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Characterization of Novel and Conventional Dielectric Barrier Discharge Actuators

Permanent Link: http://ufdc.ufl.edu/UFE0044988/00001

Material Information

Title: Characterization of Novel and Conventional Dielectric Barrier Discharge Actuators
Physical Description: 1 online resource (238 p.)
Language: english
Creator: Durscher, Ryan J
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2012

Subjects

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

Notes

Abstract: This document outlines efforts to improve upon the dielectric barrier discharge plasma actuator. These devices have been studied for use in various aerodynamic applications and have been particularly effective for freestream velocities up to ~50 m s-1. In order to be truly applicable for a wide range of applications, however, a demonstration of sufficient control authority at higher speeds is necessary. To accomplish this, the plasma actuator requires a significant improvement in output performance, whether the metric be momentum transfer or peak induced velocity. The following work presents efforts to improve these metrics, in part through the development of new actuator configurations. Actuators consisting of multiple powered electrodes are demonstrated to show a substantial reduction in the device’s power consumption, while a novel electrode layout is experimentally shown to induce a three-dimensional flow field. To date most actuator configurations used result in two-dimensional vector fields. Furthermore, two materials with extreme dielectric constants, relative to those typically investigated, are characterized. The net thrust of the actuator is shown to improve drastically while simultaneously reducing the actuator’s weight by using silica aerogel, a previously unexplored dielectric material. The problem of thrust saturation is also investigated and characterized. The physical mechanisms involved in this limiting factor are identified and a manipulation of the effect is demonstrated.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Ryan J Durscher.
Thesis: Thesis (Ph.D.)--University of Florida, 2012.
Local: Adviser: Roy, Subrata.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2012
System ID: UFE0044988:00001

Permanent Link: http://ufdc.ufl.edu/UFE0044988/00001

Material Information

Title: Characterization of Novel and Conventional Dielectric Barrier Discharge Actuators
Physical Description: 1 online resource (238 p.)
Language: english
Creator: Durscher, Ryan J
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2012

Subjects

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

Notes

Abstract: This document outlines efforts to improve upon the dielectric barrier discharge plasma actuator. These devices have been studied for use in various aerodynamic applications and have been particularly effective for freestream velocities up to ~50 m s-1. In order to be truly applicable for a wide range of applications, however, a demonstration of sufficient control authority at higher speeds is necessary. To accomplish this, the plasma actuator requires a significant improvement in output performance, whether the metric be momentum transfer or peak induced velocity. The following work presents efforts to improve these metrics, in part through the development of new actuator configurations. Actuators consisting of multiple powered electrodes are demonstrated to show a substantial reduction in the device’s power consumption, while a novel electrode layout is experimentally shown to induce a three-dimensional flow field. To date most actuator configurations used result in two-dimensional vector fields. Furthermore, two materials with extreme dielectric constants, relative to those typically investigated, are characterized. The net thrust of the actuator is shown to improve drastically while simultaneously reducing the actuator’s weight by using silica aerogel, a previously unexplored dielectric material. The problem of thrust saturation is also investigated and characterized. The physical mechanisms involved in this limiting factor are identified and a manipulation of the effect is demonstrated.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Ryan J Durscher.
Thesis: Thesis (Ph.D.)--University of Florida, 2012.
Local: Adviser: Roy, Subrata.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2012
System ID: UFE0044988:00001


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CHARACTERIZATIONOFNOVELANDCONVENTIONALDIELECTRICBARRIERDISCHARGEACTUATORSByRYANJ.DURSCHERADISSERTATIONPRESENTEDTOTHEGRADUATESCHOOLOFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENTOFTHEREQUIREMENTSFORTHEDEGREEOFDOCTOROFPHILOSOPHYUNIVERSITYOFFLORIDA2012

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c2012RyanJ.Durscher 2

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Tomyparents 3

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ACKNOWLEDGMENTS Firstofall,IwouldliketothankDr.SubrataRoy,mycommitteechair,forhisguidance.HewasalwaystherewhenIneededhim.Iwouldalsoliketothanktherestofmycommittee:Dr.LouisN.CattafestaIII,Dr.DavidArnold,andDr.DavidHahn.Ideeplyappreciatetheopportunitytoworkandconsultwiththem.IwouldalsoliketothankDr.ScottStaneldforthethoughtfultheoreticaldiscussionsandallaroundassistance;RaulChingaforthenumeroustalkswehavehadregardingtheDBDpoweringcircuitandforhelpingmemeasurevariouselectricalcomponents;toJustinZitoforalwayslendingahelpinghand;andTomasHoubaforalwayshavingananswertothenumericalquestionsIcouldnotgureoutonmyown.FinancialsupportforthisworkwasprovidedinpartthoughAirForceOfceofScienticResearch(AFOSR)grantsmonitoredbyDr.DougSmithandCharlesSuchomel.FinancialsupportwasalsoprovidedinpartthoughaDepartmentofDefense(DOD)SMARTscholarship,forwhichIamextremelygratefultohavereceived. 4

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TABLEOFCONTENTS page ACKNOWLEDGMENTS .................................. 4 LISTOFTABLES ...................................... 8 LISTOFFIGURES ..................................... 9 ABSTRACT ......................................... 16 CHAPTER 1INTRODUCTION ................................... 17 2PLASMAS,GASDISCHARGES,ANDDIELECTRICBARRIERDISCHARGES 20 2.1PlasmaBasicsandCharacterization ..................... 20 2.2GasDischarges ................................ 25 2.3DielectricBarrierDischargeClassication .................. 27 2.3.1VolumetricDielectricBarrierDischarges ............... 29 2.3.2SurfaceDielectricBarrierDischarges ................. 30 3DIELECTRICBARRIERDISCHARGEACTUATORS ............... 31 3.1CharacteristicsoftheDBDActuator ..................... 32 3.1.1ElectricalandVisualCharacteristics ................. 32 3.1.2ThrustGeneration ........................... 38 3.1.3InducedVelocityField ......................... 48 3.2NumericalModelingoftheDBDPlasmaActuator .............. 54 3.2.1EstimationofthePlasmaBodyForce ................. 54 3.2.2ReducedOrderModeling ....................... 57 3.2.3FirstPrinciplesBasedModeling .................... 60 3.3AerodynamicApplicationsoftheDBDPlasmaActuator .......... 61 3.4MotivationforCurrentWork .......................... 67 4EXPERIMENTALSETUP .............................. 69 4.1PlasmaActuatorConguration ........................ 69 4.1.1ActuatorDimensions .......................... 69 4.1.2ElectrodePhoto-fabrication ...................... 70 4.2PlasmaDischargeGeneration ........................ 71 4.3PowerMeasurements ............................. 73 4.3.1MethodologyandEquipmentDescription ............... 73 4.3.2ComparisonofPowerMeasurementTechniques .......... 76 4.4ThrustMeasurements ............................. 80 4.4.1DirectThrustEvaluation ........................ 80 4.4.1.1Inuenceofplatelength ................... 82 5

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4.4.1.2Inuenceofchambersize .................. 85 4.4.2ControlVolumeInferredForces .................... 86 4.4.2.1Controlvolumemethodology ................ 87 4.4.2.2Inuenceofcontrolvolumesize .............. 89 4.4.3ComparisonbetweenDirectandInferredThrustMeasurements .. 92 4.5FlowFieldMeasurements ........................... 94 4.5.1ParticleImageVelocimetry(PIV) ................... 94 4.5.1.1Equipmentsetup ....................... 95 4.5.1.2Processingmethodology .................. 96 4.5.1.3Statisticalconvergenceanderrorestimation ....... 97 4.5.1.4Seedmaterialselection-theory .............. 98 4.5.1.5Seedmaterialselection-implemented .......... 103 4.5.2LinearActuatorEndEffects ...................... 105 4.5.3BuoyancyEffectsontheInducedFlow ................ 107 4.5.4PitotProbeMeasurements ....................... 110 4.6ThermographyMeasurements ........................ 111 5NUMERICALFORMULATIONANDMETHODOLOGY .............. 112 5.1Drift-DiffusionApproximation ......................... 112 5.2Multi-scaleIonizedGasFlowCode ...................... 114 5.3FiniteElementFormulation .......................... 115 5.4SimulationGeometry .............................. 117 6MULTI-BARRIERACTUATORS ........................... 119 6.1MBPADesign .................................. 119 6.2EffectofGroundedElectrodeWidth ..................... 121 6.3InuenceoftheGroundedElectrodefortheMBPAConguration ..... 123 6.4ComparisonwithStandardActuatorDesign ................. 127 6.5AlternativeMBPACongurations ....................... 129 6.5.1MixingDielectricMaterial ....................... 129 6.5.2Tri-LayerMBPA ............................. 131 7THREE-DIMENSIONALACTUATION ....................... 136 7.1SerpentineActuatorDesign .......................... 136 7.2CircularSerpentineActuator ......................... 138 7.2.1FlowVisualization ........................... 138 7.2.2InducedFlowFieldMeasurements .................. 140 7.2.3EffectofVoltage ............................ 141 7.3RectangularSerpentineActuator ....................... 144 7.4ComparisonwithaLinearActuator ...................... 146 6

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8EXTREMEDIELECTRICS ............................. 152 8.1FerroelectricActuators ............................. 152 8.2AerogelActuators ............................... 154 9INVESTIGATIONOFDBDTHRUST`SATURATION' ............... 161 9.1ActuatorDesign ................................ 163 9.2SaturationEffectonThrustProduction .................... 163 9.3SaturationEffectonInducedVelocity ..................... 166 9.3.1CharacteristicsofFlowFieldPriortoSaturation ........... 168 9.3.2CharacteristicsofFlowFieldDuringSaturation ........... 170 9.4InuenceofSurfaceTemperature ....................... 173 9.4.1CharacteristicsofSurfaceTemperature ................ 177 9.4.2ManipulationoftheSaturationEffectbyLocalHeatAddition .... 183 9.5Discussion ................................... 189 10SUMMARYANDRECOMMENDATIONSFORFUTUREWORK ........ 195 10.1ExplorationoftheMulti-BarrierActuatorDesignSpace ........... 195 10.2Three-DimensionalFlowInducement ..................... 197 10.3ExploringtheFarEndsoftheDielectricSpectrum ............. 198 10.4CharacterizationoftheDBDThrust`Saturation'Effect ........... 199 APPENDIX AHIGHVOLTAGETRANSFORMERSCHEMATICSANDSPECIFICATIONS .. 202 BMEASURINGPOWERFORTHEDBDACTUATOR ............... 206 B.1ErrorAnalysis .................................. 206 B.2TemporalErrorEstimation ........................... 207 CQ-VPOWERDETERMINATION .......................... 214 DDETERMININGTHEDIELECTRICCONSTANTOFADIELECTRICMATERIAL 216 D.1Theoretical ................................... 216 D.2Measurement .................................. 218 REFERENCES ....................................... 221 BIOGRAPHICALSKETCH ................................ 238 7

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LISTOFTABLES Table page 2-1Typicalparametersfornaturallyandinducedplasmas. .............. 21 2-2Coefcients,AandB,usedtocalculatethebreakdownvoltageofagivengasbasedonPaschen'sLaw. .............................. 26 6-1Horizontaldisplacement,g,investigatedforeachactuatorconguration. .... 121 7-1Averagepowerconsumptionsforlinear,circularserpentine,andrectangularserpentineactuators(14kVppat10kHz). ..................... 151 9-1Experimentallyextractedvaluesusedinatheoreticalestimationofthetemporal,spanwiseaverage,surfacetemperatureofaDBDactuator. ........... 181 9-2Dielectricpowerlossjustpriortosaturationconditions. .............. 183 9-3Powerconsumptionforaconstantvoltage(44kVpp)andfrequency(2kHz)priortoandduringthelamentarydischargetransformation ........... 189 A-1Assortedspecicationsforthetransformersusedtogeneratethehighvoltagesrequiredtoignitethedielectricbarrierdischargeactuator. ............ 202 B-1Capacitanceandresistancevaluesforcircuitelementsusedtodeterminetheinuenceofthehighvoltageprobe. ......................... 211 8

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LISTOFFIGURES Figure page 2-1VoltageandcurrentcharacteristicforaDCdischargeinalowpressuredischargetube. .......................................... 26 2-2ExamplePaschencurvesforvariousgases. .................... 27 2-3Exampleelectrode/barriercongurationsusedtogenerateadielectricbarrierdischarge. ....................................... 28 3-1ExperimentalsetupforDBDactuationonanairfoil. ................ 32 3-2Representativevoltageandcurrenttracesforadielectricbarrierdischargeplasmaactuator. ................................... 33 3-3CurrenttraceandcorrespondinglightemissionofaDBDactuator. ....... 34 3-4Highspeedcameraimagesofadielectricbarrierdischarge. ........... 35 3-5SurfacepotentialdistributioninaDBDactuator(10kVppat3kHz). ....... 37 3-6QualitativeDCsheathnearanequipotentialwall. ................. 40 3-7TheangularvelocityofatorsionalpendulumdrivenbyaDBDactuator. .... 42 3-8Thetemporallyvaryinghorizontalandverticalcomponentsoftheplasmaforceasafunctiontime. .................................. 42 3-9Voltageandcurrenttracesforpositiveandnegativesawtoothwaveforms. ... 44 3-10Thrustasafunctionofvoltage ........................... 46 3-11Changesinthetemporalstructureoftheplasmadischargeasaresultoftheelectrodeshape. ................................... 47 3-12Saturationthrust(maximumthrustmeasured)asafunctionoftherelativedielectricconstantforvariousmaterials. ........................... 48 3-13BodyforcedistributionsforaDBDactuatorobtainedthroughtimeresolvedparticleimagevelocimetry. ............................. 49 3-14Characteristicwalljetfromadielectricbarrierdischargeplasmaactuator. ... 49 3-15PitotprobepressuresignalsasafunctionoftimenearaDBDactuator. .... 51 3-16Temporalresponseoftheinducedvelocitywithringmodulationforthedrivingfrequency(50Hz,150Hz,and300Hz). ...................... 51 3-17AsymptoticbehaviorofthemaximuminducedvelocityforaDBDactuatorasafunctionofpowerconsumption. .......................... 52 9

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3-18InducedvelocityprolesabovemultipleDBDactuators. ............. 52 3-19Experimentaldemonstrationofaplasmavortexgenerator. ............ 54 3-20Assumedtriangulardischargevolumewithheight,a,andwidth,b,inwhichtheelectriceldisassumedtovarylinearlyintheregionandisboundedbylineA-B. ........................................ 55 3-21Comparisonbetweenempiricalandrstprinciplesbasedplasmamodelsandtheirimplementationinauiddynamicssimulation. ................ 58 3-22TreatmentoftheDBDplasmaactuatorasalumpedelement. .......... 59 3-23DemonstrationofowreattachmentusingaDBDactuatoronaNACA0015airfoil. ......................................... 63 3-24Ambienttemperatureandpressureasafunctionofaltitude. ........... 66 3-25Dielectricbarrierdischargeplasmaactuatorsappliedtoasmallunmannedaerialvehicle. ..................................... 66 3-26Dielectricbarrierdischargeactuatordesignspace. ................ 68 4-1AgeneralschematicoftheDBDactuatorusedthroughoutthiswork. ...... 69 4-2Manufacturingowchartforphoto-fabricatedelectrodes. ............ 71 4-3ExamplepoweringschemesusedtodrivetheDBDactuator. .......... 72 4-4Comparisonbetweenpowerdeterminationmethods. .............. 79 4-5PercentdifferencebetweentheV-IandQ-Vpowerdeterminationmethods. .. 79 4-6ComparisonbetweentheinferredcurrentasmeasuredwithaninductivecoilandthatdeterminedfromOhm'slaw. ........................ 81 4-7Schematicofdirectthrustelevationsetup. ..................... 82 4-8Examplereadoutsfromthebalanceshowingthestabilityandrepeatabilityofthedirectthrustmeasurement(14kHzdrivingfrequency). ............ 83 4-9Schematicofactuatorusedforplatelengthtests. ................. 84 4-10Thrustmeasurementsoverarangeofinputvoltageswithvaryingactuatorplatelengths. ..................................... 84 4-11Percentageincreaseinthrust,Tx,betweenaplatelengthof2.5cmand15cmasafunctionofvoltage. ............................. 85 4-12Powerdissipationasafunctionofvoltagefordifferentplatelengths. ...... 86 4-13Effectofaventedversusun-ventedchamberontheinducedthrust. ...... 87 10

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4-14Schematicofcontrolvolumeusedtocalculatereactionforcesinducedbytheplasmadischarge. .................................. 88 4-15Velocitymagnitudecontourfora20kVppinputvoltagedrivenat14kHz. .... 90 4-16Inferredtangentialthrust,Tx,forvariousvoltagesat14kHzasafunctionofthecontrolvolume'swidth(W=x)]TJ /F3 11.955 Tf 11.96 0 Td[(xo)andheight(H=y-yo). ......... 91 4-17Inferredthrustbasedonacontrolvolumeanalysisoftheinducedoweldasafunctionoftheappliedvoltageat14kHz. .................... 92 4-18Comparisonbetweendirectthrustmeasurementsandthoseinferredfromacontrolvolumeanalysis. ............................... 93 4-19Controlvolumescalingrelations. .......................... 94 4-20Stereoscopicparticleimagevelocimetrysetup. .................. 96 4-21Convergenceplotsoftheaveragex-velocity, ux,fortwolocationsintheoweldinducedbyalinearactuator(asusedinSection 4.4.2.2 )drivenat14kHz. 98 4-22Relativestatisticaluncertaintyasafunctionofvoltageandpositionforthevelocityeldofalinearactuator(asusedinSection 4.4.2.2 )drivenat14kHz. 99 4-23ComparisonbetweenpitotmeasurementsandPIVprolesforalinearDBDactuator. ........................................ 105 4-24Schematicofactuatorusedtoinvestigatetheinuenceofelectrodeendeffectsonthemeasuredvelocityeld. ........................... 106 4-25Contoursdepictingtheratioofuztothatofux,maxforvariousdistancesfromtheedgeoftheelectrodeataxedvoltage(20kVpp). .............. 107 4-26Contoursdepictingtheratioofuztothatofux,maxforvariousdistancesfromtheedgeoftheelectrodeandvoltages. ...................... 108 5-1Schematicrepresentationofthetransformationfromanodalcoordinatesystemtoareferencebi-quadraticelement. ........................ 116 5-2SimulationdomainusedinthepresentnumericalinvestigationofaDBDplasmaactuator. ........................................ 118 6-1Actuatorcongurationstestedinmulti-barrierplasmaactuatorinvestigation. .. 120 6-2Inuenceofthegrounded,middleelectrode'swidthonthrustgeneration,forabi-layerMBPAactuator. ............................... 122 6-3Effectiveness(ratioofinducedthrusttoconsumedpower)asafunctionofvoltageforvariousgroundedelectrodewidthsinabi-layerMBPAactuator. ... 122 11

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6-4Thrustasafunctionofvoltagewith(case1)andwithout(case2)agrounded,middleelectrodeinaMBPAconguration ..................... 124 6-5Timeaveraged,non-dimensionalforce(F)vectorsandmagnitudecontoursobtainedfromnumericalsimulations(Chapter 5 ). ................ 125 6-6TotalpowerconsumedbyaMBPAactuatorwith(case1)andwithout(case2)agrounded,middleelectrode. ............................ 126 6-7PowerdistributionbetweentheexposedandencapsulatedelectrodeforaMBPAactuatorwith(case1)andwithout(case2)amiddle,groundedelectrode. ... 126 6-8SchematicrepresentationoftheelectriceldlinesforaMBPAwithandwithoutamiddle,groundedelectrode. ............................ 127 6-9Contoursofthenon-dimensionalelectricpotential,,obtainedfromnumericalsimulations(Chapter 5 ). ............................... 128 6-10EffectofvoltagesplittingontheresultantthrustforaDBDactuator. ....... 129 6-11Effectiveness(ratioofinducedthrusttoconsumedpower)forasplitpotentialactuator(case2)andastandardactuator(case3)overarangeofvoltages. .. 130 6-12Performancecharacterizationofamixeddielectricmulti-barrieractuator. .... 131 6-13Schematicofatri-layermulti-barrierplasmaactuator. .............. 132 6-14Performancecharacterizationofatri-layermulti-barrieractuator. ........ 133 6-15Instantaneousvoltageandcurrentwaveformsforatri-layerMBPA. ....... 135 7-1AcircularserpentineDBDactuatorandthenotationalinuenceontheinducedoweld. ....................................... 137 7-2Ageneralschematicoftheserpentineactuatorsinvestigated. .......... 138 7-3Locationsofspanwise(dashedlines)andstreamwise(dottedlines)planarcutsinmm. ...................................... 139 7-4Flowvisualizationoftheinducedvelocityusinglocalizedseeding. ....... 139 7-5Timeaveragedz-velocity,uz,contoursoverlaidwithx-andy-velocityvectorsforvariousplanarcutsalongthespanofacircularserpentineactuator. .... 141 7-6Timeaveragedcontourplotsandiso-surfacesofstreamwise(!x)vorticityforacircularserpentineactuatorwithaninputvoltageof14kVpp. ......... 142 7-7Temporallyaveragedspanwise(!z)vorticityiso-surfacesreconstructedfromplanarmeasurementsonacircularserpentineactuator(16kVpp). ....... 143 7-8Timeaveraged,velocitymagnitudecontoursalongacircularserpentineactuator. 145 12

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7-9Timeaveragedcontourplotsandiso-surfacesofstreamwise(!x)vorticityforarectangularserpentineactuator(14kVpp). ................... 146 7-10Temporallyaveraged,velocitymagnitudecontoursoverlaidwithx-andy-velocityvectorsforarectangularserpentineactuator(14kVpp). ............. 147 7-11Streamtracescoloredbystreamwise,!x,vorticityshowingacorkscrewlikestructureintheinducedoweld. ......................... 147 7-12Timeaveragedquantitiesforalinearactuatordrivenat14kVpp(z=0mm). .. 148 7-13Velocityprolesofuxanduyforalinear,circular,andrectangularserpentineactuator(z=0mm). ................................. 149 7-14Velocityprolesofuxanduyforalinear,circular,andrectangularserpentineactuator(z=-10mm). ................................ 150 8-1Visualandthermalcharacteristicsofaferroelectricactuatorsuppliedwitha3.5kVpp,5kHzsinusoidalinput. .......................... 153 8-2Surfacetemperatureasafunctionoftimeaboutpoint12.5mm,1.5mm(x,y). 155 8-3Thesurfacetemperatureofaferroelectricsampleasafunctionofpowerconsumption,after300secondsofoperation. .......................... 155 8-4Visualandsurfacecharacteristicsofasilicaaerogelsample. .......... 157 8-5RepresentativevelocityeldmeasuredusingPIVovertheaerogelsampleforasuppliedvoltageof36kVppat14kHz. ...................... 157 8-6Inuenceofdielectricthicknessonthrustproductionforactuatorsconstructedoutofsilicaaerogel,Kaptonandacrylicasafunctionofvoltage. ........ 158 8-7Ratioofthrustgeneratedtotheactuator'sweightforvariousdielectrics. .... 160 9-1Dischargeappearanceatsaturationconditionsforvariousfrequencies. .... 162 9-2Measuredthrustasafunctionofvoltageforvariousfrequencies. ........ 164 9-3Measuredthrustasafunctionofpowerconsumptionforvariousfrequencies. 164 9-4Powerandeffectivenessasafunctionofsuppliedvoltageforvariousfrequencies 165 9-5SaturationrelationsforaDBDactuator. ...................... 166 9-6ParticleimagevelocitmetrysetupusedtostudytheinducedoweldofaDBDactuatoratsaturationconditions. .......................... 167 9-7Timeaveragedvelocitycontours,ux,formultipleplanesabovethesurfaceofthedielectricforanappliedvoltageof40kVppat2kHz. ............. 169 13

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9-8Timeaveragedvelocitycontours,ux,forvariousvoltagespriortosaturationat2kHz. ......................................... 170 9-9Spanwisevariationsintheprimaryvelocitycomponent,ux,forvariousvoltagesatafrequencyof2kHz. ............................... 171 9-10Spanwiseuctuationsinthestreamwisevelocitycomponent, ux,asafunctionofstreamwisepositionforvariousvoltages. .................... 172 9-11Timeaveragedvelocitycontours,uz,formultipleplanesabovethesurfaceofthedielectricforanappliedvoltageof40kVppat2kHz .............. 173 9-12Spanwiseaverageofthestreamwisevelocity, ux,forvariousvoltagesandfrequenciesatdiscretestreamwisepositions. .......................... 174 9-13Timeaveragedvelocityeldpriortoandduringsaturationforanapproximatelyconstantappliedvoltageof44kVppat2kHz. ................... 174 9-14Spanwiseaverageofthestreamwisevelocity, ux,asafunctionofstreamwiseposition. ........................................ 175 9-15Instantaneousvectoreldoverlayinganimageofthedischargeduringsaturationforanappliedvoltageof44kVppat2kHz. .................... 175 9-16Timeaveragedvelocitycontours,ux,formultipleplanesabovethedielectricsurfaceforanappliedvoltageof32kVppat5kHz(lamentaryfeaturespresent). 176 9-17ThetemperaturedistributionalongthesurfaceofaDBDactuatoroperatedat36kVppand2kHzwithincreasingtime. ...................... 178 9-18ThetemperaturealongthespanofaDBDactuatoroperatedat36kVppand2kHzfordiscretestreamwiseplanes. ....................... 178 9-19Averagespanwisesurfacetemperature, T,asafunctionoftimeforvariousvoltagesat2kHz. .................................. 179 9-20Comparisonbetweenexperimentaldataandananalyticalestimationoftheaverage,spanwisesurfacetemperatureasafunctionoftimeatvariousvoltages. 181 9-21ThevisualappearanceoftheplasmaandtemperaturedistributionalongthesurfaceofaDBDactuatoroperatedat44kVppand2kHzforvarioustimes. .. 184 9-22ThevisualappearanceoftheplasmaandtemperaturedistributionalongthesurfaceofaDBDactuatoroperatedat33kVppand5kHzforvarioustimes. .. 185 9-23ThevisualappearanceoftheplasmaandtemperaturedistributionalongthesurfaceofaDBDactuatoroperatedat32kVppand5kHzforvarioustimes. .. 186 9-24Thermalandvisualimagesduringmultipleoperationalperiods(onandoff)oftheactuator(33kVppat5kHz). .......................... 187 14

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9-25ThetemperaturedistributionalongthesurfaceofaDBDactuatoroperatedat44kVppand2kHzwithincreasing(fromlefttoright)time. ............ 188 A-1CoronaMagneticsCMI5525-2highvoltagetransformer. ............. 203 A-2CoronaMagneticsCMI5528-1highvoltagetransformer. ............. 204 A-3CoronaMagneticsCMI5523highvoltagetransformer. .............. 205 B-1Powerconsumptionasafunctionofrelativephaseangleassumingsinusoidalwaveformswithpeaks10kVand20mA. ..................... 208 B-2Equivalentcircuitmodeloftheplasmaactuatorwithassociatedprobes. .... 209 B-3V-Iphaseangleasafunctionoffrequencyforaresistorandcapacitorinparallel.Thesymbolsindicateadiscretemeasurement,whilelinesaretheoretical. ... 212 B-4Inuenceofthehighvoltageprobeontherelativeshiftbetweenthevoltageandcurrentwaveforms. ............................... 213 C-1CircuitcongurationtomeasurepowerconsumedusingQ-V(orLissajous)method. ........................................ 214 C-2ExampleQ-Vcharacteristiccurve.Consumedpowerisdeterminedthroughintegrationoftheenclosedarea. .......................... 215 D-1Schematicofaparallelplatecapacitorusedtodeterminetheunknowndielectricconstantofamaterial. ................................ 217 D-2Circuitcongurationusedtomeasuretheunknowncapacitanceofamadeparallelplatecapacitor. ............................... 219 D-3ExamplevaluesfortherelativedielectricconstantbeforeandafterrejectingoutliersusingthemodiedThompsonTautechnique. .............. 220 15

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AbstractofDissertationPresentedtotheGraduateSchooloftheUniversityofFloridainPartialFulllmentoftheRequirementsfortheDegreeofDoctorofPhilosophyCHARACTERIZATIONOFNOVELANDCONVENTIONALDIELECTRICBARRIERDISCHARGEACTUATORSByRyanJ.DurscherDecember2012Chair:SubrataRoyMajor:MechanicalEngineeringThisdocumentoutlineseffortstoimproveuponthedielectricbarrierdischargeplasmaactuator.Thesedeviceshavebeenstudiedforuseinvariousaerodynamicapplicationsandhavebeenparticularlyeffectiveforfreestreamvelocitiesupto50ms)]TJ /F7 7.97 Tf 6.59 0 Td[(1.Inordertobetrulyapplicableforawiderangeofapplications,however,ademonstrationofsufcientcontrolauthorityathigherspeedsisnecessary.Toaccomplishthis,theplasmaactuatorrequiresasignicantimprovementinoutputperformance,whetherthemetricbemomentumtransferorpeakinducedvelocity.Thefollowingworkpresentseffortstoimprovethesemetrics,inpartthroughthedevelopmentofnewactuatorcongurations.Actuatorsconsistingofmultiplepoweredelectrodesaredemonstratedtoshowasubstantialreductioninthedevice'spowerconsumption,whileanovelelectrodelayoutisexperimentallyshowntoinduceathree-dimensionaloweld.Todatemostactuatorcongurationsusedresultintwo-dimensionalvectorelds.Furthermore,twomaterialswithextremedielectricconstants,relativetothosetypicallyinvestigated,arecharacterized.Thenetthrustoftheactuatorisshowntoimprovedrasticallywhilesimultaneouslyreducingtheactuator'sweightbyusingsilicaaerogel,apreviouslyunexploreddielectricmaterial.Theproblemofthrustsaturationisalsoinvestigatedandcharacterized.Thephysicalmechanismsinvolvedinthislimitingfactorareidentiedandamanipulationoftheeffectisdemonstrated. 16

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CHAPTER1INTRODUCTIONThepushtoimprovetheperformanceofaerodynamicsystemshasledresearcherstodevelopvariouscontrolmechanismstointerfacewiththeow.Thesemechanismscanbroadlybeclassiedaseitherpassive,requiringnoauxiliarypowersource,oractive,inwhichanenergy(mechanicalorelectrical)fromanexternalsourceisimpartedtotheow( Cattafestaetal. 2008 ; Gad-elHak 2001 ).Examplesofpassivecontrolmechanismsincludevarioussurfacemodicationssuchasroughnesselements( Montyetal. 2011 ),dimples( Bearman&Harvey 1993 ),riblets( Leeetal. 2005 ),andothergeometricmodications.Unlikepassivemechanisms,whichcannotsimplybeturnedoffwhennotinuse,activecontrolstrategiesofferanadditionallevelofcontroltosomeextent(generallyspeaking).Inordertointerfacewiththeow,activeowcontrolstrategiesinherentlyinvolvetheuseofactuators( Cattafesta&Sheplak 2011 ).Anoverviewofvariousuidic(zero-netmassux,unsteadyvalves,oscillators,andcombustion),movingsurface(piezoelectricaps,activedimples),andplasmabasedactuatorsisprovidedby Cattafesta&Sheplak ( 2011 ).Ingeneral,eachactuatorhasitsownuniqueadvantagesanddisadvantagesandnooneactuatorisapplicableinallows/situations.Thistextfocusesonaspecicplasmabasedactuatorknownasthedielectricbarrierdischarge(orDBD)plasmaactuator.Initssimplestform,theactuatorconsistsoftwoconductiveelectrodesplacedasymmetricallyonadielectricsubstrate.Providedthevoltagedifferentialbetweenthetwoelectrodeissufcienttoinitiateabreakdownofthesurroundinggas,aweaklyionizedplasmaformsalongthesurface.Thedischargecoupleswiththesurroundingneutrallychargedgas,typicallyair,resultinginaninducedbodyforceontheuidwhichmaybeusedtomanipulateanexternalow( Cattafesta&Sheplak 2011 ; Corkeetal. 2010 2007 ; Milesetal. 2009 ; Moreau 2007 ; Rothetal. 1998 2000 ). 17

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Sinceitwasrstwidelypublicizedinthemid1990's( Rothetal. 1998 ),theDBDactuatorhasreceivedconsiderableattentionwithintheowcontrolcommunity.Theseactuatorshavebeenshowntohaveanearinstantaneousowresponseatawiderangeofoperationalfrequencies.Thedevicesarealsopurelyelectricallydriven,inthat,theyhavenomechanicalcomponents.Thecurrentandprimarylimitationofthesedevices,however,istheirrelativelysmallvelocityoutput.Todatethishasconstrainedtheprimaryuseoftheactuatortolowsubsonicspeeds.Withinthisregimehowever,theDBDactuatorhasbeenappliedtoawiderangeofaerodynamicsurfacesandowsincludingturbinesblades( Jacobetal. 2005 ; Ramakumar&Jacob 2005 ; Rizzetta&Visbal 2007 2008 ),landinggears( Thomasetal. 2005 ),airfoils( Benardetal. 2011a 2010 ; Cho&Shyy 2011 ; Fengetal. 2012 ; Gaitondeetal. 2005 ; Littleetal. 2010 ; Post&Corke 2004 ; Rizzetta&Visbal 2011b ; Roupassovetal. 2006 ),turbulentjets( Labergueetal. 2007 ),atplateboundarylayers( Gibsonetal. 2012 ; Grundmann&Tropea 2009 ; Jacobetal. 2005 ; Rothetal. 2000 ; Schatzman&Thomas 2008 2010 ),cylindervortexshedding( Jukes&Choi 2009 ; Thomasetal. 2008 ),etc.ThecurrentexperimentalandnumericalinvestigationsoutlineeffortsaimedatimprovingtheeffectivenessoftheDBDactuatorinhopesofeventuallyextendingtheirapplicability.ThedevelopmentandcharacterizationofnovelandconventionalDBDactuatorcongurationsarepresented.Actuatorsconsistingofmultiplepoweredelectrodesaredemonstratedtoshowasubstantialreductioninthedevice'spowerconsumption(Chapter 6 ),whileanovelelectrodelayoutisexperimentallyshowntoinduceathree-dimensionaloweld(Chapter 7 ).Todatemostactuatorcongurationsusedresultintwo-dimensionalvectorelds,thoughnumericalresultshaveindicatedathree-dimensionalmixingofthelocalfreestreamuidcanhavesignicantbenets.Furthermore,twomaterialswithextremedielectricconstants,relativetothosetypicallyinvestigated,arecharacterized(Chapter 8 ).Thenetthrustoftheactuatorisshowntoimprovedrasticallywhilesimultaneouslyreducingtheactuator'sweightbyusingaerogel, 18

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apreviouslyunexploreddielectricmaterial.Theproblemofthrust`saturation'isalsoexploredandcharacterized(Chapter 9 ).Thephysicalmechanismsinvolvedinthislimitingfactorareidentiedandamanipulationoftheeffectisdemonstrated.Todate,themajorityoftheseresultshaveinfullorpart,beenpublishedorpresented( Durscher&Roy 2012a b ; Durscheretal. 2012 ; Durscher&Roy 2010 2011a b c 2012c ).Theremainingtextisorganizedinthefollowingmanner.First,adiscussiononbasicplasmaprinciples,gasdischarges,anddielectricbarrierdischargefundamentalsispresented(Chapter 2 ).Thisisthenfollowedbyareviewofthedielectricbarrierdischargeplasmaactuatorintermsofcharacterization,numericalmodeling,andaerodynamicapplications(Chapter 3 ).Fromthereadetaileddescriptionoftheexperimental(Chapter 4 )andnumericalmethods(Chapter 5 )implementedinanefforttocharacterizeandquantifythedevelopmentofthenewandconventionalactuatorcongurationsisgiven.Theresultsfromtheseinvestigationsarethenpresented(Chapters 6 7 8 ,and 9 )followedbyasummaryandrecommendationsforfuturework(Chapter 10 ). 19

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CHAPTER2PLASMAS,GASDISCHARGES,ANDDIELECTRICBARRIERDISCHARGESTheword`plasma'itselfwasrstusedbyCzechmedicalscientistJanEvangelistaPurkynetodescribetheliquidleftbehindhavingremovedvarioussuspended,corpusclesmaterialfromblood( Pinheiro 2007 ).Nearlyhalfacenturylatertheterm`plasma'wasrecoinedby Langmuir ( 1928 )todescribeaquasi-neutral(i.e.nonetcharge)regioninanionizedgascontainingions,electrons,andneutrals.Thisdenitionhasevolvedtodescribeaquasi-neutralionizedgaswhichexhibitscollectivebehavior( Chen 1984 ).Itisinthiscontextthattheterm`plasma'isusedandofinterestintheremainderofthistext.Oftendescribedastheso-calledfourthstateofmatter,plasmasaresaidtomakeup99%ofourknownuniverse.However,despiteitscelestialabundance,oureverydayexperiencewithnaturallyoccurring,terrestrialplasmasarelimited(withtheexceptionoftheoccasionallightningstrike).Intruth,man-madeplasmasaremuchmorecommoninoureverydaylivesthanmostrealize.Inducedplasmassuchasthosegeneratedinauorescentlightbulbilluminateourhomesandofcesthroughouttheyear.Thefollowingsectionsoutlinesomebasicplasmaprinciples,followedbyageneraldiscussionofaparticulartypeofplasmaknownasagasdischarge.Thephysicsofadielectricbarrierdischarge,asubsetofagasdischarge,isthenpresented. 2.1PlasmaBasicsandCharacterizationPlasmasaretypicallycharacterizedorclassiedbytwoparameters:1)electronnumberdensity,ne(m)]TJ /F7 7.97 Tf 6.58 0 Td[(3)and2)electrontemperature,Te(K).Atamicroscopicscaletemperatureisameasureoftheparticle'smotionorkineticenergy.Assuch,theelectrontemperatureisoftengivenintermsofelectronvoltswhichmayberelatedtotemperaturethough,1eV kB=1.602176510)]TJ /F7 7.97 Tf 6.58 0 Td[(19J 1.380650310)]TJ /F7 7.97 Tf 6.59 0 Td[(23JK)]TJ /F7 7.97 Tf 6.58 0 Td[(1=11604.506K (2) 20

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Table2-1. Typicalparametersfornaturallyandinducedplasmas.Adaptedfrom Goldston&Rutherford ( 1995 ). Particledensity(m)]TJ /F7 7.97 Tf 6.58 0 Td[(3)Electrontemperature(eV)Characteristiclengthscale(m) Interstellargas10611016Solarwind107101010VanAllanbelt109102106Earth'sionosphere101110)]TJ /F7 7.97 Tf 6.59 0 Td[(1105Solarcorona1013102108Gasdischarges1018210)]TJ /F7 7.97 Tf 6.58 0 Td[(2Processplasmas101810210)]TJ /F7 7.97 Tf 6.58 0 Td[(1Fusionexperiments1019-1020103-104101Fusionreactor1020104102 wherekBisBoltzmann'sconstant.Examplevaluesforelectronnumberdensityandelectrontemperatureforsomenaturallyoccurringandman-madeplasmas,takenfrom Goldston&Rutherford ( 1995 ),areprovidedinTable 2-1 .AlsoprovidedinTable 2-1 arereferencelengthscalesforvariousplasmas.Bydenitiontheplasmamustexhibitquasi-neutrality(nine)macroscopically.Heresubscripts`i'and`e'correspondtoionsandelectrons,respectively.Despitetheoverallneutralityoftheplasma,itispossibleforsignicantchargeseparationtooccur.ThelengthscaleoverwhichthisdisparitycanoccurisdenotedastheDebyelength( Lieberman&Lichtenberg 2005 ).TheDebyelengthinavacuumisgivenby( Goldston&Rutherford 1995 ; Hippleretal. 2001 ),D=s 0kB nee2(1 Te+Z Ti) (2)where0=8.85418782x1012Fm)]TJ /F7 7.97 Tf 6.59 0 Td[(1isthepermittivityoffreespaceande=1.602176565x10)]TJ /F7 7.97 Tf 6.58 0 Td[(19Cistheelementarycharge,andTiistheiontemperature.InderivingEquation 2 ,ionsareassumedtohaveachargeZeandtheelectronnumberdensityisproportionaltotheionnumberdensity(ne=Zni)farfromtheboundaries/electrode( Goldston&Rutherford 1995 ).Ingeneraltheiontermisnotincludedinthedenitionof 21

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theDebyelength.ThisreducestheDebyelengthto,D=r 0kBTe nee2 (2)forelectrons.TheDebyelengthisalsoameasureofthescaleinwhichtheplasmahastheabilitytoshieldoutelectricpotentials,formallyreferredtoasDebyeshielding( Chen 1984 ).Inawallboundedplasma,thistendencytoblockexternalelectricpotentialsgiveswaytoregionsofnon-neutralitybetweenthebulkplasmaandthewallknowasthe`sheath'( Lieberman&Lichtenberg 2005 ).Withinthesheath,largechargeseparationscanoccur(e.gforapositivelychargedwall,nine).AnimportantcharacteristicdeningaplasmaisthatitscharacteristicorreferencelengthscalemustbemuchlargerthantheDebyelength(LD)( Chen 1984 ).Similarly,asufcientnumberofparticlesmustbepresentwithinaDebyesphere,ND,suchthatNDo1fortheplasmatoexhibitcollectivebehaviorandstatisticaltreatmentoftheDebyeshieldingtobevalid( Chen 1984 ; Goldston&Rutherford 1995 ).ADebyesphereisdenedbyEquation 2 .ND=ne4 33D (2)AsshowninTable 2-1 ,theelectrontemperatureofplasmascanspanseveralordersofmagnituderangingfrom10)]TJ /F7 7.97 Tf 6.58 0 Td[(1to104eV(1,160-11.60107K).Thermodynamicequilibriumrequiresthatthetemperatureofallelectrons,ions,andneutralsbeequal(Te=Ti=Tn)withintheplasma.Thiswouldimplyanefcientenergyexchangebetweenallspecies( Bogaertsetal. 2002 ).Thiscanreadilyoccurinhightemperatureplasmas(e.g.fusionplasmas),butisrarelythecaseinlowtemperatureplasmassuchasinterstellargasesorgasdischarges( Bogaertsetal. 2002 ; Lieberman&Lichtenberg 2005 ).Totheopposition,mostplasmasaresaidtobeinnon-thermodynamicequilibrium,inwhichthetemperatureofheavierionsandtheneutralgasareapproximatelyequal(TeTiTn).Insomeplasmas,however,suchasgasdischarges,itispossibletohavelocalthermodynamicequilibrium( Bogaertsetal. 2002 ).Thisimpliesthermodynamic 22

