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Experimental Investigation of Flows from Zero-Net Mass-Flux Actuators


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ANEXPERIMENTALINVESTIGATIONOFFLOWS FROMZERO-NETMASS-FLUXACTUATORS By RYANJAYHOLMAN ADISSERTATIONPRESENTEDTOTHEGRADUATESCHOOL OFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENT OFTHEREQUIREMENTSFORTHEDEGREEOF DOCTOROFPHILOSOPHY UNIVERSITYOFFLORIDA 2006

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Copyright2006 by RyanJayHolman

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ACKNOWLEDGMENTS FinancialsupportforthisworkhasbeenprovidedbytheAirFor ceOceof ScienticResearch.Ithankmyadvisor,LouCattafesta,forhis tirelesssupportand guidancethroughoutmytenureasagraduatestudentattheUniv ersityofFlorida thatmadethisworkpossible.Specialthanksalsogotomycommit teemembers, especiallyBruceCarrollandMarkSheplak,fornumerousinsig htfuldiscussionswhich havecontributedinmanyproductivewaystothisdissertation IamgratefultoallofmymanycolleaguesintheInterdiscipli naryMicrosystems GroupandtheFluidDynamicsLaboratorywithwhomIhavebeen associatedwith overtheyears.IthankthemforwhatIhavelearnedfromthem,f ortheirhelpwith mywork,andfortheirfriendship.Inparticular,Iexpressmyg ratitudetofellow studentsQuentinGallasandAhmedElnenaeyfortheirsupportan dassistance. Finally,Ithankmyparents,ChuckandKathyHolman,fortheirc onstantencouragement.Theirneexampleofhardworkanddedicationh asalwaysmotivated metopursuemygoals. iii

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TABLEOFCONTENTS page ACKNOWLEDGMENTS .............................iii LISTOFTABLES .................................vii LISTOFFIGURES ................................viii LISTOFSYMBOLSANDABBREVIATIONS .................xv ABSTRACT ....................................xix CHAPTER1INTRODUCTION ..............................1 Background ..................................1 PreviousWork ................................3 ExperimentalStudies ..........................7 NumericalStudies ............................27 Motivation ...................................31 TechnicalObjectivesandApproach .....................32 Outline ....................................34 2PHYSICSOFSYNTHETICJETFLOWS .................36 DimensionalAnalysis .............................36 ParameterEquivalence ............................39 ParametricVariation .............................42 PublishedResults ...............................44 ProposedTestMatrix ............................46 3EXPERIMENTALSETUP .........................49 SyntheticJetDevices .............................49 DataAcquisitionSystem ...........................54 DriverDerectionMeasurement .......................55 SinusoidalController .............................60 FlowVisualizationSetup ...........................68 VelocityMeasurement ............................71 HotwireAnemometry ..........................72 ParticleImageVelocimetry .......................72 LaserDopplerAnemometry ......................83 iv

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ParticleSizingandDynamics ........................88 UncertaintyAnalysis .............................88 4RESULTSANDDISCUSSION .......................94 DeviceCharacterization ...........................94 FlowVisualization ..............................101 LaserDopplerAnemometry .........................120 ParticleImageVelocimetry .........................126 Velocity .................................127 VorticityandCirculation ........................142 ReynoldsStressandTurbulentKineticEnergy ............162 5CONCLUSIONS ...............................181 KeyFindings .................................181 RecommendationsforFutureWork .....................184 AdditionalFutureWork ...........................185 APPENDIXASOLUTIONTOFULLY-DEVELOPEDPIPEFLOWWITHANOSCILLATINGPRESSUREGRADIENT ....................186 BVORTEX-BASEDJETFORMATIONCRITERION ...........193 EectofOriceGeometry ..........................195 2Dvs.AxisymmetricJet ...........................197 ExperimentalResults .............................198 CPARAMETERCONVERSION .......................202 Ingard&Labate(1950) ...........................202 Smith&Glezer(1998) ............................203 Smith&Swift(2001) .............................204 Smith etal. (1999) ..............................205 Crook&Wood(2000) ............................206 Rediniotis etal. (1999) ............................206 Bera etal. (2001) ...............................207 Cater&Soria(2002) .............................207 Yehoushua&Seifert(2003) .........................208 Shuster&Smith(2004) ...........................209 Utturkar etal. (2003) ............................209 Rizzetta etal. (1999) .............................210 Lee&Goldstein(2002) ............................210 Summary ...................................210 v

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DFLOWINTHEPISTONGAP .......................219 FlowGeneratedbyanOscillatingWall ...................221 FlowGeneratedbyanOscillatingPressureGradient ...........223 Superposition .................................229 EMULTIVARIATEOUTLIERREJECTION ................233 LISTOFREFERENCES .............................240 BIOGRAPHICALSKETCH ............................245 vi

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LISTOFTABLES Table page 2{1Primarydimensionsofsyntheticjetdimensionalparameter s ......38 2{2Syntheticjetrowregions .........................46 2{3Testmatrixofgeometriccongurations .................48 3{1Piezoelectric-drivenZNMFactuatordetails ...............49 3{2Shaker-drivenZNMFactuatordetails ..................51 3{3Before-andafter-PIVpistonmotion ...................65 3{4LDAmeasurementdetails .........................84 3{5Uncertaintycontributionduetorandomerrorofvelocity measurements 91 3{6Percentdierenceforno-slipintegrationandslotintegr ation .....92 4{1Two-dimensionallimitofZNMFroweldsbycase ...........103 4{2Frequencyandvelocityvaluesbycase ..................127 4{3Dimensionlessturbulenttransitionbycase ................180 B{1ComparisonbetweenPIV-andLDA-acquiredReynoldsnumbers ...200 C{1AllcasesofZNMFrowsexhaustingintoaquiescentmedium .....211 vii

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LISTOFFIGURES Figure page 1{1ZNMFstudiespublishedbyyear ....................2 1{2SchematicofatypicalZNMFdevice ..................3 1{3Flowregionsinducedbyacousticstreamingthroughanori ceunder steadyillumination ..........................8 1{4Flowregion4inducedbyacousticstreamingthroughanori ceunder stroboscopicillumination .......................10 1{5Particlevelocityvs.frequencyshowingthefourrowregio ns ....11 1{6Thresholddimensionlessstrokelengthasafunctionofnorma lized viscouspenetrationdepth ......................16 1{7EectofReynoldsnumberandoriceheight-to-diameter aspectratio onsyntheticjetformation ......................19 1{8FlowregionsasafunctionofReynoldsnumber ............22 1{9Oriceplatecross-sectionsusedbyCaterandSoria(2002) .....23 1{10Oriceplatecross-sectionsusedbyShusterandSmith(2004) ....24 1{11Two-dimensionalsyntheticjetformationcriterion ..........26 1{12SymmetryplanesimposedbyRizzettaetal.(1999)forthr eedimensionalsyntheticjetcomputations ..................28 2{1Detailedschematicshowingsyntheticjetdimensionalparam eters ..37 3{1Explodedviewofmodularpiezoelectric-drivenZNMFdevi ce ....50 3{2Shaker-drivenZNMFdevice ......................51 3{3Detailedschematicofshaker-drivenZNMFdevice ..........52 3{4Relativephasingofdisplacementsensorandaccelerometer .....56 3{5Bodeplotofthecorrecteddisplacementsignal ............57 3{6Typicalpistondriverlateraldisplacement ...............59 3{7LateralpistondriverRMSposition ..................59 viii

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3{8Pistonmotiondistortion ........................60 3{9Schematicoflaserdisplacementsensor ................61 3{10Pistoncharacterizationfor h=d =1 : 46 .................62 3{11Sinusoidalcontrollerrowchart .....................66 3{12Pistonmotionbeforeandaftersinusoidalcontrol ...........66 3{13PistonmotionbeforeandafterPIVmeasurements ..........67 3{14Flowvisualizationsetupschematic ...................69 3{15Syntheticjetcoordinatesystem ....................70 3{16Schematicofthehotwireanemometrysetup .............72 3{17PhotographofthePIVsetup ......................73 3{18Framestraddlingtimingdiagramfortwo-framesingleexp osurePIV 75 3{19BlockdiagramofthePIVsetup ....................76 3{20BlockdiagramofthePIVtiming ...................77 3{21PistonmotionandPIVtriggersignals .................77 3{22PIVlaserintensityacquiredfromaphotodiode ............78 3{23TypicalPIVcalibrationimage .....................80 3{24TypicalsliceofaPIVcalibrationimage ................81 3{25PIVcalibrationimageshowingholecenters ..............82 3{26HistogramofatypicalPIVcalibration ................82 3{27SchematicoftheLDAsetupforsyntheticjetvelocityeld measurement 84 3{28LDA3-beamopticalcongurationfornear-surfaceveloc itymeasurements .................................85 3{29PhotographoftheLDA3-beamcombinersetup ...........86 3{30RawDopplerburstcreatedbythepassageofaparticlethrou ghthe probevolume .............................87 3{31TypicalhistogramfromMonteCarlosimulationof U 0 ........90 3{32TypicalhistogramfromMonteCarlosimulationof .........91 4{1CenterlineRMSvelocityvs. x=d ....................95 ix

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4{2Hotwirevelocitycharacterization, h=d =1 : 46 .............96 4{3 Re St parameterspaceenvelope ...................96 4{4Three-dimensionalparameterspaceoftestmatrixcases .......98 4{5Typicalhotwirevelocitytrace .....................98 4{6Phase-dependentturbulenceintensity,Reynoldsnumbersw eep ...100 4{7Phase-dependentturbulenceintensity,Strouhalnumbersw eep ...100 4{8Phase-dependentturbulenceintensity, h=d sweep ...........102 4{9Phase-dependentturbulenceintensitywithandwithoutsin usoidal control .................................102 4{10FlowvisualizationphotographofCase1intheXYplane ......104 4{11FlowvisualizationphotographofCase1intheXZplane ......104 4{12FlowvisualizationphotographofCase2intheXYplane ......105 4{13FlowvisualizationphotographofCase2intheXZplane ......105 4{14FlowvisualizationphotographofCase3intheXYplane ......107 4{15FlowvisualizationphotographofCase3intheXZplane ......107 4{16FlowvisualizationphotographofCase4intheXYplane ......108 4{17FlowvisualizationphotographofCase4intheXZplane ......108 4{18FlowvisualizationphotographofCase5intheXYplane ......110 4{19FlowvisualizationphotographofCase5intheXZplane ......110 4{20FlowvisualizationphotographofCase6intheXYplane ......111 4{21FlowvisualizationphotographofCase6intheXZplane ......111 4{22FlowvisualizationphotographofCase7intheXYplane ......113 4{23FlowvisualizationphotographofCase7intheXZplane ......113 4{24FlowvisualizationphotographofCase8intheXYplane ......114 4{25FlowvisualizationphotographofCase8intheXZplane ......114 4{26FlowvisualizationphotographofCase9intheXYplane ......116 4{27FlowvisualizationphotographofCase9intheXZplane ......116 x

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4{28FlowvisualizationphotographofCase10intheXYplane ......117 4{29FlowvisualizationphotographofCase10intheXZplane ......117 4{30FlowvisualizationphotographofCase11intheXYplane ......119 4{31FlowvisualizationphotographofCase11intheXZplane ......119 4{32PistondistortionbetweenCase3andCase12 ............120 4{33FlowvisualizationphotographofCase12intheXYplane ......121 4{34FlowvisualizationphotographofCase12intheXZplane ......121 4{35PIV-LDAcomparisonofstreamwiseexitvelocityprolemovi e ...122 4{36PIV-LDAcomparisonofstreamwiseexitvelocityprolestill frames 122 4{37PIV-LDAcomparisonofcross-streamexitvelocityprolemov ie ..124 4{38PIV-LDAcomparisonofcross-streamexitvelocityprolestil lframes 124 4{39PIV-LDAcomparisonofphase-averagedexitvolumerowrate ....125 4{40Phase-averagedLDAvelocityprolesintheXZplane ........125 4{41Case3meanplusphase-averagedvelocityeldmovie ........129 4{42Case3meanplusphase-averagedvelocityeldstillframes .....129 4{43Case1time-averagednormalizedverticalvelocity ..........130 4{44Case2time-averagednormalizedverticalvelocity ..........130 4{45Case3time-averagednormalizedverticalvelocity ..........131 4{46Case4time-averagednormalizedverticalvelocity ..........131 4{47Case5time-averagednormalizedverticalvelocity ..........132 4{48Case6time-averagednormalizedverticalvelocity ..........132 4{49Case7time-averagednormalizedverticalvelocity ..........134 4{50Case8time-averagednormalizedverticalvelocity ..........134 4{51Case9time-averagednormalizedverticalvelocity ..........135 4{52Case10time-averagednormalizedverticalvelocity ..........135 4{53Case11time-averagednormalizedverticalvelocity ..........137 4{54Case12time-averagednormalizedverticalvelocity ..........137 xi

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4{55Case3meanplusphase-averagedstreamwisevelocitycompon entmovie 138 4{56Case3meanplusphase-averagedstreamwisevelocitycompon entstill frames .................................138 4{57Case3meanplusphase-averagedstreamwiseexitvelocitypr olemovie 140 4{58Case3meanplusphase-averagedstreamwiseexitvelocitypr olestill frames .................................140 4{59Case3meanplusphase-averagedcross-streamexitvelocityp role movie .................................141 4{60Case3meanplusphase-averagedcross-streamexitvelocityp role stillframes ...............................141 4{61Case1meanplusphase-averagedvorticitymovie ...........143 4{62Case1meanplusphase-averagedvorticitystillframes ........143 4{63Case3meanplusphase-averagedvorticitymovie ...........145 4{64Case3meanplusphase-averagedvorticitystillframes ........145 4{65Case5meanplusphase-averagedvorticitymovie ...........146 4{66Case5meanplusphase-averagedvorticitystillframes ........146 4{67Case6meanplusphase-averagedvorticitymovie ...........147 4{68Case6meanplusphase-averagedvorticitystillframes ........147 4{69Case9meanplusphase-averagedvorticitymovie ...........149 4{70Case9meanplusphase-averagedvorticitystillframes ........149 4{71Case10meanplusphase-averagedvorticitymovie ..........150 4{72Case10meanplusphase-averagedvorticitystillframes .......150 4{73Case11meanplusphase-averagedvorticitymovie ..........151 4{74Case11meanplusphase-averagedvorticitystillframes .......151 4{75Case12meanplusphase-averagedvorticitymovie ..........153 4{76Case12meanplusphase-averagedvorticitystillframes .......153 4{77Circulationvs.phasefromtheleftvortex, Re sweep .........155 4{78Circulationvs.phasefromtherightvortex, Re sweep ........155 4{79Circulationvs.phasefromtheleftvortex, St sweep .........156 xii

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4{80Circulationvs.phasefromtherightvortex, St sweep ........156 4{81Circulationvs.phasefromtheleftvortex, h=d sweep ........158 4{82Circulationvs.phasefromtherightvortex, h=d sweep .......158 4{83Circulationvs.phasefromtheleftvortex,sinusoidal/dist ortedpiston motion .................................159 4{84Circulationvs.phasefromtherightvortex,sinusoidal/di stortedpistonmotion ..............................159 4{85Normalizedcirculationvs. Re .....................161 4{86Normalizedcirculationvs. St .....................161 4{87Case1phase-averagedReynoldsstressmovie .............164 4{88Case1phase-averagedReynoldsstressstillframes ..........164 4{89Case3phase-averagedReynoldsstressmovie .............165 4{90Case3phase-averagedReynoldsstressstillframes ..........165 4{91Case5phase-averagedReynoldsstressmovie .............166 4{92Case5phase-averagedReynoldsstressstillframes ..........166 4{93Time-averagedRSforCase5 ......................167 4{94Case6phase-averagedReynoldsstressmovie .............168 4{95Case6phase-averagedReynoldsstressstillframes ..........168 4{96Case9phase-averagedReynoldsstressmovie .............170 4{97Case9phase-averagedReynoldsstressstillframes ..........170 4{98Case10phase-averagedReynoldsstressmovie ............171 4{99Case10phase-averagedReynoldsstressstillframes .........171 4{100Case11phase-averagedReynoldsstressmovie ............172 4{101Case11phase-averagedReynoldsstressstillframes .........172 4{102Case12phase-averagedReynoldsstressmovie ............173 4{103Case12phase-averagedReynoldsstressstillframes .........173 4{104Case5phase-averagedturbulentkineticenergymovie ........175 4{105Case5phase-averagedturbulentkineticenergystillfra mes .....175 xiii

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4{106Phase-averagedcenterlineTKE,Reynoldsnumbersweep ......176 4{107Phase-averagedcenterlineTKE,Strouhalnumbersweep .......177 4{108Phase-averagedcenterlineTKE, h=d sweep ..............177 4{109Phase-averagedcenterlineTKEwithandwithoutsinusoid alcontrol 178 4{110Dimensionlessturbulenttransitionmap ................178 A{1Schematicoffully-developedpiperowwithanoscillating pressure gradient ................................186 A{2Normalizedvelocityprolevs.normalizedradius ...........189 A{3 U= ^ U vs.Stokesnumberforpiperowwithanoscillatingpressure gradient ................................190 A{4 U= ^ U vs.Stokesnumberfortwo-dimensionalchannelrowwithan oscillatingpressuregradient .....................191 B{1Detailedschematicofasyntheticjetshowingejectedvorti city ...194 B{2Normalizedjetformationdatatoaccountforradiusofcur vatureand Stokesnumber ............................197 B{3PIVvelocityvectoreldswithoverlaidvorticityconto urs ......199 B{4 U -componentvelocitycontours .....................200 B{5Jetformationcriterionforaxisymmetriccase .............201 D{1Flowinagapgeneratedbyanoscillatingpistonandoscillat ingpressuregradient .............................220 D{2Schematicofderectedpiston ......................225 D{3Relativephasingbetween r p ( t ), v p ( t ),and @p=@x ...........228 D{4Normalizedvelocityproleofrowinthepistongap .........230 D{5Comparisonofresistancetorowinthepistongapandtheventc hannel 231 E{1ExampleimageofspuriousPIVvectors ................234 E{2Exampleimageofspatial-validatedPIVvectors ...........234 E{3ExamplePIVdatasetofidentiedoutliers ..............238 E{4Exampleimageofoutlier-rejectedPIVvectors ............238 xiv

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LISTOFSYMBOLSANDABBREVIATIONS RomanSymbolsA slot(orice)area,(m 2 ) a vortexcoreradius,(m) a 0 piperadius,(m) B pressuregradientparameterforoscillatingpiperow,(m = s 2 ) c 0 speedofsoundoftheruid,(m/s) D V distancebetweenvortexcenters,(m) d slotdepth(oricediameter),(m) f driverfrequencyofoscillation,(Hz) f 0 Braggcellfrequencyshift,(Hz) f D Dopplerburstfrequency,(Hz) f p frequencybetweenPIVimagepaircaptures,(Hz) f t PIVtriggerfrequency,(Hz) h slot(orice)height,(m) I 0 impulseperunitwidth,(kg/s) K jetformationconstant K 0 proportionalityconstantofjetformation L RMSstrokelength,(m) L 0 strokelengthbasedon u 0 ( t )(m) P pressuregradientinafullydevelopedoscillatorychannelrow ,(Pa) P pistonmotionprogramfactor p constantwhichaccountsforrowseparationdueto R p averagepistondisplacementduringthehalf-cycle,(m) xv

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R slot(orice)exitradiusofcurvature,(m) R D radiusofpistondriver,(m) R p amplitudeof(sinusoidal)pistondrivermotion,(m) r p ( t )periodicpistonmotion,(m) Re ~ U Reynoldsnumberbasedon ~ U Re I 0 Reynoldsnumberbasedon I 0 Re U 0 Reynoldsnumberbasedonslotdepth(oricediameter) r t ratioofthesquarerootofthe2-squarednormoftheresidualofa Fourier seriestotheamplitudeofaperiodicsignal S Stokesnumber St Strouhalnumber dT timebetweenPIVimageframes,(s) T periodofonecycle,(s) t time,(s) U spatialaveraged,timeaveragedstreamwisecomponentofveloc ityduring expulsionattheexitplane,(m/s) ^ U amplitudeof u 0 ( t ),(m/s) ~ U commonvelocityscale,= L 0 =T ,(m/s) U 0 momentumrowvelocityattheslot(orice)exit,(m/s) U A amplitudeof u ( t ),(m/s) u timevarying,spatialaveragedstreamwisecomponentofveloci tyatthe exitplane,(m/s) u p meanstreamwisevelocitycomponentatapoint,(m/s) ~ u p phase-averagedstreamwisevelocitycomponentatapoint,(m/s) u timevarying,spatialvaryingstreamwisecomponentofvelocit yattheexit plane,(m/s) xvi

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u 0 timevaryingstreamwisecomponentofthecenterlinevelocity attheexit plane,(m/s) u p streamwisevelocityatapoint,(m/s) u 0p ructuatingstreamwisevelocitycomponentatapoint,(m/s) u pv particlevelocity,(m/s) 8 volumedisplacedbythedriverduringthehalfcycle,(m 3 ) 8 cavityvolume,(m 3 ) V I inducedvelocityofthevortexdipole,(m/s) V s averagejetsuctionvelocity,(m/s) v p meancross-streamvelocitycomponentatapoint,(m/s) ~ v p phase-averagedcross-streamvelocitycomponentatapoint,(m/ s) v p cross-streamvelocityatapoint,(m/s) v 0 p ructuatingcross-streamvelocitycomponentatapoint,(m/s) w two-dimensionalspanwiseslotwidth,(m) x streamwisecoordinatedirection y cross-streamcoordinatedirection(two-dimensionalslot) GreekSymbols s shearlayerthicknessinsidetheslot(orice),(m) slot(orice)dimensionlessradiusofcurvature,=2 R=d d phasebetweenPIV-acquiredimagepairs,(rad) dimensionlesscirculationoverhalftheslotdepth circulationproducedbyhalfofavortexpair,(m 2 = s) constantwhichdependsonvortexcoreradius a l wavelengthofLDAlaserlight,(m) dynamicviscosityoftheruid,(kg/m s) kinematicviscosityoftheruid,(m 2 = s) LDAbeamhalf-angle,(rad) xvii

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densityoftheruid,(kg/m 3 ) n v shedvortexstrength,(m 2 /s) driverfrequencyofoscillation,(rad/s) H Helmholtzfrequencyofthe(two-dimensional)cavity,(rad/s) z spanwise(orazimuthal)componentofvorticityattheexitpla ne,(1/s) AbbreviationsDNSdirectnumericalsimulationFFTfastFouriertransformJFCjetformationcriterionLDAlaserDoppleranemometryPIVparticleimagevelocimetryPMTphotomultipliertubeRANSReynolds-averagedNavier-StokesequationsRMSrootmeansquareRSReynoldsstressTHDtotalharmonicdistortionTKEturbulentkineticenergyZNMFzero-netmass-rux xviii

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AbstractofDissertationPresentedtotheGraduateSchool oftheUniversityofFloridainPartialFulllmentofthe RequirementsfortheDegreeofDoctorofPhilosophy ANEXPERIMENTALINVESTIGATIONOFFLOWS FROMZERO-NETMASS-FLUXACTUATORS By RyanJayHolman May2006 Chair:LouisN.CattafestaIIICochair:BruceF.CarrollMajorDepartment:MechanicalandAerospaceEngineering Zero-netmass-rux(ZNMF)devicesconsistofanoscillatingdriver ,acavity, andasmallopeningsuchasarectangularslotoracircularoric e.Thedriver producesaseriesofvortexpairs(orrings)attheslot/oricew hichaddmomentum andcirculationtotherow.ZNMFdevicesareusefultoolsforro wcontrolapplications suchasheattransfer,mixingenhancement,andboundarylayer separationcontrol. Todatemuchresearchhasbeendonetoqualifyandquantifythe eectsofZNMF devicesinmanyapplications,bothexperimentalandcomputa tional.However,anumberofissuesstillremain.First,thereisnouniversallyaccepte ddimensionlessparameterspace,whichmakesdevicecharacterizationandcomp arisonbetweenstudies dicult.Second,mostexperimentalstudiesdonotsucientlyq uantifytheneareldbehavior,whichhindersthefundamentalunderstanding oftheunderlyingrow physics.Ofparticularinterestaretheregimesofjetformatio n,andtransitionfrom laminartoturbulent-likerow,whicharenotwellunderstood .Finally,theaccuracy ofexperimentalmeasurementsareseldomreportedintheliter ature. xix

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Thisstudyuniestheexperimentalandnumericaldatapresent edintheliteratureforZNMFroweldsexhaustingintoaquiescentmedium.A quantitative experimentaldatabaseisalsogeneratedtocompletelycharac terizethetopological regionsofZNMFrowsoverausefulrangeofthedimensionlesspara meterspace. Thedatabaseisderivedchieryfromtwo-dimensionalvelocity eldmeasurementsusingparticleimagevelocimetryandlaserDoppleranemometry .Vorticity,circulation, Reynoldsstress,andturbulentkineticenergyisacquiredtoch aracterizetheresulting roweld. SignicantinsightintothebehaviorofvoicecoildrivenZNMF devicesisuncovered.Designimprovementsaremadebyimplementingasinuso idalcontrollerfor pistonmotionandeliminatingtheneedforasealingmembranei nthecavity.Itis shownthatthepropervelocityscaletocharacterizeaZNMFdevi ceiseitheramomentumrowvelocityoravelocityscalebasedoncirculation.I naddition,theproper scalingofaZNMFdeviceisapplication-specic.Thetwochiefp arameterswhich governZNMFrows{theReynoldsnumberandtheStrouhalnumber {areshownto aecttheroweldindierentways. xx

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CHAPTER1 INTRODUCTION Thischapterpresentssomebackgroundinformationonzero-ne tmass-ruxdevices,otherwiseknownassyntheticjets.Reviewsofanumberofst udiesintheopen literaturewhichexaminetheroweldbehaviorofsyntheticj etsarealsopresented.It isshownthatthereareinsucientdataavailabletoquantitat ivelycharacterizethe topologicalregimesgeneratedbyasyntheticjet,andthisis themotivationforthis study.Thechapterconcludeswithtechnicalobjectivesanda generaloutline. Background Inrecentyears,thescienticcommunityhasproducedalargen umberofstudies onzero-netmass-rux(ZNMF)devices.Acursoryexaminationofthe literatureshown inFigure 1{1 showstheever-increasingpopularityoftheZNMFdeviceasatop icof study. AZNMFdeviceconsistsofanoscillatingdriverattachedinsomema nnerto acavitythatcontainsasmallslotororice.Thisdrivermaybe ,forexample,a speaker,amechanicalpiston,orapiezoelectricdiaphragm.T hedriverhastheeectof periodicallydecreasingandincreasingthevolumeofthecavi ty.Thismotioncancause ruidtobealternatelycompressedandexpandedinsidethecavit y,and/orexpelledand ingestedthroughtheslot.Theextenttowhichruidiscompressed (orexpanded)as opposedtoexpelled(oringested)dependsontheruidproperti es,thedriverdynamics, andthegeometryofthedevice.Thedeviceiscalled\zero-ne tmass-rux"becauseno externalsourceofruidexists;thatis,theintegrationofthema ssrowrateacrossthe slotoveranintegernumberofcyclesisidenticallyequaltoz ero.Althoughthereisno net masstransfer toitssurroundings,theZNMFdevicehastheinterestingpropert y 1

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2 0 10 20 30 40 50 60 70 80 90 1001 991 1 992 1 993 1 994 1 995 1 996 1 997 1 9 9 8 1 9 9 9 2 0 0 0 2 0 0 1 2 0 0 2 2 0 0 3 200 4YearZNMF Studies Figure1{1:ZNMFstudiespublishedbyyear. ofcausinganiteamountof momentumtransfer toitssurroundings.Hence,other parlanceusedfortheZNMFdeviceincludes\oscillatorymoment umgenerator,"and morecommonly\syntheticjet,"althoughthelatterisactual lyalimited,albeita veryinteresting,caseofZNMFdevices. Figure 1{2 illustratesatypicalZNMFdevicebeingoperatedtoproduceasy ntheticjet.Ifthedriveramplitudeishighenough,asruidis expelledthroughthe slottheboundarylayerseparatesfromthewalland,ateithere dgeoftheslot,rolls uptoproduceavortexpair.Thisvortexpair,endowedwithci rculation,propagates awayfromtheslotunderitsownself-inducedvelocity.During thesubsequentsuction stroke,ruidisdrawnintothecavityfromthesurroundings,but thevortexpairhas movedsucientlyfarfromtheslotsoastoberelativelyunaect ed.Anewvortex pairisthenejectedandthecyclecontinues,producingatrai nofvortexpairsissuing normaltotheslot.Iftheslotisreplacedbyanaxisymmetricori ce,atrainofvortex ringsresults.Atstillhigheramplitudes,theejectedvortexpa ir(orring)maybreak

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3 downduetoturbulence.Inanycase,inatime-averagedsense,th isbehaviorcreates ajet-likerowwhichissynthesizedfromtheambientruid,henc etheterm\synthetic jet."Fortheremainderofthiswork,theterm\syntheticjet" willbeusedtodescribe anygenericZNMFdevice,inaccordancewithcommonterminolo gyfoundintheliterature.However,thereaderisremindedthatthisusageofthe termistechnicallya misnomer,sincethesyntheticjetistheproductofaspecialsubset ofZNMFdevices. Inthenextsectionweshallexaminesomeoftheinterestingprope rtiesoftheZNMF devicewhichhavebeendescribedintheopenliterature. n n r n n n n r Figure1{2:SchematicofatypicalZNMFdeviceproducingasynt heticjet:(a)instantaneousand(b)time-averaged. PreviousWork Duetoitssimplisticdesignandabilitytoproducejet-likerow swithoutexternal plumbing,thesyntheticjethasemergedasanattractivetool forresearcherstoinvestigateinthelaboratory{bothcomputationallyandexperim entally{forpotential useinrowcontrolapplications.Onesuchapplicationisjetvec toring.Forexample, Smith&Glezer ( 2002 )examinedthevectoringeectasyntheticjethadonasteady jet.Thesteadyjetexitwasnominallytwo-dimensional,measur ing76 : 2 12 : 7mm, whilethesyntheticjetslotexit,measuring76 : 2 0 : 51mm,wasmountednexttothe

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4 steadyjetatadistanceof1 : 8mmaway.Itwasfoundthatthesyntheticjetentrained ruidfromtheprimaryjetduringthesuctionstroke,causingthe primaryjettobe derectedtowardthesyntheticjet.Thisderectionwasbalanc edbyaforceonthe steadyjetchannel,whichincreasedbothwithsteadyjetveloci tyaswellassynthetic jetamplitude. Inapreviousstudy, Smith&Glezer ( 1997 )foundthatasyntheticjetwhose dimensionswereonetotwoordersofmagnitudelessthanthoseof theprimaryjet couldcauseaderectionintheprimaryjettowardthesynthetic jetof30 .Inaddition, placingthesyntheticjetsuchthatitexhaustednormaltotheste adyjetcausedthe steadyjettovectorintheoppositedirection.Inbothstudies,t hesteadyjetbegan tovectorinsideitschannelandtheturnwascompletedbyabou toneslotdepth. Pack&Seifert ( 1999 )alsoobservedavectoringeectofasyntheticjetonasteady jet,byattachingawide-anglediusertothejetexit.Thesynt heticjethadtheeect ofcausingthesteadyjetrowtoattachtothediuserwall,forbo thstreamwiseand lowamplitudecross-streamsyntheticjetrows.Forhigheramplit udecross-stream syntheticjetrows,thejetderectedawayfromthediuserwallw herethesynthetic jetwasmounted,consistentwiththeresultsof Smith&Glezer ( 1997 ). Inanumericalstudyofjetvectoring, Guo etal. ( 2003 )alsoobservedresults consistentwiththeexperimentsof Smith&Glezer ( 1997 ).Atthesameoperating conditions,theirsimulationsindicatedverygoodagreement inthevorticitycontours downstreamoftheslotexit.Theyalsoobservedthatthevectorin gangleoftheprimaryjetwasafunctionoftheangleatwhichthesyntheticjete mergedfrom,astheir simulationstestedtwocongurationsof0 and60 syntheticjetangle.Consequently, thevectoringforcewasmuchlargerforthe60 syntheticjetthanthe0 syntheticjet atthesameoperatingconditions.Finally,theynotedthatthe reexistsanoptimal frequencyandamplitudeofsyntheticjetoperation,aswella sanoptimaldistance betweenthesyntheticjetandthesteadyjet,tomaximizetheve ctoringeect.

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5 Anotherapplicationofsyntheticjetrowsismixingenhanceme nt. Wang& Menon ( 2001 )computationallyinvestigatedtheeectofsyntheticjetmix ing.They employedaLatticeBoltzmannEquation(LBE)methodtosimula tetheroweldof asyntheticmicrojetinthepresenceofafuelinjector.Itwasf oundthatoperationof thesyntheticjetresultedinsignicantlymorefuel-airmixin gthanwithoutit,butthe orientationandlocationofthesyntheticjetalsoaectedthe mixingenhancement. Chen etal. ( 1999 )experimentallyinvestigatedtheeectsofsyntheticjetmix ing byintroducingsyntheticjetrowsnormaltotheparallelrowo fcoldandhotgaseous streams.Themixingeciencywasdeducedbymeasuringthetempe raturedistributionat80diametersdownstreamofthesyntheticjets.Itwasfou nd,notsurprisingly, thatthedegreeofmixingwasafunctionofjetactuation.Atl owactuation,anexperimentallyacquiredcross-streamtemperatureproleshowed alargedierencein temperatureasthehotandcoldstreamsdidnotmixverymuch,w iththemaximum andminimumtemperaturesbeing740 Cand40 C,respectively.However,athigher actuationlevelsthetemperatureprolebecamemuchclosert ouniform,rangingfrom 360 Cto260 C.Akeybenettoutilizingsyntheticjetsformixing,theyno ted,was thattheintroductionofadditionalcolddilutionairwasno tneeded,asthesynthetic jetisaZNMFdevice.Signicantsyntheticjetmixingcanalsobe achievedbyplacinganarrayofazimuthalsyntheticjetsaroundacentralprim aryjet,asreportedin severalpapers( Davis&Glezer 1999 2000 ; Ritchie&Seitzman 1999 ; Ritchie etal. 2000 ). Anotherinterestingapplicationofsyntheticjetsisheattran sferaugmentation. Campbell etal. ( 1998 )demonstratedviaexperimentsthatasyntheticjetdevicecan beeectiveforprocessorcoolinginalaptopcomputer.Forax edactuationfrequency andamplitude,anoptimizedsyntheticjetgeometryresultedi na22%reductionin theprocessoroperatingtemperatureversusnaturalconvectio nalone.

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6 Inanotherstudy,anannularsyntheticjetdevicewastestedby Travn^cek& Tesa^r ( 2003 )togaugetheeectofmasstransfer.Thesyntheticjetrowwasdi rected towardasurfacecoatedwithnaphthalene,andthemasstransfer wasdeterminedby measuringthechangeinthicknessofthesurfaceduetosublimati on.Interestingly, throughsmokevisualizationtheyobservedtwodierentrowel ds,termed\weak" and\strong,"whichwereafunctionoftheactuationamplitud e.Asexpected,the extentofmasstransferwasgreaterforthe\strong"roweldaso pposedtothe\weak" one. Perhapsthemostpromisingapplicationofsyntheticjetsisthe irpotentialusein theactivecontrolofseparatedrows.Atwo-dimensional,NACA00 24airfoilwitha cylindricalleading-edgesectioninstrumentedwithtwosynth eticjetswasinvestigated by Smith etal. ( 1998 )andlaterby Amitay etal. ( 1999 ).Thenovelairfoildesign allowedthepositionofthetwo-dimensionalsyntheticjetstob eadjustedbyrotating thecylindricalportionoftheairfoilsection.Foranglesof attackgreaterthan5 and atachordReynoldsnumberof300,000,therowseparatedfromt heairfoilsurface.It wasfoundthatthelocationofthesyntheticjets,aswellasthe iramplitude,aected rowreattachment,withcompletereattachmentoccurringup toanangleofattackof 15 ,andpartialreattachmentupto25 Aqualitativestudywasundertakenby Crook etal. ( 1999 )whichexploredthe eectofasyntheticjetissuingnormaltothesurfaceofacylinde r.Theyfoundthat placementofthesyntheticjetjustupstreamoftheseparationlo cation,about95 causedstrongentrainmentofruidtowardtheoriceonbothside softhejet. Ravindran ( 1999 )numericallysimulatedtherowoveraNACA0015airfoilwitha syntheticjetneartheleadingedge.Itwasfoundthatasthestr engthofthesynthetic jetincreased,fortwohighanglesofattack(22 and24 ),theliftcoecientalso increased.

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7 Theeectofmultiplesyntheticjetsonaseparatedrowwasinve stigatedexperimentallybythepresentauthor( Holman etal. 2003 ).ANACA0025airfoilwas testedatanangleofattackof12 andachordReynoldsnumberof100,000.Without actuation,therowovertheairfoilseparatedbyabout25%cho rd.However,theoperationoftwocloselyspacedtwo-dimensionalsyntheticjetact uatorsneartheleading edgecausedtheseparationlocationtobemovedbacktowardthe trailingedge.The actuatorslotdepthwas0 : 5mmforeachactuator,andtheywereseparatedbyadistanceof2 : 4mm.Theactuatorpairwaslocatedat3%chord.Theexactloca tionof theseparationpointdependedonthestrengthofthesyntheticj etsandtheirposition ontheairfoilsurface,butinterestinglynotontherelativep hasingbetweenactuators. Itcanbeseenthatthereareanumberofpromisingapplications ofsynthetic jets.Despiteitspotentialuseasarowcontroldevice,however ,thefundamental natureofsyntheticjetbehaviorisstillnotwellunderstood.Ne vertheless,anumber ofinvestigatorshaveendeavoredtoelucidatetheunderlyin gphysicsofsyntheticjet rows,andthissectionpresentssomeoftheirkeyndings,divided intotwoparts: experimentalandnumericalstudies.ExperimentalStudies Althoughmostreferencestosyntheticjetsintheliteratureda tebackonlytothe pastdecade,thesuccessfuldemonstrationofthesyntheticjetmay betracedback atleastasfaras Ingard&Labate ( 1950 )inwhichtheyidentiedandcharacterized acousticstreamingaroundcircularorices.(Qualitatively, \acousticstreaming"can bedescribedasameanruidmotiongeneratedbytheimpingemen tofasoundwave onasolidboundary. Lighthill ( 1978 )providesathoroughtreatmentofthesubject.) Theirsetupconsistedofasteelcircularplatewithamachinedor iceinsertedintoa circulartubeinwhichsoundwavesweregeneratedthroughthe useofanimpedance tubeconnectedatoneend.Theotherendwassealedthroughthe useofanadjustable plungerwhichallowedtheoriceplatetobesituatedatthequ arter-wavelengthof

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8 thesoundwave.Thissetupallowedforthemeasurementoftheori ceacoustic impedanceusingthestanding-wavemethod( Blackstock 2000 ).Atotalof25orice platesofvaryingheightanddiameterweretestedwithvaryin gsoundpressurelevels atafrequencyrangeof100Hz-1kHz,and\particlevelocities"w eremeasured. Thetubeitselfwasttedwithwindowsforopticalaccess,andth erowaroundthe oricewasvisualizedwithsmokeparticles.Bothmeanillumina tionandstroboscopic illuminationwereused,allowingfortime-averagedandinsta ntaneousphotographsof theroweldtobeacquired.Thesephotographsshowedthatfour distinct\regions" ofrowestablishedthemselvesaroundtheoriceasafunctionof thefrequencyofthe soundwave,thesoundpressurelevel,andthegeometryoftheori ce(Figure 1{3 ). Figure1{3:Flowregionsinducedbyacousticstreamingthroug hanoriceunder steadyillumination,a)Region1,b)Region2,c)Region3,d)R egion4.Thewhite verticallinerepresentsthelocationoftheorice,blackho rizontalbarsrepresent theapproximateoricelocation,andblackarrowsrepresent theapproximaterow direction.Adaptedfrom Ingard&Labate ( 1950 ).

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9 Region1consistedofsteadycirculationthatwassymmetricalon eithersideof theoriceandoccurredatlowsoundintensities.Flowwasdirec tedoutfromthe oriceinthisregion.Region2wasachievedasthesoundinten sitywasincreased, andwasstillcharacterizedbysteadycirculation.However,th erowdirectedout fromtheoricereverseditselftowardtheorice.Asthesoundin tensitycontinuedto increase,turbulenceeectswereobservedandacomplicated, asymmetricalpattern ofsteadycirculationsuperposedwithpulsatoryeectsemerged asRegion3.Here theyalsoobservedwhattheytermedas\boiling"{thesporadice xchangeofparticles betweenonesideoftheoriceandtheother.Finallyonceacer tainsoundpressure levelwasreached,asudden\breakthrough"occurredinwhich vortexringswereshed andpropagatedfromeithersideoftheorice.Thisbreakthro ugh,ofcourse,isvery similartowhatisknowntodayasthesuccessfulformationofasynt heticjet.Indeed, theyobservedthat,inatime-averagedsense,rowwasdirectedo utaxiallyfromthe oriceanddirectedinradially.Ingeneral,foraxedoric egeometryandfrequency, theroweldevolvedthroughthedierentregionsasthesound pressurelevelwas increased.However,itwasfoundthatbelowacertainfrequenc y,whattheycalled the\eutectic"point,theroweldtransitionedgraduallyfr omRegion1directlyinto Region4.Figure 1{3 showsroweldsfromeachofthefourregionsundersteady illumination,andFigure 1{4 showsaroweldcharacteristicofRegion4takenwith stroboscopicillumination.InFigure 1{5 ,thefourrowregionsareshownasafunction ofparticlevelocityandactuationfrequency,andtheeutec ticpointisindicated. Itwasalsoobservedthatforaxedoscillationfrequencyandor icediameter, varyingtheoriceheight(andhencetheheight-to-diamete raspectratio)tendedto changethevalueoftheparticlevelocityrequiredtoreacha certainrowregion.Once theheight-to-diameteraspectratioreachedavalueofappro ximately2,therow boundariesbetweenregionsleveledo.Althoughthisobserva tionseemstoimply thata\fullydeveloped"rowregionexistsasafunctionofori ceaspectratio,this

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10 Figure1{4:Flowregion4inducedbyacousticstreamingthroug hanoriceunder stroboscopicillumination,thewhiteverticallinerepresent sthelocationoftheorice, blackhorizontalbarsrepresenttheapproximateoriceloca tion,andblackarrows representtheapproximaterowdirection.Adaptedfrom Ingard&Labate ( 1950 ). simplisticviewisnotcompletelyaccurate.Atpresentthereis noclear,universally accepteddenitionforfullydevelopedoscillatoryrowinap ipeorchannel.Aswill beshownlaterinChapter 2 ,thestrokelength,oraverageruidparticleexcursion, alsoplaysakeyroleindeterminingthenatureoftherowinthe orice. Althoughparticlevelocitiesattheoricearereportedasaf unctionoftherow regions,itisunfortunatethatnodescriptionofthemethodor accuracyofthedata isprovided.Notwithstandingthesesemi-qualitativendings,h owever,theresults oeratantalizinginsightintotherichlydetailedandcompl exrowphysicspresent inisolatedsyntheticjets.Inaddition,althoughpresentedinp urelydimensional form,theseresultshintattheexistenceofimportantdimension lessparametersthat characterizetheroweldofasyntheticjet.Finally,itshoul dbeemphasizedthat theserowpatternsweregeneratedviaacousticstreaming,andn otbytheperiodic oscillationofaboundarywhichistypicalofsyntheticjets.In thelattercase,the meanmotionisontheorderoftheoscillatorymotion,whilein theformer,themean motionisofsecondorder( Smith&Swift 2001 ). Nearlyvedecadeslater,inastudyofanoscillatingpiezoelec tricdiaphragm mountedrushtoaplateinawatertank, James etal. ( 1996 )observedthatwhena thresholdamplitudewasreached,aturbulentjet-likerowwa sproduced.Thisonly

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11 0 20 40 60 80 100 120 140 160 180 200 0100200300400500600700Frequency (Hz)Particle Velocity (cm/s)Region 1 Region 2 Region 3 Region 4 eutecticpoint Figure1{5:Particlevelocityvs.frequencyshowingthefourr owregionsandthe eutecticpoint.Adaptedfrom Ingard&Labate ( 1950 ). occurredwhencavitationbubblesformedonthesurfaceofthe diaphragmandthen collapsedduringeachcycle.Thethresholdamplitudeofjetfo rmationalsocorrespondedtothelowpressurenecessarytoformcavitationbubbles.I twasconjectured thatjetformationoccurredasaresultofatrainoftime-peri odicvortexringsthat formedduringeachcycleduetothepresenceofthecavitation bubblesandpropagated downstream. Shortlythereafterinaseminalpaper, Smith&Glezer ( 1998 )observedthat theformationofasyntheticjetcouldbefacilitatedbymount ingthedriverrush tothewallofacavitywhichcontainedasmallslot.Theyalsoide ntiedtwokey dimensionlessparametersthatgoverntheformationofvortex pairs.Ifoneassumesa uniformor\slug"velocityprole u 0 ( t )attheslotexit,thenthedistancethataruid particletravelswithvelocity u 0 ( t )duringtheexpulsionpartofthecycle,calledthe

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12 strokelength,maybewrittenas L 0 = Z T= 2 0 u 0 ( t ) dt (1.1) where T= 2ishalftheperiodofthecycle.Denotingtheslotdepthorori cediameteras d ,thedimensionlessstrokelength L 0 =d becomestherstkeydimensionlessparameter whichgovernsvortexpairformation.Theseconddimensionless parameteristhe Reynoldsnumber,basedontheimpulseperunitwidth Re I 0 = I 0 =d (1.2) where I 0 = d Z T= 2 0 u 20 ( t ) dt (1.3) and and aretheruiddynamicviscosityanddensity,respectively.Thech oiceof thesedimensionlessparametersaroseoutofthestudyofvortexri ngs( Didden 1979 ; Glezer 1988 ; Shari&Leonard 1992 ). Alternatively,acharacteristicoricevelocityisusedtocal culatetheReynolds number: Re ~ U = ~ Ud= (1.4) where ~ U = L 0 =T (1.5) and = = istheruidkinematicviscosity.Takenwiththefrequencyofosc illation, thedutycycle,andthegeometryofthesyntheticjetdevice(a llconstantsintheir study),theseparametersdependsolelyontheamplitudeofthed river. Fortheexperiments,theymanufacturedasyntheticjetdevice consistingofa circularpiezoceramicpatchbondedtoametaldisk,whichwas thensealedtothe undersideofacavity.Anominallytwo-dimensionalsyntheticj etwasformedviaa topplatewithasmallslotmeasuring75 0 : 5mm.Thedriverwasoperatedovera

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13 rangeofamplitudestoacquiredatafortheparameterspace5 : 3
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14 Region4of Ingard&Labate ( 1950 ).Secondly,themethodofvelocitymeasurement {hotwireanemometry{hasitsowndrawbacks,suchasdirection alambiguityin anoscillatoryroweld,largeructuationscomparedtothelo calmeanvalue,limited spatialresolutionoversmall-scaledevices,andpossiblealterat ionoftherowdueto theintrudingpresenceoftheprobe.Finally,asingledevicew asusedforalltests, whichhadaconstantslotheight-to-depthaspectratio.Thisli mitationeliminated thepossibilityofstudyinggeometriceects. Inanattempttoresolvesomeoftheseaforementionedissues,Smith andSwift,in tworelatedpapers( Smith&Swift 2001 2003 ),subsequentlyperformedexperiments onalargersyntheticjetdevice.Theoscillatorconsistedofaspe aker-drivenplenum whichallowedfrequenciesintherangeof10
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15 modelcontainedthefollowingkeyassumptions:(1)potentialr owwasassumed,(2) ajetwasformedwhentheinducedvelocityofthevortexpairw asgreaterthanthe peaksuctionvelocity,(3)thedistancebetweenthecentersof thevorticeswastheslot depth d ,and(4)thepositionofthevortexpairatthepeakofthesuctio nstrokewas takenas x= L =0 : 5.Withtheseassumptions,theyfoundathresholdstrokelength L d > 4 p 2 : 3(1.6) forjetformation.Theactualvalueofthethresholdstrokelen gthwascomputed byrstperformingschlierenvisualizationtodeterminejetfo rmationandnotingthe pressureamplitudeofthecavityandfrequencyofoscillation. Thenahotwireprole wasacquiredatthesamecavitypressureamplitudeandfrequenc ytocomputethe strokelength.Thisprocedurewasrepeatedoverthefrequenc yrangeof10
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16 0 0.05 0.1 0.15 0.2 5 5.5 6 6.5 7 7.5 8 8.5 9 d n /dL/d d=0.5 cm1.0 cm1.5 cm2.1 cm Figure1{6:Thresholddimensionlessstrokelengthasafunction ofnormalizedviscous penetrationdepthforseveralslotdepths.Adaptedfrom Smith&Swift ( 2001 ). Smith etal. ( 1999 )alsoextendedtheworkof Smith&Glezer ( 1998 )bymeasuring thevelocityelddownstreamofbothatwo-dimensional(slot)a ndanaxisymmetric (orice)syntheticjetusingphase-lockedParticleImageVelo cimetry(PIV),which gavetwo-componentvelocitymeasurementsandeliminatedth edirectionalambiguity inherentinhotwireanemometry.Cavitypressuremeasurements werealsomadeusing adynamicpressuretransducerwitharangeof1psidandabandwidt hof100kHz. Apiezoelectricdiaphragmservedastheoscillatingdriver,a ndthesharpslotexit hadaheight-to-depthaspectratioof2.5.Theactuatorwasop eratedatfrequencies of600Hzand1100Hz,andvortexpairswereseentobeejectedfrom theslotfor bothoperatingfrequenciesbycomputingthespanwisevortici tyfromthemeasured velocityelds.However,forthelowerfrequencycase,remnant sofvorticitywere observedinthewakebehindthevortexpair,ostensiblybecauset hetotalcirculation generatedbytheexpulsionstrokeexceededthemaximumamount ofcirculationthat

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17 thevortexpaircouldcontain( Gharib etal. 1998 ).Fortheaxisymmetricorice,the height-to-diameteraspectratioismuchlessthanone.Itwasf oundthatincreasing thedimensionlessstrokelengthincreasedthecavitypressure,bu talargejumpin strokelengthwasobservedforagivencavitypressurearoundastr okelengthvalue ofone.Sincetheaxialdistancebetweentheoriceandtheloc ationofthevortex ringatthestartofthesuctionpartofthecycleincreasedwithst rokelength,they postulatedthatatsmallstrokelengths,thevortexringinduced ablockageduring thesuctioncycle,sincetheringhadtheeectofpumpingruida xiallyawayfromthe orice.Oncetheringwasfarenoughremovedfromtheoricea sthestrokelength wasincreased,thisblockagewasremovedandtheheadlosswasr educed,resultingin anincreaseinstrokelengthatanominallysimilarcavitypressur e. Anotherimportantresultoftheirstudywasthatthephase-locke dvelocityprolesmeasuredinthevicinityoftheoriceweresignicantlyd ierentfromslug-like; indeed,theprolesexhibitedmaximaneartheedgesoftheor iceduringtheejection partofthecycle.ThisbehavioristermedRichardson'sannul areect,andistypical offullydevelopedpiperowsgeneratedbyoscillatingpressure gradients( White 1991 ; alsoseeAppendix A ). Duringthesuctionpartofthecycle,however,thevelocitypr olesbecamemore slug-like,suggestinganasymmetrybetweentheexpulsionanding estionstrokes.This occurredbecauseduringtheexpulsionstroke,theexitplaneof theoricecorrespondedtotheexitofthejet,whileduringthesuctionstroke,t hislocationnow becametheentranceplane.Thisbehaviorwasconrmedbyexa miningthedimensionlessphase-lockedvorticitycontoursoftherow{non-dime nsionalizedbytheoricediameterandcharacteristicvelocity{plottedinnon-di mensionalradialandaxial coordinates,acquiredforseveraldierentstrokelengths,Rey noldsnumbers,andactuationfrequencies.Thefreshlyejectedvortexring,whenpl ottedinthesedimensionlesscoordinates,wasatthesamestreamwisepositionandhadthesam edimensionless

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18 strengthofvorticity,regardlessofwhetheritwassuckedback intotheoriceorultimatelyadvectedaway.However,theremnantsofthepreviou svortexringdidnot collapsewhennon-dimensionalized,suggestingthatthesuction partofthecycleaffectedthevorticesindierentways.Specically,thesuctio ncyclehadtheeectof eitherre-ingestingthevortexringforsmallstrokelengthsor stoppingtheadvection oftheringandleavingitstationaryforslightlylargerstroke lengths.Atstilllarger strokelengths,however,theeectofthesuctionwasdiminished asthevortexring propagateddownstream. Inaqualitativeparametricstudy, Crook&Wood ( 2000 )investigatedtheeectof cavityandoricegeometryonsyntheticjetformation.Ashake r-drivenmodularsetup wasconstructedwhichallowedforinterchangeablecavityhe ightsandcircularorice plateswithvaryingheight-to-diameteraspectratio.Theru idinthecavitywasseeded withsmokeparticlesandvisualizedthroughtheuseofa50Hzpulsa tinglightsheet andvideorecorder,whichallowedforaliased\movies"ofthev ortexringformation tobegeneratedwhentheoscillatorwasrunatafrequencyof50 .1Hz.Figure 1{7 showsatwo-dimensionalmatrixofimagesoftheseededrowelda safunctionof Reynoldsnumberandoriceheight-to-diameteraspectratio .TheReynoldsnumber wascomputedbymeasuringthemaximumcenterlinevelocitydu ringtheejection phasewithahotwireanemometer,andtheappropriatelengthsc alewastakenasthe diameteroftheorice.Similarto Smith etal. ( 1999 ),itwasfoundthatamaximum valueofcirculationforavortexringwasreached,andthate xcessvorticitywhichcould notrollupintotheringemergedasatailbehindthering,whi chrolleduptoforma secondaryringiftheReynoldsnumberwashighenough.Theyal sodiscoveredthat increasingtheoriceheightwhileholdingtheReynoldsnumb erandoricediameter constanttendedtoincreasetheamountofcirculationintheri ng,presumablybecause amoredevelopedvelocityprolearoseintheorice.Similar resultswerefoundby increasingthecavityheightwhileholdingReynoldsnumber, oriceheight,andorice

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19 diameterconstant.However,itwassuggestedthatthemechanismf orthiscaseofa moredevelopedvortexringwasduetotheabilityoftheruidt ogainmorevorticity duringthesuctionstrokewhileinsidethelargercavity.Since avortexringwould forminsidethecavityasaresultofthesuctionstroke,alargerc avitywouldallow thisringtogeneratemorevorticityasitinteractedwithth ecavitywall,whichwould thenpersistintheruidthroughthefollowingexpulsionstroke. Figure1{7:EectofReynoldsnumberandoriceheight-to-d iameteraspectratioon syntheticjetformation,thewhiteverticallinerepresentst heapproximatelocationof theorice,andthewhitehorizontalbarsrepresenttheappro ximatediameterofthe orice.TheReynoldsnumberincreasesfrombottomtotop,and increasesfromleft toright.Adaptedfrom Crook&Wood ( 2000 ). Apiezoelectricsyntheticjetactuatorwasdevelopedby Chen etal. ( 2000 ).The jetissuedthroughanarrowslotmeasuring35 : 5mmby0 : 5mm,andthejetvelocity wasacquiredusinghotwireanemometry.Throughstroboscopicr owvisualization, theydiscernedtwotypesofjets.Laminarjetswereachievedat lowReynoldsnumbers

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20 andwerecharacterizedbythepresenceofdiscretevorticalstr ucturesemanatingfrom theslot.TurbulentjetsoccurredathigherReynoldsnumbers, andtypicallyonly onevortexpairwasobservedattheslot,followedbyaturbulen t-likejet,similar tothendingsof Smith&Glezer ( 1998 ).Finally,theynotedthatthetransition toturbulencedependedonboththeReynoldsnumberandthedi mensionlessstroke length,thoughtheirtransitioncriterionwassemi-qualitat iveandbasedonasmall numberofpoints. Gilarranz etal. ( 1998 )constructedasyntheticjetdeviceusingaBrueland Kjrshaker-drivenmembraneastheoscillatingdriverwithac ylindricalcavity.An axisymmetricoriceplatewithaheightof6mmandadiametero f2mmwasattached tothecavity,andtheworkingruidwaswater.PIVwasusedtoac quirephase-locked velocityvectorsinthegeneratedroweld.Approximately15 velocityvectorswere acquiredacrosstheoricediameter.Theparameterspacecove redbythisstudywas anoscillationfrequency10
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21 Bera etal. ( 2001 )alsousedPIVtomeasurethesyntheticjetvelocityelddownstreamofatwo-dimensionalsharp-edgedslotmeasuring100 1mm.Theschematic oftheirsetupindicatedtheuseofacavitygeometrywhichgrad uallycontracteddown totheslotdepth.Thedriverconsistedofaloudspeakerwhichwas runataxed frequency(200Hz)andjetrootmeansquare(RMS)velocity(14m /s).Operationof thedeviceresultedinameanjetwheretheejectedruidmovedsu cientlyfarfrom theslotduringtheexpulsionphasetobeunaectedbythesuction phase.Thismean jetroweldcontainedasaddlepointattwoslotdepthsaboveth eslot,abovewhich therowappearedsimilartoaconventionalsteadyjet.Unfortun ately,thespatial resolutionoftheirPIVmeasurementscomparedtotheslotdepth wasnotsucient toacquiremorethanoneortwovelocityvectorsacrosstheslot Inanotherexperimentalstudyofaxisymmetricsyntheticjets, Cater&Soria ( 2002 ),usingPIV,foundsimilarresultsto Smith&Glezer ( 1998 );namely,that aturbulentsyntheticjethasasimilarmeancross-streamvelocit ydistributionto aconventionalturbulentjet,butwithahigherspreadingrat eanddecayconstant. Theirsetupconsistedofapistondriverinacylindricalcavityw hichexhaustedwater througha2mmdiametercircularoriceintoalargewatertan k.Therowwasvisualizedthroughtheuseofinjecteddye,andtheydetectedfour distinctrowpatterns asafunctionoftheReynoldsnumber. First,atlowReynoldsnumbers,theyobservedasteady,laminartyperowemanatingfromtheoricewhichdidnotmixwiththesurrounding ruidandhadnot beenpreviouslyreportedintheliterature;thistheytermed alaminarjet.Asthe Reynoldsnumberincreased,individuallaminarvortexrings becameapparent.These ringsdidnotinteractwithoneanotheroverthedomainofmea surements.EventuallywithincreasingReynoldsnumber,theseparateringsbega ntocoalesceandform atransitional-typeofjet.Finally,afullyturbulentjetwa sobservedatthehighest

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22 Reynoldsnumbersandnovortexringsweredistinguishable.Fi gure 1{8 showsimages fromeachoftheidentiedrowpatterns. Figure1{8:FlowregionsasafunctionofReynoldsnumber,wh itearrowsindicate rowdirection,(a)laminarjet,(b)laminarrings,(c)transit ionaljet,(d)turbulent jet.Adaptedfrom Cater&Soria ( 2002 ). Itisclearthattheseregimesdonotcorrespondtotheregionsi dentiedby Ingard &Labate ( 1950 )inFigure 1{3 ,althoughFigure 1{4 andFigure 1{8 (b)appearstrikinglysimilar,andoveralltheseimagesareinremarkablygood qualitativeagreement withtheresultsof Crook&Wood ( 2000 )inFigure 1{7 .Itisalsonoteworthythata distinctionwasmadebetweena\laminar"syntheticjetanda\t urbulent"synthetic jet,thelatterhavingbeenstudiedextensively,buttheforme rhadnotbeenobserved previously. PIVwasusedtoacquirevelocityelddatainboththenear-el dandfar-eld regionsoftheorice.Fromthesedata,comparisonstoconvent ionalsteadyturbulent jetsweremade.Itshouldalsobenotedthattheyacquiredtheir rowvisualization imagesusingabluntoriceplatewithheight-to-diameterasp ectratioofone,but switchedtoabeveledoriceplateforthevelocitymeasuremen tstoalleviaterow separationontheinneredgeduringtheforwardstroke.Thepla tewasbeveledat45 onbothsidestoensureasymmetricalrowattheoriceduringthe expulsionand suctionstrokes.Across-sectionschematicofthetwodierentori ceplatesisshown

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23 inFigure 1{9 .Theyreportedthatqualitativerowvisualizationusingthet woorices atsimilarconditionsdidnotyieldanydierencesinthejets. 2 mm 2 mm 2 mm a) b) Figure1{9:Oriceplatecross-sectionsusedby Cater&Soria ( 2002 ),(a)blunt, (b)beveled. Yehoshua&Seifert ( 2003 )investigatedtheroweldgeneratedbyanominally two-dimensional,piezoelectric-drivensyntheticjetactua torusingphase-lockedPIV. Althoughnotspecied,theslotheight-to-depthaspectratioap pearedtobelessthan onebasedontheschematicoftheirdevice,andonlyoneslotgeom etrywasusedfor measurementsinaquiescentmedium.Theactuatorwasoperated attheHelmholtz frequencyof1060Hz,andtheyfoundthatwhenthepeakslotexit velocitydropped belowacertainvalue,theejectedvortexpairwhichresulted fromtheexpulsionstroke didnotescapetheslot,butwasinsteadre-ingestedintothecavi tyduringthesuction stroke,resultinginazeromeanverticalvelocitydownstreamo fthejet. Onepeculiaraspectofthevortexpairwhichtheyidentiedwa sthatafterit wasformedbutbeforethestartofthesuctioncycle,theindivi dualvortexstructures initiallymovedclosertooneanotherastheypropagateddown stream.Threepossible explanationsforthisbehaviorwereoered:(1)anaccelera tionofruidalongthe centerlinefromtheupstreamstagnationpointresultedinalow erstaticpressure, (2)aninducedforceduetopotentialrowmechanisms,or(3)rui dentrainmentinto thevorticesastheypropagated.

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24 Shuster&Smith ( 2004 )examinedtheeectofthreedierentoricecongurationsonsyntheticjetformation,eachwithaheight-to-diam eteraspectratioof0.5. Specically,theyusedasharporice,abeveledorice,andar oundedorice,as showninFigure 1{10 .Apiston-cylindersyntheticjetwasgeneratedwithwateras theworkingruid.Injecteddyewasusedforrowvisualizationo ftheemittedvortex rings,andvelocityeldmeasurementwasachievedwithPIV.Itw asfoundthatthe transitionofthevortexringsfromlaminartoturbulentwasa functionofboththe Reynoldsnumberandthedimensionlessstrokelength.However,t hereweremarked dierencesinthistransitionforeachofthethreeoricegeo metries.Forexample, itwasfoundthattheReynoldsnumberrequiredfortransition toturbulencecontinuallyincreasedwithincreasingstrokelengthfortheroundeda ndbeveledorices, whileforthestraightoricethetransitionReynoldsnumberb egantodecreaseata dimensionlessstrokelengthof8.Furthermore,whenholdingth eReynoldsnumber anddimensionlessstrokelengthconstant,theextenttowhichth evortexringsbroke downandlostcoherencealsodependedonwhichoricegeometry wasused.The vortexringsgeneratedwiththebeveledoricepersistedlong erthanthosegenerated bytheothertwoorices.Anotherobservationtheymadewasthat forastraight orice,theejectedvortexringwasre-ingestedbelowadimen sionlessstrokelengthof orderone. c) b) a) Figure1{10:Oriceplatecross-sectionsusedby Shuster&Smith ( 2004 ),(a)straight, (b)beveled,(c)rounded.

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25 Inacombinedexperimental/computationalwork, Mallinson etal. ( 1999 )studiedapiezoelectric-drivensyntheticjetoriginatingfroma naxisymmetricorice.Their computationalmodelconsistedofatwo-dimensional,unsteady, incompressibleNavierStokessolverwhichmodeledturbulentrowviathe k model( Pope 2001 ).The actuatorwasmodeledasasinusoidallyvaryingslugvelocitypr oleattheorice exit.Centerlinevelocitymeasurementswereacquiredwithh otwireanemometryand showedgoodagreementwithcomputationsinthefareld,butp ooragreementin thevicinityoftheorice.Thistheyascribedtopossibledevia tioninthevelocity prolefromatop-hatshape,limitationsofatwo-dimensional solverinaninherently three-dimensionalrow,and/orinaccuraciesintheexperime ntalvelocitymeasurementsduetothelargehotwireprobesize.However,aspartofap arametricstudy inwhichtheyvariedthefrequencyofoscillation,thecavity height,andtheorice diameter,itwasfoundthatalargercavityhadtheeectofre ducingthejetvelocity. Furthermore,theyperformedabriefdimensionalanalysisinw hichtheyobtaineda ReynoldsnumberandaStrouhalnumberastheimportantdimen sionlessparameters foraxedgeometrydevice.ItwasfoundthatastheReynoldsn umberwasincreased, theStrouhalnumberinitiallydecreasedbeforeincreasing. Utturkar ( 2002 )performedanumericalstudyontwo-dimensionalsyntheticjet s whichwaslatersupplementedbyexperimentaldataforbothtw o-dimensionalandaxisymmetricsyntheticjetsin Utturkar etal. ( 2003 ).Following Rampunggoon ( 2001 ), theyreasonedthatthesuccessfulformationofasyntheticjetwou lddependonthe abilityoftheejectedvortexpairtoovercomethesuction-in ducedvelocity{similar to Smith&Swift ( 2001 ){andusinganorder-of-magnitudeanalysis,itwasshown thatiftheinverseoftheStrouhalnumberwasgreaterthanaco nstant,ajetwould form.Computationalandexperimentaldataforatwo-dimensi onalslotshowedthis constanttobeoforderone,whileexperimentaldatafortheax isymmetriccaseindicatedtheconstanttobearound0.16.Thissuggestedthatori cegeometryalso

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26 playedacriticalroleinsyntheticjetrows.WhenthedataofFi gure 1{6 wasrecast intermsofReynoldsnumberandStokesnumber(1 =St = Re=S 2 ),acleartrendofjet formationresulted,shownbelowasFigure 1{11 .Itisinterestingtonotethatinthis log-logplottheeectofradiusofcurvaturehasbeencompre ssed,butitisstillreadily apparentthatajetwouldformatalowerReynoldsnumberasth e\sharpness"ofthe slotincreases.Inasubsequentpaper, Holman etal. ( 2005 )attemptedtoaccountfor theinruenceoftheradiusofcurvatureonjetformationbypr oposingamodiedjet formationcriterion.Thiscriterionaccountedfortheaddi tionaldistanceseparating thevorticesduetotheroundedexit.Theyalsonotedthatauni versalcriterionfor jetformation,validforbothtwo-dimensionalandaxisymmetr icoricegeometries, requireddetailedinformationonthesizeandseparationofth evortices,whichwas notavailableatthattime.Detailsofthisjetformationcri terioncanbefoundin Appendix B 10 20 40 100 10 2 10 3 10 4 Stokes NumberReynolds Number d=0.5 cm, R/d=1.28d=1.0 cm, R/d=0.64d=1.5 cm, R/d=0.43d=2.1 cm, R/d=0.30Re/S 2 =1 Figure1{11:Two-dimensionalsyntheticjetformationcriter ion.Thedataisfrom Smith&Swift ( 2001 ),andispresentedin Utturkar etal. ( 2003 ).

