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Subcritical and Supercritical Fuel Injection and Mixing in Single and Binary Species Systems

Permanent Link: http://ufdc.ufl.edu/UFE0044615/00001

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Title: Subcritical and Supercritical Fuel Injection and Mixing in Single and Binary Species Systems
Physical Description: 1 online resource (161 p.)
Language: english
Creator: Roy, Arnab
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2012

Subjects

Subjects / Keywords: injection -- plif -- supercritical
Mechanical and Aerospace Engineering -- Dissertations, Academic -- UF
Genre: Aerospace Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Subcritical and supercritical fluid injection using a single round injector into a quiescent atmosphere comprising single and binary species was was investigated using optical diagnostics. Different disintegration and mixing modes are expected for the two cases. In the binary species case, the atmosphere comprised an inert gas of a different composition than that of the injected fluid. In single species case, the atmosphere consisted of the same species as that of the injected fluid. Density values were quantified and density gradient profiles were inferred from the experimental data. A novel method was applied for the detection of detailed structures throughout the entire jet center plane. Various combinations of injectant and chamber conditions were tested and a wide range of density ratios were covered. The subcritical cases demonstrated the importance of surface tension and inertial forces, while the supercritical cases showed no signs of surface tension and, in most situations, resembled the mixing characteristics of a gaseous jet injected into a gaseous environment. A comparison between the single and binary species systems has also been provided. A detailed laser calibration procedure was undertaken to account for the laser absorption through the gas and liquid phases and for fluorescence in the non-linear excitation regime for high laser pulse energy. Core lengths were measured for binary species cases and correlated with visualization results. An eigenvalue approach was taken to determine the location of maximum gradients for determining the core length. Jet divergence angles were also calculated and were found to increase with chamber-to-injectant density ratio for both systems. A model was proposed for the spreading angle dependence on density ratio for both single and binary species systems and was compared to existing theoretical studies and experimental work. Finally, a linear stability analysis was performed for the jet injected into both subcritical and supercritical atmospheres. The subcritical cases showed good correlation with previous and current experimental results. The supercritical solutions, which have not yet been solved earlier by researchers, are found here through an asymptotic solution of the dispersion equation for exceedingly high Weber numbers.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Arnab Roy.
Thesis: Thesis (Ph.D.)--University of Florida, 2012.
Local: Adviser: Segal, Corin.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2014-12-31

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Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2012
System ID: UFE0044615:00001

Permanent Link: http://ufdc.ufl.edu/UFE0044615/00001

Material Information

Title: Subcritical and Supercritical Fuel Injection and Mixing in Single and Binary Species Systems
Physical Description: 1 online resource (161 p.)
Language: english
Creator: Roy, Arnab
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2012

Subjects

Subjects / Keywords: injection -- plif -- supercritical
Mechanical and Aerospace Engineering -- Dissertations, Academic -- UF
Genre: Aerospace Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Subcritical and supercritical fluid injection using a single round injector into a quiescent atmosphere comprising single and binary species was was investigated using optical diagnostics. Different disintegration and mixing modes are expected for the two cases. In the binary species case, the atmosphere comprised an inert gas of a different composition than that of the injected fluid. In single species case, the atmosphere consisted of the same species as that of the injected fluid. Density values were quantified and density gradient profiles were inferred from the experimental data. A novel method was applied for the detection of detailed structures throughout the entire jet center plane. Various combinations of injectant and chamber conditions were tested and a wide range of density ratios were covered. The subcritical cases demonstrated the importance of surface tension and inertial forces, while the supercritical cases showed no signs of surface tension and, in most situations, resembled the mixing characteristics of a gaseous jet injected into a gaseous environment. A comparison between the single and binary species systems has also been provided. A detailed laser calibration procedure was undertaken to account for the laser absorption through the gas and liquid phases and for fluorescence in the non-linear excitation regime for high laser pulse energy. Core lengths were measured for binary species cases and correlated with visualization results. An eigenvalue approach was taken to determine the location of maximum gradients for determining the core length. Jet divergence angles were also calculated and were found to increase with chamber-to-injectant density ratio for both systems. A model was proposed for the spreading angle dependence on density ratio for both single and binary species systems and was compared to existing theoretical studies and experimental work. Finally, a linear stability analysis was performed for the jet injected into both subcritical and supercritical atmospheres. The subcritical cases showed good correlation with previous and current experimental results. The supercritical solutions, which have not yet been solved earlier by researchers, are found here through an asymptotic solution of the dispersion equation for exceedingly high Weber numbers.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Arnab Roy.
Thesis: Thesis (Ph.D.)--University of Florida, 2012.
Local: Adviser: Segal, Corin.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2014-12-31

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2012
System ID: UFE0044615:00001


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SUBCRITICALANDSUPERCRITICALFUELINJECTIONANDMIXINGINSINGLEANDBINARYSPECIESSYSTEMSByARNABROYADISSERTATIONPRESENTEDTOTHEGRADUATESCHOOLOFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENTOFTHEREQUIREMENTSFORTHEDEGREEOFDOCTOROFPHILOSOPHYUNIVERSITYOFFLORIDA2012

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c2012ArnabRoy 2

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Tomyfamilyandthesupporttheyprovided 3

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ACKNOWLEDGMENTS IwouldliketoexpressmysinceregratitudetomyadvisorDr.CorinSegalforhisguidancetowardsmyresearch.Thisworkwouldnothavebeenpossiblewithouthispatienceandenthusiasm.IwouldalsoliketothankmycolleaguesintheCombustionandFluidDynamicslabforcreatingaveryfriendlyworkingenvironment.IwouldliketospecicallythankDr.JonasGustavsson,Dr.AravindVaidyanathan,JigneshSutariya,QiuyaTu,AdrianBlotandSeanKellyforsharingtheirknowledgeinvariouselds.IalsoappreciatethehelpprovidedbyMr.ClementJolyduringhisinternshipatourlab. 4

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TABLEOFCONTENTS page ACKNOWLEDGMENTS .................................. 4 LISTOFTABLES ...................................... 7 LISTOFFIGURES ..................................... 8 ABSTRACT ......................................... 11 CHAPTER 1INTRODUCTION ................................... 13 1.1TheoreticalBackground ............................ 13 1.2EarlierExperimentalWorks .......................... 16 1.3ObjectivesofCurrentWork .......................... 25 2EXPERIMENTALSETUP .............................. 27 2.1HighPressureChamber ............................ 27 2.1.1ChamberBody ............................. 27 2.1.2Injector .................................. 28 2.2LiquidandGasSupplySystem ........................ 30 2.3DataAcquisitionSystems ........................... 31 2.3.1DataAcquisitionandControl ..................... 31 2.3.2ImageAcquisition ............................ 32 2.4WorkingFluid .................................. 34 3LASERCORRECTIONANDIMAGEPROCESSING ............... 37 3.1PhotophysicsofFluoroketoneandPLIFImplementation .......... 37 3.2CalibrationthroughtheGasPhase ...................... 42 3.2.1FluorescenceIntensityDependenceonVaporDensity ....... 43 3.2.2FluorescenceIntensityDependencewithLaserPower ....... 45 3.2.3CalibrationofAbsorptionCoefcient ................. 46 3.3CalibrationthroughtheLiquidPhase ..................... 50 3.4ImageProcessing ............................... 55 4BINARYSPECIESMIXING ............................. 59 4.1ExperimentalConditions ............................ 60 4.2SubcriticalFluidintoSubcriticalAtmosphere ................ 62 4.3SubcriticalFluidintoSupercriticalAtmosphere ............... 63 4.4SupercriticalFluidintoSubcriticalAtmosphere ............... 65 4.5SupercriticalFluidintoSupercriticalAtmosphere .............. 66 4.6CoreLengthMeasurement .......................... 68 4.6.1EarlierWork ............................... 68 5

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4.6.2AlgorithmDevelopedintheCurrentStudy .............. 70 4.6.3ComparisonwithExistingData .................... 71 4.7SpreadingAngleMeasurement ........................ 74 4.7.1EarlierWork ............................... 74 4.7.2AlgorithmDevelopedintheCurrentStudy .............. 77 4.7.3ComparisonwithExistingData .................... 78 4.8Conclusions ................................... 79 5SINGLESPECIESMIXING ............................. 82 5.1ExperimentalConditions ............................ 82 5.2SubcriticalFluidintoSubcriticalAtmosphere ................ 84 5.3SubcriticalFluidintoSupercriticalAtmosphere ............... 85 5.4SpreadingAngleMeasurement ........................ 87 5.5Conclusions ................................... 88 6LINEARSTABILITYANALYSISOFASUPERCRITICALJET .......... 91 6.1EarlierWork ................................... 91 6.2BreakupRegimes ............................... 92 6.3Motivation .................................... 96 6.4TheoryofInviscidStabilityofaViscousJet ................. 97 6.4.1AnalysisoftheSurroundingEnvironment .............. 97 6.4.2AnalysisoftheInjectedFluid ..................... 100 6.5SolutiontotheDispersionEquation ...................... 102 6.6Conclusions ................................... 106 7RECOMMENDEDFUTURESTUDIES ....................... 108 APPENDIX AMATLABSCRIPTSUSEDFORDATAPROCESSING .............. 110 BADDITIONALIMAGES ................................ 143 REFERENCES ....................................... 157 BIOGRAPHICALSKETCH ................................ 161 6

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LISTOFTABLES Table page 3-1Listoftestconditionsusedforthecalibrationoftheliquidphase. ........ 52 4-1Selectedtestconditionsforthebinaryspeciesexperiments ........... 62 5-1Selectedtestconditionsforthesinglespeciesexperiments ........... 84 7

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LISTOFFIGURES Figure page 1-1Schematicofuidjetevolution ........................... 16 1-2Inuenceofgascompositiononjetbehavior ................... 17 1-3Inuenceofgastemperatureonjetbehavior ................... 18 1-4Inuenceofchamberpressureatasupercriticaltemperature .......... 19 1-5Back-illuminatedimagesofthenitrogeninjectedintoachamberofnitrogenataxedsupercriticaltemperatureofTr=2.38butvaryingsub-tosupercriticalpressure ........................................ 22 1-6Magniedimagesofthejetatitsouterboundary ................. 23 1-7Subcriticalinjectionofanoxygenjet ........................ 24 1-8Supercriticalinjectionofanoxygenjet ....................... 25 2-1Highpressurechamberschematic. ........................ 29 2-2Photographofthehighpressurechamber ..................... 29 2-3Photographoftheliquidinjector. .......................... 30 2-4Aschematicoftheopticaldataacquisitionsystem. ............... 33 2-5Atypicallasersheetproleseenfromtoptobottom. .............. 33 2-6Themolecularstructureoftheuoroketone2triuoromethyl1,1,1,2,4,4,5,5,5nonauoro-3-pentanone. .............................. 34 2-7EmissionspectrumoftheuoroketoneatSTPconditionswithanexcitationwavelengthof355nm. ............................... 36 3-1Variationofthenumberofexcitedelectronswiththenumberofexcitingphotons. ............................................. 39 3-2Intensityvariationsofthelasersheetproleasitpassesthroughthechamber 44 3-3Fluorescencesignalvs.uoroketonevapordensity ................ 45 3-4Fluorescencesignalvs.laserpower ........................ 46 3-5Detailedanalysisoflaseruorescenceintensityat14.7atm,1650C ...... 47 3-6Normalizedintensitypointsvs.thelengthtraversedbythelasersheetinpixels 48 3-7Calibrationlinefortheabsorptioncoefcientplottedagainstdensity. ...... 49 8

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3-8Normalizeduorescenceintensitiesat1.25atm.and170C. ........... 50 3-9Normalizeduorescenceintensitiesat12.7atm.and1450C. .......... 51 3-10Fluorescenceintensitiesatvaryingliquiddensities ................ 52 3-11Comparisonofthecoefcientvaluesobtainedthroughthegascalibrationtandthesumofexponentt ............................. 54 3-12Laserintensityvariationfromtoptobottomasitentersthechamber. ..... 55 3-13Jetboundarycalculatedfrompixelintensitygradients. .............. 56 3-14Atypicallasersheetprole ............................. 57 3-15Differencesindensitycausedduetoanimageuncorrectedforlaserabsorption(top)andthatwhichiscorrectedforabsorption(bottom). ............. 58 4-1Selectionoftheexperimentalconditions ...................... 61 4-2Scaledimagesofasubcriticaljetinjectedintoasubcriticalchamber ...... 64 4-3Scaledimagesofasubcriticaljetinjectedintoasupercriticalchamber ..... 65 4-4Scaledimagesofasupercriticaljetinjectedintoasubcriticalchamber ..... 67 4-5Scaledimagesofasupercriticaljetinjectedintoasupercriticalchamber .... 69 4-6Thebasisforcorelengthdetermination ...................... 72 4-7Corelengthsplottedasafunctionofchamber-to-injectantdensityratio ..... 73 4-8Thebasisforspreadingangledetermination ................... 78 4-9Jetspreadingangleplottedasafunctionofchamber-to-injectantdensityratio 80 5-1Selectionoftheexperimentalconditions ...................... 83 5-2Scaledimagesofasubcriticaljetinjectedintoasubcriticalchamber ...... 86 5-3Scaledimagesofasubcriticaljetinjectedintoasupercriticalchamber ..... 87 5-4Jetspreadingangleplottedasafunctionofchamber-to-injectantdensityratio 89 6-1Breakupregimesofajet ............................... 93 6-2SchematicdiagramofthejetbreakuplengthLvs.jetvelocityU. ........ 95 6-3Aroundjetemergingintoaquiescentatmosphereatsubcriticalandsupercriticalconditions ....................................... 98 6-4SpatialgrowthratedependenceonwavenumberforthejetinjectedatSTPconditions ....................................... 103 9

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6-5CurvesforWebernumbersrangingfrom7000to30000.Thepeakdisturbancewavenumberforeachcurvehasalsobeenshown. ............... 104 6-6Asymptotictrendofthepeakgrowthratevs.WeforRe=25000 ......... 105 6-7Variationofasymptoticwavenumberwithdensityratio .............. 106 B-1Density(A)anddensitygradient(B)imagesofsubcritical-into-subcriticalinjectioncorrespondingtocase1inTable 4-1 ........................ 143 B-2Density(A)anddensitygradient(B)imagesofsubcritical-into-subcriticalinjectioncorrespondingtocase2inTable 4-1 ........................ 144 B-3Density(A)anddensitygradient(B)imagesofsubcritical-into-subcriticalinjectioncorrespondingtocase3inTable 4-1 ........................ 145 B-4Density(A)anddensitygradient(B)imagesofsubcritical-into-subcriticalinjectioncorrespondingtocase4inTable 4-1 ........................ 146 B-5Density(A,C)anddensitygradient(B,D)imagesofsubcritical-into-supercriticalinjectioncorrespondingtocases5&6inTable 4-1 ................ 147 B-6Density(A,C)anddensitygradient(B,D)imagesofsubcritical-into-supercriticalinjectioncorrespondingtocases7&8inTable 4-1 ................ 148 B-7Density(A)anddensitygradient(B)imagesofsupercritical-into-subcriticalinjectioncorrespondingtocase9inTable 4-1 ................... 149 B-8Density(A)anddensitygradient(B)imagesofsupercritical-into-subcriticalinjectioncorrespondingtocase10inTable 4-1 .................. 150 B-9Density(A)anddensitygradient(B)imagesofsupercritical-into-subcriticalinjectioncorrespondingtocase11inTable 4-1 .................. 151 B-10Density(A)anddensitygradient(B)imagesofsupercritical-into-subcriticalinjectioncorrespondingtocase12inTable 4-1 .................. 152 B-11Density(A)anddensitygradient(B)imagesofsupercritical-into-supercriticalinjectioncorrespondingtocase13inTable 4-1 .................. 153 B-12Density(A)anddensitygradient(B)imagesofsupercritical-into-supercriticalinjectioncorrespondingtocase14inTable 4-1 .................. 154 B-13Density(A)anddensitygradient(B)imagesofsupercritical-into-supercriticalinjectioncorrespondingtocase15inTable 4-1 .................. 155 B-14Density(A)anddensitygradient(B)imagesofsupercritical-into-supercriticalinjectioncorrespondingtocase16inTable 4-1 .................. 156 10

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AbstractofDissertationPresentedtotheGraduateSchooloftheUniversityofFloridainPartialFulllmentoftheRequirementsfortheDegreeofDoctorofPhilosophySUBCRITICALANDSUPERCRITICALFUELINJECTIONANDMIXINGINSINGLEANDBINARYSPECIESSYSTEMSByArnabRoyDecember2012Chair:CorinSegalMajor:AerospaceEngineeringSubcriticalandsupercriticaluidinjectionusingasingleroundinjectorintoaquiescentatmospherecomprisingsingleandbinaryspecieswaswasinvestigatedusingopticaldiagnostics.Differentdisintegrationandmixingmodesareexpectedforthetwocases.Inthebinaryspeciescase,theatmospherecomprisedaninertgasofadifferentcompositionthanthatoftheinjecteduid.Insinglespeciescase,theatmosphereconsistedofthesamespeciesasthatoftheinjecteduid.Densityvalueswerequantiedanddensitygradientproleswereinferredfromtheexperimentaldata.Anovelmethodwasappliedforthedetectionofdetailedstructuresthroughouttheentirejetcenterplane.Variouscombinationsofinjectantandchamberconditionsweretestedandawiderangeofdensityratioswerecovered.Thesubcriticalcasesdemonstratedtheimportanceofsurfacetensionandinertialforces,whilethesupercriticalcasesshowednosignsofsurfacetensionand,inmostsituations,resembledthemixingcharacteristicsofagaseousjetinjectedintoagaseousenvironment.Acomparisonbetweenthesingleandbinaryspeciessystemshasalsobeenprovided.Adetailedlasercalibrationprocedurewasundertakentoaccountforthelaserabsorptionthroughthegasandliquidphasesandforuorescenceinthenon-linearexcitationregimeforhighlaserpulseenergy.Corelengthsweremeasuredforbinaryspeciescasesandcorrelatedwithvisualizationresults.Aneigenvalueapproachwastakentodeterminethelocationofmaximumgradientsfordeterminingthecore 11

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length.Jetdivergenceangleswerealsocalculatedandwerefoundtoincreasewithchamber-to-injectantdensityratioforbothsystems.Amodelwasproposedforthespreadingangledependenceondensityratioforbothsingleandbinaryspeciessystemsandwascomparedtoexistingtheoreticalstudiesandexperimentalwork.Finally,alinearstabilityanalysiswasperformedforthejetinjectedintobothsubcriticalandsupercriticalatmospheres.Thesubcriticalcasesshowedgoodcorrelationwithpreviousandcurrentexperimentalresults.Thesupercriticalsolutions,whichhavenotyetbeensolvedearlierbyresearchers,arefoundherethroughanasymptoticsolutionofthedispersionequationforexceedinglyhighWebernumbers. 12

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CHAPTER1INTRODUCTION 1.1TheoreticalBackgroundThemajorityoftheoriesandempiricalevaluationsofaliquidjetbreak-upandmixingprocesseshavebeenpresentedforarestrictedrangeofexperimentalconditionswherethepressureandtemperatureofthesurroundinggasarewellbelowcriticalvalues.Theanalysisofmixingundersubcriticalconditionsisbasedontheassumptionthatthereisadenedborderbetweentheliquidbeinginjectedandthesurroundinggas.Hence,itissafetoassumethattheliquiddensityisnearlyconstantandislimitedbyboilingtemperature.Thus,thepredictionsofjetordropletbreak-upandfurthermixingaremostlybasedonnon-dimensionalparametersliketheReynolds,WeberandOhnesorgenumbers.However,therearenumerousapplicationsindieselengines,gasturbinesandliquidfuelrocketengineswheretheseassumptionsarenotvalid.Theseapplicationsincludetheinjectionofauidintoanenvironmentwhosetemperatureandpressureexceedthecriticalvaluesforthepureuid.Simplethermodynamicanalysisoftherocketthrustchamber,i.e.thecombustionchamberandtheexpansionnozzleshowsthatthemotivationforachievinghigherchamberpressuresistoobtainahigherspecicimpulsefortheengine[ 1 ].Asimilartrendisalsotruefordieselandgasturbineenginestoincreasepowerandefciency.Athighenoughpressures,theinjecteduidmaynditselfnearorabovethethermodynamiccriticalpressure.Liquiddropletvaporizationandspraycombustioninsupercriticalenvironmentshavelongbeenmattersofseriouspracticalconcernincombustionscienceandtechnologymainlyduetothenecessityofdevelopinghighpressurecombustiondevicessuchasliquid-propellantrocket,gas-turbine,dieselandpulsedetonationengines.Liquidfuelsand/oroxidizersareusuallydeliveredtocombustionchambersasasprayofdroplets,whichthenundergoasequenceofvaporization,mixing,ignitionandcombustionprocessesatpressurelevelswellabovethethermodynamiccriticalpointsoftheuids. 13

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Undertheseconditions,liquidsinitiallyinjectedatsubcriticaltemperaturemayheatupandexperienceathermodynamicstatetransitionintothesupercriticalregimeduringtheirlifetimes.Theprocessexhibitsmanycharacteristicsdistinctfromthoseinasubcriticalenvironment,therebyrenderingconventionalapproachesdevelopedforlowpressureapplicationsinvalid[ 2 ].Therearedrasticchangesinsomeimportantequilibriumpropertiesofapuresubstanceasitapproachesthethermodynamiccriticalpoint.Thesharpdistinctionbetweenliquidandgasphasesdisappearsatandabovethecriticalpoint,andthesubstanceismoreproperlyconsideredtobeauidwhosedensitycanvarywidelybutcontinuouslyastemperatureischangedatxedpressure.Densitychangescanbecomeparticularlylargenearthecriticalpoint.Otherpropertiesthatvarywidelynearthecriticalpointarethermalconductivityandmassdiffusivity.Inaddition,theconstantpressurespecicheatbecomesverylargeandsurfacetensionvanishes.Undertruesupercriticalconditions,therecannotbeevaporationsincethelatentheatisnull,andasurfacecannotexist.Therefore,thetermemissionrateandemissionconstantwhichareofmoregeneralmeaningshouldbeusedinstead[ 3 ].Finally,thesolubilityofgasesintotheliquidphasebecomessignicantastheambientpressureisraised,makingitnecessarytoconsidermulti-componentphaseequilibriumornon-equilibrium.Formixtures,thedeterminationofcriticalconditions,calledthecriticalmixingtemperatureorpressure(criticallinesfortwo-componentmixtureasopposedtoacriticalpointforapuresubstance)canbecomplex.Forexample,forapurehydro-carbondropinanitrogenenvironment,theamountofnitrogendissolvedonthesurfaceoftheliquiddropincreaseswithpressure.Asaresult,thecriticalmixingtemperatureofthelayerdecreases.Thisformsalayerthatisamixtureofnitrogenandfuelthatspreadsspatiallyintime.Intheremainderofthetext,thetermssubcriticalandsupercritical,andreducedtemperatureandpressurewillrefertothecriticalconditionofthepuresubstanceusedinthejetandnotthatofthemixture.Itwasassumedformanyyearsthatsincedrop-likeentitiescanbeopticallyidentiedin 14

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thevicinityofuidjetsinjectedintosurroundingsatsupercriticalconditions,aninjecteduidthatwasliquidunderatmosphericconditionsmustremainliquidinthechamber.Thisisamisconceptionsinceopticalmeasurementsdetectanysubstantialchangeindensity,i.e.,densitygradients.Thus,thedensityratiomaybewellbelowtheorderofmagnitudethatcharacterizesitsliquid/gasvalue,butthemeasurementwillstillidentifyachangeintheindexofrefractionifthedensitygradientissteep.Thereforethereisnoinconsistencybetweentheopticalobservationof'drops'and'ligaments'andtheuids(injectedandsurrounding)beingsupercritical.Experimentswithuidsemergingfromanoriceintoachambercontaininganotheruidaremoreaptatportrayingthesituationinacombustionchamber,althoughthedatamaypresentmoreinterpretingdifculties.Inthisconguration,thedistinctionbetweenjetsandspraysispurelyintentoftheexperiment.Jetsarediscussedwhentheintentistostudytheuidcolumndisintegration,whereasspraysarediscussedinthecontextofdropsthathavealreadyseparatedfromtheincominguidjet.Similartothis,adistinctionismadebetweenatomizationanddisintegration,theformerbeingapurelysubcriticalprocessandreliesupontheexistenceofasurfacethatmustbreakup,andthelatterbeingaprocessthatmayoccurwheneverthereisaboundarywhichmaynotbeatangiblesurface.Threedistinctowregimeswereobservedcommonlyinaturbulentjet:apotentialcore,atransitionregionandafullydevelopedselfsimilarregion,asshowninFigure 1-1 .Thepotentialcore,orsimplythecorelength,onlycontainstheinjecteduidandreducesinsizeasthejetmixeswiththeentrainedsurroundinguid.Theowpropertiesalongthejetcenterlineremainnearlyconstantinthisregion.Downstreamofthepotentialcore,thereexistsatransitionregionwhereturbulentmixingtakesplace.Afullydevelopedself-similarregionisreachedfurtherdownstream,wheretheprolesofnormalizedowpropertiescollapseintosinglecurves.Foranincompressiblegasjet,Abramovich[ 4 ]statedthattheself-similarregionappearsatapproximatelyatx=Dinj20. 15

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Figure1-1. Schematicofuidjetevolution.Thethreedistinctowregimeshavebeenmarked. 1.2EarlierExperimentalWorksExperimentalinvestigationintosupercriticaluidjetdynamicsdatesbackto1971byNewmanandBrzustowski[ 5 ].TheystudiedtheinjectionofCO2uidwithaninlettemperatureof295KintoachamberlledwithamixtureofN2andCO2undernear-criticalconditions.ThecriticaltemperatureandpressureofCO2are304Kand73atmrespectively,andthoseofN2are126Kand34atmrespectively.Thechambertemperatureandpressurewaskeptbetween295-333Kand62-90atmrespectively,andtheCO2massfractionwasvariedbetween0-50%.Theshadowgraphvisualizationtechniquewasusedtoinvestigatetheoweld.SomeexperimentalimagesareshowninFigures 1-2 1-3 and 1-4 .Therearetwomainreasonswhygascompositioncanaffectthenatureofthespray.Therstissimplythatthegasdensityvarieswithcomposition.ThesecondisthattherateatwhichtheCO2liquidwillevaporatewilldependontheamountofCO2vaporintheenvironment.Allelsebeingequal,thelowertheCO2partialpressure,themoretheevaporationperunitareaofexposedliquidsurface.InFigure 1-2 ,boththeliquidandgasareatthesameinitialsubcriticaltemperatureof295K.TheamountofCO2vaporinthegasphase,however,isdifferentineachofthethree 16

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casesshown.Thepressureof75atmisabovethecriticalpressureofCO2.Thetrendtowardaner,moreuniformsprayasCO2partialpressure(andhencegasdensity)isincreasedisevident.TheobviousobservationregardingtheeffectofevaporationisthatthetotalapparentmassofliquidinthemainregionofthesprayislessthelowertheCO2partialpressure(i.e.,thehighertheevaporationrate).Thereare,however,severalcompetingeffectsthattakeplaceunderthesekindsofconditions.Thetemperature Figure1-2. Inuenceofgascompositiononjetbehavior.ThejetisinitiallyatTr=0.97isinjectedintothechamberatTr=0.97,Pr=1.04withinjectionvelocity=3.7m/sec.PartialpressureratioofCO2is0,0.5atm,saturationvaluerespectively. ofthegasenvironmentwillaffectthejetbehaviorbecause1)gasdensitydecreaseswithincreasingtemperatureforaxedcompositionandpressure,2)surfacetensiondecreaseswithincreasingtemperature,becomingzerowhentheliquidreachesitscriticaltemperatureand3)evaporationrateswouldbeexpectedtoincreasewithtemperatureforconstantliquidtemperature.Evaporationisabletoproceedrapidlyinallthreecases(CO2partialpressureiszero)andindeedwouldbeexpectedtoproceedatahigherratethehigherthegastemperature.ItisevidentfromFigure 1-3 that,astemperatureincreases,thesizeandnumberofdropletswithinthesprayissubstantially 17

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reduced.Anexaminationofthephysicalappearanceoftheliquid-gasinterfaceatashortdistancefromtheoricesuggeststhatthemajorcontributiontotheincreasedatomizationefciencyisareductionofsurfacetensioncausedbyliquidheating.In Figure1-3. Inuenceofgastemperatureonjetbehavior.ThejetisinitiallyatTr=0.97isinjectedintothechamberatPr=1.228andTr=0.97,1.05and1.10respectivelywithinjectionvelocity=2m/sec.InitialCO2partialpressure=0atm. ordertoconsidermorespecicallythepossibilityofgasication,aseriesofphotographswastakenofwhichFigure 1-4 isrepresentative.HerethereisalargepercentageofCO2intheenvironment(henceevaporationisseverelyreduced),andthegastemperatureiswellinexcessoftheliquidcriticaltemperature.At900psig,theliquidisissuingintowhatisessentiallyasuperheatedgas.Uponreachingitssaturationtemperatureatthispressure,theliquidwouldboil.Thevaporthusproducedwouldcontinuetoheatuptothegaseousstate.Theliquidcannotgasifydirectly,since61atmissubcritical.Atthepressureandcompositionofthenexttwoconditions,however,theliquidcannotboil,sincethechamberpressureissupercritical.Theliquiddropletsaresimplyheateduntiltheyreachthecriticaltemperature,atwhichpointgasicationoccurs. 18

