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Improved Visualization Algorithms for Vertical Two-Phase Annular Flow

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Title: Improved Visualization Algorithms for Vertical Two-Phase Annular Flow
Physical Description: 1 online resource (7 p.)
Language: english
Creator: KOKOMOOR,WESLEY WARREN
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2011

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Subjects / Keywords: ANNULAR -- DISTURBANCE -- PLIF -- VISUALIZATION -- WAVES
Nuclear and Radiological Engineering -- Dissertations, Academic -- UF
Genre: Nuclear Engineering Sciences thesis, M.S.
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Abstract: Annular flow is a configuration of gas-liquid two-phase flow characterized by a thin film of liquid surrounding a core of faster-moving gas. The liquid film is often a site of complex geometry where liquid mass transport occurs through base film and disturbance waves. Annular flow occurs in a wide range of industrial heat-transfer equipment, including the top of a BWR core, in the steam generator of a PWR, and in postulated accident scenarios including critical heat flux (CHF) by dryout. The present work focuses on the characterization of individual film behaviors in annular flow. Quantitative visualization techniques are discussed that provide for large-scale data collection of multiple, interrelated flow behaviors. The non-trivial data reduction codes for these techniques have been further developed in the present work to improve measurement accuracy. Film thickness distribution (base film and wave), disturbance wave length, and wave intermittency estimates have been updated using modified techniques. A system is also suggested for measuring the velocity of the gas-liquid interface. Lastly, the present observations have been applied to a recent two-region (base film and disturbance wave) annular flow model.
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 WESLEY WARREN KOKOMOOR.
Thesis: Thesis (M.S.)--University of Florida, 2011.
Local: Adviser: Schubring, Duwayne Lee.

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Rights Management: Applicable rights reserved.
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Permanent Link: http://ufdc.ufl.edu/UFE0042950/00001

Material Information

Title: Improved Visualization Algorithms for Vertical Two-Phase Annular Flow
Physical Description: 1 online resource (7 p.)
Language: english
Creator: KOKOMOOR,WESLEY WARREN
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2011

Subjects

Subjects / Keywords: ANNULAR -- DISTURBANCE -- PLIF -- VISUALIZATION -- WAVES
Nuclear and Radiological Engineering -- Dissertations, Academic -- UF
Genre: Nuclear Engineering Sciences thesis, M.S.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Annular flow is a configuration of gas-liquid two-phase flow characterized by a thin film of liquid surrounding a core of faster-moving gas. The liquid film is often a site of complex geometry where liquid mass transport occurs through base film and disturbance waves. Annular flow occurs in a wide range of industrial heat-transfer equipment, including the top of a BWR core, in the steam generator of a PWR, and in postulated accident scenarios including critical heat flux (CHF) by dryout. The present work focuses on the characterization of individual film behaviors in annular flow. Quantitative visualization techniques are discussed that provide for large-scale data collection of multiple, interrelated flow behaviors. The non-trivial data reduction codes for these techniques have been further developed in the present work to improve measurement accuracy. Film thickness distribution (base film and wave), disturbance wave length, and wave intermittency estimates have been updated using modified techniques. A system is also suggested for measuring the velocity of the gas-liquid interface. Lastly, the present observations have been applied to a recent two-region (base film and disturbance wave) annular flow model.
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 WESLEY WARREN KOKOMOOR.
Thesis: Thesis (M.S.)--University of Florida, 2011.
Local: Adviser: Schubring, Duwayne Lee.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2011
System ID: UFE0042950:00001


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IEEETRANSACTIONSONINSTRUMENTATIONANDMEASUREMENT,VOL.49,NO.5,OCTOBER20001101UncertaintyCharacterizationinImage-Based Measurements:APreliminaryDiscussionMassimoDeSanto ,Member,IEEE ,ConsolatinaLiguori ,Member,IEEE ,andAntonioPietrosanto ,Member,IEEEAbstract Therearealargenumberofapplicationfieldswhere measurementsderivingfromdigitalimagescanassumeagreatrelevance.Nevertheless,tomakeaprofitableuseofsuchmeasurements,itisindispensabletoachieveacompleteandquantitative controlonuncertaintiesthatrealsystemsintroducealongthechain ofstepsgoingfromreal-worldobjectstotheresultsofthemeasurementprocess.Thispaperdealswiththisnontrivialtaskand,in particular,withtheanalyticalexpressionofuncertaintycharacterizingtheresultsofimageprocessingsoftware.Atfirst,asimplified modelofuncertaintyofdigitalimagesisderivedandexperimentallytested;thentheCannyedgedetectoroutputuncertaintyis analyticallyexpressedandverifiedbothinartificialandreal-world images. IndexTerms Algorithms,imageedgeanalysis,imageprocessing,measurementerrors,uncertainty.I.INTRODUCTIONDIGITALimagesplayaroleofevergrowinginterestina numberofengineeringfields[1].Fromtheoneside,their continuoussuccesscanbeascribedtohuman-relatedpsychologicalmotivations:humanbeingspositivelyprefertouseimagesforexchanginginformation.Fromtheotherside,todays computersystemsmakeiteasierandeasiertoutilizeimagesbecauseofthenoticeableimprovementsinhardwareandsoftware technologiesformanagingthemintroducedinthelastfewyears. Insomefields,e.g.,inhuman-computerinterfacedesign, managingimagesisinacertainsenseaqualitativematter,even whentheyhavetobeusedasinputfortheelaborationsystem. Inotherfields,e.g.,inmorphologicalanalysisofproducts, digitalimagesareusedforquantitativepurposeswhichare inturnfunctionaltosomefinalgoals(e.g.,individuationand eliminationofdefectiveindustrialproducts).Itiseasyto understandthat,foraquantitativeuseofdigitalimages(or, evenbetter,foraquantitativeuseofthemeasurescomingfrom digitalimages),aclearcomprehensionofthewayuncertainty propagatesthroughoutthemeasurementsystemisneeded, andanextensivecontrolonboththehardwareandsoftware influencesonthequotedpropagation. Eachimage-basedmeasurementsystem(IBMS)canbe thoughtofasconstitutedbyadigitalizationinterface(e.g.,a digitalvideocamerawithappropriatecomputerinterface)andManuscriptreceivedMay26,1999;revisedJune13,2000. M.DeSantoandA.PietrosantoarewiththeDepartmentofInformationEngineeringandElectricEngineering,UniversityofSalerno,Fisciano,SA,84084, Italy(e-mail:desanto@diiie.unisa.it;pietrosa@diiie.unisa.it). C.LiguoriiswiththeDepartmentofAutomation,Electromagnetic,InformationEngineeringandIndustrialMathematics,UniversityofCassino,Cassino 03043,Italy(e-mail:liguori@ing.unicas.it). PublisherItemIdentifierS0018-9456(00)07577-X.acomputer-basedstationwhichisbuiltwithsomespecialized hardware(e.g.,apersonalcomputerhostingaDSP-based board)andsoftwaremodules,oftenhand-madebythe designerofthesystem.Itiseasytounderstandthatcharacterizationofuncertaintyinsuchasystemcanbedecomposedin thefollowingsteps: Step1)modelingtheuncertaintyoftheintensityfunction thatreachesthedigitalizationdevice(thecamera); Step2)modelingthedigitalizationprocess(framegrabbing); Step3)determiningtheuncertaintycharacterizingresultsof imageprocessingalgorithms. Referringtotheabove-definedsteps,someworkhasbeen doneinthepastyears.Letnowuspresentsomeresultspreviouslyachievedintheliterature. DorstandSmeulders[2]analyzedthelossofaccuracyindigitizedstraightlinescomingfromquantization.Theirresultsgive aquantitativeideaofdamagescomingfromoneofthesteps impliedfromdigitalizationbutareoflimitedusefulnesswhen leavingthestraightlineworld. Amilestoneinthestudyoftheeffectsofdigitalizationwas posedbyHavelock[3],[4],withtheintroductionoftheideaof locales,whicharebroadlyapplicabletotheestimationofthe positionandshapeofobjects,althoughtheiruseisshownonly forbinaryimages.AfurthersteptowardacorrectcharacterizationofdigitalizationerrorwasmadebyKamgar-Parsi[5],who introducedamathematicaltoolfortheestimationoftheaverage errorduetoquantization.Nevertheless,theiranalyticalanalysis doesnottakeintoaccountasufficientlydetailednumberoffactorstobeusefulforapracticalapplicationinevaluatingtheuncertaintyofimages. Ho[6]highlightedtheimportanceofintroducinganalytical modelstodescribethesystembehaviorandenumerateda numberoferrorcausesthataffectimageprecision,whilea veryinterestingandrecentworkbySarkar etal. [7]introduced theuseofmodulo-griddiagramstodeterminetheprobability densityfunctionassociatedwithapatternoncespecificsensor parametersaregiven.Inanycase,anexhaustiveanalysisofall theinfluenceparametersstillhastobecarriedout. AsignificantcontributionisprovidedbyNalwaandBinford [8],whostudiedtheeffectofthecharacteristicofpointspread functionofthesensorindetectingedgesandshowedthelimitationimpliedfromit.Agoodanddetailedanalysisoferror sourcesininspectionsystemshasbeendonebyGriffinandVillalobos[9],byKakaralaandHero[10],andmorerecentlyby YangandMarefat[11].However,generalapproachestothe analyticaltreatmentofuncertaintycharacterizingimage-processingalgorithmsaredifficulttobededuced.Closetothisaim0018/00$10.002000IEEE

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1102IEEETRANSACTIONSONINSTRUMENTATIONANDMEASUREMENT,VOL.49,NO.5,OCTOBER2000areHaralick etal. [12],[13],whoproposedamethodtoevaluateperformanceofedgedetectors,andinvestigatethewayin whichtheerrorsrelatedwithsuchalgorithmspropagateinmeasurementsofdistancesbetweenedgepointsonstraightlinesand circles.Intheirworks,nocontributionsaregivenabouttheapplicationofthemethodtodifferentmeasurementsandnoanalyticalexpressionsoftheuncertaintyofedgepointsareprovided. Tothebestofourknowledge,itappearsthatthemainresultswereobtainedinmodelingthedigitalizationprocesswhile adeepcomprehensionaboutthereal-worlddescription(Stepa) andabouttheintra-systempropagation(Stepc)seemsyettobe achieved.Concerningthelaststep,letusoutlinethattheuncertaintyoftheresultscomputedbyagivenimageprocessing softwarehastobecharacterizedinananalyticalway,inorderto avoidtheneedforcomplexexperimentalproceduresoftenintroducingunaffordablecosts.Moreover,theexperimentalcharacterizationofuncertaintycanbeunobtainableinpractice,when themeasurementsystemhasanhighlyvariablesoftwarepart. Startingfromthepreviousconsiderationsandonthebasis oftheirexperiencesinthefieldoftheuncertaintyanalysis [14][16],inthepresentpapertheauthorsanalyzetheproblem ofdefiningtheuncertaintyofpixelswhichbelongtoadigital image,andtheyfacetheproblemofdeterminingananalyticalrelationbetweenuncertaintyandtheparameterswhich influencethedigitalizationprocess.Then,ageneralmethod ispresentedtoanalyticallydefinetheuncertaintypropagation inasoftwaremodule,oncetheuncertaintyofthepixelsofthe inputimageisgiven.Finally,theproposedmethodisappliedto averycommonedgedetectorsuchastheCannyoperator,and validatedbymeansofexperimentaltests. II.ANALYTICALEXPRESSIONOFTHEIMAGEDIGITALIZATIONUNCERTAINTYManycontributionsareavailableinliteratureconcerningthe definitionoftheparameterswhichinfluencethewholeprocess leadingtothedigitalrepresentationofimages[7],[17].Since itisbeyondthescopeofthepresentworktopresentageneral andaccuratemodeloftheimagedigitalizationprocess,thefollowingdiscussionwillbeconstrainedinthefieldofthemorphologicalcharacterizationofobjectsinanindustrialprocess relatedwithopaquematters(e.g.,gaskets). Inthisframework,thevalidityofthefollowinghypotheses canbeassumed: Thecharacterizationisbasedonmeasurementswhichare independentfromthepositionofthemeasuredobjectin thespace(i.e.,itwillbepossibletouseanintrinsiccoordinatesystemlocatedonthemeasuredobject). Theobjectsurfaceshowsnospecularity. Thesehypothesesallowdefiningthe uncertaintyofanimage pixel astheparameterwhichquantifiestherandom changesoftheintensity ofthepixelitself.Uncertainty canbemeasuredasthestandarddeviation ofasetof samples ,obtainedby consecutiveacquisitionsofthe imageinstationaryconditionsofallthecontrollableparameters ofinfluence. Giventhoseassumptions,threemajorcausesstillinfluence theabove-defineduncertainty: 1)theimagequantizationfromthereal-continuous-worldto thecomputer-discrete-world; 2)thepresenceofvibrations;and 3)theintrinsicvariabilityofthelightsource(unstableness, flickering,etc.). Letusbrieflydiscusstheabove-mentionedcauses. Bothspatialandintensityquantizationshavetobeconsidered.Theformergivesacontributiontouncertaintywhich isproportionalforeachpixeltothegradientofintensity anddependsonthesensorspatialresolution(pixelwidth andpixelheight).Thelattergivesacontributionwhichis constantforeachpixellikethefloorinspectralanalysis anddependsonthenumberofbitsusedbytheA/Dconverter(numberoflevelsinthegrayscale). Vibrationsshouldconcurwithintensityquantizationtodeterminetheflooramplitude. Thehigheristhepixelintensity,themoresignificantare theeffectsoflightintrinsicvariability.Thisimpliesthe presenceofatermwhichisproportionalto inthe analyticalexpressionoftheuncertainty. StartingfromtheaboveconsiderationsandtakingintoaccounttheISOGUMindicationsconcerningthecombinationof uncertainty,theauthorsformulatedthefollowinganalyticalexpressionofamodelofthepixeluncertainty inrealindustrialconditions (1) where ; ,with and standarddeviationsoftriangular distributionsdefinedin (pixel width),and (pixelheight),respectively; correlationfactor,which ; ; constantforagivenimageandinparticular where isthestandarddeviationduetovibrationsand isthenumberof greylevels. ,and areconstantweightsdependingontheimage characteristics. Toexplorethisdependence,manyexperimentaltestshave beencarriedoutinrealindustrialconditions.Severalimages wereacquiredwithsignificantdifferencesintermsofdirection andintensityoflight,contrast,background,shape,androughnessofthesurfacesofmeasuredobjects.Foreachcondition, acquisitions werecarriedout,andthe uncertainty wasmeasuredforeachpixelasthestandarddeviationofintensity .Then,thebestfittingvaluesofthe constantweightsin(1)werecalculatedbyminimizingthequantityshownatthebottomofthenextpage. Forexample,Figs.1(a)and2(a)showtwoimagescharacterizedbydifferentshape,contrast,background,surfacecharacteristics,andkindofedges.Themeasureduncertainty[

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DESANTO etal. :UNCERTAINTYCHARACTERIZATIONINIMAGE-BASEDMEASUREMENTS1103 Fig.1.(a)Acquiredimageand(b)imagepixeluncertaintyU foragivenrow, measured(solid)expected(dashed),withK =1 : 7 10 ,C = )Tj/T87 1 Tf0.8283 0 TD(4 10 ,K = )Tj/T87 1 Tf0.8368 0 TD(1 : 3 10 ,U =0 : 8.solidline]andthebestfittingcalculateduncertainty[ line]dashedof throwpixelsarereportedinFig.1(b)forthe imageofFig.1(a)andinFig.2(b)fortheimageofFig.2(a). Thequotedfiguresshowhowtheabove-describedquantitiesare ingoodagreement.Thesameagreementhasbeenobservedin alltheotherrowswhichhavenotbeenreportedforthesakeof brevity. Byanalyzingthevaluesof ,and ,whichrealize thesamebestfittinginalltheotherexperimentedimagesand measurementconditions,thefollowingconclusionshavebeen drawn. Itcanbekeptconstanttothevalueof ;only inthecaseoflow-contrastimages,ithastobereduced toa50%value. Itdependsontheimageshapebutitisusuallyconstrainedwithin Itassumesverylowvaluesinhigh-contrastimages, otherwiseitdoesnotexceed Usingan8-bADCandinabsenceofsignificantvibrationsitsbestfittingvalueisabout0.5.butitincreases inlow-contrastimages(i.e.,incaseoftheroughsurfaces)until3.0;thismeans rangingfrom127to 750. Fig.2.(a)Acquiredimageand(b)imagepixeluncertaintyU foragiven row,measured(solid)expected(dashed),withK =1 : 6 e ,C =3 e ,K = )Tj/T87 1 Tf0.8368 0 TD(0 : 4 e ,U =0 : 7.However,thesensitivityoftheseweightsisnothigh;consequently,oncetypicalvalueshavebeenfoundtheymaybe keptinvariantwithimages,withoutsubstantiallyreducingthe validityofthemodel. Thepresentedanalyticalmodelallowsthe uncertaintyof imagepixels tobeestimatedandthesinglecontributionofeachinfluenceparametertobeextractedwithout theneedofmultipleacquisitionsandstatisticalelaboration whichwouldotherwisebeindispensablefortheexperimental evaluation. III.METHODFORTHEUNCERTAINTYANALYSISINIMAGEPROCESSINGALGORITHSTwodifferentapproachescanbefollowedwhentestingthe outputofImageProcessingSoftware(IPS):eitherblackbox orwhitebox.Intheformerapproachtheoutputuncertaintyis directlymeasuredwithouteitherthenecessityorthepossibility ofenumeratinganalyticalrelationshipswithinfluenceparameters.Thelatterapproachguaranteesthehigherlevelofquantitativecontrolandconsistsofthestudyofuncertaintypropagation throughtheanalyticalrelationshipsimplementedbythealgorithms.Obviously,itcanbefollowedonlyinthecaseofsystems wherealgorithmsandsourcecodeareavailable;thisassumption

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1104IEEETRANSACTIONSONINSTRUMENTATIONANDMEASUREMENT,VOL.49,NO.5,OCTOBER2000cannotbeconsideredalimitingconstraintwhenonetakesinto accountthelargenumberofcustomIPS, adhoc realizedforthis kindofapplication. Fromauthorspointofview,itisveryimportanttodefine ageneralmethodforanalyticallymodelingthecausesandthe effectsofuncertaintyinIBMS[16],andconsequently,thefollowingthree-stepapproachisproposed: 1) Theoreticalanalysis: Onceagivenandknownuncertaintyontheinputimageisassumed,ananalyticalexpressionoftheoutputuncertaintyisobtainedbyapplyingthe uncertaintypropagationlawsuggestedbytheISOGUM [18]tothenumericalrelationshipsimplementedbythe algorithm.Then,ifananalyticalmodeloftheimagedigitalizationprocessisalsoavailable,theobtainedanalytical expressionsallowtheuncertaintytobeanalyticallyestimatedfordifferenthardwareconfigurations(i.e.,camera resolutionandnumberofgraylevels),influenceparameter(i.e.,lightingandvibration),andsoftwareoperating conditions. 2) Numericalverification: Thisphaseofthemethodallows thetheoreticalapproachtobeverifiedasfarastheapplicationofthepropagationlawandtheconsideredcorrelationamongquantitiesisconcerned.NumericalverificationiscarriedoutbyrunningtheISPalgorithmonthe datasetsobtainedbytheanalyticalmodeloftheimage digitalizationsystemaffectedbyallthesourcesofuncertaintytakenintoaccountinthetheoreticalanalysis.The standarddeviationofthesimulatedoutputsgivesanestimationoftheuncertainty,whichcanbecomparedwith theresultsofstepa)toverifythetheoreticalassumptions. Obviously,thisverificationwillbecarriedoutonlyona selectednumberratherthanonallthepossibleconfigurations(asatypicalblack-boxapproachwouldrequire). 3) Experimentalvalidation: Thisphasehastheonlyaimto validatetheimagedigitalizationsystemmodelpreviously adopted;itsresultsarestrictlydependentonthehardware used.ItiscarriedoutbyrunningtheISPalgorithmonsuitablesetsofimages;theIPSoutputuncertaintyisevaluatedasthestandarddeviationoftheIPSoutputobtained insuccessiveimageacquisitions.Theexperimentalplan doesnotneedtobeexhaustive,butcanbereducedonly totheverificationofsomevaluesandtrends. IV.CANNYEDGEOPERATOR:THEORETICALANALYSISOFUNCERTAINTYPROPAGATIONEdgedetectionhasbeenchosentoillustratetheproposed approachsinceitisperhapsthemostubiquitousstepinlowlevelimageprocessing.Amongthedifferentproposedmethods, Cannysalgorithmhasbeenchosenforthreemainreasons:itis agoodexampleofanalgorithmbasedonarigorousmathematicalapproach,itisoftenusedinthescientificcommunityand, finally,ithasbeenlargelyanalyzedfromthepointofviewof performances[19]. Leavingtospecificliterature[20]theaccuratedescriptionof thealgorithm,somedetailshavetobereported.TheCannyoperatorfindsedgesbylookingforlocalmaximaofthenorm of thegradientoftheimage ;asaconsequencetwomainphases canbeidentified:1)calculationofthenormofthegradient,and 2)searchofthelocalmaxima.Consequently,theuncertainty propagationhastobeevaluatedinbothphases. 1)Thegradientoftheimage iscalculatedthroughthe convolutionbetweenthederivativealong ofa Gaussianfilter andtheimageitself. Given and weobtain (2) Inpractice,eachelementofmatrices and iscalculatedas (3) (4) where and representthenumberofcolumnsand rowsofthematrix ,respectively;andmatrices and dependonthestandarddeviationoftheGaussian filterandonitsdimension. Applyingto(2)(4)thestatisticalmethodforthecombineduncertaintyevaluationproposedbyISOGUM[18], andconsideringindependentonefromeachother(no correlationissupposed)theuncertaintiesonall pixels,weobtainthefinalcombineduncertaintyof matrixelementsasfollows: (5) where (6) (7) (8) 2)Localmaxima(relatedtoninepixelzones)areisolated in byano-maximumsuppressionalgorithm.Foreach ,thealgorithminvestigatesthegradientcomponents and ineachofthefourquadrant directions,inordertofindamaximum(Fig.3).Thealgorithmprovidesamatrix wherealltheno-maximum