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27 NumericalStudies Besidesexperimentalinvestigations,therehasalsobeenconsid erableinterestin numericallysimulatingsyntheticjetroweldsinrecentyear s.Therstsuchknown studywasperformedby Kral etal. ( 1997 )inwhichtheyusedatwo-dimensional, unsteadyReynolds-averagedNavier-Stokes(RANS)equationsolve r.Interestingly, onlytheroweldexternaltothesyntheticjetdevicewasmode led,withtheactuator, cavity,andoricebeingmodeledasaspatiallyvarying,sinuso idalvelocityprole.It wasfoundthatsettingthespatialvariationcomponenttoone( i.e.,aslugvelocity prole)cameclosesttomatchingpreviouslypublishedexperime ntaldata.Amodied pressureboundaryconditionwasalsospeciedatthelocationof theoriceexitto accountforactuatoreects.Bothlaminarandturbulentsimul ationswereperformed overarangeofStrouhalnumbers,andthecomputationalparam etersweresetsuch thattheywouldmatchtheexperimentalparametersof Smith&Glezer ( 1997 ). Itwasfoundthat,contrarytoexperimentalresults,thelamin arsimulationpredictedshedvortexpairswhichdidnotbreakdownbutpersistedt hroughoutthe computationalgriddomain.Whentheturbulencewasmodeled ,however,thecomputedroweldbegantoresemblemoreaccuratelytheexperime ntalresults;namely, thatasinglevortexpairwasformed,shed,andbrokedownintot hesubsequentturbulentjetbeforethenextcycle.Thesimulatedcross-streamvel ocityprolesalso collapsedreasonablywellnormalizedbythecenterlineveloc ity,andgoodagreement wasshownwithexperimentaldata.Thecenterlinevelocityde caywasalsoingood agreementwithexperiments. Inanattempttoimproveupontheworkof Kral etal. ( 1997 ), Rizzetta etal. ( 1999 )simulatedasyntheticjetusinganunsteady,compressibleNavierStokessolver forbothtwo-andthree-dimensionalgridsviadirectnumeric alsimulation(DNS). Heretheactualsyntheticjetoscillatingdriver,cavity,ando riceweremodeledas partofthemesh.Thelowerboundaryofthecavitywasforcedto oscillatesinusoidally

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28 tosimulatethedriver.Duetocomputationalresourcelimitat ions,forthethreedimensionalcomputations,onlyonequarterofthedomainwassi mulatedbyimposing symmetryplanesalongthedepthoftheslotat x =0andalongthemid-spanofthe slotat y =0,asshowninFigure 1{12 y=0 x=0 simulation domain Figure1{12:Symmetryplanesimposedby Rizzetta etal. ( 1999 )forthreedimensional syntheticjetcomputations. Theresultsofthetwo-dimensionalsimulationsshowedthatavor texpairalways existedinthevicinityoftheslot.First,asruidwasexpelledt hroughtheslot,a vortexpairformedatthelipandwasconvectedawayintheusua lmanner.During thesuctionstroke,however,avortexpairwithoppositesignvor ticityformedatthe innerslotlipandpropagatedtowardthelowerboundary.Atve rylowcavityheights, thissuctionvortexwasconstrainedtoremaininthevicinityo ftheslot.Forthiscase andatahigherReynoldsnumber,remnantsoftheingestedvort expairweredetected inthevicinityofthesubsequentlyexpelledvortexpair.Inal lcases,severalvortex pairsremainedcoherentdownstreamoftheslot. Forthethree-dimensionalsimulations,onlyonecoherentvort exstructurecould beidentiedabovetheslotatanygiventimeduringthecycle, consistentwithexperimentalresults.Anotherinterestingndingwasthat,despitethe largewidth-to-depth

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29 aspectratioandcorrespondingquasi-two-dimensionalityofth eroweldnearthecenteroftheslot,thevortexpairwasinfactanelongatedvortex loopconnectedatthe endsoftheslot,andspanwiseinstabilitieswerethecauseofther apiddecayofthis vortexloop.Again,theseresultsweresimilartothendingsofp reviousstudies ( Smith&Glezer 1997 1998 ).Itshouldbenoted,however,thattheexactgeometry oftheexperimentscouldnotbeduplicatedinthesesimulation sowingtorestrictions oncomputationalresources. Lee&Goldstein ( 2002 )performedtwo-dimensionaldirectnumericalsimulations onanactuatorarrayexhaustingintoaquiescentmedium.Botht hecavityandthe slotweresimulated,althoughtheslotwallwasmodeledasveryt hin,givingaslot height-to-widthaspectratioofnearlyzero.Vortexpairing wasobservedtooccur inthefareldfromtheslot,whichhadnotbeenobservedinprev ioussimulations orexperiments.Besidestheinabilityofthetwo-dimensionalsi mulationtopredict thespanwiseinstabilitieswhichnormallycausethevortexpair stobreakdown,they conjecturedthatanenclosedcomputationaldomaincausedthe vorticestoslowdown astheyapproachedthefarwall,allowingforthesubsequentvo rtexpairstocatch up.Eventuallyasteady-staterowemergedinwhichvorticesdi usedtooquicklyfor vortexpairingtobeanissue. ThesimulationparametersoftheirstudyincludedtheStrouha lnumberandthe Reynoldsnumber.Notsurprisingly,theyfoundthatataxedStr ouhalnumber,the extenttowhichvortexpairsremainedcoherentbeyondtheir formationattheslot wasafunctionoftheReynoldsnumber;i.e.,smallReynoldsnu mberrowsproduced vorticeswhichrapidlydecayed,whilelargerReynoldsnumb errowsgeneratedvortex pairswhichremainedcoherentenoughtobounceothefarbou ndary.Inaddition,at largeReynoldsnumbersacomplexcirculationpatterndevel opedinthecavitywhich neverstabilizedinaperiodicsense.WhentheStrouhalnumberw asvariedwitha xedReynoldsnumber,itwasfoundthatastheStrouhalnumbe rincreased,lessruid

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30 wasejectedduringtheexpulsionstrokebecauseoftheinversere lationshipbetween Strouhalnumberandstrokelength. Theeectofslotheight-to-depthaspectratiowasalsoexamine dforagiven ReynoldsnumberandStrouhalnumber.Asexpected,asthesloth eightincreased,a thickerboundarylayerdevelopedintherowintheslot.Thisr esultedinvortexpairs whichhadahigheradvectionvelocity,buttheyobservednoch angeinthediameters ofthevortexcores.Aroundedoriceandacusporicewerealsosi mulated,andit wasfoundthatthestrengthofthevortexpairswashigherby40 %fortherounded orice.Thiswasduetothereductioninseparationoftherowd uringthesuction stroke. Inanothertwo-dimensionalsimulationbysolvingtheincompre ssible,unsteady RANSequations, Fugal etal. ( 2004 )investigatedtheeectoftheradiusofcurvature oftheslotexitonsyntheticjetformation.Nodriverwassimulat ed;insteadan oscillatingchannelrowwassimulatedbelowtheslot.Theslothe ightwassetto threestrokelengths,toallowforfully-developedrowinthec entralthirdoftheslot duringtheentirecycle.Twodierentradiiwereexamined:a sharpedge( R =0), andaroundededge( R = h ).Theydiscoveredthatthepowerrequiredtoformajet waslargerforthesharp-edgedslot,butthatajetformedatalo werdimensionless strokelengththantheroundededge.Again,thisbehaviorisno tunexpected,since aroundededgewouldreducetheseparationontheinrow,butash arpedgewould moreeasilyallowavortexpairtorollupandpropagatedownstr eam.Thus,two competingparametersemerged,andsomeoptimalshapepossiblye xistswhichwill minimizethepowerrequirementandmaximizethestrengthoft hejet.Thisoptimum wasfoundbydeningthejeteectivenessasthenormalizedmo mentumruxachieved dividedbythenormalizedacousticpowerrequired.Whenconsi deredasafunction ofdimensionlessstrokelength,itwasfoundthattheroundeded gegaveahigherjet eectivenessthanthesharpedge.Inbothcases,theeectiveness initiallyincreased

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31 withstrokelengthandthenleveledoatsteady-statevaluesof 3 : 5and 2for theroundedslotandsharpslot,respectively. Motivation Basedontheprecedingliteraturesurvey,itisquitecleartha tawidelydiverse setofexperimentsandsimulationshavebeencarriedouttoimp rovetheunderstandingofroweldsgeneratedbythesyntheticjetexhaustinginto aquiescentmedium. However,directcomparisonoftheresultsfromeachofthesestudi esisdicult,ifnot impossible,forthefollowingreasons. First,basedonthemanydierentgeometriccongurationsasw ellasactuation characteristics,itbecomesobviousthatthereisaverylarge parameterspacein whichatypicalsyntheticjetdevicecanoperate,withseveral possibleresultingrow regions.Althoughsomeresearchershaveattemptedtoduplicate thesetupofothers (mostnotablythecomputationalistshavetriedtosimulatethe parametersofthe experimentalists),forthemostpartthisendeavorhasbeenthe exceptionratherthan therule. Second,nouniversallyacceptedsetofdimensionlessparameter sexists.Although thedimensionlessstrokelengthisoftenapopularchoice,this parameterisonly physicallymeaningfulathighStrouhalnumberswhereaslugve locityproleisa reasonableassumption( White 1991 ).Henceitbecomesachallengetoevenidentify theparameterspacecoveredbythestudiesintheopenliteratu re.Italsofollows thattheextenttowhichthephysicsofsyntheticjetrowsarego vernedbythevarious dimensionlessparametersisnotwellknownorunderstood.Furt hermore,thedierent topologicalregimesarenotsucientlycharacterizedinter msofthedimensionless parameters. Third,ifastudyreportstheresultsofanexperimentinaparam etricfashion, theresultstendtobeeitherqualitativeinnature,orcovero nlyaverylimitedregion oftheparameterspace.Finally,aswithallexperiments,quan titativeresultsare

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32 meaninglesswithoutathoroughunderstandingofthedataacqu isitionandsetup parametersandanestimateoftheaccuracyofthedata,whichsh ouldbecarefully documented.Unfortunately,amongtherelevantstudiesthisa lsotendstobethe exceptionratherthantherule.Thesevexingissuesformthemot ivationofthepresent work. TechnicalObjectivesandApproach Thetechnicalobjectivesofthisstudyarethus(1)toidentif yageneralsetof dimensionlessparameterspertinenttothestudyofasyntheticj etrowinaquiescent mediumandre-castthesalientresultsofpreviousstudiesintoa singleconsistent parameterspace;and(2)todeterminetheeectsofthesedimen sionlessparameters onthetopologicalbehaviorofthesyntheticjetroweldbype rformingasystematic, quantitative,thoroughlydocumentedparametricexperime ntalinvestigationofasyntheticjetroweldoverawiderangeofpracticaloperatingc onditions.Information onthethresholdofjetformationaswellasthetransitiontotu rbulentrowisinvestigated.Inaddition,theresultingexperimentaldatabaseco ntributestoquantifying thephysicsofsyntheticjetrows.Thisdatabaseisalsoexpectedt obeusefulasa benchmarkforcomparisonstocomputationalsimulationsofsyn theticjetrows,as wellasaidinthevalidationofsyntheticjetmodeling( Rathnasingham&Breuer 1997 ; Gallas etal. 2003 ; Yamaleev etal. 2005 ). Inordertoaccomplishthetechnicalobjectives,thefollowin gapproachistaken. First,adimensionalanalysisofagenericsyntheticjetdevicei sperformed.This analysisyieldsasetofdimensionlessparameterswhichdeneth eparameterspace ofoperationofthesyntheticjet.Thefundamentalphysicsoft hesyntheticjetroweldareaddressed.Theavailabledataintheliteratureareun iedandpresented (totheextentpossible)inthissingleparameterspaceandatestm atrixofadditionalexperimentalcasesisselected.Second,inordertoper formthequantitative parametricstudy,amodular,two-dimensionalsyntheticjetde viceisconstructedand

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33 tested,whichallowsforvariationinthegeometricparamete r h=d .Thedriverforthe deviceisanelectrodynamicshaker,capableofachievingawi derangeofReynolds andStrouhalnumbers.Thedeviceistestedinaparametricfashi onbyvaryingdriver amplitudeanddriverfrequencytoachievevariationsinthe Reynoldsnumberand Strouhalnumber. Therearethreemaintechnicalchallengeswhichpresentthem selvesaspartof thiswork.Therstchallengeisensuringthatthesyntheticjet driverisrobustand operatesconsistentlyaswellasaccurately.Mostsyntheticjet driversemploysome kindofsealingmembranetomaximizethevolumerowratethrou ghtheslot/orice, yetthisintroducesadditionalcomplexityforashaker-driv endevicebecauseavent channelmustbepresenttoallowforpressureequilibrationonbo thsidesofthepiston driver.Inaddition,arexiblesealingmembraneintroducesa nadditionalcompliance whichmayactuallylowertheeectivevolumerowrateatthesl ot.Also,themotionofanelectrodynamicshakeratverylowfrequenciesdevi atessignicantlyfrom sinusoidal,andmustbeaccountedfor.Thesecondchallengeisac quiringaccurate, high-resolutionvelocitydataoveraninherentlyunsteadyro weldwithsmallgeometricdimensions.Atypicalslot/oricescaleusedforthisstudy is1mm,soany techniquetoacquirevelocitydatashouldhavesub-millimete rresolutioninorderto capturethefullvelocityproleemanatingfromtheslot/ori ce.Third,theaccuracy ofthevelocitydataitselfshouldbethoroughlyquantied.All possibleerrorsshould becompletelyaccountedfor,andasucientnumberofdatapoi ntsmustbeacquired toensurestatisticalaccuracyandmitigaterandomerrors. Tomeetthesetechnicalchallenges,itisshownthatasealingmem branecan bereplacedbyaverythingapor\viscousseal"betweenthepisto ndriverandthe cavitywall.Asinusoidalcontrollermustalsobedevelopedande mployedforthe experiments.Inaddition,velocityeldmeasurementsemploy HotwireAnemometry forqualitativeturbulencemeasurements.BothParticleImag eVelocimetry(PIV)

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34 andLaserDopplerAnemometry(LDA)arealsobeemployedtoquanti fytheroweld andcomparesinusoidalvs.nosinusoidalcontrol.Thedetailsoft heexperimental proceduresarethoroughlydocumented.PIVandLDAarecompa redforaselect testcasetoprovidemutualverication.Theperiodic,spatial -varyingvelocityprole acrosstheoriceisacquiredtocharacterizetheroweldint ermsoftherelevant dimensionlessparameters.ThePIV-acquiredvelocityelddown streamoftheorice isusedtodeterminethevorticityeldandhencethebehavior alcharacteristicsofthe syntheticjetrow. Outline Theoutlineofthestudyisthereforeasfollows:Chapter 2 denestherelevant parameterspaceofsyntheticjetoperationandrecaststheresul tsofpreviousstudies inthisuniedframework.Inaddition,theparameterspacefo ratestmatrixofexperimentalcasesisproposedtovalidatethepublisheddataint heliteratureaswell asinvestigateinmoredetailtheeectsofgeometryandactua tionontheresulting roweld.Chapter 3 documentsthedetailsoftheexperimentalsetup.Thesyntheti c jetdevicesusedaredescribedindetail.Driverderectionmea surements,driversinusoidalcontrol,rowvisualizationprocedures,andvelocity measurementtechniques arealsodocumented.Chapter 4 describestheresultsofrowvisualization,driver derectionmeasurementandcontrol,andvelocitymeasurement .Thedatareduction andanalysistechniquesfortheresultsarepresented.Thevari oustopologicalregimes arequantiedintermsoftherelevantdimensionlessparamete rsandthevortexdynamicsoftheroweld.Finally,Chapter 5 oersconclusionsandrecommendations forfuturework. Thisstudyissupplementedbyadditionalworkfoundintheappe ndices.Appendix A givesthedetailedsolutiontoachannelrowwithanoscillatin gpressure gradient,ausefulapproximationtosyntheticjetrowsintheo rice.Thedetailsof ajetformationcriteriontofurtherquantifythesyntheticj etroweldarefoundin

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35 Appendix B .Arelativelylargenumberofcalculationsmustbeperformed toconvert theparameterspaceofpublishedresultsintotheparameterspac edenedinChapter 2 .ThedetailsofthesecalculationsaregiveninAppendix C .Themodelingof rowinthegapbetweentheoscillatingpistonandthecylindric alwallisaninterestingandrelevantissuetoZNMFrowsandisconsideredinAppendix D .Finally, Appendix E discussesanissuenotpreviouslyaddressedintheexperimentalruid dynamicsliterature{multivariateoutlierrejection.

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CHAPTER2 PHYSICSOFSYNTHETICJETFLOWS Thischapterperformsadimensionalanalysisofthesyntheticj etrowproblemto identifytheparameterspaceofoperation.Equivalencebetw eentherelevantdimensionlessparametersisderived,andspecicparametersforvar iationareidentied. Theresultsofpreviousstudiesarerecastintoasingleparamete rspace,andatest matrixofadditionalcasesisproposedtofurthertheunderstan dingofthetopological behaviorofsyntheticjetsexhaustingintoaquiescentmedium. DimensionalAnalysis Inordertoclearlyidentifytherelevant dimensionless parametersthatgovern syntheticjetrowsandrecasttheresultsofpreviousexperimen talandnumerical studiesinauniedframework,itbecomesnecessarytorstrecog nizetheappropriate dimensional parametersinvolved.Consideringagainthesimpliedschemat ic inFigure 1{2 ,showningreaterdetailinFigure 2{1 ,itispossibletoidentifythree fundamentalgroupsofparameterswhichareexpectedtoaec tthebehaviorofthe roweld.Thesethreegroupsare:(1)geometricproperties,(2 )driverproperties,and (3)ruidproperties.Thegeometricpropertiesinclude: 8 |volumeofthecavity d |slotdepth(oricediameter) h |slot(orice)height w |slotwidth(two-dimensionalcaseonly) R |radiusofcurvatureoftheslot Thedriverproperties(excludingelectromechanics)includ e: 36

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37 |frequencyofoscillation 8 |volumedisplacedbythedriver Theruidpropertiesinclude: c 0 |speedofsoundoftheruid |densityoftheruid |dynamicviscosityoftheruid Figure2{1:Detailedschematicshowingsyntheticjetdimension alparameters. Onepotentialdependentparameteris U 0 ,acharacteristicvelocityatthesurfaceof theslot(orice),asdescribedin Smith&Glezer ( 1998 ), Chen etal. ( 2000 ),and Cater&Soria ( 2002 ),amongmanyothers.Fornowthisquantityisundened.To simplifythedimensionalanalysis,itisnowassumedthattherowis incompressible. Thusthecavityvolumeandthespeedofsoundnolongeraectthe roweld.Fora detailedtreatmentofcompressibilityeects,see Gallas ( 2005 ).Furthermore,fora sharp-edgedslot,theradiusofcurvaturebecomesirrelevant .Previousstudieshave investigatedthisroundingeect( Smith&Swift 2001 ; Fugal etal. 2004 ).Also, Cater&Soria ( 2002 )notednosignicantdierencesintheresultingroweldsofa straightoriceandabeveledorice,anothercommongeometr icvariation.These assumptionsaremadebecauseasshownlaterinChapter 4 ,thesyntheticjetdevice

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38 usedforthisstudyisoperatedsolelyovertheincompressiblereg ime,andtheslotexit radiusofcurvatureisessentiallyzeroforallcases. PerformingaBuckingham-Pianalysis( Fox&McDonald 1998 ),andchoosing primarydimensionsMLt,yieldsTable 2{1 .Therearethreeprimarydimensions{ mass,length,andtime{and8parameters.Dimensionalanalysisre vealsthatthere arevedimensionlesspi-groups.Choosingtheslotdepth d ,thedriverfrequency andthedynamicviscosity astherepeatingparametersgivestheconventionalset ofpi-groupsnormallydiscussedintheliterature: 1 = hd a b c = h=d 2 = wd a b c = w=d 3 = 8 d a b c = 8 =d 3 4 = d a b c = d 2 != 5 = U 0 d a b c = U 0 =!d Table2{1:Primarydimensionsofsyntheticjetdimensionalpar ameters ParameterMLt d 010 h 010 w 010 00-1 8 030 1-30 1-1-1 U 0 01-1 Thesepi-groupsmayberearrangedinanycombination,but 0k mustincludeat least k .Thisyieldsinformationonthefunctionalformoftheveloc ity U 0 asfollows: 01 = 1 = h d ,theslot(orice)height-to-depthaspectratio 02 = 2 = w d ,theslotwidth-to-depthaspectratio

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39 03 = 3 = 8 d 3 ,dimensionlessdisplacedvolume,theratioofthedisplaced cavityvolumetothecubeoftheslotdepth(oricediameter) 04 = p 4 = s !d 2 = S ,theStokesnumber 05 = 1 5 = !d U 0 = St ,theStrouhalnumber Notethat 5 canalsoberearrangedtoyieldaReynoldsnumber, Re U 0 = 5 4 = U 0 !d !d 2 = U 0 d (2.1) ThustheReynoldsnumberasthedependentparameterisafunc tionoffourother dimensionlessparameters, Re U 0 = f h d ; w d ; 8 d 3 ;S (2.2) Thatis,theroweldgeneratedbyasyntheticjetexhaustingint oaquiescentmedium (assumingincompressiblerowandnoslotexitradiusofcurvature eects)isafunctionofallofthedimensionlessparametersgiveninEq.( 2.2 ).Notethatforthe axisymmetriccase,thepi-group w=d vanishes.Itisdesiredtoobservechangesinthe Reynoldsnumber(andhencetheroweld)asafunctionofasing ledimensionless parameter,inordertogaugethatparameter'seectonthero weld.AnotableparameterwhichisabsentfromEq.( 2.2 ),butwhichoftenappearsintheliteratureis thedimensionlessstrokelength,denedastheratioofthestrok elengthasdenedin Eq.( 1.1 )totheslotdepth(oricediameter), L 0 =d .Inthenextsection,equivalence betweenthisparameterandthoseofEq.( 2.2 )isshown. ParameterEquivalence Athoroughunderstandingofhowallthedimensionlessparamete rsaectone anotherisusefulforcomparisonofthevariousstudieswhichra relyemploythesame

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40 parameters.First,wenotefromEq.( 2.1 )aninterestingrelationshipbetweenthe Strouhal,Reynolds,andStokesnumbers.Thisrelationshipis Re U 0 =(1 =St ) = (1 =S 2 ), andthisequivalenceismoreeasilyobservedasfollows: 1 St = U 0 !d = U 0 d= !d 2 = = Re U 0 S 2 (2.3) ThusfromEq.( 2.3 )specifyinganytwooftheseparametersxesthethird. Itisnowdesiredtondarelationshipbetweenthedimensionless strokelength andtheparametersofEq.( 2.3 ).Todothis,thevelocityscale U 0 mustbeexplicitly dened.Thereareanumberofvelocityscaleswhichmaybeusedt orepresent U 0 ; howeverthemostgeneralscaleispreferred.Sincethereisbot hspatialandtemporal variationinthevelocityatthesurfaceoftheslot,avelocity scalewhichdoesnot integratethevelocityprolebothspatiallyandtemporally isinappropriate.Further, sincetheexpulsionandingestiontimesmaynotbeequal,anaver ageexpulsionvelocitymaynotnecessarilyequalanaverageingestionvelocity,an dthisimpliesthatthe temporalintegrationshouldbeoveranentirecycle.Thisthe npresentsadilemma becauseaquantitysuchasmassrowratebydenitionintegrates tozerooveran integernumberofcyclesatthesurfaceoftheslot(orice).How ever,sincethedevice impartsaniteamountofmomentumtothesurroundingsduring acycle,avelocity scalebasedonthismomentumisperhapsmoreappropriate.Foll owing Cater&Soria ( 2002 ),themomentumrowvelocityscaleischosentorepresent U 0 U 0 = 1 A 1 T Z A Z T 0 [ u ( A;t )] 2 dtdA 1 = 2 (2.4) where A istheslot(orice)area,and u ( A;t )isthetimevarying,spatialvarying streamwisecomponentofvelocityattheexitplane.Forthelim itingcaseofaslug velocityprolewhichvariessinusoidally, U 0 istheRMSvelocityattheslot(orice). However,itshouldbenotedthatwhenthevelocityprolevarie sspatially, U 0 is

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41 not theRMSofthespatial-averagedvelocity.Forexample,foran oscillatingtwodimensionalchannelrowatverylowStokesnumber,thespatial velocityproleis parabolic(seeAppendix A ). U 0 forthiscaseis58%largerthantheRMSofthe spatial-averagedvelocity.Thisfactorappearsbyseparatin gthespatialintegration fromthetemporalintegrationinEq.( 2.4 ), U 0 = R A u 2 ( A;t ) dA 1 = 2 R A u ( A;t ) dA 1 T Z T 0 [ u ( t )] 2 dt 1 = 2 (2.5) Itthenfollowsthatanaveragestrokelengthshouldbedenedb asedon U 0 as L = U 0 T (2.6) Physically, L isanalogoustotheRMSdistancethataruidparticletravelsn earthe surfaceoftheslot(orice)duringacycle,althoughasstatedp reviouslyitisnot exactlytheRMSdistance.Thisdenitionofthestrokelengthw illnowbeused insteadof L 0 becauseitisthemostgeneral. FromthedenitionoftheReynoldsnumberandfromEq.( 2.6 ),itfollowsthat Re U 0 = U 0 d = Ld T = Ld! 2 = L d !d 2 1 2 (2.7) RearrangingEq.( 2.7 )andrecallingEq.( 2.3 ),thefollowingparameterequivalence isobtainedbetweenReynoldsnumber,Strouhalnumber,Stok esnumber,anddimensionlessstrokelength: 1 St = Re U 0 S 2 = L=d 2 (2.8) Itisimportanttonotethatthisparameterequivalenceisva lidforperiodicmotion regardlessofthetemporalorspatialshapeofthevelocitypro le.Thisisanimportant pointfortworeasons.First,spatialvariationofthevelocityp rolecanbesignicant atlowStokesnumbers( White 1991 ).Second,non-linearitiesinthedrivermotion and/orrownon-linearitiesinthecavityand/ortheslot(ori ce)mayresultina non-sinusoidalvelocityproleintime.Thiswouldyielddie rentaveragevelocities

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42 duringexpulsionandingestion,andtheselectionofonetodescr ibetheroweld wouldcomeattheexpenseoflosinginformationabouttheother .Whileonemay expecttheexpulsionpartofthecycletodominatetheroweld ,theingestionpartof thecyclecanalsobesignicantandprobablyshouldnotbeignor ed.Thispointis furtheremphasizedinChapter 4 ,whereitisshownthataReynoldsnumberbased oncirculationissensitivetothesuctionpartofthecycle. ParametricVariation Nowthatallofthecommondimensionlessparametersusedtochara cterizesyntheticjetshavebeendened,itremainstobedeterminedhow theseparametersaect theoutputofthedeviceandtheresultingroweld.Jetformat ionisthemostcommon characteristicofaZNMFdevice,andasmentionedinChapter 1 ,severalresearchers haveinvestigatedthephenomenonofjetformation. Holman etal. ( 2005 )publisheda detailedjetformationcriterionbasedonthevortexstrength ofthevortexpair(ring) emergingfromtheslot(orice).Itwasfoundthatthecritica lparameterindeterminingjetformationistheStrouhalnumber;specically,thatw hentheStrouhalnumber wasbelowacriticalvalue,jetformationwastheresult.Above thisvalue,notype ofrowwasobservedfromtheslot(orice).Thecriticalvaluew asapproximately 1forsharp-edgedtwo-dimensionalslotsand6forsharp-edgedax isymmetricorices. FromEq.( 2.8 ),itcanbeseenthatthisthresholdcriterioncorrespondstoat hreshold strokelengthforjetformation.Additionaldetailsonthejet formationcriterioncan befoundinAppendix B ThejetformationcriterionindicatesthattheStrouhalnum berplaysacritical roleindeterminingtheresultingroweld.Inaddition,based onrowvisualization resultsdescribedlaterinChapter 4 ,theReynoldsnumberalsocontributestothe roweldcharacteristics.Itisalsoknownthattheslot(orice) height-to-depth(diameter)aspectratiosignicantlyaectstheroweld( Gallas etal. 2004 ).These threeparametersarethemostpracticallyrelevantforchara cterizingasyntheticjet,

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43 andnotcoincidentally,theyallappearinEq.( 2.2 ){theStrouhalnumberemerging viatheequivalenceofEq.( 2.8 ).Fortwo-dimensionalslots,intheneareldregion theroweldremainsessentiallytwo-dimensionalas w=d ischanged. Foraxedgeometry,Eq.( 2.2 )revealsthat changes intheReynoldsnumberare afunctionof Re U 0 = f 8 d 3 ;S (2.9) Or,alternatively, S canbereplacedbytheStrouhalnumber.Theusualphysical parameterstovarywhenoperatingaZNMFdevicearethefreque ncyandtheamplitudeofdrivermotion.FromEq.( 2.9 ),thefrequencydependencemanifestsitself intheStrouhalnumber,whilethedrivermotiondependencea ppearsinthedimensionlessdisplacedvolume.Itisdesiredtoxalldimensionlesspa rametersexcept foroneandobservechangesintheresultingroweldasthatpar ametervaries.For ReynoldsnumbervariationwithaxedStrouhalnumber,both thefrequencyandthe amplitudemustbevaried,because U 0 mustchangetovaryReynoldsnumber,and consequently mustalsochangetokeeptheStrouhalnumberconstant.Conversel y, forStrouhalnumbervariationwithaxedReynoldsnumber,o nlythefrequencymust bevaried. Thenalparameterofinteresttoinvestigateistheheight-to -depth(diameter) aspectratio h=d .Variationsin w=d maybebypassedbecauseinapracticalsense, w=d 1formostapplicationsandisnotrelevantatallfortheaxisym metriccase. Also,threedimensionaleectsarenegligibleintheneareld. Iftheoscillation frequencyanddriveramplitudearexed,thisimpliesthat U 0 isxedaswelland hencetheonlychangesintheroweldwouldbearesultofchang esin h=d .Itmust alsobenotedthattheresultsofaparametricvariationareonl yvalidatthexed valuesoftheotherdimensionlessparameters.

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44 PublishedResults Quiteanumberofdescriptionshavebeenreportedintheopenl iteratureconcerningsyntheticjetrowelds. Ingard&Labate ( 1950 ), Smith&Glezer ( 1998 ), Crook& Wood ( 2000 ),and Cater&Soria ( 2002 ),amongmanyothers,usedescriptiveterms likelaminarjet,laminarrings,transitionaljet,turbulent jet,jetformation,suction row,boiling,interactingvortices,non-interactingvorti ces,reingestedvortices,and manyothers.Itiscertainlyadauntingtasktotrytounifyallo fthesestudiesinto asingleparameterspace,butbydoingso,onemayobservetrendsi nsyntheticjet behavioraswellasidentifyregionsoftheparameterspacewh ichhavenotbeen studiedextensivelyandrequirefurtherexploration.Unfortu nately,therelevantdimensionlessparameterswhichweredenedpreviouslycannotal waysbedetermined conclusivelybasedonthepublishedresults.Forexample,oftena Reynoldsnumber willbereportedbasedonlyonacenterlinevelocityamplitud e,whichisinsucient tocompute Re U 0 .However,theproblemoffully-developedrowwithanoscillat ing pressuregradientservesasausefulapproximationwhensucient quantitativedatais lacking.Therelevantdimensionlessparameterscanbeestimat edfromtheavailable dataandthesolutiontothisproblem,whichisprovidedinAppe ndix A Theexperimentalresultsofeachstudymustbecarefullymatche dinorderto realizeavalidcomparisonandidentifytrends.Thismeanstha talloftheresultsmust bere-castintermsofthedimensionlesspi-groupsofEq.( 2.2 ).Ingeneral,astudy reportsaqualitativerowdescriptionasafunctionofeither thedimensionalparametersofthestudysuchasvelocity,frequencyofoscillation,an doricediameter,oras afunctionofseveraldimensionlessparameterswhicharerarel ymatchedidentically inotherstudies.Sometimestheroweldresultsarequantitati ve,suchasvorticity contoursoftherowelddownstreamoftheoriceorameanvelo cityeld.Foreach rowdescription,thedataprovidedmustbeconvertedasaccura telyaspossibletothe parameterspaceofEq.( 2.2 ).Thedetailsofthenecessarycalculationstoconvertthe

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45 parameterscanbefoundinAppendix C foreachstudyanalyzed.Table C{1 gives theresultsofthiscomparison. Atrstglance,onemayconcludethattheparameterspacehasbe enwell-covered. However,forthetwo-dimensionalcases,mostofthedataavailabl ecomesfrom Smith &Swift ( 2001 ),whoonlyreportedresultsofjetformation.Theothertwo-d imensional studiesareconnedtolowparametervalues.Itshouldalsobenot edthatthedata of Smith&Swift ( 2001 )containvariationsinthedimensionlessradiusofcurvature butalltheotherstudiesreporteduseeitherasharp-edgedori ceorabeveled-shaped orice.Fortheaxisymmetriccases,themajorityofthedatacom esfrom Ingard& Labate ( 1950 ),wherethemethodandaccuracyofthevelocitywerenotrepo rted. Therangeoftheoriceheight-to-diameteraspectratio h=d isalsosmallerforallof theseaxisymmetricstudiesthanthetwo-dimensionalstudies.Asca nbeseen,there remainsmuchinformationontherowcharacteristicstoberel iablyobtainedover justthesethreedimensionlessparameters( Re U 0 St ,and h=d ).Inaddition,itcannot beemphasizedenoughthatthemajorityofthedataavailablei ntheliteratureis insucienttoaccuratelydeterminetheReynoldsnumber Re U 0 ,andthereisalmost neveranyinformationprovidedontheaccuracyofthecomput edReynoldsnumber. ThemostobviouscharacteristicofanoperatingZNMFdeviceisw hetherasyntheticjetisformedornot,andseveralstudieshaveeithernot edthisphenomenonor studieditindetail( Smith&Swift 2001 ; Utturkar etal. 2003 ; Yehoshua&Seifert 2003 ; Shuster&Smith 2004 ).However,othershavenotedvariousothertypesof \regions"ofrow( Ingard&Labate 1950 ; Cater&Soria 2002 )whichmayormay notbeclassiedintermsofjetformationandmaycontainsub-re gionsoftheirown. Generallyspeaking,alloftheresultspublishedintheliterat uremaybeclassiedinto oneofseveralbroadcategories,andtheinstantaneousandtime -averagedrowelds mayappeardierently.Table 2{2 summarizesthesecategories.Itisimportantto notethatthenumberedregionsdenedinTable 2{2 applyonlytothisstudyand

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46 shouldnotbecompareddirectlywithregionsidentiedinpre viousstudies.Ingeneral,ifalltheotherparametersarexed,theroweldtransi tionsfromoneregion tothenextasthenon-dimensionaldriveramplitude 8 =d 3 (andhencetheReynolds number Re U 0 )increases.However,otherparameterssuchastheStokesnumber and theoriceheight-to-diameteraspectratiomayalsoaectthi stransition.Forexample,iftheStokesnumberislow,transitionfromRegion2dire ctlytoRegion5may beobserved( Utturkar etal. 2003 ). Table2{2:Syntheticjetrowregions. Regioninstantaneousroweldtime-averagedroweld 1novorticityformedorvorticesreingestednotypeofrowobse rved 2vorticitystrengthincreasessomerowobserved3vorticespossiblyshedbutreingestedsuction-typerow,'boili ng' 4vorticesareshedbutareweaktransitiontoajet-likerow5trainoflaminarvortexringslaminar-typejet6ringsbegintobecometurbulentjettransitionstoturbulen t 7fullyturbulentrings,maybreakdownturbulentjet ProposedTestMatrix Smith&Swift ( 2001 )arguedthattherewasathresholddimensionlessstroke lengthforjetformation,while Utturkar etal. ( 2003 )reasonedthatathresholdinverse Strouhalnumberdictatedthesuccessfulformationofasyntheti cjet.BasedonEq. ( 2.8 ),thefundamentalequivalencebetweenthesetwoideasbecom esobvious.Furthermore,sincejetformationisanessentialcharacteristicof asyntheticjet,andthis dependsonthedimensionlessstrokelength(oralternativelyt heStrouhalnumber), itisvitalthatvariationsinthisparameterbeinvestigated .Inaddition, Gallas etal. ( 2004 ){focusingontheinruenceofrowintheoriceonthesynthetic jetroweld behavior{demonstratedthattheoriceheighttodiameterasp ectratio( h=d )was anotherkeyparameterwhichgovernedsyntheticjetrows.Spec ically,theyfound thattherowintheoricewasdominatedby\major"losseswhich scaledlinearly

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47 withtheructuatingstreamwisevelocitycomponentwhentheor iceheightsignificantlyexceededthestrokelength.Atlongerstrokes,however ,\minor"nonlinear lossesassociatedwithentranceeectsweredominant.Hencethis furtherunderscores themotivationforexploringvariationsin h=d .Asmentionedpreviously,theresultsof Ingard&Labate ( 1950 )alsosuggestthat h=d isakeyparametergoverningsynthetic jetrows. Transitionfromalaminar-likejettoaturbulent-likejetis alsoofinterestand hasonlybeenreportedsparselyintheliterature. Chen etal. ( 2000 )developedatransitioncriterionforsyntheticjetrowsbutitwasbasedoofonl yafewpointswhich variedwithbothdimensionlessstrokelengthandReynoldsnumb er.Thestudiesby Gharib etal. ( 1998 )and Glezer ( 1988 ),thoughofvortexringsandnotsyntheticjets, neverthelesshintatthepossibilityofaturbulentsyntheticje temergingduetoan upperlimitonthecirculationthatcanbecontainedwithina vortexpair.Insucha casetheexcessvorticitytrailsthevortexpairandthismayfa cilitatethebreakdown toturbulence.ThisalsomotivatesthestudyofReynoldsnumbe reects. BoththeReynoldsnumberandtheStrouhalnumberwillbevari edovertheir usablerangeinordertocapturetherowregionsthathavebeen identiedbypreviousresearchers.Aparametricstudyoftheheight-to-depthaspe ctratio h=d willbe undertakenforsharp-edgedslotcongurations.Table 2{3 givesthetestcasestobe performed,alongwiththerelevantdimensionalparameterst ofacilitatecomparisonto otherresults.TheactualvaluesoftheReynoldsnumberandStr ouhalnumberarenot known apriori ;rather,thetestmatrixisinitiallybasedonrowvisualizatio nresults describedinChapter 4 .Quantitativevelocitymeasurementsareutilizedtocomput e Re and St ,andthesevaluesareshowninTable 2{3 forclarication.Anominalcase (Case3)ischosenandbothReynoldsnumbervariations(Cases15)andStrouhal numbervariations(Cases6-9)areperformed.Thentheslothei ght-to-depthaspect ratio h=d isvaried(Cases10,11)whilemaintainingthenominalStrouh alnumberand

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48 Reynoldsnumber.Asmall h=d ischosen,butitislargeenoughsuchthatcompliance eectsdonotarise( Horowitz etal. 2002 ).Also,alarge h=d istestedtoinvestigate acasethatmayresultinfully-developedrowintheslot.Finall y,thenominalcaseis repeated(Case12),butforadistorteddrivermotionwhichisc ommonforvoice-coil drivers.MoredetailsofthedriveraregiveninChapter 3 Table2{3:Testmatrixofgeometriccongurations. Case Re U 0 St U 0 h=dw=df (Hz) U 0 (m/s) d (mm) 1430.841.4614.889.260.213.082840.861.4614.8818.520.423.0831610.781.4614.8832.420.803.0842800.801.4614.8857.891.403.0855550.811.4614.88115.772.763.0861590.531.4614.8821.580.793.0871550.631.4614.8825.240.773.0881541.001.4614.8839.530.773.0891391.301.4614.8846.670.693.08101750.730.3215.4835.400.902.97111610.793.3215.9837.390.862.87121430.881.4614.8832.420.713.08 ForcaseswithdesiredxedReynoldsnumber,thestandarddevia tionamong themeasuredReynoldsnumbersisonly7%ofthemeanReynoldsn umber,while fordesiredxedStrouhalnumber,thestandarddeviationisju st6%ofthemean Strouhalnumber.Thissuggeststhatchangesintherowelddue tovariationofeither parameterbylargeramountsthanthesedeviationsareprobab lynotsignicantdue tominorvariationsintheotherparameterwhichisdesiredto bexed.Rather,the roweldchangesarelikelytoresultprimarilyfromchangesi ntheparameterwhich isvaried,asdesired.

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CHAPTER3 EXPERIMENTALSETUP Thischapterprovidesthedetailsofdesignandspecications oftheZNMFdevicesusedforthisstudy.Thedataacquisitionhardwareisdiscu ssed.Adescriptionof driverderectionmeasurementsisprovided,aswellasthefee dforwardsinusoidalcontrollerused.Therowvisualizationtechniqueisdocumented. BoththePIVandLDA velocitydataacquisitionandreductionproceduresarethor oughlydiscussed.Finally, estimatesofthesourcesofuncertaintyareprovidedfortheco mputedquantities. SyntheticJetDevices TwodierentZNMFdevicesareconstructedandemployedinthis study.The rstdeviceconsistsofapiezoelectric-drivenactuatordiscmo untedtothesideof acavity.Thisactuatorisusedtoverifythejetformationcri teriondescribedin Chapter 2 .Thedriverdiscconsistsofapiezoelectricpatchwhichisbond edtoa metallicshim.Anaxisymmetricoriceplatemountedatthetopo fthecavityserves toformthesyntheticjetroweld.Anexplodedviewofthismodu larsyntheticjet deviceisshowninFigure 3{1 .Theconstructionofthecavityandthepiezoelectric driverarenearlysimilartoCase2describedin Gallas etal. ( 2003 ),andthegeometric parametersofthisdevicearegiveninTable 3{1 Table3{1:Piezoelectric-drivenZNMFactuatordetails. PropertyValue Cavityvolume(m 3 )5 : 50 10 6 Oricediameter(typical)(mm)2 : 00 Oriceheight(mm)1 : 65 Thisdeviceisconstructedspecicallytooperateinthelow-t o-moderateStokes numberrange, S< 50.Thedatapublishedintheopenliteratureinthisrange 49

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50 issomewhatscatteredasdescribedinChapter 2 .Acquiringreliableexperimental dataatlowStokesnumberswouldproveusefulinapplications involvinglarge-scale rowcontrolexperimentsandenginenacelleacousticliners( Horowitz etal. 2002 ). Thepiezoelectric-drivendeviceisalsooneofthemostcommon implementationsof syntheticjetsduetoitsmodularandcompactdesign.Inadditi on,onlyasmall wireneedstobesolderedtothepiezoelectricpatchtoprovid ethedriversignal, thusthisdesignisapotentiallypromisingrealizationofasyn theticjetinreal-world applications. Figure3{1:Explodedviewofmodularpiezoelectric-driven ZNMFdevice. ThesecondZNMFdeviceisdesignedtohavelargergeometricdime nsions.It consistsofaBruelandKjr(B&K)model4810mini-shakerwitha nattachedaluminumpistonplateasthedriver.Athincylindricalshellmoun tsandsealstothe shakerframetoformthecavity,andthedesignallowsforinter changeableslotplates tobeattachedtothetop.Aperspectiveviewofthisdeviceissh owninFigure 3{2 Amoredetailedcross-sectionalviewisshowninFigure 3{3 .Table 3{2 givesthegeometricparameters.Thepistondoesnotsealtotheouterclamppl ateshell;rather,a viscoussealiscreatedbymakingthegapbetweenthepistonandt hewallverysmall (seeAppendix D fordetails).

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51 "# $% %# & %' &() &+ !' ) ( !' %# & ./ 0/ 1 21 Figure3{2:Shaker-drivenZNMFdevice,a)explodedview,b)a ssembledview. Table3{2:Shaker-drivenZNMFactuatordetails. PropertyValue Uppercavityvolume(m 3 )7 : 38 10 6 Lowercavityvolume(m 3 )5 : 67 10 6 Pistongapthickness(mm)0 : 127 Pistondiameter(mm)45 : 46 Slotdepth(mm)3Slotheight(mm)1 ; 4 : 5 ; 10 Thecavityvolumeofthisdeviceis 8 =7 : 38 10 6 m 3 ,thewidthoftheslotis w =45 : 9mm,andtheslotdepthis d =3mm.Theslotheightisvariedbychanging theslotplates,whichhave h =1mm,4 : 5mm,and10mm.ThustheHelmholtz frequency H rangesbetween2 : 4kHzand7 : 5kHz,whichisanorderofmagnitude higherthanthefrequencyofoperationofthedevice.Hence,c ompressibilityeects inthecavityarenegligible( Gallas 2005 ). Thenatureofthisvoicecoilactuatordesignmeansthatthede viceisaccelerationlimitedathigherfrequencies,whileitisdisplacement-limi tedatlowerfrequencies. Theshiftfromdisplacement-limitedtoacceleration-limite disafunctionofthemass loadingontheshakertable.Nevertheless,atlowfrequencieson theorderof10Hz,

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52 3 4 567 89 :; <= > ?? 67 89 :; <= ? ; @ < 4A B 9 ? @ 3 4 < ? 3 9 < 6 C DE @F 9G 67 ? ; @ < 4A Figure3{3:Detailedschematicofshaker-drivenZNMFdevice. largedisplacementsareachievable.Thisallowsforinvestig ationofsyntheticjet characteristicsatlowStokesnumbers S< 10.Onedisadvantageofthisdeviceis thatitdrawsrelativelyhighcurrent,especiallyatthedesir edhigheramplitudes ofmotion.Thiscurrentcausesundesirableheating,whichcon vectsawayfromthe shakerasaplumejet-likerow.Forthisreason,whenacquiring rowvisualization imagesorvelocitydata,theshakerisoperatedfortheminimu mamountoftime necessarytoobtainresults.Also,thepistonmotioncanbesignican tlydistorted fromasinusoidalshapeathighamplitudesand/orlowfrequenci es.Forthisreason, asinusoidalcontrollerisdevelopedtoensureasinusoidalpiston motion,andthisis discussedinfurtherdetaillater. Whilethisparticulardesignmaynotbeassuitableforpractic alapplications asthepiezoelectric-driverdesign,thereareanumberofadv antagestoutilizingthis

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53 deviceforlaboratoryexperiments.First,thelargerdimensio nsallowforatwodimensionalsyntheticjetdesigntobetested.Second,theshaker -drivenpistonis physicallyabletoachieveamuchlargeramplitudeofderecti onatlowerfrequencies aspreviouslystated,therebyallowingmoreoftheparametersp acetobeinvestigated. Third{andperhapsmostimportantly{theshaker-drivendevic eisbelievedtobe morerobustthanthepiezoelectric-drivendeviceduetothei rdierencesinelectromechanicaltransduction.Thisisbecausethepiezoelectricdia phragmismorelikelyto failordegradeovertimethantheshaker,impedingtherepeat abilityandreliabilityof theresultsobtained.Thisdegradationcanoccursuddenlyift hedepolarizationvoltageofthepiezoelectricmaterialisapplied,orgraduallyo vermanycyclesofoscillation astheelectricalcontactsdegrade,thepiezoelectricmate rialitselfbeginstooxidize, orthepatchbecomesde-bondedfromthemetallicshim.Incont rast,theB&Kshaker electromechanicalmechanismconsistsofapermanentmagnetwi thacoilembeddedin oneplane.Asanoscillatingcurrentisappliedtothemagnet,a mechanicalvibration isinduced.Asuspensionsystemconnesthisvibrationtorectili nearmotion.This typeofdeviceisrobustenoughtobecommonlyusedforaccelero metercalibration andmechanicalimpedancemeasurements.However,overmanycyc lesthepistonmotiondoesinfactchangeinshape,thoughnotnecessarilyinampl itude.Thisproblem isovercomethroughtheuseofthesinusoidalcontrollerwhichi susedimmediately priortorowvisualizationandvelocitymeasurement,ensuring thepistonmotionis bothsinusoidalandatthedesiredamplitude. Inthecaseofbothsyntheticjetdevices,anAgilentmodel33120A functiongeneratorservesasthesignalsource.Thesignalfromthefunctiong eneratorisappliedto anamplier(PCBPiezotronics790SeriesPowerAmplierfort hepiezoelectric-driven syntheticjet,B&Kpowerampliertype2718fortheshaker-dri vensyntheticjet),and theampliedsinusoidalinputvoltagesignalisthenappliedto thedriver,whichconvertsthevoltageintoamechanicalderection.Bychangingb oththefrequencyof

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54 oscillationandtheamplitudeofthefunctiongenerator,one maysystematicallyadjust theStrouhalnumberandtheReynoldsnumber. DataAcquisitionSystem Inordertodeterminetherelativephasingbetweentheinputsi gnal,thedriver derection,andthecorrespondingperiodicvolumerowrateas determinedbythe velocitymeasurementattheslot,itisnecessarytoacquirephase -lockedmeasurements ofthesequantities.UsingthesyncsignaloftheAgilent33120Afunc tiongenerator, therelativephasingbetweenthemeasuredquantitiescanbede terminedifphaselockeddataisacquired.Inaddition,itisimperativethate achquantitybeacquired simultaneously,andmostcommondataacquisitioncardsdonotpr ovidethisfeature. Hence,aNationalInstrumentsmodelNI-4552dynamicsignalanaly zerPCIcardis usedfordataacquisition(DAQ). TheDAQcardis16-bitandcansampleupto4channelsofanalogi nputsimultaneouslyandhasabandwidthofapproximately200kHz,whichi swell-suitedfor thepresentstudy.However,abuilt-intwo-partanti-aliasing ltermustbeconsidered.Therstpartconsistsofalowpassanaloglterwithacuto frequencyof 4MHz,whichiswellabovethefrequenciesconsideredhereandm aybeconsidered tohavezerophaseosetinthepassband.Secondly,adigitallte rremovesallfrequencycomponentsabovetheNyquistfrequency.ThisDAQcardi nterfaceswitha standardPCthroughNationalInstruments'LabVIEWsoftware.LabVI EWisalso usedtocontrolthetraverseforLDAvelocitymeasurementsassho wninFigure 3{27 andinterfacewiththeDantecBSAFlowsoftwareusedtocontrol theLDAsystem. Alldata{inputsignal,driverderection,andvelocitymeasure ments{areacquired andaveragedoverasucientnumberofcyclestoensurestatistic alaccuracyofthe results.Thenumberofblocksofdataaveragedtypicallyrange sfrom100-1000,with aphaseresolutionthatissimilartothevelocitymeasurements.

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55 DriverDerectionMeasurement Bymeasuringthedisplacementofthedriverasitoscillates,the volumedisplacementofthedrivercanbedetermined.Furthermore,byexperi mentallymeasuringthe volumevelocityofthesyntheticjetattheorice,onemaydet erminetheextentto whichruidiscompressedandexpandedinsidethecavityasoppose dtoejectedand ingested,respectively.Forthecasestobetested,itisalready knownthat !=! H 1, thustherearenegligiblecompressibilityeectsinthecavit y.Theextenttowhich thevolumevelocitydoesnotmatchthedrivermotion,then,i sanindicatorofeither leaksinthevariouscomponentsofthedeviceoredgeeectsi nthecaseofthetwodimensionalslot.Whileallleaksareminimizedthroughtheuse ofRTVsealantor vacuumgreaseateveryjoint,therearesomeinevitablelossesdu etoleakage. Fortheshaker-drivendevice,arigidpistonservesastheoscill atorandhencea singlepointmeasurementofthedisplacementallowsfordeterm inationofthevolume velocity.ThedisplacementisacquiredusingaMicro-Epsilonm odelILD-200010laser displacementsensor.Thissensorfunctionsontheprincipleoftr iangulation,andthe deviceisfactory-calibratedtogiveanoutputsignalof1V/mm ,witharesolutionof 5 mandasamplerateof10kHz,whichissucientforthisstudy.Ofpa rticular importance,however,isthelaginthedigital-to-analogco nversionofthesignal.The manufacturerreportsthatthereisafourcyclelagbetweenm easuredlocationand outputsignal.Ata10kHzsamplerate,thistranslatestoaconstan ttimedelayof 0 : 4ms.Thisfurtherresultsinalinearphaseshiftbetweeninputan doutputsignals. Toverifyboththedisplacementsensorcalibrationaswellasth econstanttime delay,aB&Kmodel45063-axisaccelerometerismountedonth etopofthepiston driveratthecenteroftheplate,andtheaccelerationfromt heaccelerometerismeasured.Inadditionthemotionoftheaccelerometerismeasured simultaneouslyusing thelaserdisplacementsensoroverafrequencyrange0
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56 plateisremoved.Theaccelerometerisaxedtothealuminum pistonplateviasuper glue;itwasfoundthatatlargeforcinglevelsawaxbondwasi nsucientandthe accelerometerbecamedislodgedfromthepiston.Theaccelera tionsignalisintegrated twiceandtheconstantofintegrationremovedtoyieldpositio n.Figure 3{4 shows therelativephasingbetweenboththedisplacementsensorandth eaccelerometerto theinputsignal,aswellasthephasedierencebetweenthetwo .Thephasedierenceisaroughlylinearline.Thustheslopeofthislineiscon stantandhasunits oftime{phase( !t rad)dividedbyfrequency( rad/s).Thevalueoftheslopeis approximately0 : 4ms,whichagreeswiththemanufacturer'sspecications. 0 50 100 150 200 250 300 350 400 -180 -120 -60 0 60 120 180 Frequency (Hz)Phase (deg) Phase Difference Disp. Sensor Phase Accel. Phase Figure3{4:Relativephasingofdisplacementsensorandacceler ometer. Whenthisphasecorrectionisappliedtothedisplacementsensor signal,the displacementasmeasuredbythedisplacementsensorisidentical tothedisplacement asmeasuredbytheaccelerometer,bothinmagnitudeandphase. Figure 3{5 givesa bodeplotofthemagnitudeandphasebetweenthedisplacementa smeasuredbythese twomethods.Asanadditionalcheck,asecondaccelerometerwas mountedtothe

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57 housingofthelaserdisplacementsensortoinvestigatetheeecto fpossiblevibration inducedinthelaserdisplacementsensorbytheshaker.However,th ismotionwas foundtobenegligibleatallfrequenciesandamplitudesove rtherangeofoperation ofthedevice.Thuswhenthephasecorrectionisapplied,thed isplacementsensor properlymeasuresthepistonmotion. 0 50 100 150 200 250 300 350 400 0 0.5 1 1.5 2 Frequency (Hz)Magnitude 0 50 100 150 200 250 300 350 400 -30 -15 0 15 30 Frequency (Hz)Phase (deg) Figure3{5:Bodeplotofthecorrecteddisplacementsignal. Inordertomaximizetheresistancetorowthroughthegapbetwe entheoscillatingpistondriverandthecylindricalwall,thegapthicknesssh ouldbeminimized,as showninAppendix D .Fortheshaker-drivendevice,theprimaryconcerninminimi zingthegapthicknessistoensurethatthepistondoesnotrubaga instthecylindrical wall.Whilethemanufacturerreportsthatthelateralmotio noftheshakerisminimizedduetoradialrexuralsprings,itisdesiredtoquantifyt hislateralmotionas awaytosetalimitonthegapthickness.Withapistonplatehaving arelatively largegapthicknessof5mm,thereisnodangerinrubbingandth eshakermaybe takenthroughitsentireoperationaldomaintodetermineth elateraldisplacement.

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58 Thedriveramplitudeisxedatthemaximumsustainablevaluew ithoutexceeding thecurrentlimitwhilethefrequencyisvariedfrom10Hzto40 0Hz. LateraldisplacementmeasurementsareacquiredusingthesameB &K3-axis accelerometermountedatthetop-centerofthepistonplate. Thelateraldisplacement issimilarlydeterminedfromthelateralcomponentsoftheac celerometersignaland atypicalresultisshowninFigure 3{6 .Here,thelateralcomponentsXandY aresomewhatarbitrarybecausetheslotplateisremoved;theyc orrespondtothe planeofthepiston.Thephase-lockedaverageoftheRMSpositio noftheseXand Ycomponentsofdisplacementareplottedvs.frequencyinFigu re 3{7 .Itcanbe seenthatthemaximumlateraldisplacementdecreasesroughlym onotonicallywith frequency.Atlowfrequenciestheamplitudeofthelaterald isplacementintheX directionisapproximately0.25mm,whileathigherfrequen cies(likethedataof Figure 3{6 )thelateraldisplacementdecreasesaslowasontheorderofmi crons. Onemaynotethatthetwolateralcomponentsarenotidentica l,whichindicatesthat theaccelerometerisnotperfectlycenteredontopofthepist on.Itisbelievedthat thisasymmetry,ifanything,wouldcausethelateraldisplacem enttoincrease.One mayalsoexpectthepresenceofthemassoftheaccelerometertoc auseanincrease inthelateraldisplacementbecauseofthisasymmetry.Hencewit houtthepresence oftheaccelerometerthelateraldisplacementwouldprobabl yeitherremainthesame orbesmallerthanthesemeasuredvalues.Thusifthepistongapiso ntheorder of0 : 25mm,thethicknessofthegapissmallenoughtoallowittoacta saviscous sealwhilestillbeinglargeenoughtoavoidcontactwiththecy linderovertheentire frequencyrangeofinterest.

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59 0 60 120 180 240 300 360 -8 -6 -4 -2 0 2 4 6 8 x 10-6 Phase (deg)Position (m) X component Y component Figure3{6:Typicalpistondriverlateraldisplacementat f =300Hz. 0 50 100 150 200 250 300 350 400 10-6 10-5 10-4 10-3 Frequency (Hz)RMS Position (m) X Direction Y Direction Figure3{7:LateralpistondriverRMSposition.

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60 SinusoidalController Onecriticalaspectofavoicecoildeviceisthedistortionint hepistonmotion r p ( t ).Whileatlowamplitudesandhighfrequenciesthepistonmot ionisfairlylinear, atverylowfrequenciesandathigheramplitudestheshapeoft hepistonmotioncan deviatesignicantlyfromsinusoidalgivenasinusoidalinput.F igure 3{8 showsthe pistonmotionacquiredwiththelaserdisplacementsensor,appro priatelycorrected forthephaselag,forCase2inTable 2{3 .Itisclearthatthepistonmotionisnot sinusoidal.InChapter 4 ,itisshownthatthisdistortionaectsthenatureofthe roweld.Therefore,tohavecondenceinexperimentalresul ts,asinusoidalpiston motionmustbeensuredasthisisthemostcommon\program"forsyn theticjet drivermotionandisthemostprevalentintheliterature. 0 60 120 180 240 300 360 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 Phase (deg)Voltage (V) Input Signal Piston Motion (mm) Figure3{8:Pistonmotiondistortion, f =18 : 5Hz. Giventheneedtohavesinusoidalmotionofthedriver,afeedba ckcontrolleris requiredwhichusespistonmotionasthefeedbacksignal.Adisti nctdisadvantage oftheshaker-drivendeviceisthatthepistondriver,beingsea ledinsidethecavity,

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61 provideslimitedaccessformeasurementofmotion.Theonlypr acticalwaytomeasurethepistonmotionisbymountingthelaserdisplacementsensor abovetheslot toachieveopticalaccessofthepistonasshowninFigure 3{9 .Clearlythissetup isimpracticalforsimultaneouslyacquiringroweldmeasurem ents,whetherrowvisualizationorquantitativevelocitydata,duetotheblocka gepresentedbythelaser displacementsensor.Thesinusoidalcontrollermustthereforebe ofafeed-forward natureinwhichfeedbackisrstinitiallyusedtoobtainaninp utwaveformwhich generatesasinusoidalsignal,thenthiswaveformisusedasthei nputtotheamplier duringroweldmeasurements. Figure3{9:Schematicoflaserdisplacementsensor. Themethodofemployingthesinusoidalcontrollerisasfollow s.First,thepiston motionisacquiredforsinusoidalinputsovertheentirefrequ encyandamplituderange ofinterestinordertocharacterizethedevice.Ithasalread ybeenstatedthatthe frequencyrangeofinterestis0
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62 viarowvisualizationwhichshowedthatatthemaximumvoltage input,nosignicant rowwasachievedoutofthesyntheticjetdeviceabove400Hz.Th eamplituderange isxedaccordingtothemaximumcurrentof1 : 8ARMSwhichcorrespondsroughly to6Vpp.Sincetheimpedanceseenbytheoscillatingpistonisafu nctionoftheslot geometry,aseparatecharacterizationmustbeperformedfore achslotconguration. InFigure 3{10 ,thenormalizedRMSpistonpositionisplottedvs.frequency.Ab ove 100Hz,thedatacollapsetoasingleline,thusforadesiredRMSpi stonpositionat agivenfrequencyfor h=d =1 : 46,thisquantitydictatestherequiredRMSvoltage inputtotheshaker.Atlowerfrequenciesthereissomescatteri nthedata,butan averagevaluemaybetakentocomputetheinitialestimateoft herequiredRMS voltageinput. 0 50 100 150 200 250 300 350 400 100 101 102 103 Frequency (Hz)Normalized RMS position (Vpp/mm) 1 Vpp 2 Vpp 3 Vpp 4 Vpp 5 Vpp 6 Vpp Figure3{10:Pistoncharacterizationfor h=d =1 : 46. Thepurposeofthesinusoidalcontrolleristogenerateawavefo rmwhichgivesa sinusoidalpistonmotionataparticularfrequencyandamplitu de.ThedesiredfrequencyandamplitudearedeterminedfromthedesiredReynold snumberandStrouhal

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63 number.Since d and arexed,thismeansthatforagiven Re U 0 isdetermined. Thenforadesired St ,thefrequencyofoscillation isdetermined,anditremainsto determinethevoltageamplitudeofpistonmotionfromthegiv en U 0 .Thisiseasily donebymakinguseofthepistoncharacterizationfromFigure 3{10 ,andassuming continuitybetweenthepistonplateandtheslot,whichisexpl ainedindetailnext. Letthesinusoidalpistonmotionbedescribedby r p ( t )= R p cos( !t )(3.1) where R p istheamplitudeofthepistondrivermotion,andthecosineisu sedbecause forincompressiblerow,thepistonmotionwillbe90 outofphasewiththevolume rowrate.Let R p bedenedasthestrokeofthepistonduringeitherexpulsionor ingestion.Forsinusoidalmotion, R p isidenticallyequaltotheamplitudeasshown inEq.( 3.1 ).However,ifthemotionofthepistonisnotsinusoidal,thevalu eofthe pistonstroke R p mustbetakenashalfthetotalstroke,whichisthedistancebetw een thepointofmaximumexpulsionandmaximumingestion.Thisisd onetoensure thatthevolumeexpelledisidenticallyequaltothevolumei ngested{anecessary conditionforaZNMFdevice. Returningtothecaseofsinusoidalpistonmotion,foracircular pistonofradius R D ,thetotalchangeinvolume 8 duringthehalf-cycle(forincompressiblerow)is 8 =2 R 2 D R p (3.2) ThefactoroftwoinEq.( 3.2 )arisesbecausethetotalpistonderectionduringexpulsion(oringestion)istwicetheamplitude.Forsimplicity,aslu gvelocityprolewhich variessinusoidallyintimewithamplitude U A shallnowbeassumedatthesurfaceof theslot,suchthatbycontinuity 8 =2 R 2 D R p = Uwd (3.3)

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64 ThentheRMSpositionofthepistonissimply R p = p 2andasstatedinChapter 2 U 0 istheRMSvelocityattheslotsuchthat U =(2 = ) U A and U 0 = U A = p 2therefore U = 2 p 2 U 0 (3.4) andsubstitutingEq.( 3.4 )intoEq.( 3.3 )andsolvingfortheRMSpistonposition gives R p p 2 = wdU 0 !R 2 D (3.5) Giventhegeometricparametersofthedeviceandthedesired U 0 and asdetermined bythedesiredReynoldsandStrouhalnumbers,thedesiredRMSpi stonposition cannowbecomputedandtogetherwiththepistoncharacteriza tionasshownin Figure 3{10 ,thisyieldsthenecessaryRMSvoltageoftheinputsignal. Next,thepistonmotionisacquiredphase-lockedtotheinputsig nalwiththe laserdisplacementsensorandappropriatelycorrectedforthep haselag.Bothsignals aresimultaneouslysampledtoeliminatephaseerrorsduetodata acquisition.The signalsareacquiredusingtheDAQsystemdescribedpreviously.Th esamplerate issetsuchthat100samplesareacquiredperperiod,phase-locke dtothefunction generatorinputsignal,andveperiodsareaveragedtocreat ethepistonmotion waveform.Thetotalharmonicdistortion(THD)ofthiswavefor misdeterminedby ttingaFourierserieswithinitially7harmonicsusinganonlinearleastsquares algorithmtothepistonmotion.Letthesquarerootofthe2-squa rednormofthe residualofthettedsignalappropriatelynormalizedbythea mplitudeofthepiston motionwaveformbedenedas r t .If r t islargerthan1%,anotherharmonicisadded andanewFourierseriesisgenerated.Harmonicsarecontinual lyaddeduntil r t falls below1%,ensuringthattheFourierseriesisanaccuraterepre sentationofthepiston motion.ThentheTHDiscomputedastheratioofthetotalpower inallofthe harmonicsintheFourierseriestothepowerinthefundamenta l.

