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Control of Three-Dimensional Flow over a Turret

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Title:
Control of Three-Dimensional Flow over a Turret
Physical Description:
1 online resource (343 p.)
Language:
english
Creator:
Palaviccini, Miguel Ra
Publisher:
University of Florida
Place of Publication:
Gainesville, Fla.
Publication Date:

Thesis/Dissertation Information

Degree:
Doctorate ( Ph.D.)
Degree Grantor:
University of Florida
Degree Disciplines:
Aerospace Engineering, Mechanical and Aerospace Engineering
Committee Chair:
Cattafesta, Louis Nicholas, Iii
Committee Members:
Dixon, Warren E
Sheplak, Mark
Arnold, David P

Subjects

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

Notes

Abstract:
Airborne optical systems are susceptible to large losses in performance due to aero-opticdistortion. For the case of laser-based systems, as the laser beam propagates through re-gions of high turbulence, the transmitted energy and focus of the beam are reduced. Astudy of the flow physics around a surface mounted turret with a flat aperture is described.The baseline flow is characterized by steady pressure measurements over the centerline ofthe model, unsteady pressure measurements on the aperture, and oil flow visualizationalong the surface for the range of Reynolds numbers from ReH = 2.27 × 105 - 5.10 × 105(Ma = 0.09-0.26). The evaluation of the static pressure measurements provides quanti-tative information on the separation location along the centerline of the turret. Oil flowvisualization provides information on the three-dimensional flow topology over the turret.Spectra from unsteady pressure measurements impart information on unsteady fluctuationtrends along the aperture. Several passive flow control configurations using pins are stud-ied. The evaluation of flow control performance is performed by analyzing both the surfacestreamlines from oil flow visualization and measurements of unsteady pressure fluctuationsalong the flat window. Results show that pins that penetrated though the boundary layerand were spaced less than four boundary layer thicknesses apart provided a reduction inthe rms pressure on the aperture, a slight delay in separation, and an elongation of therecirculation region.
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 Miguel Ra Palaviccini.
Thesis:
Thesis (Ph.D.)--University of Florida, 2013.
Local:
Adviser: Cattafesta, Louis Nicholas, Iii.

Record Information

Source Institution:
UFRGP
Rights Management:
Applicable rights reserved.
Classification:
lcc - LD1780 2013
System ID:
UFE0045001:00001

MISSING IMAGE

Material Information

Title:
Control of Three-Dimensional Flow over a Turret
Physical Description:
1 online resource (343 p.)
Language:
english
Creator:
Palaviccini, Miguel Ra
Publisher:
University of Florida
Place of Publication:
Gainesville, Fla.
Publication Date:

Thesis/Dissertation Information

Degree:
Doctorate ( Ph.D.)
Degree Grantor:
University of Florida
Degree Disciplines:
Aerospace Engineering, Mechanical and Aerospace Engineering
Committee Chair:
Cattafesta, Louis Nicholas, Iii
Committee Members:
Dixon, Warren E
Sheplak, Mark
Arnold, David P

Subjects

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

Notes

Abstract:
Airborne optical systems are susceptible to large losses in performance due to aero-opticdistortion. For the case of laser-based systems, as the laser beam propagates through re-gions of high turbulence, the transmitted energy and focus of the beam are reduced. Astudy of the flow physics around a surface mounted turret with a flat aperture is described.The baseline flow is characterized by steady pressure measurements over the centerline ofthe model, unsteady pressure measurements on the aperture, and oil flow visualizationalong the surface for the range of Reynolds numbers from ReH = 2.27 × 105 - 5.10 × 105(Ma = 0.09-0.26). The evaluation of the static pressure measurements provides quanti-tative information on the separation location along the centerline of the turret. Oil flowvisualization provides information on the three-dimensional flow topology over the turret.Spectra from unsteady pressure measurements impart information on unsteady fluctuationtrends along the aperture. Several passive flow control configurations using pins are stud-ied. The evaluation of flow control performance is performed by analyzing both the surfacestreamlines from oil flow visualization and measurements of unsteady pressure fluctuationsalong the flat window. Results show that pins that penetrated though the boundary layerand were spaced less than four boundary layer thicknesses apart provided a reduction inthe rms pressure on the aperture, a slight delay in separation, and an elongation of therecirculation region.
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 Miguel Ra Palaviccini.
Thesis:
Thesis (Ph.D.)--University of Florida, 2013.
Local:
Adviser: Cattafesta, Louis Nicholas, Iii.

Record Information

Source Institution:
UFRGP
Rights Management:
Applicable rights reserved.
Classification:
lcc - LD1780 2013
System ID:
UFE0045001:00001


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CONTROLOFTHREE-DIMENSIONALFLOWOVERATURRET By MIGUELPALAVICCINI ADISSERTATIONPRESENTEDTOTHEGRADUATESCHOOL OFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENT OFTHEREQUIREMENTSFORTHEDEGREEOF DOCTOROFPHILOSOPHY UNIVERSITYOFFLORIDA 2013 1

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2013MiguelPalaviccini 2

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IdedicatethistoAnaandAlberto.Icouldn'thaveaskedforabetterpairofsiblingsto constantlyremindmetoenjoylifetothefullest. 3