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DESANTO etal. :UNCERTAINTYCHARACTERIZATIONINIMAGE-BASEDMEASUREMENTS1105 Fig.3.Schematicdiagramoftheno-maximumsuppressionalgorithm.pixelsarezeroed.Thealgorithmdecidesifapixelmust besuppressedornotbymeansofasequenceoflogictests whicharebasedoncomparisonsamongthecomponents ofthegradientsofcontiguouspixels.Ofcourse,thefinal resultofthissequenceofcomparisonsisnotdeterministicduetotheuncertaintyof and matrixelements.Asaconsequence,once ,and areknown,foreachelement theprobability ofbeinganedgecanbeevaluatedasthe probabilitythatthealgorithmfollowsoneofthefourindependentpathswhicharepresentinitsfluxdiagram.Each pathisinturnmadeofthreesteps,eachoneconsistingof theresultofalogictestcarriedoutonaconditionsuch asthefollowing: .Theprobability oftruthofsuchaconditionisevaluatedbyconsidering [and inothercases]asnormal randomvariableshavingameanequaltothemeasured valueandastandarddeviationequaltotheuncertainty. Finally,theprobabilityassociatedateachpathisgivenas theproductoftheprobabilitiesofallthethreesteps.So,the probabilitythatapixelofcoordinates isanedgepoint canbeobtainedasthesumoftheprobabilityvaluesassociated ateachpathdrivingtothedetection. V.NUMERICALVERIFICATIONANDEXPERIMENTALVALIDATIONAspreviouslydiscussed,numericalverificationconsistsof comparingtheresultsoftheoreticalanalysiswithresultsofa numericalsimulation.Tothisaimasetof images isgeneratedstartingfromareferencenoiselessimage .Each pixelofthe thimage isobtainedbymeansofarandom functionwithmeanvalueequalto ,andstandarddeviationequalto [ isthepixeluncertaintyprovidedbytheaforementionedanalyticalmodel].Then,the and matricesareobtainedforeach thimageoftheset bytheCannyoperator.Finally,the and matricesareobtained: isequaltothestandarddeviationofthe elements ,and isequaltotheratio betweenthenumberof thatarenotzeroand Fig.4.(a)Hexagon,forthe12throw;(b)thepercentagerelativeuncertaintyu %;and(c)Pversusthecolumnindex,measured(solid)expected(dashed). Fig.5.(a)Circle,forthe12throw;(b)thepercentagerelativeuncertaintyu %;and(c)Pversusthecolumnindex,measured(solid)expected(dashed).and cannowbecomparedwiththeirequivalentobtainedby thetheoreticalanalysis. Theabove-mentionedverificationhasbeencarriedoutontwo referenceimages,anhexagon andacircle [seeFigs.4(a) and5(a)]whicharebothcharacterizedby: spatialresolution,8bintensityresolution,twocolorimages( fortheback-

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1106IEEETRANSACTIONSONINSTRUMENTATIONANDMEASUREMENT,VOL.49,NO.5,OCTOBER2000 Fig.6.(a)Cannyalgorithmoutputforimage2;forthe200throw;(b)the percentagerelativeuncertaintyu %;and(c)P,versusthecolumnindex, measured(solid)expected(dashed).ground,and fortheobject).Testshavebeenconductedfor differentvaluesof and andwith usingMatlab. Figs.4(b)and5(b)reportthe percentagerelativeuncertainty ,whileFigs.4(c)and5(c) showtheprobability evaluatedintestswith and forFig.4,and and forFig.5.Percentagerelative %ratherthanabsolute uncertaintyisreportedbecause and arenotconstrainedinthe8-bgrayscale.Ineachcaseanexcellentagreementbetweentheoretical(dashed)andsimulation (solid)resultsisshown,thusconfirmingthecorrectnessofthe analyticalformulation.Moreover,itcanbenotedthatforthe chosenimagecharacteristics(shape,contrast,andnoise)the achievedresultshighlightthattheuncertaintyon alwaysinfluencestheno-maximumsuppressionalgorithmonlyinrelationtothefewpixelswherethestepedgeisconsistent. Afterthenumericalverification,anexperimentalvalidation ofthetheoreticalanalysiswascarriedouttoconfirmtheaccuracyoftheadopteduncertaintymodel.Thesamestepsofthenumericalverificationwerefollowedexcepttheimagegeneration. Inthiscase,infact,thesetof images isobtained through cameraacquisitionsofthesameimage,allperformed inthesameexternalconditions.Forthesakeofbrevity,onlyresultsconcerningtheobjectofFig.2(a)arereported.Fig.6(a) showstheoutput oftheno-maximumsuppressionalgorithm.Boththecalculatedvalues(dashed)andthemeasured values(solid)of %andof provetobe ingoodagreementinFig.6(b)and(c),respectively,thusconfirmingtheconsiderationmadeonthenumericalverification results.Finally,bothnumericalandexperimentalresultsconcerningonerowarecharacterizedbythesamedegreeofagreementoftheotherrows. VI.CONCLUSIONSAmethodfortheapplicationofthewhiteboxapproachtothe metrologicalcharacterizationofimageprocessingalgorithms hasbeenpresentedandappliedtotheCannyedgedetector. Namely,ananalyticalexpressionofCannyoperatoroutputuncertaintyisgiventhatavoidstheneedforburdensomeexhaustivesetsofexperimentaltests.Thistheoreticalanalysisofthe edgedetector,extendedtotheno-maximumsuppressionalgorithm,hasledtoastatisticaltreatmentoftheuncertaintyof theedgedetectionprocess.Bothnumericalverificationandexperimentalvalidationfullyagreewiththetheoreticalresults, showingthesignificantinfluenceofthedigitalizationuncertaintyontherepeatabilityoftheedgedetectionprocess.Further effortswillbedriventoenumeratetheanalyticalrelationship betweentheprobability andtheuncertaintyofthemorphologicalmeasurementsmadeusingedgepoints. ACKNOWLEDGMENTTheauthorswishtothankDr.T.FerrareseandDr.S.Amico forthehelpgivenintheexperimentalwork. REFERENCES [1]R.Chelappa etal. ,Thepast,present,andfutureofimageandmultidimensionalsignalprocessing, IEEESignalProcessingMag. ,vol.15, no.2,pp.21,Mar.1998. [2]L.DorstandA.W.M.Smeulders,Discreterepresentationofstraight lines, IEEETrans.PatternAnal.MachineIntell. ,vol.PAMI-6,pp. 450,July1984. [3]D.I.Havelock,Geometricprecisioninnoise-freedigitalimages, IEEE Trans.PatternAnal.MachineIntell. ,vol.11,pp.1065,Oct.1989. [4] ,Thetopologyoflocalesanditseffectsonpositionuncertainty, IEEETrans.PatternAnal.MachineIntell. ,vol.13,pp.380,April 1991. [5]B.Kamgar-ParsiandB.Kamgar-Parsi,Evaluationofquantizationerror incomputervision, IEEETrans.PatternAnal.MachineIntell. ,vol.11, pp.929,Sept.1989. [6]C.Ho,Precisionofdigitalvisionsystems, IEEETrans.PatternAnal. MachineIntell. ,vol.PAMI-5,pp.593,Nov.1983. [7]P.Sarkar,G.Nagy,J.Zhou,andD.Lopresti,Spatialsamplingof printedpatterns, IEEETrans.PatternAnal.MachineIntell. ,vol.20, pp.344,Mar.1998. [8]V.S.NalwaandT.O.Binford,Ondetectingedges, IEEETrans.PatternAnal.MachineIntell. ,vol.PAMI-8,pp.699,Nov.1986. [9]P.M.GriffinandJ.R.Villalobos,Processcapabilityofautomatedvisualinspectionsystems, IEEETrans.Syst.,Man,Cybern. ,vol.22,pp. 441,May1992. [10]R.KakaralaandA.Hero,Onachievableaccuracyinedgelocalization, IEEETrans.PatternAnal.MachineIntell. ,vol.14,pp.777,July 1992. [11]C.C.YangandM.M.Marefat,Spatialquantizationerrorsinactive visioninspection,in Proc.IEEEInt.Conf.Syst.,Man,Cybern., ,vol.1, SanAntonio,TX,1994,pp.67. [12]S.Yi,R.M.Haralick,andL.G.Shapiro,Errorpropagationinmachine vision,machinevisionandapplications, Mach.Vis.Applicat. ,vol.7, pp.93,1994. [13]T.Kanungo,M.Y.Jaishima,J.Palmer,andR.M.Haralick,Amethodologyforquantitativeperformanceevaluationofdetectionalgorithms, IEEETrans.ImageProcessing ,vol.4,pp.1667,Dec.1995. [14]G.Betta,C.Liguori,andA.Pietrosanto,Uncertaintyanalysisindigital signalprocessingalgorithms,in Proc.XIVIMEKOWorldCongress vol.IV,Tampere,Finland,Giugno1997,pp.267. [15] ,UncertaintyanalysisinfastFouriertransformalgorithms,in AttidelXIMEKOTC-4ISDDMI ,Napoli,Italy,Settembre1998,pp. 747.

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DESANTO etal. :UNCERTAINTYCHARACTERIZATIONINIMAGE-BASEDMEASUREMENTS1107[16] ,Astructuredapproachtoestimatethemeasurementuncertainty indigitalsignalprocessingalgorithms,in IEEProc.Sci.Meas. Technol. ,vol.146,Jan.1999,pp.21. [17]G.J.Klinker,S.A.Shafer,andT.Kanade,Aphysicalapproachtocolor imageunderstanding, Int.J.Comput.Vis. ,vol.4,pp.7,1990. [18]ISOguidetotheexpressionofuncertaintyinmeasurement(GUM),, 1993. [19]H.D.TagareandR.J.P.deFigueiredo,Onthelocalizationperformancesmeasureandoptimaledgedetection, IEEETrans.PatternAnal. MachineIntell. ,vol.PAMI-12,pp.1186,Dec.1986. [20]J.Canny,Acomputationalapproachtoedgedetection, IEEETrans. PatternAnal.MachineIntell. ,vol.PAMI-8,pp.679,Nov.1986. MassimoDeSanto (M)graduatedinelectronicengineeringandreceived thePh.D.degreeincomputersciencefromtheUniversityofNapoli,Napoli, Italy. Since1993,hehasbeenaSeniorResearcherandAssistantProfessorinthe DepartmentofInformationTechnologyandElectricEngineeringoftheUniversityofSalerno,Fisciano,Italy,whereheismemberoftheArtificialVision ResearchGroup.Since1985,hehasbeenactiveinthefieldofcomputernetworks,imageprocessing,andpatternrecognition.Heisauthorofmorethen60 researchworks.HeisScientificCoordinatorofseveralresearchprojectsfunded bytheItalianMinistryofUniversityandbyEuropeanCommunity.Hismain presentresearchinterestsconcerndistributedmultimediaapplicationforeducationandimagecompressionformultimedia. Dr.DeSantoisaMemberoftheACM. ConsolatinaLiguori (M)wasborninSolofra (AV),Italy,in1969.ShereceivedtheM.S.degree inelectronicengineeringfromtheUniversityof Salerno,Fisciano,Italy,in1993,andthePh.D. degreeinindustrialengineeringfromtheUniversity ofCassino,Cassino,Italy,in1997. Since1997,shehasbeenAssistantProfessorof electricalandelectronicmeasurementsattheUniversityofCassino.Hercurrentresearchinterestsare concernedwithdigitalsignalprocessing,software characterization,measurementsbasedonimage processing,andmeasurementsystemsforfaultdetectionanddiagnosis. AntonioPietrosanto (M)wasborninNapoli, Italy,in1961.HereceivedtheM.S.andPh.D. degreesinelectricalengineeringfromtheUniversity ofNapoliin1986and1990,respectively. In1991,hebecameAssistantProfessorofelectricalandelectronicmeasurementsattheUniversity ofSalerno,Fisciano,Italy,wherehehasbeenAssociateProfessorofelectricalandelectronicmeasurementssince1999.Heisprincipallyconcernedwith researchintoinstrumentfaultdetectionandisolation, digitalsignalprocessingsoftwarecharacterization,sensorrealizationandcharacterization,andVXI-basedinstruments.



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IMPROVEDVISUALIZATIONALGORITHMSFORVERTICALTWO-PHASEANNULAR FLOW By WESLEYWARRENKOKOMOOR ATHESISPRESENTEDTOTHEGRADUATESCHOOL OFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENT OFTHEREQUIREMENTSFORTHEDEGREEOF MASTEROFSCIENCE UNIVERSITYOFFLORIDA 2011

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IdedicatethistotheashesoftheDepartmentofNuclearandRadiologicalEngineering. 2

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ACKNOWLEDGMENTS TheauthorgratefullyacknowledgestheteachingguidanceofDr.DuWayneSchubring, whohasdemonstratedacommittmenttothesuccessofhisstudentsandtotheoverallqualityof thermalhydraulicresearch. TheauthorrecognizesandappreciatesthematchingnancialsupportfortheNRCFaculty DevelopmentGrantProgramfromtheUniversityofFloridaCollegeofEngineeringandDepartmentofNuclearandRadiologicalEngineering.Additionalfundingforresearchequipmenthas alsobeengraciouslyprovidedbytheUniversityofFloridaDivisionofSponsoredResearch. 3

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TABLEOFCONTENTS page ACKNOWLEDGMENTS....................................3 LISTOFTABLES.......................................7 LISTOFFIGURES.......................................8 LISTOFSYMBOLS......................................11 ABSTRACT...........................................15 CHAPTER 1INTRODUCTION....................................16 1.1AnnularFlowOverview...............................16 1.2QuantitativeVisualization..............................17 1.3Objectives......................................18 2LITERATUREREVIEW.................................20 2.1RegimeIdentication................................20 2.2FlowVisualization.................................24 2.3AnnularFlowModeling...............................28 2.3.1SchubringandSheddPredictionofFilmThickness............30 2.3.2SchubringandSheddPredictionofWaveBehavior,EntrainedFraction, andPressureGradient............................32 2.4ApplicationofLiterature..............................35 3PLIFEDGEIDENTIFICATION.............................37 3.1PLIFOptics.....................................37 3.2PLIFProcessing...................................38 3.2.1PLIFImageProcessing...........................39 3.2.2CodeModications.............................42 3.2.3PLIFOutlier-SelectionGUI.........................43 3.2.4PLIFDataProcessing............................45 3.3PLIFResults....................................47 3.3.1PLIFImageComparison..........................47 3.3.2PLIFSingle-ZoneComparison.......................47 3.3.3PLIFBaseandWaveComparison......................55 3.3.3.1CriticalStandardDeviationMultiplierMethod.........55 3.3.3.2IntermittencyInputMethod...................60 4PLIFINTERFACETRACKING.............................66 4.1PLIFImagePairProcessing.............................66 4

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4.1.1PLIFImagePairEdgeProcessing......................68 4.1.2PLIFImagePairDivisions.........................68 4.1.3PLIFImagePairCross-Correlation.....................68 4.1.4PLIFImagePairDataProcessing......................69 4.1.4.1PLIFImagePairOutlierRemoval................72 4.1.4.2VanDriestModelDataFitting..................72 4.2PLIFImagePairResults..............................73 5VERTICALWAVELENGTHMEASUREMENT....................77 5.1VerticalWaveVideoAcquisition..........................77 5.2VerticalWaveLengthProcessing..........................79 5.3VerticalWaveLengthResults............................81 5.3.1IndividualWaveLengthResults......................81 5.3.2AverageWaveLengthResults........................82 5.3.3WaveCorrelations..............................83 6GLOBALMODELAPPLICATION...........................85 6.1Re-CorrelatedFilmBehavior............................85 6.1.1PLIFObservationsFEPTestSection...................85 6.1.2VerticalWaveObservations.........................86 6.2ModelAdjustments.................................87 6.3ComparisontoVerticalDataFEPTube......................88 6.4ComparisontoVerticalDataQuartzTube....................89 7CONCLUSIONS.....................................94 7.1PLIFConclusions..................................94 7.2PLIFImagePairConclusions............................95 7.3VerticalWaveConclusions.............................96 7.4GlobalModelConclusions.............................97 7.5OverallConclusions.................................98 7.6RecommendedFutureWork............................99 APPENDIX APLIFDATA........................................101 BPLIFHISTOGRAMS:BASEANDWAVE........................104 CPLIFHISTOGRAMS:STANDARDDEVIATIONMULTIPLIERMETHOD.....107 DPLIFHISTOGRAMS:INTERMITTENCYMETHOD.................115 EPLIFIMAGEPAIRDATA................................126 FMEANINTERFACIALVELOCITYPLOTS......................127 5

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GVERTICALWAVELENGTHDATA...........................130 HVERTICALWAVELENGTHEXAMPLEIMAGES..................132 REFERENCES.........................................138 BIOGRAPHICALSKETCH..................................143 6

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LISTOFTABLES Table page 3-1InitialcropwidthsforPLIFimageprocessing.......................39 3-2Errorcomparisonforlmthicknessrelativeroughnesscorrelation............55 3-3Errorcalculationsforbase-to-waveratiocorrelation...................62 5-1Frameratesandvideolengthsforverticalwavevideos.................79 5-2Performanceofvertical-specicwavecorrelations....................84 6-1PerformanceofpresentglobalmodelforverticalFEPlmthicknessdata........88 6-2Performanceofpresentglobalmodelforverticalquartztubedata............89 A-1VerticalFEPtubedata...................................101 A-2PLIFdatausing k c method.................................102 A-3PLIFdatausing INT w method...............................103 E-1FlowconditionsforPLIFimagepairsets.........................126 G-1Verticalquartztubewavedata.............................130 G-2Verticalquartztubewavedata.............................131 7

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LISTOFFIGURES Figure page 1-1PLIFimagesofbaselm..................................17 1-2Back-litimagesofdisturbancewaves...........................18 2-1Verticalowregimes,asshownbyHewittandHallTaylor................21 2-2Schematicillustrationofoodingandowreversal....................23 3-1TestsectionforPLIFmeasurements.Flowisoutoftheplaneofthepage........38 3-2ExamplerejectedPLIFimages...............................46 3-3ExampleprocessedPLIFimagesforowcondition121F.................48 3-4ExampleprocessedPLIFimagesforowcondition162F.................49 3-5Histogramsoflmthicknessbaseandwavecomparisontooriginalresults.......50 3-6Histogramsoflmthicknessbaseandwavecomparisontooriginalresults.......51 3-7Histogramsoflmthicknessbaseandwavecomparisontooriginalresults.......52 3-8Histogramsoflmthicknessbaseandwavecomparisontooriginalresults.......53 3-9Totallmthicknesstrendcomparison...........................54 3-10Histogramsofbaselmusing k c methodforselectedowconditions..........56 3-11Histogramsofbaselmusing k c methodforselectedowconditions..........57 3-12Baselmthicknesstrendsusing k c methodforselectedowconditions.........58 3-13Histogramsofwaveheightusing k c methodforselectedowconditions.........59 3-14Histogramsofwaveheightusing k c methodforselectedowconditions.........60 3-15Waveheighttrendsusing k c method............................61 3-16Ratioofwaveheighttobaselmusing k c method....................62 3-17Baselmthicknesstrends, k c methodversus INT w method...............63 3-18Waveheighttrends, k c methodversus INT w method...................64 3-19Ratioofwaveheighttobaselm, k c methodversus INT w method............65 4-1DiagramofprocessingpathforPLIFinterfacetracking..................67 4-2PLIFcross-correlationexamplegraphs..........................70 8

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4-3PLIFcross-correlationexampleimages..........................71 4-4 y + vs. u + i plotsforselectedowconditions.......................74 4-5 y + vs. u + i plotsforselectedowconditions.......................75 4-6Average y + vs. u + i ,by U sg .................................75 4-7PLIFinterfacialvelocitydatawithvanDriestmodel..................76 5-1Schematicofverticalowloopwithquartztestsection..................78 5-2Visualizationsectionforverticalwaves,includingmeasurementforphysicalscale...78 5-3Schematicofverticalwavelengthmeasurementtechniques................80 5-4Examplewavelengthcomparisonimagesforvaryinggasvelocities............82 5-5Wavelengthandintermittencytrendswithcomparisonofmeasurementtechniques..83 5-6Wavelengthandintermittencycorrelationperformance..................84 6-1ModelresultspertainingtolmthicknessforverticalFEPtube..............90 6-2Componentsof i frommodelforverticalFEPtube....................91 6-3Performanceofmodelinverticalquartztube.......................92 6-4Modeledentrainedfraction, E mod ,inverticalquartztube. Left By U sl Right By U sg .93 B-1Histogramsoflmthicknessbaseandwaveforselectedowconditions........104 B-2Histogramsoflmthicknessbaseandwaveforselectedowconditions........105 B-3Histogramsoflmthicknessbaseandwaveforselectedowconditions........106 C-1Histogramsofbaselmthicknessusing k c methodforselectedowconditions.....107 C-2Histogramsofbaselmthicknessusing k c methodforselectedowconditions.....108 C-3Histogramsofbaselmthicknessusing k c methodforselectedowconditions.....109 C-4Histogramsofbaselmthicknessusing k c methodforselectedowconditions.....110 C-5Histogramsofwaveheightusing k c methodforselectedowconditions.........111 C-6Histogramsofwaveheightusing k c methodforselectedowconditions.........112 C-7Histogramsofwaveheightusing k c methodforselectedowconditions.........113 C-8Histogramsofwaveheightusing k c methodforselectedowconditions.........114 D-1Histogramsofbaselmthicknessusing INT w methodforselectedowconditions...116 9

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D-2Histogramsofbaselmthicknessusing INT w methodforselectedowconditions...117 D-3Histogramsofbaselmthicknessusing INT w methodforselectedowconditions...118 D-4Histogramsofbaselmthicknessusing INT w methodforselectedowconditions...119 D-5Histogramsofbaselmthicknessusing INT w methodforselectedowconditions...120 D-6Histogramsofwaveheightusing INT w methodforselectedowconditions......121 D-7Histogramsofwaveheightusing INT w methodforselectedowconditions......122 D-8Histogramsofwaveheightusing INT w methodforselectedowconditions......123 D-9Histogramsofwaveheightusing INT w methodforselectedowconditions......124 D-10Histogramsofwaveheightusing INT w methodforselectedowconditions......125 F-1PLIFinterfacialvelocitydataplotsforselectedowconditions..............127 F-2PLIFinterfacialvelocitydataplotsforselectedowconditions..............128 F-3PLIFinterfacialvelocitydataplotsforselectedowconditions..............129 H-1Verticalwavelengthexampleimagesforowcondition139Q..............132 H-2Verticalwavelengthexampleimagesforowcondition140Q..............133 H-3Verticalwavelengthexampleimagesforowcondition141Q..............133 H-4Verticalwavelengthexampleimagesforowcondition143Q..............134 H-5Verticalwavelengthexampleimagesforowcondition145Q..............134 H-6Verticalwavelengthexampleimagesforowcondition147Q..............135 H-7Verticalwavelengthexampleimagesforowcondition149Q..............135 H-8Verticalwavelengthexampleimagesforowcondition151Q..............136 H-9Verticalwavelengthexampleimagesforowcondition153Q..............136 H-10Verticalwavelengthexampleimagesforowcondition155Q..............137 H-11Verticalwavelengthexampleimagesforowcondition157Q..............137 10

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LISTOFSYMBOLS,NOMENCLATURE,ORABBREVIATIONS A aream 2 A r functionofroughnessfromNikuradseequation avedarki averagedarknessaxialinverticalwavevideoimages avedarkX average,time-independentdarknessaxialinverticalwavevideoimages base assubscriptpertainstobaselm c B parameterinHurlburt etal. rough-tubefrictionfactor C f Fanningfrictionfactor core assubscriptpertainstothegascore crit assubscriptcritical D diameterm D h hydraulicdiameterm ddarki normalizedaveragedarknessaxialinverticalwavevideoimages E entrainedfraction f wave wavefrequencys )]TJ/F22 7.9701 Tf 6.586 0 Td [(1 FEP ourinatedethylenepropylene film assubscriptpertainstoliquidlm fps framesperseconds )]TJ/F22 7.9701 Tf 6.587 0 Td [(1 fric assubscriptpartduetofriction g accelerationduetogravity g assubscriptpertainstogasphase G massuxkgm )]TJ/F22 7.9701 Tf 6.586 0 Td [(1 s )]TJ/F22 7.9701 Tf 6.586 0 Td [(2 11

