionof RE = SE , b = 4 :8 ˙ U 2 rel d 1 ˆ f ( d 2 d 1 ) ;(3.43) where,thedimensionlessfunction f ( d 2 d 1 ) isgivenbytheequation 29 f d 2 d 1 = 2 6 4 1+ d 2 d 1 2 + ( 1+ d 2 d 1 3 ) 2 3 3 7 5 " 1+ d 2 d 1 3 # 11 3 d 2 d 1 6 1+ d 2 d 1 2 (3.44) 3.4TheO'RourkeCollisionModel TheO'Rourkemodelhasbeenwidelyutilizedinnumericalstu diesofspraysandusesastatistical approachtopredicttheoutcomesofcollisionevents.Thism odelonlyconsiderscollisionsof dropletsthatareinthesamecomputationalcell.Thustheco llisionfrequencyoflargerdroplets againstallsmalleronesis[67]: ˛ 21 = N 1 V cell ˇ 4 ( d 1 + d 2 ) 2 U rel ;(3.45) where V cell isthecellvolume.O'RourkeassumedaPoissondistribution ofdropletsizesand showedthattheprobabilityofnocollisionwas[49]: P 0 = e ( ˛ 21 t ) :(3.46) Inthismodel,threecollisionoutcomesareconsidered:str etchingseparationwithnogenerated satellitedroplets;bounce;andpermanentcoalescence.Ar andomnumber ˘ issampledfroma uniformdistributionbetween 0 and 1 .Ifitisgreaterthantheprobabilityofnocollision,colli - siontakesplacebetweenthetwodroplets;otherwisenocoll isionoccursbecausethetwodroplets bounce.Thecriticalimpactparameterthatdelineatesperm anentcoalescencefromstretchingsep- arationisshowninFig.3.5[68].Thevalueofthecriticalim pactparameter( CIP )isestimatedas 30 Figure3.5EffectofdropletdiameteroncoalescenceŒstret chingseparationinabinarycollisionof thesamesizedroplets thesquarerootof " coal ,where " coal isthecoalescenceefciencyandisdenedas: " coal = min ˆ 1 ;2 :4 We s 1 3 2 :4 2 + 2 :7 ˙ ;(3.47) We s = ˆU 2 rel ( d 1 + d 2 ) 2 ˙ ;(3.48) where We s istheWebernumberbasedontheamplitudeoftherelativevel ocityandthediameter ofeachdroplet.Ifarandomnumberbetween 0 and 1 isgreaterthanthe CIP ,stretchingseparation withnogeneratedsatellitedropletstakesplace.Otherwis eitisconsideredtobeapermanentcoa- lescence.Theconservationofmassandmomentumequationsr equirethepost-collisionproperties ofthepermanentcoalescenceregimetobe: d new = d 3 1 + d 3 2 1 3 ;(3.49) 31 U new = d 3 1 U 1 + d 3 2 U 2 d 3 new ;(3.50) wherethesubscript new denotesthevalueaftercollision.Inastretchingseparati onthatgenerates nosatellitedroplets,bothdropletsareassumedtoretaint heirsize.Thevelocitiesofthedroplets aftercollisioncanbeobtainedfromtheenergyandmomentum conservationequationsas: U new;i = d 3 i U i + d 3 j U j + d 3 j U i U j b p " coal 1 p " coal d 3 i + d 3 j ;i;j 2f 1 ;2 g ;i 6= j: (3.51) Inthebouncingprocess,bounceddropletspreservetheiror iginaldiameters,whiletheirvelocities areobtainedfromthemomentumconservationequation: U new;i = d 3 i U i + d 3 j U j + d 3 j U i U j d 3 i + d 3 j ;i;j 2f 1 ;2 g ;i 6= j: (3.52) 3.5ModelingtheGenerationofSatelliteDroplets AlthoughtheO'Rourkemodelonlypermitspermanentcoalesc encebetweentwodroplets,many researchershaveshownthatsatellitedropletsareformeda ftercollision[50Œ52]andthatstretching andreexiveseparationmaytakeplace.Modelsthatinclude theseeffectsaredescribedbriey below. 3.5.1StretchingSeparationwithGeneratedSatelliteDrop lets VisualizationdatareportedbyAshgrizandPoo[50]andQian andLaw[51]suggestedthat,during thestretchingseparationprocess,aportionoftheinterac tionvolumeformssatellitedropletswhile therestremainsintheoriginalcollidingdroplets.Theref orewhentwodropletsexperiencestretch- 32 ingseparation,theinteractingportionbetweenthemcreat esaligamentwhichultimatelyforms satellitedroplets,whereasthenon-interactingportionc reatestwodropletscalled`headdroplets.' AccordingtoAshgrizandPoo[50],whentwodropletscollide atahighimpactparameter,onlya fractionofthemcomeintodirectcontact,asshowninFig.3. 4.Thisfractioncanbecalculatedas: 8 > < > : 1 = 1 C VS 2 = 2 C VS (3.53) 1 = 8 > > < > > : 1 1 4 3 (2 ˝ ) 2 (+ ˝ ) forh> d 1 2 ˝ 2 4 3 (3 ˝ ) forh< d 1 2 (3.54) 2 = 8 > < > : 1 1 4 (2 ˝ ) 2 (1+ ˝ ) forh> d 2 2 ˝ 2 4 (3 ˝ ) forh< d 2 2 ;(3.55) where h , V , and b aretheinteractionheight,dropletvolume,sizeratioofdr opletsandimpact parameter,respectivelyand ˝ =(1 b )(1+) ;(3.56) h = ( d 1 + d 2 )(1 b ) 2 :(3.57) MannannurandReitz[69]proposedaseparationvolumecoef cienttodeterminethetemporalcre- ationofaligamentthatiscomposedoftheinteractingvolum esofthetwodroplets.Theseparating volumeissmallerthantheinteractionvolume.Toaccountfo rthesephenomena,thepresentmodel denestheseparationvolumecoefcientbyassumingthatth eseparatingvolumeisproportionalto theratiooftheenergyrequiredforseparationtothetotale nergyofthetwodroplets.Theseparation volumecoefcientofstretchingcollisionisdenedas: 33 C VS = E st E ten E dis E st + E ten + E dis ;(3.58) where E st isthetotalkineticenergy, E ten isthesurfacetensionenergyintheinteractingarea, and E dis istheviscousdissipation,oftenassumedtobe 30% ofthetotalkineticenergy[69]. E st = 1 2 ˆU 2 rel ˇ 6 d 3 1 2 6 4 3 1+ 3 2 3 7 5 h 1+ 3 1 b 2 1 + 3 2 i ;(3.59) E ten = ˙ r d 1 ˝ 1 + 3 2 2 ˇ ˇ 6 d 3 1 :(3.60) AccordingtoMunnannureandReitz[69],therstshapeofthe interactingareaafterthecollision isacylindricalligament.Fig.3.6showstheprocessofstre tchingseparationandligamentand satellite-dropletformation.Themassconservationequat ionforthestretchingseparationwitha ligamentiswrittenas: ˇ 6 d 2 1 + ˇ 6 d 2 2 =(1 1 ) ˇ 6 d 2 1 +(1 2 ) ˇ 6 d 2 2 + ˇr 2 L: (3.61) Thediameterofthetwo`headdroplets'aftertheseparation canbewrittenas: d 1 af = h (1 1 ) d 3 1 i 1 3 ;(3.62) d 2 af = h (1 2 ) d 3 2 i 1 3 ;(3.63) wheresubscript af indicatesthestatusofdropletpropertiesaftercollision .Thevelocitiesofthe 34 Figure3.6Thestretchingseparationprocess `headdroplets'canbecalculatedfromEq.3.11.Assumingth eseparationprocesstakesplace rapidlyenough,noheatorworktransfertakesplaceandsoth econservationofenergyequation canbeexpressedas: 1 2 ˆ ˇ 6 d 3 1 U 2 1 + d 3 2 U 2 2 + ˇ˙ d 2 1 + d 2 2 = 1 2 ˆ ˇ 6 (1 1 ) d 3 1 U 2 1 +(1 2 ) d 3 2 U 2 2 + ˆ 1 2 ˇr 2 U r + ˇ˙d 1 af 0 B @ d 1 af 2 + s d 2 1 f 4 r 2 1 C A + ˇ˙d 2 af 0 B @ d 2 af 2 + s d 2 2 f 4 r 2 1 C A + ˙ 2 ˇr + '; (3.64) where ' istheviscousdissipation, r isthecylindricalligamentradius, istheligamentlength, and U r istheaveragevelocityoftheuidinsidetheligament.Inth ismodel,itisassumedthatthe dropletvelocities(beforeandaftercollision)andthevol umeoftheligamentareindependentof time.Alsotheradiusoftheligamentisassumedtobemuchsma llerthanthediametersofdroplets 35 aftercollision.Makingtheseassumptionsanddifferentia tingEq.3.64withrespecttotime, U 2 r _ 4 ˙ _r ˆr 2 + 2_ ' ˆˇr 2 =0 ;(3.65) where _denotesaderivativewithrespecttotime.Theinitialshape ofthemassthatconnectsthe bulbousend-dropsisassumedtobeauniformcylinderofleng thequaltoitsradius,so ˇr 2 = ˇr 2 0 r 0 ;(3.66) where r 0 istheinitialradiusoftheligament r 0 = 1 6 1 d 3 1 + 2 d 3 2 1 = 3 :(3.67) Theaverageuidvelocityinthestretchingligamentisassu medtobeproportionaltotherateof stretchingso U r = C _; (3.68) where C isaconstantassumedtobeunity[70].Theviscousdissipati onrateforapureextensional owcanbegivenby[69]: _' = ˇr 2 _ 2 2 :(3.69) SubstitutingfromEq.3.65and3.68,wendthat r = 3_ r 2 r + r 4 2 ˆr 6 0 ( ˙ _r ) ;(3.70) MannunnarandReitzshowedthat,asanalternativetosolvin gthenon-lineardifferentialEq.3.30, 36 anapproximationsolutioncanbefoundbyobtainingthenon- dimensionalradius R ofthefollow- ingequation[69]: 3 4 p 2 k 1 k 2 We 0 :5 0 R 3 :5 + R 2 1=0 ;(3.71) where k 1 and k 2 areconstantsforthespecicconditions.Thediameterofth egeneratedsatellite dropletsisgivenby: d sat =3 :78 r 0 R: (3.72) Thenumberofsatellitedropletsgeneratedis: N sat = 3 4 r 0 r sat 3 (3.73) Thevelocityofthesatellitedropletscanalsobefoundfrom theconservationofmomentum. 