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ACKNOWLEDGMENTS Theworkpresentedinthisdissertationwouldnothavebeenpossiblewithoutthe contributionsfrommycommitteemembers.First,IwouldliketothankDr.Louis CattafestaforhisguidanceandmentorshipduringmytimeatUF.Hisrelentlessand passionatenaturealwayspushedmetobecomeabetterexperimentalist,moldingmeinto theresearcherthatIamtoday.IwouldalsoliketothankDr.MarkSheplak,forfostering myinterestinaerodynamicsandpushingmetodigintothefundamentalsofevery problem.IowemyinteresttotheeldofcontrolstotheanimatednatureofDr.Warren Dixon'steachingstyle.IwouldalsoliketothankDr.DavidArnoldforhisparticipation andfeedback. IthankalloftheInterdisciplinaryMicrosystemsGroupfortheconstantinteraction andthoughtfuldiscussionstheyprovide.Thegrouptrulyisoneofakindwithits stimulatingandenjoyableworkenvironment.IwouldparticularlyliketothankMatias Oyarzun,BrandonBertolucci,andDrewWetzelwhomwereindispensablecolleaguesanda positiveinuenceinandoutofthelab.AspecialthanksAdamEdstrandandJohnGrin forshowingmethattruesuccessisthesumofsmalleortsdayinanddayout.Iowea particularthankstoNikolasZawodny-Iwillalwaysadmirethededicationthathepours intoeverythinghedoes.Additionally,IMGisfullofencouragingpeople,makingiteasyto cometothelabeveryday.ThesepeopleincludedAshleyJones,MattWilliams,FeiLiu, JasonJune,CaseyBarnard,TianyReagan,DylanAlexander,DavidMills,ChrisMeyer, andDavidMartin.Ihavealsoworkedwithmanysuperbundergraduatesatseveralstages inthisproject,allofwhomdeserverecognition:BenjaminGeorge,MikeAguilar,Ben Johnson,andKyleO'Connor. Finally,Iwanttoacknowledgemyfamilyfortheirinvaluableadviceand unconditionallove.Myparentssacricedatremendousamountintheirlivestoensure thatIhadeveryopportunitytosucceedinallofmyendeavors.ForthatIamtruly grateful.Iowemyattentiontodetail"mentalitytomydadwhotaughtmetoalways 4

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dothingstherightway.Mymomhasalwaysprovidedmewithapositiveoutlook,and islargelyresponsiblefortheoutgoingpersonthatIhavebecome.Mysiblings,twoof themostimportantpeopleinmylife,areandcontinuetobeoutstandingpersonalrole models.Myfour-leggedbestfriend,Ollie,hasgreatlycontributedtomyhappinessand well-being.Thebestoutcomefromthesepastveyearshasbeenndingmybestfriend andwife,Megan.Icouldn'thavedonethiswithoutherconstantmotivationandsupport. 5

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TABLEOFCONTENTS page ACKNOWLEDGMENTS.................................4 LISTOFTABLES.....................................10 LISTOFFIGURES....................................12 ABSTRACT........................................20 CHAPTER 1INTRODUCTION..................................22 1.1Motivation....................................23 1.2Background...................................25 1.2.1GenericTurretModels.........................26 1.2.2FluidDynamics.............................26 1.2.2.1Two-dimensionalFlowSeparation..............27 1.2.2.2Three-dimensionalFlowSeparation.............28 1.2.2.3GeneralFlowFeaturesAroundaTurret..........31 1.2.3Aero-optics................................32 1.2.3.1SourcesofOpticalDegradation...............32 1.2.3.2MeasureofOpticalAberrations...............34 1.2.3.3ToolsforMeasuringAero-opticDistortion.........36 1.2.3.4OPD rms Non-DimensionalAnalysis.............40 1.2.4FlowControl...............................45 1.2.4.1ApplicationstotheAero-opticProblem...........45 1.2.4.2TerminologyandClassications...............46 1.2.4.3FurtherDiscussiononFlowControlParameters......50 1.3Objectives....................................51 1.4Approach....................................52 1.5Outline......................................52 2LITERATUREREVIEW..............................63 2.1OriginsofFlowoveraTurret.........................63 2.1.1EarlyLiteratureonFlowsoverHemisphericalObjects........63 2.1.2FlowoverTurretProtuberance.....................66 2.2RecentAdvancesinFlowoveraHemisphericalTurret............68 2.2.1BaselineCharacterization........................68 2.2.2PassiveControl.............................71 2.2.3Open-LoopControl...........................75 2.2.4Closed-LoopControl..........................80 2.3UnresolvedTechnicalIssues..........................82 6

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3EXPERIMENTALSETUP.............................92 3.1TurretModel..................................92 3.2UniversityofFloridaLowSpeedWindTunnelFacility...........93 3.3WindTunnelCharacterization.........................94 3.3.1IncomingBoundaryLayer.......................94 3.3.2TunnelAcoustics............................96 3.4BaselineFlowMeasurements..........................97 3.4.1SteadyPressure.............................97 3.4.2UnsteadySurfacePressure.......................98 3.4.3OilFlowVisualization.........................99 3.4.4Hot-wireAnemometry.........................100 3.4.5ParticleImageVelocimetry.......................101 3.4.5.1TurretApexBoundaryLayer................102 3.4.5.2StereoscopicWakeMeasurements..............103 3.4.5.3sPIVUncertainty.......................104 3.5Aero-OpticMeasurements...........................104 3.5.1Aero-OpticImaging...........................104 3.5.2MalleyProbe..............................105 3.5.2.1TunnelVibrations......................106 3.5.2.2EquipmentandSetup....................107 3.5.2.3DataAcquisitionandProcessing..............107 3.5.2.4CoherentStructureConvectiveSpeed............108 3.6FlowControlImplementation.........................109 3.6.1PassiveFlowControl..........................109 3.6.1.1PinConguration.......................109 3.6.1.2AssessmentofControl....................110 3.6.2ActiveFlowControl...........................110 3.6.2.1TurretModel.........................111 3.6.2.2AirDeliverySystem.....................112 3.6.2.3JetVelocityMeasurement..................112 3.6.2.4AssessmentofControl....................113 4BASELINERESULTS................................130 4.1WindTunnelCharacterization.........................130 4.1.1IncomingBoundaryLayer.......................130 4.1.2AcousticNoiseFloor..........................131 4.2FlowMeasurements...............................132 4.2.1StaticPressureDistribution......................132 4.2.2UnsteadyPressure............................134 4.2.2.1SpatialAveragingEects..................134 4.2.2.2ParameterNon-dimensionalization.............135 4.2.2.3TripTapeLocation......................136 4.2.2.4FluctuatingPressureSpectraAcrossTurretWindow...137 4.2.2.5CoherentStructureConvectionSpeed............138 7