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HEA assubscriptpertainstomodelofHurlburt etal. i assubscriptevaluatedatgas-liquidinterface INT w waveintermittency k c PLIFstandarddeviationmultiplier KE s supercialkineticenergydynamicpressureJm )]TJ/F22 7.9701 Tf 6.586 0 Td [(3 l assubscriptpertainstoliquidphase L wave lengthofadisturbancewavem LF linearfractionfromlmthicknessmodel m massowratekgs )]TJ/F22 7.9701 Tf 6.587 0 Td [(1 m + non-dimensionalmassowrate mod assubscriptpertainstoamodeledresult n FC numberofowconditionsconsidered n frames numberofframesinaverticalwavevideo n pairs numberofPLIFimagepairs nom assubscriptnominalvalue OH assubscriptpertainstotheOwenandHewittmodel P pressurePa PLIF planarlaser-inducedourescence Q volumetricowratem 3 s )]TJ/F22 7.9701 Tf 6.586 0 Td [(1 Quartz pertainstoquartztestsection R D dropletdepositionuxkgm )]TJ/F22 7.9701 Tf 6.586 0 Td [(2 s )]TJ/F22 7.9701 Tf 6.586 0 Td [(1 Re Reynoldsnumber 12

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Re ? roughnessReynoldsnumber rough assubscriptpartduetoroughnessasopposedtodrag Score wavescore Sr Strouhalnumber SS assubscriptpertainstoacorrelationintheworksofSchubringand Shedd t timegenerals t video lengthofhigh-speedvideos trans assubscriptrelatedtothetransitionfrombaselmzonetowavezone u axialvelocityms )]TJ/F22 7.9701 Tf 6.587 0 Td [(1 U velocitygeneralms )]TJ/F22 7.9701 Tf 6.587 0 Td [(1 U + non-dimensionalvelocitygeneral u + non-dimensionalaxialvelocity u ? liquidfrictionvelocityms )]TJ/F22 7.9701 Tf 6.586 0 Td [(1 U D velocityofdepositingdropletsms )]TJ/F22 7.9701 Tf 6.586 0 Td [(1 U E velocityofentrainingdropletsms )]TJ/F22 7.9701 Tf 6.586 0 Td [(1 U s supercialvelocityvolumeuxms )]TJ/F22 7.9701 Tf 6.587 0 Td [(1 UVP universalvelocityprole v fric;g gasfrictionvelocityms )]TJ/F22 7.9701 Tf 6.587 0 Td [(1 v wave wavevelocityms )]TJ/F22 7.9701 Tf 6.587 0 Td [(1 wave assubscriptpertainstowaves voidfraction lmthicknessm 13

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+ wallcoordinatelmthicknessnon-dimensional t timedifferencePLIFimagepairss roughnessheightm ^ non-dimensionalroughnessheight eff effectiveroughnessm vonK arm anconstant dynamicviscositykgm )]TJ/F22 7.9701 Tf 6.587 0 Td [(1 kinematicviscositym 2 s )]TJ/F22 7.9701 Tf 6.587 0 Td [(1 RR parameterinlmthicknessmodel densitykgm )]TJ/F22 7.9701 Tf 6.586 0 Td [(3 surfacetensionNm )]TJ/F22 7.9701 Tf 6.587 0 Td [(1 shearPa 14

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AbstractofThesisPresentedtotheGraduateSchool oftheUniversityofFloridainPartialFulllmentofthe RequirementsfortheDegreeofMasterofScience IMPROVEDVISUALIZATIONALGORITHMSFORVERTICALTWO-PHASEANNULAR FLOW By WesleyWarrenKokomoor May2011 Chair:DuWayneSchubring Major:NuclearEngineeringSciences Annularowisacongurationofgas-liquidtwo-phaseowcharacterizedbyathinlm ofliquidsurroundingacoreoffaster-movinggas.Theliquidlmisoftenasiteofcomplex geometrywhereliquidmasstransportoccursthroughbaselmanddisturbancewaves.Annular owoccursinawiderangeofindustrialheat-transferequipment,includingthetopofaBWR core,inthesteamgeneratorofaPWR,andinpostulatedaccidentscenariosincludingcriticalheat uxCHFbydryout. Thepresentworkfocusesonthecharacterizationofindividuallmbehaviorsinannular ow.Quantitativevisualizationtechniquesarediscussedthatprovideforlarge-scaledata collectionofmultiple,interrelatedowbehaviors.Thenon-trivialdatareductioncodesfor thesetechniqueshavebeenfurtherdevelopedinthepresentworktoimprovemeasurement accuracy.Filmthicknessdistributionbaselmandwave,disturbancewavelength,andwave intermittencyestimateshavebeenupdatedusingmodiedtechniques.Asystemisalsosuggested formeasuringthevelocityofthegas-liquidinterface.Lastly,thepresentobservationshavebeen appliedtoarecenttwo-regionbaselmanddisturbancewaveannularowmodel. 15

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CHAPTER1 INTRODUCTION Gas-liquidtwo-phaseowiscommontomanyindustrialapplications,especiallyin boilingorcondensingheattransferequipment.Nuclearpowerplantscontaintwo-phaseowin severalsystemsoflightwaterreactors,includingboilinginthecoreofaBWRandinthesteam generatorofaPWR.ThecoreofaPWRmayalsobethesiteofsaturatedboilinginoff-normal conditionsoraccidentscenarios. Thecontinuingstudyoftwo-phaseowisnecessaryduetothecomplexityofinteractions attheinterfacesbetweenphases.Mostdescriptionsoftheseinteractionsbeginbyrecognizing andcategorizingthegeneralarrangementofthetwo-phases,referredtoasaowregime.A morecomprehensivelookintoowregimecategories,traits,andidenticationisincludedin Section2.1. 1.1AnnularFlowOverview Thecurrentworkfocusesontheannularowregime,characterizedbyacoreoffast-moving gassurroundedbyaliquidlmalongthechannelwall.Annularowoccursthroughawide rangeofgasandliquidowrates.Innuclearsystems,annularowmaybeobservednearthetop ofthecoreinaBWRandinthesteamgeneratorofaPWR.Thisregimeisalsothenalstagein channelboilingbeforegas-dropletowoccursincriticalheatuxCHFbydryoutpostulated BWRaccidentscenario. Theliquidlmisoftenasiteofcomplexgeometry.Theliquidmovesslowlyrelativetothe gascoreandmaytransportasmallfractionofthegasasbubbles,whichcanaffectboilingheat transfer.Theremainderoftheliquidlmcanbedividedintobaselmanddisturbancewaves. Thebaselmoccupiesmostofthetotallmarea,creatingarelativelysmoothinterface withthegascore.SomeexampleimagesofbaselmareshowninFigure1-1,takenusinga planarlaser-inducedourescencePLIFtechniqueandprocessedusingthemethoddiscussedin Chapter3.Eachimagehasbeenrotated90 counter-clockwise,sotheverticalupowisshownas righttoleft.Thegasvelocityforthetopfourimagesisconsiderablylessthanforthetopfour 16

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ms )]TJ/F22 7.9701 Tf 6.587 0 Td [(1 vs. 78ms )]TJ/F22 7.9701 Tf 6.587 0 Td [(1 .Theimagesindicatethatanincreasedgasowratehasaslimmingeffecton baselmthickness. Figure1-1.PLIFimagesofbaselm. U sl =6.3cms )]TJ/F22 7.9701 Tf 6.587 0 Td [(1 U sg = topfour 46ms )]TJ/F22 7.9701 Tf 6.586 0 Td [(1 bottomfour 78ms )]TJ/F22 7.9701 Tf 6.586 0 Td [(1 Disturbancewavestravelalongtopofthebaselm,exchangingliquidmasswiththebase lmandtravelingatamuchhighervelocity.Someexamplebacklitwaveimages,processed usingthemethoddiscussedinChapter5,areshowninFigure1-2.Thewavesintheseimages arevisibleasdarkpatchesbecauselesslightistransferredthroughthethickerlmsections, indicativeofwavebehavior. Inadditiontobaselmandwaves,someliquidistransportedthroughthetubeasdroplets entrainedinthegascore.Thestudyofliquidentrainmentrequiresdifcultandoftenintrusive measurementsthatarenotamongthepresentvisualizationtechniques.However,thequalitative assessmentofentrainmentisanimportantaspectofannularowmechanics;entrainedliquid behavioriscloselytiedtodisturbancewavebehavior. 1.2QuantitativeVisualization Quantitativevisualizationreferstoafamilyofdataacquisitiontechniquesbasedon themanipulationanddetectionofradiationinaoweld.Thecenterofthevisualization processisanexperimentalapparatus,reconstructingaowscenariowithnecessarycontroland 17

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Figure1-2.Back-litimagesofdisturbancewaves. U sl =15.3cms )]TJ/F22 7.9701 Tf 6.587 0 Td [(1 U sg =52ms )]TJ/F22 7.9701 Tf 6.587 0 Td [(1 measurementability.Dependingonthetechnique,auiddyeortracermayalsobeanintegral partoftheapparatus. Theuid,dye,ortracerisbombardedbyaradiationsource e.g. laserandthesubsequent reactionisrecorded.Therecordeddatacanbeinawiderangeofformatsincludingintensity measurements,images,holograms,etc.andusuallyrequiresanon-trivialdatareductioncode specictotheexperiment.Theimplementationofmostquantitativevisualizationtechniques ismechanicallyandcomputationallyexpensive.However,withcarefulsetup,itpermitsoneto visualizecomplexoweldsnearlyinstantaneouslywithhighspatialandtemporalresolution. Thecurrentworkfocusesontwosystemsforquantitativevisualizationofannularow: planarlaser-induceduorescencePLIF,Chapters3and4forlmthicknessandhigh-speed videoChapter5forwavedata.Bothsystemsemployuser-developeddataregressioncodesin MATLAB. 1.3Objectives Theprimarygoalofthepresentresearchistoimprovetheunderstandingofverticalannular owbehaviorthroughtheimprovementofspecicbehaviordatabanks.Thisgoalhasbeensplit intotwomainobjectives: 18

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1.DeveloporimproveexistingMATLABcodefortheextractionofdatafromannularow images,including aFilmthicknessandroughnessfromPLIFimages, bInterfacialvelocityprolefromPLIFimages, cDisturbancewavevelocityandintermittencyfromback-littubeimages 2.Enhancebehaviorinterrelationshipsby aRe-assessmentandcorrelationofowparameterobservations,and bRe-optimizationoftheSchubringandShedd[1]modelforannularowbehavior. Allofthecorrelations,re-correlations,andmodeladjustmentsarescrutinizedbasedonthree measurementsoferror:meanerror,meanabsoluteerrorMAE,androot-meansquarederror RMS: MeanError = 1 n n X i =1 F i )]TJ/F23 11.9552 Tf 11.956 0 Td [(Y i Y i 100% MAE = 1 n n X i =1 F i )]TJ/F23 11.9552 Tf 11.955 0 Td [(Y i Y i 100% RMS = v u u t 1 n n X i =1 F i )]TJ/F23 11.9552 Tf 11.956 0 Td [(Y i Y i 100% 2 where F i isthepredictedvalue, Y i isthetrueexperimentalvalue,and n isthenumberofdata points. 19

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CHAPTER2 LITERATUREREVIEW Thischaptersummarizesliteraturereleventtothepresentresearch.Fundamentaltwo-phase owbehaviorandvisualizationtechniquesareoutlined,followedbyliteratureonthefollowing annularowbehaviorsofinterest: Baselmthickness, Disturbancewavevelocity,frequency,andlength, Liquidentrainment. Thebehaviorinterrelationshipsarediscussedusingtheglobal 2.1RegimeIdentication Thecharacterizationoftwo-phaseowthroughachannelhasbeenthesubjectofresearch formanydecadesduetothecomplexinteractionsattheinterfacesbetweenphases.Thecontrast betweensingleandmulti-phasesystemdynamicsisstark,butcertainelementsarestillrelevent, suchasturbulence.Single-phaseturbulencehasbeenwellestablishedinuiddynamicstext e.g. Kays etal. [2]andHolman[3]byuseofthedimensionlessReynoldsnumber, Re D : Re D = u l D h l where u l istheaverageliquidvelocity, l istheliquidkinematicviscosityand D h isthehydraulic diameterusedtocharacterizechannelgeometries.Foragivengeometry,anupperlimitfor laminarbehaviorcanbeformedintermsof Re D ,abovewhichtransitionalorfullyturbulent behaviorprevail. Incontrast,textssuchasWhalley[4]havedemonstratedtheseverechangesinthephysical natureoftwo-phasegas-liquidowsoverarangeofowparameters.Theinteractionbetween phasesinamulti-phasechanneloftenbecomesverycomplex,leadingtodistinctcongurations, orowregimes,asafunctionofuidpressure,gasandliquidowrates,uidproperties,and channelgeometry.HewittandHallTaylor[5]suggestedfourbasicowregimesforverticalow, 20

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showninFigure2-1:thebubblyregime,wherevaporbubblesareevenlydispersedthroughout acontinuousliquidphase;slug,wherelargebubblesslugstakeupmuchofthevolume;churn, wherethefastermovinguidscreatecomplexoscillations;andannular,whereacontinuouscore ofgasissurroundedbyathinlmofslower-movingliquid. Figure2-1.Verticalowregimes,asshownbyHewittandHallTaylor[5].Fromleft-to-right: bubblyow,slugow,churnow,andannularow. Inaddition,awispy-annularregimehasbeenobservedsuchasbyHewittandRoberts [6]forhighgasandhighliquidow,causingalargefractionofliquidtotravelthroughthegas coreaswispstructures.Oneofthecharacteristicsofthewispy-annularregime,asdiscussed byHawkes etal. [7],isthesignicantuctuationinpressuregradient.Theyalsodevelopeda mechanismforpredictingthetransitionintothisregimebasedonconservationequationsandthe developmentofsustainedliquidwavesinthegascore. Modelingattemptsfortwo-phaseowareoftenspecictooneoftheseregimesduetothe differencesinphaseinteractions.Theconsequencesofnonregime-specic,orpatternless, modelinghavebeendiscussesindetailbyThome[8,9]withaheattransferperspective.Several negativeeffectswerediscussedbyThome,including: 1.Failuretopredicttheonsetofdryoutorthesharpdeclineintwo-phasevoidfractionduring certaindryoutscenarios. 2.Theneglectofproperannularlmheattransfer. 21

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3.Theneglectofproperturbulentandthermalboundarylayertheoryforheattransfer. Thedeterminationofverticaltwo-phaseregimesbasedonbasicowparametershasbeen addressedfrommanyangles.Severalattemptshavebeenmadeintheliteraturetoplotregime transitionsonspeciedcoordinates.Ashortsummaryofthisconcept,referredtoasregime mapping,hasbeenprovidedbyWhalley[4].Oneoftheearliestattemptsatregimemapping Baker[10]reliedontheobservationoftransitionsbytheauthor.Theplottingcorrdinatesfor theBakermaparethemassuxesofthegasandliquidwithcorrectionsforuidproperties.The usefulnessofthismapislimitedtosmalltubediameters < 0.05mandforair/waterowsfor whichthemapwasdeveloped. TheHewittandRoberts[6]mapwasalsoproducedbyobservationforair/watersystems, thistimeforverticalowandwithmappingcoordinatesofmomentumux,calculatedfrom themassux G anddensity .Theinclusionofdensityinthemappingcoordinatescreates somesensitivitytopressureintheowsystem.However,therelianceofobservationinthe developmentofthemapisstillinherentlysubjective.TheworkofTaitel etal. [11]wasone attempttocreateregimetransitioncriteriafrommechanicalprinciples.Manyofthesetheoretical processes,however,havebeenunderscrutinyduetoquestionablephysicalprinciplesWhalley [4].AcritiqueoftheTaitel etal. principleshasalsobeenprovidedbyHewitt[12]. MishimaandIshii[13]havealsodevelopedtransitioncriteriabasedonprinciplesofuid mechanics.Ofparticularinteresttothecurrentworkisthechurn-to-annulartransition,whichhas beendevelopedintheone-dimensionaldriftuxmodelbyHibikiandIshii[14]anddescribedby twomechanisms. Therstmechanismrelatestheonsetofannularowtotheabsenceofowreversalinthe liquidlmsectionalonglargebubbles.Thisiscloselyrelatedtotheconceptsofowreversaland oodingthetransitionbetweencountercurrentandcocurrentow,showninFigure2-2.Fowler andLisseter[15]haveprovidedareviewofmechanicalprinciplesfortheonsetofcocurrentow oodingusingatwo-uidmodel.Floodingisanalagoustothechurn-to-annulartransition, consideringcountercurrentowaslargebubblesinaslugregime. 22

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Figure2-2.Schematicillustrationofoodingandowreversal,asshownbyFowlerandLisseter [15]. ThesecondannulartransitionmechanismdescribedbyHibikiandIshiiisthedestruction ofliquidslugsorwavesbyentrainmentordeformation.Thiswouldoccuratasupercialgas velocity, U sg ,sufcienttoentrainliquidinthecore.Equation2hasbeenderivedbyaforce balancebetweentheshearingforceofthevapordragandthesurfacetensionoftheliquid.The applicationofthismodelhasbeenlimitedtotubediameterslargerthanthecriterionshownin Equation2forroundtubegeometry. U sg g 2 g 1 = 4 N )]TJ/F22 7.9701 Tf 6.586 0 Td [(0 : 2 f 23

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D> r g N )]TJ/F22 7.9701 Tf 6.586 0 Td [(0 : 4 f [ )]TJ/F15 11.9552 Tf 11.956 0 Td [(0 : 11 C o =C o ] 2 N f = f f s g # )]TJ/F22 7.9701 Tf 6.586 0 Td [(1 = 2 C o =1 : 2 )]TJ/F15 11.9552 Tf 11.955 0 Td [(0 : 2 s g f 2.2FlowVisualization Flowvisualizationreferstotheidenticationofvisiblepatternsinuidmotionandthesubsequentqualitativeorquantitativeanalysis.Thepresentdiscussionfocusesonthosetechniques thatenhancetheunderstandingofannulartwo-phaseow. Perhapsthemostbasicapplicationofowvisualizationisbydirectimagemanipulationand processing.Ohta etal. [16]hasdemonstratedearlyimagethresholdingmethodsfordetermining velocityoweldsforbubbles.Theuseofhigh-speedvideoandimageprocessingfortwo-phase owhasbeendemonstratedbyRezkallah etal. [17,18]todeterminelocalgasphasevelocities andinstantaneousvoidfractions.Thesestudiesaresensitivetotwo-phaseowregimesand provideregime-specicdataandearlyestimationsoferror. Recently,Schubring etal. [19]hasprovidedaquantitative,statisticalapproachtovertical annularowwavemeasurementsbyimagemanipulationandprocessing.Theimagesusedin thestudywereobtainedbyhigh-speedvideoofabacklittube.Thevisualizationofdisturbance waveshasalsobeenspecicallystudiedbyBelt etal. [20]throughtheuseofconductance-based lmthicknesssensors.Thesensorswereappliedinanarraythatfacilitatedthetime-resolved, three-dimensionalvisualizationofdisturbancewaves,whichisalsoreleventtothepresentwork onwavecharacteristics.Thevalidityofconductanceprobesaslmthicknessmeasurement deviceshasbeenscrutinizedbyRodr guez[21]forafailuretorecognizebubblesintheliquid lm.Thedevicesarealsooftenplacedintotheowandarethusinvasivetotheexperiment. Flowvisualizationmethodsareconstantlyadaptingtotechnologicaladvancements,notably lasercapabilitiesandcomputationalpower.Arecentandcomprehensivereviewofachievements 24

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intheareaisprovidedbySmitsandLim[22].Theabilitytoobtainandanalyzeinformation onparticlesinuidmotionhasbeenanextremelypowerfuladvancementoverthepastthree decades.Areviewofmeasurementsbyuidparticletechniquesonthemicroandmacroscale hasbeenprovidedbySinton[23].Popularparticle-basedvisualizationtechniquesincludelaserdopplervelocimetryLDV,particleimagevelocimetryPIV,andparticletrackingvelocimetry PTV. Two-beamLDVisoneoftheearliestlasersystemsforowmeasurement,popularin practicesincethemid1970s.MacroscaleLDVhasbeensuccessfullyappliedtotwo-andthreedimensionalowpatterns,includingthree-dimensionalturbulentboundarylayersbyCompton andEaton[24].InageneralLDVsystem,asmallvolumeofuid,seededwithreective particles,isexposedtotheinterferencepatterncreatedbytheintersectionoftwolasers.Flow velocitycanthenbedeterminedbycalculatingtheDopplerfrequencyinagivencontrolvolume. Thegoalformostuidvisualizationtechniquesistoachievespatialandtemporalresolution neenoughtoobservemicroscaleturbulentmotion.However,microscaleLDVhasbeen limitedtechnologicallybylaserdiameter,whichlimitsthesizeoftheinterferencesection,and statisticallybyreducingthenumberofparticlesintheinterferencesection.TheworkofCompton andEatondisplaystwo-dimensionalinterferencesectionsassmallas35 m 66 m .Further advancementshavebeenmadebyTieu etal. [25]withLDVvelocitymeasurementsascloseas 18 m toachannelwall. ParticleimagevelocimetryPIVinvolvesafundamentallydifferentapproachtoparticle motioninuids,addingtheabilitytotrackvelocityanddirectionforseverallocationsof interestatonce.Thehistoriesofmultipleseedparticlesinaowarerecordedbytime-elapsed photographyandareanalyzedinaseparateprocesstodeterminevelocityvectors. GeneralPIVsetupsallowanareatobeinstantaneouslyobservedthroughtheuseofa planarilluminationsource,usuallyapulsedlasersheet,andoneormorecameras.Theworkof Adrian[26]demonstratesthevarietyofinstrumentationtechniquesunderthegeneraltheoryof PIV.SeveralphysicallimitationsexistforaPIVsystemthatmustbeaddressedsimultaneously, 25

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includingsizeofthecontrolvolume,particledensity,particleresponse,andmethodsfortimeelapsedphotography.TheoptimizationofPIVsystemsfortwo-pulseimagingandmulti-pulse imaginghasalsobeendevelopedbyKeaneandAdrian[27,28]. AnotherlimitationofPIVisthecomputationalpowerrequiredforstatisticalimagecorrelation.Theextractionofquantitativedatafromparticleimagesisoftenthemostimportantstepin PIVmeasurements,asdescribedbyHinsch[29].Thecorrelationofmultipleparticleimagesis achievedbyautocorrelationorbycross-correlation.Autocorrelationisperformedbyshiftingan imageandcorrelatingwithitself,whichisusedinPIVsystemsthatacquireasingle,multipleexposedimage.Limitationstoautocorrelation,includingtheapparentlackofpositive/negative direction,havebeenmitigatedbyMarzoukandHart[30]. Incontrast,cross-correlationrequirestwoseparateimagesandknowledgeofthetime betweenthem.Theadvantageofcross-correlationistheknowledgeofdirectionduetothe independentlyexposedimages.TheworkKeaneandAdrian[31]hasshownconsiderable advancementincross-correlationtechniquesspecicallyfortheuseofPIVmeasurements.The disadvantagestothismethodincludemoreexpensiveinstrumentationcameraspeed,increased storagecapacitydoubletheimages,andincreasedcomputationalpowerimagemanipulation. TheusualapplicationofPIVcandevelopvelocityvectoreldsintwodimensions-D foraxedtime.SeveralinnovativetechniqueshavebeendevelopedtoapplyPIVtothree dimensions-Dtofullyunderstandvolumetricuidmotion.Arecentreviewofleading3DPIVtechniqueshasbeendiscussedbyHinsch[32].Theutmostinmulti-dimensionalow visualizationinvolvestheresolutionofthreevelocitydemensionsoverthreespacialdimensions withtime.Theonlyvisualizationtechniqueadvancedenoughtostoresuchahighquantityof data,todate,isholographicPIV. TheapplicationofPIVtoachievemicroscaleowsistermedasmicro-PIV,whichis especiallyusefulforlowvelocitiessuchasnear-wallowsorlowReynoldsnumberows. Santiago etal. [33]demonstratemicro-PIVmeasurementswithspatialresolutionsthatapproach onemicron. 26