3.5.2ReexiveSeparationandGenerationofSatelliteDrop lets Tennisonetal.consideredreexiveseparationasanadditi onaloutcomewhentheWebernumber denedinEq.3.36isgreaterthanacriticalWebernumberof We crit = 3 " 7 1+ 3 2 3 4 1+ 2 # 1+ 3 2 6 1 + 2 ;(3.74) where 1 =2(1 ) 2 q 1 2 1 ;(3.75) 2 =2( ) 2 q 2 2 3 ;(3.76) = 1 2 b (1+) :(3.77) 37 Fig.3.7showsthedropletformationprocessofreexivesep aration.Ascanbeseenfromthis gure,allsatellitedropletsgeneratedfromtheseparatio nareassumedtohavethesamesize,sono head-dropletisformedinthisprocess. Figure3.7Theprocessofreexiveseparation Thevelocityofthesatellitedropletsinreexiveseparati oncanbeobtainedfromEq.3.51. U new;i = d 3 i U i + d 3 j U j + d 3 j U i U j r 1 We crit We s d 3 i + d 3 j ;i;j 2f 1 ;2 g ;i 6= j: (3.78) Thediameterofthesatellitedropletscanbecalculatedfro mEq.(3.31)and(3.32)withtheinitial ligamentradiusof: r 0 = 1 8 d 3 1 + d 3 2 1 3 :(3.79) 3.6SingleDropletTrajectories Predictionsofthetrajectoryofadiscrete-phasedropletc anbeobtainedbyintegratingtheforce balanceonthedroplet,writteninaLagrangianreferencefr ame.Theinherentthree-dimensional 38 characterofthedropletsisaccountedforthroughanaerody namicdragforce.Asaparticlemoves throughtheuid,itexperiencesaforceequivalenttotheco mpositedragforceofthedroplets movingrelativetotheambientuid.Inter-dropleteffects ontheaerodynamicdragareneglected. Theforcebalanceequatesthedropletinertiawiththeforce sactingonthedropletand,inthe z direction,canbewrittenas dU p dt = F D U U p + g ˆ p ˆ ˆ p + F z ;(3.80) where F D( U U p )isthedragforceperunitdropletmassand F D= 18 ˆ p d 2 p C DRe 24 ;(3.81) where U istheenvironmentalgasphasevelocity, U p isthedropletvelocity, isthegasphase viscosity, ˆ g isthegasdensity, ˆ p isthedropletdensity,and d p isthedropletdiameter. Re isthe Reynoldsnumber,whichisdenedas Re = ˆd p U p U :(3.82) Thedragcoefcient, C Dcanbefoundfrom C D= a 1 + a 2 Re + a 3 Re 2 ;(3.83) where a 1 , a 2 and a 3 areconstantsthatapplyforsmoothsphericalparticlesove rseveralranges of Re givenbyMorsiandAlexander[3].Figure3.8showsthedragco efcientdiagramforthese rangesofReynoldsnumbers. 39 101102103104012345678910ReCdFigure3.8DragofasphericaldropletoverarangeofReynold snumbers[3]. Thesemodelsforthebehaviorofdropletsundergoingcollis ionswillbeexaminedinlatersec- tionsofthisdissertation.Theywillbeusedtodetermineho wwellexperimentalmeasurementsof dropletsizedistributionsinsprayscanbeexplainedbydro pletcollisiontheories.Theevaporation modelswillbeusedtoassesswhetherevaporationisasigni cantcontributortochangesindroplet sizemeasuredalongtheaxisofaspray. 40 Chapter4 ExperimentalMethods Inthischapter,theexperimentalapparatususedtosprayfu elinacontrolledmanner,andtomea- surethemacroscopicfeaturesofthesprayandthedropletsi zedistributionisdescribed.The apparatusconsistsofvemainparts:thefueldeliverysyst em;theinjectorcontrolsystem;thefuel heatingsystem;themacroscopicvisualizationsystem;and thedropletsizemeasurementsystem. Fig.4.1showsaschematicoftheexperimentalsetup.Afueli njectorissuppliedwithfuelfroma pressurizedtankthroughafuelline.Acomputercontrolsys temisusedtosetinjectionparameters suchastimedurationandtimedelayafteratimingpulse,toa llowaspeciedvolumeoffuelto beinjected/sprayed.Acapabilitywasalsoprovidedtoheat thefuelinthelineupstreamofthe injector,toexploreeffectsoffueltemperatureonspraybe havior.AhighspeedCCDcamerawas usedtorecordthespraypropagationintoquiescentsurroun dingswhich,afterimageprocessing, couldbeusedtomakemacroscopiccharacterizationsofthes pray.ASpraytecdiffraction-based laserdropletsizingsystemwasusedtodeterminemicroscop icspraycharacteristicssuchasdroplet sizedistribution.Eachofthesecomponentsisdescribedin detailinthefollowingsections. 41 Figure4.1Schematicofthepresentexperimentalsetup 42 4.1FuelDeliverySystem Intheseseriesofexperimentsn-heptanewasusedasthefuel .Thefueldeliverysystemisshown inFig.4.1.Tosupplyfueltotheinjector,acylinderofnitr ogenisusedtopressurizethefueltank atapressurecontrolledbythecylinderregulator.Asecond pressuregageisinstalledonthefuel tank,whichcomprisestwochambers.Onecontainsliquidfue landitsoutowisconnectedtothe injectorsupplyline.Theotherisacompressedgasaccumula torŠacylinderwithtwochambers thatareseparatedbyaoatingpistonŠconnectedtothenitr ogenreservoir.Asthevolumeof thecompressedgaschanges,thepressureofthegas(andthep ressureontheuid)changes.An injector(intheseseriesofexperiments,acommercialBosc hModelPA66)isconnectedbyafuel linetotheaccumulator,sothatitspressureprovidesaowo ffuelwhentheneedleoftheinjector isenergized.Thisinjectorisatypeofcommercialinjector susedincommonrailfuelinjection systemwhichusuallyoperatesatpressuresbetween 100 and 300 MPa .Theoriginalinjectorwas a7-holetypewitha 0 :3 mm eachholediameter.Inordertostudythepuresingleplunges pray development,6holeswereblockedoutbyusingacommercials uperglue.Fuelisthensprayed fromtheinjector.Inordertorelltheaccumulatorwithfue landchangetheinjector,threehigh- pressurevalvesarepositionedasshowninFig.4.1.Withthi ssystem,theinjectorcanoperateover arangeofpressureslimitedonlybythatofthenitrogeninth ecylinder. InFig.4.2,atypicalheavy-dutyfuelinjectorwithelectro magneticfuelinjectioncontrolis shown.Thiskindoffuelinjectorconsistsofthreemainpart s:asolenoidspring;acontrolchamber; andanozzlechamber.Intheclosedposition,boththecontro landnozzlechambersarepressurized. Becausetheareaabovethecontrolplungerislargerthanthe areaofthenozzlechamber,thereis anetclosingforceandsonofuelleavesthenozzle.Whenthes olenoidisenergized,theresulting magneticforceraisestheballvalveand,becausethez-thro ttleareaissmallerthantheA-throttle 43 area,thepressureinthecontrolchamberdrops.However,th enozzlechamberisstillpressurized andsothereisanetopeningforcethatraisesthecontrolplu nger.Theneedletipisthenraised andfuelisinjected.Whenthesolenoidisnolongerenergize d,thesolenoidspringpushestheball valvetoitsoriginalseatandterminatesinjection. Figure4.2Schematicofacommonrailfuelinjector 4.2FuelHeatingSystem Toinvestigatespraybehavioratfueltemperaturesaboveam bient,aheatingsystemisused.As fuelsareammable,ahighcapacitywaterheaterisusedtora isethefueltemperatureusinga cross-owheatexchanger.Thecirculatingwaterpassesthr oughinsulatedlinesandtransfersheat totheinjector.Table4.1showsthewaterheaterspecicati ons. 44 Table4.1Waterheaterspecication Item WaterHeater Type Residential Tank( Gal ) 10 Voltage 120 Phase 1 Totalwatts 2000 Numberofelements 1 Height/Topoftheheater( in ) 23 Jacketdiameter( in ) 15 3 = 4 Waterconnection 3 = 4 inNPT Temperaturerange 90 to 220 F Weight( lb ) 47 :05 Model 1PZ78 4.3InjectionControllerSystem AFireLynxenginecontrollersystemisusedtocustomizethe injectionperiodanddelayinthese experiments.TheFireLynxisaprogrammableenginecontrol lerdesignedtooperateinenviron- mentsfrom-40 Cto+75 Cwithbuilt-inover-voltage,over-currentandover-tempe ratureprotec- tion.Thissystemalsopermitsindependentexternalwavefo rmcontrolofmultipleinjectors,with atemporalresolutionof0.01ms.Theoutputvoltagetothein jectorcanbescaledfromtheinput supplyvoltageorthebuilt-in5 V powersupplyandtheperiodofinjectioncantakeanyvalue above0.1 ms ,howevertheinjectionpulsewidthwas2.4 ms inallexperiments. 