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Figure1-4. Inuenceofchamberpressureatasupercriticaltemperature.ThejetisinitiallyatTr=0.97isinjectedintothechamberatTr=1.05andPr=0.85,1.04and1.228respectivelywithinjectionvelocity=3.35m/sec. Birketal.[ 6 ]alsoperformedwaterdisintegrationexperimentsinnitrogenwherethetemperaturesandpressureswereconsiderablyhigherandwellintothesupercriticalregime.Theexperimentswerecarefullyconductedanddocumentedinordertoidentifyglobaldifferencesbetweenvisualaspectsatvariousoperatingconditions;inparticularthechambertemperatureandpressureasafunctionoftimewererecordedandpresented.Waterinjectedthrougha1mm.circularoriceapparentlydisintegratedintolargedrops.VisualcomparisonsofsprayX-rayrecordsfornon-evaporating,subcritical,transcriticalandsupercriticalconditionsconductedbyBirketal.[ 7 ]clearlyshowedmarkeddifferences.Theobservationshowedthatthejetcoreisnotwelldenedundersupercriticalconditions,butitisrathertheregionoftheowwherethereisalargeconcentrationofworkinguid.Conductingevaporativeexperimentswhereboththepressureandthetemperaturewereabovethecriticalpointoftheworkinguid,theauthorsdetected(underthisnewdenitionofthecore)anincreasedcorepenetrationwithincreasingpressurewhichtheyspeculativelyattributedtotheattainmentofthecriticaltemperatureincloseproximitytotheinjectionlocation,andthereforetoaslow 19

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jetdisintegrationthatcouldproducealongercore.Theseauthorsalsoinvestigatedthedifferencebetweenfullconeandannularjets,anddetectedinthelatteracylindricalshellcomposedofstreamwiseligamentswhich,whenmagnied,exhibitedthehelicalstructureidentiedinthecoresoffullconesprays.Thisaspectofbehaviorisconsistentwiththeshellbehavinglocallyastheshearlayeratthesurfaceoffullconesprays.Anunexplainedpeculiarityofsupercriticalannularsprayswasaninwardcollapseoftheshellclose(1-2shelldiameters)totheinjectionlocationandafurtherspatialdivergencewhichoccurredclosertotheinjectionpointwithincreasingambientpressureandtemperature.ThedifferencesbetweensubcriticalandsupercriticaljetbehaviorwasalsoexaminedbyChehroudi[ 8 ]andMayeretal.[ 9 ].ChehroudistudiedaN2jetinjectedintoaN2environmentwiththechamberpressuresrangingfromsubcriticaltosupercriticalandatsupercriticalchambertemperatures.TheeffectswerephotographicallyobservedanddocumentedneartheinjectorexitregionusingaCCDcamerailluminatedbyashort-durationback-litstrobelight.Figure 1-5 showsimagesoftheN2jetinjectedintoN2ataxedsupercriticalchambertemperaturebutvaryingsub-to-supercriticalpressure.Onthehighresolutionprintsoftheprocessedimagesonecanrecognizeobjectswithrealsizeofabout30micronsandlarger,witha7micronbandwidth.Whatweseeintheseimagesaredemarcationofregionswherechangesinindexofrefractionoccurduetodensityvariations.AtthelowestsubcriticalchamberpressureinFigure 1-5 thejetisliquid-likewithsurfaceinstabilitiesthatgrowdownstreamwhereithastwistedappearance.AtProf0.43allinstabilitiesarefurtheramplieduntilatthenexthigherpressurewheremanysurfaceligamentsanddropsareseenejectedfromthejet.AtProf0.83verynedropsareseensurroundingthejetandit'sspanwisedimensionnoticeablygrowsawayfromtheinjectorexitplane(i.e.jetdiverges).AtProf1.03theN2jetentersintoasupercriticaltemperatureandpressureenvironment.Therearedrasticchangesindetailsoftheinterface.Therearenodetectabledropsunderthisconditionwiththehighestsoftwaremagnicationusedtoviewthesehighresolution 20

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images.Therearethread-likeornger-likeentitiesemergingfromthejetwhicharenotbrokenupintodropletsasbeforebutareseeminglydissolvedataspectrumofdistancefromthedarkcore.This,inasense,formsamixinglayerinwhichphasetransitionand/orlargelocaldensitynon-uniformitiesoccur.Anyfurtherincreaseofchamberpressuredecreasesthelengthandthethicknessoftheinternaldarkcoreandimagesprogressivelyresembleinjectionofagaseousturbulentgasjetintoagaseousenvironment.Figure 1-6 showsthemagniedimagesofthemixinglayeratthreesubcritical,transitional,andsupercriticalchamberpressures.Gradualtransitionfromclassicalliquid-likeligamentanddropformationsattheinterface,seeninliquidatomizationregime,toacomb-likestructurenearthecriticalpointandnallytowheresubmergedturbulentjetappearanceemergescanbeobserved.Inspectingalargesetofimagesathighmagnications,noevidenceofdropformationisseeninthisgas-likejetregime.TheseobservationsarealsoconsistentwithimagespresentedbyMayer[ 9 ].Insummary,forN2intoN2injectionatthesupercriticalambienttemperaturetested,thereappearstobetwostructuraltransitions.Oneiswhentheintactjetwithirregularly-lookingsurfacewavesanddownstreamshinytwisted-shapedcolumnturnsintoasomewhatdivergingjetwithligamentsandmanysmalldroplets.Theotheriswhenthelatterstructurechangesintoagas-likejetappearancenearbutbelowthepointwherethemediumpressurechangesfromsub-tosupercriticalconditions,basedoninjectorcriticalpressure.Thereasonforthisbehavior,particularlyforthechangeintogas-jetbehavior,shouldbesoughtinprogressivereductionofsurfacetensionandheatofvaporizationuntiltheybothvanishatandabovethecriticalpoint.Mayeretal.[ 9 ]studiedtheinjectionandcombustionprocessesinaliquidoxygen/gaseoushydrogen(LOX/GH2)rocketenginecombustorsthroughowvisualizationsandmeasurementsofinjection,sprayformation,andsupercriticalmixingatchamberpressuresupto10MPa.Thecriticalpressuresofoxygenandhydrogenare5.09and1.31MPa,andthecriticaltemperaturesare154.8and33.2K,andhence 21

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Figure1-5. Back-illuminatedimagesofthenitrogeninjectedintoachamberofnitrogenataxedsupercriticaltemperatureofTr=2.38butvaryingsub-tosupercriticalpressure.Forthersttworows,chamberpressuredecreasesleft-to-rightfromupper-lefttolower-rightcorner:ChamberPr=2.74,2.44,2.03,1.64,1.23,1.03,0.83,0.63,0.43,and0.23.Lowertworowimagesarecorrespondingimagesfortheupperonesbutfurtherdownstream.Reynoldsnumberrange:25,000to75,000;Injectionvelocityrange:10to15m/s. 22

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Figure1-6. Magniedimagesofthejetatitsouterboundaryshowingtransitiontothegas-jetlikeappearancestartingatjustbelowthecriticalpressureoftheinjectant.ImagesareatxedsupercriticalchambertemperatureofTr=2.38. thechamberpressureswerealwayssupercriticalwithrespecttoboththespecies.Thetemperatureoftheliquidoxygenwas100K,andthatofthegaseoushydrogenwas300K,andhencesubcriticalforoxygenbutsupercriticalforhydrogen.Figure 1-7 showsthephotographsofthe1.5MPacondition(testcase1)takenwithastandardshadowgraphsetup.AtchamberpressuresmuchlessthanthecriticalpressureofoxygentheLOXjetisatomizedformingaspraycomparabletotheowpatternofcoldowatomizationbeforeignition.LigamentsaredetachedfromtheLOXjetsurface,whichformrounddropletsandnallyevaporate.Atthe1.5MPachamberpressureexperiments,secondarybreakup(dropletvibrational-and-bag-typebreakup)couldbeobserved.Becauseoftherapidvaporizationofthedropletsinaburningspray,thedropletnumberdensityisratherlowcomparedtothecoldowcase.Mostofthedropletsarenotspherical.TheverysmoothsurfaceoftheLOXjetclosetotheinjectorisalsonoted.Uponapproachingandexceedingsupercriticalpressure,dropletsnolongerexistasshowninFigure 1-8 .FromtheLOXjetcore,thread-likestructuresdevelop 23

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andgrow,whichdonotdetach,butrapidlydissolveandfadeaway.SeveraltensofjetdiametersfurtherdownstreamtheLOXcorebreakupintolargeLOXlumps,whichdissolveinthesamemanner.Thejetbreakuplength(averagelengthofconnectedLOX)decreaseswithincreasingchamberpressure.Inthe6.0MPacaseshowninFigure 1-8 ,mixingisnotcompleteattheendofthevisualizedarea.Onequestionthatmightarisegiventheexperimentalevidenceofadifferenttypeofuiddisintegrationundersubcriticalandsupercriticalfareldconditionsiswhetherasupercriticalsprayactuallyexists.Theguresshownhereclearlydisplaythedifferencebetweensubcriticalandsupercriticalmixingandignition. Figure1-7. Subcriticalinjectionofanoxygenjet.Injectionconditions:Oxygenvelocity10m/s,hydrogenvelocity300m/s,d=1mm,chamberpressure1.5MPa.Fromleft-rightandtop-bottom:Axialpositionx=0,12,24,36,48,60mm. Itmustbeunderstoodthatthethermodynamicstate(subcriticalorsupercritical)oftheinjecteduidwithrespecttotheimposedfareldconditionsisinitiallyknown,butthatthefurtherstateoftheuidatdifferentlocationsisafunctionoftheinter-diffusionofexistingspecies,ofheattransfer,ofsolubilityeffectsandveryimportantly,ofconvectivemixing.Thus,transportproperties,thermodynamicpropertiesoftheequationofstateandtheReynoldsnumberallcontributetodeterminingthethermodynamicstate: 24

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Figure1-8. Supercriticalinjectionofanoxygenjet.Injectionconditions:Oxygenvelocity30m/s,hydrogenvelocity300m/s,d=1mm,chamberpressure6.0MPa.Fromleft-rightandtop-bottom:Axialpositionx=0,12,24,36,48,60mm. pressure(P),temperature(T),andmass-fractionofthespecies(Yi)ateachlocationwithintheuid.Sincethecriticalpointofamixturedependsupon(P,T,Yi),accordingtothemixtureandthedevelopmentoftheow,subcriticalregionsmayormaynotexist.Iftheuidissupercriticalatalltimes,traditionalatomizationwillnotoccur.Iftheuidremainssubcriticalinsomeregionslongenoughtosustainformationofinstabilities,classicalatomizationmayoccur,however,theevolveddropsmaybecomechunksofsupercriticaluidatfurthertimes.Clearly,manypossibilitiesaretheoreticallyconceivable.However,thereisnotenoughexperimentalevidencetocurrentlysupportauniedviewofuiddisintegrationoverthesubcritical/supercriticalregimes. 1.3ObjectivesofCurrentWorkThisintroductionwasusedtogiveaperspectiveofthesupercriticalmixingexperimentsundertakenbyseveralotherresearchers.Thisproblemhasbeenactivelyapproachedbytheresearchcommunity,withsignicantsuccess.Nevertheless,thereareafewproblemswhichdidnotattractenoughattentionsofar,forexamplehowasecondspeciescanfundamentallyinuencethemixingprocess,includinghowthe 25

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corelengthsandspreadinganglesareaffected,whetherpreheatingtheinjecteduidcanaffectthemixingprocessandhowthestabilityofthejetisaffectedatsupercriticalconditions.Asithasbeenmentionedbefore,mixingathighpressuresandtemperaturesappearsinmanyapplicationsincludingliquidrocket,dieselandgasturbineengines,wherepressureandtemperaturecaneasilyexceedcriticalvaluesfortheuid.Yet,thereislimitedtheoreticalaswellasconceptualunderstandingofthefundamentalprincipleswhicharegoverningthisprocess.Thegoalofthisworkistogainsomeinsightintofundamentalfeaturesofsupercriticalmixingforsinglespeciesandbinaryspeciessystems,aswellastoexpandthedatabaseofreliableexperimentalmeasurementsofdensitydistributionduringthesupercriticalliquid/gasmixingdoneinthesamefacilitybyPolikhov[ 10 ]. 26

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CHAPTER2EXPERIMENTALSETUPThedetailsoftheexperimentalsetuphavebeengivenbyPolikhov[ 10 ],andhenceabriefoverviewisincludedhere. 2.1HighPressureChamberThechamberhastoprovidemaximalexibilityintermsofopticalaccessandinjectorscongurations.Secondly,thechamberhastosustainhighpressuresandelevatedtemperaturestoexceedcriticalconditionsofworkinguid.ThedesignisshowninFigures 2-1 and 2-2 .Thechamberconsistsofthreemainparts:(i)theuppercomponentwhichincorporatesgasandliquidsupply,(ii)thebodyand(iii)theexhaust.Thechamberiscapableofsustainingthepressuresofupto150atm(2200psi)attemperatureashighas3500C.Foroperationalsafetythelimitwassettopressuresupto70atm(1000psi)andtemperaturesupto3000C.Brasswaschosenasthematerialforthechambersinceitcansustainhighpressuresandtemperatureswhileprovidingfastenoughheattransfertopreventlocaloverheatingandensureuniformtemperaturesfromtheinjectortiptothechamberexhaust. 2.1.1ChamberBodyThechamberdimensionsare1.81.89(45.7245.72228.6mm).Suchdimensionswerechosentopreventhighlyundesirableliquiddepositiononthewindowsduetojetappingandsplashingfromthebottom.Moreover,tofullltherequirementsofmaximumeldofviewforopticalaccess,thechambercross-sectionwasdesignedtobesquareinsteadofround.Fourround0.26(6.6mm)diameterslotsweredrilledinthechambercornerstoinsertfour6(152.4mm)longOmegaCIR-1060/240Vcartridgeheaters.Eachheaterisabletodeliver0.4kW.OmegaPX303-1KG10Vpressuretransducershavebeenusedtomeasurethepressureinthehighpressurechamber,liquidsupplyandgassupplylines.OmegaK-typethermocouplesofdifferentlengthsareusedtomeasurethetemperaturesatvariouslocationsoftheexperimentalfacility. 27

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Topreventleaks,O-ringswereusedtosealthefacility.Foropticalaccess,thewindowswerechosensuchthattheywouldprovideaccesstothelaterstagesofthejetbreak-up,andwouldalsobeushwiththeinnersideofthechambertopreventinterferencewiththegasow.Figures 2-1 and 2-2 showthefourcutoutstomountthewindows.Quartzwindowsofdimensions3.801.350.70(96.534.317.8mm.)wereused[ 11 ].Thesewindowsaredesignedtowithstandtemperaturesashighas10000Candpressuresaround70atm(withasafetyfactorof7).Afterinstallationofthewindowsintotheanges,theeldofviewis3.30.84(83.821.3mm).Thewindowsareheldinplacebyinsertslocatedintheangecavitieswhicharetightenedbysocketscrews.Afterthewindowisinsertedintoitsslottheclearancebetweenwindowandslotislledwith100%liquidsiliconerubber.Ittakesabout2hoursforsiliconerubbertodryanabout24hourstoformthebondcompletely.Thisinstallationprocedureinsuresushmountingandholdsthewindowsinplacermenoughtoprovidesealingbetweenthewindowandtheange.ThenextstepistoplacetheO-ringintothegroovesandmountwindowanges.Allexperimentsdonotneedallfourwindows,hencetosimplifythesetupmaintenancedummyangeswithnocutsforopticalaccessweremanufacturedfortheseexperimentstoeasilyandreliablyblockunusedcut-outs. 2.1.2InjectorTheupperpartofthetestsectionincorporatestheinjectorassemblyandisdesignedtoprovidethecapabilitytostudysingleinjectionaswellasco-axialinjection.Theliquidsupplyisthesameforbothcases,suppliedvia1/8Swagelokstainlesssteeltubing.Thenalinjectordiameterischosentobe0.08(2mm).Ahoneycomblikestructureisweldedtotheinjectorjustbeforethetiptostraightenthegasowbeforeinjectionintothechamberfortheco-axialinjectioncase,andalsotoreducetheinjectorpostvibration.Inthecaseofsingleinjectionaspresentedhere,thegasowthroughtheannuluschannelisblocked.Instead,thegasissuppliedviafourchannelsdrilledintothelidbodyupstreamofthehoneycombstructure.Additionally,thegasowisinthedirect 28

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Figure2-1. Highpressurechamberschematic. Figure2-2. Photographofthehighpressurechamber.Theliquidandgasinjectionportshavealsobeenshown.Thechambercanbeheatedandpressurizedto3500Cand150atmrespectively. 29

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vicinityofthewindowsandhencepreventsliquiddeposition.Thelengthtodiameterratiooftheinjectortipwaskeptabove2.5tokeeptheowlaminarwhenit'sinjected.AphotographoftheliquidinjectorisshowninFigure 2-3 Figure2-3. Photographoftheliquidinjector. 2.2LiquidandGasSupplySystemInthecaseofsingleinjectionwithasingleroundinjection,thegassupplylineisusedtopressurizethehighpressurechamberandmaintainthedesiredtemperatureduringtheexperiment.Thegasentersthechamberfarenoughfromtheliquidinjectortopreventanyliquid-gasinteractions.Whentheco-axialinjectionisgoingtobestudied,thegasowalsohastobeprovidedwithcontrolledtemperatureandvelocityinadditiontobeingusedtopressurizethechamber.AllowlinesarecontrolledbyOmegaSV-128solenoidvalveswithanoperationalpressurerangeof0.3-100atm(5-1500psi).Theow-ratesarecontrolledbySwagelokneedlevalves.ThegasowrateismeasuredusinganOmegaFLMG12050SS-MAowmeterwhichhasanoperationalpressureandowraterangesof1-100atmand0-50standardcubicfeetpermeterrespectively.ThepressureinthegaslineismeasuredusinganOmegapressuretransducer.Thegasisheatedviaanelectricalheaterlocateddownstreamofthetransducerwhichuses 30

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sixOmegaCIR-2121/240cartridgeheatersgivingatotalpoweroutputof6kW.Thegastemperatureismeasuredusingthermocouplesattachedtotheheatercoreandthechamberlidwhichallowsthecontroloftheinjectedgastemperaturewithoptimalprecision.Thefuelintheliquidlineissuppliedbythefueltankwhichispressurizedwithnitrogen.TheowinthislineisalsocontrolledusingSwagelokneedleandballvalves.TheowrateismeasuredusingaturbinetypeSponslerLo-Floprecisionow-meterMF-125-MB-PH-A-4X-N1.Thisow-meterprovidesfrequencyoutputandhasameasuringrangeof5-100cc/secwitha+ 0.25%linearity[ 12 ].Oneofthemajordrawbacksofthistypeofow-meteristhatitssignalisdominatedbythe60Hzfrequencyanditsharmonicsfromelectromagneticdevicessuchasthesolenoidvalves.Hence,theow-meterwasshieldedforlowliquidowexperiments.Thedesignoftheliquidheaterissimilartothegasheater,theonlydifferencebeingthetotallength.Thetotalpoweroutputis3kW.Thedesignallowsthetemperatureoftheinjectedliquidtobeconstantfor30secondsataowrateof50cc/sec.Theheatercoreandtheinjectedliquidtemperaturesaremeasuredusingthermocouplesplacedinsidethecoreandthechamberlid. 2.3DataAcquisitionSystems 2.3.1DataAcquisitionandControlThesystemisoperatedfromacomputerusingaPCI6259dataacquisitioncard.Thecardhas32analog12bitinputchannelsand2analogoutputchannelswithamaximuminput/outputrangeof+ 10V.ThiscardisconnectedtothesignalconditionerandchannelmultiplierSCXI-1000.TherearethreemodulesinvolvedinthedatacollectionprocesswhicharecontrolledbyaprogramwritteninLabVIEW8.2graphicalprogrammingenvironment.ThetemperaturesaremeasuredviaSCXI-1100withaSCXI-1303connectorblock.Thepressuresandtheow-ratesaremeasuredviaSCXI-1140withaSCXI1301connectorblock.ThecontrolfunctionsofthesystemareimplementedbyaSCXI-1124modulewithaSCXI-1325connectorblock.Thedetailsof 31

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theLabVIEWprogramandthedataacquisitionhardwaresetupschematichavebeenprovidedintheearlierworkofPolikhov[ 10 ]. 2.3.2ImageAcquisitionPlanarlaserinduceduorescence(PLIF)isusedastheopticaltechniquetostudythemixingprocess.TheopticaldataacquisitionsystemisshownasaschematicinFigure 2-4 .ThesystemconsistsofaContinuumSureliteIINd:YAGlaser,3dichroicmirrors,3cylindricallenses,abandpasslterandaPIMAXIIIntensiedChargedCoupledDevice(ICCD)camera.Thethirdharmonicorthe355nmwavelengthofthelaserwasusedintheuorescenceexcitationprocess.Averageenergyperpulsewas150mJat10Hzwithapulsedurationof10ns.Thebeamwasreectedoff3dichroicmirrorstoeliminateanyresidual532nmthatmighthaveemanatedfromthelaser.Thus,afterreectionthebeamcontainsabout0.002%oflightwithwavelengthsotherthan355nm.Thebeamwasthenpassedthrough3cylindricallensestoformasheet25mmwideand0.1mmthickatthecenterofthechamber.AtypicalbeamprolehasbeenshowninFigure 2-5 .Theuorescenceimageswererecordedwiththecamerakeptat900tothebeampath.Oneoftwoseparatecameraswithdifferentresolutionswasusedbasedonexperimentalneeds.Forexperimentswheretheaxialdistance-todiameterratiotobecapturedwas8,acamerawitharesolutionof512512pixelswasused,andincaseswheretheratiotobecapturedwas20orgreater,acamerawitharesolutionof10241024pixelswasused.Theactualimagewascroppedtoeither311512pixelsorto3811024pixelstoincreasetheacquisitionrateofthecamerafrom7Hzto10Hzandhencetomatchthelaserfrequency.Cameraspatialresolutionof44m/pixelverticallyhorizontallywasachieved.AbandpasslterofFWHMat420nmwasplacedinfrontofthecameratoeliminatethecollectionofanyelasticscattering.ThecameraandthelaserweresynchronizedusingaStanfordinstrumentsdelaygeneratorDG-535.Theexposuretimewaskeptto150nstoreduceanybackgroundlightandtocaptureonlytheuorescence. 32

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Theentiresetupismountedonanopticaltabletofacilitatetheopticalacquisitionsystemadjustment. Figure2-4. Aschematicoftheopticaldataacquisitionsystem. Figure2-5. Atypicallasersheetproleseenfromtoptobottom. 33

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2.4WorkingFluidTheworkinguidusedinalloftheexperimentsisaperuorinatedketoneandistechnicallyreferredtoas2-triuoromethyl-1,1,1,2,4,4,5,5,5-nonauoro-3-pentanone,alsoknownasFK-5-1-12[ 13 ].ThemolecularstructureisshowninFigure 2-6 .Thisuoroketonehasseveralinterestingfeaturesthatmakeitausefulcompoundforresearch[ 14 ].Ithasahighvaporpressureatambienttemperaturemakingitagoodmodelforstudiesofthebreak-upandmixingofvolatilefuelsandenablinghighseedingdensities.Ithasalowcriticalpressureof18.4atmandcriticaltemperatureof1680C(441K),facilitatingthestudyofnear-criticalandsupercriticalphenomenawithrelativeeaseascomparedtowaterforexample.Itsstronguorescencewithbroadbandexcitationmakesowtracingpossibleusingcommonhigh-powerlasers,suchasthethirdandfourthorderharmonicsofanNd:YAGlaser.It'sinertandhencecompatiblewithmostcommonconstructionmaterialsanddoesnotexhibitthermaldecompositionbelow5000Cinair[ 15 ].Moreover,itisnonammableandsafeforuseinlargequantities,haslowtoxicityandisenvironmentallyacceptable.Forexperimentsathightemperaturesandpressures,uoroketoneoffersasaferalternativetoacetone.FK-5-1-2exhibitsstrongabsorptioninthenearUV,withpeakabsorptionlocatedat307nm.At355nmexcitationwavelengththeabsorptioncross-sectionreducesquitesignicantlyandisshowninthenextchaptertobearound3.8110)]TJ /F5 7.97 Tf 6.59 0 Td[(19cm2/molecule.Thebeam Figure2-6. Themolecularstructureoftheuoroketone2triuoromethyl1,1,1,2,4,4,5,5,5nonauoro-3-pentanone. attenuationvariesbasedonwhetherasinglecomponentexperimentisperformedora 34

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dualcomponentone.Inthecaseofthedualcomponentsystem,asthebeamentersthechamberittravelsthroughinertnitrogenrstwhereabsorptionisnegligible,thenthroughthecircularjetwhereitisabsorbedtoproduceuorescence,andthenthroughnitrogenagainandexitsthechamber.Inthesinglespeciesexperiments,thebeamtravelsthroughgaseousuoroketonerstwhereitmaybeabsorbedsignicantlybasedonthedensityofthemedium,thenthroughthejetwhereitabsorbedagain,andagainthroughthegaseousuoroketoneenvironmentwhichabsorbssomemore.Thus,adetailedlasersheetcorrectionneedstobeperformedtocorrectlyanalyzethedensityanddensitygradientsofthejet.Moreover,sincethepowerofthelaserbeamisveryhigh,theuorescenceisnolongerinthelinearregime.Anon-linearuorescencetheoryhasbeendevelopedinthenextchapterandappliedtoallourexperimentstoobtaindependabledensityprolesofthejetatvariousconditionsoftemperatureandpressureforbothsingleanddualcomponentsystems.Somebeamattenuationcanbeattributedtothebeamsteeringeffectsratherthantotheabsorptionphenomenon,butthiseffectisconsiderednegligiblecomparedtotheabsorption.AnotherconcerninthePLIFapplicationiswhethertheemissiondependsonthepressureandtemperature.EmissionspectrumatSTPconditionsisshowninFigure 2-7 .Asitcanbeseenfromtheplot,therangeofwavelengthfrom400to500nmappearstobethemostattractiveintermsofuorescenceintensity.Thebehaviorofemissionspectrawithinthisrangeofwavelengthsdependingonpressureandtemperaturewasstudiedearlier[ 10 ]andindicatesthattherewasnosignicantdependenceoftheemissionspectraontheenvironmentconditionswithinarangeof400-500nm.Thus,basedontheobtainedemissionspectrathecenterwavelengthoftheopticallterforPLIFmeasurementshasbeenchosentobe420nmwith10nmFWHMwidth.Inadditiontogooduorescentpropertiestheuidhaswelldocumentedthermodynamicproperties[ 15 ].ThePeng-Robinson-Stryjek-Vera(PRSV)equationofstatecanbeusedtopredictthethermodynamicpropertiesoftheuoroketonewith2%uncertainty 35

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Figure2-7. EmissionspectrumoftheuoroketoneatSTPconditionswithanexcitationwavelengthof355nm. withinapressurerangeof0.01atmto100atmandtemperaturesofand150Kto600K.ThisdensitycalculationwasdoneinMATLAB.Inthenextchapter,adetailedaccountofthelasercorrectiontechniqueandtheimageprocessingmethodhasbeenprovided.Separatemethodswereadoptedforcoldjetandheatedjetinjections.Aftertheimageswereprocessed,aquantitativeestimateofthedensitiesanddensitygradientscouldbemade,alongwithotherestimatessuchasthecorelengthandspreadingangles. 36

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CHAPTER3LASERCORRECTIONANDIMAGEPROCESSING 3.1PhotophysicsofFluoroketoneandPLIFImplementationFluorescenceisaradiativedecayprocessofatomsormoleculesthathavebeenexcitedtoahigherenergystate,generallybyphotonsofashorterwavelength.Fluoroketone,atroomtemperatureandatmosphericpressure,hasabroadbandexcitationfrom260nmto355nm.Fluorescenceisemittedfrom350nmto550nm.AdifferentialvolumedVisconsidered,equaltothedifferentiallengthdltraversedbythelaser,timestheareaAperpendiculartothedirectionoflaserpropagation.ThenumberofmoleculesinthegroundstateisNgandexcitedstateisNe,withabsorptioncrosssectionsofganderespectively.IfthenumberofphotonsincidentononefaceofthisvolumebeNph,thenthenumberofmoleculesexcitedfromthegroundstatecanbecalculatedas:Ne=Nph ANgg (3)Similarly,thenumberofmoleculesremovedfromtheexcitedstateduetostimulatedemissionis:)]TJ /F8 11.955 Tf 9.29 0 Td[(Ne=Nph ANee (3)Laserindependentlossprocessesduringtheexcitationlikespontaneousemission,inter-systemcrossing,internalconversionandcollisionalquenchinghavenotbeentakenintoconsiderationsinceweassumethatthepulsedurationofthelaserisshortcomparedtotheseprocesses.Hence,laseruencythroughtheareaAcanbecalculatedas:dNe dt=dNph dt(Ngg)]TJ /F3 11.955 Tf 11.96 0 Td[(Nee)1 A=_Nph A(Ngg)]TJ /F3 11.955 Tf 11.96 0 Td[(Nee) (3) 37