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AlsoofparticularinterestistheapplicationofPIVtomultiphasegas-liquidows.The abilitytoresolvetwophaseswithmicro-PIVhasbeendemonstratedbyHassan[34]forbubbly air-waterowinaverticalchannel.Wavyandwavy-annularowregimeshavealsobeen successfullycharacterizedbySchubring etal. [35]usingmicro-PIV. ParticletrackingvelocimetryPTVattemptstoincreaseresolutionbytrackingindividual particlesratherthanlocations.TheclearadvantageoverPIV,whichrequiresapproximately20 particlesperinterrogationareatoobtainanaccuratevelocityvectorSinton[23],isthatPTV providesupto20individualvelocityvectors.Inpractice,however,individualparticletracking requiresmorethantwoimagespercorrelationsetandafractionofparticlesarelostintracking. Toprovideenoughowinformationtoaccuratelytrackindividualparticles,PTVtheory hasbeencoupledwithPIVcorrelations,oftenphrasedassuper-resolutionPIVanalysis.This wasrstaccomplishedbyKeane etal. in1995[36],whoimprovedthespacialresolutionof normalPIVmeasurementsby250 % .MorerecenteffortsbyTakehara etal. [37]haveshown improvementsofover500 % withsimilarmethods. Theadvancementsinlaserpowerandpulsefrequencycapabilitieshaveopenedupnew realmsofowvisualizationbasedonlaser-induceduorescenceLIF[22].MostLIFapplicationsforthetwo-dimensionalvisualizationofuidowarecollectivelyreferredtoasplaner laser-induceduorescencePLIF,whichhasbeenstudiedasearlyas1988byHanson[38]. PLIFusesalaseratanappropriatefrequencytoexcitetheseedmoleculesinauid,whichsubsequentlyouresce.Theresultisanearlyinstantaneouscross-sectionalimageofauid,making PLIFaveryattractivemethodforhigh-velocityturbulentowimaging.Kychakoff etal. [39] demonstratedtheearlyabilityofPLIFtovisualizehighlyturbulentamegases.Theworkof Hanson[40]furtherdemonstratedtheuseofPLIFforpressurizedcombustionprocesses. ThetransformationofPLIFimagesintoquantitativedataoftenrequiresunique,non-trivial imageprocessingandcanbeverycomputationallyexpensive.Earlyeffortstounderstandthe capabilitiesofPLIFbyvanCruyningen etal. [41]forowthroughanozzleemphasizedthe resolutionanderrorcalculationsofmeasurements.TheuseofPLIFtostudyannularowlm 27

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thicknessisamorerecentdevelopmentbyRodr guezandShedd[42],renedbySchubring et al. [43,44]. 2.3AnnularFlowModeling Thedataanalysisinthepresentworkisfocusedonthecharacteristicsofindividualthin-lm mechanismsliquidlmanddisturbancewavestatisticsandtheeffectsofthosemechanisms onannularowbehavior.Inatwo-zonemodelwavesandbaselm,disturbancewavesare modeledasseparatestructuresthanbaselmorentraineddroplets.Thetwo-zonemethodrelies heavilyonaccuratecharacterizationsofwavebehaviors. ReviewsofwavebehaviorareprovidedbyAzzopardiin1989[45]andagainin1997asa partofalargerreviewofentrainment[46].Forverticalupow,NeddermanandShearer[47]and HallTaylor etal. [48]observedthatwavevelocitiesandfrequenciesincreasewithincreasing gasandliquidowrate.Martin[49]hasobservedaninverseeffectoftubediameteronwave frequency.Aninverserelationshipbetweenliquidkinematicviscosityandwavefrequencyhas alsobeenobservedbyMori etal. [50]. Someresearch,suchasthatbyMori etal. [51],hassuggestedthepresenceoftwodistinct wavestructuresinverticalow,termeddisturbancewavesandhugewaves.Thelatterhave greateraveragevelocityandliquidmass.Hugewavesareobservedclosertotheannular-churn boundary,outsideoftherangeofthepresentwork. Fortheestimationofwavevelocity, v wave ,amechanisticmodelandanempiricalcorrelation havebeendevelopedbyPearce[52]thatincludeadependenceonliquidinterfacevelocity, U l;i However,thismeasurementismorechallengingthanthatof v wave itself.Kumar etal. [53] developeda v wave predictionbasedonsupercialvelocitiesandReynoldsnumbers: v wave;Kumar = C kumar U sg + U sl 1+ C Kumar C Kumar =5 : 5 g l 1 = 2 Re l Re g 1 = 4 Re l = m l D l 28

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Re g = m g D g Wavefrequencymodeling,suchasthatbySekoguchi etal. [54]andAzzopardi[45],often reliesoncorrelationwiththeStrouhalnumber, Sr : Sr wave = f wave D U sg ThecorrelationisoftenafunctionoftheliquidReynoldsnumber, Re l equation2.Onerecent correlationfor Sr hasbeendevelopedbySawant etal. [55]: Sr Sawant =0 : 086 Re l 0 : 27 l g )]TJ/F22 7.9701 Tf 6.587 0 Td [(0 : 64 Thereisalsoagreatemphasisinthewavefrequencyliteratureontheeffectofthevelocity distributionsonwavecoalescenceAzzopardi[45],HallTaylorandNedderman[56].Waves withawidervelocitydistributionhaveagreaterchanceofcollidingandcoalescingwithother waves,affectingtheoverallfrequency. Thelengthofdisturbancewaves, L wave ,referstothesizeofthestructuresratherthanthe spacingbetweenwavesandhasnotbeenwidelycorrelatedintheliterature. L wave isrelatedto waveintermittency,usedinglobalmodels e.g. SchubringandShedd[1],Hurlburt etal. [57]. Acorrelationfor L wave hasbeendevelopedbySchubring etal. [19]basedontubediameterand owquality: L wave;SS =0 : 53 x )]TJ/F22 7.9701 Tf 6.587 0 Td [(0 : 6 D Theunderlyinggoalofannularowresearchisthedevelopmentofaglobalmodelto predictallrelevantowcharacteristicsbasedonfew,easilyobtainableinputssuchasowrates, geometry,andthermodynamicstates.Desirableoutputsforaglobalmodelarepressuredrop, wavestatistics,lmthickness,lmvelocity,turbulence,andheattransfer.Informationregarding theinitiationofphasesinthechannelintroductionofphasesortransitionintoannularowis required. 29

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TheglobalmodelofSchubringandShedd[1]hasbeenchosenforfurtherdiscussion. SimilartotheHurlburt etal. [57]model,theSchubringandSheddmodelemploysatwo-zone base/wavelmroughnessconcepttolinkinterfacialshearandlmthickness.TheHurlburt et al. model,however,requireslmthicknessandentrainedfractionasinputs.TheSchubringand Sheddmodeladdressestheseissuesbyonlyrequiringowrates,uidpropertiesandgeometryas inputs.Theoutputsofthemodelincludepressuregradient,lmthicknesswithzoneseparation, anddisturbancewavevelocity.Thereisagreateremphasisonthebehaviorsintheliquidlm ratherthanonmodelingentrainmentordeposition. 2.3.1SchubringandSheddPredictionofFilmThickness Thepredictionoflmthicknessesoriginateswiththecorrelationofafrictionfactor,the sensitivityofwhichhasbeendescribedbytheauthorsasnegligible.Twocorrelationsforthe Fanningfrictionfactorhavebeenprovided.TherstistheBlasiusrelationEquation2 increasedbyafactor RR ,where Re core;base isdenedastheReynoldsnumberofthegascore overthebaselm.Experimentaldatahasbeenusedtocorrelate RR ,showninEquation2. Re core;base = g U core;base D core;base g C f;i;base =0 : 079 RR Re )]TJ/F22 7.9701 Tf 6.586 0 Td [(0 : 25 core;base RR =1 : 9 x 0 : 1 ThesecondisthefrictionfactorofHurlburt etal. [57],whosettheempiricalconstant c B;base to0.8: C f;i;base =0 : 58 2 )]TJ/F15 11.9552 Tf 21.771 8.088 Td [(ln^ base ^ base )]TJ/F15 11.9552 Tf 11.955 0 Td [(1 2 )]TJ/F15 11.9552 Tf 11.955 0 Td [(ln c B;base +1 : 05+ 1 2 ^ base +1 ^ base )]TJ/F15 11.9552 Tf 11.955 0 Td [(1 )]TJ/F22 7.9701 Tf 6.587 0 Td [(2 Theroughnessisevaluatedusing: base =2 )]TJ/F23 11.9552 Tf 11.955 0 Td [(LF base base ^ base = 2 base D )]TJ/F23 11.9552 Tf 11.955 0 Td [( base 30

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where LF base isthefractionoflmthatfollowsalinearvelocityprole.Theremainderofliquid lmisobservedasripplesatthegas-liquidinterfaceandismodeledaswell-mixedconstant velocity.Theripplesizewasrelatedtothestandarddeviationofbaselmheight,provided bytheexperimentaldataofSchubring etal. [43,44]as30%oftheaveragebaselm.The remaining70%isassumedtoowwithalinearviscousvelocityprole LF base =0.7. Theliquidvelocityattheinterface U l;i;base andlmowrate m film;base areestimated throughacomputationofshear: i;base = C f;i;base g U 2 core;base 2 u ? base = r i;base l + base = base u ? base l U + l;i;base = + base LF base U l;i;base = U + l;i;base u ? base m + film;base = LF 2 base 2 + LF base )]TJ/F23 11.9552 Tf 11.955 0 Td [(LF base )]TJ/F23 11.9552 Tf 5.479 -9.684 Td [( + base 2 m film;base =_ m + film;base D l Thevelocityofthegascoreoverthebaselm U core;base andcorevelocity U g;base are computedfromthefollowing: D core;base = D )]TJ/F15 11.9552 Tf 11.955 0 Td [(2 base A core;base = D 2 core;base 4 U core;base = U g;base )]TJ/F23 11.9552 Tf 11.955 0 Td [(U l;i;base U g;base = U sg A A core;base U sg = m g g A 31

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Themodelisclosedwitharelationofwaveheighttobaselmheight.Theaveragewave heightwasobservedtobeapproximatelydoubletheaveragebaselmheight: wave =2 base 2.3.2SchubringandSheddPredictionofWaveBehavior,EntrainedFraction,and PressureGradient Thetotalmodeledshearinthewavezone, i;wave ,isseparatedintotwotermsEquation2 32.Therst, i;wave;rough ,relatestotheroughnessofwavesandiscomputedinananalogous mannerasthebaselmroughness.Thesecond, i;wave;trans ,relatestothesuddentransitionsfrom owoverbaselmtoowoverwaves.Arough-tubefrictionfactor, C f;i;wave ,isestimatedto compute i;wave;rough ,where c B;wave isanempiricalconstantsettothevalueof2.4suggestedby Hurlburt etal. [57]: i;wave = i;wave;rough + i;wave;trans i;wave;rough = C f;i;wave g U 2 core;wave 2 C f;i;wave =0 : 58 2 )]TJ/F15 11.9552 Tf 21.771 8.087 Td [(ln^ base ^ base )]TJ/F15 11.9552 Tf 11.955 0 Td [(1 2 )]TJ/F15 11.9552 Tf 11.955 0 Td [(ln c B;wave +1 : 05+ 1 2 ^ base +1 ^ base )]TJ/F15 11.9552 Tf 11.955 0 Td [(1 )]TJ/F22 7.9701 Tf 6.587 0 Td [(2 TheSchubring etal. modelrequiresanapproximationforwaveroughness,whichwas calculatedasaconstant40%ofthemeanwaveheight.Waveroughnessisthereforecomputed with: wave =0 : 4 wave ^ wave = 2 wave D )]TJ/F23 11.9552 Tf 11.955 0 Td [( wave ThesuddentransitionsbetweenbaselmandwaveshavebeendescribedbySchubring andSheddassimilartoanobstacleinthetube.Wavepropertiesarethereforeimportanttothe calculationofgas-to-liquidmomentumtransferproportionaltocorekineticenergydensityfor anobstruction.Anempiricalcorrelation,developedbySchubring[58],isusedtoestimatethe lengthofthedisturbancewaves, L wave ,presentedinEquation2 32

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Thecharacteristicgasvelocityatthebase-wavetransition, U g;trans ,isfoundusing: U g;trans = U l;i;base )]TJ/F23 11.9552 Tf 11.955 0 Td [(U l;i;wave + r i;base g s 1 + g;trans Z + g;trans 0 [ u + y + ] 2 dy + + g;trans = wave )]TJ/F23 11.9552 Tf 11.955 0 Td [( base g r i;base g Thenon-dimensionaldistance + g;trans representsthepenetrationofthewaveintotheboundary layerformedoverthebaselm.ThecharacteristicvelocityconsidersboththeRMSvelocityin thegasobstructedbythelmsecondterm,righthandsideandthechangeininterfacialvelocity betweenthewaveandbaselmzonesrstterm,righthandside. Forturbulentgasandliquidvelocityapproximations,auniversalvelocityproleUVPis assumedaspresentedbyWhalley[4],where u + and y + aredenedas: u + y = u y u ? l y + = yu ? l l + = u ? l l u + = 8 > > > > < > > > > : y + if y + < 5 )]TJ/F15 11.9552 Tf 9.298 0 Td [(3+5ln y + if 5 30ofthelm,simplifyingthevelocityprolecalculation.Theinterfacial velocityofthewaves U l;i;wave = v wave andwavezoneliquidlmowrate, m film;wave ,are 33

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computedfromthefollowing: U + l;i;wave =5 : 5+2 : 5ln )]TJ/F23 11.9552 Tf 5.479 -9.684 Td [( + wave U l;i;wave = U + l;i;wave u ? wave m + film;wave = )]TJ/F15 11.9552 Tf 9.298 0 Td [(64+3 + wave +2 : 5 + wave ln )]TJ/F23 11.9552 Tf 5.479 -9.684 Td [( + wave m film;wave =_ m + film;wave D l Thedensityofthecoregasandentraineddroplets, core ,isestimatedbymassconservation intheliquidphaseandanassumedhomogeneousmodelinthecore: m l;Ent =_ m l )]TJ/F15 11.9552 Tf 15.449 0 Td [(_ m l;film;base )]TJ/F23 11.9552 Tf 11.955 0 Td [(INT w )]TJ/F15 11.9552 Tf 15.449 0 Td [(_ m l;film;wave INT w E = m l;Ent m l core = m l;Ent +_ m g A U sg + U sl E Thewaveintermittency, INT w ,isestimatedbyanempiricalcorrelationdevelopedby Schubring etal. [19]: INT w;SS =0 : 1+ Re l 40000 Re l = l U sl D l Thedropletdepositionux, R D ,isrequiredintheevaluationofpressuredrop.ThecorrelationofIshiiandMishima[59]Equation2isusedtocomputethis,whichincorporatesthe entrainedfractionthroughtheuseofcoredensity, core R D =0 : 022 core )]TJ/F23 11.9552 Tf 11.955 0 Td [( g U sg Re )]TJ/F22 7.9701 Tf 6.586 0 Td [(0 : 25 g g core )]TJ/F23 11.9552 Tf 11.955 0 Td [( g 0 : 26 Re g = g U sg D g Estimationofaveragepressurelossisaccomplishedbyindependentlysolvingthefollowing baseandwaveinterfacialshearequationsfortheirrespective dP=dz values,asfromtheworkof Fore etal. [60]Equations2and2.Thetotalpressurelossisthencalculatedusingthe 34

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waveintermittency, INT w : i;base = )]TJ/F23 11.9552 Tf 10.494 8.088 Td [(D core;base 4 1 )]TJ/F23 11.9552 Tf 13.15 9.321 Td [( core U 2 g;base P abs dP dz base )]TJ/F23 11.9552 Tf 9.298 0 Td [( core g D core;base 4 )]TJ/F23 11.9552 Tf 11.955 0 Td [(R D U core;wave )]TJ/F23 11.9552 Tf 11.956 0 Td [(U l;i;wave i;wave = )]TJ/F23 11.9552 Tf 10.494 8.087 Td [(D core;wave 4 1 )]TJ/F23 11.9552 Tf 13.15 9.167 Td [( core U 2 g;wave P abs dP dz wave )]TJ/F23 11.9552 Tf 9.298 0 Td [( core g D core;wave 4 )]TJ/F23 11.9552 Tf 11.956 0 Td [(R D U core;wave )]TJ/F23 11.9552 Tf 11.955 0 Td [(U l;i;wave dP dz = )]TJ/F23 11.9552 Tf 11.955 0 Td [(INT w dP dz base + INT w dP dz wave Inasimilarfashion,thetime-averagedlmthicknessiscomputedby: = )]TJ/F23 11.9552 Tf 11.955 0 Td [(INT w base + INT w wave Thenaloutputsofthismodelincludelmheight,interfacialvelocitywavevelocityforthe wavezone,pressuregradient,andlmowrate.Themodelperformancewasevaluatedusing annularowdataobtainedbySchubring etal. [43,44].Outputsforpressuregradientandwave velocityarereasonableandonparwithempirical,single-behaviorestimates. 2.4ApplicationofLiterature Theresearcheffortsdiscussedinthischapterrepresentonlyasmallfractionofow visualizationandannularowliterature.Thepapersselectedforthisreviewhavebeeninline withthegoalofthecurrentworktoimprovethemeasurementandmodelingofindividual annularowphenomena.Theemphasisonthespecicbehaviorsofannularowisanimportant steptounderstandingthephysicsoftheowregimeasawhole.Thedesirableoutputsofannular modelingpressuregradientandheattransferwillbenetfromtheunderstandingofthese behaviors. Thefollowingchaptersfocusontheapplicationoftwouidvisualizationtechiniques:PLIF imagingandhigh-speedvideo.Severalannularowobservationsintheliteraturearestudied 35

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andupdatedusingthesemethods,includingbaselmandwavedistributions,interfacialvelocity, disturbancewavelengths,andwaveintermittency. 36

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CHAPTER3 PLIFEDGEIDENTIFICATION Filmthicknesshasbeendescribedintheliteratureusingatwo-zonecharacterization, composedofbaselmanddisturbancewaveswithdrasticbehaviordifferences.Duetothe periodicnatureofdisturbancewaves,themeasurementoflmthicknessbymosttechniquesis preferentialtobaselm.Thepurposeofthisworkistocharacterizebothzonesoftheliquidlm usingPLIFimagesobtainedbySchubring etal. [43].Thecurrentworkincludesrevisionsand improvementstotheoriginalalgorithm. 3.1PLIFOptics AschematicofthetestsectionusedforthePLIFimageacquisitionisshowninFigure3-1. Themaincomponentsintheexperimentalsetuparetheowtube,laserlightsource,ourescing dye,digitalcamera,andlens.FlourinatedethylenepropyleneFEPwasselectedastheowtube materialduetotheproximityofitsrefractiveindex.337tothatofwater.333.Thisallowed foraccuratenear-wallmeasurementsofbaselmthicknesses,whicharegenerallyontheorderof 100 m.TheFEPsectionwasencompassedbyasquare,water-lledchamberandpaintedblack toreduceambientlightandimproveimagecontrast. ThelaserlightsourcewasaNewWaveResearchSoloPIVNd:YAGthatusedacommerical lightsheetattachment.Thelasersheetenteredtheenclosureata90 anglethroughaviewing windowtoavoidrefractionattheair-FEPtransition.RhodamineBwasusedastheourescing dye.ARoper-Scientic1300YHS-DIFcameraby1030pixels,inter-linetransferCCD wasaimedthroughanotherviewingwindowata90 angletothelasersheettoviewtheliquid cross-sectionmadevisiblebytheourescingdye. ThecurrentworkisbasedonimagesetstakenfromalensMitutoyoTelecentricObjective 3x,NA=0.07,nominalworkingdistance72.5mm,depthoffocus56 mthatyieldedpixels 3.14 mineachdirectiontotalaxiallength:approximately4mm.Alloftheowconditions usedforthecurrentworkareshowninTableAalongwithgasandliquidsupercialvelocities. 37

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Figure3-1.TestsectionforPLIFmeasurements.Flowisoutoftheplaneofthepage. 3.2PLIFProcessing PLIFprocessingusesMATLABcodeinthreesections:imageprocessing,outlier-removal, anddataprocessing.Theexpectedshapeoftheliquidedgeisasmooth,continuous,unbroken linethroughthelengthoftheimage.Ametricwasdevelopedfortheoriginalcode,chaos,asa measurementforthelackofcontinuityintheedgeandhasbeenmaintainedinthecurrentwork. Whenadjacentaxiallocationsbothcontaindetectededges,thedifferenceinheightbetweenthe edgelocationsistakentothepowerof1.5,withalloftheseresultssummedforeachimageasthe chaosvalue. Anoutlier-removalprocedureisperformedforthesmallfractionofPLIFimagesthatare incorrectlyprocessed.AgraphicaluserinterfaceGUIwasdevelopedtolocate,tag,andpurge poorlyprocessedimages.Thenaldataprocessingsectionhasbeendevelopedtoquantifylm thicknessdataandgenerategures. 38

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3.2.1PLIFImageProcessing Someobstaclesovercomeintheliquidedge-ndingroutineinclude: 1.Imagecontrast 2.Single-pixelimagenoise 3.Bubblesinthegas-liquidinterface 4.Out-of-planefeatures,includingdropletsneartheinterface Theimageprocessingisaccomplishedinthefollowingsteps. Crop .Theimageiscroppedtoaspeciedwidthtoreducetheimageprocessingtimeand reducetheimpactofdropletsattheouterrangeoftheimages.Theinitialcropwidthsarea functionofthegasowrates,basedonthemaximumobservedlmthicknessforeachliquid ow.ThesevalueshavebeenpresentedinTable3-1. Table3-1.InitialcropwidthsforPLIFimageprocessing. Q g;nom Width Lmin )]TJ/F22 7.9701 Tf 6.587 0 Td [(1 m 8002000 10001500 12001250 14001100 1600800 AxialBlur .Toreducesingle-rownoise,theimageissubjectedtoave-pixelblurring processintheaxialdirection.Thecenterpixelintheprocessisaweightedaverage;thecenteris weighted3,thenextadjacentweighted2,andtheendsweighted1.Thisprocesshasanegligible effectonthenaledgeshapebeyondreducingnoise-relatederrorsintheedge. MedianFilter .Single-pixelnoiseintheimageisreducedbyapplyingamedianlter,found intheMATLABimageprocessingtoolboxasmedlt2.Thelterwindowissetto3pixelsinall directions. ContrastAdjustment .Therawimagesareinitiallytoodarkforviewingbythehuman eye.ThepixelrangeoftheimagesisadjustedusingaMATLABfunction,imadjust.Themain operationinimadjustisshowninEquation3where J istheoutputimage, I istheinputimage, 39