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4.2.3SurfaceOilFlowVisualization.....................139 4.2.4BoundaryLayeratTurretApex....................140 4.2.5NearWakeRegionCharacterization..................142 4.2.5.1AccuracyofsPIVMeasurements..............142 4.2.5.2MeanCharacteristics.....................144 4.2.5.3Second-orderMomentsandVorticity............144 4.2.5.4VelocitySpectra.......................146 4.2.5.5NearWakeRegionRemarks.................146 4.3Aero-OpticMeasurements...........................147 4.3.1Aero-OpticImaging...........................148 4.3.2MalleyProbeMeasurements......................148 4.3.2.1MeasurementLocations...................150 4.3.2.2AberratingStructureConvectiveSpeed...........150 4.3.2.3DeectionAngleSpectra...................151 4.3.2.4RelationshipBetweenDeectionSpectraandOPD rms ...152 4.3.2.5One-DimensionalApertureFilter..............153 4.3.2.6DeectionSpectraLow-frequencyFit............155 4.3.2.7Low-frequencyCut-o....................155 4.3.2.8OPD rms CalculationRemarks................156 4.3.3CorrelatingAero-opticsandUnsteadyPressure............157 4.3.3.1OrdinaryCoherenceFunction................159 4.3.3.2ConditionedAutospectra...................160 4.3.3.3PartialConditionedAutospectra..............160 4.4BaselineFlowConcludingRemarks......................162 5FLOWCONTROLRESULTS............................203 5.1Introduction...................................203 5.2PassiveFlowControl..............................204 5.2.1Aero-OpticMeasurements.......................205 5.2.2UnsteadyPressureMeasurements...................207 5.2.3OilFlowVisualization.........................209 5.2.4DirectShearLayerMeasurements...................211 5.2.4.1Hot-wireAnemometry....................212 5.2.4.2sPIV..............................214 5.3ActiveFlowControl..............................216 5.3.1Aero-OpticMeasurements.......................216 5.3.2FlowVisualization............................218 5.3.3DirectWakeMeasurements.......................219 5.4FlowControlConcludingRemarks......................221 6SUMMARYANDFUTUREWORK........................248 6.1ResearchSummary...............................248 6.1.1BaselineFlow..............................248 6.1.2FlowControl...............................251 8

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6.1.2.1PassiveFlowControl.....................251 6.1.2.2ActiveFlowControl.....................252 6.2ResearchImpact................................253 6.3RecommendationsforFutureWork......................255 APPENDIX ATURRETMODELTECHNICALDRAWINGS..................258 A.1TunnelModications..............................258 A.2BaselineModel.................................258 A.3PassiveControlModel.............................259 A.4SteadyBlowingModel.............................259 BSPIVUNCERTAINTY................................271 B.1SampleCountandConvergence........................271 B.2RandomUncertainty..............................271 B.3BiasUncertainty................................271 B.3.1SatisfyingSub-pixelAccuracy.....................272 B.3.2Root-Sum-SquareAnalysis.......................273 CCONDITIONALSPECTRALANALYSIS.....................279 C.1Multiple-input,Single-outputNoise-freeModel................279 C.2Auto-spectralandCross-spectralAnalysis..................280 C.3NoiseConsiderations..............................281 C.4ConditionalSpectralAnalysis.........................282 C.5RemovingTunnelVibrationEects......................285 C.5.1AccelerometerCalibration.......................285 C.5.2EectonAero-opticSignal.......................285 C.5.3OrdinaryCoherenceFunction.....................287 C.5.4PartialCoherenceFunction.......................288 DEXTENDEDPASSIVECONTROLRESULTS..................296 REFERENCES.......................................333 BIOGRAPHICALSKETCH................................343 9

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LISTOFTABLES Table page 1-1PrimarydimensionsofOPD rms dimensionalparameters..............62 2-1BoundarylayerdetailsusedinstudybyToy etal. 1983.............88 2-2Summaryofearlystudiesonowsoverhemisphericalobjects...........88 2-3Summaryofinitialowoveraturretprotuberancestudies............88 2-4Flowcontrolscreeningmethodologies........................89 2-5Summaryofrecentbaselineowcharacterization.................89 2-6Summaryofrecentpassivecontrolstudies.....................89 2-7SummaryofReynolds etal. 2012passivecontrolmodels............90 2-8Summaryofrecentopen-loopcontrolstudies....................91 2-9Summaryofrecentclosed-loopcontrolstudies...................91 3-1Randomuncertainty95%condenceintervalestimatesofcomputedvelocity andReynoldsstressterms..............................128 3-2Shearlayermeasurementlocations.........................128 3-3MalleyProbepositionsensingdeviceparameters..................128 3-4Passiveowcontrolcongurations.........................129 3-5Massowcontrollerdevicespecications......................129 3-6ActiveControlSteadyBlowingCases........................129 4-1Incomingboundarylayerparametersforfreestreamvaluesof40and90m/s..202 4-2Thirdoctavebandfrequencylimitsusedtocreateunsteadypressurecontour plots..........................................202 4-3AccelerometersensitivityvaluesmV/G......................202 4-4OPDrms mand SRfortwodistinctcalculationmethods............202 5-1OPD rms forallpassivecontrolcases.......................243 5-2P rms forallpassivecontrolcases.........................243 5-3Oilowvisualizationresultsforpassivecontrolcases...............244 5-4Shearlayermeasurementresultsforpassivecontrolcases.............244 10

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5-5Summaryofpassiveowcontrolresultsfortallpincongurations h> ....245 5-6Summaryofpassiveowcontrolresultsforshortpincongurations h< ...246 5-7OPD rms forallactivecontrolcases........................247 5-8OPD rms forallactivecontrolcases........................247 5-9 k=U 2 1 forallactivecontrolcases..........................247 B-1Randomuncertainty95%condenceintervalestimatesofcomputedvelocity andReynoldsstressterms..............................276 B-2Relevantparametersusedtoestimatetheprojectednominalparticlediameter forthebaselineandpassivecontrolcases......................277 B-3Relevantparametersusedtoestimatetheprojectednominalparticlediameter fortheactivecontrolcases..............................277 B-4Relevantparametersusedtodeterminethebiasuncertaintyforthebaseline andpassivecases...................................277 B-5Relevantparametersusedtodeterminethebiasuncertaintyfortheactive controlcases......................................277 B-6Biasuncertaintiesinm/sateachmeasuredsPIVplaneforthebaselineand passivecases......................................278 B-7Biasuncertaintiesinm/sateachmeasuredsPIVplanefortheactivecontrol cases..........................................278 11