4.4MacroscopicandMicroscopicVisualizationSystems Theopticaltechniquesusedinsprayvisualizationcanbedi videdintotwosub-categories:direct imagingandnon-imagingtechniques.Directimagingindire ctinjectionspraydiagnosticshas focusedonobservationofthespraystructureandgeometry, suchassprayconeangle,cluster break-up,andpenetrationlength.Non-imagingopticaltec hniquesmeasurespatialandtemporal 45 dropletsizedistributionandvelocities. 4.4.1MacroscopicVisualizationSystem Directimagingisusedforevaluatingthemacroscopicchara cteristicsofasprayandconsistsof takingphotographswithacharge-coupleddevice(CCD)came ratocaptureimagesofthespray orspraydroplets.Illuminationiscarriedoutwithaashli ghtorpulsedlaser,whichcreatesa highintensitylightsourceofshortduration.Theprimaryr equirementindeterminingthespray geometricparametersisthattheentirespraybeimaged.Aun iformlightsource,adiffuser,and aPhotronCCDcamerawereconguredtogeneratebacklitimag esoftheentirespray(Fig.4.3). Thiscameracanbeusedwithdifferentratestorecordthespr aydevelopment.For10,000and 300,000framepersecondrates,theresolutionis896X848an d256X64pixels,respectively.The correspondingphysicalresolutioninimagesisapproximat ely51 m /pixel.Thesefootprintshave 16Bitgraycolor.Tofreezethemotionofthedropletsinthes pray,atriggeredashlampwith sub-microseconddurationwasused. Figure4.3Schematicofthemacroscopicvisualizationsyst em 46 AcontinuouslightsourceandaCCDcamerawithaveryshortex posuretimewereusedto recordsprayimages.Thelightand/orcameratriggerswerea ctivatedwithtime-delayedsignals fromaninjectordrivercircuit.Additionalelectroniccon trolswereusedtosynchronizeandphase theinjection,thelightsourceandthecamerashutter.Assh owninFig.4.4,backlitilluminationwas usedforuniformimagingofthesprayandwaseffectiveforre solvingthesprayedges.Toevaluate theprincipalsprayparameterssuchasthesprayangleandax ialspraypenetrationdistance,the edgesofthesprayweredetermined.Todenethespraybounda ry,imageprocessingtechniques wereusedtodistinguishbetweendropletsatthespraybound aryandopticalnoise. Figure4.4BacklitimageofadirectDieselinjectionspray 47 4.4.2Laplacian-GaussianEdgeDetection Edgedetectionalgorithmsarecommonlyusedforevaluating oftheDieselspraymacroscopic characteristicsproperties.Thesealgorithmsndedgesth atformaclosedcontourandcompletely boundanobject.Theintensityofanimagechangesattheedge sofaspecicshapeisshownin Fig.4.5. Figure4.5Intensityandspatialintensityderivativefunc tionsneartheedges Iftheintensityproleofanimagechangescontinuously,it indicatesthepresenceofanedge. TheLaplacianisa2-Disotropicmeasureofthesecondspatia lderivativeofanimageandin2-D imagescanbedenedas: r 2 f ( x;y )= @ 2 f @x 2 + @ 2 f @y 2 :(4.1) TheLaplacianofanimagehighlightsregionsofrapidintens itychangeandthereforecanbeused foredgedetection.However,asasecond-orderderivative, theLaplacianisverysensitivetonoise andsoisappliedtoimagesthathaverstbeensmoothed.This pre-processingstepreducesthehigh frequencynoisecomponentspriortothedifferentiationst ep.Onepossiblepreprocessingtoolis 48 theGaussiansmoothing.TheGaussiandistributionfunctio nintwovariables g ( x;y ) isillustrated inFig.4.6andisdenedas g ( x;y )= 1 2 ˇ˙ 2 e ( x 2 + y 2 ) 2 ˙ 2 ;(4.2) where s isthestandarddeviationrepresentingthewidthoftheGaus siandistribution.Theshapeof thedistributionandhencetheamountofsmoothingcanbecon trolledbyvarying s . Figure4.6TheGaussiandistributionintwovariables Inordertosmoothanimagewiththeintensityfunctionof f ( x;y ) ,itisconvolvedwith g ( x;y ) toproduceasmoothedimagewiththeintensityfunctionof s ( x;y ) . s ( x;y )= f ( x;y ) g ( x;y ) :(4.3) AftersmoothingtheimagewithaGaussianoperator,theLapl acianofthesmoothedimageistaken, 49 whichisequivalenttoconvolvingtheoriginalimage f ( x;y ) withaLaplacianofaGaussian(LOG) operator.Fig.4.7showstheLOGoperator. Figure4.7TheLOGoperator ThezerocrossingisthelocationinaLaplacianofanimagewh erethevalueoftheLaplacian passesthroughzero.Suchpointsoftenoccurattheedgesini mageswheretheintensityofthe imagechangesrapidly.Fig.4.5showsthatintheapproachto achangeinintensity,theLaplacian responseispositiveonthedarkerside,andnegativeonthel ighterside.Thusthereisasharpedge betweentworegionsofuniformbutdifferentintensitiesan dtheLaplacianresponseis:zeroata longdistancefromtheedge;positivejusttoonesideofthee dge;negativejusttotheothersideof theedge;andzeroatsomepointinbetween,ontheedgeitself .Oncetheimagehasbeenconverted bytheLaplacianofaGaussianlter,thealgorithmdetectst hezerocrossings.Fig.4.9showsa Dieselsprayshapebeforeandaftertheimageprocessing. 50 Figure4.8StepsofaLOGoperator Figure4.9(a)n-heptanespraywithroughedgesbeforetheim ageprocessing.(b)Thesamespray afterimplementingedgedetectionimageprocessing 51 4.4.3MicroscopicMeasurementSystems Specializedlaboratoryinstrumentshavebeendevelopedfo rmeasurementofdropletsinautomo- tivefuelspraysaslaserdiffractioninstrumentsandphase -Dopplerinstruments.Theselaser-based instrumentsmaybeusedtomeasureandrecordthesizesofdro pletswithinfuelsprays.However, theydonotnecessarilygiveidenticalresultsinthesamesp ray.Phase-Dopplersystemsmeasure thesizedistributionofasprayinaverysmallprobevolumew hichiscreatedattheintersectionof twoormorefocusedlaserbeams.Laserdiffractionmeasures dropletsizedistributionsbymeasur- ingtheangularvariationinintensityoflightscatteredas alaserbeampassesthroughadispersed dropletsample.Largedropletsscatterlightatsmallangle srelativetothelaserbeamandsmall dropletsscatterlightatlargeangles,asillustratedinFi g.4.10.Theangularscatteringintensity dataisthenanalyzedtocalculatethesizeoftheparticlesr esponsibleforcreatingthescattering pattern,usingtheoriesoflightscattering.Thedropletsi zeisreportedasavolumeequivalent spherediameter.Thusinlaserdiffractionmethods,thesiz edistributionresultisobtainedfrom theregionofthespraywithinthelaserbeamcrosssectionas opposedtotheprobevolumein phase-Doppleranemometry.Theneedtomovetheprobevolume throughnumerouspositions inthespraymakesphase-Dopplermeasurementssignicantl ymoretimeconsumingthanlaser diffractionones.Inbothmethods,thedropletsizingparam etersobtainedfromthesizedistribution curvesaretheSauterMeanDiameter(SMD)andthedropletdia meterscorrespondingtothe 50% or 90% cumulativevolumepointonthedropletsizedistributioncu rve: Dv 50 and Dv 90 respectively. 