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andsubscripts min max ,and n representtheminimum,maximum,andcurrentpixelvaluein theimage,respectively.Theexponentialweightingfactor, ,hasbeensetto1.5andwieghts theoutputtowardsthelowerpixelvaluestohelpreduceblurinthegascore.Thisversionofthe image,referredtoastheadjustedimage,isalsousedlaterintheprocessastheuser-viewable version. J n = J min + J max )]TJ/F23 11.9552 Tf 11.955 0 Td [(J min I n )]TJ/F23 11.9552 Tf 11.955 0 Td [(I min I max )]TJ/F23 11.9552 Tf 11.955 0 Td [(I min Stretch .Theadjustedimageisthenenhancedasecondtimebyapplyingarow-by-row linearstretchofthepixelvalues,creatingabetterdenededgeforlowcontrastregions.A stretchingthresholdisimplementedtoensurethataregionisnotblurredbythisprocess.A minimum-to-maximumpixeldifferenceof74outof255isrequiredforarowbeforeitis linearlystretched. Thenewlystretchedimage Temp str isthenaddedtothepreviousadjustedimage Adjusted asinEquation3.Theweightingfactorfortheadditionwasdeterminedbyvisualinspectiontoreducetheaxialnoisecreatedbythestretchingprocess. Stretched =0 : 8 Temp str +0 : 2 Adjusted Opening/Closing .Amorphologicalopeningandclosingisappliedtothestretched imagewithbuilt-inMATLABfunctionsimopenandimclosetoreducetheeffectsofsmall-scale defectsintheedge.Thersttimethroughtheprocessing,adiskofradius3pixelsisusedasthe morphologicalstructure.Allotheriterations,whichcontainedgedataandupdatedimagesize, useavariablesystemofmorphologicaldiskradiidescribedinEquation3unitsofpixels. Animagecanbesubjecttothreedifferentopen/closeradii R oc dependingonthedistance fromthechannelwall y andthearrayofedgelocations Edge .Theparameters C 1 and C 2 are distancesfromthechannelwallwherethemorphologicalradiuschanges,andarebasedonthe heightandroughnessstandarddeviationoftheliquidedge.Thissystemwasdevelopedsince higheredgelocations e.g. ,wavesshowmorechaoticedgebehavior,largerbubbles,andmore 40

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edgedefects.Thelargerradiiaremoreeffectiveatsmoothingthisbehavior. C 1 = Edge +2 s Edge C 2 =1 : 6 C 1 R oc z = 8 > > > > < > > > > : 1 for y z C 1 6 for C 1
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EdgeCleaner .Aniterativeprocessisperformedtoeliminateedgelocationsthatareat least120 mfromtheedgemeannotincludingedgelocationsrecordedaszeroandgreater than2.4standarddeviationsfromthemean.Thisstepismoreeffectiveateliminatingincorrect patchesoftheedgethatcouldnotbespecicallyidentied. WidthIteration .Theresultingedgevectoristhenusedtosetanewimagewidthandthe entireprocessisiterated,startingwiththecrop.Theiterationcontinuesuntilthewidthofthe imageceasestochangeadifferenceoflessthan20 morafter10iterations.Thisreductionof imagesizegreatlyreducestherequiredcomputationofeachsubsequentiterationandallowsfor easierimagestorage. ImageStorage .Toenableavisualinspection,thenaledgearrayissuperimposedonto theadjusted,viewableimageasalightbluecyanline.Theattemptsattheiterativeedgexing methodidentiededgepointsthatwerenotselectedareindicatedontheimageasgreenlines. Bubbleremovalsareindicatedbysmallredlinesatthebottomofimages.Allofthedatafrom theprocessisthenstoredforthefollowingoutlier-removalanddataprocessing. 3.2.2CodeModications Manyofthefeaturesinthecurrentalgorithmaresimilartotheoriginal.Theprocess describedinSection3.2.1includesthefollowingchangesfromtheoriginalcode. InitialCropWidth .Theoriginalcropwidthsweredeterminedbasedontotalinternal reectionTIRmeasurementsbySchubring[58].TheinitialcropwidthspresentedinTable3-1 havebeenincreasedduetolargerobservedlmheightsandincreasedcomputationalpower. ContrastMethods .Theuseofthe variableintheMATLABfunctionimadjustwasnot implementedintheoriginalcode.Thisvariableweightstheimagestowardsthedarkerpixelsand createsimageswithbettercontrastanddenededges. StretchThreshold .Thestretchingthresholdwasincludedinthecurrentversionto eliminateissueswithnoiseandblurringfromtheoriginalprocess.Thenalstepinthisprocess linearlyaddingtheadjustedimagetothenewlystretchedimagewasalsoaddedtoreducenoise. 42

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MorphologicalRadii .Theoriginalcodeonlyperformedthemorphologicalopeningand closingprocesswithonestructureandaconstantradiuspixel.Thecurrentvariableradius methodusesradiithatrangefrom1pixelto13pixels,dependingonthelengthoftheedge.This isthemostcomputationallyexpensiveoperationinthePLIFprocessingalgorithm,doublingthe processingtimeforeachimage. FilmThreshold .Thebinarythresholdforthecurrentcodehasbeendecreasedsignicantly fromtheoriginalduetonewcontrastingmethods.Theoriginalimagelmthresholdwas175out of255andisnowreducedto85. EdgeIteration .Theconceptofedgeiterationwasintroducedinthenewcodeasan alternativetolocatingandxingbubbles.Ittakesadvantageoftheiterationthatalreadytook placeintheoriginalcenteredaroundreducingtheimagesize. BubbleDetection .Thepurposeofthebubbledetectionintheoriginalalgorithmwastond andeliminateregionsoftheedgethatwereperturbedbyabubble,describedasalengthofedge 150 mandameandepressionofatleast15 mrelativetothesurroundinglmheight.This wasaconstantcriteriadesignedaroundtheaverageobservedbubbleattheinterface.Thecurrent processdetectsvariablelengthsofbubbles,oranysimilaredgedefects,thatrangefrom0to200 m ImageStorage .Theedgedatafromtheoriginalalgorithmwassuperimposedontothe currentimagesatredlines.ExampleimagesshowingbothsetsofdataareshowninFigure3-3 andFigure3-4. 3.2.3PLIFOutlierSelectionGUI Therearecertainfeaturesoftheliquidlmthatcancauseerrorsintherecordedliquidedge. Somesuchissuescausefailureintheedgendingroutine.Itispreferabletolocateandreject suchoutlierimages.Anymeasurementofstandarddeviationorchaosisnotsufcientgrounds forimagerejectionhighlychaoticedgevectorshaveoccasionallybeenobservedtobeaccurate. Forthisreason,agraphicaluserinterfaceGUIwasproducedusingMATLABtoaidinthe visualidenticationofoutliers. 43

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TheGUIloadsonesetofprocessedowdataatatimeandcalculatesthemeanandstandard deviationofalledgevalues.Alistofpotentialoutliersisproducedforwhichthemeanofthe edgevectorliesoutsideofacriticalrange.Thedefaultcriticalrangeiscalculatedas2standard deviationsawayfromthemean,butcanbemodiedintheGUI.Thiscriterionprimarilylocates edgevectorsthatareuncharacteristicallyhigh.Asimilarcriterionisevaluatedusingchaos values,attemptingtolocateerraticedgevectors.Fromthislist,theusercanselectanimage, viewtheimageandedgedata,anddeterminewhetheritqualiesasanoutlier.Imageswereonly rejectediftherecordededgerepresentedthelmincorrectlyasaresultofthefollowing: Coreliquid .Someimagesshowdropletsorlargersectionsofliquidtravelingthrough thecore.Thisisoftenmuchfartherfromthewallthantheliquidlmandcanskewthedataif detected.However,errorsofthiskindaregenerallysmaller,asmostoftheowstestedhavelow levelsofentrainment.Evenifdetected,liquidinthecorehasbeenobservedtoaffect,atmost, 10 % ofanimage.Duetothedisparityintherecordedvalues,anyfalselydetectedliquidinthe corethataffectsmorethan5 % ofarecordededgebyvisualestimationisremoved. Out-of-planefeatures .Somefeatures,unidentiableaspartoftheliquidlm,showup inimagesaslarge,blurrypatches.Someoftheseissuesmaybeexacerbatedbythestretching routineintheimageprocessing.Thesesections,muchlikethecoreliquid,resultinextreme overestimationofthelm.Out-of-planefeaturesalsooccurinmuchlargersections,often affectingover15 % ofarecordededge.Alloftheimageswiththistypeofissuearerejected. Erraticlmsections .Someimagesshowaliquidedgethatisextremelyerraticandnot wellcharacterizedbytheimageprocessing.Thiscanbecausedbyseveralmechanisms,such asalargeconcentrationofbubblesattheinterface,alargewavewithliquidtearingfromthe surface,ortherolling/breakingofalargewave.Errorsofthistypeoccuratvaryinglevelsof severitydisparitybetweentherecordededgeandthetrueedgelocationandarerejectedona case-by-casebasis. SomeexampleimagesthatwereselectedasoutliershavebeenshowninFigure3-2.The numberofoutliersremovedforeachowcondition Rej isshownintheright-handcolumnof 44

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TableA.Typically,between1%and5%ofthetotalimagesinaowconditionareselectedas outliers.AnarrayiscreatedbytheGUIthatindicateswhichimageswereselected,laterusedin thedataanalysis. 3.2.4PLIFDataProcessing Therststepinthedataanalysisprocedureistoconverttheresultsfromimageprocessing toaphysicalscale,takingintoaccountmisalignmentfromtheexperimentalprocedure.The entiredatasetwasobservedtobeslightlyskewed-thewalllocationatthetopoftheimagewas foundtobe6pixels mtotherightofthatatthebottom.Eachimagewaslinearlyadjusted tocompensateforthismisalignment. Filmthicknessdataarethensplitintotworegionsusingoneoftwomethods.Therstis basedontheworkofRodr guez[21]andusesacriticalstandarddeviationmultiplier, k c ,to createtheseparationcriterion.Filmheightmeasurementsgreaterthan k c standarddeviations fromthemeanbaselmheightareassumedtobewavemeasurements.Basedontheworkof Schubring[58],a k c valueof2isusedforthisanalysis.Theevaluationofthiscriterionmustbe performediteratively.Theinitialassumptionforthisprocedureisthatthestandarddeviationof thebaselmisthesameasthestandarddeviationforalllmpoints.Thisiterationcontinues untilthebaselmdistributionconverges. Analternatemethodistousewaveintermittencydataasaninputforthecalculation.Values for INT w fromChapter5havebeenusedasinputsforthismethod.Themaindiscrepancy betweenthe INT w andthePLIFdataistheuseofslightlydifferenttubediameters.Thereis alsoanerrorassociatedwiththe INT w measurementsbasedonthewavelength,velocityand frequencymeasurementsthatcouldcompoundtheerrorforthebase/wavedivision. Afterthezoneseparation,severalguresareproducedfordataanalysis.Waveandbase distributionsarerepresentedbyhistograms.Themeanandstandarddeviationofwaveandbase lmarecalculatedandplottedasfunctionsof U sg and U sl .Otherinformationisalsoobtainedthat isusefulfortheoptimizationofthecode,includingchaosvaluesforthedatasetandthenumber ofpointswherenoedgewasdetected. 45

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Figure3-2.ExamplerejectedPLIFimagesforowconditions toptobottom 185F,166F,147F, 128F,and109Fconstant U sl =21.1cms )]TJ/F22 7.9701 Tf 6.587 0 Td [(1 46

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3.3PLIFResults Averagelmthickness ,baselmthickness base ,andwaveheight wave ;their respectiveroughnessesestimatedbysamplestandarddeviations;andwaveintermittency INT w areshownforall26testsinTableA k c methodandTableA INT w method. 3.3.1PLIFImageComparison ExampleprocessedPLIFimagesareshowninFigure3-3owcondition121Fand Figure3-4owcondition162F.Eachimageindicatestheedgefromtheoriginalcoderedline alongwiththeedgefromthecurrentcodebluelinetohighlightthecodemodicationsinthe caseofbothedgeindicatorsexistinginthesamespace,theredlineisvisible. Forbaselm,thedifferenceinedgelocationisvisiblynegligible.Mostofthedifferences areduetolargerwavesandbubbles,wheretheinterfaceisnotasclearlydened.Theimages chosenforthiscomparisonallshowstructuresthatthecurrenteffortsweredirectedatimproving. Itcanbeseenfromtheimagesthatthecurrentcodendsslightlyhighervaluesatmost locationsduetothemoreaggressivecontrastingmethodsusedintheprocessing.Forlargewaves, thisdiscrepancybecomesmuchmoreapparent,indicatingthattheoriginalcodeunder-predicted waveheights.Thecurrentcodealsodoesabetterjobatignoringthestructuresinthelm, includingbubbles. 3.3.2PLIFSingle-ZoneComparison Allofthegurespresentedforthissectionincludetheresultsoftheoriginalcodealongwith thecurrentresultsforcomparison.Figures3-5and3-6showlmthicknessdistributionsforve owconditionswithconstantliquidowrate U sl =21.1cms )]TJ/F22 7.9701 Tf 6.587 0 Td [(1 .Figures3-7and3-8showlm thicknessdistributionsforveowconditionswithconstantgasowrate U sg =57ms )]TJ/F22 7.9701 Tf 6.586 0 Td [(1 .All lmthicknessdistributionsareshowninAppendixB. Themaineffectofincreasingthegasowrateisashiftofthedistributionpeaktothe leftlowerlmthickness.Asimilartrendisseeninthecurrentresults,buttheshapeofthe distributionsaregenerallytallerandnarrower.Thenarrowershapeismostapparentinthelowest 47

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Figure3-3.ExampleprocessedPLIFimagesforowcondition121F.Redlineshowsoriginal results,lightbluelineshowscurrentresults. 48

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Figure3-4.ExampleprocessedPLIFimagesforowcondition162F.Redlineshowsoriginal results,lightbluelineshowscurrentresults. 49

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Figure3-5.Histogramsoflmthicknessbaseandwave,originalresults left versuscurrent results right .Flowconditions toptobottom 109F,128F,and147Fconstant U sl = 21.1cms )]TJ/F22 7.9701 Tf 6.587 0 Td [(1 50

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Figure3-6.Histogramsoflmthicknessbaseandwave,originalresults left versuscurrent results right .Flowconditions toptobottom 166Fand185Fconstant U sl =21.1 cms )]TJ/F22 7.9701 Tf 6.586 0 Td [(1 gasows U sg =36.3ms )]TJ/F22 7.9701 Tf 6.586 0 Td [(1 ,indicatingthatthegreatestdiscrepancyinresultsoccursatlower gasowrateshigherlmthicknesses. FilmthicknesstrendsareshowninFigure3-9withlmroughness,estimatedherebya standarddeviation.Theaveragelmthicknesstrendsforthenewdataaresimilartothoseofthe original.Thelmthicknesssteadilydecreaseswithincreasinggassupercialvelocity,withthe decreaseslightlysteeperthanwiththeoriginalcode.Thelmthicknessalsotendstoincrease withliquidsupercialvelocityoveralargerrangethantheoriginal mversus100 m. 51

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Figure3-7.Histogramsoflmthicknessbaseandwave,originalresults left versuscurrent results Right .Flowconditions toptobottom 140F,143F,and147Fconstant U sg = 57ms )]TJ/F22 7.9701 Tf 6.586 0 Td [(1 52

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Figure3-8.Histogramsoflmthicknessbaseandwave,originalresults left versuscurrent results Right .Flowconditions toptobottom 151Fand153Fconstant U sg =57m s )]TJ/F22 7.9701 Tf 6.586 0 Td [(1 Theaveragelmthicknessvaluesareallconsiderablyhigher.Thishasbeenobserved visuallyintheimagecomparisons,asthenewcodegenerallydetectshigherlmthickness values,especiallyforwavesections. Thelmroughnesstrendsarealsosimilarbutshowaconsiderableincreaseinlmroughnessvalues.Thecurrentcodeappearedtoproducesmootheredgeresults,whichindicatesthatthe higherroughnessisanothereffectofdetectinglargerwaves.Therelativeroughnessisalsohigher andappearstobeaweakfunctionofgasandliquidsupercialvelocity.Anempiricalcorrelation wasdevelopedusingowquality x toexpressthisdependence,showninEquation3.The errorforthiscorrelationisshowninTable3-2alongwiththeerrorfromapproximatingthe 53

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Figure3-9.Totallmthicknesstrends,originalresults left versuscurrentresults right Top Averagelmthickness, middle averagelmroughnessstandarddeviationoflm thickness, bottom Ratiooflmroughnesstolmthickness. 54

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datafromtheaverage.508.Theaveragevalueproducesareasonableestimate,indicating thattherelativeroughnessisnearconstant.However,themeanabsoluteerrorMAEandthe root-mean-squarederrorRMSareimprovedbyaround50%withthecorrelation. s =0 : 33 x )]TJ/F22 7.9701 Tf 6.587 0 Td [(0 : 33 Table3-2.Errorcomparisonforlmthicknessrelativeroughnesscorrelation. MethodError % MAE % RMS % Average )]TJ/F15 11.9552 Tf 9.298 0 Td [(2 : 9314 : 3319 : 15 NewCorr. )]TJ/F15 11.9552 Tf 9.298 0 Td [(0 : 747 : 929 : 47 3.3.3PLIFBaseandWaveComparison Thetotallmthicknessdistributionshavebeendividedintobaseandwavezonesusingthe twomethodsdescribedinSection3.2.4criticalstandarddeviationmultipliermethod, k c ,and intermittencyinputmethod, INT w 3.3.3.1CriticalStandardDeviationMultiplierMethod Figures3-10and3-11showbaselmthicknessdistributionsforveowconditions constantliquidow, U sl =21.1cms )]TJ/F22 7.9701 Tf 6.586 0 Td [(1 .Theshapeofthebaselmdistributionshavechanged verylittlewiththenewcode.Thelocationandmagnitudeofthepeaksarecomparable,although dataareextendedtotheright. Thebaselmtrends,showninFigure3-12,supporttheseobservations.Themagnitudes andslopeshavechangedverylittleforboththeaveragebaselmthicknessandtheaverage roughness.Therelativeroughnessindicatesaconstantratioofbaseroughnesstobaseheight .3,consistentwiththemodelingeffortofSchubringandShedd[1].Onlyaweakdependence ongasowrateremains. Figures3-13and3-14showwaveheightdistributionsforthesameowconditions.All ofthedistributionsshowamorepronouncedtailtotheright,indicatinghigherwaveheight measurements.Forsomegasowrates e.g. 1400Lmin )]TJ/F22 7.9701 Tf 6.586 0 Td [(1 themaximummeasuredwaveheight hasbeenincreasedbyover200 m. 55

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Figure3-10.Histogramsofbaselmusing k c method,originalresults left versuscurrentresults right .Flowconditions toptobottom 109F,128F,and147Fconstant U sl =21.1 cms )]TJ/F22 7.9701 Tf 6.587 0 Td [(1 56

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Figure3-11.Histogramsofbaselmusing k c method,originalresults left versuscurrentresults right .Flowconditions toptobottom 166Fand185Fconstant U sl =21.1cm s )]TJ/F22 7.9701 Tf 6.587 0 Td [(1 Thewaveheighttrends,showninFigure3-15,showthattherehasbeenadramaticincrease inaveragewaveheightvalues.Waveheightalsoappearsasamuchstrongerfunctionofgasow rateasindicatedbythesteeperslope.Theroughnesshasalsoincreaseddramatically,showing amuchhigheructuationwithinthewavezone.Therelativeroughnesshasincreasedfrom about0.2toabout0.3andshowsanewdependenceongasowratealthoughveryslight.The wave-to-baseratios,showninFigure3-16,indicatethatthenewcodeindeedndshigherwaves, showinganincreaseinaveragewave-to-baseratiofromabout2to2.5. Theremainderofthelmthicknessdistributionsgeneratedusingthe k c methodareshown inAppendixC. 57

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Figure3-12.Baselmthicknesstrendsusing k c method,originalresults left versuscurrent results right Top Averagelmthickness, middle averagelmroughness standarddeviationoflmthickness, bottom Ratiooflmroughnesstolm thickness. 58

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Figure3-13.Histogramsofwaveheightusing k c method,originalresults left versuscurrent results right .Flowconditions toptobottom 109F,128F,and147Fconstant U sl =21.1cms )]TJ/F22 7.9701 Tf 6.587 0 Td [(1 59

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Figure3-14.Histogramsofwaveheightusing k c method,originalresults left versuscurrent results right .Flowconditions toptobottom 166Fand185Fconstant U sl =21.1 cms )]TJ/F22 7.9701 Tf 6.587 0 Td [(1 3.3.3.2IntermittencyInputMethod The INT w distributionsarenotcompareddirectlytotheoriginalcodeinthesamemanner asthe k c distributions.Thecurrentdataprocessinguses INT w valuesfromChapter5thatdiffer fromthoseusedintheworkofSchubring[58],whichwouldunderminesuchacomparison. Instead,thelmthicknesstrendsofthe k c and INT w methodshavebeencomparedtoeachother inFigures3-17through3-19.Thebaseandwavedistributionsgeneratedusingthismethodare showninAppendixD. AveragebaselmtrendsareshowninFigure3-17.Thevaluesforthe INT w methodare generallyhigherandshowasteeperslope,indicatingastrongerdependenceongasowrate.The 60

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Figure3-15.Waveheighttrendsusing k c method,originalresults left versuscurrentresults right Top Averagelmthickness, middle averagelmroughnessstandard deviationoflmthickness, bottom Ratiooflmroughnesstolmthickness. 61

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Figure3-16.Ratioofwaveheighttobaselmusing k c method,originalresults left versus currentresults right relativeroughnesshasalsoincreasedbyafewpercent.Manyofthetrendsdiscussedwithdata fromthe k c methodarestillapparent. AveragewaveheighttrendsareshowninFigure3-18.Similartothebaselm,theaverage waveheightvalueshaveincreasedandtheslopehasbecomesteeper.Thisistobeexpectedif the INT w methodcreatesaseparationcriterionhigherthanthe k c methodbothaverageswill increase.Theroughnessinthewavezoneisconsistentbetweenbothmethods,whichcreatesa decreaseintherelativeroughnessfor INT w byafewpercent. Figure3-19showswave-to-baseratiosafterthezoneseparation.The INT w valuesare directlyrelatedtotheseratios,whichclearlyshowfunctionsofbothgasandliquidowrates. Thelowerwaterowrates,800and1000Lmin )]TJ/F22 7.9701 Tf 6.587 0 Td [(1 ,showveryerraticbehaviorasafunctionof gasow.Thewave-to-baseratiohasbeenempiricallycorrelatedusingowquality x ,shownin Equation3.Theerrorforthiscorrelationhasalsobeencalculated,showninTable3-3. wave base =1 : 86 x )]TJ/F22 7.9701 Tf 6.587 0 Td [(0 : 18 Table3-3.Errorcalculationsforbase-to-waveratiocorrelation. Error % MAE % RMS % )]TJ/F15 11.9552 Tf 9.298 0 Td [(0 : 256 : 748 : 13 62

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Figure3-17.Baselmthicknesstrends, k c method left versus INT w method right Top Averagelmthickness, middle averagelmroughnessstandarddeviationoflm thickness, bottom Ratiooflmroughnesstolmthickness. 63