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LISTOFFIGURES Figure page 1-1Sourcesofopticaldegradation............................53 1-2Eectofnear-eldowfeaturesonlaserintensity.................54 1-3Genericturretmodels................................54 1-4Turretmodelgeometricparameters.........................55 1-5Separationovera2-Dcurvedsurface........................55 1-6Three-dimensionalboundarylayerinacrossow..................56 1-7Limitingstreamlinesalongayawedairfoil.....................56 1-8Limitingstreamlinesnearthree-dimensionalseparationline............57 1-9Complexowoveraturret..............................57 1-10Sourcesofaero-opticaldegradationatlowsubsonicows.............58 1-11Interactionofwavefrontwithpotentialoweldaroundaturret.........58 1-12Planarwavefrontandprobebeamdistortionmechanismthroughavariant indexofrefractionow................................59 1-13Malleyprobeschematic...............................59 1-14Surfacemountedconformal-windowturretscaling.................60 1-15Conformal-windowedturretmountedonacylindricalbasescaling........60 1-16Two-dimensional,surfacemountedat-windowedturretscaling.........61 1-17Categorizationofapproachestoowcontrol....................61 1-18Vortexgenerators...................................62 2-1ModelsusedbyTaylor1992............................84 2-2ModelusedbySchonberger etal. 1982......................84 2-3PassivecontroldevicesusedbyGordeyev etal. 2005..............85 2-4PassivesplitterplateusedbyVukasinovic&Glezer2007............85 2-5ModelusedbyVukasinovic&Glezer2007....................86 2-6PassivecontroldeviceusedbyWoszidlo etal. 2009...............86 2-7TurretmodelwithsyntheticjetactuatorsusedbyVukasinovic etal. 2009 b ..87 12

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2-8TurretmodelwithhybridcontrolusedbyVukasinovic etal. 2010 b .......87 2-9TurretmodelwithhybridcontrolusedbyWallace etal. 2008..........87 3-1Modeldimensionsandrelevantparameters.....................114 3-2Turretmodelimagesfromseveralperspectives...................114 3-3Boundarylayertriptape...............................115 3-4Boundarylayerhot-wiresetup............................115 3-5Noseconemountedonmicrophonefortunnelacousticmeasurements......116 3-6Staticpressureportlocations............................116 3-7Unsteadypressuresensorlocationsonatwindow.................117 3-8Turretaperturewithunsteadypressuresensors..................117 3-9Oilowdropletlocations...............................118 3-10Oilowvisualizationset-up.............................118 3-11Shearlayermeasurementlocations.........................119 3-12Particleimagevelocimetryschematic........................120 3-13Particleimagevelocimetrysetup..........................120 3-14SPIVSetup......................................121 3-15Aero-opticimagingset-up..............................121 3-16USAFResolutionTestChart............................122 3-17MalleyProbewindtunnelset-up..........................123 3-18Malleyprobebeamlocations.............................124 3-19Malleyprobesensor,hood,andlter........................124 3-20Beamdisplacementcoordinatesystem.......................125 3-21Passiveowcontrolsetup..............................125 3-22Passivecontrolcongurations............................126 3-23Steadyblowingslotdimensions...........................127 3-24Steadyblowingmodel................................127 4-1Incomingboundarylayerforfreestreamvelocityof40m/s............164 13

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4-2Incomingboundarylayerforfreestreamvelocityof40m/s............165 4-3Dimensionlessboundarylayervelocityproles...................166 4-4Windtunnelacousticnoiseoor...........................167 4-5Windtunnelacousticsnormalized.........................168 4-6Acousticcontaminationwithandwithoutmodelinstalledintestsection....168 4-7Eectofacousticcontaminationonunsteadypressurereadings..........169 4-8Staticpressuredistribution.............................169 4-9Unsteadypressuremeasurementlocations.....................170 4-10Unsteadypressurespatialaveragingeects.....................170 4-11Unsteadypressurespectranon-dimensionalization.................171 4-12EectoftriptapelocationforRe=3.40 10 5 ...................172 4-13EectoftriptapelocationforRe=5.10 10 5 ...................173 4-14Eectoftriptapelocationfor0 o windoworientation,loc.1...........173 4-15Pressurespectraasafunctionoflocation......................174 4-16UnsteadypressurespectraalongatwindowforRe H =5.10 10 5 ........175 4-17Unsteadypressurecontoursonturretwindowatlowfrequencies.........176 4-18Unsteadypressurecontoursonturretwindowatmidfrequencies.........177 4-19Unsteadypressurecontoursonturretwindowathighfrequencies........178 4-20Coherentstructureconvectionspeed........................179 4-21OilowdevelopmentoverthesurfaceoftheturretforRe H =5 : 10 10 5 ....180 4-22OilowvisualizationresultsforRe H =2 : 27 10 5 .................181 4-23OilowvisualizationresultsforRe H =5 : 10 10 5 .................182 4-24Boundarylayeratapexofturret..........................183 4-25sPIVmeasurementplanes..............................183 4-26Meanspeedandstreamlinesinthenearwakeregion...............184 4-27NormalReynoldsstresscomponentsextractedfromsPIV.............185 4-28NormalReynoldsstresscomponentsextractedfromsPIV.............186 14