52 Figure4.10Scatteringoflightfromsmallandlargeparticl es 4.4.4MalvernSpraytec TheMalvernSpraytecwasdesignedasalaserdiffractionsys temtomeasuredropletsizedistribu- tionsfromlightscatteredbythespraydropletsinacylindr icalbeamoflaserlight,asillustrated inFig.4.11.Thelightscatterfromdropletsiscollectedby theSpraytecafterrsttakingaback- groundmeasurement.Thescatteredlightisthenusedtoinfe raspatiallyintegrateddropletsize distribution.Thediffractedlightfromthedropletswithi ntheworkingdistanceandsizerangeof thereceivingopticsiscollectedinanannulararrayofphot odetectorsanditsintensitymeasured. TherecordedscatteringpatternisthenanalyzedusingaMie scatteringmodeltoyieldasizedis- tribution.Theangularrangeoverwhichscatteringmeasure mentsaremadehasbeenoptimized withintheSpraytectoensurepoly-dispersesizedistribut ionsarefullyresolved.Particlesizecal- culationsarethencarriedoutusingamultiplescatteringa lgorithm.Thisensuresaccurateparticle sizedistributionscanbemeasuredatup 98% obscuration,beyondtherangeofoperationoftradi- tionallaserdiffractionsystems.Toproperlycalculateth edropletsizedistribution,thesoftwarehas theuserinputtheopticalpropertiesofthematerialbeingm easured.Laserdiffractionsystemsyield 53 Figure4.11TheSpraytecspraymeasurement asizedistributionmeasurementfromscatteringdatacoinc identintime,asasinglemeasurement fromtheentirescatteringvolume.Nomeasurementofdrople tvelocitydistributionwasmade.The maincomponentsofaSpraytecsystemareshowninFig.4.12. Figure4.12KeycomponentsofaSpraytecsystem 54 4.4.5OpticalSupportBench(X-bar) TheopticalsupportbenchorX-barsupportsthetransmitter andreceivermodules.TheX-bar allowsthetransmitterandreceivercanbemovedtodifferen tpositions,withthedetectoroptics remainingalignedtothetransmitterlaserpath. 4.4.6Transmitter Thetransmittercontainsthelasersourcewhichproducesac ollimatedbeamof14 mm diameter withawavelengthof632.8 nm .Thelaserbeamfromthetransmitterpassesthroughthemeas ure- mentzonewithinthespray,thenthroughalensandprotectiv ewindowstothedetectorarrayinthe receiver.Theresultantscatteredlightisdetectedbythed etectorsinthereceiver.Whennosprayis presentinthemeasurementzone,thetransmissionlevelis1 00 % .However,somelightisblocked whendropletsarepresentinthebeam. 4.4.7Receiver Thereceiverholdsthelensassemblyandphotodiodedetecto relements.A300 mm lensfocuses scatteredlightontothedetectorsandbyusingMiescatteri ngtheory,thesizedistributionofscat- teringdropletsisdetermined.Thereceiverhas36detector sthatsensethescattered-lightintensity ofdropletsassmallas0.5 m .Miescatteringtheoryisapplicabletohomogeneousandsph erical dropletsofarbitrarysizeilluminatedbyplanewaves[71]. AccordingtoMietheory,theintensity ofthescatteredlightwhichreachesanobserverisafunctio noftheincidentlightintensityand scatteringfunction.Mietheoryrequiresknowledgeoftheo pticalpropertiessuchastherefractive indexofthedroplet-gasinterface.AtypicalMiescatterin gpatternisshowninFig.4.13.Each barinthehistogramrepresentsthescatteredlightcapture dbyoneofthedetectorsandsorelates 55 directlytothesizeoftheparticles. Figure4.13Asnapshotofascatteringpatternofthedetecto rarray 4.5ExperimentalPlan Theoverallexperimentalplanistomakemeasurementsofimp ulsivelystartedfuelspraysundera rangeofcontrolledconditionsthatwillprovidenewdatafo rthedesignoffuelingsystemsandtar- getdataforassessingthevalidityofdropletevaporationa nddropletcollisionmodelsinpredicting themicrostructureofsprays.Sincediffraction-basedmea surementsofdropletsizedistributioncan onlybemadereliablywelldownstreamofthenozzle,itispla nedtomakethesemeasurementsat aseriesofsuchlocationsalongthesprayaxis.Thesizedist ributiondataatthelocationclosestto thenozzlecanthenbeusedasaninitialconditionfortestin gtheabilityofcollisionandevapora- tionmodelstopredictthedropletsizedistributionatmult iplelocationsfurtherdownstream.Since dropletevaporationisknowntobesensitivetothetemperat uredifferencebetweentheliquidand thesurroundinggas,itisalsoplannedtomeasurethesedata overarangeoffueltemperatures,and soprovidetargetdatafortestingthetemperaturesensitiv ityofevaporationmodels.Theplanis 56 tomakethesemeasurementsusingn-heptaneasthefuelbecau seitisapuresubstancewithwell knownpropertiesandisrepresentativeofgasoline. Theoverallexperimentalplanistherefore: i )Measuretheshapeandsprayangleofn-heptanespraysunder ambientconditionsasafunc- tionoftimeandpenetrationdistance,todescribetheirmac roscopicstructure; ii )Carryoutthemeasurementsof i )forfueltemperaturesatacontrolledrangeofvaluesabove ambienttodeterminetheeffectoffueltemperatureonmacro scopicspraystructure; iii )Measurethedropletsizedistributionattheclosestlocat iontothenozzleatwhichreliable diffraction-basedmeasurementscanbemade,asindicatedb ythelighttransmissionef- ciency,foruseasaninitialconditionfortestingevaporat ionandcollisionmodelsandfor characterizingthemicro-structureofthespray; iv )Measurethedropletsizedistributionataseriesofdownst reamlocations,andaton-and off-axislocations,tocharacterizethemicrostructureof thesprayandprovidetargetdatafor collisionandevaporationmodelsinsprays;and v )Repeatthemeasurementsof iii )and iv )atdifferentfueltemperatures,todeterminetheef- fectoffueltemperatureonspraymicrostructureandtoprov idetargetdataforspraymodel testing. 57 Chapter5 ExperimentalResults Inthischapter,experimentalresultsarepresentedofthes praygeometryandthesizedistributionof dropletsinthefareldofthespray.Theliquidwaschosenas n-Heptane,whichisrepresentativeof gasoline,andanimpulsivelystartedspraywasgeneratedus ingalowpressureBosch7-holeinjector withallbutoneholeblocked.Thiscongurationwaschosena sspraysfromsingleoricesprovide bettertargetdataforcomputationalmodelingthanthosefr ommultipleorices,asthecomplexity ofmergingspraysisavoided.Theinjectorholediameterwas 0 :3 mm .Whileinjectoractuation isalmostperfectlyrepeatablefromeventtoevent,thenatu reofbreak-upisbelievedtodepend oninstabilityinthepresenceofsmalldisturbancesandsot hesubsequentevolutionofspraysis stochasticinnature.Forthisreason,multiplemeasuremen tsaremadeofeachinjectioneventso thatbothinstantaneousandaveragedatacanberecorded.Th ereporteddropletsizedistributions aretimeaveragedduringthesprayeventandincludeanavera gesizedistributionalongthewhole sprayfromthefrontedgetothetail. 