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ThetotalnumberofmoleculesN=Ng+Neisassumedtoremainconstant,i.e.photodissociationeffectshavebeenneglected.Thus,rearrangingtheaboveequationyields:dNe dt=_Nph A(Ng)]TJ /F3 11.955 Tf 11.96 0 Td[(Ne(e+g)) (3)Duringsteadystate,i.e.,atsaturation,theaboveequationisequatedtozero,yielding:Ng=Ne,sat(e+g))Ne,sat=Ng g+e (3)WhenEquation( 3 )issolvedwiththeinitialconditionNe(0)=0,thesolutionis:Ne=Ng e+g1)]TJ /F3 11.955 Tf 11.96 0 Td[(e)]TJ /F12 5.978 Tf 10.68 1.33 Td[(_Nph(g+e)t A (3)Ifexpressedintermsoftotalnumberofphotonsdeliveredinonepulse,theaboveequationcanberepresentedas:Ne=Ng e+g1)]TJ /F3 11.955 Tf 11.95 0 Td[(e)]TJ /F13 5.978 Tf 5.76 0 Td[(Nph(g+e) A (3)ThefunctionobtainedinEquation( 3 )hasbeenplottedinFigure 3-1 .Toestablisharegionwherethecurvecanbeapproximatedasbeinglinear,astraightlineisdrawntangentiallytothecurvethroughtheoriginuntilitintersectsthesaturationline,andapointNphisfoundasshowninthegure.Hence,forthelinearregime,Nph<
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Figure3-1. Variationofthenumberofexcitedelectronswiththenumberofexcitingphotons. uorescencecanbewrittenas:N=Ng e+g1)]TJ /F3 11.955 Tf 11.95 0 Td[(e)]TJ /F13 5.978 Tf 5.76 0 Td[(Nph(g+e) A' (3)Here'istheuorescenceyield.Accordingtosomeworks[ 17 19 ],'istakentobeafunctionofthelaserwavelength,pressureandtemperatureofthesubstance.Otherworks[ 20 ]havestatedthat'isafunctionofthelaserintensityI.Inthiswork,'hasbeentakentobeafunctionofalltheabovementionedparameters,i.e.,'=f(P,T,I,).Thenumberofincidentphotons,Nph,canbewrittenasfollows:Nph=I hc=A (3)HereIisthelaserintensity,and(hc=)istheenergyofanincidentphotonatthelaserwavelength.Itshallalsobeassumedinthisworkthat(g+e)gorsimply.Thetransmissionefciencyofthecollectionopticsandthecollectionanglealsohavetobe 39

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takenintoaccount.Ifopticisthecollectionopticefciencyand(=4)isthefractionalsolidangleforcollection,thetotalnumberofphotonscollectedduetouorescencecanbewrittenas:N,coll=optic 4Nh1)]TJ /F3 11.955 Tf 11.95 0 Td[(e)]TJ /F4 7.97 Tf 6.58 0 Td[(I( hc)i' (3)Thecollectionopticsefciency,fractionalsolidangle,photontosignalcountconversionfactorandotherconstantsaregroupedintoafactorF.Ifthex-directionistakenasthedirectionofpropagationofthelaser,andthey-directionisthedirectionperpendiculartothex-axisandintheplaneofthelasersheet,thenI=f(x,y).ThetotalnumberoftheabsorbingmoleculesNisproportionaltothedensityofthevaporuoroketone(x,y).Thentheequationforuorescencesignalrecordedonapixelforaspeciclaserexcitationwavelengthcanbewrittenas:S(px,py)=F(x,y)'h1)]TJ /F3 11.955 Tf 11.95 0 Td[(e)]TJ /F4 7.97 Tf 6.59 0 Td[(I( hc)i (3)Equation( 3 )hasadifferentformthanthatadoptedbyothers[ 21 22 ]duetoitsnon-linearity.Inthecurrentwork,thedensityoftheuoroketonevaporischangedbychangingthetemperatureandpressureofthechamber.Moreover,iftheabsorbingspeciesisuniformlydistributedthroughoutthechamber,thenisnotafunctionoftheposition(x,y).Thedecreaseoftheintensityofthelasersheetalongitslineofpropagationalsoneedstobeconsidered[ 23 ].Forconditionswherescatteringcanbeneglected,thedropinlaserintensityduetoabsorptionshouldfollowtheBeer-Lambert'slaw,whichcanbeexpressedas:I(x,y)=I(0,y)e)]TJ /F16 7.97 Tf 7.99 6.42 Td[(Rx0ndx (3)Thelimitsoftheintegralforourexperimenthavebeentakentobefromthewindow(x=0)toanypositionxalongthelineofpropagationofthelaser.Fortheexperimentsdescribedbelow,sincetheconcentrationofuoroketonevaporisuniforminsidethe 40

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chamber,nisnotafunctionofthepositionx.Hence,Equation( 3 )canbesimpliedas:I(x,y)=I(0,y)e)]TJ /F15 7.97 Tf 6.59 0 Td[(nx (3)PluggingthisexpressionofI(x,y)intoEquation( 3 ),thefollowingrelationisobtained:S(px,py)=F(x,y)'h1)]TJ /F3 11.955 Tf 11.96 0 Td[(e)]TJ /F4 7.97 Tf 6.59 0 Td[(I(0,y)( hc)e)]TJ /F14 5.978 Tf 5.76 0 Td[(nxi (3)Inthiscase,forasinglephase,theabsorptioncrosssectionhasbeenassumedtobeaconstant.Thishasalsobeenveriedthroughourtests.Thus,Equation( 3 )canbesimpliedas:S(px,py)=F(x,y)'h1)]TJ /F3 11.955 Tf 11.96 0 Td[(e)]TJ /F4 7.97 Tf 6.59 0 Td[(ke)]TJ /F14 5.978 Tf 5.76 0 Td[(nxi (3)Herealltheconstantsintheexponenttermhavebeengroupedunderasingleconstantk.ObtainingconcentrationvaluesfromtheuorescencesignalbyPLIFmeasurementsrequiresanaccuratedeterminationof'.Inthecurrentwork,focushasbeengiventothestudyof'undervaryinguoroketonevaporconcentrations.Thevalueof'canbeaffectedbyprocessessuchasquenching,whichisanon-radiativerelaxationprocessresultingfromthecollisionbetweentheuoroketoneandasecondspeciessuchasoxygen.Thus,anyairpresentinsidethechambermayleadtoquenchingeffects.Phosphorescenceisanotherradiativerelaxationprocesswithcharacteristictimesmuchlongerthanuorescence.Ithasbeenreportedthattheinuenceofquenchingonphosphorescenceismoresignicantthanonuorescenceinacetone[ 24 ].Asimilarphenomenonisassumedforuoroketone.Photolysishasalsobeenneglectedinthisanalysis.Inmostnon-reactingenvironments,wheretheconcentrationofvaporisessentiallyuniforminsidethechamberandlaserexcitationiswithincertainlimits,itmaybeexpectedthat'isaconstant.Thishasbeenvalidatedinthecurrentworkthrough 41

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variouscalibrationtests.Thecalibrationprocedureinvolvesobtainingtheuorescencesignalforvariousuoroketonevapordensitiesandlaserintensities.Intheabsenceofsaturation,ifboth'andareconstants,theuorescencesignalshouldbelinearwiththevapordensity(forxedlaserintensity).Itisonlythenthattheimageprocessingfordensitycalculationsisreliable. 3.2CalibrationthroughtheGasPhaseTostudythelaserabsorptionthroughtheuoroketonegasphase,thechamberwaspartlylledwithuoroketoneandthevaporandliquidphasesareallowedtoreachequilibrium.Thevaporconcentrationinsidethechamberwascontrolledbyadjustingthechamberwalltemperature.Toobtainhighervaluesofvaporconcentration,thechamberwallswereheatedtothesaturatedvaportemperature,whichinturnheatedtheliquidphase,producingmorevapor.Thisalsoincreasedthepressureinsidethechambersincethevolumeisconstant.Thelasersheetwasthenpassedthroughthenearlyuniformvaporphasetoobtaintheintensityproleofthesheetandalsotoobservehowtheintensityoftheuorescencechangesasthelaserpassesthroughthechamber.Figure 3-2 showsthelasersheetprolestakenatfourdifferenttemperaturesandpressures,averagedforatotalof50images.Thelaserentersthechamberatcolumn1andleavesatcolumn512.Figure 3-2 Ashowstheproleat2.7atmchamberpressureand850Cchambertemperature.Thevapordensityinthiscaseis0.032g/cm3.Thegureshowsthatthatthelaserprolesatthefourdifferentcolumnpositionsareverysimilartoeachother.Therearesomevariationsinintensitybuttheoveralleffectisnotassignicantastheothercasestofollow.Figure 3-2 Bshowstheproleat5.9atmchamberpressureand1100Cchambertemperature,atavapordensityof0.074g/cm3.Thisplotshowsagreatervariationofthelaserproleshapeandintensity,implyingthattheabsorptionhasincreased.Figure 3-2 Cshowstheproleat10.4atmchamberpressureand1500Cchamberpressure,whenthevapordensityis0.13g/cm3.Thisplotissignicantly 42

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differentfromtheprevioustwo,andshowsclearsignsoflaserintensitydropandproleshapechange.Alargedecreaseinintensityandamajorchangeinproleshapeareobserved.Theprolevariationsreduceconsiderably,anditbecomesmoreuniform.Figure 3-2 Dshowstheproleat14.7atmchamberpressureand1650C.Thevapordensityisthehighestinthiscaseandisequalto0.207g/cm3.Thetemperatureisnearlycriticalwithrespecttothecriticaltemperatureof1680C,butthepressureisstillsubcriticalcomparedtothecriticalpressureof18.4atm.Thelaserintensitydropsto30%ofthe100thcolumnatcolumn200andisreducedtoapproximately10%atthe300thcolumn.Inthefollowingsections,thedependenceofuorescenceonvapordensityandlaserintensityhasbeeninvestigatedandarelationbetweenabsorptioncoefcientandvapordensityhasbeenobtained. 3.2.1FluorescenceIntensityDependenceonVaporDensityTounderstandhowtheuorescencesignaldependsonthevapordensity,thecamerawaszoomedtoaregionveryclosetothewindowwherethelasersheetenteredthechamber.Thisregionwaschosensothatthelasersheetwouldnotbeattenuatedbyabsorption.TheresultsareshowninFigure 3-3 .Theplotshowsaweaksecond-orderdependenceoftheuorescencesignalwiththevapordensity.Forlowvaluesofvapordensity,thecurvecloselyapproximatesastraightline,whileforhighervalues,approachingthecriticalpoint,non-linearitiesstarttobecomeimportant[ 25 ].FromEquation( 3 )itcanbeseenthatforxedvaluesofincidentlaserintensityI(0,y),opticsefciencyFandabsorptioncross-section,theuorescencesignalSisproportionaltothedensityifthequantumyield'isaconstant.Thusatx=0,i.e.atthewindowthroughwhichthelasersheetenters,Equation( 3 )reducesto:S(px,py)=F(x,y)'1)]TJ /F3 11.955 Tf 11.95 0 Td[(e)]TJ /F4 7.97 Tf 6.58 0 Td[(k)S(px,py)=K (3)HerealltheconstantshavebeengroupedunderK.Fromtheplot,itisseenthat'isaconstantforvapordensityvaluestoabout0.15g/cm3,butstartstovarywhen 43

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A B C DFigure3-2. Intensityvariationsofthelasersheetproleasitpassesthroughthechamber.Thelaserentersthechamberatcolumn1,andexitsthechamberatcolumn500.Itcanbeobservedthatthevariationsaresignicantastheconcentrationofvaporincreases.ThepressureandtemperatureconditionsforthecasesareA)2.7atm,850C.B)5.9atm,1100C.C)10.4atm,1500C.D)14.7atm,1650C. 44

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Figure3-3. Fluorescencesignalvs.uoroketonevapordensity.Forlowvaluesofvapordensity,thecurvecloselyapproximatesastraightline,whileforhighervalues,especiallynearthecriticalpoint,non-linearitiesstarttobecomeimportant. thedensitiesarehigher.Sincethevapordensityinthecurrentexperimentswaschangedbyheatingthechamberwalls,itcanbestatedthatclosertothecriticalpointofuoroketone,'deviatesonlyslightlyfromaconstant. 3.2.2FluorescenceIntensityDependencewithLaserPowerToobtaintheuorescenceintensitydependenceonlaserpower,thedensityoftheuoroketonevaporinsidethechamberwaskeptxedandtheincidentlaserintensityI(0,y)wasvaried.AnexponentialdependenceofthesignalwithlaserpowerisobservedasshowninFigure 3-4 .Asmentionedearlier,theuorescenceisclearlynotinthelinearregime.Forxedvaluesofdensity,constantopticsefciencyFandabsorptioncross-section,theuorescencesignalSisdependentontheincidentlaserintensityI(0,y)asshowninEquation( 3 )ifthequantumyield'isaconstant.S(px,py)=a1)]TJ /F3 11.955 Tf 11.95 0 Td[(e)]TJ /F4 7.97 Tf 6.59 0 Td[(bI(0,y) (3) 45

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Figure3-4. Fluorescencesignalvs.laserpower.Anon-lineardependenceofthesignalwithlaserpowerisobservedintheoperatingrangeusedforthecurrentexperiments. Allconstantshavebeengroupedunderaandb.ReferringbacktotheplotinFigure 3-4 ,thedatapointsandthecurvettedtothesepointsaccordingtoEquation( 3 )showcloseagreement.Itcanhencebeconcludedthatthevalueof'isconstantovertherangeoflaserpowerusedforthecurrentexperiments. 3.2.3CalibrationofAbsorptionCoefcientTocloselyexaminehowthevariationoflaserintensityoccursacrossthelengthandwidthofthechamber,asampleimageischosenandanalyzed.Figure 3-5 showsplotsofthelasersheetuorescenceintensityatachamberpressureof14.7atmandachambertemperatureof1650C.Theactualintensityplotshavebeenshownontheleft,andthenormalizedintensityplotshavebeenshownontheright.Allimageshavearesolutionof512512pixels.Theplotonthetopleftcornershowsthevariationofuorescenceintensityfromtoptobottomforallthecolumnsoftheimage,i.e.,512.Similarly,theplotonthebottomleftcornershowsthevariationofuorescenceintensity 46

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fromlefttorightforalltherowsoftheimage,i.e.,512.Thenormalizedimageswereobtainedbydividingthepixelintensityofaspeciccolumnorrowbythemaximumintensityforthatcolumnorrowrespectively,andthentakingtheirmean.Fromthenormalizedlaseruorescenceintensityvariationfromlefttoright,itcanbeseenthatthereisadecreasefrom1toabout0.05within300pixelsoflaserpropagationdistance.Sincethechamberislledwithuniformdensityvapor,thisvariationcanbesolelyattributedtotheactuallaserintensitydrop.Hence,itcanbeinferredthatthelaserintensityvariationacrossthechambercannotbeneglectedasitwasfortheexperimentswithbinaryspecies,e.g.auoroketonejetinjectedintoinertnitrogengas.Thiscallsforarigoroustreatmenttodealwithsuchvariationsinuorescenceintensityforaspeciedchambertemperatureandpressure,asdescribedinthefollowingsections.Ithasbeen Figure3-5. Detailedanalysisoflaseruorescenceintensityat14.7atm,1650C.Actualintensitieshavebeenplottedontheleftandthenormalizedintensitieshavebeenplottedontheright.Allplotsshowsignicantvariationoflaseruorescenceintensityacrossthechamber. 47

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showninprevioustwosectionsthatthevalueof'isessentiallyaconstantandthusEquation( 3 )isvalid.Itcanthenbestatedthat:S(px,py)=A(x,y)'h1)]TJ /F3 11.955 Tf 11.96 0 Td[(e)]TJ /F4 7.97 Tf 6.59 0 Td[(ke)]TJ /F14 5.978 Tf 5.76 0 Td[(nxi (3)WherethenewconstantA=F'.Hence,itisseenthatforaspecicrowoftheimage,andhenceforaspecicvalueofI(0,y),theuorescencesignalalsoundergoesanexponentialdropinintensityalongthelineofpropagationofthelasersheet.Thishasbeenveriedthroughtheobtainedexperimentaldata.Fromthenormalizedlaserintensitydiagram(fromlefttoright),weselectaportionoftheplotwhereauniformdecreaseofuorescenceintensityisnoted.AcurveisthenttedtothedatapointsaccordingtoEquation( 3 )asshowninFigure 3-6 .The Figure3-6. Normalizedintensitypointsvs.thelengthtraversedbythelasersheetinpixels.Whenanexponentialtrendisttedtotheplot,theabsorptioncoefcientisobtainedasgivenbytheBeer-Lambert'slaw. exponentialcoefcientintheequationofthettedcurveisessentiallytheabsorptioncoefcient.Thisvalueoftheabsorptioncoefcientisvalidforthespeciedconcentration 48

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ofvaporataparticularchamberpressureandtemperature,i.e.,14.7atmand1650C.Thehigherthepressuresandtemperaturesare,thegreateristheconcentrationofvapor,andthusthevalueoftheabsorptioncoefcient.AbsorptioncoefcientsforvariousvaporconcentrationswereobtainedbytheabovementionedprocessandacalibrationcurvewasobtainedasshowninFigure 3-7 .Itcanbeseenthatthecalibrationcurveisastraightline,indicatingthattheslopeisaconstantthroughoutthevaporphase.Now,theabsorptioncoefcientandcrosssectionarerelatedas:=n=NA M (3)Itisseenthattheslopeofthecalibrationcurveisproportionaltotheabsorptioncrosssection,andhenceiscanbeapproximatedtobeaconstantfortherangeofdensitiesplotted.Thisvalidatestheassumptionthatwasmadeearlierintheanalysis,thattheabsorptioncrosssectionisalsoconstantthroughoutthevaporphase.Usingthisdata Figure3-7. Calibrationlinefortheabsorptioncoefcientplottedagainstdensity. andthemolecularweightofuoroketone(316g/mol),theabsorptioncrosssectionin 49

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thevaporphasewascalculatedtobe3.8110)]TJ /F5 7.97 Tf 6.58 0 Td[(19cm2/molecule.Theuorescenceyieldwasthusfoundtobeconstantuptovapordensitiesof0.25g/cm3. 3.3CalibrationthroughtheLiquidPhaseCalibrationofthelasersheetabsorptionthroughtheliquidphaseyieldedinterestingresults.Theprocedurewassimilartocalibrationthroughthegasphase.Thechamberwasinitiallylledwithliquiduoroketoneatroomtemperatureandpressureandthenheatedtothedesiredtemperature.Thepressureinsidethechambergraduallyreachedthevaporpressureoftheliquidatthattemperature.Afterasteadystatetemperaturewasreached,thelasersheetwaspassedthroughtheliquidandtheuorescencewascapturedusingthecameraplacedat90degreestothelaserpath.AnexampleoftheuorescencemeasurementhasbeenshowninFigure 3-8 belowforchamberpressure1.25atmandtemperature170C. Figure3-8. Normalizeduorescenceintensitiesat1.25atm.and170C. Twoseparatetshavebeenusedforthedataset.Therstoneisthesameasusedduringthecalibrationofthegas,andthesecondoneusesasumofexponents.Itisobservedthatthegasphasecalibrationtdoesnotfollowthedatapointsaswellasthesumofexponentialtsdoes.Thiscouldbeduetoseveralreasons.Thereis 50

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agreaterchanceofuorescencetrappingathigherdensitiessincetheabsorptionishigherforliquidphasethanthegas.Theabsorptioncrosssectionvaluesmaydifferandquenchingmightalsobeapossibility.Asseenintheliteratureforketoneuorescence,quenchingoccursprimarilyinthepresenceofoxygen,anditaffectsthephosphorescencesignicantlymorethantheuorescence.Henceweassumethatasimilarphenomenonoccursforuoroketonetoo.Tounderstandhowdifferentlytheuorescenceintheliquidphasebehavescomparedtothegas,uorescencedatawascollectedforlowerdensitiesofliquidapproachingthecriticalpoint.Figure 3-9 showsonesuchcaseatachamberpressureof12.7atmandchambertemperatureof1450C. Figure3-9. Normalizeduorescenceintensitiesat12.7atm.and1450C. Itcanbeobservedfromtheplotthatboththecurvetsarealmostidentical,andtheyfollowtheexperimentaldataclosely.Torevealthereasonforsuchanobservation,thecoefcientsofthettedcurveswereanalyzed.Incaseofthetcomprisingthesumofexponents,coefcientcwastwoordersofmagnitudelessthana,therebyprovingthatthesecondexponenttermisoflittleimportanceatlowerdensitiesoftheliquid.Whenthesametwasanalyzedforthecasewhentheliquiddensitywashigher,thecoefcientsaandcwereofthesameorderofmagnitudessignifyingboththeterms 51

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wereequallyimportant.ThiscanbeunderstoodfromFigure 3-10 whichshowstheuorescencedataatvaryingliquiddensitiesandtheircorrespondingts.Table 3-1 showsasetoftestconditions.Thechambertemperaturesandpressureshavebeenlisted,alongwiththecorrespondingliquiddensities. Figure3-10. Fluorescenceintensitiesatvaryingliquiddensities.Thepressuresandtemperaturesforeachdatasethavebeenindicatedinthelegend. Table3-1. Listoftestconditionsusedforthecalibrationoftheliquidphase. Pressure(atm)Temperature(0C)Density(kg/m3) 1.25171623.92.40701444.43.00801401.73.91901354.24.931001302.86.221101245.67.721201182.58.401251146.69.401301109.810.301351069.011.401401025.412.70145980.8 Thus,whentheplotinFigure 3-10 isanalyzedweseethatthecalibrationcurveobtainedforthegasphaseworkswellforliquiddensitieslowerthan1401.7kg/m3,i.e., 52

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at3atmand800C.Thusthenon-lineareffectsthatcreatethedifferencesbetweentheliquidandgasuorescencebecomelessimportantatlowerliquiddensities.Sincetheonlyuniversaltthatrepresentstheliquiduorescencecloselyisthesumofexponents,thecoefcientbwassoughtastheprimarycalibrationvariable,andwasplottedfortherangeofliquiddensitiestestedtoseeifanytrendcanbenoted.Toseehowwellthegascalibrationtdoesincomparison,itscoefcientcisalsoplottedonthesamegraphalongwithbinFigure 3-11 .Itcanbeobservedfromtheplotsthatthedifferenceinthevalueslieprimarilyathigherdensitiesoftheliquidphase.Below1350kg/m3,theyconvergetonearlyidenticalvaluesandoscillateabout0.0045.Henceitcanbeinferredfromtheplotthatinbothcases,thecoefcientvaluesdropverysteeplyfromdensitiesaround1600kg/m3to1350kg/m3,andthenbecomesrelativelyindependentofthedensity.Thisisnotrepresentativeoftheabsorptioncoefcient,sinceitsvalueshoulddecreasewithdecreasingdensity.Henceitcanbeconcludedthattherearecertainothercompetingphenomenawhichcannotbeestimatedwiththeexistingdata.Thetscanbeusedwhentheliquidexistsatsimilarconditionsasthetestconditions.Hence,thestudyoftheopticalpropertiesofaperuorinatedketoneundertakenatsubcriticalconditionsandnearcriticalconditionsrevealedinterestingresults.Atheoreticalanalysisofuorescenceinthenon-linearregimeofexcitationenergywasdeveloped.ThecriteriathatneedtobesatisedtousethisketoneasameansforstudyingquantitativePLIFapplicationswereveried.Theseincludethelinearvariationofuorescenceintensitywithconcentrationforxedlaserintensity,andtheexponentialvariationofuorescenceintensitywithlaserintensityforaxedconcentration.Boththesecriteriawerefoundtobetrueforthevaporphaseofuoroketonefromdensitiesrangingfrom20kg/m3to200kg/m3andlaserintensitiesvaryingfrom20mJ/pulseto140mJ/pulse.Thiswasdonetojustifythatthequantumuorescenceyieldisaconstantwithintherangeoflaserintensityandconcentrationsthatwereusedforourexperiments.Acalibrationcurvewasobtainedforthevaporphaseofuoroketonefrom 53

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A BFigure3-11. Comparisonofthecoefcientvaluesobtainedthroughthegascalibrationtandthesumofexponentt.Thedifferenceprimarilyliesathigherdensities,whileatlowerdensitiestheyconvergetonearlyidenticalvalues. 54

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densitiesrangingfrom0.03to0.24g/cm3.Thiscurvewasastraightline,verifyingthattheslopeoftheline,whichisessentiallytheabsorptioncrosssection,isaconstantasassumedinthebeginning.Asimilartechniquewasalsoappliedtotheliquidphaseofuoroketone,butacalibrationlinecouldnotbedevelopedasinthevaporphase.Theabsorptioncrosssectionofthevaporwasfoundtobe3.8110)]TJ /F5 7.97 Tf 6.58 0 Td[(19cm2/molecule.Thesevaluesofabsorptioncoefcientsandcrosssectionscanthusbeusedforanyexperimentsinvolvingthisuidundersimilarexperimentalconditions. 3.4ImageProcessingThreesetsofinformationarerequiredtoobtainaquantitativedensitydistributioninsidethejet:abackgroundimage,lasersheetintensitydropthroughthechamberandtheexperimentalimageofthejet.Thelasersheetisrstpassedthroughauniformvaporphasetoestimatethelaserprolevariationfromtoptobottom.AtypicalprolehasbeenshowninFigure 3-12 ,thoughitvariesforeachsetofexperiments.Itisusuallyadvisabletousethemoreuniformpartofthelaserproleasmuchaspossible.The Figure3-12. Laserintensityvariationfromtoptobottomasitentersthechamber. nextstepistoestimatethelaserintensityvariationasittravelsthroughthechamber.Thelasersheetrstpassesthroughavaporphase,thenthehigherdensityjet,andthen 55

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nallythroughanothersectionofvaporphasebeforeexitingthechamber.Eachtimethesheetencountersanabsorbingmedium,itlosesitsintensityasittravelsthroughit.Thelossismoreinadensermedium,whichisthejetinthiscase,andhencethejetboundariesneedtobecalculatedfromtheexperimentalimages.Around50imagesareaveraged,andtheboundaryiscalculatedfromthepixelintensitygradientsasshowninFigure 3-13 .Onlythelaserintensityvariationsfromtoptobottomaretakenintoaccountwhilecalculatingthejetboundary.Incasesofhigherabsorption,manualthresholdvaluescanalsobeprovidedasanoptioniftheboundaryisnotproperlyidentied. Figure3-13. Jetboundarycalculatedfrompixelintensitygradients. Oncethejetboundarieshavebeenidentied,andtheabsorptioncrosssectionsforthesurroundingvaporandthejethavebeenfoundfromthecalibrationlinesdescribedinthesectionsabove,alasersheetintensityproleiscalculated.AtypicallasersheetprolehasbeenshowninFigure 3-14 .Herethenormalizedlaserintensityhasbeenplottedagainstthelengthtraversedbythelasersheet.Thedropinintensityishigherinsidethejetthanoutsideofitduetoitshigherdensity.Oncethelaserintensityhasbeendenedacrosstheeldofview,theexperimentalimageisdividedpoint-by-pointby 56

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thelaserprolematrixtogetacorrectedimage,i.e.amatrixofpixelintensitieswherethelaserabsorptionhasbeentakenintoaccount. Figure3-14. Atypicallasersheetprole.Normalizedintensityhasbeenplottedagainstthelengthtraversedbythesheet.Thedropinintensityishigherinsidethejetthanoutsideofitduetoitshigherdensity. Toconvertthepixelintensitiestodensityvalues,areferencedensityatanareaclosetotheinjectorischosen.ThisdensityiscalculatedusingthePRSVequationofstatebasedontheknownconditionsofinjection,andthenthepixelintensitiesthroughouttheimageareconvertedtoquantitativedensityvalues.Thedifferencesbetweenanimageuncorrectedforlaserabsorptionandonethat'scorrectedhasbeenshowninFigure 3-15 ,justifyingtheimportanceoftheprocessoflasersheetcorrectionbeforeanyfurtheranalysis.Hence,itisseenfromthegurethatanuncorrectedimagecanleadtoincorrectdensityanddensitygradients.Oncethelasersheetabsorptionhasbeentakenintoaccount,theimagescanbeusedforfurtheranalysis. 57

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Figure3-15. Differencesindensitycausedduetoanimageuncorrectedforlaserabsorption(top)andthatwhichiscorrectedforabsorption(bottom). 58