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equilibriumisachievedinlocalizedareaswithintheplasma.Foragasdischargethedistinctionbetweennon-andlocalequilibriumisgenerallydependentonthepressureintheplasma( Bogaertsetal. 2002 ).Anotherimportantdeningquantityofaplasmaisthedegreeofionization,,whichisgivenby,=ni ni+nn (2)Forafullyionizedplasmathisratioapproachesunity,whileforratiosslightlylessthanonetheplasmaisconsideredpartiallyionized.Similarly,forvaluesmuchlessthanone(1),theplasmaisconsideredweaklyionized( Goldston&Rutherford 1995 ; Lieberman&Lichtenberg 2005 ).Asdescribedby Goldston&Rutherford ( 1995 ),thedegreeofionizationwilldictatethecollisionalinteractionbetweenchargedandneutralspecies.Forplasmaswithdegreesofionizationaslowas10)]TJ /F7 7.97 Tf 6.59 0 Td[(3,collisionsbetweenchargedparticlestendtodominateovercollisionsbetweenchargedandneutralparticlesasaresultofCoulombinteractions( Goldston&Rutherford 1995 ).However,inweaklyionizedplasmas(e.g.ionospheric,processplasma,andmostlow-currentgasdischarges)collisionsbetweenchargedandneutralparticleswilltendtodominate( Goldston&Rutherford 1995 ; Raizer 1991 ).Consideringonlyelasticcollisions,inaweaklyionizedplasmaanelectron-neutralcollisionwillalteronlytheelectron'smomentumduetothelargedisparityinsizebetweenthetwospecies( Bellan 2008 ).Converselyinanion-neutralcollision,bothmomentumandenergy(aswellasachargeexchange,alternatively)maybetransfered( Lieberman&Lichtenberg 2005 ).Sinceionshaveapproximatelythesamemassasneutrals,thisenergyexchangeoftenresultsintheions'temperatureapproachingthatoftheneutralstemperature(Ti=Tn)inaweaklyionizedplasma( Bellan 2008 ).Furthermore,dependingontheneutralgas(whetheratomisticormolecular),inelasticprocessessuchasexcitation,ionization, 23

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dissociation,dissociativerecombination,attachment,vibrationexcitation,rotationalexcitation,etc.mayalsooccur( Lieberman&Lichtenberg 2005 ).Thetimebetweencollisionsestablishesanotherimportantcharacteristicoftheplasma.Ingeneral,thecollisionfrequencyisgivenby,=nv (2)whereisthecollisionalcrosssectionofthe`target'particles,nisthenumberdensityofthe`target'particles,andvisthe`impacting'particle'svelocity.Thecollisionalcrosssectionisdependentontheparticlesinvolved(ion-electron,ion-ion,electron-electron)andscatteringprocess(e.g.Coulombcollisions,polarizationscattering,etc.)( Lieberman&Lichtenberg 2005 ).Anexampleformulaforanelectron-electroncollisionfrequencyasderivedby Bellan ( 2008 )is,ee=410)]TJ /F7 7.97 Tf 6.58 0 Td[(12nln T3=2e (2)wherelnistheCoulomblogarithm(typicallyrangesfrom8-25,see Huba ( 2002 ))andTeistheelectrontemperatureinelectronvolts.InreferencetoTable 2-1 ,eecanrangefrom10)]TJ /F7 7.97 Tf 6.58 0 Td[(5to104s)]TJ /F7 7.97 Tf 6.59 0 Td[(1forsolarwindandfusionplasmas,respectively( Bellan 2008 ).Additionalformalurayforion-ionandelectron-ioncollisionfrequenciesmaybefoundin Chen ( 1984 ).Tothispointthebasicconceptsbehindplasmashavebeenpresented.Readersarereferredtothefollowingreferencesforamorecompletediscussionofthetopic: Bellan ( 2008 ); Bogaertsetal. ( 2002 ); Chen ( 1984 ); Goldston&Rutherford ( 1995 ); Lieberman&Lichtenberg ( 2005 );and Raizer ( 1991 ).Asoutlinedabove,plasmarelatedresearchisabroadscienticeldthatrangesfromthestudyofinterstellarmediumtothecommonuorescentlightbulb.Withinthisbroadrangeamultitudeoftemporalandspatialscalesarespanned.Theremainderofthetext,however,isfocusedoninducedgasdischarges. 24

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Inparticularthedielectricbarrierdischarge(DBD)anditsapplicationsinowcontrolareinvestigated. 2.2GasDischargesThetermgasdischargeisusedtodescribetheowofanelectriccurrentthroughanionizedgasortheactofionizingagasbyanappliedelectriceld( Raizer 1991 ).ThetreatmentofgasdischargesinliteraturetypicallybeginswiththeapplicationofaDCvoltageacrossagasgap,howeverACvoltagesmaybeusedtodrivethedischarge.Inaninstantaneousrespect,anACdrivendischargeisDC-like.Althoughthefundamentalbreakdowncharacteristicsremainthesame,theplasmastructurechanges(e.g.andmodesofradiofrequencycapacitivelycoupleddischarges)whenusingalternatingorpulsedvoltagesources( Fridman 2008 ; Howatson 1976 ; Raizer 1991 ).ADCgasdischargemaybeclassiedintothreemaintypesbasedondeliveredcurrent:darkdischarge,glowdischarge,andarcdischarge.Figure 2-1 outlinestheseregimesasafunctionofvoltageandcurrent.Adarkdischargeischaracterizedbyverylittlelightemission.Thedischargeinthisregimeissaidtobeselfsustaininginwhichforaconstantpotential(andelectriceld)theelectronnumberdensitybeginstomultipleinwhatisreferredtoasan`electronavalanche'( Raizer 1991 ).Theinitialseedelectronsmustbeprovidedbyexternalagentssuchascosmicraysand/orphoto-ionization( Howatson 1976 ).Asthecurrentbeginstorise,abreakdownofthegasensues,duringwhichthegasbecomesluminous.Thebreakdownvoltageofthegasisafunctionoftheworkingpressure(p)anddischargegap(d)accordingtoPaschen'slaw.Foragivengasthebreakdownvoltage,VB,isgivenbyVB=B(pd) ln(pd)+C,C=lnA ln(1=+1) (2)whereAandBaregasdependentconstantsandisthesecondaryelectroncoefcientforthecathode.ExamplevaluesforAandBareprovidedinTable 2-2 forselectgases.Assumingasecondaryelectroncoefcientof10)]TJ /F7 7.97 Tf 6.58 0 Td[(1,examplePaschencurvesforthe 25

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Figure2-1. VoltageandcurrentcharacteristicforaDCdischargeinalowpressuredischargetube.Takenfrom Roth ( 1995 ). Table2-2. Coefcients,AandB,usedtocalculatethebreakdownvoltageofagivengasbasedonPaschen'sLaw.Adaptedfrom Fridman ( 2008 ). GasA(1 cmTorr)B(V cmTorr) CO220466Air15365N210310H25130Ne4100He334 gasesfoundinTable 2-2 arepresentinFigure 2-2 .Forlargergaps,thebreakdownvoltagepredictedbyEquation 2 becomeslesssensitivetothesecondaryelectroncoefcientofthecathode( Fridman 2008 ).Furthermore,Paschen'slawhasbeenreportedtofailasthegapdecreasesbelow5m( Torres&Dhariwal 1999 ).Oncebreakdownoccurs,theplasmaissaidtoentertheglowdischargeregime.Plasmasinthisregimeareprimarilysustainedthroughsecondaryelectronemissionatthecathode( Howatson 1976 ).Thedielectricbarrierdischarge,discussedinSection 2.3 ,operatesinthisregime.Ifthecurrentisallowedtoincrease,thedischarge 26

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Figure2-2. ExamplePaschencurvesforvariousgases.ValuesarecalculatedfromEquation 2 usingthecoefcientsinTable 2-2 eventuallytransitionstoanarcdischarge,duringwhichthevoltagedropssignicantly.Thehighcurrentspresentduringanarcdischargeareoftenaccompaniedbyhightemperaturesatthecathode( Raizer 1991 ).Readersarereferredtothefollowingreferencesforamorein-depthdiscussionongasdischarges: Conrads&Schmidt ( 2000 ); Fridman ( 2008 ); Howatson ( 1976 );and Raizer ( 1991 ). 2.3DielectricBarrierDischargeClassicationIngeneral,thedielectricbarrierdischarge(DBD)occursuponthegenerationofasufcientlyhighelectriceldbetweentwoconductingelectrodesseparatedbyoneormoredielectric(non-conducting/insulating)layers.SinceaDCcurrentcannotpassthroughadielectric,analternatingvoltagemustbeused.Thedischargecaneitheroccuronthesurfaceofthebarrierorinthegasgapbetweenthedielectricandtheelectrode/dielectricdependingontheparticulararrangement.Todistinguishbetweenthetwo,theformeristypicallyreferredtoasasurfacedischargewiththelatterknownasavolumetricdischarge.ExamplecongurationsforsurfacedischargesareshowninFigures 2-3 A-C,whileFigures 2-3 D,Erepresentvolumetricarrangements. 27

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Figure2-3. Exampleelectrode/barriercongurationsusedtogenerateadielectricbarrierdischarge.ImagesA,B,C)correspondtosurfacedischarges,whileD,E)arevolumetricdischarges. ThepresenceofadielectricinaDBDlimitstheaveragecurrentdensityallowingthedischargetooperateatelevatedpressureswithouttransitioningtoanarcdischarge( Kogelschatz 2003 ).TypicalDBDoperatingpressuresrangefrom0.1to10bar(0.1to10atm)( Conrads&Schmidt 2000 ).Atatmosphericpressuresthedielectricbarrierdischargeisclassiedasanon-equilibriumgasdischarge( Kogelschatz 2003 ),suchthatTeTiTn.Furthermore,atatmosphericpressures,typicalvaluesofcharacteristicplasmaparametersforadielectricbarrierdischargearene=1020to1021m)]TJ /F7 7.97 Tf 6.59 0 Td[(3andTe=2to10eV( Conrads&Schmidt 2000 ; Kogelschatz 2003 ).Bycomparisontheneutralnumberdensityofdryairis2.51025m)]TJ /F7 7.97 Tf 6.59 0 Td[(3,whichbasedonEquation 2 ,givesadegreeofionizationof410)]TJ /F7 7.97 Tf 6.59 0 Td[(6to410)]TJ /F7 7.97 Tf 6.59 0 Td[(5.ThisclassiestheatmosphericDBDasaweaklyionizedplasma(Section 2.1 )andfurtherjustiesthenon-thermodynamicequilibriumassumption.Thedielectricbarrierdischargehasalonghistorystemmingbackto1857,inwhich Siemens ( 1857 )iscreditedwithitsdiscovery.Inhisexperiments Siemens ( 1857 )appliedanoscillatingelectriceldbetweentwocoaxialglasstubesseparatedby 28

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asmallannulargaptogenerateozone.Forthelast155years,researchersfromaroundtheglobehaveinvestigatedthephysicssurroundingtheDBD,aswellasdevelopapplicationswhichutilizethedevice.AthoroughreviewofthehistoryofDBDispresentedby Kogelschatz ( 2003 ).Although,theDBDwasoriginallyusedasameansofozonegeneration( Siemens 1857 ),ithassincefounduseinnumerousindustrialapplicationssuchasbiomedicalsterilization( Fridmanetal. 2006 2007 ; Leietal. 2004 ),surfacemodication( Cui&Brown 2002 ; Geyteretal. 2006 ),pollutioncontrol( Chang&Lee 1995 ; Hackam&Aklyama 2000 ),CO2( Yagi&Kuzumoto 1995 )andexcimer( Eliasson&Kogelschatz 1988 ; Mildren&Carman 2001 )laserexcitation,andplasmadisplaypanels( Boeuf 2003 ; Rauf&Kushner 1999 ; Whang&Kim 2005 ).Alongwiththeaforementionedapplications,thedielectricbarrierdischargemayalsobeusedasauidicactuatorforowcontrol( Cattafesta&Sheplak 2011 ; Corkeetal. 2010 2007 ; Milesetal. 2009 ; Moreau 2007 ; Rothetal. 1998 2000 ). 2.3.1VolumetricDielectricBarrierDischargesAtatmosphericpressuresthedischargeinavolumetriccongurationsuchas 2-3 D,Eistypicallycomprisedoflamentarymicro-dischargeswhichformdiscretechannelsstemmingfromtheelectrodetothedielectricsurface( Gibalov&Pietsch 2000 ; Kogelschatz 2003 ; Xu 2001 ).Oncethemicro-dischargereachesthesurface,chargeisdeposited.Theaccumulatedchargeinturnreducesthelocalelectriceldandextinguishesthemicro-discharge,creatingaself-limitingeffect.Awayfromthedischarge,however,theundisturbedelectriceldisstillhigh,whichallowsforthegenerationofadditionalmicro-discharges.Inturn,theself-limitingbehaviorofasinglemicro-dischargeallowsforanaturalexpansionofthedischargeovertheentiresurface.Diffuseorglow(see Kogelschatz ( 2002 ))dischargesmayalsobeattainedatatmosphericpressures,thoughthistypicallyinvolvesspecialelectrodelayouts( Okazakietal. 1993 )and/orusingheliumoramixtureofastheworkinggas( Kanazawa 29

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etal. 1988 ; Massinesetal. 1998 ; Yokoyamaetal. 1990 ).Aglowdischargeiseasilyattainablebydecreasingtheworkingpressureaswell( Kogelschatz 2003 ). 2.3.2SurfaceDielectricBarrierDischargesTheDBDactuatoroperatesasasurfacemodedischargesuchasshowninFigure 2-3 A,buttheprinciplesofthedischargeoutlinedinSection 2.3.1 foravolumetriccongurationremainthesame.However,unlikeinavolumetricdischarge,nodistinctgasgapexistsinasurfacearrangement.Assuch,chargetransferoccursinathinlayeronthesurfaceofthedielectricastheplasmaexpandsawayfromtheelectrode( Gibalov&Pietsch 2000 ).Theplasmavolumeforasurfacedischarge,ingeneral,isfairlysmallwhenoperatedatatmosphericpressures.Typicalestimateddimensionsofthevolumeconsistofa1mmthickness(fromthesurface)extending5to20mmalongthesurface(inthestreamwisedirection).Theelectrodelength(orspan)can,ofcourse,vary.Thesmallplasmavolumeresultsinadverseconditionsforconventionalplasmadiagnostictechniques,suchasLangmuirprobes,makingcharacterizationdifcult.Theproblemisexacerbatedbythetransient,non-equilibriumdynamicsoftheplasma.Furthermore,numericalmodelingofasurfacedischargeisformidableduetotheinherenttwo-dimensionalnatureoftheconguration( Boeufetal. 2009 ; Boeuf&Pitchford 2005 ; Royetal. 2006a ).Theremainderofthistextisfocusedontheeffortstocharacterizethedielectricbarrierdischargeplasmaactuatoranditsapplicationsinowcontrol. 30

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CHAPTER3DIELECTRICBARRIERDISCHARGEACTUATORSThemostreadilyinvestigatedcongurationofthedielectricbarrieractuatorisshowninFigure 2-3 A.Insubsequentchapters(Chapters 6 7 8 ,and 9 )additionaldesignconceptswillbeexplored,buttheunderlyinggeneralitieswillremainthesame.Initsbasicform,theactuatoriscomprisedoftwothinelectrodesplacedasymmetricallyonasingledielectricsubstrate.Theexposedelectrodeispoweredwitharadiofrequency(0.5-50kHz),highvoltagewaveform(5-80kVpp),whilethebottomelectrodeisgroundedandusuallyencapsulatedtopreventadischargefromoccurringonthelowersurface.Thehighpotentialdifferencebetweenthetwoelectrodesinitiatesabreakdownofthesurroundinggascreatingaweaklyionizedplasmainthevicinityoftheexposedelectrode.Aswillbediscussedinmoredetailinthefollowingsections,thesurfacedischargecoupleswiththesurroundingneutrallychargedgas(typicallyair)resultinginaninducedbodyforceontheuid.Explorationoftheaerodynamicbenetsfromtheseactuatorswasrstpublicizedinthemid1990sby Rothetal. ( 1998 ).Scarceearlierdocumentation(Figure 3-1 )maybefoundinliterature(e.g. Mhitaryanetal. ( 1964 )),thoughtheseworksareoftenuntranslatedand/ornotreadilyavailable.Similarly,reportsusingacoronadischargeorion/electricwind( El-Khabiry&Colver 1997 ; Okress 1969 ; Rosendaleetal. 1988 )asowcontroldevicesmayalsobefoundthatpredate Rothetal. ( 1998 ).Onesuchexampleisapatentby Okress ( 1969 ),whichenvisionsanaerodynamicvehiclepropelledbythethrustproducedfromacoronadischarge.Acoronadischargeissimilartothedielectricbarrierdischarge,though,nodielectricisnecessary.Assuch,aDCvoltagemaybeused.Interestingly,inhispatent, Okress ( 1969 )describeshowthethrustmaybeincreasedusingshortdurationpulses(ontheorderofnanoseconds)asopposedtoaDCvoltage.Thisideaofusingnanosecondpulseshasgainedpopularity( Opaitsetal. 2009 ; Roupassovetal. 2009 ; Starikovskiietal. 2009 )foruseintheDBD 31

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Figure3-1. ExperimentalsetupforDBDactuationonanairfoil.Takenfrom Mhitaryanetal. ( 1964 )(inRussian). arrangementandwillbediscussedingreaterdetailinlatersections.Similarly,coronadischargesandtheiraerodynamicapplicationsarestillanareaofactiveresearch( El-Khabiry&Colver 1997 ; Labergueetal. 2005 ; Mestirietal. 2010 ).Despitepotentialpre-existingwork, Rothetal. ( 1998 )iscreditedherewithlaunchingtheconceptofDBDactuationintothemainstreamowcontrolcommunity.Itisherethatwewillbeginourdiscussionofthedielectricbarrierdischargeactuator. 3.1CharacteristicsoftheDBDActuator 3.1.1ElectricalandVisualCharacteristicsRepresentativevoltageandcurrenttracesresultingfromaDBDactuatoraregiveninFigure 3-2 .Thecurrentwaveform,fromFigure 3-2 ,maybedecomposedintodisplacementandconductivecurrents,withtheprimarybeingthelarge(sinusoidal)displacementcurrent.Thisindicatesalargelycapacitiveloadasdeterminedbythe90ophaseshiftbetweenthewaveforms.Superimposedonthedisplacementcurrentistheconductivecurrentwhichmanifestsitselfasshort-lived(orderofnanoseconds)spikes.Thesespikesareindicativeofthemicro-dischargespreviouslydiscussedin 32

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Figure3-2. Representativevoltageandcurrenttracesforadielectricbarrierdischargeplasmaactuator. Section 2.3 .AsshowninFigure 3-2 ,thedischargeoccurontherisingandfallingslopesofthevoltagewaveform.However,themagnitudeandregularitybetweenthetwooccurrencesisclearlynotthesame.Thisqualitativelyprovidesevidencethattwodistinctdischargeregimesexistduringasingleperiod,withtheeventsbeingdependentonthepolarityoftheexposedelectrode. Enloeetal. ( 2004a )usedaphotomultipliertube(PMT)totemporallyresolvetheradiationemittedbytheactuatoroveracompleteperiodoftheinputvoltage.Themeasuredradiationwasfoundtobedirectlycorrelatedtothedischargespikes(Figure 3-3 ).Asindicatedbythecurrent,thelightemissionconrmedthattheplasmaisquenchedtwicewithinanappliedperiod.Theemittedradiationwasalsofoundtobedistinctivelydifferentbetweentherisingandfallingslopesofthevoltagewaveform.Arelativelyuniformlightemissionwasobservedforanegativevoltageslope,while 33

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Figure3-3. CurrenttraceandcorrespondinglightemissionofaDBDactuator.A)GeneralandB)detailedviewsareprovided.Takenfrom Enloeetal. ( 2004a ). theemissionwasmoreirregularforapositivevoltageslope.Thedifferentdischargeregimesbecomemoreapparentusinghigh-speedphotography(Figure 3-4 ).Distinctdischargechannelsareobservedwhentheelectrodeispositivelycharged,whereasamorediffuseglow-likedischargeisseenduringthenegativehalfcycle.Interestingly,thesebasicdischargepatternsonthedielectricsurfaceareindependentoftheelectrodearrangement,whetheritbeasurfaceorvolumetricconguration( Gibalov&Pietsch 2000 ).Tothenakedeye,however,thedischargeappearsasadiffuseglow-likestate.Asaresultofthepolaritydependentdischargeregimes,variousterminologyhasbeenadoptedwithintheDBDactuatorcommunitytodistinguishbetweentherisingandfallingslopesoftheappliedvoltagewaveform.Toavoidlaterconfusion,itispertinenttodiscernandgeneralizethesuggestedterms.Thetermsforward,forward-stoke( Enloeetal. 2008b 2006 2004a b ; Kimetal. 2007 ),andpositivelygoing( Enloeetal. 2008b )areoftenusedintheliteraturetodescribetherisingedgeoftheinputvoltage.Similarly,backward,backward-stoke( Enloeetal. 2008b 2006 2004a b ; Kimetal. 2007 ),andnegativelygoing( Enloeetal. 2008b )describethefallingedge.Thenegativehalfcycleandpositivehalfcycle( Staneldetal. 2009 )havealsobeenusedtodenotethepolarityoftheappliedvoltage.Itisthisterminologythatisadoptedhereandwillbeusedintheremainderofthistext. 34

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Figure3-4. Highspeedcameraimagesofadielectricbarrierdischarge.ImageA)correspondstoaDBDactuator(Figure 2-3 A),whileB)acoplanarconguration(Figure 2-3 C).Twodistinctplasmadischargesareobserveddependingonthepolarityoftheelectrode.ImageA)istakenfrom Enloeetal. ( 2008b ),whileB)isfrom Gibalov&Pietsch ( 2004a b ); Hulka&Pietsch ( 2002 ) Theplasmasweepvelocity,orthespeedinwhichtheplasmapropagatesalongthedielectricsurfaceonceignited,wasmeasuredby Enloeetal. ( 2004a )andfoundtobeapproximatelyequalforthepositiveandnegativehalfcycles.Thevelocitywasfoundtobevoltagedependent(atconstantfrequency)andontheorderof80ms)]TJ /F7 7.97 Tf 6.59 0 Td[(1( Enloeetal. 2004a ).Similarresultswereobtainedby Orlovetal. ( 2007 2006 )andusedasvericationofalumpedelementmodel(seeSection 3.2.2 ).Aspointedoutby Staneld ( 2009 ),the(voltage)polarityindependencedoesnotagreethestructuraldifferenceseenbetweenthetwoplasmaregimes.Thediffuseappearanceofthedischargeduringthenegativehalfcycleisreminiscentofaglow-likedischargewhereasthepositivehalfcycleseemstobecomposedofcathode-directedstreamers.Cathode-directedstreamersarecharacterizedasthin,ionizedplasmachannels.Thestreamersaresustainedthroughphotoionizationduetothehighlynonuniformlocalelectriceldinthepositivelychargedstreamerhead.Thevelocityofapropagatingstreamerhasbeenestimatedasbeingontheorderof106ms)]TJ /F7 7.97 Tf 6.58 0 Td[(1( Pancheshnyietal. 2005 2001 ; Pancheshnyi&Starikovskii 35

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2003 ).Thedissimilarityinresultsbetweenthetwospeedsforthepositivehalfcycleislikelyduetothelargecollectionvolumeusedby Enloeetal. ( 2004a );theresultsobtainedwouldbespatiallyaveragedquantities,asopposedtoindividualdischargeeventswerebeingcaptured.AspreviouslydiscussedinSection 2.3.2 ,astheplasmaexpandsacrossthesurfaceofthedielectricchargeisdeposited.Thedepositedcharge,inturn,raisesthepotentialonthesurfacereducingthelocalelectriceld.Interestingly,thisriseinthesurfacepotentialhasbeenfoundtonotonlyoccurnearthedischargevolumeitself,butmuchfurtherdownstream.Thechargehasshowntoremainonthesurface(ontheorderofminutes)evenaftertheactuatoristurnedoff( Enloeetal. 2008a ).Anexamplestreamwisesurfacepotentialdistribution,asmeasuredby Opaitsetal. ( 2008b ),isshowninFigure 3-5 .Relativetotheappliedpeakvoltage,5kV(10kVpp),themaximumaveragesurfacepotentialmeasured(+1.5kV)ispositiveandisquitecomparableinmagnitude.Similarresultshavebeenshownby Gibalov&Pietsch ( 2000 ). Enloeetal. ( 2008a )measuredthetemporalcharacteristicsofthesurfacepotentialandfoundthatthesurfaceaccruesthenetpositivechargewithintherstperiodoftheplasmadischarge.Thepresenceofaconstantbiasinthesurfacepotentialcreatesanasymmetryintheelectriceldnearthesurfacebetweenthepositiveandnegativehalfcycles.Asmeasuredby Enloeetal. ( 2008a ),themagnitudeofthemaximumeldis50%largerduringthenegativehalfcycle.Usingthesametechnique, Fontetal. ( 2010 )investigatedtheinuenceofoxygenonthetemporalcharacteristicsofthesurfacecharging.Aswithpreviousstudies,alarge(kV's)positivebiaswasobservedattypicalatmosphericlevelsofoxygen(20%).Intheabsenceofoxygen(0%),however,asmallnegativebiasisprevalentonthesurfacefardownstreamoftheexposedelectrodebutalternatesbetweenpositiveandnegativevoltagesneartheelectrode.Unliketheaforementionedexperimentswhichusedprobestomeasureorinferthesurfacepotential,arecentreportby Takeuchietal. ( 2011 )takesadvantage 36

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Figure3-5. SurfacepotentialdistributioninaDBDactuator(10kVppat3kHz).Takenfrom Opaitsetal. ( 2008b ). ofanelectro-opticeffectknownasPockelseffecttomeasurethesurfacechargeaccumulation.Inthepresenceofanelectriceldcertaincrystals,suchasBismuthSiliconOxide(BSO),becomebirefringent;meaningasinglelightraymaybesplitintotwounequallyreectedortransmittedwavesbasedontheanisotropicrefractiveindexofthematerial.Thebirefringenceisdirectlyproportionaltotheappliedelectriceld.Pockelseffecthasbeenpreviouslyusedwithsuccessforvariouslowpressure,volumetricdielectricbarrierdischarges( Jeongetal. 2005 ; Sakurai 2007 ; Stollenwerketal. 2007 ).Intheirexperiments, Takeuchietal. ( 2011 )embeddedasmallBSOcrystalintoaDBDactuatorconstructedoutofalargerdielectricsubstrate(glass).Theexperimentalresultsindicatedthattherewasnobiasinthesurfacechargeaccumulationandthechargesimplyfollowedtheappliedvoltagewithasmallphaselag.Thedifferenceintheseresultsandthosepreviouslydiscussedisnoteasilyexplained.However,asoutlinedinSection 3.1.2 ,theexistenceofachargebiasdoesaidinexplainingthrustproductiontrendsobservedinparametricstudies,aswellasthetemporalthrustcharacteristics. 37

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Beforepreceding,abriefdiscussiononsomeattemptstolimitorsuppressasurfacechargeaccumulationiswarranted. Opaitsetal. ( 2008a )demonstratedthatchargeaccumulationdecreasedtheeffectiveelectriceldinaplasmageneratedbyrepetitivenanosecondpulseswithDCandlowfrequency,sinusoidalbiases.Itwasfoundthattheaccumulatedsurfacechargecouldberemovedbyswitchingthebiaspolarityperiodically,requiringspecializedequipment,orbysimplyleavingaportionofthelowerelectrodeunexposedbythedielectricdownstream(withtheformerbeingmoreeffective).Asamodicationtothelaterapproach, Opaitsetal. ( 2009 )proposedtheuseofaconductivedielectricinordertodepletethesurfacechargebetweenthepulses.Intheirexperimentstwomaterialswereconsideredasslightlyconductivedielectrics,zincoxideandlinen-basedphenolic.Neithermaterialwaswidelysuccessfulwiththerstbeingtooconductive,whilethesecondtooresistive.However,itdoesopenuptheideaoftailoringthedielectricbasedonidentiedtrends.Followingasimilarlogic, Guoetal. ( 2009 2010 )placedathinconductivelayerbetweenathirddownstreamelectrodeandtheprimaryexposedelectrode.Bothelectrodeswereconnectedtoahighvoltagesource,though,adiodewasplacedinlinebetweenthevoltagesupplyandthethirddownstreamelectrode.Thepresenceofthediodedictatesthatcurrent(orcharge)canonlyowinonedirection.Thisdesignwouldpresumablyhelpmitigatesurfacechangeaccumulationbyallowingittobleedoffthroughthedownstreamelectrode.Forasinusoidalappliedvoltage,a70%improvementinthrustproductionwasreported Guoetal. ( 2009 2010 ). 3.1.2ThrustGenerationInthepresenceoftheplasma,abodyforceisimposedonthesurroundinguid.Inthecontextofthistexttheterm`force'willstrictlyreferencethisplasmainducedbodyforce,whiletheterm`thrust'willrepresentthe`neteffectoftheplasma'whichincludesotheruidicforcessuchasshear.ThedistinguishingcharacteristicbetweenthetwotermsisfurtheraddressedinSection 4.4.2 .Ingeneral,itissimplertomeasurethe 38

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actuator'sthrust.Aswillbepresentedlaterinthesection,numerousparametricstudieshaveusedtheactuator'sthrustasametricforoptimizationanddesignimprovements.Beforethis,however,adiscussiononthetemporalcharacteristicsandmechanismsinvolvedintheactuator'sforcegenerationiswarranted.TheLorentzforce,~Fparticle,onachargedparticleisgivenby,~Fparticle=q[~E+(~v~B)] (3)whereqistheelectricalchargeoftheparticle,~Eistheelectriceld,~visthevelocityoftheparticle,and~Bisthemagneticeld.MagneticeldsaretypicallynotusedforatmosphericDBDactuatorsduetothelargeeldsrequiredtomakeasubstantialcontribution.Assuch,Equation 3 reducesto,~Fp=e(n+i)]TJ /F3 11.955 Tf 11.95 0 Td[(ne)]TJ /F3 11.955 Tf 11.95 0 Td[(n)]TJ /F5 7.97 Tf -.3 -8.28 Td[(i)~E (3)whereFpistheLorentzianforcedensityoftheplasmaduetoaspacechargeseparation.Hereqhasbeenreplacedbythenetchargeseparation.n+i,ne,andn)]TJ /F5 7.97 Tf -.3 -8.28 Td[(irepresentthenumberdensitiesofpositiveions,electrons,andnegativeions,respectively.eistheelementalchargepreviouslydened(Section 2.1 ).FromEquation 3 ,theLorentzianforceisproportionaltotheappliedelectriceldandtheseparatedspacecharge,suchthattheforcemaybeincreasedbyeitherraisingtheelectriceldorincreasingthespacechargeseparation.Bydenition,however,thebulkofaplasmaisquasi-neutral.Thisindicatesthatthemajorityoftheforceisgeneratedwithintheplasmasheath(Figure 3-6 )wherethechargeseparationisthegreatest(Section 2.1 ).Furthermore,themomentumexchangebetweentheplasmaandthesurroundingneutralgasisacollisiondominatedprocess.Giventherelativesizediscrepancybetweenelectronsandneutralgasparticlesitislogicaltoassumethatlittlemomentumwouldbetransferedinacollision(Section 2.1 ),thusindicatingthationsaretheprimarysourceofforcegeneration.However,thedielectricbarrierdischargeisaweaklyionized 39

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Figure3-6. QualitativeDCsheathnearanequipotentialwall.Amendedfrom Lieberman&Lichtenberg ( 2005 ). plasma(inthesenseofaDBDactuatoratatmosphericpressures).FromSection 2.3 typicaldegreesofionizationfortheDBDareontheorder10)]TJ /F7 7.97 Tf 6.59 0 Td[(6-10)]TJ /F7 7.97 Tf 6.59 0 Td[(5,meaningatbestforevery105neutralmoleculesthereisonly1ion.Duetotherelativelylargedifferenceinnumberdensities,theplasmamaybethoughtofasaporouspistonpushingagainsttheneutralsurroundinggas.Inthisanalogyofthecollisionprocess,asproposedby Likhanskiietal. ( 2008 ),amajorityoftheworkinggaswouldsimplyslipthroughtheplasmapistonsignicantlyreducingthepotentialLorentzianforce(giveninEquation 3 )transferedtotheneutralgas.Additionally,thetemporallyvaryingstructureoftheplasmaduringthepositiveandnegativehalfcycleswouldlikelycausetheplasmatointeractwiththeuiddifferently.Thequestionremainsthen,whichspecies(orion)isgeneratingthemajorityoftheforceandduringwhichpartoftheACcycledoesitoccur?Thisquestionhasbeenwidelydiscussed( Bairdetal. 2005 ; Boeufetal. 2009 ; Debienetal. 2012a ; Enloeetal. 2009 2008b ; Font 2006 ; Fontetal. 2010 ; Kotsonisetal. 2011 ; Polivanovetal. 2011 ; Porteretal. 2007 ; Royetal. 2006a ; Singh&Roy 2008 )intheDBDactuatorcommunitywiththequestionoftenreducingtoisita`push-pull',`pull-push',or`push-push'scenario.Here`push'indicatesapositiveforceinthestreamwisedirection,while`pull'representsanegativeforce.Thepositiveandnegativehalfcyclesaredistinguishedbytherespectiveorder.Forexample,'pull-push' 40

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wouldindicatethatanegativeforcewasgeneratedduringthepositivehalfcycle,whileapositiveforcewasproducedforthenegativehalfcycle.Bymountinganactuatortoatorsionalpendulum, Enloeetal. ( 2009 )wasabletodeducefromtheangularvelocityofthependulum(Figure 3-7 )thatapositivethrustwasgeneratedforboththepositiveandnegativehalfcycles.Thethrustproducedduringthenegativehalfcycle,however,wassignicantlygreater.Thisdescriptionisconsistentwithotherreportsindicatingthat97%ofthemomentumistransferedduringthenegativehalfcycle( Enloeetal. 2008b ).Usingthesameexperimentalsetup, Fontetal. ( 2010 2011 )reducedtheoxygencontentoftheworkinggastoinvestigatetheinuenceofoxygenionsonthetemporalforcecharacteristics.Previousresultshaveindicatedtheimportanceofoxygeninthrustgeneration( Enloeetal. 2006 ; Kimetal. 2007 ).Consistentwiththepreviousestablished`push-push'scenario,thetemporalmeasurementsshowedthattheplasmapositivelyacceleratestheairtwiceduringeachhalfcycleregardlessofoxygencontent(includingpurenitrogen).Theresultsindicatedthattheforceproductionmechanismisdominatedbyoxygenconcentrationdowntoalevelof5%,withthemajorityofthrustagainbeinggeneratedduringthenegativehalfcycle.Basedontheseresultsitcanbeinferredthattheroleofnegativeoxygenionsplayanimportantandprimaryroleinthrustgeneration.Interestingly,though,inpurenitrogenthedominateforceproducedoccursduringthepositivehalfcycleasopposedtothenegativecycleat20%oxygencontent(air)( Fontetal. 2010 2011 ).Totheopposition,however,recentreportsby Debienetal. ( 2012a )showthatapositiveforceisgeneratedduringthepositivehalfcyclewhilethereisanegativeforceduringthenegativehalfcycle(Figure 3-8 ).Thiswouldindicatea`push-pull'scenario.Unlikethethrust(a'neteffect'quantity)measurementsof Enloeetal. ( 2009 ), Debienetal. ( 2012a )usedtimeresolvedparticleimagevelocimetryandacontrolvolumeanalysisoftheNavier-Stokesmomentumequationtoestimatetheplasmabodyforce.Attestingtotheaccuracyoftheirmeasurement, Debienetal. ( 2012a )provides 41

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Figure3-7. TheangularvelocityofatorsionalpendulumdrivenbyaDBDactuator.Theresultsindicatethatapositiveforceisgeneratedduringboththepositiveandnegativehalfcycles.Takenfrom Enloeetal. ( 2009 ). Figure3-8. Thetemporallyvaryinghorizontalandverticalcomponentsoftheplasmaforceasafunctiontime.Theresultsindicatethatapositiveforceisgeneratedduringthepositivehalfcycle,whilethereisanegativeforceduringthenegativehalfcycle.Takenfrom Debienetal. ( 2012a ). temporallyaveragedthrustvalueswhicharereasonableclosetootherresearchersreportedvalues,wherethependulumbasedmeasurementsonlyallowedforqualitativeobservationsoftheunsteadyforce.Aswiththeaforementionedexperimentalstudies,mixedresultsarefoundinliteratureregardingnumericaleffortsaimedatdeterminingthetemporalnatureofthe 42

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plasmaforce.Forexample, Likhanskiietal. ( 2008 )demonstratedthatdependingontheappliedvoltage,drivingfrequency,andlengthscaleoftheplasma(dictatedbythelengthoftheelectrode),anegativeforcecouldbegeneratedduringthenegativehalfcycle.However,byincreasingtheplasmalength,raisingthevoltage,anddecreasingthefrequencythisforcecouldbereversedwithapositiveforcenowbeinggeneratedduringboththepositiveandnegativehalfcycles.Similarly, Boeufetal. ( 2009 )foundpositiveforcesweregeneratedduringbothhalfcycleswiththeforceduringthepositivehalfcyclebeingaresultofpositiveions,whilenegativeionswereattributetothenegativehalfcycleforcegeneration.Therelativemagnitudeoftheseforces,however,wasdependentontheappliedvoltageandfrequency.Forhighfrequenciesandlowvoltages,themajorityofthenetforcewasgeneratedduringthepositivehalfcycle,whileatlowfrequenciesandhighvoltagestheforceduringthenegativehalfcyclewasdominate.TodatethereisstillcontroversywithintheDBDactuatorcommunityregardingthetemporalcharacteristicsoftheplasmaforceduetotheconictingexperimental/numericalreports.However,qualitativeargumentsregardingtheforcemaybemadebasedonthetimevaryingstructureoftheplasmadescribedinSection 3.1.1 .Duringthenegativehalfcycletheplasmaappearsasadiffusedischarge,whilethepositivehalfcycleiscomprisedofcathode-directedstreamers.Althoughlargeelectriceldsexistattheirtips,thethinchannelsofthestreamerswouldlikelyinteractwithasmallervolumeofthesurroundingairthanthatofthediffusedischarge.Returningtotheporouspistonanalogy,thepistonwouldbesubstantiallymoreporousduringthepositivehalfcycle.Theinuenceofsurfacechargeaccumulationwouldalsocontributetoanegativehalfcyclebiasing.AsestablishedinSection 3.1.1 ,alargepositiveoffsetinthesurfacepotentialisknowntoexistonthedielectric.Thiswouldlikelyreducetheelectriceldduringthepositivehalfcycle,whileenhancingitduringthenegativehalf.Furthermore,itmaybeinferredthatthenegativehalfcycleistheprimaryforcegeneratorfromparametricstudiesontheDBDactuator.Inparticular,theuseofpositiveandnegative 43

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Figure3-9. Voltageandcurrenttracesforpositiveandnegativesawtoothwaveforms.Takenfrom Balconetal. ( 2009 ). sawtooth(orramp)waveformshavebeenshowntoproducedifferentthrusts( Benard&Moreau 2012 ; Enloeetal. 2004a ; Thomasetal. 2009 )andresultantvelocities( Balconetal. 2009 ).Ingeneral,apositiverampisseenasdetrimentalasitlimitsthedischargeonthenegativehalfcycle,resultinginanoverallmorelamentarydischarge.Thiscanbeseeninthedischargecurrent,asshowninFigure 3-9 ,whichcomparesthevoltage-currentcharacteristicsforapositiveandnegativesawtoothwaveform.Furthermore,theuseofanegativesawtoothwaveformhasbeenshowntoproducesubstantiallylargerthruststhanasinusoidalwaveform( Thomasetal. 2009 ).Regardlessofthetemporalstructureoftheplasmabodyforceitsneteffectresultsinanaccelerationofsurroundinggas.Thisforcemayalsobedescribedastheactuator'sthrustwhichisacombinationtheplasmabodyforceandotheruidicforcessuchasshear(seeSection 4.4.2 ).Forasinusoidalinput,theinducedthrustandpowerhavebeenshowntoscalewiththeappliedvoltage,V,suchthat,Thrust/Power/V (3)whereatypicalvalueofis3.5( Enloeetal. 2004a ; Littleetal. 2010 ; Thomasetal. 2009 ).Thepowerrelationbetweentheinducedthrustandvoltagedoesnotincreaseindenitely,however.Thethrustisknowntoeventually`saturate'whichisvisuallycharacterizedbyatransformationfromadiffusetolamentarydischarge( Thomasetal. 44

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2009 ).Asshownby Thomasetal. ( 2009 ),thefrequencyalsoplaysapredominantroleinthethrustgeneration(Figure 3-10 A).Foragivenvoltage,anincreaseinthrustmaybeachievedbyraisingthedrivingfrequency.However,bydecreasingtheappliedfrequency,largervoltagesmaybeappliedbeforethesaturationlimitisreached.Thisultimatelyincreasestheinducedthrust.ThetopicofthrustsaturationinaDBDactuatorisfurtherdiscussedandinvestigatedinChapter 9 .TheideaofusingnanosecondpulsesasopposedtoAC,sinusoidalwaveformshasalsobeeninvestigated( Opaitsetal. 2008a 2009 ; Starikovskiietal. 2009 ). Opaitsetal. ( 2009 )measuredthethrustproducedusingananosecondpulsewithandwithoutaDCbias.ThethrustsgeneratedwerelessthanthatofaDBDactuatordrivenwithahighfrequency(10kHz),lowvoltage(15kVpp)sinusoidalwaveform.Similarly,inducedvelocitieshavebeenreportedasnearzero(<1ms)]TJ /F7 7.97 Tf 6.58 0 Td[(1)fornanosecondpulses( Starikovskiietal. 2009 ).Duetotherapidenergyinputofthenanosecondpulse,theinducedvelocityandthrustisnolongeraresultofadirect,collisional,momentumexchange.Instead,itismostlikelyasideeffect,broughtonbyathermalizationoftheworkinggas.Althoughdirectlytransferringlittlemomentumtotheworkinggas,thenanosecondpulsedDBDactuatorhasbeenusedwithpromisingresults. Roupassovetal. ( 2009 )demonstratedeffectiveowcontrolforMachnumbersupto0.85usingnanosecondpulsedactuators.Alongwithapplyingvariouswaveforms,othergeometricparametersoftheactuatorsuchaselectrodesize,electrodespacing,electrodematerial,electrodeshape,dielectricthickness,anddielectricmaterialhavebeenextensivelystudied( Abeetal. 2007 2008 ; Corkeetal. 2007 ; Enloeetal. 2004b ; Hoskinson&Hershkowitz 2010 ; Hoskinsonetal. 2008 ; Kotsonis&Ghaemi 2012 ). Hoskinsonetal. ( 2008 )reportedthattheexposedelectrodematerialhadlittleeffectontheinducedthrust,whileadecreaseintheelectrodediameter(inthiscasewirewasused)hadasubstantialinuence.Thethrustwasfoundtoincreaseexponentiallywithareductionindiameter.Thisresultis 45