5.1MeasurementErrorandMalvernInstrumentCalibration Tobetterunderstandingoftheexperimentresults,itisimp ortanttocalculatetheorderofmag- nitudeoferrorintheexperiments.Inthisstudy,spraytipp enetrationandangleareobtainedby implementingimageprocessing;explainedinpreviouschap ter;ontherawimages.Inorderto 58 calculatethefuelspraytippenetration,thelocationofth einjectortipandsprayfrontedgeare necessary,themaximumerrorofreadingtheselocationscan be2pixelsasFig.5.1shows.Since themaximumlengthofeachpixelinthestudyis 50 m ,themaximumerrorinndingspraytip penetrationis 0 :1 mm .Inthesimilarway,itisobviousthatthemaximumerrorofre adingpixels forcalculatingsprayangleistwopixelsat60diametersdow nstreamoftheinjectortip[1].By usingEq.5.1,itcanbeshownthatthemaximumerrorinreadin gthesprayangleisalmost 0 :3 . ˇ tan = 2 50 60 300 rad ˇ 0 :3 (5.1) Figure5.1Errorinmeasuringfuelsprayangleandpenetrati on Inthisstudy,theMalvernSpraytecinstrumentwasusedforl aser-diffractionmeasurement. Forventilationpurpose,avacuumsystemcollectsfuelafte rspraying.Inordertoshowthatthis vacuumsystemhasnegligibleeffectonfuelspraydevelopme ntintheexperiments,twodifferent approachesweretakentoinvestigatetheinuenceofthevac uumsystemonmeasurementresults. Intherstapproach,theambientairvelocitywasmeasureda ttheentranceofthedrainsystem. Sincethisvelocitywastoolowtobemeasuredbyconventiona lpitottubedevice,theairvelocity 59 wasmeasuredatthehorizontalsectionofthevacuumdrainsy stemasitisshowninFig.5.2,then byusingincompressibleowassumption,theairowvelocit ywascalculatedatthedrainentrance asitisshownbelow: Figure5.2Flowvelocitymeasurementinvacuumsystem Q = A 1 v 1 = A 2 v 2 ! v 2 = D1 D2 2 v 1 = 16 :5 60 2 3=0 :23 m s (5.2) Thecalculatedairowvelocityatthevacuumentranceisneg ligiblecomparedtothefuelspray velocitywhichisorderof50 m=s .Inthesecondapproach,thedropletsizedistributionata xed injectionpressureandtemperaturewasmeasuredfortwocas es:havingthevacuumsystemon andoff.Fig.5.3showsthatthedropletsizedistributionis almostidenticalforbothcaseswhich indicatesthatthevacuumsystemhasalmostnoeffectonthee xperimentalresults. InordertoassesstheaccuracyandlimitationsoftheMalver ninstrument,itisnecessaryto simulatethedensesprayenvironmentwithatwo-phasemediu mofknownparticlenumberdensity anddistribution.Thiswasaccomplishedusingadispersion ofSolidSodaLimemicrospheres indistilledwaterinastirredglasstestcell.Inordertoma kesurethatusingaglasscontainer 60 Figure5.3Effectofthevacuumsystemoperationonmeasurem entresults(injectionpressureand temperatureare5 MPa ,25 C,respectively doesnotaffecttheMalverndevicemeasurementresult,itis builtfromnemicroscopicslidesand itisplacedsuchthattheMalvernlaserbeamisperpendicula rtothesidesofthecontainer.A testmeasurementofparticlesizedistributionwasalsocon ductedtoinvestigatetheeffectofthis containerontheperformanceoftheMalverndevice.Inthist estfuelspray,thesizedistributionfor n-Heptanewasmeasuredwithandwithoutthecontainer,assh owninFig.5.4.Fig.5.4showsthe resultsofthistestwhichdemonstratesthattheglassconta inerhasalmostnoeffectontheMalvern deviceperformance.Thepulsedsprayranfor50pulsesandea chpulsehadthedurationof2 ms withthefrequencyof40 Hz (Fig.5.5).BasedonthepulsedsprayWebernumberrangeinth is experiment,nodropletsplashinginterferedwiththeMalve rnmeasurement[72]. InordertocalibratetheMalverninstrument,1 gr ofSolidSodaLimeglassmadebyCospheric Inc.(whichhasmicrospheresintherangeof37-40 m )wasagitatedin200 ml distillatewater intheglasscontainer.Agitationwasperformedtopreventt heparticlesfromcoagulating.The Malverninstrumentindicatedthat95.4percentofparticle swereintherangeof34-40 m ,as showninFig.5.6,whichisthesameasthecerticationforpa rticlesbyCosphericInc. ItisalsonoteworthythattheAirForceResearchLaboratory releasedatechnicalbulletinoncal- ibratingtheMalvernSprayTechdevice[4].Thegoaloftheir studywastoassessthecapabilityand 61 Figure5.4Effectofusingaglasscontainerinmeasuringdro pletsizedistribution Figure5.5Thepulsedspraydurationwhichwasusedbytheinj ectorinallexperiments Figure5.6CalibrationresultsofMalvernSpraytecwith37- 40 m microspheres limitationsofthelaserdiffractiontechniqueindensespr ays.Thisinvolvedarelativelybroadrange ofsizesfromtensofmicronstonearlyamillimeterindiamet er.Inordertoassesstheaccuracyand limitationsoftheinstrument,itwasnecessarytosimulate thedensesprayenvironmentwithatwo- phasemediumofknownparticlenumberdensityanddistribut ion.Thiswasaccomplishedusinga dispersionofsolid,sphericalpolystyrenemicrospheresa nddistilledwaterinamagneticallystirred glasstestcell.Separateexperimentswereconductedwithe achinstrumentusingbothmonodis- 62 persedmicrospheresatconcentrationsrangingfrom 1% to 90% transmissionandsizesranging from 30 to 650 m .Experimentswerealsoconductedwithpolydispersedmixtu resofbeadsover thesamerangeofconcentrationsandsizes.Thepolydispers edmixturesconsistedofsixdiffer- entbeadsizesinrelativeconcentrationsthatapproximate dlog-normalsizedistributionstypicalof large-scalerocketinjectors.Theirresultsfromthepolyd ispersedexperimentswerepresentedasa percenterrorinthevolume-weightedvolumemeandiameterf romtheactualsize.Volumemean diameterwaschosenasarepresentativeindicatorofaccura cydistributionbecausetheinstrument usesaprocessofinvertingthelightscatteringdatatoobta inaparticlevolumedistributionandis thusgearedtowardprovidingmaximumaccuracyinavolumeme andiameter.Fig.5.7contains plotsofmeasurementerrorwhichtheyobtained,expresseda sapercentageofvolumemeandi- ameterasafunctionoftransmissionforeachofthepolydisp ersedbeadmixtures.TheMalvern Spraytecinstrumentshowsveryhighaccuracyovertherange oftransmissionsstudiedinthisthe- sis.Theinstrumentwasaccuratetowithin+/-10 % inthetransmissionrangeof2 % to90 % .The instrumentproducesreasonablygoodresultsevenatatrans missionof1 % .Howevertheminimum erroroccurredatabove60 % transmissionforallthedistributionswhichisalwaysthec aseinthe experimentofthisdissertation. 5.2DropletSizeDistributionwithinaPulsedn-HeptaneSpr ay Duringasingleinjectionfromapulsedfuelinjector,thela bdatashowedavariationofthedroplet sizedistributionalongthespray.Theleadingedgeofthesp rayhaslargerdropletsthanthetrailing edgeasshowninFig.5.8,wherethedropletsizedistributio nisplottedatthesprayleadingedge, middlesection,andtrailingedge.Thesedistributionswer econstructedfrom50ensemblesofdata, witheachofthethreedistributionsdeterminedfrom0.3 ms ofdata,withtheentirepassageofthe 63 Figure5.7Percenterrorinmeasuredvolumemeandiameterve rsestransmissionfor SprayTech[4] spraythroughthemeasuringvolumetaking2 ms .Thecorrespondingvaluesof D43 and Dv 50 in thesepartsofthespray,measuredat50 mm fromtheinjectornozzle,were 27 :73 m , 23 :1 m , 19 :93 m and 23 :16 m , 18 :43 m , 15 :35 m ,respectively.Forasinglesprayinjection,the minimumspraydropletmeandiameteroccursnearthesprayta il.Inthisstudy,allsubsequent dropletsizedistributionsplottedareaveragedovertheen tirelengthofthesprayandrepresentative ofthesizedistributioninthecenterofthespray. Figure5.8Dropletsizedistributionvariationalongan-He ptanesinglesprayinjection 64 5.3TheGeometryofaLowPressuren-HeptaneSprayatAm- bientFuelTemperature Experimentshavebeencarriedoutusingthemethodologydes cribedinthepreviouschapterfor n-Heptanepulsedinjectionintoanambientatmospherecond itionsat20 C,1 bar atfuelsupply pressuresbetween5and10 