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Figure3-18.Waveheighttrends, k c method left versus INT w method right Top Average lmthickness, middle averagelmroughnessstandarddeviationoflm thickness, bottom Ratiooflmroughnesstolmthickness. 64

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Figure3-19.Ratioofwaveheighttobaselm, k c method Left versus INT w method right 65

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CHAPTER4 PLIFINTERFACETRACKING MostofthePLIFimageshavebeentakenwithaverylargetimeseparationtoensure independentmeasurements.BytakingPLIFimagesatmuchshortertimeintervals,themovement ofthegas-liquidinterfacecanbeobserved.Globalmodelsrequireandestimateofthis,for whichalinearrelationshipSchubringandShedd[1]ortheUVPEquation2,Owenand Hewitt[61]inthelmhasbeenassumed. Thecharacterizationofthegas-liquidinterfaceishighlydependentondisturbancewave behavior,asdemonstratedintheliterature e.g. ,Azzopardi[45,46].PLIFimagesallowforthe separationofbaselmandwavebehavior,unavailablebyotherlmthicknessmeasurement techniques. TherawdataforshorttimedelayPLIFpairswasacquiredbySchubring[58]withthesame apparatususedinChapter3.Thetimedelaysforeachimagesetwereselectedtoproducepairs appropriateforcross-correlationroughly50pixelsindistance.Theowconditionstestedfor thiswork,alongwiththetimedelayforeachset,areshowninTableE-1.Thecurrentchapter includespreliminaryndingsaswellaschallengesandsuggestionsforfuturework. 4.1PLIFImagePairProcessing FourstagesofprocessingareusedtotransformPLIFimagepairsintoreviewabletrendplots forinterfacialvelocity.Adiagramofstages1through3isshowninFigure4-1. 1.Eachimageisprocessedtoidentifytheliquidedge. 2.Eachpairissplitintosectionsandindividuallycorrelatedtoidentifytheappropriatelag distances. 3.Therawdataisprocessedthroughoutlierremoval,conversiontophysicalscale,and non-dimensionalization. 4.Theprocesseddataiscomparedtoliquidvelocitymodels,including aTheuniversalvelocityproleforindividualowconditions,and bThevanDriestmodelforcontinuouslawofthewallformultipleowconditions. 66

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Figure4-1.DiagramofprocessingpathforPLIFinterfacetracking. 67

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4.1.1PLIFImagePairEdgeProcessing TheworkofSchubring[58]discussedsomedifcultiesassociatedwithcross-correlating PLIFedgevectors.Mostoftheissueswerefocusedonaccuratelydetectingtheliquidedge,often complicatedbybubblesintheinterface.Manyoftheseissueshavebeenaddressedbyadjusting thePLIFedgendingroutine,outlinedinChapter3.Theedgeprocessingfortrackingtheliquid interfaceutilizestheedgeprocessingcodedevelopedinSection3.2.Theactualimageprocessing andedgendingroutinesareidenticalexceptforthelmthicknessthreshold,whichneededtobe adjustedduetoreducedcontrastbetweengasandliquidforthePLIFimagepairs. Thevaryinglevelofqualityfromoneimagetothenextmadeaconstantthresholddifcult todetermine.ThisversionofthePLIFedgendingcodeemploysahistogram-basedthreshold selectionmethoddevelopedbyOtsu[62].Otsu'smethoditerativelydeterminesthemostaccurate thresholdvaluebasedonthereductionofvarianceinthethresholdedsection.Ithasbeen observedtocreateaccurateresultsinahigherrangeofimagequalitiesbyvisualinspection. 4.1.2PLIFImagePairDivisions Eachimagehasanaxialdistanceof1300pixels,orabout4mm.Asaresult,thelm thicknessmayvaryfrombasetowavewithinanimage.Largebubblesmayalsoobscure interface.Thisposesaproblemtocorrelatingtheimagepairs,asdifferentlmheightsandlm featuresmoveatdifferentvelocities.Thisalsoposesaproblemfordevelopingvelocityasa functionofdistancefromthewallifthewallheightforanimagepairisnotclearlydened. Eachimagepairissplitintotwosections,each650pixelsinlength.Theremainderofthe imagepairprocessingschemeisperformedoneachsectionindividually.Othernumbersof sectionswereconsidered.However,asthesizeoftheimagepairsdecreased,thechancesofpoor correlationincreaseduetoalackoffeaturesintheliquidedge.Splittingtheimagesintotwo sectionsyieldedthemostconsistentcross-correlationsuccess. 4.1.3PLIFImagePairCross-Correlation Thisstageoftheprocessingusescross-correlationtodeterminethemostaccuratedistance lagbetweentheedgevectors.Thecross-correlationisperformedusingabuilt-inMATLAB 68

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function,whichtakeseachedgevectorasaninputandreturnsanarrayofcorrelationvalues between-1and1,termed Xcorr .Thevaluesof Xcorr correspondtothedistancesthatthe edgevectorswerelagged,termed Lag Theappropriatecorrelateddistancebetweenanimagepairisfoundasthemaximumvalue of Xcorr for Lag valuesbetween-100and600pixels.Anegativevaluefor Lag wouldrepresent anegativevelocity,whichmaybephysicallyaccurateinsomecasesduetolocalooding. However, Lag valueslessthan-100pixels-0.3mmmostoftencorrespondtobrokensectionsof lmortheincorrectcorrelationoffeatures.High Xcorr valuesmayoftenoccurneartheendsof theedgevectors Lag> 600.Thisisgenerallyduetocoincidentalagreementattheedgeends, andsoany Lag valueover600pixels.9mmisignored. Thisstageofthecodealsooutputsguresforvericationoftheedgendingandcorrelation process.Agraphof Xcorr versus Lag isproducedforeachoriginalimagepairthatincludesa lineforeachimagesection.Thisgurealsoincludestherecordedvalueof Lag foreachimage section.AnexamplecorrelationgraphforeachgasowrateisshowninFigure4-2. Acombinedimageisproducedforeachcorrelatedimagepairthatincludeseachedgevector superimposedononeimage,shiftedbytherecorded Lag valueforverication.Thecompiled imagesthatcorrespondtothecorrelationgraphsinFigure4-2areshowninFigure4-3.Each imagehastherstimageofthepairontopandthesecondonethebottom.Theyellowlineisthe liquidedgeoftherstimage,shiftedandsuperimposedontheliquidedgeofthesecondimage cyanline. 4.1.4PLIFImagePairDataProcessing Thisstageoftheimagepairprocessingusesthephysicalpixelscaleoftheimagesand a priori knowledgeofowconditionstoinputuidpropertiesforvelocityanddistancecalculation. Therawinterfacialvelocity, u i ,iscalculatedfromthephysicaldistancetraveledbythelmover theknownelapsedtime, t .Thedistancefromthewall, y ,wascalculatedastheaverageofboth edgevectorsforanimagepairnotincludingzeros.Thenon-dimensionalizationisperformed 69

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Figure4-2.PLIFcross-correlationexamplegraphsfromowconditions topleft 105F, top right 126F, middleleft 143F, middleright 164F, bottom 181F. fromthefollowing: u + i = u i u ? y + = yu ? l 70

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Figure4-3.PLIFcross-correlationexampleimages, left section1, right section2.Takenfrom owconditions toptobottom 105F,126F,143F,164F,and181F. u ? = r i;wave l where u i isthemeasuredinterfacialvelocity, u + i isthedimensionlessinterfacialvelocity, y + isa wallunit,and i;wave iscalculatedfromEquation2. EachPLIFimagepairismarkedaswaveorbaselmusingintermittencydatafrom Chapter5.Thedivisionisbasedontheaveragelmthicknessofeachcorrelatedpair,not includingzerosintheedgevectors.Thetotallistoflmpointsisthensortedandseparatedbased 71

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ontherecordedwaveintermittencyforthatowcondition.Datapointsthatrepresentwavelm aredisplayedasreddotsandbaselmsectionsaredisplayedasbluedots. 4.1.4.1PLIFImagePairOutlierRemoval ItwasdemonstratedinSection3.2.3thatthereisanerrorassociatedwithPLIFprocessing thatresultsinpoorlyidentiedliquidedgesupto5 % ofthetime.PLIFinterfacetracking requiresthatbothimagesinapairbecorrectlyprocessed,whichcompoundsthaterror.In addition,theuseofcross-correlationisdependentonfeaturesoftheinterfacebeingpresentand identiedinbothimages. Animagepairisacceptedasadatapointifitmeetsallthreeofthefollowingcriteria: 1.Thelagdistancemustbewithinthreestandarddeviationsawayfromthemeanlagfora owcondition. 2.Themaximum Xcorr valuemustbegreaterthan0.25. 3.Overhalfoftheedgevectormustberecordedasanedgenotazero. 4.1.4.2VanDriestModelDataFitting Thenon-dimensionalizeddatapointsforthe800Lmin )]TJ/F22 7.9701 Tf 6.587 0 Td [(1 and1200Lmin )]TJ/F22 7.9701 Tf 6.586 0 Td [(1 gasow rateconditionswerecombinedforamorecomprehensivedatat.TheVanDriestmodelfora continuouslawofthewall,describedinKays etal. [2],hasbeenusedforthispurpose.The modelintroducesanempiricalconstant, A + ,andanintegralthatmustbeevaluatednumerically: Z u + u + o du + = 1 Z y + y + o dy + y + h 1 )]TJ/F23 11.9552 Tf 11.955 0 Td [(exp )]TJ/F24 7.9701 Tf 11.43 5.256 Td [(y + A + i where isthevonKarmanconstant.41,and u + o and y + o arethelowerboundsofthemodel. ThevanDriestmodelwasdevelopedtoextendtotheviscoussublayer,eliminatingtheneedfor abufferlayerintheUVP.Therefore,thevaluesbelowtheboundsofthevanDriestmodelare assumedtoobeytheviscoussublayer u + = y + andthelowerboundsaresetequaltoeachother. Thevaluefor u + o isthendeterminedbysolvingthefollowing: 1 = u + o 1 )]TJ/F23 11.9552 Tf 11.955 0 Td [(exp )]TJ/F23 11.9552 Tf 11.55 8.088 Td [(u + o A + 72

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Theempiricalconstant A + wasdeterminedbytrialanderror,beginningwiththevalue of25.0suggestedinKays etal. Thegoodnessoftwasoptimizedusingthecoefcientof determination, R 2 .Similartotheindividualowcongurationplots,thedataforthisstudyhas beendividedintobasesectionsblueandwavesectionsredusingintermittencyinputsfrom Chapter5. 4.2PLIFImagePairResults Non-dimensionalinterfacialvelocity u + i graphsforselectedowconditionsareshownin Figure4.2Lmin )]TJ/F22 7.9701 Tf 6.587 0 Td [(1 gasowratesandFigure4-5Lmin )]TJ/F22 7.9701 Tf 6.586 0 Td [(1 gasowrates.Graphs fortheremainderoftheowconditionsareshowninAppendixF.Allvelocitygraphsareshown asafunctionofwallunits y + andincludecomparisonlinesfortheUVPdashedlineandan extensionoftheviscoussublayer u + i = y + ,solidline.Average u + i andaverage y + foreachow conditionareshowninTableE-1. Noneoftheowconditionsshowdistincttrendsof y + versus u + .Thereisaslighttrendof increasingvelocitywithincreasedlmthickness,asexpected.Thevelocitymeasurementsalso becomemuchmoresporadicwithincreasinglmthickness.Themaximumvelocityandlm thicknessmeasurementsalsoincreasewithincreasingliquidowrate. TheUVPshowsareasonableagreementwiththedata,buttendstounder-predict y + or over-predict u + i forthemajorityofthebaselm.TheUVPisanacceptabletrendlineforthe wavedata,butthespreadistoowidebythatpointforanyaccuratepredictionofwavebehavior. Theviscoussublayerlineisaneffectiveminimumfor y + valuesformostowconditions. Figure4-6showsthemean u + i and y + valuesforeachowcondition,linkedbysimilar valuesofsupercialgasvelocity.Thelowestvaluesofaverage y + correspondtothelowestliquid owand y + increaseswith U sl .However,neithergasorliquidowrateshaveastrongeffecton u + i ,whichcouldbeapproximatedwithanaveragevalueof9.Thisisdifferentfromwhatwould beexpctedforwavevelocitiesalone,whichhavebeenobservedtoincreasewithincreasinggas ow. 73

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Figure4-4. y + vs. u + i plotsforowconditions topleft 102F, topright 105F, bottomleft 109F,and bottomright 113F.Approximate U sg =36ms )]TJ/F22 7.9701 Tf 6.586 0 Td [(1 TheresultofthevanDriestmodeldatatisshowninFigure4-7usingavalueof34.0for A + .AswithUVPcurvesforindividualowcondtions,thismodeltendstounder-predictthe baselmvelocity.Themodelalsoturnsupwardssharply,failingtopredictany u + i valuesmuch over20.However,thewidedistributionoflmthicknessandvelocitymeasurementswouldmake ttingthisdatadifcultwithanymodel,asevidentinthewavesection. 74

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Figure4-5. y + vs. u + i plotsforowconditions topleft 140F, topright 143F, bottomleft 147F, bottomright 151F.Approximate U sg =57ms )]TJ/F22 7.9701 Tf 6.586 0 Td [(1 Figure4-6.Average y + vs. u + i ,by U sg 75

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Figure4-7.PLIFinterfacialvelocitydatawithvanDriestmodel.Flowconditionsincluded: 102F,105F,109F,113F,140F,143F,147F,and151F. 76

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CHAPTER5 VERTICALWAVELENGTHMEASUREMENT High-speedvideosofmanyverticalannularowconditionswereacquiredandanalyzedin theworkofSchubring,SheddandHurlburt[19]andinthedissertationofSchubring[58].The twomajorobjectivesofthestudieswereto: Demonstratetheuseofhigh-speedvideotoestimatethevelocities,lengths,andtemporal spacingsofindividualwaves. Usetheseindividualwavemeasurementstodevelopaveragevelocites,lengths,frequencies andintermittenciesofdisturbancewavesasfunctionsofgasandliquidowrates. Thecurrentworkisanextensionofoneaspectoftheoriginalverticalwaveprocessingcode wavelengthmeasurement.Anewwavelengthmeasurementtechniquehasbeendevelopedto addressthecircumferentialasymmetryofdisturbancewavestravelingthroughaverticaltube. Allotheraspectsoftheprocessingareidenticalincludingidentication,velocity,andfrequency measurements.Thegoalofthecurrentworkistousethenewprocessingmethodtostudythe effectofcircumferentialasymmetryonwavebehavior. 5.1VerticalWaveVideoAcquisition Averticaltestfacilitywasconstructedaroundaquartztubewithaninnerdiameterof0.0234 m.4mm,showninFigure5-1.Allaspectsofthisowloopareidenticaltothatusedfor thePLIFmeasurementsChapter3withtheexceptionofthetestsectiontubematerialand diameter.Liquidandgasmassowratesandsupercialvelocitieswererecordedusingow meterscoupledwithstaticpressuremeasurements.Liquidsupercialvelocitiesinthepresent workrangefrom0.04to0.39m/s,withgassupercialvelocitiesbetween36and82m/s.Test sectionpressuresrangedfrom100to116kPa. A0.303mlongregionofthetubewasbacklitwithvelightsandimagedwithanIntegratedDesignToolsX-StreamVISIONXS-3high-speedCMOSdigitalcamerain8-bit grayscale.Wavesappearinthetestregionasdarkpatchesthatpassovereachofthevelights insequence.Theconversiontophysicalscalewasaccomplishedbyalsorecordingvideoofa ruler,showninFigure5-2.Thepixelswere242 msquares.Thetotalimageresolutionwas1252 77

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Figure5-1.Schematicofverticalowloopwithquartztestsection. pixelsaxiallengthby112or120pixelswidth.Regionsexposedtoeachlightwereusedas virtualdetectorsfortheidenticationandtrackingofdisturbancewaves. Figure5-2.Visualizationsectionforverticalwaves,includingmeasurementforphysicalscale. Theframerateforthevideoaqcuisitionwasvariedbasedontheobservationthatwave velocityincreaseswithincreasinggasow.Theframeratewasincreasedwithincreasinggas velocityasindicatedinTable5-1.Thevideodurationwasalsoalteredtomaintainaconsistent numberofframesforprocessing.Theinitialvideooutputssavedas.avileswereseparated intouncompressed.tifimagesforanalysis. Everyaspectoftheoriginalverticalhigh-speedvideoprocessingcodeMATLAB-based hasbeenmaintainedexceptforthewavelengthmeasurementmethod.Thecodebeginswith 78

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Table5-1.Frameratesandvideolengthsforverticalwavevideos Q g;nom [Lmin )]TJ/F22 7.9701 Tf 6.587 0 Td [(1 ] fps [s )]TJ/F22 7.9701 Tf 6.586 0 Td [(1 ] t video [s] n frames [-] 800400114400 1000500105000 120060095400 140070085600 160080075600 180090065400 waveidentication,accomplishedusingthe score ofwave,ametricdevelopedbySchubring etal. [19]forwavetracking.The score iscalculatedasafunctionofthepeak-normalized darkness,summedoverthreeconsecutivevideoframes.Thecodeproceedswithwavetracking unchanged,wavevericationunchanged,andwavelengthmeasurementdiscussedbelow. 5.2VerticalWaveLengthProcessing Twomeasurementtechniqueshavebeenappliedtoestimatethelengthofdisturbancewaves, asingle-sectionmeasurementoriginalcodeandamulti-sectionmeasurementcurrentcode.A schematicofthetwomeasurementtechniquesisshowninFigure5-3,where L 1 representsthe originalestimateand L 2 isthecurrentestimate.Thesingle-sectionmethodproceedsbylocating thecenterofthewavedarkestsection,thenscanninginbothdirectionstondtheforward andrearedgesofthewave.Thewaveisthenrecordedasthedifferencebetweenthetwoedge recordings.AmoredetaileddescriptionoftheoriginalprocessingcodeisprovidedbySchubring etal. [19]. Themulti-sectionmethodproceedsbyidentifyingthecenterofthewaveinthesamemanner astheoriginalcode.Theimageisthensplitintofourequalsections Img sec sec =1through 4alongthetubewidth.Eachsectionisthenaveragedalongitswidthtoproduce avedarki sec thennormalizedbythetime-independentaveragefortheentireowcondition avedarkX to produce ddarki sec ,showninEquation5.AlloftheelementsinEquation5arearrays withapixellengthequaltothelengthofthetestsection. ddarki sec = Img sec )]TJ/F23 11.9552 Tf 11.956 0 Td [(avedarkX 79

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Figure5-3.Schematicofverticalwavelengthmeasurementtechniques. Athresholdisthenappliedto ddarki sec tolocatethepassingwave,producing ddarkiBW sec .Duetothevaryinglevelofcontrastineachimage,thewavethreshold, Th wave sec ,isafunctionoftheaverageandstandarddevationofeachsection,shownin Equation5. Th wave sec = ddarki sec + k sec s ddarki sec ddarkiBW sec = ddarki sec >Th wave sec Thevariationincontrastalsoappearedtobeastrongfunctionofliquidowrate,which wasalsofoundinChapter3tohavethestrongestimpactonwaveheight.Thestandarddeviation multiplier, k sec ,islinearlyalteredbetween-1.0and-0.45asafunctionof Q l .Thismethod producesaccuratelocationsofwaveedgeswithalowsensitivityto k sec variation. Startingatthecenterofthewaverecordedearliereach ddarki sec arrayissearchedleft towardsthefrontofthewaveandrighttowardsthebackofthewavetondthefrontand backwaveedges.Thesearchcontinuesineachdirectionuntil3consecutivenon-wavepixelsare identied.Thelengthforeachsectionisrecordedasthedifferencebetweenthefrontandback 80

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edges.Thewavelengthfortheimage L wave isrecordedastheaverageofallfourwavesection measurements L sec ,Equation5andconvertedtoaphysicalscale.Thewaveintermittencyfor theowconditionisthencalculatedfromthefollowing: INT w = L wave f wave v wave L wave = 1 4 4 X i =1 L sec;i Theprogramoutputstheoriginalimagewithallfourwavesectionmeasurementssuperimposedassolidlinesandtheresultsofthesingle-sectionmeasurementfromtheoriginalcodeas dashedlines.Averagevaluesofwavelength L wave ,wavefrequency f wave ,andwavevelocity v wave arecalculatedforeachowcondition. 5.3VerticalWaveLengthResults Wavelength L wave andwaveintermittency INT w measurementsarerecordedin AppendixGforallowconditionsalongwithgasandliquidsupercialvelocities. 5.3.1IndividualWaveLengthResults ExampleimageswithbothwavelengthmeasurementtechniquesareshowninFigure5-4for increasinggasow,wheredashedlinesindicatethesingle-measurementmethodandsolidlines indicatethemulti-measurementmethod.Additionalwavemeasurementexamplesareshownin AppendixHforincreasingliquidow. Disturbancewavesarenotalwayssymmetricaroundthecircumferenceofthetube.Awave isoftenobservedtobethickerincertainsectionsortravelwithaslantthroughthetube.The observationofassymetryindisturbancewaveshasalsobeenaddressedbyBelt[20]throughthe useofthree-dimensionalconductanceprobemeasurements. Thesingle-sectionmeasurementtechniquerecordsallwaveedgesattheleftandright extremes,andisthereforeover-estimatingthelengthofassymetricalfeatures.Thiscanbeseen inFigure5-4,wherethedistancebetweendashedlinesisconsistentlylargerthanbetweensolid lines. 81

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Figure5-4.Examplewavelengthcomparisonimagesforvaryinggasvelocities, U sl =7.8cms )]TJ/F22 7.9701 Tf 6.587 0 Td [(1 U sg toptobottom=32ms )]TJ/F22 7.9701 Tf 6.586 0 Td [(1 ,41ms )]TJ/F22 7.9701 Tf 6.587 0 Td [(1 ,50ms )]TJ/F22 7.9701 Tf 6.586 0 Td [(1 ,60ms )]TJ/F22 7.9701 Tf 6.587 0 Td [(1 ,70ms )]TJ/F22 7.9701 Tf 6.586 0 Td [(1 5.3.2AverageWaveLengthResults AveragetrendsforwaveintermittencyandwavelengthareshowninFigure5-5forthe single-sectionandmulti-sectionmeasurementtechniques.Themulti-sectionmethodproduces slightlylowerresultsforwavelengthsto10%,onaverage,whichwasconrmedbyvisual inspection.Inaddition,thewavelengthshowsamoreconsistentfunctionofliquidow, especiallyforhighgasowrates. Wavevelocityhasbeenobservedtoincreaseprimarilyasafunctionofgasowrate, accordingtotheworkofSchubring[58].Themulti-sectionmethodhasthegreatesteffecton highergasow,indicatingthatdisturbancewavesbecomeincreasinglyassymetricasthevelocity increases. Theintermittencytrendsalsoshowageneraldecreasein INT w valuesandasmoother functionofliquidowforthemulti-sectionmethod.Thisistobeexpected,astheonlychanging variableintheintermittencycalculationEquation5is L wave .However, INT w valueshave previouslybeenattributedtoaxiallocationsbyassumingsymmetryacrossdisturbancewaves. 82