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Figure3-10. Thrustasafunctionofvoltage:A)varyingfrequency(6.35mmquartz)andB)varyingdielectricsandthicknesses.Takenfrom Thomasetal. ( 2009 ). notsurprising,however,giventheLorentzianforceisproportionaltotheelectriceldwhich,fromelectrostatics,scalesasE_1=r(r=radius)foracylindricalconductor.Althoughnaturallyincreasingtheelectriceld, Hoskinson&Hershkowitz ( 2010 )foundthatthecathodedirectedstreamerstypicallyseenduringthepositivehalfcycle(Figure 3-4 )couldbeinhibitedbyusinga25mdiameterwireasopposedtotheconventionalrectangularelectrode.ChangesinthetemporalstructureoftheplasmaareshowninFigure 3-11 forthedifferentelectrodeshapes.Furthermore, Debienetal. ( 2012a )foundthatthestructuraldifferencesbetweenthedischargesaffectedthetemporalforce,withapositiveforcebeinggeneratedduringboththepositiveandnegativehalfcycleswhenawireelectrodewasused.Asshownby Thomasetal. ( 2009 ),thethicknessofdielectricandthedielectricmaterialalsodeterminetheultimatethrustthatcanbeachieved(Figures 3-10 Band 3-12 ).Ingeneral,thickerdielectricsallowlargervoltagestobeappliedresultinginlargerthrusts(Equation 3 ).However,foraconstantvoltagetheelectriceld,andconsequently,thethrustwillbehigherforathinnerdielectric(Figure 3-10 B).Similarly,amaterialwithlowrelativedielectricconstantispreferred(Figure 3-12 ). 46

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Figure3-11. Changesinthetemporalstructureoftheplasmadischargeasaresultoftheelectrodeshape.A)TimingdiagramandB)ICCDimagesforarectangularelectrode(80mthick),a100mwireelectrode,anda13mwireelectrode.Takenfrom Debienetal. ( 2012b ) Thethrustmeasurementsdescribedsofarhavebeen(primarily)obtaineddirectlyusingaforcebalancesimilartothatdescribedinSection 4.4.1 .However,theplasmaforce(orthrust)maybeinferredfrommeasurementsoftheinducedoweld( Baughnetal. 2006 ; Hoskinsonetal. 2008 ; Kotsonisetal. 2011 ).Forexample, Kotsonisetal. ( 2011 )usedtimeresolvedparticleimagevelocimetrytospatiallyandtemporallyresolvethevelocityeldsurroundingaDBDactuator.TheNavier-Stokesmomentumequationswerethendecomposedandthespatialdistributionoftheplasmabodyforcewasestimated.AsshowninFigure 3-13 ,thenotedtrendsareinlinewiththosepreviously 47

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Figure3-12. Saturationthrust(maximumthrustmeasured)asafunctionoftherelativedielectricconstantforvariousmaterials.Takenfrom Thomasetal. ( 2009 ). discussed.Foraconstantfrequency,thespatialdistributionandmagnitudeoftheplasmaforcegrowswithincreasingvoltage.Thesameoccurswithincreasingfrequencyataconstantvoltage. 3.1.3InducedVelocityFieldForalinearactuator(Figure 2-3 A)theplasmabodyforcemanifestsitselfasatangentialwalljetalongthesurfaceofthedielectric.ArepresentativeexampleoftheaveragevelocityeldisshowninFigure 3-14 alongwithdiscretevelocityproles.Thejetischaracterizedbyathin(1-3mm)regionofhighvelocityneartheexposedelectrodewhichdecreasesandexpandsasitpropagatesdownstream.Thedownstreamcharacteristicsoftheinducedwalljetmaybeapproximatedusingananalyticalself-similarsolutionforaviscouswalljet( Opaitsetal. 2010 ).Uponapplicationofthehighvoltagesignal,thejetbecomesquasi-steadyafter40msduringwhichtheimpulsecausesaninitialvortextoformandconvectdownstream( Kotsonisetal. 2011 ). 48

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Figure3-13. BodyforcedistributionsforaDBDactuatorobtainedthroughtimeresolvedparticleimagevelocimetry:A)varyingvoltage(at2kHz)andB)varyingfrequency(at10kVpp).Theexposedelectrodeendsatx=0mm.Takenfrom Kotsonisetal. ( 2011 ). Figure3-14. Characteristicwalljetfromadielectricbarrierdischargeplasmaactuator.A)TheentireoweldandB)discretevelocityprolesforvariousstreamwiseplanes.Takenfrom Santhanakrishnanetal. ( 2006 ). 49

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Theunequalforcingduringthenegativeandpositivehalfcyclesbecomesprevalentintheuidsresponse( Benard&Moreau 2009 2010a ; Kotsonis&Ghaemi 2011 ; Kotsonis&Veldhuis 2010 ; Leonovetal. 2010 ; Polivanovetal. 2011 ).AsshowninFigure 3-15 A,duringthenegativehalfcycletheuidexperiencesalargeincreaseinvelocity(positiveacceleration),whilenoincreaseisseenduringthepositivehalfcycle.Usingtimeresolvedpitotstaticmeasurements, Leonovetal. ( 2010 )showedhowever,thatalargervelocitymaybeinducedduringthepositivehalfcycle(incomparisontothenegativehalfcycle)thoughtheuseofatippedelectrode(Figure 3-15 B).Thesignicantincreaseinvelocitywasattributedtothehighelectriceldneartheelectrode'stip.Thiswouldinturnamplifytheotherwiseineffectivestreamer.Adecelerationoftheuidensueswhiletheplasmaisquenched,whichaspreviouslydiscussedoccurstwiceperperiodasindicatedbythecurrenttracesandcorrespondingradiationemission(Section 3.1.1 ).Thisresultsinthefrequencyresponseoftheinducedoweldcorrespondingtotheappliedexcitationfrequencyoftheplasma( Benard&Moreau 2009 2010a ; Forteetal. 2007 ). Benard&Moreau ( 2010a )showedthatsingletonesfrom150to1500Hzmaybetransmittedtothesurroundingairaswellasmodulatedsignalsconsistingofmultiplefrequencies(Figure 3-16 ).Aswiththedirectforce/thrustmeasurements,numerousparametricstudieshaveusedtheinducedvelocityasametricforimprovingtheactuatordesign( Borghietal. 2008 ; Forteetal. 2007 ; Jolibois&Moreau 2009 ; Ponsetal. 2005 ; Roth&Dai 2006 ).Thesamegeneraltrendsaspreviouslydiscussedremainthesame(Figure 3-17 ),withonenotablecaveat.Todate(tothebestoftheauthor'sknowledge)themaximuminducedvelocityexperimentallymeasuredhasnotexceeded7-8ms)]TJ /F7 7.97 Tf 6.59 0 Td[(1( Forteetal. 2007 ),regardlessofappliedfrequencyandvoltage.However,asshowninFigure 3-10 ,themaximumthrustachievedmaybeincreasedthroughtheuseofthickerdielectricsandhighervoltagesatlowdrivingfrequencies.Thiswouldimplythattheregionofhighvelocityisgrowing,resultinginhigherthrusts(anintegratequantity),asopposedto 50

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Figure3-15. PitotprobepressuresignalsasafunctionoftimenearaDBDactuator.A)AconventionalstraightelectrodedesignandB)atippedelectrodedesign.Temporaldelaysinthepressuresignalwerenotcorrectedforinthegure.Amendedfrom Leonovetal. ( 2010 ). Figure3-16. Temporalresponseoftheinducedvelocitywithringmodulationforthedrivingfrequency(50Hz,150Hz,and300Hz).Takenfrom Benard&Moreau ( 2010a ). 51

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Figure3-17. AsymptoticbehaviorofthemaximuminducedvelocityforaDBDactuatorasafunctionofpowerconsumption.A)VaryingvoltageandfrequencyforaPMMAactuatorandB)varyingdielectricmaterials.Takenfrom Forteetal. ( 2007 ). Figure3-18. InducedvelocityprolesabovemultipleDBDactuators.A)Twoactuatorswithappliedvoltagesof20,25,and30kVppat1kHzandB)fouractuatorswithasuppliedvoltageof20kVppat1kHz.Takenfrom Forteetal. ( 2007 ). thevelocityincreasinginaxedregion.Inlinewithexperimentalresults,numericalpredictionshaveindicatedamaximumachievablevelocityof10ms)]TJ /F7 7.97 Tf 6.58 0 Td[(1forasingleDBDactuator( Likhanskiietal. 2010 ).Thenetvelocitymaybeincreased,though,usingmultipleactuatorssimultaneouslyasshowninFigure 3-18 ( Benardetal. 2009b ; Forteetal. 2007 ; Thomasetal. 2009 ). 52

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ForthetypicallinearDBDactuator,theinducedowisconcentratednearthedielectricsurfaceunderquiescentconditions(Figure 3-14 ).Intermsofowcontrolapplications,thiswouldimplythatmomentumwouldonlybeinjectedveryclosetothesurfacewithintheviscousboundarylayer.Thismayormaynotbedesirabledependingontheparticularemployment.Variouselectrodearrangementshavebeeninvestigatedwhichmanipulatetheorientationoftheinducedjet.OnesuchvariationistheplasmasyntheticjetactuatororPSJA( Santhanakrishnan&Jacob 2006 2007 ; Santhanakrishnanetal. 2006 ).ThePSJAcreatesaverticaljetawayfromthedielectricsurfacebyarrangingtheexposedelectrodeinaclosedloopsuchthatopposingdischargesaregenerated.Whentheinducedowsfromthetwodischargescollided,theyaredirectedupward.Thesameeffectmaybeaccomplishedusingopposinglinearactuators( He 2008 ; Liuetal. 2011 ; Porteretal. 2009 ; Santhanakrishnanetal. 2009 ; Schatzman&Thomas 2008 2010 ; Zhangetal. 2011 ). Schatzman&Thomas ( 2010 )demonstratedthatanarrayoflinearplasmasyntheticjetactuatorsmaybeusedtocreatesequentialverticaljets(Figure 3-19 ).Thiscongurationwasusedasameansofintroducingstreamwisevorticitytoanincomingow.Spatiallydistributedforcingandjetvectoringwasinvestigatedby Porteretal. ( 2009 ).Intheseexperimentsvectoringwasachievedusingasetoftwoopposingplasmaactuatorsofdifferentstrengths.Thejetanglecouldbecontrolledbasedontheappliedvoltageratiobetweentheelectrodes.Theelectrodecongurationsdescribedsofarareinherentlytwo-dimensional. Roy&Wang ( 2009 )numericallyinvestigatedaserpentinelikeelectrodecongurationwhichintroducesathree-dimensionalitytotheinducedow.Thesimulationalsoshowssimilarvortexgeneratingcapabilitiestothatoftheactuatorcongurationusedby Schatzman&Thomas ( 2010 ).Thevectoredangleoftheinducedowfortheserpentinecongurationwasfoundtobeafunctionofthegeometricparameters( Wangetal. 2011 ). 53

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Figure3-19. Experimentaldemonstrationofaplasmavortexgenerator.A)TheelectrodearrangementusedandB)theresultinginducedoweld.Takenfrom Schatzman&Thomas ( 2008 ). 3.2NumericalModelingoftheDBDPlasmaActuatorThenumericalmodelingeffortsfortheDBDactuatormaybegeneralizedintothreecategories:1)estimationoftheplasmabodyforcefromphenomenologyorhigherordermodels,2)reducedordermodeling,and3)rstprinciplemodeling.Therstcategoryprovidesasimple,empiricalestimationofthespatialdistributionoftheplasmabodyforcewhichcanbeincorporatedintouidicsolvers.Thesecondcategoryaimsatsimplifyingthespatiallydistributedplasmaintodiscreteelementsthatapproximateitsbehaviorundercertainassumptions.Thisallowsonetorapidlyinvestigatevariousparametricparameterswithreducedcomputationalexpense.Theaforementionedcategoriesonlyprovidedestimationswithlittletonophysicaldescriptionofthemechanismsinvolved.Firstprinciplesmodelingisthereforenecessarytofullyandaccuratelycapturethefundamentaldynamicsofthedischargeprocess. 3.2.1EstimationofthePlasmaBodyForceOneofthesimplestplasmamodelswasproposedby Shyyetal. ( 2002 ).Inthismodelnoneoftheprincipleplasma/electrodynamicequationsaresolved.Therefore,itoffersonlyaheuristicviewofthedischarge.Itdoes,however,provideasimpledesigntooltoapproximatetheinducedbodyforcewhichcaneasilybeincorporatedintouidicsimulations.Forthemodel,thedischargevolumeisassumedtooccupyatriangular 54

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Figure3-20. Assumedtriangulardischargevolumewithheight,a,andwidth,b,inwhichtheelectriceldisassumedtovarylinearlyintheregionandisboundedbylineA-B.Takenfrom Shyyetal. ( 2002 ). regionwithdimensionsa(height)andb(width)neartheedgeoftheexposed/topelectrode(Figure 3-20 ).Furthermore,theelectriceldisassumedtovarylinearlywithintheplasmavolumewiththemagnitudeoftheeldgivenbyEquation 3 .Themaximumelectriceld,E0,isbasedontheappliedvoltage(V)andthehorizontaldisplaced(d)betweenthetwoelectrodes,suchthatE0=V d.Theelectriceldattheboundingregionsofthedischargevolumeisassumedtobethebreakdownvoltageofthemedium,Eb,allowingonetosolveforconstantsk1andk2inEquation 3 .jEj=E0)]TJ /F3 11.955 Tf 11.96 0 Td[(k1x)]TJ /F3 11.955 Tf 11.95 0 Td[(k2y (3)ThecomponentsoftheelectriceldfromthismodelaregivenbyEquation 3 .Thetwo-dimensionalLorentzianbodyforcewithcomponents,FxandFy,arethencalculatedfromEquation 3 wherecistheassumedchargedensityandeistheelementaryparticlecharge.Ex=jEjk2 p k12+k22,Ey=jEjk1 p k12+k22 (3)Fx=Exce,Fy=Eyce (3) 55

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FurthercomplexitymaybeaddedtoEquation 3 byassumingtheinducedforceactsonlyduringagivenportionofthetotalACperiod,thereforeallowingatimeaveragedforcetobeusedforagiveninputfrequency.Similarly,acorrectionfactortoaccountforcollisionalefciencymaybeadded.Althoughmanyassumptionsmustbemadetoeffectivelyusethismodel,theresultingbodyforceisabletoproducerealisticeffectswhentheinputparametersarechosenappropriately. Singh&Roy ( 2008 )developedananalyticalexpression(Equations 3 and 3 )oftheplasmaforcebasedonrstprinciplesimulations( Singh&Roy 2007 )usingairchemistry.TheparametersFx0andFy0correspondtotheaverageelectrodynamicforceobtainedfromthesimulations,whilexandyareadjustedsuchthattheinducedvelocityprolesmatchedwiththepriornumericaldata.x0andy0correspondtothestartinglocationsfortheactuatorinthex-ycoordinateframe.Thetshowsa4thpowerrelationwithappliedvoltage(0),whichagreesreasonablywelltothe3.5exponent( Enloeetal. 2004a ; Thomasetal. 2009 )experimentallymeasured.Furthermore,comparisonsbetweentheinducedoweldresultingfromtheapproximatedandcalculatedforcesshowreasonableagreement.Thevoltagerangeinthesesimulationsrangedfrom800to1200V,however,whichiswellbelowthetypicaloperatingvoltage(generally5kV)ofaDBDactuator.Therefore,duetotheapparent4thpowerrelation,cautionshouldbeexercisedwhentryingtoextrapolatethemodeltohighervoltages.Fx=Fx004exp )]TJ /F6 11.955 Tf 10.49 8.09 Td[((x)]TJ /F3 11.955 Tf 11.96 0 Td[(x0)]TJ /F6 11.955 Tf 11.96 0 Td[((y)]TJ /F3 11.955 Tf 11.96 0 Td[(y0)) y2)]TJ /F9 11.955 Tf 11.96 0 Td[(x(y)]TJ /F3 11.955 Tf 11.96 0 Td[(y0)2! (3)Fy=Fy004exp )]TJ /F6 11.955 Tf 10.5 8.09 Td[((x)]TJ /F3 11.955 Tf 11.96 0 Td[(x0) y2)]TJ /F9 11.955 Tf 11.96 0 Td[(y(y)]TJ /F3 11.955 Tf 11.96 0 Td[(y0)2! (3)Evenwiththemostefcientalgorithm,itwouldbeanimpossiblerequesttosimultaneouslysolvethegoverningelectrodynamicanduiddynamicequationsonatypicalaerodynamicbodyforaplasma'stemporalandspatialscales,thatis,todosoinatimelymanner(1year).Thisimpliesthatthetwoproblemsmustbedecoupledand 56

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solvedseparately.Forthisdecoupling,theuseofDBDactuationincomputationaluiddynamicsistypicallyassumedtobeaonewaystreet;meaningtheplasmainuencestheow,buttheowdoesnotinuencetheplasma.Ingeneralthisassumptionisnotacorrectone( Erfanietal. 2012 ; Kriegseisetal. 2012 2011c ).Ithasbeenshownthatforevenmodestexternalows(50ms)]TJ /F7 7.97 Tf 6.59 0 Td[(1)adecreaseinactuatorperformance(comparedtoquiescentconditions)isinevitable,withtheeffectsbecomingmorepronouncedathigherspeeds( Kriegseisetal. 2012 ).However,againduetothecomputationallimitationsitisanecessaryinaccuracythatonemustincur.Bymakingthedecoupledassumptionitallowsonetoonlyhaveknowledgeofthespatialdistributionoftheplasmabodyforceforimplementationintouidicsolvers.Hereinliestheutilitariannatureofthebodyforceestimationsdiscussedabove.Theyprovideanempiricalrelationthatcaneasilybeimplemented.Oftentheresultsbetweentheserelationsandhigherordermodelsaresimilar.Forexample,Figure 3-21 comparesthecoefcientofpressure(Cp)onahighlyloadedturbinebladefortwodifferentplasmamodels.Slightlydifferentresultsareseenbetweenthetwocases,buttheneteffectremainsthesame. 3.2.2ReducedOrderModelingAlumped-elementcircuitwasproposedby Enloeetal. ( 2004a )whichreducedtheactuatortoasimplenetworkofresistorsandcapacitors. Orlovetal. ( 2007 2006 )laterextendedthisconcepttoincludennumberofthesecircuitsinparallel(Figure 3-22 ).Eachsub-circuitaccountsforthecapacitanceoftheairanddielectricalongwitharesistiveelementtorepresentthepresenceoftheplasma.Zenerdiodesarealsoaddedtoeachsub-circuitinordertosettheminimumthresholdvoltageforplasmaformation.Furthermore,thetwozenerdiodesareusedtochangetheplasma'sresistance,whichvariesthecurrent'smagnitudedependingonitsdirection.Thisaccountsforthedifferencesexperimentallyobservedinthedischargecurrentduringthepositiveandnegativehalfcyclesoftheappliedvoltage. 57

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Figure3-21. Comparisonbetweenempiricalandrstprinciplesbasedplasmamodelsandtheirimplementationinauiddynamicssimulation.A)Contoursofthex-andy-forcecomponentsandtheresultantforcevectorfromanempirical( Shyyetal. 2002 )andrstprinciplesbasedplasmamodel( Royetal. 2006b ).B)Coefcientofpressure(Cp)onahighlyloadedturbinebladewithandwithoutplasmaactuation.Takenfrom Rizzetta&Visbal ( 2008 ). Thecapacitanceoftheairforthenthcircuitisgivenas,Can=0aAn ln (3)where0isthepermittivityoffreespace,aistherelativedielectricconstantofair,Anthecross-sectionalareaoftheelement,andlnthelengthoftheelementrelativetotheedgeoftheexposedelectrode.Thecrosssectionoftheelementisbasedonthesurfacenormalextensionoftheelementandtheoutplanelengthoftheactuator(referringtoFigure 3-22 ).Thecapacitanceofdielectricisdeterminedinasimilarfashionby,Cdn=0dAd ld (3)wheredistherelativedielectricconstantofthedielectric,Adthecross-sectionalareaoftheelement(basedonthewidthoftheelementparalleltothesurfaceanditsoutofplaneextension),andldisthethicknessofthedielectric. 58

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Figure3-22. TreatmentoftheDBDplasmaactuatorasalumpedelement.A)Adivisionoftheactuatorintonparallelsub-circuitsandB)theequivalentelectricalcircuitmodel.Takenfrom Orlov ( 2006 ). TheplasmaresistanceisgivenbyEquation 3 whereaistheeffectiveresistivityofair.Rn=aln An (3)ThesurfacepotentialforthenthbranchinthecircuitissolvedusingEquation 3 ,wherethecurrentthroughtheplasmaresistor,Ipn(t),isgivenby 3 .ThetimevaryingappliedpotentialacrossthecircuitisrepresentedbyVapp(t).kninEquation 3 representsthezenerdiodebeingopen(kn=1)orclosed(kn=0)withtheplasmaresistance,Rn,changingdependingonthecurrent'sdirection.dVn(t) dt=dVapp(t) dtCan Can+Cdn+knIpn(t) Can+Cdn (3)Ipn(t)=1 Rn[Vapp(t))]TJ /F3 11.955 Tf 11.96 0 Td[(Vn(t)] (3) 59

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Usingthismodel Orlovetal. ( 2007 2006 )wasabletoobtainreasonableagreementwithexperimentaldatafortheplasmasweepvelocityandmaximumextentofplasmaasafunctionofbothvoltageandfrequency.Theplasmavelocityobtained,however,wasbetween75to110ms)]TJ /F7 7.97 Tf 6.59 0 Td[(1(inagreementwith Enloeetal. ( 2004a ))whichissignicantlylowerthanthevelocityofacathodedirectedstreamerasdiscussedinSection 3.1.1 .Thishighlightsthelimitationofthelumpedapproachasonlyaveragedquantilesmaybeobtained.Usingthesurfacepotentialresultingfromthelumpedelementmodelasatime-dependentboundarycondition, Orlovetal. ( 2006 )solved,r(r)= 2d (3)forthepotential,,distributionaroundtheexposedelectrode.HeredistheDebyelength.TheLorentzianbodyforceisthengivenas,~fp=)]TJ /F11 11.955 Tf 11.3 16.85 Td[(0 2d~E (3)fromknowledgeofthepotentialdistribution.Asis,thismodeldoesnotinherentlyaccountforspatialvariationsinthechargedspeciesoftheplasma.Therefore,acompensationweightingofthebodyforce,whichreliesonexperimentalobservations,isnecessary( Orlovetal. 2006 ). 3.2.3FirstPrinciplesBasedModelingThemodelspresentedthusfardonotquantitativelycapturefundamentalaspectsofthedischarge.Todosoonemustturntoarstprinciplesapproachandmodeltheplasmabasedonthegoverningelectrodynamicequations.However,modelingthecompletecontinuity,momentum,andenergyequationsformultiplechargedspecies/particlesbecomescomputationallyprohibited.Assuch,adrift-diffusionapproximationisoftenmade,simplifyingtheequationsystem.ThisapproachhasbeenwidelyusedtomodeltheDBDactuator( Boeufetal. 2009 ; Boeuf&Pitchford 60

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2005 ; Likhanskiietal. 2007 2008 ; Royetal. 2006a b ; Soloviev&Krivtsov 2009 ).Althoughslightvariationsexistthroughouttheliterature,thesamebasicoutlineisused.Thecontinuityequationforparticle,,intermsofnumberdensityn,isgivenby,@n @t+r~)]TJ /F14 7.97 Tf 6.78 -1.8 Td[(=)]TJ /F6 11.955 Tf 11.96 0 Td[( (3)whereandaresourceandsinktermsbasedonionization,attachment,dissociation,recombination,etc.,andmayaccountforotherrelevantphysicssuchasphoto-ionization.Thedrift-diffusionapproximationallowstheparticlesux)]TJ /F1 11.955 Tf 10.1 0 Td[((=n~V,where~Vistheparticle'svelocity)tobeestimatedby,~)]TJ /F14 7.97 Tf 6.77 -1.8 Td[(=n~V=sgn(e)n~E)]TJ /F3 11.955 Tf 11.95 0 Td[(Drn (3)withoutsolvingthefullmomentumequation.andDrepresentthechargedparticlesmobilityanddiffusivity.CoupledwithPoisson'sequationfortheelectriceld,E,r~E=c (3)aclosedformsolutionmaybeobtained.cisthenetchargedensity(=ePsgn(e)nintheplasmaand=0inthedielectric).Furthermore,isthepermittivityoftheparticularmedium(gasordielectric).NotethatE=r,whereistheelectricpotential;aprescribedboundaryconditionattheelectrode.Atthedielectric-gasinterface,surfacechargemayalsobetakenintoaccount.Speciesincluded,reactionsconsidered,andtreatmentofthemobility/diffusivityvarywithintheliteratureandarenoteasilygeneralized.Similarly,theinitialandboundaryconditionsimplementedchangedependingonthephysicsconsidered.Oncesolved,Equation 3 maybeusedtondthespatialandtemporalvariationsintheplasmabodyforce. 3.3AerodynamicApplicationsoftheDBDPlasmaActuatorTheDBDactuatorhasbeenappliedtoarangeofaerodynamicsurfacesincluding,butnotlimitedto,turbinesblades( Jacobetal. 2005 ; Ramakumar&Jacob 2005 ; 61

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Rizzetta&Visbal 2007 2008 ),landinggears( Thomasetal. 2005 ),airfoils( Benardetal. 2011a 2010 ; Cho&Shyy 2011 ; Fengetal. 2012 ; Gaitondeetal. 2005 ; Littleetal. 2010 ; Post&Corke 2004 ; Rizzetta&Visbal 2011b ; Roupassovetal. 2006 ),turbulentjets( Labergueetal. 2007 ),andvariousconicalows(e.g.atplateboundarylayers( Gibsonetal. 2012 ; Grundmann&Tropea 2009 ; Jacobetal. 2005 ; Rothetal. 2000 ; Schatzman&Thomas 2008 2010 ),cylindervortexshedding( Jukes&Choi 2009 ; Thomasetal. 2008 ),etc.).Ingeneral,thefreestreamvelocitiesintheseexperimentsarerelativelylow(550ms)]TJ /F7 7.97 Tf 6.59 0 Td[(1)duetothelimitedcontrolauthorityoftheDBDactuator.Aspreviouslydiscussed,themaximumvelocityoftheinducedwalljetis7-8ms)]TJ /F7 7.97 Tf 6.59 0 Td[(1.Assuch,successfulimplementationoftheactuatorhingesonitsstrategicplacementatreceptivelocationsalongtheaerodynamicsurface.Forexample,inthecaseofanairfoilatahighangleofattackatornearstallconditions,theoweldischaracterizedbyaseparationoftheshearlayerneartheleadingedge.Thisresultsinlargescalevorticalstructureswhichpropagatealongthechordintothewake.Ingeneral,anactuatorplacedalongthemid-chordortrailingedgewouldlackthenecessaryauthoritytoreattachthisow.However,byplacingoftheactuatorattheleadingedgeneartheshearlayerseparation,onecanleverageinstabilitieswithintheoweldallowingreattachment. Post&Corke ( 2004 )demonstratedreattachmentonaNACA663-018airfoilusingaleadingedgeplasmaarrangementforaReynoldsnumberupto3.33105(freestreamvelocity=30ms)]TJ /F7 7.97 Tf 6.59 0 Td[(1).Theuseofplasmaactuationallowedthestallangletoraiseby8oalongwitha400%increaseinthelift-to-dragratio.Similarly, Benardetal. ( 2010 )demonstratedthataDBDactuatorplacedattheleadingedgeofaNACA0015(freestreamvelocities=10to30ms)]TJ /F7 7.97 Tf 6.59 0 Td[(1,chordRe=1.3105to4105)couldbeincorporatedintoaclosed-loopcontrolsystemtoachievepartialorfullreattachment(Figure 3-23 ).Exceptionstotheleadingedgeplacementoftheactuatormayfoundinliterature,however.Forexample, Vorobievetal. ( 2008 )usedtrailing-edge-mountedplasmaactuatorsforliftenhancementandrollcontrolona 62

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Figure3-23. DemonstrationofowreattachmentusingaDBDactuatoronaNACA0015airfoil.A)AnaturallyseparatedowwiththeplasmaactuatoroffandB)areattachedowasresultoftheplasmaactuation.Thefreestreamvelocityis20ms)]TJ /F7 7.97 Tf 6.59 0 Td[(1withaReynoldsnumberof2.6105andanangleofattackof16o.Theactuatorislocatedattheleadingedgeandwassuppliedwithavoltageof18kVat1kHz.Takenfrom Benardetal. ( 2010 ). NACA0009airfoil.Improvementsinliftwerereported,thoughthefreestreamvelocitieswerelimitedto10ms)]TJ /F7 7.97 Tf 6.59 0 Td[(1(Re=1.34105).Thelimitedfreestream/ReynoldsnumberrangeoftheDBDhaspromptedmanyresearcherstoinvestigatetheuseofDBDactuationformicro-airvehicle(MAV)applications.MAV'sarecharacterizedashavingamaximumdimensionoflessthan6inches(15.24cm)andightspeedsontheorder15ms)]TJ /F7 7.97 Tf 6.59 0 Td[(1( Pines&Bohorquez 2006 ). Rizzetta&Visbal ( 2011a c )numericallyexploredtheuseofDBD'sonaappingandstationaryairfoil(SD7003)representativeofmicro-airvehicle(MAV)applications.Inthecaseoftheappingairfoil,DBDactuationwasfoundtodecrease,butnotcompletelyeliminate,themassiveseparationthatoccursduringtheunsteady,oscillatingmotion.Overtheentireappingcycle,however,an80%reductionindraganda5timesincreaseinlift-to-dragwasreported.Forthestationaryairfoil, Rizzetta&Visbal ( 2011c )found 63

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thatfarbetterperformancewasachievedbyusingunsteadyasopposedtosteadyactuation.Hereunsteadyactuationimpliesadutycycleisused,meaningthedeviceisonlyoperatedorturnedonduringsomeportionofasetcarrierfrequency.Thecarrierfrequencyinthiscasecorrespondstosomeuidictimescale,suchasthefrequencyofsheddingvortices,nottheplasmadrivingfrequency.Similarresultsusingunsteadyactuationmaybefoundinliterature.Forowoveracylinder, Thomasetal. ( 2008 )showedthatbothsteadyorunsteadyactuation(25%dutycycle)couldcompletelyeliminateKarmanshedding,whilereducingturbulencelevelsandnear-eldsoundpressure(13.3dBreduction)levelsinthewake.However,inthecaseofunsteadyplasmaactuation,thenetpowerconsumptionwassignicantlyreducedduetotheactuatoronlybeingon25%ofthetime.AlthoughtheoverwhelmingmajorityofexamplesreportedinliteratureinvolvetheuseofthesinusoidaldrivenDBDactuatoratlowfreestreamvelocities,afewcasesathigherspeedshavebeenreportedwithmodestsuccess( Imetal. 2010 ; Schuele 2011 ).Forexample, Imetal. ( 2010 )examinedtheuseofadielectricbarrierdischargeplasmaactuatortomanipulatetheturbulentboundarylayerofasupersonicow(Ma=4.7)overacompressionrampmodel(congruenttoascamjetinletduct).Theactuatorwasorientedparalleltotheow,astocreateadisturbanceinthecross-owdirection.Athinningoftheboundarylayerwasobservedwhich,assuggestedby Imetal. ( 2010 ),couldprevent/delayinletunstartofascramjetengine.Theunstartphenomenonoccursastheshocksystemintheengine'sinletmovesoutoftheinletthroatresultinginnoowenteringtheengine.Thisinturncausestheenginetoshutdown;apotentiallycatastrophicoccurrence.Furthermore,asnotedinSection 3.1.2 thenanosecondpulsedDBDhasfoundapplicationsinhigherspeedows( Nishiharaetal. 2011 ; Roupassovetal. 2009 ).IngeneraltheDBDactuatoristestedunderideallaboratoryconditions,unrealisticofrealworldapplications.Variousstudieshavelookedatthebehavioroftheactuator 64

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atdifferenttemperatures( Segawaetal. 2007 ; Versaillesetal. 2010 ),pressures( Abeetal. 2007 2008 ; Benardetal. 2008 ; Nichols&Rovey 2012 ; Versaillesetal. 2010 ; Wuetal. 2008 ),andhumidities( Benardetal. 2009a ). Abeetal. ( 2008 )demonstratedthattheinducedthrustincreasedslightlyastheambientpressure(atconstanttemperature)decreasedfrom1atmto0.8atm,afterwhichthethrustdecreasedatalinearratewithafurtherreductioninpressure(downto0.25atm).Similartemperaturedependenttrendshavebeenobserved. Versaillesetal. ( 2010 )reportedthatthethrustincreasedlinearlyasthetemperaturewasincreasedfrom30oCto180oC,while Segawaetal. ( 2007 )showedadeterioratingperformancefortemperaturesabove200oC.However,totrulysimulateenvironmentalightconditionsofanaircraftfromtakeofftocruisingaltitude,onemustvarybothtemperatureandpressure(Figure 3-24 ). Benard&Moreau ( 2010b )investigatedtheperformanceofaDBDactuatorplacedinaquiescent,altitudechamber,inwhichthepressureandtemperatureweresimultaneouslyvariedtomimicightconditionsfromgroundlevelupto10,000m.Theresultsindicatedthatathighaltitudetheinuenceofpressuredominatesascomparedtotheeffectoftemperature.Thehighaltitudeoperationwasalsoaccompaniedwithanincreaseinmaximuminducedvelocity(3ms)]TJ /F7 7.97 Tf 6.59 0 Td[(1atgroundlevelto4ms)]TJ /F7 7.97 Tf 6.59 0 Td[(1at10,000m).Theoverallstructureoftheplasmaduringthenegativeandpositivehalfcycleswasfoundtobeunaffectedbyvariationsinthealtitude( Benardetal. 2011b ).Besideslaboratorybasedexperiments,afewighttestsutilizingDBDactuatorshavebeenreported. Sidorenkoetal. ( 2008 )mountedanactuatortotheleadingedgeofasailplanewinginanefforttomanipulatepre-stallandpost-stallightconditions.Similarly, Grundmannetal. ( 2009 )implementedtheDBDonasmall,remotelypilotedplane(Figure 3-25 ).Inbothcasestheactuatorwasfoundtohaveaseeminglypositiveeffect. Grundmannetal. ( 2009 )reportsthatthestallspeed(aproductofowseparation)oftheplanewasloweredonaverageby3.6ms)]TJ /F7 7.97 Tf 6.58 0 Td[(1.However,inboth 65

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Figure3-24. Ambienttemperatureandpressureasafunctionofaltitude.Dryairisassumed. Figure3-25. Dielectricbarrierdischargeplasmaactuatorsappliedtoasmallunmannedaerialvehicle.Takenfrom Grundmannetal. ( 2009 ). experimentsmoredataneedstobecollectedinordertodenitivedeclaresuccessfortheDBDactuator. 66

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3.4MotivationforCurrentWorkAsdiscussedabove,thedielectricbarrierdischargeplasmaactuatorhasshowntremendouspromiseforvariousowcontrolapplications.It'sprimarylimitationhowever,isitslackofuidiccontrolathighspeeds.Numerousparametricstudieshavebeenundertakeninanefforttoimproveuponwhatisconsideredthestatusquo.ThedesignspaceoftheDBDactuator,asshowninFigure 3-26 ,isquitebroad.Aspectssuchasdielectricmaterial,electrodegeometry,inputvoltage,drivingfrequency,etc.havebeenextensivelystudiedforthelinearDBDactuator.TheaimofthisworkistoexpandthedesignspaceoftheDBDactuatorandinvestigatepreviouslyunexploredcongurations.Intheremainingchapters,adetaileddescriptionoftheexperimental(Chapter 4 )andnumericalmethods(Chapter 5 )implementedinanefforttocharacterizeandquantifythedevelopmentofthenewandconventionalactuatorcongurationsisgiven.Theresultsfromtheseinvestigationsarethenpresented(Chapters 6 7 8 ,and 9 )followedbyasummaryandrecommendationsforfuturework(Chapter 10 ).Withinthecompletedresearch,threedifferentactuatorcongurationsareinvestigated.Therstconsistsofusingmultipledielectricsubstratesandpoweredelectrodescombinedintoasingleactuator(Chapter 6 ).Theresultspresentedshowthatasubstantialreductioninthedevice'spowerconsumptionispossibleusingthisconguration.Second,theelectrodelayoutoftheDBDactuatorismanipulatedtoinduceafullythree-dimensionaloweld(Chapter 7 ),unlikethetwo-dimensionalactuationpreviouslydiscussed.Stereoscopicparticleimagevelocimetryisusedtoquantifytheseeffectsandprovideathree-dimensionalviewofthevectoreld.Thethirdcongurationevaluatestheuseofdielectricmaterialswithextremepermittivitiesasplasmaactuators(Chapter 8 ).Thesematerialsprocessrelativedielectricconstantsonthefarendsofthedielectricspectrum.Thethrustproductionoftheactuatorisshowntoimprovedrasticallywhilesimultaneouslyreducingtheactuator'sweightbyusingsilicaaerogel,apreviouslyunexploreddielectricmaterial.Theuseofthismaterialnotonlyhelpsextend 67

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Figure3-26. Dielectricbarrierdischargeactuatordesignspace. theapplicabilityoftheDBDtohigherspeedows,butalsotheimplementationoftheactuatorsonmicro-airvehiclesduetoitsreducedweight.Thelimitingeffect,oftenreferredastheactuator'sthrust`saturation',isalsoexplored(Chapter 9 ).Itisshownthatthesaturationeffectcanbemanipulatedbychangingthesurfacetemperatureofthedielectric,resultingintheinitiationoftheionizationoverheatinginstabilitychain.Theseresultsprovideaphysicsbasedexplanationfortheobservationsofthemanyparametricstudiesreported. 68

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CHAPTER4EXPERIMENTALSETUPThefollowingsectionsoutlinethefabricationandgeneraldimensionsoftheactuatorcongurationstested.Thetechniquesusedtoevaluatethepowerconsumption,thrust,inducedvelocity,andsurfacetemperatureofthesedesignsisthenpresented. 4.1PlasmaActuatorCongurationThroughoutthisworkamultitudeofdifferentelectrodearrangementsareinvestigated.Therefore,inanefforttoavoidlaterconfusion,itislogicaltosavethedetaileddescriptionofeachdesigntoitsrespectivesection.Acommonclericalnotationforeachdesignmaybeestablished,however,andisoutlinedbythegenericactuatorschematicprovidedinFigure 4-1 4.1.1ActuatorDimensionsThedimensionalnotationandcoordinatedsystemoutlinedinFigure 4-1 willbeusedthroughouttheremainderofthetext.Theupperandlowerelectrodewidthsaregivenasw1andw2,respectively.Theelectrodesareconstructedoutofadhesivelybackedcoppertapewhichhasanominalthicknessof0.07mm(70m).Theelectrodesarehorizontallydisplacedbyadistanceofgandspanalengthoflalongthedielectric.Thedielectricsubstrateusedhasathicknesstandarelativedielectricconstantdenotedbyr.Inthisexampletheinduceduidowisconsidertobelefttoright,suchthatthecardinalcoordinatesx,y,andzrepresentthestreamwise,surfacenormal,andspanwise Figure4-1. AgeneralschematicoftheDBDactuatorusedthroughoutthiswork.A)SideandB)topviewstheDBDactuator. 69

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directions.Ingeneral,thelowerelectrodeoftheactuatorwasencapsulatedtopreventanunwanteddischargeonthelowersurfaceoftheactuator.Thiswasaccomplishedbyeitherplacingacouplepiecesofelectricaltapeovertheelectrodeorsealingtheelectrodeinepoxy.Thoughbothmethodswereequallyeffective,thelatermethodwaspreferred.Similarly,0.084mm(84m)thickKaptontapewasoftenplacedovertopthebackedgeoftheexposedelectrodetopreventbreakdown(notshowninFigure 4-1 ). 4.1.2ElectrodePhoto-fabricationIngeneral,theactuatorswereconstructedbycuttingtheadhesivelybackedcoppertapewitharazorbladeandlayingthestripsofmetalonthedielectricsubstratebyhand.ThissimplisticmethodworkswellforrudimentaryelectrodecongurationssuchasthestraightlinelayoutshowninFigure 4-1 ,but,forobviousreasons,becomesimpossibleformorecomplicateddesigns(e.g.curvedelectrodes).Forsuchdesignsaphoto-fabricationmethod,typicallyusedforin-houseprintedcircuitboard(PCB)construction,wasadopted.Thefollowingstepsoutlinetheprocess.Sheetsofcoppertapewererstadheredtobothsidesofthedielectricsubstrateandcoveredbyaphotosensitivenegativedrylmresist(step1).Adhesionoftheresisttothecopper/acrylicwasaccomplishedbylightlyblowinghotairfromaheatgunonbothsidesoftheactuator.Theactuatordesignwasthenprintedonatransparentlmwiththedesiredfeaturesoutlinedbyadarkbackground.Thelmsusedhadaminimumfeatureresolutionof25m,whichiscertainlybelowthemillimeterdimensionsofmostdesigns.ThetransparencieswerethenalignedonbothsidesofthedielectricsubstrateandplacedunderaUVsourcefor15minutes(eachside)inordertoexposetheresist(step2and3).Oncedone,anegativelmdeveloperwasgentlybrushedontotheactuator'ssurfacetoremovetheunexposedresist.Thisresultsinamaskwiththedesiredactuatordesigncoveringthecoppertape.Theactuatoristhensubmergedinaferricchloridebathtoremove(viawet/chemicaletching)theunwantedcopper(step4).Theremnantsoftheadhesiveglueleftbehindbythecoppertapewasthenremoved 70

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Figure4-2. Manufacturingowchartforphoto-fabricatedelectrodes. usingasolventsuchasmethanoloracetone(step5).Figure 4-2 providesapictorialowchartofthedescribedprocess. 4.2PlasmaDischargeGenerationAswiththedesigncongurations,differentpoweringschemeswhereuseddependingontheparticularactuatortested.Again,thespecicarrangementusedinthecongurationwillbereportedinitsrespectivesection.However,thelayoutsandtheequipmentusedmaybediscussedwithoutalossingenerality.Figure 4-3 schematicallyoutlinesthethreedischargegenerationcongurationsusedthroughoutthistext.HighvoltageamplicationisachievedthroughthecombineduseofanaudioamplierandahighvoltagetransformerincongurationsAandBofFigure 4-3 .Theaudioamplier(QSCaudioamplierModelRMX2450)stepsupthesinusoidaloutputsignalofanarbitrarywaveformgenerator(TektronixModelAFG3022B).Theoutputfromtheaudioamplieristhenfedtoacustommade,CoronaMagneticsInc.,highvoltagetransformerwherethehighvoltagesrequiredtoignitetheplasmadischargearereached.Overthecourseoftheseexperimentsthreedifferenttransformerswereused 71