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65 IfthemeasuredTHDisaboveapredeterminedthreshold,thenane rrorsignal iscalculatedbydividingeachpointinthesinetbythecorre spondingpointinthe actualpistonmotion.Toavoidlargeructuationsinthecontr oller,thiserrorsignal isthenclippedatapreviouslyspeciedlevel,whichisanalog oustosettingasmall valueof k p inaproportionalcontrollertoavoidinstability.Thisclip pederrorsignal isthenmultipliedbytheinputsignal,andanew,distortedinp utsignalresults. Theamplitudeofthepistonmotionisalsocomputedandtherati oofthedesired amplitudetothisquantityisdeterminedtoappropriatelysc aletheamplitudeofthe inputsignal.Thenewdistortedinputsignalisthenfedtothesha ker,andthenew pistonmotionisacquiredwiththelaserdisplacementsensor.The processrepeats untiltheTHDfallsbelowthedesiredthreshold.Theentireproc edureisdepicted schematicallyinFigure 3{11 .Figure 3{12 showstheresultingwaveformgenerated bythesinusoidalcontrollerforthesamecaseasFigure 3{8 .TheTHDoftheinitial pistonmotionis0 : 823%,whiletheTHDofthenalpistonmotionis0 : 0067%,adrop inTHDofnearlytwoordersofmagnitude.Qualitatively,the nalpistonmotionalso appearssinusoidal. Table3{3:Before-andafter-PIVpistonmotion. Case BeforeTHD(%) AfterTHD(%) RMSDis-placementBefore(mm) RMSDis-placementAfter(mm) RMSDis-placement%di. 10.00910.04550.6620.6961.2620.00670.03230.6630.6670.1330.00930.08210.6630.7051.5340.00840.04490.6660.7322.3550.01500.02030.7450.7440.0260.00910.12430.9861.0511.6170.00310.09870.8520.9292.1780.00860.02340.5730.5810.3790.00790.05380.4600.5172.90100.00850.01930.6070.6280.87110.00850.01850.6850.7050.72121.00881.13820.6330.6270.27

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66 H IJ KLM NLKILM O PQJ R J KSN H I J KLMJI T M UV W SM SX U KS YZ [ L\XISXJSXI SJ L] ^ U XNLMI ` J YZabc d eSJ f ` LN g \ KS hiO ^ L ^ j ^ k b l LN g \ KS SXX LX JI T M UV l V I g SXX LX JI T M UV m M g \ Kn Uo S]LXN p ` UV S IM g \ K JI T M UV q R SXX LX JI T M UV hiO V SJJK_ U MK_X SJ_L Vr LX N Us t I KSX U KILMJ X S U` _S r d eSJ ^ L [IM UV IM g \ K n Uo S] LXN Figure3{11:Sinusoidalcontrollerrowchart. 0 60 120 180 240 300 360 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 Phase (deg)Voltage (V) Initial Input Signal Initial Piston Motion (mm) Final Input Signal Final Piston Motion (mm) Figure3{12:Pistonmotionbeforeandaftersinusoidalcontrol f =18 : 5Hz.

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67 0 60 120 180 240 300 360 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 Phase (deg)Piston Motion (mm) Before PIV (THD=0.0067%) After PIV (THD=0.0323%) Figure3{13:PistonmotionbeforeandafterPIVmeasurements, f =18 : 5Hz. Whilethefeedforwardcontrolleddeviceisinvariantforth etimerequiredtocompleterowvisualizationandvelocitymeasurements,theshakerm otiondoeschange graduallyafterextendeduseovermanycycles.Forthisreason, thesinusoidalcontrollerisemployedimmediatelybeforebothacquisitionofr owvisualizationimages andvelocitymeasurementforeachcase.Thenthepistonmotioni sacquiredafter theexperimentforcomparison.Figure 3{13 showsthepistonmotionasmeasuredby thelaserdisplacementsensorbothbeforeandafterPIVacquisiti on.Whilethetwo signalsappearnearlyidentical,anexaminationoftheTHDrev ealsthatthepiston motionhasbecomemoredistorted.Thisisanunfortunatebutu navoidablesideeect ofthefeedforwardcontrollersetup.However,theTHDisstillqu itesmall,indicating theshapeisstillpracticallysinusoidal.Furthermore,therei sonlya0 : 13%dierence intheRMSpositionofthepistonbetweenbeforeandafterPIVme asurement.Consequently,accordingtoEq.( 3.5 ),theRMSvelocity U 0 alsoonlychangesby0 : 13%.

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68 Table 3{3 showthecomparisonofthepistonmotionbeforeandafterPIVmea surements.ThepercentdierenceinRMSpistonmotionislessthan3% forallcases.It isthereforeexpectedthattheslightchangesexhibitedinth epistonmotionduring velocitymeasurementdonotadverselyaecttheresultingrow eld.ThehighTHD inCase12isexpectedbecausethisisthe\uncontrolled"case. FlowVisualizationSetup Figure 3{14 illustratestherowvisualizationsetup.Alargetankmeasuring 600mmby600mmby1200mmisconstructedtohousethesyntheticje tassembly andtheresultingroweld.A600mmby600mmglassplateservesas theceiling, andthisplateisremovabletofacilitateevacuationofthese edparticlesfromthetank attheconclusionofanexperiment.Thetankwallsandceiling aremadeofglassto enableopticalaccesstotheresultingroweld.Theacousticre sonancefrequenciesof thetankarecomputedaccordingto Beranek ( 1993 ),andthelowestacousticresonance frequencyisfoundtobe143Hz,whichisbelowthemaximumfreq uencyofoperation ofthesyntheticjetof115Hz.Thus,acousticresonancesarenotex pectedtoadversely aecttheroweld.Thebottomofthetankisopentoallowfori nsertionofthe syntheticjetdevice.Aplatemadeofplywoodmeasuring525mmb y525mmserves astheroorofthetank,andthisroorisraised150mmoofthebo ttomsurface andsupportedwithopticalposts.Thebottomsurfaceisanoptica lbreadboardwith threaded1 = 4 20holesspacedeveryinch.Theglasstankitselfisalsoraised100 mm othebottomsurfaceandsupportedwithunistrutbars,tofacili tateinsertionofthe syntheticjetdevicefromtheunderside.Theroorplateiscare fullycenteredwith respecttothetankanda50mmdiametercircularholeiscutint heroorplateto allowthesyntheticjetslotexittoberush-mountedtotheroorp late.Theedgesof theroorplatearesealedtothewallsoftheglasstankusingduct tape,thusensuring thattheentiretankissealedandisolatedfromairrowcurrent sinthelaboratory.In addition,theentireopticaltableareaisenclosedusing6mil thickblackconstruction

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69 plastictofurtherisolatetheroweldfromtheairrowcurrent sinthelaboratory, aswellastominimizetheeectofexternallightsourcesinth elaboratorysuchas computermonitordisplays,LEDreadoutsofinstruments,etc. uv w xy z v { x |} z ~xy }€y x z ~ xy ‚ y } w x  ƒ z v { „ y v ~z z x{ ‚… xy v ~z z x{ †z ~ x{z }€y x ‡ v |… „ x |~… ~ w z x x v z v { † ƒ { |… x | v ˆx | ~  |€ ~ |}y |y ~ ‰ xy v {† |~†x |y ~ ‰ xy v { † |~†x x x „ x „ u z } ‡ uv xz „ z v †… | … xx | Š‹ ‹ ŒŒ  Ž‹‹ ŒŒ Figure3{14:Flowvisualizationsetupschematic. Thesyntheticjetdeviceismountedona2-axismanualtraverse whichhasa degreeoffreedominthe x -directiontoallowrush-mountingoftheslottotheroor plateandarotationaldegreeoffreedomaboutthe x -directionenablingviewsofeither the xy planeorthe xz planeasshowninFigure 3{15 .Becausethesyntheticjetslot ismountedpreciselyatthecenteroftheglasstankandbecauseo ftherelativelylarge sizeofthetankcomparedtotheslotdepth,recirculationcurr entsinthetankare minimized,andtheimagescapturedviarowvisualizationrep resentthetruenature ofaroweldgeneratedbyaZNMFdeviceexhaustingintoaquiesce ntmedium. ThelasersourceisaSpectra-Physics2020argon-ioncontinuou s-wattlaserwith anominalpowerlevelof3watts.Duetospacelimitations,thela serismounted onaseparateopticalbreadboardtable.Theopticalcomponen tsoftheLDAsystem (describedindetaillater)areusedtoextractthe514 : 5nmlineofthelaseranda

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70   ‘ Figure3{15:Syntheticjetcoordinatesystem. beropticcableisemployedtotransmitthislinetotheLDAla serprobeasshown inFigure 3{14 .ThefocusinglensoftheLDAprobeisremovedsuchthatthelaser beamrunsparalleltothebottomsurfaceinsteadoffocusingata nangletoapoint. The514 : 5nmlineischosenbecauseitexhibitsthehighestpowerofallth elinesin theargon-ionlaser.A 142mmfocallengthcylindricallensdivergesthebeamintoa lightsheet,anda500mmfocallengthsphericallensreducesth elightsheetthickness tolessthan1mmatthefocalpoint.Theopticsareappropriate lyplacedsuchthat thecenterofthesyntheticjetslotcoincideswiththefocalpo int,andthecenterof thelightsheetisprojectedontothe yz planesincethisisthelocationofmaximum intensityforaGaussianbeam.TheLDAprobeismountedonasingle stagetraverse toallowthelightsheettobepreciselypositionedatthecenter oftheslot,eitherin the xy planeorthe xz planedependingontheorientationoftheslotwithrespect tothelightsheet.Imagesareacquiredinthe xz planeprincipallytodeterminethe extenttowhichtherowistwo-dimensional. FlowvisualizationimagesareacquiredusingaNikonSLRD70out t6megapixel camerawithaNikonAFMicroNikkor200mmtelephotolenstoallow forhighly resolvedimagesoftherowneartheslot.Thiscameraisidealfo rrowvisualization becauseitmaybecontrolledremotelywithaPCviaaUSBinterfa ceandtheaperture openingandshutterspeedcanbothbecontrolledmanually.Ado vetailopticalrail (notshown)protrudesalongeitherthe y or z axisoftheslotdependingonthe orientationandthecameraismountedtothisrailviaoptica lpostsandamanual

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71 3-axislinearstagetraverse,whichallowsforpreciseposition ingoftheeldofview ofthecamerawithrespecttotheoriginofthecoordinatesystem ofthesyntheticjet device. ThetankisseededwithLeMaitrefogruidparticlesusingaTSIm odel9302 singlejetatomizer.Accordingtothemanufacturer'sspecica tions,theparticleshave ameandiameterof1 m.Theseparticlesarelargeenoughtobeobservedaspathlines intheroweldintherowvisualizationimagesbutarestillsmal lenoughtofaithfully followtherow.Thesectiononparticlesizinganddynamicspro videsmoredetailsto conrmthis. VelocityMeasurement Forroweldcharacterization,themostimportantmeasurable quantityofasyntheticjetdeviceisthevelocityeldinducedintheruidabo vetheslotexit.The velocityproleattheslotexit,ifmeasuredcarefully,yield sthejetReynoldsnumber. Inaddition,takingthecurlofthevelocityyieldsthevorti cityeld,whichmaybeused todeterminethebehavioroftheshedvortexpairs.Ifasignica ntlylargenumber ofvelocitymeasurementsareacquired,theninformationont heturbulentnatureof theroweldmayalsobededuced.Thus,itisimperativethatana ccuratetechnique beemployedtoacquirevelocitydata.Giventheunsteadynatu reofsyntheticjet rows,theinherentsmallgeometricsizeoftheslottoachievelow Stokesnumbers, andthepurelyoscillatorynatureoftherowattheslot,hotwir eanemometryisnot wellsuitedtothetask.Ahighspatialresolution,non-intrusive techniqueisdesired. BothParticleImageVelocimetry(PIV)andLaserDopplerAnemom etry(LDA),if properlyused,canyieldhighlyaccurateresultsfromwhichth eroweldgenerated bythesyntheticjetdevicecanbequantied.Ofteninthelite rature,thedetails ofthevelocitymeasurementtechniqueareabridgedoromitte dcompletely.Here,a completedescriptionofthesetwomethodsisgiventoassistinpro vidingathorough characterizationoftheresults.

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72 HotwireAnemometry WhilenotacceptableforquantitativemeasurementsofZNMFro welds,hotwire anemometrycanbeusefulforqualitativedeterminationoftu rbulentcharacteristics. Pastresearchers( Winter&Nerem 1984 ; Lodahl etal. 1998 )havenotedthephenomenonofconditionalturbulencearisinginpulsatilerows,d enedasoscillatory rowswiththesuperpositionofameanrow.Thisphenomenonhasn everbeeninvestigatedforsyntheticjetrowelds,andwouldprovidevaluabl einsightintothenature oftheserowelds.Figure 3{16 showsthehotwiresetup.Atwoaxistraverseisused topositionthewireatthecenteroftheslot,rightatthesurfac e.Velocitytraces arethenacquiredfromthehotwiresignalviathedataacquisit ionsystemdescribed later.Itisexpectedthattheanalysisofthesetracesforeach ofthecasesacquired willassistindeterminingthenatureoftheturbulenceinthere sultingroweld. ’ “” •– — • ™ š— • › — œ ™— Ÿ   ’ •¡ Ÿ œ — ¡ ’— – ¢ • £ ¡ — Figure3{16:Schematicofthehotwireanemometrysetup. ParticleImageVelocimetry Near-eldvelocitymeasurementsareacquiredabovethesurfac eofthesynthetic jetdeviceusingParticleImageVelocimetry(PIV).Theneareldisdenedasthe distanceextending2-3strokelengthsdownstreamoftheslot,wh ere1-2vortexpairs remainvisibleintheeldofview.ThesetupofthePIVsystemisne arlythesame astherowvisualizationsetupschematicshowninFigure 3{14 .Aphotographof thePIVsetupisshowninFigure 3{17 .Insteadofthefogruidasusedforrow

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73 visualization,thetankisseededwithincensesmokeforPIVmeasu rements.The incenseparticleshaveameandiameterontheorderofamicron ,andmoredetailson theparticlesizingisgivenlater.Astickofburningincenseis placedexactlyatthe centerofthetanktominimizetheestablishmentofrowrecircu lationpatternsinthe tank.Asinglesticktakesapproximately20minutestoburnand providesasucient densityofseedparticlesforPIVmeasurementsforaboutonehou r. ¤ ¦§¨ ¦¨ § ¤ ¦ § § ¦ § ¤ § ¤ § ¦ §¨ ¦ § § ¦ ¤ Figure3{17:PhotographofthePIVsetup. ThelasersourceconsistsofapairofNewWavemodelMinilase-IIINd: YAG lasers.Theselasersarettedontoasingleassemblyandalinearstag etraverseis usedtopositionthelightsheet,similartotherowvisualization setup.Thediameters ofthetwobeamsareboth3 : 5mm,andthepulsewidthisapproximately6ns.Internal opticsinthelaserassemblyalignthetwobeamssuchthattheyfol lowthesameoptical

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74 path.Thebeamsthenpassthrougha 6 : 35mmfocallengthcylindricallensanda 500mmfocallengthsphericallenstogeneratealightsheet.Th ewaistofthelight sheetoccursatthefocallengthofthesphericallens.Atthislo cation,thelightsheet is0 : 09mmthickwithadivergenceof6 : 82 m/mmalongtheopticalaxis.Alsoatthe waist,thelightsheetheightis272mmandtheheightdivergenc eis30degrees.Note thatthedirectionoftheprojectedlightsheetisnormaltoth edirectionoftherow, whichminimizesthererectivelightscatternearthesurfaceo ftheorice.Also,the centerofthelightsheetinthe x directionispositionedat x =0,duetotheGaussian intensityofthelightsheet. ATSImodel630157PowerviewPlus2MP10-bitCCDcameraisused tocapture images.Thiscameracontains1600 1200pixelswhicharespaced7.4 mapart. ThesameNikon200mmmicrolensusedforrowvisualizationisusedt ofocusand obtaintheimages.Thissetupallowsforexcellentspatialresol utionofapproximately 13 m/pixel,whichgivesaeldofviewintheverticaldirection ofabout6slotdepths downstreamofthesyntheticjetdevice. ThelaserpulsingandcameraexposureiscontrolledbyaTSIMode l610032 synchronizerwhichisconguredtoacquiretwo-framesinglee xposureimagesusing TSIINSIGHTSoftwareversion6.1.1.Inordertoachievethemini mumtimebetween pulses,thesynchronizertimesthepulseoftherstlasertooccura ttheendofthe exposuretimeofthecamerafortherstframe.Theimageisthen transferredoof thecameraCCDarraythroughshiftregisters,andthesecondlaser pulseoccursat thebeginningoftheexposuretimeofthecameraforthesecondf rame.Thisprocess isdepictedschematicallyinFigure 3{18 ,where dT representsthetimebetweenexposures.Thecorrectchoiceof dT isapplicationspecic.Forlowamplitudesynthetic jetrows, dT shouldbelargerthanforhigheramplitudesyntheticjetrows.T he timingoftheinitialcameratriggerpulsecanbecontinuous,a ndtherateatwhich imagepairsareacquiredislimitedonlybytherepetitionra teofthecameraand

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75 laser,whichis15Hz.Foraninherentlyperiodicrow,however, phase-lockedtiming isdesiredandcanbeachievedthroughtheuseofanexternaltri ggersourcefedinto thesynchronizer. Figure3{18:Framestraddlingtimingdiagramfortwo-framesi ngleexposurePIV. AblockdiagramoftheentirePIVsetupisshowninFigure 3{19 .Toacquire phase-lockedvelocityfromthePIVsystem,twoAgilentmodel331 20Afunctiongeneratorsareemployed.Therstfunctiongeneratorservesasth einputsignaltothe shakerviathepoweramplier,whilethesecondfunctiongener ator,phase-lockedto therst,isusedtotriggerthePIVacquisition.Whenphase-lock ed,itispossible toachieveadesiredrelativephasebetweenthetwofunctionge nerators.Hence,the phaseofthesecondfunctiongeneratorisadjustedasrequiredt oobtainthevelocity eldatthedesiredphase.Boththerstfunctiongeneratorsigna landtheoutput ofthelaserdisplacementsensorareacquiredbythedataacquisit ionsystemforthe sinusoidalcontroller.Thesesignals,alongwiththesecondfunct iongeneratorTTL triggersignal,areacquiredanddisplayedonaTektronixmode lTDS-2014digitaloscilloscopetofacilitatedeterminationoftherelativephase .Here,zerophaseisdened asthepointwherethevolumerowrateiszerowithpositiveslop e.Whilethisvalue cannotbequantitativelydetermined apriori ,itcanbeapproximatedasthetime

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76 inthecycleofthepistonmotionwherethemaximumderectiono fthepistonaway fromtheslothasoccurred.Thesignalfromthelaserdisplacemen tsensorispositive downwardasdepictedinFigure 3{9 ,thereforezerophaseistakenasapproximately thepointinthelaserdisplacementsignalexhibitingmaximumv oltage.Therelative phasingbetweenthetwofunctiongeneratorsisthenadjustedt ocorrespondtothis denitionofzerophase.Later,oncethevelocitydatahasbee nreduced,amore preciseestimateforzerophaseisfoundbyinterpolatingtheph ase-lockedvolume rowrate. "" "" " " " Figure3{19:BlockdiagramofthePIVsetup. ToverifythePIVtiming,bothfunctiongeneratorsignals,the laserdisplacement signal,theQ-switchsignalsfromthesynchronizertothelasers,a ndaphotodiode signalareacquiredphase-lockedontheoscilloscope.TheQ-swit chsignalsaretrigger signalsusedtoforcethelaserstoreapulse.Ablockdiagramoft hissetupisshown inFigure 3{20 Thepistonmotion,triggersignal,andbothQ-switchsignalsare showninFigure 3{21 foratypicalcaseataphaseof150 .ItisapparentthattheQ-switchsignals occurattheinstantaTTL-highsignalisachievedfromthetrig ger.Thisismore

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77 n r r n r r rn !" # $ % & % ( )* + -. / 01 2 / 3 n r 4 01 2 5 6 n rn r 01 2 7 01 2 7 r r r Figure3{20:BlockdiagramofthePIVtiming. 0 60 120 180 240 300 360 -2 -1 0 1 2 3 4 5 Phase (deg)Voltage (V) Piston Motion (mm) Trigger Signal Q-switch 1 Q-switch 2 Figure3{21:PistonmotionandPIVtriggersignalsforaphaseof 150

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78 easilyobservedinFigure 3{22 ,whichshowsboththesynchronizationbetweenthe triggersignalandtheQ-switchsignalsalongwiththemeasuredp hotodiodevoltage signal.Basedonthephotodiodesignal,itisapparentthatthel asersreattheinstant theQ-switchsignalstriggerthem.Itshouldalsobenotedthatth ewidthofeachlaser pulseisnotasindicatedbythephotodiode;rather,thesignal fromthephotodiode isprobablybestmodeledasasecondordersystemresponsetoanimpu lse;hence theapparentringinginthephotodiodesignal.Boththetimeb etweenpulses dT and thepulsedelaytime,denedasthetimebetweenthetriggerpu lseandtherstlaser pulse,wereveriedwiththissetup.Thepurposeofthepulsedela ytimeistoalign theexposuretimesofeachframeonthePIVcamerawiththeligh tsheetpulses. -400 -200 0 200 400 600 800 -12 -10 -8 -6 -4 -2 0 2 4 6 Time ( m s)Voltage (V) Trigger Signal Qswitch 1 Qswitch 2 Photodiode Signal Figure3{22:PIVlaserintensityacquiredfromaphotodiode. Althoughthepistonmotionhasbeencorrectedforitsphaselag; Figure 3{22 indicatesthatthereisstillaslighterrorinthephase,duetot hefactthattheactual phaseofthePIV-acquiredvelocitydataisbestestimatedasthem idpointbetween thetwoQ-switchsignals,ratherthanthestartofthetriggersign al.Forthiscase,

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79 theerrorbetweenthetriggersignalandthecenteroftheQ-swi tchsignalsisabout 300 s.Foratypicaloperatingfrequencyof50Hz,thiserroramount stoonly1 : 5%of theperiod.Whilethismayseeminsignicant,itisneverthele ssultimatelyaccounted forwhenthetruephaseiscomputedviathevolumerowratemeasu rements. Beforecomputingthevelocityeldforagivenimagepair,im agecalibrationis requiredtoobtainscalefactorsin m/pixel.Athinsiliconplatemeasuringoneinch byoneinchandperforatedwithagridofcircularholesisused forimagecalibration. Thefabricationoftheplateisatwostepprocess.First,achrome maskofthe gridofholesisgeneratedwitharesolutionontheorderofone micron.Second,the siliconplateismanufacturedfromthemaskusingphotolithogr aphyanddeepreactive ionetch(DRIE).Thisproceduregivesanexcellentaccuracy intheholespacingfrom whichPIVimagecalibrationcanbeaccuratelydetermined.T heprocessoffabrication ofthesiliconplateisdescribedindetailin Chandrasekharan etal. ( 2006 ). Withtheshakerremovedfromthetank,theplateismountedint heplaneofthe lightsheet.Arashlightfromabovethepositionofthecamerais usedtoilluminatea smallwhitebackgroundbehindthecenterofthetank(seeFigur e 3{17 ).Someofthe diusedlightfromthisbackgroundisscatteredthroughtheho lesandcapturedby thePIVcamera,thustheimagegeneratedappearsasregularl yspacedcircularholes ofhighintensitysurroundedbyadarkbackground.Anexampleca librationimage (showninafalsecolorscale)isshowninFigure 3{23 .Notethatthe x direction isverticalwhilethe y directionishorizontalinthisview.SincetheCCDarray measures1600pixelsby1200pixels,yetthesyntheticjetrowe ldexhaustsvertically, thecameraisrotated90degreestoallowformoreroweldinf ormationfurtheraway fromtheslot. OncethePIVcalibrationimageisacquired,thethresholdoft heholeedges mustbedeterminedbyplottingasliceoftheintensitythrought he y directionand determiningthesmallestintensityabovethenoiseroor.Anexamp lesliceisshown

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80 y (pixels)x (pixels) 200 400 600 800 1000 1200 1400 1600 200 400 600 800 1000 1200 0 1 2 3 4 5 6 x 104 Figure3{23:TypicalPIVcalibrationimage. inFigure 3{24 ,andfromthisdata,forthisexampleanintensitythresholdof 5000is appropriate. Anedgedetectionschemeisnextdevelopedtoultimatelydeter minethecenters oftheholesasfollows.First,theregionofexaminationofasin gleholeisdetermined byspecifyinganestimateoftheholediameterandthedistanceb etweenholesin pixelsviaFigure 3{24 .Next,slicesaremadehorizontallyacrosseachrowofpixelsto determinethetwopixelvaluesthatcrossthethresholdintensi ty,andthemidpoint betweenthesetwopixelvaluesistakenasasampleoftheholece nterinthehorizontal direction.Allrowsofpixelsarescannedmovingdownthehole, eachrowyielding anestimateofthehorizontalcenterofthehole.Themeanofth eseestimatesis thencomputedasthe y locationofthecenter.Theprocessisthenrepeatedinthe verticaldirectiontodeterminethe x locationofthecenter.Thiswholeprocessis thenrepeatedforeveryholeintheimage,asshowninFigure 3{25

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81 0 200 400 600 800 1000 1200 1400 1600 0 10,000 20,000 30,000 40,000 50,000 60,000 y (pixels)intensity Figure3{24:TypicalsliceofaPIVcalibrationimage. Everyhorizontalandverticalcombinationofdistancesbetw eenholesiscomputed inpixels,andeachoftheseyieldsacalibrationvaluein m/pixel.Astatistical distributionofthecalibrationcanthenbedetermined,sucht hatnotonlyisthe valueofthecalibrationcomputed,buttheuncertaintyinth ecalibrationiscomputed aswell.Figure 3{26 plotsahistogramofthecalibrationfortheimageofFigure 3{23 Inthiscasethecalibrationisdeterminedtobe12 : 999 0 : 00097 m/pixel. Thecomputationofthevelocityeldbeginsbydividingthei mageintoagridof interrogationwindows.Thesewindowsare32 32pixels.Toincreasethenumberof resultingvectors,a50%overlapisemployedwhicheectively yields16pixelsbetween vectors.Thevelocityisdeterminedbytheknowndistancethat aparticleisdisplaced (asdeterminedbytheimagecalibration)duringtheknownti me dT .Specically,a fastFouriertransform(FFT)cross-correlationprocessisutili zedinconjunctionwith aGaussianpeaksearchalgorithm.Thedetailsofthisprocessare internaltothe INSIGHTsoftware.Avelocityvectorisacceptedforaninterrog ationwindowifthe

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82 y (pixels)x (pixels) 200 400 600 800 1000 1200 1400 1600 200 400 600 800 1000 1200 0 1 2 3 4 5 6 x 104 Figure3{25:PIVcalibrationimageshowingholecenters. 12.96 12.97 12.98 12.99 13 13.01 13.02 13.03 13.04 0 10 20 30 40 50 60 70 Calibration ( m m/pixel)Counts Figure3{26:HistogramofatypicalPIVcalibration.

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83 valueofthemaximumpeakisatleast50%higherthanthenexthi ghest(noise)peak andisatleast10timeshigherthanthenoiseroor.Atotalof100 imagepairsare acquiredatagivenphase,andthecycleisdividedevenlyamon g15phases;thus thereareatotalof2400imagepairswhichareprocessedtogene ratevectorelds. Unlikeconventionalvalidationschemeswhichusespatiallter ingtoremovespurious vectors,anovelmultivariateoutlierrejectiontechniquei semployedoneachofthe 100velocitysamplesateverypointintheimagedomain,forev eryphase.Thedetails ofthistechniqueareprovidedinAppendix E LaserDopplerAnemometry Althoughusefulforfull-eldmeasurements,PIVhasitsownuniq uesetoflimitations.Mostimportantly,currentdatastoragelimitsdictatet hatonlyasmallnumber ofvelocitysamplesmaybeacquiredateachpoint.Althoughthe condenceinthe velocitydataacquiredwiththecurrentPIVsetupishigh,asec ond,independent velocitymeasurementtechniquewouldproveusefultovalidat ethePIVdata.For thisreason,LaserDopplerAnemometry(LDA)measurementsareacq uiredforselect cases,andcanserveasacheckagainstPIV-obtainedresults.Figure 3{27 showsa schematicoftheLDAsystem,thedetailsofwhicharefoundinTab le 3{4 Thesameenclosureisusedtohousethesyntheticjetandtheresulti ngroweld, andthesameincensesmokeisusedtoprovideseedparticles.TheLDA probeis mountedonamotorizedtwo-axistraversetoallowpreciseposit ioningoftheprobe volumeovertheslot,bothinthe x and y directions.Thelasersourceisthesame Spectra-Physics2020argon-ionlaserthatwasusedforrowvisua lization.Thebeam isseparatedinto488nmand514 : 5nmwavelengthsfortwo-component,coincident velocitymeasurementsusingaDantecFiberFlowsystem.Thetwob eamsarethen eachsplitforatotaloffourbeamsandaBraggcellisusedtogen eratea f 0 = 40MHzshiftingfrequencyintwoofthebeamstoeliminatedirec tionalambiguity inthevelocitymeasurements.Thetwounshiftedbeamsaretheno pticallyaligned

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84 Table3{4:LDAmeasurementdetails. PropertyLDA1LDA2 Wavelength(nm)514.5488Focallength(mm)401.9401.9Beamdiameter(mm)1.351.35Expanderratio11Beamspacing(mm)26.8726.87Numberoffringes2525Fringespacing( m)7.7007.303 Beamhalf-angle(deg)1.9151.915Probevolume{dx(mm)0.1950.185Probevolume{dy(mm)0.1950.185Probevolume{dz(mm)5.8375.537 89 :; < = > ?9 :@ A BC<9 C< F GH B I = C E9 B J <9 C< Figure3{27:SchematicoftheLDAsetupforsyntheticjetveloc ityeldmeasurement.

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85 andtransmittedalongasingleberopticline,whiletheshifte dbeamstravelalong separateberopticlines.Thethreebeamsthenreachtheprobe ,wheretheyare focusedusinga401 : 9mmsphericallenstoaprobevolume.Thisistheso-calledthre e beamcombinerconguration,whichisusefulformakingveloc itymeasurementsvery neartosolidsurfaces,andisshownschematicallyinFigure 3{28 .Adirectioncosine matrixmustthenbeappliedtotheacquiredvelocitycomponen tsLDA1andLDA2 toextracthorizontalandverticalvelocity.Aphotographo fthe3-beamcombiner congurationoverthesurfaceofthesyntheticjetslotisshowni nFigure 3{29 K L MN O P MQNR S O T UV WX U SQ Y WZZ SQ N O[Q \ O] [L [ ^ O UV WX U SQ [S T WZ Z SQ N O[Q_ R S ^` O ` MLR a MS ^ [b ]b [ SO \ c S ^` O ^ R deO ^ [d ^f [ ^ ML gh i V gh i j k f l m L MS ^ k R O no p M] qR O n \ R T O qR O n Figure3{28:LDA3-beamopticalcongurationfornear-surfa cevelocitymeasurements. TheLDAsystemisoperatedinthebackscattermode,whichsimpli esthealignmentandsetupsincethereceivingopticsarecontainedwithin thesameprobeassemblyasthetransmittingoptics.Tocheckthequalityoftheacqu iredDopplerbursts,

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86 Figure3{29:PhotographoftheLDA3-beamcombinersetup. anoscilloscopewasusedtomeasurearawburst.Atypicalburstissho wninFigure 3{30 .Notethatnotonlyisthebursteasilydetectable,butthenumbe roffringes intheburstis24-25,whichcorroboratesthesetupparameters ofTable 3{4 Oncethebackscatteredlighttravelsthroughthereceivingo ptics,acolorseparatorsplitsthe514 : 5nmand488nmwavelengthsandtransmitsthelighttotwo separatephotomultipliertubes(PMTs).ThePMTsconverttheD opplersignalto avoltage,anditisthenpassedthroughahigh-passltertoremo vetheDoppler pedestal.Thesignalisthenadditionallylteredwithabandpassltertoremove noiseinthesignaloutsideoftheexpectedvelocityrange.Next, theFFTsofthe signalsarecomputed,andtheDopplerburstisvalidatedbyensu ringthatthepower inthehighestpeakisatleastfourtimesgreaterthanthepower inthenexthighestpeak.OncetheDopplerfrequency f D isdetermined,thevelocityiscomputed accordingtotheformula u pv =( f D f 0 ) l 2 sin ( = 2) (3.6)

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87 -50 -40 -30 -20 -10 0 10 20 30 40 0 0.05 0.1 0.15 0.2 0.25 Time (s)PMT Voltage (V) Figure3{30:RawDopplerburstcreatedbythepassageofapartic lethroughthe probevolume.where l isthewavelengthofthelaserlightand = 2isthebeamhalfangle.Finally, sincetwocomponentsofvelocityaremeasured,acoincidence lterisappliedtoensure thataDopplersignalispresentonbothchannelsatthesameinsta ntintime. SinceLDAisapoint-by-pointmeasurementtechnique,fulleldvelocityinformationcannotbeacquiredsimultaneously;rather,thetraversin gprobemustbemoved frompointtopoint.Nevertheless,theprincipleadvantageofL DAisthatwitha sucientlyhighdatarate,manymorevelocitysamplescanbeac quiredatapointin spacethanispracticallypossiblewiththePIVsystem.ThustimeresolvedinformationmayalsobedeterminedfromLDAvelocitydataifthedatar ateishighenough. LDAsurveysareperformedatthesurfaceoftheslotandatapprox imately y=d =5 downstream,correspondingtotheminimumandmaximumrangeso fthePIVdata. Inaddition,velocitymeasurementsinthe xz planeareacquirednearthesurfaceof

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88 theslottodeterminethetwo-dimensionalityoftheroweldin thevicinityofthe oricealongwiththerowvisualizationimages. ParticleSizingandDynamics SincebothPIVandLDArequireseedparticlesforvelocitymea surement,great caremustbetakentoensurethattheparticlesfaithfullyfoll owtherow.Thisis becausethevelocityoftheroweldisnotactuallymeasured;i tisthevelocityof theseedparticlesthatismeasured.Aspreviouslystated,theman ufacturerofthe atomizerusedforrowvisualizationreportsameanparticlesiz eontheorderofone micron.Atypicalparticlesizeforincensesmokeis1 2microns. Onceparticlesizeisdetermined,thefrequencyrangeofunste adyandturbulent rowsmustbedeterminedatwhichtheparticlesfaithfullytra cktherow.Inastudy whichmodeledthemotionofparticlesinaturbulentruid, Hjelmfelt&Mockros ( 1966 )showedthataparticlesizeof2 misacceptableforfrequenciesupto10kHz. Sincetheactuationfrequenciesforallsyntheticjetcasesar eontheorderof100Hz orless,itisexpectedthattheseedparticlesuseddoindeedfoll owtheroweld.Thus anyresultsderivedfromvelocitymeasurementswillinfactbe avalidindicatorofthe actualsyntheticjetroweld. UncertaintyAnalysis Inordertogaugetheaccuracyofthevariouscomputedparame terssuchas Reynoldsnumber,Strouhalnumber,anddimensionlesscircula tion,theuncertainty intheseparametersmustbeestimated.Severalfactorscontrib utetotheoveralluncertaintyofthesemeasurements.First,thereisuncertaintyin themeasuredvelocity valueswhichmaybeanalyzedusinggeneraluncertaintyanaly sisandMonteCarlo methods( Coleman&Steele 1999 ).Second,thereisuncertaintyinthesequantities duetothevelocitymeasurementsbeingobtainedatanitedist anceothesurface oftheslot.Third,becauseofthespatialdiscretizationandsubse quentnumerical integration,thereisuncertaintyintheseparametersdueto spatialresolutioneects.

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89 Finally,becauseofthephaseresolutionof15degreesbetweenm easurements,there isatemporaldiscretizationeectwhichcontributestotheu ncertaintyofthemeasurements.Eachofthesecontributionstotheuncertaintyisco nsiderednext. AMonteCarloanalysisisperformedtoevaluatetheuncertain tyintheReynolds number,Strouhalnumber,anddimensionlesscirculation.Wit hknowledgeofthe meanandstandarddeviationofthevelocityateachpoint,ara ndomvalueisgenerated which(withsucientnumberofpoints)hasanormaldistributio ncorrespondingto themeanandstandarddeviationatthatpoint.Arandomvaluei sgeneratedfor eachpointandthecorrespondingvelocityscale(orvorticity rux)iscomputedvia integration.Theprocessisthenrepeatedtoyieldanotherva lueofthevelocityscale (orvorticityrux).Withsucientrepetition,thelocusofth esecomputedvalues themselvesformanormaldistributionfromwhichmeanandstand arddeviationvalues ofthenalquantitiesmaybeextracted.Thisthenisameasure oftherandomerror contributiontothesequantities. Figure 3{31 showsatypicaldistributionofthevelocityscale U 0 forCase1, Re =43, St =0 : 84, h=d =1 : 46.Theuncertaintyisapproximately0.4%ofthe meanvalueof U 0 .Thisuncertaintyisquitelow,likelyduetothefactthatth e doubleintegrationofthevelocityprolemitigatestheee ctoftherandomnoise intheindividualvelocitymeasurements.Usinggeneraluncerta intyanalysis,the uncertaintyintheReynoldsnumberis U Re = s @Re U 0 2 U 2 U 0 (3.7) wherethevaluesoftheslotdepth d andthekinematicviscosity havebeenassumed exactly.From( 3.7 ),itcanbeseenthatthepercentuncertaintyin U 0 isequivalentto thepercentuncertaintyin Re .FortheStrouhalnumber,generaluncertaintyanalysis reveals U S t = s @St U 0 2 U 2 U 0 (3.8)

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90 whichalsoreducestotheuncertaintyinthevelocityscale.Th usthepercentuncertaintyin U 0 isalsothepercentuncertaintyinboththeReynoldsnumberan dthe Strouhalnumber. 0.212 0.213 0.214 0.215 0.216 0.217 0 50 100 150 200 250 300 350 U 0 (m/s)Counts Figure3{31:TypicalhistogramfromMonteCarlosimulationof U 0 Figure 3{32 showsatypicaldistributionofthecirculationforthesameca se consideredpreviously.Theuncertaintyhereissignicantlyh igherthantheuncertaintyin U 0 ,approximately9.6%.Howeverthisisbecausethevalueofthec irculation isclosetozeroandhencethepercentuncertaintybecomeshig h.SincetheMonte Carlosimulationrequirescomputationofthevorticityusing perturbedvelocityvalues,theuncertaintyismagniedbydierentiatingtheveloc itytoobtainvorticity. Theuncertaintyinthedimensionlesscirculation isfoundusinggeneraluncertainty analysisasbefore, U = s U 2 + U U 0 U 0 2 (3.9)

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91 -2.8 -2.6 -2.4 -2.2 -2 -1.8 x 10-3 0 50 100 150 200 250 300 G (m 2 /s)Counts Figure3{32:TypicalhistogramfromMonteCarlosimulationof Table3{5:Uncertaintycontributionduetorandomerrorofve locitymeasurements. Case U 0 (m/s) ReSt 10.21 5 : 01 10 4 43 0 : 200.84 3 : 84 10 3 3.58 0 : 34 20.43 8 : 73 10 4 84 0 : 340.86 3 : 46 10 3 2.04 0 : 27 30.81 4 : 51 10 3 161 1 : 770.78 8 : 58 10 3 2.98 0 : 86 41.43 1 : 63 10 2 280 6 : 280.80 1 : 80 10 2 2.38 1 : 75 52.84 4 : 14 10 2 555 15 : 840.81 2 : 32 10 2 0.91 2 : 30 60.82 5 : 97 10 3 159 2 : 270.53 7 : 56 10 3 4.95 1 : 52 70.80 4 : 43 10 3 155 1 : 690.63 6 : 90 10 3 3.86 0 : 99 80.77 5 : 16 10 3 154 2 : 021.00 1 : 31 10 2 1.50 0 : 83 90.71 5 : 65 10 3 139 2 : 191.30 2 : 05 10 2 0.15 0 : 84 100.95 8 : 35 10 3 175 3 : 020.73 1 : 26 10 2 4.22 1 : 96 110.88 5 : 26 10 3 161 1 : 880.79 9 : 18 10 3 2.55 0 : 85 120.72 3 : 13 10 3 143 1 : 230.88 7 : 53 10 3 2.33 0 : 64

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92 Table 3{5 showsthe95%condenceintervalsin U 0 Re St ,and foreachcase ofPIVdataasdescribedinChapter 4 .Itisapparentthattheuncertaintyinthe dimensionlesscirculationisquitelargeforthehighestReyno ldsnumberandhighest Strouhalnumbercases. Toevaluatetheuncertaintyduetothevelocitymeasurements beingtakenanite distanceothesurface,thepercentdierencebetweenquanti tiesintegratedoverthe extentoftheslotandquantitiesintegratedtotheno-slipcon ditionisobtained.To determinetheno-slipcondition,thelimitsofintegrationa redenedasthepoints wherethetotalvalueoftheintegralisbetween1%and99%.Ta ble 3{6 shows thispercentdierenceforboth[ u ( A;t )] 2 and u z foreachcase.Itisapparent thatthesquaredvelocityerrorisverysmall,whileitissigni cantforthevorticity rux.Nevertheless,thesepercentagesarenotablysmallerthanth oseofTable 3{5 suggestingthatthisno-slipeectisnegligiblecomparedtoth erandomnoiseinthe velocitymeasurements. Table3{6:Percentdierenceforno-slipintegrationandslot integration. Case[ u ( A;t )] 2 u z 10.11%7.71%20.01%15.10%30.05%6.99%40.14%9.32%50.20%21.50%60.14%6.16%70.17%7.84%80.07%12.70%90.66%24.60%100.03%6.78%110.53%19.70%120.08%9.82% Next,theuncertaintyduetospatialresolutionisevaluatedby consideringthe LDAvelocitydata.Sincetheresolutionofthesevelocitymeasu rementsistwice asgoodasthePIVmeasurements,comparisonbetweenthecompute dvelocityscale

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93 usingjusthalftheLDAmeasurementsofthevelocityproletoth efullvelocityprole isareasonableindicatorofthesensitivityoftheuncertainty tospatialresolution. Unfortunately,thisinformationisonlyavailableforoneca se,Case3, Re =161, St =0 : 84, h=d =1 : 46.However,itisexpectedthattheothercases,beingnear thisnominalcaseintheparameterspace,wouldhavesimilarresu lts.Thepercent dierencebetweenthePIV-computedandLDA-computedReynold snumbersand Strouhalnumbersare0 : 008%and0 : 009%,respectively.Remarkably,thisverysmall dierenceindicatesthatthespatialdiscretizationissucie nt,andnotexpectedto adverselyaecttheuncertaintymeasurements. Finally,theeectofphaseresolutionisexaminedbycomparin gtheintegration ofthesquareofaperfectsinewaveoveronecycletothesquareof anapproximated sinewavewithaphaseresolutionof15degrees,theresolutionused forthisstudy. Exactintegrationgives Z T 0 [sin( !t )] 2 dt =0 : 5(3.10) whilenumericalapproximationofthisintegralwithaphaser esolutionof15degrees givesavalueof0.4986.Thus,itisexpectedthatthediscretiz ationofthephaseresults inanuncertaintyofabout0.3%forallcases,forthevelocitym easurements.Since thevorticityruxisalsoaperiodicsignal,itisexpectedthat thiserroriscomparable. Theinvestigationofthesefoursourcesofuncertaintyhasshown thattheuncertaintyinthecomputedquantitiesisduechierytotheran domcomponentofthe velocitymeasurements.Spatialresolutionandtemporalresolu tioneectsarenegligible,asistheerrorduetotheintegrationofquantitiesat anitedistanceothe surface.TheuncertaintyintheReynoldsnumbersandtheStro uhalnumbersarelow forallcases,whiletheuncertaintyinthedimensionlesscircul ationishigher,especiallyforthehigherReynoldsnumbercases.Thisislikelydue totheuncertaintyin thevorticitycalculation,andabettervorticitycalculat iontechnique( Soria 1996 ) couldimprovethis.

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CHAPTER4 RESULTSANDDISCUSSION Thischapterpresentssomeofthekeyndingsobtainedbyopera tingtheshakerdrivensyntheticjetdevicedescribedinChapter 3 .Hotwireanemometryvelocity tracesareusedtogiveinitialestimatesoftheparameterspace andtodetermine thenatureoftheroweldneartheslot.Flowvisualizationpho tographsqualitatively documenttheroweldregions.LDAmeasurementsareacquireda tthesurfaceofthe slottoquantifythevelocityeld.Finally,PIVmeasurements areperformedforall casesinthetestmatrixofTable 2{3 .Velocity,vorticity,circulation,andturbulence quantitiesareanalyzedandtheirimpactdiscussed. DeviceCharacterization InordertodeterminethetestmatrixofcasesofTable 2{3 ,theshaker-driven ZNMFdevicemustrstbecharacterizedinsomemannersuchthatthe envelopeof theparameterspaceisdened.Initially,thisisdoneusingho twireanemometryto obtaininitialestimatesoftheReynoldsnumberandStrouhal number.First,the maximumoutputofthedeviceisdeterminedbymountingaslotp latewithvery small d =1mm,andmeasuringtheRMScenterlinevelocityatseveral x=d locations. Thisisdonetodeterminehowwelltheoutputofthecurrentsha ker-drivenZNMF devicematchestheresultsofotherstudieswhichtypicallyre portpeakvelocitieson theorderof10 50m/s.Figure 4{1 revealsthattheshakerdeviceiscapableof achievingapproximately25m/sRMSvelocityatthesurfaceof theslot,whichis comparabletodevicesusedinotherstudies.Itshouldbenotedth atthehotwire signalisnotderectiedbeforetheRMSvelocityiscomputed; hencethisquantityis onlyaqualitativeestimateoftheoutputofthedevice.Howeve r,thevoltageinput 94

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95 requiredtoachievethisrowisontheorderof6Vrms,whileoth erelectrodynamic shaker-drivendevicesrequiredoublethisvoltagetoachiev esimilarresults. 0 2 4 6 8 10 12 14 16 100 101 102 x/dU RMS (m/s) Figure4{1:CenterlineRMSvelocityvs. x=d Tochecktheperformanceenvelopefromwhichtodevelopthet estmatrix,the frequencyrangeofthedeviceissetaccordingtopreliminary rowvisualizationexperimentstoensurethatonlytherangewhichyieldsinterestingr oweldsfromarow controlperspective(laminarjets,turbulentjets,etc.)isco nsidered.Thentheamplitudeisvarieduptothemaximumallowablevaluewithoute xceedingthecurrent limit.Theshakerdeviceisnotsinusoidal-controlledinthesec ases,sinceatthispoint measurementsareperformedonlytoobtaininitialestimates.F igure 4{2 showsthe performanceenvelopeoftheshakerinfrequency-velocitypa rameterspace.ThesevaluesarethenconvertedtoestimatesoftheReynoldsnumberand Strouhalnumberby computinganestimateof U 0 ,theRMSvelocityattheslot,fromthehotwirevelocity traces,asshowninFigure 4{3 .Notethatthepeakoutputoftheshakerdeviceat agivenvoltageinputisafunctionofbothReynoldsnumberan dStrouhalnumber.

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96 0 50 100 150 200 250 300 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 Frequency (Hz)U RMS (m/s) 1 Vrms 2 Vrms 3 Vrms 4 Vrms 5 Vrms 6 Vrms Figure4{2:Hotwirevelocitycharacterization, h=d =1 : 46. 10-1 100 101 102 101 102 103 Strouhal NumberReynolds Number 1 Vrms 2 Vrms 3 Vrms 4 Vrms 5 Vrms 6 Vrms Test Matrix Figure4{3: Re St parameterspaceenvelopewithtestmatrixvaluessuperimposed, h=d =1 : 46,thejetformationthresholdisindicatedbythesolidverti calline.

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97 Withthetestmatrixsuperimposed,itcanbeseenthatthecasescho sencoverawide rangeoftheparameterspaceenvelopeoftheshakerdevice.Whi lethereisalarge regionofhighStrouhalnumbersthatisnotconsidered,itmust berememberedthat thispartoftheparametermapisbelowthejetformationthre shold( St 1forjet formation)andthereforeisnotexpectedtoyieldinterestin groweldsfromarow controlperspective. Preliminaryrowvisualizationisemployedtochecktherowto pologyandthe nominalcase, Re U 0 =161, St U 0 =0 : 78, h=d =1 : 46,ischosenbecauseitexhibits transitionaljet-likecharacteristics.CaseswhichyieldReyn oldsnumber,Strouhal number,andslotheight-to-depthaspectratiosweepsarethenc hosenforcomparison tothenominalcase.Itisimportanttonotethatthisprocessis quiteinvolved becauseitisiterative{requiringvelocitymeasurementtode terminethelocationin theparameterspace,andthenrowvisualizationtodeterminet heroweldtopology. Theprocessisrepeateduntilthedesiredpointsarefoundinth eparameterspace. Figure 4{4 illustratesthethree-dimensionalparameterspacemap.Theno minalcase iswherethethreelinesintersect. AtypicalhotwirevelocitytraceisshowninFigure 4{5 ,forCase1, Re =43, St =0 : 84, h=d =1 : 46.Thewireispositionedjustinsidethesurfaceoftheslot alongthecenterline y =0.Thesignalappearssimilartoarectiedsinewave,due tothedirectionalambiguity.Expulsionoccursduring0 << 180 ,whileingestion occursduring180 << 360 .Thedierenceinthepeaksindicatesthatthe velocityduringexpulsionishigherthanthatofingestion.How ever,thevelocityvalues reportedaresuspectattheminimumvaluesbecauseoftheinaccu raciesassociated withhotwireanemometrydiscussedinChapter 3 .Nevertheless,withasucient numberofcyclesacquired,thesetracescanyieldinformatio nonthephase-dependent turbulentbehavioroftherowattheslot,andthisisexamined next.

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98 10-1 100 101 10-1 100 101 101 102 103 Strouhal Number h/d Reynolds Number Figure4{4:Threedimensionalparameterspaceoftestmatrixca ses. 0 60 120 180 240 300 360 0.36 0.38 0.4 0.42 0.44 0.46 0.48 0.5 Phase (deg)Hotwire Velocity (m/s) Figure4{5:Typicalhotwirevelocitytrace, Re =43, St =0 : 84, h=d =1 : 46.

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99 Figure 4{6 showsthephase-dependentturbulenceintensityforthecasesma king uptheReynoldsnumbersweep.Onethousandphase-lockedhotwir evelocitytraces areacquiredandaveraged,andtheturbulenceintensityatea chpointinthecycleis denedasthestandarddeviationofthese1 ; 000samplesdividedbytheRMSvelocity. Sincethevelocityvaluesmeasuredbythehotwirearesuspect,i tmustberemembered thatthisisonlyaqualitativeproceduretodeterminethena tureoftheturbulence, andthatthevaluescomputedarenotquantitative. Overall,theturbulenceintensityincreaseswithReynoldsnu mber,asexpected andthisagreeswiththerowvisualizationphotographsshowni nthenextsection.For thethreelowestReynoldsnumbers,thereisasharpdropinthetu rbulenceintensity betweenexpulsionandingestion,whentherowisessentiallyqui escent.Atthetwo highestReynoldsnumbers,however,thereisnodrop,suggesting thatturbulenteddies persistintheslotevenwhenthereisnonon-zerophase-averaged row.Evenmore interestingforthesecasesisthataftertheturbulenceintensi tyreachesitsminimum valueduringthesuctionpartofthecycle,itbeginstorisedur ingexpulsionand reachesamaximumduringtheearlypartofexpulsion, 30 ,beforequicklyfalling again.Thiscouldbeindicativeofconditionalturbulencei napurelyoscillatory row,andwhilethisphenomenonhasbeenrecognizedandrepor tedintheliterature forpulsatilerows( Winter&Nerem 1984 ; Lodahl etal. 1998 ),ithasneverbeen reportedforapurelyoscillatoryrow.Amorequantitativean alysisoftheturbulence oftheseroweldsisundertakenlater. TheturbulenceintensityforthecasesoftheStrouhalnumbersw eepisshownin Figure 4{7 .Whilethereisvariationinturbulenceintensitysimilartot heprevious casesexamined,namelythattheturbulenceintensitydropsto verylowvaluesbetween expulsionandingestion,itisapparentthatthereisnotassign icantachangeinthe overallturbulenceintensitybetweencasescomparedtotheRe ynoldsnumbersweep.

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100 0 60 120 180 240 300 360 10-5 10-4 10-3 10-2 10-1 100 Phase (deg)Turbulence Intensity Re=43 Re=84 Re=161 Re=280 Re=555 Figure4{6:Phase-dependentturbulenceintensity,Reynolds numbersweep, St =0 : 8, h=d =1 : 46. 0 60 120 180 240 300 360 10-3 10-2 10-1 100 Phase (deg)Turbulence Intensity St=0.53 St=0.63 St=0.78 St=1.0 St=1.3 Figure4{7:Phase-dependentturbulenceintensity,Strouhal numbersweep, Re =160, h=d =1 : 46.

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101 ThissuggeststhatturbulenceeectsinZNMFrowsareindepende ntoftheStrouhal number. Consideringnextthechangeinslotheight-to-depthaspectrat io,Figure 4{8 thesamedropinturbulenceintensitybetweenexpulsionanding estionisobserved. Furthermore,itappearsas h=d decreases,theoverallturbulenceincreases.Once again,thisiscorroboratedbytherowvisualizationphotogr aphsinthenextsection. Thelargeincreaseinturbulenceintensityatthebeginningof ingestionfor h=d =0 : 32 isprobablyduetoturbulenteddiesfrompreviouscyclesbei ngreingested. Finally,examiningFigure 4{9 ,whichcomparesturbulenceintensitywithand withoutsinusoidalcontrol,theoverallturbulenceintensity ofthetwocasesarevery similar.However,itappearsthatthepeaksofhigherturbulen ceintheuncontrolled caseareduetothepresenceoftheharmonicsinthedistorteddri vermotion.Again, thisconclusionisreasonablewhenconsideringtherowvisualiz ation,whichindicated thattheuncontrolled,distorteddrivermotionprogramresul tedinamoreturbulent row. FlowVisualization UsingthesetupforrowvisualizationdescribedinChapter 3 ,Figure 3{14 ,photographsareacquiredforeachcaseinboththeXYplaneandtheXZ plane(dened usingthecoordinatesystemofFigure 3{15 )andReynoldsnumbervariationsareexamined.Theexposuretimeforallimagesis1 = 30s,andtheaperturewasadjusted toensuretheoptimumcontrastbetweentheparticlesandtheba ckground. TheroweldsgeneratedbytheZNMFactuatorarethoroughlyqu antiedin theXYplane,asdescribedlater.Whiletherowremainsfairlyt wodimensionalat leastuptotheorderofastrokelengthdownstreamfromtheslot,a highlythreedimensionalpatterneventuallyemergesforallcases.Theimag esoftheroweldin theXZplaneareincludedheretodeterminetheextentoftwo-d imensionality.Let thetwo-dimensionalitybequalitativelydenedastheregio noverwhichtheobserved

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102 0 60 120 180 240 300 360 10-3 10-2 10-1 100 Phase (deg)Turbulence Intensity h/d=0.32 h/d=1.46 h/d=3.32 Figure4{8:Phase-dependentturbulenceintensity, h=d sweep, Re =160, St =0 : 8. 0 60 120 180 240 300 360 10-2 10-1 100 Phase (deg)Turbulence Intensity Controlled Uncontrolled Figure4{9:Phase-dependentturbulenceintensitywithandwi thoutsinusoidalcontrol, Re =160, St =0 : 8, h=d =1 : 46.

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103 pathlinesintheimageremainparallelandthewidthoftheje tisatleasttwothirds oftheslotwidth.Table 4{1 showsthelimitoftwo-dimensionalityintermsofthe dimensionlessdistancedownstreamoftheslot.Alsoincludedisthe dimensionless RMSparticleexcursion L=d .Fromthistableandthesubsequentphotographsfound below,itisapparentthatthetwo-dimensionalitydoesnotsca lewithasingleparameter.However,ingeneralforveryshortstrokelengths(largeS trouhalnumber)and forverysmallslotheight-to-depthaspectratios,thetwo-dime nsionalityisconned toonlyaboutoneslotdepthdownstream.Conversely,forveryla rgestrokesorlarge h=d ,thetwo-dimensionalityextendsquitefar. Table4{1:Two-dimensionallimitofZNMFroweldsbycase. Case Re U 0 St U 0 h=d 2Dlimit( x=d ) L=d 1430.841.462.67.52840.861.465.67.331610.781.462.08.042800.801.461.37.855550.811.461.97.761590.531.463.011.971550.631.462.29.981541.001.460.76.391391.301.461.14.8101750.730.320.98.6111610.793.324.58.0121430.881.461.27.1 InFigure 4{10 andFigure 4{11 ,thepathlinesgeneratedbytheZNMFdevice forCase1intheXYplaneandXZplaneareshown,respectively.The eldofview is23mminthe x direction(vertical)by35mminthe y direction(horizontal)for theXYplane,and43mminthe x direction(vertical)by65mminthe y direction (horizontal)fortheXZplane.Astationaryvortexpairstructu reisapparentatabout 1slotdepthdownstreamoftheslot,andthepathlinesofseedpart iclescaughtinthe vortexduringtheexposuretimeofthecameraareclearlyvisib le.Thereisverylittle entrainmentofruidintothejetintheXYplane,asevidencedb ythenearlystationary

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104 Figure4{10:FlowvisualizationphotographofCase1intheXYpl ane, Re U 0 =43, St U 0 =0 : 84, h=d =1 : 46. Figure4{11:FlowvisualizationphotographofCase1intheXZpl ane, Re U 0 =43, St U 0 =0 : 84, h=d =1 : 46.

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105 Figure4{12:FlowvisualizationphotographofCase2intheXYpl ane, Re U 0 =84, St U 0 =0 : 86, h=d =1 : 46. Figure4{13:FlowvisualizationphotographofCase2intheXZpl ane, Re U 0 =84, St U 0 =0 : 86, h=d =1 : 46.

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106 pathlinesofparticlesoutsidethejetwidth.However,thegro wthofthejetwidthin theXYplaneindicatessomeentrainmentofruid,andinameansen se,thisroweld appearsremarkablysimilartoalaminarjetaspathlinesinth ejetremainessentially paralleltooneanother.Thereisalsoaclearvectoringofthe jettowardtheleftof theimage.Itisbelievedthatthisvectoringiscausedeither byslightrecirculating currentsinthetank,slightimperfectionsintheslotplate,o rsomecombinationof both.Althoughthecurrentsinthetankareweak,Case1isavery weakjetandso ismorelikelytobeinruencedbythesecurrents. ForCase2,whichcorrespondstoalmostdoubletheReynoldsnumb erofCase1, thevortexstructuresarestillvisibleneartheslotsurfacebuta renowslightlymore chaotic,asseeninFigure 4{12 fortheXYplaneandFigure 4{13 fortheXZplane. Thejetbehaviorisstilllaminar,howeverthenarrowjetappe arstosuddenlyexpand atabout3slotdepthsdownstreamintheXYplane,andthencontin uesgrowing asruidisentrainedintothejet.Someruidisdrawntowardth eslotneartheslot surface.Thisjetisnowstrongenoughsuchthatweakrecirculat ioncurrentsdo notcausevectoring.Thetwo-dimensionalityofthejetextend sconsiderablyfurther downstreamthanthepreviouscase. Figure 4{14 showstheroweldintheXYplaneforCase3,withahigher Re U 0 = 161and St =0 : 8,denotedasthenominalcase.TheXZplaneisshowninFigure 4{15 andtheregionoftwo-dimensionalityhasnowshrunkcomparedt othepreviouscase. IntheXYplane,ruidcontinuestobedrawnmoretowardtheori cethanentrained intothejetitself,butnowthisisevenstronger,likelyaresul tofthesuctionpartofthe cycle.Avortexpairstructureisstillvisible,butisnowat2slo tdepthsdownstream oftheslotandcontinuestoappearmorechaotic.Therowinthe vicinityofthe vortexstructuresalsoappearsmoreerraticandturbulent.How ever,by3slotdepths downstream,vortexstructuresarenolongervisibleandasudden expansionofthe jetangleensues,theshearlayerofwhichisclearlyvisibleasth epathlinestraced

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107 Figure4{14:FlowvisualizationphotographofCase3intheXYpl ane, Re U 0 =161, St U 0 =0 : 78, h=d =1 : 46. Figure4{15:FlowvisualizationphotographofCase3intheXZpl ane, Re U 0 =161, St U 0 =0 : 78, h=d =1 : 46.

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108 Figure4{16:FlowvisualizationphotographofCase4intheXYpl ane, Re U 0 =280, St U 0 =0 : 80, h=d =1 : 46. Figure4{17:FlowvisualizationphotographofCase4intheXZpl ane, Re U 0 =280, St U 0 =0 : 80, h=d =1 : 46.

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109 outbytheparticlesoutsidethejetareveryshortcomparedtot hoseinsidethejet. Throughouttheentireimagedomainthepathlinesneartheco reofthejetremain parallel.Alsoofinterestisanapparentstagnationpointinthe jetrowalongthe centerlineatabout1slotdepthawayfromthesurface,abovewh ichthejetemerges. Asimilarobservationwasmadeby Yehoshua&Seifert ( 2003 ),andisduetothe suctionpartofthecycle.Thiscaseisdeemedatransitionaljet ,exhibitingneither purelylaminarnorpurelyturbulentcharacteristics. ThejetstrengthcontinuestoincreaseastheReynoldsnumberi sincreasedto 280whiletheStrouhalnumberremainsxedinCase4,showninFi gure 4{16 forthe XYplaneandFigure 4{17 fortheXZplane.Thedrawingofruidfromoutsidethe jettowardtheslotcontinuesintheXYplane,butruidalsoconti nuestobeentrained intothejet,andapossiblestagnationpointcanstillbediscerne dclosetothesurface oftheslot.Thechaoticpathlinesthroughouttheentireimag edomainindicatethejet isbecomingincreasinglyturbulent.Consequently,theregio noftwo-dimensionality hasbeenreducedfurtherfromthepreviouscase. TheroweldgeneratedbyCase5,withthehighestReynoldsnumb erequalto 555,isshowninFigure 4{18 fortheXYplaneandFigure 4{19 fortheXZplane. OnceagainruidisdrawntowardtheslotintheXYplane,butstron gentrainmentis alsoobserved,bothintheXYplaneandtheXZplane.Here,thebound aryofthejet isnotasdistinguishableasthejetisclearlyturbulentthrou ghouttheimagedomain. Nevertheless,thejetemergesfromtheslotandexpandsrapidly, thestagnationpoint observedpreviouslyisnolongervisible.Thetwo-dimensionali tyisnowessentially unchangedfromthepreviouscase,andextends1 2slotdepthsdownstream.Thus, itcanbeseenthatasallthejetparametersarexedandonlyth eReynoldsnumber isvaried,aninitiallylaminar-likejetundergoestransiti onaroundaReynoldsnumber of160,andthenultimatelybecomesaturbulent-likejet,ju stasforsteadyjets.

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110 Figure4{18:FlowvisualizationphotographofCase5intheXYpl ane, Re U 0 =555, St U 0 =0 : 81, h=d =1 : 46. Figure4{19:FlowvisualizationphotographofCase5intheXZpl ane, Re U 0 =555, St U 0 =0 : 81, h=d =1 : 46.

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111 Figure4{20:FlowvisualizationphotographofCase6intheXYpl ane, Re U 0 =159, St U 0 =0 : 53, h=d =1 : 46. Figure4{21:FlowvisualizationphotographofCase6intheXZpl ane, Re U 0 =159, St U 0 =0 : 53, h=d =1 : 46.

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112 Strouhalnumbervariationsareperformedaboutthenominal caseandtherow visualizationrevealsinterestingchangesintheresultingro welds.Case6,thelowest Strouhalnumber, St =0 : 53,andnominalReynoldsnumber Re =160,alsohas thehigheststrokelengthandsothevortexstructureshereappea rmuchfurther downstream,atabout4slotdepths.TheXYplanerowvisualization isshownin Figure 4{20 ,andtheXZplanerowvisualizationisshowninFigure 4{21 .The stagnationpointhasmovedslightlyfurtherdownstreamcompar edtothenominal case,andtheregionoftwo-dimensionalityhasbeenextendedf urtherdownstream. Whileforothercasesentrainmentofruidintothejettendsto bederectedslightly awayfromtheshearlayerofthejetandtowardthevicinityoft heslot,herethe ruidisdrawnnearlycompletelyinthedirectiontowardthesl ot.Thisisespecially apparentintheupperhalfoftheimageoutsideofthejet,aspa thlinesrevealruid beingdrawntowardtheslotevenverynearthevicinityofthesh earlayerwhere itwouldbeexpectedtobeentrainedandthenconvectedaway. Thisisduetothe relativelylargestrokelengthofthedriver,whichallowsth eeectsofthesuctionpart ofthecycletobefeltfurtherawayfromtheslot.Thejetwidth islargerthanthe nominalcase,andthejetitselfappearsmoreturbulent;thoug hnotnearassoas Case5. Asthestrokelengthisreduced(andhencetheStrouhalnumberi sincreasedto 0 : 63)forCase7,thejetbeginstoappearmorelaminar-to-transi tionalasshownin Figure 4{22 fortheXYplane,andFigure 4{23 fortheXZplane.Thevortexpair structureshavemovedslightlymoretowardtheslot,ashasthest agnationpoint. Thetwo-dimensionalityinthiscaseisessentiallyunchangedfr omthepreviouscase. Thereisstillevidenceofruidbeingpreferentiallydrawnto wardtheslotasopposed tobeingentrainedintothejet,butnowonemaynotewhatappe arstobealarge recirculationpatternintheentireimagedomainleftofthe jetintheXYplane.Once

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113 Figure4{22:FlowvisualizationphotographofCase7intheXYpl ane, Re U 0 =155, St U 0 =0 : 63, h=d =1 : 46. Figure4{23:FlowvisualizationphotographofCase7intheXZpl ane, Re U 0 =155, St U 0 =0 : 63, h=d =1 : 46.