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4-29TurbulentkineticenergyandlateralvorticityextractedfromsPIV........187 4-30Hot-wireanemometryresultsinthenearwakeregion x=H< 1 : 5........188 4-31Hot-wireanemometryresultsinthefarwake x=H> 1 : 5............189 4-32Aero-opticimagingresults..............................190 4-33ModiedMalleyprobewindtunnelset-up.....................191 4-34ResultingoutputautospectraafterCSAisapplied.................192 4-35Phaseplotusedtodeterminetheeectoftip/tilt.................192 4-36CoherenceandphaseofMalleyprobebeams....................193 4-37Beamdeectionspectra...............................194 4-38ContourplotofmeanvelocitywithMalleyprobebeamlocations.........195 4-39ContourplotofturbulentkineticenergywithMalleyprobebeamlocations...196 4-40Aperturelterusedtoremovetip/tilteects....................197 4-41Rawandltereddeectionspectra.........................197 4-42Malleyprobebeamlocations.............................198 4-43Vibrationalanalysisparticlecoherence.......................198 4-44Ordinarycoherencefunctionforpressureandaero-optics.............199 4-45ConditionedordinarycoherencefunctionforP1B1.................199 4-46ConditionedautospectraforP1B1..........................200 4-47SystemmodelstodescribeoutputfromPSD....................200 4-48Outputautospectrafromsystemmodels......................201 5-1Flowtopologyoveraverticallymountedpin....................223 5-2OPD rms %asafunctionofpinorientationforpassiveowcontrol......223 5-3DeectionspectraforpassivecasesP3,P7,andP9................223 5-4 P rms %trendsasafunctionofpinorientationforpassiveowcontrol....224 5-5OPD rms vs P rms %trendsforpassiveowcontrol..............224 5-6UnsteadypressurespectraforpassiveowcontrolcaseP3............225 5-7 x R =H %trendsasafunctionofpinorientationforpassiveowcontrol...225 15

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5-8Oilowvisualizationforbaseline,P8,andP9atMa=0.26............226 5-9Oilowvisualizationforbaseline,P3,andP7atMa=0.26............227 5-10Separationlineandrearstagnationpointforbaseline,P3,andP7atMa=0.26.227 5-11OPD rms asafunctionof x R =H forpassiveowcontrol............228 5-12 I 2 %trendsasafunctionofpinorientationforpassiveowcontrol......228 5-13OPD rms asafunctionof k=U 2 1 forpassiveowcontrol............229 5-14ShearlayerspectraforbaselineandpassivecontrolcasesP8andP9.......230 5-15ShearlayerspectraforbaselineandpassivecontrolcasesP3andP7.......231 5-16ContourplotofturbulentkineticenergyforpassivecontrolwithMalleyprobe beamlocationsat z=H =0..............................232 5-17OPD rms asafunctionofsPIV k=U 2 1 forpassiveowcontrol.........233 5-18ContourplotofturbulentkineticenergyforpassivecontrolwithMalleyprobe beamlocationsat z=H = )]TJ/F15 11.9552 Tf 9.298 0 Td [(0 : 31...........................234 5-19ContourplotofturbulentkineticenergyforpassivecontrolwithMalleyprobe beamlocationsat z=H = )]TJ/F15 11.9552 Tf 9.298 0 Td [(0 : 62...........................235 5-20Contourplotofstreamwisevorticityforbaseline,P3,andP7congurations...236 5-21OPD rms and asafunctionof C foractiveowcontrol...........237 5-22Deectionangletimesconvectivespeedspectraorbaseline )]TJ/F15 11.9552 Tf 9.299 0 Td [(andselected activecontrolcases..................................237 5-23Instantaneousowvisualizationimagesforallactivecontrolcases........238 5-24Oilowvisualizationforselectactivecontrolcases................239 5-25Contourplotofmeanvelocityforselectactivecontrolcases...........240 5-26ContourplotofturbulentkineticenergyforactivecontrolwithMalleyprobe beamlocationsat z=H =0 : 0.............................241 5-27ContourplotofturbulentkineticenergyforactivecontrolwithMalleyprobe beamlocationsat z=H = )]TJ/F15 11.9552 Tf 9.298 0 Td [(0 : 31and )]TJ/F15 11.9552 Tf 9.298 0 Td [(0 : 62.....................242 A-1Tunneloorforturretmodels............................260 A-2Baselineturretmodel.................................261 A-3Turretwindowforsteadyandunsteadypressuremeasurements.........262 16

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A-4Opticallyclearturretwindow............................263 A-5Safetybarusedtosecurewindowtoturretmodel.................264 A-6Passiveowcontrolinsertforthinpins.......................265 A-7Passiveowcontrolinsertforthickpins......................266 A-8Turretwindowforunsteadypressuremeasurements................267 A-9Steadyblowingturretmodel.............................268 A-10Steadyblowingturretmodel,alternateview1...................269 A-11Steadyblowingturretmodel,alternateview2...................270 B-1PIVcontourTKEandconvergenceplots......................275 B-2IllustrationofageneralsPIVcamerasetup.....................276 C-1LinearSISOandMISOmodels...........................289 C-2MISOmodelincludinganoisecomponent......................289 C-3ConditionedMISOmodel...............................290 C-4LinearSISOandMISOmodels...........................290 C-5Accelerometercalibration..............................291 C-6Autospectraoftunnelvibrations..........................292 C-7Autospectraoftunnelvibrations..........................292 C-8Two-input,single-outputsystemrepresentingtheopticalmeasurements.....293 C-9Vibrationalanalysisautospectra...........................293 C-10Vibrationalanalysiscross-spectra..........................293 C-11Vibrationalanalysisordinarycoherencefunction..................294 C-12Vibrationalanalysisconditionedautospectra....................294 C-13Resultingoutputautospectra............................295 D-1Illustrationofallpassivecontrolcongurations..................296 D-2SeparationlineandextentofrecirculationforpassivecontrolcaseP1......297 D-3UnsteadypressurespectraforpassivecontrolcaseP1...............297 D-4ShearlayerspectraforpassivecontrolcaseP1...................298 17