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Figure4-3. ExamplepoweringschemesusedtodrivetheDBDactuator.IncongurationsAandBthehighvoltagesneededtogenerateaplasmadischargeareobtainedthroughtheuseofhighvoltagetransformers,whereahighvoltageamplierisutilizedincongureC. dependingonthedrivingfrequencyandpeakoutputvoltagerequired.TheschematicsanddesignspecicationsforthesetransformersmaybefoundinAppendix A .CongurationBdiffersfromtheconventionalDBDpoweringscheme(congurationA)inthatbothelectrodesarepowered.Thisarrangementisprimarilyusedinthemulti-barrieractuatordesign(Chapter 6 ),butmayalsobeusedasanalternativetothestandardschemeasameansofreducingthecurrentloadonanindividualtransformer.Duetothexedbandwidthofthetransformer,alternativewaveforms(e.g.squarewaves)cannotreadilypassthroughwithoutadistortionoftheoriginalsignal.Insuchacaseitisadvantageoustoreplacetheaudioamplierandtransformerwithahighvoltageamplier(TrekModel30/20A).Theamplierusedhasaxedgainof3kV:1Vandiscapableofoutputvoltagesintherangeof0to30kVDCorpeakAC.The 72

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amplierhasalargesignalbandwidthofDCto>5kHz(2%distortion)andasmallsignalbandwidthofDCto>30kHz(-3dB).Theprimarylimitationoftheamplierisitslimitedcurrentoutput(0to20mADCorpeakAC)whichcaneasilybeexceededduringoperationofanactuator.Assuch,congurationCisonlyusedwhentheknownpowerrequirementoftheactuatorisrelativelysmall. 4.3PowerMeasurementsMeasuringthepowersuppliedtothedielectricbarrierdischargeactuatorisanimportantpropertytoquantifyinordertoproperlyevaluatethetrueeffectivenessofthedevice.Thefollowingsectionsdescribethemethodologyandequipmentused(Section 4.3.1 ),aswellasacomparisonbetweencommonpowermeasurementtechniquesfortheDBDactuator(Section 4.3.2 ). 4.3.1MethodologyandEquipmentDescriptionTheinstantaneouspower,P(t),consumedbytheactuatorisgivenby,P(t)=V(t)I(t) (4)whereV(t)andI(t)areinstantaneousvaluesofthetemporarilyvaryingvoltageandcurrent.Equation 4 maybeintegratedoverncompleteperiodstodeterminetheaveragedissipatedpower, P,bytheactuator.Theaveragepowerisdenedas, P=1 nTZnT0P(t)dt=1 nTZnT0V(t)I(t)dt (4)whereTistheperiodofoscillation(=1=f,fisthedrivingfrequency).Thedeterminationoftheaverageconsumedpowerrequiresthattwoquantitiesbeaccuratelymeasured:1)thevoltageand2)thecurrent.Intheexperimentsoutlinedinthistext,thevoltageismeasureddirectlyusingahighvoltageprobeasdepictedinFigure 4-3 .TheprobeusedisaTektronix(ModelP6015A)passiveprobewhichhasa1000xattenuation.TheprobehasafrequencyrangeofDCto75MHzanditiscapableofmeasuringDCvoltagesupto20kVorpeakACvoltagesof40kVwitharated 73

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accuracyof3%.Theinputimpedancecharacteristicsoftheprobe,asrated,are100Mand3pF(whencompensatedproperly).Intheorytheimpedancecharacteristicsofanyprobeneedstobemuch,muchgreaterthanthemeasuredloadsuchthatthepresenceandinuenceoftheprobeisnegligible.Unfortunately,theimpedanceofthehighvoltageprobeisonthesameorderasthatofthetypicalDBDactuator( Kriegseisetal. 2011a b ; Zitoetal. 2010 ).Thisraisesconcernsontheinuenceoftheprobeonthemeasuredpower.Theseissueswereinvestigatedanditwasdeterminedthatthehighvoltageprobehaslittletonoeffectontheactuator.AdetaileddescriptionofthesetestsisprovidedinAppendix B .Theotherquantitythatneedstobeknowninordertodeterminethepowerconsumptionisthecurrent.Therearethreeapproachesthataretypicallyused:1)ashuntresistance,2)aninductivecoil,and3)aLissajous(Q-V)Figure.Ashuntresistanceinvolvesmeasuringthevoltagedropacrossaknownresistanceplacedinlinewiththegroundedelectrode.ThecurrentisthendeterminedfromOhm'slaw.ThesecondmethodinvolvestheuseofaninductiveRogowskicoilplacedaroundtheinputhighvoltageleadtoindirectlyinferthecurrent.ThistechniqueisprimarilyusedinthistextasshowninFigure 4-3 .BothaPearsonElectronic's(Model2100)andBergoz's(ModelCT-F1.0-B)ammetershavebeenused.Theprimarydifferencebetweenthetwodifferentammetersistheirrespectivebandwidthlimits,whichhadcorrespondingupperlimitsof20and100MHz.Bothprobeshaveaxed1V:1Againandaratedaccuracyof1%.Probeindependencewasobservedwhenusedsimultaneouslytodetermineanactuator'sconsumedpower.Thethirdmethodcommonlyusedtocapturethecurrentrequiresaknowncapacitorbeplacedinlinewiththegroundelectrode.Muchliketheshuntresistance,thecurrentmaybedeterminedbydifferentiatingthevoltagedropacrossthecapacitor.Asanalternative,thecharge,Q,onthecapacitormayalsobeusedtoformaLissajousgurewiththehighvoltagesignal,V.TheQ-VLissajous 74

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guremaythenbeintegratedtodeterminethedissipatedpower( Manley 1943 ).ThisprocedureisoutlinedinAppendix C .Adigitizingoscilloscopeisusedtocapturetheprobes'analogoutput.TwoTektronixoscilloscopes(ModelDPO3014andModelDPO2014)areusedthroughoutthiswork.Bothdeviceshaveabandwidthof100MHz.However,theDPO3014iscapableofsamplingratesupto2.5GSa/s,whereastheDPO2014islimitedto1GSa/s.Inanycase,thisisnotaconcernasthesamplingrateduringoperationoftheactuatorisontheorderofMSa/s.AcustomLabVIEW(NationalInstrument)interfacewasmadetointeractwiththeoscilloscopesandallowsthedigitizeddatatoquicklyandeasilybedownloaded.TheLabVIEWprogramexportsthedatainMATLAB's(Mathworks)inherentbinaryformat,MAT-le(*.mat),forcomputationalefciency.Oncethevoltageandcurrentwaveformsareobtained,adiscreteformofEquation 4 ,writtenas, P=1 NNXi=1ViIi (4)isusedtocalculatetheaveragepowerdeliveredtotheactuator.HereNcorrespondstothenumberofpointscapturedbytheoscilloscope.ForasinusoidalvoltageNmustcorrespondtocompleteperiods(suchthatN=SamplingratenT)toensureanunbiasedaverage.ForpoweringschemessuchascongureBinFigure 4-3 ,inwhichbothelectrodesarepowered,thetotalaveragepowerisconsideredtobealinearcombinationoftheaveragepowerineachbranch(Equation 4 ).Thetwocircuitbranchesaredenotedas1and2.AnerroranalysisofEquations 4 and 4 isprovidedinAppendix B P=1 NNXi=1Vi,1Ii,1+1 NNXi=1Vi,2Ii,2 (4) 75

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4.3.2ComparisonofPowerMeasurementTechniquesAsdiscussedinSection 3.1.1 thecurrentintheDBDactuatorcircuitisrepresentedbyasinusoidaldisplacementcurrentsuperimposedwithanerraticconductivecurrent.Theshort-livedspikesduringtherisingandfallingedgesoftheappliedvoltageareindicativeoftheconductivecurrentasshowninFigure 3-2 .Duringthepositivehalfcyclethemagnitudeoftheconductivecurrentcanberelativelylargecomparedtothedisplacementcurrent.Forexample,fromFigure 3-2 (arepresentativecurrenttraceforaDBDactuator)theconductivecurrentduringthepositivehalfcycle,althoughshort-lived,reachesamaximumvalueof45mA;thepeakofthedisplacementcurrentisonly18mA.Inordertoavoidclippingthelargeconductivespikes,thedynamicrangeontheoscilloscopemustbesetaccordingly.Asaresult,thenerdetailsofthecurrentsignalsufferduetoareducedresolution.Thisinturnreducesthesignal-to-noiseratiooftheoverallsignal.Thedischargecurrentmaybemeasuredthrougheithera1)shuntresistance,2)indirectlyusinganinductivecoil,or3)fromthechargeonaninlinecapacitor,aspreviouslystated.ThersttwomethodsleadtothecurrenttracesasshowninFigure 3-2 .Withknowledgeofthevoltageandcurrent,Equation 4 maybeusedtodeterminetheconsumedpower.Forthethirdmethod,thechargeonthecapacitoristypicallyusedtoformaLissajousgure(seeAppendix C )fromwhichthepowermaybeascertained.WithintheDBDactuatorliteratureitiscommontondoneofthethreemethodsindiscriminatelyselectedtodeterminethepowerconsumption.However,duetothelargeconductivecurrentsthatmaybepresent,someresearchershavestatedapreferencetotheLissajousgure(orQ-Vmethod)citingabettersignal-to-noiseratioshouldbeachievedasthecapacitoressentiallyintegratesthecurrent( Grundmann&Tropea 2009 ; Kriegseisetal. 2011b ).Inastudyby Ashpisetal. ( 2012 ),instantaneouspowermeasurementsobtainedusingashuntresistortomeasurethecurrentwerecomparedwiththatofaLissajous 76

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gure.Itwasconcludedthatthelowsignal-to-noiseinthecurrentsignalmeasuredwiththeshuntresistorledtoinaccurateresults,thoughgoodagreementbetweenthetwomethodscouldbeachievedthroughtheuseofanonlinear,signalcompressioncircuit.Thecircuitservedtocompresstheamplitudeofthecurrentspikes(inthecurrentobtainedwiththeshuntresistance),suchthatthedynamicrangeofthesignalcouldbereduced,whicheffectivelyincreasedthesignal-to-noiseratio.Itisimportanttonote,however,thattheinherentuncertaintyinthemeasurementprobeswerenottakenintoaccountinthisstudyasnoerrorboundsinthecalculatedpowerwereprovided.Ingeneral,theinstantaneouspowerisoflittleconcernwiththeaveragepowerbeingtheprimaryreportedvalue.Hereaninvestigationwascarriedout,todeterminehowtheaveragepowerdifferedbetweenthepreviouslydescribedmethods.Aplasmadischargewasgeneratedonanactuatorconstructedoutof3mmthickborosilicateglassusingpoweringschemeAinFigure 4-3 .Theelectrodewidthswerew1=10mmandw2=50mmwiththelengthoftheelectrode(l)being10cm.Avoltageandfrequencyrangefrom14to44kVppand2to14kHzwereinvestigated,respectively.Resultsfortheaverageconsumedpoweroverthetestedvoltage/frequencyrangesareprovidedinFigure 4-4 .The`V-I'notationindicatesthatEquation 4 wasusedtodeterminethepowerwherethecurrentwasinferredusinganinductiveRogowskicoil.Conversely,the`Q-V'notationindicatesthepowerwascalculatedfromaLissajousgureasdescribedinAppendix C .FortheQ-Vmethod,acapacitorwithacapacitanceof18nF(5%)wasplacedinlinebetweentheencapsulatedelectrodeandtheground.Thecurrentasmeasuredwithashuntresistorwasnotcomparedinthisstudy,astheprimarypowerdeterminationmethodusedinthistextinvolvesmeasuringthecurrentwithaninductivecoil.Although,forcompleteness,allthreemethodsshouldbecompared,similarresultsareexpectedasboththeinductivecoilandshuntresistancewillbothsufferfromthesameresolution/signal-to-noiseissues. 77

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AsshowninFigure 4-4 ,thesamequantitativetrendsareobservedregardlessofthepowerdeterminationmethod.Asexpectedforagivenfrequencythepowerincreasesatanexponentialratewithappliedvoltage.Ingeneral,however,itisobservedthattheV-ImethodresultsinahighercalculatedpowerthanthatoftheQ-Vmethod.Theseresultswerefoundtoberepeatablewiththecalculatedpowerconsistentlyfallingwithintheerrormarginonrepeatedtestsfortherespectivemethod.Theerrorbarsshownaccountfortheinherentuncertaintyintheprobesused,withtheadditionaluncertaintyofthecapacitor'scapacitancefortheQ-Vmethod.Likewise,thestatisticaluncertaintyofthenitesamplesizewastakenintoaccount.Inrecordingtherawwaveformstheoscilloscopewassettocaptureonemillionpointsatasamplingrateappropriatetovisualizemultiplecompletecycles.Thesewaveformpacketswerethendownloaded10timesateachinputvoltage.Toillustrate,fora14kHzdrivingfrequency,theoscilloscopewassettoasamplingrateof250MSas)]TJ /F7 7.97 Tf 6.59 0 Td[(1.Inasingleacquisitionthiscorrespondsto56completeperiodsbeingdownloaded,withrepeatingtheprocess10timescorrespondingtothepowerbeingaveragedover560periods.Whenfactoringinstatisticaluncertainty,however,anitesamplesizeof10wasusedtoensureindependence.Thisprocesswasusedthroughoutthetextwhendeterminetheaveragepower.AmorequalitativecomparisonofthemethodsisprovidedinFigure 4-5 ,whichdepictsthepercentdifferencebetweenthetwomethodsgivenbyj1)]TJ /F5 7.97 Tf 13.82 5.95 Td[(PQ)]TJ /F12 5.978 Tf 5.76 0 Td[(V PV)]TJ /F12 5.978 Tf 5.75 0 Td[(Ij.Allfourfrequenciesexhibitthesamecharacteristicswiththepercentdifferencebeinghigheratthelowerendoftheirrespectivevoltageranges,butdecreasesasthevoltageisincreased.However,dotothisdependence(aswellastheapparentfrequencydependence)itisdifculttomakeabroadstatementregradingtheerrorbetweenthetwomethods.Theaveragepercentdifferencebetweenallthemeasurementsis15%;whenincludingthenetmarginoferror,however,thedifferencebetweenthetwomethodscouldbeanywherebetween9%and21%. 78

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Figure4-4. Comparisonbetweenpowerdeterminationmethods.The`V-I'notationindicatesthatthepowercalculationinbasedonthevoltage-currentproductwherethecurrentwasinferredusinganinductiveRogowskicoil.The`Q-V'notationindicatesthepowerwascalculatedfromacharge-voltagerelationinwhichaLissajousgure(seeAppendix C )wasused. Figure4-5. PercentdifferencebetweentheV-IandQ-Vpowerdeterminationmethods.Here`V-I'indicatesthatthepowerwascalculatedfromavoltage-currentproductwiththecurrentbeinginferredusinganinductiveRogowskicoil,while`Q-V'indicatesthepowerwasbasedoncharge-voltagerelationinwhichaLissajousgure(Appendix C )wasused. 79

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Basedontheseresultsitisbelievedthatbothmethodsprovideareasonableestimationoftheconsumedpower,thoughahighervalueisgivenwhenusingtheV-Imethod.Thisislikelyduetothereducedresolutionand/orinaccuracieswiththeinductivecoilforsuchsmallcurrents,O(mA).Asstatedpreviously,theratedaccuracyofthecurrentprobes,asprovidedbythemanufacture,is1%;nominimumdetectionvalueisprovided,however.Tofurtherillustratedhowresolutionand/ortheprobeinaccuraciesmayinuencetheresultingpowerfortheV-Imethod,asimpletestcircuitwasconstructed.Thecircuitconsistedofavoltagesourceandaknownresistance(98.8).Aninductivecoilwasusedtoinferthecurrentinthecircuit,whilethevoltagedropacrosstheresistor,fromwhichOhm'slawmaybeusedtodeterminethecurrent,wassimultaneouslymeasured.TherelativemagnitudeofthetwosignalswasdrasticallydifferentwiththevoltagesignalbeingofO(V)whilethecurrentwasofO(mA).Assuchthestrongervoltagesignalismoreeasily/betterresolvedcomparatively.AcomparisonbetweenthetwosignalsisshowninFigure 4-6 ,withtheinductivecurrentmeasurementbeingconsistently16%largerthanthatdeterminedfromOhm'sLaw.Theseresultswerenotdependentontheparticularammeterused(PearsonElectronic'sModel2100orBergoz'sModelCT-F1.0-B),leadingonetobelievethatresolutionissues(duetotheoscilloscope'sdynamicrange)islikelytheculprit. 4.4ThrustMeasurements 4.4.1DirectThrustEvaluationTheresultantthrustproducedbyanactuatormaybemeasureddirectlyusingaprecisionbalance.HereanOhausAdventurerTMPro(ModelAV313C)witha1mgresolutionwasused.Measurementswereobtainedbyattachingtheactuatortoanacrylicstandwhichprotrudedapproximately20cmfromthetopsurfaceofanaluminumFaraday'scage.Thecagewasconstructedusingaluminum(3.18mmthick)andwasusedtoshieldthebalancefromanyelectromagneticinterferenceproducedduringoperationoftheactuator.Thedimensionsofthecagewere30cm38cm23.0cm 80

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Figure4-6. ComparisonbetweentheinferredcurrentasmeasuredwithaninductivecoilandthatdeterminedfromOhm'slaw. (widthxdepthxheight).Thissetupwascontainedwithinalargerquiescentchamberconstructedfromacrylicpanelsandanaluminumframe.Thechamber'sdimensionswere0.61m0.61m1.22m(widthxdepthxheight).Inordertominimizecircuitlosses,heavilyinsulatedhighvoltagewirewasfedthroughtheoorofthechamberfortheinputleads.Topreventsaggingwiresfrominuencingtheforcemeasurements,thinmagneticwire(34AWG)connectedtheinputleadstotheactuator.ThebalancewasconnectedtoadataacquisitioncomputerwhichallowedthesystemtobecontrolledremotelythroughadedicateduserinterfacecreatedinLabVIEW.Theprogramallowedtheusertoremotelyre-zerothebalance,aswellasviewandrecorditsreadout.AschematicofthesetupisgiveninFigure 4-7 .Asimilarexperimentalcongurationhasbeenusedby Hoskinsonetal. ( 2008 )and Opaitsetal. ( 2009 ).Ingeneral,15measurementswererecordedfromthescaleovera30secondspanonceaninitialstablereadingwasreached.AnexampleoutputfromthebalanceisshowninFigure 4-8 forvariousvoltages.Themaximumuncertaintyassociatedwithagivenmeasurementisestimatedtobelessthan4%(to95%condence),basedonrepeatedmeasurements(ataconstantvoltage)andthescale'sinherentuncertainty. 81

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Figure4-7. Schematicofdirectthrustelevationsetup. Furthermore,theerrorinthethrustmeasurementduetothescalescross-axissensitivitywasinvestigatedandfoundtobenegligible.Thiswasdeterminedbyorientingtheactuatoronthemassbalancetomeasurethez-componentoftheforce(referringtoFigure 4-1 ).Insuchanarrangementthescalewouldbeaffectedbyboththexandycomponentsinthecross-axisdirection.Given,thatthez-componentshouldbezeroforalinearactuator,aregisteredthrustreadingbythebalanceshouldpresumablybearesultofitssensitivitytocross-axisforces.Nothrustwasmeasuredasthebalancereadzeroovertheentirerangeofinputvoltages. 4.4.1.1InuenceofplatelengthThenearwallowasaresultofactuationgivesrisetoaself-induceddrag( Font 2010 ),forwhichtheplatesizewouldlikelyhaveasignicantimpactonthemeasuredthrust.Theplatesize,however,isnottypicallyreportedintheliterature.Inordertoevaluatetheeffectoftheactuator'splatelength(L),asshowninFigure 4-9 ,differentplatelengthsweretested.Thesameactuatorwasusedthroughouttheexperiments 82

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Figure4-8. Examplereadoutsfromthebalanceshowingthestabilityandrepeatabilityofthedirectthrustmeasurement(14kHzdrivingfrequency).Takenfrom Durscher&Roy ( 2012b ). withtheplatelength,L,beingreducedeachtime.Lengthscorrespondingto15,10,5,and2.5cmwereinvestigatedoverarangeofvoltages(14kVppto28kVpp).Aplatelengthof15cmwaschosenastomimicatypicalplatelengthusedforoweldmeasurements.Alimitinglengthof2.5cmwasimposedtoavoidthepossibilityoftheplasmaarcingaroundthedielectricsubstrate(3mmthickacrylic),sincethewidthoftheencapsulatedelectrodeitselfwas(w2=)2cm.10cmand5cmwerechosenarbitrarilyasincrementallengths.InreferencetoFigure 4-1 ,theelectrodelength,l,was12cmandthewidthoftheexposedelectrodewasw1=5mm.TheactuatorwaspoweredusingcongurationBinFigure 4-3 withdrivingfrequencies7kHzand14kHz.Theresultsofthisstudy,presentedinFigure 4-10 ,indicatethatthereislittlevariationintheresultantthrustregardlessofthelengthoftheplateforlowerinputvoltages.Thistrenddoesnothold,however,asthevoltageincreases.Atthehighervoltagesinvestigated,anincreaseinthrustisobservedastheactuator'splatelengthisdecreased.Thisincreaseisindependentofthetwofrequenciesinvestigated.Atthemaximumvoltagestested,adifferenceof5and7mN/mwasmeasuredbetweenplatelengthsof15cmand2.5cmfor14kHzand7kHz,respectively.Thiscorrespondstoa 83

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Figure4-9. Schematicofactuatorusedforplatelengthtests. Figure4-10. Thrustmeasurementsoverarangeofinputvoltageswithvaryingactuatorplatelengths.A)Thedrivingfrequencyis14kHz,whileinB)theappliedis7kHz.Takenfrom Durscher&Roy ( 2012b ). 20%increaseinmeasuredthrustinbothcases(Figure 4-11 ).Suchalargediscrepancycouldproveproblematicwhentryingtocomparebetweendifferentresearchers'results,iftheplatelengthhasnotbeenspecied. 84

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Figure4-11. Percentageincreaseinthrust,Tx,betweenaplatelengthof2.5cmand15cmasafunctionofvoltage.Takenfrom Durscher&Roy ( 2012b ). Becausetheviscousdragrapidlydecreasesinthedownstreamdirectionasthewalljetoftheactuatorexpandsanddissipates,thedifferenceinitsintegratedeffectbecomeslesssevereastheplatelengthisincreasedbeyondacertainthreshold(e.g.L=10cm).Thisresultsinnearlyidentical(plateindependent)thrustvaluesforthelongerplatelengths(L=10cmand15cm).Forshorterplatelengths,however,theimpactoftheviscousdragoverallwouldbesignicantlylessthanthelongerplates,resultinginhigherrecoverablethrustreadings.Itisalsoplausiblethatashorteningofthedielectricplateaffectsthesurfacechargeaccumulationandthustheelectriceldandinducedforceontheuid.Thesurfacechargehasbeenshowntopersistseveralcentimetersdownstreamofanactuator( Enloeetal. 2008a ; Opaitsetal. 2008b ).Regardlessoftheexactmechanism,Figure 4-12 veriesthatthepowerconsumptionandthuspowerdeliveredtoplasmaloadremainsconstantregardlessoftheplatelengthindicatinganominalconstantbodyforceisgenerated. 4.4.1.2InuenceofchambersizeThechamberinwhichthescaleishousedisonlyslightlyventedtopreventpotentiallydangerousamountsofozone(abyproductofthedischarge)fromcontinuously 85

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Figure4-12. Powerdissipationasafunctionofvoltagefordifferentplatelengths.Takenfrom Durscher&Roy ( 2012b ). spreadingintothelaboratoryenvironment.Asaconsequenceonecouldarguethatforparticularlylongrunsoftheactuator,theairchemistryinsideofthechamberisbeingmodied.Toinvestigatethisargument,twotestswerecarriedoutoverarangeoninputvoltagesusingthesameactuatorcongurationdescribedinSection 4.4.1.1 withaplatelengthof10cm.Inonecase,the0.74m2doortothechamberwasclosedduringtesting,whileitwasleftwideopenintheother.ThemeasuredthrustfromthesetestsareshowninFigure 4-13 ,wherenotventedandventedcorrespondtothedoorbeingclosedandopen,respectively.AsevidentfromFigure 4-13 ,theresultantthrustwasnearlyidenticalregardlessofventilation.Thisresultwouldlikelychangeifthevolumeofthequiescentofchamberwasreduced,thoughtheresultsseemindifferentforthecurrentexperimentalsetup.Theseresultsareexpectedtoholdwhenusingthechamberforvelocitymeasurementsaswell. 4.4.2ControlVolumeInferredForcesAsanalternativetoadirectmeasurement,thethrustproducedbyanactuatormaybeindirectlyinferredfromacontrolvolumeanalysisoftheinducedoweld.The 86

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Figure4-13. Effectofaventedversusun-ventedchamberontheinducedthrust.Theplatelength(L)was10cm.Takenfrom Durscher&Roy ( 2012b ). followingsectionsoutlinethecontrolvolumemethodology(Section 4.4.2.1 )andtheinuenceofthecontrolvolume'ssizeontheextractedthrust(Section 4.4.2.2 ). 4.4.2.1ControlvolumemethodologyAnexamplerectangularcontrolvolumeisshowninFigure 4-14 .Thetwocomponent,reactionforceimpartedtothedielectriciscalculatedbyintegratingthemomentumuxthrougheachsurfaceofthevolume.Thex-andy-thrustcomponentsarefoundusingtheconservativeformofthemomentumequationsassumingtimeindependencegivenbyEquations 4 and 4 ,respectively.Aswritten,twodimensionalityisassumedwithTxandTybeingnormalizedbytheactuator'slength.Tx=Fp,x+Fs=)]TJ /F11 11.955 Tf 11.29 16.27 Td[(ZHyou2x,leftdy+ZWxoux,topuy,topdx+ZHyou2x,rightdy (4)Ty=Fp,y=)]TJ /F11 11.955 Tf 11.29 16.27 Td[(ZHyouy,leftux,leftdy+ZWxou2y,topdx+ZHyouy,rightux,rightdy (4)AsshowninFigure 4-14 ,thenetthrustproducedwouldbethesummationofthewallshearstress(Fs),pressuredifferential,andtheplasmainducedbodyforce(Fp),actingwithinandonthecontrolvolume.Ifthecontrolvolumeboundariesare 87

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Figure4-14. Schematicofcontrolvolumeusedtocalculatereactionforcesinducedbytheplasmadischarge. signicantlyremovedfromthebulkplasmahowever,aconstantpressureassumptionmaybemade( Kotsonisetal. 2011 ),inwhichthenetthrustinthex-directionmaybedecomposedintothex-componentoftheplasmaforce(Fp,x)andtheshearstress(Fs)alongthesurfaceofthedielectric.Tyisequivalenttothey-componentoftheplasmaforce(Fp,y).Inthecasesoutlinedinthistext,onlythenetreactionthrusts,TxandTy,impartedtothedielectricareofconcern;noattemptsare,therefore,madetoseparatetheplasmabodyforceandtheuidicshearingeffects.Furthermore,theairdensity,,istypicallyassumedconstant.IngeneralforthestandardDBDconguration,TxismuchgreaterthanTy,suchthatthey-componentisoftenignored.Similarly,itcaneasilybeshownthatthenetthrustinthex-directionmaybeapproximatedbyonlyconsideringthemomentumuxthroughtherightsideboundary( Kotsonis&Ghaemi 2011 ).ThisleadstothefollowingsimplicationTxZHyou2x,rightdy (4)whichissometimesusedintheliterature( Hoskinsonetal. 2008 ).InordertofullysolveEquation 4 bothvelocitycomponents(uxanduy)mustbeknownonallthree 88

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sidesofthecontrolvolume.ThisissimpliedbyEquation 4 ,whichonlyrequiresonecomponentononeboundarytobeknown. 4.4.2.2InuenceofcontrolvolumesizeAlthoughtheoreticallyproducingidenticalresults,inliteratureacomparisonbetweenthedirectandinferredthrustmeasurementmethodshasbeenoftenmetwithmixedresults.Forexample, Hoskinsonetal. ( 2008 )reportedafactoroftwodifferenceinthecalculatedthrustbetweenthetwotechniques(attributedtosimplicationsmade),while Kotsonisetal. ( 2011 )showedareasonableagreementbetweenthetwomethods.Apossibleexplanationbetweenthesedifferencescouldbearesultofthecontrolvolumesizeimplemented.Inordertoevaluatetheeffectofthecontrolvolume'ssize,two-componentparticleimagevelocimetry(additionaldetailsprovidedinSection 4.5.1 )wasusedtocapturetimeaveragedmeasurementsoftheinducedoweld.AnexamplevelocityeldisshownFigure 4-15 .Theactuatorwasconstructedfrom3mmthickacrylicwith,inreferencetoFigure 4-1 ,theelectrodewidthsbeingw1=5mmandw2=20mm;theelectrodelength,lwas12cm.TheactuatorwaspoweredusingcongurationBinFigure 4-3 withadrivingfrequencyof14kHz.Inordertoextractthereactionthrustsonthecontrolvolume,theintegralsontheright-handsideofEquations 4 and 4 werenumericallyintegratedinMatlabusingthetimeaverageddata.Acompositetrapezoidalrulewasusedfortheintegrationscheme.Itwasfoundthatthestartingx-location,xo,intheintegralshadlittleinuenceontheresultantthrustcalculatedaslongasitwaschosenbehindtheedgeoftheexposedelectrode(i.e.xo
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Figure4-15. Velocitymagnitudecontourfora20kVppinputvoltagedrivenat14kHz.Thedashedlineslabeledathroughecorrespondtocontrolvolumewidths(W=x)]TJ /F3 11.955 Tf 11.95 0 Td[(xo=x)]TJ /F6 11.955 Tf 11.95 0 Td[([)]TJ /F1 11.955 Tf 9.3 0 Td[(5]mm)of10,20,30,40,and45mm,respectively.Takenfrom Durscher&Roy ( 2012b ). neartheactuatorwerelessthan2%oftheambientdensity.Here,theairdensitywastakenas1.184kgm)]TJ /F7 7.97 Tf 6.58 0 Td[(3.Figure 4-16 depictstypicalplotsoftheinferredtangentialthrustcomponent,Tx,andhowitvarieswiththewidth(W=x-xo)andtheheight(H=y-yo)ofthecontrolvolume(referringtoFigure 4-14 )forvariousvoltages.Theplotindicatesthatthethrustisindependentoftheheightabovethedielectricsurfaceinwhichthecontrolvolumeistakenbeyondagivenpoint(10mmforallcasesinvestigated).Thispointcorrespondstothetotalencapsulationoftheinducedwalljet'sboundarylayer.Theboundarylayercreatedbythejetincreaseswithbothappliedvoltageanddownstreamlocation.However,fortherangeofvoltagesinvestigated,theboundarylayerwaslessthan10mmthickforthegiveneldofview.Moreimportantthantheheightofthecontrolvolumeisitswidth,asFigure 4-16 reveals.Thecalculatednetthrustishighlydependentonthepointatwhichthecontrolvolumeends.Ifthewidthistoosmallthethrustmaybegrosslyoverpredictedascomparedtoamuchwidercontrolvolume.ThetangentialandnormalthrustcomponentsareplottedinFigures 4-17 Aand 4-17 B,respectively,overtherangeofinputvoltagesinvestigated.Ateachvoltage,thethrustwasextractedforvedifferentcontrolvolumewidthsfromdatasimilartoFigure 90

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Figure4-16. Inferredtangentialthrust,Tx,forvariousvoltagesat14kHzasafunctionofthecontrolvolume'swidth(W=x)]TJ /F3 11.955 Tf 11.95 0 Td[(xo)andheight(H=y-yo).Takenfrom Durscher&Roy ( 2012b ). 4-16 .TheverticaldashedlinesinFigure 4-15 correspondtocontrolvolumewidthsof10,20,30,40,and45mm.Theheightofthecontrolvolumechosenwas10mm,whichisasuitablechoiceforreasonspreviouslydiscussed.Overtherangeofsuppliedvoltagesthecalculatedtangentialthrustshowsastrongdependencyonthewidthofthecontrolvolume.Thisdependencebecomesmorepronouncedathighervoltages.Thecalculatedthrustsdobegintoplateauasthedownstreamextentofthecontrolvolumeisincreased.ThisisaresultoftheasymptoticnatureofthecurvesshowninFigure 4-16 .Itisimportanttonotethatthethrustdoescontinuallydecreaseasthedownstreamextentisincreasedduetheperpetualadditionofviscousdrag.However,therateofthisdecreasebeginstoslowasthewalljetexpandsanddissipates.Thenormalthrustcomponentdeviatesfromthistrendwithitsvaluesremainingapproximatelyconstantasthewidthofthecontrolvolumeisincreased(Figure 4-17 B).Theexception,however,tothisobservationisthesmallestcontrolvolumeplotted(W=10mm).Regardless,themagnitudeofthenormalcomponentissignicantlylessthanthatofthetangential.Thelargedisparitybetweenthenormalandtangentialcomponentsisinlinewithotherreports( Cheongetal. 2011 ). 91

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Figure4-17. Inferredthrustbasedonacontrolvolumeanalysisoftheinducedoweldasafunctionoftheappliedvoltageat14kHz.A)Tangentialcomponentofthrust,Tx,andB)normalcomponentofthrust,Ty,forvariouscontrolvolumewidths(W=x-xo).Takenfrom Durscher&Roy ( 2012b ). 4.4.3ComparisonbetweenDirectandInferredThrustMeasurementsCombiningtheresultsfromSections 4.4.1.1 and 4.4.2.2 ,acomparisonbetweenthecontrolvolumeanalysisandthedirectthrustmeasurementisshowninFigure 4-18 .Twodifferentcontrolvolumewidths(W=20mmand40mm)arepresented,aswellasthedirectthrustmeasurementswithanactuatorplatelengthof10cm(notethatthedifferencebetweenL=10and15cmwasfoundnegligibleinSection 4.4.1.1 ).Resultsindicatethatthemeasuredandinferredthrustsareingoodagreementovertheentirevoltagerangeforthewider(W=40mm)controlvolume.Itisalsoevidentthatifthecontrolvolumeisofinsufcientsize,thatthrustmaybeoverpredictedandeludesthatthereisaminimumlengthdownstreamoftheactuatorthatthecontrolvolumeneedstoconsider.Thatlengthhoweverisdirectlytiedtotheappliedvoltageasthereisadecentagreementforthesmallercontrolvolumewidthatlowerinputvoltages.Identifyingtheplateindependentdirectthrustwithasingleparametercouldbeusefulforpracticalpurposes.Anon-invasiveparameterofchoice,assuggestedby Kriegseisetal. ( 2011a b ),istheplasmalength(Lp)whichresultsfromthecombination 92

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Figure4-18. Comparisonbetweendirectthrustmeasurementsandthoseinferredfromacontrolvolumeanalysis.Thedrivingfrequencyandplatelength,L,are14kHzand10cm,respectively.Takenfrom Durscher&Roy ( 2012b ). ofgeometricandelectricalinputs.Forthecurrentresultstheplasma'slengthisdeterminedfromphotographsobtainedusingaNikonD90digitalcamerattedwitha105mmlens(8sexposure,f/7.1).Thecolorimageswererstconvertedtograyscale,thenbinarizedusingathresholdvalueof0.08.Atracingalgorithmthenmappedouttheplasmaextensionandanaveragevaluewasdetermined.ThisvalueisplottedinFigure 4-19 AagainsttheplateindependentdirectthrustmeasurementsforL=10cmpresentedinFigure 4-18 .Alinearrelationshipwasfoundbetweenthedirectthrustdata(Tx,Direct)inmNm)]TJ /F7 7.97 Tf 6.58 0 Td[(1andtheplasmalength(Lp)inmm.Tx,Direct=6.57Lp)]TJ /F6 11.955 Tf 11.96 0 Td[(18.9 (4)Todeterminetheminimumthresholdforthecontrolvolumesizeforreasonablypredictingthrust,thesamescalingmetric(Lp)wasstudied.Alinearrelationoftheformxmin=7.12Lp)]TJ /F6 11.955 Tf 11.96 0 Td[(11.1 (4) 93

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Figure4-19. Controlvolumescalingrelations.A)ThrustasafunctionplasmalengthandB)thepercentdifferencebetweendirectandinferredthrustsusingaxedandscaledcontrolvolume.Takenfrom Durscher&Roy ( 2012b ). wasobtainedfortheminimumcontrolvolume'sdownstreamextent(xmin=Wmin+xo).ThisrelationwasfoundbymatchingthedirectthrustdatafromFigure 4-18 (L=10cm)withPIVinferredthrustdata,representedinFigure 4-16 ,forgivenvoltages.ThedifferencebetweentheinferredthrustusingtheminimumcontrolvolumeextensionandthedirectmeasurementsareprovidedinFigure 4-19 Bonapercentagebasis.Asacomparison,thepercentagedifferenceinusingaxedcontrolvolumeisalsoshown.Ingeneral,theresultsusingtheminimumcontrolvolumeextentfollowthatofthexedwidthforW=40mm.Furthermore,theplotalsoemphasizestheoverpredictionofthethrustwhenusingacontrolvolumeofinsufcientsize(inthiscaseW=20mm). 4.5FlowFieldMeasurements 4.5.1ParticleImageVelocimetry(PIV)UnlikeLaserDopplerVelocimetry/Anemometry(LDV/LDA)andhotwireanemometry,whichonlyprovidepoint-wisemeasurements,ParticleImageVelocimetry(PIV)maybeusedtogeneratespatiallyresolveddatasetsoftheentireoweld.Ingeneral,PIVinvolvesseedingtheuidwithtracerparticleswhicharethenilluminatedbyalasersheet.Stillimagesoftheparticleswithintheilluminatedplanearecapturedusinga 94

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digitalcamera.Theimagesarethenbrokenupintowhatisknownasinterrogationwindows.Individualwindowsarethencorrelatedbetweenconsecutiveframesinordertodeterminetheparticles'motion.Thetimeseparationbetweentheframesispreciselyknownallowingforthedeterminationoftheuid'svelocity. 4.5.1.1EquipmentsetupFortheexperimentsinthistext,theactuatorwassetupinthesamequiescentchamberasdescribedabove(Section 4.4.1 ).Theoorofthechamberisconnectedtoasingleaxismanualtraverse(VelmexModelA1503P40-S1.5),whichallowstheoortotranslatehorizontally19mmoffcenter.Thiseliminatestheneedtocontinuouslyreadjusttheopticsinordertoimagevariouslocationsalongtheactuator.ThenecessarylightsheetisgeneratedusingaNd:YAG,dualcavitypulsed532nmlaser(NewWaveResearchModelSoloPIVII30).Connectedtothelaserwasanadjustablefocallengthoptics,whichallowedforneadjustmentstothewaistofthelasersheet,andadivergentcylindricallens(f=-10mm).ALaVision'sCCD(ModelImagerProX4M)camerawasusedtocapturethePIVimages.Thecamerahasarepetitionrateof7.2Hz(whenoperatedindualframemode)andapixelresolutionof20482048pixels.Ingeneral,aNikon105mmlenswasconnectedtothecamerawithorwithouta1.4x(or2x)teleconverter,dependingonthedesiredeldofview(FOV).Likewise,eitheratwo-componentorstereoscopic(three-component)measurementwasmadedependingontheactuatorcongurationandparticularassessment.Onlyasinglecameraisrequiredinorderofobtaintwo-components,wheretwoarenecessaryforthelater.Inasinglecamerasystem,thecameraisalignednormaltothelightsheet.Forasteroscopicsetup,asshowninFigure 4-20 ,thecamerasareobliquetothelightsheetandhavearelativeangleof58obetweenthem.TimingbetweenthecameraandlaserwashandledbyLaVision's(ModelPTU-9)programmabletimingunit(PTU).ThePTUhasasynchronizationresolutionof10nswith<1nsjitter. 95

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Figure4-20. Stereoscopicparticleimagevelocimetrysetup. 4.5.1.2ProcessingmethodologyLaVision'sDaVis7.2PIVsoftwarepackagewasusedtocalibrate,capture,pre-process,process,andpost-processthePIVimages.Imagecalibrationwasperformedwitha40mmx40mm,two-tieredcalibrationplate(LaVisionType7).Thefollowingoutlinesthegeneralstepsimplementedindeterminingthevectoreldfromtherawcameraimages.Firstanaverageimageintensityforeachframeinagivendatasetwascalculated.Theseaverageswerethensubtractedfromtherawimagesinordertoincreasetherelativecontrastbetweentheparticlesandthebackground,increasingthesignal-to-noiseratio.Alocalparticleintensitycorrectionisthenappliedinwhichtheparticleintensitiesarenormalizedoverawindowof4pixels(typical,butcase 96

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dependent).Thisallowsforsmallerparticlestocontributemoreeffectivelyinthecorrelation( GmbH 2007 ).Havingmaskedthesurfaceoftheactuator,eachimagepairwasthensubjectedtoacross-correlationmulti-gridprocedure.Againthespecicsizesoftheinterrogationwindowsvarieddependingontheeldofviewinvestigatedfortheparticularactuatorconguration.AnexamplecorrelationprocessforastandardlinearactuatorwithaFOVof48x48mmconsistedofaninitialpasswitha32x32pixel2interrogationwindowwitha50%overlap,followedbytworeningpasseswith16x16pixel2windowsagainwith50%overlaps.Fortheinitialpass,a1:1Gaussianweightwasappliedtotheintegrationwindows,whilea2:1wasappliedonthereningpasses.Thisresultedinaresolutionof5.26vectorspermm.Outliersweredetectedandremovedusingarecursivespatialoutlierdetection( Westerweel 1994 )inbetweenmulti-gridpassesaswellasonthenalvectoreld. 4.5.1.3StatisticalconvergenceanderrorestimationInacquiringtimeaveragedquantities,itisimportanttoensureastatisticalconvergenceofthedatasets.Thenumberofsamplesrequiredtoachievethisvariesdependingontheactuatorcongurationandoperatingparameters.Atypicalconvergenceplotforastandardlinearactuator(asusedinSection 4.4.2.2 )isshowninFigure 4-21 .Forthisparticulardataset,300imagepairsweretakenforeachoperatingvoltage.Theconvergenceplotsdepicttherunningaverageofthetangentialvelocitycomponent( ux)fortwolocationsinthevelocityeld.Therstpoint,(5,0.5)mm,isrepresentativeofthehighvelocityregionnearthedischarge(Figure 4-21 A),whilethesecondposition,(35,1.5),iswithinthefullydevelopedwalljet(Figure 4-21 B).After200samples,theaveragevaluesbegintoconvergetoaconstantvalueforbothpoints.Therelativestatisticaluncertainty,,forthesetwopointsisshowninFigure 4-22 ascalculatedfrom,=tN)]TJ /F7 7.97 Tf 6.59 0 Td[(1,95% x ux (4) 97

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Figure4-21. Convergenceplotsoftheaveragex-velocity, ux,fortwolocationsintheoweldinducedbyalinearactuator(asusedinSection 4.4.2.2 )drivenat14kHz.A)Point(x,y)=(5,0.5)mmandB)(x,y)=(35,1.5)mm.Takenfrom Durscher&Roy ( 2012b ). wheretN)]TJ /F7 7.97 Tf 6.59 0 Td[(1,95%isthetestimator(N-1degreesoffreedom,95%condenceinterval), xisthestandarddeviationofthemeanvelocity,and uxisthemeanvelocity(x-component).Theresultsindicateamaximumrelativeerrorof4%inthevelocitymeasurements.Althoughtheseresultspertaintoaspecicactuatorcongurationandoperatingparameters,theymaybeconsideredrepresentativeofthedatapresentedinthistext. 4.5.1.4Seedmaterialselection-theoryChoosingtheappropriateseedingmaterialforuseinparticleimagevelocimetryisanimportantparameter.Theparticleneedstobesmallenoughtoaccuratelycapturetheuiddynamicswithoutalteringtheuidorowproperties.Anestimationtotheaccuracyinwhichatracerparticlefollowstheowisrepresentedbythenon-dimensionalStokesnumber.TheStokesnumberisdenedasSt=particleuref Lref (4)whereparticleistherelaxationtimeoftheparticle,urefisthecharacteristicreferencevelocity(typicallythefreestreamvelocity),andLrefisthecharacteristicreferencelength. 98