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CHAPTER4BINARYSPECIESMIXINGTounderstandthebreakupmechanismsforinjectionundersubcriticalandsupercriticalconditions,asimpleandfundamentalcasewasconsidered.Thisincludedtheinjectionofasingleroundjetofuoroketoneintoanenvironmentofnitrogen,thusconstitutingabinaryspeciessystem.Inthecurrentstudy,planarlaserinduceduorescence(PLIF)wasusedtogenerateasectionthroughthejet,thusaccuratelyidentifyingboththeboundaryandthejetcorestructures.Inthepreviousstudiesusingthesamefacility[ 26 27 ]ajetatambienttemperaturewasinjectedintoasubcriticalandsupercriticalenvironment.Inthepresentstudy,thejetwasheatedtosubcriticalandsupercriticaltemperaturesbeforeinjectionintothechamberwhichwasmaintainedessentiallyatsupercriticalpressures.Fourdifferentmixingregimeshavebeenconsidered: (i) Subcriticalinjectionintoasubcriticalenvironment; (ii) Subcriticalinjectionintoasupercriticalenvironment; (iii) Supercriticalinjectionintoasubcriticalenvironment; (iv) Supercriticalinjectionintoasupercriticalenvironment;Theobjectiveofthisworkwastoanalyzehowthemixingandjetdisintegrationprocesseswouldbeaffectediftheinjectant(initiallyatsupercriticalpressures)waspreheatedtoeitheraboveorbelowthecriticaltemperatureandinjectedintosubcriticalandsupercriticalchamberconditions.Corelengthsandspreadingangleswerecalculatedandtheirvariationwithrespecttoarangeofchamber-to-injectantdensityratioswasinferred.Planarlaserinduceduorescence(PLIF)wasusedastheopticaldiagnostictechniqueinallcasestoidentifythedetailedstructuresthroughthejetcenterplane.TheexperimentswereperformedusingtwoseparateICCDcamerastocapturetwodifferentaxiallength-to-jetdiameterratios(x=D).Therstsetofexperiments,whichprimarilyfocusedonthersttwomixingregimes,consistedofimageswithx=D=8.The 59

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secondsetfocusedonthelasttwomixingregimesandcapturedaratioofx=D=20.Thiswasdonetoidentifythebreakupandmixingprocessesfurtherdownstreamofinjector,andledtothediscoveryofseveralinterestingdisintegrationandnucleationfeaturesthatwerenotcapturedusingthesmallereldofview.Thus,thedatabaseofreliableexperimentalmeasurementsofdensityanddensitygradientdistributionsinthesupercriticalregimedoneinthesamefacilitybyPolikhov[ 10 ]wasexpandedthroughthisstudy. 4.1ExperimentalConditionsTheexperimentalconditionsareshowninFigure 4-1 onareducedpressure(Pr=P=Pcr)andreducedtemperature(Tr=T=Tcr)diagram.Thegoalwastospanarangeofpressuresandtemperatureswithparticularfocusaroundthecriticalpoint.Chamberandinjectantconditionshavebeenmarkedseparately.Thesetofexperimentswheretheuidwasinjectedatroomtemperature(Tr=0.66)hasbeenindicatedontheplotas`coldinjection',whilethesetwheretheuidwaspreheatedbeforeinjectionhavebeenmarkedas`heatedinjection'.Inthisstudy,focushasbeengiventotheheatedinjectiontests,primarilywhentheinjectantandchamberareatsupercriticalpressures.Previousstudies[ 28 29 ]haveshownthatsupercriticalbehaviormaybeencounteredevenwhenonlyoneoftheparameters,ProrTr,iscritical.Inthisstudy,itwasfoundthattemperatureplaysagreaterrolethanpressureindeningthesupercriticalstateoftheuid.Hence,fromthispointonwards,theterm`supercritical'shallbereferredtocaseswherebothtemperatureandpressurearesupercritical,while`subcritical'shallbereferredtocaseswhereonlythetemperatureissubcritical(whilepressurescanbesubcriticalorsupercritical).Asweepofpressuresforgiventemperatureswereselectedalongwithconditionsthatkeptthepressureessentiallyconstantandincreasedthetemperature.Thehighestpressurestestedwerenearly2Pr(37atm),whilethehighesttemperaturestestedwerearound1.32Tr(583K).Thiswasdonetoensurethat 60

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supercriticalconditionswereachievedevenifthemixtureeffectsshiftedthecriticalpoint[ 30 ]. Figure4-1. Selectionoftheexperimentalconditions.Reducedtemperaturesandpressureshavebeenselectedtocoverthesubcriticaltosupercriticalregime.Theplotreferstoboththechamberandtheinjectantconditionsindependently.Theselectedcombinationswillbeemphasizedinthefollowingsectionsdiscussingtheresults. AfewselectedtestconditionshavebeenlistedinTable 4-1 .Forallthetests,themassowratewaskeptrelativelyconstant.Velocitydifferencesexistedduetothelargechangesindensitynearthecriticalpoint,anditrangedbetween3to30m/sec.Pressuresweremaintainedsupercriticalforalltestconditions(exceptforcase1)toisolatetheeffectsoftemperatureinthedisintegrationandmixingprocesses.Itshallbepertinentinthesectionstofollowthatthetemperatureeffectwasfoundtobethedeterminingfactorinidentifyingwhetherthestateoftheinjecteduidwassupercriticalornot.Cases1-4representsubcritical-into-subcriticalinjections,5-8representsubcritical-into-supercriticalinjections,9-12representsupercritical-into-subcritical 61

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injectionswhilethe13-16representsupercritical-into-supercriticalinjections.BuoyancyeffectscanbeignoredinfavoroftheinertialforcesforallthetestcasessincetheowismomentumdominatedaccordingtothecriterionbyChenandRodi[ 31 ]. Table4-1. Selectedtestconditionsforthebinaryspeciesexperiments CaseTr,gTr,lPr,gPr,lUl(m/sec)_m(g/sec) 10.660.770.790.883.5616.4720.690.931.401.483.9815.2830.690.971.261.334.3515.4540.690.991.001.065.9715.7851.220.661.611.823.7919.3161.100.881.181.403.6414.8371.070.931.531.734.1119.3181.150.971.901.953.0919.3190.691.131.381.5120.9819.31100.721.211.861.9717.9518.33110.761.291.881.9820.3117.24120.801.311.381.5130.0016.99131.041.001.261.347.0717.82141.061.081.371.4714.5616.78151.081.081.411.5014.4717.35161.091.181.471.6720.5718.64 4.2SubcriticalFluidintoSubcriticalAtmosphereTheexperimentsdoneundertheseconditionsinvolverelativelylowertemperaturesfortheinjectantandthechamber,whilethepressuresarekeptsupercritical(exceptforcase1).Somerepresentativetestcases1through4havebeenlistedinTable 4-1 .Thecaseshavebeenchosensuchthatchamberandinjectanttemperaturesareinincreasingorderofmagnitude.Figure 4-2 showstherespectiveimagesofthelistedtestcases.Densityanddensitygradientimageshavebeenshownontherstandsecondrowsrespectively.Theimagesareshownfor20jetdiametersfromtheinjector.Itcanbeobservedthatsurfacetensionandinertiaforcesdominateundertheseconditionswithdropletformationobservedoncetheuiddetachesfromthejet.Theshortereldofviewtestscouldnotcapturethedropletformation,buttheimagesthatcapturedlonger 62

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axialdistanceindicateddropletformationbeyond10jetdiameters.Thedropletshadanellipsoidorroundshape,i.e.,thesurfacetensionforceswererelativelystrong.Pronounced`ligament'formationisobservedundertheseconditions.Asusedhere,aligamentisadistinctprotrusionfromthesurfaceoftheliquidjetcausedbytheinterfaceshear.Theyappearwithcertainperiodicityandcorrespondtothesurfacewavinesscausedbyinstabilities.Thechamberandinjectanttemperaturesincreasefromlefttorightinthegure.Theincreaseintheinjectanttemperaturesismuchmoresignicantthanthechambertemperaturessinceitreachesanearcriticalvalueincase4.Itcanbeobservedthatthedropletsizedecreasesfromlefttoright,whilethejetspreadingangleincreases.Thisobservationcanbeexplainedbythedecreaseinsurfacetensionandhenceitiseasierforportionsbreakofffromthemainbodyofthejet.Thishappensusuallybeyond10jetdiametersfromtheinjectorwherethesurfaceinstabilitieshavegrownconsiderablyandhaveenoughenergyforthebreakupprocess. 4.3SubcriticalFluidintoSupercriticalAtmosphereTheexperimentsdoneundertheseconditionsinvolverelativelyhighertemperaturesforthechamberthaninthepreviousregime.Somerepresentativetestcases5through8havebeenlistedinTable 4-1 .Thecaseshavebeenchosensuchthatinjectanttemperaturesareinincreasingorderofmagnitude,whileallotherparametershavebeenkeptsupercritical.Figure 4-3 showstherespectiveimagesofthelistedtestcases.Densityanddensitygradientimageshavebeenshownontherstandsecondrowsrespectively.Thecharacteristicfeatureofthisregionistheapparentdecreasedimportanceofsurfacetensionthanthepreviousregime,thatmanifeststhroughthesmootheningoftheliquid-gasinterface.Ligamentformationtendstosignicantlydecrease.Duetothedecreasedsurfacetensionforces,theligamentshavea`cluster'or`nger-like'appearance.Atlowerinjectanttemperaturesasseenincases5and6,thesurface 63

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A B C D E F G HFigure4-2. Scaledimagesofasubcriticaljetinjectedintosubcriticalchamberconditions.Testconditionscorrespondtocases1-4inTable 4-1 .Figures(a)-(d)representdensityimageswhile(e)-(h)representdensitygradientimages. ofthejetiscorrugatedandwavyduetosurfaceinstabilitiesandtherelativelygreaterimportanceofsurfacetension.Someoftheclustersgetdetachedfromthemainbodyofthejetandformdrops.Athigherinjectanttemperatures,thesurfacebecomessmootheranddropsarenolongerobserved.Sincedropsareobservedforthisandthepreviousregimeevenatsupercriticalpressures,itcanbeinferredthattemperatureisthemoredominantparameterindeterminingthesupercriticalstateoftheuid,sinceitwastheonlyparameterthatwaskeptsubcritical. 64

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Theimagescapturedinthisregimehadshortereldofview,andhencethedownstreamdisintegrationcouldnotbevisualized.ThevalueofthemaximumdensityanddensitygradientsdecreaseaswegofromlefttorightinFigure 4-3 ,whilethespreadingangleincreases. A B C D E F G HFigure4-3. Scaledimagesofasubcriticaljetinjectedintosupercriticalchamberconditions.Testconditionscorrespondtocases5-8inTable 4-1 .Figures(a)-(d)representdensityimageswhile(e)-(h)representdensitygradientimages. 4.4SupercriticalFluidintoSubcriticalAtmosphereInthesetestcases,theuidwaspreheatedtosupercriticaltemperaturesbeforeinjectionintothechamberwhichwasmaintainedatsubcriticalconditions.Bothwereatsupercriticalpressures.Somerepresentativetestcases9through12havebeenlistedinTable 4-1 .Thecaseshavebeenchosensuchthatchamberandinjectanttemperaturesareinincreasingorderofmagnitude.Figure 4-4 showstherespectiveimagesofthelistedtestcases.Densityanddensitygradientimageshavebeenshownontherstandsecondrowsrespectively. 65

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Sincetheuidisinasupercriticalstatewhenitisbeinginjected,thesurfacetensioneffectsarenegligibleintheinitialmixingregion,whichisveryclosetotheinjectorataround5-10injectordiameters.Typicalcharacteristicsofsupercriticalinjectionarenotedinthisregion,includingasmoothjet-gasinterfaceandoccasionalformationof`ligaments'andclusters.Furtherdownstreamoftheinjector,thejetinterfacechanges.Incase1,itcanbeseenthatseveraldropletsformbeyond10injectordiametersfromtheinjectoranddetachfromthemainbodyofthejet.Thisiscausedduetotheheattransferredfromthejetasitisinjectedintoasignicantlycoolermedium,andhencetheconditionsbecomelocallysubcritical.Anyportionofthejetthatbreaksoffwillcoolbelowthecriticaltemperatureandformsphericaldropletsduetosurfacetensionforcesgainingimportance.Thiseffectismostprominentinthersttwocases,wherethetemperatureofthechamberisthelowest,causingthegreatestheattransfer.AswegofromlefttorightinFigure 4-4 ,thetemperatureofthechamberincreasesanddropletsgraduallydisappearsincelocalconditionsarenotcoolenoughintheregioncapturedtocausesubcriticalphenomenatoexist.Densityanddensitygradientvaluesalsograduallydecreasefromlefttorightwhichisduetotheincreaseintemperatureofboththesurroundingsandtheinjectant. 4.5SupercriticalFluidintoSupercriticalAtmosphereInthesecases,thesupercriticaluidwasinjectedintothechambermaintainedatsupercriticalconditions.Bothwereagainatsupercriticalpressures.Representativetestcases13through16havebeenlistedinTable 4-1 inincreasingorderofchamberandinjectanttemperaturesandpressures.Figure 4-5 showstherespectiveimagesofthelistedtestcasesasintheearliercase.Densityanddensitygradientimageshavebeenshownontherstandsecondrowsrespectively.Theuidintheseinjectionconditionsexhibitcompletesupercriticalbehavior.Noeffectsofsurfacetensionordropletformationisseenasfaras20jetdiametersfromtheinjectorevenatlowerchambertemperatures.Therearesomenger-likeentities 66

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A B C D E F G HFigure4-4. Scaledimagesofasupercriticaljetinjectedintosubcriticalchamberconditions.Testconditionscorrespondtocases9-12inTable 4-1 .Figures(a)-(d)representdensityimageswhile(e)-(h)representdensitygradientimages. thatemergefromthejetbutdonotbreakupintodropletsasthepreviouscase.TheimagesinFigure 4-5 progressivelyresembletheinjectionofagaseousturbulentjetintoagaseousenvironmentwithincreasingtemperaturesandpressuresasobservedbyotherresearchers[ 1 30 ].Thejetspreadingangleincreasesfromlefttoright,andhencewithincreasingchamber-to-injectantdensityratio.Thedensity-gradientmagnitudesalsocontinuetodecrease. 67

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ThersttwosetsofimagesinFigure 4-4 appeartostartinthesecondwind-inducedzoneaccordingtotheclassicalbreakuptheory[ 32 ].Whentheconditionsapproachsupercriticalforthechamber,beforeassumingtheatomizationcharacterthejetgraduallybeginstotaketheappearanceofagasjetasseeninFigure 4-5 .Thisdeparturefromtheclassicalbehavioroccursduetotwoprimaryfactors:thereductionofsurfacetensionandtheheatofvaporizationtoanearzerovalue.Asthechamber-to-injectantdensityratiosareincreasedfromlefttorightofbothsetsofimagesshown,thevalueapproaches0.1andabovewhichcanbeobservedforgas/gasjets.Inthefollowingsections,thecorelengthsandspreadingangleshavebeencalculatedfortheabovementionedtestconditionsandafunctionaldependencewithchamber-to-injectantdensityratiohasbeenobtained. 4.6CoreLengthMeasurementTheterm'corelength'usuallyreferstotheintactsectionofthejetwhichishigherindensitythantheremainingareas.Thecorelengthdoesnothaveanyuniquedenitionamongresearchers.Varioustermssuchastheintactlength,potentialcore,dark-corelength,andbreak-uplengthhavebeenusedalongwithvariousmeasurementtechniquestodeterminethesamephysicalquantity.Inthissection,abriefoverviewofearlierworkdonetodeterminethecorelengthshallbepresented,followedbythemethoddevelopedinthecurrentstudyandhowitcomparestoexistingmodelsandtheories. 4.6.1EarlierWorkAccordingtothetheoryofAbramovich[ 4 ],thelengthofthepotentialcoreinisothermal,uniformdensity,axisymmetricandtwodimensionaljetsisestimatedtobe6to10injectordiameters.Also,fornon-isothermalcoldjetsinjectedintohotenvironments,thelengthcanbeupto25injectordiametersdependingonthejettemperature.Chehroudi[ 33 ]calculatedtheintactcorelengthofdieselliquidspraysandmodeleditasbeingdependentonthechambertoinjectantdensityratioas 68

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A B C D E F G HFigure4-5. Scaledimagesofasupercriticaljetinjectedintosupercriticalchamberconditions.Testconditionscorrespondtocases13-16inTable 4-1 .Figures(a)-(d)representdensityimageswhile(e)-(h)representdensitygradientimages. Lc=Cd(g=l)1=2.Here`d'istheeffectivejetdiameterattheinjectorexitandCisaconstantthatvariesfrom3.3to11.Earlierworksofmeasuringtheliquidcoreanddarkcorelengthsofdifferentjetsfromphotographswereperformedbyseveralresearchers[ 29 30 34 35 ].Quantitativemeasurementsofcorelengthsfromimagesofjetsposemanydifculties.Ifastrobelightorlasersourceisbeingusedforcapturingimages,theintensityofthelightsourcemayvaryfromshottoshot.Anotherchallengeistheselectionofacriteriontodeterminethelocationoftheendofthecore.Furthermore, 69

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withtheuseofdigitalcameraswithhighframeacquisitionrates,manualmeasurementofthecorelengthisnotaviableoption.Hence,toaccountforalltheabovementioneddifculties,itisnecessarytocreateanalgorithmforautomatedcomputerprocessingoftheimagesandsubsequentcorelengthdetermination.Themethodofcalculatingthedark-coreusedintherecentworksofDavisandChehroudi[ 35 ]involvedthechoiceofasuitablethresholdlevelonthebrightnessscaleofanimage.Thealgorithmwasdesignedsuchthattheseparatethresholdlevelsforeachcomponentwasidentiedforeachimage.Thenumberofpixelshavinggraylevelsbetweenthetwospeciclowthresholdvaluesmarkthecorelength.Otherregionssuchasthebackgroundandinjectorareidentiedsimilarlyusingdifferentthresholdvalues.Sincetheexactthresholdvalueschangeforeachimageduetoshottoshotvariationandchangesinexperimentalconditions,athresholdvaluecorrespondingtoacertainslopeofthebroadbackgroundpeakwasdetermined,andwasassignedtobee)]TJ /F5 7.97 Tf 6.59 0 Td[(1.Thisvaluewaschosensuchthatresultingvalueofcorelengthconformedtovisualinspection.Finally,anaveragevalueof30imageswastakenandthecorelengthvalueofaspecicexperimentalcasewasdetermined. 4.6.2AlgorithmDevelopedintheCurrentStudyThecorelengthisdenedinthisstudyastheintactsectionofthejet,measuredalongitsaxiallength,beyondwhichaconsiderablechangeofdensityoccurs.Thealgorithmdevelopedheretocalculatethecorelengthstartswithasinglejetimage.Theimageisscaledusingthepixelintensities.EachshadeinthescaledimagecorrespondstoalocaldensityrangeasshowninFigure 4-6 A.Thusthebrightestpixelcorrespondstothehighestdensity.Theanalyzedimagesarestoredasamatrixoflocaldensityvalueswhichisthenusedfordeterminingthecorelength.Therstrowofthedensitymatrixisscannedtondthewidthofthejetattheinjector.Thiswidthisusedtocreateindividualsquaredensitymatricesorblocksalongtheentirelengthofthejet,whereeachblockstartsonerowafterthepreviousblockas 70

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showninFigure 4-6 A.Theaverageandtheeigenvaluesofeachofthesematricesarethencomputed.ThedeterminantsoftheeigenvaluematricesareplottedinFigure 4-6 B.Apolynomialisttedtothisplotanditspointsofinexioncorrespondtoasignicantchangeindensityacrosstheaxiallengthofthejet.Ateachpointofinexiontheaveragedensitymatrixiscomparedtoitsneighboringones.Thepointthatcorrespondstothemaximumdensitychangewithrespecttoitsimmediateneighborsistakentobethecorelength.AscanbeseenfromFigure 4-6 ,thepointofinexionbetweenpixelnumber500and600isfoundtobethecorelengthandithasbeenmarkedinbothgures.Foreachexperiment,thecorelengthswerecalculatedforallimages,andthenanaverageofthisvaluewastaken.Itshouldalsobenotedthatthismethodofcalculatingthecorelengthissensitivetocoreseparation;hencethelengthbeforeseparationistakentobethecore.Insomecases,themethodoverpredictsthecorelengthduetotheapproximationinvolvedinttingthepolynomialandcalculatingthepointsofinexion,andhencethesecaseshavebeendiscarded.Mostcasesalsoagreewellwiththecorelengthdeterminedusingvisualinspection. 4.6.3ComparisonwithExistingDataSincethecorelengthdoesnothaveauniquedenitionamongresearchers,differentmeasuringtechniquescanchangehowitsabsolutemagnitudeisreported.Thus,moreemphasisshouldbemadeonthetrendsthattheyhavewithdifferentoperatingconditions.Figure 4-7 showsaplotofthecorelengthasafunctionofthechamber-to-injectantdensityratioalongwithexistingmodelsandtheories.Inthecurrentwork,thejetcorelengthremainsrelativelyconstantat11.5jetdiametersforchamber-to-injectantdensityratiosvaryingfrom0.01to0.12,thuscoveringmorethananorderofmagnitudefordensityratiovalues.ItcanbeobservedinFigure 4-7 thatourdataliesslightlybeyondthetheorypredictedbyAbramovichforturbulentnon-isothermalsubmergedcoldgasjets,wherethecorelengthstaysconstantat10jetdiameters.Thisobservationindicatesthatwhenajetisinjectedatsupercriticalconditions,itbehaves 71

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A BFigure4-6. Thebasisforcorelengthdetermination.Theshadedareain(A)istheportionofthejetwhereindividualdensitymatricesorblocksarechosen.Thedeterminantsoftheeigenvaluematricesoftheseblocksareplottedagainstthepixeldistancein(B).Thecalculatedcorelengthisalsoshownonbothgures. 72

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verysimilartoagasjetinjectedintoagaseousmedium.Thisisirrespectiveofwhetherthejetisinitiallyatsubcriticalorsupercriticalconditions.Theeffectofpreheatingthejetessentiallymanifestsitselfaschangingthechamber-to-injectantdensityratio,andthushaslittleeffectinalteringthecorelengthvalue.Itshouldbenotedthatthejetinjectedundersupercriticalconditionsdoesnotbehaveassubcritical,liquiddieselsprayswhosecorelengthdecreaseswithincreasingdensityratio,aspredictedbyChehroudi'smodel,butmorelikethetheoryputforthbyAbramovich[ 4 ]forturbulentgasjets. Figure4-7. Corelengthsplottedasafunctionofchamber-to-injectantdensityratio.OurdatapointsandproposedmodellieslightlyabovethetheoryofAbramovichforturbulentsubmergedcoldgasjetsbutfollowasimilartrend.Thecorelengthstaysrelativelyconstantatabout11.5jetdiameters. Theclassicaltwostreammixinglayerstartsfromtheinjectorexittoapproximatelytheendofthecorelength.AnimportantassumptionmadehereisthatthecorelengthsmeasuredinourpresentstudyandtheworkofDaviset.al.[ 35 ]playthesameroleastheintactcoreorpotentialcore.ItisonlythenthattheabovecomparisonwithexistingliteratureasshowninFigure 4-7 canbeappropriatelyjustied. 73

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4.7SpreadingAngleMeasurementAnotherimportantgeometricalparameterthathasbeenevaluatedquantitativelyisthejetspreadingangleorthedivergenceangle.Measurementsandestimationsofthespreadinganglehasbeenthesubjectofintenseresearch,sinceitprovidesameasureofthemixinganddevelopmentofthejet.Thissectionincludesabriefsummaryofthepreviousresearchdonetodeterminethisquantityfordifferentkindsofows,thealgorithmusedtomeasureitinthecurrentstudyandnallyacomparisonofourdatatothoseofearliermodelsandtheories. 4.7.1EarlierWorkTheexperimentalresultsofBrownandRoshko[ 36 ]areconsideredhererst,whereheliumandnitrogenwereusedinasubsonictwodimensionalincompressibleturbulentgaseousmixinglayer.Shadowgraphy,concentrationprobesandPitottubedynamicpressuremeasurementswereusedtoinferthespreadingofthemixinglayer.TheyconcludedthatatlowMachnumbersquaredvalues,thereisnodistinctionbetweenmixinglayersoftwostreamshavingdifferentmolecularweights,temperaturesorcompressibilityeffects.Theirresultsareconsideredheresincetheinitialmixingregionforaxisymmetricjetscanbeapproximatedastwo-dimensionalmixinglayers.PapamoschouandRoshko[ 37 ]usedschlierenphotographyandPitottubemeasurementstocalculatethespreadingcharacteristicsforsubsonicandsupersonictwo-dimensionalturbulentmixinglayers.Theyobservedthatinadditiontocompressibility,thespreadinganglealsodependsonvelocityanddensityratiosofthemixinglayers.Toisolatetheeffectsofcompressibility,aconvectivevelocityUcandaconvectiveMachnumberMcweredenedasshownbelowtomoreappropriatelyexplainthemixingcharacteristicsratherthantheMachnumbersoftheindividualstreams.Uc=(U1p 1+U2p 2) (p 1+p 2)Mc=(U)]TJ /F3 11.955 Tf 11.95 0 Td[(Uc) a 74

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Theseparameterswereusedtorepresentarateofchangeofvisualthickness0visinthestreamwisedirectionforincompressiblevariabledensitymixinglayers,whichwascalculatedas:0vis=0.17h1)]TJ /F4 7.97 Tf 13.15 4.88 Td[(U2 U1i1+2 11 2 1+U2 U12 11 2Here(1,U1)and(2,U2)arethedensityandvelocityofeachstreamandtheconstant0.17hasbeendeterminedexperimentally.Inthecasewhereoneofthestreamsisstationary,U2=U1=0andhencetheequationsimpliesto:0vis=0.17"1+2 11 2# (4)Dimotakis[ 38 ]observedexperimentallythataspatiallygrowingshearlayerentrainsunequalamountsofuidfromeachstream,resultinginamixeduidcompositionthatfavorsthehighspeeduid.Heproposedarelationforthegrowthoftheturbulentmixinglayerbasedonthegeometricalpropertiesofthelargescalestructuresofthesubsonic,fullydeveloped,two-dimensionalmixinglayerwhichdependedonthedensityandvelocityratiosofthestreams.Asinthepreviouscase,whenoneofthestreamsisstationary,therelationsimpliesto:0vis=0.17"1+2 11 2)]TJ /F8 11.955 Tf 13.16 8.08 Td[(1)]TJ /F8 11.955 Tf 11.95 0 Td[((2=1)1 2 3.9# (4)Theimagesshownearlierforthecurrentworkexhibitbothliquidandgaslikecharacteristics,andhencethespreadingangleforliquidspraysproducedfromsingle-holenozzles(asindieselengines)isalsobrieydiscussedhere.Theatomizationofliquidspraysdependsonseveralfactorsincludinginjectorgeometry,ambientdensity,viscosity,surfacetension,initialturbulence,cavitationandliquidsupplypressureoscillations[ 1 ].AccordingtoReitzandBraccointheirfamousworks[ 39 41 ],thesprayanglecanbedeterminedbycombiningtheradialvelocityofthefastestgrowingunstablewaveswiththeaxialjetvelocity.Theequationobtainedbytheirmethodsreproducesthe 75

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dependenceofsprayangleonsquarerootofambienttoinjectantdensityratioandviscosity.Themeasurementsweremadeveryclosetothenozzleexitplanewhichiscomparabletoourspatialregionofmeasurementalso.Sincethespreadingangledependsoninjectorgeometryandnozzledesign,differentnozzleL=Dvaluescanyieldspreadingangles.OneoftheirrelationsforL=D=85isgivenby:=0.27g l1 2 (4)AseriesofrecentstudiesatAFRLandDLRdoneoninjectionofN2intoenvironmentsofN2,HeandAr[ 29 ]indicateseveralinterestingfeaturesbasedongasicationandseparationtimesofdropletsandligamentsrespectively.Thebulgeformation/separationtimecharacterizestheformationandseparationofbulgesfromtheinterfaceoftheturbulentliquidjetproducingisolatedligamentsanddrops.ThegasicationtimecharacterizestheevaporationofdropsandfollowstheD2Lawfordrops.Itwasproposedherethatifthesecharacteristictimesbecomenearlyequalinmagnitude,thentheinterfacebulgescannotdetachtoformdrops/ligamentssincetheyaregasiedassoonastheyseparatefromthejetsurface.Hencethetransitionbetweenliquid-likeandgas-likebehavioriswhenthesetimescalesarenearlyequal,andthishasbeenusedforinjectionatsupercriticalpressures.Thisproposedtheoryenabledthemtoformulatearelationforthespreadingangleasfollows:=0.27"Fxg l+g l1 2# (4)wheretheshapeofthefunctionFisgivenbyFg l=5.325g l+0.0288wheng l<0.0885Fg l=0.5wheng l0.0885 76