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D-5MalleyproberesultsforpassivecontrolcaseP1..................299 D-6SeparationlineandextentofrecirculationforpassivecontrolcaseP2......300 D-7UnsteadypressurespectraforpassivecontrolcaseP2...............300 D-8ShearlayerspectraforpassivecontrolcaseP2...................301 D-9MalleyproberesultsforpassivecontrolcaseP2..................302 D-10SeparationlineandextentofrecirculationforpassivecontrolcaseP3......303 D-11UnsteadypressurespectraforpassivecontrolcaseP3...............303 D-12ShearlayerspectraforpassivecontrolcaseP3...................304 D-13MalleyproberesultsforpassivecontrolcaseP3..................305 D-14SeparationlineandextentofrecirculationforpassivecontrolcaseP4......306 D-15UnsteadypressurespectraforpassivecontrolcaseP4...............306 D-16ShearlayerspectraforpassivecontrolcaseP4...................307 D-17MalleyproberesultsforpassivecontrolcaseP4..................308 D-18SeparationlineandextentofrecirculationforpassivecontrolcaseP5......309 D-19UnsteadypressurespectraforpassivecontrolcaseP5...............309 D-20ShearlayerspectraforpassivecontrolcaseP5...................310 D-21MalleyproberesultsforpassivecontrolcaseP5..................311 D-22SeparationlineandextentofrecirculationforpassivecontrolcaseP6......312 D-23UnsteadypressurespectraforpassivecontrolcaseP6...............312 D-24ShearlayerspectraforpassivecontrolcaseP6...................313 D-25MalleyproberesultsforpassivecontrolcaseP6..................314 D-26SeparationlineandextentofrecirculationforpassivecontrolcaseP7......315 D-27UnsteadypressurespectraforpassivecontrolcaseP7...............315 D-28ShearlayerspectraforpassivecontrolcaseP7...................316 D-29MalleyproberesultsforpassivecontrolcaseP7..................317 D-30SeparationlineandextentofrecirculationforpassivecontrolcaseP8......318 D-31UnsteadypressurespectraforpassivecontrolcaseP8...............318 18

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D-32ShearlayerspectraforpassivecontrolcaseP8...................319 D-33MalleyproberesultsforpassivecontrolcaseP8..................320 D-34SeparationlineandextentofrecirculationforpassivecontrolcaseP9......321 D-35UnsteadypressurespectraforpassivecontrolcaseP9...............321 D-36ShearlayerspectraforpassivecontrolcaseP9...................322 D-37MalleyproberesultsforpassivecontrolcaseP9..................323 D-38SeparationlineandextentofrecirculationforpassivecontrolcaseP10.....324 D-39UnsteadypressurespectraforpassivecontrolcaseP10..............324 D-40ShearlayerspectraforpassivecontrolcaseP10..................325 D-41MalleyproberesultsforpassivecontrolcaseP10..................326 D-42SeparationlineandextentofrecirculationforpassivecontrolcaseP11.....327 D-43UnsteadypressurespectraforpassivecontrolcaseP11..............327 D-44ShearlayerspectraforpassivecontrolcaseP11..................328 D-45MalleyproberesultsforpassivecontrolcaseP11..................329 D-46SeparationlineandextentofrecirculationforpassivecontrolcaseP12.....330 D-47UnsteadypressurespectraforpassivecontrolcaseP12..............330 D-48ShearlayerspectraforpassivecontrolcaseP12..................331 D-49MalleyproberesultsforpassivecontrolcaseP12..................332 19

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AbstractofDissertationPresentedtotheGraduateSchool oftheUniversityofFloridainPartialFulllmentofthe RequirementsfortheDegreeofDoctorofPhilosophy CONTROLOFTHREE-DIMENSIONALFLOWOVERATURRET By MiguelPalaviccini August2013 Chair:LouisN.CattafestaIII Major:AerospaceEngineering Airborneopticalsystemsaresusceptibletolargelossesineciencyastheoptical beamstravelsthroughhighlyturbulentcompressibleows.Itiswellknownthat compressibleturbulentowcausedbyowseparationoverathree-dimensionalturret hasanadverseeectonaero-opticapplications.Therefore,understandingthevarious three-dimensionalowfeaturesandtheireectsontheaero-opticenvironmentisakey challengethatneedstobeaddressed. Astudyofthebaselineowphysicsaroundasubmergedhemisphericalturretwith aatapertureatMa < 0.26ischaracterized,identifyingpotentialsourcesofaero-optic distortion.Spectralanalysisofunsteadypressurerevealsthattherecirculationregion andseparatedshearlayeraretwodominantregionscontributingtotheunsteadiness oftheow.Oilow-visualizationillustratethethreedimensionalseparationlineand lengthofrecirculationregion,bothinvestigatedaspossiblemetricsforowcontrol applications.StereoscopicPIVandhot-wireanemometryareusedtocharacterizethe separatedshearlayerwithbothspatialevolutionandtemporalspectracalculations ofthevelocityeld.Malleyprobemeasurementsaremadealongtheatwindow, providingone-dimensionalslicesofopticalwavefrontsinthedirectionofthebeam propagationvector.OPD rms iscalculatedviaspectralmethods,andwhennormalizedby thesuggestedscalingintheliterature,theowisfoundtobetwiceasopticallyactive asthatsurroundingasurface-mountedconformal-windowturret.Conditionalspectral 20

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analysisoftheaero-opticandunsteadypressuremeasurementsrevealthatalargeportion oftheaero-opticdistortionisaccountedforbyunsteadypressureuctuations. Onceaclearunderstandingofthebaselineowisestablished,themaingoalshifts towardtheevaluationandimplementationofowcontrolstrategies.Leveragingresearch intheowcontrolcommunity,bothpassiveandactivecontrolareimplementedto suppressunfavorableowdisturbancesand,inturn,mitigateaero-opticdistortion.First, passivecontroleortsareperformedbyusingcylindricalpinstogeneratestreamwise vorticesthatpromotecrossstreammixingbetweenthehighmomentumfreestreamand thelowermomentumboundarylayer.Flowvisualizationdeterminedthatseparation delayshouldnotbeusedasametricwhenassessingaero-opticdistortions.Instead,the lengthoftherecirculationregionshowsadirectcorrelationwiththemeasuredaero-optics. TheresultsfromallcongurationsshowthatthecauseoftheincreaseinOPD rms istiedtoboththethickeningoftheshearlayerandincreaseinmaximumturbulent uctuations.Activeowcontrolisachievedviasteadyblowingalongthetopportionof theataperture.Forincreasing C valuesupto0.21,thespectraforthebeamdeection angleincreasemonotonically.Furtherblowingresultsinadecreaseinthecalculated changeinmeasuredbeamdeectionangle,withtheminimumoccurringfor C 0 : 38. CalculatingOPD rms showsthattheminimumoccursfor C =0 : 26,suggestingthatthere isanoptimumamountofsteadyblowing,withanyexcessresultinginadegradationof theopticalenvironment.BothowvisualizationandmeanvelocityprolesfromsPIV demonstratethatfullreattachmentalongthewindowneednotbenecessarytoachievea reductioninOPD rms 21