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114 Figure4{24:FlowvisualizationphotographofCase8intheXYpl ane, Re U 0 =154, St U 0 =1 : 0, h=d =1 : 46. Figure4{25:FlowvisualizationphotographofCase8intheXZpl ane, Re U 0 =154, St U 0 =1 : 0, h=d =1 : 46.

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115 againthisisthoughttobeduetothelargestrokelengthinrue nceonthesuction partofthecycle. Themeanpositionofthevortexpaircontinuestomovecloserto theslotas theStrouhalnumbercontinuestoincreasetoavalueof1forCa se8,showninthe XYplaneinFigure 4{24 andtheXZplaneinFigure 4{25 .Thestagnationpointis slightlymorediculttodiscern,andithasmovedclosertothesl otintheXYplane. Herethejetappearssomewhatweakerandthevectoringeectdu etorecirculationin thetankmanifestsitselfonceagain.Thedrawingofruidtowar dtheslot,whilestill signicant,isnotassevereastheprevioustwocasesexamined. Theroweldisclearly three-dimensionalbeyondaboutoneslotdepth,andaninterest ingthree-dimensional patternmanifestsitselfaroundthecornersofthejet.Anymeasu rementsacquiredfar fromtheslotsuchasvelocityorvorticitymustberegardedason lysemi-qualitative. InCase9, St =1 : 3,Figure 4{26 fortheXYplaneandFigure 4{27 fortheXZ plane,aninterestingrowpatterndevelopswhichdoesnotapp earasajetatall; rather,thereappearstoberuiddrawntowardthesurfaceanda nerraticplumeof pathlinesemanatingfromtheslotintheXYplane.TheXZplanesho wsacomplex recirculatingpatternwithajetcorenearthecenterlinean drecirculationoverthe outerthirdoftheslotoneitherside.IntheXYplane,apossiblesta gnationpointis locatedatabouthalfaslotdepthawayfromtheslot,andslightl yo-centertothe left.However,sincetheStrouhalnumberherehasincreasedabo veone,itisquite possibletheregionofjetformationhasbeencrossed( Holman etal. 2005 )andany furtherincreasesinStrouhalnumberwouldresultinnosignic antrow.Thus,as theStrouhalnumbervariesforaxedReynoldsnumber,theex tenttowhichruidis drawntowardtheslotvs.entrainedintothejetalsovaries.Ifat hresholdStrouhal numbervalueisexceeded,thennorowresults. Changesintheslotheight-to-depthaspectratioareobservedb yxingthe ReynoldsnumberandStrouhalnumberattheirnominalvalues of Re =160and

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116 Figure4{26:FlowvisualizationphotographofCase9intheXYpl ane, Re U 0 =139, St U 0 =1 : 3, h=d =1 : 46. Figure4{27:FlowvisualizationphotographofCase9intheXZpl ane, Re U 0 =139, St U 0 =1 : 3, h=d =1 : 46.

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117 Figure4{28:FlowvisualizationphotographofCase10intheXYp lane, Re U 0 =175, St U 0 =0 : 73, h=d =0 : 32. Figure4{29:FlowvisualizationphotographofCase10intheXZp lane, Re U 0 =175, St U 0 =0 : 73, h=d =0 : 32.

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118 St =0 : 8andexaminingtheroweldsusingdierentslotplateswhichh avedierent h=d .InFigure 4{28 h=d =0 : 32,Case10,theXYplaneisshown.TheXZplane forthiscaseisshowninFigure 4{29 ,andthetwo-dimensionalityagainonlyextends aboutoneslotdepthdownstream.Itcanbeseenthataverythinslo tplateresults inaveryturbulentrow,similartothehigherReynoldsnumber rows.Thismaybe duetothedominanceof\minor"lossesintherowintheslotwhich islikelynotfully developed.Henceturbulentvortexstructuresarereingestedd uringsuction,andthen reintroducedtotheroweldduringthenextexpulsionstroke. Withaverylargeslotheight, h=d =3 : 32,Case11{Figure 4{30 fortheXY planeandFigure 4{31 fortheXZplane{aweaker,thin,laminar-likejetemerges fromtheslot.Italsoappearsthesuctionstrokestronglyinruenc estheroweldas ruidisdrawntowardtheslot,andalargerecirculationpatte rnappearstotherightof thejet,similartoCase7inFigure 4{22 .Itisalsointerestingtonotethattheregion oftwo-dimensionalitynowextendsfardownstream.Theseresult stendtosuggest thatstrongervortexstructuresareejectedintotheroweldf orsmaller h=d ,though thetrueparameterwhichaectsthisislikely L 0 =h ( Gallas etal. 2004 ),theratioof theparticleexcursionattheslottotheslotheight. InCase12, Re U 0 St U 0 h=d ,andeven 8 =d 3 arematchedtothenominalcase, butthepistonmotionprogramisallowedtobedistorted,toobse rvechangesinthe roweldduesolelytothisdistortion.Figure 4{32 showsthepistonmotionprogram, whichisclearlysinusoidalforCase3butdistortedforCase12.Fr omTable 3{3 ,the totalharmonicdistortionforCase12istwoordersofmagnitud ehigherthanthatof Case3. Figure 4{33 showstheresultingroweldforthisdistortedcaseintheXYplane whichcertainlyappearsmoreturbulentthanthatofthenomi nalcase,Figure 4{14 TheroweldintheXZplaneisshowninFigure 4{34 ,whichappearsremarkably similartotheroweldintheXZplaneforthesinusoidal-control ledcase,Figure 4{15

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119 Figure4{30:FlowvisualizationphotographofCase11intheXYp lane, Re U 0 =161, St U 0 =0 : 79, h=d =3 : 32. Figure4{31:FlowvisualizationphotographofCase11intheXZp lane, Re U 0 =161, St U 0 =0 : 79, h=d =3 : 32.

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120 0 60 120 180 240 300 360 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 Phase (deg)Piston Motion (mm) Case 3 Case 12 Figure4{32:PistondistortionbetweenCase3(THD=0.0093)andC ase12 (THD=1.0088).Thereisstillastagnationpointataboutoneslotdepthdownstre amofthesurface intheXYplane,butbothentrainmentofruidintothejetandth edrawingofruid towardtheslotsurfacearemarkedlystronger.Perhapsmoststrik ingistheturbulent natureofthejet.Thisisthoughttooccurduetoharmonicdist ortionsinthepiston motionmanifestingthemselvesashigherfrequencydisturbanc eswhichmorerapidly breakdowntoturbulence.Thisobservationunderscorestheim portanceofensuring adesireddrivermotionprogramandthedangerinassumingthatt heinputsignal programcorrespondstothedrivermotionprogram. LaserDopplerAnemometry ToincreasethecondenceinthePIVvelocityeldmeasurement sandthesubsequentcomputedquantitieswhicharediscussedindetailinthe nextsection,LDA isperformedveryclosetothesurfaceoftheslotat x=d =0 : 07forthenominalcase, Case3, Re U 0 =161, St U 0 =0 : 78, h=d =1 : 46,andcomparedtothePIVdataat

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121 Figure4{33:FlowvisualizationphotographofCase12intheXYp lane, Re U 0 =143, St U 0 =0 : 88, h=d =1 : 46. Figure4{34:FlowvisualizationphotographofCase12intheXZp lane, Re U 0 =143, St U 0 =0 : 88, h=d =1 : 46.

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122 -1.5 -1 -0.5 0 0.5 1 1.5 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 y/d( u +~ u ) =U 0(Click to play movie) PIV LDA Figure4{35:PIV-LDAcomparisonofstreamwiseexitvelocitypro lemovie, Re U 0 = 161, St U 0 =0 : 78, h=d =1 : 46. -1.5 -1 -0.5 0 0.5 1 1.5 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 y/d( u +~ u ) =U 0 PIV LDA (a) -1.5 -1 -0.5 0 0.5 1 1.5 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 y/d( u +~ u ) =U 0 PIV LDA (b) -1.5 -1 -0.5 0 0.5 1 1.5 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 y/d( u +~ u ) =U 0 PIV LDA (c) -1.5 -1 -0.5 0 0.5 1 1.5 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 y/d( u +~ u ) =U 0 PIV LDA (d) Figure4{36:PIV-LDAcomparisonofstreamwiseexitvelocitypro lestillframes, Re U 0 =161, St U 0 =0 : 78, h=d =1 : 46,(a)0 ,(b)90 ,(c)180 ,(d)270

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123 x=d =0 : 12.InFigure 4{35 ,amovieofthephase-averagedstreamwisecomponentof velocityattheexitplane,normalizedby U 0 ,isshowncomparingthePIVandLDA measuredvelocities.Notethatallanimationsinthisstudyarea ctivatedbyclicking onthegure.Providedwitheachanimationisagureofthe4p hases0 ,90 ,180 and270 .Figure 4{36 showsthesestillframes.Acounter-clockwiserotatingphasor isincludedintheanimation,wherethephaseangleofthephaso rcorrespondstothe phaseangleofthevolumerowrate.Zerophase,then,correspond stothepointof zerovolumerowratewithpositiveslope;i.e.,thebeginningo ftheexpulsionpartof thecycle.TheLDAvelocitymatchesreasonablywelltothePIV velocity,although itisnotassymmetricasthePIVvelocityaboutthecenterline y=d =0.SinceLDA isapoint-by-pointtechnique,andtheexperimentmeasuredt hevelocityfromleftto right,itispossiblethatthepistonmotionchangesslightlydur ingtheexperiment, andthisisareasonablecauseofthisasymmetry. Thephase-averagedcross-streamvelocityatthesurfaceoftheslo tcomparedbetweenPIVandLDAfor Re U 0 =161, St U 0 =0 : 78, h=d =1 : 46isshowninFigure 4{37 StillframesofthiscaseareincludedinFigure 4{38 .Again,theagreementisquite goodoverthesurfaceoftheslot,buttheslightasymmetryintheL DAvelocityprole isapparent. Thephase-lockedvolumerowrateisdeterminedforboththePI VandLDA velocityproles,andthiscomparisonisillustratedinFigure 4{39 .Theagreementis excellentbetweenthetwomethods,andthecomputedReynolds numbersdierby only5%.Itshouldalsobenotedthattheseexperimentswereperf ormedseveralweeks apart,indicatingtherepeatabilityoftheshakerdevice.Ano therimportantnoteis thattheLDAparametersweresettoobtainanorderofmagnitud emorevelocity pointsperphasethanthePIV.Sincetheresultsmatchupwell,th issuggeststhat 100phase-averagedvelocityeldsissucienttoaccuratelyr epresenttheroweld.

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124 -1.5 -1 -0.5 0 0.5 1 1.5 -1.5 -1 -0.5 0 0.5 1 1.5 y/d( v +~ v ) =U 0(Click to play movie) PIV LDA Figure4{37:PIV-LDAcomparisonofcross-streamexitvelocitypr olemovie, Re U 0 = 161, St U 0 =0 : 78, h=d =1 : 46, x=d PIV =0 : 15 ;x=d LDA =0 : 07. -1.5 -1 -0.5 0 0.5 1 1.5 -1.5 -1 -0.5 0 0.5 1 1.5 y/d( v +~ v ) =U 0 PIV LDA (a) -1.5 -1 -0.5 0 0.5 1 1.5 -1.5 -1 -0.5 0 0.5 1 1.5 y/d( v +~ v ) =U 0 PIV LDA (b) -1.5 -1 -0.5 0 0.5 1 1.5 -1.5 -1 -0.5 0 0.5 1 1.5 y/d( v +~ v ) =U 0 PIV LDA (c) -1.5 -1 -0.5 0 0.5 1 1.5 -1.5 -1 -0.5 0 0.5 1 1.5 y/d( v +~ v ) =U 0 PIV LDA (d) Figure4{38:PIV-LDAcomparisonofcross-streamexitvelocitypr olestillframes, Re U 0 =161, St U 0 =0 : 78, h=d =1 : 46, x=d PIV =0 : 15 ;x=d LDA =0 : 07,0 corresponds totheonsetofexpulsion,(a)0 ,(b)90 ,(c)180 ,(d)270

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125 0 50 100 150 200 250 300 350 -3 -2 -1 0 1 2 3 4 5 x 10-3 Phase (deg)Volume flowrate (m 3 /s) PIV LDA Figure4{39:PIV-LDAcomparisonofphase-averagedexitvolume rowrate. -0.03 -0.02 -0.01 0 0.01 0.02 0.03 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 z (mm)Vertical Velocity (m/s) Figure4{40:Phase-averagedLDAvelocityprolesintheXZpla ne,thevertical dashedlinesindicatetheextentoftheprobevolume,thevert icalsolidlinesindicate theextentoftheslotdepth.

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126 Animportantcaveattothisanalysisistheresolutionofthevel ocitymeasurements.WhilethePIVvelocitydataisacquiredinaplanewitht hicknessontheorder of100micronsinthespanwise z -direction,theLDAprobeextendsnearly6mmin the z -direction.Therefore,LDAvelocitymeasurementsareacqui rednear x=d =0in theXZplanetodeterminethetwo-dimensionalityoftheveloci ty.Figure 4{40 shows thephase-averagedvelocityprolesacrossthecenterofthesl otintheXZplane.The dashedlinesindicatetheextentoftheprobevolume,whileth esolidverticallines indicatetheextentoftheslotdepth.Itcanbeseenthattherow remainsrelatively two-dimensionalovertheentireslot,withtheexceptionofth eslotcornerswhereend eectsareclearlynoticeable.Thevelocityprolesherear ebiasedlowandareonly qualitativebecausetheprobevolumeinthe y -directionextends1 : 5mmoneither sideoftheslot.Nevertheless,theseresultsindicatethereismini malvariationinthe velocityprolealongtheslot,consistentwiththerowvisualiz ationobservations. ParticleImageVelocimetry ThroughtheuseofPIV,theroweldemanatingfromatwo-dimensi onalZNMF devicemaybethoroughlyquantied.AsdescribedinChapter 3 ,100phase-locked PIVimagepairsareeachobtainedfor24phaseswitharesolutio nof15 foreach case.Velocityvectoreldsaregenerated,andthevelocityv ectorateachpointis completelycharacterizedviaatripledecomposition( Davis&Glezer 2000 ; Kotapati etal. 2006 )as u p = u p +~ u p + u 0p (4.1) where u p isthevelocitymeasuredexperimentallyatagivenpoint, u p isitsaverage velocityoveranentirecycle,whichisindicativeofthemea nrow,~ u p isitsphaseaveragedvelocity,and u 0p istheructuatingcomponent.Notethatthevelocityat eachpointcontainstwocomponents, u p and v p .Foreachpointinthedomain,then, thereisameanvelocity,24phase-averagedvelocities(onep erphase),and2 ; 400ructuatingvelocities(100perphasetimes24phases).Typically, PIVdataarespatially

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127 validatedandthentherejectedvectorsarelledinviainte rpolation.Herehowever, beforethemeanandphase-averagedquantitiesarecomputed, multivariateoutlier rejectionisemployedtoremovespuriousvelocityvectors.Th istechniqueismorereliablethanspatialvalidation,especiallywhenconsideringt urbulencequantities(see Appendix E ). Inthefollowingsections,thevelocity,Reynoldsstress,andtur bulentkinetic energyeldsarenormalizedby U 0 .Thevorticityeldsarenormalizedby .Table 4{2 providesthesefrequenciesandRMSvelocitiesofallcasesfor convenience.Also includedis U ,thespatial-averaged,time-averagedstreamwisecomponento fvelocity duringtheexpulsionpartofthecycle,measuredatthesurfaceo ftheslot.The variationbetweenthesetwovelocityscalesissmall;however, themomentumrow velocityscale U 0 isusedbecauseitismoregeneral. Table4{2:Frequencyandvelocityvaluesbycase. CaseFrequency(rad/s) U 0 (m/s) UU 0 = U 158.20.210.191.122116.40.410.371.113203.70.800.721.114363.71.391.271.095727.42.762.591.076135.60.790.731.087158.60.770.701.108248.40.760.681.139293.20.690.641.0710222.40.900.801.1311234.90.850.811.0512203.70.710.611.15 Velocity Atypicalphase-lockedmovieofthemeanplusphase-averagedv elocityeld u p +~ u p isshowninFigure 4{41 forthenominalcase, Re =161, St =0 : 78, h=d =1 : 46. Figure 4{42 showstheseframesfromtheanimation.Everyothervectorispl ottedas arrowsforclarity{anexcellentspatialresolutionallowsfo rapproximately15vectors

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128 tobeacquiredoverthesurfaceoftheslot.Theperiodicexpulsi onandingestionat thesurfaceoftheslotisapparent,asistherollingupandadve ctiondownstreamof avortexpaironeithersideoftheslot. Theresultsofrowvisualizationmaybefurtherveriedbyconsi deringcontour plotsofthemeanstreamwisecomponentofvelocity u p foreachcase.Forallcontour plotsinthisstudy,thelowest-valuedcontourlinecorrespond stothenotedincrement. Inallcases,thevelocityiszeroatthesurfaceoftheslot,asexp ectedforaZNMF device.Figure 4{43 ,Case1, Re =43, St =0 : 84showsajet-likerowwhichbegins expandingimmediatelyafterexitingtheslot.Thepointofma ximumvelocityoccurs alongthecenterlineofthejet,atabout x=d =1 : 5,andisequaltoabout60%of U 0 Thejetvectorstotheleft,perhapsduetotheinruenceofrec irculationeectsinthe tankapparatus,asnotedintherowvisualizationimage,orthe vectoringisdueto asymmetriesinthecavity/slot( Utturkar etal. 2002 ).Anotherpossibilityisthatby thispointdownstream,three-dimensionaleectsbegintodom inate.Thereisalsoa weaknegativevelocitycomponentoneithersideoftheslot. InFigure 4{44 ,Case2,withReynoldsnumberdoubledto Re =84,thestrength ofthejethasgrown,andthebeginningsofjetgrowtharenoti ceableat x=d =2. Thepointofmaximumvelocityisunchanged,andthisjet,whi lestrongerthanthe previouscase,stillvectorsslightlytotheleft. Figure 4{45 showstheverticalvelocityforCase3, Re =161.Thepointof maximumvelocityisstillat x=d =1 : 5,butwhilethejetremainsrelativelynarrow until x=d =2,thebeginningsofsuddenjetexpansionarenoticeable.Thi sresultis consistentwithobservationsoftherowvisualizationimagefor thiscase.Thejetstill vectorsslightlytotheleft. ThejetstructurechangessignicantlybyCase4,Figure 4{46 Re =280.While theslightsuctiontowardthesurfaceoneithersideoftheslotisu nchanged,thejet nowundergoesrapidgrowthnear x=d =1 : 7,andthepointofmaximumvelocityhas

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129 -1.5 -1 -0.5 0 0.5 1 1.5 0 0.5 1 1.5 2 2.5 3 y/dx/d(Click to play movie) Figure4{41:Case3meanplusphase-averagedvelocityeldmov ie, Re =161, St = 0 : 78, h=d =1 : 46. -1.5 -1 -0.5 0 0.5 1 1.5 0 0.5 1 1.5 2 2.5 3 y/dx/d (a) -1.5 -1 -0.5 0 0.5 1 1.5 0 0.5 1 1.5 2 2.5 3 y/dx/d (b) -1.5 -1 -0.5 0 0.5 1 1.5 0 0.5 1 1.5 2 2.5 3 y/dx/d (c) -1.5 -1 -0.5 0 0.5 1 1.5 0 0.5 1 1.5 2 2.5 3 y/dx/d (d) Figure4{42:Case3meanplusphaseaveragedvelocityeldstill frames, Re =161, St =0 : 78, h=d =1 : 46,(a)0 ,(b)90 ,(c)180 ,(d)270

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130 y/dx/d -2 -1 0 1 2 1 2 3 4 5 6 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 Figure4{43:Case1time-averagednormalizedverticalveloc ity, Re U 0 =43, St U 0 = 0 : 84, h=d =1 : 46,incrementbetweencontourlinesis0.1,negativecontou rsareindicatedbydashedlines. y/dx/d -2 -1 0 1 2 1 2 3 4 5 6 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 Figure4{44:Case2time-averagednormalizedverticalveloc ity, Re U 0 =84, St U 0 = 0 : 86, h=d =1 : 46,incrementbetweencontourlinesis0.1,negativecontou rsareindicatedbydashedlines.

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131 y/dx/d -2 -1 0 1 2 1 2 3 4 5 6 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 Figure4{45:Case3time-averagednormalizedverticalveloc ity, Re U 0 =161, St U 0 =0 : 78, h=d =1 : 46,incrementbetweencontourlinesis0.1,negativecontou rs areindicatedbydashedlines. y/dx/d -2 -1 0 1 2 1 2 3 4 5 6 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 Figure4{46:Case4time-averagednormalizedverticalveloc ity, Re U 0 =280, St U 0 =0 : 80, h=d =1 : 46,incrementbetweencontourlinesis0.1,negativecontou rs areindicatedbydashedlines.

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132 y/dx/d -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 1 2 3 4 5 6 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 Figure4{47:Case5time-averagednormalizedverticalveloc ity, Re U 0 =555, St U 0 =0 : 81, h=d =1 : 46,incrementbetweencontourlinesis0.1,negativecontou rs areindicatedbydashedlines. y/dx/d -2 -1 0 1 2 1 2 3 4 5 6 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 Figure4{48:Case6time-averagednormalizedverticalveloc ity, Re U 0 =159, St U 0 =0 : 53, h=d =1 : 46,incrementbetweencontourlinesis0.1,negativecontou rs areindicatedbydashedlines.

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133 shiftedslightlytowardthesurfaceatabout x=d =1 : 3,likelyduetotheincreasing inruenceofthesuction.Thejetstrengthneartheedgeofthene areld, x=d =6, ismorespreadoutcomparedtopreviouscases,indicatingthatt hisjetisbecoming moreturbulent.Onceagain,thiscorroboratestherowvisual izationimageforthis case. ThejetstrengthcontinuestogrowinCase5,Figure 4{47 Re =555,asdoes thejetwidth.Basedonthecontourlines,thisjetappearstobe widerthanthe previouscases.Thewideningshearlayerneartheedgeoftheima geindicatesa strongturbulentjet. ConsideringnowchangesintheStrouhalnumber,Case6,Figure 4{48 Re =159, St =0 : 53,thepointofmaximumvelocityissignicantlyfurtherdow nstreamthan theothercases,at x=d =3,likelyduetothelargestrokelength.Thejetremains relativelystrongthroughouttheimagedomain,butalsostaysf airlynarrowcompared tothepreviouscase.Thissuggestsamorelaminar-likejet. InFigure 4{49 ,Case7,withStrouhalnumberincreasedto0.63,theroweld appearsverysimilartoCase6,exceptthepointofmaximumvelo cityhasshifted towardthesurface,atabout x=d =2 : 5.Thespreadingofthejetisnolongeras uniformeither,asabove x=d =3thejettendstospreadmorerapidlythanbelow. ByCase8,Figure 4{50 St =1,thejetwidthhasdecreasedconsiderably,and thepointofmaximumvelocityhasshiftedfurthertowardthesu rface,at x=d =1. AnotherinterestingresultoftheincreasingStrouhalnumberis theincreasingstrength ofthesuctionregionsoneithersideoftheslot.AstheZNMFdevice isapproaching thejetformationthreshold,itisexpectedthatthesuctionpa rtofthecyclebecomes strongerrelativetotheself-inducedvelocityofthejet( Holman etal. 2005 ).Thejet strengthisnowbarelydiscernibleattheedgeoftheimagedoma in. ConsideringnowCase9,Figure 4{51 St =1 : 3,thejetisnowquiteweak. Themaximumvelocityoccursveryclosethesurface, x=d =0 : 5,andthejetdoes

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134 y/dx/d -2 -1 0 1 2 1 2 3 4 5 6 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 Figure4{49:Case7time-averagednormalizedverticalveloc ity, Re U 0 =155, St U 0 =0 : 63, h=d =1 : 46,incrementbetweencontourlinesis0.1,negativecontou rs areindicatedbydashedlines. y/dx/d -2 -1 0 1 2 1 2 3 4 5 6 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 Figure4{50:Case8time-averagednormalizedverticalveloc ity, Re U 0 =154, St U 0 =1 : 0, h=d =1 : 46,incrementbetweencontourlinesis0.1,negativecontou rs areindicatedbydashedlines.

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135 y/dx/d -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 1 2 3 4 5 6 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 Figure4{51:Case9time-averagednormalizedverticalveloc ity, Re U 0 =139, St U 0 =1 : 3, h=d =1 : 46,incrementbetweencontourlinesis0.1,negativecontou rs areindicatedbydashedlines. y/dx/d -2 -1 0 1 2 1 2 3 4 5 6 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 Figure4{52:Case10time-averagednormalizedverticalvelo city, Re U 0 =175, St U 0 =0 : 73, h=d =0 : 32,incrementbetweencontourlinesis0.1,negativecontou rs areindicatedbydashedlines.

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136 notpenetratepast x=d =3.Thereisnoticeablestrengthinthesuctionregionson eithersideoftheslot,andmostlikelythejetformationthresho ldhasbeencrossed. ThroughoutallofthecaseswhichhavexedReynoldsnumber,t hereisnotalarge changeinthejetwidthlikeforthecasesofvaryingReynoldsn umber.Liketherow visualizationimages,thissuggeststhattheReynoldsnumbera ectsturbulencein theroweldandthattheseeectsareessentiallyStrouhalnumb erindependent. Changesintheslotheight-to-depthaspectratio h=d arenowaddressed.A verywidejetemergesfromtheslotforCase10,Figure 4{52 ,whichhas h=d = 0 : 32, Re =175, St =0 : 73.Again,thisisveriedbytherowvisualization,which showedaturbulent-likejetemanatingfromtheverythinslot. Furthermore,thereis anoticeableasymmetryinthevelocityofruidtowardthesloto neitherside,with therightsideexhibitingmoresuctionthantheleftside.Becau setheslotissothin, itisconjecturedthatimperfectionsinthemanufactureoft heslotplateareamplied, andthisislikelythecauseofthisasymmetry,aswellasthejet vectoring. ForCase11,Figure 4{53 h=d =3 : 32,thejetisnowmuchmorenarrow,indicative ofalaminarjet.Thepointofmaximumvelocityhasonlymoved slightly,butthe suctionofruidtowardtheslotisnoticeablystronger.Alarge h=d ,itwouldseem,is notconducivetowardformingastrongjet. FinallyforCase12,Figure 4{54 ,anunusualjetproleemerges.Recallthiscase isperformednearthesamenominalvaluesofthedimensionlessp arametersasCase 3, Re =143, St =0 : 88, h=d =1 : 46.Thesuddenexpansionforthisuncontrolled caseisstrongerthanCase3,whichsuggestamoreturbulentjet.Wh ilethepointof maximumvelocityandthestrengthofthesuctiononeithersideo ftheslotiscomparabletoCase3,thereisaninteresting\bubble"ofhigher-vel ocityruidcenterednear x=d =4.Thereasonforthisbehaviorisnotconclusivelyknown,but ishypothesized tobeduetothenon-linearitiespresentduetothedistorteddr ivermotion.

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137 y/dx/d -2 -1 0 1 2 1 2 3 4 5 6 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 Figure4{53:Case11time-averagednormalizedverticalvelo city, Re U 0 =161, St U 0 =0 : 79, h=d =3 : 32,incrementbetweencontourlinesis0.1,negativecontou rs areindicatedbydashedlines. y/dx/d -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 1 2 3 4 5 6 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 Figure4{54:Case12time-averagednormalizedverticalvelo city, Re U 0 =143, St U 0 =0 : 88, h=d =1 : 46,incrementbetweencontourlinesis0.1,negativecontou rs areindicatedbydashedlines.

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138 (Click to play movie) y/dx/d -2 -1 0 1 2 1 2 3 4 5 6 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 Figure4{55:Case3phase-averagedstreamwisevelocitycompone ntmovienormalized by U 0 Re U 0 =161, St U 0 =0 : 78, h=d =1 : 46,incrementbetweencontourlinesis0.2, negativecontoursareindicatedbydashedlines. y/dx/d -2 -1 0 1 2 1 2 3 4 5 6 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 (a) y/dx/d -2 -1 0 1 2 1 2 3 4 5 6 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 (b) y/dx/d -2 -1 0 1 2 1 2 3 4 5 6 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 (c) y/dx/d -2 -1 0 1 2 1 2 3 4 5 6 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 (d) Figure4{56:Case3meanplusphaseaveragedstreamwisevelocity componentstill framesnormalizedby U 0 Re U 0 =161, St U 0 =0 : 78, h=d =1 : 46,incrementbetween contourlinesis0.2,negativecontoursareindicatedbydash edlines,(a)0 ,(b)90 (c)180 ,(d)270

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139 Aphase-lockedmovieofthemeanplusphase-averagedstreamwise velocitycomponentnormalizedby U 0 forthenominalcase,Case3, Re =161, St =0 : 78, h=d =1 : 46isshowninFigure 4{55 .StillframesofthismoviearegiveninFigure 4{56 .Itisinterestingtonotethatduringexpulsion,thepointofm aximum velocitymovesawayfromtheslot,remainingrelativelyunch anged.However,once thesuctionpartofthecyclebegins,themaximumvelocitystart stoweakenconsiderably.However,theinitialvelocityremainsstrongenought ocontinueforwardat about x=d =5throughouttheentirecycle.Similarresultswerefoundfo rallother cases(notshown). Amovieofthenormalizedmeanplusphase-averagedstreamwisee xitvelocity prole u p +~ u p isshowninFigure 4{57 .Stillframesofthismoviearegivenin Figure 4{58 .Whilethevelocityproleduringexpulsionresemblesfullyd eveloped piperowwithanoscillatingpressuregradient,thevelocitydu ringthesuctionpartof thecycleismuchmoreslug-likeanddoesnotreachthesamecent erlinemagnitudeas expulsion.Thiswasobservedqualitativelyinthehotwiremea surements,andfurther underscorestheneedtouseavelocityscalebasedontheentirecy cle,ratherthan justexpulsionoringestion. Themeanplusphase-averagedcross-streamexitvelocityprole v p +~ v p normalizedby U 0 isshownasamovieinFigure 4{59 .Thestillframesofthismovieare showninFigure 4{60 .Notethatthehorizontalvelocityremainszerothroughoutt he cycleonlyatthecenteroftheslot.Themagnitudeofthehoriz ontalvelocityisalso similartotheverticalvelocity.Thus,ifoneusedhotwireanem ometrytogeneratea velocityproleacrosstheslot,therewouldinherentlybeerr orsintheresultsdueto thedirectionalambiguity.The u and v normalizedexitvelocityprolesfortheother casesweresimilartothenominalcase,andarenotshownhereforb revity.

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140 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 y/d( u +~ u ) =U0(Click to play movie) Figure4{57:Case3meanplusphase-averagedstreamwiseexitvel ocityprolemovie normalizedby U 0 Re U 0 =161, St U 0 =0 : 78, h=d =1 : 46. -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 y/d( u +~ u ) =U 0 (a) -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 y/d( u +~ u ) =U 0 (b) -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 y/d( u +~ u ) =U 0 (c) -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 y/d( u +~ u ) =U 0 (d) Figure4{58:Case3meanplusphaseaveragedstreamwiseexitvelo cityprolestill framesnormalizedby U 0 Re U 0 =161, St U 0 =0 : 78, h=d =1 : 46,(a)0 ,(b)90 (c)180 ,(d)270

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141 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 y/d( v +~ v ) =U0(Click to play movie) Figure4{59:Case3meanplusphase-averagedcross-streamexitve locityprolemovie normalizedby U 0 Re U 0 =161, St U 0 =0 : 78, h=d =1 : 46. -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 y/d( v +~ v ) =U 0 (a) -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 y/d( v +~ v ) =U 0 (b) -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 y/d( v +~ v ) =U 0 (c) -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 y/d( v +~ v ) =U 0 (d) Figure4{60:Case3meanplusphaseaveragedcross-streamexitvel ocityprolestill framesnormalizedby U 0 Re U 0 =161, St U 0 =0 : 78, h=d =1 : 46,(a)0 ,(b)90 (c)180 ,(d)270

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142 VorticityandCirculation Besidesthevelocityproles,muchusefulinformationonthero weldphysicsmay bededucedbyconsideringthevorticityoftheroweld,aswel lasthecirculation.For two-dimensionalvelocitymeasurements,thevorticityis z = r ~ V z = @v @x @u @y v x u y (4.2) whichcanbeapproximatedfortheexperimentalvelocitydat abyusingacentral dierencescheme, z v i;j +1 v i;j 1 x j +1 x j 1 u i +1 ;j u i 1 ;j y i +1 y i 1 (4.3) Notethatnearthesurfaceoftheslot,therowistwo-dimensional pertherowvisualizationphotographs.Themeanplusphase-averagedvortic ityeldiscomputed forallcases,thennormalizedbytheoscillationfrequency ,andvorticitymoviesare shownnextforseveralcases.Thecasesnotshownexhibitsimilarcha racteristicsto thosecaseswhichbracketthemintheparameterspace. Itisnotablethatthestrengthofthevorticescollapsesreason ablywellwhen normalizedbytheoscillationfrequency .However,theoverallbehaviorofthe vorticityevolutiondoesnotcollapse. Smith etal. ( 1999 )notedthisandobserved thatthesuctionpartofthecycleaectedthevorticesindie rentways.Later,itis shownthattheproductionandevolutionofthecirculationat thesurfaceoftheslot alsoaectsthevorticityoftheroweld. Figure 4{61 showsamovieoftheevolutionofthevortexstructuresforthe weakestcase,Case1, Re =43, St =0 : 84, h=d =1 : 46.Stillframesofthismovieare includedinFigure 4{62 .Avortexpairisejectedfromtheslotandbeginspropagating downstreamunderitsownself-inducedvelocity.Atabouthalf waythroughthecycle, thevortexpairpinchesofromthesurface,andthenbecomese longatedandweaker duringthesuctionstroke.Duringthistime,opposite-signvort icityisgeneratedalong thesurfaceoftheslot,whichisindicativeofruidbeingdrawn intotheslot.

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143 y/dx/d(Click to play movie) -2 -1 0 1 2 1 2 3 4 5 6 -10 -8 -6 -4 -2 0 2 4 6 8 10 Figure4{61:Case1meanplusphase-averagedvorticitymovien ormalizedby Re U 0 =43, St U 0 =0 : 84, h=d =1 : 46,incrementbetweencontourlinesis1,negative contoursareindicatedbydashedlines. y/dx/d -2 -1 0 1 2 1 2 3 4 5 6 -10 -8 -6 -4 -2 0 2 4 6 8 10 (a) y/dx/d -2 -1 0 1 2 1 2 3 4 5 6 -10 -8 -6 -4 -2 0 2 4 6 8 10 (b) y/dx/d -2 -1 0 1 2 1 2 3 4 5 6 -10 -8 -6 -4 -2 0 2 4 6 8 10 (c) y/dx/d -2 -1 0 1 2 1 2 3 4 5 6 -10 -8 -6 -4 -2 0 2 4 6 8 10 (d) Figure4{62:Case1meanplusphaseaveragedvorticitystillfra mesnormalizedby Re U 0 =43, St U 0 =0 : 84, h=d =1 : 46,incrementbetweencontourlinesis1,negative contoursareindicatedbydashedlines,(a)0 ,(b)90 ,(c)180 ,(d)270

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144 Atthenominalcase,Case3, Re U 0 =161, St U 0 =0 : 78, h=d =1 : 46,asshown inFigure 4{63 ,amorecoherentvortexpairdevelopsduringexpulsion,anda lso pinchesohalfwaythroughthecycle.Thestillframesforthi scaseareincludedin Figure 4{64 .Theelongationofthevortexpairismorenoticeableduring suction,and thepairreachesapproximately x=d =2 : 5beforestalling.However,thesubsequent expulsionstrokepushesthevortexpairouttonearly x=d =4,beforeitbecomes indistinguishablefromthebackground. Figure 4{65 givesthevorticitymovieofCase5, Re U 0 =555, St U 0 =0 : 81, h=d =1 : 46.StillframesareshowninFigure 4{66 .Again,averycoherentvortex pairisgenerated,expelled,andpinchesofromtheslotatab outthemidpointof thecycle.Thistimehowever,thevorticityrapidlydissipate snear x=d =1 : 5andis essentiallygoneatthestartofthenextcycle.Diusionisapossib lecause;asper therowvisualizationtheroweldremainsroughlytwo-dimen sionalinthisregion. Nevertheless,theturbulentnatureoftherowsuggeststhree-dim ensionaleectsmay alsocontributetothevorticitydecay. Thevorticitygeneratedbyaverylargestrokelength(lowStr ouhalnumber) andnominalReynoldsnumber,Case6, Re U 0 =159, St U 0 =0 : 53, h=d =1 : 46,is showninFigure 4{67 .StillframesofthiscaseareincludedinFigure 4{68 .These vortexstructuresarequitelarge,indicatinghighvorticit y,andpropagaterapidly downstream,reaching x=d =2 : 5halfwaythroughthecycle.Thevortexdoesnottruly pincho;rather,atrailingtailofvorticityisapparentfr om =135 to =225 Thistailquicklybecomesindistinguishablefromthemainvor texpair,whichreaches x=d =5attheendofthecycle,andthenisquicklypushedoutofthei magedomain atthestartofthefollowingcycle.Thiscouldbeindicativeo fmaximumcirculation beingachievedandexcessvorticityresultinginthetail( Gharib etal. 1998 ). AtCase9, Re U 0 =139, St U 0 =1 : 3, h=d =1 : 46,havingverysmallstrokelength andhencelargeStrouhalnumber,verylittlevorticitypene tratestheroweldasseen

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145 y/dx/d(Click to play movie) -2 -1 0 1 2 1 2 3 4 5 6 -10 -8 -6 -4 -2 0 2 4 6 8 10 Figure4{63:Case3meanplusphase-averagedvorticitymovien ormalizedby Re U 0 =161, St U 0 =0 : 78, h=d =1 : 46,incrementbetweencontourlinesis1,negative contoursareindicatedbydashedlines. y/dx/d -2 -1 0 1 2 1 2 3 4 5 6 -10 -8 -6 -4 -2 0 2 4 6 8 10 (a) y/dx/d -2 -1 0 1 2 1 2 3 4 5 6 -10 -8 -6 -4 -2 0 2 4 6 8 10 (b) y/dx/d -2 -1 0 1 2 1 2 3 4 5 6 -10 -8 -6 -4 -2 0 2 4 6 8 10 (c) y/dx/d -2 -1 0 1 2 1 2 3 4 5 6 -10 -8 -6 -4 -2 0 2 4 6 8 10 (d) Figure4{64:Case3meanplusphaseaveragedvorticitystillfra mesnormalizedby Re U 0 =161, St U 0 =0 : 78, h=d =1 : 46,incrementbetweencontourlinesis1,negative contoursareindicatedbydashedlines,(a)0 ,(b)90 ,(c)180 ,(d)270

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146 y/dx/d(Click to play movie) -2 -1 0 1 2 1 2 3 4 5 6 -10 -8 -6 -4 -2 0 2 4 6 8 10 Figure4{65:Case5meanplusphase-averagedvorticitymovien ormalizedby Re U 0 =555, St U 0 =0 : 81, h=d =1 : 46,incrementbetweencontourlinesis1,negative contoursareindicatedbydashedlines. y/dx/d -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 1 2 3 4 5 6 -10 -8 -6 -4 -2 0 2 4 6 8 10 (a) y/dx/d -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 1 2 3 4 5 6 -10 -8 -6 -4 -2 0 2 4 6 8 10 (b) y/dx/d -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 1 2 3 4 5 6 -10 -8 -6 -4 -2 0 2 4 6 8 10 (c) y/dx/d -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 1 2 3 4 5 6 -10 -8 -6 -4 -2 0 2 4 6 8 10 (d) Figure4{66:Case5meanplusphaseaveragedvorticitystillfra mesnormalizedby Re U 0 =555, St U 0 =0 : 81, h=d =1 : 46,incrementbetweencontourlinesis1,negative contoursareindicatedbydashedlines,(a)0 ,(b)90 ,(c)180 ,(d)270

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147 y/dx/d(Click to play movie) -2 -1 0 1 2 1 2 3 4 5 6 -10 -8 -6 -4 -2 0 2 4 6 8 10 Figure4{67:Case6meanplusphase-averagedvorticitymovien ormalizedby Re U 0 =159, St U 0 =0 : 53, h=d =1 : 46,incrementbetweencontourlinesis1,negative contoursareindicatedbydashedlines. y/dx/d -2 -1 0 1 2 1 2 3 4 5 6 -10 -8 -6 -4 -2 0 2 4 6 8 10 (a) y/dx/d -2 -1 0 1 2 1 2 3 4 5 6 -10 -8 -6 -4 -2 0 2 4 6 8 10 (b) y/dx/d -2 -1 0 1 2 1 2 3 4 5 6 -10 -8 -6 -4 -2 0 2 4 6 8 10 (c) y/dx/d -2 -1 0 1 2 1 2 3 4 5 6 -10 -8 -6 -4 -2 0 2 4 6 8 10 (d) Figure4{68:Case6meanplusphaseaveragedvorticitystillfra mesnormalizedby Re U 0 =159, St U 0 =0 : 53, h=d =1 : 46,incrementbetweencontourlinesis1,negative contoursareindicatedbydashedlines,(a)0 ,(b)90 ,(c)180 ,(d)270

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148 inFigure 4{69 .ThestillframesareshowninFigure 4{70 .Themainvortexpair barelybreaksawayfromtheslotbutremainsstationarynearth esurface,andis thenelongatedduringsuctionasitdissipates.Anotherinteresti ngobservationof thisroweldistheformationofavortexpairofoppositesensea t =45 which residesinsidethemainvortexpair.Thisvorticityisshort-li ved,however,andhas dissipatedby =90 Averyinterestingvortexpairisgeneratedbythethinslotpla te, h=d =0 : 32,Case 10, Re U 0 =175, St U 0 =0 : 73,asseeninFigure 4{71 (movie)andFigure 4{72 (still frames).Notethattheblankregionnearthecoreoftherightvo rtexinFigure 4{72(b) isanartifactofpost-processingwherethevorticityisslightl yhigherthanthelimit ofthecontourplot,andnotindicativeofaregionofnodata. Astrongvortexpairis ejectedandreaches x=d =1,thenthedistancebetweenthevortexcentersincreases duringthesuctionpartofthecycleasthevortexpairreaches x=d =2.Thepair thenrapidlydissipatesandisnearlygonebythestartofthefol lowingcycle.Thisis mostlikelyabreakdowntoturbulence,asevidencedbybothth erowvisualization andthemeanvelocityeldforthiscase. Incontrast,Figure 4{73 showstheevolutionofvorticityforCase11, Re U 0 =161, St U 0 =0 : 79, h=d =3 : 32.StillframesofthismovieareprovidedinFigure 4{74 Here,thevortexpairremainsfairlycoherentthroughoutthe entirecycleandreaches x=d =2attheendofthecycle.Thevortexpairpersistsuntilnearly theendofthe followingcycle,althoughitisapparentthatthesuctionstro kesignicantlystretches outthevortexafterithaspinchedofromthesurface. Case12presentsaninterestingvorticityeldinFigure 4{75 .Thestillframesof thismoviearefoundinFigure 4{76 .Becauseofthedistortioninthepistonmotion, thevortexpairdoesnotevolvesmoothlyduringexpulsionbutr atherslowlyemerges duringthersthalfofexpulsion,0 << 90 .Thenthevortexpairsuddenlybursts intotheroweld,getselongatedbacktowardtheslotduetoth esuction,andreaches

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149 y/dx/d(Click to play movie) -2 -1 0 1 2 1 2 3 4 5 6 -10 -8 -6 -4 -2 0 2 4 6 8 10 Figure4{69:Case9meanplusphase-averagedvorticitymovien ormalizedby Re U 0 =139, St U 0 =1 : 3, h=d =1 : 46,incrementbetweencontourlinesis1,negative contoursareindicatedbydashedlines. y/dx/d -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 1 2 3 4 5 6 -10 -8 -6 -4 -2 0 2 4 6 8 10 (a) y/dx/d -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 1 2 3 4 5 6 -10 -8 -6 -4 -2 0 2 4 6 8 10 (b) y/dx/d -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 1 2 3 4 5 6 -10 -8 -6 -4 -2 0 2 4 6 8 10 (c) y/dx/d -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 1 2 3 4 5 6 -10 -8 -6 -4 -2 0 2 4 6 8 10 (d) Figure4{70:Case9meanplusphaseaveragedvorticitystillfra mesnormalizedby Re U 0 =139, St U 0 =1 : 3, h=d =1 : 46,incrementbetweencontourlinesis1,negative contoursareindicatedbydashedlines,(a)0 ,(b)90 ,(c)180 ,(d)270

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150 y/dx/d(Click to play movie) -2 -1 0 1 2 1 2 3 4 5 6 -10 -8 -6 -4 -2 0 2 4 6 8 10 Figure4{71:Case10meanplusphase-averagedvorticitymovie normalizedby Re U 0 =175, St U 0 =0 : 73, h=d =0 : 32,incrementbetweencontourlinesis1,negative contoursareindicatedbydashedlines. y/dx/d -2 -1 0 1 2 1 2 3 4 5 6 -10 -8 -6 -4 -2 0 2 4 6 8 10 (a) y/dx/d -2 -1 0 1 2 1 2 3 4 5 6 -10 -8 -6 -4 -2 0 2 4 6 8 10 (b) y/dx/d -2 -1 0 1 2 1 2 3 4 5 6 -10 -8 -6 -4 -2 0 2 4 6 8 10 (c) y/dx/d -2 -1 0 1 2 1 2 3 4 5 6 -10 -8 -6 -4 -2 0 2 4 6 8 10 (d) Figure4{72:Case10meanplusphaseaveragedvorticitystillfr amesnormalizedby Re U 0 =175, St U 0 =0 : 73, h=d =0 : 32,incrementbetweencontourlinesis1,negative contoursareindicatedbydashedlines,(a)0 ,(b)90 ,(c)180 ,(d)270

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151 y/dx/d(Click to play movie) -2 -1 0 1 2 1 2 3 4 5 6 -10 -8 -6 -4 -2 0 2 4 6 8 10 Figure4{73:Case11meanplusphase-averagedvorticitymovie normalizedby Re U 0 =161, St U 0 =0 : 79, h=d =3 : 32,incrementbetweencontourlinesis1,negative contoursareindicatedbydashedlines. y/dx/d -2 -1 0 1 2 1 2 3 4 5 6 -10 -8 -6 -4 -2 0 2 4 6 8 10 (a) y/dx/d -2 -1 0 1 2 1 2 3 4 5 6 -10 -8 -6 -4 -2 0 2 4 6 8 10 (b) y/dx/d -2 -1 0 1 2 1 2 3 4 5 6 -10 -8 -6 -4 -2 0 2 4 6 8 10 (c) y/dx/d -2 -1 0 1 2 1 2 3 4 5 6 -10 -8 -6 -4 -2 0 2 4 6 8 10 (d) Figure4{74:Case11meanplusphaseaveragedvorticitystillfr amesnormalizedby Re U 0 =161, St U 0 =0 : 79, h=d =3 : 32,incrementbetweencontourlinesis1,negative contoursareindicatedbydashedlines,(a)0 ,(b)90 ,(c)180 ,(d)270

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152 x=d =2bythestartofthenextcycle.Someremnantsofvorticityar eseennear x=d =4untilthesuctionpartofthefollowingcycle. Therelationshipbetweenvorticityandcirculationisfound viaStokes'theorem, whichwasshownby Didden ( 1979 )torelatethetimerateofchangeofcirculationto thevorticityruxthroughtheplane x=d =0foravortexring, d dt = Z 1 0 ( x =0 ;y;t ) u ( x =0 ;y;t ) dy (4.4) Forthecaseofatwo-dimensionalZNMFdevicewithslotdepth d ,thevorticitycan beapproximatedastwovorticesofoppositesignwhichrollupo neithersideofthe slot,thusthetimerateofchangeofcirculationduetothelef tvortexis d L dt = Z 0 d= 2 ( x =0 ;y;t ) u ( x =0 ;y;t ) dy (4.5) andsimilarlyfortherightvortex, d R dt = Z d= 2 0 ( x =0 ;y;t ) u ( x =0 ;y;t ) dy (4.6) wherethelimitsofintegrationaresetbecauseruidcanonlypa ssthroughtheplane x=d =0overtheextentoftheslot.EvaluationoftheintegralsinE qs.( 4.5 )and ( 4.6 ),andthensubsequentintegrationofthesequantitiesduringo necycle,yieldsthe totalcirculationimpartedtotheroweldbytherollingupo feachvortexinthepair. Itshouldbenotedthatthetwohalvesofthevortexpairarenot separate,but rathertheyarebothpartofacontinuousvortexloopwhichme etsateitherendofthe slotinthe z -direction.Thisisessentiallyare-statementofHelmholtz'sl aw,which statesthatavortexlamentmustbeeithercontinuousorendat theruidboundary, assumingtheviscousforcesarenegligibleaftertheruidobtai nsvorticity( Panton 1996 ).StillfurtherinsightmaybeattainedbyconsideringKelvin 'stheorem,which statesthatforaninviscidruid,thecirculationaboutaclosed curvemovingwiththe ruidisconstant( Panton 1996 ; White 1991 ). Didden ( 1979 ),workingwithvortex

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153 y/dx/d(Click to play movie) -2 -1 0 1 2 1 2 3 4 5 6 -10 -8 -6 -4 -2 0 2 4 6 8 10 Figure4{75:Case12meanplusphase-averagedvorticitymovie normalizedby Re U 0 =143, St U 0 =0 : 88, h=d =1 : 46,incrementbetweencontourlinesis1,negative contoursareindicatedbydashedlines. y/dx/d -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 1 2 3 4 5 6 -10 -8 -6 -4 -2 0 2 4 6 8 10 (a) y/dx/d -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 1 2 3 4 5 6 -10 -8 -6 -4 -2 0 2 4 6 8 10 (b) y/dx/d -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 1 2 3 4 5 6 -10 -8 -6 -4 -2 0 2 4 6 8 10 (c) y/dx/d -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 1 2 3 4 5 6 -10 -8 -6 -4 -2 0 2 4 6 8 10 (d) Figure4{76:Case12meanplusphaseaveragedvorticitystillfr amesnormalizedby Re U 0 =143, St U 0 =0 : 88, h=d =1 : 46,incrementbetweencontourlinesis1,negative contoursareindicatedbydashedlines,(a)0 ,(b)90 ,(c)180 ,(d)270

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154 ringsexpelledinwater,observedthatthechangeincirculat ionduetodiusionwas negligible,thusitisreasonabletoestimatethattheringspr opagatedthroughan inviscidruid.However,thisassumptionismoreproblematicint hecaseofZNMF rows.Theexpelledvortexpairsmovethroughruidregionsae ctedbyprevious cycles,makingthesevortexstructuresmorelikelytobreakdow ntoturbulenceand henceviolatetheassumptionofaninviscidruid( Smith etal. 1999 ). Figure 4{77 andFigure 4{78 showthecirculationgeneratedbytheleftandright vortex,respectively,forCases1-5.Anumberofobservationsi ntothephysicsofthe resultingroweldmaybededucedfromthesegures.First,theci rculationimparted toeachvortexisnearlysymmetricalforeachcase,suggestingth atthesameamount ofcirculationisproducedineachvortex,withoppositesign, asexpected.Second, theinitialcirculationiszero,andthenrisestoamaximumva luenearthemidpoint ofthecycle,indicatingtheexpulsionpartofthecycle.Howev er,whilethecirculation thenremainsrelativelyconstantforCases1-4,itisapparent thatthecirculationof Case5dropsduringthesuctionstrokebeforestabilizing.AstheR eynoldsnumber increases, 8 increasesandthesuctionpartofthecyclebeginstomorestrong lyaect theroweld.Itisinterestingtonotethatamonotonicincrea seinReynoldsnumber doesnotcorrespondtoamonotonicincreaseinthecirculation forthesecases;instead, apointisreachedbeyondwhichthecirculationcannotincre aseduetothegrowing inruenceofthesuctionpartofthecycle. Smith etal. ( 1999 )notedthattomaximize theimpulseimpartedtotheroweld,theblowingstrokeshouldb eshortandofhigh amplitude,whilethesuctionstrokeshouldbelongerwithlower amplitude.Suchan analogycanalsoapplytocirculation. Next,variationsintheStrouhalnumberareexaminedforthel eftandrightvortexinFigure 4{79 andFigure 4{80 ,respectively.Notsurprisingly,forxedReynolds number,astheStrouhalnumberisdecreased(increasingstroke length),thetotal circulationincreases.Nowhowever,itisthecaseofhighestStro uhalnumber(lowest

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155 0 60 120 180 240 300 360 -12 -10 -8 -6 -4 -2 0 2 x 10-3 Phase (deg)G L (m 2 /s) Re=43 Re=84 Re=161 Re=280 Re=555 Figure4{77:Circulationvs.phasefromtheleftvortex, Re sweep, St =0 : 82, h=d =1 : 46. 0 60 120 180 240 300 360 -2 0 2 4 6 8 10 12 x 10-3 Phase (deg)G R (m 2 /s) Re=43 Re=84 Re=161 Re=280 Re=555 Figure4{78:Circulationvs.phasefromtherightvortex, Re sweep, St =0 : 82, h=d =1 : 46.

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156 0 60 120 180 240 300 360 -14 -12 -10 -8 -6 -4 -2 0 2 x 10-3 Phase (deg)G L (m 2 /s) St=0.53 St=0.63 St=0.78 St=1.00 St=1.30 Figure4{79:Circulationvs.phasefromtheleftvortex, St sweep, Re =154, h=d = 1 : 46. 0 60 120 180 240 300 360 -2 0 2 4 6 8 10 12 14 x 10-3 Phase (deg)G R (m 2 /s) St=0.53 St=0.63 St=0.78 St=1.00 St=1.30 Figure4{80:Circulationvs.phasefromtherightvortex, St sweep, Re =154, h=d =1 : 46.

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157 strokelength)thatlosescirculationduringthesuctionstroke .ForagivenReynolds numberthen,oneshouldminimizetheStrouhalnumbertoachie vethehighestcirculation.However, Gharib etal. ( 1998 )notedthatanupperlimitexistsbeyondwhich nomorecirculationcanbecontainedinavortexbutwillinste adtrailbehindthe vortex.Thisbehaviorwasobservedby Crook&Wood ( 2000 )foraZNMFdevice. Apparentlythislimitwasnotachievedforthecurrenttestmat rixofcases.Surpassingthislimitismostlikelytoincreasetheturbulenceofth eresultingroweld. HencethoughforthesecasesatagivenReynoldsnumberthemeanr oweldsappear laminar,itisreasonabletoexpectthatforalargeenoughstro kelength,therow couldbecometurbulentduetotheexcesscirculationtrailin gthevortexstructures. Theeectofslotheight-to-depthaspectratiooncirculation isexaminedinFigure 4{81 andFigure 4{82 .Theresultsareintuitive;asmaller h=d {andhence larger L 0 =h because 8 isxed{resultsinmorecirculationbeingimpartedtothe roweld.ItisalsonoteworthythatforthesexedvaluesofRey noldsnumberand Strouhalnumber,changesintheslotheight-to-depthaspectr atiocauseonlyminimal changesincirculationduringthesuctionstroke. Thecirculationimpartedtotheroweldisverysensitivetoth eshapeofthe velocityprole.InFigure 4{83 andFigure 4{84 ,thecirculationissignicantlyhigher forthecaseofsinusoidalcontrol,Case3, Re U 0 =161, St U 0 =0 : 78, h=d =1 : 46,vs. thecaseofdistortedpistonmotion,Case12, Re U 0 =143, St U 0 =0 : 88, h=d =1 : 46. Atrst,onemayexpecttheprogramfactorsofthesetwocasestob edierentsince thisaectsthecirculation( Glezer 1988 ).However,theprogramfactorsofthesetwo casesarenearlyidentical,suggestingthatevenaminorchange intheshapeofthe motionofthedrivercansignicantlyalterthecirculationi mpartedtotheroweld. Programfactorishistoricallydenedforvortexringsasthe ratiobetweenthemeansquaredpistondisplacementtothesquareoftheaveragepistondi splacement.For anoscillatorypistonmotion,however,theaveragepistondispl acementiszero,hence

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158 0 60 120 180 240 300 360 -12 -10 -8 -6 -4 -2 0 2 x 10-3 Phase (deg)G L (m 2 /s) h/d=0.32 h/d=1.46 h/d=3.32 Figure4{81:Circulationvs.phasefromtheleftvortex, h=d sweep, Re =154, St =0 : 82. 0 50 100 150 200 250 300 350 -12 -10 -8 -6 -4 -2 0 2 x 10-3 Phase (deg)G R (m 2 /s) h/d=0.32 h/d=1.46 h/d=3.32 Figure4{82:Circulationvs.phasefromtherightvortex, h=d sweep, Re =154, St =0 : 82.

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159 0 60 120 180 240 300 360 -8 -7 -6 -5 -4 -3 -2 -1 0 1 x 10-3 Phase (deg)G L (m 2 /s) Controlled Uncontrolled Figure4{83:Circulationvs.phasefromtheleftvortex,sinusoi dal/distortedpiston motion, Re =154, St =0 : 82, h=d =1 : 46. 0 60 120 180 240 300 360 -1 0 1 2 3 4 5 6 7 8 x 10-3 Phase (deg)G R (m 2 /s) Controlled Uncontrolled Figure4{84:Circulationvs.phasefromtherightvortex,sinuso idal/distortedpiston motion, Re =154, St =0 : 82, h=d =1 : 46.

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160 theaveragepistondisplacementduringthehalf-cycle, R p ,isused, P = R p 2 R p 2 (4.7) Theprecedingresultssuggestthepossibilityofscalinglawsrela tingthecirculationimpartedtotheroweldasafunctionofthedimensionl essparameters Re and St .Thechangeinthecirculation,normalizedbytheproductof themomentum velocityandtheslotdepth,isshownasafunctionofReynoldsn umberforconstant StrouhalnumberinFigure 4{85 .Ifthesecondpointisrejectedasanoutlier,then afunctionalformisfoundwhichasymptoticallyapproachesz eroathighReynolds number,andlevelsoatanitevalueatlowReynoldsnumber. Whileitmaynot seemintuitivelycorrectforthenormalizedcirculationtol eveloas Re 0,it mustberememberedthat U 0 alsoapproacheszero,andhencel'H^opital'srulemust beinvoked.Thisresultalsosuggeststhatthenormalizedcircul ationimpartedto theroweldactuallydecreasesasafunctionofReynoldsnumb er,likelyduetothe strongerinruenceofthesuctionpartofthecycleathigherRey noldsnumbers. AsimilarresultisfoundinFigure 4{86 ,whichplotsthenormalizedcirculation asafunctionoftheStrouhalnumberforxedReynoldsnumber .Notsurprisingly,at verylowStrouhalnumber,thelargestrokelengthcausesaninc reaseintotalcirculationimpartedtotheroweld.AthigherStrouhalnumbers( lowerstrokelengths), thecirculationisreduced.Anintriguingpossibilityforfutu reworkistocontinueto decreasetheStrouhalnumberandobserveifthereisa\levelin go"ofthecirculation duetothemaximumvalueofcirculationbeingattainedforav ortex( Gharib etal. 1998 ).Withtheacquisitionofmorecasesatothervaluesof h=d ,ascalinglawcould alsobedevelopedwhichincorporatesslotheight-to-depthasp ectratio. Insummary,theseresultsonvorticityandcirculationsuggestth attheproper operationofaZNMFdeviceisapplicationspecic.Forapplica tionsinvolvingheat transfer,momentumimpartedtotheroweldataxeddistancef romtheslotis

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161 0 100 200 300 400 500 600 1 1.5 2 2.5 3 3.5 4 Reynolds Number¡ =U 0 d Data 1/[0.28+(1.6e-6)Re 2 ] Figure4{85:Normalizedcirculationvs. Re St =0 : 8, h=d =1 : 46. 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 0 1 2 3 4 5 6 Strouhal Number¡ =U 0 d Data 4.15St -1 -2.5 Figure4{86:Normalizedcirculationvs. St Re =160, h=d =1 : 46.