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Figure4-22. Relativestatisticaluncertaintyasafunctionofvoltageandpositionforthevelocityeldofalinearactuator(asusedinSection 4.4.2.2 )drivenat14kHz.Redsquarescorrespondtopoint(x,y)=(5,0.5)mmwhileblackcirclesrepresent(x,y)=(35,1.5)mm.Takenfrom Durscher&Roy ( 2012b ). AStokesnumber1indicatestheparticlewillpoorlyfollowtheow,whileaStokesnumberapproachingzero(St!0)impliesaperfecttracer.Foraconstantacceleratingowtheparticlerelaxationtimeisparticle=d2particle(particle)]TJ /F9 11.955 Tf 11.96 0 Td[(uid) 18uiduid (4)wheredparticleistheparticle'sdiameter,particletheparticledensity,uidtheuiddensity,anduidthekinematicviscosityoftheuid.ThevalueofisdependentontheparticleReynoldsnumberbutmaybetakenasone(=1)forStokesiandragatlowReynoldsnumbers( Adrian&Westerweel 2011 ).Ingeneral,thedynamicsofasuspendedparticlearemuchmorecomplicated(see Adrian&Westerweel ( 2011 )),however,Equation 4 providesareasonableestimationoftheparticles'response( Raffeletal. 2007 ).Inmostapplicationstheelectrodynamiceffectsontheparticlesarenegligibleandcanbeignored.However,considerationiswarrantedinmeasuringtheinducedoweldresultingfromplasmaactuationduetothelargeelectriceldsrequiredtoinitiatea 99

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breakdownoftheair.IndoingsothePIVimageswillbebrokenintotworegions:1)thedischargevolumeitselfand2)everythingelseawayfromthevicinityofthedischargevolume. Seedingthefar-eldoftheow.Startingwiththelaterregionrst,consideranotherwiseelectricallyneutralatomormoleculeplacedinastaticelectriceld,~E.Assumingthattheeldisnotstrongenoughtoionizetheparticle,thechargedistributionoftheatomormoleculewillbecomedistorted,resultinginapolarizationoftheparticle.Thenowpolarizedparticlehasaninduceddipolemoment,~p,whichisproportionaltotheelectriceldandwhatisknownastheelectronicpolarizability,,asshownbelow.~p=~E (4)Whenplacedinanonuniformelectriceld,adipolemomentwillresultinanettorqueontheparticleasitattemptstoalignitselfwiththeeld.Ifanequilibriumpositioncannotbeattained,asisthecaseinanonuniformeld,therewillbeanetforceontheparticle.Theforce,~Fdipole,onadipoleinanonuniformelectriceldisgivenby,~Fdipole=(~pr)~E (4)InordertosolveEquation 4 ,onemustknowthevalueoftheelectronicpolarizability,whichdependsonthedetailedstructureoftheparticleandistypicallyexperimentallydetermined.However,itmaybeestimatedbyconsideringanatomwithapointnucleuswithchange(+q)surroundedbyasphericalelectroncloudofcharge()]TJ /F3 11.955 Tf 9.3 0 Td[(q)( Grifths 1999 ).IftheatomofradiusaisplacedinastaticelectriceldE,thenucleuswillshiftbyadistanceinanefforttobalancethecharge(hereisassumedtobesmallenoughthatthesphericalshapeoftheelectroncloudispreserved).Atequilibrium,theappliedelectriceldwillbebalancedbytheinducedinternalelectriceld(Eind)createdbytheshiftedelectroncloud.Fromelectrostatics,theelectriceldatadistancefroma 100

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uniformlychargedsphereisgivenbyE=Eind=1 40q a3 (4)Equation 4 mayberearrangedsuchthatp=q=40a3E (4)wheretheelectronicpolarizabilityis=40a3 (4)Althoughderivedforanatom(equations 4 and 4 ), Bruus ( 2008 )extendsthepriorlogictoadielectricsphereofradiusaandrelativedielectricconstantr,spherebeingplacedintoadielectricuidwithapermittivityofr,uid.Subjectingtheuidtoauniformelectriceldonearrivesthat~p=40r,uidKa3~E (4)whereKistheClausius-MossottifactorgivenbyK(r,uid,r,sphere)=r,sphere)]TJ /F9 11.955 Tf 11.95 0 Td[(r,uid r,sphere+2r,uid (4)SubstitutingEquation 4 intoEquation 4 andsimplifying(notethat(~Er)~E=r~E2ifr~E=0fromelectrostatics)yields,~Fdipole=20r,uidKa3r~E2 (4)whichrepresentsthedielectrophoreticforceexertedonadielectricparticleinadielectricuidundertheinuenceofanonuniformelectriceld.Inthepresenceofanonuniformeld,thederivationofEquation 4 fortheinduceddipolebecomesmorecomplicated.However,Equation 4 and,consequently,Equation 4 remainsvalidiftheradiusofthesphereismuchsmallerthanthedistanceoverwhichtheappliedelectrical 101

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eldvaries( Bruus 2008 ).Similarly,Equation 4 maybeextendedtoACelectriceldsbysubstitutingintherootmeansquare(rms)oftheelectriceld(~Erms)andincludingcomplexpermittivitiesforthedielectrics(see Adrian&Westerweel ( 2011 )or Bruus ( 2008 )).Here,however,onlythestaticcaseisconsidered,whichissufcientforillustrativepurposes.Theaboveanalysiswasdevelopedasameanstoestimatetheinduceddipolemomentfromanotherwiseneutralatomormolecule.Thoughduetotheirmorecomplexatomicstructure,somemoleculessuchaswatercanhavepermanentdipolemoments.Inthecaseofwater,thedipolemomentisequalto6.110)]TJ /F7 7.97 Tf 6.58 0 Td[(30Cm.ConsideringStokesiandrag(FStokes)asabove,forthedielectrophoreticforcetobeconsiderednegligibleitshouldbesignicantlylessthantheshearforceonthetracerparticle(FdipoleFStokes).ThefrictionalforcebasedonStokes'lawisgivenbyFStokes=6uiduidrparticleVparticle (4)whererparticleandVparticleistheparticle'sradiusandvelocity. Seedingtheplasmavolume.Withinthedischargevolume,twoscenariosareenvisionedtopossiblyunfold.First,thetracerparticlemaybecomeionizedfundamentallyalternatingtheplasmachemistry.Alternatively,theparticlemaybecomeelectricallycharged(forexamplethroughattachment)inwhichtheparticlebehavesaspartoftheplasmafollowingelectromagneticlaws(similartoadustyplasma)asopposedtouidictracer.Arudimentarycounterargumenttotherelativeimpactofeitherscenario(inparticularthesecond)maybemadebasedontheparticleconcentrationinrelationtotheionnumberdensityintheabsenceoftracerparticles.Inasealedchambertheparticles'concentration(nparticle-#particles/m3)maybeestimatedbynparticle=Qton 8particle8chamber (4) 102

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whereQistheowrateoutoftheparticlegenerator,tonisthelengthoftimeinwhichthegeneratoristurnedon,8particleisthevolumetricsizeoftheparticle(=4/3r3particleforasphericalparticle),and8chamberisthevolumeofthetestchamber.Iftheparticleconcentrationismuchlessthantypicalionnumberdensityoftheplasma(nparticleni)therelativeimpactofthetracerparticlecanarguablybeignored.Furthermorethepresenceofadditionalchargedparticlesshouldhaveanimpactofthemeasureddischargecurrentandconsequentlythepowerconsumption. 4.5.1.5Seedmaterialselection-implementedForexperimentsoutlinedinthistext,vaporizedOndinaoil(Shell917)wasusedtoseedthechamber.TheoilwasvaporizedusingaTSIatomizer(Model9302)which,whenpressurizedat25psi,producesadropletwithameandiameterof0.8m(rparticle=a0.4m)( TSI 2000 ).Takingairastheworkinguidandsubstitutingtheparticle'sdiameterintoEquation 4 (alongwithparticle=854kgm)]TJ /F7 7.97 Tf 6.58 0 Td[(3,uid=1.184kgm)]TJ /F7 7.97 Tf 6.58 0 Td[(3,anduid=15.6810)]TJ /F7 7.97 Tf 6.59 0 Td[(6m2s)]TJ /F7 7.97 Tf 6.59 0 Td[(1)givesarelaxationtimeof1.6310)]TJ /F7 7.97 Tf 6.58 0 Td[(6s.Substitutingacharacteristicvelocityof5ms)]TJ /F7 7.97 Tf 6.59 0 Td[(1andareferencelengthof1mmintoEquation 4 givesaStokesnumberof8.210)]TJ /F7 7.97 Tf 6.59 0 Td[(3(orSt1).Ondinawasassumedtobedipoleneutralaswelland,thus,believedrelativelyunaffectedbythehighelectriceldneartheactuators.Thismaybeveriedbyconsideringthetworegionsconsideredabove(theplasmavolumeandthefar-eld).First,considerthefar-eldinwhichthedipoleforceontheparticleisgivenbyEquation 4 .Inthisanalysistheelectriceldwillbetakenas3,000kVm)]TJ /F7 7.97 Tf 6.59 0 Td[(1(or30kVcm)]TJ /F7 7.97 Tf 6.59 0 Td[(1thebreakdowneldforairatatmosphericpressure).Furthermore,forsimplication,considerthegradientoftheelectriceldinEquation 4 toscalewiththeparticlesdiametersuchthat,rE2E2 rparticle (4) 103

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Thisisanticipatedtobeaworstcasescenarioforthebulkoftheplasmavolume.TheexactvalueoftherelativedielectricconstantforOndinawasnotreportedbythemanufacture,soavalueof4(typicalforoils)isassumed.Againusingairastheworkinguid,Equation 4 givesaforceduetopolarizationoftheparticleof4.010)]TJ /F7 7.97 Tf 6.58 0 Td[(11N.Similarly,applyingEquation 4 ,theStokesdragontheparticlebecomes7.010)]TJ /F7 7.97 Tf 6.59 0 Td[(10N.AlthoughFStokesisonlyanorderofmagnitudehigherthanFdipole,equation 4 isconsideredtobeaworstcasescenario.Thepolarizationforceisthereforeconsiderednegligible.Furthermore,onaveragetheatomizerwasrunforapproximately10secondstoseedthe0.45m3quiescentchamber.Theowrateoutoftheparticlegeneratorwas1.0810)]TJ /F7 7.97 Tf 6.59 -.01 Td[(4m3s)]TJ /F7 7.97 Tf 6.58 -.01 Td[(1asspeciedbythemanufacturer( TSI 2000 ).SubstitutionintoEquation 4 givesanestimatedparticleconcentrationof91015m)]TJ /F7 7.97 Tf 6.59 0 Td[(3.AgainrelativetoionconcentrationofaweaklyionizedplasmageneratedinaDBDactuator(1021m)]TJ /F7 7.97 Tf 6.59 0 Td[(3)theseedparticledensityis6ordersofmagnitudesmaller.Thisprovidesarudimentaryapproximationthatthepresenceoftheseedmaterialwillhaveanegligibleimpactontheplasmavolume.Furthermore,theseedmaterialstrueimpactshouldbecomeapparentinthedischargecurrent,fromwhichnoevidenceofinuencewasobserved.TofurtherexperimentallyverifytheuseofOndinaasasuitableseedmaterial,acomparisonstudywasdonethatcomparedPIVvelocityprolesusingOndinaagainstmeasurementsobtainedusingapitotprobe(Section 4.5.4 ).ThevelocitymeasurementsshowninFigures 4-23 Aand 4-23 Bweretaken25mmand35mmdownstreamoftheexposedelectrode,respectively.Reasonablygoodagreementisseenbetweenthetwodatasetsbothintermsofmagnitudeandshapegivingsomeindicationthatelectrodynamiceffectsmaybenegligibleinthecurrentexperimentalsetup. 104

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Figure4-23. ComparisonbetweenpitotmeasurementsandPIVprolesforalinearDBDactuator.ProlesaretakenA)25andB)35mmdownstreamoftheexposedelectrode.Theappliedvoltageanddrivingfrequencyare20kVppand14kHz.Theactuatorwasconstructedfrom3mmthickacrylicwithelectrodewidthsofw1=5mmandw2=20mm.Ondinaoilwasusedforthetracerparticles.Takenfrom Durscher&Roy ( 2012b ). 4.5.2LinearActuatorEndEffectsThelinearactuatorisgenerallyconsideredtobeatwo-dimensionaldevice,howeveriftheobservationplaneistooclosetotheedgeoftheniteelectrodeendeffectscouldinuencethemeasuredvelocityeld.Toinvestigatethiseffect,stereoscopic-PIVwascarriedoutonalinearactuatorinordertomeasureallthreecomponentsofthevelocityvector.AsoutlinedinFigure 4-24 thelasersheetwasalignedalongthecenterlineofactuator.Theinitiallengthoftheelectrode(l)was160mm,butwasincrementaldecreasedwhilekeepingthelasersheetxed.Theproximityofthelasersheettotheedgeoftheelectrodeisgivenbyl,inwhichlengthsof80mm(initialelectrodelength),40mm,20mm,10mm,5mm,and0mmwereinvestigated.TheresultsofthisstudyarepresentedinFigures 4-25 and 4-26 .ForalltestspoweringcongurationA(fromFigure 4-3 )atadrivingfrequencyof14kHzwasused,withthedielectricbeing3mmthickacrylic.Theelectrodegeometryconsistedofw1=5mmfortheexposedelectrodeandw2=20mmfortheencapsulatedelectrode. 105

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Figure4-24. Schematicofactuatorusedtoinvestigatetheinuenceofelectrodeendeffectsonthemeasuredvelocityeld. AsshownintheFigure 4-25 foraconstantvoltageof20kVpp,asthemeasurementplanegetsclosertotheedgeoftheelectrode,theoutofplanevelocitycomponent(uz)begantohaveastrongerinuencewithinthevectoreld.Thedataintheguresarenormalizedbythemaximumx-componentofvelocity,ux,max,whichistypicallytheprimaryvelocitycomponentforalinearactuator.Forthelongerelectrodelengths(l=80and40mm)thereisanegligiblerelativez-velocitycomponentpresent.Astheelectrodewasfurthershortened,however,asignicantoutofplanecomponentwasobservedaroundy=4mm(justabovethewalljet).Furthermore,asshowninFigure 4-25 Fasubstantialinuencewasobservedwhentheedgeoftheelectrodewasdirectlyalignedwiththemeasurementplane(l=0mm).Thesetrendswereconsistentregardlessoftheinputvoltage(whichdirectlyaffectsux,max)asshowninFigure 4-26 .Theseresultsindicatethataslongasthemeasurementplaneissufcientlyfarwayfromtheedgeoftheexposedelectrode(>40mm)anyedgeeffectsmaybeconsiderednegligibleandthelinearactuatorisperformingasaquasi-two-dimensionaldevice.Foralloftheexperimentsoutlined(unlessspecicallynoted)inthistext,themeasurement 106

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Figure4-25. Contoursdepictingtheratioofuztothatofux,maxforvariousdistancesfromtheedgeoftheelectrodeataxedvoltage(20kVpp).A)l=80mm,B)l=40mm,C)l=20mm,D)l=10mm,E)l=5mm,andF)l=0mm. planewastakenalongthecenterlineoftheactuator,forwhichtheoverallelectrodelengthwasatleast100mmlong. 4.5.3BuoyancyEffectsontheInducedFlowAlthoughclassiedasanon-thermaldischarge,thetemperatureofthelocalsurroundinguidwillnaturallyincreaseslightly,duetothedischarge.Furthermore,thesurfacetemperatureofthedielectricwillincreaseasaresultofpowerdissipationwithinthedielectric(additionaldetailsarediscussedinChapter 9 )whichcouldalsocontributetoariseinlocalgastemperature.Inturn,anelevatedlocalairtemperaturecouldleadtoabuoyancyforceontheuidwhichcouldinuencethedynamicsoftheinducedow 107

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Figure4-26. Contoursdepictingtheratioofuztothatofux,maxforvariousdistancesfromtheedgeoftheelectrodeandvoltages.A)l=40mmand13kVpp,B)l=0mmand13kVpp,C)l=40mmand18kVpp,andD)l=0mmand18kVpp. eld.Forthetypicalhorizontallyorientedactuator,thebuoyancyforcewouldactnormaltodielectricsurfaceinthey-direction(Figure 4-1 ).Foraverticallyorientedactuator,suchasshowninFigures 4-7 and 9-6 ,thebuoyancyforcewouldalign/couplewiththeprimarycomponentoftheinducedow,inthex-direction.Toestimatetherelativeimpactofbuoyancyontheoweld,ascalingargumentbasedonthenon-dimensionalRichardsonnumber,Ri,maybemade.TheRichardsonnumberrepresentstherelativeimportanceofnaturalconvection(buoyancydriven)toforcedconvectionandisdenedas,Ri=Gr Re2 (4) 108

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whereGristheGrashofnumberandReistheReynoldsnumber.TheGrashofnumberforaverticallyorientedatplateisgivenby,Gr=g(Tw)]TJ /F3 11.955 Tf 11.95 0 Td[(T1)L3ref 2 (4)whereg(9.81ms)]TJ /F7 7.97 Tf 6.59 0 Td[(2)isthegravitationalacceleration,Twisthewall/surfacetemperature,andLrefisareferencelength.Thethermalexpansioncoefcient,temperature,andkinematicviscosityoftheambientgasarerepresentedby,T1,and.TheGrashofnumberrepresentstheratioofthebuoyancytoviscousforcesactingonauid.TheReynoldsnumber,whichcorrespondstotheratioofinertialtoviscousforces,isgivenby,Re=urefLref (4)whereurefisacharacteristicreferencevelocityofthegas.TheRichardsonnumbermaybeestimatedbyconsideringairat25oC(=298K=T1)astheworkinggas(=310)]TJ /F7 7.97 Tf 6.59 0 Td[(3K)]TJ /F7 7.97 Tf 6.58 0 Td[(1and=15.6810)]TJ /F7 7.97 Tf 6.59 0 Td[(6m2s)]TJ /F7 7.97 Tf 6.59 0 Td[(2)owingoveraverticalatplateatavelocity,uref,of3ms)]TJ /F7 7.97 Tf 6.59 0 Td[(1;arepresentativevaluefortheinducedvelocityofaDBDactuatoroperatedinquiescentair.Furthermoreconsideringareferencelength,Lref,of50mm(approximateeldofviewforaPIVimage)andawalltemperatureof100oC(=373K=Tw)theRichardsonnumberbecomes0.012.ForaRichardsonnumbermuchlessthanone(Ri1)buoyancyeffectsmaybeignored,indicatingthattheoweldisunaffectedbybuoyancyduringoperationoftheDBDactuator.Evenifthewalltemperaturewasincreased200%to300oC(=573K=Tw),avaluefarbeyondthatseeninexperiments(Chapter 9 ),thebuoyancyeffectremainsinsignicantasRi0.045. 109

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4.5.4PitotProbeMeasurementsTheuseofapitotprobeprovidesameanstoinfertheinducedoweldwithouthavingtorelyonparticleseeding.However,thepresenceoftheprobedoescreateanobstructionintheoweld.Similarly,thediameteroftheprobebecomesalimitingfactorfornearwallresolution.Althoughaprobeconstructedfromanon-conductivematerial(suchasglass)isidealduetothehighelectriceldsneartheactuator,ndingaprobewithasuitablediameterprovedtobechallenging.AssuchanUnitedSensorCorp.stainlesssteelboundarylayerprobe(ModelBR-.025-12-C-11-.120)havinganinnerandouterdiameterof0.4318mmand0.635mmwasused.Thedesignoftheprobestiphoweverisattened(thediameterisreducedbyhalf)whichsignicantlyreducesitspresenceinthewallnormaldirection.Positioningoftheprobewascontrolledusingatwo-axistraverse(VelmexMN10-0150-M02-21)withaminimumstepsizeof5m.ThepressuremeasurementsweremadeusingaFurnessControls(ModelFCO332)differentialmanometercalibratedto25Pawitha10Voutput.ThevoltageoutputfromthemanometerwasrecordedusingaNationalInstrumentsdataacquisitionmodule(ModelPCI-6133),atwhich800voltagereadingswereobtainedatasamplingrateof20Hz.Thedifferentialpressure,P,measurementswereconvertedtovelocitiesusingBernoulli'sequation,givenas,ux=s 2P air (4)wheretheairdensity,air,isassumedconstantandwastakenas1.184kgm)]TJ /F7 7.97 Tf 6.59 0 Td[(3.Astandarderroranalysiswascarriedoutontheobtaineddatawhichtookintoaccounttheaccuracyofthetransducer(0.5%Pa),theaccuracyofthevoltagereading(5mV),andthestatisticaluncertaintyofthesampledset.Theuseofametallicprobelimitedtheproximityinwhichameasurementmaybemadeneartheplasma.Furthermore,measurementsnearthedielectricsurfacewere 110

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alsoprohibitedasarcingwasobservedbetweentheprobeandthedielectricwhentheprobeitselfwasincontractwiththesurface.Theseproblemswerealleviated,however,bytakingreadingssufcientlyfardownstream(>25mm)andkeepingtheprobeawaythedielectricsurface(>0.5mm). 4.6ThermographyMeasurementsInfraredthermographyprovidesanon-intrusivediagnostictoolwhichmaybeutilizedtomeasurethesurfacetemperatureofaDBDactuator.Fortheexperimentsoutlinedinthistext,aFLIR(ModelA325)infraredcameraoperatinginthefarinfraredrange(7.5-13m)wasused.Thecamerahasapixelresolutionof320240pixels2.Theusermayselectbetweentwocalibratedranges(-20oCto120oCor0oCto+350oC)dependingonthetemperaturesexpected.Theratedaccuracyofthecamerais2oCor2%ofreading(whicheverishigher).OperationofthecameraiscontrolledthroughFLIR'sExaminIRMaxsoftwarewhichisusedtocaptureandprocessthethermographicimages.Thesoftwareprovidestheusertheabilitytocompensatedforavarietyofaspectsthatwillaffectanaccuratetemperaturemeasurement.Ingeneralthedielectric'semissivity,thecamerasworkingdistancefromtheactuator,reectedtemperatures,aswellastheambienttemperatureandhumiditywereallconsideredinthetemperaturemeasurements.Thedielectric'semissivitywasdeterminedbyheatingthedielectrictoaquasi-uniformtemperaturewiththeaidofelectrichotplateandrecordingthecamera'sreadout.Theemissivitywastheniterativelyadjustedwithinthesoftwareuntiltheresultsmatchedthetemperaturesobtainedfrommultiplesurfacemountedthermocouples.ANIUSBthermocouplemodule(ModelUSB-9211)wasusedtorecordtheoutputfromthethermocouples.Themodulehas4channelsandiscapablesamplingratesupto14Samples/swithaoperatingrangeof-40oCto70oC. 111

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CHAPTER5NUMERICALFORMULATIONANDMETHODOLOGYTheplasmaactuatorwillbemodeledusingtheunsteadytransportequationsforelectronsandionsintheformofmassconservation.Adrift-diffusionapproximationismadeallowingthespeciesmomentumtobesolvedinacomputationallyreducedmanner.Thefollowingsectionsoutlinethenumericalmethodologyused,includingthemodel'sequationsystemandtheniteelementformulation. 5.1Drift-DiffusionApproximationThedriftdiffusionequationsfollowfromSection 3.2.3 ,whichoutlinesthegeneralformoftheequationsystem.Diatomicnitrogen,N2,isusedastheworkinggasinwhichonlytwospeciesareconsideredN+2andelectrons.Assuch,themodelonlyincludesionizationanddissociativerecombinationasoutlinedinEquation 5 .Attachmentwasnotconsidered,thoughwouldcertainlybewarrantedifoxygen,O2,wasincludedinthedischargechemistry.Ionizatione+M!M++2eDissociativerecombinatione+M+!M (5)Thecontinuityequationforionandelectronnumberdensities,n,isgivenas,@n @t+@nV,j @xj=j)]TJ /F5 7.97 Tf 6.77 -1.8 Td[(ej)]TJ /F3 11.955 Tf 17.93 0 Td[(rpnine (5)whereVisthevelocityofspecies,.Thefollowingnotationisadoptedtodistinguishbetweenelectrons(=e)andpositiveions(=i)throughouttheremainderofthesection.Subscriptj(=1or2)correspondstoxandycardinalcoordinates.ThetermsontherighthandsideofEquation 5 representthespeciesionizationandrecombinationandaredeterminedasfollows.Therecombinationrate,rp,wastakenhasaconstantequalto210)]TJ /F7 7.97 Tf 6.58 0 Td[(13m3s)]TJ /F7 7.97 Tf 6.58 0 Td[(1( Surzhikov&Shang 2004 ),whileionizationwassupportedthroughaTownsend 112

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ionizationschemegivenby,=ApeB jEj=p (5)wherepistheambientpressureandjEjisthemagnitudeoftheelectriceld(jEj=p E2x+E2y).AandBareconstantsequalto12cm)]TJ /F7 7.97 Tf 6.58 0 Td[(1Torr)]TJ /F7 7.97 Tf 6.58 0 Td[(1and342Vcm)]TJ /F7 7.97 Tf 6.59 0 Td[(1Torr)]TJ /F7 7.97 Tf 6.59 0 Td[(1takenfrom Raizer ( 1991 ),respectively.Thenetelectronmomentumux,j)]TJ /F5 7.97 Tf 6.78 -1.8 Td[(ej,foundinEquation 5 isgivenby,j)]TJ /F5 7.97 Tf 6.78 -1.79 Td[(ej=q (neVe)2x+(neVe)2y (5)wherethespeciesmomentumuxis,nV,j=sgn(e)n@ @xj)]TJ /F3 11.955 Tf 11.96 0 Td[(D@n @xj (5)Theelectricpotentialisdenotedby,whiletheconstantsandDcorrespondtothespeciesmobilityanddiffusionrate,respectively.Themobilitiesareapproximatedfrome=4.4105 pcm2 sVandi=1.45103 pcm2 sV (5)wherepisthegaspressureinTorr( Raizer 1991 ).Similarly,thediffusionratesareestimatedusingEinstein'sformulas( Howatson 1976 )givenbyDe=eTecm2 sandDi=iTicm2 s (5)Forthesimulationsoutlinedinthistextaworkingpressureof760Torrwasused,suchthattheelectronandionmobilitieswere579cm2s)]TJ /F7 7.97 Tf 6.59 0 Td[(1V)]TJ /F7 7.97 Tf 6.58 0 Td[(1and1.9cm2s)]TJ /F7 7.97 Tf 6.59 0 Td[(1V)]TJ /F7 7.97 Tf 6.59 0 Td[(1.Similarly,xedtemperatureswereassumedfortheelectrons(Te=1eV=11,600K)andions(Ti=0.0258eV=300K),wheresubstitutionintoEquation 5 givesrespectivediffusionratesof579cm2s)]TJ /F7 7.97 Tf 6.58 0 Td[(1and0.049cm2s)]TJ /F7 7.97 Tf 6.58 0 Td[(1. 113

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Closingthesystemofequations,theelectricpotentialwasdeterminedfromPoisson'sequation:@2 @x2j=eXsgn(e)n (5)whereeistheelementalchargeandisthepermittivityofthemedium.NotethatbydenitiontheelectriceldisgivenbyE=r (5)Normalcomponentsoftheelectriceldaretakenaszeroatallboundariesexceptatthedielectricsurfacewhichisdiscontinuousbytheseparatedcharge.Similarly,noelectronorioncurrentowintothedielectricwasconsidered.Thesystemofequationsarenormalizedusingthefollowingscheme:t=t t0,xj=xj d,n=n no,=e kBTe,V,j=V,j VB (5)wheret0(=1.510)]TJ /F7 7.97 Tf 6.58 0 Td[(9s)isareferencetimescale,d(=0.1mm)isareferencelengthbasedontheactuatorgeometrysimulated,no(=1017m)]TJ /F7 7.97 Tf 6.58 0 Td[(3)isareferencenumberdensity,eistheelementalcharge,kBistheBoltzmannconstant,andVBistheBohmvelocity.TheBohmvelocityisgivenby,VB=r kBTe mi (5)wheremiistheatomicmassofdiatomicnitrogen(=281.6610)]TJ /F7 7.97 Tf 6.59 0 Td[(27kg). 5.2Multi-scaleIonizedGasFlowCodeTheMulti-scaleIonizedGas(MIG)owcode,developedattheUniversityofFlorida,isutilizedtosolvethepartialdifferentialequationsapproximatelyusinganiteelementalgorithm.ThesolutionmethodologyisbasedontheGalerkinWeakStatement(GWS)oftheequationsystemwhichisfurtherdiscussedinSection 5.3 .Aniterativesparse 114

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matrixsolver,GeneralizedMinimalRESidual(GMRES),isusedtotosolvetheinherentlystiffmatrix.TemporalintegrationishandledthroughtheNewton-Raphsonscheme. 5.3FiniteElementFormulationLikenitedifference(FD)andnitevolume(FV)schemes,niteelement(orniteelementmethod-FEM)isanumericaltechniquewhichcanbeutilizedtosolvepartialdifferentialequations.Intheniteelementmethod,thecomputationaldomainissubdividedintodiscretesectionsknownaselements.Abasisortrialfunctionisthenusedtoapproximatethesolutionineachelement.HeretheniteelementmethodisbasedontheGalerkinWeakStatement(GWS)ofthelinearoperatorL().Denotingthedifferentialequationsfoundin 5 5 ,and 5 byL(),onecanrewritethecompactformas,L(q)=@q @t+@ @xj(f,j)]TJ /F3 11.955 Tf 11.95 0 Td[(fv,j)=0 (5)whereqisavectorofthestatevariablesne,ni,and.Convectiveanddissipativeuxvectorsaredenotedbyf,jandfv,j,respectively.Multiplyingbythebasisfunction,,andintegratingoverthediscretizeddomain,,theGalerkinWeakStatementofEquation 5 isgivenas,GWSh=SeZeL(qe)de=0 (5)whereedenotesanelement.Serepresentsthenon-overlappingsumofelements,whilethesuperscripthindicatesaspatialdiscreteform.Thestatevariablesforeachelementareapproximatedbytheniteelementbasisfunction,,whicharetypicallyconstructedfromLagrange,Chebyshev,orHermiteinterpolatingpolynomialsofvariousdegrees.Forthisworktheniteelementbasissetiscomprisedofbi-quadratic(4thorderaccurate)Lagrangepolynomials.Thebasissetforabi-quadraticelementisgivenby, 115

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Figure5-1. Schematicrepresentationofthetransformationfromanodalcoordinatesystemtoareferencebi-quadraticelement.TheelementintheCartesianreferenceframeisdenedbytheelement'sheight(he)andlength(le),whereinthetransformedcoordinatesystemtheelementextendsfrom-1to1. =0BBBBBBBBBBBBBBBBBBBBBBBB@12(1+1)(2+1) 412(1)]TJ /F7 7.97 Tf 6.58 0 Td[(1)(2+1) 412(1)]TJ /F7 7.97 Tf 6.58 0 Td[(1)(2)]TJ /F7 7.97 Tf 6.58 0 Td[(1) 412(1+1)(2)]TJ /F7 7.97 Tf 6.58 0 Td[(1) 4)]TJ /F14 7.97 Tf 10.49 6.25 Td[(2(2+1)(21)]TJ /F7 7.97 Tf 6.59 0 Td[(1) 2)]TJ /F14 7.97 Tf 10.49 6.25 Td[(1(1)]TJ /F7 7.97 Tf 6.58 0 Td[(1)(22)]TJ /F7 7.97 Tf 6.59 0 Td[(1) 2)]TJ /F14 7.97 Tf 10.49 6.25 Td[(2(2)]TJ /F7 7.97 Tf 6.58 0 Td[(1)(21)]TJ /F7 7.97 Tf 6.59 0 Td[(1) 2)]TJ /F14 7.97 Tf 10.49 6.25 Td[(1(1+1)(22)]TJ /F7 7.97 Tf 6.59 0 Td[(1) 2(21)]TJ /F6 11.955 Tf 11.95 0 Td[(1)(22)]TJ /F6 11.955 Tf 11.95 0 Td[(1)1CCCCCCCCCCCCCCCCCCCCCCCCA (5)where1and2arethetransformedcoordinatesofareferenceelement.Inthetransformedcoordinatesystem,1and2eachextendfrom-1to1(Figure 5-1 ).ExpandingEquation 5 andformingtheglobalmatricesonemaywritethefollowingordinarydifferentialequation:GWSh=[M]dq dt+[R]=f0g (5) 116

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where[M]isgivenby,[M]=SeZde0de (5)FormulationssimilartothatofEquation 5 aredenotedbythe[R]matrixfortheconvectiveandviscousterms.A-implicitTaylorseriesisusedtotemporaldiscretizeEquation 5 ,suchthat,fFg=[M]fqn+1)]TJ /F3 11.955 Tf 11.96 0 Td[(qng+t(fRgn+1+(1)]TJ /F6 11.955 Tf 11.95 0 Td[()fRgn)=f0g (5)where=1and=0correspondtofullyimplicit(usedinthiswork)andexplicitschemes,respectively.Thecurrenttemporalstepisdenotedbyn.ThewellestablishedNewton-RaphsoniterativeschemeisusedtonumericallysolveEquation 5 :[J]pn+1fqp+1n+1)]TJ /F3 11.955 Tf 11.95 0 Td[(qpn+1g=)]TJ /F3 11.955 Tf 9.3 0 Td[(Fpn+1 (5)wherethematrixJacobian,J,is,[J]=@F @q (5)Iterations,denotedbyp,continueduntiltheresidual,F,wasdriventothedesiredconvergencecriteria(10)]TJ /F7 7.97 Tf 6.58 0 Td[(5). 5.4SimulationGeometryThesimulationdomainusedinthecurrentnumericalinvestigationispresentedinFigure 5-2 .Themeshconsistedof188,160bi-quadraticelements.Inthey-direction,thedielectric(r=4.5)extendedfrom0to0.4,atwhichtheremainderofthedomainwasnitrogen.Thedielectric-plasma/uidinterfaceisdenotedbyared(dashed)line.AsshowninFigure 5-2 ,thegridwaslocallyrenedneartheelectrodesanddielectricsurface,butgeometricallystretchedtowardstheboundariesofthedomain.TheinsetimageinFigure 5-2 denotestheelectrodeplacement.ThespecicdetailsregardingthesuppliedpotentialstotheseelectrodesisreservedforChapter 6 117

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Figure5-2. SimulationdomainusedinthepresentnumericalinvestigationofaDBDplasmaactuator.Themeshconsistsof188,160bi-quadraticelementsandislocalrenedneartheelectrodes.Thered(dashed)lineindicatesthedielectric-plasma/uidinterface. 118

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CHAPTER6MULTI-BARRIERACTUATORSThemulti-barrierplasmaactuator(MBPA)isanextensiononthestandarddielectricbarrierdischargeactuator.Unliketheconventionalcongurationthatutilizesonedielectricandonepoweredelectrode,theMBPAdesignincorporatesmultipledielectriclayersandphaselaggedpoweredelectrodes.Theaimofthisdesignistocreateastrongerdischargeleadingtoanincreasedmomentumtransferwiththesurroundinguid. 6.1MBPADesignAdoptingthenotationestablishedinSection 4.1.1 ,Figure 6-1 outlinesthedevicestested.Case1representswhatisconsideredtobethebi-layerMBPA,whilecase2isadualpoweredandcase3isasinglepoweredactuator.Incases1and2,thetoporexposedelectrodeispoweredwithapeakpotential,atsomereferencephaseangle!.Thelowerelectrodeforthesecongurationsarealsosuppliedwithapotential,howeveritisnowtemporallyshifted180degreesrelativetotheexposedelectrode.Inordertomaintainaconstantnetsuppliedpotentialbetweenthedesigns,theexposedelectrodeincase3issuppliedwithavoltageof2,duetothelowerelectrodebeinggrounded.ThepreviouslydiscussedpoweringschemeB(seeFigure 4-3 )wasusedincases1and2,whilecircuitlayoutAisusedforcase3.ThethrustproducedbythethreecasesismeasureddirectlyasdescribedinSection 4.4.1 .Inthemulti-barrierdesign,electrodesaresandwichedbetweendielectriclayers.Toaccomplishthisatwopartepoxywasusedtoholdindividualdielectricsubstratestogether.Theepoxylayerswerefoundtohavethicknessesvaryingfrom60-150mdependingontheactuator.Itisassumed,however,thattheepoxyhasanegligibleeffectontheplasmaformationduetoitsrelativelysmallthickness(comparedtothedielectricitself).Althoughnotnecessary,theactuatorsincases2and3wereconstructedinthislayeredmannertofurthernegatetheinuenceoftheepoxyinacomparativesense. 119

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Figure6-1. Actuatorcongurationstestedinmulti-barrierplasmaactuatorinvestigation.Case1representswhatisconsideredtobethebi-layerMBPA,whilecase2isadualpoweredandcase3isasinglepoweredactuator. Acryliclayerswitharelativedielectricconstantof3werecombinedforanoverallthickness,t,of6mmforallthecongurations.Similarly,alldesignshadanelectrodelength,l,of120.0mm.Again,keepingwiththenotationfromSection 4.1.1 ,allthecongurationstestedhadanexposedelectrode'swidth,w1,of5mm.Similarly,thehorizontalfootprintofeachdesignremainedconstant,suchthat3w1=g+w2.Multiplehorizontaldisplacements,g,wereinvestigatedforeachdesignasoutlinedinTable 6-1 .Thedifferentcongurationsarereferencedasa,b,andc.Sinusoidalwaveformswithconstantdrivingfrequenciesof14kHzwereusedinalltests.ThehighvoltagesignalswherecapturedasdescribedinSection 4.3.1 ,withtheaveragepowerconsumptioncalculatedbyEquations 4 and 4 .Themeasuredpowerwasaveragedover560periods. 120

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Table6-1. Horizontaldisplacement,g,investigatedforeachactuatorconguration. CongurationCase1Case2Case3 a3mm0mm0mmb5mm5mm5mmc10mm10mm6.2EffectofGroundedElectrodeWidthInapriorinvestigation, Forteetal. ( 2007 )foundthatthepeakvelocityinducedbyastandardDBDactuatorchangedasthehorizontaldisplacement/gapbetweenthetwoelectrodeswasvaried.AsimilarinuencewouldbeexpectedfortheMBPAcongurationasthewidthofthegroundedelectrodeisvariedinthedesign.PlottedinFigure 6-2 istheresultantthrustforcases1a-cand2aasafunctionoftotalvoltage.Forthedualpoweredcongurationsthetotalvoltageisthenetpotentialacrossthedevice.Forexample,iftheexposedandencapsulatedelectrodesareeachsuppliedwitha12kVpppotential,duetothe180ophaseshiftofthelowerelectrode,thetotalvoltagewouldbe24kVpp.Cases1a-ccorrespondstowidths3,5,and10mm,whilecase2arepresentsnohorizontaldisplacement(or0mm).AsshowninFigure 6-2 ,foraconstantvoltagetheresultantthrustincreasessignicantlyasthewidthofthegroundedelectrodedecreases.However,therelativedifferenceinthethrustdoesdecreasewithdecreasingwidth.ThisislikelyduetothemodicationoftheelectriceldandconsequentlytheLorentzianforceonthechargedparticles(seeSection 3.1.2 ).Foraconstantvoltage,thelocalelectriceldcanonlyincreaseasthewidthbetweentheelectrodesisdecreased.However,whenconsideringtheactuator'seffectiveness,denotedbyEquation 6 ,anelectrodewidthof5mm(case1b)representsanoptimaldisplacement(Figure 6-3 ).Theactuator'seffectivenesstakesintoaccounttheactuator'spowerconsumptionnecessarytoachieveadesiredthrust.=Thrust Power (6) 121

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Figure6-2. Inuenceofthegrounded,middleelectrode'swidthonthrustgeneration,forabi-layerMBPAactuator. Figure6-3. Effectiveness(ratioofinducedthrusttoconsumedpower)asafunctionofvoltageforvariousgroundedelectrodewidthsinabi-layerMBPAactuator. 122

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6.3InuenceoftheGroundedElectrodefortheMBPACongurationThesimilaritybetweentheresultsof Forteetal. ( 2007 )andthoseshowninFigure 6-2 raisesquestionsregardingtherelativeimportanceofthemiddlegroundedelectrodeintheMBPAconguration.Doesthepresenceofthegroundedelectrodeinuencethemomentumtransfermechanismordoesitsimplyactasaspacerbetweentheexposedandencapsulatedelectrodes?PresentedinFigure 6-4 isthemeasuredresultantthrustbetweencases1b,cand2b,cforvariousvoltages.Again,theonlydifferencebetweenthesetwocongurationsisthepresenceofthemiddlegroundedelectrode.Regardlessofthegapwidth,thesamenominalthrustproductionisseenforeachconguration.Thiswouldindicatethatthemiddlegroundedelectrodeprovidesnosignicantadvantageintermsofthrustgeneration.Anumericalinvestigationofthesetwodesigncongurations,asoutlinedinChapter 5 ,alsoprovedtoyieldsimilarresults.AsshowninFigure 6-5 thetimeaveraged,non-dimensionalbodyforce,F,producedremainsapproximatelythesamebetweenthetwodesigns.Itshouldbepointedout,however,thatforthelongergapwidth(10mm,cases1cand2c)amoreuniformplasmawasestablishedforloweroperatingvoltagesasaresultofthemiddlegroundelectrode(case1c).Conversely,themiddleelectrodealsolimitedtheuppervoltagerangeforthelongergapwidth,astheactuatormorequicklyapproached`saturation'conditions(seeChapter 9 fordetailspertainingtothiscondition)limitingtheoverallmaximumthrustproduction(Figure 6-4 ).Withinthemeasurablevoltagerangethetotalpowerconsumption(Figure 6-6 )bythedeviceswasalsofoundtoberelativelyunaffectedbythepresenceofthemiddlegroundedelectrode.Differencesareobservableatthehighvoltagesinvestigatedforeachdesign,thoughthegeneraltrendsremainthesame.Conversely,thepresenceofthemiddleelectrodedoeshaveasubstantialinuenceonthepowerdistributionsuppliedtothetwoelectrodes(Figure 6-7 ).Whenthemiddleelectrodewaspresent(case1),theupper(orexposed)electrode'scircuitconsumedsignicantlymorepowerthanthelower(orencapsulated)electrode'scircuit.Inthiscase80-100%ofthetotal 123