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CHAPTER1 INTRODUCTION Airborneopticalsystemshaverecentlyattractedmuchattentionbecauseoftheir nearzeropropagationtimeandselectiveenergydeposition.Thegoaloftheseairborne systemsistoproduceanaircraftmountedlasercapableofengagingspeciedtargets.The mostcommonofthesesystemsconsistofaphotonsource,abeamtransportsystemasa meansoftransferringenergyfromthelasertoatelescope,andatrackingsystemusedto focusonanintendedtarget.Ingeneral,alaserbeammustbecreatedinsideanaircraft, thenpropagatedecientlytotheoptics,andnallydirectedtoaspeciedtargetwhile travelingthroughagenerallycompressibleturbulentoweld. Whenalaser-opticalsystemismountedwithinaprotuberanceonamovingaircraft, theresultingapparatusistermedanaero-opticalaircraftturret.Theimmediateow eldsurroundingaturretischaracterizedbyattachedowontheupstreamportionof theturretandthenseparatedandfullyturbulentowontheaftportion.Theseparation locationishighlydependentontheowparametersCherry etal. 2008andresults inaoweldthatishighlythreedimensional.Atthehighspeedstypicalofaircraft applications,theresultingwakestructurescauseasignicantlevelofaberrationonthe opticalsystem,thuseectivelyeliminatingalargeportionoftheturret'srearquadrantas ausefuleldofvision. Itiswellknownthatairborneopticalsystemsareaectedbyunsteadydensity uctuationscausedbyowseparation.Asalasertravelsthroughahighlyvariantindexof refractionoweld,itissubjecttorefractionbydensitygradients,inturncausingoptical pathdierences.Thisresultsinthescatteringoflightandreductionoflaserintensityon theintendedtarget,whichisdetrimentaltotheperformanceofairborneopticalsystems. Researchhasshownthatalaser'sintensitycouldbereducedtounder10%ofitsotherwise idealperformanceforanopticalturretatightMachnumbersofaslowas0.7Cicchiello &Jumper1997. 22

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Inordertomitigateunwantedowfeaturesandassesstheimpactonaero-optic distortion,eectiveowcontroltechniquesarerequired.Recentowcontrol implementationshaveshownpromiseformeetingperformancerequirementsby suppressingundesirableowfeaturesinvarioustwo-dimensionalows.However,owover aturretpresentschallengestoowcontrolbeyondthoseassociatedwithtwo-dimensional aerodynamicsurfaces.Understandingthevariousthree-dimensionalowfeaturesand theireectsonopticaldistortionisachallengingtask.Nevertheless,applyingcurrent owcontroltechniquesonaero-opticsystemstoimprovethenear-eldaero-opticscan haveavarietyofpotentialapplications.Theseinclude,butarenotlimitedto,missiles withopticalseekers,airbornetelescopes,free-spacecommunicationsystems,andlaser weaponsystemsGilbert&Otten1982.Additionalmotivationforthisresearchdirection isdiscussedinthefollowingsection. 1.1Motivation Therstknownquantitativeobservationofaero-opticdegradationwasmadeinthe mid1960'sGilbert&Otten1982.Itdealtwithablurringeectofcelestialimages takenfromastar-imaginginterferometermountedonboardanAirForceKC-135aircraft. Sincethen,researchershavefocusedonbothstudyingthemechanismsresponsibleforthe distortionsaswellasrecenteortstoleverageowcontroltechniquesinanattemptto reducethem. AgeneralschematicofpossibleaeroopticdegradationsourcesisdepictedinFigure 1-1.Theschematicshowseachcomponentofanairborneopticalsystemalongwith someoftheassociatedopticaldegradationsourcesusedindeterminingtheeciencyof thesystem.Thesecomponentsincludethedevicethatpowersthelaser,abeamcontrol system,aero-opticalinteractions,andatmosphericpropagationeects.Theaero-optic problemisspecicallyinvolvedwiththeinteractionoftheairbornelaserbeamwiththe near-eldsurroundingatmosphere.Near-eldowfeaturesthatcausetheseundesirable eectsincludeturbulentboundarylayers,shearlayers,separatedows,shocks,andow 23