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162 likelytobethechiefparametertomaximize;whileforbound arylayerseparation controlapplications,thecirculationisprobablythebestpa rametertomaximize. Indeed,averystrongsyntheticjetissuingnormaltoanaerodyna micsurfacemay causeaseparationbubbletoformandhinderitsoperation,whi leaweakerroweld whichcreatesvortexstructuresthatcanbesweptdownstreamwi thoutpinchingo thesurfacemaybemoresuitedforboundarylayerseparationcon trolapplications ( Holman etal. 2003 ). ReynoldsStressandTurbulentKineticEnergy Reynoldsstress(RS)andturbulentkineticenergy(TKE)provi deinformation onthenatureoftheturbulenceintheZNMFroweld.Thesequant itiescanbe computedeitherphase-averaged,bytakingtheapproximatel y100valuesof u 0 and v 0 atagivenphase,ortheymaybecomputedusingallvelocityruct uations(2 ; 400 values)duringtheentirecycletogetapictureoftheoverall turbulentstructureof theroweld.TheReynoldsstressiscomputedas RS= u 0 v 0 U 2 0 (4.8) whiletheturbulentkineticenergyis TKE= u 0 2 + v 0 2 2 U 2 0 (4.9) Thephase-averagedRSisexaminedforthenominalcaseandthel imitingcases onReynoldsnumber,Strouhalnumber,andslotheight-to-dep thaspectratio.While notallcasesareshown,theonesomittedexhibitsimilarcharac teristicstothecases whichbracketthem.Figure 4{87 showsaphase-lockedmovieoftheRSforCase1, Re U 0 =43, St U 0 =0 : 84, h=d =1 : 46.Thecorrespondingstillimagesareshownin Figure 4{88 .First,itisnotedthattheoverallproleremainsremarkabl yconstant duringtheentirecycle.Thisindicatesthatthereisnochan geintheturbulenceof theroweldduringacycle.BecausetheRSisnormalizedby U 2 0 fromEq.( 4.8 ),it

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163 isapparentthatthedimensionalvalueoftheRSforthiscaseis verysmall.Again, thisisexpectedbecausethiscaseexhibitslaminarjetcharac teristics. Figure 4{89 showsthephase-averagedRSforCase3,thenominalcase, Re U 0 = 161, St U 0 =0 : 78, h=d =1 : 46.StillframesforthiscasearefoundinFigure 4{90 ThereisanunusuallylargeregionofnegativeRSintheupperl eftquadrantofthe image.Thiscouldbeduetorecirculationcurrentsinthetan kalteringtheroweld, orthree-dimensionaleects,andtheseeectsmayappearampli edsincetheRS isnormalizedbyarelativelysmallRMSvelocity.Whatisvery interestinginthis case,however,isthatwhiletheRSremainsfairlyconstantint hevicinityoftheslot, x=d< 1 : 5,thereisaveryclearincreaseinRSduringthersthalfofthe suction partofthecycle,180 << 270 ,at x=d =2.Thislocationcorrespondstothe suddenexpansionofthejetasobservedinthevelocityeldmeasu rementsandthe rowvisualizationphotographs.Thislocalizedregionofhigh RSthenpropagates awayfromtheslot,reaching x=d =2 : 5bytheendofthecycleandcontinuingpast x=d =3duringthenextcyclebeforeeventuallydecayingat =90 Thisbehaviorimpliesthataninitiallylaminarvortexpair isejectedfromthe oriceandthentransitionstoturbulent,whichresultsinenh ancedmixingwithlow momentumruidsurroundingthejetandhenceasuddenspreadingo fthejet.Furthermore,since x=d =2marksthelimitoftwo-dimensionalityforthisrow,the transitiontoturbulencemostlikelyoccursduetospanwiseriblikeinstabilitieswhich developinthevortexpair( Smith&Glezer 1998 ).Thustheturbulenceatthispoint isnotduetoreingestedturbulentstructuresduringsuctionwh icharesubsequently expelledduringthenextcycle. TheRSeldofCase5, Re U 0 =555, St U 0 =0 : 81, h=d =1 : 46,showninFigure 4{91 ,presentsyetadierentpattern.Thestillimagesofthispatt ernarefoundin Figure 4{92 .TheRSisratherhighthroughouttheentiredomain,andthej etwidth iseasilyobservedfrom x=d> 1.Furthermore,acleardisturbancepropagatesfrom

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164 y/dx/d(Click to play movie) -2 -1 0 1 2 1 2 3 4 5 6 -0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1 Figure4{87:Case1phase-averagedReynoldsstressmovie, Re U 0 =43, St U 0 =0 : 84, h=d =1 : 46,incrementbetweencontourlinesis0.01,negativeconto ursareindicated bydashedlines. y/dx/d -2 -1 0 1 2 1 2 3 4 5 6 -0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1 (a) y/dx/d -2 -1 0 1 2 1 2 3 4 5 6 -0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1 (b) y/dx/d -2 -1 0 1 2 1 2 3 4 5 6 -0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1 (c) y/dx/d -2 -1 0 1 2 1 2 3 4 5 6 -0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1 (d) Figure4{88:Case1phaseaveragedReynoldsstressstillframes, Re U 0 =43, St U 0 = 0 : 84, h=d =1 : 46,incrementbetweencontourlinesis0.01,negativeconto ursare indicatedbydashedlines,(a)0 ,(b)90 ,(c)180 ,(d)270

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165 y/dx/d(Click to play movie) -2 -1 0 1 2 1 2 3 4 5 6 -0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1 Figure4{89:Case3phase-averagedReynoldsstressmovie, Re U 0 =161, St U 0 =0 : 78, h=d =1 : 46,incrementbetweencontourlinesis0.01,negativeconto ursareindicated bydashedlines. y/dx/d -2 -1 0 1 2 1 2 3 4 5 6 -0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1 (a) y/dx/d -2 -1 0 1 2 1 2 3 4 5 6 -0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1 (b) y/dx/d -2 -1 0 1 2 1 2 3 4 5 6 -0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1 (c) y/dx/d -2 -1 0 1 2 1 2 3 4 5 6 -0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1 (d) Figure4{90:Case3phaseaveragedReynoldsstressstillframes, Re U 0 =161, St U 0 = 0 : 78, h=d =1 : 46,incrementbetweencontourlinesis0.01,negativeconto ursare indicatedbydashedlines,(a)0 ,(b)90 ,(c)180 ,(d)270

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166 y/dx/d(Click to play movie) -2 -1 0 1 2 1 2 3 4 5 6 -0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1 Figure4{91:Case5phase-averagedReynoldsstressmovie, Re U 0 =555, St U 0 =0 : 81, h=d =1 : 46,incrementbetweencontourlinesis0.01,negativeconto ursareindicated bydashedlines. y/dx/d -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 1 2 3 4 5 6 -0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1 (a) y/dx/d -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 1 2 3 4 5 6 -0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1 (b) y/dx/d -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 1 2 3 4 5 6 -0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1 (c) y/dx/d -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 1 2 3 4 5 6 -0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1 (d) Figure4{92:Case5phaseaveragedReynoldsstressstillframes, Re U 0 =555, St U 0 = 0 : 81, h=d =1 : 46,incrementbetweencontourlinesis0.01,negativeconto ursare indicatedbydashedlines,(a)0 ,(b)90 ,(c)180 ,(d)270

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167 thesurfaceoftheslotduringthecycle,thentheRSeldstabili zesby =270 .This suggeststhataturbulentvortexpairisejectedfromtheslot,w hichcorroboratesthe previousobservationsthatthiscaseisafullyturbulentjet. Thetime-averagedRS isshownforthiscaseinFigure 4{93 .Itisremarkablethatthephase-averagedRS isverysimilartothetime-averagedRS,indicatingthat100sa mplesisadequateto obtainphase-averagedturbulencequantities. y/dx/d -2 -1 0 1 2 1 2 3 4 5 6 -0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1 Figure4{93:Time-averagedRSforCase5, Re U =555, St U =0 : 81, h=d =1 : 46, incrementbetweencontourlinesis0.01,negativecontours areindicatedbydashed lines. Figure 4{94 showstheRSevolutionduringacycleforCase6, Re U 0 =159, St U 0 =0 : 53, h=d =1 : 46,thestillframesofwhicharefoundinFigure 4{95 .The RSeldremainsfairlyconstantthroughouttheentireimaged omainuntiltheonset ofthesuctionpartofthecycle,wherealocalizedregionofin creasedRSmanifests itselfat x=d =2andthenpropagatesdownstream.Thisregionmovesto x=d = 4 : 5duringthefollowingexpulsionstroke,andthisbehaviorisv erysimilartothat observedinFigure 4{89 forCase3,exceptthelocationofthelocalizedregionisfurt her

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168 y/dx/d(Click to play movie) -2 -1 0 1 2 1 2 3 4 5 6 -0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1 Figure4{94:Case6phase-averagedReynoldsstressmovie, Re U 0 =159, St U 0 =0 : 53, h=d =1 : 46,incrementbetweencontourlinesis0.01,negativeconto ursareindicated bydashedlines. y/dx/d -2 -1 0 1 2 1 2 3 4 5 6 -0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1 (a) y/dx/d -2 -1 0 1 2 1 2 3 4 5 6 -0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1 (b) y/dx/d -2 -1 0 1 2 1 2 3 4 5 6 -0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1 (c) y/dx/d -2 -1 0 1 2 1 2 3 4 5 6 -0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1 (d) Figure4{95:Case6phaseaveragedReynoldsstressstillframes, Re U 0 =159, St U 0 = 0 : 53, h=d =1 : 46,incrementbetweencontourlinesis0.01,negativeconto ursare indicatedbydashedlines,(a)0 ,(b)90 ,(c)180 ,(d)270

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169 downstream.Thisisexpectedbecausesincethiscasehasaveryhi ghstrokelength, thevortexpairmovesfurtherdownstreambeforebreakingdow ntoturbulence.This isfurthercorroboratedbyconsideringthatthecutooftwodimensionalityforthis casehasnowincreasedto x=d =3. Forveryshortstrokelength(Case9), Re U 0 =139, St U 0 =1 : 3, h=d =1 : 46, Figure 4{96 ,theRSisprincipallyconnedtotheregion x=d< 2,althoughstarting at =90 thereisalocalizedregionofhigherRScenteredaround x=d =0 : 75.The stillframesforthiscasearefoundinFigure 4{97 .Thisregiondoesnotcompletely dissipatebeforebeingre-energizedbythenextcycle.Fromth erowvisualizationand velocitymeasurements,itisknownthattheregionbeyond x=d =2haslittlerow, andthisexplainswhythereisnosignicantReynoldsstressher e. InFigure 4{98 ,Case10, Re U 0 =175, St U 0 =0 : 73, h=d =0 : 32,theRSvariesconsiderablyduringthecycle,andtheregionofhighestRSreache s x=d =2 : 5.Thestill framesareshowninFigure 4{99 .Thisregionthendecaysduringthefollowingexpulsionstroke.Thispatternisindicativeofaturbulentvortexp ropagatingdownstream, andthisisconrmedbytherowvisualizationandvelocitymea surements. Forverylarge h=d ,Case11, Re U 0 =161, St U 0 =0 : 79, h=d =3 : 32,Figure 4{100 thereisonlyasmallvariationinRSduringthecycle.Thestill frameshereare foundinFigure 4{101 .Thisvariationisalsoconnedto90 << 180 .Itisalso interestingtonotethatastableregionofhigherRSmaybeobser vedat x=d =2,and thereisnegligibleRSbeyondthis.Fromtherowvisualization andvelocitydata,it isknownthatthisisbecausetheroweldremainslaminarinth atregion. TheRSeldforCase12, Re U 0 =143, St U 0 =0 : 88, h=d =1 : 46,shownin Figure 4{102 (movie)andFigure 4{103 (stillframes),isremarkablysimilartothat ofCase3,Figure 4{89 .ThesameregionofhighnegativeRSexistsintheupper leftquadrantoftheimagedomain,andatime-dependentregi onofhigherRSforms

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170 y/dx/d(Click to play movie) -2 -1 0 1 2 1 2 3 4 5 6 -0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1 Figure4{96:Case9phase-averagedReynoldsstressmovie, Re U 0 =139, St U 0 =1 : 3, h=d =1 : 46,incrementbetweencontourlinesis0.01,negativeconto ursareindicated bydashedlines. y/dx/d -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 1 2 3 4 5 6 -0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1 (a) y/dx/d -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 1 2 3 4 5 6 -0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1 (b) y/dx/d -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 1 2 3 4 5 6 -0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1 (c) y/dx/d -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 1 2 3 4 5 6 -0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1 (d) Figure4{97:Case9phaseaveragedReynoldsstressstillframes, Re U 0 =139, St U 0 =1 : 3, h=d =1 : 46,incrementbetweencontourlinesis0.01,negativeconto urs areindicatedbydashedlines,(a)0 ,(b)90 ,(c)180 ,(d)270

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171 y/dx/d(Click to play movie) -2 -1 0 1 2 1 2 3 4 5 6 -0.1 -0.05 0 0.05 0.1 0.15 Figure4{98:Case10phase-averagedReynoldsstressmovie, Re U 0 =175, St U 0 =0 : 73, h=d =0 : 32,incrementbetweencontourlinesis0.0075,negativecon toursareindicated bydashedlines. y/dx/d -2 -1 0 1 2 1 2 3 4 5 6 -0.1 -0.05 0 0.05 0.1 0.15 (a) y/dx/d -2 -1 0 1 2 1 2 3 4 5 6 -0.1 -0.05 0 0.05 0.1 0.15 (b) y/dx/d -2 -1 0 1 2 1 2 3 4 5 6 -0.1 -0.05 0 0.05 0.1 0.15 (c) y/dx/d -2 -1 0 1 2 1 2 3 4 5 6 -0.1 -0.05 0 0.05 0.1 0.15 (d) Figure4{99:Case10phaseaveragedReynoldsstressstillframes, Re U 0 =175, St U 0 = 0 : 73, h=d =0 : 32,incrementbetweencontourlinesis0.0075,negativecon toursare indicatedbydashedlines,(a)0 ,(b)90 ,(c)180 ,(d)270

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172 y/dx/d(Click to play movie) -2 -1 0 1 2 1 2 3 4 5 6 -0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1 Figure4{100:Case11phase-averagedReynoldsstressmovie, Re U 0 =161, St U 0 = 0 : 79, h=d =3 : 32,incrementbetweencontourlinesis0.01,negativeconto ursare indicatedbydashedlines. y/dx/d -2 -1 0 1 2 1 2 3 4 5 6 -0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1 (a) y/dx/d -2 -1 0 1 2 1 2 3 4 5 6 -0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1 (b) y/dx/d -2 -1 0 1 2 1 2 3 4 5 6 -0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1 (c) y/dx/d -2 -1 0 1 2 1 2 3 4 5 6 -0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1 (d) Figure4{101:Case11phaseaveragedReynoldsstressstillframes, Re U 0 =161, St U 0 =0 : 79, h=d =3 : 32,incrementbetweencontourlinesis0.01,negativeconto urs areindicatedbydashedlines,(a)0 ,(b)90 ,(c)180 ,(d)270

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173 y/dx/d(Click to play movie) -2 -1 0 1 2 1 2 3 4 5 6 -0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1 Figure4{102:Case12phase-averagedReynoldsstressmovie, Re U 0 =143, St U 0 = 0 : 88, h=d =1 : 46,incrementbetweencontourlinesis0.01,negativeconto ursare indicatedbydashedlines. y/dx/d -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 1 2 3 4 5 6 -0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1 (a) y/dx/d -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 1 2 3 4 5 6 -0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1 (b) y/dx/d -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 1 2 3 4 5 6 -0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1 (c) y/dx/d -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 1 2 3 4 5 6 -0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1 (d) Figure4{103:Case12phaseaveragedReynoldsstressstillframes, Re U 0 =143, St U 0 =0 : 88, h=d =1 : 46,incrementbetweencontourlinesis0.01,negativeconto urs areindicatedbydashedlines,(a)0 ,(b)90 ,(c)180 ,(d)270

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174 duringtheingestionpartofthecycleat x=d =1 : 5.Thisregiondissipatesduringthe followingexpulsionstrokeasitreaches x=d =3. TheTKEroweldresultsmimictheRSroweldinthatthehigher Reynolds numbercasesexhibitmoreturbulence.Notethatthesamecolorsc aleisusedfor conveniencebutthatvaluesofTKEarestrictlypositive.These roweldsarenot includedhereforbrevity,butanexampleroweldforCase5, Re U 0 =555, St U 0 = 0 : 81, h=d =1 : 46,isshowninFigure 4{104 .Thestillframesofthiscasearefoundin Figure 4{105 .Thiscaseisparticularlyinterestingbecauseatabout =90 ,theTKE ofthevortexpairisclearlyvisibleasthepairissuesfromthesl otandpropagates downstream.However,theTKEthenquicklymergeswiththesurro undingTKEand awavecanbeseenpropagatingdownstream,reaching x=d =1 : 2attheonsetofthe suctionstroke. Furtherinsightintothenatureoftheturbulenceattheslotma ybefoundby examiningthephase-averagedTKEatthesurfaceoftheslot,att hecenterline.These datamaybecomparedtothequalitativehotwireturbulencei ntensitydata,butsince theyarequantitative,moredenitiveobservationsmaybema deconcerningtheturbulence. Figure 4{106 showsthephase-averagedTKEforCases1-5,whichhavevarying Reynoldsnumber.ItisremarkablethatforCases1-3,theTKEi ncreasesasthe Reynoldsnumberincreases,butthereareessentiallynovariati onsinTKEduring thecycle.ForCase4andCase5especially,however,therearesig nicantchanges inTKEduringthecourseofacycle.ConsideringCase5, Re =555,thereisa largeriseinTKEfrom60 << 120 .Furthermore,thereisasecondriseinTKE duringsuctionwhichbeginsat =240 .Itisquitepossiblethatthesuddenrisein TKEduringexpulsionisinruencedbyconditionalturbulence intheslot;however, atpresentthenatureoftheturbulencecannotbedenitively stated{moredatais neededathigherReynoldsnumbers.

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175 y/dx/d(Click to play movie) -2 -1 0 1 2 1 2 3 4 5 6 -0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25 Figure4{104:Case5phase-averagedturbulentkineticenergy movie, Re U 0 =555, St U 0 =0 : 81, h=d =1 : 46,incrementbetweencontourlinesis0.03. y/dx/d -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 1 2 3 4 5 6 -0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25 (a) y/dx/d -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 1 2 3 4 5 6 -0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25 (b) y/dx/d -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 1 2 3 4 5 6 -0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25 (c) y/dx/d -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 1 2 3 4 5 6 -0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25 (d) Figure4{105:Case5phaseaveragedturbulentkineticenergyst illframes, Re U 0 = 555, St U 0 =0 : 81, h=d =1 : 46,incrementbetweencontourlinesis0.03,(a)0 ,(b)90 (c)180 ,(d)270

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176 0 60 120 180 240 300 360 10-2 10-1 100 Phase (deg) u 0 2 + v 0 2 2 U 0 2 Re=43 Re=84 Re=161 Re=280 Re=555 Figure4{106:Phase-averagedcenterlineTKE,Reynoldsnumb ersweep, St =0 : 8, h=d =1 : 46. ThecenterlineTKEforvariousStrouhalnumbersisplottedi nFigure 4{107 ThereislittlevariationintheTKEamongthesecases,similarto theturbulence intensitymeasurementsinFigure 4{7 .However,thereisinterestingTKEbehavior duringtheingestionstrokefor St =1 : 3.Here,theTKEishigherthantheothercases andclearlyrisesnearthestartofthesuction.Becausethestroke lengthissoshort, theformedvortexpairatthecornersoftheslotisalmostimmed iatelyreingested, andthisaccountsfortheriseinTKEduringthispartofthecyc le. AninterestingvariationinTKEisseenfordierentaspectratio s,showninFigure 4{108 .Whilefor h=d =1 : 46and h=d =3 : 32theTKEremainssteadythroughout thecycle,theTKEfor h=d =0 : 32variesconsiderablyandhasasignicantlyhigher valuethantheothertwocases.Sincetheregionoftwo-dimensio nalityforthiscase issmall,itislikelythattheriseinTKEduringingestionisdue tothereingestionof vortexstructures,andthesubsequentexpulsionduringthefollo wingcycle.

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177 0 60 120 180 240 300 360 10-2 10-1 100 Phase (deg) u 0 2 + v 0 2 2 U 0 2 St=0.53 St=0.63 St=0.78 St=1.0 St=1.3 Figure4{107:Phase-averagedcenterlineTKE,Strouhalnumb ersweep, Re =160, h=d =1 : 46. 0 60 120 180 240 300 360 10-2 10-1 100 Phase (deg) u 0 2 + v 0 2 2 U 0 2 h/d=0.32 h/d=1.46 h/d=3.32 Figure4{108:Phase-averagedcenterlineTKE, h=d sweep, Re =160, St =0 : 8.

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178 0 60 120 180 240 300 360 10-2 10-1 Phase (deg) u 0 2 + v 0 2 2 U 0 2 Controlled Uncontrolled Figure4{109:Phase-averagedcenterlineTKEwithandwithou tsinusoidalcontrol, Re =160, St =0 : 8, h=d =1 : 46. 101 102 103 100 101 102 ¡ = L=d Laminar Transitional Turbulent Figure4{110:Dimensionlessturbulenttransitionmap.

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179 ThecenterlineTKEiscomparedatthenominalcaseforcontrol ledanduncontrolledpistonmotioninFigure 4{109 .Inneithercaseisthereevidenceofconditional turbulenceorreingestionofvortexstructures.However,itisi nterestingtonotethat theTKEishigherforthesinusoidal-controlledcase,whichseem stodisagreewith thehotwiremeasurementsofturbulenceintensityinFigure 4{9 .Itmustberecalled, however,thattheTKEmeasurementsaretakenfromPIVvelocit ydatawhichis acquiredslightlyabovetheslot,whilethehotwireisposition edjustinsidetheslot. Itisalsoimportanttonotethatthehotwirevelocitytracesc onsistof1 ; 000samples overacycle,whilethePIV-derivedTKEmeasurementscontaino nly24phasesin thecycle.Thepeakswhichoccurinthehotwiredatamayhaveb eenmissedbythe coarserphaseresolutionofthePIV. ThissectionhasshownthatReynoldsstressandturbulentkineti cenergymeasurementsareveryusefulinquantifyingtheturbulentnature ofaZNMFroweld. Twodierentmechanismswhichcreateaturbulentroweldhav ebeenobserved.For higherReynoldsnumbersandlower h=d ,thevortexejectedfromtheslotisturbulent,andhenceaturbulentroweldexistsatalltimesduring thecycle.Forlower ReynoldsnumbersandalsolowerStrouhalnumbers,alaminarvo rtexpairejected fromtheslotcanbreakdowntoturbulentatsomedistancefromth eslotsurface whichscaleswiththestrokelength,resultinginasuddenwideni ngofthejetand transitiontoturbulence. Figure 4{110 givesatransitionmaptoturbulenceinthesameparameterspace as Glezer ( 1988 ).ItappearsatransitiontoturbulenceforZNMFrowsoccursat = =400.Whileitisdiculttomakeconclusionsbasedononlyafew cases, itisapparentthatahighercirculationimpartedtotherow eldresultsinamore turbulentrow.Thereisalsoadiscrepancybetweenthetransiti onalandturbulent caseswhichhasnotbeenobservedforvortexrings.Thisislikel yduetotheinruence ofthesuctionpartofthecycle.Furthermore,althoughtheva lueoftransitiondoes

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180 notmatchthecriterionin Glezer ( 1988 ),itisimportanttonotethatthiscriterion isforaxisymmetricvortexrings,whileatwo-dimensionalZNMFd eviceisconsidered here.Table 4{3 tabulatesthevaluesofFigure 4{110 bycase. Table4{3:Dimensionlessturbulenttransitionbycase. Case = L=d topology 1153.97.5laminar2182.07.3laminar3494.08.0transitional4718.87.8turbulent5653.37.7turbulent6830.811.9transitional7630.19.9transitional8231.06.3laminar992.84.8laminar10776.08.6turbulent11380.68.0laminar12377.17.1transitional

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CHAPTER5 CONCLUSIONS Thischaptersummarizestheimportanceandrelevanceofther esultsobtained forthisstudy.PreviouslyunknownndingsontheZNMFdeviceop erationand subsequentroweldcharacterizationaredetailed.Suggestio nsarealsoprovidedfor possiblefuturework. KeyFindings Anumberofsignicantresultshavebeenuncoveredbythisstudy whichhavenot beenreportedbeforeintheopenliterature.Thesendingsca nbeclassiedintotwo broadcategories:ZNMFsetupndingsandZNMFrowndings.Whilet heZNMF setupndingsaremorerelevantforresearchersdesiringtousev oicecoilshaker-driven syntheticjetdevices,theresultsobtainedfromtheexperimen tstoquantifyZNMF roweldsarerelevantforanysyntheticjetdevice. Forvoicecoil,shaker-drivensyntheticjets,acommonconstruc tionhasarigid pistondriverwhichissealedinsomemannertoformacavity.The sealingmembrane maybeforgonethroughtheuseofapistondriverwhichgivesave rysmallgap clearancealongthewallofthecavity.Suchacongurationh asbeentermedaviscous sealandithasbeenshownthatatpracticaloperatingconditio ns,theresistanceto rowinthisgapisashighasatypicalventchannel.Withoutth emembrane,the ventchannelisnolongerneededandthecomplexityofdesigna ndconstructionof theZNMFdeviceisreduced.Furthermore,themembraneintrod ucesanadditional compliancetothedevicewhichcanhinderitsrangeofoperat ion,thusthedeviceis moreoptimizedwithoutthesealingmembrane. 181

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182 Shaker-drivensyntheticjetdevicesarelikelytonduseinap plicationsatlow frequencieswheretheiroutputismaximized.Underthesecirc umstances,however, thedrivermotioncanbecomedistortedanddeviatesignicant lyfromtheinputwaveformsignal.Forthecaseofsinusoidalactuation,thisdistorted pistonmotioncanbe modeledasaFourierseries,andtheconcomitantharmonicshav etheeectofaltering theresultingroweldtoamoreturbulentstate.Thisisespecia llyimportantbecause evenwithalltherelevantdimensionlessparametersmatched, twodierentdevices mayproducetwodierentresultingroweldsiftheprogramfa ctorsofthedriversare evenslightlydierent.Therefore,asinusoidalcontrollerha sbeendevelopedtoensure thatnotonlyare Re St ,and 8 matched,butthepistondrivermotionisforced tobesinusoidal.Inthismanner,anyotherZNMFdevice,regardl essofactuation (piezoelectric,speaker-driven,etc.),willyieldthesamer oweldifalloftherelevant dimensionlessparametersarematched. Onceexperimentalvelocitydataareacquiredbutbeforepro cessingtodetermine relevantparameters,thedatamustbereducedtoeliminatenoi sewhichappears asspuriousvelocityvectors.Whilemanydierentspatialvali dationschemesare availabletotheresearcher,theyallhavetheinherentrawof distortingthevelocity gradientsintherow,whichcanbesignicantforZNMFdevices.A multivariate outlierrejectionschemehasthereforebeenadaptedforther equirementsoftwodimensionalruidrowvelocitymeasurement,takingintoaccou ntconstraintsonboth robustnessandcomputationaltime.Suchaschemeismoreaccura tethananyspatial lteringtechniquebecausetherawvelocitydataarenotmodi ed;rather,theyare merelyacceptedorrejectedandstatisticsfreefrombiaserro rsmaybecomputed. Anumberofobservationsofsyntheticjetroweldshavebeenma dewhichcontributesignicantlytothestateoftheart.First,theproperc haracterizationofthe outputofaZNMFdevicemusttakeintoaccountthespatial-varyi ng,time-varying velocityatthesurfaceoftheslot/orice.Thereasonforthisi stwo-fold:rst,spatial

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183 variationsinthevelocityprolecanbesignicant,particu larlyatlowerStokesnumberswheretherowresemblesfully-developedpiperowwithan oscillatingpressure gradient.Second,duetopossiblenon-linearbehaviorinthesl ot,theexitvelocity maynotmimicthevelocityprogramofthedriver.Henceanyvel ocitycomputation whichassumesanexactperiodicformsuchasasinewaveislikelyt obeincorrect.Determinationofthecorrectvelocityproleisalsocriticalf oraccuratecomputationof themomentuminjectedtotheroweld,aswellasknowingthec irculationimparted. Fromtheseresults,ithasbeenshownthatthescalingofaZNMFdevic eis application-specic.Forapplicationswhichrelyonthesucc essfulformationand advectionofvorticesintoaroweldsuchasmixingenhanceme ntorheattransfer, theReynoldsnumberbasedonthemomentumvelocityscaleismost appropriatein characterizingtheroweld,aschangesinthisparameterdi rectlyaecttheextentto whichthesyntheticjetpenetratesintothequiescentmediuma ndtheturbulencelevels intherow.Ontheotherhand,forboundarylayerseparationco ntrolapplications, thedesiredeectofanembeddedZNMFdevicemaybesimplytoimpa rtcirculation totherow,whichcanthenassistinthemixingofhighmomentumru idinthefree streamwithlowmomentumruidintheboundarylayerastheyare sweptdownstream ( Holman etal. 2003 ).Inthiscase,thecirculationisamorerelevantparameter, and aReynoldsnumberbasedoncirculationmaybeemployed( Glezer 1988 ). Anotherinterestingresultfromthisstudyistherelativeeect oftheReynolds numberandStrouhalnumber.Overtheparameterspaceconsider ed,theReynolds numberchierygovernstransitionfromalaminartoaturbulen t-likeroweld.This transitionoccursaroundaReynoldsnumberof400.Incontrast ,whilechangesinthe Strouhalnumberaectthebehavioroftheroweld,thispara meterbestcharacterizes jetformation,asveryhighStrouhalnumbers(andhencelowst rokelengths)donot formajetbutverylowStrouhalnumbers(highstrokelengths)d o.Forthecases

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184 consideredinthisstudy,theStrouhalnumberwasvariedwhile holdingtheReynolds numberxed,andallcasesappearedessentiallylaminar. Signicantinsightintothephase-averagedturbulentnature ofZNMFdevices hasbeenattained.Regardinghotwireanemometry,thisshoul donlybeusedasa qualitativetoolwhenconsideringZNMFrows.Thisisduetotheu nreliabilityof hotwiremeasurementsnearzero-velocity,andthedirection alambiguitywhichcan causesignicanterrorssincetheroweldnearthesurfaceofthe ZNMFdevicehasa non-trivialcross-streamcomponent.Thusanyvelocitydataac quiredwithhotwireis onlyreliableforsemi-qualitativeinformationsuchasturbu lenceandinitialestimates oftheparameterspace.Morequantitativeinformationcanon lybeobtainedvia othervelocitymeasurementssuchasparticleimagevelocimet ryandlaserDoppler anemometry. Thisstudyhasrevealedthatdierentmechanismscanberesponsi bleforthe emergenceofaturbulentstructurefromaZNMFdevice.IftheRe ynoldsnumber ishighenough,thentheroweldundergoesatransitiontotur bulence,similartoa steadyjet.Athighstrokelengths,however,alaminarvortexma ybeexpelledwhich undergoestransitiontoturbulencesomewheredownstreamofth eslot. RecommendationsforFutureWork ConsideringagainFigure 4{3 ,itmaybepossibletoachievebothslightlyhigher ReynoldsnumbersandhigherStrouhalnumbers.Specically, itisexpectedthat conditionalturbulencemaymanifestitself,similartothebeh aviorofpulsatilerows atcertainconditions.Understandingofthisphenomenonwould provequiteuseful forimprovingnumericalsimulationofsyntheticjetrows,whic hoftenassumelaminar rowandwouldthusbedecientinaccuratelycharacterizing aroweldsubjectedto conditionalturbulence.

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185 Anotherphenomenonofinterestthataroseinthestudyofvortexr ingsisthe formationofatrailingtailofvorticitybehindavortexrin gwhichcontainsthemaximumamountofcirculation( Gharib etal. 1998 ). Crook&Wood ( 2000 )qualitatively observedthisforasyntheticjet,anditispossiblethatthisrow patternisathird methodbywhichasyntheticjetmaybecometurbulent.Forappl icationswhichrequirestrongmixingthen,itmaybepossibletoobtainaturbulen tjetatrelativelylow Reynoldsnumber,buthighenoughstrokelengthtoinducethet railingtail.With moredatapointsathighervaluesof St and Re ,areasonablescalinglawmaybe developedwhichcorrelatesthecirculationtotherelevant dimensionlessparameters. AdditionalFutureWork Possibilitiesforfutureworkbeyondthescopeofthisresearchi ncludeextensionof theexperimentaldatabasetootherareasoftheparameterspac esuchasinvestigating slot/oriceradiusofcurvatureeects,theeectsofchangin gcavityvolume,driver dynamics,etc.Forthecaseofacompressiblerow,itmaybepossible toachievea highervolumerowrateoutoftheslotforagiveninputamplitu dethaniftherow wereincompressible.Thedetailedquanticationandmeasurem entofcompressibility eectsinZNMFdevices,then,isaninterestingtopicofstudy. AnotherreasonableextrapolationofthisworkisthestudyofZNM F-induced rowsinteractingwithacross-rowboundarylayersuchasazeropressure-gradient boundarylayeroralongacurvedsurfacesuchasanairfoilshape .Whiletherehas beensomeeorttomodeltheserows,suchasin Gallas ( 2005 ),todatethereis notyetsucient,quantitativevelocitymeasurementsofthen eareldofsuchrows. Inaddition,similartothestudiesofrowsinaquiescentmedium ,mostoftheresearchtodateontheinteractionofsyntheticjetswithacross-r owhasbeenscattered throughoutanon-standardizedparameterspacewhereaccurac yofresultsisseldom reported.

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APPENDIXA SOLUTIONTOFULLY-DEVELOPEDPIPEFLOWWITHANOSCILLATING PRESSUREGRADIENT Theproblemoffully-developedpiperowwithanoscillatingp ressuregradientis themostreasonableexactsolutionavailabletomodelrowseman atingfromtheorice ofaZNMFdevice.Figure A{1 showsaschematicofthisproblem.Aninnitepipe ofradius a 0 issubjectedtoanoscillatingpressuregradientrepresentedby Pe i!t andtheradialandaxialcoordinatesarealsoindicated. r s t u v wx y FigureA{1:Schematicoffully-developedpiperowwithanosci llatingpressuregradient.Theappropriateassumptionsforthisproblemareasfollows: 1.Fully-developedrow2.Incompressiblerow3.Axisymmetricrow4.Parallelrow( v r =0) 5. v z ( r;t )= Re f f ( r ) e i!t g 6.Ignorebodyforces Beginningwiththeexpandedformofthe z -momentumNavier-Stokesequation incylindricalcoordinatesandcancellingoutappropriate termsbasedontheabove 186

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187 assumptions: @v z @t + (4) v r @v z @r + > (3) 1 r v @v z @ + (1) v z @v z @z = 1 @p @z + > (6) g z + 2664 1 r @ @r r @v z @r + > (3) 1 r 2 @ 2 v z @ 2 + (1) @ 2 v z @z 2 3775 (A.1) ThenEq.( A.1 )reducesto @v z @t = 1 @p @z + r @ @r r @v z @r (A.2) Withboundaryconditions v z ( r = a 0 ;t )=0 ;v z ( r =0 ;t )=nite(A.3) Nowlet B P= ,thenbyassumption(5), @v z @t = i!fe i!t ; @p @z = Pe i!t ; @v z @r = f 0 e i!t i!fe i!t = Be i!t + r @ @r rf 0 e i!t i!fe i!t = Be i!t + r rf 00 e i!t = f 0 e i!t i!f = B + f 00 + r f 0 f 00 + 1 r f 0 i! f = B (A.4) Introducingtheparameter y = r p i!= ,theresultingexpressionEq.( A.4 )becomes r = y= p i!= dy dr = r i! d 2 f dr 2 = d dr df dr = d dy dy dr df dy dy dr = i! d 2 f dy 2 df dr = df dy dy dr = r i! df dy i! d 2 f dy 2 + 1 y r i! r i! df dy i! f = B f 00 + 1 y f 0 + f = B i! (A.5)

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188 NowexaminingjustthehomogeneouspartofEq.( A.5 ), y 2 f 00 + yf 0 + y 2 f =0(A.6) RecognizingthisexpressionastheBesselequation,thishasthe generalsolution f ( y )= AJ 0 ( y )+ B 0 Y 0 ( y )(A.7) Where J 0 ( y )and Y 0 ( y )arethezeroorderBesselfunctionsoftherstandsecond kind,respectively.Theterm Y 0 ( y ) !1 as y 0,andsincethevelocityhasa nitevalueat r =0,theconstant B 0 mustbeequaltozero.Nowapplyingtheno-slip boundaryconditionatthepoint r = a 0 0= AJ 0 a 0 r i! e i!t + v z;part: (A.8) Assumingnowaparticularsolutionoftheform v z;part: = B i! e i!t (A.9) Thisimpliesthat 0= AJ 0 a 0 r i! e i!t B i! e i!t B i! AJ 0 a 0 r i! !# e i!t =0 A = B i!J 0 a 0 q i! (A.10) Andrearrangingthisexpression,thesolutionbecomes v z ( r;t )= B i! e i!t 24 1 J 0 r p i!= J 0 a 0 p i!= 35 (A.11) Nowtonon-dimensionalizethisexpression,areferencevelocit yscaleandlength scalemustbedened.Forsteady-statePoiseuillerow,themaximu mvelocityoccurringalongthecenterline r =0forpressuregradient B is v z; max = a 20 B= 4 Non-dimensionalizingtheradialcoordinate r bytheradiusofthepipegives r =

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189 r=a 0 .NowintroducingtheStokesnumberas S = p 4 a 20 != = p !d 2 = ,thenondimensionalsolutionforthevelocityprolebecomes v z v z;max = i 16 S 2 1 J 0 0 : 5 r S p i J 0 0 : 5 S p i # e i!t (A.12) AplotofthevelocityproleisgiveninFigure A{2 forseveralStokesnumbercases. 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 r*v z /v z,maxS=1 S=5 S=10 S=15 S=40 FigureA{2:Normalizedvelocityprolevs.normalizedradius. Withthevelocityprole u ( r;t )nowcompletelydetermined,theratiobetween thetime-averaged,spatial-averagedvelocityduringtheex pulsionpartofthecycle U andthecenterlinevelocityamplitude ^ U cannowbecomputedasafunctionof theStokesnumber.Figure A{3 showsthisratio.Onemaynotice,inparticular, thatatlowStokesnumberthisratioapproaches1 = ,whileathighStokesnumberit asymptotesto2 = .Physicallythismakessense,becauseatveryhighStokesnumber therowfromtheoriceisessentiallyslug-like,suchthatthece nterlinevelocityis

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190 alsothespatial-averagedvelocityandhence U = Z =! 0 ^ Usin ( !t ) dt = 2 ^ U (A.13) Also,atverylowStokesnumber,therowresemblesPoiseuillerow ,withaspatialaveragedvelocityequaltohalfthecenterlinevelocity(fo raxisymmetricrow)atany instantintime;thusforthiscaseitisexpectedthat U= ^ U =1 = {halfthevaluefor highStokesnumber. 10-1 100 101 102 103 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 U= ^ UStokes Number 1/ p 2/ p FigureA{3: U= ^ U vs.Stokesnumberforpiperowwithanoscillatingpressuregradi ent. Wemayquantifytheterms\highStokesnumber"and\lowStoke snumber"by examiningthevaluesatwhichtheratio U= ^ U deviatesby5%fromitsasymptotic values.If S< 6,thentaking U= ^ U =1 = isareasonableapproximation.Likewise, if S> 55,thentaking U= ^ U =2 = isalsoreasonable.Intherange6 S 55,one mustconsultFigure A{3 togetthecorrectratio U= ^ U .Itmustbenoted,however, thattheseresultsareonlyestimateswhichassumetherowattheex itresembles

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191 fully-developedpiperowwithanoscillatingpressuregradien t.Especiallyinthecase ofathinoriceplate, h=d< 1,theassumptionoffully-developedrowisproblematic. Nevertheless,intheabsenceofactualdataforthevelocitypro lesfromthevarious studiesreviewedhere,thissolutionisdeemedthemostreasonab lealternativefor computing U andhencetheReynoldsnumber. 10-1 100 101 102 103 0.4 0.45 0.5 0.55 0.6 0.65 Stokes Number U= ^ U2/ p 4/3 p FigureA{4: U= ^ U vs.Stokesnumberfortwo-dimensionalchannelrowwithanoscil latingpressuregradient. Forthecaseofatwo-dimensionalslot,theanalysisissimilarexc eptthenal solutionconsistsofhyperboliccosinesinsteadofBesselfunction s: u ( y;t ) u max = i 8 S 2 1 cosh y S p i cosh 0 : 5 S p i # (A.14) Figure A{4 showstheratio U= ^ U asafunctionoftheStokesnumberforthetwodimensionalcase.WenotethatthehighStokesnumberapproxim ation, U= ^ U =2 = isnowvalidfor S> 29inthiscaseandisthesameresultastheaxisymmetriccase becauseinbothcases,ahighStokesnumberrowyieldsaslugveloc ityprole.The

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192 lowStokesnumberapproximationhaschangedhowever, U= ^ U =4 = 3 for S< 5, becauseforthecaseoftwo-dimensionalpressure-drivenrow,the averagevelocityis nowtwo-thirdsthecenterlinevelocity.FortheStokesnumb errange5 S 29and foratwo-dimensionalslot,onemustconsultFigure A{4 forthepropervalueof U= ^ U Onceagain,thecaveattothisanalysisisthatthesyntheticje troweldismodeledas afully-developedtwo-dimensionalchannelrowwithanoscill atingpressuregradient.

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APPENDIXB VORTEX-BASEDJETFORMATIONCRITERION Acriterionforpredictingonsetofjetformationisespeciall yusefulformany syntheticjetapplicationswhichrelyonthesuccessfulformati onandsubsequentadvectionofvortexpairs(orrings).Figure B{1 illustratesavortexpair(orring) emanatingfromaslot(ororice).Theabilityofthepairtoov ercomethesuction velocityduringtheingestionstrokedependsonitsself-induc edvelocity,whichinturn isafunctionofthevortexstrength.Thestrengthofeachshedvo rtexn v hasbeen shownby Didden ( 1979 )toberelatedtotheruxofvorticitythrougha( x;y ) planar sliceofthehalf-slotduringtheejectionphaseofthecycle n v = Z T= 2 0 Z d= 2 0 z ( y;t ) u ( y;t ) dydt (B.1) where z ( y;t )isthespanwise(orazimuthal)vorticitycomponentattheexi tfora two-dimensional(oraxisymmetric)case.InFigure B{1 s isthesizeoftheshear rowregioncharacterizedbynon-zerovorticity.Theinduce dvelocityofthedipole V I isthusproportionalton v =d .Anorder-of-magnitudeanalysisofEq.( B.1 )resultsin n v U s U s 1 U 2 (B.2) where U isthespatialaveraged,timeaveragedstreamwisecomponentof velocity duringexpulsionattheexitplane.Asanaside,itisnotedthate venthoughthejet formationcriterionisdevelopedusingthevelocityscale U ,itisreasonabletoassume U U 0 forthisorder-of-magnitudeanalysis. 193

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194 Ifitisassumedthatajetwillformwhentheinducedvelocityof thedipole V I is somewhatlargerthantheaveragejetsuctionvelocity V s U ,itfollowsthat V I V s n v =d U U !d = 1 St U = Ud= !d 2 = = Re U S 2 >K (B.3) where K isan O (1)constant.Eq.( B.3 )statesthatajetisformedwhentheStrouhal numberisbelowacriticalvalue.Ofcourse,itisexpectedtha tthevalueoftheconstant K inEq.( B.3 )willbeaectedbytheoricegeometry,namelytheaspectrat io h=d andtheexitedgeshape(sharporrounded).Theconstantisalsoex pectedto assumedierentvaluesfortwo-dimensionalandaxisymmetricmo delshavingsimilar oricegeometry,duetodierentfunctionalformsofsolutio nstofully-developedunsteadypressure-drivenrowinapipevs.atwo-dimensionalchanne l( White 1991 ; seealsoAppendix A ).Theinruenceoftheaforesaidfactorsonthescalingconstant isrecognizedandbrierydiscussednext. FigureB{1:Detailedschematicofasyntheticjetshowingeject edvorticity.

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195 EectofOriceGeometry Theinruenceoftheoricegeometryonthevalueoftheconstan t K canbe reasonablyexplainedbyasimpleextensiontotheabovescaling. Eq.( B.1 )canbe adaptedforajetwitharoundededgeto n v = Z T 2 0 Z d 2 + R 0 @u ( y;t ) @y u ( y;t ) dydt (B.4) where R istheradiusoftheroundededge,andthecenterlineandno-sl ipboundary conditionson u ( y;t )are u (0 ;t )= u 0 ( t )and u ( d= 2+ R;t )=0,respectively.The spatialintegrationyields n v = Z =! 0 1 2 u 20 dt (B.5) whichcanbeevaluatedbyassumingasinusoidalformofthecenter linevelocity u 0 ( t )= ^ U sin( !t )andemploying U= ^ U ,theratioofthetime-averaged,spatial-averaged velocitytothecenterlinevelocityamplitudeasdiscussedinAp pendix A : n v = 1 4 U 2 U ^ U 2 (B.6) Employingthenon-dimensionalexitradiusofcurvature, =2 R=d ,thefollowing heuristicexpression( Saman 1997 ; Pierrehumbert 1980 )canbeusedtoestimate theinducedvelocity V I = n v 2 D V = n v 2 d (1+ ) p (B.7) bymodelingthedistancebetweenthevortexcenters( D V inFigure B{1 )asequal to d (1+ ) p .Here,theexponent p< 1accountsgrosslyforrowseparationdueto theexitcurvature,and isaconstantthatdependsontheratioofthevortexcore radius( a )todistancebetweenthetwovortexcenters( D V ).SubstitutingEq.( B.6 ) intoEq.( B.7 )gives V I = U 2 8 !d U ^ U 2 (1+ ) p (B.8)

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196 Next,let V s = U ,then V I V s = U 8 !d U ^ U (1+ ) p (B.9) RecallingEq.( B.3 ), V I V s Re U S 2 >K (B.10) RecognizingtheformoftheStrouhalnumberinEq.( B.9 ): Re U S 2 8 U ^ U 2 (1+ ) p >K (B.11) RearrangingEq.( B.11 )yieldsthemodiedcriterionforjetformation 1 St U = Re U S 2 > 8 K U ^ U (1+ ) p = K 0 (B.12) where K 0 isanewproportionalityconstant. TherearetwosignicantimplicationsofEq.( B.12 ).First,itindicatesalower jetformationconstantfororiceswithasharpexit(small )ascomparedtothose withaniteradiusofcurvature( ).Inotherwords,alletradiuswilltendtodelay theformationofdiscretevortices,althoughthisdoesnotimp lyanythingaboutthe eciencyofjetformation{see Fugal etal. ( 2004 ). Bycomparison,itisdesiredtominimizethecombinedinruence ofexitcurvatureandStokesnumberonthedataofFigure 1{11 (via U= ^ U )bynormalizingthe Reynoldsnumberbytheconstant8( U= ^ U )(1+ ) p ,asderivedfromEq.( B.12 ).This normalizationoftheReynoldsnumberattemptstounifythej etformationanalysisfor syntheticjetswithvaryingexitcurvatureandoperatingove rawiderangeofStokes numbers.Theexponent p =0 : 62providesthebestqualitativeagreementwithinthe wide-rangingexperimentaldataof Smith&Swift ( 2001 ),asdepictedinFigure B{2 Despitetheapparentagreement,itisimportanttonotethatt hisanalysisis inadequatetopreciselymodelallcomplexitiesoftherowint hejetorice,andonly servestoestimatetheimpactofthesignicantfactorsonthesca lingconstant.In

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197 10 20 40 100 101 102 103 Stokes NumberRe / [8(U/U)2(1+ e )p] d=0.5 cm, e =2.4 d=1.0 cm, e =1.2 d=1.5 cm, e =0.8 d=2.1 cm, e =0.6 (modified) Re/S2=0.17 Jet No Jet FigureB{2:Normalizedjetformationdatatoaccountforradi usofcurvatureand Stokesnumber.Thedataisfrom Smith&Swift ( 2001 ),andispresentedin Holman etal. ( 2005 ). particular,thereisinsucientinformationatpresenttocal culatetheconstant in Eq.( B.12 )duetoalackofknowledgeofthevortexsizeandspacing. Second, K 0 isdirectlyproportionaltothesquareof U= ^ U 1whichis,inturn, aectedbythegeometryoftheoriceandtheStokesnumber( White1991 ,Appendix A ).Furthermore, K 0 / 1 = where inEq.( B.7 )dependsonwhethera vortexdipole(inthecaseofaslot)orring(inthecaseofanori ce)isconsidered ( Saman 1997 ; Pierrehumbert 1980 ).Thedistinctionbetweenatwo-dimensional slotandanaxisymmetriccircularoriceisdiscussedfurtherbel ow. 2Dvs.AxisymmetricJet Saman ( 1997 )and Pierrehumbert ( 1980 )haveestimatedtheconstant inEq. ( B.7 )asafunctionof a=D V inthecaseoftwo-dimensionalvortexdipolesandaxisymmetricvortexrings.For0
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198 asnotedinAppendix A .Forlarge S ,thevalueof U= ^ U tendsto2 = (aslugprole)forbothcases.Consequently,thesecombinedeectssuggestt hattheformation constant K 0 foraxisymmetricjetsissignicantlylower,byuptoalmostano rder ofmagnitude,thanitstwo-dimensionalcounterpart.Thisis validatedbynumerical simulationsperformedby Utturkar ( 2002 )andexperimentsdescribedbelow. ExperimentalResults Anaxisymmetric,piezoelectric-drivensyntheticjetdevicei sconstructedand testedtosupplementtheworkof Smith&Swift ( 2001 ).Thedetailsofthefabrication ofthisdevicearegiveninChapter 3 .PIV-basedrowvisualizationisrstused todeterminetheonsetofjetformation.Anovelaliasingtechn iqueisemployed toacquiresuccessiveimagepairsoverthecycletoaccuratelyc apturetheroweld behaviorwhilesimultaneouslyminimizingthenumberofacqui redimagepairs.This techniqueinvolvessettingtheoscillationofthedriver(and hencethetriggersignalto thePIVsystem)atafrequencysuchthatthePIVframerateissligh tlydierentthan asubmultipleofthisactuationfrequency,aprocesssimilarto theschlierenimaging of Smith&Glezer ( 1998 ).Eachimagepairthenshowsanewvortexringataslightly dierenttimeduringthecycle,resultinginan\aliasedmovie "oftheroweld.Given theactuationfrequency f ,thefrequencybetweenPIVimagepaircaptures f p ,and thedesiredphasebetweenimagepairs d ,thenecessarytriggerfrequencybecomes f t = f f p d 360 (B.13) Velocityvectoreldsoveronealiasedcycleofthesyntheticj etareacquired,and vorticitycontoursarecomputedforeachframe.Theresultin galiasedmovieofthe vortexsheddingisthenusedtodeterminejetformation.Jetfo rmationisdenedas thesheddingofavortexringfromthesurfaceoftheoricewhic hissucientlystrong topropagateawayunderitsownself-inducedvelocity,result inginatime-averaged jet-likerowemanatingfromtheorice.Figure B{3 showstheevolutionofvorticity

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199 duringtheminimumandmaximumcavityvolumestagesofthecyc lefor S =18under nojet,transitional,andclearjetformationconditionsresp ectively.Themeanrow fromtheoriceispresentedinFigure B{4 forthecorrespondingcasesinFigure B{3 Indeed,theformationofameanjet,evidentinFigure B{4 (c),correspondstothe caseofvortexsheddinginFigure B{3 (c). z{ | { }{ FigureB{3:PIVvelocityvectoreldswithoverlaidvortici tycontoursforminimum (leftcolumn)andmaximum(rightcolumn)cavityvolumestage srespectively, S =18, axisymmetricorice,(a)nojet( Re U =44),(b)transition( Re U =82),(c)jet ( Re U =121). VelocityprolesareacquiredusingbothPIVandLDAtechniqu estoprovide mutualverication.TheReynoldsnumberiscomputedbyinte gratingthevelocity

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200 y/d x/d 1 0.5 0 0.5 1 0 0.5 1 1.5 2 y/d x/d 1 0.5 0 0.5 1 0 0.5 1 1.5 2 y/d x/d 1 0.5 0 0.5 1 0 0.5 1 1.5 2 ~ €  FigureB{4: U -componentvelocitycontourscorrespondingtoFigure B{3 ,increment betweencontourlinesis0.05m/s, S =18,circularorice,(a)nojet( Re U =44),(b) transition( Re U =82),(c)jet( Re U =121). prolestoyieldthevolumerowrates.Table B{1 summarizesthecomparisonbetween thecomputedReynoldsnumberusingPIVandLDA,fortwodieren tStokesnumber cases.Thedataagreetowithinthe95%condenceintervalsfor allcases,evenat slightlydierent x=d locations,indicatingthatthevelocitydataacquiredareac curate. TableB{1:ComparisonbetweenPIV-andLDA-acquiredReynoldsn umbers. MeasurementTechniqueandLocation S =12,nojet formation S =18,clear jetformation PIV, x=d =0 : 0817 : 8 3%121 : 2 3 : 7% LDA, x=d =0 : 0818 : 9 3%121 : 4 3% LDA, x=d =0 : 0318 : 1 3%126 : 9 3% Oncejetformationhasbeendetermined,theReynoldsnumber isdetermined asdescribedpreviously.Thejetformationdatafromthecurre ntexperimentsalong

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201 withtheaxisymmetricdatafrom Ingard&Labate ( 1950 )and Smith etal. ( 1999 )are comparedinFigure B{5 .Itisfoundthattheavailabledataisconsistentwiththejet formationcriterionwithanempiricallydeterminedconstan t K equaltoabout0.16. ComparingFigure B{2 andFigure B{5 ,onemaybetemptedtodrawtheconclusion that K 0 : 16isauniversalconstantofjetformationforboththetwo-dim ensional andaxisymmetricgeometries.However,thisisnotthecasedueto thereasonsdiscussedpreviously.Thefactthatthemodiedconstantforthetwo -dimensionalcase wasnearlyequaltotheunmodiedconstantoftheaxisymmetric caseinvestigated hereisostensiblycoincidental. 10 20 40 100 100 101 102 103 104 Stokes Number Reynolds Number FigureB{5:Jetformationcriterionforaxisymmetriccase:( )thresholdjetformation valuesof Ingard&Labate ( 1950 ),( )thresholdjetformationvaluesof Smith etal. ( 1999 ),( N )maximumvaluesofnojetformationacquiredforthecurrent study,and ( F )minimumvaluesofobservedjetformationacquiredforthecu rrentstudy.

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APPENDIXC PARAMETERCONVERSION Inordertoperformadirectcomparisonbetweenresultspublish edintheliterature,acareful,systematicapproachmustbetakentoconvertth ereportedvaluesof thesestudiestotheparameterspacedenedinChapter 2 .Foreachstudyconsidered here,theobservedroweldisnotedalongwiththereportedde nitionsoftherelevant parametersandthereportedaccuracyofthoseparameters.Fur thermore,ifinformationnecessaryforparameterconversionoraccuracyismissingor ambiguous,thatis notedaswell.Eachstudyshallbeexaminedintheorderthatitw asintroducedin Chapter 1 Ingard&Labate(1950) Fourseparaterowregionsweredenedby Ingard&Labate ( 1950 )asnotedin Chapter 1 .Therowregionthresholdwasreportedasafunctionofthefol lowingdimensionalparameters:oricediameter( d ),oriceheight( h ),frequencyofoscillation ( f ),and\particlevelocity"( u p ).Thustheoriceheight-to-diameteraspectratio h=d isreadilyobtained.Theworkingruidwasair,sotheStokesnu mberisfoundby setting =2 f .Althoughtheparticlevelocity u p wasanambiguousquantity,ina laterpaper, Ingard ( 1953 )clariedthisasanRMSvelocity.Itshallbeassumedthat u p istheRMSvelocityatthecenterlinesuchthat ^ U = p 2 u p (C.1) 202

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203 Mostofthereportedresultshave S> 55,soforthisaxisymmetricsyntheticjet theanalysisofAppendix A allowsonetocomputetheReynoldsnumberasfollows: Re U = 2 p 2 u p d (C.2) Noinformationontheaccuracyofthevelocitydataisprovide dinthisstudy.Once again,itisnotedthateventhoughtheprinciplevelocitysca leusedforthisstudyis U 0 ,quantitiesbasedon U followthesametrendsasquantitiesbasedon U 0 because U U 0 asreportedinAppendix B Smith&Glezer(1998) Anominalcasedescribedasasinglevortexpairfollowedbyatur bulent-likejet characterizedtheworkof Smith&Glezer ( 1998 ).Thetwo-dimensionalslotdimensionsweregivenandarenotedintheliteraturereview,andth eheightwasreported in Lee&Goldstein ( 2002 )tobe2 : 5 d .Thefrequencyofthenominalcasewasreported inHertzandtheworkingruidwasair,thusthegeometricparam etersandtheStokes numbercanbeobtained.Comparingthedenitionoftheveloc ityscaleusedintheir work,Eq.( 1.5 ),thefollowingequivalenceinReynoldsnumberisfound: Re U =2 Re U 0 (C.3) Thereisnoreportedinformationontheaccuracyoftheveloc itymeasurements. Inaddition,theStokesnumberiscomputedtobe S = r !d 2 = s (2 f ) d 2 air = s (2 )(1140Hz)(0 : 5 10 3 m) 2 (1 : 536 10 5 m 2 = s) =10 : 8(C.4) andthisvalueistoolowtoconsiderthevelocityeldattheex ittobespatially uniform.ThustheanalysisofAppendix A mustbeappliedheretodetermine U Nowitremainstobedeterminedwhattherelationshipisbetwee ntheamplitude ofthecenterlinevelocity ^ U andthevelocityscale U 0 .RecallingEqs.( 1.1 )and ( 1.5 ),andassumingthatthecenterlinevelocity u 0 ( t )issinusoidalintime,givesthe

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204 following: U 0 = 2 Z =! 0 ^ Usin ( !t ) dt = ^ U (C.5) Hencethisimpliesthat ^ U = U 0 (C.6) andamorepreciseexpressionfortheequivalenceoftheReynold snumbersthanEq. ( C.3 )isobtained: Re U = U ^ U Re U 0 (C.7) ForthisStokesnumbercase,fromAppendix A U= ^ U 0 : 45,thusEq.( C.7 ) becomes Re U =1 : 41 Re U 0 (C.8) Thisexerciseunderscorestheimportanceofmeasuringtheenti revelocityprole asopposedtojustthecenterlinevelocitytocomputetheReyno ldsnumber.Ifone assumedaslugvelocityproleforthiscase, Re U wouldhavebeenoverestimatedby about40%. Smith&Swift(2001) Inapaperwhichexaminedajetformationthreshold, Smith&Swift ( 2001 ) utilizedadevicewhichallowedforadjustmentoftheirtwo-d imensionalslotdepth. Sincetheedgesoftheslotwererounded,thegeometricparame ters h=d w=d ,and werevariedsystematically.Althoughadirectcomparisonwitho therresultsfrom sharp-edgedslotsofdierentgeometriesisnotfeasible,with and w=d xed,changes intheStrouhalnumberarenotaectedbytheseparameters,the reforetheseresults canstillbeinstructiveandprovideinsightintotherowbehavi or. Thegeometricparametersweregiven,aswastheratioofthev iscouspenetration depth = p =f totheslotdepth d ,sotheStokesnumbercanbedeterminedas S = p 2 ( =d ) (C.9)

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205 Thedimensionlessstrokelengthwasalsogiven,buthereitwasco mputedbymeasuringthecross-streamdistributionofthevelocityattheexitp lane,asopposedto relyingsolelyonthecenterlinevelocity.Thustheratio U= ^ U isnotneededhere,but anexpressionfortheReynoldsnumberparametermustbeobtaine dintermsofthe dimensionlessstrokelength L=d andtheratiooftheviscouspenetrationdepthtothe slotdepth =d .Here, L istheaveragestrokeaparticlemovesduringexpulsionwith velocity U .RecallingEq.( C.3 ),itcanbeseenthatthevelocityscalesarerelatedby U =2 U 0 .FromEq.( 1.5 )then,itfollowsthat U =2 Lf (wehavereplaced L 0 by L sincethespatial-averagedvelocityisused),sotheReynoldsnu mbercanbeexpressed as Re U = 2 Lfh =2 L h h 2 f (C.10) ThelasttermontheRHSofEq.( C.10 )canbewrittenintermsoftheviscous penetrationdepthtoslotdepthratio: f = 1 1 d 2 ( =d ) 2 (C.11) ThusapplyingEq.( C.11 )toEq.( C.10 )andsimplifyingyields Re U 0 = 2( L=d ) ( =d ) 2 (C.12) Informationontheaccuracyofthedatawasnotpresented. Smith etal. (1999) Bothanaxisymmetricoriceandtwo-dimensionalslotgeometri eswerestudiedin Smith etal. ( 1999 ).Inthecaseoftheaxisymmetricorice,asmentionedpreviou sly, alargejumpinstrokelengthwasobservedatagivencavitypressu reasthevortex ringescapedtheinruenceofthesuctioncycle.This,presumably ,correspondstothe onsetofjetformation.Forthetwo-dimensionalslot,PIVwasuse dtoacquirethe velocityeldandfromthisthevorticitycontoursoftherow eldwerecomputed. Thesecontoursdemonstratedthatatleasttwovortexpairsrema inedcoherentafter

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206 ejectionfromtheslot.Themeanrowstreamfunctioncontoursi ndicatedthepresence ofajet.Theworkingruidwasair,andtherelevantgeometric parameterswere supplied,aswasthedriverfrequency.Thisallowsforcomput ationoftheaspectratio andStokesnumber.ThevelocityscaleusedtocomputetheReyno ldsnumberwas thesameas Smith&Glezer ( 1998 ), ~ U = L 0 =T .Sincethereisnospecicdiscussion onwhether u 0 ( t )isacenterlineorspatial-averagedvelocity,andbecauseth eauthors specicallyfollowthemethodologyof Smith&Glezer ( 1998 ),itisassumedthat u 0 ( t ) isthecenterlinevelocityandtheratio U= ^ U mustbeappliedtotheirtwo-dimensional datainordertoproperlycomputetheReynoldsnumber.Forth eaxisymmetriccases, S> 55andso U= ^ U =2 = .AlthoughPIV-generatedvelocityprolesaregiven,no informationontheaccuracyofthesedataisprovided. Crook&Wood(2000) Severalroweldsgeneratedbyaxisymmetricsyntheticjetswe reidentiedby Crook&Wood ( 2000 )asafunctionofReynoldsnumberandoricegeometry.No meanrowresultswerepresented,butonlyphase-lockedinstanta neousrowelds. Theobservedpatternsincludedinteractinglaminar-likevo rtexrings,non-interacting laminarrings,andringswhichbegantoappearturbulentandc ontainedtrailingtails ofexcessvorticity.Theworkingruidwasair,theoriceheig htanddiameterwere given,andallresultswereacquiredforaxedfrequency.The velocityscaleusedto determinetheReynoldsnumberwastheamplitudeoftheruidv elocityattheorice exit,whichwasassumedtobeslug-like.AtaStokesnumberofapp roximately22, however,thecorrectionfactor U= ^ U mustbedeterminedfromFigure A{3 inorder tocomputethecorrectReynoldsnumber Re U .Hotwireanemometrywasusedto acquirethevelocitydata,butthereisnoinformationonthe accuracyofthisdata. Rediniotis etal. (1999) Twointerestingrowpatternsareobservedoveranaxisymmetric oriceproducingasyntheticjetinwaterby Rediniotis etal. ( 1999 ).Therstisasuction-likerow,

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207 whilethesecondismorecharacteristicofasyntheticjet.Fore achpattern,theorice diameterandheightarenoted,aswellasthefrequencyofact uation,whichgivesthe geometricparametersaswellastheStokesnumber.Phase-loc kedPIVmeasurements revealedthattheamplitudeofthecenterlinevelocityfore achcasewasapproximately 0.1m/s.ThereforetheReynoldsnumbermaybecalculatedbyco mputingtheratio U= ^ U foreachcase.Onceagain,noinformationontheaccuracyofth edatais provided. Bera etal. (2001) Bera etal. ( 2001 )observedastrongjetbeingformedfromatwodimensional slitmeasuring100mmlongand1mmwide.Theircavitygeometryw assomewhat unusual,startingatthebottomwiththeloudspeaker-actuator andtaperingotothe slotdepthatthetop.AlthoughtheStokesnumberoftherowwasl ow(approximately 9),thespatialresolutionoftheirPIVmeasurementswasnearly thesameastheslot depth.Therefore,theRMSvelocityvaluetheymeasuredwasin deedaspatially averagedvelocity,analgousto U 0 ,andtheReynoldsnumberbasedon U canbe computed.Somedetailsareprovidedontheaccuracyoftheda ta.Specically,they notedthataveragingthephase-averageddataproducedthesam emeanasrandomly acquireddata.However,therearenootherspecicdetails. Cater&Soria(2002) Usingwaterastheworkingruid, Cater&Soria ( 2002 )identiedseveralrow regionsasafunctionoftheirReynoldsnumberandStrouhaln umber,includinga seriesoflaminarrings,alaminarjet,andaturbulentjet.The Reynoldsnumberwas basedonthemomentumrowvelocityscale U 0 whichwascomputedbyintegratingthe squareofthevelocityproleovertheoriceandduringoneen tirecycleandtaking thesquareroot(seeChapter 2 ).Theamplitudeofthespatial-averagedvelocityis foundbysimplymultiplyingthemomentumrowvelocityby p 2.Theappropriate geometricparametersaregiven,andtheStokesnumbercanbe computedfromtheir

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208 Re 0 and St 0 asfollows: Re 0 St 0 = U 0 d fd U 0 = 1 2 2 fd 2 = S 2 2 (C.13) Thus S = p 2 Re 0 St 0 (C.14) NowwithknowledgeoftheStokesnumberandtheamplitudeofth espatial-averaged velocity U A Re U canbedeterminedbecause U =2 U A = .Fortheirvorticitycalculations,theycomputedbothabiasandarandomerror. Therowvisualizationworkof Cater&Soria ( 2002 )hasanimportantcaveat whichdeservesspecialattention.Becausetheworkingruidwas wateranddyeinjectionwasusedtovisualizetherow,caremustbetakenwheninterp retingtheresults. Thedyeitselfmayleadtoanerroneousconclusionabouttherow eld,becausedye maybepresentinregionsofnovorticity.Indeed,foranappar entlylaminar-typerow, thecomputedReynoldsnumberseemedunusuallyhigh, Re O (10 4 ),andiscause forconcernwhencomparingresultsfromotherstudies.Thisdisc repancyunderscores themotivationforthiswork{theopenliteraturetodateisn otconsistentinthe descriptionofsyntheticjetroweldsevenwhenthedimensionl essparameterspace isseeminglyidentical. Yehoushua&Seifert(2003) Usingphase-lockedPIV, Yehoshua&Seifert ( 2003 )studiedtheevolutionof ejectedvortexpairsfromapiezoelectric-drivensynthetic jetdevice.Althoughthe mainemphasisoftheirpaperwasonquantifyingtheeectofasy ntheticjetwhen placedinthepresenceofacross-rowboundarylayer,theyexami nedanumberof caseswherethesyntheticjetexhaustedintoaquiescentmedium. Specically,they observedthetransitionfrom\nojet"to\clearjet"basedonwhe thertheejected vortexpairescapedtheslotduringthesuctionpartofthecycle .Theworkingruid wasair,andtheyprovidedtherelevantgeometricparameter saswellastheactuation

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209 frequency.Foreachrowconditiontheyalsonotedthepeakexi tvelocityattheslot. ThisquantitymaybeusedinconjunctionwiththeStokesnumbe randtheratio U= ^ U toprovideanestimatefortheReynoldsnumber Re U .AcomparisonbetweenPIV andhotwirevelocitymeasurementswasalsomade,anditwasfou ndthatatclose distancestotheslot,PIV-acquiredvelocitydatadidnotmatch hotwiredata.One possibleexplanationforthiswasbecausethephaseresolutionof thePIVwaspoor. Shuster&Smith(2004) Quantitativeresultsareprovidedfortwodierentaxisymmet ricoricecongurationsby Shuster&Smith ( 2004 ):astandardsharp-edgedorice,andanorice whichwasbeveledontheexitplaneside.Theydescribedtheeme rgingrowpatterns fromoneringwhichbrokedownintoaturbulentjet{similarto Smith&Glezer ( 1998 ){toatrainofvortexringswhichdidnotbreakdownwithinth emeasurement domain.Althoughtheyassumedaslugvelocityprole,forthemost partthiswasa reasonableassumptionbecausetheStokesnumbersoftheirtestca sesweregenerally above55,withtheexceptionofafewcasesforwhichthecorrec tionfactor U= ^ U will havetobeappliedinordertocomputetheReynoldsnumbercor rectly.Thenecessarygeometricparameterswereprovided,alongwiththedime nsionlessstrokelength andtheReynoldsnumberbasedon U 0 ,theaveragecenterlinevelocityduringthe expulsionstroke.Sinceboth L 0 and U 0 aregiven, canbedeterminedandhence theStokesnumber.Alsosince U 0 =2 ^ U= forasinusoidalvelocityprole, ^ U can becomputedandwiththeStokesnumber, Re U maybereadilyobtained.However, informationontheuncertaintyandaccuracyofthedatawasn otprovided. Utturkar etal. (2003) Bothexperimentalandcomputationaldatawerepresentedin Utturkar etal. ( 2003 )andlaterin Holman etal. ( 2005 ).Theirstudyfocusedspecicallyonajet formationcriterion;i.e.,thepointatwhichtheejectiona ndsubsequentadvectionof vorticesfromtheoricebecameapparent.Theyexaminedcase sofnojet,transition,