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Herex=1.0forN2injectedintoN2,0.2forN2injectedintoHeand1.2forN2injectedintoAr.Theformulationabovealsosuggestsadominanteffectofthedensityratioparameterforinjectionofasinglejetintoastationaryatmosphere. 4.7.2AlgorithmDevelopedintheCurrentStudyTheprocessofmeasuringthespreadingangleinthecurrentworkissimilartothatmentionedinpreviousstudiesandisbasedonatwodimensionalapproachasshowninFigure 4-8 A.Therststepistoidentifythegas-jetinterfaceandcalculatethejetboundaries.Thishasbeendonebyidentifyingthelocationofhighestdensitygradientsatthejetsurfaceforaspecicrow.Theintensityvalueatthislocationisusedasthethresholdintensityfortheimage,andanythingbelowthisthresholdvalueisassignedtozerointensity.Oncethejethasbeenseparatedfromitssurroundings,anoutlineofthejetstructurewasdrawnasshownbytheredlinesinFigure 4-8 A.Straightlineswerettedtothisoutline,oneoneachsideofthejetbutusingonlyaboutone-thirdsofthelengthofthejetandthusstayingveryclosetotheinjectorexitplane.Thiswasdonesinceonlytheinitialmixingregionofaxisymmetricjetscanbeapproximatedastwodimensionalmixinglayersassuggestedbyseveralresearchers.Thesumoftheanglesthateachstraightlinemakeswiththeverticaldenesthespreadingangleofthejet.Sincethetotalaxiallengththatwasconsideredwasone-thirdoftheaxiallengthcapturedforthatspecicframe,imagesthathadashorteraxialdistance(x=D=8)couldalsobeusedalongwiththosethathadlongereldofview(x=D=20).Figure 4-8 showsarepresentationofhowanimagewithaxialdistance-to-jetdiameterratioofaround20wasusedtocalculatethespreadingangle.Thedensitygradientsattheinterfaceforaspecicrowhasbeenshown,alongwiththejetboundariesandthecalculatedangles.Thespreadingangleswerecalculatedforeachindividualimageforeachexperimentalcase,andthenaveragedforallimages.Thestandarddeviationsforeachcasewasalsomeasuredandpointslyingbeyondonestandarddeviationwerediscardedorthespecicexperimentwasrepeated. 77

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Figure4-8. Thebasisforspreadingangledetermination.Thegureshowstheanalyzedimagewiththeoutlinesdrawn,thestraightlinesttedtoit,andthemeasuredspreadinganglesoneachsideofthejet.Theangleincludedbetweentheselinesisthetotaljetdivergenceangle. 4.7.3ComparisonwithExistingDataAcomparisonofthecurrentresultswiththosepreviouslyobtainedbyotherresearchershasbeenshowninFigure 4-9 .OurdatafollowatrendthatliesbetweenthetheoreticalcurveofDimotakis[ 38 ]andtheproposedmodelbyReitzandBracco[ 32 ]fordieselspraysusingalargelength-to-diameterrationozzle(L=D=85).Beyondadensityratioof0.08,thedatapointsappeartobeanexactaverageofthetwocurvesmentionedabove.Belowthisdensityratio,thedatatendstobeclosertothatofReitzandBraccoanddeviatesawayfromthatofthetwodimensionalmixingshearlayers.Thisisexpectedsinceatlowerdensityratios,thetemperaturesand/orpressuresaretypicallysubcritical,andhencethejetenterstheclassicalbreakupregime.ThedataalsohasamarkedsimilaritywiththatobtainedbyChehroudi[ 1 ]forN2-N2injectionat 78

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subcriticalandsupercriticalconditions,thereforeindicatingthatsupercriticalinjectionusingdifferentuidsbehavesimilarlywithrespecttospreadingangle.Accordingtoourdata,thespreadingangleofauoroketonejetinjectedintoaN2environmentinsubcriticalandsupercriticalconditionsvariesasfollows:=0.40g l1 2 (4)Theaboveequationwasobtainedusingacurvettoallthedatapointsextendingfromsubcriticaltosupercriticaltestconditions.Itisalsoclearfromtheplotthatbeyondthedensityratioswhereeitherthejetortheambientisatsupercriticalconditionswithrespecttotheinjectant,thedataobtainedfromthecurrentworkhaspropertiesofbothliquidandgas.Theimagesnotonlyhaveagasjet-likeappearancebutbehavesimilarlywithrespecttospreadingangle.Thevaluesareslightlylowerthananactualgas-gasmixinglayer,buthigherthantypicallyatomizedjetsfordieselengines.Thejetsshowthesignsofclassicalbreakupinthesecondwind-inducedregimeatlowerdensityratios,i.e.atsubcriticalconditions.Disagreementofourdatawiththeliquidspraysathigherdensityratios,i.e.,typicallyintheatomizationregimeoccursduetotherestrictionofsupercriticaljetstoreachtheatomizationstateduetotheabsenceofsurfacetensionandtheheatofvaporization. 4.8ConclusionsAstudyofajetatsubcriticalandsupercriticalconditionsinjectedintosubcriticalandsupercriticalchamberconditionswasundertaken.Theimageswereobtainedusingplanarlaserinduceduorescencethroughthejetcenterplane.Theimagesindicatethecharacteristicsofsubcriticalandsupercriticalmixingasmentionedinthetheories,buttemperaturewasfoundtobethedominantparameterindeterminingthestateoftheinjecteduid.Thisworkcomplementsthelimitedexperimentalstudiesdedicatedtosupercritical-into-subcriticalinjectionandsubsequentnucleation,andspreadingangleaswellascorelengthdependenceondensityratio. 79

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Figure4-9. Jetspreadingangleplottedasafunctionofchamber-to-injectantdensityratio.OurdatapointsandproposedmodelliebetweenthoseproposedbyReitzandBraccofordieselsprays(L=D=85)andChehroudi'smodelforN2injectedintosupercriticalN2environment. Inthecaseofasubcriticaljetinjectedintoasubcriticalenvironment,dropletformationwasobservedastheuiddetachedfromthemainbodyofthejetduetosurfacetensionbeingthedominantparameter.Thesizeofthedropletsgraduallydecreasedastheinjectanttemperaturewasincreasedtonearcriticalvalues.Whenthesubcriticaljetwasinjectedintosupercriticalenvironments,theimportanceofsurfacetensionprogressivelydecreased.Withincreasinginjectanttemperature,thejetsurfacebecamesmootherwithminimalsurfaceirregularities,butdownstreamdisintegrationcouldnotbeinvestigatedsincetheimageshadashortereldofview.Inthecaseofasupercriticaljetinjectedintoasubcriticalenvironment,dropletswereobservedtoformatbeyond10jetdiametersdownstreamoftheinjectoratlowerchambertemperatures.Thiswasduetotheheattransferfromthejettothesurroundingsandhencetheexistenceoflocalsubcriticalconditionswheresurface 80

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tensiongainedimportance.Agradualincreaseofchambertemperatureinhibitedtheformationofdropsandthejet-gasinterfacebecamesmoother.Whenthesupercriticalwasjetinjectedintosupercriticalenvironments,thejetsurfaceexhibitedcompletesupercriticalbehaviorwithnoformationofdropletsnoted.Surfacetensiondisappearedcompletely,andthesurfacebecamesmoothwithminimalirregularities.Withincreasedtemperatureandpressure,thedensitygradientvaluesdecreaseandthejetresembledthatofaturbulentgasjetinjectedintoagaseousatmosphere.Thecorelengthswerecalculatedforallthetestconditionsusingapreviouslydevelopedmethodandwereplottedasafunctionofthechamber-to-injectantdensityratio.Thecorelengthvalueswerefoundtoremainunaffectedwithdensityratiosrangingfrom0.01to0.12andwasfoundtobe11.5jetdiameters.ThiswasobservedtobesimilartothetheorypredictedbyAbramovichforturbulentnon-isothermalsubmergedcoldgasjets,wherethecorelengthstaysconstantat10jetdiameters.Amodelwasfoundforthejetspreadingangleswhichpredictedthattheanglewasproportionaltothesquare-rootofthechamber-to-injectantdensityratio,followingacurvemidwaybetweenthemodelsofDimotakisandReitzforturbulent,gaseous,subsonic,mixinglayersanddieselspraysrespectively.Itshouldbementionedthatalltherelevantparameterswerenotconsideredindeterminingtheaxes.Moreover,disagreementsinthedifferentmeasurementsbyvariousresearcherscanalsoberesponsiblefordifferencesinthespreadingangle.Thiscanbeattributedtothedifferentdenitionsofmixinglayerthicknessesandthecorrectionfactorsusedtoconvertthemintoequivalentvisualthicknesses. 81

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CHAPTER5SINGLESPECIESMIXINGInthischapter,themixingcharacteristicsandjetdisintegrationprocessesinasinglespeciesenvironmenthasbeenstudied.Thegoalofthisworkistoexpandtheexistingdatabaseofreliableexperimentalmeasurementsofsinglespeciessupercriticalmixingaswellasgainsomeinsightintofundamentalfeaturesofthebinaryspeciesmixingprocess.Thejetisheatedfromsubcriticaltosupercriticalconditions,andisinjectedintoanatmospherewhichisthegaseousphaseofthesame.Thisstudyisexpectedtogenerateabasefortheunderstandingofsubcriticalandsupercriticalmixinginnon-similaruids. 5.1ExperimentalConditionsTheexperimentalconditionsareshowninFigure 5-1 onareducedpressure(Pr)andreducedtemperature(Tr)diagram.Thegoalwastospanarangeofpressuresandtemperatureswithparticularfocusaroundthecriticalpoint.Chamberandinjectantconditionshavebeenmarkedseparately.Thesetofexperimentswheretheuidwasinjectedatroomtemperature(Tr=0.66)hasbeenindicatedontheplotas`coldinjection',whilethesetwheretheuidwaspreheatedbeforeinjectionhavebeenmarkedas`heatedinjection'.Asinthecaseofthetwospeciesmixing,itwasfoundthattemperatureplaysagreaterrolethanpressureindeningthesupercriticalstateoftheuid.Hence,forsinglespeciesmixingcases,theterm`supercritical'shallbereferredtocaseswheretemperatureissupercritical,while`subcritical'shallbereferredtocaseswhereonlythetemperatureissubcritical(pressuresaresubcriticalinmostcases).Asweepofpressuresforgiventemperatureswereselectedalongwithconditionsthatkeptthepressureessentiallyconstantandincreasedthetemperature.Thehighesttemperaturestestedwerearound1.04Tr(1850C).Theexperimentalpointscoveredforthesinglespeciescasesarenotasextensiveasthebinaryspeciescases.The 82

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imagesobtainedinthesubcriticalandsupercriticalcategorieshavebeenanalyzedinthesectionstofollow. Figure5-1. Selectionoftheexperimentalconditions.Reducedtemperaturesandpressureshavebeenselectedtocoverthesubcriticaltosupercriticalregime.Theplotreferstoboththechamberandtheinjectantconditionsindependently.Theselectedcombinationswillbeemphasizedinthefollowingsectionsdiscussingtheresults. AfewselectedtestconditionshavebeenlistedinTable 5-1 .Forallthetests,themassowratewaskeptrelativelyconstantbutvelocitydifferencesexistedduetothelargechangesindensitynearthecriticalpoint.Thesevalueshavenotbeenindicatedinthetable.Pressuresweresubcriticalforalltestconditions(exceptforcase7and8)toisolatetheeffectsoftemperatureinthedisintegrationandmixingprocesses.Asmentionedbefore,temperaturewasfoundtobethedeterminingfactorinidentifyingwhetherthestateoftheinjecteduidwassupercriticalornot.Cases1-4representsubcritical-into-subcriticalinjectionswhile5-8representsubcritical-into-supercritical 83

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injections.Buoyancyeffectsareagainignoredinfavoroftheinertialforcesforallthetestcasesasdiscussedinthepreviouschapter. Table5-1. Selectedtestconditionsforthesinglespeciesexperiments CaseTr,gTr,lPr,gPr,l 10.860.650.170.2920.880.850.290.3330.920.900.430.4940.980.940.700.7451.000.660.620.7261.030.660.790.9171.000.950.731.0381.040.981.011.22 Inbothregimesofinjection,thedensityanddensitygradientproleshavebeencalculated,andimportantmixingpropertieshavebeenidentied.Spreadingangleshavebeencalculatedforbothsingleanddualcomponentsystemsandcomparedwithexistingtheoriesandmodels.Acomparisonbetweensingleanddualcomponentmixingprocesseshasalsobeenprovided. 5.2SubcriticalFluidintoSubcriticalAtmosphereTheexperimentsdoneunderthiscategoryinvolvesubcriticaltemperaturesandpressuresfortheinjectantandthechamber.Somerepresentativetestcases1through4havebeenlistedinTable 5-1 .Thecaseshavebeenchosensuchthatchamberandinjectanttemperaturesandpressuresareinincreasingorderofmagnitude.Figure 5-2 showstherespectiveimagesofthelistedtestcases.Densityanddensitygradientimageshavebeenshownontherstandsecondrowsrespectively.Allthetestcasesforthesinglespeciesmixingexperimentsweredoneusingashortereldofview,andthustheimagesshow8jetdiametersfromtheinjector.Similarphenomenaareobservedasinthebinaryspeciessystem.Surfacetensionandinertiaforcesdominateundertheseconditions.Thus,dropletformationisobservedoncetheuiddetachesfromthebodyofthejet.Atlowertemperatures,thejetsurfaceiscorrugatedandwavy,indicatingagainthatthesurfacetensionforcesareimportant. 84

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Athighertemperatures,thejetsurfacegraduallybecomessmootherasitapproachesthecriticalpoint,whenthesurfacetensiondecreasestoanear-zerovalue.Thedensitygradientprolesindicatethatthemaximumvalueofthegradientsdecreaseasthetemperatureofthejetduringinjectionisincreased.Inallcases,thevalueofthedensitygradientisthehighestattheliquid-gasinterface,andisthelowestinsidethecoreofthejet.Itcanalsobeenseenthatthelasercorrectionmethodadoptedworkswellforallofthesecases.Thedensityproleinsidethejetdoesnotshowapreferentialweightingornon-uniformdensitydistributiontowardsanyside,whichindicatestheabsorptioncoefcientpredictedforthesubcriticalinjectionconditionsofthejetisquiteaccurate.Thejetdivergenceangleisgreaterinthecaseofthesinglespeciessystemthaninthebinaryspecies.Thiscanbeattributedtothehigherdiffusionandhigherheattransfertothejetfromthesurroundingsintheformercase,causingincreasedpenetrationintothegasphaseandhenceenhancedmixing.ThechamberandinjectanttemperaturesincreasefromlefttorightinFigure 5-2 .Theincreaseintheinjectantandchambertemperaturesismuchmoresignicantthanthepressurerisesincethetemperaturesreachanearcriticalvalueincase4.Itcanbeobservedthatthedropletformationanditssizedecreasesfromlefttoright,whilethejetspreadingangleincreasesasobservedforthebinaryspeciesmixingcases. 5.3SubcriticalFluidintoSupercriticalAtmosphereTheexperimentsdoneundertheseconditionsinvolverelativelyhighertemperaturesforthechamberthaninthepreviousregime.Somerepresentativetestcases5through8havebeenlistedinTable 5-1 .Thecaseshavebeenchosensuchthatinjectanttemperaturesareinincreasingorderofmagnitude,whilethechambertemperatureshavebeenkeptessentiallyconstant.Pressuresarevariedfromsubcriticaltosupercriticalforthechamberandtheinjectant.Figure 5-3 showstherespectiveimagesofthelistedtestcases.Densityanddensitygradientimageshavebeenshownontherstandsecondrowsrespectively. 85

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A B C D E F G HFigure5-2. Scaledimagesofasubcriticaljetinjectedintosubcriticalchamberconditions.Testconditionscorrespondtocases1-4inTable 5-1 .Figures(a)-(d)representdensityimageswhile(e)-(h)representdensitygradientimages. Thecharacteristicfeatureofthisregionistheapparentdecreasedimportanceofsurfacetensionthatmanifeststhroughthesmootheningoftheliquid-gasinterface.Ligamentformationtendstosignicantlydecrease.Duetothedecreasedsurfacetensionforces,theligamentshaveaclusterornger-likeappearancefromwhichparcelsofliquiddetachasseenforthebinaryspeciescases.Forsimilarconditionsofinjection,itwasobservedthatinthebinaryspeciessystem,someoftheclustersgetdetachedfromthemainbodyofthejetandformdrops,whilesuchanobservationcannotbemadeinthesinglespeciessystem.Duetointeractionsatthesurface,instabilitiesleadtodisturbancesthatmanifestassurfacewaves.ThevalueofthemaximumdensityanddensitygradientsdecreaseaswegofromlefttorightinFigure 5-3 ,whilethespreadingangleincreases.Moreover,we 86

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seecompletesupercriticalbehaviorandtheresemblanceofagaseousjetinjectedintoagaseousenvironmentevenwhenthepressuresarekeptsubcritical,restatingtheimportanceoftemperatureeffectsoverpressureeffects.Itisnotedherethatthegurestendtogetprogressivelynoisieratthehigherdensityratiosduetotheincreasedabsorptionofthelasersheet,leadingtoincorrectvaluesofdensitygradientincase8.Analternativewayoflasercorrectionneedstobeadoptedforsuchsituations. A B C D E F G HFigure5-3. Scaledimagesofasubcriticaljetinjectedintosubcriticalchamberconditions.Testconditionscorrespondtocases5-8inTable 5-1 .Figures(a)-(d)representdensityimageswhile(e)-(h)representdensitygradientimages. 5.4SpreadingAngleMeasurementAsstatedinthepreviouschapter,animportantgeometricalparameterthathasbeenevaluatedquantitativelyisthejetspreadingangleorthedivergenceangle.Acomparisonofthesinglespeciesdatatothoseofthebinaryspeciescasesdoneearlier,andalsowithearliermodelsandtheorieshasbeenshowninFigure 5-4 87

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ItisobservedthatbothsinglespeciesandbinaryspeciescasesfollowatrendthatliesbetweenthetheoreticalcurveofDimotakis[ 38 ]andtheproposedmodelbyReitzandBracco[ 32 ]fordieselspraysusingalargelength-to-diameterrationozzle(L=D=85).Athighdensityratios(beyond0.18),thecurveforthesinglespeciesmixingtendstomergewiththoseofPapamoschou,ChehroudiandDimotakis.Atlowdensityratios,thebothcasesarequiteclosetoeachotheranddeviateawayfromthatofthetwodimensionalmixingshearlayers.Thisisexpectedsinceatlowerdensityratios,thetemperaturesand/orpressuresaretypicallysubcritical,andhencethejetenterstheclassicalbreakupregime.ThesinglespeciesdataalsohasamarkedsimilaritywiththatobtainedbyChehroudi[ 1 ]forsinglespeciesN2-N2injectionatsubcriticalandsupercriticalconditions,buttheanglesarealwayslowerinmagnitude.Accordingtoourdata,thespreadingangleofauoroketonejetinjectedintoauoroketoneenvironmentinsubcriticalandsupercriticalconditionsvariesasfollows:=0.52g l1 2 (5)Theaboveequationwasobtainedusingacurvettoallthedatapointsextendingfromsubcriticaltosupercriticaltestconditionsaswasdoneforthebinaryspeciescases.Similarobservationsaremadeforboththesingleandbinaryspeciesmixingcases,theonlymajordifferencebeingthemagnitudeofthespreadinganglebeinghigherinthesinglespeciescases. 5.5ConclusionsAstudyofajetinjectedintoagaseousenvironmentcomprisingasinglespecieswasundertakenatsubcriticalandsupercriticalconditions.Thelaserintensitylossthroughthechamberandthejetwastakenintoaccount.Thisledtobetteridenticationofdensityanddensitygradientwhichcouldbeusedforfurtheranalysisofcorelengthmeasurements. 88

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Figure5-4. Jetspreadingangleplottedasafunctionofchamber-to-injectantdensityratio.OurdatapointsandproposedmodelliebetweenthoseproposedbyReitzandBraccofordieselsprays(L=D=85)andChehroudi'smodelforN2injectedintosupercriticalN2environment.thesinglespeciesmixingcasesproducehigherspreadinganglesthanthebinaryspeciescases.Bothhavebeenindicated. Forasubcriticaljetinjectedintoasubcriticalenvironment,surfacetensionandinertiaforcesdominatedthejetbreakupprocess,anddropletformationwasobserved.Thesizeofthedropletsdecreasedasthechamberandinjectanttemperatureswereincreased,keepingthepressuressubcriticaluntilalmostnodropletswereseenatnear-criticalconditions.Inthecaseofasubcriticaljetinjectedintoasupercriticalenvironmentthejetsurfacechangedcompletelyasresembledgas-gasmixingcharacteristics.Thesurfaceofthejetbecamesmootherthaninthepreviouscaseandbothdropletformationandirregularlyshapedmaterialwereobservedwhenaportionofthejetbrokeoff.Thedensitygradientvalueswerehigherinthecaseofthe 89

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binaryspeciessystemthoughinbothsystemsthehighestgradientswereatthejet-gasinterface.Amodelwasfoundforthejetspreadingangleswhichpredictedthattheanglewasproportionaltothesquare-rootofthechamber-to-injectantdensityratioasinthecaseofthebinaryspeciesmixing,followingacurvemidwaybetweenthemodelsofDimotakisandReitzforturbulent,gaseous,subsonic,mixinglayersanddieselspraysrespectively.Themajordifferenceinthetwocaseswasthemagnitudeofthespreadinganglewhichwashigherinthecaseofsinglespeciesmixing,indicatinghigherdiffusionandheattransfertothejetsurfacefromthesurroundings,andthereforeenhancedmixing. 90

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CHAPTER6LINEARSTABILITYANALYSISOFASUPERCRITICALJETAlinearstabilityanalysiswasperformedonaviscousjetinjectedintosubcriticalandsupercriticalatmospheres.Onlythebinaryspeciessystemsareconsideredinthisanalysis,sothateffectsofthesecondspeciesonjetdisintegrationcouldbeinspected.Thesubcriticalcasesshowedgoodcorrelationwithpreviousexperimentalresults.Thesupercriticalsolutions,whichhavenotyetbeensolvedpreviously,arefoundherethroughanasymptoticsolutionofthedispersionequationforexceedinglyhighWebernumbers. 6.1EarlierWorkThebreakupofaliquidjetissuingfromanoriceintoanotheruidhasbeenstudiedforoveracentury.Thejetdisintegrationoccursaccordingtomanyfactorsincludingtheoricegeometry,upstreamconditionsandtheenvironmentintowhichthejetisinjected.Ultimately,thejetbreaksdownduetotheinuenceofhydrodynamicinstability,andthisbreak-upbroadlyoccursundertwocategories:largedropformationandnesprayformation.Thesetwobreakupregimesarecontrolledbydifferentphysicalforcesonthejetanditsreactiontoapplieddisturbances,andbetweenthemexistintermediateregimesofbreakup.LiquidjetbreakupinthesubcriticalregimehasbeenextensivelystudiedbeginningwiththepioneertheoreticalworksbyRayleigh[ 42 ]whosuggestedthataroundliquidjetisnotenergeticallystableandtheinstabilityonsetleads,ultimately,tothejetdisintegration.Neglectingtheambientuid,theviscosityofthejetliquid,andgravity,heshowedthatacircularcylindricalliquidjetismostsusceptibletowavelengthsthatare1.437timesthecircumference.Chandrasekhar[ 43 ]accountedfortheliquidviscosityanddensityandconcludedthatviscosityreducesthebreakuprateandincreasesthedropsize.Healsoshowedthatthemechanismofthebreakupiscapillarypinching.ThetheoreticalpredictionsofWeber[ 44 ]whoconsideredtheeffectofliquidviscosityand 91

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ambientgasdensitydidnotmatchwellwiththeexperimentaldataandwasimproveduponwithpartialsuccessbySterlingandSleicher[ 45 ].ItwasrstshownbyTaylor[ 46 ]thattheambientgasdensityhasasignicanteffectonthejetbreakup.Forasufcientlyhighratioofgasdensitytosurfacetensionforceperunitinterfacialarea,dropletsformwhosediameterismuchlessthanthatofthejet.Thismodeofbreakupiscalledatomization.Inthefollowingsection,thedifferentregimesofjetbreakuphavebeendiscussedinbrief. 6.2BreakupRegimesWhenaliquidjetisinjectedintochamberofstagnantgasthroughacircularorice,fourmainregimesofjetbreakupareidentied.Thesearebasedonthedifferencesintheappearanceofthejetastheoperatingconditionsarechanged,andisprimarilyduetotheactionofthedominantforcesonthejet[ 41 ].Theregimescorrespondtodifferentcombinationsofliquidinertia,surfacetensionandaerodynamicforcesactingonthejet,andhavebeennamedas:Rayleigh,rstwind-induced,secondwindinducedandatomizationregimes[ 39 ].PhotographsofthesefourbreakupregimesofthejethavebeenshowninFigure 6-1 .Forlowjetvelocities,thejetbreakupoccursmanyinjectordiametersdownstreamandyieldsdropsofdiameterlargerthanthejet.ThisistheRayleighregimeandthebreakupoccursduetothegrowthofaxisymmetricoscillationsontheliquidjetsurfaceinducedbysurfacetension.Asthejetvelocityisincreasedorotheroperatingconditionsareappropriatelychanged,theinertialeffectsofthesurroundinggasbecomeimportant.Thejetbreaksupintodropswhosediametersareoftheorderofthejetdiameter.Thesurfacetensionforcesareaugmentedbytherelativemotionoftheambientgasandtheliquidjet,andthisacceleratesthebreakupprocess.ThismechanismwaspointedoutbyWeber[ 44 ]andiscalledtherstwind-inducedregime.Withafurtherincreaseinjetvelocity,thedropsformedfromthejetbreakupprocesshaveanaveragediametermuchlessthanthejetdiameter.thebreakupoccursdue 92

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Figure6-1. Breakupregimesofajet:(a)Rayleighbreakup.Dropdiameterslargerthanthejetdiameter.Breakupoccursmanynozzlediametersdownstreamofnozzle.(b)Firstwind-inducedregime.Dropswithdiametersoftheorderofjetdiameter.Breakupoccursmanynozzlediametersdownstreamofnozzle.(c)Secondwind-inducedregime.Dropsizessmallerthanthejetdiameter.Breakupstartssomedistancedownstreamofnozzle.(d)Atomizationregime.Dropsizesmuchsmallerthanthejetdiameter.Breakupstartsatnozzleexit. 93

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totheunstablegrowthofshortwavelengthdisturbancesonthejetsurface.Thewavegrowthiscausedbytherelativemotionofthegasandliquidjet,butitisopposedbysurfacetension.Thisregimeistermedasthesecondwindinducedbreakupregime.Asthejetvelocityisincreasedfurther(orotheroperatingconditionsareappropriatelychanged),thebreakupresultsinasprayformationwhichdivergesimmediatelyfromthenozzleexit.Thespraycontainsdropletswithaveragediametermuchlessthanthejetdiameter.Thisistheatomizationregime,andthemechanismthatcontrolsthishasnotyetbeendeterminedeventhoughseveralhavebeenproposed.Adetailedevaluationofproposedatomizationtheoriesshowsthataerodynamiceffects,liquidturbulence,jetvelocityprolerearrangementeffectsandliquidsupplypressureoscillationscannotaloneexplainthebreakupprocess.However,amechanismthatincludesboththeaerodynamicinteractionandnozzlegeometryeffectswasfoundcompatiblewithearliermeasurements[ 40 ],thoughthespecicprocessbywhichnozzlegeometryinuencesatomizationisstillunidentied.Thenozzleinternaloweffectsareincludedempiricallyinmostbreakuptheoriesandareknowntobeimportantespeciallyforhighspeedjetbreakup.Whenaliquidjetissuedfromanozzledoesnothavesufcientmomentum,acontinuousjetcannotbeformed.Whentheliquiddischargeisincreasedbeyondacertainrate,theintermittentreleaseofdropsturnsintoasteadystreamingjet.Theliquidnearthenozzleappearstobeundisturbed,butwavydisturbancesattheliquidsurfacebecomevisibleatacertaindistancedownstream.Theamplitudeofthewaveincreasesdownstreamandwhenitbecomesequaltothejetradius,therstdropispinchedfromthejet.Thisdistancebetweenthenozzletipandthepointbeforewhichtherstdropisformedistermedastheintactlengthorbreakuplength[ 47 ].Thislengthincreasesalmostlinearlyinitiallyasthejetvelocityincreases.TherateofincreasedecreasesbeforetheintactlengthreachesamaximumasshownbetweenpointsAandBinFigure 6-2 .Furtherincreaseinjetvelocitycausesadecreaseintheintactlength.PointA 94

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markstheendofdrippingandthebeginningofasteadyjet.ThedropsformingbetweenpointsAandBarealmosttwicethatofthejetradius,whilebetweenBandCarenearlythesameasthejetradius.BeyondCthedropletsstartstrippingofffromthesurfaceandandaveragedropletsizebecomessmaller.asthevelocityincreasesbeyondD,thejetiscompletelyatomizedexceptnearthetipwhereasmallcoreofliquidremains,andistermedasaspray.Theaveragesizeofdropletsinaspraydecreasewithincreasingjetvelocity.ThedevelopmentofatomizationbeyondDiscomplexandtheintactlengthcanalsobemadetogrowagainwithaspeciallydesignedoriceedgegeometry. Figure6-2. SchematicdiagramofthejetbreakuplengthLvs.jetvelocityU. 95