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Figure6-4. Thrustasafunctionofvoltagewith(case1)andwithout(case2)agrounded,middleelectrodeinaMBPAconguration powerconsumedbythedevicewassuppliedtotheexposedelectrode.Whenremoved(case2),however,theconsumedpowerbetweentheupperandlowerelectrodecircuitswasapproximatelyequal.Theseresultsforthepowerdistributionmaybeexplainedbyconsideringtheexpectedelectriceldlinesforthearrangements(Figure 6-8 ).Forthecaseinwhichthegroundedelectrodeisnotpresent(case2),theeldlineswillbedrawnsolelyfromtheexposedelectrodetotheencapsulatedpoweredelectrode(Figure 6-8 A).ThedirectionoftheeldlineswouldobviouslybedependentonwhichparttotheACsignaloneistalkingabout,butasaresulttheworkdonebyeachpowersupplyshouldberoughlyequallydistributedbetweenthetwosinceeachelectrodeshouldcontributetotheionizationprocess.Conversely,whenthegroundedelectrodeispresent,analternativepathwayor`steppingstone'isprovided(Figure 6-8 B).Theeldlinesforthiscongurationstemmingfromtheexposedelectrodemayterminateatthegroundedelectrodeor,ifthepotentialsarehighenough,maystretchtothepoweredencapsulatedelectrode.ThisisschematicallyshowninFigures 6-8 Band 6-8 Cinwhich1isgreaterthan2.Intherstcasethepotentialonthelowerelectrodeislowenoughthatit 124

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Figure6-5. Timeaveraged,non-dimensionalforce,F,vectorsandmagnitudecontoursobtainedfromnumericalsimulations(Chapter 5 ).Non-dimensionalvoltages,,ofA,B)200,C,D)300,andE,F)400arepresented.ImagesA,C,E)correspondtoactuatorgeometrycase1(referringtoFigure 6-1 ),whileB,D,F)representcase2.Thedashedwhitelinerepresentsthedielectricsurface. virtuallydoesnotexistandcontributeslittletonothingtotheplasmaformation.Forthiscase,thelowercircuitshouldactroughlyasanidealcapacitorconsuminglittletonopower.However,asthesuppliedpotentialisincreased,thepresenceofthelowerelectrodeisseenanditbeginscontributingtotheionizationprocessand,thus,thetotalpowerconsumedbytheactuator.Thesetrendsarefoundinboththeexperimentaldata(Figure 6-7 )andnumericalsimulations(Figure 6-9 ).Fromtheexperimentaldata,Figure 6-7 ,atthelowervoltagesthepowerusedbytheencapsulatedelectrodewhenthegroundedelectrodeispresentisapproximatelyzero,butbeginstoincreaseasthe 125

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Figure6-6. TotalpowerconsumedbyaMBPAactuatorwith(case1)andwithout(case2)agrounded,middleelectrode. Figure6-7. PowerdistributionbetweentheexposedandencapsulatedelectrodeforaMBPAactuatorwith(case1)andwithout(case2)amiddle,groundedelectrode.A)g=5mmandB)g=10mm. 126

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Figure6-8. SchematicrepresentationoftheelectriceldlinesforaMBPAwithandwithoutamiddle,groundedelectrode.A)Nogroundedelectrodeispresent,B)groundedelectrodeispresentbutthesuppliedpotentialislow,andC)groundedelectrodeispresentandthesuppliedpotentialisofsufcientstrengththattheelectriceldismodiedbythepresenceofthelower,encapsulatedelectrode. potentialisincreased.SimilarlyFigure 6-9 showsamodicationtotheelectriceldasaresultofthegroundedelectrodepresencesatlowervoltages(Figures 6-9 Aand 6-9 B).However,asthevoltageisincreasedthisinuencedisappears(Figure 6-9 C-F).WithinFigure 6-9 ,themodicationoftheelectriceldisvisualizedbythenon-dimensionalelectriceldequivalentof30kVcm)]TJ /F7 7.97 Tf 6.59 0 Td[(1,therequiredeldtoionizeairatatmosphericpressures,indicatedbyasolidblackline. 6.4ComparisonwithStandardActuatorDesignAsacomparisonwiththestandardactuatorconguration(case3),thediscussionwillbelimitedtosolelyconguration2,sinceintheprevioussection,itwasshownthatthedifferencebetweencases1and2wasnegligible.FromFigure 6-1 ,theonlyvariationbetweencases2and3ishowthevoltageissuppliedtothedevice.Forcase2,aphaselagisusedtosplitthesuppliedpotentialbetweenthetwoelectrodes,whileonlythetopelectrodeispoweredincase3.Comparingthetwocases,Figure 6-10 presentstheinducedthrustasafunctionofappliedvoltage.Theresultsindicatethatthereislittledifferencebetweencases2aand3aasbothdesignsproducenominallythesamethrust(althoughslightlyhigherforcase3)foragivenvoltage.Thereisasignicantdifference, 127

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Figure6-9. Contoursofthenon-dimensionalelectricpotential,,obtainedfromnumericalsimulations(Chapter 5 ).TheappliedpotentialisequaltoA,B)=200,C,D)=300,andE,F)=400.ReferringtoFigure 6-1 ,imagesA,C,E)correspondtotheactuatorgeometrydenotedbycase1,whileB,D,F)representcase2.Thenon-dimensionalelectriceldequivalentof30kVcm)]TJ /F7 7.97 Tf 6.59 0 Td[(1,therequiredeldtoionizeairatatmosphericpressures,isoutlinedbyasolidblackline,wherethedashedwhitelinerepresentsthedielectricsurface. 128

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Figure6-10. EffectofvoltagesplittingontheresultantthrustforaDBDactuator.Thevoltagesuppliedtocase2issplitbetweentheupperandlowerelectrodes,whileonlyvoltageisappliedtothetopelectrodeincase3. however,betweencases2band3b.Foragivenvoltage,thestandardactuator(case3b)resultsinalargerinducedthrustcomparedtocase2b,thoughthisincreasedthrustisassociatedwithasubstantialincreaseinconsumedpower.Thisleadstoadecreasedeffectiveness(givenbyEquation 6 )forcase3incomparisontocase2(Figure 6-11 ).Basedontheeffectivenessmerit,againof30%maybeachievedbysplittingthesuppliedvoltage. 6.5AlternativeMBPACongurations 6.5.1MixingDielectricMaterialAsastartingpointtothebroaddesignspaceofmixeddielectrics,asinglecombinationforabi-layerMBPA(case1fromFigure 6-1 )wasinvestigated.Resultsfortheinducedthrust,power,andeffectivenessarepresentedinFigure 6-12 .Thebi-layermixtureconsistedofacrylicandTeonlayerswhicheachhadathicknessof1.5mm,foratotalthickness,t,of3mm.Therelativedielectricconstantsforthetwomaterialsare2and3forTeonandacrylic,respectively.Thenotation`Teon-Acrylic'showninFigure 6-12 indicatesthatTeonistherst(ortop)dielectricandacrylicisthe 129

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Figure6-11. Effectiveness(ratioofinducedthrusttoconsumedpower)forasplitpotentialactuator(case2)andastandardactuator(case3)overarangeofvoltages.Thevoltagesuppliedtocase2issplitbetweentheupperandlowerelectrodes,whileonlyvoltageisappliedtothetopelectrodeincase3. second(orbottom)dielectricreferringtoFigure 6-1 .TheelectrodedimensionsremainthesameasdescribedinSection 6.1 forcase1b.Animprovementinthrustisshownforthe`Acrylic-Teon'arrangementoverthe`Teon-Acrylic'conguration.Thisimprovementislikelyduetodifferencesintherelativedielectricconstantsofthetwomaterials.PreviousoptimizationstudiesonconventionalDBDactuatorshaveshownthatforagivenvoltageamaterialwithahigherrelativedielectricconstantwillresultinahigherachievablethrust( Thomasetal. 2009 ).Thesessamestudies,however,haveindicatedthattheuseofdielectricswithlowerpermittivitiesultimatelyincreasesthemaximumvoltagethatmaybeapplied.Thehighervoltagesresultinanoverallincreaseinthrustproduction(seeChapters 8 and 9 foradditionaldetailsonthistopic).ThetrendobservedinFigure 6-12 Aisconsistentwiththesestudiesasthehigherdielectricconstantmaterial,acrylic,isusedasthetoplayerinthe`Acrylic-Teon'conguration.However,ifhighervoltageswouldhavebeeninvestigated,the`Teon130

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Figure6-12. Performancecharacterizationofamixeddielectricmulti-barrieractuator.A)Thrust,B)power,andC)effectivenessresults.Thenotation`Teon-Acrylic'indicatesTeonwastherst(ortop)dielectricandacrylicisthesecond(orbottom)dielectricandviceversafor`Acrylic-Teon'. Acrylic'designwouldhavelikelyresultedinlargerthrustseventually.Theincreasedthrustproductionofthe`Acrylic-Teon'arrangementwasassociatedwithanincreasedpowerconsumption(Figure 6-12 B),resultinginalowereffectivenesscomparatively(Figure 6-12 C). 6.5.2Tri-LayerMBPAAnaturalextensiontothebi-layerMBPA(case1fromFigure 6-1 )isthetri-layerconguration,whereanotherdielectriclayerandpoweredelectrodeisadded(Figure 6-13 ).Allelectrodeswere5mmwide(w1=w2)and120mminlength,l.Thetotal 131

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Figure6-13. Schematicofatri-layermulti-barrierplasmaactuator. thickness(t)oftheactuatorwas6mmwitheachlayerbeingconstructedoutofacrylic.Asintheprevioussections,all4electrodesofthetri-layerdesignweresuppliedwiththesamepotentialbutwithrelativephaseanglesbetweenthesignals.Alinearprogressionintherelativephaseanglesforthesandwichedelectrodeswasused.ReferringtoFigure 6-13 ,1and2wereequal60oand120o,respectively,whiletheencapsulatedelectrodehadan180ophaseshift.Positivevaluesofrefertoa`leading'arrangementwhilenegativevaluesareconsidered`lagging'.ExamplevoltagewaveformsareshowninFigures 6-15 Aand 6-15 Cforleadingandlaggingcongurationsrespectively.Resultsforthemeasuredthrust,consumedpower,andeffectivenessarepresentedinFigure 6-14 againstthetotalvoltage.Forthetri-layeractuator,thetotalvoltage(asdescribedpreviously)isthenetvoltageacrossthedeviceasallelectrodesaresuppliedwithequal,thoughtemporallyshifted,potentials.UsingthesameexampleasdescribedinSection 6.2 ,iftheexposedandlowestelectrode(andallotherelectrodes)areeachsuppliedwitha12kVpppotential,duetothe180ophaseshiftofthelowestelectrode,thetotalvoltagewouldbe24kVpp.Thethrustmeasurements(Figure 6-14 A)indicatethatthereisalargediscrepancyintheproducedthrustbetweentheleadingandlaggingcircuits,especiallysincetheconsumedpowerisrelativelythesame(particularlyatlowvoltages)betweenthecongurations(Figure 6-14 B).Thisleadstoasubstantialimprovement,comparatively,ineffectivenessfortheleadingcircuitconguration(Figure 6-14 C).Forexample,at12 132

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Figure6-14. Performancecharacterizationofatri-layermulti-barrieractuator.A)Thrust,B)power,andC)effectivenessresults.Thenotation`Leading'referstopositivephaseangles,while`Lagging'indicatesnegativephaseangles. kVppanimprovementineffectivenessof85%inseenbetweentheleadingandlaggingconguration.Apotentialexplanationforsucharesultmaybefoundinthevoltageandcurrentwaveforms(Figure 6-15 ).AsdescribedinChapter 3 ,ithasbeenwidelydocumentedbothexperimentallyandnumericallythattheplasmabehavesquitedifferentlyoverasingleperiodoftheappliedvoltage.AsshowninFigures 6-15 Band 6-15 Ctheevolutionofthecurrentsignalismodiedbytheparticularlead-lagconguration.Thesemodicationsareeasilyseenbytheshiftinglocationsofthelargeirregularcurrent 133

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spikes.Itisbelievedthattherelativephaseanglesare`diminishing'theplasma'smomentumtransfer,relatively,foralaggingcircuitcongurationbyeffectivelyreducingthenetelectriceldneartheexposedelectrodeduringthenegativehalfcycle.Incomparison,however,tothebi-layer(case1orcase2)andthestandard(case3)actuator,thetri-layercongurationissignicantlyoutperformedinallmetricswhetheritbethrustoreffectiveness.Althoughadditionalcongurations(i.e.alternativedielectrics,phaseangles,electrodewidths,dielectricthickness,etc.)shouldbetested,basedonthecurrentresultsthetri-layeractuatorappearstobeapooractuatordesignchoice. 134

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Figure6-15. Instantaneousvoltageandcurrentwaveformsforatri-layerMBPA.ThevoltagetoeachwaveformisshowninimagesA)andC),whileonlytheexposedelectrode'svoltagesignalisshowninB)andD)withthecurrentmeasuredateachelectrode.NotethatapositivereferstoaA,B)leadingphaseangle,whilenegativevaluesareconsideredC,D)lagging. 135

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CHAPTER7THREE-DIMENSIONALACTUATIONTheinducedoweldresultingfromthestandardlinearactuatorandtheplasmasyntheticjetactuator(Section 3.1.3 )areinherentlytwo-dimensional.Combiningthesetwodesigns,however,theserpentineactuator(Figure 7-1 )ensuresafullythree-dimensionalvectoreld.Intuitively,asonemovesalongthespanoftheactuator,thereisaspreadingoftheuidatthecrestwhilethereisapinchinginthetrough.Suchadisturbanceshouldresultinanenhancedmixingofthesurroundinguidasnumericallypredictedby Roy&Wang ( 2009 ).Thefollowingsectionaimstocharacterizetheinducedoweldgeneratedbytwodifferentserpentinecongurationsinquiescentair.Therstdesignisconstructedfrompatternedcirculararcs,whilethesecondfrompatternedrectangles.Thenon-intrusiveowdiagnostictechniqueofparticleimagevelocimetry(PIV)isusedtoquantifytheeffectsoftheseactuators.Astereo-PIVsystem(Section 4.5.1 )isusedtocapturetimeaveraged(200imagepairs),spatiallyresolveddatasetsofthevectoreldsalongspanwiseandstreamwisecuts.Thetwo-dimensionalplanesarethenreconstructedtogiveathree-dimensionalviewoftheinducedoweld.Comparisonswithalinearactuatoraremadeaswell. 7.1SerpentineActuatorDesignGeneralschematicsofthetwoserpentinedesignsinvestigatedinthisworkareshowninFigure 7-2 :onewithpatternedcirculararcs( 7-2 B),andonewithpatternedrectangles( 7-2 C).Thephoto-fabricationmethoddescribedinSection 4.1.2 wasusedtoconstructthecontinuouscurvedsurfacesoftheserpentineactuator.InreferencetoFigure 4-1 ,forbothdesignstestedthewidthoftheexposedelectrode,w1,wasxedat2mmandtherewasnohorizontaldisplacementbetweentheelectrodes(g=0mm).3.0mmthickacrylicwasusedasthedielectricsubstrate(r=3.0). 136

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Figure7-1. AcircularserpentineDBDactuatorandthenotationalinuenceontheinducedoweld.Takenfrom Durscher&Roy ( 2012c ). InthepatternedcirculararcsdesignFigure( 7-2 B)theradiioftheinneredgeoftheexposedelectrodeare6(r1)and4(r2)mm.Thelowergroundedelectrodeinthisdesignhasawidth,w2,of5mmwhichfollowsalongtheinnerradiusoftheexposedelectrode.ThedimensionsforthepatternedrectangulardesignareshowninFigure 7-2 C,whereg1=2r1=12mm,g2=r1+r2=10mm,g3=w2=5mm,andg4=2r2=8mm.Thegroundedelectrodeforthisdesignagainfollowsalongthewindingsoftheexposedelectrode,butforsimplicityoffabrication,theexcessgroundedelectrodewasnotremovedinthetroughregion.Thewavelength(p),orthelengthoverwhichthepatternrepeatsitself,forbothdesignswas20mm.Topreventendeffectsfrominuencingthevelocitymeasurements,theactuatorstestedconsistedof8and9wavelengthsforthecircularandrectangulardesigns,respectively.Thiscorrespondstooverallspanwise(z-direction)lengths,l,of160mmand180mm.Asinusoidalvoltagewaveformwithadrivingfrequencyof10kHzwassuppliedtotheactuatorsusingpoweringcongurationAfromFigure 4-3 .Thedissipatedpowerwascalculatedfromtheaveragedproductofthevoltageandcurrentwaveformsmeasuredattheexposedelectrode(Equation 4 ). 137

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Figure7-2. Ageneralschematicoftheserpentineactuatorsinvestigated.A)AsideproleandtopviewsoftheB)circularandC)rectangularserpentineactuatorstested.Takenfrom Durscher&Roy ( 2012c ). Inordertofullycapturethethree-dimensionalnatureoftheinducedoweldinthequiescentchamber,bothspanwiseandstreamwisecutsweretakenalongtwo-dimensionalplanesoftheactuator.Forthespanwisecuts,9planeswereimagedstartingatz=0mmandendingatz=-20mmin-2.5mmincrements.Notethatthetotalwavelengthofthedeviceis20mm;acompletewavelength,therefore,wascapturedinthespanwisescan.Similarly,10planeswerecapturedinthestreamwisedirectionstartingatx=-2.5mmandendingatx=20mm,againin2.5mmincrements.Figure 7-3 providesanexampleofspanwiseandstreamwiseplanarcutsrepresentedbydashedanddottedlines,respectively.Thefollowingsectionpresentstheresultsofthesemeasurementsandhighlightshowtheserpentinedesigndiffersfromthatofalinearactuator. 7.2CircularSerpentineActuator 7.2.1FlowVisualizationAsasimplerststep,thelasersheetwaspositionedtoilluminatethespanwiseplanecuttingthroughthetroughofcircularserpentineactuator(z=0mm).Alitincensestickwasplaced5mmupstreamoftheexposedelectrode,theactuatorwasturnedon,andtheimagewascapturedusingaNikonD90SLRcamera.Theresultofthisrudimentarytestindicatesaverticallyvectoredmomentumcomponentalongtheplane. 138

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Figure7-3. Locationsofspanwise(dashedlines)andstreamwise(dottedlines)planarcutsinmm.Takenfrom Durscher&Roy ( 2012c ). Figure7-4. Flowvisualizationoftheinducedvelocityusinglocalizedseeding.TheowpatternproducedbyA)acircularpatternedserpentineactuatorforaplanetakenalongthetrough(z=0mm)andB)astandardlinearactuator.Takenfrom Durscher&Roy ( 2012c ). Theowispushedawayfromthesurfaceatapproximatelya43oangle(Figure 7-4 A).Asacomparison,smokeowvisualizationwithastandardlinearactuatorshowsthattheinducedjetcreatesa12oanglewiththesurface(Figure 7-4 B).Theobservedpinchingoftheuidintheserpentinecongurationisaresultofcollidingstreamsofuidacceleratedduetotheplasmabodyforce.Thisforceactsperpendiculartothecurvatureoftheexposedelectrodedrivingtheuidparalleltothedielectricsurface.However,sincetheserpentinedesignalsoconsistsofaneighboringspreadingregionatthecrestoftheactuator,theexistenceofatrulythree-dimensionaloweldisnatural. 139

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7.2.2InducedFlowFieldMeasurementsIftheserpentineactuatoristrulyathree-dimensionaldevice,asonemovesalongthespanoftheactuator,thez-componentofvelocity,uz,andresultingowstructureshouldvary.ThisfactisshowninFigure 7-5 whichdepictscontoursofuzforselectspanwiselocationsforaninputvoltageof14kVpp.Figure 7-5 showsthatatthetrough(z=0mm)andthecrest(z=-10mm)oftheactuatortheowdirectionisprimarilyinthex-yplane(ortwo-dimensional).Fortheotherlocations(z=-2.5and-17.5mm)presentedinFigure 7-5 B,D,onecanseethattheactuatorisaddinganoutofplanecomponenttothenetmomentumimpartedtotheuid.Itwillbeshownthatthisoutofplanecomponentresultsinstreamwisecounter-rotatingvortexpairs(CVPs).Thepaired,anti-symmetricvelocitycontoursinandoutofplaneshowninFigure 7-5 B,DarefurtherevidenceoftheCVPs.Althoughthetimeaverageoweldatz=0mmand-10mmshowsnoindicationofasignicantz-componentinthevelocityvector,aninstantaneousimageindicatesaquitedifferentscenario.Notshownhereforbrevity,astaggeredstructureinuzwasobserved,whichresultedinanetcancellationinthetimeaverage.Futureeffortswilladdressthetemporalnatureofthisactuatorcongurationthroughphaselockedstereo-PIVmeasurements.SelectresultsfromthestreamwisescanofthecircularserpentineactuatorareshowninFigure 7-6 ,whichdepictscontoursofthestreamwise(!x)vorticity.Theseresultsshowpairsofvectoredcounter-rotatingvorticeswhicharecenteredalongthez=0and-20mmplanes(thetroughsoftheactuator).Thevorticesbegintoformaroundtheinectionpoint(x=6mm)ofthecurvemakinguptheexposedelectrodeandcontinuetogrowinmagnitudeastheypropagatedownstream.ThegrowthofthevortexpairsisclearlyseeninFigure 7-6 D.Theseresultsagreewellwithpriornumericalprediction( Roy&Wang 2009 ; Wangetal. 2011 )oftheexistenceofsuchaowstructure.However,onemayalsonoticethelackofsymmetrybetweenthevortexpairlocatedatz=0mmand-20mm.Theasymmetryappearstoworsenthefurther 140

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Figure7-5. Timeaveragedz-velocity,uz,contoursoverlaidwithx-andy-velocityvectorsforvariousplanarcutsalongthespanofacircularserpentineactuator.Theappliedvoltageis14kVpp.A)z=0mm,B)z=-2.5mm,C)z=-10mm,andD)z=-17.5mm.Takenfrom Durscher&Roy ( 2012c ). downstream.Sucharesultismostlikelyduetoslightvariationsintheplasmabodyforcealongthespanoftheactuatorwhichresultsinanon-uniformityintheoweld. 7.2.3EffectofVoltageToinvestigatetheinuenceofinputvoltageonthestructureoftheinducedow,thesuppliedvoltagewasincreasedfrom14to16kVpp.Forvoltagesabove16kVpptheextensionoftheplasmabegantoapproachtheedgeofthegroundedelectrode.Athighervoltagesthisinsufcientlengthinthegroundedelectrodecouldhaveresultedinasuppressionoftheplasmabodyforceandtheresultingvelocity.( Forteetal. 2007 ) 141

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Figure7-6. Timeaveragedcontourplotsandiso-surfacesofstreamwise(!x)vorticityforacircularserpentineactuatorwithaninputvoltageof14kVpp.A)x=7.5mm,B)x=12.5mm,C)x=17.5mm,andD)athree-dimensionalperspectiveview(thegreenplaneindicatesx=0mm).Takenfrom Durscher&Roy ( 2012c ). Highervoltageswere,therefore,notinvestigated.Futureexperimentswilladdressthislimitationintheelectrodearrangements.Figure 7-7 presentsreassembledthree-dimensionalperspectivesandplanarcontoursofthetimeaveragedspanwisevorticity(!z)forthehigherdrivingpotential.Theresultsaresimilartothatfoundforthelowerinputvoltage.Thez-vorticityshowscharacteristicsofatypicalwalljetproducedbyalinearactuator(Figure 7-12 C)overmostofthespanofthedevice,withtheexceptionbeingatthetroughs(z=0and-20mm).Attheselocationstheopposingplasmaforces 142

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Figure7-7. Temporallyaveragedspanwise(!z)vorticityiso-surfacesreconstructedfromplanarmeasurementsonacircularserpentineactuator(16kVpp).A)PerspectiveandB)topviews,wherethegreenplaneindicatesx=0mm,alongwithcontoursandstreamtracesextractedatC)z=0andD)z=-10mm.Takenfrom Durscher&Roy ( 2012c ). resultsinapinchingoftheuidwhichisthenpropelledupward.Theonlydifferenceobservedwiththehigherinputvoltageisanincreaseinvorticitystrengthparticularlyclosetothewall.ThisincreaseisnotsurprisinggiventhattheplasmaforceanditsinuenceonthesurroundinguidvelocityisknowntoincreasewithvoltageforaDBDactuator.Thus,thespanwisevorticitycomponentwillincreaseclosetoanoslipwall.AnincreaseinvelocityisindeedoccurringasshowninFigure 7-8 .Despitethisincrease,thevelocityprolesdonotappeartochangeasFigure 7-8 revealsfor 143

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locationsz=0and-10mm.Atthetroughspecically,theresultantowangleremainsapproximatelyat38oasshowninFigure 7-8 A,Cbyasolidblackline.ThisangleisinagreementwiththeangleestimatedfromowvisualizationsdescribedinFigure 7-4 previously.Thisindifferencetovoltageontheimpingementangleisnotconclusiveduetothelimitedrangeofvoltageexplored.Itis,however,plausible.Whilethevelocityoftheimpinginguidisgrowingwithincreasingvoltage,itincreasesuniformlyalongthecurvatureoftheelectrode.Thisuniformityandthexedgeometryoftheserpentinedesignimpliesthattheuidispushedatanominallyconstantangleregardlessoftheappliedvoltage.Toensureatrulycontrollablejet,asegmentedelectrodestructurewithavariablevoltage,similartothetwoopposinglinearplasmaactuatorsof Porteretal. ( 2009 ),maybewarranted. 7.3RectangularSerpentineActuatorTheoverallstructureoftheresultantoweldinducedbytherectangularserpentinedesignwitha14kVppinputisremarkablysimilartothatofthecircularconguration.However,thereareafewnotabledifferencesstartingwiththestreamwisevorticitygeneration.AsFigure 7-9 ,showstherectangulardesignproducespairsofcounterrotatingvorticescenteredaboutz=0mmand-20mm,aswell.Thedifference,though,liesinthestrengthandareaoverwhichthevortexacts.Sincetherectangulardesignismadeupofstraightlinesasopposedtothecurvedcircularactuator,itiseasytoseefromFigure 7-2 Cthatalargerportionoftheplasmageneratedalongtheactuator'swavelengthwillacceleratetheowinopposingz-directions.Thisresultsinadditionalstreamwisevorticitygeneration.Theothernoteworthydifferenceisinthemagnitudeoftheresultantvelocityatthetroughandcrestoftheactuator(Figure 7-10 ).Thestructureoftheowatz=0mmand-10mmisroughlyidenticaltothatfoundinFigure 7-8 .Theimpingementowanglealsoremainsconstantat38o.However,atz=0mmthevelocitymagnitudehasincreasedcomparedtothecircularserpentinedesignforthesameinputvoltage,14kVpp.The 144

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Figure7-8. Timeaveraged,velocitymagnitudecontoursalongacircularserpentineactuator.TheappliedvoltagesareA,B)14kVppandC,D)16kVpp.ImagesA)andC)correspondtoz=0mm,whileB)andD)representz=-10mm.Theimpingementangleintheowwasfoundtobe38oasindicatedbytheblacksolidline.Takenfrom Durscher&Roy ( 2012c ). increaseinvelocitylocallyatthetroughandnotthecrestislikelyduetothestraightlinedesignanditsinuenceontheoutofplanevelocitycomponent.Thecombinationofbothspanwiseandstreamwisevorticitygenerationcreatesauniquestructureintheinducedoweldfortheserpentinecongurations.AsshownbythestreamtracesinFigure 7-11 ,whicharereconstructedfromthestreamwisescan,theuidfollowsacorkscrewlikepathasitisentrainedinthetroughsoftheactuator.Thevectoredpinchingoftheuidinthisregionpushestheuidforwardandawayfromthesurfaceasuzimpartsaspinonitspath.Theuidatthecrestoftherectangularactuator 145

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Figure7-9. Timeaveragedcontourplotsandiso-surfacesofstreamwise(!x)vorticityforarectangularserpentineactuator(14kVpp).A)x=7.5mm,B)x=12.5mm,C)x=17.5mmandD)athree-dimensionalperspectiveview(thegreenplaneindicatesx=0mm).Takenfrom Durscher&Roy ( 2012c ). issimplypushedforward.Asimilarcorkscrewlikepathwasobtainedfromthespanwisescan,aswellasforthecircularserpentinedesign. 7.4ComparisonwithaLinearActuatorAsameansofcomparison,stereomeasurementsweremadealongthespanofastandardlinearDBDactuatoraswell.ReferringtoFigure 4-1 ,w1=2mmandw2=5mmfortheelectrodewidthsandtheoveralllength,l,oftheactuatorwas160mm.Forthisactuatoronlythreeplanes(z=0,-5,and-10mm)wereinvestigatedallyieldingapproximatelyidenticalresults.Thez-velocity,x-velocity,andz-vorticitycontoursalong 146

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Figure7-10. Temporallyaveraged,velocitymagnitudecontoursoverlaidwithx-andy-velocityvectorsforarectangularserpentineactuator(14kVpp).Twoplanesareshown,A)z=0mmandB)z=-10mm.Theblacksolidlineindicatestheimpingementangleintheow,38o.Takenfrom Durscher&Roy ( 2012c ). Figure7-11. Streamtracescoloredbystreamwise,!x,vorticityshowingacorkscrewlikestructureintheinducedoweld.Takenfrom Durscher&Roy ( 2012c ). 147

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Figure7-12. Timeaveragedquantitiesforalinearactuatordrivenat14kVpp(z=0mm).ImageA)correspondstothez-velocity,B)thex-velocity,andC)thez-vorticity.Takenfrom Durscher&Roy ( 2012c ). thez=0mmplaneareshowninFigure 7-12 fora14kVppinputvoltage.Thevelocitycontoursindicatethattheoutofplanecomponentofvelocity(uz)isminutecomparedtothatofthex-component.Thisfurthervalidatestheassumptionthatthelinearactuatorisaprimarilytwo-dimensionaldevice(consistentwiththatpresentedinSection 4.5.2 )Theuxanduyvelocityprolesfortwodifferentspanwiselocations(x=15and20mm)arepresentedinFigures 7-13 and 7-14 .Thespanwisecutsfortheserpentinecasesweretakenalongthetrough(x=0mm)inFigure 7-13 whilethecutsweretakenatthecrest(x=10mm)inFigure 7-14 .Bothoftheselocationswereshownabovetobequasitwo-dimensional.TheresultingprolespresentedinFigures 7-13 and 7-14 highlightkeydifferencesinthelinearandserpentinedesigns.InthecaseofthelinearDBD,themomentuminjectionisprimarilyinthex-directionwhichislocalizednear 148

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Figure7-13. Velocityprolesofuxanduyforalinear,circular,andrectangularserpentineactuator(z=0mm).ThestreamwisepositionoftheprolescorrespondtoA,C)x=15mmandB,D)x=20mm.Furthermore,thecutistakenalongz=0mmfortheserpentinecases.Theappliedvoltagewas14kVpp.Takenfrom Durscher&Roy ( 2012c ). thewall.Asaresultthereisnegligiblevertical(y)oroutofplane(z)componentsofvelocity.Theserpentineconguration,however,introducesbothx,y,andz(referringtoFigures 7-5 and 7-13 )momentumtotheuid,particularlyatthetrough.Atthecrestoftheactuator(Figure 7-14 ),thevelocityproleoftheserpentineactuatorsiscomparabletothewalljetproducedbythelinearactuator. 149

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Figure7-14. Velocityprolesofuxanduyforalinear,circular,andrectangularserpentineactuator(z=-10mm).ThestreamwisepositionoftheprolescorrespondtoA,C)x=15mmandB,D)x=20mm.Furthermore,thecutistakenalongz=0mmfortheserpentinecases.Theappliedvoltagewas14kVpp.Takenfrom Durscher&Roy ( 2012c ). TheaveragecalculatedpowerconsumptionforeachdeviceispresentedinTable 7-1 .Whennormalizedbythespanwiselength,l,thelinearactuatorclearlyusedtheleastamountofpower,whiletherectangulardesignconsumedthemost.However,consideringthetotallengthoftheelectrode,ltot,thataccountsforthewindingelectrode,thenormalizedpowervariationsbetweenthedesignsdrasticallyreduces.Thisresultindicatesthattheionizationprocessmaynotbeaffectedbythegeometricmanipulation 150

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Table7-1. Averagepowerconsumptionsforlinear,circularserpentine,andrectangularserpentineactuators(14kVppat10kHz).Takenfrom Durscher&Roy ( 2012c ). Ptot(W)Ptot=l(Wm)]TJ /F7 7.97 Tf 6.59 0 Td[(1)Ptot=ltot(Wm)]TJ /F7 7.97 Tf 6.58 0 Td[(1) Linear2.60.516.33.116.33.1Circularserpentine4.80.630.03.719.12.4Rectangularserpentine7.20.840.04.420.02.2 oftheelectrodes.Intheserpentinedesignoneisonlyaffectingthedirectioninwhichtheplasmabodyforceisoriented.However,fromadesignperspective,theultimategoalistoapplytheseactuatorstorealworldaerodynamicowssuchasoveranairfoil.Insuchacasetheactuatorwouldmostlikelybeappliedoversomeunitlengthoftheairfoil,wherePtot/lwouldbethemoreappropriatedesignparameter. 151

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CHAPTER8EXTREMEDIELECTRICSAsshowninFigure 3-12 ,thedielectricmaterialusedhasasubstantialeffectontheactuator'sthrustproduction.Inapriorexperimentalinvestigation, Thomasetal. ( 2009 )showedthatforaxedplatethicknessandfrequency,thesaturationthrust(ormaximumthrustachieved)decreasedastherelativedielectricconstantincreasedfrom2to6.Thefollowingexperimentsexploretheextremeupperandlowerrangesofdielectricconstantsusedthusfarinliterature. 8.1FerroelectricActuatorsTotesttheupperextremeofdielectricpermittivity,theuseofaferroelectric(ModiedLeadZirconate-Titanate,PZT)materialwasinvestigated.Theferroelectricsamplehadanominalrelativedielectricconstant(r)of1750.Thedimensionsoftheferroelectricsamplewere40mmx12mmx3mm(x,y,t).ReferringtoFigure 4-1 ,thewidthofexposedandencapsulatedelectrodeswerew1=w2=5mm.TheactuatorwaspoweredusingcongurationCinFigure 4-3 .Theferroelectricmaterialallowedforadischargeignitionatamuchlowerinputvoltageascomparedtomaterialsofthesimilarthicknesswithlowerdielectricconstants.ArepresentativepictureofthedischargegeneratedisshowninFigure 8-1 Aforaninputvoltageof3.5kVppat5kHz.AsshownintheFigure,thedischargeisconcentratedaroundtheexposedelectrode'sedge.Athighervoltages(>5kVpp,5kHz),forthisthicknessofferroelectric,dielectricheatingbecameaproblemwithtemperaturesreaching200oCafteronly10'sofsecondsofoperation.Atthispoint,keepingtheadhesivelybackedcoppertapeelectrodesadheredtothesurfacewasdifcult.Evenatthesehighervoltagesthedischargeneverappearstopropagatedownstreamaswouldanactuatorconstructedfromalowerdielectricconstant.Thisislikelyduetohighsurfacechargeaccumulatedduetohighcapacitanceofferroelectricmaterialincreasingthesurfacepotentialandreducingtheelectriceldlocally.Thiswould 152

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Figure8-1. Visualandthermalcharacteristicsofaferroelectricactuatorsuppliedwitha3.5kVpp,5kHzsinusoidalinput.A)ApictureoftheplasmadischargeandB)thecorrespondingsurfacetemperature.Temperaturemeasurementistakenafter300secondsofoperation.Takenfrom Durscher&Roy ( 2012a ). limittheexpansionoftheplasmaalongthesurface.Adirectthrustmeasurement,asdescribedinSection 4.4.1 ,wasusedtoquantifytheactuator'sperformance.Sincethethrustproducedisdirectlytiedtovoltage,overtherangeofinputstested(1.5to3.5kVppat14kHz)nomeasurablethrustwasdetected.Withnothrustbeingachieved,thedielectricheatingofthedevicewasinvestigated.AninfraredcameraasdescribedinSection 4.6 wasused.Theambienthumidity(55%RH)andtemperature(22oC),distancefromactuator(0.33m),andmaterialemissivity(0.960.02)wereallconsideredindeterminingthesurfacetemperature.Asmentionedinthepreviousparagraph,thehightemperaturesobservedduringinitialtestswerefoundtoexceedtheboundariessetbythecurrentactuatorconguration,assuchtheoperationalvoltage/frequencyregimesweresetastonotexceedtheselimits.Temperaturemeasurementsweremadeoverarangeofvoltages(1.5to4kVpp)at5kHzaswellasoverarangeoffrequencies(DCto14kHz)at3kVpp. 153

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Figure 8-1 Bshowsarepresentativesurfacetemperaturedistributionafter300secondsofoperation.Lookingatatimetrace(Figure 8-2 )forapointtakenatx=12.5mmandy=1.5mm,thesurfacetemperatureshowsasharpinitialincreaseandthengraduallyrisestoitssteadystatetemperature.TheprolespresentedinFigure 8-2 areconsistentwiththatof Joussotetal. ( 2010 ).ThemeasurementsshowninFigure 8-2 correspondtoaninitial5secondsofnon-actuation,afterwhichthedevicewasturnedonfor300seconds.Onceturnedoff,another40secondsofdataacquisitioncontinued.Notingtheseeminglystrongdependenceonfrequencyandvoltage,aplotofthetemperatureriseafter300seconds(atx=12.5mm,y=1.5mm)asafunctionofpowershowsalinearrelationshipproportionalto0.87oCW)]TJ /F7 7.97 Tf 6.58 0 Td[(1m(Figure 8-3 .Thisproportionalityissolelydependentofpowerconsumptionandthusindependentoftheinputfrequencyorvoltage,atrendalsoobservedby Joussotetal. ( 2010 ).However,asshowninFigure 8-2 A,foraconstantvoltageonemayreachthesamesurfacetemperaturefasterusingahigherfrequency.Theresultsindicateapossibilityofoperatingatanevenhigherfrequencytogeneratethermalloadingatafastertimescale.Thissameargumentalsocanbemadeforaconstantfrequencywithamodulatedvoltage(Figure 8-2 B). 8.2AerogelActuatorsSilicaaerogelwasusedtoinvestigatethelowendofthedielectricspectrum.Ingeneralsilicaaerogelsconsistofacomplexmicrostructureofsilicondioxideinwhichairoccupiesamajorityofthevolume.Forthesamplestested,95%ofthedielectric'svolumewasairresultinginadensityrangingfrom0.04to0.12gcm)]TJ /F7 7.97 Tf 6.59 0 Td[(3withresultsbeingreportedforsampleshavingadensityof0.11gcm)]TJ /F7 7.97 Tf 6.59 0 Td[(3.Silicaaerogelsinthisrangeofdensitieshavearelativedielectricconstant(r)of1.1-1.2( Hrubeshetal. 1993 ).ThesampleofaerogelusedinthisworkisshowninFigure 8-4 Aalongwithaninsetimageofaplasmadischargebeingignitedonasmallersampleasaproofofconceptdemonstration.Forthesilicaaerogeltests,theelectrodewidthswerew1=5andw2= 154

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Figure8-2. Surfacetemperatureasafunctionoftimeaboutpoint12.5mm,1.5mm(x,y).A)Variousfrequenciesareappliedataconstantvoltage(3kVpp)andB)variousvoltagesataconstantfrequency(5kHz).Takenfrom Durscher&Roy ( 2012a ). Figure8-3. Thesurfacetemperatureofaferroelectricsampleasafunctionofpowerconsumption,after300secondsofoperation.Resultsforamodulatedfrequencyat3kVpp(redsquare)andamodulatedvoltageat5kHz(greentriangle)arepresentedinA)linearandB)logarithmicscales.Takenfrom Durscher&Roy ( 2012a ). 155

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20mm.TheactuatorspresentedinthissectionwerepoweredusingcongurationBinFigure 4-3 witha14kHzdrivingfrequency.Thesurfacemorphologyofsilicaaerogelactuatorsobtainedusingnon-contactatomicforcemicroscopy(AFM)isshowninFigure 8-4 Bona5mx5msurfacearea.Thearithmeticmeansurfaceroughness(Sa)rangedfrom15to102nmoverthreerandomlyselectedsurfaceareasof4,25,and100m2.Relativetothethicknessoftheexposedcopperelectrode(70m)themeasuredsurfaceroughnesswasatleastanorderofmagnitudesmaller.Presumably,thedistributedroughnessoftheaerogelmaterialwillhavelesserinuenceinsidetheboundarylayerascomparedtothethicknessoftheelectrode.Theeffectsoftheinhomogeneousaccumulationofsurfacechargeduetothesurfaceroughnesswerenotinvestigated.Suchaphenomenonmayaffecttheoverallstructureoftheplasmaformation.However,thetemporalcharacteristicsofthedischargecurrentforthesilicaaerogelactuatorswereconsistentwiththatofFigure 3-2 .TheinducedthrustproducedbyactuatorsusingKapton(r=3.5),acrylic(r=3),andaerogeldielectricsforvariousthicknessesarepresentedinFigure 8-6 .Overtherangeofvoltagestested,nonoticeablesurfacedamagewasobservedforaerogel.TheopensymbolsfoundinFigure 8-6 and 8-7 indicateadirectthrustmeasurementmadeusingtheforcebalancepreviouslydescribed(Section 4.4.1 ).Theclosedsymbolsrepresentthrustmeasurementsinferredfromacontrolvolumeanalysisontheinducedvelocityeldrecordedusingtwo-componentparticleimagevelocimetry(Sections 4.4.2 and 4.5.1 ).Arepresentativetime-averaged(300imagepairs)oweldisshowninFigure 8-5 fora36kVppinput,wherethedashedlinescorrespondtothesidesofthecontrolvolume.Thereactionforceimpartedtothedielectricwascalculatedusingtheconservedformofthemomentumequationinthex-direction(Equation 4 )usingthepreviouslystatedassumptions.Theairdensitywastakenas1.184kgm)]TJ /F7 7.97 Tf 6.58 0 Td[(3.A 156

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Figure8-4. Visualandsurfacecharacteristicsofasilicaaerogelsample.A)ApictureofthesilicaaerogelsampleandB)thecorrespondingsurfacetopography.InimageA)theactualsampleofsilicaaerogelusedforcollectingdataisshown,withtheinsetimageshowingaplasmadischargeonasmallersampleofsilicaaerogel.Thesurfacetopographyofthesilicaaerogelwasmeasuredusingatomicforcemicroscopy.Takenfrom Durscher&Roy ( 2012a ). Figure8-5. RepresentativevelocityeldmeasuredusingPIVovertheaerogelsampleforasuppliedvoltageof36kVppat14kHz.Thedashedlinesindicatetheboundariesofthecontrolvolumeconsidered.Takenfrom Durscher&Roy ( 2012a ). 157