MPa .Atypicalimageoftheresultingspray,0.3msafterinjecti on, isshowninFig.5.9.Itcanbeseenthatthesprayforasingleh oleinjectorisasymmetriccone shapewithasprayangleofapproximately15 .Thesprayappearstobelessdenseatitsedges andfront,possiblybecausetheproximitytotheambientair enhancesevaporation.InFig.5.10, Figure5.9n-Heptanesprayoverallshape thedevelopmentofann-heptanesprayinjectedatanupstrea mpressureof10 MPa isshown. Thedevelopmentofthebreak-upcorecanbeseeninthisseque nceofimages.Thefrontedge ofthespraygetssharperasitmovesanditcanbeseenthatthe break-upstartsalmostfromthe centerofthespray.Thesprayislessdenseatitssidesandth edropletsarenerinthisarea thanthecenter.Becauseofthestochasticnatureofsprays, severalexperimentswereperformed 65 Figure5.10Developmentofn-heptanesprayat10 MPa ,25 C todeterminehowthesprayconeangleandpenetrationwouldc hangeunderdifferentinjection conditions.Forthispurpose,thevarianceisdenedasthea verageofthesquaresofthedifferences betweentheindividualexperimentalvaluesandtheiravera gedvalue.Standarddeviationisdened asthesquarerootofthevarianceandisusedtoexpresshowme asurementsforagrouparespread outfromtheaverage.Fig.5.11showsthebehaviorofthecone anglevalueataninjectiontimeof 2 ms attwodifferentinjectionpressures,for50independentex perimentsatthesameconditions. Astheinjectionpressuredoubledfrom5 MPa to10 MPa ,thesprayangledecreasedbyabout 3degrees.Theverticallinesshowthenumbersbetweenthemi nimumandmaximummeasured valuesduringtheexperiments.Becauseofthestochasticna tureofthesecondarybreakup[73], thesprayedgesvarywithtime.FromFig.5.11,itcanbeinfer redthatthesprayanglevaried duringtheinjection[1]andthisisthoughttobeduetotheun steadynatureofthesprayformation. Themeasurementerrorofconeangleintheexperimentalseri esislessthan0.3degrees,sothe variationsseeninFig.5.11andFig.5.13arenotnoise. Fig.5.12showstheaveragedvalueofthespraytippenetrati onof50observationsatthesame 66 Figure5.11Dependenceofsprayangleontimeandinjectionp ressureatafueltemperatureof 25 Cina25 Cambient. conditions,fortwodifferentinjectionpressures.Asthei njectionpressureincreased,thespray liquid-jetReynoldsandWebernumbersincreased,andtheti pofthespraydevelopedfaster. Figure5.12Effectofinjectionpressureonthespraytippen etrationatafueltemperatureof25 C ina25 Cambient. 67 5.4TheEffectofFuelTemperatureontheGeometryofaLow Pressuren-HeptaneSpray Fig.5.13showsthebehavioroftheconeangleataninjection timeof2msfordifferentn-heptane temperatures,for50independentexperimentsperformedat thesameconditions.Atthehigher fueltemperature(by50 C ),thesprayangledecreasedbyseveraldegrees.Thevertica llinesshow thevaluesbetweentheminimumandmaximummeasuredvaluesd uringtheexperiments.From thisgure,itwasinferredthatthesprayanglevarieddurin gtheinjectionandwasagainduetothe unsteadynatureofthepulsedspray.Fig.5.14showstheaver agedvaluesofthespraytippenetration Figure5.13Dependenceofsprayangleontimeandonfueltemp erature of50observations,atthesameconditions,butfortwofuelt emperaturesthatdifferedby50 C.At thehigherfueltemperature,evaporationwasthoughttobea moreimportantphenomenonandso theincreasedrateofdropletevaporationmadethefrontoft hespraydevelopmoreslowly. 5.5TheMicroscopicCharacteristicsofann-HeptaneSpray Inthissection,dataobtainedfromlaserdiffractionmeasu rementsofdropletdiametersinapulsed spray,usingthetechniquesdescribedinthepreviouschapt er,arepresented.Thesizesofdroplets 68 Figure5.14Effectoffueltemperatureonspraytippenetrat ion inthesprayaredescribedbyalog-normaldistribution,ass howninFig.5.15.Inthisgure,the logarithmicabscissasrepresentboththevolumefrequency andcumulativevolumepercentagesfor dropletswhichhavethesamerangeofdiameters.Thesedistr ibutionsarethetimeaveragesof50 experimentaldistributionsmeasuredundernominallyiden ticalexperimentalconditions. InTable5.1,stochasticparametersofthedatapresentedin Fig.5.15areshown,withDv50 andDv90asthedropletdiametersatwhich50and90percentof thevolumeofspraydropletsis smallerandtherestislarger.Dv50valueisalsoknownasthe MassMedianDiameter(MMD), andindicatesthemidrangeofthedistribution.Theterm`Tr ans'isameasureoftheamountof (transmitted)laserlightreachingthebeampowerdetector .Somelightisblockedwhendroplets passthroughthemeasurementarea.Whenthetransmittedlig htismorethanabout80%,there aretoofewdropletsintheareaofmeasurement;whenitisles sthanabout20%,thesprayinthe regionofinterrogationistoodense.Ineitherofthesecase s,diffractionmeasurementsmaynotbe trustworthy. TheMalverninstrumenthastheabilitytomeasurethedrople tsizedistributionintimeintervals asshortas0.4 ms .Fig.5.16showsthevariationofdifferentdropletsizemea nvaluesduring asingleinjection.Inthisgure,thesolidblacklinerepre sentsthevariationofreceivedlaser 69 Figure5.15Atypicalsizedistributionofdropletsinthefa reldofann-heptanesprayatan injectionpressureof5MPaandafuelandenvironmenttemper atureof25 C Table5.1StochasticvaluesofFig.5.15distribution property average standarddeviation min max Trans(%) 63.3 9.3 54 87 Dv50( m) 22.17 1.463 21.06 26.42 Dv90( m) 49.1 2.06 48.16 55.46 SMD( m) 16.15 1.019 15.45 19.24 intensity.Itisclearthatasthespraydevelopsthetransmi ssionpercentagereduces,showingthat themiddleofasinglesprayisdenser.Afterthedenseregion ofthesprayandnearthetailofthe spraythetransmissionpercentageincreases.Fromdiffere ntaverageddropletdiameters,itisclear thatthefrontleadingedgeofthesprayconsistsoflargerdr opletscomparedtothemiddleandtail ofthespray.BasedonFig.5.16,duringasingleinjection,t hesprayfrontleadingedgeSauter MeanDiameter(SMD)is 26% morethantheminimumSMD;happeningnearthespraytail.Thi s relativepercentageis35and45forDv50and d 43 ,respectively.Inthisstudyinordertoinvestigate thespraycharacteristics,atimeaverageddataofseveralm easurementswereused. Fig.5.18and5.17showtheeffectoftheinjectionpressureo ndropletssizedistributionat adistanceof19 mm fromtheinjectortipŠtheclosestlocationatwhichreliabl emeasurement 70 Figure5.16Variationofdropletsizemeanvaluesduringasi ngleinjection couldbemade.Eachgraphisthetimeaverageof50experiment almeasurementsattheambient temperatureof25 Candismeasuredat19 mm and25 mm belowtheinjectortiprespectively. Fromthesegures,itappearsthatincreasingtheinjection pressuremovesthedistributiontothe leftinFig.5.15,implyingtherearemoresmallerdroplets. FromFig.5.18,ataninjectionpressure of5 MPa ,approximately99%ofdropletshavediameterslessthan160 m,whileat10 MPa , thismeasureofdiameterdropsto100 m.Thusthedropletsizedistributionisverysensitiveto theinjectionpressure.Table5.2showstheSMDandDv50valu esandtheirstandarddeviations fortheseexperiments. Table5.2MeandropletsizesofFig.5.17 InjectionPressure MeanSize Average StandardDeviation 5.0MPa Dv50( m) 23.16 2.173 SMD( m) 16.87 1.465 5.0MPa Dv50( m) 23.16 2.173 SMD( m) 16.87 1.465 5.0MPa Dv50( m) 23.16 2.173 SMD( m) 16.87 1.465 Fig.5.19showsthesizedistributionofdropletsatdiffere ntaxiallocationswhentheambient andfueltemperatureare25 