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6.3MotivationThemostsignicantfeatureofasupercriticaluidisthedisappearanceofsurfacetension;hencethetermliquidisnolongerapplicable.Thelatentheatdisappearsanduidelementsleavingthejetaregovernedbymassdiffusionratherthanevaporation.Experimentswithuidinjectedinasupercriticalenvironmentclearlyillustratethedifferencebetweensubcriticalandsupercriticalmixing,althoughtheinterpretationoftheresultsmaynotbestraightforward.Sincefollowinginjectiontheuidmixeswiththesurroundinggas,thecriticalpropertiesoftheuidcannotbeconsideredasxedvaluesbutdynamicparametersdependingonthelocalconditions[ 48 49 ].Experimentalstudies[ 9 27 ]suggestedthat,duetothedisappearanceofsurfacetensionandvanishingofevaporationenthalpy,mixingbetweeninjecteduidandsurroundinggasexhibitsgas-gasmixingbehavioroncethecriticalvaluesarereached.Theabsenceofsurfacetensioncausesthediffusionprocesstodominateoverthejetatomization.Variouscomputationalstudies[ 2 3 50 ]suggestthatifthegasandjetdensitiesaresubstantiallydifferentasupercriticaljetbehavesdifferentlyfromitssubcriticalcounterpartsincethedensitydifferencecausesturbulencedamping.Thiscausesittohavealongerunmixedcorelengthcomparedtotheturbulentsubcriticalgaseousjets[ 4 ].Inthecurrentstudy,alinearstabilityanalysishasbeenperformedtounderstandthejetbreakupmechanismsinsubcriticalandsupercriticalenvironmentsforaccompanyingexperimentalcases.Thestabilityanalysishasbeendoneonaviscousjet,showingfeaturessimilartothoseobtainedinearlierstudiesforthesubcriticalcases[ 47 ],buttheanalysisfailstopredictthestabilityatsupercriticalcases.ThisisprimarilyduetothedisappearanceofatermcontainingtheWebernumberinthedispersionequation,whichcausesthesolutiontodivergeindenitely.Hence,anasymptoticanalysishasbeen 96

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suggestedheretopredictthewavenumberofthelargestinstabilityatexceedinglyhighWebernumbers. 6.4TheoryofInviscidStabilityofaViscousJetAbriefreviewofthederivationofthedispersionequationisgivenforlinearstabilityofaroundsymmetricaljetinjectedintoasubcriticalatmosphere.Theanalysisaimstopredictthesurfacewavenumberaccordingtotheinitialandboundaryconditionsofthejet.Figure 6-3 showsaroundjetemergingintoaquiescentatmosphereforsubcriticalandsupercriticalconditions.InFigure 6-3 A,thesubcriticalcaseshowscleardevelopmentofsurfaceinstabilityandwavinesswhileinFigure 6-3 B,thesurfaceofthesupercriticaljetbecomesconsiderablysmootherindicatingalowerexpecteddisturbancewavelength.Thegoverningequationsofmassandmomentumconservationareshown,followingasimilarderivationasSegalandPolikhov[ 27 ].Theliquidjetandthesurroundinggaseousatmosphereareanalyzedseparatelybelow,withtheapplicationofappropriateboundaryconditionswhichassumethat: (a) Thejetisbeinginjectedintoastationarygaseousenvironment. (b) Allperturbationsthatareappliedaresmallandperiodicinspaceandtime. (c) Thejet-gasinterfaceisaperiodicfunction. 6.4.1AnalysisoftheSurroundingEnvironmentThejetisinjectedintoaninertenvironment,whichintheseexperimentsisnitrogen.Theprimaryassumptionsforthegasowarethatitisinviscid,incompressible,nobodyforcesexist,theowisaxiallysymmetricandthedisturbancesaresmall.Hencethegoverningequationsofmass,r-momentumandz-momentumfortheowcanbewrittenasfollows:1 r@ @r(rurg)+@uzg @z=0[ContinuityEquation] 97

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A BFigure6-3. Aroundjetemergingintoaquiescentatmosphereatsubcriticalandsupercriticalconditionshasbeenshown.Ing(A),thesubcriticalcaseshowscleardevelopmentofsurfaceinstabilityandwavinesswhileing(B),thesurfaceofthesupercriticaljetbecomesconsiderablysmootherindicatingalowerexpecteddisturbancewavelength. @urg @t+urg@urg @r+uzg@urg @z=)]TJ /F8 11.955 Tf 13 8.08 Td[(1 g@pg @r[r)]TJ /F3 11.955 Tf 11.95 0 Td[(MomentumEquation]@uzg @t+urg@uzg @r+uzg@uzg @z=)]TJ /F8 11.955 Tf 13.01 8.08 Td[(1 g@pg @z[z)]TJ /F3 11.955 Tf 11.96 0 Td[(MomentumEquation]Whereuindicatesthevelocity,pisthepressureandisthedensity.Subscriptsgandlindicatethegasorliquidphaserespectively.Sincetheowofthesurroundinggasisessentiallypotentialow,istakentobethevelocitypotentialfunction.Hence,the 98

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continuityequationcanbewrittenas:1 r@ @rr@ @r+@2 @z2=0 (6)Aperturbationisappliedtothisvelocitypotentialsuchasfollows:=C1z+F2(r)ei(kz+!t) (6)Substitutedinto( 6 )ityields:1 r@ @r[rF2(r)]=k2F2(r) (6)Thesolutiontothedifferentialequationis:F2(r)=C2K0(kr)+C3I0(kr) (6)HereI0andK0aremodiedBesselfunctionsofrstandsecondkindswhichareexponentiallyincreasinganddecreasingrespectively.Sincethesolutionneedstobeboundedatalltimes,C3=0,asI0(1)tendstoinnity.Thus,thevelocitypotentialcanbewrittenas:=C1z+C2K0(kr)ei(kz+!t) (6)Thisvelocitypotentialisusedtocalculatetheradialandaxialgasvelocitiesandthensubstitutedintothez-momentumequation.Theboundaryconditionthathasbeenusedhereisuzg=)]TJ /F3 11.955 Tf 9.3 0 Td[(W1asrtendsto1,whereW1isthejetexitvelocityatthenozzleandtheco-ordinatesystemhasbeenxedonthejet,thenthefollowingequationisobtainedforthepressuregradient:)]TJ /F7 11.955 Tf 10.49 8.08 Td[(@pg @z=g[!kC2K0(kr)ei(kz+!t)+()]TJ /F3 11.955 Tf 9.29 0 Td[(W1)k2C2K0(kr)ei(kz+!t)] (6) 99

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Thepressuredisturbanceisassumedas:p0g=Pg(r)ei(kz+!t) (6)WhensubstitutedintothepressuregradientequationandsolvedforPg(r),thenalexpressionforthegaspressureis:p0g=igC2K0(kr)(!)]TJ /F3 11.955 Tf 11.95 0 Td[(W1k)ei(kz+!t), (6)Abriefanalysisofthejetow,theinterfacematchingboundaryconditionsandtheformationofthedispersionequationaregivennext. 6.4.2AnalysisoftheInjectedFluidTheprimaryassumptionsofthejetowarethatitisviscous,incompressible,bodyforcesdonotexist,andthatthedisturbancesaresmallandsymmetric.Similarly,thegoverningequationsforthisowcanbewrittenas:1 r@ @r(rurl)+@uzl @z=0[ContinuityEquation]@url @t=)]TJ /F8 11.955 Tf 11.96 8.09 Td[(1 l@pl @r+@2url @r2+1 r@url @r)]TJ /F3 11.955 Tf 13.15 8.09 Td[(url r2+@2url @z2[r)]TJ /F3 11.955 Tf 11.95 0 Td[(MomentumEquation]@uzl @t=)]TJ /F8 11.955 Tf 11.95 8.09 Td[(1 l@pl @z+@2uzl @r2+1 r@uzl @r+@2uzl @z2[z)]TJ /F3 11.955 Tf 11.95 0 Td[(MomentumEquation]Thisowisnowdividedintoapotentialowandaviscousow.Thus:url=urlp+urlv=@ @r)]TJ /F8 11.955 Tf 13.15 8.09 Td[(1 r@ @z (6)uzl=uzlp+uzlv=@ @z)]TJ /F8 11.955 Tf 13.15 8.09 Td[(1 r@ @r (6) 100

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Similarlyasinthecaseofthegasow,theseequationsaresubstitutedintothecontinuityequationtoobtain:1 r@ @rr@ @r+@2 @z2=0 (6)Followingasimilaranalysisasbefore,thepressuredisturbanceinsidethejetcanbeexpressedas:p0l=lC0I0(kr)i!ei(kz+!t) (6)Theconstantsintheaboveequationcanbeeliminatedbyusingtheinterfacematchingboundaryconditions.Therstsuchboundaryconditionisthatthesurfaceco-ordinateofthejetisexpressedas:R1=R+0ei(kz+!t) (6)Moreover,thepressurematchingboundaryconditionsatthejetsurfaceinvolvesthebalanceofnormalpressureforces,viscousforcesandsurfacetensionforces.Thiscanbeexpressedas:pl=pg+2l@url @r+1 R1+1 R2 (6)Whereisthedynamicviscosityandisthesurfacetensionofthejet.Thus,aftersubstitutingtheexpressionsofgaspressureandtheliquidjetpressureintoEquation( 6 )andundergoingadditionalsimplications[ 27 ],thefollowingdispersionrelationisobtained:( !+ k)2I0( k) I1( k))]TJ /F8 11.955 Tf 13.15 8.08 Td[(2i k2 Rel( !+ k)I0( k) I1( k)+I01( k) I1( k)+!2g lK0( k) K00( k))]TJ /F8 11.955 Tf 13.76 8.08 Td[(4 k3 Re2l kI01( k) I1( k))]TJ ET q .478 w 416.47 -538.06 m 420.31 -538.06 l S Q BT /F3 11.955 Tf 416.47 -548.03 Td[(lI01( l) I1( l)+ k Wel(1)]TJ ET q .478 w 411.82 -573.23 m 418.71 -573.23 l S Q BT /F3 11.955 Tf 411.82 -583.2 Td[(k2)=0 (6) 101

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TheReynoldsnumberhasbeendenedas:Rel=(RW1)=andtheWebernumberhasbeendenedas:Wel=(RlW12)=.Thewavenumberandtheradialfrequencyweretransformedtoanon-dimensionalformasfollows: !=0.5(d1=u1), k=0.5kd1and l2= k2+i !2Rel.Equation( 6 )hasalsobeenobtainedby[ 47 ]inaslightlymodiedformforaviscousaxisymmetricallyperturbedjetinjectedintoasurroundinggas.ForReynoldsnumbersof10,000andabove,thefourthtermintherelationcanbeneglectedcomparedtotheothers.Hencethesimpliedformofthedispersionrelationis:( !+ k)2I0( k) I1( k))]TJ /F8 11.955 Tf 13.15 8.09 Td[(2i k2 Rel( !+ k)I0( k) I1( k)+I01( k) I1( k)+!2g lK0( k) K00( k)+ k Wel(1)]TJ ET q .478 w 381.59 -181.29 m 388.48 -181.29 l S Q BT /F3 11.955 Tf 381.59 -191.27 Td[(k2)=0 (6)Thishasalsobeenusedforthesameboundaryconditionsinsubcriticalcasesbyotherresearchers[ 43 51 ].InsupercriticalcaseswhenWeltendstoinnity,thelastterminequations( 6 )and( 6 )tendstozero,andnosolutioncanbefound.Inthefollowingsection,thesolutiontothedispersionequationisgivenwiththegoalofachievingasolutionforexceedinglylargeWebernumbers. 6.5SolutiontotheDispersionEquationThesolutiontothedispersionequationwasfoundnumerically,sincenoanalyticsolutioncouldbefound.Onlyspatialdisturbanceswereconsidered,sinceatlargeWebernumbers,thetemporalvariationsaremuchlesssignicantthanthespatialvariations.Thus,thenon-dimensionalfrequency !wasconsideredtobepurelyreal,whilethenon-dimensionalwavenumberwasselectedas k= kr+i ki.TheinitialrootswereguessedusingGaster'stheorem[ 52 ],whichstates: kr= !r+O(We)]TJ /F5 7.97 Tf 6.59 0 Td[(2l) (6)ThesolutionforthedispersionequationforthejetinjectedatSTPconditionsisshownbelowinFigure 6-4 .Itcanbeseenthatthefastestgrowingdisturbancesarewhen k=2.6)]TJ /F3 11.955 Tf 12.71 0 Td[(i0.034,whichcorrespondsto =1.2,wherethewavelengthhasbeennon-dimensionalizedbasedontheinjectororicediameter. 102

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Figure6-4. SpatialgrowthratedependenceonwavenumberforthejetinjectedatSTPconditions.Re=11,500,We=7000,andg=l=6.2510)]TJ /F5 7.97 Tf 6.59 0 Td[(4fortheexperiment. Thedispersionequation(Equation 6 )hassolutionsonlyforsubcriticalcases,i.e.,caseswherethejetisinliquidphaseandhencesurfacetensionexists.Whenthecriticalpointisgraduallyapproached,thevalueofthesurfacetensiondecreases,andatthecriticalpointitcompletelydisappears.ThisindicatesthattheWebernumbertendstoinnityatthecriticalpoint,causingthelastterminthedispersionequationtobecomezero.Nonumericalsolutioncouldbefoundforthiscasesincetheconvergencecriterionisnotmet.Thus,toquantifythestabilityofthejetatcriticalconditions,thecriticalpointwasapproachedhereasymptotically.Tounderstandhowthesolutionchangesastheowconditionsapproachsupercriticalconditions,thesurfacetensionwasgraduallyreduced,i.e.,theWebernumberwasgraduallyincreased.TheplotshowninFigure 6-5 belowshowsthestabilitycurvesforWebernumbersupto30000.Fortheaboveplots,theReynoldsnumberandthedensityratiohavebeenkeptxedattheSTPvalues,implyingthatallthecoefcientsofthedispersionequationwaskeptxedexcepttheWebernumber.Theprocessofreachingthecriticalconditions 103

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Figure6-5. CurvesforWebernumbersrangingfrom7000to30000.Thepeakdisturbancewavenumberforeachcurvehasalsobeenshown. asymptoticallyinvolvedobtainingthestabilitycurvesforincreasinglyhighWebernumbersandplottingthetrendsofthemostamplieddisturbance,whichisthepeakofthestabilitycurve.OnlyalimitednumberofstabilitycurveshavebeenshownintheplotinFigure 6-5 .Figure 6-6 isaplotofthemostamplieddisturbancewavenumberagainstWebernumberataReynoldsnumberof25000.TheWebernumbershavebeenincreaseduptoonehundredmillion,whichisconsideredlargeenoughtoapproximatesupercriticalcases.Fivedifferentgas-to-injectantdensityratioshavebeenplottedseparately,andallofthemshowasimilartrend.ThewavenumbersincreaseverysteeplyuptoWebernumbersofabout100000,andthengraduallyreachanasymptoteafterWe=1000000.Sincethiswavenumbercorrespondstoanextremelysmallvalueofthedisturbancewavelength,itindicatesthatinsupercriticalconditions,thejetisunstabletoanyperturbationmadetoitsow.ThedisturbancewavelengthsolutionisapproachedasymptoticallyataroundthesameWebernumberforalldensityratios. 104

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Figure6-6. Asymptotictrendofthepeakgrowthratevs.WeforRe=25000.Thesymbolsindicatevedifferentdensityratios,chosenforaccompanyingexperimentalcases. SimilarobservationswerealsomadeforotherReynoldsnumbers.ThevariationoftheasymptoticwavenumberwithdensityratioforvaryingReynoldsnumbersisshowninFigure 6-7 .Asseenfromtheplot,thewavenumbervarieslinearlywiththedensityratioforallthreecasesassumedhere.ThelinesbecomesteeperastheReynoldsnumberisincreased,indicatingthatthedisturbancewavelengthdecreasesforthesamevalueofthedensityratio.ThisismostlikelyduetothestrongerresponsetoinertialforcesathigherReynoldsnumbers.Inallthesecases,themostamplieddisturbancewavelengthrangesfrom10-20microns,andhencethejetinthesupercriticalphaseisunstabletoevenverysmallperturbationsinitsow.Thisalsoexplainsthesmootherappearanceofthejetnearthenozzlewheninjectedintosupercriticalenvironments,asseenfromearlierexperiments.Thedifcultyofobtainingasolutiontothedispersionequationisfurtheremphasizedbythefactthatevenwhileusingtheasymptoticapproach,solutionsarefoundforonlyalimitednumberofdensityratiosduetonumericalconvergence 105

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issuesatsuchhighWebernumbers.OurresultsarehencelimitedtoowswithReynoldsnumbersofupto40000andchamber-to-injectantdensityratioofupto0.015. Figure6-7. Variationofasymptoticwavenumberwithdensityratio.ThelinesbecomesteeperastheReynoldsnumberisincreased,indicatingthatthedisturbancewavelengthdecreasesforthesamevalueofthedensityratio. 6.6ConclusionsThus,alinearstabilityanalysisofaroundsymmetricaljetinjectedintoasupercriticalenvironmentwasundertakenfollowinganasymptoticapproachtoreachthesolution.TheasymptoticapproachinvolvedplottingthemostampliedwavenumberagainstWebernumbertoobserveanytrends.ThecurvesreachedanasymptoteatWebernumbersofaround1000000.ThiswasobservedforallthreeselectedReynoldsnumbercases,andthevedifferentdensityratios.Theasymptoticwavenumbersfortheselectedcasescorrespondtodisturbancewavelengthsrangingfrom10to20microns.Itcanthusbeinferredthatthejetinjectedintoasupercriticalenvironmentisunstabletoanysmallperturbationstoitsow.Thisalsoexplainsthesmoothappearanceof 106

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thejetnearthenozzlewheninjectedatsupercriticalconditionsasseeninpreviousexperiments.ItwasalsoobservedthatforaspecicReynoldsnumber,themostamplieddisturbancewavelengthdecreaseswithdensityratio.Similarly,foraspecicdensityratio,thedisturbancewavelengthdecreaseswithReynoldsnumber.ThisismostlikelyduetoastrongerresponsetoinertialforcesathigherReynoldsnumbers. 107

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CHAPTER7RECOMMENDEDFUTURESTUDIESTheresearchtillnowhasfocusedprimarilyonthesubcriticalandsupercriticalmixingcharacteristicsofasingleroundjetinjectedintoanenvironmentconsistingofthevaporofthesamespeciesorofadifferentspecies.ThetestconditionsforthebinaryspeciesmixingexperimentshavebeenvariedfromPr=0.20to1.95andTr=0.66to1.22,andforthesinglespeciesexperimentstheconditionsvaryfromPr=0.17to1.22andTr=0.66to1.04.Whilethestudydescribedherecoverssufcientlythebinaryspeciesdomainoverallfourmixingregimes(subcritical-into-subcritical,subcritical-into-supercritical,supercritical-into-subcriticalandsupercritical-into-supercritical),thereisaneedtocoveralltheregimesforthesinglespecies;onlythersttwowereinvestigatedhere.Oneadditionaltopicofinterestistheidenticationofanon-dimensionalparameterthatwillcollapsethecorelengthsandjetspreadinganglesbetterwhentherearesignicantvariationsininjectionvelocity,sincethecasesconsideredinthisstudycoveredanarrowvelocityrange.Todate,thereisalargespreadinresultsobtainedindifferentstudies.Reynoldsnumbermightneedtobeincorporatedalongwithdensityratioinsomeform,astheothernon-dimensionalparametersliketheWebernumberandOhnesorgenumberceasetoexistatsupercriticalconditionsduetotheabsenceofsurfacetension.Anotherareathatcanbeexpandedisintermsofspatialresolutionofimagesobtained.Decreasingcamerafocusingdistanceorbyusingahigherspatialresolutioncamera,thejet-gasinterfacecanbecloselymonitored.Itappearsthatmostofthephysicallyinterestingprocessestakeplaceinthedirectvicinityoftheinterfaceandhenceitisreasonabletozoomintothisarea.Thestudyofsupercriticalmixingcanbefurtherextendedfromsinglejetinjectiontoco-axialinjection.Thecurrentexperimentalfacilityisfullycapableofco-axialinjection 108

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experimentswiththereplacementoftheinjector.Eitherathirdelementcouldbeusedfortheco-axialjet,andhencemakingitathreespeciessystem,oritcanstillremainabinarysystemwhereN2oranyotherinertgascouldbeusedastheco-axialjetandthesurroundingenvironment,whileuoroketoneisinjectedasthecentraljet.Thecomparisonofcorelengthsandjetdivergenceangleswiththeothertwomixingcasescouldrevealinterestingresultsaboutthefundamentalfeaturesofmulti-speciesmixing. 109

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APPENDIXAMATLABSCRIPTSUSEDFORDATAPROCESSINGTheMatlabscriptsusedfordataprocessingareprovidedhere: Background.m:Programusedfortheeliminationofbackgroundemissions.Thisprogramcreatesabackgroundintensitylecalled`background.mat'andmustbeexecutedpriortoanyimageanalysis. Beam Correction.m:Functiontocalculatethevariationinthelasersheetspatialprole.Thefunctioncorrectsforthelaserintensityvariationfromtoptobottom,andalsoalongthelengthtraversedbythelasersheetasitisabsorbedbymultiplephases.Ittakesintoaccounttheabsorptionthroughthegasphaseusingthecalibrationoftheabsorptioncoefcient,andalsotheabsorptionthroughtheliquidphasethroughuser-denedliquidabsorptioncoefcients. Core Length.m:Functiontocalculatethejetpenetrationlength(corelength).Thecorelengthiscalculatedasfollows:Thejetisdivided(usingthewidthoftheinjector)intosub-matricesandtheaveragedensityiscalculatedforeach.Usingtheeigenvaluesandaveragedensityofeachsub-matrix,themostsignicantchangeindensityalongthecenter-lineofthejetisfound.Thislocationsigniestheendofthecore,anditsdistancefromtheinjectorisdenedasthecorelength. Data Analysis.m:Programtoperformdataanalysisforaspecicsetoftestsbycallingfunctionssuchascorelength,spreadingangle,andmoviemaker.Theprogramcalculatesthemean,standarddeviationofeachquantityandalsoeliminatesanypossibleoutliersinthedata.Thedataisthenwritteninanexcelspreadsheetwhosecellrangehastobespeciedbytheusereachtime. Divergence Angle.m:Functiontocalculatethejetdivergenceanglebyusingthelimitsofthejetboundaryandapplyingalineartfromtheinjectoruptoone-thirdsofthejetlength.Theslopesofthesetsareusedtodeterminetheangle. Goodeqn liq.m:Functiontocalculatethedensityoftheliquid/supercriticalphaseapproachedbyheatingtheliquidusingthePRSVequationofstate.DiffersonlyslightlyatandbeyondthecriticalpointfromthevaluesobtainedbyGoodeqn vap.m. Goodeqn vap.m:Functiontocalculatethedensityofthevapor/supercriticalphaseapproachedbyheatingthevapor,alsousingthePRSVequationofstate.DiffersonlyslightlyatandbeyondthecriticalpointfromthevaluesobtainedbyGoodeqn liq.m. Idealgas.m:Programtocalculatethedensityofnitrogeninbinaryspeciesmixingexperiments,usingtheidealgasequationofstate. 110

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Image Processor.m:Programforconvertingtherawimageleintoquantieddensityanddensitygradientimageswhichareassignedcolorsbasedonvalue.TheprogramcallsthefunctionBeam Correction.mandusesthemodiedlasersheettocorrecttheimageforanyspatiallossoflaserintensity.Itcreatesthe`*d.mat'(densitymatrix),`*g.mat'(densitygradient)and`*.emf'(image)lesinthe`ProcessedFiles'folderofeachexperiment. Jet boundary latest.m:Functiontocalculatethejetboundaryofeachimage.Ittakesintoaccountthelaserintensityvariationfromtoptobottomonly,andworksbasedonthresholdvaluesprovidedbytheuser. Laser Proles.m:Programusedtoviewthelaserprolevariationinbothdirectionsofthesheet.Thiswasoriginallyusedtodeterminetheabsorptioncoefcientofuoroketoneinthegasphaseforvaryingdensitiesforlasercalibrationandabsorptioncross-sectiondetermination,usingthe`cftool'function. Movie Maker.m:Functionusedtocreatemovielesinthe`*.avi'formatfromthedensityimageles.Theframeratehasbeenkeptto2framespersecond,andthelengthofeachvideodependsonthenumberofworkableprocessedimages.Acompressioncodeccalled`Cinepak'isusedherethatmayormaynotworkbasedontheversionofMATLABbeingused. Run Preview.m:Programthatconvertsalltherawdataintoaprocessedandorganizedtextlenamed`ProcessedData.txt'.Thecolumnsofthistextleincludetime,injectiontemperature,chambertemperature,camerasynchronization,chamberpressure,injectionpressure,andinjectantowrate. Spreading Angle.m:Functionthatcalculatesthejetspreadingangle.Thisfunctionisusuallycalledbythe`Data Analysis.m'program,andusesthefunction`Divergence Angle.m'duringthecalculation. Stability Analysis.m:ProgramtocalculatethestabilitycurvesforspeciedWebernumbers.Thisprogramsolvesthedispersionequationusinganiterativemethod,andworksbetteriftherangeofthesolutionisclosetotheactualsolution.Theoutputconsistsofplotsofkivs.krandidentiesthemostamplieddisturbancewavelength.ThisvalueislaterusedtocalculatethestabilityforsupercriticalcasesusingtheasymptoticmethodwithincreasingWebernumbers. Test Conditions.m:Programtodeterminethetestconditionsduringasetofexperiments.Ithastheabilitytocorrectowmeterdatausingtemperaturedataiftheowmeterdidnotworkforthatspecicrun.Thenalresultiswritteninaexcelspreadsheetandincludesthemassowrateandvelocityforeachrun.Multipleexperimentalconditionscanbeanalyzedatonce. 111

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Background.m clearall[filename,pathname]=uigetfile(`*.*',`Findbackgroundimage',`D:\Till_December_2011\Tests\');location=[pathnamefilename];iffilename==0fprintf(`Nofilewasselected!\n')returnendX=double(imread(location,1));vert=length(X(:,1))horz=length(X(1,:))sum=zeros(vert,horz);know=imfinfo(location);nimg=length(know);total=0;fork=1:nimgX=double(imread(location,k));sum=sum+X;total=total+1;endbackground=sum/total;figure(1);image(background*64/max(max(background)));doit=input(`Wouldyouliketosavethisimagey/n?',`s');ifdoit==`y'eval([`save'pathname(1:end)`\background.matbackground']);elsefprintf(`Thiswasnotsaved.\n');end 112

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Beam Correction.m %ModifiedLaserSheetProgram%%Takesintoaccountthelossofintensitythroughthejet%%Thismatrixhastobeusedforpoint-by-pointdivisionwiththeImage%%PreparedbyArnabRoyon20thOctober,2011%function[mod_laser,Origin_new,degree]=Beam_Correction(pathname,origin,Noz)%DefiningthelocationoftheLaserSheetProfileandBackgroundImage%location=strcat(pathname(1:42),`Laser_Sheet_Profile\Laser_Sheet.TIF');bckgrdlocate=[pathname(1:42)`Background\background.mat'];bckgrd=load(bckgrdlocate);background=bckgrd.background;size(background);%CreatinganAverageLaserSheetProfile%know=imfinfo(location);n=length(know);sum1=0;fori=1:nX=double(imread(location,i));X1=X;X1=X1-background;sum1=sum1+X1;endprofile=sum1/n;[row,col]=size(profile);avgprof=mean(profile(:,1:25)')';profile=avgprof/max(avgprof);profile=profile(Noz:end);%Findingthestartandtheendpointsofthejetforeachrow%location2=strcat(pathname,`Test.TIF');[start,finish,imgtemp]=Jet_boundary_latest(location,location2,origin,Noz);clrimg=imgtemp*64/max(max(imgtemp));mymap=(load(strcat(location(1:end-15),`mymap.txt')));ans1=`n';while(ans1==`n')degree=input(`Angleofrotation(clockwise):');clrimg1=imrotate(clrimg,-degree,`crop');figure(3)colormap(mymap);image(clrimg1);gridon;gridminor;ans1=input(`Satisfiedwithimagerotation?(y/n):',`s');endOrigin_new=input(`Enterneworigin:'); 113