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Figure8-6. Inuenceofdielectricthicknessonthrustproductionforactuatorsconstructedoutofsilicaaerogel,Kaptonandacrylicasafunctionofvoltage.Theopensymbolscorrespondtodirectthrustmeasurements,whileclosedsymbolsareinferredfromacontrolvolumeanalysisontheinducedoweld.Takenfrom Durscher&Roy ( 2012a ). comparisonbetweeninferredanddirectthrustmeasurementsisshowninFigure 8-6 ,withgoodagreement,fora3mmthickacrylicactuator.Aspreviouslymentionedinaprioroptimizationstudy, Thomasetal. ( 2009 )showedthatforaconstantthicknesshighervoltagescanbeappliedresultinginlargerthrustswhenusingamaterialwithalowerdielectricconstant.ThisisdemonstratedinFigure 8-6 ,incomparingthet=6mmthickacrylicandaerogelsamples.Interestinglyforthisfrequency,theinducedthrustforanacrylicactuatorasymptoteatabout34mNm)]TJ /F7 7.97 Tf 6.59 0 Td[(1.Thesilicaaerogeldemonstratesamuchhigherthrust,47mNm)]TJ /F7 7.97 Tf 6.59 0 Td[(1,withnosignofsaturation.Thevoltagerangetestedinthisreportwasupto36kVpp,thoughhighervoltageswouldhavebeenpossiblefortheaerogelactuator.Itisalsonotablethatforagivenvoltagetheacrylicactuatorgeneratesmorethrustuptoitssaturationpoint.Anaddedbenetoftheaerogelisitslowdensity,aparameterthatwouldbecriticalwhenapplyingtheseactuatorstomediumtosmall/micro-airvehicles.ThebenetsofusingathickerdielectricintheDBDactuatordesignhavebeenpreviously 158

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discussedinSection 3.1.2 .ConsistentwiththetrendsshowninFigure 3-10 ,Figure 8-6 showsthat,byincreasingthethicknessofthedielectriclayer,largervoltagescanbeappliedtotheactuator.Theadditionalvoltageincreasesthemaximumthrustthatmaybeachieved.Atrade-offofincreasingthedielectricsthickness,however,isthattheweightoftheactuatoralsoincreases.Althoughthiswouldbelessdetrimentalforlarge-scaleapplications,itcouldprovecriticalatsmallerscalesseekingtobenetfromtheincreasedbodyforceassociatedwiththickerdielectrics.AsdiscussedinSection 3.3 ,theuseofDBDactuationonmicro-airvehiclesisagrowingareaofinterest.Figure 8-7 re-plotsthedatashowninFigure 8-6 onathrusttoactuatorweightratiodenedbyEquation 8 .Alldimensionsareincentimeters(referringtoFigure 4-1 )andthedensity(dielectric)ofacrylic,aerogel,andKaptonweretakenas1.20gcm)]TJ /F7 7.97 Tf 6.59 0 Td[(3,0.11gcm)]TJ /F7 7.97 Tf 6.58 0 Td[(3,and1.42gcm)]TJ /F7 7.97 Tf 6.59 0 Td[(3,respectively.Thrust Weight=f tl(w1+w2)dielectric (8)Fortheconventionaldielectricstested(Kaptonandacrylic)athinnerdielectricisbenecialbasedonathrust-to-weightbasis.However,whenthesilicaaerogelisconsidered,thebenetofthisextremelylowdensitymaterialisevident(Figure 8-7 ).ReferringtoFigure 8-7 A,foragiventhickness(t=6mm),thenetthrust-to-weightratiomeasuredhasincreasedfrom1.810)]TJ /F7 7.97 Tf 6.59 0 Td[(2(at30kVpp)to2.910)]TJ /F7 7.97 Tf 6.59 0 Td[(1(at36kVpp)fortheacrylicandaerogelsamples,respectively.Thenetthrust-to-weightratioforKaptonis1.410)]TJ /F7 7.97 Tf 6.58 0 Td[(1at12kVpp.Thisincreasedthrust-to-weightbasiscomeswithnoaddedpowerconsumptionfortheactuatorasshowninFigure 8-7 B.Specically,atlowerpowerthebenetofusingaerogelasadielectricissubstantial. 159

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Figure8-7. Ratioofthrustgeneratedtotheactuator'sweightforvariousdielectrics.ResultspresentedasafunctionofA)appliedvoltageandB)powerconsumption.Actuatorsareconstructedoutofsilicaaerogel,Kaptonandacrylic;withopensymbolscorrespondingtodirectthrustmeasurements,whileclosedsymbolsareinferredfromacontrolvolumeanalysisontheinducedoweld).Takenfrom Durscher&Roy ( 2012a ). 160

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CHAPTER9INVESTIGATIONOFDBDTHRUST`SATURATION'AspreviouslydiscussedinSection 3.1.2 ,theplasmaimpartsbodyforceonthesurroundingneutrallychargeduid.Thismomentumexchangeisoftencharacterizedbytheactuatorsthrustwhichhasbeeninterpretedasameasureofthereactionforceonthedielectricplateasaresultoftheplasmainducedbodyforceanduidicshearingeffects(Section 4.4.2 ).ThethrustproducedinquiescentairbyasinusoidallydrivendielectricbarrierdischargeactuatorhasbeenshowntobeproportionaltoV(Equation 3 ),whereVistheappliedvoltageandisaproportionalityconstant.AsgiveninSection 3.1.2 ,atypicalvaluereportedforisapproximately3.5.Forvoltagesgreaterthanathreshold,theexponentofthepowerlawreduces,limitingthethrustincrease.Inanoptimizationstudyby Thomasetal. ( 2009 )itwasshownthatthedielectricthickness,dielectricconstant,anddrivingfrequencyhadastrongeffectontheamountofthrustgenerated(Figures 3-10 and 3-12 ).Inthisinvestigation,thedielectricthickness,dielectricconstant,anddrivingfrequencyrangedfrom0.15-6.35mm,2.0-6.0,and1-8kHz,respectively.Moreover,thethrustproducedwasshowntoincreasebasedonEquation 3 withincreasingvoltageuptoathresholdvoltage.Forvoltagesgreaterthanthisthresholdvoltage,thethrustnolongerincreasedandtheDBDactuatorwassaidtohave`saturated',limitingtheuseofthedevice.Theonsetofthissaturationeffectwasassociatedwithasharpincreaseinpowerconsumption,andvisuallycorrelatedwiththeinitiationoflamentarydischargeevents(Figure 9-1 B-E).AsdescribedinSection 3.1.1 ,thevisualappearanceofaDBDactuatoristypicallydescribedasmanydiffuse,glow-likeeventsdistributedalongthespanoftheelectrode(Figure 9-1 A).Tosummarizetheresultsof Thomasetal. ( 2009 ),theuseofthickerdielectricswithlowerdielectricconstantsandlowerdrivingfrequencieswerefoundtodelaythesaturationtransition,allowinghighervoltagestobeapplied.Thisinturnmaximizedthethrustproduction 161

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Figure9-1. Dischargeappearanceatsaturationconditionsforvariousfrequencies.A)Atypicalnon-saturateddischargeat1kHzandB-E)saturateddischargesat1,2,4,and8kHz.Takenfrom Thomasetal. ( 2009 ). oftheDBDactuator,whichfromanapplicationsstandpoint,mightimprovetheuidiccontrolauthorityofthedevice.Todatethesaturationeffecthasbeenprimarilyquantiedbytheactuator'sthrust.Inthefollowingsectionsthetrendsobservedby Thomasetal. ( 2009 )areveriedandextendedusingdirectthrustmeasurements.ThevelocityeldinducedbytheDBDactuatorinquiescent,atmosphericpressureairisalsocharacterizedusingparticleimagevelocimetryforconditionspriortoandduringsaturation.Furthermore,withtheuseofinfraredthermography,itisshownthatthesurfacetemperatureofthedielectricbarrierplaysacrucialroleinthetransitionoftheglow-likedischargeeventstolamentarydischargeevents.Basedontheseresults,itisshownthatthesaturationeffectcanbemanipulatedbychangingthelocalsurfacetemperatureofthedielectric.Moreover,theresultspresentedwithinprovideaphysicalexplanationfortheempiricalndingsdeducedfromparametricstudies. 162

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9.1ActuatorDesignKeepingwiththenotationofFigure 4-1 ,theexposedandencapsulatedelectrodesweremadeoutofcopperandhadalengthofl=10cm,withwidthsofw1=10mmandw2=50mm,respectively.Thedielectricmaterialusedwas3mmthickborosilicateglass.Theplatelength,L,oftheactuatorwas8.5cm,whichisonlyslightlybelowtherecommendedvaluesuggestedinSection 4.4.1.1 .Thedischargewasgeneratedbypoweringbothelectrodeswithsinusoidalvoltagesofequalmagnitude,butopposingpolarity(congurationBfromFigure 4-3 ).Thedissipatedpowerwascalculatedfromtheaveragedproductofthevoltageandcurrentwaveformsmeasuredateachelectrode(Equation 4 ). 9.2SaturationEffectonThrustProductionDirectthrustmeasurementsweremadeontheactuatorasdescribedinSection 4.4.1 .ResultsoverarangeofvoltagesandfrequenciesarepresentedinFigure 9-2 .Aspreviousreportshaveobserved,foragivenvoltage,largerthrustsmaybeachievedwhenoperatingathigherfrequencies( Thomasetal. 2009 ).However,bydecreasingthefrequency,highervoltagesmaybeappliedtotheactuatorresultinginultimatelylargerobtainedthrusts.Atsaturation,denotedbytheinexionpointattheapexofthethrustmeasurement(moreeasilyseenfortheloweroperatingfrequencies),adecreaseinmeasuredthrustwasrecorded.Thisconditionwasassociatedwiththeglow-to-lamentarytransitionasshowninFigure 9-1 .Oncethetransitionoccurs,asharpincreaseinpowerconsumptionisobserved(Figure 9-3 ).ThepowerconsumptionandeffectivenessassociatedwiththesemeasurementsasafunctionofvoltageareprovidedinFigure 9-4 .Aclearadvantageintermsofincreasedthrustproductionwhilesimultaneouslyreducingpowerrequirementscanbeseenforloweroperatingfrequencies.Denotingthemaximumthrustachievedbytheactuatorasthe`saturationthrust',anassociating`saturationvoltage'mayalsobedenedforagivenfrequency.The 163

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Figure9-2. Measuredthrustasafunctionofvoltageforvariousfrequencies.Foragivenvoltage,largerthrustsmaybeachievedwhenoperatingathigherfrequencies.However,bydecreasingthefrequency,highervoltagesmaybeappliedtotheactuatorresultinginamaximumthrustoutput. Figure9-3. Measuredthrustasafunctionofpowerconsumptionforvariousfrequencies.Foragivensuppliedpower,largerthrustsmaybeachievedwhenoperatingatlowerfrequencies. 164

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Figure9-4. Powerandeffectivenessasafunctionofsuppliedvoltageforvariousfrequencies:A)powerandB)effectiveness saturationvoltageasafunctionoffrequency,thesaturationthrustasafunctionoffrequency,andthesaturationthrustasafunctionofsaturationvoltagearepresentedinFigure 9-5 .Boththesaturationvoltageandthrustshowapowerrelationoftheform,bfa,wherefistheappliedfrequencyandaandbareconstants(Figures 9-5 Aand 9-5 B).Theexponentaisequalto-0.3and-0.5forthesaturationvoltageandthrust,respectively.Thecorrespondingcoefcientofdetermination(orR2value)fortheregressionlinesare0.92and0.94.Thesevalueswouldlikelychangeifadifferentdielectricmaterialand/orthicknesswasused,asindicatedby Thomasetal. ( 2009 ).Besidesapowerrelation,asshowninFigure 9-5 C,alinearregression,withaslopeof2.4mNm)]TJ /F7 7.97 Tf 6.58 0 Td[(1kVpp)]TJ /F7 7.97 Tf 6.59 0 Td[(1(R2=0.99),mayalsobettedtothesaturationthrust-voltagerelation.Itispertinenttonotethatinsubsequentinvestigationsregardingthesaturationeffect(asoutlinedinthefollowingsections),foraspeciedfrequencythesaturationvoltagewasfoundtovaryslightly.Toaccountforthisvariation,errorbarsof2.0kVppareshowninFigure 9-5 forthesaturationvoltage.Theimpactofvoltagevariationonthesaturationthrustwasnotaccountedfor.Similartothepreviousdescribedrelationbetweensaturationvoltage/thrustandfrequency,otherinuencessuchasdielectricthicknessanddielectricconstantwere 165

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Figure9-5. SaturationrelationsforaDBDactuator.A)Saturationvoltageasafunctionoffrequency,B)saturationthrustasafunctionoffrequency,andC)saturationthrustasafunctionofsaturationvoltage. validatedinChapter 8 .Intheaforementionedchapter,theuseofmaterialsonthefarendsofthedielectricspectrum,suchassilicaaerogel(r1.2)andferroelectric(r1750)wereinvestigated.Ingeneral,asubstantialimprovementinthrustproductionwasdemonstratedforthickerdielectricmaterialswithlowerdielectricconstants. 9.3SaturationEffectonInducedVelocityThevelocityoweldwasmeasuredusingaparticleimagevelocimetrysystemasdetailedinSection 4.5.1 .Unliketheconventionalsetupinwhichthelightsheetisorientednormaltothedielectricinthex-yplane(asrequiredtoprovideasideproleof 166

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Figure9-6. ParticleimagevelocitmetrysetupusedtostudytheinducedoweldofaDBDactuatoratsaturationconditions. theinducedwalljet);intheseexperimentsthelaserlightsheetwaspositionedparalleltothesurfaceoftheDBD,inthex-zplane,asshowninFigure 9-6 .AsshowninSection 4.4.2 ,themeasuredthrustisavolumeintegrated,notalocal,quantity.Furthermore,thelamentaryfeatureswereobservedtooccurquasi-randomlyalongthespanoftheactuator.Ifonlyasinglex-yplanewasinvestigated,theriskofonlycapturinglocalmaximum/minimumvaluescouldexistifspanwisevariationswerepresent.Inordertoreducethisriskandtogetatruesenseoftheoweldalongtheelectrodespan,thex-zplanewasinvestigated.Furthermore,timeaveragedquantitiesareprimarilypresented,whereateachappliedvoltage,1,000imagespairswerecapturedandaveraged.However,duetotherandomtemporalnatureofthelamentaryfeaturesduringsaturation,thenumberofimagepairswasreducedto400.Althoughthisreductionslightlyincreasesthestatisticalerrorbetweenthepre-andpost-saturationdatasets,itisarelativelysmallincrease.TheuncertaintyestimationoutlinedinSection 4.5.1.3 isstillappropriateforbothcases. 167

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9.3.1CharacteristicsofFlowFieldPriortoSaturationMultipleplanesabovethesurfaceofthedielectricwereinitiallyinvestigated,asindicatedinFigure 9-6 ,byy.Distancesof0.5mmto6.0mmin0.5mmincrementswereexplored.ExamplemeasurementsareshowninFigure 9-7 ,wherethehighestvelocitieswerefoundtooccuraty=0.5mm.Thisisconsistentwithmeasurementsmadealongthex-yplane(e.g.Figure 4-15 ).Assuch,fortheremainderofthissection,themeasurementpresentedcorrespondtothemeasurementplaneaty=0.5mmunlessotherwisespecicallyspecied.Asexpected,anincreaseinvelocitywascorrelatedtoanincreaseinvoltage(Figure 9-8 ),foraconstantfrequency.Furthermore,thetimeaveragedcontoursshowsignicantstructureinthespanwisedistributionofthevelocityeld,althoughtheforcefromaDBDactuatorisgenerallyconsideredtobeuniformalongtheelectrodespan.Spanwisevariationsintheprimaryvelocitycomponent,ux,aremoreclearlyshowninFigure 9-9 fortwodiscretestreamwisecuts,x=10mmandx=20mm.Forbothlocationstheuctuationsarecomparativelysmallattheloweroperatingvoltages,butincreaseasthevoltageisincreased.TheseuctuationsarequantiedinFigure 9-10 werethestandarddeviationsalongdiscretespanwisecutsarepresentedasafunctionofstreamwiseposition.Thestandarddeviationswerefoundtobeashighas0.5ms)]TJ /F7 7.97 Tf 6.59 0 Td[(1(or10%ofthemaximumvelocity)atthehigherfrequenciesinvestigated(5and7kHz).Theseresults,however,donotconictwiththatofSection 4.5.2 or 7.4 ,inwhichthez-componentofthevelocityeldalongdiscretex-yplaneswerepresentedforalinearactuator.Inthecurrentmeasurementsthez-componentofvelocity(Figure 9-11 )isstillsmallrelativetotheprimaryx-componentasindicatedbythestereoscopicPIVmeasurements(Sections 4.5.2 and 7.4 ).BycomparingFigures 9-9 and 9-11 ,themaximumz-componentisonly6%ofthemaximumx-component.ConsistentwiththethrustmeasurementsfromFigure 9-2 ,foragivenvoltage,largervelocitiesmaybeachievedwhenoperatingathigherfrequencies.However, 168

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Figure9-7. Timeaveragedvelocitycontours,ux,formultipleplanesabovethesurfaceofthedielectricforanappliedvoltageof40kVppat2kHz.A)y=0.5mm,B)y=1.0mm,C)y=1.5mm,andD)athreedimensionalreconstructionwhichincludesallmeasurementplanes. bydecreasingthedrivingfrequency,highervoltagesmaybeappliedtotheactuatorresultinginultimatelylargerobtainedvelocities.ThesetrendsareshowninFigure 9-12 inwhichthespanwiseaverageofthestreamwisevelocityispresentedfordiscretestreamwisepositions.Alsoconsistentwiththethrustmeasurements,theobservedvelocityisshowntosaturate,resultinginadecreasedvelocity.Again,thevisualappearanceoftheplasmawascharacterizedbyaglow-to-lamentarytransition.Floweldcharacteristicsatsaturationarediscussedinthefollowingsection(Section 9.3.2 ). 169

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Figure9-8. Timeaveragedvelocitycontours,ux,forvariousvoltagespriortosaturationat2kHz.A)24kVpp,B)28kVpp,C)36kVpp,andD)42kVpp. 9.3.2CharacteristicsofFlowFieldDuringSaturationItwasobservedthatatparticularvoltages,theglow-to-lamentarytransitionwasveryrapid,andwastreatedasinstantaneouswithrespecttothePIVsystem;thebreakdownprocesswasdelayedbyapproximately10-100'sofsecondsatpotentialsslightlybelowthisthresholdvoltage.AsshowninFigure 9-13 ,thisdelayedtransitionprocessallowsforadirectcomparisonbetweenthemeasuredvelocityeldspriorto(Figure 9-13 A),andimmediatelyaftertransitionofthedischarge(Figure 9-13 B)foranapproximatelyconstantappliedvoltageof44kVppat2kHz.InFigure 9-13 ,thetimeaveragedvelocityeldsubstantiallydecreasedasthedischargeeventstransitionedfromaglow-likestatetoalamentaryone. 170

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Figure9-9. Spanwisevariationsintheprimaryvelocitycomponent,ux,forvariousvoltagesatafrequencyof2kHz.PlanestakenalongA)x=10mmandB)x=20mm. ThedecreaseintheaveragedvelocityeldduringthelamentarymodeismoreclearlyseeninFigure 9-14 A,whichdepictsthespanwiseaverageofthestreamwisevelocity, ux,asafunctionofstreamwisepositionforvariousvoltagesat2kHz.Aspreviouslydiscussed(Section 9.3.1 ),anincreaseinvelocityisassociatedwithanincreaseinvoltagepriortosaturation.Oncethedischargetransitionedtoalamentarymodeatapproximately44kVppfor2kHz,however,asubstantialdecreaseinvelocitywasmeasured.Athighervoltages,ontheorderof46kVpp,thetransitionprocesswasseeminglyinstantaneous,andagainadecreaseinvelocitywasmeasured.Thesetrendswereindependentoffrequency,asshowninFigure 9-14 B.Thesaturationeffectoftheactuatorhasbeenpreviouslyassociatedwithadecreaseinmeasuredthrust(Section 9.2 ).Giventhatthrustisameasureofthetransferredmomentum,aquantityintegratedovertheentiredischargevolume;areductionintheaverageinducedvelocityoverthedischargevolumeisexpected.Thatdoesnotmean,although,thattheinstantaneousvelocityeldaftersaturationcannothavecomparable,localpeakvalues.AsshowninFigure 9-15 ,thevelocitiesmeasurednearthelamentswerefoundtobecomparabletothatofthevelocitiesprior 171

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Figure9-10. Spanwiseuctuationsinthestreamwisevelocitycomponent, ux,asafunctionofstreamwisepositionforvariousvoltages.Theuctuationsalongthespanoftheactuatorarerepresentedbythestandarddeviation, x.A)2kHz,B)5kHz,andC)7kHzdrivingfrequencies. tosaturation.However,duetherandomspatialandtemporalnatureofthelamentsanetreductionisseeninthetimeaveragedoweld.Furthermore,thisresultwouldindicatethatthemajorityofthetransferableenergyintheplasma-(neutral)gascouplingwasbeingexpendedwithinthelament,asopposedtobeingmoreevenlydistributedalongthespanoftheactuator,asisthecaseinthepre-saturateddischarge.Toinsuregeneralityinthepresentedresults,multipleplaneswereagaininvestigatedwhileoperatingtheactuatorinthelamentarymode(Figure 9-16 ).Aswiththevelocity 172

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Figure9-11. Timeaveragedvelocitycontours,uz,formultipleplanesabovethesurfaceofthedielectricforanappliedvoltageof40kVppat2kHz.A)y=0.5mm,B)y=1.0mm,C)y=1.5mm,andD)athreedimensionalreconstructionwhichincludesallmeasurementplanes. eldpriortosaturation,thehighestvelocities(althoughlowerthanthepre-lamentaryoweld)wereagainfoundtooccuraty=0.5mm,correspondingtotheplaneclosesttothedielectricsurface. 9.4InuenceofSurfaceTemperatureAspreviouslydescribedinSection 9.3.2 ,foragivenfrequencyitwasfoundpossibletodelaytheglow-to-lamentarytransitionprocessbycarefullychoosingtheappliedvoltage.Insomeexperimentsthistransitionprocesswasfoundtobedelayedby 173

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Figure9-12. Spanwiseaverageofthestreamwisevelocity, ux,forvariousvoltagesandfrequenciesatdiscretestreamwisepositions.PlanestakenalongA)x=10mmandB)x=20mm. Figure9-13. Timeaveragedvelocityeldpriortoandduringsaturationforanapproximatelyconstantappliedvoltageof44kVppat2kHz.A)Nolamentaryfeaturesarepresentinthedischarge,whileinB)theglow-to-lamentarytransitionhastakenplace.Takenfrom Durscheretal. ( 2012 ). 174

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Figure9-14. Spanwiseaverageofthestreamwisevelocity, ux,asafunctionofstreamwiseposition.A)Variousvoltagesat2kHzarepresentedwhileB)demonstratesfrequencyindependence.Conditionscorrespondingtothepresenceoflamentaryfeaturesaredenotedbysolidsymbols.Takenfrom Durscheretal. ( 2012 ). Figure9-15. Instantaneousvectoreldoverlayinganimageofthedischargeduringsaturationforanappliedvoltageof44kVppat2kHz.Takenfrom Durscheretal. ( 2012 ). 175

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Figure9-16. Timeaveragedvelocitycontours,ux,formultipleplanesabovethedielectricsurfaceforanappliedvoltageof32kVppat5kHz(lamentaryfeaturespresent).A)y=0.5mm,B)y=1.0mm,C)y=1.5mm,andD)athreedimensionalreconstructionwhichincludesallmeasurementplanes. 10-100'sofseconds.Suchadrasticrelativedifferencebetweenthetransitiondelayandtheappliedfrequencyledtothebeliefthatdielectricheating,whichoperatesonasubstantialslowertimescale,maybeplayingaroleinthetransitionprocess.Toinvestigateitseffect,thesurfacetemperatureoftheactuatorandthevisiblelightemissionoftheplasmawererecordedsimultaneously.AninfraredcameraasdescribedinSection 4.6 ,wasusedtodeterminethesurfacetemperatureofthedielectricduringoperationoftheDBDactuator.Thecamerawas 176

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alignedatarelativeangleof11o0.2otothesurface.Theworkingdistancebetweentheactuatorandinfraredcamera,theambienttemperatureandhumidity,andtheemissivityoftheborosilicateglassweremeasuredas0.30.005m,202oC,663%RH,and0.890.03,respectively.Thesequantitieswereallconsideredforthesurfacetemperaturemeasurements.Thefollowingsectionsdescribethecharacteristicsofthesurfacetemperature(Section 9.4.1 )andthemanipulationofthesaturationeffectbylocalheataddition(Section 9.4.2 ). 9.4.1CharacteristicsofSurfaceTemperatureRepresentativespatialtemperaturedistributionsalongthesurfaceoftheactuatorareshowninFigure 9-17 forvariousoperatingtimes.Intuitively,thedielectrictemperatureincreasesastimeprogresseswiththehighesttemperaturesoccurringneartheedgeoftheexposedelectrode.Alongthespanoftheactuatortheinitialtemperaturedistributionissporadicbutbecomesmorehomogeneouswithincreasingtime.Thisinitialspanwisevariationsandlaterquasi-uniformityofthesurfacetemperaturearehighlightedinFigure 9-18 forvariousstreamwisecuts.Thepointedendsoftherectangularelectrodedoresultinincreasedtemperaturesneartheedgesoftheexposedelectrodeatlatertimes,howevertheseincreasesarerelativelysmall.ReferringtoFigure 9-18 B,thereisonlya5%differencebetweenthesurfacetemperatureneartheendoftheelectrode(z=50mm)andthecenterline(z=0mm)fory=2mm.Asthetemperatureisapproximatelyconstantalongthespan,anaveragespanwisetemperature, T,maybeconsidered.ThetemporalevolutionoftheaveragespanwisetemperatureforvariousappliedvoltagesarepresentedinFigure 9-19 .Fromthegure,foragivenoperatingtimethesurfacetemperatureofthedielectricincreaseswithincreasingvoltage.Overall,however,thegeneraltemporalcharacteristicsareindependentoftheappliedvoltage.Forpredictionpurposes Jukesetal. ( 2008 )and Joussotetal. ( 2010 )proposedthatthetemporalcharacteristicsofthedielectricnear 177

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Figure9-17. ThetemperaturedistributionalongthesurfaceofaDBDactuatoroperatedat36kVppand2kHzwithincreasingtime.A)t=5s,B)t=10s,C)t=20s,D)t=80s,E)t=120s,andF)t=140s. Figure9-18. ThetemperaturealongthespanofaDBDactuatoroperatedat36kVppand2kHzfordiscretestreamwiseplanes.A)t=10sandB)t=120s. 178

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Figure9-19. Averagespanwisesurfacetemperature, T,asafunctionoftimeforvariousvoltagesat2kHz.PlanestakenalongA)x=2mmandB)x=10mm. theexposedelectrodeforaDBDactuatormaybeestimatedbytheone-dimensional,transientheatequationgivenby@2TDielectric @y2=1 @TDielectric @t (9)whereTDielectricisthetemperatureofthedielectricandisthethermaldiffusivityofthedielectricmaterial.ThepresenceoftheplasmaistreatedasahotgaswithtemperatureTPlasmapositioneddirectlyabovethedielectricwithathermalconductivityofkandaninitialtemperatureofTInitial.Theplasma-surfaceinterfaceistreatedasaconstantheatuxatthesurfacewithaheattransfercoefcientofh.Thisleadstothefollowinginitial(Equation 9 )andboundaryconditions(Equations 9 and 9 ):TDielectric(y=,t=0)=TInitial (9)TDielectric(y=,t>0)=TInitial (9)h[TPlasma)]TJ /F3 11.955 Tf 11.96 0 Td[(TDielectric(y,t)]jy=0=k@TDielectric @yjy=0 (9) 179

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AclosedformsolutiontoEquation 9 withtheaforementionedinitialandboundaryconditionsmayreadilybefoundinliterature( Arpacietal. 1999 ),withthesolutionatthedielectricsurface(y=0)simplifyingto:TDielectric(t)=[TPlasma)]TJ /F3 11.955 Tf 11.95 0 Td[(TInitial][1)]TJ /F6 11.955 Tf 11.96 0 Td[(exp(t)erfc(p t)]+TInitial (9)whereisacharacteristictimeconstantgivenby=h2 k2 (9)ThetemporaltemperatureprolesshowninFigure 9-19 AwerettedwithEquation 9 andacomparisonbetweentheexperimentaldataandthetheoreticalpredictionispresentedinFigure 9-20 .Consistentwith Jukesetal. ( 2008 )and Joussotetal. ( 2010 )reasonableagreementisseenbetweentheexperimentaldataandtheanalyticalestimation.Furthermore,theextractedvaluesfortheplasmatemperature(TPlasma),characteristictimeconstant(),andheattransfercoefcient(h)arepresentedinTable 9-1 foreachcurve.ForthelowerdrivingpotentialstheplasmatemperatureisconsiderablelowerthanthetemperaturesdeducedfromspectroscopyforaDBDactuator( Staneld 2009 ; Staneldetal. 2009 ).Therefore,asmentionedby Jukesetal. ( 2008 ),itwouldbeincorrecttoestimatetheplasma'stemperatureinthismanner;themethodcould,however,beusedtodescribethesteadystatetemperatureoftheactuator'ssurface( Joussotetal. 2010 )forthelowerdrivingpotentials.However,althoughabletostillanalyticallydescribethecharacteristicsofthetemporaltemperatureproles,theexactedparametersbecomenon-physicalastheactuatorapproachessaturationconditions(44kVppat2kHz).FromTable 9-1 ,thepredictedsteadystatetemperatureis48,300oCforanappliedvoltageof44kVpp.AprimarysimplicationofEquation 9 istheomissionofinternalheatgenerationduetopowerlossinthedielectric.Itwasdemonstratedby Roth&Dai ( 2006 )thatforaDBDactuatorthedielectricpowerlossescouldbecomparabletothepowerinputtothe 180

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Figure9-20. Comparisonbetweenexperimentaldataandananalyticalestimationoftheaverage,spanwisesurfacetemperatureasafunctionoftimeatvariousvoltages.Thedrivingfrequencyis2kHzandthepointistakenforastreamwisedistanceofx=2mm. Table9-1. Experimentallyextractedvaluesusedinatheoreticalestimationofthetemporal,spanwiseaverage,surfacetemperatureofaDBDactuator.ThevalueswereobtainedbyttingthecurvesofFigure 9-19 AwithEquation 9 Voltage(kVpp)TPlasma(oC)(s)]TJ /F7 7.97 Tf 6.59 0 Td[(1)h(Wm)]TJ /F7 7.97 Tf 6.58 0 Td[(2K)]TJ /F7 7.97 Tf 6.59 0 Td[(1) 2432.18.810)]TJ /F7 7.97 Tf 6.59 0 Td[(31.331022835.67.810)]TJ /F7 7.97 Tf 6.59 0 Td[(31.251023240.47.610)]TJ /F7 7.97 Tf 6.59 0 Td[(31.241023653.92.910)]TJ /F7 7.97 Tf 6.59 0 Td[(37.6510140116.53.410)]TJ /F7 7.97 Tf 6.59 0 Td[(42.621014448,3001.810)]TJ /F7 7.97 Tf 6.59 0 Td[(96.0210)]TJ /F7 7.97 Tf 6.59 0 Td[(2 plasma.Thisdissipatedpowerdirectlyresultsinheatingofthedielectricmaterial.Thepowerlosspervolume(PLoss)inadielectricisgivenbyPLoss=2f00r0E2 (9)wherefistheappliedfrequency,00ristheimaginarypartofthecomplexrelativepermittivity,0isthepermittivityoffreespace,andEtheappliedelectriceld.Conventionally,theimaginarypartoftherelativepermittivityisimplicitlytakenintoaccountthrougha`losstangent'.Thelosstangentofadielectric(,thematerialsconductivity0)isgiven 181

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bytan=2f00+ 2f000 000r0 0r000r 0r (9)where00istheimaginarypartofthecomplexpermittivity(=00r0)and0istherealpartofthecomplexpermittivity(=0r0).Customarilytherealpartoftherelativepermittivity(0r)isrepresentedsimplybyr(ashasbeenadoptedinthistext).SubstitutingEquation 9 intoEquation 9 yieldsanalternativeformforthepowerlossinadielectricperunitvolumePLoss=2fr0E2tan (9)IndeterminingthepowerlossesinthedielectricoftheDBDactuatortheelectriceld,E,willbeestimatedastheratioofthepeakvoltagetothedielectricthickness(=VPeak=t);thevoltageconsideredwillbetheappliedvoltage(VPeak=VPeak)]TJ /F5 7.97 Tf 6.58 0 Td[(to)]TJ /F5 7.97 Tf 6.59 0 Td[(Peak=2)justpriortosaturation(Figure 9-5 A)foragivendrivingfrequency,f.Furthermoreborosilicate,thedielectricmaterialused,hasareportedlosstangent,tan,of0.005andameasured(Appendix D )relativedielectricconstant,r,of4.7.SubstitutingthesevaluesintoEquation 9 thepowerloss,PLoss,inthedielectricperunitvolumemaybeestimated(Table 9-2 ).Consideringacrosssectionalareaconsistingofthedielectric'sthicknessandthelowerelectrode'swidth(tw2=1.510)]TJ /F7 7.97 Tf 6.59 0 Td[(4m2)thepowerlossonaperunitlengthbasismaybedetermined.Thisallowsforadirectcomparisonwiththenetpower,PNet,consumedbytheactuatorperelectrodelengthastakenfromFigure 9-4 A.Increasingwithfrequency,theestimatedpowerlostinthedielectricaccountsfor7%to19%ofthetotalpower.Notethatapeakvaluewasconsideredfortheelectriceld,thusthetimeaveragepowerlossinthedielectricwouldlikelybeslightlylowerthancurrentlyestimated.AsdemonstratedinTable 9-2 ,Equation 9 dictatesthatthepowerdissipated,andthusheatgenerated,inthedielectricincreaseswiththeappliedfrequency.Furthermore, 182

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Table9-2. Dielectricpowerlossjustpriortosaturationconditions. f(kHz)VPeak(kV)PNet(Wm)]TJ /F7 7.97 Tf 6.58 0 Td[(1)PLoss(kWm)]TJ /F7 7.97 Tf 6.58 0 Td[(3)PLoss(Wm)]TJ /F7 7.97 Tf 6.59 0 Td[(1)PLoss=PNet(%) 1.032.031514922.371.526.024214722.192.021.018912819.2103.018.019214121.2115.015.522217426.2127.014.526721432.11214.013.043034451.61221.011.039536955.41428.010.032340761.019 thepowerlostinthedielectricisalsodependentontherelativedielectricconstantofthematerial.AsdiscussedinfurtherdetailinthefollowingsectionsitisbelievedthatforaDBDactuatoroperatinginquiescentair,thesurfacetemperatureplaysanimportantroleintheglow-to-lamentarytransitionobservedatsaturation. 9.4.2ManipulationoftheSaturationEffectbyLocalHeatAdditionAsnotedinSection 9.3.2 ,itwasobservedthatatparticularvoltagestheglow-to-lamentarytransitionwasveryrapid;thebreakdownprocess,however,wasdelayedbyapproximately10-100'sofsecondsatpotentialsslightlybelowthisthresholdvoltage.Forthesevoltages,itwasfoundthatthelamentaryfeaturesdonotbecameprominentuntilthesurfacetemperatureoftheborosilicateglasswasapproximatelygreaterthan50oC(thisvaluewasfoundtovaryslightlydependingontheappliedvoltage/frequency).ThistemperaturedependenceisdemonstratedinFigures 9-21 9-22 ,and 9-23 ,wherethevisualappearanceofthedischargeiscomparedwithathermalimageofthesurfacetemperaturefordiscreteoperatingtimesoftheactuator.Thedrivingparametersoftheactuatorfortherespectiveguresare44kVppat2kHz,33kVppat5kHz,and32kVppat5kHz.AsestablishedinFigure 9-19 ,thedielectrictemperatureincreaseswithincreasingvoltageforagivenoperatingtime.Theincreasedrateofdielectricheatingwithvoltageanditsimpactonthetransformationtimefortheglow-to-lamentarytransitionisexhibitedinFigures 9-22 and 9-23 ,astheappliedvoltageisreducedfrom 183

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Figure9-21. ThevisualappearanceoftheplasmaandtemperaturedistributionalongthesurfaceofaDBDactuatoroperatedat44kVppand2kHzforvarioustimes.A,B)t=60s,C,D)t=80s,E,F)t=85s,andG,H)t=90s. 33kVppto32kVppforaconstantoperatingfrequency.Forthelowervoltage(32kVpp,Figure 9-23 )ittook85sfortheglow-to-lamentarytransitiontooccur,whileitonlytook45satthehighervoltage(33kVpp,Figure 9-22 ).Itwasalsoobservedthatthetransformationtimecouldbedrasticallyreducedbyturningontheactuatoroncethesurfacewasatanelevatedtemperature.Thiswasinitiallydemonstratedbyrunningtheactuatoruntiltheglow-to-lamentarytransitionoccurred.Theactuatorwasthenturnedoff,allowingthesurfacetoslightlycool.After 184

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Figure9-22. ThevisualappearanceoftheplasmaandtemperaturedistributionalongthesurfaceofaDBDactuatoroperatedat33kVppand5kHzforvarioustimes.A,B)t=20s,C,D)t=40s,E,F)t=45s,andG,H)t=50s. ashortdelay,theglow-to-lamentarytransitionwasseeminglyinstantaneousuponturningtheactuatorbackon.FromFigure 9-22 ,theglow-to-lamentarytransitiontookapproximately45secondsforanappliedvoltageof33kVppat5kHzwhenthestartingtemperatureofthedielectricsurfacewasequaltothatoftheambient(T20oC).However,whenstartingatanelevatedtemperature(obtainedbyinitiallyrunningtheactuatoruntilaglow-to-lamentarytransitionoccurred)thetransformationtimewassubstantiallyreduced(Figure 9-24 ).Theseresultswerefoundtoberepeatableas 185

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Figure9-23. ThevisualappearanceoftheplasmaandtemperaturedistributionalongthesurfaceofaDBDactuatoroperatedat32kVppand5kHzforvarioustimes.A,B)t=60s,C,D)t=80s,E,F)t=85s,andG,H)t=90s. demonstratedinFigure 9-24 ,inwhichtheactuatorwascycledonandoffmultipletimes.Eachcycleresultedinrestartingtheactuatorwithaninitialtemperaturedistribution.Thepeaksurfacetemperatureswere45-50oCwhenrestartingtheactuator.Althoughindicatingastronginuenceofsurfacetemperature,theresultsofFigure 9-24 donotnegatetheinuentialeffectssurfacechargemayhave.AsdescribedinSection 3.1.1 ,substantialsurfacecharginghavebeenfoundtooccurontheactuatorsurfaceevenaftertheactuatorasbeenturnedoff( Enloeetal. 2008a ; Fontetal. 186

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Figure9-24. Thermalandvisualimagesduringmultipleoperationalperiods(onandoff)oftheactuator(33kVppat5kHz).Areducedglow-to-lamentarytransformationtimeusingapreheatedsurfaceisdemonstrated.Theinitialtemperaturedistributionwasobtainedbyturningontheactuatoruntiltheglow-to-lamentarytransitionoccurred.Points(redcircles)correspondtothefollowingtemporallocations:A)t=0s,B)t=1s,C)t=9s,D)t=84s,E)t=85s,F)t=144s,andG)t=145s. 2010 ; Gibalov&Pietsch 2000 ; Opaitsetal. 2008b ).Althoughsurfacechargedoesnotinitselfexplainthedrasticrelativedifferencebetweentheinitialtransitiondelayandtheappliedfrequency(thetimescalerelativetothesurfacecharge),attemptstomanipulatedtheglow-to-lamentarytransitionwithoutinitiallyrunningtheactuatorwereinvestigated.Itwasfoundthataglow-to-lamentarytransitioncouldbeselectivelyrealizedwithoutaffectingotherregionsofthedischargebylocallyheatingtheborosilicateglass.Toaccomplishthis,theborosilicateglasswaslocallyheatedusingahotairguntoatemperatureofapproximately90oC.AsshowninFigure 9-25 D,wherethe 187

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Figure9-25. ThetemperaturedistributionalongthesurfaceofaDBDactuatoroperatedat44kVppand2kHzwithincreasing(fromlefttoright)time.A-C)Noinitialheatadditionwasprovided,whileinD-F)therighthalfandG-I)thelefthalfwereinitiallyheatedto90oC.Thecorrespondingvisualappearanceofthedischargeisprovidedintheinsetimages.Takenfrom Durscheretal. ( 2012 ). rightsideoftheactuatorwaslocallypre-heated,thelamentaryfeaturesimmediatelyoccurredwhenthedischargewasestablished.Moreover,thelamentaryfeaturesareinitiallyconcentratedontherightsideoftheactuator.Overtimethelamentsdidbegintoencompasstheentirespanoftheexposedelectrode(Figure 9-25 E,F).Theseresultswererepeatedsothattheleftsideoftheactuatorwaspre-heatedasopposedtotheright,asshowninFigure 9-25 G-I.Inbothcases,thepreheatedorlamentarysideextendedinthestreamwisedirectionwellpasttheunheatedglow-likeside.Forcomparativepurposes,noinitialheatadditionwasprovidedinFigure 9-25 A-C.Furthermore,asoutlinedinTable 9-3 ,thepresenceofthelamentsincreasedthenetpowerconsumptionofthedeviceby30-40%forthesameappliedvoltage.Thisincreasewasindependentofwhetherornottheglow-to-lamentarytransitionwas 188

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Table9-3. Powerconsumptionforaconstantvoltage(44kVpp)andfrequency(2kHz)priortoandduringthelamentarydischargetransformation.Takenfrom Durscheretal. ( 2012 ). Power(W)jPFilamentary PNon)]TJ /F12 5.978 Tf 5.76 0 Td[(Filamentary)]TJ /F6 11.955 Tf 11.96 0 Td[(1j(%) Noheataddition(non-lamentary)23.50.8-Noheataddition(lamentary)33.22.44111Righthalfheated(lamentary)32.21.9379Lefthalfheated(lamentary)30.71.7318 induced(bypre-heatingthesurface)oroccurrednaturally(byallowingtheactuatortorunforanextendedperiodoftime). 9.5DiscussionThetemperaturedifferencesbetweenelectrons,vibrationalstates,andneutralspeciesinthenon-equilibriumdischargeoftheDBDismaintainedbyabalancebetweenexcitationandrelaxationprocesses.Thisbalancemaybedisrupted,however,byrandomperturbations,resultinginaninstability.Whenaninstabilitydoesarise,thevisualappearanceoftheplasmamaybebroadlydescribedbyeitherastriationorcontraction( Fridman&Kennedy 2004 ; Raizer 1991 ),withthelaterbeingofpracticalinteresthere.Astriationinstabilityisvisuallydescribedasalternatingbrightanddarkregionswithintheplasma( Raizer 1991 ).ExamplesofplasmastraticationmayreadilybefoundintheliteratureforthepositivecolumnofaDCdischarge( Raizer 1991 ; Staacketal. 2005 ),ionosphereplasma( Linson&Workman 1970 ),andplasmadisplaypanels( Ouyangetal. 2007 ; Shon&Lee 2001 ).Thepresenceofstriationsinaplasmadonotsignicantlychangeitsparameters( Fridman&Kennedy 2004 ).Acontraction,orselfcompression,oftheplasma,ontheotherhand,iscorrelatedwiththeplasmareducingtooneormorebrightcurrentlaments( Fridman&Kennedy 2004 ).Withinthecontraction,thenon-equilibriumsystemattemptstorestoreitselftoaquasi-equilibriumstate( Fridman&Kennedy 2004 ).Thelamentarydischargeeventsobservedatsaturationareconsistentwiththedescriptionofaconstrictingplasma.Atatmosphericpressures,aconstrictionofthe 189