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210 andclearjetformation.Theirgeometricparameterswereno ted,asweretheStokes numberandtheproperReynoldsnumber Re U .Inaddition,estimatesontheaccuracy oftheReynoldsnumberwereprovided,basedontheuncertaint yofthevelocity measurementsandtheuncertaintyoftheoricediameter.The workingruidforthis studywasair. Rizzetta etal. (1999) Inanumericalsimulationofatwo-dimensionalsyntheticjetro w, Rizzetta etal. ( 1999 )observedcoherentejectedvortices.Withaxedfrequencyan dgeometric parameters,allrelevantdimensionlessparameterscanbedete rmined.TheReynolds numberiscomputedbasedonthepeak-to-peakvelocityamplit ude,whichcanbe usedinconjunctionwiththeratio U= ^ U tocompute Re U asinseveralotherstudies. Lee&Goldstein(2002) Lee&Goldstein ( 2002 )alsoperformednumericalsimulations.Theyexamineda numberofcaseswhichincludedroweldsthatwerecharacteri zedbyrelativelyweak vorticityejectionandothersinwhichstrongejectedvortic eswereobserved.They reportedtherelevantgeometricparametersaswellasthefr equencyofoscillation. TheirReynoldsnumberwasbasedontheslothalfwidthandthespa tial-averaged maximumvelocityattheslotexit,whichcanbeconvertedinto < U inasimilarmanner tootherstudies. Summary Twokeypointsshouldbetakenfromthisparameterconversionst udy.First, thecomputationoftheReynoldsnumber Re U requiredthetheoretical U= ^ U valuefor everycaseexceptfortheresultsof Smith&Swift ( 2001 ), Bera etal. ( 2001 ), Cater &Soria ( 2002 ), Utturkar etal. ( 2003 ),and Lee&Goldstein ( 2002 ).Thismeans thatonly28%ofallthecasesreportedintheliteratureactua llycontainenough informationtoevencompute Re U .AsmentionedinAppendix A ,theassumption offully-developedpiperowwithanoscillatingpressuregradi entmaynotalwaysbe

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211 valid,thusonecannotplacetoomuchcondenceinapproxima tely72%oftheresults providedintheliterature. Second,almostnoinformationontheaccuracyofthereported dataisgiven. Only Cater&Soria ( 2002 ), Yehoshua&Seifert ( 2003 ),and Utturkar etal. ( 2003 ){ followedlaterby Holman etal. ( 2005 ){providesomeinformationontheaccuracy ofthecomputeddata,representing9%ofthecasesexamined.Hen ceforthevast majorityoftheresultsprovidedintheopenliterature,noto nlyistheReynolds numberambiguous,butthecondenceofthedataisalsounknown Fromallofthesestudies,atotalof228separatecaseshavebeenan alyzedand convertedintotheparameterspaceofEq.( 2.2 ). Re U S ,and h=d arenotedforeach case.InthecaseofReynoldsnumber,theactualvaluegivenis Re U ,becausethe computationof Re U 0 requiresknowledgeofthephase-locked,spatial-varyingcro ssstreamvelocitycomponentwhichisnotgiven.Asimilarargume ntholdsforthe Strouhalnumberwhichalsodependson U 0 ,thustheStokesnumberisprovidedand anestimateoftheStrouhalnumbermaybeobtainedviaEq.( 2.3 ).Oftenthereis insucientdatatodeterminetheremainingparameters.Alloft heseresultsaregiven hereintabularform,Table C{1 .Theinformationprovidedincludesthereference,the rowdescriptionintheterminologyofthatreference,theshap e(two-dimensionalor axisymmetric),theReynoldsnumber,theStokesnumber,andt heheight-to-diameter (depth)aspectratio. TableC{1:AllcasesofZNMFrowsexhaustingintoaquiescentmediu mreportedin theopenliteratureforwhichtheparameterspaceisknown(or estimated). ReferenceFlowDescriptionShape Re U Sh=d Smith&Glezer(1998) onevortexpair,breaksdowntoformaturbulentjet(nominalcase) 2D 540 10.8 2.5 Ingard&Labate(1950) Region2threshold axisym 199 67.3 0.1 Ingard&Labate(1950) Region2threshold axisym 208 82.1 0.1 Ingard&Labate(1950) Region2threshold axisym 278 96.7 0.05 Ingard&Labate(1950) Region2threshold axisym 309 117 0.05 Ingard&Labate(1950) Region2threshold axisym 315 136 0.05 Ingard&Labate(1950) Region2threshold axisym 352 163 0.05

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212 TableC{1:Continued. ReferenceFlowDescriptionShape Re U Sh=d Ingard&Labate(1950) Region2threshold axisym 331 132 0.04 Ingard&Labate(1950) Region2threshold axisym 378 166 0.04 Ingard&Labate(1950) Region2threshold axisym 408 190 0.04 Ingard&Labate(1950) Region2threshold axisym 451 231 0.04 Ingard&Labate(1950) Region2threshold axisym 244 157 0.03 Ingard&Labate(1950) Region2threshold axisym 320 192 0.03 Ingard&Labate(1950) Region2threshold axisym 471 231 0.03 Ingard&Labate(1950) Region2threshold axisym 473 270 0.03 Ingard&Labate(1950) Region2threshold axisym 543 328 0.03 Ingard&Labate(1950) Region2threshold axisym 167 47.9 0.65 Ingard&Labate(1950) Region2threshold axisym 172 47.9 1.29 Ingard&Labate(1950) Region2threshold axisym 144 47.9 2.54 Ingard&Labate(1950) Region2threshold axisym 151 47.9 3.83 Ingard&Labate(1950) Region2threshold axisym 292 95.7 0.05 Ingard&Labate(1950) Region2threshold axisym 292 95.7 0.31 Ingard&Labate(1950) Region2threshold axisym 290 95.7 1.26 Ingard&Labate(1950) Region2threshold axisym 289 95.7 1.89 Ingard&Labate(1950) Region2threshold axisym 334 134 0.04 Ingard&Labate(1950) Region2threshold axisym 334 134 0.23 Ingard&Labate(1950) Region2threshold axisym 328 134 0.46 Ingard&Labate(1950) Region2threshold axisym 328 134 0.89 Ingard&Labate(1950) Region2threshold axisym 334 134 1.36 Ingard&Labate(1950) Region2threshold axisym 223 138 0.04 Ingard&Labate(1950) Region2threshold axisym 245 138 0.22 Ingard&Labate(1950) Region2threshold axisym 249 138 0.53 Ingard&Labate(1950) Region2threshold axisym 258 138 0.9 Ingard&Labate(1950) Region2threshold axisym 284 138 1.37 Ingard&Labate(1950) Region3threshold axisym 237 67.1 0.1 Ingard&Labate(1950) Region3threshold axisym 380 82.5 0.1 Ingard&Labate(1950) Region3threshold axisym 328 97.1 0.05 Ingard&Labate(1950) Region3threshold axisym 504 117 0.05 Ingard&Labate(1950) Region3threshold axisym 623 137 0.05 Ingard&Labate(1950) Region3threshold axisym 709 163 0.05 Ingard&Labate(1950) Region3threshold axisym 434 131 0.04 Ingard&Labate(1950) Region3threshold axisym 637 166 0.04 Ingard&Labate(1950) Region3threshold axisym 759 190 0.04 Ingard&Labate(1950) Region3threshold axisym 975 230 0.04 Ingard&Labate(1950) Region3threshold axisym 293 157 0.03 Ingard&Labate(1950) Region3threshold axisym 453 192 0.03 Ingard&Labate(1950) Region3threshold axisym 804 232 0.03 Ingard&Labate(1950) Region3threshold axisym 947 270 0.03 Ingard&Labate(1950) Region3threshold axisym 1290 327 0.03

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213 TableC{1:Continued. ReferenceFlowDescriptionShape Re U Sh=d Ingard&Labate(1950) Region3threshold axisym 183 47.9 0.64 Ingard&Labate(1950) Region3threshold axisym 199 47.9 1.28 Ingard&Labate(1950) Region3threshold axisym 199 47.9 2.54 Ingard&Labate(1950) Region3threshold axisym 198 47.9 3.82 Ingard&Labate(1950) Region3threshold axisym 351 95.7 0.05 Ingard&Labate(1950) Region3threshold axisym 362 95.7 0.32 Ingard&Labate(1950) Region3threshold axisym 360 95.7 1.27 Ingard&Labate(1950) Region3threshold axisym 371 95.7 1.89 Ingard&Labate(1950) Region3threshold axisym 460 134 0.04 Ingard&Labate(1950) Region3threshold axisym 514 134 0.22 Ingard&Labate(1950) Region3threshold axisym 460 134 0.46 Ingard&Labate(1950) Region3threshold axisym 492 134 0.89 Ingard&Labate(1950) Region3threshold axisym 476 134 1.36 Ingard&Labate(1950) Region3threshold axisym 354 138 0.04 Ingard&Labate(1950) Region3threshold axisym 479 138 0.24 Ingard&Labate(1950) Region3threshold axisym 483 138 0.53 Ingard&Labate(1950) Region3threshold axisym 558 138 0.9 Ingard&Labate(1950) Region3threshold axisym 600 138 1.36 Ingard&Labate(1950) Region4threshold axisym 29.2 39.2 0.1 Ingard&Labate(1950) Region4threshold axisym 56.9 48 0.1 Ingard&Labate(1950) Region4threshold axisym 122 55.8 0.1 Ingard&Labate(1950) Region4threshold axisym 180 59.3 0.1 Ingard&Labate(1950) Region4threshold axisym 393 67.4 0.1 Ingard&Labate(1950) Region4threshold axisym 560 82.7 0.1 Ingard&Labate(1950) Region4threshold axisym 449 97 0.05 Ingard&Labate(1950) Region4threshold axisym 704 117 0.05 Ingard&Labate(1950) Region4threshold axisym 843 136 0.05 Ingard&Labate(1950) Region4threshold axisym 942 163 0.05 Ingard&Labate(1950) Region4threshold axisym 509 130 0.04 Ingard&Labate(1950) Region4threshold axisym 781 165 0.04 Ingard&Labate(1950) Region4threshold axisym 1090 190 0.04 Ingard&Labate(1950) Region4threshold axisym 1250 229 0.04 Ingard&Labate(1950) Region4threshold axisym 393 156 0.03 Ingard&Labate(1950) Region4threshold axisym 611 192 0.03 Ingard&Labate(1950) Region4threshold axisym 1050 231 0.03 Ingard&Labate(1950) Region4threshold axisym 1500 271 0.03 Ingard&Labate(1950) Region4threshold axisym 1830 327 0.03 Ingard&Labate(1950) Region4threshold axisym 73.4 47.9 0.11 Ingard&Labate(1950) Region4threshold axisym 460 47.9 0.64 Ingard&Labate(1950) Region4threshold axisym 471 47.9 1.29 Ingard&Labate(1950) Region4threshold axisym 390 47.9 2.54 Ingard&Labate(1950) Region4threshold axisym 378 47.9 3.83

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214 TableC{1:Continued. ReferenceFlowDescriptionShape Re U Sh=d Ingard&Labate(1950) Region4threshold axisym 468 95.7 0.05 Ingard&Labate(1950) Region4threshold axisym 1120 95.7 0.31 Ingard&Labate(1950) Region4threshold axisym 1300 95.7 0.64 Ingard&Labate(1950) Region4threshold axisym 1110 95.7 1.26 Ingard&Labate(1950) Region4threshold axisym 1070 95.7 1.88 Ingard&Labate(1950) Region4threshold axisym 553 134 0.04 Ingard&Labate(1950) Region4threshold axisym 2250 134 0.47 Ingard&Labate(1950) Region4threshold axisym 2200 134 0.9 Ingard&Labate(1950) Region4threshold axisym 2050 134 1.34 Ingard&Labate(1950) Region4threshold axisym 491 138 0.04 Smith&Swift(2001) jetformationthreshold 2D 247 10.7 45.2 Smith&Swift(2001) jetformationthreshold 2D 381 13.1 45.2 Smith&Swift(2001) jetformationthreshold 2D 539 15.2 45.2 Smith&Swift(2001) jetformationthreshold 2D 683 17 45.2 Smith&Swift(2001) jetformationthreshold 2D 876 18.6 45.2 Smith&Swift(2001) jetformationthreshold 2D 1250 21.4 45.2 Smith&Swift(2001) jetformationthreshold 2D 1570 24 45.2 Smith&Swift(2001) jetformationthreshold 2D 1820 26.3 45.2 Smith&Swift(2001) jetformationthreshold 2D 2210 28.4 45.2 Smith&Swift(2001) jetformationthreshold 2D 2480 30.3 45.2 Smith&Swift(2001) jetformationthreshold 2D 2880 32.2 45.2 Smith&Swift(2001) jetformationthreshold 2D 3190 33.9 45.2 Smith&Swift(2001) jetformationthreshold 2D 3490 35.6 45.2 Smith&Swift(2001) jetformationthreshold 2D 902 20.7 23.5 Smith&Swift(2001) jetformationthreshold 2D 1360 25.3 23.5 Smith&Swift(2001) jetformationthreshold 2D 1950 29.2 23.5 Smith&Swift(2001) jetformationthreshold 2D 2460 32.7 23.5 Smith&Swift(2001) jetformationthreshold 2D 3000 35.8 23.5 Smith&Swift(2001) jetformationthreshold 2D 3970 41.3 23.5 Smith&Swift(2001) jetformationthreshold 2D 4820 46.2 23.5 Smith&Swift(2001) jetformationthreshold 2D 5740 50.6 23.5 Smith&Swift(2001) jetformationthreshold 2D 6550 54.6 23.5 Smith&Swift(2001) jetformationthreshold 2D 7440 58.4 23.5 Smith&Swift(2001) jetformationthreshold 2D 9140 65.3 23.5 Smith&Swift(2001) jetformationthreshold 2D 1710 30.8 15.7 Smith&Swift(2001) jetformationthreshold 2D 2520 37.7 15.7 Smith&Swift(2001) jetformationthreshold 2D 3550 43.5 15.7 Smith&Swift(2001) jetformationthreshold 2D 5460 53.3 15.7 Smith&Swift(2001) jetformationthreshold 2D 6890 61.6 15.7 Smith&Swift(2001) jetformationthreshold 2D 8770 68.8 15.7 Smith&Swift(2001) jetformationthreshold 2D 10400 75.4 15.7 Smith&Swift(2001) jetformationthreshold 2D 13100 81.4 15.7

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215 TableC{1:Continued. ReferenceFlowDescriptionShape Re U Sh=d Smith&Swift(2001) jetformationthreshold 2D 15100 87.1 15.7 Smith&Swift(2001) jetformationthreshold 2D 17100 92.3 15.7 Smith&Swift(2001) jetformationthreshold 2D 3550 42.5 11.4 Smith&Swift(2001) jetformationthreshold 2D 5120 52 11.4 Smith&Swift(2001) jetformationthreshold 2D 6690 60.1 11.4 Smith&Swift(2001) jetformationthreshold 2D 8390 67.2 11.4 Smith&Swift(2001) jetformationthreshold 2D 9700 73.6 11.4 Smith&Swift(2001) jetformationthreshold 2D 11700 79.5 11.4 Smith&Swift(2001) jetformationthreshold 2D 13100 85 11.4 Smith&Swift(2001) jetformationthreshold 2D 15400 95 11.4 Smith etal. (1999) jetisformed,2vortexpairsvisibledownstream 2D 455 7.96 2.5 Smith etal. (1999) jetisformed,2vortexpairsvisibledownstream 2D 455 10.8 2.5 Smith etal. (1999) jetformationthreshold axisym 1700 86.2 0.19 Smith etal. (1999) jetformationthreshold axisym 2640 107 0.19 Smith etal. (1999) jetformationthreshold axisym 3520 124 0.19 Crook&Wood(2000) ringsinteract,areelongatedbysuc-tionpartofcycle axisym 186 22.6 2 Crook&Wood(2000) ringsinteract,areelongatedbysuc-tionpartofcycle axisym 186 22.6 2 Crook&Wood(2000) lessringinteraction,appearlaminar axisym 371 22.6 2 Crook&Wood(2000) lessringinteraction,appearlaminar axisym 371 22.6 2 Crook&Wood(2000) laminarrings,distinct`tail'behindrings axisym 371 22.6 2 Crook&Wood(2000) laminarrings,distinct`tail'behindrings axisym 551 22.6 2 Crook&Wood(2000) laminarrings,distinct`tail'behindrings axisym 551 22.6 2 Crook&Wood(2000) laminarrings,distinct`tail'behindrings axisym 551 22.6 2 Crook&Wood(2000) ringsbegintotransitiontoturbu-lence,strongtrailingtailsofexcessvorticity axisym 919 22.6 2 Crook&Wood(2000) ringsbegintotransitiontoturbu-lence,strongtrailingtailsofexcessvorticity axisym 919 22.6 2 Crook&Wood(2000) ringsbegintotransitiontoturbu-lence,strongtrailingtailsofexcessvorticity axisym 919 22.6 2 Crook&Wood(2000) ringsbegintotransitiontoturbu-lence,strongtrailingtailsofexcessvorticity axisym 1290 22.6 2

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216 TableC{1:Continued. ReferenceFlowDescriptionShape Re U Sh=d Crook&Wood(2000) ringsbegintotransitiontoturbu-lence,strongtrailingtailsofexcessvorticity axisym 1290 22.6 2 Crook&Wood(2000) ringsbegintotransitiontoturbu-lence,strongtrailingtailsofexcessvorticity axisym 1290 22.6 2 Crook&Wood(2000) ringsinteract,areelongatedbysuc-tionpartofcycle axisym 186 22.6 0.4 Crook&Wood(2000) ringsinteract,areelongatedbysuc-tionpartofcycle axisym 186 22.6 1 Crook&Wood(2000) ringsinteract,areelongatedbysuc-tionpartofcycle axisym 186 22.6 2 Crook&Wood(2000) laminarrings,nointeraction,notails axisym 371 22.6 0.4 Crook&Wood(2000) laminarrings,nointeraction,notails axisym 371 22.6 1 Crook&Wood(2000) laminarrings,nointeraction,notails axisym 371 22.6 2 Crook&Wood(2000) laminarrings,nointeraction,notails axisym 371 22.6 0.4 Crook&Wood(2000) laminarrings,distinct`tail'behindrings axisym 371 22.6 1 Crook&Wood(2000) laminarrings,distinct`tail'behindrings axisym 371 22.6 2 Crook&Wood(2000) ringsbegintotransitiontoturbu-lence,strongtrailingtailsofexcessvorticity axisym 371 22.6 0.4 Crook&Wood(2000) ringsbegintotransitiontoturbu-lence,strongtrailingtailsofexcessvorticity axisym 371 22.6 1 Crook&Wood(2000) ringsbegintotransitiontoturbu-lence,strongtrailingtailsofexcessvorticity axisym 371 22.6 2 Crook&Wood(2000) ringsappearturbulent,multipletrail-ingtailsofvorticity axisym 371 22.6 0.4 Crook&Wood(2000) ringsappearturbulent,multipletrail-ingtailsofvorticity axisym 371 22.6 1 Crook&Wood(2000) ringsappearturbulent,multipletrail-ingtailsofvorticity axisym 371 22.6 2 Rediniotis etal. (1999) suctionrow{likeIngardRegion2 axisym 120 50.1 3 Rediniotis etal. (1999) jetformation axisym 120 15.9 3 Bera etal. (2001) strongjetisformed 2D 821 9.05 1 Cater&Soria(2002) strongturbulentjet axisym 9000 9.71 1 Cater&Soria(2002) ringsinteract{`laminarjet' axisym 3000 25.1 1 Cater&Soria(2002) seriesoflaminarrings axisym 7010 24.2 1 Cater&Soria(2002) transitionaljet axisym 10000 25.1 1 Cater&Soria(2002) turbulentjet axisym 60300 61.5 1 Shuster&Smith(2004) onering,thenanapparentlyturbu-lentjet axisym 1270 44.7 0.5

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217 TableC{1:Continued. ReferenceFlowDescriptionShape Re U Sh=d Shuster&Smith(2004) onering,thenanapparentlyturbu-lentjet(actually2rings) axisym 3180 50 0.5 Shuster&Smith(2004) turbulent-likeringspersistdown-stream axisym 2390 36.5 0.5 Shuster&Smith(2004) onering,thenanapparentlyturbu-lentjet axisym 6370 70.7 0.5 Shuster&Smith(2004) vortexringspersistfurtherdown-stream axisym 1150 22.4 0.5 Shuster&Smith(2004) vortexringspersistfurtherdown-stream axisym 6370 50 0.5 Shuster&Smith(2004) onlyoneringvisible axisym 3180 70.7 0.5 Shuster&Smith(2004) vortexringspersistfurtherdown-stream axisym 3010 40.8 0.5 Shuster&Smith(2004) secondvortexringpresent axisym 6370 100 0.5 Shuster&Smith(2004) strongersecondvortexring axisym 6370 57.7 0.5 Shuster&Smith(2004) strongcoherentrings axisym 3180 70.7 0.5 Shuster&Smith(2004) strongcoherentrings axisym 3180 50 0.5 Shuster&Smith(2004) strongcoherentrings axisym 3010 40.8 0.5 Shuster&Smith(2004) strongercoherentrings axisym 6370 100 0.5 Shuster&Smith(2004) strongercoherentrings axisym 6370 57.7 0.5 Shuster&Smith(2004) trainofrings,no'breakdown'toajet axisym 637 70.7 0.5 Utturkar(2002) nojet 2D 190 15.8 1 Utturkar(2002) transition 2D 254 15.8 1 Utturkar(2002) jetformation 2D 480 15.8 1 Lee&Goldstein(2002) ejectedvortices 2Dsim 133 5.12 0.2 Lee&Goldstein(2002) ejectedvortices 2Dsim 530 10.2 0.2 Lee&Goldstein(2002) veryweakvorticityejected 2Dsim 133 10.2 0.2 Lee&Goldstein(2002) strongejectedvortices 2Dsim 133 0.82 0.2 Lee&Goldstein(2002) strongejectedvortices 2Dsim 133 5.12 2 Yehoshua&Seifert(2003) clearvorticesejected 2-D 698 20.8 1 Yehoshua&Seifert(2003) vorticesreingested 2-D 349 20.8 1 Yehoshua&Seifert(2003) strongerjet,clearvortices 2-D 1670 20.8 1 Yehoshua&Seifert(2003) transitiontojetformation 2-D 465 20.8 1 Rizzetta etal. (1999) ejectedvortices 2Dsim 198 10.1 1 Rizzetta etal. (1999) ejectedvortices 2Dsim 198 10.1 1 Rizzetta etal. (1999) strongerejectedvortices 2Dsim 395 10.1 1 Utturkar etal. (2003) nojet{vorticesreingested axisym 2.71 6.06 0.83 Utturkar etal. (2003) nojet{vorticesreingested axisym 12.9 12.1 0.83 Utturkar etal. (2003) nojet{vorticesreingested axisym 44.3 18.2 0.83 Utturkar etal. (2003) nojet{vorticesreingested axisym 100 24.2 0.83 Utturkar etal. (2003) nojet{vorticesreingested axisym 115 30.3 0.83 Utturkar etal. (2003) nojet{vorticesreingested axisym 182 36.4 0.83 Utturkar etal. (2003) jetformationthreshold axisym 6.18 6.06 0.83

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218 TableC{1:Continued. ReferenceFlowDescriptionShape Re U Sh=d Utturkar etal. (2003) jetformationthreshold axisym 34 12.1 0.83 Utturkar etal. (2003) jetformationthreshold axisym 121 18.2 0.83 Utturkar etal. (2003) jetformationthreshold axisym 164 24.2 0.83 Utturkar etal. (2003) jetformationthreshold axisym 218 30.3 0.83 Utturkar etal. (2003) jetformationthreshold axisym 266 36.4 0.83

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APPENDIXD FLOWINTHEPISTONGAP OnefundamentalaspectofaZNMFdeviceisthatthecavityshould besealed withtheexceptionoftheslot(orice)throughwhichruidisp eriodicallyexpelled andingested,inordertomaximizetheperiodicvolumerowrat ethroughtheslot. Forthecaseofarigiddriver,thisisusuallyaccomplishedbyin cludingasealing membranebetweenthedriverpistonandthecavityitself.Unfor tunately,thereare severaldisadvantageswhenusingsuchamembrane.First,thememb ranepresence increasestheoverallcomplexityofZNMFconstruction.Second ,themeanpressure, orDCcomponentofpressure,ontheundersideofthecavitymustal waysbeequalto theDCcomponentofpressureinthecavityitself.Thereasonfort hisisbecauseif thereisameanpressuredierencebetweenthetwosidesoftheme mbrane,abiasor osetderectionofthedrivercanresult,reducingtheoverall eectivenessofthedriver. Forexample,ifaZNMFdeviceisrush-mountedinawindtunnelte stsection,the lowerstaticpressure\seen"bythecavitywouldcausethedrivert oderecttowardthe testsectioninameansense.Thussomekindofaventchannelwouldb enecessaryto equilibratetheDCpressures,resultinginadditionalcomplexi tyoftheZNMFdevice. Finally,themembraneitselfcanbethoughtofasacompliance ,thestretchingofwhich introducesanadditionalperiodicforceonthedriverwhich opposesthedrivermotion. Hence,anovel\viscousseal"isproposedtoreplacethesealingme mbrane.While thismaybeconsideredanexactsolutionofacanonicalrowprob lem,athorough literaturereviewdidnotrevealthesolutiontothisproblem .Hence,thesolutionis includedhereforcompleteness. 219

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220 Aviscoussealcanbeformedbetweentwocavitiesseparatedbyan oscillating pistonifthegapbetweenthepistonandthewallissmallenough. Ifthegapissmall comparedtotheradiusofthepistonandthepistonissuciently thick,thentherow inthegapcanbemodeledasafullydevelopedtwo-dimensional channelrowwithan oscillatingwall.Inaddition,anoscillatingpressuregradien tisgeneratedacrossthe pistonduetoitsmotion,asshowninFigure D{1 FigureD{1:Flowinagapgeneratedbyanoscillatingpistonand oscillatingpressure gradient. Assuminganincompressible,laminar,fullydeveloped,two-dime nsional,parallel rowwithnobodyforces,thenthemomentumequationreducesto @u @t = 1 @p @x + @ 2 u @y 2 (D.1) Withboundaryconditions u ( y =0 ;t )= U 0 e i!t u ( y = h;t )=0(D.2) Thepressuregradientis @p @x = P L e i ( !t = 2) (D.3) Thereasonforthephaseshiftinthepressuregradientwithrespect totheboundary conditionat y =0isclariedlater.SincetheconvectivetermsinEq.( D.1 )have

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221 vanished,thesolutionislinearandsuperpositioncanbeused.Th eproblembecomes simplertosolveifitisbrokendownintoarowgeneratedbyanosc illatingwallalone, andarowgeneratedbyanoscillatingpressuregradientalone.T hesetwoproblems shallbeconsideredseparately. FlowGeneratedbyanOscillatingWall Forthispartoftheproblem,thegoverningequationis @u 1 @t = @ 2 u 1 @y 2 (D.4) Withboundaryconditions u 1 ( y =0 ;t )= U 0 e i!t u 1 ( y = h;t )=0(D.5) Makingtheassumptionthatthesteady-stateoscillatingsolution tothisproblemis variableseparable, u 1 ( y;t )= < f 1 ( y ) e i!t (D.6) SubstitutionofEq.( D.6 )intoEq.( D.4 )yields i!f 1 e i!t = f 00 1 e i!t f 00 1 i! f 1 =0(D.7) Withtransformedboundaryconditions f 1 ( y =0)= U 0 f 1 ( y = h )=0(D.8) ThesolutiontoEq.( D.7 )isreadilyobtainedas f 1 ( y )= C 1 cosh y r i! + C 2 sinh y r i! (D.9)

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222 ApplyingtheboundaryconditionsEqs.( D.8 )toEq.( D.9 )gives f 1 ( y )= U 0 8><>: cosh y r i! cosh h r i! sinh y q i! sinh h q i! 9>=>; (D.10) Introducingthedimensionlessparameters y = y=h S = p !h 2 = = !t ,and u 1 = u 1 =U 0 ,where S istheStokesnumber,thenon-dimensionalsolutionbecomes u 1 ( y ; )= < (" cosh y S p i cosh S p i sinh y S p i sinh S p i # e i ) (D.11) The(complex)dimensionlessvolumerowrate Q 1 ( )canbecomputedbyintegrating Eq.( D.11 )withrespectto y .Theproblembecomessimplerbydeninganew variable y 0 = y S p i ,andintegratingwithrespectto y 0 ,inwhichcasethevalueof theintegrationbecomes Q 1 ( )= e i S p i ( sinh S p i + cosh S p i sinh S p i h 1 cosh S p i i ) (D.12) ResortingtoMapletocomputethevelocityprole,therealpa rtofEqn.( D.11 ),the followingisobtained: u 1 ( y ; )= 1 cos 2 S= p 2 +cosh 2 S= p 2 n cos( )sin S= p 2 cos S= p 2 cosh y S= p 2 sin y S= p 2 sin( )sin S= p 2 cos S= p 2 sinh y S= p 2 cos y S= p 2 cos( )cosh y S= p 2 cos y S= p 2 cos 2 S= p 2 +cos( )cosh y S= p 2 cos y S= p 2 cosh 2 S= p 2 cos( )cosh S= p 2 sinh S= p 2 sinh y S= p 2 cos y S= p 2 +sin( )sinh y S= p 2 sin y S= p 2 cos 2 S= p 2 sin( )sinh y S= p 2 sin y S= p 2 cosh 2 S= p 2 +sin( )cosh S= p 2 sinh S= p 2 cosh y S= p 2 sin y S= p 2 o (D.13)

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223 FlowGeneratedbyanOscillatingPressureGradient Forthesecondpartoftheproblem,thegoverningequationist hesameasEq. ( D.1 ), @u 2 @t = 1 @p @x + @ 2 u 2 @y 2 (D.14) Buttheboundaryconditionsnoware u 2 ( y =0 ;t )=0 u 2 ( y = h;t )=0(D.15) Againassumingthesteady-stateoscillatingvelocityisvariable separable,butthis timeintroducingaxedphaseshiftintothesolution, u 2 ( y;t )= < f 2 ( y ) e i ( !t = 2) (D.16) Thenthegoverningequationbecomes i!f 2 e i ( !t = 2) = P L e i ( !t = 2) + f 00 2 e i ( !t = 2) f 00 2 i! f 2 = P L (D.17) Withtransformedboundaryconditions f 2 ( y =0 ;t )=0 f 2 ( y = h;t )=0(D.18) ThesolutiontoEq.( D.17 )isthesumofahomogeneouspartandaparticular part, f 2 ( y )= f 2 ;H + f 2 ;P (D.19) Thesolutiontothehomogeneouspartis f 2 ;H = C 3 cosh y r i! + C 4 sinh y r i! (D.20)

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224 Byinspection,itcanbeseenthattheparticularsolutionis f 2 ;P = P i!L = P i!L (D.21) Thentheexpressionfor f 2 is f 2 = C 3 cosh y r i! + C 4 sinh y r i! P i!L (D.22) WhereapplyingtheboundaryconditionsEqs.( D.18 )gives f 2 ( y )= P i!L 8><>: cosh y r i! + 1 cosh h r i! !# sinh y q i! sinh h q i! 1 9>=>; (D.23) Usingthesamedimensionlessparametersasbefore,thesolutionbe comes u 2 ( y ; )= < P i!LU 0 h cosh y S p i + h 1 cosh S p i i sinh y S p i sinh S p i 1 # e i ( = 2) ) (D.24) ThersttermontheRHSofEq.( D.24 )isdimensionless,butitwouldbe convenienttoexpressitintermsofcommondimensionlessparam eters.Inaddition, arelationshipbetweentheamplitudeofthepressuregradient P andtheamplitude ofthevelocityoftheoscillatingpiston U 0 wouldproveusefulingainingphysical insightintotheproblem.Inordertoobtainthisrelationship ,bothcavitiesoneither sideofthepistonaremodeledassealedwithidenticalvolumesa ndcontainingairat STP,asshowninFigure D{2 .Thisisadeparturefromthesyntheticjetconguration, butneverthelessisanecessarysteptosimplifytheproblem.Init ially,bothcavities haveidenticalproperties, p 1 = p 2 8 1 = 8 2 ,and T 1 = T 2 .Thisimpliesthat 1 = 2 and m 1 = m 2 .Nowletprimesdenotequantitieswhenthepistonisderecteda sshown inFigure D{2 .Forthepurposeofdeterminingtheamplitudeofthepressurech ange P acrossthepiston,thegapisnowassumedtobesealed,suchthat m 01 = m 02 =

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225 m 1 = m 2 .Also,itfollowsthatthevolumesarenow 8 01 = 8 1 b 2 d 8 02 = 8 2 + b 2 d (D.25) Thusthedensitiesare 01 = m 01 8 01 = m 1 8 01 = 1 8 1 8 01 02 = m 02 8 02 = m 2 8 02 = 2 8 2 8 02 (D.26) FigureD{2:Schematicofderectedpiston.

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226 Nextitisassumedthattheruidisisentropic.Thisisareasonable assumptionif thetimescaleoftheoscillatingrowismuchlessthanthetimesca leofheattransfer: 1 =! h 2 = 1 = !h 2 = 1 1 S 2 Pr 1(D.27) Taking Pr =0 : 7forair, S 2 Pr< 0 : 1for S> 4.Lateritshallbeseen,however,that theassumptionoftwoseparatecavitiessealedbythepistonisonl yvalidforhigh frequencies,whichtranslatestohighStokesnumbers.Therefo re,thismodelcanonly beusedathighfrequencieswheretheassumptionofisentropicro wisinfactvalid. Sincethepressureinregion1isincreasedbythesameamountasth epressurein region2isdecreased,andbytheisentropicequationofstate, p 1 + 1 2 P = 01 RT 0 1 p 2 1 2 P = 02 RT 0 2 (D.28) Inaddition,iftheratio d=H 1,thentheperiodictemperaturechangeinboth cavitiesisalsoverysmallandmaybeneglected,soitmaybeassume dthat T 0 1 = T 0 2 = T .Becausetheshakerdevicebecomesacceleration-limitedath ighfrequencies wherethismodelisapplied,thedisplacement d getsverysmall(typically < 1mm) anditcanbeassumedthattheprocessisisothermal.Takingthedi erencebetween Eqs.( D.28 )gives P = RTb 2 H 1 b 2 ( H d ) 1 b 2 ( H + d ) (D.29) SimplifyingEq.( D.29 )gives P = RT 2 Hd H 2 d 2 (D.30) Anditremainstoexpresstheamplitudeofderectionofthepisto n d intermsof theamplitudeoftheoscillationofthepiston U 0 .Thepositionofthepistoncanbe

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227 expressedas r p ( t )= d sin( !t )(D.31) Thusthevelocityofthepistonis v p ( t )= !d cos( !t )= U 0 cos( !t )(D.32) ThenfromEq.( D.32 ), d = U 0 =! andtheamplitudeofthepressuregradientis P L = RT L 2 !HU 0 2 H 2 U 2 0 (D.33) NowthereasonforthephaseshiftinEq.( D.3 )becomesapparentbyconsidering therelativephasingbetween r p ( t ), v p ( t ),and @p=@x showninFigure D{3 .Whenthe pistonisatitsnominalposition,thevelocityisatamaximum( orminimum),while thepressuregradientiszero.Atthemaximumpositionofthepist on,thepressure gradientisatitsmaximumvaluebecauseofthesignconvention fromFigure D{1 Thusitcanbeseenthatthepressuregradientlagsthepistonvelo cityinphase by90 ,requiringaxedphaseshiftinthesolutionto u 2 ( y;t ).Notethatatthe maximumvalueofthepressuregradient,therowinducedintheg apisinthenegative x direction. SubstitutingEq.( D.33 )intoEq.( D.24 )gives P i!LU 0 = RT i!L 2 !H 2 H 2 U 2 0 = i 2 L=H RT 2 ( H 2 d 2 ) (D.34) SodeningapistonlengthtocavityheightratioandanEckert numberbasedonthe oscillationfrequency L = L=H Ec = 2 ( H 2 d 2 ) RT (D.35)

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228 0 60 120 180 240 300 360 -1 -0.5 0 0.5 1 Phase (deg)Normalized Quantity Piston Position Piston Velocity Pressure Gradient FigureD{3:Relativephasingbetween r p ( t ), v p ( t ),and @p=@x ThenEq.( D.24 )becomes u 2 ( y ; )= < i 2 L Ec h cosh y S p i + h 1 cosh S p i i sinh y S p i sinh S p i 1 # e i ( = 2) ) (D.36) Thedimensionlessvolumerowrateisfoundsimilartobefore, Q 2 ( )= i 2 e i ( = 2) L Ec S p i n sinh S p i + 1 cosh S p i sinh S p i h cosh S p i 1 i S p i ) (D.37)

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229 ResortingagaintoMapletoacquiretherealpartofEq.( D.36 )givesthecomponent ofvelocityduetothepressuregradient: u 2 ( y ; )= 2 L Ec cosh S p 2 = 2 +cos S p 2 = 2 n sin( = 2)cosh S p 2 = 2 +sin( = 2)cosh S p 2 = 2 cosh y S p 2 = 2 cos y S p 2 = 2 +cos( = 2)cosh S p 2 = 2 sinh y S p 2 = 2 sin y S p 2 = 2 +sin( = 2)sinh S p 2 = 2 sinh y S p 2 = 2 cos y S p 2 = 2 +sin( = 2)sin S p 2 = 2 cosh y S p 2 = 2 sin y S p 2 = 2 +cos( = 2)sinh S p 2 = 2 cosh y S p 2 = 2 sin y S p 2 = 2 +cos( = 2)sin S p 2 = 2 sinh y S p 2 = 2 cos y S p 2 = 2 +sin( = 2)cos S p 2 = 2 +sin( = 2)cos S p 2 = 2 cosh y S p 2 = 2 cos y S p 2 = 2 +cos( = 2)cos S p 2 = 2 sinh y S p 2 = 2 sin y S p 2 = 2 o (D.38) Superposition ThenalsolutiontothisrowproblemisthesumofEq.( D.6 )andEq.( D.38 ). Takingdimensionlessparametervalues S =21, Ec =5 : 8,and L =0 : 2,allreasonablevaluesforthisstudy,thevelocityproleinthegapisco mputedandshownat onephaseinFigure D{4 Aspreviouslystated,thepurposeofusingaviscoussealistoelimin atetheneed forasealingmembraneontopofthepistonandacorrespondingve ntchannelto equilibratetheDCpressuresintheupperandlowercavities.Th elowfrequency approximationoftheacousticresistancetorowinthisventcha nnel R aVC wasgiven in Gallas etal. ( 2003 )tobe R aVC = 8 L VC a 40 (D.39)

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230 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 u*=u/U 0y*=y/h FigureD{4:Normalizedvelocityproleofrowinthepistongap S =21, Ec =5 : 8, L =0 : 2. whichisderivedfromsteady-statePoiseuillerowinapipe.Here L VC isthelength oftheventchanneltubeand a 0 isitsradius.Theresistancetorowinthepistongap istherealpartoftheacousticimpedanceofthegap Z aG ,denedas Z aG = P Q (D.40) where Q isfoundbysummingthetwonon-dimensionalvolumerowratesan dsubsequentlydimensionalizingthem, Q =( Q 1 + Q 2 ) U 0 h (2 b )(D.41) FromEqs.( D.12 )and( D.37 )itcanbeseenthattheterm e i maybefactoredout. Similarly,thenumeratorinEq.( D.40 )isproperlyexpressedas Pe i ( = 2) ,thusthe arbitraryphase vanishesandwhatremainsisthecomplexexpressionfor Z aG which isStokesnumberdependent.Therealpartofthisexpressionis theresistance,while

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231 theimaginarypartisthereactance.Next,typicalvaluesare assumedfordensity, viscosity,temperature,andspeedofsoundofair,aswellasagap thicknessof1mm, acavityheightof100mm,aconstantpistonderectionamplitud eof0.5mm,anda cylinderradiusof50mmtocomputetheresistancetorowintheg apasafunctionof Stokesnumber.Figure D{5 comparestheresistanceofthepistongaptothatofthe lowfrequencyapproximationfortheventchannelgiveninEq .( D.39 ).Clearlyfor thesevalues,theresistancetorowintheventchannelishighert hantheresistanceto rowinthepistongap.However,notethattheresistancetorowint hegapasymptotes atlowfrequenciestothevalueforsteady-statePoiseuillerow inatwo-dimensional channel. 10-1 100 101 102 104 105 106 107 Resistance Piston Gap Vent Channel 10-1 100 101 102 100 105 1010 Stokes NumberReactance FigureD{5:Comparisonofresistancetorowinthepistongapandt heventchannel fortypicalvalues. Despitethehigherresistanceoftheventchannel,thismodelin dicatesthatthe resistanceincreasessignicantlyathigherStokesnumbers,ase xpected.Inaddition, sinceitisassumedthattherowisisentropic,itisknownthatthe modelcanonlybe

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232 appliedathighStokesnumbersasdiscussedpreviously.Onemusta lsoconsiderthe resistancetorowthroughtheslot(orice),whichisinparalle lwiththepistongap, todeterminethesignicanceoftherowinthegap.Also,sinceapr essuregradient generatedbythemotionofapistonbetweentwosealedcavities wasassumed,itis expectedthatthiswillonlybevalidathigherfrequenciesa swell{wherethetypical timescaleforsteady-statePoiseuillerowinatwo-dimensionalc hannelismuchlarger thantheoscillationtimescale.Finally,asdescribedinChapt er 3 ,theactualpiston gapforthedeviceemployedis0 : 13mmandtheresultingdierenceintherowin theslotbetweenthisandasealedgapisnegligible,indicatin gthataviscoussealis achievedandisinfactaviableoptionforsyntheticjetexper iments.

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APPENDIXE MULTIVARIATEOUTLIERREJECTION Whenconsideringtwo-dimensionalexperimentalvelocitydat a,oftenthereare badvectorswhicharenotrepresentativeoftheroweld.This isespeciallytruefor measurementsnearsolidsurfaces,wherethepresenceofthesurfac ecaninterferewith thevelocitymeasurement.Thisappendixfocusesonamultivar iateoutlierrejection technique( Hadi 1992 )appliedtoPIVvelocitydatafortheremovalofspurious vectors. Figure E{1 showsanexampleinstantaneousvectoreldacquiredusingPIVf or Case5, Re =555, St =0 : 81, h=d =1 : 46,averyturbulentcase.Thisparticularimage showspartofthesuctioncycle,asthevectorsaredirectedtow ardtheslotsurface (notshown).Itisapparentthatintheregion1
PAGE 254

234 0 1 2 3 4 5 6 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 x (mm)y (mm) FigureE{1:ExampleimageofspuriousPIVvectors,notethatth emissingvectors arepointswhichfailedtheinitialcorrelationanalysis. 0 1 2 3 4 5 6 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 x (mm)y (mm) FigureE{2:Exampleimageofspatial-validatedPIVvectors,o btainedusingamedian lterandinterpolation,thensmoothing.

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235 WhilethevalidatedvectoreldinFigure E{2 maybevisuallypleasing,itis quitepossiblethatsomelegitimateinformationontheroweld hasbeenlostor altered.Thisisbecausealthoughthistechniquemaybesuitab leforsomerows wherevelocitygradientsaresmall,manyruidrowsmaynotbea menabletothis methodsuchasshearlayerrows,vortexrings,boundarylayers,et c.whichhave largevelocitygradients.CertainlyaZNMFrowintheneareld alsofallsunder thiscategory.Thesevelocitygradientsarereducedormaybe eliminatedcompletely duringthespatialvalidationprocess,andallquantitiesderi vedfromthevelocity (suchasvorticityandReynoldsstress)thenbecomesuspect.Forth isexample,it isapparentthatthevelocitygradientatthesurfacehasbeen reducedduetothis smoothingeect.Anotherpotentialproblemwiththistechniq ueisifthereisa regionofmanybadvectors.Thespatialvalidationrequiresco mparisonofavectorto itsneighbors,soaneighborhoodregionoflegitimatelybadve ctorsmaybepermitted sincetheyaresimilartooneanother. OfteninPIVexperiments,relativelyfewimagesareacquired .Indeed,spatial lteringtechniquesofPIVdatahaveattainedpopularitybe causetheycanbeperformedonasingleimage.AsPIVimageacquisitionandstoragetec hniquesimprove, however,andascomputingtechnologybecomesmoreecienta tprocessingPIVdata, manyimages(andhencevectorelds)canbeobtainedforasingl erowconditionand statisticaloutlierrejectionbecomesaviablealternativet ospatialvalidation. Sinceexperimentalvelocityelddataisatleasttwo-dimensi onal,amultivariate techniqueisrequiredtodeterminethethresholdforoutlier rejectionofavelocity vector.Duetocurrentcomputationallimits,therobustnessof thetechniquemust bebalancedbyitscomputationaltime.Here,\robustness"refer stotheabilityof theoutlierrejectionalgorithmtoproperlyrejectalloutl iersandpermitalllegitimate points.Totheauthor'sknowledge,themostrobusttechniqueis theso-called\FASTMCD"algorithmdescribedin Rousseeuw&Driessen ( 1999 ).Unfortunately,dueto

PAGE 256

236 currentlimitsoncomputationalresources,thisalgorithmis impracticalforapplication tothecurrentPIVdataset.Anotheralgorithmwhichisnotasro bustbutuses signicantlylesscomputationtimeisoutlinedin Hadi ( 1992 )andisdescribednext. Thetechniquedescribedby Hadi ( 1992 )proceedsasfollows.Therststepis termedinitialordering.Beginningwithadatasetof n samplesby p variates( p =2 fortwo-dimensionalvelocityvectordata),theco-ordinate wisemedians C M arerst computedbytakingthemedianofeachvariateinthedataset.T hemediansare chosenasopposedtothemeanstominimizetheskewingoftheinit ialestimatesdue tothe(potential)outliers.Thenthescaleestimators S M arecomputedaccordingto S M = 1 n 1 n X i =1 ( x i C M )( x i C M ) T (E.1) Next, D i {thedistancesfromeachsampletothecenterlocation C M {iscomputed using S M asthemeasureofdispersion, D i ( C M ;S M )= q ( x i C M ) S M 1 ( x i C M )(E.2) Thesedistancesarethenarrangedinascendingorder,andther st h samplesare usedtocomputetherobustcenterlocations C R andtherobustcovariancematrix estimator S R ,where h istheintegerpartof( n + p +1) = 2.Thereasonforthischoice of h isbecausethedatasetispermittedtohaveatmost n h outliers( Hadi 1992 ). C R iscomputedbytakingthemeanoftherst h samples,and S R isthecovariance matrixoftherst h samples. Next,therobustdistancesarecomputedusingEq.( E.2 ),butsubstituting C R and S R inplaceof C M and S M ,respectively.Therobustdistancesarethensortedin ascendingorder.Atthispoint,Hadi'stechniquespeciesden ingabasicsubsetof p +1samples,computingthemeanandcovariancematrix C b and S b ,andreordering thedistancesaccordingtothesenewestimates.Theprocessisthe nrepeateduntil thebasicsubsetcontains h samples.Toreducecomputationaltime(admittedlyat

PAGE 257

237 theriskofreducingrobustness),thebasicsubsetisdenedimmedia telyastherst h samplesoftherobustdistances,andthenassumingthatthebasicsubse tisoffull rank.Thenaldistancesarethencomputedforallthesamplesu sing C b asthemean and c b S b asthecovariancematrix,where c b isacorrectionfactortoaccountfora multivariatenormaldistribution{see Hadi ( 1992 )fordetailsofthiscorrectionfactor. Atthispointtheproblemisonlypartlycompleted;asuitable thresholdof D i isnextrequiredtodeterminewhichpointsareoutliers.Tabl eXXXIIin Barnett& Lewis ( 1994 )isusedtodeterminethethresholdforoutlierrejectiongive nthenumber ofsamples n andthenumberofvariates p .Figure E{3 showsatypicaldatasetof PIVvectorsatasinglepoint,andtheoutliersrejectedareco mparedusingtheFASTMCDmethod,themodiedHadimethodwithlevelofsignicance =0 : 05,andthe modiedHadimethodwithlevelofsignicance =0 : 01.TheFAST-MCDmethod requiresapproximately2stocomplete,whilethemodiedHad itechniquerequires only0 : 02sofcomputationaltimeonaPCwithanAMDAthlonXP2500+proc essor and1.5gigabytesofRAM.Foravectoreldof70 90vectorsand24phaseseach for12cases,thecomputationtimeoftheFAST-MCDmethodis42da ys,whilethe modiedHaditechniquerequiresonly10hours. FromFigure E{3 ,itcanbeseenthattheFAST-MCDmethodisthemostrobust, rejectingthemostoutliers.ForthemodiedHadimethodwith =0 : 05,thenumber ofrejectedoutliersisreduced,butismorethanthemodied Hadimethodwith =0 : 01.ItisalsoimportanttonotethatthemodiedHadimethodwit h =0 : 05 doesnotrejectanypointswhicharenotalsorejectedbytheFAS T-MCDmethod. CertainlythismethodisnotasrobustastheFAST-MCDmethod,b utitischosendue toitscloseapproximationtotheFAST-MCDmethodanditsconsid erablereduction ofcomputationaltime. WhenmultivariateoutlierrejectionisappliedtoFigure E{1 ,theresultisquite interesting,showninFigure E{4 .Surprisingly,noneoftheapparentlybadvectors

PAGE 258

238 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 u (m/s)v (m/s) Sample Dataset Rejected by FAST-MCD Rejected by Hadi modified ( a =0.05) Rejected by Hadi modified ( a =0.01) FigureE{3:ExamplePIVdatasetofidentiedoutliers. 0 1 2 3 4 5 6 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 x (mm)y (mm) FigureE{4:Exampleimageofoutlier-rejectedPIVvectors,t herejectedvectorlocationsarecircled,notethattheothermissingvectorsarepo intswhichfailedthe initialcorrelationanalysis.

PAGE 259

239 nearthecenter-leftoftheimagehavebeenrejected,andthr eepointswhichdonotlook likeoutliersinFigure E{1 arerejected.Nevertheless,itisimportanttorememberthat thevectorsarerejectedbasedonthedatasetof100vectorsatt hatpoint,andnoton theappearanceofneighboringvectors.Hence,multivariateo utlierrejectionisabetter toolforvelocityvectorvalidationthanspatiallteringbe causeitsimultaneously retainsgoodvectorsandrejectsbadvectors,whilespatiall teringcandotheopposite.

PAGE 260

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242 Holman,R.,Gallas,Q.,Carroll,B.&Cattafesta,L. 2003Interactionof adjacentsyntheticjetsinanairfoilseparationcontrolappl ication.Orlando,FL: AIAAPaper2003-3709. Holman,R.,Utturkar,Y.,Mittal,R.,Smith,B.L.&Cattafesta ,L. 2005Formationcriterionforsyntheticjets. AIAAJ. 43 ,2110{2116. Horowitz,S.,Nishida,T.,Cattafesta,L.&Sheplak,M. 2002Characterizationofcompliant-backplateHelmholtzresonatorsfor anelectromechanical acousticliner. InternationalJournalofAeroacoustics 1 ,183{205. Ingard,U. 1953Onthetheoryanddesignofacousticresonators. J.Acous.Soc. Am. 25 ,1037{1061. Ingard,U.&Labate,S. 1950Acousticcirculationeectsandthenonlinear impedanceoforices. J.Acous.Soc.Am. 22 ,211{218. James,R.D.,Jacobs,J.W.&Glezer,A. 1996Aroundturbulentjetproduced byanoscillatingdiaphragm. Phys.Fluids 8 ,2484{2495. Kotapati,R.B.,Mittal,R.&Cattafesta,L. 2006Numericalstudyofa transitionalsyntheticjetinquiescentexternalrow. J.FluidMech. InPress Kral,L.D.,Donovan,J.F.,Cain,A.B.&Cary,A.W. 1997Numerical simulationofsyntheticjetactuators.SnowmassVillage,CO:AIAAP aper19971824. Lee,C.Y.&Goldstein,D.B. 2002Two-dimensionalsyntheticjetsimulation. AIAAJ. 40 ,510{516. Lighthill,S.J. 1978Acousticstreaming. J.SoundVib. 61 ,391{418. Lodahl,C.R.,Sumer,B.M.&Fredse,J. 1998Turbulentcombinedoscillatoryrowandcurrentinapipe. J.FluidMech. 373 ,313{348. Mallinson,S.G.,Hong,G.&Reizes,J.A. 1999Somecharacteristicsof syntheticjets.Norfolk,VA:AIAAPaper1999-3651. Meunier,P.&Leweke,T. 2003Analysisandtreatmentoferrorsduetohigh velocitygradientsinparticleimagevelocimetry. Exp.Fluids 35 ,408{421. Pack,L.G.&Seifert,A. 1999Periodicexcitationforjetvectoringandenhanced spreading.Reno,NV:AIAAPaper1999-0672. Panton,R.L. 1996 IncompressibleFlow ,2ndedn.JohnWiley&Sons. Pierrehumbert,R.T. 1980Afamilyofsteady,translatingvortexpairswith distributedvorticity. J.FluidMech. 99 ,129{144. Pope,S.B. 2001 TurbulentFlows .CambridgeUniversityPress.

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243 Rampunggoon,P. 2001Interactionofasyntheticjetwitharatplateboundary layer.PhDthesis,UniversityofFlorida,Gainesville,Florida. Rathnasingham,R.&Breuer,K. 1997Coupledruid-structuralcharacteristics ofactuatorsforrowcontrol. AIAAJ. 35 ,832{837. Ravindran,S.S. 1999Activecontrolofrowseparationoveranairfoil.Hampton, VA:NASA/TM-1999-209838. Rediniotis,O.K.,Ko,J.,Yue,X.&Kurdila,A.J. 1999Syntheticjets,their reducedordermodelingandapplicationstorowcontrol.Ren o,NV:AIAAPaper 1999-1000. Ritchie,B.D.,Mujumdar,D.R.&Seitzman,J.M. 2000Mixingincoaxial jetsusingsyntheticjetactuators.Reno,NV:AIAAPaper2000-0404. Ritchie,B.D.&Seitzman,J.M. 1999Acetonemixingcontroloffueljetsusing syntheticjettechnology:scalareldmeasurements.Reno,NV:AIAAP aper19990448. Rizzetta,D.P.,Visbal,M.R.&Stanek,M.J. 1999Numericalinvestigation ofsynthetic-jetrowelds. AIAAJ. 37 ,919{927. Rousseeuw,P.J.&Driessen,K.V. 1999Afastalgorithmfortheminimum covariancedeterminantestimator. Technometrics 41 (3),212{223. Saffman,P.G. 1997 VortexDynamics .CambridgeUniversityPress. Shariff,K.&Leonard,A. 1992Vortexrings. Ann.Rev.FluidMech. 24 ,235{ 279. Shuster,J.M.&Smith,D.R. 2004Astudyoftheformationandscalingofa syntheticjet.Reno,NV:AIAAPaper2004-0090. Smith,B.L.&Glezer,A. 1997Vectoringandsmall-scalemotionsaectedin freeshearrowsusingsyntheticjetactuators.Reno,NV:AIAAPaper19 97-0213. Smith,B.L.&Glezer,A. 1998Theformationandevolutionofsyntheticjets. Phys.Fluids 10 ,2281{2297. Smith,B.L.&Glezer,A. 2002Jetvectoringusingsyntheticjets. J.FluidMech. 458 ,1{34. Smith,B.L.&Swift,G.W. 2001SyntheticjetsatlargeReynoldsnumberand comparisontocontinuousjets.Anaheim,CA:AIAAPaper2001-3030. Smith,B.L.&Swift,G.W. 2003Acomparisonbetweensyntheticjetsand continuousjets. Exp.Fluids 34 ,467{472.

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244 Smith,B.L.,Trautman,M.A.&Glezer,A. 1999Controlledinteractionsof adjacentsyntheticjets.Reno,NV:AIAAPaper1999-0669. Smith,D.,Amitay,M.,Kibens,V.,Parekh,D.&Glezer,A. 1998Modicationofliftingbodyaerodynamicsusingsyntheticjetsactuat ors.Reno,NV:AIAA Paper1998-0209. Song,X.,Yamamoto,F.,Iguchi,M.&Murai,Y. 1999AnewtrackingalgorithmofPIVandremovalofspuriousvectorsusingDelaunayt essellation. Exp. Fluids 26 (371{380). Soria,J. 1996Aninvestigationofthenearwakeofacircularcylinderusi ngavideobaseddigitalcross-correlationparticleimagevelocimetryt echnique. Exp.Therm. FluidSci. 12 ,221{233. Tr avn ^ cek,Z.&Tesa ^ r,V. 2003Annularsyntheticjetusedforimpingingrow mass-transfer. Int.J.HeatMassTran. 46 ,3291{3297. Utturkar,Y. 2002Numericalinvestigationofsyntheticjetrowelds.Master' s thesis,UniversityofFlorida,Gainesville,Florida. Utturkar,Y.,Holman,R.,Mittal,R.,Carroll,B.,Sheplak,M.& Cattafesta,L. 2003Ajetformationcriterionforsyntheticjetactuators.Re no, NV:AIAAPaper2003-0636. Utturkar,Y.,Mittal,R.,Rampunggoon,P.&Cattafesta,L. 2002Sensitivityofsyntheticjetstothedesignofthejetcavity.Reno, NV:AIAAPaper 2002-0124. Wang,H.&Menon,S. 2001Fuel-airmixingenhancementbysyntheticmicrojets. AIAAJ. 39 ,2308{2319. White,F.M. 1991 ViscousFluidFlow .Boston,MA:McGrawHill. Winter,D.C.&Nerem,R.M. 1984Turbulenceinpulsatilerows. Ann.Biomed. Eng. 12 ,357{369. Yamaleev,N.K.,Carpenter,M.H.&Ferguson,F. 2005Reduced-order modelforecientsimulationofsyntheticjetactuators. AIAAJ. 43 ,357{369. Yehoshua,T.&Seifert,A. 2003Boundaryconditioneectsonoscillatorymomentumgenerators.Orlando,FL:AIAAPaper2003-3710.

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BIOGRAPHICALSKETCH RyanJayHolmanwasbornonNovember20 th ,1975,inDeLand,Florida.After graduatingfromDeLandHighSchoolin1993,heattendedDayto naBeachCommunityCollege,whereheearnedtheAssociateofArtsdegreein19 97.Hethen transferredtotheUniversityofFloridainGainesvilletoconti nuehisundergraduate studies,receivingtheBachelorofScienceinAerospaceEnginee ringdegreein2000. Decidingtocontinuehiseducation,heenrolledintheGradu ateSchoolattheUniversityofFloridaandsubsequentlywasawardedtheMasterofScienc edegreein2003. HeiscurrentlyadoctoralstudentpursuingaPh.D.,andaftergr aduationwillbegin employmentatLockheedMartinAeronauticsCompanyinFortWo rth,Texas,asa SeniorAeronauticalEngineer.Hisresearchinterestsincludeu nsteadyaerodynamics, activerowcontrol,andexperimentalruiddynamics. 245


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AN EXPERT I TAL INVESTIGATION OF FLOWS
FROM ZERO-NET MA-"-, PLUX ACTUATORS















By

RYAN JAY HOLMAN


A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREi: TS FOR THE DEGREE OF
DOCTOR OF PIIILOSOPHY

UNIVERSITY OF FLORIDA


_.(i ( 14 -,

































Copyright 2006

by

Ryan .1-- Iolman















ACKNOWLEDGMENTS

Financial support for this work has been provided by the Air Force C0li,:e of

Scientific Research. I thank ri- advisor, Lou Cattafesta, for his tireless support and

guidance throughout ,-; tenure as a graduate student at the University of Florida

that made this work possible. Special thanks also go to my committee members,

Specially Bruce Carroll and Mark "'.1, i.1 i for numerous in ,iu, 1 discussions which

have contributed in i.: ,* productive --,- to this dissertation.

I am grateful to all of my ? -:i- colleagues in the Interdis(cili' : :y Mi. .. i. I, .

Group and the Fluid Dynamics Labocr i-- r .r with whom I have been associated with

over the years. I thank them for what I have learned from them, for their help with

n-- work, and for their friendship. In particular, I express n-, gratitude to fellow

students Quentin Gallas and Ahmed F1I,. .. d for their support and assistance.

Finally, I thank r..-- parents, C i.:. I and Kathy Holman, for their constant en-

couragement. Their fine example of hard work and dedication has al- ---. motivated

me to pursue rn-- goals.















TABLE OF CONTENTS


ACKNOWLEDGMENTS .............

LIST OF TABLES .................

LIST OF FIGURES ...............

LIST OF SYMBOLS AND ABBREVIATIONS .

ABSTRACT ....................

CHAPTER

1 INTRODUCTION .............

Background ..................
Previous Work ...............
Experimental Studies ..........
Numerical Studies ............
M otivation . . . . .
Technical Objectives and Approach .....
O utline . . . . .

2 PHYSICS OF SYNTHETIC JET FLOWS .

Dimensional Analysis .............
Parameter Equivalence ............
Parametric Variation .............
Published Results .............
Proposed Test Matrix ............

3 EXPERIMENTAL SETUP .........

Synthetic Jet Devices .............
Data Acquisition System ...........
Driver Deflection Measurement .......
Sinusoidal Controller .............
Flow Visualization Setup .. .........
Velocity Measurement .. ..........
Hotwire Anemometry .. ........
Particle Image Velocimetry .......
Laser Doppler Anemometry ......


page

iii


xv









Particle Sizing and Dynamics ........ . . .. 88
Uncertainty Analysis .................. ........ .. .. 88

4 RESULTS AND DISCUSSION .................. ... 94

Device C'!i 1 'Iterization .................. ........ .. 94
Flow Visualization .................. ........... .. 101
Laser Doppler Anemometry .................. .... 120
Particle Image Velocimetry ............. ... ..... 126
Velocity ............... ............ 127
Vorticity and Circulation . . ..... ..... 142
Reynolds Stress and Turbulent Kinetic Energy . . ... 162

5 CONCLUSIONS ............... ........... .. 181

Key Findings .. .......... .. ....... ...... 181
Recommendations for Future Work ................ ... 184
Additional Future Work ............... ....... 185

APPENDIX

A SOLUTION TO FULLY-DEVELOPED PIPE FLOW WITH AN OSCIL-
LATING PRESSURE GRADIENT ........ . . 186

B VORTEX-BASED JET FORMATION CRITERION . . 193

Effect of Orifice Geometry ............... .... .. 195
2D vs. Axisymmetric Jet .................. ...... .. 197
Experimental Results .................. .......... 198

C PARAMETER CONVERSION .................. ...... 202

Ingard & Labate (1950) .................. ...... .. .. 202
Smith & Glezer (1998) .................. ......... .. 203
Smith & Swift (2001) .................. .......... .. 204
Smith et al. (1999) .................. ........... .. 205
Crook & W ood (2000) .................. ....... .. .. 206
Rediniotis et al. (1999) .................. ......... .. 206
B1 ra et al. (2001) . . . . . . .. 207
Cater & Soria (2002) .................. ........ .. .. 207
Yehoushua & Seifert (2003) ................ ... .. 208
Shuster & Smith (2004) ............... ....... ..209
Utturkar et al. (2003) ............ . . .. 209
Rizzetta et al. (1999) .................. .......... .. 210
Lee & Goldstein (2002) .................. ......... .. 210
Summary .................. ................ .. 210









D FLOW IN THE PISTON GAP ....................... 219

Flow Generated by an Oscillating Wall ........ ......... 221
Flow Generated by an Oscillating Pressure Gradient . .... 223
Superposition .................. .............. .. 229

E MULTIVARIATE OUTLIER REJECTION ..... . . 233

LIST OF REFERENCES .................. .......... .. 240

BIOGRAPHICAL SKETCH .................. ......... .. 245















LIST OF TABLES
Table page

2-1 Primary dimensions of synthetic jet dimensional parameters ..... 38

2-2 Synthetic jet flow regions .................. ..... .. 46

2-3 Test matrix of geometric configurations ................ 48

3-1 Piezoelectric-driven ZNMF actuator details .............. ..49

3-2 Shaker-driven ZNMF actuator details ................. 51

3-3 Before- and after-PIV piston motion ................ .. 65

3-4 LDA measurement details .................. ..... .. 84

3-5 Uncertainty contribution due to random error of velocity measurements 91

3-6 Percent difference for no-slip integration and slot integration . 92

4-1 Two-dimensional limit of ZNMF flowfields by case . .... 103

4-2 Frequency and velocity values by case ................. 127

4-3 Dimensionless turbulent transition by case ............... ..180

B-1 Comparison between PIV- and LDA-acquired Reynolds numbers 200

C-1 All cases of ZNMF flows exhausting into a quiescent medium ..... .211















LIST OF FIGURES
Figure page

1-1 ZNMF studies published by year .................. ... 2

1-2 Schematic of a typical ZNMF device ................. .. 3

1-3 Flow regions induced by acoustic streaming through an orifice under
steady illumination ................... ... 8

1-4 Flow region 4 induced by acoustic streaming through an orifice under
stroboscopic illumination ................ .... 10

1-5 Particle velocity vs. frequency showing the four flow regions . 11

1-6 Threshold dimensionless stroke length as a function of normalized
viscous penetration depth .................. ..... 16

1-7 Effect of Reynolds number and orifice height-to-diameter aspect ratio
on synthetic jet formation .................. ..... 19

1-8 Flow regions as a function of Reynolds number . ..... 22

1-9 Orifice plate cross-sections used by Cater and Soria (2002) . 23

1-10 Orifice plate cross-sections used by Shuster and Smith (2004) .. 24

1-11 Two-dimensional synthetic jet formation criterion . .... 26

1-12 Symmetry planes imposed by Rizzetta et al. (1999) for three dimen-
sional synthetic jet computations ................. 28

2-1 Detailed schematic showing synthetic jet dimensional parameters 37

3-1 Exploded view of modular piezoelectric-driven ZNMF device .. 50

3-2 Shaker-driven ZNMF device .................. ..... 51

3-3 Detailed schematic of shaker-driven ZNMF device . .... 52

3-4 Relative phasing of displacement sensor and accelerometer . 56

3-5 Bode plot of the corrected displacement signal ........... ..57

3-6 Typical piston driver lateral displacement .............. ..59

3-7 Lateral piston driver RMS position ................. .. 59









Piston motion distortion .. ...................