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Figure5-5. Top L wave vs. U sl ,by U sg Bottom INT w vs. U sl ,by U sg Left Single-section wavelengthmeasurementtechnique. Right Multiple-sectionwavelength measurementtechnique. Theapplicationofthemulti-sectionmethodremovestheassumptionofsymmetry,andthereby relocateswavebehaviorfromanaxiallocationtoalocationontheliquidlm.Thischangein locationhasadirectimpactontwo-zonemodelingefforts,includingHurlburt etal. [57]and Schubring etal. [1],ansismoreconsistentwithanapplicationoflmmodeling. 5.3.3WaveCorrelations Empricalcorrelationsweredevelopedforthesingle-sectiondataintheworkofSchubring[58]. Thecorrelationsfor L wave and INT w havebeenre-optimizedforthemulti-sectiondata: L wave;KS =0 : 43 D x 0 : 63 INT w;KS =0 : 07+ Re l 49000 83

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Thesecorrelations'performanceisshowninFigure5-6;allvertical-speciccorrelationsare judgedasshowninTable5-2,basedonowswith Q g;nom of800to1600Lmin )]TJ/F22 7.9701 Tf 6.587 0 Td [(1 i.e. ,those plottedinthischapter. Table5-2.Performanceofvertical-specicwavecorrelations CorrelatedParameterMeanError[%]MAE[%]RMS[%] L wave;KS )]TJ/F15 11.9552 Tf 9.299 0 Td [(1 : 5815 : 9120 : 50 INT w;KS )]TJ/F15 11.9552 Tf 9.299 0 Td [(1 : 109 : 4712 : 13 Figure5-6.Wavecorrelationperformance.Seriesofconstant U sg Right Seriesofsimilar U sl Top L wave;KS Bottom INT w;KS 84

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CHAPTER6 GLOBALMODELAPPLICATION TheglobalmodelofSchubringandShedd[1]describedinChapter2hasbeenmodied basedontheresultsofChapters3and5.Theoptimizationofthemodelproceedsbyrst updatingthelmbehaviorcorrelationsdevelopedinthecurrentwork.Thesecondstepis determiningwhichparametersinthemodelempiricalandphysicalcanbeadjustedtoimprove agreementwithdataandtomoreaccuratelyreectthephysicsofannularow. Themetricsofoptimizationforthisworkaretheerrorsbetweencorrelatedparameters andmeasuredoutputs,whichvarydependingonthemeasurementtestsection.FortheFEP testsectionusedforPLIFlmmeasurement,averagelmthickness ,baselmthickness base ,andwaveheight wave dataareavailable.Forthequartztestsection,pressuregradient dP=dz anddisturbancewavevelocity v wave dataareavailable.Thecurrentmodelresultsare alsocomparedqualitativelytotheresultsoftheoriginalmodel,presentedinthedissertationof Schubring[58]. 6.1Re-CorrelatedFilmBehavior TheupdatedPLIFmeasurementtechniqueinChapter3andtheupdatedverticalwavelength measurementtechniqueinChapter5haveresultedinchangestolmbehaviorapproximations relevanttotheSchubringandSheddmodel.Thespeciccontributionsoftheseadjustmentstothe globalmodelaredescribedbytestsection. 6.1.1PLIFObservationsFEPTestSection TheSchubringandSheddmodelreliesonobservationsofroughnessinthebasezone, roughnessinthewavezone,andanapproximationofwave-to-baselmheightratio.The followingobservationshavebeenmadeinthecurrentworkthatupdatethoseobservationsinthe model: BaseFilmRoughness .Thebaselmroughnessiscalculatedinthecurrentworkastwice standarddeviationofbaselmdatasameastheoriginalworkandisusedtwowaysinthe model: 85

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1.IntheroughnessfrictionfactorfromHurlburt etal. ,showninEquation2. 2.Toapproximatethefractionofbaselmthattravelswithalinearprolelinearfraction, LF base Theoriginalobservationagreeswellwiththecurrentwork,demonstratingaconstantrelative roughnessof0.6anda LF base of0.7. WaveHeightRoughness .Thewaveroughnessiscalculatedasthestandarddeviationof wavedataandisappliedintheroughnessfrictionfactorshowninEquation2.Theroughness inthewavezonehasbeenobservedinthecurrentworkas60%of wave anincreasefromthe originalobservationof40%. Wave-to-BaseRatio .Theoriginalworkestimatedmeanwaveheightas2timesthemean baseheight,whichdidnotexplainsomelowliquidowbehaviors.Thecurrentworkshowsthat theratioisactuallyafunctionofgasandliquidowrate.Anempiricalcorrelationwasdeveloped toexpressthisratioasafunctionofowqualityEquation3,shownagainhere: wave base =1 : 86 x )]TJ/F22 7.9701 Tf 6.587 0 Td [(0 : 18 6.1.2VerticalWaveObservations Theupdatedwavelength L wave measurementcodedevelopedinChapter5resultedin differentobservationsofwavelengthandwaveintermittency INT w thantheoriginalwork. WaveLengthObservations .Thewavelengthdistributionsinthecurrentworkshow generallyshortervaluesfor L wave thanpreviouslyobserved.Thecorrelationfor L wave developed bySchubring[19]Equation2hasbeenre-optimizedtotthenewmeasurements: L wave;KS =0 : 43 D x 0 : 63 WaveIntermittencyObservations INT w iscloselylinkedto L wave ,andtherefore showedsimilardeparturesfromtheoriginalmodel.Thecorrelationfor INT w developedby Schubring[19]Equation2hasbeenre-optimizedtotthenewmeasurements: INT w;KS =0 : 07+ Re l 49000 86

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6.2ModelAdjustments SomeparametersintheSchubringandSheddmodelarepurelyempirical.Thegoalofa globalmodelistodescribeannularowfromphysicalprinciples.Thecalculationofwaveshear fromsharpbase-wavetransitions, i;wave;trans ,isoneviolationofthisgoalbyemployingapurely empiricalfactorof2.Thisparameterhasbeenremoved,effectivelyloweringthecontributionof transitionshear: i;wave;trans = core U g;trans 2 wave )]TJ/F23 11.9552 Tf 11.955 0 Td [( base L wave Thebaseandwavezonesub-modelsbothusetheroughtubefrictionfactorsuggestedby Hurlburt etal. [57]andemploytheempiricalconstants c B;base and c B;wave .Theseconstantsare observedintheequationsasthesubjectsofanaturallogarithm,sobysettingthemto1.0inthe currentmodeltheyareeffectivelyeliminated: C f;i;base =0 : 58 2 )]TJ/F15 11.9552 Tf 21.771 8.088 Td [(ln^ base ^ base )]TJ/F15 11.9552 Tf 11.955 0 Td [(1 2 +1 : 05+ 1 2 ^ base +1 ^ base )]TJ/F15 11.9552 Tf 11.956 0 Td [(1 )]TJ/F22 7.9701 Tf 6.586 0 Td [(2 C f;i;wave =0 : 58 2 )]TJ/F15 11.9552 Tf 21.771 8.088 Td [(ln^ wave ^ wave )]TJ/F15 11.9552 Tf 11.955 0 Td [(1 2 +1 : 05+ 1 2 ^ wave +1 ^ wave )]TJ/F15 11.9552 Tf 11.955 0 Td [(1 )]TJ/F22 7.9701 Tf 6.587 0 Td [(2 Thepredictionoflmthicknessbothzonesandvelocityisverysensitivetothefriction correlation,includingtheempiricalenhancer, RR .Theequationfor RR hasbeenadjustedfrom itsoriginalformEquation2tothefollowing: RR =2 : 18 x )]TJ/F22 7.9701 Tf 6.587 0 Td [(0 : 1 Theoriginalmodelobservedapoorcorrelationofwavevelocityoutputsforseriesof constantliquidow,whichincreasedtooquicklywithincreasinggasowrate.Thiscanbe attributedtoanover-predictionofwavevelocitybytheuniversalvelocityprole.Toremedythis, therelativeroughnessofthewavezoneisusedtopredictthefractionofthewavethattravels withtheprescribedproletermedthewavevaryingfraction, VF wave creatingthefollowing 87

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expressionforwavevelocity: U + l;i;wave =5 : 5+2 : 5ln )]TJ/F15 11.9552 Tf 5.479 -9.684 Td [( )]TJ/F23 11.9552 Tf 11.955 0 Td [(VF wave + wave U l;i;wave = U + l;i;wave u ? wave VF wave =0 : 3 Thisassumesthattheupperportionofthewaveroughfractiondoesnotincreasethewave velocitywell-mixedow.ThisisinagreementwiththepreliminaryresultsofPLIFinterface trackinginChapter4,whichindicatesaconsistentover-pridictionofwavevelocitybytheUVP asafunctionofwaveheight. 6.3ComparisontoVerticalDataFEPTube TheoriginalmodelwasdevelopedrstwithconsiderationoftheverticalFEPtubeow conditions,usedprimarilyforthePLIFlmthicknessmeasurements.Theseparationbetween baseandwavezoneshasbeenperformedusingthe INT w valuesfromdisturbancewave visualization.Averagevaluesfor base ,and wave areavailableforeachowconditionfrom PLIFresultsandarecomparedtothemodeloutputsforerrorestimation. Table6-1showstheaccuracyofthepredictionsforthesethreeresultsforPLIFows investigatedwith Q g;nom of1600Lmin )]TJ/F22 7.9701 Tf 6.586 0 Td [(1 andbelow.Flow189Fwasimagedtwice;both comparisonsareincludedintheresults. Table6-1.PerformanceofpresentglobalmodelforverticalFEPlmthicknessdata. CorrelatedParameterMeanError[%]MAE[%]RMS[%] -0.108.7011.11 base 0.178.9311.49 wave 0.429.8214.31 Figure6-1showsthepredicted base ,and wave withseriesofliquidowrate,alongwith theperformanceofthemodelforlmthickness.Thecurrentmodelperformsverywellfor and base ,withslightinaccuraciesinconstantliquidseries.Thisobservationisconsistentwith theoriginalmodelandismostlikelyrelatedtothesameissues:experimentalerrorsnotably 88

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locatingthetubewallthatvarywithowrates.Theoriginalmodelalsoperformedverywell forPLIFlmthicknessdataandshowedsimilartrends. 6.4ComparisontoVerticalDataQuartzTube Flowconditionsstudiedinthequartztubeallowfortwodirectcomparisonsofmodeled resultsandexperimentaldata:pressuregradientandwavevelocity.Atotalof54owconditions Q g;nom of1600Lmin )]TJ/F22 7.9701 Tf 6.587 0 Td [(1 andbelowareavailable.Theperformanceofthemodelwithrespectto thesetwoquantitiesisshowninTable6-2.Themodeledandexperimentalresultsarecompared forthequartztubeinFigure6-3. Table6-2.Performanceofpresentglobalmodelforverticalquartztubedata. CorrelatedParameterMeanError[%]MAE[%]RMS[%] dP=dz 0.4517.4223.22 v wave 10.8819.1420.99 Forpressureloss,theresultsshowsimilartrendsasfromtheoriginalmodel.Theoverpredictionof dP=dz withhighgasandliquidowappearstobeachronicissuewiththemodel andthesehighowrates.Theerrorestimatesaregood,andonparwithempiricalpressureloss estimators.Thewavevelocityisalsowell-predictedinthequartztube,althoughtherangeof v wave withincreasinggasowrateissomewhatunderestimatedasintheoriginalmodel.The changeappliedtothe U l;i;wave calculationshowsanimprovementforvelocityestimatesathigh gasowrates. Theestimateofentrainedfractionfromthemodel, E mod ,isshowninFigure6-4asa functionofgasandliquidowrate.Thisestimateisevaluatedqualitativelyduetothelackof entrainmentdataforcomparison. Thevaluesfor E mod decreaseacrosstheboardforthenewmodelwhilemaintainingthe sametrends.Theincreaseswithgasandliquidowrateareconsistentwiththeoriginalmodel, wavevideos,andentrainmentliterature.Theincreasewithliquidowrateandthesharpdrop towardsanentrainedfractionof0atlow U sl areinagreementwiththeexcessliquidconcept. 89

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Figure6-1.ModelresultspertainingtolmthicknessforverticalFEPtube. Left Resultsfor seriesof U sl Right Performancecomparison. Top Middle base Bottom wave 90

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Figure6-2.Componentsof i frommodelforverticalFEPtube. Left By U sl Right By U sg Top Baselmroughness, i;base )]TJ/F23 11.9552 Tf 11.955 0 Td [(INT w Middle Waveroughness, i;wave;rough INT w Bottom Wavedrag, i;wave;trans INT w 91

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Figure6-3.Performanceofmodelinverticalquartztube. Left By U sl Right By U sg Top dP=dx predictions. Middle dP=dx comparisons. Bottom v wave comparisons. 92

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Figure6-4.Modeledentrainedfraction, E mod ,inverticalquartztube. Left By U sl Right By U sg 93

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CHAPTER7 CONCLUSIONS Thecurrenteffortontwo-phasemodelingisjustiedbythenumerousapplicationsto industrialheat-exchangeequipment,notablyinnuclearBWRandPWRsystems.Theannular regimeexiststhroughlargerangeofowratesandisfoundinthecoreofaBWR,thesteam generatorofaPWR,andinseveralpostulatedaccidentscenariosincludingCHFinaBWR. Gas-liquidannularowischaracterizedbyacoreoffast-movinggaswithentrained liquiddroplets,surroundedbyathinlmofliquid,complicatedbythepresenceofdisturbance wavesandentrainedgasbubbles.Thecomplexfeaturesofannularowareintricatelyrelated, producinguctuationsinpressurelossandheattransfer,whichareofparticularinterestin industrialapplications. Manyfeaturesofannularowhavebeenstudiedbypreviousresearchers.Severalfeatures, includinglmthicknessdistributions,disturbancewavedistributions,andlmvelocityproles areintegraltotheowmechanicsandmodelingefforts.Chapter2outlinesseveralofthese efforts,culminatingwiththeglobalmodelingeffortsofSchubringandShedd[1].Thegoalofthe SchubringandShedd[1]modelistocharacterizeannularowthroughquantitativevisualization ofindividualowfeatures. Theconclusionsforeachchapterinthecurrentworkarepresented,followedbyabrief summary/conclusionofthetotaleffortandsuggestionsforfuturework. 7.1PLIFConclusions TheplanarlaserinduceduorescencePLIFannularlmmeasurementtechniqueof Schubring etal. [43,44]hasbeenmodiedinChapter3.Manyoftheguresusedtopresentthe originaldatahavebeenduplicatedandshownforcomparison. Theresultsofthenewalgorithmhavebeencomparedvisuallytothepreviousandhave demonstratedmoreaccurateresultsforedgelocation.Theproblemswithdetectingbubblesin theinterfacehavebeenlimited,whilethemeasurementoflarger,moreerraticwaveshasbeen 94

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improved.AnaccurateGUImethodoflocatingandeliminatingpoorlyprocessedimageshas beenadded. Thenewalgorithmhasbeencomparedquantitativelytothepreviousbyuseofthe k c method,demonstratingdifferencesinlmthicknessdistribution.Anewcorrelationhas beenpresentedforlmthicknessrelativeroughnessasafunctionofowquality.Alarge impactisalsoseenonwaveheightdistributionsandaveragewavevalues,whichshowagreater dependencyongasowrate.Relativeroughnessforthewavezoneisnowestimatedas0.3, basedontheinterpretationofroughnessasstandarddeviation.Thismeasurementhasadirect impactontheSchubringandShedd[1]modelforpredictingfrictioninthewavezone. Verylittleimpactonbaselmthicknessdistributionsortrendsisseen.Theoriginalcode didnotshowanyproblemswithbaselmmeasurement;thecodemodicationsweredirectedat thicker,moreerraticsectionsofthelm.Thewave-to-baseratiohasbeenaffectedduetolarger wavemeasurements,withacorrelationpresentedtopredictthisbehaviorasafunctionofow quality.Therelativeincreaseinwaveheightwillincreasethecontributionofthewavezoneshear. The k c methodforseparatingbaselmfromwaves,developedbyRodr guez[21],was comparedtobase-waveseparationsusing INT w inputs.The INT w resultswerecomparable inmagnitude,butshowedhigheraveragelmthicknessvaluesforbaseandwaveandstronger dependenceofgasowrate. 7.2PLIFImagePairConclusions AMATLABprogrammingschemewasdevelopedtoaccepttime-elapsedPLIFimage pairsofannularowandestimatethevelocityofthegas-liquidinterfaceChapter4.These measurementshavebeenusedtostudythenon-dimensionalinterfacialvelocity, u + i ,asafunction ofwallunits, y + .Therearestillseveralaspectsofthisstudythatrequirefutureeffort,whichmay bejustiedbythecurrentwork.Someissuesthatneedtobeaddressedinclude: PLIFImageQuality .Achievingcross-correlationwithasuccessratenecessaryforthis studyrequiresextremelyaccurateliquidedgemeasurements.Manyoftheissueswithpoorly 95

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processedimagesandbadcross-correlationsstemfromblurryPLIFimages.Avigorousoutlierremovalprocessisemployedtocompensatefortheseproblemsinthecurrentdata,whichmay skewtheresults.Morespecically,baselmsectionsaredifculttotrackduetothelackof featuresofbaselm.Increasedimagequalitywouldallowmoreaccurateprocessingandbetter overallvelocitymeasurements. FunctionDevelopment .NeithertheUVPorthelinear/viscousapproximationshowgood agreementwiththe u + i measurementsforindividualowrates.Abetteruniversalfunctionfor interfacialvelocityneedstobedevelopedwithrespecttodistancefromthechannelwall.It hasbeendemonstratedthatsuchafunctiondoesexistalbeitweaklyandthatsupercial gasvelocityhaslittleeffect.TheuseofthevanDriestmodelhasnotbeenprovensignicantly accurateasauniversalapproximationof u + i ,especiallyconsideringtheincreasedempiricismand computationrequired.TheUVPisalsoaninnaccurateapproximation,butisrelativelyeasyto apply. ThePLIFimagepairshavebeendividedintobaseandwavezonesusingintermittencydata fromChapter5.Thetwozoneshave,insomeowconditions,showndifferentvelocitybehavior. Thewavezoneshowsamuchwiderrangeofinterfacialvelocitiesandlmthicknesses.Itmay beusefulinfutureeffortstocorrelatethedataintwozonestocompensateforthedifferencein behavior. 7.3VerticalWaveConclusions Thehigh-speedvideoprocessingcodeforwavelengthmeasurement L wave developed bySchubring etal. [19]hasbeenmodiedtoaccommodateasymmetricdisturbancewavesby splittingeachimageintomultiplesectionsChapter5.Thetwomethods,single-andmultisection,havebeencomparedvisuallyandquantitativelytoassesstheimpactofasymmetryon L wave estimation. Themulti-sectionmethodproducesmoreaccuratewavelengthmeasurementsforindividual wavesandgenerallyshorterestimatesforindividualandaverage L wave values.Thewavelength 96

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trendsalsoappearassmootherfunctionsofgasandliquidowrates.Thewaveintermittency INT w ,calculatedasafunctionof L wave ,showssimilarchanges. Theassumptionofdisturbancewavesymmetryhasbeenkeyinthedenitionof INT w :the fractionoftimethatdisturbancewavesarepresentatanaxiallocation.Thelackofsymmetry impliesthatwaveintermittencyisapplicabletoalocationontheliquidlm. 7.4GlobalModelConclusions Severallimitationstotheoriginalmodelhavebeenaddressedinthecurrentworkthrough updatedmeasurementtechniquesandre-correlationofindividualparametersChapter6.The determinationofvelocityinthebaselmusingrelativeroughnesstoidentifyalinearfraction LF base hasbeenstrengthenedbyanimprovedagreementwiththenewmeasurements. Performanceofthemodelhasbeenimprovedforlow-liquidowsthroughthecorrelationof wave-to-baseratio,previouslyassumedconstant. Severallimitationsofthemodelstillexistinthefrictionfactorcorrelationsandassumed velocityproles.Therelianceontheuniversalvelocityproleforestimatesinthewavezone hasnotbeenveried.Incontrast,thecurrentworkoninterfacialtrackingChapter4shows preliminaryresultsthatquestionsuchanassumption.Theinclusionofawell-mixedlayeron thewavezonehasmitigatedsomeover-predictioninwavevelocity,butitismorelikelythatthe universalvelocityprolenotsuitedfor U l;i;wave prediction. Theempiricalfactorof2inEquation2transitioneffecthasbeenremovedand continuestoproduceaccurateresults.Arelianceontheuniversalvelocityprolestillexists throughthe U i;wave;trans term,whichmayrequirefutureadjustment.Apredominantformof empiricismistheuseofsamplestandarddeviationasanestimationofroughness,usedinseveral calculationsofvelocityandshear. TheuseoftheHurlburt etal. [57]frictionfactorsrequiresanempiricalassignmentofthe valuesfor c B .Theremainderofthemodeladjustmenthasbeenperformedbytweaking RR ,a purelyempiricalt.Themodelcouldbeimprovedwithamorephysicaldeterminationoffriction factors,perhapseliminatingtheneedforsuchanadjustmentparameter. 97

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Inspiteofthecontinuedlimitations,themodelproducesanumberofaccuratepredictions withreducedempiricismwhilerequiringnoinformationbeyondowrates,tubediameter,and uidproperties.Allpredictionsareaccuratetowithin20%MAE;manyaresignicantly superiortothis.Thepredictionsforlmheightandwavevelocityareaccuratetowithin10% and15%MAE,respectively,includinganydifferencesthatmayberelatedtotheexperimental facilityFEP vs. quartztubing.Theaccuracyofthepredictionfor v wave isnotable,especially giventhelackofdirectwavezonevelocityproleinformation. 7.5OverallConclusions Theculminationofthecurrentworkisthere-correlationoftheSchubringandSheddglobal model[1]inChapter6.Muchofthecurrentefforthasbeenspentupdatingmeasurementtechniquesanddatasetsforthebetterunderstandingofannularowbehavior.Therealverication fortheseindividualbehavioralobservationsreliesontheirinterrelationshipsandtheimproved predictionofannularowparameters.TheSchubringandSheddmodelhasbeenusedasametric fortheseimprovements,showingsimilaroftenimprovedobservationalagreementsinoutput parameterswithreducedempiricism. Onethemeofthecurrentworkistheapplicationofquantitativevisualizationformeasurementsinannularow.ThePLIFmeasurementshavebeenshowntoproducevisuallyaccurate lmthicknessresultsbaselmandwavewithoutintrusiveinstrumentation.Theverticalwave videohasdemonstratedsimilarachievements,withtheadditionoftemporalresolution. Onelimitingfactortobothtechniquesandquantitativevisualizationingeneralisthe relianceofmeasurementsonuniquedataregressioncode.Thecurrentworkshowshowsome observationscanvarybasedonmeasurementtechniquesaftertherawdatacollection.Several originalobservations,includingbaselmroughnessestimates,havebeenrevisedbythenew code.However,theadjustmentofwave-to-baseratioandwaveintermittencytrendshasanotable impactonglobalmodeloutputs.Theobjectivedevelopmentofdatareductioncode,andthe knowledgeofalllimitations,iskeytotheaccuracyofameasurement. 98