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%CreatingtheModifiedLaserImagewithexponentialdecaysaftertheJetstartsandends%%location3=strcat(pathname,'ProcessedData.txt');%Pdata=load(location3);%samples=length(Pdata);%TimeIndex=1;%gradflow=gradient(Pdata(:,LiqFlowCol));%forl=1:samples%if(gradflow(l)==max(gradflow))%TimeIndex=l;%break;%end%end%LiqTemp=mean(Pdata(TimeIndex:end,LiqTempCol));%LiqPres=mean(Pdata(TimeIndex:end,LiqPresCol));%ChmTemp=mean(Pdata(TimeIndex:end,ChmTempCol));%ChmPres=mean(Pdata(TimeIndex:end,ChmPresCol));%alpha_gas=(goodeqn_vap(Tg,Pg)*4e-5)+0.00092;%alpha_liq=(goodeqn_liq(Tl,Pg)*1.2e-6)+0.0029;%Forheatedjetinjectionalpha_liq=0.003;%Forcoldjetinjectionalpha_gas=0;%Forbinaryinjectionans2=`n';while(ans2==`n')%Usingthenewlyderivednon-linearformulaforlaserabsorptioninsidethejetandbeyondit%fork=1:row-Nozfori=1:start(k)mod_laser(k,i)=profile(k)*4.55*(1-exp(-.25*exp(-alpha_gas*i)));endendfork=1:row-Nozfori=start(k):finish(k)-1mod_laser(k,i+1)=mod_laser(k,start(k))*(1-exp(-.25*exp(-(alpha_liq*(i-start(k)))-alpha_gas*start(k)))))/(1-exp(-.25*exp(-alpha_gas*start(k))));endfori=finish(k)+1:colmod_laser(k,i)=mod_laser(k,finish(k))*(1-exp(-.25*exp(-(alpha_gas*(i-finish(k)))-(alpha_liq*(finish(k)-start(k)))-(alpha_gas*start(k)))))/(1-exp(-.25*exp(-(alpha_liq*(finish(k)-start(k)))-(alpha_gas*start(k)))));endendmod_laser=mod_laser/max(max(mod_laser));clrimg_new=clrimg(1:end-1,:)./mod_laser;clrimg_new=imrotate(clrimg_new,-degree,`crop');clrimg_new=clrimg_new/max(max(clrimg_new)); 114

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figure(3)image(clrimg_new*64);colormap(mymap);count=1;forl=1:25:row-Noz-24avg_profile(count,:)=mean(clrimg_new(l:l+24,:));grad_profile(count,:)=gradient(avg_profile(count,:));count=count+1;endcount=count-1;xlimit1=round(0.15*col);xlimit2=round(2*Origin_new-0.15*col);figure(4)plot((xlimit1:xlimit2),avg_profile(:,xlimit1:xlimit2)');gridon;holdon;plot(ones(count,1)*Origin_new,(0:1/(count-1):1),`r');holdoff;figure(5)plot((xlimit1:xlimit2),grad_profile(:,xlimit1:xlimit2)');gridon;holdon;plot(ones(count,1)*Origin_new,(0-max(max(grad_profile)):2*max(max(grad_profile))/(count-1):max(max(grad_profile))),`r');holdoff;ans2=input(`Satisfiedwithimagequality?(y/n):',`s');alpha_liq=alpha_liq+0.0005;enddisp(strcat(`Thealphausedforthisinjectioncasewas:',num2str(alpha_liq-0.0005)));figure(6)plot(mod_laser');title(`Correctedlaserprofileimage');xlabel(`Length(Pixels)');ylabel(`ActualIntensity');sum=0;fori=1:length(mod_laser)sum=sum+(mod_laser(i,:)/max(mod_laser(i,:)));endsum=sum/length(mod_laser);figure(7);plot(sum);title(`Meannormalizedlaserintensityfromlefttoright');xlabel(`Length(Pixels)');ylabel(`NormalizedIntensity'); 115

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Core Length.m functioncore_std=Core_Length(location,count,origin)JetDia=0.2;per1=0.1;diffeig1=0.9;core(1:count)=0;fori=1:countclearoutlinecoremaybelengthDensityAVGHVDMgHgHrootsgHrootsrxy1y2y3p1p2p3limitrcountercjkgrr1startfinishcenterlcount1count2;img=load(location(i,:));Density=img.DensMatrix;mymap=load([location(1,1:end-54)`Laser_Sheet_Profile\mymap.txt']);[rowcol]=size(Density);count1=0;start=origin-25;finish=origin+25;width=50+1;width2=50+1;height2=10+1;center=origin;forr=1:length(Density)-width-1M(1:width,1:width)=Density(r:r+width-1,center-((width-1)/2):center+((width-1)/2));M2(1:height2,1:width2)=Density(r:r+height2-1,center-((width2-1)/2):center+((width2-1)/2));AVG(r)=sum(M2(:))/numel(M2);[V,D]=eig(M);H(r)=abs(det(eye(size(D))+D));ifAVG(r)<0.5*max(AVG);breakendendx=1:r;p1=polyfit(x,log(H(1:r)),20);y1=p1(1)*x.^20+p1(2)*x.^19+p1(3)*x.^18+p1(4)*x.^17+p1(5)*x.^16+p1(6)*x.^15+p1(7)*x.^14+p1(8)*x.^13+p1(9)*x.^12+p1(10)*x.^11+p1(11)*x.^10+p1(12)*x.^9+p1(13)*x.^8+p1(14)*x.^7+p1(15)*x.^6+p1(16)*x.^5+p1(17)*x.^4+p1(18)*x.^3+p1(19)*x.^2+p1(20)*x.^1+p1(21)*x.^0;gH=gradient(y1);gHroots=roots([20*p1(1)19*p1(2)18*p1(3)17*p1(4)16*p1(5)15*p1(6)14*p1(7)13*p1(8)12*p1(9)11*p1(10)10*p1(11)9*p1(12)8*p1(13)7*p1(14)6*p1(15)5*p1(16)4*p1(17)3*p1(18)2*p1(19)1*p1(20)]);gHrootsr=floor(abs(gHroots));counter=1; 116

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g=length(gHrootsr);whileg>=1if(g>1&&gHrootsr(g)==gHrootsr(g-1)&&(gHrootsr(g)1)&&(gHrootsr(g)=.025);per=per1;while(core1<=0)&&(per<=0.99)forj=2:counter-2if(abs(H20(j)-H20(j-1))>diffeig&&AVG(coremaybe(j))/AVG(coremaybe(j-1))0.1*row)core1=coremaybe(j);breakendendper=per+.025;enddiffeig=diffeig-.025;endcore2=0;per=per1;while(core2<=0)&&(per<=0.99)diffeig=diffeig1;while(core2<=0)&&(diffeig>=.025);forj=2:counter-2if(abs(H20(j)-H20(j-1))>diffeig&&AVG(coremaybe(j))/AVG(coremaybe(j-1))0.1*row)core2=coremaybe(j);breakend 117

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enddiffeig=diffeig-.025;endper=per+.025;endcore(i)=min(core1,core2)/(JetDia/0.0044);%Normalizewiththeinjectordia.figure(1);colormap(mymap);scale=64/max(max(Density));image(Density*scale);holdon;plot(1:col,core(i)*(JetDia/0.0044));end%Eliminatingoutliersandplotting%cnt=1;fori=1:countif(abs(core(i)-mean(core))
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Data Analysis.m clcclearall;closeall;holdoff;JetDia=0.2;pathname=`G:\Till_December_2011\Tests\';[filename1,pathname1]=uigetfile(`*.mat',`PickfirstimagefiletoProcess',pathname);[filename2,pathname2]=uigetfile(`*.mat',`PicklastimagefiletoProcess',pathname1);start=str2double(filename1(1:2));finish=str2double(filename2(1:2));count=1;fori=start:finishif(i<10)location(count,:)=[pathname1strcat(`0',num2str(i)),`d.mat'];elselocation(count,:)=[pathname1strcat(num2str(i)),`d.mat'];endfid=fopen(location(count,:));if(fid~=-1)count=count+1;endendcount=count-1;fprintf(`Therearethe%dfilelocationsyouhavechosen:\n',count);disp(location);Origin=input(`Entertheorigin:');warningoff;core_std=Core_Length(location,count,Origin);angle_std=Spreading_Angle(location,count,Origin);core_angle=[core_stdangle_std];xlswrite(`G:\Till_December_2011\Tests\Sup_Sub.xlsx',core_angle,`Sheet1',`I67:L67');Movie_Maker(location,count); 119

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Divergence Angle.m %Spreadinganglecalculationfunction%%PreparedbyArnabRoyon1stApril,2012%function[alpha1,alpha2]=Divergence_Angle(clrimg,origin,row)%Storingtheboundariesofthejetforeachrow%initial(1:row)=0;fori=1:rowforj=1:originif((clrimg(i,j)>0)&&(clrimg(i,j+1)>0))initial(i)=j;break;endendendfinal(1:row)=0;fori=1:rowforj=311:-1:originif((clrimg(i,j)>0)&&(clrimg(i,j-1)>0))final(i)=j;break;endendendplot(final,1:row,`k');plot(initial,1:row,`r');p2=polyfit((1:round(row/3)),initial(1:round(row/3)),1);y2=p2(1)*(1:round(row/3))+p2(2);p3=polyfit((1:round(row/3)),final(1:round(row/3)),1);y3=p3(1)*(1:round(row/3))+p3(2);plot(y2,(1:round(row/3)));plot(y3,(1:round(row/3)));alpha1=atan(p2(1));alpha2=atan(p3(1)); 120

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Goodeqn liq.m functiondensity=goodeqn_liq(To,Po)%Peng-Robinson-Stryjek-Veraequationofstateappliedtofluoro-ketone%T=(0:1:600)'+273.15;R=8.3144;Tc1=441.81;Pc1=18.646E5;rhoc1=639;omega1=0.471;kappa11=0.052;Mw1=.316046;%FKpropertiesmolarweightkg/m^3Tc2=748;Pc2=40.5E5;rhoc2=315.29;omega2=0.30295;kappa12=0.03297;Mw2=.12817;x1=1;x2=0.0;%molarfractionsMw=x1*Mw1+x2*Mw2;rho=0.1:1:1800;V=Mw./rho;%m3/moleb1=0.077796*R*Tc1/Pc1;b2=0.077796*R*Tc2/Pc2;Tr1=T/Tc1;Tr2=T/Tc2;kappa01=0.378893+1.4897153*omega1-0.1713185*omega1^2+0.0196554*omega1^3;kappa02=0.378893+1.4897153*omega2-0.1713185*omega2^2+0.0196554*omega2^3;kappa1=kappa01+kappa11*(1+Tr1.^0.5).*(0.7-Tr1);kappa2=kappa02+kappa12*(1+Tr2.^0.5).*(0.7-Tr2);alpha1=(1+kappa1.*(1-Tr1.^0.5)).^2;alpha2=(1+kappa2.*(1-Tr2.^0.5)).^2;a1=alpha1*0.457235*(R*Tc1)^2/Pc1;a2=alpha2*0.457235*(R*Tc2)^2/Pc2;a=x1^2*a1+2*x1*x2*sqrt(a1.*a2)+x2^2*a2;b=x1*b1+x2*b2;p=R*T*(1./(V-b))-a*(1./(V.*(V+b)+b*(V-b)));pb=p/10^5;To=To+273.15;[vl,Ind]=min(abs(T-To));fori=length(pb(Ind,:)):-1:1if(pb(Ind,i)-Po)<0breakendenddensity=rho(i)*.97; 121

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Goodeqn vap.m functiondensity=goodeqn_vap(To,Po)T=(0:1:600)'+273.15;R=8.3144;Tc1=441.81;Pc1=18.646E5;rhoc1=639;omega1=0.471;kappa11=0.052;Mw1=.316046;%FKpropertiesmolarweightkg/m^3Tc2=748;Pc2=40.5E5;rhoc2=315.29;omega2=0.30295;kappa12=0.03297;Mw2=.12817;x1=1;x2=0.0;%molarfractionsMw=x1*Mw1+x2*Mw2;rho=0.1:1:1800;V=Mw./rho;%m3/moleb1=0.077796*R*Tc1/Pc1;b2=0.077796*R*Tc2/Pc2;Tr1=T/Tc1;Tr2=T/Tc2;kappa01=0.378893+1.4897153*omega1-0.1713185*omega1^2+0.0196554*omega1^3;kappa02=0.378893+1.4897153*omega2-0.1713185*omega2^2+0.0196554*omega2^3;kappa1=kappa01+kappa11*(1+Tr1.^0.5).*(0.7-Tr1);kappa2=kappa02+kappa12*(1+Tr2.^0.5).*(0.7-Tr2);alpha1=(1+kappa1.*(1-Tr1.^0.5)).^2;alpha2=(1+kappa2.*(1-Tr2.^0.5)).^2;a1=alpha1*0.457235*(R*Tc1)^2/Pc1;a2=alpha2*0.457235*(R*Tc2)^2/Pc2;a=x1^2*a1+2*x1*x2*sqrt(a1.*a2)+x2^2*a2;b=x1*b1+x2*b2;p=R*T*(1./(V-b))-a*(1./(V.*(V+b)+b*(V-b)));pb=p/10^5;To=To+273.15;[vl,Ind]=min(abs(T-To));fori=1:length(pb(Ind,:))if(pb(Ind,i)-Po)>0breakendenddensity=rho(i)*.97;Idealgas.m functiondensityN2=idealgas(T,P)Ru=8.314;Mw=28;Tch=T+273.15;Tch=T+273.15;Pch=P*101.325;densityN2=(Pch*Mw)/(Ru*Tch); 122

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Image Processor.m %Modified`run_processor.m'Programforsinglecomponentinjection%%Accountsforpoint-by-pointdivisionwiththeLaserImage%%PreparedbyJohnGaebler.ModifiedbyArnabRoyon7thApril,2010%clearall;closeall;%DeclarationofVariablesandInitialization%DataCols=7;CamHz=10;x=0.044;%mmperonepixely=0.044;%mmperonepixelJetDia=0.2;%incmTimeCol=1;%Colstandsforcolumn,inProcessedData.txtLiqTempCol=2;ChmTempCol=3;ExtSyncCol=4;ChmPresCol=5;LiqPresCol=6;LiqFlowCol=7;ExtSyncSpikeLev=4;TotalFrames=50;%ChoosingtheFilestoprocess%pathname=`G:\Till_December_2011\Tests\Data_05_25_12\';[filename,pathname]=uigetfile(`*.*',`PickProcessedData.txtfilefordataruntoProcess',pathname);%Loadingthenecessaryfilesfromtheirrespectivelocations%location=[pathnamefilename];Pdata=Manual_Fudge(location);TotalFrames=round(length(Pdata)/1100);samples=length(Pdata);%Totalnumberofsamplesstep=Pdata(2,TimeCol);%Thispositionisfirststepfromtime(1)=0Noz=input('\nEnterstartofnozzle:');Origin_init=input('Enterorigin:');[weight,Origin,degree]=Beam_Correction(pathname,Origin_init,Noz);[row,col]=size(weight);xlimit=round(0.45*col);ylimit=round(0.9*row);weight=weight(1:ylimit,:);holdoff;location=[pathname(1:42)`Background\background.mat'];eval([`load'location`background'])%Loadingthebackgroundimagebackground=background(Noz:ylimit+Noz-1,:);ImageLocate=[pathname`Test.TIF'];location=[pathname(1:42)`Laser_Sheet_Profile\mymap.txt']; 123

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mymap=load(location);%Loadingthecolormaptobeusedforimagesclearlocationfid%Findingtheindexofeachimagewrt'ProcessedData.txt'%Frame=0;LengthCounter=0;check=0;fork=1:samplesifPdata(k,ExtSyncCol)>=ExtSyncSpikeLevLengthCounter=LengthCounter+1;IndexOfSpike(LengthCounter)=k;check=1;elseifcheck==1Frame=Frame+1;FrameIndex(Frame)=round(mean(IndexOfSpike));check=0;LengthCounter=0;clearIndexOfSpikeendendend%CalculationoftheTimeIndex%TimeIndex=1;%forl=1:samples%if(Pdata(l,LiqFlowCol)==max(Pdata(:,LiqFlowCol)))%TimeIndex=l;%break;%end%endgradflow=gradient(Pdata(:,LiqFlowCol));forl=1:samplesif(gradflow(l)==max(gradflow))TimeIndex=l;break;endendclearLengthCountercheckiifFrame==0%checkifthereareanyimagespresentfprintf(`Therearenoimagesassociatedwiththisdata.\n')fprintf(`Checktest.TIFandExternalSyncChannelinDAQ\n')returnendInitialFrame=TotalFrames-Frame+1;creenSize=double(imread(ImageLocate,1));X=0:x:(length(ScreenSize(1,:))-1)*x;%convertingpixelstomm. 124

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Y=0:y:(length(ScreenSize(:,1))-1)*y;%convertingpixelstomm.clearScreenSizescrsz=get(0,`ScreenSize');%Analysingeachimageseparatelystartshere%forpic=1:FrameCurrent=InitialFrame+pic-1;ifCurrent>TotalFramesbreakendImageMatrix=double(imread(ImageLocate,Current));ImageMatrix=ImageMatrix(Noz:ylimit+Noz-1,:);ImageMatrix=ImageMatrix-background;%Imageisweightedpoint-by-ImageMatrix=ImageMatrix./weight;%pointusingLaserWeightmatrix%Checkforneedtoprocessthefile%ImageMatrix1=imrotate(ImageMatrix,-degree,`crop');figure(1)YZ=ImageMatrix1*64/max(max(ImageMatrix1));Pdata(FrameIndex(pic),TimeCol);colormap(mymap);image(YZ);%xz=input(`Doyouwantthisimagetobeprocessed?(y/n)(1/anything)');%ifxz~=1%clearYZ%close(figure(1))%endxz=1;%ImageProcessingstartshere%%ConvertseachimagefromIntensityMatrixtoDensityMatrix%if(xz==1)clearYZclose(figure(1))count1=1;high=0;form=1:5:length(ImageMatrix)/2mat_avg(count1,:)=mean(ImageMatrix(m:m+4,:));if(count1>1)if(max(mat_avg(count1,:))>high)pos=count1;high=max(mat_avg(count1,:));endendcount1=count1+1;endtop_avg=mat_avg(pos,:);form=1:length(top_avg) 125

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if(top_avg(m)==max(top_avg))loc=m;endendif(max(top_avg)==0)loc=Origin;endleft=loc-5;right=loc+5;RefInt=mean(top_avg(left:right));%StoringtheTemperature,Pressure,VelocityandMassFlowrate%Time=Pdata(FrameIndex(pic)+TimeIndex,TimeCol);LiqTemp=Pdata(FrameIndex(pic)+TimeIndex,LiqTempCol);ChmTemp=Pdata(FrameIndex(pic)+TimeIndex,ChmTempCol);ChmPres=Pdata(FrameIndex(pic)+TimeIndex,ChmPresCol);LiqPres=Pdata(FrameIndex(pic)+TimeIndex,LiqPresCol);MassFlow=1.61*Pdata(FrameIndex(pic)+TimeIndex,LiqFlowCol);%g/sRefDen=goodeqn_liq(LiqTemp,ChmPres);%Units(kg/m^3)Velocity=10*MassFlow/(RefDen*(pi/4)*JetDia^2);%Units(m/s)%CalibratingImageIntensityMatrixtoDensityMatrix%%%%DensitySlope=RefDen/RefInt;%CalibrationnumberDensMatrix=ImageMatrix*DensitySlope;%MatrixofDensitiesDensMatrix1=DensMatrix;fork=1:length(DensMatrix(1,:))DensMatrix1(:,k)=smooth(DensMatrix(:,k),5);end%SmootheningtheDensityMatrixfork=1:length(DensMatrix(:,1))DensMatrix1(k,:)=smooth(DensMatrix1(k,:),5);endCutOff_low=0;%SettingthecutoffsforthedensityCutOff_high=RefDen;%if(ChmTemp>LiqTemp)%CutOff_high=RefDen;%else%CutOff_high=goodeqn_liq(ChmTemp,ChmPres);%endfork=1:length(DensMatrix(1,:))forj=1:length(DensMatrix(:,1))ifDensMatrix(j,k)CutOff_high 126

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DensMatrix(j,k)=CutOff_high;endendendsf=64/max(max(DensMatrix));clearij;X=X-X(Origin);Y=Y-Y(Noz);%FormingDensityGradientfromtoDensityMatrix%[DX,DY]=gradient(DensMatrix1,x,y);clearDensMatrix1GradMatrix=sqrt(DX.^2+DY.^2);%FormingtheGradientMatrixclearDXDYgmcv=sort(reshape(GradMatrix,numel(GradMatrix),1));gma=numel(GradMatrix)*x*y;RefGrad=gmcv(round(length(gmcv)*(1-1/gma)));mingrad=0;fork=1:length(GradMatrix(1,:))forj=1:length(GradMatrix(:,1))ifGradMatrix(j,k)RefGradGradMatrix(j,k)=RefGrad;endendendsf2=64/max(max(GradMatrix));DensMatrix=imrotate(DensMatrix,-degree,`crop');GradMatrix=imrotate(GradMatrix,-degree,`crop');trim=Noz+round(tan(degree*pi/180)*(col-Origin));%Plottingtheimageandsavingthefiles%h=figure(`Name',`Density/GradientPlotWindow',`NumberTitle',`off',`Position',[22scrsz(3)scrsz(4)-70]);image(X(Origin-xlimit:Origin+xlimit),Y(trim:ylimit),DensMatrix(trim-Noz+1:end,Origin-xlimit:Origin+xlimit)*sf);gridon;gridminor;%axisij%axissquareaxisequalaxistightcolormap(mymap);colorbar;xlabel('Distance(mm.)','Fontsize',16) 127

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ylabel('Distance(mm.)','Fontsize',16)bet=strcat(`T_c_h=',int2str(ChmTemp),`^o','C,T_i_n_j=',int2str(LiqTemp),'^o',`C,P_c_h=',num2str(ChmPres,'%.1f'),`atm,P_i_n_j=',num2str(LiqPres,'%.1f'),`atm,',`u_i_n_j=',num2str(Velocity,'%.1f'),`m/sec,Time=',num2str(Time,'%.2f'),`secs.');title(bet,`Fontsize',16)k=get(gcf,`Children');set(k(1),`YLim',[164]);set(k(1),`YTick',1:63/8:64);set(k(1),`YTicklabel',num2str(roundn((0:63/8:64)'./sf,1)),`Fontsize',16);set(k(2),`XTick',-6:2:6,`Fontsize',16);set(get(k(1),`YLabel'),`String',`\rho(kg/m^3)');set(get(k(1),`YLabel'),`Fontsize',16);ifCurrent<10saveloc=strcat(pathname,`ProcessedFiles\',int2str(0),int2str(Current),`d.fig');saveas(h,saveloc)saveloc=strcat(pathname,`ProcessedFiles\',int2str(0),int2str(Current),`d.emf');saveas(h,saveloc)eval([`save'pathname`ProcessedFiles\'int2str(0)int2str(Current)`d.matDensMatrixXY']);elsesaveloc=strcat(pathname,`ProcessedFiles\',int2str(Current),`d.fig');saveas(h,saveloc)saveloc=strcat(pathname,`ProcessedFiles\',int2str(Current),`d.emf');saveas(h,saveloc)eval([`save'pathname`ProcessedFiles\'int2str(Current)`d.matDensMatrixXY']);endclose(h)clearDensMatrixh=figure(`Name',`Density/GradientPlotWindow',`NumberTitle',`off',`Position',[22scrsz(3)scrsz(4)-70]);image(X(Origin-xlimit:Origin+xlimit),Y(trim:ylimit),GradMatrix(trim-Noz+1:end,Origin-xlimit:Origin+xlimit)*sf2);gridon;gridminor;%axisij%axissquareaxisequalaxistight 128

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colormap(mymap);colorbar;title(bet,`Fontsize',16)xlabel(`Distance(mm.)',`Fontsize',16);ylabel(`Distance(mm.)',`Fontsize',16);m=get(gcf,`Children');set(m(1),`YLim',[164]);set(m(1),`YTick',1:63/8:64);set(m(1),`YTicklabel',num2str(roundn((0:63/8:64)'./sf2,1)),`Fontsize',16);set(m(2),`XTick',-6:2:6,`Fontsize',16);set(get(m(1),`YLabel'),`String',`d\rho/dx(kg/m^4)');set(get(m(1),`YLabel'),`Fontsize',16);ifCurrent<10saveloc=strcat(pathname,`ProcessedFiles\',int2str(0),int2str(Current),`g.fig');saveas(h,saveloc)saveloc=strcat(pathname,`ProcessedFiles\',int2str(0),int2str(Current),`g.emf');saveas(h,saveloc)eval([`save'pathname`ProcessedFiles\'int2str(0)int2str(Current)`g.matGradMatrix']);elsesaveloc=strcat(pathname,`ProcessedFiles\',int2str(Current),`g.fig');saveas(h,saveloc)saveloc=strcat(pathname,`ProcessedFiles\',int2str(Current),`g.emf');saveas(h,saveloc)eval([`save'pathname`ProcessedFiles\'int2str(Current)`g.matGradMatrix']);endifCurrent<10fid=fopen(strcat(pathname,`ProcessedFiles\',int2str(0),int2str(Current),`t.txt'),`w');fprintf(fid,bet);fclose(fid);elsefid=fopen(strcat(pathname,`ProcessedFiles\',int2str(Current),`t.txt'),`w');fprintf(fid,bet);fclose(fid);endclose(h)clearGradMatrix 129

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endendclearFrameFrameIndexscrszJet boundary.m %Jetboundarycalculationfunction%%PreparedbyArnabRoyon14thJune,2010%function[initial,final,imgtemp]=Jet_boundary_latest(location1,location2,origin,Noz)%CreatinganAverageLaserSheetProfile%bckgrdlocate=[location2(1:41)`\Background\background.mat'];bckgrd=load(bckgrdlocate);know=imfinfo(location1);n=length(know);sum1=0;fori=1:nX=double(imread(location1,i));X1=X;X1=X1-bckgrd.background;sum1=sum1+X1;endprofile=sum1/n;profile=profile(Noz:end,:);[row,col]=size(profile);%Creatingalaserweightingprofile%%consideringthetoptobottomvariationinintensity%sum2=0;fori=1:length(profile)sum2(i)=sum(profile(i,:));endweight=sum2/max(sum2);%plot(weight);%Choosingtheimagesofthejettobeaveragedandaveragingthem%Pdatalocate=[location2(1:62)`ProcessedData.txt'];Pdata=load(Pdatalocate);camcol=Pdata(:,4);tot=length(camcol);fori=1:totif(camcol(i)>4)start=i;break;endendfori=tot:-1:1 130

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if(camcol(i)>4)finish=i;break;endendFrames=round((finish-start)/1100);InitialFrame=round(tot/1100)-Frames+1;%InitialFrame=1;shuru=InitialFrame;%startingframenumbershesh=shuru+20;%endingframenumbersum3=0;fori=shuru:sheshX=double(imread(location2,i));X=X-bckgrd.background;sum3=sum3+X;endimgtemp=sum3/(shesh-shuru);imgtemp=imgtemp(Noz:end,:);%Weighingthejetverticallyandcreatingacoloredimage%fori=1:length(imgtemp)img(i,:)=imgtemp(i,:)./weight(i);endclrimg=(img/max(max(img)))*64;%Settingthecolorofthejetsurroundingstowhite%halfnoz=0;%Halfwidthofnozzlefori=1:rowforj=1:colif((j<(origin-halfnoz))&&(clrimg(i,j)<25))%20clrimg(i,j)=0;endif((j>(origin+halfnoz))&&(clrimg(i,j)<20))%15clrimg(i,j)=0;endendend%clrimg(:,1:(origin-50))=0;Anything50pixelsaway%clrimg(:,(origin+50):end)=0;%%fromtheoriginissettowhitefigure(2);image(clrimg);colormap(load([location1(1:42)`Laser_Sheet_Profile\mymap.txt']));%Storingtheboundariesofthejetforeachrow%initial(1:row)=origin;final(1:row)=origin;fori=1:rowforj=1:origin 131

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if((clrimg(i,j)>0)&&(clrimg(i,j+1)>0))initial(i)=j;break;endendendfori=1:rowforj=col:-1:originif((clrimg(i,j)>0)&&(clrimg(i,j-1)>0))final(i)=j;break;endendif((final(i)==origin)&&(i>1))final(i)=final(i-1);endendholdon;plot(final,1:length(final),`k.');plot(initial,1:length(initial),`r.');Laser Proles.m clearall;%DefiningthelocationoftheLaserSheetProfileandBackgroundImage%[filename,pathname]=uigetfile(`*.*',`Findlaserprofile',`G:\Till_December_2011\Tests\');location=[pathnamefilename];bckgrdlocate=[pathname(1:41)`\Background\background.mat'];eval([`load'bckgrdlocate`background']);%CreatinganAverageLaserSheetProfile%know=imfinfo(location);n=length(know);sum=0;fori=1:nX=double(imread(location,i));X1=X;X1=X1-background;sum=sum+X1;endprofile=sum/n;figure(99)subplot(2,2,1);plot(profile);title(`Lasersheetintensityfromtoptobottom',`Fontsize',12,`Fontweight',`bold'); 132