C.Thesemeasurementsweremadedownstreamofthelocationa t whichtheprimaryandsecondarybreak-uptakeplace.Fromth isgure,itcanbeseenthatthesize 71 Figure5.17Effectofinjectionpressureonspraydropletss izedistribution Figure5.18Effectofinjectionpressureoncumulativespra ydropletsizecurve distributionisshiftedtowardsalargerensembleofdrople tdiameterswithincreasingdownstream distance.Thisobservationisimportantbecauseitsuggest sthatthereisagreaterproportionof largerdropletsinthesprayasaxialdistanceincreases.Th isshifttolargerdropletsinthedistri- butioncouldbecausedeitherbytheremovalofsmalldroplet sthroughevaporation,orbydroplet collisionyieldingmorelargerdroplets. Fig.5.20showsthevariationof SMD withaxialdistancefromtheinjectortip.Thisgure 72 Figure5.19Dropletsizedistributionatdifferentaxiallo cations,ataninjectorpressureof5MPa andfueltemperatureof25 C(here z istheaxialdistancefromtheinjectortip) showsunambiguouslythattheaveragedropletdiametergrow swithaxialdistanceandthattheshift inthedropletdistributiontolargerdiametersisnotanart ifactoftheremovalofsmalldropletsfrom thedistribution.Thereforedropletcollision,whichcany ieldlargerdiameterdroplets,appearsto beanimportantmechanismduringspraydevelopment.Itisal sopossiblethatdropletcoalescence takesplaceasaresultofcollisions,leadingtoanincrease inthe SMD ofdropletswithaxial distance. Figure5.20Axial SMD variationfortheinjectionconditionsofFig.5.19 Fig.5.21showsthe SMD ofdropletsatdifferent-onandoff-axiallocations,atamb ientand fueltemperaturesof25 C.Fromthisgure,itappearsthatdropletsarenerattheed gesofsprays, 73 whereevaporationismoreprevalentandtherearefeweroppo rtunitiesforcollisions. Figure5.21Thevariationofdroplets SMD fordifferentoff-axiallocationsatambientfuel temperatureat25 C 5.6TheEffectofFuelTemperatureontheMicroscopicChar- acteristicsofann-HeptaneSpray Figs.5.22and5.23showtheeffectofthefueltemperatureon thedropletsizedistributioninan impulsivelystartedn-heptanespray.Eachgraphshowsthet imeaveragedof50experimentalmea- surementsataninjectionpressureof5 MPa andanaxiallocationof100 mm fromtheinjector tip.Fromthesegures,itisclearthatincreasingthefuelt emperaturefrom25to75 Cshiftsthe sizedistributionfunctiontotheright,whichcorresponds tofewersmallerdropletsandagreater proportionoflargerdroplets.Thiseffectisthoughttobed uetoevaporation,whichismorepro- nouncedathigherfueltemperaturesanddepletesthesprayo fitssmallestdroplets.Table5.3shows the SMD ,Dv50andstandarddeviationsforthedatainthesegraphs. Fig.5.24showsdropletsizedistributionsatdifferentaxi allocationsinan-heptanesprayat 74 Figure5.22Effectoffueltemperatureonthespraydroplets izedistribution Figure5.23Effectoffueltemperatureonthespraydroplets izecumulativedistributioncurve Table5.3SpraymeandropletsizesofFig.5.22 FuelTemperature MeanDiameter Average StandardDeviation 25 Dv50( m) 30.65 3.633 SMD( m) 23.04 2.982 50 Dv50( m) 24.22 3.25 SMD( m) 18.17 2.373 70 Dv50( m) 22.97 0.963 SMD( m) 16.9 0.556 75 afuel-linetemperatureof75 C-atemperatureatwhichdropletevaporationwasshowntobe signicantinFig.5.22.However,fromthisgraph,itcanbes eenthat,evenwhenevaporation issignicant,theeffectofincreasingaxialpositionisst illtoshiftthedropletsizedistribution curvetotheright,indicatingagreaterproportionoflarge rdropletswithincreasingdownstream distance.Themostlikelyexplanationforthiseffectistha tdropletcoalescencethroughcollision playsadominantroleinthedownstreamevolutionofaspray. Thiseffectwillbeexaminedthrough simulationsinthefollowingchapter. Figure5.24Dropletsizedistributionatdifferentaxiallo cations,ataninjectionpressureof 5 MPa andafueltemperatureof75 C ,where z istheaxialdistancefromtheinjectortip. Fig.5.25representsthe SMD ofdropletsfordifferent-onandoff-axiallocationsforfu el temperatureat25,75 C.Forelevatedfueltemperatures,thedropletsarestilln erattheedgesof thespray. 76 Figure5.25Thevariationofdroplets SMD fordifferentoff-axiallocationsatdifferentfuel temperaturesat5 MPa injectionpressure 77 Chapter6 FuelSprayModeling Inthischapterasimpliednumericalapproachtomodelingt hefareldoflow-speedspraysis presented. 6.1Introduction Althoughseveralbreak-upmodelshavebeenproposedrecent lytoestimateinitialdropletsizedis- tributioninspraymodeling,noneofthemcanpredictthegen eratedfueldropletsizedistribution withahighlevelofaccuracy.Theabilitytomeasuredroplet ssizewithaMalvernSprayteclaser diffractiondeviceprovidesauniqueopportunitytouseexp erimentalmeasurementsasinitialcon- ditionsinsimulations. Simulationofthedetailedevolutionoflow/mediumpressur efuelspraysrequiresnumerical solutionofthevelocity,temperatureandconcentratione ldsinthegasphasesurroundingthe droplets,andcoupledsolutionsofthemotionofindividual droplets,possiblyincludingtheirin- ternalliquidmotionandsurfacephasechange([74],[75])a ndiscomputationallyveryexpensive. Simulationofthebreak-upofliquidstreamsintodropletsc anhaveevengreatercomputational expense.Itisthereforeimportantandusefultoexploresim pliedandcomputationallycheaper approachestomodelingtheevolutionofsprays.Sincetrust worthymeasurementsofthesizedistri- butionofdropletsatdifferentdownstreamlocationsinafu elspraycanbemade,theadequacyof 78 simpliedmodelingapproachesforthefareldofafuelspra ycanbeexploredbyusingmeasured dropletsizedistributionsneartheinjectornozzleasinit ialconditionsandmeasuredfareldsize distributionsastargetdataforevaluationofspraymodelp erformance.Inthisthesis,thesimplied modelingapproachexploredisoneinwhichalargenumberofs phericaldroplets,ofachosen sizedistributionandinitialvelocityeld,eachmoveinaL agrangianframe,governedbyNew- ton'ssecondlawofmotion.Asimpleevaporationmodelisuse dtodescribephasechange,and severalmodelsfordropletcollisions-whicharebelievedt obethemaincauseofchangesinsize distributionintheexperimentsofthisstudy-areexplored .Asimplesphericaldropletdragforce modelisused,andinthiswaythebehaviorofdropletsinspra ysismodeledwithouttheconsid- erableexpenseofhavingtosolveforthecompaniongasphase ,theinternalvelocitywithineach droplet,orthenon-sphericityofdroplets.Theadequacyof thissimpliedmodelingapproachfor low-pressurefuelspraysistheassessedbycomparingpredi ctedwithmeasureddropletsizedistri- butions.Thenumericalsimulationusedinthisstudywaspro grammedusingMATLAB.Ensembles ofdropletswithrandomdiameterswhichhavethesamesizedi stributionastheonesmeasuredfrom theMalvernSpraytecinstrumentcanbegeneratedrelativel yeasilybycomputer.Usingthesegen- erateddropletstomatchtheinitialsizedistributioninth efuelsprayandimplementingevaporation andcollisionmodelstosimulatetheLagrangiandevelopmen tofdropletsresultistheessenceof thisfuelspraymodel.SincetheMalvernSpraytecdevicehas theabilitytomeasurethedroplet sizedistributionatdifferentlocations(Fig.6.1),thed elityofsimulationresultscanbetestedby comparingthemwithmeasureddataatdownstreamlocations. Thereareimportantassumptionsthatareusedinthesimulat ion: i )Thedropletsareassumedsphericalandtheenvironmentala irdragforceistheonlyforce participatedintheequations. 