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TheeffortspentonliquidinterfacetrackingChapter4hasnotbeenappliedtotheglobal modelinChapter6.Thateffortcouldbeusefultotheunderstandingofinterfacialvelocityand shear.Thecurrentlimitationstointerfacialtrackingareprimarilydependentonimagequality. 7.6RecommendedFutureWork ThecurrentworkhasshownimprovementsintheuseofPLIFandhigh-speedvideodata forannularow,alongwithimprovedglobalmodeling.However,severallimitationstillexist inpursuitoftheoverallgoalacompletelyclosedmodelforindustrialannularow.The achievementofthatgoaliswellbeyondthescopeofthecurrentwork.Thefollowingareas requirefurtherstudytoachievethisgoal. Time-elapsedPLIF .Thesedatawouldfacilitatetheanalysisofmomentumtransferat thegas-liquidinterfaceandabetterunderstandingofthelmroughnessconcept.Themain limitationtothismeasurementisthelackofcontrastinPLIFimagepairs,limitingtheaccuracy ofliquidedgeidentication.Anew,comprehensivesetoftime-elapsedPLIFimagesisrequired forfutureanalysis.Thefutureworkfordevelopinginterfacialvelocityasafunctionoflm heighthasalsobeendiscussedinSection7.2. Inadditiontothegas-liquidinterface,bubbleswithintheliquidcoreareoftenvisiblewith apossibilityoftracking.Thereliableidenticationofbubblesisamuchmoredifculttask,as bubblesshowupthrougharangeofintensitiesandcontrasts.Thethree-dimensionalshapeand locationofbubblesalsoposeproblems,astheidenticationofbubblesoutsidethelaserplane couldresultininaccuratemeasurements. Entrainment .Liquidentrainmentinthegascoreisparticularlydifculttodescribe. Thefurtherdevelopmentofglobalmodelsrequiresabetterunderstandingofentrainedliquid behavioranditscomplexdependenceongasandliquidvelocities.Theinvolvementofcomplex entrainmentscenariosintotheglobalmodelmayreducetheempiricisminsomeofthese behaviors. Forfuturedataacquisition,thelocationandtrackingofentrainedliquidinannularow wouldbeinvasiveforalmostanyphysicalmeasurementtechnique.Theuseofmultiplecameras 99

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withthree-dimensionalreconstruction,orothermulti-dimensionalvisualizationtechniques,may beapplicable. PropertyEffects .Thisworkfocusedonbehaviorsofanair-watersystem,rarelyseenin industrialapplications.Anaccurateproperty-dependentannularowmodelisideal,requiring multipleuidpairsandawiderangeofuidpropertiesforcomparison.Thiswouldimprove therelationoflaboratoryworktotherealmsofrefrigerants,steam-watersystems,andother condensiblegasesprevalentinindustrialsystems.Onasmallerscale,moreattentioncouldbe focusedoncorrelatingparameterstouidpropertiessuchasdensity,viscosity,orsurfacetension. HeatTransfer .Whiletheoutputsofthecurrentworkhaveadirecteffectonheattransfer modeling,thecouplingofconvectiveheattransferintheliquidlmcouldenhancethemodel's industrialapplication.Abetterunderstandingofturbulence-enhancedconvectiveheattransfer mayalsoprovideinsighttothin-lmmechanics. Thescopeofthecurrentworkhasbeenlimitedtotherawdataavailable.Advancementof theSchubringandShedd[1]globalmodeltoaclosed,physicalengineeringdesigncoderequires agreatadditionofthoughtfulexperimentalwork,supplementedwithdatareductioneffortsona similarscale. 100

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APPENDIXA PLIFDATA TableA-1.VerticalFEPtubedata. Flow Q g;nom Q l U sg U sl Total Rej [Lmin )]TJ/F22 7.9701 Tf 6.586 0 Td [(1 ][Lmin )]TJ/F22 7.9701 Tf 6.586 0 Td [(1 ][ms )]TJ/F22 7.9701 Tf 6.587 0 Td [(1 ][cms )]TJ/F22 7.9701 Tf 6.586 0 Td [(1 ][images][images] 102F 8001 : 535 : 76 : 34004 105F 8003 : 035 : 812 : 74005 109F 8005 : 036 : 321 : 14008 113F 8007 : 037 : 229 : 640016 115F 8008 : 037 : 333 : 840018 121F 10001 : 545 : 06 : 34005 124F 10003 : 045 : 412 : 74003 128F 10005 : 046 : 221 : 14006 132F 10007 : 047 : 829 : 640012 134F 10008 : 047 : 933 : 840013 140F 12001 : 554 : 76 : 34001 143F 12003 : 055 : 312 : 74004 147F 12005 : 056 : 521 : 14002 151F 12007 : 059 : 329 : 640015 153F 12008 : 059 : 433 : 84005 159F 14001 : 564 : 46 : 34002 162F 14003 : 065 : 212 : 74004 166F 14005 : 066 : 921 : 14002 170F 14007 : 072 : 129 : 640017 172F 14008 : 071 : 733 : 84006 178F 16001 : 575 : 06 : 34001 181F 16003 : 076 : 112 : 74000 185F 16005 : 078 : 021 : 14003 189Fa 16007 : 083 : 529 : 64009 189Fb 16007 : 083 : 529 : 640016 191F 16008 : 083 : 533 : 83006 101

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TableA-2.PLIFdatausing k c method. Flow s base s base wave s wave [ m][ m][ m][ m][ m][ m] 102F 223 : 9116 : 0183 : 857 : 0412 : 5135 : 5 105F 260 : 8157 : 2199 : 962 : 6491 : 8190 : 1 109F 294 : 3165 : 4222 : 372 : 0532 : 9163 : 5 113F 337 : 8205 : 3242 : 874 : 7608 : 5217 : 9 115F 342 : 7196 : 7250 : 678 : 6602 : 1197 : 7 121F 187 : 278 : 0164 : 847 : 1332 : 782 : 4 124F 187 : 8107 : 5150 : 544 : 2357 : 6142 : 2 128F 239 : 7143 : 8177 : 954 : 4439 : 6160 : 1 132F 262 : 6160 : 8190 : 755 : 4469 : 1183 : 9 134F 267 : 6148 : 4202 : 061 : 2473 : 9152 : 8 140F 145 : 057 : 7127 : 633 : 2247 : 764 : 0 143F 153 : 181 : 5122 : 335 : 9277 : 794 : 4 147F 174 : 694 : 6133 : 737 : 4304 : 6103 : 4 151F 201 : 5109 : 2151 : 943 : 1347 : 5113 : 7 153F 206 : 9116 : 0151 : 641 : 8354 : 9121 : 6 159F 116 : 543 : 2102 : 024 : 9190 : 041 : 4 162F 116 : 647 : 5100 : 326 : 1194 : 549 : 0 166F 146 : 178 : 2111 : 531 : 2252 : 982 : 9 170F 171 : 783 : 3136 : 136 : 1293 : 584 : 2 172F 167 : 991 : 4130 : 841 : 6307 : 792 : 4 178F 91 : 631 : 281 : 318 : 1144 : 930 : 6 181F 91 : 133 : 179 : 418 : 6145 : 231 : 6 185F 100 : 052 : 478 : 320 : 9173 : 359 : 7 189Fa 158 : 173 : 9123 : 726 : 5250 : 480 : 9 189Fb 152 : 476 : 5117 : 334 : 7260 : 868 : 2 191F 135 : 665 : 8105 : 828 : 2231 : 360 : 4 102

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TableA-3.PLIFdatausing INT w method. Flow s base s base wave s wave [ m][ m][ m][ m][ m][ m] 102F 223 : 9116 : 0197 : 168 : 4496 : 0146 : 3 105F 260 : 8157 : 2219 : 780 : 4623 : 1198 : 5 109F 294 : 3165 : 4237 : 084 : 1595 : 6161 : 2 113F 337 : 8205 : 3258 : 487 : 7677 : 7217 : 7 115F 342 : 7196 : 7261 : 286 : 9641 : 7198 : 1 121F 187 : 278 : 0165 : 647 : 6336 : 782 : 8 124F 187 : 8107 : 5160 : 152 : 6432 : 0151 : 2 128F 239 : 7143 : 8193 : 067 : 3522 : 2159 : 5 132F 262 : 6160 : 8201 : 163 : 9518 : 2188 : 0 134F 267 : 6148 : 4207 : 265 : 2494 : 9153 : 2 140F 145 : 057 : 7131 : 836 : 8270 : 968 : 5 143F 153 : 181 : 5130 : 943 : 3328 : 498 : 8 147F 174 : 694 : 6145 : 047 : 1359 : 0106 : 5 151F 201 : 5109 : 2162 : 051 : 3390 : 6114 : 5 153F 206 : 9116 : 0159 : 948 : 6388 : 6122 : 0 159F 116 : 543 : 2106 : 128 : 2208 : 842 : 9 162F 116 : 647 : 5104 : 329 : 4212 : 652 : 1 166F 146 : 178 : 2122 : 440 : 5306 : 283 : 0 170F 171 : 783 : 3144 : 142 : 7330 : 582 : 6 172F 167 : 991 : 4132 : 743 : 1316 : 392 : 3 178F 91 : 631 : 283 : 219 : 5153 : 031 : 5 181F 91 : 133 : 181 : 720 : 4154 : 332 : 6 185F 100 : 052 : 483 : 725 : 5201 : 062 : 3 189Fa 158 : 173 : 9133 : 234 : 4292 : 784 : 0 189Fb 152 : 476 : 5126 : 342 : 2293 : 065 : 8 191F 135 : 665 : 8112 : 534 : 0260 : 055 : 6 103

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APPENDIXB PLIFHISTOGRAMS:BASEANDWAVE FigureB-1.Histogramsoflmthickness,baseandwave.Flowconditions: TopLeft 102F. Top Right 105F. MiddleLeft 113F. MiddleRight 115F. BottomLeft 121F. Bottom Right 124F. 104

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FigureB-2.Histogramsoflmthickness,baseandwave.Flowconditions: TopLeft 132F. Top Right 134F. MiddleLeft 159F. MiddleRight 162F. BottomLeft 170F. Bottom Right 172F. 105

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FigureB-3.Histogramsoflmthickness,baseandwave.Flowconditions: TopLeft 178F. Top Right 181F. BottomLeft 189Fa. BottomRight 191F. 106

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APPENDIXC PLIFHISTOGRAMS:STANDARDDEVIATIONMULTIPLIERMETHOD FigureC-1.Histogramsofbaselmthicknessusing k c method.Flowconditions: TopLeft 102F. TopRight 121F. MiddleLeft 140F. MiddleRight 159F. Bottom 178F. 107

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FigureC-2.Histogramsofbaselmthicknessusing k c method.Flowconditions: TopLeft 105F. TopRight 124F. MiddleLeft 143F. MiddleRight 162F. Bottom 181F. 108

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FigureC-3.Histogramsofbaselmthicknessusing k c method.Flowconditions: TopLeft 113F. TopRight 132F. MiddleLeft 151F. MiddleRight 170F. Bottom 189aF. 109

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FigureC-4.Histogramsofbaselmthicknessusing k c method.Flowconditions: TopLeft 115F. TopRight 134F. MiddleLeft 153F. MiddleRight 172F. Bottom 191F. 110

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FigureC-5.Histogramsofwaveheightusing k c method.Flowconditions: TopLeft 102F. Top Right 121F. MiddleLeft 140F. MiddleRight 159F. Bottom 178F. 111

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FigureC-6.Histogramsofwaveheightusing k c method.Flowconditions: TopLeft 105F. Top Right 124F. MiddleLeft 143F. MiddleRight 162F. Bottom 181F. 112

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FigureC-7.Histogramsofwaveheightusing k c method.Flowconditions: TopLeft 113F. Top Right 132F. MiddleLeft 151F. MiddleRight 170F. Bottom 189aF. 113

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FigureC-8.Histogramsofwaveheightusing k c method.Flowconditions: TopLeft 115F. Top Right 134F. MiddleLeft 153F. MiddleRight 172F. Bottom 191F. 114

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APPENDIXD PLIFHISTOGRAMS:INTERMITTENCYMETHOD FigureD-1.Histogramsofbaselmthicknessusing INT w method.Flowconditions: TopLeft 102F. TopRight 105F. MiddleLeft 109F. MiddleRight 113F. Bottom 115F. 115

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FigureD-2.Histogramsofbaselmthicknessusing INT w method.Flowconditions: TopLeft 121F. TopRight 124F. MiddleLeft 128F. MiddleRight 132F. Bottom 134F. 116

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FigureD-3.Histogramsofbaselmthicknessusing INT w method.Flowconditions: TopLeft 140F. TopRight 143F. MiddleLeft 147F. MiddleRight 151F. Bottom 153F. 117

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FigureD-4.Histogramsofbaselmthicknessusing INT w method.Flowconditions: TopLeft 159F. TopRight 162F. MiddleLeft 166F. MiddleRight 170F. Bottom 172F. 118

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FigureD-5.Histogramsofbaselmthicknessusing INT w method.Flowconditions: TopLeft 178F. TopRight 181F. MiddleLeft 185F. MiddleRight 189F. Bottom 189Fa. 119

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FigureD-6.Histogramsofwaveheightusing INT w method.Flowconditions: TopLeft 102F. TopRight 105F. MiddleLeft 109F. MiddleRight 113F. Bottom 115F. 120

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FigureD-7.Histogramsofwaveheightusing INT w method.Flowconditions: TopLeft 121F. TopRight 124F. MiddleLeft 128F. MiddleRight 132F. Bottom 134F. 121

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FigureD-8.Histogramsofwaveheightusing INT w method.Flowconditions: TopLeft 140F. TopRight 143F. MiddleLeft 147F. MiddleRight 151F. Bottom 153F. 122

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FigureD-9.Histogramsofwaveheightusing INT w method.Flowconditions: TopLeft 159F. TopRight 162F. MiddleLeft 166F. MiddleRight 170F. Bottom 172F. 123

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FigureD-10.Histogramsofwaveheightusing INT w method.Flowconditions: TopLeft 178F. TopRight 181F. MiddleLeft 185F. MiddleRight 189F. Bottom 189Fa. 124

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APPENDIXE PLIFIMAGEPAIRDATA TableE-1.FlowconditionsforPLIFimagepairsets. Flow Q g;nom Q l t + u + i Lmin )]TJ/F22 7.9701 Tf 6.586 0 Td [(1 Lmin )]TJ/F22 7.9701 Tf 6.587 0 Td [(1 ms[-][-] 102F 8001 : 50 : 2125 : 528 : 53 105F 8003 : 00 : 1726 : 888 : 88 109F 8005 : 00 : 1433 : 568 : 78 113F 8007 : 00 : 1241 : 399 : 54 120F 10001 : 00 : 1919 : 086 : 86 122F 10002 : 00 : 1719 : 919 : 15 126F 10004 : 00 : 1425 : 9110 : 4 130F 10006 : 00 : 1232 : 9510 : 5 134F 10008 : 00 : 1043 : 5310 : 16 140F 12001 : 50 : 1516 : 877 : 28 143F 12003 : 00 : 1320 : 837 : 42 147F 12005 : 00 : 1221 : 6110 : 5 151F 12007 : 00 : 1032 : 9610 : 56 158F 14001 : 00 : 1514 : 638 : 23 160F 14002 : 00 : 1314 : 817 : 27 164F 14004 : 00 : 1219 : 6510 : 3 168F 14006 : 00 : 1124 : 229 : 9 172F 14008 : 00 : 0934 : 0711 : 62 178F 16001 : 50 : 1314 : 238 : 35 181F 16003 : 00 : 1115 : 858 : 05 185F 16005 : 00 : 1021 : 749 : 51 189F 16007 : 00 : 1025 : 4712 : 05 125

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APPENDIXF MEANINTERFACIALVELOCITYPLOTS FigureF-1.PLIFinterfacialvelocitydataplotsforowconditions topleft 120F, topright 122F, middleleft 126F, middleright 130F, bottom 134F. 126

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FigureF-2.PLIFinterfacialvelocitydataplotsforowconditions topleft 158F, topright 160F, middleleft 164F, middleright 168F, bottom 172F. 127

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FigureF-3.PLIFinterfacialvelocitydataplotsforowconditions topleft 178F, topright 181F, bottomleft 185F, bottomright 189F. 128

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APPENDIXG VERTICALWAVELENGTHDATA TableG-1.Verticalquartztubewavedata. Flow Q g;nom Q l U sg U sl L wave INT w [Lmin )]TJ/F22 7.9701 Tf 6.586 0 Td [(1 ][Lmin )]TJ/F22 7.9701 Tf 6.587 0 Td [(1 ][ms )]TJ/F22 7.9701 Tf 6.587 0 Td [(1 ][cms )]TJ/F22 7.9701 Tf 6.586 0 Td [(1 ][cm][-] 101Q 8001 : 032 : 73 : 91 : 920 : 072 102Q 8001 : 532 : 85 : 82 : 140 : 090 103Q 8002 : 032 : 47 : 82 : 390 : 086 105Q 8003 : 033 : 011 : 62 : 740 : 104 107Q 8004 : 033 : 315 : 52 : 810 : 142 109Q 8005 : 033 : 619 : 43 : 270 : 163 111Q 8006 : 034 : 823 : 33 : 450 : 181 113Q 8007 : 034 : 527 : 13 : 780 : 195 117Q 8009 : 035 : 434 : 94 : 260 : 208 119Q 80010 : 035 : 738 : 84 : 970 : 226 120Q 10001 : 041 : 43 : 91 : 750 : 073 121Q 10001 : 541 : 55 : 82 : 270 : 119 122Q 10002 : 041 : 27 : 82 : 200 : 086 124Q 10003 : 041 : 911 : 62 : 380 : 107 126Q 10004 : 042 : 315 : 52 : 510 : 130 128Q 10005 : 042 : 719 : 42 : 770 : 145 130Q 10006 : 044 : 823 : 32 : 890 : 174 132Q 10007 : 044 : 427 : 13 : 270 : 195 134Q 10008 : 044 : 731 : 03 : 710 : 214 136Q 10009 : 045 : 534 : 93 : 740 : 222 138Q 100010 : 045 : 838 : 84 : 190 : 231 139Q 12001 : 050 : 43 : 91 : 790 : 086 140Q 12001 : 550 : 55 : 82 : 000 : 097 141Q 12002 : 050 : 37 : 82 : 120 : 092 143Q 12003 : 051 : 111 : 62 : 290 : 121 145Q 12004 : 051 : 715 : 52 : 160 : 124 147Q 12005 : 052 : 319 : 42 : 300 : 138 149Q 12006 : 055 : 723 : 32 : 660 : 157 151Q 12007 : 055 : 327 : 12 : 900 : 177 153Q 12008 : 055 : 531 : 03 : 170 : 205 155Q 12009 : 056 : 534 : 93 : 480 : 224 157Q 120010 : 056 : 638 : 83 : 780 : 242 129

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TableG-2.Verticalquartztubewavedata. Flow Q g;nom Q l U sg U sl L wave INT w [Lmin )]TJ/F22 7.9701 Tf 6.586 0 Td [(1 ][Lmin )]TJ/F22 7.9701 Tf 6.587 0 Td [(1 ][ms )]TJ/F22 7.9701 Tf 6.587 0 Td [(1 ][cms )]TJ/F22 7.9701 Tf 6.586 0 Td [(1 ][cm][-] 158Q 14001 : 059 : 63 : 91 : 670 : 122 159Q 14001 : 559 : 55 : 81 : 810 : 108 160Q 14002 : 059 : 77 : 81 : 860 : 103 162Q 14003 : 060 : 411 : 61 : 830 : 121 164Q 14004 : 061 : 115 : 51 : 600 : 128 166Q 14005 : 062 : 119 : 41 : 510 : 121 168Q 14006 : 067 : 223 : 31 : 860 : 139 170Q 14007 : 067 : 227 : 12 : 170 : 149 172Q 14008 : 067 : 131 : 02 : 690 : 190 174Q 14009 : 075 : 734 : 92 : 950 : 217 176Q 140010 : 076 : 738 : 83 : 270 : 235 177Q 16001 : 069 : 63 : 91 : 190 : 131 178Q 16001 : 569 : 55 : 81 : 320 : 123 179Q 16002 : 069 : 87 : 81 : 370 : 115 181Q 16003 : 070 : 711 : 61 : 420 : 123 183Q 16004 : 071 : 415 : 51 : 320 : 129 185Q 16005 : 072 : 519 : 41 : 270 : 132 187Q 16006 : 077 : 723 : 31 : 540 : 152 189Q 16007 : 077 : 927 : 11 : 420 : 140 191Q 16008 : 078 : 331 : 01 : 770 : 153 193Q 16009 : 088 : 634 : 92 : 400 : 182 195Q 160010 : 090 : 538 : 82 : 690 : 226 196Q 18001 : 080 : 33 : 90 : 830 : 136 197Q 18001 : 580 : 35 : 80 : 900 : 127 198Q 18002 : 080 : 57 : 80 : 920 : 119 200Q 18003 : 081 : 511 : 61 : 040 : 119 202Q 18004 : 082 : 515 : 51 : 130 : 132 204Q 18005 : 083 : 319 : 41 : 160 : 132 206Q 18006 : 088 : 623 : 31 : 270 : 152 208Q 18007 : 088 : 927 : 11 : 300 : 172 210Q 18008 : 089 : 631 : 01 : 480 : 158 212Q 18009 : 0101 : 534 : 91 : 610 : 164 214Q 180010 : 0105 : 038 : 82 : 380 : 200 130

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APPENDIXH VERTICALWAVELENGTHEXAMPLEIMAGES Thefollowingguresincludeexamplewaveimagesforvertialannularowfor Q g;nom = 1200Lmin )]TJ/F22 7.9701 Tf 6.586 0 Td [(1 approximately U sg =53ms )]TJ/F22 7.9701 Tf 6.586 0 Td [(1 andareshowninorderofincreasingliquidow U sl from3.9to38.8cms )]TJ/F22 7.9701 Tf 6.586 0 Td [(1 FigureH-1.Verticalwavelengthexampleimagesforowcondition139Q. 131

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FigureH-2.Verticalwavelengthexampleimagesforowcondition140Q. FigureH-3.Verticalwavelengthexampleimagesforowcondition141Q. 132

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FigureH-4.Verticalwavelengthexampleimagesforowcondition143Q. FigureH-5.Verticalwavelengthexampleimagesforowcondition145Q. 133

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FigureH-6.Verticalwavelengthexampleimagesforowcondition147Q. FigureH-7.Verticalwavelengthexampleimagesforowcondition149Q. 134

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FigureH-8.Verticalwavelengthexampleimagesforowcondition151Q. FigureH-9.Verticalwavelengthexampleimagesforowcondition153Q. 135

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FigureH-10.Verticalwavelengthexampleimagesforowcondition155Q. FigureH-11.Verticalwavelengthexampleimagesforowcondition157Q. 136

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BIOGRAPHICALSKETCH WesleyWarrenKokomoorwasbornin1985astheyoungestofthreechildren.Hewas bornandraisedinEnglewood,Florida,graduatingfromLemonBayHighSchoolin2004.He earnedhisB.S.inMechanicalEngineeringfromtheUniversityofFloridain2008withaminorin MaterialSciencesEngineering. WesleybegainhisgraduateworkattheUniversityofFloridaDepartmentofNuclearand RadiologicalEngineeringintheFallof2009undertheguidanceofDr.DuWayneSchubring.His researchhasbeenfocusedonthecomputer-aidedvisualizationoftwo-phaseowphenomena, specicallyverticalannularow.UponcompletionofhisM.S.degree,Wesleyplanstopursuea carreerinprivateindustry. 142