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ylabel(`Intensity(toptobottom)',`Fontsize',16);xlabel(`Length(Pixels)',`Fontsize',16);m=get(gcf,`Children');set(m(1),`Fontsize',16);subplot(2,2,2);plot(mean(profile')/max(mean(profile')));title(`Meanlasersheetintensityfromtoptobottom','Fontsize',12,`Fontweight',`bold');ylabel(`NormalizedIntensity',`Fontsize',16);xlabel(`Length(Pixels)',`Fontsize',16);m=get(gcf,`Children');set(m(1),`Fontsize',16);%CreatingaplotshowingtheintensityofLaserBeamfromLtoR%sum2=0;fori=250:length(X)prof_norm(i,:)=profile(i,:)/max(profile(i,:));sum2=sum2+prof_norm(i,:);endsubplot(2,2,3);plot(profile');title(`Lasersheetintensityfromlefttoright',`Fontsize',12,`Fontweight',`bold');ylabel(`Intensity(lefttoright)',`Fontsize',16);xlabel(`Width(Pixels)',`Fontsize',16);avg_norm=sum2/length(250:length(X));subplot(2,2,4);plot(avg_norm);title(`MeanlasersheetIntensityfromlefttoright',`Fontsize',12,`Fontweight',`bold');ylabel(`NormalizedIntensity',`Fontsize',16);xlabel(`Width(Pixels)',`Fontsize',16);Movie maker.m %Programtomakeamoviefromstillcorrectedframes%%MadebyArnabRoyon1stMay,2012%functionMovie_Maker(location,count)TotalFrames=50;JetDia=0.2;TimeCol=1;LiqTempCol=2;ChmTempCol=3;ExtSyncCol=4;ChmPresCol=5;LiqPresCol=6;LiqFlowCol=7;loadloc=(strcat(location(1,1:end-35),`\ProcessedData.txt'));Pdata=load(loadloc); 133

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samples=length(Pdata);%Totalnumberofsamplesstep=Pdata(2,1);%Thispositionisfirststepfromtime(1)=0%Identifyingtheindexforeachframe%Frame=0;LengthCounter=0;check=0;fork=1:samplesifPdata(k,4)>=4LengthCounter=LengthCounter+1;IndexOfSpike(LengthCounter)=k;check=1;elseifcheck==1Frame=Frame+1;FrameIndex(Frame)=round(mean(IndexOfSpike));check=0;LengthCounter=0;clearIndexOfSpikeendendend%CalculationoftheTimeIndex%TimeIndex=1;gradflow=gradient(Pdata(:,LiqFlowCol));forl=1:samplesif(gradflow(l)==max(gradflow))TimeIndex=l;break;endendCurrent=TotalFrames-Frame;%Creatingeachframeandstackingtomakemovie%fori=1:countFrameno=str2double(location(i,90:91))-Current;Time=Pdata(FrameIndex(Frameno)+TimeIndex,TimeCol);LiqTemp=Pdata(FrameIndex(Frameno)+TimeIndex,LiqTempCol);ChmTemp=Pdata(FrameIndex(Frameno)+TimeIndex,ChmTempCol);ChmPres=Pdata(FrameIndex(Frameno)+TimeIndex,ChmPresCol);LiqPres=Pdata(FrameIndex(Frameno)+TimeIndex,LiqPresCol);MassFlow=1.61*Pdata(FrameIndex(Frameno)+TimeIndex,LiqFlowCol);%g/sRefDen=goodeqn_liq(LiqTemp,ChmPres);%Units(kg/m^3)Velocity=10*MassFlow/(RefDen*(pi/4)*JetDia^2);%Units(m/s)img=load(location(i,:));density=img.DensMatrix;RefDen=goodeqn_liq(LiqTemp,ChmPres);%Units(kg/m^3) 134

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sf=64/max(max(density));mymap=load(`G:\Till_December_2011\Tests\Data_05_25_12\Laser_Sheet_Profile\mymap.txt');colormap(mymap);image(img.X,img.Y,density*sf);gridon;gridminor;set(gcf,`Position',[50501366768]);axisequal;axistight;colorbar;xlabel(`Distance(mm.)',`Fontsize',14)ylabel(`Distance(mm.)',`Fontsize',14)bet=strcat(`T_c_h=',int2str(ChmTemp),`^o',`C,T_i_n_j=',int2str(LiqTemp),`^o',`C,P_c_h=',num2str(ChmPres,`%.1f'),`atm,P_i_n_j=',num2str(LiqPres,`%.1f'),`atm,',`u_i_n_j=',num2str(Velocity,`%.1f'),`m/sec,Time=',num2str(Time,`%.2f'),`secs.');title(bet,`Fontsize',14)m=get(gcf,`Children');set(get(m(1),`YLabel'),`String',`\rho(kg/m^3)');set(get(m(1),`YLabel'),`Fontsize',14);set(m(1),`YTicklabel',num2str(roundn((0:63/8:64)'./sf,2)),`Fontsize',14);f=getframe(gcf);M(:,:,:,i)=f.cdata;endmov=immovie(M);saveloc=(strcat(location(1,1:77),`Movie.avi'));movie2avi(mov,saveloc,`compression',`Cinepak',`fps',2);Run Preview.m %Tomakesuretargettemperaturesandpressureshavebeenhit%Savesdatainprocessedandmeaningfulformto'ProcessedData.txt'%Thisprogrammustberunbeforefullprocessingcanbedone%Foldersmustbeorganizedpriortorunningthisprogramclearall[filename,pathname]=uigetfile(`*.*',`Findruntoprocess',`G:\Till_December_2011\Tests\Data_05_09_12\');location=[pathnamefilename];fid=fopen(location);data=fscanf(fid,`%f%f%f%f%f%f%f',[7inf]);%Ithassevenrowsnow.data=data';%Transposeto7columnsfclose(fid);%Closethefile,allrelevantdatahasbeenstoredsamples=length(data);%Totalnumberofsamplestime=data(:,1);%Firstcolumnofdatarepresentstimeinstepsstep=time(2);%Thispositionisfirststepfromtime(1)=0 135

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fs=1/step;%Samplerate%Processingliquidflowdata:Column7[num1,den1]=butter(6,0.1);f_data=filter(num1,den1,data(:,7));data(:,7)=f_data;NofB=20;%Numberofblocksthatwillbefitintotaltimedelta=step*floor((samples-1)/NofB);%lengthintimeofblockchunk=floor((samples-1)/NofB);%indexedsizeofblockfori=1:NofBBlock(:,i)=data(chunk*(i-1)+2:chunk*i+1,7);BlockTime(i)=delta*(i-1/2);%atcenterofblockendfori=1:NofB[Pxx,f]=pwelch(Block(:,i),[],[],[],fs);[val,ind]=max(Pxx);domfreq(i)=floor(f(ind));end%liqflow=.0808*domfreq+1.5095;%Doublecheckthisequation!liqflow=6.545151*(0.0054*domfreq+0.2483);%Processingtempandpresdata:Columns2,3,5,6Fc=fs/200;%CarrierfrequencyF=Fc/fs;%ChangeFtovarythefilter'scutofffrequency.[num,den]=butter(6,F);%DesignButterworthfilter.scrsz=get(0,`ScreenSize');h=figure(`Name',`Sensoroutputplots',`NumberTitle',`off',`Position',[22scrsz(3)scrsz(4)-70]);spot=filter(num,den,data(:,2));%Temporaryvariabletofilterdatasubplot(2,2,1);plot(time,spot)data(:,2)=spot;holdon%Alltemperature'sappearonsameplotspot=filter(num,den,data(:,3));plot(time,spot,`r')data(:,3)=spot;title(`TemperatureReadings')xlabel(`Time(s)')ylabel(`Temperature({\circ}C)')legend(`Liquid',`Chambertop',1)[num2,den2]=butter(6,F);f_data_1=filter(num2,den2,data(:,5));f_data_2=filter(num2,den2,data(:,6));data(:,5)=f_data_1;data(:,6)=f_data_2;subplot(2,2,2);plot(time,data(:,5),`r')holdon%Allpressuresappearonthesameplotplot(time,data(:,6),`b') 136

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title(`PressureReadings')xlabel(`Time(s)')ylabel(`Pressure(atm)')tempmax=max(data(:,6));%followingfindsmaxpressuretoscaleaxisifmax(data(:,5))>tempmaxtempmax=max(data(:,5));endymax=1.1*tempmax;%maxfoundsoaxisisprettyENDaxis([010ymax])axis`autox'legend(`Chamber',`Liquid',1)subplot(2,2,3);plot(BlockTime,liqflow);holdon;plot(BlockTime,liqflow,`r.');holdoff;%spot)forq=1:NofBdata(chunk*(q-1)+1:chunk*q,7)=liqflow(q);enddata(chunk*q:end,7)=liqflow(q);title(`LiquidFlowMeterdata')xlabel(`Time(s)')ylabel(`Flow(cc/s)')ymax=1.1*max(liqflow);axis([010ymax])axis`autox'subplot(2,2,4);plot(time,data(:,4),`g')title(`CameraSyncoutput')%CameraSyncOutputisconnectedtotheNotScanoutputoftheST-133(Ch1labeled).xlabel(`Time(s)')ylabel(`Voltage(V)')hgsave([pathname`PDI_'filename(9:end)`.fig']);newloc=[pathname`ProcessedData.txt'];eval([`save'newloc`data-ascii-tabs']);Spreading Angle.m functionangle_std=Spreading_Angle(location,count,origin)sprangle(1:count,1:2)=0;totspread(1:count)=0;thres(1:count)=0;%Calculatingthethresholddensityforjetboundaryusingpeakdensitygradients%fork=1:countcurrent=char(location(k,:));colormap(load([current(1:42)`Laser_Sheet_Profile\mymap.txt']));img=load(current);clrimg=round(64*img.DensMatrix/max(max(img.DensMatrix))); 137

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if(k==1)image(clrimg);%inp=input(`Doyouwanttoinputthresholdvaluemanually?(y/n)',`s');inp=`n';if(inp==`n')%ans1=input(`SupercriticalTest?(y/n)',`s');ans1='y';%ans2=input(`SingleSpecies?(y/n)',`s');ans2=`n';if(ans2==`n')lower=10;upper=30;endif(ans1==`y')&&(ans2==`y')lower=35;upper=45;endif(ans1==`n')&&(ans2==`y')lower=20;upper=35;endelselower=input(`Enterlowerthresholdvalueforjetboundary:');upper=input(`Enterupperthresholdvalueforjetboundary:');enddisp(strcat(`Lowerthreshold=',num2str(lower)));disp(strcat(`Upperthreshold=',num2str(upper)));closeall;endgrad=abs(gradient(img.DensMatrix(50,:)));[peak,locs]=findpeaks(grad);nozwidth=40;forl=1:length(locs)if(locs(l)>(origin-nozwidth))&&(locs(l)<(origin+nozwidth))if((clrimg(50,locs(l))>lower)&&(clrimg(50,locs(l))
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if(thres(i)~=0)thresh(cnt)=thres(i);cnt=cnt+1;endendthreshold=min(thresh);%Calculatingthejetspreadingangle%fork=1:countcurrent=char(location(k,:));img=load(current);clrimg=round(64*img.DensMatrix/max(max(img.DensMatrix)));%Settingthecolorofthejetsurroundingstowhite%row=length(clrimg);fori=1:rowforj=1:311ifclrimg(i,j)
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plot((1:count),avg_spr,`g',(1:count),avg_spr-std(totspread),`r-.',(1:count),avg_spr+std(totspread),`r-x');avg_final=mean(angle_final);plot(avg_final*ones(1,cnt),`k');xlabel(`No.ofimagesconsidered',`Fontsize',14);ylabel(`SpreadingAngle',`Fontsize',14);legend(`Allangles',`Meanspreadingangle',`Lowerstandarddeviation',`Upperstandarddeviation',`Modifiedmean');disp(strcat(`Averagespreadingangleis:',num2str(avg_final),`degrees'));disp(strcat(`Standarddeviationis:',num2str(std(angle_final)),`degrees'));angle_std=[avg_finalstd(angle_final)];Stability Analysis.m clearall;R=(0.84e-3)/2;Re=25000;denrat=0.0122;cnt3=1;forWe=1000:100:10000Wecnt2=0;pos=0;forkr=0.1:0.1:70cnt=0;cnt2=cnt2+1;forki=0:-0.1:-5k=kr+(i*ki);w=-kr;cnt=cnt+1;f(cnt)=(((w+k)^2)*besseli(0,k)/besseli(1,k))-((2*(k^2)*(w+k)/(Re*besseli(1,k)))*(besseli(0,k)+besseli(0,k)-besseli(1,k)/k))+((w^2)*denrat*besselk(0,k)/besselk(1,k))+((k-k^3)/We);endpos=(find(f==min(f)));if(pos>1)ki_final(cnt2)=(-0.1*(pos-1));elseki_final(cnt2)=0;endendkr=(0.1:0.1:70);plot(kr,-ki_final,`g');holdon;xlabel(`k_r',`Fontsize',14); 140

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ylabel(`-k_i',`Fontsize',14);%title(`LinearStabilityCurve',`Fontsize',14);pos2=(find(ki_final==min(ki_final)));lamd=2000*pi/(kr(pos2(1))/R);x(cnt3)=kr(pos2(1));y(cnt3)=-ki_final(pos2(1));cnt3=cnt3+1;endplot(x,y,`r');Test Conditions.m closeallclearallJetDia=0.2;TimeCol=1;LiqTempCol=2;ChmTempCol=3;ExtSyncCol=4;ChmPresCol=5;LiqPresCol=6;LiqFlowCol=7;pathname=`D:\Till_December_2011\Tests\';count=0;whiletrue[filename,pathname]=uigetfile(`*.fig',`PickPDIfiletoProcess',pathname);iffilename==0ifcount==0returnendbreakendcount=count+1;paths(count,:)=cellstr(pathname);files(count,:)=cellstr(filename);endfprintf(`Thesearethe%dfilelocationsyouhavechosen:\n',count)Locations=strcat(deblank(char(paths)),deblank(char(files)))fprintf(`Ifthisisinerrorpress'`Ctrl+c'`tocancel');clearLocationsflowmeter=input(`Doesflowmeterworkforthiscase(s)?(y/n)',`s');fori=1:countpathname=deblank(char(paths(i)));filename=deblank(char(files(i))); 141

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location=[pathname`ProcessedData.txt'];Pdata=load(location);samples=length(Pdata);TimeIndex=1;if(flowmeter==`y')gradflow=gradient(Pdata(:,LiqFlowCol));forl=1:samplesif(gradflow(l)==max(gradflow))TimeIndex=l;break;endendelsegradtemp=gradient(Pdata(5500:end-5500,LiqTempCol));fork=5500:samples-5500if(gradtemp(k-5500+1)==max(gradtemp))TimeIndex=k;break;endendendLiqTemp(i)=mean(Pdata(TimeIndex:end,LiqTempCol));LiqPres(i)=mean(Pdata(TimeIndex:end,LiqPresCol));ChmTemp(i)=mean(Pdata(TimeIndex:end,ChmTempCol));ChmPres(i)=mean(Pdata(TimeIndex:end,ChmPresCol));MassFlow(i)=1.61*mean(Pdata(TimeIndex:end,LiqFlowCol));RefDen=goodeqn_liq(LiqTemp(i),ChmPres(i));Velocity(i)=mean(10*MassFlow/(RefDen*(pi/4)*JetDia^2));DenRat(i)=idealgas(ChmTemp(i),ChmPres(i))/goodeqn_liq(LiqTemp(i),LiqPres(i));%disp(strcat(`Meanliquidtemperatureis=',num2str(LiqTemp(i)),`C'));%disp(strcat(`Meanchambertemperatureis=',num2str(ChmTemp(i)),`C'));%disp(strcat(`Meanliquidpressureis=',num2str(LiqPres(i)),`atm'));%disp(strcat(`Meanchamberpressureis=',num2str(ChmPres(i)),`atm'));%disp(strcat(`Meanmassflowis=',num2str(MassFlow(i)),`g/s'));%disp(strcat(`Meaninjectionvelocityis=',num2str(Velocity(i)),`m/s'));endTestMatrix=[ChmTemp'LiqTemp'ChmPres'LiqPres'MassFlow'Velocity'];xlswrite(`H:\Till_December_2011\Tests\Sup_Sub_2012.xlsx',TestMatrix,`B36:G46');xlswrite(`H:\Till_December_2011\Tests\Sup_Sub_2012.xlsx',DenRat',`P36:P46'); 142

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APPENDIXBADDITIONALIMAGES A BFigureB-1. Density(A)anddensitygradient(B)imagesofsubcritical-into-subcriticalinjectioncorrespondingtocase1inTable 4-1 143

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A BFigureB-2. Density(A)anddensitygradient(B)imagesofsubcritical-into-subcriticalinjectioncorrespondingtocase2inTable 4-1 144

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A BFigureB-3. Density(A)anddensitygradient(B)imagesofsubcritical-into-subcriticalinjectioncorrespondingtocase3inTable 4-1 145

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A BFigureB-4. Density(A)anddensitygradient(B)imagesofsubcritical-into-subcriticalinjectioncorrespondingtocase4inTable 4-1 146

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A B C DFigureB-5. Density(A,C)anddensitygradient(B,D)imagesofsubcritical-into-supercriticalinjectioncorrespondingtocases5&6inTable 4-1 147

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A B C DFigureB-6. Density(A,C)anddensitygradient(B,D)imagesofsubcritical-into-supercriticalinjectioncorrespondingtocases7&8inTable 4-1 148

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A BFigureB-7. Density(A)anddensitygradient(B)imagesofsupercritical-into-subcriticalinjectioncorrespondingtocase9inTable 4-1 149

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A BFigureB-8. Density(A)anddensitygradient(B)imagesofsupercritical-into-subcriticalinjectioncorrespondingtocase10inTable 4-1 150

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A BFigureB-9. Density(A)anddensitygradient(B)imagesofsupercritical-into-subcriticalinjectioncorrespondingtocase11inTable 4-1 151

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A BFigureB-10. Density(A)anddensitygradient(B)imagesofsupercritical-into-subcriticalinjectioncorrespondingtocase12inTable 4-1 152

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A BFigureB-11. Density(A)anddensitygradient(B)imagesofsupercritical-into-supercriticalinjectioncorrespondingtocase13inTable 4-1 153

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A BFigureB-12. Density(A)anddensitygradient(B)imagesofsupercritical-into-supercriticalinjectioncorrespondingtocase14inTable 4-1 154

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A BFigureB-13. Density(A)anddensitygradient(B)imagesofsupercritical-into-supercriticalinjectioncorrespondingtocase15inTable 4-1 155

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A BFigureB-14. Density(A)anddensitygradient(B)imagesofsupercritical-into-supercriticalinjectioncorrespondingtocase16inTable 4-1 156

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REFERENCES [1] Chehroudi,B.,Talley,D.G.,andCoy,E.,VisualCharacteristicsandInitialGrowthRatesofRoundCryogenicJetsatSubcriticalandSupercriticalPressures,PhysicsofFluids,Vol.14,2002,pp.850. [2] Yang,V.,ModelingofSupercriticalVaporization,MixingandCombustionProcessesinLiquid-FueledPropulsionSystems,ProceedingsofCombustionInstitute,Vol.28,2000,pp.925. [3] Bellan,J.,Supercritical(andSubcritical)FluidBehaviorandModeling:Drops,Streams,ShearandMixingLayersandSprays,ProgressinEnergyandCombus-tionScience,Vol.26,2000,pp.329. [4] Abramovich,G.N.,TheTheoryofTurbulentJets,MITPress,1963. [5] Newman,J.A.andBrzustowski,T.A.,BehaviorofaLiquidJetneartheThermodynamicCriticalRegion,AIAAJournal,Vol.12,No.6,1996,pp.1137. [6] Birk,A.,McQuaid,M.,andBliesener,G.,ReactingLiquidMonopropellantSprays-ExperimentswithHighVelocityFullConeSpraysin33MPa,500CNitrogen,FinalReportARL-TR,Vol.17,1992. [7] Birk,A.,McQuaid,M.,andGross,M.,LiquidCoreStructureofEvaporatingSpraysatHighPressures-FlashX-rayStudies,ProceedingsofICLASS-94,1994. [8] Chehroudi,B.,Coy,E.,andTalley,D.G.,InitialGrowthRateandVisualCharacteristicsofaRoundJetintoaSub-toSupercriticalEnvironmentofRelevancetoRocket,GasTurbineandDieselEngines,37thAerospaceSciencesMeetingandExhibit,AIAA,Reno,NV,Jan.1999. [9] Mayer,W.andTamura,H.,PropellantInjectioninaLiquidOxygen/GaseousHydrogenRocketEngine,JournalofPropulsionPower,Vol.19,1971,pp.1595. [10] Polikhov,S.A.,ExperimentalStudyofSubcriticaltoSupercriticalMixing,Ph.D.thesis,UniversityofFlorida,Gainesville,FL,Aug.2007. [11] PropertiesofFusedQuartz,2000. [12] Lo-FloSeriesPrecisionFlow-meters,http://www.sponsler.com/pdfs/loo.pdf,2000. [13] Owens,J.G.,UnderstandingtheStabilityandEnvironmentalCharacteristicsofaSustainableHalonAlternative,Proceedingsofthe13thHalonOptionsTechnicalWorkingConference,Vol.61,NIST,Albuquerque,NM,May2007,pp.903. 157

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[14] Gustavsson,J.P.R.andSegal,C.,FluorescenceSpectrumof2-triuoromethyl-1,1,1,2,4,4,5,5,5,-nonauoro-3-pentanone,AppliedSpectroscopy,2003,pp.984. [15] Owens,J.G.,PhysicalPropertiesof3MNovec649Fluid,PrivateCommunication,2007. [16] Hanson,R.K.,Mungal,M.G.,Grisch,F.,Thurber,M.C.,Smith,S.H.,andHasselbrink,E.F.,TemperatureandMixtureFractionImagingofGaseousFlowsusingAcetonePLIF,27thFluidDynamicsConference,AIAA,NewOrleans,LA,June1996. [17] Thurber,M.,Grisch,F.,Kirby,B.,Votsmeier,M.,andHanson,R.K.,MeasurementsandModelingofAcetoneLaser-InducedFluorescencewithImplicationsforTemperatureImaging-Diagnostics,AppliedOptics,Vol.37,1996,pp.4963. [18] Koch,J.andHanson,R.K.,TemperatureandExcitationWavelengthDependenciesof3-pentanoneAbsorptionandFluorescenceforPLIFApplications,AppliedPhysicsB,Vol.76,2003,pp.319. [19] Frackowiak,B.,Strzelecki,A.,andLavergne,G.,ALiquidVaporInterfacePositioningMethodAppliedtoPLIFMeasurementsaroundEvaporatingMonodisperseDropletStreams,ExperimentsinFluids,Vol.46,2008,pp.671. [20] Melton,L.A.andLipp,C.W.,CriteriaforQuantitativePLIFExperimentsusingHighPowerLasers,ExperimentsinFluids,Vol.35,2003,pp.310. [21] Karasso,P.S.andMungal,M.G.,PLIFMeasurementsinAqueousFlowsUsingtheNd:YAGLaser,ExperimentsinFluids,Vol.23,1997,pp.382. [22] Muhlfriedel,K.andBaumann,K.H.,ConcentrationMeasurementsDuringMassTransferAcrossLiquidPhaseBoundariesUsingPlanarLaserInducedFluorescence,ExperimentsinFluids,Vol.28,2000,pp.279. [23] Crimaldi,J.,PlanarLaserInducedFluorescenceinAqueousFlows,ExperimentsinFluids,Vol.44,2008,pp.851. [24] Thurber,M.andHanson,R.K.,PressureandCompositionDependencesofAcetoneLaser-InducedFluorescencewithExcitationat248,266,and308nm,AppliedPhysicsB,Vol.69,1999,pp.229. [25] Tran,T.,Kochar,Y.,andSeitzman,J.,AcetonePhotophysicsatNearCriticaltoSupercriticalConditions,46thAerospaceSciencesMeetingandExhibit,AIAA,Reno,NV,Jan.2008. [26] Polikhov,S.A.andSegal,C.,ExperimentalStudyofSubcriticaltoSupercriticalJetMixing,45thAerospaceSciencesMeetingandExhibit,AIAA,Reno,NV,Jan.2007. 158

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[27] Segal,C.andPolikhov,S.A.,SubcriticaltoSupercriticalMixing,PhysicsofFluids,Vol.20,No.5,2008,pp.052101. [28] Mayer,W.,Telaar,J.,Branam,R.,andSchneider,G.,CharacterizationofCryogenicInjectionatSupercriticalPressures,37thJointPropulsionConferenceandExhibit,AIAA,SaltLakeCity,UT,July2001. [29] Chehroudi,B.,Talley,D.G.,Mayer,W.,Branam,R.,Smith,J.J.,Schik,A.,andOschwald,M.,UnderstandingInjectionintoHighPressureSupercriticalEnvironments,FifthInternationalSymposiumonLiquidSpacePropulsion,NASA,Huntsville,AL,Oct.2003. [30] Oschwald,M.,Branam,R.,Hussong,J.,Schik,A.,Chehroudi,B.,andTalley,D.G.,InjectionofFluidsintoSupercriticalEnvironments,CombustionScienceandTechnology,Vol.178,2006,pp.49. [31] Chen,C.J.andRodi,W.,VerticalTurbulentBuoyantJets-AReviewofExperimen-talData,PergamonPress,1980. [32] Reitz,R.D.andBracco,F.V.,OntheDependenceofSprayAngleandOtherSprayParametersonNozzleDesignandOperatingCondition,SAEInternationalCongressandExposition,SAE,Detroit,MI,Feb.1979. [33] Chehroudi,B.,Chen,S.H.,Bracco,F.V.,andOnuma,Y.,OntheIntactCoreofFull-ConeSprays,SAEInternationalCongressandExposition,SAE,Detroit,MI,Feb.1985. [34] Eroglu,H.,Chigier,N.,andFarago,Z.,Co-axialAtomizerIntactLengths,PhysicsofFluidsA,Vol.3,No.2,1991,pp.303. [35] Davis,D.W.andChehroudi,B.,MeasurementsinanAcousticallyDrivenCoaxialJetunderSub-,Near-,andSupercriticalConditions,JournalofPropulsionandPower,Vol.23,No.2,2007,pp.364. [36] Brown,G.andRoshko,A.,OnDensityEffectsandLargeStructureinTurbulentMixingLayers,JournalofFluidMechanics,Vol.64,1974,pp.775. [37] Papamoschou,D.andRoshko,A.,TheCompressibleTurbulentShearLayer:AnExperimentalStudy,JournalofFluidMechanics,Vol.197,1988,pp.453. [38] Dimotakis,P.E.,Two-dimensionalShearLayerEntrainment,AIAAJournal,Vol.24,No.11,1986,pp.1791. [39] Reitz,R.D.andBracco,F.V.,Ultra-High-SpeedFilmingofAtomizingJets,PhysicsofFluids,Vol.22,1979,pp.1054. [40] Reitz,R.D.andBracco,F.V.,MechanismofAtomizationofaLiquidJet,PhysicsofFluids,Vol.25,1982,pp.1730. 159

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[41] Lin,S.P.andReitz,R.D.,DropandSprayFormationfromaLiquidJet,AnnualReviewofFluidMechanics,Vol.30,1998,pp.85. [42] Rayleigh,L.,OntheInstabilityofJets,ProceedingsofLondonMathematicalSociety,Vol.10,1879,pp.4. [43] Chandrasekhar,S.,HydrodynamicandHydromagneticStability,OxfordUniversityPress,London,1961. [44] Weber,C.,DisintegrationofLiquidJets,JournalofAppliedMathematicsandMechanics,Vol.11,1931,pp.136. [45] Sterling,A.M.andSleicher,C.A.,Theinstabilityofcapillaryjets,JournalofFluidMechanics,Vol.68,1975,pp.477. [46] Taylor,G.I.,ScienticPapersofG.I.Taylor,CambridgeUniversityPress,Cambridge,1962. [47] Lin,S.P.,BreakupofLiquidSheetsandJets,CambridgeUniversityPress,Cambridge,2003. [48] Chehroudi,B.andTalley,D.G.,Thefractalgeometryofroundturbulentcryogenicnitrogenjetsatsubcriticalandsupercriticalpressures,AtomizationandSprays,Vol.14,2004,pp.50. [49] Oschwald,M.,Smith,J.J.,Branam,R.,Hussong,J.,Schik,A.,Chehroudi,B.,andTalley,D.G.,Injectionofuidsintosupercriticalenvironments,CombustionScienceandTechnology,Vol.49,2006,pp.179. [50] Zong,N.,Meng,H.,Hsieh,S.H.,andYang,V.,CryogenicFluidInjectionandMixingunderSupercriticalConditions,PhysicsofFluids,Vol.16,2004,pp.4248. [51] Ponstein,J.,InstabilityofRotatingCylindricalJets,AppliedScienceResearch,Vol.8,1959,pp.425. [52] Gaster,M.,ANoteontheRelationBetweenTemporallyIncreasingandSpatiallyIncreasingDisturbancesinHydrodynamicStability,JournalofFluidMechanics,Vol.14,1962,pp.222. 160

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BIOGRAPHICALSKETCH ArnabRoyhailsfromCalcutta,thecapitalofthehistoricalIndianstateofWestBengal.HisearlychildhoodwasspentinPhiladelphia,PAbeforehisfamilymovedbacktohishometownwherehenishedhishighschoolintheyear2003.Hereceivedhisbachelor'sdegreeinmechanicalengineeringfromJadavpurUniversityinCalcutta,Indiaintheyear2007.Inthesameyear,hejoinedtheUniversityofFloridatopursueaPhDinaerospaceengineering,specializinginPLIFmeasurementsinhighpressureandhightemperaturefuelinjectionandmixingexperiments.Hisresearchinterestsincludecombustionprocessesinautomotiveenginesandgasturbines,andlaser-basedowdiagnostics. 161