Schematic of laser displacement sensor .. .............

Piston characterization for h/d = 1.46 .. ..............

Sinusoidal controller flowchart .. .................

Piston motion before and after sinusoidal control .. .........

Piston motion before and after PIV measurements .. ........

Flow visualization setup schematic .. ................

Synthetic jet coordinate system .. ................

Schematic of the hotwire anemometry setup .. ..........

Photograph of the PIV setup .. ..................

Frame straddling timing diagram for two-frame single exposure PIV

Block diagram of the PIV setup .. ................

Block diagram of the PIV timing .. ...............

Piston motion and PIV trigger signals .. ..............

PIV laser intensity acquired from a photodiode .. ..........

Typical PIV calibration image .. .................

Typical slice of a PIV calibration image .. .............

PIV calibration image showing hole centers .. ............

Histogram of a typical PIV calibration .. .............

Schematic of the LDA setup for synthetic jet velocity field measurement

LDA 3-beam optical configuration for near-surface velocity measure-
m ents . . . . . . . . .

Photograph of the LDA 3-beam combiner setup .. .........

Raw Doppler burst created by the passage of a particle through the
probe volum e . . . . . . . .

Typical histogram from Monte Carlo simulation of Uo .. ......

Typical histogram from Monte Carlo simulation of .. .......

Centerline RMS velocity vs. x/d .. .................










4-2 Hotwire velocity characterization, h/d = 1.46 .. .........

4-3 Re St parameter space envelope .. ..............

4-4 Three-dimensional parameter space of test matrix cases .....

4-5 Typical hotwire velocity trace .. ...............

4-6 Phase-dependent turbulence intensity, Reynolds number sweep

4-7 Phase-dependent turbulence intensity, Strouhal number sweep


Phase-dependent

Phase-dependent
control .


turbulence intensity,

turbulence intensity


4-10 Flow visualization photograph of Case


Flow

Flow

Flow

Flow

Flow

Flow

Flow

Flow

Flow

Flow

Flow

Flow

Flow

Flow

Flow

Flow

Flow


visualization photograph

visualization photograph

visualization photograph

visualization photograph

visualization photograph

visualization photograph

visualization photograph

visualization photograph

visualization photograph

visualization photograph

visualization photograph

visualization photograph

visualization photograph

visualization photograph

visualization photograph

visualization photograph

visualization photograph


of Case

of Case

of Case

of Case

of Case

of Case

of Case

of Case

of Case

of Case

of Case

of Case

of Case

of Case

of Case

of Case

of Case


h/d sweep .....

with and without


1 in the XY plane

1 in the XZ plane

2 in the XY plane

2 in the XZ plane

3 in the XY plane

3 in the XZ plane

4 in the XY plane

4 in the XZ plane

5 in the XY plane

5 in the XZ plane

6 in the XY plane

6 in the XZ plane

7 in the XY plane

7 in the XZ plane

8 in the XY plane

8 in the XZ plane

9 in the XY plane

9 in the XZ plane


sinusoidal










4-28 Flow visualization photograph of Case 10 in the XY plane ......

4-29 Flow visualization photograph of Case 10 in the XZ plane ......

4-30 Flow visualization photograph of Case 11 in the XY plane ......

4-31 Flow visualization photograph of Case 11 in the XZ plane ......

4-32 Piston distortion between Case 3 and Case 12 .. ..........

4-33 Flow visualization photograph of Case 12 in the XY plane ......

4-34 Flow visualization photograph of Case 12 in the XZ plane ......

4-35 PIV-LDA comparison of streamwise exit velocity profile movie .

4-36 PIV-LDA comparison of streamwise exit velocity profile still frames

4-37 PIV-LDA comparison of cross-stream exit velocity profile movie .

4-38 PIV-LDA comparison of cross-stream exit velocity profile still frames

4-39 PIV-LDA comparison of phase-averaged exit volume flowrate ..

4-40 Phase-averaged LDA velocity profiles in the XZ plane ........


4-41 Case 3 mean plus phase-averaged velocity field mov


mean plus phase-averaged velocity field still

time-averaged normalized vertical velocity


time-averaged

time-averaged

time-averaged

time-averaged

time-averaged

time-averaged

time-averaged


normalized

normalized

normalized

normalized

normalized

normalized

normalized

normalized


vertical

vertical

vertical

vertical

vertical

vertical

vertical

vertical


velocity

velocity

velocity

velocity

velocity

velocity

velocity

velocity


4-51 Case 9 time-averaged


10 time-averaged normalized vertical velocity

11 time-averaged normalized vertical velocity

12 time-averaged normalized vertical velocity


ie ....... 129

frames .... 129

. . . 130

. . . 130

. . . 131

. . . 131

. . . 132

. . . 132

. . . 134

. . . 134

. . . 135

. . . 135

. . . 137

. . . 137


Case

Case

Case

Case

Case

Case

Case

Case

Case


Case

Case

Case










4-55 Case 3 mean plus phase-averaged streamwise velocity component movie138

4-56 Case 3 mean plus phase-averaged streamwise velocity component still
frames ................... .... .......... 138

4-57 Case 3 mean plus phase-averaged streamwise exit velocity profile moviel40

4-58 Case 3 mean plus phase-averaged streamwise exit velocity profile still
frames ................... .... .......... 140

4-59 Case 3 mean plus phase-averaged cross-stream exit velocity profile
movie ............................. ..... 141

4-60 Case 3 mean plus phase-averaged cross-stream exit velocity profile
still frames ................... ........... 141


4-61 Case 1 mean p


Case

Case

Case

Case

Case

Case

Case

Case


mean

mean

mean

mean

mean

mean

mean

mean


p

p

p

p

p

p

p

p


4-70 Case 9 mean p

4-71 Case 10 mean

4-72 Case 10 mean

4-73 Case 11 mean

4-74 Case 11 mean

4-75 Case 12 mean

4-76 Case 12 mean

4-77 Circulation vs.

4-78 Circulation vs.

4-79 Circulation vs.


lus phase-averaged vorticity movie .

lus phase-averaged vorticity still frames .

lus phase-averaged vorticity movie .

lus phase-averaged vorticity still frames .

lus phase-averaged vorticity movie .

lus phase-averaged vorticity still frames .

lus phase-averaged vorticity movie .

lus phase-averaged vorticity still frames .

lus phase-averaged vorticity movie .

lus phase-averaged vorticity still frames .

plus phase-averaged vorticity movie .

plus phase-averaged vorticity still frames

plus phase-averaged vorticity movie .

plus phase-averaged vorticity still frames

plus phase-averaged vorticity movie .

plus phase-averaged vorticity still frames

phase from the left vortex, Re sweep .

phase from the right vortex, Re sweep

phase from the left vortex, St sweep .










4-80 Circulation vs.

4-81 Circulation vs.

4-82 Circulation vs.

4-83 Circulation vs.
motion .

4-84 Circulation vs.
ton motion


N..

N..


phase from the right vortex, St sweep .. ......

phase from the left vortex, h/d sweep .. ......

phase from the right vortex, h/d sweep ...

phase from the left vortex, sinusoidal/distorted piston


phase from the right vortex, sinusoidal/distorted pis-


,1i. .1 circulation vs. Re .

Ji1. .1 circulation vs. St .


4-87 Case 1

4-88 Case 1

4-89 Case 3

4-90 Case 3

4-91 Case 5

4-92 Case 5

4-93 Time-a

4-94 Case 6

4-95 Case 6

4-96 Case 9

4-97 Case 9


phase-averaged Reynolds stress

phase-averaged Reynolds stress

phase-averaged Reynolds stress

phase-averaged Reynolds stress

phase-averaged Reynolds stress

phase-averaged Reynolds stress

averaged RS for Case 5 .....

phase-averaged Reynolds stress

phase-averaged Reynolds stress

phase-averaged Reynolds stress

phase-averaged Reynolds stress


movie ......

still frames .

movie ......

still frames .

movie ......

still frames .



movie ......

still frames .

movie ......

still frames .


10 phase-averaged Reynolds stress movie .....

10 phase-averaged Reynolds stress still frames

11 phase-averaged Reynolds stress movie .....

11 phase-averaged Reynolds stress still frames .

12 phase-averaged Reynolds stress movie .....

12 phase-averaged Reynolds stress still frames .

5 phase-averaged turbulent kinetic energy movie .


4-105 Case 5 phase-averaged turbulent kinetic energy still frames .


Case

Case

Case

Case

Case

Case

Case









4-106 Phase-averaged centerline TKE, Reynolds number sweep ..... ..176

4-107 Phase-averaged centerline TKE, Strouhal number sweep ...... ..177

4-108 Phase-averaged centerline TKE, h/d sweep ............. ..177

4-109 Phase-averaged centerline TKE with and without sinusoidal control 178

4-110 Dimensionless turbulent transition map . . .... 178

A-1 Schematic of fully-developed pipe flow with an oscillating pressure
gradient .. .. .. ... .. .. .. .. .. .. .. .. ..... 186

A-2 N ,ini. I.,1 velocity profile vs. normalized radius . .... 189

A-3 U/U vs. Stokes number for pipe flow with an oscillating pressure
gradient .................. ............. .. 190

A-4 U/U vs. Stokes number for two-dimensional channel flow with an
oscillating pressure gradient .................. .. 191

B-1 Detailed schematic of a synthetic jet showing ejected vorticity 194

B-2 N. .11-i l. .1 jet formation data to account for radius of curvature and
Stokes number .................. ......... 197

B-3 PIV velocity vector fields with overlaid vorticity contours ..... ..199

B-4 U-component velocity contours ................ . 200

B-5 Jet formation criterion for axisymmetric case . . ... 201

D-1 Flow in a gap generated by an oscillating piston and oscillating pres-
sure gradient .................. .......... .. 220

D-2 Schematic of deflected piston .................. ..... 225

D-3 Relative phasing between rp(t), vp(t), and p/x . . ... 228

D-4 N. i in i!i. .1 velocity profile of flow in the piston gap . ... 230

D-5 Comparison of resistance to flow in the piston gap and the vent channel231

E-1 Example image of spurious PIV vectors . . ..... 234

E-2 Example image of spatial-validated PIV vectors . .... 234

E-3 Example PIV dataset of identified outliers ............. ..238

E-4 Example image of outlier-rejected PIV vectors . . ... 238














LIST OF SYMBOLS AND ABBREVIATIONS


Roman Symbols

A slot (orifice) area, (m2)

a vortex core radius, (m)

ao pipe radius, (m)

B pressure gradient parameter for oscillating pipe flow, (m/s2)

Co speed of sound of the fluid, (m/s)

Dv distance between vortex centers, (m)

d slot depth (orifice diameter), (m)

f driver frequency of oscillation, (Hz)

fo Br, -- cell frequency shift, (Hz)

fD Doppler burst frequency, (Hz)

f, frequency between PIV i. i7 pair captures, (lHz)
ft PIV tri frequency, (Hz)

h slot (orifice) height, (m)

lo impulse per unit width, (kg/s)
K jet formation constant

K' proportionality constant of jet formation

L RMS stroke length, (m)

Lo stroke length based on uo(t) (m)

AP pressure gradient in a ili- developed oscillatory channel flow, (Pa)

P piston motion program factor

p constant which accounts for flow separation due to F
Rp average piston displacement during the half-cycle, (m)









R slot (orifice) exit radius of curvature, (m)

RD radius of piston driver, (m)
Rp amplitude of sinusoidall) piston driver motion, (m)

rp(t) periodic piston motion, (m)
Re, RB. nolds number based on U

Re10 R.-nolds number based on Jo

PF. P .. nolds number based on slot depth (orifice diameter)

rt ratio of the square root of the 2 :i: ed norm of the residual of a Fourier

series to the amplitude of a periodic signal

S Stokes number

St. ;- :.,! .1 number

dT time between PIV image frames, (s)

T' period of one ( 1 (s)

t time, (s)

U i ..i i averaged, time averaged streamwise < ..:. :onent of velocity during

expulsion at the exit plane, (m/s)

U amplitude of uo(0), (m/s)

U common velocity scale, = Lo/T, (m/s)

Uo momentum flow velocii at the slot (orifice) exit, (m/s)

UA amplitude of u(i), (m/s)

u time varyi i spatial averaged streamwise component of velocity at the

exit plane, (m/s)

Mean streamwise velocity component at a point, (m/s)

UP, phase-averaged streanmwise velocity component at a point, (m/s)

It time varying, spatial varying streamwise component of velocity at the exit

plane, (m/s)









uo time varying streamwise component of the centerline velo,-itr at the exit

plane, (rn/s)

streamwise velocity at a point, (m/s)

u' fluctuating streamwise velocity component at a point, (m/s)

Up,, particle velocity, (m/s)

AV volume displaced !b-- the driver during the half cycle, (rn3)

V cavity volume, (m3)

IV induced velocity of the vortex dipole, (m/s)

V. average i. suction velocity, (m/s)

mean cross-stream velocity component at a point, (m/s)

ivp phase-averaged cross-stream velocity component at a point, (m/s)

cross-stream velo-it.r at a point, (m/s)

vt fluctuating cross-stream velocity component at a point, (m/s)
w two-dimensional spanwise slot width, (m)

x streamwise coordinate direction

y cross-stream coordinate direction (two-dimensional slot)

Greek Symbols

6, shear 1 ---r thickness inside the slot (orifice), (m)

e slot (orifice) dimensionless radius of curvature, 2R/d

dq) phase between PIV-acquired image iI' H (rad)

F* dimensionless circulation over half the slot depth

F circulation produced by half of a vortex pair, (in2/s)

K constant which depends on vortex core radius a

Az wavelength of LDA laser light, (m)

, dynamic viscosity of the fluid, (kg/m s)

v kinematic viscosity of the fluid, (nn2/s)

0 LDA beam half-angle, (rad)


xvii









p :-itv of the fluid, (kg/m 3)

fQ, shed vortex strength, (nm/s)

a) driver frequency of oscillation, (rad/s)

LIH Helmholtz frequency of the (two-dimensional) cavity, (rad/s)

z spanwise (or azimuthal) component of vorticity at the exit plane, (1/s)

Abbreviations

DNS direct numerical simulation

FFT fast Fourier 1t :, *.,i:,

JFC jet formation criterion

LDA laser Doppler anemometry

PIV particle image velocimetry

PMT photomultiplier tube

RANS Reynolds-,,, i. .1 ", -ier-Stokes equations

RMS root mean square

RS R.- -nolds stress

THD total harmonic distortion

TKE turbulent kinetic energy

ZNMF zero-net mass-flux


xviii















Abstract of Dissertation Presented to the Graduate School
of the University of Fi..: 1 i in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosoi h--

AN EXPERT "- -' TAL INVESTIGATION OF FLOWS
FROM ZERO-NET MASS-FLUX ACTUATORS

By

R -i: .IL.-- Holman

'", 2006

C(. "I : Louis N. Cattafesta III
Cochair: Bruce F. Carroll
Ma i-: Department: Mechanical and Aerospace Engineering

Zero-net mass-flux (ZNMF) devices consist of an oscillating driver, a cavity,

and a small opening such as a rectangular slot or a circular orifice. Tli. driver

produces a series of vortex i"i' (or rings) at the slot/i .: I:.. which add momentum

and circulation to the flow. ZNMF devices are useful tools for flow control .i, .tions

such as heat transfer, mixing enhancement, and boundary I:-.-- separation control.

To date much research has been done to qualify and quantify the effects of ZNMF

devices in many applications, both experimental and computational. However, a num-

ber of issues still remain. First, there is no universally accepted dimensionless pa-

rameter space, which makes device characterization and comparison between studies

di:il,.ult. Second, most experimental studies do not sit !:il quantify the near-

field behavior, which hinders the ii.li ..1 .. I understanding of the t ..1. i1 ;._ flow

physics. Of particular interest are the regimes of i1. formation, and transition from

laminar to turbulent-like flow, which are not well understood. Finally, the accuracy

of experimental measurements are seldom reported in the literature.









This study unifies the experimental and numerical data presented in the lit-

erature for ZNMF flowfields exhausting into a quiescent medium. A quantitative

experimental database is also generated to completely characterize the topological

regions of ZNMF flows over a useful range of the dimensionless parameter .

Tli database is derived chiefly from two-dimensional velocity field measurements us-

ing !'ticle image velocimetry and laser Doppler anemometry. Vorticity, circulation,

.- -nolds stress, and turbulent kinetic energy is acquired to characterize the resulting

flowfield.

'- ti .;. :i insight into the behavior of voice coil driven ZNMF devices is un-

covered. Design improvements are made by implementing a sinusoidal controller for

piston motion and eliminating the need for a sealing membrane in the cavity. It is

shown that the proper velocity scale to characterize a ZNMF device is either a mo-

mentum flow velocity or a velocity scale based on circulation. In addition, the 1:... i

scaling of a ZNMF device is application-specific. Ti. two chief parameters which

govern ZNMF flows the P.- -nolds number and the Strouhal number are shown to

affect the flowfield in different -.... -.
















CHAPTER 1
INTRODUCTION

This chapter presents some background information on zero-net mass-flux de-

vices, otherwise known as synthetic jets. Reviews of a number of studies in the open

literature which examine the flowfield behavior of synthetic jets are also presented. It

is shown that there are insufficient data available to quantitatively characterize the

topological regimes generated by a synthetic jet, and this is the motivation for this

study. The chapter concludes with technical objectives and a general outline.

Background

In recent years, the scientific community has produced a large number of studies

on zero-net mass-flux (ZNMF) devices. A cursory examination of the literature shown

in Figure 1-1 shows the ever-increasing popularity of the ZNMF device as a topic of

study.

A ZNMF device consists of an oscillating driver attached in some manner to

a cavity that contains a small slot or orifice. This driver may be, for example, a

speaker, a mechanical piston, or a piezoelectric diaphragm. The driver has the effect of

periodically decreasing and increasing the volume of the cavity. This motion can cause

fluid to be alternately compressed and expanded inside the cavity, and/or expelled and

ingested through the slot. The extent to which fluid is compressed (or expanded) as

opposed to expelled (or ingested) depends on the fluid properties, the driver dynamics,

and the geometry of the device. The device is called i ,-net mass-flux" because no

external source of fluid exists; that is, the integration of the mass flow rate across the

slot over an integer number of cycles is identically equal to zero. Although there is no

net mass 'i i.n- er to its surroundings, the ZNMF device has the interesting property











100
90
80
70
60
50
40
30
20
10
0
N- C IA C,1,1,1,1:


Year


Figure 1-1: ZNMF studies published by year.


of causing a finite amount of momentum 'i.nu,-er to its surroundings. Hence, other

parlance used for the ZNMF device includes oscillatoryy momentum generator," and

more commonly -3yii!1. ii: jet," although the latter is actually a limited, albeit a

very il. ii -l ii.- case of ZNMF devices.

Figure 1-2 illustrates a typical ZNMF device being operated to produce a syn-

thetic jet. If the driver amplitude is high enough, as fluid is expelled through the

slot the boundary 1 .-r separates from the wall and, at either edge of the slot, rolls

up to produce a vortex pair. This vortex pair, endowed with circulation, propagates

away from the slot under its own self-induced velocity. During the subsequent suction

stroke, fluid is drawn into the cavity from the surroundings, but the vortex pair has

moved sufficiently far from the slot so as to be relatively unaffected. A new vortex

pair is then ejected and the cycle continues, producing a train of vortex pairs issuing

normal to the slot. If the slot is replaced by an axisymmetric orifice, a train of vortex

rings results. At still higher amplitudes, the ejected vortex pair (or ring) may break









down due to turbulence. In any case, in a time-averaged sense, this behavior creates

a jet-like flow which is synthesized from the ambient fluid, hence the term -ynii. Ii

jet." For the remainder of this work, the term -iyni !, 'ic jet" will be used to describe

any generic ZNMF device, in accordance with common terminology found in the lit-

erature. However, the reader is reminded that this usage of the term is technically a

misnomer, since the synthetic jet is the product of a special subset of ZNMF devices.

In the next section we shall examine some of the interesting properties of the ZNMF

device which have been described in the open literature.
U

shed vortex pairs





slot slot
cavity cavity
--::------------222--:=- .:--------------------------,



a) oscillating driver b) oscillating driver

Figure 1-2: Schematic of a typical ZNMF device producing a synthetic jet: (a) in-
stantaneous and (b) time-averaged.


Previous Work

Due to its simplistic design and ability to produce jet-like flows without external

plumbing, the synthetic jet has emerged as an attractive tool for researchers to inves-

tigate in the laboratory -both computationally and experimentally for potential

use in flow control applications. One such application is jet vectoring. For example,

Smith & Glezer (2002) examined the vectoring effect a synthetic jet had on a steady

jet. The steady jet exit was nominally two-dimensional, measuring 76.2 x 12.7 mm,

while the synthetic jet slot exit, measuring 76.2 x 0.51 mm, was mounted next to the









steady jet at a distance of 1.8 mm away. It was found that the synthetic jet entrained

fluid from the primary jet during the suction stroke, causing the primary jet to be

deflected toward the synthetic jet. This deflection was balanced by a force on the

steady jet channel, which increased both with steady jet velocity as well as synthetic

jet amplitude.

In a previous study, Smith & Glezer (1997) found that a synthetic jet whose

dimensions were one to two orders of magnitude less than those of the primary jet

could cause a deflection in the primary jet toward the synthetic jet of 30. In addition,

placing the synthetic jet such that it exhausted normal to the steady jet caused the

steady jet to vector in the opposite direction. In both studies, the steady jet began

to vector inside its channel and the turn was completed by about one slot depth.

Pack & Seifert (1999) also observed a vectoring effect of a synthetic jet on a steady

jet, by attaching a wide-angle diffuser to the jet exit. The synthetic jet had the effect

of causing the steady jet flow to attach to the diffuser wall, for both streamwise and

low amplitude cross-stream synthetic jet flows. For higher amplitude cross-stream

synthetic jet flows, the jet deflected away from the diffuser wall where the synthetic

jet was mounted, consistent with the results of Smith & Glezer (1997).

In a numerical study of jet vi liin:.- Guo et al. (2003) also observed results

consistent with the experiments of Smith & Glezer (1997). At the same operating

conditions, their simulations indicated very good agreement in the vorticity contours

downstream of the slot exit. They also observed that the vectoring angle of the pri-

mary jet was a function of the angle at which the synthetic jet emerged from, as their

simulations tested two configurations of 0 and 600 synthetic jet angle. Consequently,

the vectoring force was much larger for the 600 synthetic jet than the 0 synthetic jet

at the same operating conditions. Finally, they noted that there exists an optimal

frequency and amplitude of synthetic jet operation, as well as an optimal distance

between the synthetic jet and the steady jet, to maximize the vectoring effect.









Another application of synthetic jet flows is mixing enhancement. Wang &

Menon (2001) computationally investigated the effect of synthetic jet mixing. They

employ, -l a Lattice Boltzmann Equation (LBE) method to simulate the flowfield of

a synthetic microjet in the presence of a fuel injector. It was found that operation of

the synthetic jet resulted in significantly more fuel-air mixing than without it, but the

orientation and location of the synthetic jet also affected the mixing enhancement.

C'!l i et al. (1999) experimentally investigated the effects of synthetic jet mixing

by introducing synthetic jet flows normal to the parallel flow of cold and hot gaseous

streams. The mixing efficiency was deduced by measuring the temperature distribu-

tion at 80 diameters downstream of the synthetic jets. It was found, not surprisingly,

that the degree of mixing was a function of jet actuation. At low actuation, an ex-

perimentally acquired cross-stream temperature profile showed a large difference in

temperature as the hot and cold streams did not mix very much, with the maximum

and minimum temperatures being 740C and 40C, respectively. However, at higher

actuation levels the temperature profile became much closer to uniform, ranging from

360C to 260C. A key benefit to utilizing synthetic jets for mixing, they noted, was

that the introduction of additional cold dilution air was not needed, as the synthetic

jet is a ZNMF device. Significant synthetic jet mixing can also be achieved by plac-

ing an array of azimuthal synthetic jets around a central primary jet, as reported in

several papers (Davis & Glezer, 1999, 2000; Ritchie & Seitzman, 1999; Ritchie et al.,

2000).

Another interesting application of synthetic jets is heat transfer augmentation.

Campbell et al. (1998) demonstrated via experiments that a synthetic jet device can

be effective for processor cooling in a laptop computer. For a fixed actuation frequency

and amplitude, an optimized synthetic jet geometry resulted in a 2"'". reduction in

the processor operating temperature versus natural convection alone.









In another study, an annular synthetic jet device was tested by Trdvnfcek &

Tesar (2003) to gauge the effect of mass transfer. The synthetic jet flow was directed

toward a surface coated with naphthalene, and the mass transfer was determined by

measuring the change in thickness of the surface due to sublimation. Interestingly,

through smoke visualization they observed two different flowfields, termed .."

and -I i..:- which were a function of the actuation amplitude. As expected, the

extent of mass transfer was greater for the -i i flowfield as opposed to the v-, .1"

one.

Perhaps the most promising application of synthetic jets is their potential use in

the active control of separated flows. A two-dimensional, NACA 0024 airfoil with a

cylindrical leading-edge section instrumented with two synthetic jets was investigated

by Smith et al. (1998) and later by Amitay et al. (1999). The novel airfoil design

allowed the position of the two-dimensional synthetic jets to be adjusted by rotating

the cylindrical portion of the airfoil section. For angles of attack greater than 50 and

at a chord Reynolds number of 300,000, the flow separated from the airfoil surface. It

was found that the location of the synthetic jets, as well as their amplitude, affected

flow reattachment, with complete reattachment occurring up to an angle of attack of

15, and partial reattachment up to 25.

A qualitative study was undertaken by Crook et al. (1999) which explored the

effect of a synthetic jet issuing normal to the surface of a cylinder. They found that

placement of the synthetic jet just upstream of the separation location, about 95,

caused strong entrainment of fluid toward the orifice on both sides of the jet.

Ravindran (1999) numerically simulated the flow over a NACA 0015 airfoil with a

synthetic jet near the leading edge. It was found that as the strength of the synthetic

jet increased, for two high angles of attack (220 and 240), the lift coefficient also

increased.









The effect of multiple synthetic jets on a separated flow was investigated exper-

imentally by the present author (Holman et al., 2003). A NACA 0025 airfoil was

tested at an angle of attack of 120 and a chord Reynolds number of 100,000. Without

actuation, the flow over the airfoil separated by about 25' chord. However, the op-

eration of two closely spaced two-dimensional synthetic jet actuators near the leading

edge caused the separation location to be moved back toward the trailing edge. The

actuator slot depth was 0.5 mm for each actuator, and they were separated by a dis-

tance of 2.4 mm. The actuator pair was located at ;:' chord. The exact location of

the separation point depended on the strength of the synthetic jets and their position

on the airfoil surface, but interestingly not on the relative phasing between actuators.

It can be seen that there are a number of promising applications of synthetic

jets. Despite its potential use as a flow control device, however, the fundamental

nature of synthetic jet behavior is still not well understood. Nevertheless, a number

of investigators have endeavored to elucidate the underlying physics of synthetic jet

flows, and this section presents some of their key findings, divided into two parts:

experimental and numerical studies.

Experimental Studies

Although most references to synthetic jets in the literature date back only to the

past decade, the successful demonstration of the synthetic jet may be traced back

at least as far as Ingard & Labate (1950) in which they identified and characterized

acoustic streaming around circular orifices. (Qualitatively, ... i-I str( iniii;' can

be described as a mean fluid motion generated by the impingement of a sound wave

on a solid boundary. Lighthill (1978) provides a thorough treatment of the subject.)

Their setup consisted of a steel circular plate with a machined orifice inserted into a

circular tube in which sound waves were generated through the use of an impedance

tube connected at one end. The other end was sealed through the use of an adjustable

plunger which allowed the orifice plate to be situated at the quarter-wavelength of









the sound wave. This setup allowed for the measurement of the orifice acoustic

impedance using the standing-wave method (Blackstock, 2000). A total of 25 orifice

plates of varying height and diameter were tested with varying sound pressure levels

at a frequency range of 100 Hz 1 kHz, and 'p article velocil were measured.

The tube itself was fitted with windows for optical access, and the flow around the

orifice was visualized with smoke particles. Both mean illumination and stroboscopic

illumination were used, allowing for time-averaged and instantaneous photographs of

the flowfield to be acquired. These photographs showed that four distinct s,,is

of flow established themselves around the orifice as a function of the frequency of the

sound wave, the sound pressure level, and the geometry of the orifice (Figure 1-3).


Figure 1-3: Flow regions induced by acoustic streaming through an orifice under
steady illumination, a) Region 1, b) Region 2, c) Region 3, d) Region 4. The white
vertical line represents the location of the orifice, black horizontal bars represent
the approximate orifice location, and black arrows represent the approximate flow
direction. Adapted from Ingard & Labate (1950).









Region 1 consisted of steady circulation that was symmetrical on either side of

the orifice and occurred at low sound intensities. Flow was directed out from the

orifice in this region. Region 2 was achieved as the sound intensity was increased,

and was still characterized by steady circulation. However, the flow directed out

from the orifice reversed itself toward the orifice. As the sound intensity continued to

increase, turbulence effects were observed and a complicated, .,-ii'., Ii ical pattern

of steady circulation superposed with pulsatory effects emerged as Region 3. Here

they also observed what they termed as "boiling the sporadic exchange of particles

between one side of the orifice and the other. Finally once a certain sound pressure

level was reached, a sudden Ii iI:l !i'oil! occurred in which vortex rings were shed

and propagated from either side of the orifice. This breakthrough, of course, is very

similar to what is known tod i, as the successful formation of a synthetic jet. Indeed,

they observed that, in a time-averaged sense, flow was directed out axially from the

orifice and directed in radially. In general, for a fixed orifice geometry and frequency,

the flowfield evolved through the different regions as the sound pressure level was

increased. However, it was found that below a certain frequency, what they called

the eutecticc" point, the flowfield transitioned gradually from Region 1 directly into

Region 4. Figure 1-3 shows flowfields from each of the four regions under steady

illumination, and Figure 1-4 shows a flowfield characteristic of Region 4 taken with

stroboscopic illumination. In Figure 1-5, the four flow regions are shown as a function

of particle velocity and actuation frequency, and the eutectic point is indicated.

It was also observed that for a fixed oscillation frequency and orifice diameter,

varying the orifice height (and hence the height-to-diameter aspect ratio) tended to

change the value of the particle velocity required to reach a certain flow region. Once

the height-to-diameter aspect ratio reached a value of approximately 2, the flow

boundaries between regions leveled off. Although this observation seems to imply

that a "fully d, 1, !1p.' i flow region exists as a function of orifice aspect ratio, this




















Figure 1-4: Flow region 4 induced by acoustic streaming through an orifice under
stroboscopic illumination, the white vertical line represents the location of the orifice,
black horizontal bars represent the approximate orifice location, and black arrows
represent the approximate flow direction. Adapted from Ingard & Labate (1950).


simplistic view is not completely accurate. At present there is no clear, universally

accepted definition for fully developed oscillatory flow in a pipe or channel. As will

be shown later in ('! Ilpter 2, the stroke length, or average fluid particle excursion,

also pl. i, a key role in determining the nature of the flow in the orifice.

Although particle velocities at the orifice are reported as a function of the flow

regions, it is unfortunate that no description of the method or accuracy of the data

is provided. Notwithstanding these semi-qualitative findings, however, the results

offer a tantalizing insight into the richly detailed and complex flow physics present

in isolated synthetic jets. In addition, although presented in purely dimensional

form, these results hint at the existence of important dimensionless parameters that

characterize the flowfield of a synthetic jet. Finally, it should be emphasized that

these flow patterns were generated via acoustic streaming, and not by the periodic

oscillation of a boundary which is typical of synthetic jets. In the latter case, the

mean motion is on the order of the oscillatory motion, while in the former, the mean

motion is of second order (Smith & Swift, 2001).

Nearly five decades later, in a study of an oscillating piezoelectric diaphragm

mounted flush to a plate in a water tank, James et al. (1996) observed that when a

threshold amplitude was reached, a turbulent jet-like flow was produced. This only









200

180

160 -
Region 4
4 140
E / Region 3
120

2 100-
0 Region 2
I, 80----/ ^^

S60

0e Region 1
20 point


0
0 100 200 300 400 500 600 700
Frequency (Hz)

Figure 1-5: Particle velocity vs. frequency showing the four flow regions and the
eutectic point. Adapted from Ingard & Labate (1950).


occurred when cavitation bubbles formed on the surface of the diaphragm and then

collapsed during each cycle. The threshold amplitude of jet formation also corre-

sponded to the low pressure necessary to form cavitation bubbles. It was conjectured

that jet formation occurred as a result of a train of time-periodic vortex rings that

formed during each cycle due to the presence of the cavitation bubbles and propagated

downstream.

Shortly thereafter in a seminal paper, Smith & Glezer (1998) observed that

the formation of a synthetic jet could be facilitated by mounting the driver flush

to the wall of a cavity which contained a small slot. They also identified two key

dimensionless parameters that govern the formation of vortex pairs. If one assumes a

uniform or -! ,g" velocity profile uo(t) at the slot exit, then the distance that a fluid

particle travels with velocity uo(t) during the expulsion part of the cycle, called the









stroke length, may be written as
T/2
Lo \ uof(t)dt (1.1)

where T/2 is half the period of the cycle. Denoting the slot depth or orifice diameter as

d, the dimensionless stroke length Lo/d becomes the first key dimensionless parameter

which governs vortex pair formation. The second dimensionless parameter is the

Reynolds number, based on the impulse per unit width

Reio = o/pd (1.2)

where
T/T/2
Io pd j U(t)dt (1.3)

and p and p are the fluid dynamic viscosity and density, respectively. The choice of

these dimensionless parameters arose out of the study of vortex rings (Didden, 1979;

Glezer, 1988; Shariff & Leonard, 1992).

Alternatively, a characteristic orifice velocity is used to calculate the Reynolds

number:

Reu = Ud/v (1.4)

where

S= Lo/T (1.5)

and v = p/p is the fluid kinematic viscosity. Taken with the frequency of oscillation,

the duty cycle, and the geometry of the synthetic jet device (all constants in their

study), these parameters depend solely on the amplitude of the driver.

For the experiments, they manufactured a synthetic jet device consisting of a

circular piezoceramic patch bonded to a metal disk, which was then sealed to the

underside of a cavity. A nominally two-dimensional synthetic jet was formed via a

top plate with a small slot measuring 75 x 0.5 mm. The driver was operated over a









range of amplitudes to acquire data for the parameter space 5.3 < Lo/d < 25 and

1400 < Reo < 30, 000 (corresponding to 104 < Rea < 489). The experiments were

divided into two parts: flow visualization using schlieren photography enabled via

injection of a small amount of tracer gas, and fluid velocity measurements using hot

wire anemometry.

Schlieren visualization at the nominal case of Re, = 383 revealed that during a

cycle, a vortex pair was shed which initially appeared laminar, transitioned to tur-

bulent, and then ultimately lost coherence and became indistinguishable as spanwise

rib-like vortices enveloped the vortex pair. Velocity measurements of the vortex pair

trajectories performed with hot wire anemometry over a range of positions above

the slot indicated that these trajectories scaled with the stroke length. Furthermore,

although the vortical structures appeared to break down, a time-periodic component

of the velocity persisted through the measurement domain of 180 slot depths down-

stream of the slot. In addition, a non-zero time-invariant mean velocity component

emerged, which was found to be a function of downstream distance. Analysis of

the time-averaged and fluctuating components of velocity far downstream of the slot

demonstrated that the velocity profile collapsed, indicating that similarity had been

achieved, analogous to the conventional two-dimensional jet but with some notable

differences. Namely, the synthetic jet flow achieved similarity much sooner, the cen-

terline velocity d. ,i .1 more rapidly, and both the jet width and volume flow rate

decreased more rapidly than conventional two-dimensional jets. These differences

were attributed to the constant loss of momentum flux associated with the suction

portion of the cycle (Smith & Glezer, 1998).

Although these experimental results represented a benchmark for characterizing

synthetic jet flows from which several other studies were based, several important

questions remained unanswered. First, the range of operation of their device was

limited to the higher dimensionless stroke length range, most likely corresponding to









Region 4 of Ingard & Labate (1950). Secondly, the method of velocity measurement

-hot wire anemometry -has its own drawbacks, such as directional ambiguity in

an oscillatory flowfield, large fluctuations compared to the local mean value, limited

spatial resolution over small-scale devices, and possible alteration of the flow due to

the intruding presence of the probe. Finally, a single device was used for all tests,

which had a constant slot height-to-depth aspect ratio. This limitation eliminated

the possibility of studying geometric effects.

In an attempt to resolve some of these aforementioned issues, Smith and Swift, in

two related papers (Smith & Swift, 2001, 2003), subsequently performed experiments

on a larger synthetic jet device. The oscillator consisted of a speaker-driven plenum

which allowed frequencies in the range of 10 < f < 100 Hz to be achieved. The

two-dimensional slot depth could be adjusted such that 0.51 < d < 2.0 cm, while

the spanwise width of the slot was fixed at 15.2 cm, giving a width-to-depth aspect

ratio 7.6 < w/d < 30.4. The height of the slot was fixed at 24 cm; thus the height-

to-depth aspect ratio varied as 12 < h/d < 47. Also, a rounded radius of curvature

of 0.64 cm was present on either side of the slot exit to mitigate separation effects

during the suction stroke. Thus, a new geometric parameter was introduced: the

dimensionless radius of curvature, defined as the radius of curvature divided by the

slot depth, 0.32 < R/d < 1.25. The parameter space of the dimensionless stroke

length and Reynolds number was extended beyond that of Smith and Glezer such

that 13.5 < Lo/d < 80.8 and 695 < ReK < 14, 700. Although hot wire anemometry

was employ, ,1 to acquire velocity measurements, the large slot depth allowed for good

spatial resolution in the measured velocity profile, and consequently the time-varying

velocity profile uo(t) from Eq. (1.1) was no longer used, but u(t), the cross-stream

averaged exit-plane velocity, was used to compute the Reynolds number.

Smith & Swift (2001) developed a model for jet formation, independently of

Rampunggoon (2001), which yielded a threshold dimensionless stroke length. The









model contained the following key assumptions: (1) potential flow was assumed, (2)

a jet was formed when the induced velocity of the vortex pair was greater than the

peak suction velocity, (3) the distance between the centers of the vortices was the slot

depth d, and (4) the position of the vortex pair at the peak of the suction stroke was

taken as x/L = 0.5. With these assumptions, they found a threshold stroke length

L 4
> 2.3 (1.6)
d

for jet formation. The actual value of the threshold stroke length was computed

by first performing schlieren visualization to determine jet formation and noting the

pressure amplitude of the cavity and frequency of oscillation. Then a hot wire profile

was acquired at the same cavity pressure amplitude and frequency to compute the

stroke length. This procedure was repeated over the frequency range of 10 < f <

110 Hz for four slot depths: d = 0.5, 1.0, 1.5, and 2.1 cm. It was found that the

threshold stroke length was not a constant of approximately 2.3 as the model predicted

but in fact was significantly higher between 5 and 8, and varied as a function of the

viscous penetration depth normalized by the slot depth, as shown in Figure 1-6.

Possible explanations for this discrepancy included the model assumptions, deviation

from a slug-flow velocity profile, radius of curvature effects, and turbulent transition

in the slot.

Since hot wire anemometry was used to acquire the velocity data, accuracy

issues still existed, and the authors acknowledged that the velocity measurements

were strictly limited to regions of small cross-stream velocity compared to the local

mean streamwise velocity component. As will be shown in ('! Ilpter 4, this is not

the case for velocity measurements very near the exit plane, and the potential for

computing an incorrect Reynolds number and stroke length based on the hot wire-

measured velocity profile exists.









9
d=.5 cm
8.5 ---------- 1.0cm
1.5 cm
2.1 cm
8 --

7.5 -

7.5 ------------ -----------F T----------- T------------
i i
6.5

6 ----

5.5 --

5
0 0.05 0.1 0.15 0.2
8 /d
V

Figure 1-6: Threshold dimensionless stroke length as a function of normalized viscous
penetration depth for several slot depths. Adapted from Smith & Swift (2001).


Smith et al. (1999) also extended the work of Smith & Glezer (1998) by measuring

the velocity field downstream of both a two-dimensional (slot) and an axisymmetric

(orifice) synthetic jet using phase-locked Particle Image Velocimetry (PIV), which

gave two-component velocity measurements and eliminated the directional ambiguity

inherent in hot wire anemometry. Cavity pressure measurements were also made using

a dynamic pressure transducer with a range of 1 psid and a bandwidth of 100 kHz.

A piezoelectric diaphragm served as the oscillating driver, and the sharp slot exit

had a height-to-depth aspect ratio of 2.5. The actuator was operated at frequencies

of 600 Hz and 1100 Hz, and vortex pairs were seen to be ejected from the slot for

both operating frequencies by computing the spanwise vorticity from the measured

velocity fields. However, for the lower frequency case, remnants of vorticity were

observed in the wake behind the vortex pair, ostensibly because the total circulation

generated by the expulsion stroke exceeded the maximum amount of circulation that









the vortex pair could contain (Gharib et al., 1998). For the axisymmetric orifice, the

height-to-diameter aspect ratio is much less than one. It was found that increasing

the dimensionless stroke length increased the cavity pressure, but a large jump in

stroke length was observed for a given cavity pressure around a stroke length value

of one. Since the axial distance between the orifice and the location of the vortex

ring at the start of the suction part of the cycle increased with stroke length, they

postulated that at small stroke lengths, the vortex ring induced a blockage during

the suction cycle, since the ring had the effect of pumping fluid axially away from the

orifice. Once the ring was far enough removed from the orifice as the stroke length

was increased, this blockage was removed and the head loss was reduced, resulting in

an increase in stroke length at a nominally similar cavity pressure.

Another important result of their study was that the phase-locked velocity pro-

files measured in the vicinity of the orifice were significantly different from slug-like;

indeed, the profiles exhibited maxima near the edges of the orifice during the ejection

part of the cycle. This behavior is termed Richardson's annular effect, and is typical

of fully developed pipe flows generated by oscillating pressure gradients (White, 1991;

also see Appendix A).

During the suction part of the cycle, however, the velocity profiles became more

slug-like, s,-l-:. -1 iir; an .i-vmmetry between the expulsion and ingestion strokes. This

occurred because during the expulsion stroke, the exit plane of the orifice corre-

sponded to the exit of the jet, while during the suction stroke, this location now

became the entrance plane. This behavior was confirmed by examining the dimen-

sionless phase-locked vorticity contours of the flow -non-dimensionalized by the ori-

fice diameter and characteristic velocity -plotted in non-dimensional radial and axial

coordinates, acquired for several different stroke lengths, Reynolds numbers, and ac-

tuation frequencies. The freshly ejected vortex ring, when plotted in these dimension-

less coordinates, was at the same streamwise position and had the same dimensionless









strength of vorticity, regardless of whether it was sucked back into the orifice or ul-

timately advected away. However, the remnants of the previous vortex ring did not

collapse when non-dimensionalized, -i-i-:. i ir; that the suction part of the cycle af-

fected the vortices in different v--iv. Specifically, the suction cycle had the effect of

either re-ingesting the vortex ring for small stroke lengths or stopping the advection

of the ring and leaving it stationary for slightly larger stroke lengths. At still larger

stroke lengths, however, the effect of the suction was diminished as the vortex ring

propagated downstream.

In a qualitative parametric study, Crook & Wood (2000) investigated the effect of

cavity and orifice geometry on synthetic jet formation. A shaker-driven modular setup

was constructed which allowed for interchangeable cavity heights and circular orifice

plates with varying height-to-diameter aspect ratio. The fluid in the cavity was seeded

with smoke particles and visualized through the use of a 50 Hz pulsating light sheet

and video recorder, which allowed for aliased in,. ~;" of the vortex ring formation

to be generated when the oscillator was run at a frequency of 50.1 Hz. Figure 1-7

shows a two-dimensional matrix of images of the seeded flowfield as a function of

Reynolds number and orifice height-to-diameter aspect ratio. The Reynolds number

was computed by measuring the maximum centerline velocity during the ejection

phase with a hot wire anemometer, and the appropriate length scale was taken as the

diameter of the orifice. Similar to Smith et al. (1999), it was found that a maximum

value of circulation for a vortex ring was reached, and that excess vorticity which could

not roll up into the ring emerged as a tail behind the ring, which rolled up to form a

secondary ring if the Reynolds number was high enough. They also discovered that

increasing the orifice height while holding the Reynolds number and orifice diameter

constant tended to increase the amount of circulation in the ring, presumably because

a more developed velocity profile arose in the orifice. Similar results were found by

increasing the cavity height while holding Reynolds number, orifice height, and orifice









diameter constant. However, it was -.-.-,- -1i I1 that the mechanism for this case of a

more developed vortex ring was due to the ability of the fluid to gain more vorticity

during the suction stroke while inside the larger cavity. Since a vortex ring would

form inside the cavity as a result of the suction stroke, a larger cavity would allow

this ring to generate more vorticity as it interacted with the cavity wall, which would

then persist in the fluid through the following expulsion stroke.


Figure 1-7: Effect of Reynolds number and orifice height-to-diameter aspect ratio on
synthetic jet formation, the white vertical line represents the approximate location of
the orifice, and the white horizontal bars represent the approximate diameter of the
orifice. The Reynolds number increases from bottom to top, and increases from left
to right. Adapted from Crook & Wood (2000).


A piezoelectric synthetic jet actuator was developed by C', i1 et al. (2000). The

jet issued through a narrow slot measuring 35.5 mm by 0.5 mm, and the jet velocity

was acquired using hot wire anemometry. Through stroboscopic flow visualization,

they discerned two types of jets. Laminar jets were achieved at low Reynolds numbers









and were characterized by the presence of discrete vortical structures emanating from

the slot. Turbulent jets occurred at higher Reynolds numbers, and typically only

one vortex pair was observed at the slot, followed by a turbulent-like jet, similar

to the findings of Smith & Glezer (1998). Finally, they noted that the transition

to turbulence depended on both the Reynolds number and the dimensionless stroke

length, though their transition criterion was semi-qualitative and based on a small

number of points.

Gilarranz et al. (1998) constructed a synthetic jet device using a Briiel and

Kjaer shaker-driven membrane as the oscillating driver with a cylindrical cavity. An

axisymmetric orifice plate with a height of 6 mm and a diameter of 2 mm was attached

to the cavity, and the working fluid was water. PIV was used to acquire phase-locked

velocity vectors in the generated flowfield. Approximately 15 velocity vectors were

acquired across the orifice diameter. The parameter space covered by this study was

an oscillation frequency 10 < f < 100 Hz and an actuator oscillation amplitude

ranging between 25 and 75 pm, although the results of only two cases are reported:

f = 10 Hz, amp.= 75 pm, and f = 100 Hz, amp.= 25 pm. It was found that,

in general, higher amplitudes produced jet-like flows due to the escaping train of

vortex rings, while for lower amplitudes, the jet flow was reversed and appeared

as suction in a mean sense. The observation of this suction flow is reminiscent of

Region 2 from Ingard & Labate (1950). In a related study, Rediniotis et al. (1999)

showed that this difference in mean flow behavior was due to an order-of-magnitude

difference in the Strouhal number between the two cases. The case of mean suction

was characteristic of the higher Strouhal number, indicating that the ratio of unsteady

inertia to steady inertia was higher and therefore the effect of the synthetic jet was

unable to "pen( I ii. as far into the ambient fluid, analogous to the Stokes oscillating

plate problem.









B6ra et al. (2001) also used PIV to measure the synthetic jet velocity field down-

stream of a two-dimensional sharp-edged slot measuring 100 x 1 mm. The schematic

of their setup indicated the use of a cavity geometry which gradually contracted down

to the slot depth. The driver consisted of a loudspeaker which was run at a fixed

frequency (200 Hz) and jet root mean square (RMS) velocity (14 m/s). Operation of

the device resulted in a mean jet where the ejected fluid moved sufficiently far from

the slot during the expulsion phase to be unaffected by the suction phase. This mean

jet flowfield contained a saddle point at two slot depths above the slot, above which

the flow appeared similar to a conventional steady jet. Unfortunately, the spatial

resolution of their PIV measurements compared to the slot depth was not sufficient

to acquire more than one or two velocity vectors across the slot.

In another experimental study of axisymmetric synthetic jets, Cater & Soria

(2002), using PIV, found similar results to Smith & Glezer (1998); namely, that

a turbulent synthetic jet has a similar mean cross-stream velocity distribution to

a conventional turbulent jet, but with a higher spreading rate and decay constant.

Their setup consisted of a piston driver in a cylindrical cavity which exhausted water

through a 2 mm diameter circular orifice into a large water tank. The flow was visu-

alized through the use of injected dye, and they detected four distinct flow patterns

as a function of the Reynolds number.

First, at low Reynolds numbers, they observed a steady, laminar-type flow em-

anating from the orifice which did not mix with the surrounding fluid and had not

been previously reported in the literature; this they termed a laminar jet. As the

Reynolds number increased, individual laminar vortex rings became apparent. These

rings did not interact with one another over the domain of measurements. Eventu-

ally with increasing Reynolds number, the separate rings began to coalesce and form

a transitional-type of jet. Finally, a fully turbulent jet was observed at the highest









Reynolds numbers and no vortex rings were distinguishable. Figure 1-8 shows images

from each of the identified flow patterns.















Figure 1-8: Flow regions as a function of Reynolds number, white arrows indicate
flow direction, (a) laminar jet, (b) laminar rings, (c) transitional jet, (d) turbulent
jet. Adapted from Cater & Soria (2002).


It is clear that these regimes do not correspond to the regions identified by Ingard

& Labate (1950) in Figure 1-3, although Figure 1-4 and Figure 1-8(b) appear strik-

ingly similar, and overall these images are in remarkably good qualitative agreement

with the results of Crook & Wood (2000) in Figure 1-7. It is also noteworthy that a

distinction was made between a "1 ,iiiii synthetic jet and a "turbil. ili synthetic

jet, the latter having been studied extensively, but the former had not been observed

previously.

PIV was used to acquire velocity field data in both the near-field and far-field

regions of the orifice. From these data, comparisons to conventional steady turbulent

jets were made. It should also be noted that they acquired their flow visualization

images using a blunt orifice plate with height-to-diameter aspect ratio of one, but

switched to a beveled orifice plate for the velocity measurements to alleviate flow

separation on the inner edge during the forward stroke. The plate was beveled at 450

on both sides to ensure a symmetrical flow at the orifice during the expulsion and

suction strokes. A cross-section schematic of the two different orifice plates is shown









in Figure 1-9. They reported that qualitative flow visualization using the two orifices

at similar conditions did not yield any differences in the jets.

2mm
D- 2 mm,- 2 2 mmc-






a) b)


Figure 1-9: Orifice plate cross-sections used by Cater & Soria (2002), (a) blunt,
(b) beveled.


Yehoshua & Seifert (2003) investigated the flowfield generated by a nominally

two-dimensional, piezoelectric-driven synthetic jet actuator using phase-locked PIV.

Although not specified, the slot height-to-depth aspect ratio appeared to be less than

one based on the schematic of their device, and only one slot geometry was used for

measurements in a quiescent medium. The actuator was operated at the Helmholtz

frequency of 1060 Hz, and they found that when the peak slot exit velocity dropped

below a certain value, the ejected vortex pair which resulted from the expulsion stroke

did not escape the slot, but was instead re-ingested into the cavity during the suction

stroke, resulting in a zero mean vertical velocity downstream of the jet.

One peculiar aspect of the vortex pair which they identified was that after it

was formed but before the start of the suction cycle, the individual vortex structures

initially moved closer to one another as they propagated downstream. Three possible

explanations for this behavior were offered: (1) an acceleration of fluid along the

centerline from the upstream stagnation point resulted in a lower static pressure,

(2) an induced force due to potential flow mechanisms, or (3) fluid entrainment into

the vortices as they propagated.









Shuster & Smith (2004) examined the effect of three different orifice configura-

tions on synthetic jet formation, each with a height-to-diameter aspect ratio of 0.5.

Specifically, they used a sharp orifice, a beveled orifice, and a rounded orifice, as

shown in Figure 1-10. A piston-cylinder synthetic jet was generated with water as

the working fluid. Injected dye was used for flow visualization of the emitted vortex

rings, and velocity field measurement was achieved with PIV. It was found that the

transition of the vortex rings from laminar to turbulent was a function of both the

Reynolds number and the dimensionless stroke length. However, there were marked

differences in this transition for each of the three orifice geometries. For example,

it was found that the Reynolds number required for transition to turbulence contin-

ually increased with increasing stroke length for the rounded and beveled orifices,

while for the straight orifice the transition Reynolds number began to decrease at a

dimensionless stroke length of 8. Furthermore, when holding the Reynolds number

and dimensionless stroke length constant, the extent to which the vortex rings broke

down and lost coherence also depended on which orifice geometry was used. The

vortex rings generated with the beveled orifice persisted longer than those generated

by the other two orifices. Another observation they made was that for a straight

orifice, the ejected vortex ring was re-ingested below a dimensionless stroke length of

order one.


a)



b)



c)

Figure 1-10: Orifice plate cross-sections used by Shuster & Smith (2004), (a) straight,
(b) beveled, (c) rounded.









In a combined experimental/computational work, Mallinson et al. (1999) stud-

ied a piezoelectric-driven synthetic jet originating from an axisymmetric orifice. Their

computational model consisted of a two-dimensional, unsteady, incompressible Navier-

Stokes solver which modeled turbulent flow via the k E model (Pope, 2001). The

actuator was modeled as a sinusoidally varying slug velocity profile at the orifice

exit. Centerline velocity measurements were acquired with hot wire anemometry and

showed good agreement with computations in the far field, but poor agreement in

the vicinity of the orifice. This they ascribed to possible deviation in the velocity

profile from a top-hat shape, limitations of a two-dimensional solver in an inherently

three-dimensional flow, and/or inaccuracies in the experimental velocity measure-

ments due to the large hot wire probe size. However, as part of a parametric study

in which they varied the frequency of oscillation, the cavity height, and the orifice

diameter, it was found that a larger cavity had the effect of reducing the jet velocity.

Furthermore, they performed a brief dimensional analysis in which they obtained a

Reynolds number and a Strouhal number as the important dimensionless parameters

for a fixed geometry device. It was found that as the Reynolds number was increased,

the Strouhal number initially decreased before increasing.

Utturkar (2002) performed a numerical study on two-dimensional synthetic jets

which was later supplemented by experimental data for both two-dimensional and ax-

isymmetric synthetic jets in Utturkar et al. (2003). Following Rampunggoon (2001),

they reasoned that the successful formation of a synthetic jet would depend on the

ability of the ejected vortex pair to overcome the suction-induced velocity -similar

to Smith & Swift (2001) -and using an order-of-magnitude analysis, it was shown

that if the inverse of the Strouhal number was greater than a constant, a jet would

form. Computational and experimental data for a two-dimensional slot showed this

constant to be of order one, while experimental data for the axisymmetric case in-

dicated the constant to be around 0.16. This -i-i:.- -1 .'1 that orifice geometry also










p11 i,- 1I a critical role in synthetic jet flows. When the data of Figure 1-6 was recast

in terms of Reynolds number and Stokes number (1/St = Re/S2), a clear trend of jet

formation resulted, shown below as Figure 1-11. It is interesting to note that in this

log-log plot the effect of radius of curvature has been compressed, but it is still readily

apparent that a jet would form at a lower Reynolds number as the -i ,rpness" of the

slot increases. In a subsequent paper, Holman et al. (2005) attempted to account for

the influence of the radius of curvature on jet formation by proposing a modified jet

formation criterion. This criterion accounted for the additional distance separating

the vortices due to the rounded exit. They also noted that a universal criterion for

jet formation, valid for both two-dimensional and axisymmetric orifice geometries,

required detailed information on the size and separation of the vortices, which was

not available at that time. Details of this jet formation criterion can be found in

Appendix B.



10 U ,
4 .. .. ..

U
10 -- -- -
E *m +
z S

S10 *

7r 1 ------------------
S* d=0.5 cm, R/d=1.28
Sd=1.0 cm, R/d=0.64
S* d=1.5 cm, R/d=0.43
d=2.1 cm, R/d=0.30
Re/S2=1
2
10
10 20 40 100
Stokes Number

Figure 1-11: Two-dimensional synthetic jet formation criterion. The data is from
Smith & Swift (2001), and is presented in Utturkar et al. (2003).









Numerical Studies

Besides experimental investigations, there has also been considerable interest in

numerically simulating synthetic jet flowfields in recent years. The first such known

study was performed by Kral et al. (1997) in which they used a two-dimensional,

unsteady Reynolds-averaged Navier-Stokes (RANS) equation solver. Interestingly,

only the flowfield external to the synthetic jet device was modeled, with the actuator,

cavity, and orifice being modeled as a spatially varying, sinusoidal velocity profile. It

was found that setting the spatial variation component to one (i.e., a slug velocity

profile) came closest to matching previously published experimental data. A modified

pressure boundary condition was also specified at the location of the orifice exit to

account for actuator effects. Both laminar and turbulent simulations were performed

over a range of Strouhal numbers, and the computational parameters were set such

that they would match the experimental parameters of Smith & Glezer (1997).

It was found that, contrary to experimental results, the laminar simulation pre-

dicted shed vortex pairs which did not break down but persisted throughout the

computational grid domain. When the turbulence was modeled, however, the com-

puted flowfield began to resemble more accurately the experimental results; namely,

that a single vortex pair was formed, shed, and broke down into the subsequent tur-

bulent jet before the next cycle. The simulated cross-stream velocity profiles also

collapsed reasonably well normalized by the centerline velocity, and good agreement

was shown with experimental data. The centerline velocity decay was also in good

agreement with experiments.

In an attempt to improve upon the work of Kral et al. (1997), Rizzetta et al.

(1999) simulated a synthetic jet using an unsteady, compressible Navier-Stokes solver

for both two- and three-dimensional grids via direct numerical simulation (DNS).

Here the actual synthetic jet oscillating driver, cavity, and orifice were modeled as

part of the mesh. The lower boundary of the cavity was forced to oscillate sinusoidally









to simulate the driver. Due to computational resource limitations, for the three-

dimensional computations, only one quarter of the domain was simulated by imposing

symmetry planes along the depth of the slot at x = 0 and along the mid-span of the

slot at y = 0, as shown in Figure 1-12.

x=0






----------- ------ ----------------y=



simulation domain




Figure 1-12: Symmetry planes imposed by Rizzetta et al. (1999) for three dimensional
synthetic jet computations.


The results of the two-dimensional simulations showed that a vortex pair alv--,i

existed in the vicinity of the slot. First, as fluid was expelled through the slot, a

vortex pair formed at the lip and was convected away in the usual manner. During

the suction stroke, however, a vortex pair with opposite sign vorticity formed at the

inner slot lip and propagated toward the lower boundary. At very low cavity heights,

this suction vortex was constrained to remain in the vicinity of the slot. For this case

and at a higher Reynolds number, remnants of the ingested vortex pair were detected

in the vicinity of the subsequently expelled vortex pair. In all cases, several vortex

pairs remained coherent downstream of the slot.

For the three-dimensional simulations, only one coherent vortex structure could

be identified above the slot at any given time during the cycle, consistent with experi-

mental results. Another interesting finding was that, despite the large width-to-depth









aspect ratio and corresponding quasi-two-dimensionality of the flowfield near the cen-

ter of the slot, the vortex pair was in fact an elongated vortex loop connected at the

ends of the slot, and spanwise instabilities were the cause of the rapid decay of this

vortex loop. Again, these results were similar to the findings of previous studies

(Smith & Glezer, 1997, 1998). It should be noted, however, that the exact geometry

of the experiments could not be duplicated in these simulations owing to restrictions

on computational resources.

Lee & Goldstein (2002) performed two-dimensional direct numerical simulations

on an actuator array exhausting into a quiescent medium. Both the cavity and the

slot were simulated, although the slot wall was modeled as very thin, giving a slot

height-to-width aspect ratio of nearly zero. Vortex pairing was observed to occur

in the far field from the slot, which had not been observed in previous simulations

or experiments. Besides the inability of the two-dimensional simulation to predict

the spanwise instabilities which normally cause the vortex pairs to break down, they

conjectured that an enclosed computational domain caused the vortices to slow down

as they approached the far wall, allowing for the subsequent vortex pairs to catch

up. Eventually a steady-state flow emerged in which vortices diffused too quickly for

vortex pairing to be an issue.

The simulation parameters of their study included the Strouhal number and the

Reynolds number. Not surprisingly, they found that at a fixed Strouhal number, the

extent to which vortex pairs remained coherent beyond their formation at the slot

was a function of the Reynolds number; i.e., small Reynolds number flows produced

vortices which rapidly d. i, '1 while larger Reynolds number flows generated vortex

pairs which remained coherent enough to bounce off the far boundary. In addition, at

large Reynolds numbers a complex circulation pattern developed in the cavity which

never stabilized in a periodic sense. When the Strouhal number was varied with a

fixed Reynolds number, it was found that as the Strouhal number increased, less fluid









was ejected during the expulsion stroke because of the inverse relationship between

Strouhal number and stroke length.

The effect of slot height-to-depth aspect ratio was also examined for a given

Reynolds number and Strouhal number. As expected, as the slot height increased, a

thicker boundary 1livr developed in the flow in the slot. This resulted in vortex pairs

which had a higher advection velocity, but they observed no change in the diameters

of the vortex cores. A rounded orifice and a cusp orifice were also simulated, and it

was found that the strength of the vortex pairs was higher by 40'. for the rounded

orifice. This was due to the reduction in separation of the flow during the suction

stroke.

In another two-dimensional simulation by solving the incompressible, unsteady

RANS equations, Fugal et al. (2004) investigated the effect of the radius of curvature

of the slot exit on synthetic jet formation. No driver was simulated; instead an

oscillating channel flow was simulated below the slot. The slot height was set to

three stroke lengths, to allow for fully-developed flow in the central third of the slot

during the entire cycle. Two different radii were examined: a sharp edge (R = 0),

and a rounded edge (R = h). They discovered that the power required to form a jet

was larger for the sharp-edged slot, but that a jet formed at a lower dimensionless

stroke length than the rounded edge. Again, this behavior is not unexpected, since

a rounded edge would reduce the separation on the inflow, but a sharp edge would

more easily allow a vortex pair to roll up and propagate downstream. Thus, two

competing parameters emerged, and some optimal shape possibly exists which will

minimize the power requirement and maximize the strength of the jet. This optimum

was found by defining the jet effectiveness as the normalized momentum flux achieved

divided by the normalized acoustic power required. When considered as a function

of dimensionless stroke length, it was found that the rounded edge gave a higher jet

effectiveness than the sharp edge. In both cases, the effectiveness initially increased









with stroke length and then leveled off at steady-state values of ~ 3.5 and ~ 2 for

the rounded slot and sharp slot, respectively.

Motivation

Based on the preceding literature survey, it is quite clear that a widely diverse

set of experiments and simulations have been carried out to improve the understand-

ing of flowfields generated by the synthetic jet exhausting into a quiescent medium.

However, direct comparison of the results from each of these studies is difficult, if not

impossible, for the following reasons.

First, based on the irn ir different geometric configurations as well as actuation

characteristics, it becomes obvious that there is a very large parameter space in

which a typical synthetic jet device can operate, with several possible resulting flow

regions. Although some researchers have attempted to duplicate the setup of others

(most notably the computationalists have tried to simulate the parameters of the

experimentalists), for the most part this endeavor has been the exception rather than

the rule.

Second, no universally accepted set of dimensionless parameters exists. Although

the dimensionless stroke length is often a popular choice, this parameter is only

physically meaningful at high Strouhal numbers where a slug velocity profile is a

reasonable assumption (White, 1991). Hence it becomes a challenge to even identify

the parameter space covered by the studies in the open literature. It also follows

that the extent to which the physics of synthetic jet flows are governed by the various

dimensionless parameters is not well known or understood. Furthermore, the different

topological regimes are not sufficiently characterized in terms of the dimensionless

parameters.

Third, if a study reports the results of an experiment in a parametric fashion,

the results tend to be either qualitative in nature, or cover only a very limited region

of the parameter space. Finally, as with all experiments, quantitative results are









meaningless without a thorough understanding of the data acquisition and setup

parameters and an estimate of the accuracy of the data, which should be carefully

documented. Unfortunately, among the relevant studies this also tends to be the

exception rather than the rule. These vexing issues form the motivation of the present

work.

Technical Objectives and Approach

The technical objectives of this study are thus (1) to identify a general set of

dimensionless parameters pertinent to the study of a synthetic jet flow in a quiescent

medium and re-cast the salient results of previous studies into a single consistent

parameter space; and (2) to determine the effects of these dimensionless parameters

on the topological behavior of the synthetic jet flow field by performing a systematic,

quantitative, thoroughly documented parametric experimental investigation of a syn-

thetic jet flowfield over a wide range of practical operating conditions. Information

on the threshold of jet formation as well as the transition to turbulent flow is inves-

tigated. In addition, the resulting experimental database contributes to quantifying

the physics of synthetic jet flows. This database is also expected to be useful as a

benchmark for comparisons to computational simulations of synthetic jet flows, as

well as aid in the validation of synthetic jet modeling (Rathnasingham & Breuer,

1997; Gallas et al., 2003; Yamaleev et al., 2005).

In order to accomplish the technical objectives, the following approach is taken.

First, a dimensional analysis of a generic synthetic jet device is performed. This

analysis yields a set of dimensionless parameters which define the parameter space

of operation of the synthetic jet. The fundamental physics of the synthetic jet flow-

field are addressed. The available data in the literature are unified and presented

(to the extent possible) in this single parameter space and a test matrix of addi-

tional experimental cases is selected. Second, in order to perform the quantitative

parametric study, a modular, two-dimensional synthetic jet device is constructed and









tested, which allows for variation in the geometric parameter hid. The driver for the

device is an electrodynarnic shaker, capable of I:. I;, 1,,.1 a wide range of IReynolds

and Strouhal numbers. Ti:.- device is tested in a parametric fashion by varying driver

.-;i. :ude and driver frequency to achieve variations in the Reynolds number and

Strouhal number.