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plasmatypicallyarisesduetoanionizationoverheatinginstability(IOI)( Fridman 2008 ; Fridman&Kennedy 2004 ; Raizer 1991 ).Asdiscussedfurther,theionizationoverheatinginstabilityisbelievedtobetheprimarycauseoftheglow-to-lamentarytransition( Fridman 2008 )observedduringsaturationoftheDBDactuator.Asdescribedby Staacketal. ( 2009 ),theglow-to-lamentarytransitionofaninitiallystableDCglowdischargeinamonoatomicgascanbedescribedbytheionizationoverheatinginstability,whichisgivenbythefollowingpositivefeedbackloop:"T)#n)"E n)"Te)"ki)"ne)"T (9)whereisthedifferentialoperator,Tistheneutralgastemperature,nisthenumberdensityoftheneutralspecies,E=nisthereducedelectriceld,Teistheelectrontemperature,kiistheionizationrateconstant,andneistheelectronnumberdensity.Althoughtheinstabilitymaybeinitiatedatanystep,fromEquation 9 aninitialdifferentialincreaseingastemperatureresultsinadecreaseingasdensity(assumingconstantpressureandtheneutralspeciesmaybetreatedasanidealgas).Furthermore,assumingaconstantelectriceld,thedecreaseddensityeffectivelyincreasesthereducedelectriceldwhichincreasesthedependentelectrontemperature.Duetothestrongdependenceonelectrontemperature,theionizationrateincreaseswithelectrontemperature( Fridman&Kennedy 2004 ),whichleadstoanincreaseinelectronnumberdensity.Closingthefeedbackloop,thegastemperaturefurtherrisesasaresultofincreasingcollisionalexchangesduetothehigherelectronconcentration.FurtherdescriptionoftheIOIchain(Equation 9 )by Raizer ( 1991 )clariesthatanincrementalincreaseinelectronnumberdensityresultsinanincreasedelectriccurrentdensity,j,duetotheadditionalchargecarries.Foraconstantelectriceldthiswouldimplyanincreaseinpowerdissipation(=jE)intheplasma,suchthat"ne)"(jE))"T. 190

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WhenexpandingEquation 9 toamoleculargas,asisthecaseofaDBDactuatoroperatedinair,intermediatevibrationalmodes(TVib)mustbeconsidered( Fridman&Kennedy 2004 ).Asaresultanincreaseinelectronconcentrationdoesnotleaddirectlytogasheating("ne)"TVib)"T),thoughtherestoftheprocessesdescribedinEquation 9 remainthesame.InEquation 9 ,adifferentialincrease(ordecrease,asisthecaseforthenumberdensity)resultsinanunboundedgrowthoftheseparameterswithintheglowdischargeuntilglow-to-lamentarytransitionoccurs.Fromtheprevioussection(Section 9.4.2 ),initiationoftheIOIchainbyheatingthesurfaceoftheborosilicateglassisthoughttooccurbyincreasingthenearwallgastemperatureand/orincreasingthenearwallelectronnumberdensityduetodesorption.Basedonthecurrentexperimentalobservations/measurementsandthenonspecicinitializingnatureofEquation 9 ,separatingthesetwomechanismswouldbemisguided.However,regardlessofthespecicdetailsassociatedwithinitiationoftheIOIchain,whichisbelievedtocausetheonsetofthesaturationeffect,thedata(Section 9.4.2 )indicatesthatchangingthesurfacetemperatureofthedielectricmediumofaDBDactuatorcouldstabilizetheglow-to-lamentarytransition,delayingthesaturationeffectandincreasingthebodyforce,therebypotentiallyimprovingthecontrolauthorityoftheactuator.Fromthecurrentexperimentalobservationsandmeasurements,theionizationoverheatinginstabilityisbelievedtobetheprimarycauseoftheglow-to-lamentarytransitionobservedduringsaturationoftheDBDactuator.However,duetothecomplexchemistryinvolved(i.e.multiplespecies)andtherelativelycomplicatednatureofthedischargeandactuatorgeometry,whichmakesitdifculttodeneplasmaparametersandspatialandtemporalscales,adenitivedeclarationoftheresponsibilityoftheIOIchaincannotbemade(basedonthecurrentmeasurementspresented).Additionalargumentsinfavoroftheionizationoverheatinginstability,however,maybemade 191

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byexaminingsimilardischarges,negatingotherpossibilities,andconsideringtheobservationsofthemanyparametricstudiesreported.Tobeginwith,thecurrentdataindicates(Section 9.4.2 )thatatparticularvoltages/frequenciesthelamentaryfeaturesdidnotbecameprominentuntilthesurfacetemperatureoftheborosilicateglasswasapproximatelygreaterthan50oC.Ifthenearwallgastemperatureisalsoassumedtoreachatemperatureof50oC,foranambienttemperatureof20oC,thiswouldcorrespondtoanincreaseingastemperatureof30oC.Asdemonstratedmathematicallyby Raizer ( 1991 ),forahomogeneousglowdischargeinamonatomicgas(ofwhichtheDBDactuatoroperatedinairsharessimilarlyqualities),aconstrictionoftheplasmainatubeorplanechannelcanbetriggeredbyheatingthegasbyonly10to20%aboveambient.Relativetothissimpliedexample,anincreaseof150%ismorethancomparable.Furthermore,theinclusionofotherinstabilitymodesmustalsobeconsidered.Forexample,theelectronattachmentinstabilityisanothercommoninstability(althoughnotasgeneralastheionizationoverheatinginstability)whichcanoccurwhenelectronegativegasesarepresent( Fridman&Kennedy 2004 ).Anattachmentinstabilityonlymanifestsitselfifelectrondeattachmentsubstantiallycompensatesforattachment( Raizer 1991 ).Asnotedby Fridman&Kennedy ( 2004 ),thishasbeenobservedforglowdischargeswhenuctuationsintheelectronnumberdensitydonotaffectthecurrent.Fromtheobtainedresults,suchaninstabilityseemsunlikelyastheincreasedpowerconsumptionofthedevice,asoutlinedinTable 9-3 ,indicateasubstantialincreaseincurrentforthenominallyconstantvoltage.Forcompleteness,additionalinstabilitymechanisms,whicharelessgeneralandlesslikelyincludetheionizationinstability(controlledbydissociationofmolecules),thestepwiseionizationinstability,theelectronMaxwellizationinstability,andaninstabilityduetofastoscillatingelds( Fridman&Kennedy 2004 ).Theseremaininginstabilitiesrequireveryspeciccircumstancessuchashighcurrentsorfrequencies(relativetotheDBDactuator)andarenotconsideredplausiblebased 192

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onthecurrentexperimentalobservationsandmeasurements;untiladditionaltestsareundertaken,however,theyshouldnotbeexcluded.AsdiscussedinChapter 2 and 3 ,thedielectricplaysacrucialroleinthedynamicsofthedischargeinaDBD.Additionalconsiderationssuchaschangingdielectricpropertieswereinvestigatedasothertemperaturedependentsourceswhichcouldalterthedischarge.Onesuchpropertyisthedielectricconstantofthematerial.AsshowninChapter 8 thedielectricconstantcanhaveasubstantialeffectofactuator'sthrustgeneration.AdescriptionoftheexperimentalmethodusedtodeterminetherelativedielectricconstantisdescribedinAppendix D .Foraborosilicatesubstrate,therelativedielectricconstantwasdeterminedtobe4.7atambienttemperatures(20oC).Thesamplewasthenheatedtoaquasi-uniformtemperatureof100oCandtherelativedielectricconstantwasremeasured.Auctuationofthelessthan4%wasobserved,indicatingconstantelectricallypropertiesforthedielectric,withinexperimentalaccuracyforthetemperatureregimesshowninSection 9.4.1 .Similarly, Uchiikeetal. ( 1976 )reportedatemperatureindependentsecondaryelectronemissioncoefcientforaquartz(similartoborosilicate)sampleattemperaturebelow100oC.Gasdischarges(seeSection 2.2 )operatingintheglowdischargeregimeareprimarilysustainedthroughsecondaryelectronemissionatthecathode( Howatson 1976 ).Althoughadditionalconsiderationshavebeenpresentedtoexplaintheglow-to-lamentarytransitionobservedatsaturation,themechanismsinvolvedwiththeionizationoverheatinginstabilityagreewellwithreportedparametricstudiesaimedatoptimizingtheDBDactuator.Asdescribedatthebeginningofthechapter,theuseofthickerdielectricswithlowerdielectricconstantsandlowerdrivingfrequencieshavebeenfoundtodelaythesaturationtransition,allowinghighervoltagestobeapplied.ThisinturnmaximizesthethrustproductionoftheDBDactuator.Whileparametricallyfoundtoinuencetheactuator'sthrustgeneration,theseparametersalsoinuencethepowerdissipated,andthusheatgenerated,inthedielectric.Equation 9 dictatesthatthe 193

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powerdissipatedinthedielectricincreaseswiththerelativedielectricconstantofthematerial,thedrivingfrequency,andtheappliedelectriceld(=voltage/thickness).Tofurtherillustrate,considerthatthemaximumthrustproducedissolelydependentontheglow-to-lamentarytransitionwhichisinverselydependentonthesurfacetemperature.Thesurfacetemperatureisthenproportionaltothepowerlossinthedielectric.FromEquation 9 ,inordertoreducethepowerloss(foraconstantvoltage)oneneedstousethickdielectrics(toreducetheelectriceld)withlowerdielectricconstantsandlowerdrivingfrequencies;thesametrendsobservedparametricallytomaximizethrustgeneration.Furthermore,asidefromjustheatgenerationwithinthedielectric,thenecessitytooperateatlowerfrequenciesplaysanadditionalseparate,butsimilarrole.Areductioninthedrivingfrequencyinherentlyincreasesthetimebetweendischarges(asdescribedinSection 3.1.1 thedischargeextinguishestwiceperperiod).Thisallowsmoretimeforheat(andreactivespecies)todissipate,resultinginreducedoperatingtemperatures. 194

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CHAPTER10SUMMARYANDRECOMMENDATIONSFORFUTUREWORKAsdescribedinChapter 3 thedielectricbarrierdischargeplasmaactuatorhasbeenappliedtovariousaerodynamicapplicationsandhavebeenparticularlyeffectiveforlowerfreestreamvelocities(50ms)]TJ /F7 7.97 Tf 6.58 0 Td[(1).Inordertobetrulyapplicableforawiderangeofapplications,however,ademonstrationofsufcientcontrolauthorityathigherspeedsisnecessary.Toaccomplishthistheplasmaactuatorrequiresasignicantimprovementinoutputperformance,whetherthemetricbemomentumtransferorpeakinducedvelocity.TheobjectiveofthisworkwastoexploreandcharacterizenovelandconventionalDBDactuatorsinanefforttoimprovethesemetrics.Resultsforactuatorsconsistingofmultiplepoweredelectrodes,actuatorswiththree-dimensionalelectrodelayouts,actuatorsconsistingofdielectricmaterialswithextremepermittivities,andtheproblemofthrust`saturation'werepresentedinthepreviouschapters.Thefollowingsectionshighlightandsummarizetheprimaryndingsoftheseinvestigations,aswellasproviderecommendationsforfutureworkintheseareas. 10.1ExplorationoftheMulti-BarrierActuatorDesignSpaceInChapter 6 ,anexplorationofthemulti-barrierplasmaactuator(MBPA)designspacewaspresented.Theinuenceonperformanceofthemiddleelectrode'swidthinthebi-layerMBPAwasascertained.Awidthof5mmwasfoundtobeanoptimumoperatingpointintermseffectiveness,ratioofinducedthrusttoconsumedpower.However,basedonthesendingsitwasspeculatedthatthemiddleelectrodeplayednosignicantroleinthrustproductionandthatbychangingitswidthonewassimplyvaryingtherelativegapbetweentheexposedandencapsulatedelectrode.Toverifythispostulate,themiddleelectrodewasremovedfromthebi-layercongurationandtheexperimentswererepeated.Althoughhavinglittleeffectontheinducedthrustortotalpowerconsumed,themiddleelectrodewasfoundtoplayanimportantroleinhowtheconsumedpowerwasdistributedamongstthepoweredelectrodes.Whenremoved, 195

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eachbranchinthebi-layerMBPAcircuitcontributedroughlyequallytotheoverallpowerconsumption.Whenthegroundedelectrodewaspresent,however,theexposedelectrode'scircuitsuppledsignicantlymorepower(especiallyatlowervoltages)thantheencapsulatedelectrode'spoweringcircuit.Thisbehaviorinthepowerdistributionwasattributedtoa`steppingstone'effectthatthegroundedelectrodecreatesfortheelectriceldlines;aphenomenonwhichwasveriednumerically.Intermsofpurethrustgeneration,thestandardactuatorwasfoundtoproducehigherinducedthrustsforagivenvoltageovertheMBPAdesigns.Whenpowerconsumptionwastakenintoaccount,however,splittingthevoltageamongthetwoelectrodesresultedinasignicantreductioninpowerconsumption.Thiswasshownbytheeffectivenessparameter.Animprovementineffectivenessof30%wasobtainedusingthesplitelectrodeconguration(MBPA)overthestandardactuator.Futuretest,however,shouldlookattheactuators`efciency'inwhichtheeffectivenesscouldbemultipliedbythepeakvelocityproduced.AdditionalMBPAcongurationssuchasmixingdielectricmaterialandatri-layeractuatorwerealsoinvestigated.ForthemixeddielectricMBPA,theorderofthedielectricsinthedesignwasfoundtoinuencethethrustproduction.Seemingly,amaterialwithahigherrelativedielectricconstantforthetoplayerresultedinlargerthrustsataxedvoltage.However,onlymaterialswithrelativelysmalldifferencesindielectricconstantsweretested.Itissuggestedthatfutureexperimentsinvestigatelargelydisparatedielectricmaterials.Furthermore,theeffectofrelativephaseangleontheperformanceofatri-layerMBPAwasexplored.Largediscrepanciesintheresultantthrustandconsumedpowerwerefoundbetweenleadingandlaggingcircuitcongurations.Relativetotheotherdesignstested(bi-layerMBPAandstandardactuator),thetri-layerMBPAwassignicantlyoutperformedinboththrustproductionandeffectiveness.Additionalinvestigationschangingtherelativephaseangle,electrodewidths,anddielectricsusedis,however,warrantedandfurthertestsareadvised. 196

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10.2Three-DimensionalFlowInducementStereo-PIVwasusedtocaptureandcharacterizethecomplicatedthree-dimensionaloweldinducedbyserpentineplasmaactuatorsinaquiescentenvironmentinChapter 7 .Twodifferentdesignswereinvestigatedinthisstudy:oneconstructedfrompatternedcirculararcsandonefrompatternedrectangles.Bothdesignswerefoundtoinjectx,y,andzmomentumresultinginthree-dimensionalvorticalstructures.Inparticular,notonlywasspanwisevorticitygenerated,butalsocounter-rotatingvortexpairsinthestreamwisedirection.Thesevortexpairsweregeneratedperiodicallyalongthespanoftheactuator.TheserpentinecongurationcombinestheeffectsofalinearplasmasyntheticjetactuatorandthatofalinearDBDactuator,bothofwhichareinherentlyquasi-two-dimensional.Asaresult,thereisavectorednaturetothevortexgenerationintheserpentinedesign.Thiswasshowntoresultinacorkscrewlikestructureintheinducedoweld.Theserpentineactuatorswerefurthercomparedwithastandardlinearactuatorwhereanominallytwodimensionaloweldwasobserved.Suchadevicehasnumerousaerodynamicapplicationswhereanincreasedmixingofthelocaluidisdesired.Animprovementinowturbulizationcouldsignicantlyenhancethedesiredoutputintheareasofboundarylayertransition,convectiveheattransfer,andplasmaassistedcombustion(PAC).Anexperimentalstudyusingaserpentineactuatoronafreestreamboundarylayerofsuchanapplicationremainsopenforevaluationinfutureefforts.Thegeometricdesignoftheserpentinedevicewouldlikelybedependentontheboundarylayercharacteristicsofthedesiredapplication,andoptimizing/tailoringthedevicewouldberequired.Theserpentinedesignstestedtodatehavebeenshowntopushuidawayfromthesurfaceataprescribedangle.Thisangleremainedapproximatelyconstantat38owithregardstothetwocongurationstested(circularandsquare)andappearedtobeindependentoftheappliedvoltageaswell.Forbothdesignsexplored,thefundamentalwavelengthandamplitudeofthe 197

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congurationsremainedthesame.Thereforeinordertotrulyapplythisactuator,aparametricinvestigationiswarrantedtostudytheeffectsofgeometryontheinducedoweld.Furthermore,theinuenceonowstructureandcontrollablevectoringofasegmentedserpentinedesignandtheadditionofadutycycletothesupplyvoltageshouldalsobeevaluated. 10.3ExploringtheFarEndsoftheDielectricSpectrumInChapter 8 ,dielectricspossessingextremerelativedielectricconstantsof1.2(silicaaerogel)and1750(ferroelectric)werepresented.Silicaaerogelwasfoundtoahaveastrongeffectonthethrustgeneration.Signicantlyhighervoltagesweresustainablecomparedtoothermaterialsofsimilarthickness,duetosuchalowdielectricconstant.Theaerogel'sminimalweightpenaltyandhigherthrustsmaybeusefulforpracticalapplicationslikemediumtosmall/micro-airvehicles.Thefriabilityofthecurrentsamplesofsilicaaerogel,however,makesthemchallengingfordirectintroductiontoapplications.Though,thepotentialbenetofalargeimprovementinthethrust-to-weightratio,withnopowerpenalty,usingsuchlightweightmaterialsisencouraging.Furthermore,duetothebrittlenessofthecurrentsamples,thereportedthrustmeasurementshavebeeninferredfromacontrolvolumeanalysisonthevelocityeldobtainedusingparticleimagevelocimetry.Forcompletenesstheseresultsneedtobeveriedusingadirectmeasurementtechnique.Additionally,themaximumvoltagethatmaybeappliedtoasilicaaerogelactuatorneedstobeinvestigated.Duetotherelativelysmallsizeofthecurrentsamples,anarcingaroundthedielectricensuedbeforeabreakdownofthedielectricwasobserved.Aninvestigationusingmorerobustaerogelsisalsowarranted.AlthoughnotpresentedinChapter 8 ,preliminarytestsusingRF(Resorcinol-Formaldehyde)aerogelwereundertaken.Liketheirsilicabasedcounterpart,RFaerogelhasaverylowdensity(0.2gcm)]TJ /F7 7.97 Tf 6.58 0 Td[(3)andrelativedielectricconstant(1.4)( Hrubeshetal. 1993 ).Despitebeingslightlyheavierthansilicabasedaerogels,RFaerogelissignicantlystronger. 198

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Thecurrentlyobtainedsamplescouldbebentslightlywithoutfracturing;afeatnotpossiblewiththebrittlesilicabasedsamples.Preliminarytestsindicated,aswiththesilicaaerogelsamples,asustainableplasmacouldbegeneratedonthesurfacewithoutbreakingdownthedielectric.Voltagescomparabletothatusedforthesilicaaerogeltestswereapplied.Thismaterial,however,stillneedstobeevaluatedforthrustgeneration.Fortheferroelectricmaterialstudied,signicantheatingofthesurfaceresultedwhilenothrustwasobservedovertherangeoftestedvoltagesandfrequencies.Theresultsindicatethepossibilityofoperatingatahigherfrequency(orvoltage)togeneratethermalloadingatafastertimescale.Thismayhavepossibleimplementationasaheatbumpinhighspeedowcontrolapplications.Thinner,highpermittivitymaterialshouldalsobeexaminedforthrustgeneration. 10.4CharacterizationoftheDBDThrust`Saturation'EffectThemechanismsandfeaturesoftheDBDactuator'sthrustsaturationwereexploredinChapter 9 .Extendingonreportedobservations,directthrustmeasurementswereusedtoquantifytheactuator'sthrust.Additionally,theoweldforaDBDactuatorpriortoandduringsaturationwasinvestigated.Itwasshownthattheaverageuidvelocitydecreasedupontheinceptionoflamentarydischargeevents,whichisconsistentwiththereportedthrustmeasurements.Furthermore,withtheuseofinfraredthermography,thesurfacetemperatureofthedielectricbarrierwascharacterized.Itwasshownthatthesurfacetemperatureofthedielectricbarrierplaysacrucialroleinthetransitionoftheglow-likedischargeeventstolamentarydischargeevents.Itwasalsoshownthatthesaturationeffectcanbemanipulatedbychangingthesurfacetemperatureofthedielectric,resultingintheinitiationoftheionizationoverheatinginstabilitychain.Theseresultsprovideaphysicsbasedexplanationfortheobservationsofthemanyreportedparametricstudiesonthethrustsaturationphenomenon. 199

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Todate,onlytimeaveragedquantities,relativetothedrivingfrequencyoftheappliedvoltage,havebeencharacterizedforanactuatoroperatingatsaturationconditions.UsinganICCD(IntensiedCharge-CoupledDevice)cameraitwouldbepossibletovisualizetheperiodic,temporalcharacteristicsoftheplasmabeforeandaftertheglow-to-lamentarytransition.Theseimageswouldprovideadditionalinsightintotheactuator'ssaturationeffect.Furthermore,theuseofatime-resolvedparticleimagevelocimetrysystemwouldprovideafurtherunderstandingoftheuid'sinteractionwiththeplasmaandhowthisinteractionchangesastheglow-to-lamentarytransitionoccurs.Suchresultscouldalsobeusedtotrackthetemporalchangesintheplasmainducedbodyforceusingacontrolvolumeanalysis( Debienetal. 2012a )orbacksubstitutionintotheNavier-Stokesmomentumequations( Kotsonisetal. 2011 ).Additionalprobingintotheionizationoverheatinginstabilityisalsowarranted.Timeresolvedspectroscopicmeasurementscouldprovidedadditionalinformationintotherelativeconcentrationsandtemperaturesofselectspecies,whichmayprovidedpertinentinformation.Lastly,theresultspresentedinChapter 9 suggestthatasuppressionorstabilizationoftheglow-to-lamentarytransitionispossiblebyalteringthesurfacetemperatureofthedielectricmedium.Adelayofthesaturationeffectwouldincreasetheinducedbodyforceandlikelyextend/improvethecontrolauthorityoftheactuator.Asimpleexperimenttosuppresstheglow-to-lamentarytransitionwastried,inwhichthedielectricwasinitiallycooled(0oC)priortoturningontheactuator.However,priortoobtainingusabledata,watervaporwouldquicklycondenseonthesurface,detrimentallyalternatingthedischargepropertiesandchemistry.Moresophisticatedmeansoftestingthispostulateshouldbeexplored,whichinvolvetheuseofdry(0%RH)air.Furthermore,theapplicationofanexternal,freestreamvelocitymaybesufcienttoreducethetemperature,delayingthesaturationeffect.Additionalexperimentscould 200

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alsoentailheatingtheairdirectly,asopposedtothedielectricsurface,andstudyingthetransition. 201

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APPENDIXAHIGHVOLTAGETRANSFORMERSCHEMATICSANDSPECIFICATIONSTable A-1 highlightskeyspecications(i.e.turnratio,frequencyrange,voltagerating,andcurrentrating)forthethreetransformersusedthroughoutthisworktogeneratethehighvoltagesrequiredtoignitetheplasmadischarge.SchematicsoftheindividualtransformersarealsoprovidedinFigures A-1 A-2 ,and A-3 TableA-1. Assortedspecicationsforthetransformersusedtogeneratethehighvoltagesrequiredtoignitethedielectricbarrierdischargeactuator.Frequencyrangesareestimates. Model#TurnratioFrequencyrange(kHz)Voltagerating(kVrms)Currentrating(Arms) CMI5525-21=3570.9-5250.20CMI5528-11=2458-30250.08CMI55231=1=4327-30180.07 202

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FigureA-1. CoronaMagneticsCMI5525-2highvoltagetransformer. 203

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FigureA-2. CoronaMagneticsCMI5528-1highvoltagetransformer. 204

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FigureA-3. CoronaMagneticsCMI5523highvoltagetransformer. 205

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APPENDIXBMEASURINGPOWERFORTHEDBDACTUATORMeasuringthepowersuppliedtothedielectricbarrierdischargeactuatorisanimportantpropertytoquantifyinordertoproperlyevaluatethetrueeffectivenessofthedevice.Thissectionoutlinesfurtherdetailsregardingthesemeasurements. B.1ErrorAnalysisTheinstantaneouspowerconsumedbytheplasmaactuatorisgivenbyEquation 4 inSection 4.3.1 .Therootmeansquarederrorinaninstantaneousmeasurementisgivenas,P(t)error=s @P(t) @VV2+@P(t) @II2+@P(t) @2 (B)whereVandIaretheassociateduncertaintiesinthemeasuredvoltageandcurrent,respectively.Thetemporaluncertaintywhichwouldleadtoanerrorintherelativephasedifferencebetweenthetwowaveformsisgivenby.Fornowanytemporalerrorwillbeignored(=0),butfurtherdetailswillbediscussedinSection B.2 .Giventheuncertaintiesinthevoltageandcurrentasapercentageofthemeasuredvoltage,V=VV(t),andcurrent,I=II(t);Equation B mayberewrittenasP(t)error=p (I(t)VV(t))2+(V(t)II(t))2 (B)Uncertaintyvaluesforthevoltage(V)andcurrent(I)probesusedareprovidedinSection 4.3.1 Rearrangingandsimplifying,theaboveequationmaybeexpressedas,P(t)error=V(t)I(t)q 2V+2I (B) 206

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whichgivestheerrorintheinstantaneouspowerduetoprobeuncertainties.Equation B maybetemporallyaveragedandexpresseddiscretelyas,Perror=p 2V+2I NNXi=1ViIi=q 2V+2VP (B)wheretheaveragepower,P,isgivenbyEquation 4 .Similarlyforthecaseinwhichtwopowersuppliesareused(Equation 4 ),theaverageerrorintheconsumedpowerisgivenby,Perror=q (2V+2I)(P21+P22) (B)whereP1andP2arethepowersuppliedineachcircuitbranch(Figure 4-3 B).Notethatthenetpowerconsumedbythedeviceistakenasalinearsuperpositionofthepowersuppliedtoeachbranch. B.2TemporalErrorEstimationThetemporaluncertaintyinthepowermeasurementismoreeasilyseenbytreatingthevoltageandcurrentwaveformsaspuresinusoidalfunctionsofarbitraryamplitudes(AandB)andfrequency(f).Examplefunctionsaregivenby,V(t)=Asin(f2t),I(t)=Bsin(f2t+) (B)Thetemporalphaseshiftbetweenthetwosignalsisgivenby.Thetimeaveragepower(similartoEquation 4 )isgivenby, P=fZf0V(t)I(t)dt=VrmsIrmscos() (B)whereVrmsandIrmsaretherootmeansquaredvalueofthevoltageandcurrent.Notethattheaboveequationonlyholdsinthecaseofpuresinusoidalfunctions.Thetemporalerrorbetweenthetwosignalsisnowgivenbytherelativeerrorinthephaseshift,,aswasoriginallydenotedinEquation B .Theimpactofthephaseshiftisbestexaminedthroughanexample.ReplacingtheamplitudesinEquation B withtypical 207

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FigureB-1. Powerconsumptionasafunctionofrelativephaseangleassumingsinusoidalwaveformswithpeaks10kVand20mA.Forlargeanglesalinearapproximationmaybemadeshowing1.7Wattsperdegreevariation. valuesfortheDBDactuator(A=10,000VandB=0.02A),agraphofthecalculatedpowerverserelativephaseshiftcanbemade(Figure B-1 ).Hereaphaseshiftof0owouldcorrespondstoapurelyresistiveload,whileashiftof90oispurelycapacitive.AsdiscussedinSection 3.1.1 theDBDactuatorisprimarilycapacitive.Furthermore,thepowerisroughlyproportionaltotherelativephaseshiftbetween60oand90o.FromFigure B-1 thisresultsina1.7Wattsperdegreerelation,meaningthatifthemeasuredsignalsaretemporallyoffbyasingledegree,thenthecalculatedpowerwilldifferby1.7Wfromthetruevalue.Temporalerrorsmayarisedotointernaldelaysintheacquisitionequipment,however,thisseemsunlikelyduetothehighbandwidthratingsoftheequipment(MHz)usedrelativetotheoperatingfrequencies(kHz).Amorelikelysourceoferrorwouldbeduetotheprobe'spresencephysicallyalteringthemeasuredload.Intheorythe 208

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FigureB-2. Equivalentcircuitmodeloftheplasmaactuatorwithassociatedprobes. idealimpedancecharacteristicsofanyprobeneedstobemuch,muchgreaterthanthemeasuredloadsuchthatthepresenceandinuenceoftheprobeisnegligible.Unfortunately,theimpedanceofthehighvoltageprobeusedintheseexperimentsisonthesameorderasthatofthetypicalDBDactuator( Kriegseisetal. 2011a b ; Zitoetal. 2010 ).Toevaluatetheprobeseffectontheactuator,theelectricalcharacteristicsofthedielectricbarrierdischargeactuatorwillbetreatedasasimplelumpedelementmodelconsistingofaresistorandcapacitorinparallel. Alonsoetal. ( 2003 )demonstratedthatthiswasareasonableapproximationforasurfaceDBDconguration.TheequivalentcircuitisshowninFigure B-2 ,whereR,C,andLrepresentresistive,capacitive,andinductiveelements.Subscripts`Plasma',`HV,probe',`LV,probe',and`Current,probe'denotetheplasma,highvoltageprobe,lowvoltageprobe,andRogowskicurrentprobe,respectively.CLissajousrepresentsacapacitiveelementusedtodeterminethecurrentasdescribedinAppendix C .Ingeneral,theimpedancecharacteristicsoftheRogowskicoilmaybeconsiderednegligible.Astheprobedoesnotphysicallyinteractwiththecircuittherestiveelementissmall(ontheorderm's).Furthermore,thepresenceoftheprobeshouldreduce 209

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thecircuitsinductancedototheprobe'scoupling.However,theDBDloadisprimarilycapacitivesoanyreductionintheinductancewouldbeinconsequential.Thepresenceoftheprobedoescreateanadditionalcapacitiveelementthatisinparallelwiththeactuatorthatneedstobeconsidered.Itsinuencemaybeestimatedbyconsideringthecapacitancebetweentwoconcentriccylindersgivenby,C=20L ln() (B)whereListhelengthofthecylinder,0isthepermittivityoffreespace,andisthediameterratioofthetwocylinders.ForthecurrentprobesoutlinedinSection 4.3.1 ,L=25mmand=11(assumingaconductivewirediameterof5mm).EvaluatingintoEquation B yieldsacapacitanceof0.57pF.Sincetheprobescapacitanceisinparallelwiththeplasmaloaditmaybeignoredduetoitsrelativelysmallvalue.IgnoringtheRogowskicurrentprobethecircuit'sequivalentcapacitancebecomes,Ceq=(1 Cplasma+1 CLissajous+CLV,probe))]TJ /F7 7.97 Tf 6.59 0 Td[(1+CHV,probe (B)Ifthein-linecapacitor,CLissajous,isverylargecomparatively,thetermincludingitmaybeneglectedreducingthecapacitanceto,Ceq=Cplasma+CHV,probe (B)Similarly,theresistanceofthelowvoltageprobemaybeignoredrelativetotheresistanceofanon-idealcapacitor.Theequivalentresistancethenbecomes1 Req=1 Rplasma+1 RHV,probe (B)Justifyingtheseapproximations,Table B-1 outlinestypicalvaluesoftheprobesdiscussedinSection 4.3.1 FromEquations B and B itbecomesapparentthatthehighvoltageprobe'scapacitanceshouldbemuchsmallerthantheplasma's,whiletheresistanceshouldbe 210

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TableB-1. Capacitanceandresistancevaluesforcircuitelementsusedtodeterminetheinuenceofthehighvoltageprobe. Capacitance,CResistance,R Plasma??HV,probe3pF100MLissajous9nF1LV,probe8pF10M muchlargerinordertohaveanegligibleeffect.Toinvestigatetheprobesinuence,highvoltageresistors(Rideal)andcapacitors(Cideal)wereusedasideal,knownsubstitutesfortheDBDactuator.ThecapacitorandresistorvalueswerechoseninanefforttomatchtheexpectedvaluesinaDBDactuator.Thecapacitorutilizedhadaratednominalvalueof47pF9.4pF,thoughindependentmeasurementsindicatedacapacitanceof55pF5pFoverthetestedfrequencyrange.Fourresistorswithmeasuredresistances148k,1.16M,2.32M,and4.65M(1%)wereused.Ifthepresenceoftheprobehadasignicantinuence(oranyinternaltimedelay),thecircuit'sresponseshoulddeviatefromtheidealcasegivenbythetransferfunction,VHV,probe I=Rideal 1+sRidealCideal (B)whereIisthecurrentmeasuredwiththeRogowskicurrentprobeandsistheLaplacevariable.TheseresultsareshowninFigure B-2 whichplotsthecircuitstheoreticalphaseresponseasafunctionfrequency.Thesymbolsindicateadiscretemeasurement.Asonecansee,goodagreementisseenbetweenthemeasuredandtheoreticalresults.Tofurthertesttheinuenceofthehighvoltageprobe,readingsweremadewithandwithoutitconnectedtoaDBDactuatorcircuit.Thecurrentsignal,asmeasuredbytheRogowskicurrentprobe,wasusedasthereferencesignalwhilethelowvoltagesignalacrosstheLissajouscapacitorwassampledwithandwithoutthehighvoltageprobebeingconnectedtothecircuit..Ashiftintherelativephasebetweenthecurrentandthelowvoltagesignalsshouldbeapparentifthereisasubstantialinuence.TheseresultsareshowninFigure B-4 andagainthehighvoltageprobeseemstohavea 211

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FigureB-3. V-Iphaseangleasafunctionoffrequencyforaresistorandcapacitorinparallel.Thesymbolsindicateadiscretemeasurement,whilelinesaretheoretical. negligibleimpactontheplasmaload.Thisindicatesthatthetemporalerrorinthethepowermeasurementmaybeignored. 212

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FigureB-4. Inuenceofthehighvoltageprobeontherelativeshiftbetweenthevoltageandcurrentwaveforms.Thecurrentsignal,asmeasuredbytheRogowskicurrentprobe,isusedasthereferencesignalwhilethelowvoltagesignalacrosstheLissajouscapacitorissampledwithandwithoutthehighvoltageprobebeingconnectedtothecircuit.Averagedsignalsareshown. 213

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APPENDIXCQ-VPOWERDETERMINATIONALissajousgure(alsoknownasaBowditchcurve),describesthegraphicalpatternproducedwhenplottingtwoparametricequations(typicallysinusoidal).TheLissajousgurecreatedbythecharge(Q)andhighvoltage(VHV)tracesinadielectricbarrierdischargecanbeusedtodeterminethedissipatedpower,assuggestedby Manley ( 1943 ).Thetemporalchargeasdenedby,Q(t)=CLissajousVLV(t) (C)isobtainedbymeasuringthevoltagedrop(VLV)acrossacapacitor(CLissajous)placedinseriesbetweentheactuator'slower(grounded)electrodeandtheearthground(Figure C-1 ).Thein-linecapacitorintegratesthecurrentpassingthoughtheactuatorasshownbyI(t)=CLissajousdVLV(t) dt (C)Replacingthecurrent,I(t),previouslyusedtodenetheaveragepower(Equation 4 )withEquation C ,onearrivesatP=1 TZT0VHV(t)I(t)dt=1 TZT0VHV(t)CLissajousdVLV(t) dtdt (C) FigureC-1. CircuitcongurationtomeasurepowerconsumedusingQ-V(orLissajous)method. 214

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FigureC-2. ExampleQ-Vcharacteristiccurve.Consumedpowerisdeterminedthroughintegrationoftheenclosedarea. where,Tistheperiodofoscillation(T=1 f,fistheappliedfrequency).FromEquation C ,however,theproductofCLissajousdVLV(t)isnothingmorethanthedifferentialcharge,dQ.Simplifying,Equation C maythenrecastasP=1 TZT0VHV(Q)dQ (C)AnexampleLissajousgure(orQ-Vcurve)isshowninFigure C-2 .FromEquation C ,theaveragepowerisobtainedbyintegratingtheenclosedarea.Oftentheinstantaneousmeasurementofthevoltageacrosstheinlinecapacitorisnoisydotothehighconductivecurrentsexperiencedduringthemicro-discharges.Assuchthetwosignalsareoftenaveraged. 215

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APPENDIXDDETERMININGTHEDIELECTRICCONSTANTOFADIELECTRICMATERIALThemethoddescribedheretodeterminethedielectricconstantofamaterial,hasbeenadoptedfrom Staneld ( 2009 ).ThetechniqueconsistsofcreatingaparallelplatecapacitorbysandwichingamaterialofunknowndielectricconstantbetweentwoparallelconductorsasshowninFigure D-1 .Thevoltageacrossandcurrentpassingthroughthecapacitorarethenmeasuredandusedtodetermineitscapacitance,fromwhichthedielectricconstantmaybeobtained.Tobeginwith,thetheoreticalaspectsarerstdiscussed,whichisthenfollowedbydetailingtheactualmeasurements. D.1TheoreticalGauss'slawisoftenwrittenas,I~Dd~a=Q (D)whereDisknownastheelectricdisplacementeldandQisthetotalfreecharge( Grifths 1999 ).Theelectricdisplacementeldisgivenby~D=0~E+~P (D)suchthat0isthepermittivityoffreespace(8.8541878210)]TJ /F7 7.97 Tf 6.59 0 Td[(12C2N)]TJ /F7 7.97 Tf 6.58 0 Td[(1m)]TJ /F7 7.97 Tf 6.58 0 Td[(2),~Eistheelectriceld(inVm)]TJ /F7 7.97 Tf 6.59 0 Td[(1orNC)]TJ /F7 7.97 Tf 6.59 0 Td[(1),and~Pisthematerial'spolarization(inCm)]TJ /F7 7.97 Tf 6.59 0 Td[(2).Foralineardielectric(asmostmaterialsare),~Pcanbeconsideredproportionaltotheappliedelectriceld:~P=0e~E (D)whereeistheelectricsusceptibilityofthematerial.SubstitutingEquation D intoequation D yields,~D=0(1+e)~E=~E (D) 216

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FigureD-1. Schematicofaparallelplatecapacitorusedtodeterminetheunknowndielectricconstantofamaterial. whereisthepermittivityofthematerial.Therelativepermittivity,ordielectricconstant,isthereforegivenbyr= 0=1+e (D)Foraparallelplatecapacitorwithappliedcharges+Qand)]TJ /F3 11.955 Tf 9.3 0 Td[(Q(Figure D-1 )equation D maybesolvedanalyticallygiventhattheplate'sarea,A,isrelativelylargecomparedtotheseparationdistance,d,(i.e.Ad2)suchthatendeffectsmaybeneglected.Therefore,displacementeldbetweentheplatesis,~D=)]TJ /F3 11.955 Tf 10.5 8.09 Td[(Q A^y (D)wheresubstitutionofEquation D yieldsanexpressionfortheelectriceld:~E=)]TJ /F3 11.955 Tf 18.77 8.08 Td[(Q Ar0^y (D)Integratingtheelectriceldyieldsthevoltagedifference,V,acrossthedielectricsubstrate:V=)]TJ /F11 11.955 Tf 11.29 16.28 Td[(Zd0~Ed~l=Qd Ar0 (D) 217

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Usingthedenitionofcapacitance(C=Q V),anexpressionforthedielectricconstantofamaterialisthengivenasr=dC 0A (D)withtheonlyunknownnowbeingthecapacitance,C. D.2MeasurementTheunknowncapacitanceofthematerialisdeterminedbyconsideringthecurrent-voltagerelationforacapacitor,suchthatI(t)=CdVCapacitor(t) dt (D)whereVCapacitoristhevoltagedropacrossthecapacitorandIisthecurrent.ThesevaluesareeasilyobtainableusingthesimpletestcircuitshowninFigure D-2 .Theresistor,R(=98.8),showninthecircuitwasusedtodeterminethecurrentwithinthecircuitbasedonOhm'slaw:I(t)=VR(t) R (D)whereVRisthevoltagedropacrosstheresistor.SubstitutionofEquations D and D intoEquation D yieldsananalyticalexpressionfortheunknowndielectricconstant:r=d 0AVR R dVCapacitor dt (D)Althoughastaticvalue,usingthismethodtodeterminethedielectricconstantledtosomevariationsinitsvalue.Thesedeviationsareprimarilyduetoerrorsinapproximatingthetemporalderivative,butwerealsoaresultofsmalluctuationsinboththecurrentanddifferentialvoltagesignals.Assuchincalculatingthedielectricconstant,itisnecessarytoaveragethevaluesafteroutlierswererstremovedusingthemodiedThompsonTautechnique(seeFigure D-3 ).TheexampledataintheFigure 218

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FigureD-2. Circuitcongurationusedtomeasuretheunknowncapacitanceofamadeparallelplatecapacitor. D-3 correspondstoamadeborosilicatecapacitorwithathickness,d,of3mmandaplatearea,A,of76.2cm2(referringtoFigure D-1 ).Theaveragerelativedielectricconstant, r,wascalculatedas4.7whichiswithinthereportedrangeof4.6-5.1(at1MHz,valueswerecollectedfrompubliclyavailablematerialdatasheets).Althoughwithinthereportedrange,mostmanufacturerslistavalueof4.6fortherelativedielectricconstantofborosilicate;thiscorrespondstoa2%differencefromthecurrentlyobtainedresult. 219

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FigureD-3. ExamplevaluesfortherelativedielectricconstantbeforeandafterrejectingoutliersusingthemodiedThompsonTautechnique.A)AgeneralviewofthedatasetandB)azoomedinview.Theexamplevaluescorrespondtodataobtainedforaborosilicatecapacitorwithathickness,d,of3mmandaplatearea,A,of76.2cm2).Theaveragevalueafterremovingoutliersfortherelativedielectricconstantwasdeterminedtobe4.7. 220

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BIOGRAPHICALSKETCH In2003RyanbeganattendingtheUniversityofFloridawherehewentontoreceivebachelordegreesinmechanicalengineeringandaerospaceengineering.Uponnishinghisundergraduatecurriculum,hewasawardedaSMARTscholarshipfromtheDepartmentofDefense,aswellasanassistantshipfromtheUniversityofFlorida.UndertheguidanceofDr.SubrataRoy,RyanbeganworkingtowardshisDoctorofPhilosophyinmechanicalengineeringin2008.Uponcompletion,hewillacceptaresearchpositionintheAirVehiclesDirectorateatWrightPattersonAirForcebase. 238