79 Figure6.1SchematicoftheabilityoftheSpraytecinstrume nttomeasuresizedistributionsat differentlocations ii )Theenvironmentalgasphaseisstagnantduringthesprayin geventandthegasphaseentrain- mentisassumedtobenegligible. iii )Noturbulentequationissolvedduringthesprayingevent. 6.2TestCalculationsandResults 6.2.1SimulationProcedure InordertotesttheLagrangianspraymodelanditsdependenc eonthechoiceofcollisionmodel, thefollowingstepsaretaken: 1.Dropletsizedistributionismeasuredexperimentallyat adesiredlocationfarenough(more than30 mm )fromtheinjectortipthattheMalverndeviceissupposedto measuretrust- worthydata.Thesizedistributionatthislocationisthein itialconditioninspraymodeling. Additionalmeasurementsarealsoperformedoffueldroplet sizedistributionatlocations 80 beyondtherstone. 2.Sphericaldropletsaregeneratedbycomputerwithrandom diameterswhichhavethesame sizedistributionasmeasuredinexperiments.Thesedrople tsandtheirdiametersareconsid- eredastheinitialconditionsinthenumericalsimulation. 3.Velocitiesofdropletsaredeterminedfromtheexperimen talconditions. 4.Linearmomentumequationsaresolvedfortheinitialense mblesofdropletsinacontrol volumearoundthespraytoobtainthevelocityeldofalldro pletsatthenexttimestep. Whentwodropletsoccupypartsofthesamevolume,theyareco nsideredtohavecollided. Theappropriatecollisionmodelisthenimplementedtodete rminetheoutcome,andthis procedureiscontinuedatsubsequenttimesteps. 6.2.2EffectofNumberofDropletsontheConvergenceofSize -Distribution Statistics Asshownintheexperimentalresultschapter,dropletsized istributioninapulsedfuelsprayhas alog-normalshape.Inordertohavingarealisticnumerical simulation,itisessentialtogenerate initialdropletswithrandomdiameterswhichhavealog-nor malsizedistribution.Theproperway ofgeneratingrandomdropletsshouldnotonlybeindependen tofthenumberofdroplets,butalso hasthesamerangeoffuelconcentrationintheair-fuelmixt ureasintheexperiments.Fig.6.2 showstheinuenceofthenumberofgenerateddropletsonsiz edistributionforspecicmeanand standarddeviationvalues. Accordingtofollowingdenitions,thefuelsprayReynolds andWebernumberinthiscaseare 81 52 ;000 and 102 ;000 ,respectively. Re = ˆvd ;We = ˆv 2 d ˙ (6.1) where ˆ isfueldensity, d isinjectororicediameter, ˙ isfuelsurfacetensionand v isfuelspray averagevelocity.BoschinjectormodelPA66withasingleho lediameterof0.3 m andspraywide angleof12degreeswasusedtogeneratedropletswiththemea ndiametervalueof35 m . 82 Figure6.2Generatedrandomdropletsizedistributionford ifferentnumberofdroplets 83 AccordingtoFig.6.2increasingthenumberofgenerateddro pletsfrom2000to10,000has negligibleinuenceonthesizedistributionhoweveritinc reasesthecalculationcostsignicantly. Takingintoaccountthatintheexperimentsn-heptaneconce ntrationsweremeasuredintherange of10 ppm to30 ppm ,choosing2000initialdropletsresultsinafuelconcentra tioncompati- bletotheexperimentalmeasurementsasdescribedbelow.In thisstudysimulations,sincethe MalvernSprayteclaserbeamdiameteris16 mm ,thecontrolvolumedimensionsarechosentobe 10 mm x10 mm x16 mm .Assumingtheaveragediameterofdropletstobe30 m ,fueldroplets concentrationiscalculatedasfollows: V controlvolume =10 10 16 mm 3 =16 10 7 m 3 (6.2) d mean =30 m (6.3) V droplets =2000 ˇ 6 (30 10 6 ) 3 =28 :27 10 15 m 3 (6.4) V controlvolume V droplets =56 :6 10 6 =56 :6 Million (6.5) PPM = 2000 56 :6 =35 :3 (6.6) Itisdeducedthatusing2000dropletsastheinitialnumbero fdropletsinthisstudysimulations notonlyresultsinhavinganindependentsmoothdistributi on,butalsomakestheair-fuelmixture concentrationintherightrange. 84 6.2.3EffectofMeanValueofInitialVelocitiesonDownstre amStatistics Theaveragevalueofinitialvelocityofdropletsatinjecto rtipis100 m=s .Itisassumedthatthe sprayissymmetricandthateachdroplethasaninitialveloc ityvectorinthedirectionfromthe centeroftheinjectortiptothecenterofthedroplet,shown inFig.6.3.Toinvestigatetheeffectof theinitialmeanvelocityofdropletsondownstreamstatist ics,thedownstreamsizedistributionis calculatedfordifferentinitialmeanvelocitiesforarepr esentativeinitiallog-normalsizedistribu- tion.Alldropletvelocitiesareassumedtohaveaninitialv elocityequaltothemeanvelocity,and theO'Rourkemodelisusedforpredictingthecollisionoutc omes.Thissimulationiscarriedout atambienttemperatureforn-Heptanedroplets,forwhichev aporationisassumedtobenegligible atroomtemperature.BasedonthedenitiongiveninEq.6.1a ndthesizedistributionchosen,the Webernumberrangewasbetween0.5and86.7.TheReynoldsnum berisintherangeof600to 6,400. Figure6.3Dropletsinitialvelocity 85 Fig.6.4showsthathigherinitialvelocitiesresultinslig htlylargerdropletsdownstream,which canbeexplainedbythefactthatincreasingtheinitialdrop letvelocityincreasestheWebernumber whichresultsinmorecoalescencethroughhead-oncollisio ns,makingthesizedistributionmove slightlytotheright.Howeverthiseffectbecomesmuchless signicantwhentheinitialmean velocityisreducedto80 m=s or40 m=s . Figure6.4Simulateddropletsizedistributionat50 mm downstreamfordifferentinitialmean velocities 86 6.2.4EffectofSyntheticTurbulenceinInitialVelocityon DownstreamStatis- tics Inthissection,theeffectofaddinguctuationstoinitial velocitiesofafewpercentondownstream dropletsizedistributionisinvestigated.Arandomnumber between 1 , 1 (RAN)iscreatedfor eachdroplet,sotheinstantaneousinitialdropletvelocit ycanbemodeledas: v V =1+ ( RAN ) ;(6.7) Thedirectionofeachdropletvelocityisassumedtobethesa measdescribedintheprevious section.Fig.6.5showstheeffectofupstreamvelocityuct uationsondownstreamdropletsize distributionfortwodifferent valuesof 0 :05 and 0 :1 .Itisclearthatthiseffectisverysmallinthis study.Thefollowingstatisticalequationsareusedtocalc ulateuctuationintensityfordifferent initialvelocities. u p;i = u p;i + u 0 p;i ;p 2f x;y;z g (6.8) U p = 1 N N X i =1 u p;i ;p 2f x;y;z g (6.9) U 0 p = 1 N N X i =1 u 0 p;i ;p 2f x;y;z g (6.10) U = q U 2 x + U 2 y + U 2 z (6.11) 87 U 0 = r 1 3 U 0 2 x + U 0 2 y + U 0 2 z (6.12) I = U 0 U (6.13) Basedontheaboveequations,theuctuationintensity( I )is 2 :3 and 5 :6 percentfor valuesof 0 :05 and 0 :1 ,respectively. Figure6.5Simulateddropletsizedistributionat50 mm downstreamforsyntheticturbulencesin initialvelocities 88 6.2.5DropletCollision Inthisstudyfourcollisionoutcomesareconsideredasposs ibleresultsofabinarycollisionasitwas showninChapter3.Inthisstudyincaseofcollisionbetween twodroplets,thevalueoftheimpact parameterisobtainedanalyticallybasedonwhatitwasprop osedbyTaskiran[76],whichmakes thecollisionmodeldescribedinthepreviouschaptermorea ccurate.Inotherprevioussimulation works,theimpactparameterischosenasapositiverandomnu mberlessthanone,howeverthis assumptioncaninuencetheresultofcollisionsimulation signicantly,especiallywherethereare manyhead-oncollisions. 6.2.5.1BinaryCollisionImpactParameter Considertwosphericaldroplets(Fig.6.6)whichhavediame tersof d 1 , d 2 ( d 1