Ti,. i are three main technical challenges which present themselves as -. !'t of

this work. The first challenge is ensuring that the --nthetic i. I driver is robust and

ci,. i :1. consistently as well as accurately. Most synthetic I drivers ~ipI.. some

kind of sealing membrane to maximize the volume flow rate through the slot/orifice,

yet this introduces additional complexity for a shaker-driven device because a vent

channel must be present to allow for pressure equilibration on both sides of the piston

driver. In addition, a flexible sealing membrane introduces an additional compliance

which -.i actually lower the ( i:. i ve volume flow rate at the slot. Also, the mo-

tion of an electrod-:. ,. shaker at -. I,- low frequencies deviates significantly from

sinusoidal, and must be accounted for. The second challenge is acquiring accurate,

high-resolution velocity data over an inherently unsteady flowfield with small geo-

metric dimensions. A typical slot/orifice scale used for this study is 1 mm, so any
...i.i.::. to acquire velocity data should have sub-millimeter resolution in order to

capture the full velocity profile emanating from the slot/orifice. Third, the accuracy

of the velocity data itself should be thoroughly ilvl .i I.. d. All possible errors should

be completely accounted for, and a sufficient number of data points must be acquired

to ensure statistical accuracy and mitigate random errors.

To meet these technical challenges, it is shown that a sealing membrane can

be replaced by a very thin gap or ...:, i between the .; I..-,, driver and the

cavity wall. A sinusoidal controller must also be developed and (:, .-1.-. d for the

experiments. In addition, velocity field measurements employ Hotwire Anemometry

for qualitative turbulence measurements. Both Particle Image Velocimetry (PIV)









and Laser Doppler Anemometry (LDA) are also be emplo,, 1 to quantify the flowfield

and compare sinusoidal vs. no sinusoidal control. The details of the experimental

procedures are thoroughly documented. PIV and LDA are compared for a select

test case to provide mutual verification. The periodic, spatial-varying velocity profile

across the orifice is acquired to characterize the flowfield in terms of the relevant

dimensionless parameters. The PIV-acquired velocity field downstream of the orifice

is used to determine the vorticity field and hence the behavioral characteristics of the

synthetic jet flow.

Outline

The outline of the study is therefore as follows: C'!i lpter 2 defines the relevant

parameter space of synthetic jet operation and recasts the results of previous studies

in this unified framework. In addition, the parameter space for a test matrix of ex-

perimental cases is proposed to validate the published data in the literature as well

as investigate in more detail the effects of geometry and actuation on the resulting

flowfield. ('!i lpter 3 documents the details of the experimental setup. The synthetic

jet devices used are described in detail. Driver deflection measurements, driver si-

nusoidal control, flow visualization procedures, and velocity measurement techniques

are also documented. ('!i lpter 4 describes the results of flow visualization, driver

deflection measurement and control, and velocity measurement. The data reduction

and analysis techniques for the results are presented. The various topological regimes

are quantified in terms of the relevant dimensionless parameters and the vortex dy-

namics of the flowfield. Finally, ('! Ilpter 5 offers conclusions and recommendations

for future work.

This study is supplemented by additional work found in the appendices. Ap-

pendix A gives the detailed solution to a channel flow with an oscillating pressure

gradient, a useful approximation to synthetic jet flows in the orifice. The details of

a jet formation criterion to further quantify the synthetic jet flowfield are found in







35

Appendix B. A relatively large number of calculations must be performed to convert

the parameter space of published results into the parameter space defined in C'! ip-

ter 2. The details of these calculations are given in Appendix C. The modeling of

flow in the gap between the oscillating piston and the cylindrical wall is an inter-

esting and relevant issue to ZNMF flows and is considered in Appendix D. Finally,

Appendix E discusses an issue not previously addressed in the experimental fluid

dynamics literature -multivariate outlier rejection.
















CHAPTER 2
PHYSICS OF SYNTHETIC JET FLOWS

This chapter performs a dimensional analysis of the synthetic jet flow problem to

identify the parameter space of operation. Equivalence between the relevant dimen-

sionless parameters is derived, and specific parameters for variation are identified.

The results of previous studies are recast into a single parameter space, and a test

matrix of additional cases is proposed to further the understanding of the topological

behavior of synthetic jets exhausting into a quiescent medium.

Dimensional Analysis

In order to clearly identify the relevant dimensionless parameters that govern

synthetic jet flows and recast the results of previous experimental and numerical

studies in a unified framework, it becomes necessary to first recognize the appro-

priate dimensional parameters involved. Considering again the simplified schematic

in Figure 1-2, shown in greater detail in Figure 2-1, it is possible to identify three

fundamental groups of parameters which are expected to affect the behavior of the

flowfield. These three groups are: (1) geometric properties, (2) driver properties, and

(3) fluid properties.

The geometric properties include:

SV volume of the cavity

d -slot depth (orifice diameter)

h slot (orifice) height

w slot width (two-dimensional case only)

R -radius of curvature of the slot

The driver properties (excluding electromechanics) include:









frequency of oscillation

AV volume displaced by the driver

The fluid properties include:

co -speed of sound of the fluid

p -density of the fluid

p dynamic viscosity of the fluid



ih




AV R




Co

Figure 2-1: Detailed schematic showing synthetic jet dimensional parameters.


One potential dependent parameter is Uo, a characteristic velocity at the surface of

the slot (orifice), as described in Smith & Glezer (1998), C'!i. i et al. (2000), and

Cater & Soria (2002), among many others. For now this quantity is undefined. To

simplify the dimensional analysis, it is now assumed that the flow is incompressible.

Thus the cavity volume and the speed of sound no longer affect the flowfield. For a

detailed treatment of compressibility effects, see Gallas (2005). Furthermore, for a

sharp-edged slot, the radius of curvature becomes irrelevant. Previous studies have

investigated this rounding effect (Smith & Swift, 2001; Fugal et al., 2004). Also,

Cater & Soria (2002) noted no significant differences in the resulting flowfields of a

straight orifice and a beveled orifice, another common geometric variation. These

assumptions are made because as shown later in C'! lpter 4, the synthetic jet device









used for this study is operated solely over the incompressible regime, and the slot exit

radius of curvature is essentially zero for all cases.

Performing a Buckingham-Pi analysis (Fox & McDonald, 1998), and choosing

primary dimensions MLt, yields Table 2-1. There are three primary dimensions

mass, length, and time -and 8 parameters. Dimensional analysis reveals that there

are five dimensionless pi-groups. C'!In.... the slot depth d, the driver frequency w,

and the dynamic viscosity p as the repeating parameters gives the conventional set

of pi-groups normally discussed in the literature:

1 hd"bb h/d

II2 ,= '.ibpc w/d

I3 AVdbc AV/d3

HI4 pdWbc pd2a/p

I1s Uod b Uo/ud

Table 2-1: Primary dimensions of synthetic jet dimensional parameters

Parameter M L t
d 0 1 0
h 0 1 0
w 0 1 0
w 0 0 -1
AV 0 3 0
p 1 -3 0
p 1 -1 -1
Uo 0 1 -1


These pi-groups may be rearranged in any combination, but 1H must include at

least Ilk. This yields information on the functional form of the velocity Uo as follows:



1 = Iii -, the slot (orifice) height-to-depth aspect ratio



II'2 = the slot width-to-depth aspect ratio
dA








AV
II' = s = dimensionless displaced volume, the ratio of the displaced

cavity volume to the cube of the slot depth (orifice diameter)


VII' = S, the Stokes number
v /

1 (wdN
II' -- ) St, the Strouhal number


Note that II5 can also be rearranged to yield a Reynolds number,

(Uo p o'd2
Reuo = nUs5n4 ( d) ) pUd (2.1)

Thus the Reynolds number as the dependent parameter is a function of four other

dimensionless parameters,

ReCU f ,d d S3 (2.2)


That is, the flowfield generated by a synthetic jet exhausting into a quiescent medium

(assuming incompressible flow and no slot exit radius of curvature effects) is a func-
tion of all of the dimensionless parameters given in Eq. (2.2). Note that for the

axisymmetric case, the pi-group w/d vanishes. It is desired to observe changes in the

Reynolds number (and hence the flowfield) as a function of a single dimensionless

parameter, in order to gauge that parameter's effect on the flowfield. A notable pa-

rameter which is absent from Eq. (2.2), but which often appears in the literature is

the dimensionless stroke length, defined as the ratio of the stroke length as defined in

Eq. (1.1) to the slot depth (orifice diameter), Lo/d. In the next section, equivalence

between this parameter and those of Eq. (2.2) is shown.

Parameter Equivalence

A thorough understanding of how all the dimensionless parameters affect one

another is useful for comparison of the various studies which rarely employ the same









parameters. First, we note from Eq. (2.1) an interesting relationship between the

Strouhal, Reynolds, and Stokes numbers. This relationship is Reu = (1/St) / (1/S2),

and this equivalence is more easily observed as follows:

1 Uo Uod/v Reu (2.3)
St ud wd2/v S2

Thus from Eq. (2.3) specifying any two of these parameters fixes the third.

It is now desired to find a relationship between the dimensionless stroke length

and the parameters of Eq. (2.3). To do this, the velocity scale Uo must be explicitly

defined. There are a number of velocity scales which may be used to represent Uo;

however the most general scale is preferred. Since there is both spatial and temporal

variation in the velocity at the surface of the slot, a velocity scale which does not

integrate the velocity profile both spatially and temporally is inappropriate. Further,

since the expulsion and ingestion times may not be equal, an average expulsion veloc-

ity may not necessarily equal an average ingestion velocity, and this implies that the

temporal integration should be over an entire cycle. This then presents a dilemma

because a quantity such as mass flow rate by definition integrates to zero over an

integer number of cycles at the surface of the slot (orifice). However, since the device

imparts a finite amount of momentum to the surroundings during a cycle, a velocity

scale based on this momentum is perhaps more appropriate. Following Cater & Soria

(2002), the momentum flow velocity scale is chosen to represent Uo,

S1 1 r0T 11/2
U O= [u (A, t)]2 dtdA (2.4)

where A is the slot (orifice) area, and u(A, t) is the time varying, spatial varying

streamwise component of velocity at the exit plane. For the limiting case of a slug

velocity profile which varies sinusoidally, Uo is the RMS velocity at the slot (orifice).

However, it should be noted that when the velocity profile varies spatially, Uo is









not the RMS of the spatial-averaged velocity. For example, for an oscillating two-

dimensional channel flow at very low Stokes number, the spatial velocity profile is

parabolic (see Appendix A). Uo for this case is 5-'-. larger than the RMS of the

spatial-averaged velocity. This factor appears by separating the spatial integration

from the temporal integration in Eq. (2.4),

[JA u2 (A, t) dA] 1/2 { jT 2 1/2 (2.5)
A u (A, t) dA T (t

It then follows that an average stroke length should be defined based on Uo as


L = UoT (2.6)


Physically, L is analogous to the RMS distance that a fluid particle travels near the

surface of the slot (orifice) during a cycle, although as stated previously it is not

exactly the RMS distance. This definition of the stroke length will now be used

instead of Lo because it is the most general.

From the definition of the Reynolds number and from Eq. (2.6), it follows that

Uod Ld Ldu L \(d2 1
Reuo = Tv 2v -d (2.7)
v TV 2 d V 27

Rearranging Eq. (2.7) and recalling Eq. (2.3), the following parameter equivalence

is obtained between Reynolds number, Strouhal number, Stokes number, and dimen-

sionless stroke length:
1 ReU, L/d
St S2 2-

It is important to note that this parameter equivalence is valid for periodic motion

regardless of the temporal or spatial shape of the velocity profile. This is an important

point for two reasons. First, spatial variation of the velocity profile can be significant

at low Stokes numbers (White, 1991). Second, non-linearities in the driver motion

and/or flow non-linearities in the cavity and/or the slot (orifice) may result in a

non-sinusoidal velocity profile in time. This would yield different average velocities









during expulsion and ingestion, and the selection of one to describe the flowfield

would come at the expense of losing information about the other. While one may

expect the expulsion part of the cycle to dominate the flowfield, the ingestion part of

the cycle can also be significant and probably should not be ignored. This point is

further emphasized in ('! plter 4, where it is shown that a Reynolds number based

on circulation is sensitive to the suction part of the cycle.

Parametric Variation

Now that all of the common dimensionless parameters used to characterize syn-

thetic jets have been defined, it remains to be determined how these parameters affect

the output of the device and the resulting flowfield. Jet formation is the most common

characteristic of a ZNMF device, and as mentioned in ('! i pter 1, several researchers

have investigated the phenomenon of jet formation. Holman et al. (2005) published a

detailed jet formation criterion based on the vortex strength of the vortex pair (ring)

emerging from the slot (orifice). It was found that the critical parameter in determin-

ing jet formation is the Strouhal number; specifically, that when the Strouhal number

was below a critical value, jet formation was the result. Above this value, no type

of flow was observed from the slot (orifice). The critical value was approximately

1 for sharp-edged two-dimensional slots and 6 for sharp-edged axisymmetric orifices.

From Eq. (2.8), it can be seen that this threshold criterion corresponds to a threshold

stroke length for jet formation. Additional details on the jet formation criterion can

be found in Appendix B.

The jet formation criterion indicates that the Strouhal number p1 i',- a critical

role in determining the resulting flowfield. In addition, based on flow visualization

results described later in ('!Ci pter 4, the Reynolds number also contributes to the

flowfield characteristics. It is also known that the slot (orifice) height-to-depth (di-

ameter) aspect ratio significantly affects the flowfield (Gallas et al., 2004). These

three parameters are the most practically relevant for characterizing a synthetic jet,









and not coincidentally, they all appear in Eq. (2.2) -the Strouhal number emerging

via the equivalence of Eq. (2.8). For two-dimensional slots, in the near field region

the flowfield remains essentially two-dimensional as w/d is changed.

For a fixed geometry, Eq. (2.2) reveals that l,.;,jh in the Reynolds number are

a function of

AReu0 f ( 3-, S (2.9)

Or, alternatively, S can be replaced by the Strouhal number. The usual physical

parameters to vary when operating a ZNMF device are the frequency and the am-

plitude of driver motion. From Eq. (2.9), the frequency dependence manifests itself

in the Strouhal number, while the driver motion dependence appears in the dimen-

sionless displaced volume. It is desired to fix all dimensionless parameters except

for one and observe changes in the resulting flowfield as that parameter varies. For

Reynolds number variation with a fixed Strouhal number, both the frequency and the

amplitude must be varied, because Uo must change to vary Reynolds number, and

consequently w must also change to keep the Strouhal number constant. Conversely,

for Strouhal number variation with a fixed Reynolds number, only the frequency must

be varied.

The final parameter of interest to investigate is the height-to-depth (diameter)

aspect ratio h/d. Variations in w/d may be bypassed because in a practical sense,

w/d > 1 for most applications and is not relevant at all for the axisymmetric case.

Also, three dimensional effects are negligible in the near field. If the oscillation

frequency and driver amplitude are fixed, this implies that Uo is fixed as well and

hence the only changes in the flowfield would be a result of changes in h/d. It must

also be noted that the results of a parametric variation are only valid at the fixed

values of the other dimensionless parameters.









Published Results

Quite a number of descriptions have been reported in the open literature concern-

ing synthetic jet flowfields. Ingard & Labate (1950), Smith & Glezer (1998), Crook &

Wood (2000), and Cater & Soria (2002), among many others, use descriptive terms

like laminar jet, laminar rings, transitional jet, turbulent jet, jet formation, suction

flow, boiling, interacting vortices, non-interacting vortices, reingested vortices, and

many others. It is certainly a daunting task to try to unify all of these studies into

a single parameter space, but by doing so, one may observe trends in synthetic jet

behavior as well as identify regions of the parameter space which have not been

studied extensively and require further exploration. Unfortunately, the relevant di-

mensionless parameters which were defined previously cannot alv--x be determined

conclusively based on the published results. For example, often a Reynolds number

will be reported based only on a centerline velocity amplitude, which is insufficient

to compute Reu0. However, the problem of fully-developed flow with an oscillating

pressure gradient serves as a useful approximation when sufficient quantitative data is

lacking. The relevant dimensionless parameters can be estimated from the available

data and the solution to this problem, which is provided in Appendix A.

The experimental results of each study must be carefully matched in order to

realize a valid comparison and identify trends. This means that all of the results must

be re-cast in terms of the dimensionless pi-groups of Eq. (2.2). In general, a study

reports a qualitative flow description as a function of either the dimensional parame-

ters of the study such as velocity, frequency of oscillation, and orifice diameter, or as

a function of several dimensionless parameters which are rarely matched identically

in other studies. Sometimes the flowfield results are quantitative, such as vorticity

contours of the flowfield downstream of the orifice or a mean velocity field. For each

flow description, the data provided must be converted as accurately as possible to the

parameter space of Eq. (2.2). The details of the necessary calculations to convert the









parameters can be found in Appendix C for each study analyzed. Table C 1 gives

the results of this comparison.

At first glance, one may conclude that the parameter space has been well-covered.

However, for the two-dimensional cases, most of the data available comes from Smith

& Swift (2001), who only reported results of jet formation. The other two-dimensional

studies are confined to low parameter values. It should also be noted that the data

of Smith & Swift (2001) contain variations in the dimensionless radius of curvature,

but all the other studies reported use either a sharp-edged orifice or a beveled-shaped

orifice. For the axisymmetric cases, the ii, j.i iily of the data comes from Ingard &

Labate (1950), where the method and accuracy of the velocity were not reported.

The range of the orifice height-to-diameter aspect ratio h/d is also smaller for all of

these axisymmetric studies than the two-dimensional studies. As can be seen, there

remains much information on the flow characteristics to be reliably obtained over

just these three dimensionless parameters (Reuo, St, and h/d). In addition, it cannot

be emphasized enough that the majority of the data available in the literature is

insufficient to accurately determine the Reynolds number Reuo, and there is almost

never any information provided on the accuracy of the computed Reynolds number.

The most obvious characteristic of an operating ZNMF device is whether a syn-

thetic jet is formed or not, and several studies have either noted this phenomenon or

studied it in detail (Smith & Swift, 2001; Utturkar et al., 2003; Yehoshua & Seifert,

2003; Shuster & Smith, 2004). However, others have noted various other types of

i, 'i's" of flow (Ingard & Labate, 1950; Cater & Soria, 2002) which may or may

not be classified in terms of jet formation and may contain sub-regions of their own.

Generally speaking, all of the results published in the literature may be classified into

one of several broad categories, and the instantaneous and time-averaged flowfields

may appear differently. Table 2-2 summarizes these categories. It is important to

note that the numbered regions defined in Table 2-2 apply only to this study and









should not be compared directly with regions identified in previous studies. In gen-

eral, if all the other parameters are fixed, the flowfield transitions from one region

to the next as the non-dimensional driver amplitude AV/d3 (and hence the Reynolds

number Reuo) increases. However, other parameters such as the Stokes number and

the orifice height-to-diameter aspect ratio may also affect this transition. For exam-

ple, if the Stokes number is low, transition from Region 2 directly to Region 5 may

be observed (Utturkar et al., 2003).

Table 2-2: Synthetic jet flow regions.

Region instantaneous flowfield time-averaged flowfield
1 no vorticity formed or vortices reingested no type of flow observed
2 vorticity strength increases some flow observed
3 vortices possibly shed but reingested suction-type flow, 'boiling'
4 vortices are shed but are weak transition to a jet-like flow
5 train of laminar vortex rings laminar-type jet
6 rings begin to become turbulent jet transitions to turbulent
7 fully turbulent rings, may break down turbulent jet


Proposed Test Matrix

Smith & Swift (2001) argued that there was a threshold dimensionless stroke

length for jet formation, while Utturkar et al. (2003) reasoned that a threshold inverse

Strouhal number dictated the successful formation of a synthetic jet. Based on Eq.

(2.8), the fundamental equivalence between these two ideas becomes obvious. Fur-

thermore, since jet formation is an essential characteristic of a synthetic jet, and this

depends on the dimensionless stroke length (or alternatively the Strouhal number),

it is vital that variations in this parameter be investigated. In addition, Gallas et al.

(2004) -focusing on the influence of flow in the orifice on the synthetic jet flowfield

behavior -demonstrated that the orifice height to diameter aspect ratio (h/d) was

another key parameter which governed synthetic jet flows. Specifically, they found

that the flow in the orifice was dominated by i11, I. r" losses which scaled linearly









with the fluctuating streamwise velocity component when the orifice height signif-

icantly exceeded the stroke length. At longer strokes, however, "minor" nonlinear

losses associated with entrance effects were dominant. Hence this further underscores

the motivation for exploring variations in h/d. As mentioned previously, the results of

Ingard & Labate (1950) also sI--,: -I that h/d is a key parameter governing synthetic

jet flows.

Transition from a laminar-like jet to a turbulent-like jet is also of interest and

has only been reported sparsely in the literature. C'!, i1 et al. (2000) developed a tran-

sition criterion for synthetic jet flows but it was based off of only a few points which

varied with both dimensionless stroke length and Reynolds number. The studies by

Gharib et al. (1998) and Glezer (1988), though of vortex rings and not synthetic jets,

nevertheless hint at the possibility of a turbulent synthetic jet emerging due to an

upper limit on the circulation that can be contained within a vortex pair. In such a

case the excess vorticity trails the vortex pair and this may facilitate the breakdown

to turbulence. This also motivates the study of Reynolds number effects.

Both the Reynolds number and the Strouhal number will be varied over their

usable range in order to capture the flow regions that have been identified by previ-

ous researchers. A parametric study of the height-to-depth aspect ratio h/d will be

undertaken for sharp-edged slot configurations. Table 2-3 gives the test cases to be

performed, along with the relevant dimensional parameters to facilitate comparison to

other results. The actual values of the Reynolds number and Strouhal number are not

known a priori; rather, the test matrix is initially based on flow visualization results

described in ('! Ilpter 4. Quantitative velocity measurements are utilized to compute

Re and St, and these values are shown in Table 2-3 for clarification. A nominal case

(Case 3) is chosen and both Reynolds number variations (Cases 1-5) and Strouhal

number variations (Cases 6-9) are performed. Then the slot height-to-depth aspect

ratio h/d is varied (Cases 10,11) while maintaining the nominal Strouhal number and









Reynolds number. A small h/d is chosen, but it is large enough such that compliance

effects do not arise (Horowitz et al., 2002). Also, a large h/d is tested to investigate

a case that may result in fully-developed flow in the slot. Finally, the nominal case is

repeated (Case 12), but for a distorted driver motion which is common for voice-coil

drivers. More details of the driver are given in C'! lpter 3.

Table 2-3: Test matrix of geometric configurations.


Stuo h/d w/d


0.84
0.86
0.78
0.80
0.81
0.53
0.63
1.00
1.30
0.73
0.79
0.88


1.46
1.46
1.46
1.46
1.46
1.46
1.46
1.46
1.46
0.32
3.32
1.46


14.88
14.88
14.88
14.88
14.88
14.88
14.88
14.88
14.88
15.48
15.98
14.88


f (Hz) Uo (m/s)
9.26 0.21
18.52 0.42
32.42 0.80
57.89 1.40
115.77 2.76
21.58 0.79
25.24 0.77
39.53 0.77
46.67 0.69
35.40 0.90
37.39 0.86
32.42 0.71


For cases with desired fixed Reynolds number,

the measured Reynolds numbers is only 7'. of the


d (mm)
3.08
3.08
3.08
3.08
3.08
3.08
3.08
3.08
3.08
2.97
2.87
3.08


the standard deviation among

mean Reynolds number, while


for desired fixed Strouhal number, the standard deviation is just i'. of the mean

Strouhal number. This -, r.-.- -1 that changes in the flowfield due to variation of either

parameter by larger amounts than these deviations are probably not significant due

to minor variations in the other parameter which is desired to be fixed. Rather, the

flowfield changes are likely to result primarily from changes in the parameter which

is varied, as desired.


Case
1
2
3
4
5
6
7
8
9
10
11
12


Reu,
43
84
161
280
555
159
155
154
139
175
161
143
















CHAPTER 3
EXPERIMENTAL SETUP

This chapter provides the details of design and specifications of the ZNMF de-

vices used for this study. The data acquisition hardware is discussed. A description of

driver deflection measurements is provided, as well as the feedforward sinusoidal con-

troller used. The flow visualization technique is documented. Both the PIV and LDA

velocity data acquisition and reduction procedures are thoroughly discussed. Finally,

estimates of the sources of uncertainty are provided for the computed quantities.

Synthetic Jet Devices

Two different ZNMF devices are constructed and employ, ,1 in this study. The

first device consists of a piezoelectric-driven actuator disc mounted to the side of

a cavity. This actuator is used to verify the jet formation criterion described in

C'! lpter 2. The driver disc consists of a piezoelectric patch which is bonded to a

metallic shim. An axisymmetric orifice plate mounted at the top of the cavity serves

to form the synthetic jet flowfield. An exploded view of this modular synthetic jet

device is shown in Figure 3-1. The construction of the cavity and the piezoelectric

driver are nearly similar to Case 2 described in Gallas et al. (2003), and the geometric

parameters of this device are given in Table 3-1.

Table 3-1: Piezoelectric-driven ZNMF actuator details.
Property Value
Cavity volume (m3) 5.50 x 10-6
Orifice diameter (typical) (mm) 2.00
Orifice height (mm) 1.65


This device is constructed specifically to operate in the low-to-moderate Stokes

number range, S < 50. The data published in the open literature in this range









is somewhat scattered as described in C'! ipter 2. Acquiring reliable experimental

data at low Stokes numbers would prove useful in applications involving large-scale

flow control experiments and engine nacelle acoustic liners (Horowitz et al., 2002).

The piezoelectric-driven device is also one of the most common implementations of

synthetic jets due to its modular and compact design. In addition, only a small

wire needs to be soldered to the piezoelectric patch to provide the driver signal,

thus this design is a potentially promising realization of a synthetic jet in real-world

applications.

orifice plate




J:'* *j % *



*S*

top plate body plate diaphragm clamp plate
/ mount
access hole for
microphone

Figure 3-1: Exploded view of modular piezoelectric-driven ZNMF device.


The second ZNMF device is designed to have larger geometric dimensions. It

consists of a Briiel and Kjaer (B&K) model 4810 mini-shaker with an attached alu-

minum piston plate as the driver. A thin cylindrical shell mounts and seals to the

shaker frame to form the cavity, and the design allows for interchangeable slot plates

to be attached to the top. A perspective view of this device is shown in Figure 3-2.

A more detailed cross-sectional view is shown in Figure 3-3. Table 3-2 gives the geo-

metric parameters. The piston does not seal to the outer clamp plate shell; rather, a

viscous seal is created by making the gap between the piston and the wall very small

(see Appendix D for details).












Sorifice plate
cavity ring
piston
clamp plate
B&K shaker









a) b)



Figure 3-2: Shaker-driven ZNMF device, a) exploded view, b) assembled view.

Table 3-2: Shaker-driven ZNMF actuator details.

Property Value
Upper cavity volume (m3) 7.38 x 10-6
Lower cavity volume (m3) 5.67 x 10-6
Piston gap thickness (mm) 0.127
Piston diameter (mm) 45.46
Slot depth (mm) 3
Slot height (mm) 1,4.5,10


The cavity volume of this device is V = 7.38 x 10-6 m3, the width of the slot is

w = 45.9 mm, and the slot depth is d = 3 mm. The slot height is varied by changing

the slot plates, which have h = 1 mm, 4.5 mm, and 10 mm. Thus the Helmholtz

frequency WH ranges between 2.4 kHz and 7.5 kHz, which is an order of magnitude

higher than the frequency of operation of the device. Hence, compressibility effects

in the cavity are negligible (Gallas, 2005).

The nature of this voice coil actuator design means that the device is acceleration-

limited at higher frequencies, while it is displacement-limited at lower frequencies.

The shift from displacement-limited to acceleration-limited is a function of the mass

loading on the shaker table. Nevertheless, at low frequencies on the order of 10 Hz,









piston
slot plate


piston gap



upper cavity





lower cavity

B&K shaker






Figure 3-3: Detailed schematic of shaker-driven ZNMF device.

large displacements are achievable. This allows for investigation of synthetic jet

characteristics at low Stokes numbers S < 10. One disadvantage of this device is

that it draws relatively high current, especially at the desired higher amplitudes

of motion. This current causes undesirable l. ;ii:.- which convects away from the

shaker as a plume jet-like flow. For this reason, when acquiring flow visualization

images or velocity data, the shaker is operated for the minimum amount of time

necessary to obtain results. Also, the piston motion can be significantly distorted

from a sinusoidal shape at high amplitudes and/or low frequencies. For this reason,

a sinusoidal controller is developed to ensure a sinusoidal piston motion, and this is

discussed in further detail later.

While this particular design may not be as suitable for practical applications

as the piezoelectric-driver design, there are a number of advantages to utilizing this









device for laboi-,lt -i- experiments. First, the larger dimensions allow for a two-

dimensional synthetic jet design to be tested. Second, the shaker-driven i.1 i..: is

physically able to achieve a much larger amplitude of deflection at lower :. pI, 1:. 1, -i

as previously stated, thereby allowing more of the parameter space to be investigated.

Third -and perhaps most importantly the shaker-driven device is believed to be

more robust than the piezoelectric-driven device due to their differences in electrome-

chanical transduction. This is because the piezoelectric diaphragm is more likely to

fail or degrade over time than the shaker, impeding the : i" i :1 ,ility and reliability of

the results obtained. Ti degradation can occur suddenly if the depolarization volt-

age of the piezoelectric material is .,i .i.d, or gradually over many cycles of oscillation

as the electrical contacts degrade, the piezoelectric material itself begins to oxidize,

or the patch becomes de-bonded :"i -.: the metallic shim. In contrast, the B&K shaker

electromechanical mechanism consists of a permanent magnet with a coil embedded in

one plane. As an (.-. ii i:. current is applied to the magnet, a mechanical vibration

is induced. A suspension system confines this vibration to rectilinear motion. This

type of device is robust enough to be commonly used for accelerometer calibration

and mechanical impedance measurements. However, over many cycles the ; I .. ,i mo-

tion does in fact change in shape, 1-.., ,!. not necessarily in .i.:l_; iiT, This problem

is overcome through the use of the sinusoidal controller which is used immediately

prior to flow visualization and velocity measurement, ensuring the piston motion is

both sinusoidal and at the desired amplitude.

In the case of both nthetic jet devices, an Agilent model 331_', i..'\t:lion gen-

erator serves as the signal source. The signal :. .;:. the 'it:- I ..:. generator is applied to

an i 1-.1 r (PCB Piezotronics 790 Series Power Amplifier for the piezoelectric-driven

-.i1, tic ij-t B&K power amplifier 1,e 2718 for the shaker-driven synthetic jet), and

the amplified sinusoidal input voltage signal is then applied to the driver, which con-

verts the voltage into a mechanical deflection. By changing both the frequency of









oscillation and the amplitude of the function generator, one may systematically adjust

the Strouhal number and the Reynolds number.

Data Acquisition System

In order to determine the relative phasing between the input signal, the driver

deflection, and the corresponding periodic volume flow rate as determined by the

velocity measurement at the slot, it is necessary to acquire phase-locked measurements

of these quantities. Using the sync signal of the Agilent 33120A function generator,

the relative phasing between the measured quantities can be determined if phase-

locked data is acquired. In addition, it is imperative that each quantity be acquired

simultaneously, and most common data acquisition cards do not provide this feature.

Hence, a National Instruments model NI-4552 dynamic signal analyzer PCI card is

used for data acquisition (DAQ).

The DAQ card is 16-bit and can sample up to 4 channels of analog input simul-

taneously and has a bandwidth of approximately 200 kHz, which is well-suited for

the present study. However, a built-in two-part anti-aliasing filter must be consid-

ered. The first part consists of a low pass analog filter with a cutoff frequency of

4 MHz, which is well above the frequencies considered here and may be considered

to have zero phase offset in the passband. Secondly, a digital filter removes all fre-

quency components above the Nyquist frequency. This DAQ card interfaces with a

standard PC through National Instruments' LabVIEW software. LabVIEW is also

used to control the traverse for LDA velocity measurements as shown in Figure 3-27

and interface with the Dantec BSA Flow software used to control the LDA system.

All data -input signal, driver deflection, and velocity measurements -are acquired

and averaged over a sufficient number of cycles to ensure statistical accuracy of the

results. The number of blocks of data averaged typically ranges from 100-1000, with

a phase resolution that is similar to the velocity measurements.









Driver Deflection Measurement

By measuring the displacement of the driver as it oscillates, the volume displace-

ment of the driver can be determined. Furthermore, by experimentally measuring the

volume velc. i of the synthetic l at tie orifice, one 1n! determine the extent to

which fluid is compressed and expanded inside the cavity as opposed to ei.. !d and

ingested, respectively. For the cases to be tested, it is already known that w/wH t 1,

thus there are negligible compressibility effects in the cavity. The extent to which

the volume velocity does not match the driver motion, then, is an indicator of either

leaks in the various components of the device or edge effects in the case of the two-

dimensional slot. While all leaks are minimized through the use of RTV sealant or

vacuum grease at .-r* i..i,( there are some inevitable losses due to leakage.

For the shaker-driven device, a rigid piston serve s as the oscillator and hence a

single point measurement of the (di-.1 n. n.1i allows for determination of the volume

velocity. The displacement is acquired using a Micro-Eli. I... model ILD- 1',l0 laser

displacement sensor. This sensor functions on the principle of triangulation, and the

device is factory-calibrated to give an output signal of 1 V/mm, with a resolution of

5 pmn and a sample rate of 10 kHz, which is .i.!: i n. for this study. Of particular

importance, however, is the lag in the digital-to-analog conversion of the signal. The

manufacturer :- .orts that there is a four ( 1.- lag between measured location and

output signal. At a 10 kHz sample rate, this translates to a constant time 1. 1 .-- of

0.4 ms. This further results in a linear phase shift between input and output signals.

To verify both the displacement sensor calibration as well as the constant time

<1. 1, a B&K model 4506 3-axis accelerometer is mounted on the top of the piston

driver at the center of the plate, and the acceleration from the accelerometer is mea-

sured. In addition the motion of the accelerometer is measured simultaneously using

the laser 11: ii ,. .- i. sensor over a frequency range 0 < f < 400 Hz, corresponding

to the frequency range of interest of the shaker. Due to size constraints, the orifice










plate is removed. The accelerometer is affixed to the aluminum piston plate via super

glue; it was found that at large forcing levels a wax bond was insufficient and the

accelerometer became dislodged from the piston. The acceleration signal is integrated

twice and the constant of integration removed to yield position. Figure 3-4 shows

the relative phasing between both the displacement sensor and the accelerometer to

the input signal, as well as the phase difference between the two. The phase differ-

ence is a roughly linear line. Thus the slope of this line is constant and has units

of time -phase (At rad) divided by frequency (a rad/s). The value of the slope is

approximately 0.4 ms, which agrees with the manufacturer's specifications.


-60


0 50 100 150 200 250 300 350 400
Frequency (Hz)


Figure 3-4: Relative phasing of displacement sensor and accelerometer.


When this phase correction is applied to the displacement sensor signal, the

displacement as measured by the displacement sensor is identical to the displacement

as measured by the accelerometer, both in magnitude and phase. Figure 3-5 gives a

bode plot of the magnitude and phase between the displacement as measured by these

two methods. As an additional check, a second accelerometer was mounted to the


Phase Difference
Disp. Sensor Phase
S- Accel. Phase






S ,'..' '-' '-.'. '.': '-'



I
&-

4,'. "
1








57

housing of the laser displacement sensor to investigate the effect of possible vibration

induced in the laser displacement sensor by the shaker. However, this motion was

found to be negligible at all frequencies and amplitudes over the range of operation

of the device. Thus when the phase correction is applied, the displacement sensor

properly measures the piston motion.


2 1 i i i p 1

1.5 .
()
E 1

0.5

0 ----------------------------
0 50 100 150 200 250 300 350 400
Frequency (Hz)
30

15





-30
0 50 100 150 200 250 300 350 400
Frequency (Hz)


Figure 3-5: Bode plot of the corrected displacement signal.


In order to maximize the resistance to flow through the gap between the oscillat-

ing piston driver and the cylindrical wall, the gap thickness should be minimized, as

shown in Appendix D. For the shaker-driven device, the primary concern in minimiz-

ing the gap thickness is to ensure that the piston does not rub against the cylindrical

wall. While the manufacturer reports that the lateral motion of the shaker is min-

imized due to radial flexural springs, it is desired to quantify this lateral motion as

a way to set a limit on the gap thickness. With a piston plate having a relatively

large gap thickness of 5 mm, there is no danger in rubbing and the shaker may be

taken through its entire operational domain to determine the lateral displacement.









The driver amplitude is fixed at the maximum sustainable value without exceeding

the current limit while the frequency is varied from 10 Hz to 400 Hz.

Lateral displacement measurements are acquired using the same B&K 3-axis

accelerometer mounted at the top-center of the piston plate. The lateral displacement

is similarly determined from the lateral components of the accelerometer signal and

a typical result is shown in Figure 3-6. Here, the lateral components X and Y

are somewhat arbitrary because the slot plate is removed; they correspond to the

plane of the piston. The phase-locked average of the RMS position of these X and

Y components of displacement are plotted vs. frequency in Figure 3-7. It can be

seen that the maximum lateral displacement decreases roughly monotonically with

frequency. At low frequencies the amplitude of the lateral displacement in the X

direction is approximately 0.25 mm, while at higher frequencies (like the data of

Figure 3-6) the lateral displacement decreases as low as on the order of microns.

One may note that the two lateral components are not identical, which indicates that

the accelerometer is not perfectly centered on top of the piston. It is believed that

this .-i-vii.iii I ry, if anything, would cause the lateral displacement to increase. One

may also expect the presence of the mass of the accelerometer to cause an increase

in the lateral displacement because of this .,-vmmetry. Hence without the presence

of the accelerometer the lateral displacement would probably either remain the same

or be smaller than these measured values. Thus if the piston gap is on the order

of 0.25 mm, the thickness of the gap is small enough to allow it to act as a viscous

seal while still being large enough to avoid contact with the cylinder over the entire

frequency range of interest.




































60 120 180 240
Phase (deg)


300 360


Figure 3-6: Typical piston driver lateral displacement at f


50 100 150 200 250
Frequency (Hz)


Figure 3-7: Lateral piston driver RMS position.


x 10-6


300 Hz


10-6
0


300 350 400










Sinusoidal Controller

One critical aspect of a voice coil device is the distortion in the piston motion

rp(t). While at low amplitudes and high frequencies the piston motion is fairly linear,

at very low frequencies and at higher amplitudes the shape of the piston motion can

deviate significantly from sinusoidal given a sinusoidal input. Figure 3-8 shows the

piston motion acquired with the laser displacement sensor, appropriately corrected

for the phase lag, for Case 2 in Table 2-3. It is clear that the piston motion is not

sinusoidal. In Chapter 4, it is shown that this distortion affects the nature of the

flowfield. Therefore, to have confidence in experimental results, a sinusoidal piston

motion must be ensured as this is the most common pi,'_'i oi, for synthetic jet

driver motion and is the most prevalent in the literature.


2 I----------------
S Input Signal
1.5 -- Piston Motion (mm)




0.5


0 -
-0.5 :
%r

-1

-1.5 -

-2 I
0 60 120 180 240 300 360
Phase (deg)


Figure 3-8: Piston motion distortion, f = 18.5 Hz.


Given the need to have sinusoidal motion of the driver, a feedback controller is

required which uses piston motion as the feedback signal. A distinct disadvantage

of the shaker-driven device is that the piston driver, being sealed inside the cavity,










provides limited access for measurement of motion. The only practical way to mea-

sure the piston motion is by mounting the laser displacement sensor above the slot

to achieve optical access of the piston as shown in Figure 3-9. Clearly this setup

is impractical for simultaneously acquiring flowfield measurements, whether flow vi-

sualization or quantitative velocity data, due to the blockage presented by the laser

displacement sensor. The sinusoidal controller must therefore be of a feed-forward

nature in which feedback is first initially used to obtain an input waveform which

generates a sinusoidal signal, then this waveform is used as the input to the amplifier

during flowfield measurements.




Laser displacement sensor





Transmitted beam
projected through slot

Reflected beam projected
through slot
through Rigid driver surface


S r(t /
\ p



/ / / / / / // / // / / / / / / //


Figure 3-9: Schematic of laser displacement sensor.


The method of employing the sinusoidal controller is as follows. First, the piston

motion is acquired for sinusoidal inputs over the entire frequency and amplitude range

of interest in order to characterize the device. It has already been stated that the

frequency range of interest is 0 < f < 400 Hz. This frequency range was determined











via flow visualization which showed that at the maximum voltage input, no significant

flow was achieved out of the synthetic jet device above 400 Hz. The amplitude range

is fixed according to the maximum current of 1.8 A RMS which corresponds roughly

to 6 Vpp. Since the impedance seen by the oscillating piston is a function of the slot

geometry, a separate characterization must be performed for each slot configuration.

In Figure 3-10, the normalized RMS piston position is plotted vs. frequency. Above

100 Hz, the data collapse to a single line, thus for a desired RMS piston position at

a given frequency for h/d = 1.46, this quantity dictates the required RMS voltage

input to the shaker. At lower frequencies there is some scatter in the data, but an

average value may be taken to compute the initial estimate of the required RMS

voltage input.


103
S. .I . . .. I . .. . . . . . .








. . . . . . . . . . . .. ..4 V p p
102

O



1
.N 101: :1 : : Vpp
E .. ......6 .... .. ... -. .. 2 V pp
.. 3.. . . .. . .. .V p p
.. 4 Vpp
-... ....... ... 5 Vpp
....... 6 Vpp
100
0 50 100 150 200 250 300 350 400
Frequency (Hz)


Figure 3-10: Piston characterization for h/d = 1.46.


The purpose of the sinusoidal controller is to generate a waveform which gives a

sinusoidal piston motion at a particular frequency and amplitude. The desired fre-

quency and amplitude are determined from the desired Reynolds number and Strouhal









number. Since d and v are fixed, this means that for a given Re, Uo is determined.

Then for a desired St, the frequency of oscillation u is determined, and it remains to

determine the voltage amplitude of piston motion from the given Uo. This is easily

done by making use of the piston characterization from Figure 3-10, and assuming

continuity between the piston plate and the slot, which is explained in detail next.

Let the sinusoidal piston motion be described by


r,(t) = R cos(wt) (3.1)


where Rp is the amplitude of the piston driver motion, and the cosine is used because

for incompressible flow, the piston motion will be 900 out of phase with the volume

flowrate. Let Rp be defined as the stroke of the piston during either expulsion or

ingestion. For sinusoidal motion, Rp is identically equal to the amplitude as shown

in Eq. (3.1). However, if the motion of the piston is not sinusoidal, the value of the

piston stroke Rp must be taken as half the total stroke, which is the distance between

the point of maximum expulsion and maximum ingestion. This is done to ensure

that the volume expelled is identically equal to the volume ingested -a necessary

condition for a ZNMF device.

Returning to the case of sinusoidal piston motion, for a circular piston of radius

RD, the total change in volume AV during the half-cycle (for incompressible flow) is

AV 27R R, (3.2)


The factor of two in Eq. (3.2) arises because the total piston deflection during expul-

sion (or ingestion) is twice the amplitude. For simplicity, a slug velocity profile which

varies sinusoidally in time with amplitude UA shall now be assumed at the surface of

the slot, such that by continuity


AV 2wRR = Uwd-


(3.3)









Then the RMS position of the piston is simply Rp/ /2 and as stated in C'!i ipter 2, Uo

is the RMS velocity at the slot such that U = (2/7) UA and Uo = UA/V2 therefore


U 2 Uo (3.4)
7-

and substituting Eq. (3.4) into Eq. (3.3) and solving for the RMS piston position

gives
R, wdUo
R wdU0 (3.5)
V2 DwRS
Given the geometric parameters of the device and the desired Uo and w as determined

by the desired Reynolds and Strouhal numbers, the desired RMS piston position

can now be computed and together with the piston characterization as shown in

Figure 3-10, this yields the necessary RMS voltage of the input signal.

Next, the piston motion is acquired phase-locked to the input signal with the

laser displacement sensor and appropriately corrected for the phase lag. Both signals

are simultaneously sampled to eliminate phase errors due to data acquisition. The

signals are acquired using the DAQ system described previously. The sample rate

is set such that 100 samples are acquired per period, phase-locked to the function

generator input signal, and five periods are averaged to create the piston motion

waveform. The total harmonic distortion (THD) of this waveform is determined by

fitting a Fourier series with initially 7 harmonics using a non-linear least squares

algorithm to the piston motion. Let the square root of the 2-squared norm of the

residual of the fitted signal appropriately normalized by the amplitude of the piston

motion waveform be defined as rt. If rt is larger than 1 another harmonic is added

and a new Fourier series is generated. Harmonics are continually added until rt falls

below 1 ensuring that the Fourier series is an accurate representation of the piston

motion. Then the THD is computed as the ratio of the total power in all of the

harmonics in the Fourier series to the power in the fundamental.









If the measured THD is above a predetermined threshold, then an error signal

is calculated by dividing each point in the sine fit by the corresponding point in the

actual piston motion. To avoid large fluctuations in the controller, this error signal

is then clipped at a previously specified level, which is analogous to setting a small

value of kp in a proportional controller to avoid instability. This clipped error signal

is then multiplied by the input signal, and a new, distorted input signal results.

The amplitude of the piston motion is also computed and the ratio of the desired

amplitude to this quantity is determined to appropriately scale the amplitude of the

input signal. The new distorted input signal is then fed to the shaker, and the new

piston motion is acquired with the laser displacement sensor. The process repeats

until the THD falls below the desired threshold. The entire procedure is depicted

schematically in Figure 3-11. Figure 3-12 shows the resulting waveform generated

by the sinusoidal controller for the same case as Figure 3-8. The THD of the initial

piston motion is 0.82 :'. while the THD of the final piston motion is 0.011.7'. a drop

in THD of nearly two orders of magnitude. Qualitatively, the final piston motion also

appears sinusoidal.


Table 3-3: Before- and after-PIV

RMS Dis-
After placement
.) THD ( .) Before (mm)
0.0455 0.662
0.0323 0.663
0.0821 0.663
0.0449 0.666
0.0203 0.745
0.1243 0.986
0.0987 0.852
0.0234 0.573
0.0538 0.460
0.0193 0.607
0.0185 0.685
1.1382 0.633


piston motion.

RMS Dis-
placement
After (mm)
0.696
0.667
0.705
0.732
0.744
1.051
0.929
0.581
0.517
0.628
0.705
0.627


RMS Dis-
placement
diff.
1.26
0.13
1.53
2.35
0.02
1.61
2.17
0.37
2.90
0.87
0.72
0.27


Case
1
2
3
4
5
6
7
8
9
10
11
12


Before
THD (
0.0091
0.0067
0.0093
0.0084
0.0150
0.0091
0.0031
0.0086
0.0079
0.0085
0.0085
1.0088














































Figure 3-11: Sinusoidal controller flowchart.


60 120 180 240
Phase (deg)


300 360


Figure 3-12: Piston motion before and after sinusoidal control, f = 18.5 Hz.


-1


-1.5-


-2
0












Before PIV (THD=0.0067%)
0.8 After PIV (THD=0.0323%)

0.6

0.4

E 0.2
0
0 0

.Ph -0.2(

-0.4 -

-0.6 -

-0.8

-1
0 60 120 180 240 300 360
Phase (deg)


Figure 3-13: Piston motion before and after PIV measurements, f = 18.5 Hz.



While the feedforward controlled device is invariant for the time required to com-

plete flow visualization and velocity measurements, the shaker motion does change

gradually after extended use over many cycles. For this reason, the sinusoidal con-

troller is employ, l1 immediately before both acquisition of flow visualization images

and velocity measurement for each case. Then the piston motion is acquired after

the experiment for comparison. Figure 3-13 shows the piston motion as measured by

the laser displacement sensor both before and after PIV acquisition. While the two

signals appear nearly identical, an examination of the THD reveals that the piston

motion has become more distorted. This is an unfortunate but unavoidable side effect

of the feedforward controller setup. However, the THD is still quite small, indicating

the shape is still practically sinusoidal. Furthermore, there is only a 0.1;:' difference

in the RMS position of the piston between before and after PIV measurement. Con-

sequently, according to Eq. (3.5), the RMS velocity Uo also only changes by 0.1;:';









Table 3-3 show the comparison of the piston motion before and after PIV measure-

ments. The percent difference in RMS piston motion is less than ;:'. for all cases. It

is therefore expected that the slight changes exhibited in the piston motion during

velocity measurement do not adversely affect the resulting flowfield. The high THD

in Case 12 is expected because this is the "uncontill .!!. case.

Flow Visualization Setup

Figure 3-14 illustrates the flow visualization setup. A large tank measuring

600 mm by 600 mm by 1200 mm is constructed to house the synthetic jet assembly

and the resulting flowfield. A 600 mm by 600 mm glass plate serves as the ceiling,

and this plate is removable to facilitate evacuation of the seed particles from the tank

at the conclusion of an experiment. The tank walls and ceiling are made of glass to

enable optical access to the resulting flowfield. The acoustic resonance frequencies of

the tank are computed according to Beranek (1993), and the lowest acoustic resonance

frequency is found to be 143 Hz, which is below the maximum frequency of operation

of the synthetic jet of 115 Hz. Thus, acoustic resonances are not expected to adversely

affect the flowfield. The bottom of the tank is open to allow for insertion of the

synthetic jet device. A plate made of plywood measuring 525 mm by 525 mm serves

as the floor of the tank, and this floor is raised 150 mm off of the bottom surface

and supported with optical posts. The bottom surface is an optical breadboard with

threaded 1/4 20 holes spaced every inch. The glass tank itself is also raised 100 mm

off the bottom surface and supported with unistrut bars, to facilitate insertion of the

synthetic jet device from the underside. The floor plate is carefully centered with

respect to the tank and a 50 mm diameter circular hole is cut in the floor plate to

allow the synthetic jet slot exit to be flush-mounted to the floor plate. The edges of

the floor plate are sealed to the walls of the glass tank using duct tape, thus ensuring

that the entire tank is sealed and isolated from air flow currents in the laboratory. In

addition, the entire optical table area is enclosed using 6 mil thick black construction










plastic to further isolate the flowfield from the air flow currents in the laboratory,

as well as to minimize the effect of external light sources in the laboratory such as

computer monitor di-pli, LED readouts of instruments, etc.

600 mm
glass enclosure with .ii
detachable ceiling . . .

cylindrical spherical seeded flowfield
lens lens syntheticjet

light traversin....................
The synthetic jet device is mountsheet staged on a 2axis manual traverse which has a
thlaser the xz ple as s n in F e 35.200. B t s mm
source
laser
probe \



traversing _"



Figure 3 14: Flow visualization setup schematic.


The synthetic jet device is mounted on a 2-axis manual traverse which has a

degree of freedom in the 3 wat-direction to allow flush-imounting of the slot to the mounteoor

plate and a rotational degree of freedom about the ical -direction enabling views of either

the scribplane or the later) plane as shown in Figure 315. Because the synthetic jet slot

is mounted precisely at the center of the glass tank and because of the relatively large

size of the tank compared to the slot depth, recirculation currents in the tank are

minimized, and the images captured via flow visualization represent the true nature

of a flowfield generated by a ZNMF device exhausting into a quiescent medium.

The laser source is a Spectra-Physics 2020 argon-ion continuous-watt laser with

a nominal power level of 3 watts. Due to space limitations, the laser is mounted

on a separate optical breadboard table. The optical components of the LDA system

(described in detail later) are used to extract the 514.5 nm line of the laser and a







70

x









Figure 3-15: Synthetic jet coordinate system.


fiber optic cable is employ, ,1 to transmit this line to the LDA laser probe as shown

in Figure 3-14. The focusing lens of the LDA probe is removed such that the laser

beam runs parallel to the bottom surface instead of focusing at an angle to a point.

The 514.5 nm line is chosen because it exhibits the highest power of all the lines in

the argon-ion laser. A -142 mm focal length cylindrical lens diverges the beam into a

light sheet, and a 500 mm focal length spherical lens reduces the light sheet thickness

to less than 1 mm at the focal point. The optics are appropriately placed such that

the center of the synthetic jet slot coincides with the focal point, and the center of

the light sheet is projected onto the yz plane since this is the location of maximum

intensity for a Gaussian beam. The LDA probe is mounted on a single stage traverse

to allow the light sheet to be precisely positioned at the center of the slot, either in

the xy plane or the xz plane depending on the orientation of the slot with respect

to the light sheet. Images are acquired in the xz plane principally to determine the

extent to which the flow is two-dimensional.

Flow visualization images are acquired using a Nikon SLR D70 outfit 6 megapixel

camera with a Nikon AF Micro Nikkor 200 mm telephoto lens to allow for highly

resolved images of the flow near the slot. This camera is ideal for flow visualization

because it may be controlled remotely with a PC via a USB interface and the aperture

opening and shutter speed can both be controlled manually. A dovetail optical rail

(not shown) protrudes along either the y or z axis of the slot depending on the

orientation and the camera is mounted to this rail via optical posts and a manual









3-axis linear stage traverse, which allows for precise positioning of the field of view

of the camera with respect to the origin of the coordinate : of the synthetic jet

device.

Ti.- tank is seeded with Le Maitre fog fluid -. 'ticles using a TSI model '2 :;2

single 1 I atomizer. According to the manufacturer's specifications, the particles have

a mean diameter of 1 pm. Ti -. particles are large enough to be observed as 1,11 11 ,

in the flowfield in the flow visualization images but are still small enough to faithfully

follow the flow. The section on particle ;j and dynamics provides more details to

confirm this.

Velocity Measurement

For flowfield characterization, the most important measurable quantity of a syn-

thetic i. I device is the velocity field induced in the fluid above the slot exit. T:i.

velocity I .1._.1 at the slot exit, if measured carefully, yields the 1. R :. .1.14 number.

In addition, taking the curl of the velocity yields the vorticity field, which n1: be used

to determine the behavior of the shed vortex pairs. If a significantly large number

of velomt-.r measurements are acquired, then information on the turbulent nature of

the flowfield l- also be deduced. Thus, it is imperative that an accurate technique

be :.: 1J..1-- .1 to acquire velocity data. Given the unsteady nature of ---:.11, tic jet

flows, the inherent small geometric size of the slot to achieve low Stokes numbers,

and the purely oscillatory nature of the flow at the slot, hot wire anermometry is not

well suited to the task. A high spatial resolution, non-intrusive techni(i. is desired.

Both Particle Image Velocimetry (PIV) and Laser Doppler Anemometry (LDA), if

properly used, can yield highly accurate results fror which the flowfield generated

by the synthetic jet device can be quantified. Often in the literature, the details

of the veloii measurement technique are abridged or omitted completely. Here, a

complete description of these two methods is given to assist in providing a thorough

characterization of the results.









Hotwire Anemometry

While not acceptable for quantitative measurements of ZNMF flowfields, hotwire

anemometry can be useful for qualitative determination of turbulent characteristics.

Past researchers (Winter & Nerem, 1984; Lodahl et al., 1998) have noted the phe-

nomenon of conditional turbulence arising in pulsatile flows, defined as oscillatory

flows with the superposition of a mean flow. This phenomenon has never been inves-

tigated for synthetic jet flowfields, and would provide valuable insight into the nature

of these flowfields. Figure 3-16 shows the hotwire setup. A two axis traverse is used

to position the wire at the center of the slot, right at the surface. Velocity traces

are then acquired from the hotwire signal via the data acquisition system described

later. It is expected that the analysis of these traces for each of the cases acquired

will assist in determining the nature of the turbulence in the resulting flowfield.

hotwire



jet ,2-axis
synthetic et averse
device traverse
device/







Figure 3-16: Schematic of the hotwire anemometry setup.


Particle Image Velocimetry

Near-field velocity measurements are acquired above the surface of the synthetic

jet device using Particle Image Velocimetry (PIV). The near-field is defined as the

distance extending 2-3 stroke lengths downstream of the slot, where 1-2 vortex pairs

remain visible in the field of view. The setup of the PIV system is nearly the same

as the flow visualization setup schematic shown in Figure 3-14. A photograph of

the PIV setup is shown in Figure 3-17. Instead of the fog fluid as used for flow









visualization, the tank is seeded with incense smoke for PIV measurements. The

incense particles have a mean diameter on the order of a micron, and more details on

the particle sizing is given later. A stick of burning incense is placed exactly at the

center of the tank to minimize the establishment of flow recirculation patterns in the

tank. A single stick takes approximately 20 minutes to burn and provides a sufficient

density of seed particles for PIV measurements for about one hour.

synthetic
jet slot
/


laser light 200 mm PIV
source sheet telephoto camera
optics lens

Figure 3-17: Photograph of the PIV setup.


The laser source consists of a pair of New Wave model Minilase-III Nd:YAG

lasers. These lasers are fitted onto a single assembly and a linear stage traverse is

used to position the light sheet, similar to the flow visualization setup. The diameters

of the two beams are both 3.5 mm, and the pulse width is approximately 6 ns. Internal

optics in the laser assembly align the two beams such that they follow the same optical









path. The beams then pass through a -6.35 mm focal length cylindrical lens and a

500 mm focal length spherical lens to generate a light sheet. The waist of the light

sheet occurs at the focal length of the spherical lens. At this location, the light sheet

is 0.09 mm thick with a divergence of 6.82 pm/mm along the optical axis. Also at the

waist, the light sheet height is 272 mm and the height divergence is 30 degrees. Note

that the direction of the projected light sheet is normal to the direction of the flow,

which minimizes the reflective light scatter near the surface of the orifice. Also, the

center of the light sheet in the x direction is positioned at x = 0, due to the Gaussian

intensity of the light sheet.

A TSI model 630157 Powerview Plus 2MP 10-bit CCD camera is used to capture

images. This camera contains 1600 x 1200 pixels which are spaced 7.4 Pm apart.

The same Nikon 200 mm micro lens used for flow visualization is used to focus and

obtain the images. This setup allows for excellent spatial resolution of approximately

13 /pm/pixel, which gives a field of view in the vertical direction of about 6 slot depths

downstream of the synthetic jet device.

The laser pulsing and camera exposure is controlled by a TSI Model 610032

synchronizer which is configured to acquire two-frame single exposure images using

TSI INSIGHT Software version 6.1.1. In order to achieve the minimum time between

pulses, the synchronizer times the pulse of the first laser to occur at the end of the

exposure time of the camera for the first frame. The image is then transferred off of

the camera CCD array through shift registers, and the second laser pulse occurs at

the beginning of the exposure time of the camera for the second frame. This process

is depicted schematically in Figure 3-18, where dT represents the time between ex-

posures. The correct choice of dT is application specific. For low amplitude synthetic

jet flows, dT should be larger than for higher amplitude synthetic jet flows. The

timing of the initial camera tri. ._ v r pulse can be continuous, and the rate at which

image pairs are acquired is limited only by the repetition rate of the camera and










laser, which is 15 Hz. For an inherently periodic flow, however, phase-locked timing

is desired and can be achieved through the use of an external tri --r source fed into

the synchronizer.

Camera time
trigger


Camera Image 1
Camera Image 1 Image 2 exposure
exposure exposure
III
III
Camera
ea Image 1 readout Image 2 readout
readout
I
II

Laser
pulses_

Figure 3-18: Frame straddling timing diagram for two-frame single exposure PIV.


A block diagram of the entire PIV setup is shown in Figure 3-19. To acquire

phase-locked velocity from the PIV system, two Agilent model 33120A function gen-

erators are employ. -1 The first function generator serves as the input signal to the

shaker via the power amplifier, while the second function generator, phase-locked to

the first, is used to tri --. --r the PIV acquisition. When phase-locked, it is possible

to achieve a desired relative phase between the two function generators. Hence, the

phase of the second function generator is adjusted as required to obtain the velocity

field at the desired phase. Both the first function generator signal and the output

of the laser displacement sensor are acquired by the data acquisition system for the

sinusoidal controller. These signals, along with the second function generator TTL

tri .- -r signal, are acquired and di-p11 .i. I1 on a Tektronix model TDS-2014 digital os-

cilloscope to facilitate determination of the relative phase. Here, zero phase is defined

as the point where the volume flow rate is zero with positive slope. While this value

cannot be quantitatively determined a prior, it can be approximated as the time










in the cycle of the piston motion where the maximum deflection of the piston away

from the slot has occurred. The signal from the laser displacement sensor is positive

downward as depicted in Figure 3-9, therefore zero phase is taken as approximately

the point in the laser displacement signal exhibiting maximum voltage. The relative

phasing between the two function generators is then adjusted to correspond to this

definition of zero phase. Later, once the velocity data has been reduced, a more

precise estimate for zero phase is found by interpolating the phase-locked volume

flowrate.


Inputs PIV System Outputs


Function Amplifier B&K Shaker Laser Displacement
F- Ge ^Amplifier B&K Shaker -
Generator 1 Sensor
phase
locked
Function PIV Synchronizer t- PIV Laser DAQ card
Generator 2


PIV Camera Oscilloscope



PC (INSIGHT
software)


Figure 3-19: Block diagram of the PIV setup.


To verify the PIV timing, both function generator signals, the laser displacement

signal, the Q-switch signals from the synchronizer to the lasers, and a photodiode

signal are acquired phase-locked on the oscilloscope. The Q-switch signals are trigger

signals used to force the lasers to fire a pulse. A block diagram of this setup is shown

in Figure 3-20.

The piston motion, trigger signal, and both Q-switch signals are shown in Fig-

ure 3-21 for a typical case at a phase of 1500. It is apparent that the Q-switch signals

occur at the instant a TTL-high signal is achieved from the trigger. This is more
















Function


PIV Camera


Figure 3-20: Block diagram of the PIV timing.


0 60 120


180 240
Phase (deg)


300 360


Figure 3-21: Piston motion and PIV trigger signals for a phase of ~ 1500.


phase
locked


Laser Displacement
Sensor


Oscilloscope








78


easily observed in Figure 3-22, which shows both the synchronization between the

tri- -. -r signal and the Q-switch signals along with the measured photodiode voltage

signal. Based on the photodiode signal, it is apparent that the lasers fire at the instant

the Q-switch signals trigger them. It should also be noted that the width of each laser

pulse is not as indicated by the photodiode; rather, the signal from the photodiode

is probably best modeled as a second order system response to an impulse; hence

the apparent ringing in the photodiode signal. Both the time between pulses dT and

the pulse delay time, defined as the time between the trigger pulse and the first laser

pulse, were verified with this setup. The purpose of the pulse delay time is to align

the exposure times of each frame on the PIV camera with the light sheet pulses.


6

4

2

0

-2

-4

-6

-8

-10

-12
-40


--







---C
--F


0


4 Itaba wa'nsmn
I II

i! II
i! ii

i! II
i! ii

i_! II

rigger Signal i- ii
switch 1 i! II
Switch 2 g II
'hotodiode Signal


-200


0 200
Time (ps)


Figure 3-22: PIV laser intensity acquired from a photodiode.


Although the piston motion has been corrected for its phase lag; Figure 3-22

indicates that there is still a slight error in the phase, due to the fact that the actual

phase of the PIV-acquired velocity data is best estimated as the midpoint between

the two Q-switch signals, rather than the start of the trigger signal. For this case,









the error between the trigger signal and the center of the Q-switch signals is about

300 ps. For a typical operating frequency of 50 Hz, this error amounts to only 1.5' of

the period. While this may seem insignificant, it is nevertheless ultimately accounted

for when the true phase is computed via the volume flowrate measurements.

Before computing the velocity field for a given image pair, image calibration is

required to obtain scale factors in pm/pixel. A thin silicon plate measuring one inch

by one inch and perforated with a grid of circular holes is used for image calibration.

The fabrication of the plate is a two step process. First, a chrome mask of the

grid of holes is generated with a resolution on the order of one micron. Second, the

silicon plate is manufactured from the mask using photolithography and deep reactive

ion etch (DRIE). This procedure gives an excellent accuracy in the hole spacing from

which PIV image calibration can be accurately determined. The process of fabrication

of the silicon plate is described in detail in Chandrasekharan et al. (2006).

With the shaker removed from the tank, the plate is mounted in the plane of the

light sheet. A flashlight from above the position of the camera is used to illuminate a

small white background behind the center of the tank (see Figure 3-17). Some of the

diffused light from this background is scattered through the holes and captured by

the PIV camera, thus the image generated appears as regularly spaced circular holes

of high intensity surrounded by a dark background. An example calibration image

(shown in a false color scale) is shown in Figure 3-23. Note that the x direction

is vertical while the y direction is horizontal in this view. Since the CCD array

measures 1600 pixels by 1200 pixels, yet the synthetic jet flowfield exhausts vertically,

the camera is rotated 90 degrees to allow for more flowfield information further away

from the slot.

Once the PIV calibration image is acquired, the threshold of the hole edges

must be determined by plotting a slice of the intensity through the y direction and

determining the smallest intensity above the noise floor. An example slice is shown











x 104

6
200
5

400
4

.x 600
3

800


1000 1


1200 0
200 400 600 800 1000 1200 1400 1600
y (pixels)


Figure 3-23: Typical PIV calibration image.


in Figure 3-24, and from this data, for this example an intensity threshold of 5000 is

appropriate.

An edge detection scheme is next developed to ultimately determine the centers

of the holes as follows. First, the region of examination of a single hole is determined

by specifying an estimate of the hole diameter and the distance between holes in

pixels via Figure 3-24. Next, slices are made horizontally across each row of pixels to

determine the two pixel values that cross the threshold intensity, and the midpoint

between these two pixel values is taken as a sample of the hole center in the horizontal

direction. All rows of pixels are scanned moving down the hole, each row yielding

an estimate of the horizontal center of the hole. The mean of these estimates is

then computed as the y location of the center. The process is then repeated in the

vertical direction to determine the x location of the center. This whole process is

then repeated for every hole in the image, as shown in Figure 3-25.