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accelerationsproducedbystreamwisepressuregradientsGilbert&Otten1982.Figure 1-2depictstheinteractionofalaserbeamwiththesurroundingoweld.Asshown, anyindexofrefractionuctuationcanleaddirectlytoascatteringoflaserbeamenergy, causingadecreaseinfar-eldintensity. ResultsfromCress etal. 2008;Gordeyev etal. 2004 b ;Vukasinovic etal. 2009 b revealthataero-opticdistortionsgrowapproximatelyas s Ma 2 .Severalstudieshave shownastrongcorrelationbetweenowfeaturesandaero-opticdistortions.Gordeyev etal. 2004 b haveusedahot-wireanemometertomeasurevelocityuctuationsatseveral locationsneartheopticalatofaturretmodel.Correlatingthisdatawithaero-optical measurements,theyfoundthatopticaldistortionsoveraatwindowweregreatly governedbytheseparatedshearlayerinanadversepressuregradient.Wallace etal. 2008focusedonreducingopticaldistortionbyhomogenizingthewakeoftheturretover theapertureareausingactivecontroltechniques.OtherresearchersAndino&Glezer 2010;Wallace etal. 2009,2010havealsoattemptedtoimprovetheopticalqualityofow byusingunsteadypressuremeasurementsasametric.Theystatethatevenwhendirect measurementsofaero-opticsarenotavailable,turbulenceintensitymeasurementsprovide astrongindicatoroftheopticalqualityoftheow.Specically,Vukasinovic etal. 2010 a notedtheparticularlydestructivenatureoftheshearlayeronotherwiseaberration-free owsduetothepresenceofthevorticalstructuresthatinducestrongpressuregradients. Earlystudiesfocusedoncorrectingtheaero-opticproblemsgeneratedbyatmospheric propagationeects.Inthesimplestterms,amethodtermedadaptiveopticswasusedin whichthesystemsensestheaberrationandcorrectsadeformablemirrortooptimizethe focusandfar-eldintensitywithoutalteringtheowitselfNightingale etal. 2006.While adaptive-optictechniqueshaveadequatebandwidthtocorrectfortheslowtime-varying atmosphericpropagationproblem,thespatialandtemporalfrequenciesassociatedwith theneareldaero-opticproblemareatleastandorderofmagnitudegreaterJumper& Fitzgerald2001. 24

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Itwasnotuntilthispastdecadethatresearchersbegantoexploreowcontrol techniquestosuppressundesiredowstructuresinhopesofimprovingthenear-eldoptic owregion.Severalresearchgroupshavetackledtheproblembyusingeitherpassiveor open-loopcontrolandallhaveuseddierentmetricstoevaluatetheeectivenessofthe control.InitialresultsbyVukasinovic etal. 2005showedthatatRe D =6 : 06 10 5 Ma=0.09,anopen-loopcontrolschemeresultedinowattachedtothesurfacefor approximatelytwentydegreesfurtherdownstreamcomparedtoseparationintheabsence ofcontrol.In2010,Andino&Glezerreportedtheuseofhighfrequencyactuationon aturretatRe D =3 : 0 10 5 Ma=0.10toreduceturbulencelevelsbyaround25%in thewakeoftheturret.Whileresearchershaveshownsimilarresultsatlowowspeeds Ma < 0 : 3,thecombinationofactuatorlimitationsandowcontroltechniqueshave resultedindiminishedsuccessathigherspeedows. In1982Gilbert&Ottenstated, ...theimportanceofrstunderstandingthe separatedoweectsforrear-lookinglasermissionscannotbeoverstressed ."Therefore, inordertomaximizetheeectivenessofairbornelaser-basedweapons,animproved understandingoflow-speedturretowphysicsisnecessary.Asthelaserturretsystems continuetoevolve,itisimportanttoalsoinvestigateadvancedowcontroltechniquesfor complexthreedimensionalowsoveraircraftturretcongurations.Thisdissertationwill focusonidentifyingpotentialsourcesofaero-opticdistortion,andinaneorttoreduce theadverseeects,theuseofbothpassiveandactiveowcontrolwillbeexploredand implemented.Theapproachestakenwillleverageresearchintheowcontrolcommunity, resultinginowdisturbancesuppressionandaconcomitantdecreaseinaero-optic distortion. 1.2Background Thissectionisbrokenupintofourparts.Therstintroducesthegenericturret modelsthathavebeenstudiedinearlierliterature.Then,somephysicalunderstandingof theowaroundbothtwo-andthree-dimensionalblubodiesispresented.Aquickreview 25

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ofaero-opticalsourcesandterminologyisthenaddressed.Thelastsectionintroducesow controlnomenclatureandbrieydiscussesbothpassiveandactivemethods. 1.2.1GenericTurretModels Theparametersthatmakeupagenericturretmodelarerstdiscussedbefore anyuiddynamicsoraero-opticphenomenaisintroduced.Figure1-3showsthefour congurationsthatarecommonlyusedinresearchapplications.Mostmodelsaredened byahemisphericalcapwithdiameter D andagenerallyaft-facingaperturewindowwith diameter d .Theaperturewindowcanbeeitherconformaltothehemisphericalbody orcanbeaatcutthroughthebody.Themodelitselfistheneitherxedontopa cylindricalbaseofheight H orissurfacemounted.Theresearchpresentedhereindeals withtheowaroundasurfacemountedturretwithaatapertureFigure1-3D. Anillustrationofallrelevantparametersofahemispheremountedonacylindrical basewithaatapertureisshowninFigure1-4.Thedirectionoftheaftfacingwindow, whetherconformalorat,ischaracterizedbyazimuthalandwindowangles, and respectively.Notethatanothercommonlyusedparameteristheelevationangle,whichis denedasthecomplimenttothewindowangle, =180 o )]TJ/F22 11.9552 Tf 12.287 0 Td [( .Thecoordinatesystemis orientedsuchthat x isalongthedirectionoftheow, y ispassingthroughtheapexofthe hemisphere,and z isperpendiculartothe x )]TJ/F22 11.9552 Tf 12.271 0 Td [(y plane.Thewindowangle isdenedas theanglefromthe x )]TJ/F15 11.9552 Tf 9.298 0 Td [(axistotheoutwardbeamdirectionvectoronthe x )]TJ/F22 11.9552 Tf 12.221 0 Td [(y plane.The azimuthangleistheangleinthe x )]TJ/F22 11.9552 Tf 12.069 0 Td [(z planebetweentheprojectedbeamdirectionvector andthereferencefreestreamvelocityvector. 1.2.2FluidDynamics Thissectionisdesignedtointroducesomeofthebasicowfeaturesoveraturret-like object.Itbeginswithasimpledescriptionoftwo-dimensionalowseparationandthen extendstosomeoftheimportantthree-dimensionalowfeatures. 26

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1.2.2.1Two-dimensionalFlowSeparation Afundamentalunderstandingoftwo-dimensionalowisneededbeforedivinginto thecomplexityofowaroundablunt,three-dimensionalmodel.Thissectionusesboth physicalunderstandingandmathematicstodescribethefundamentalsoftwo-dimensional owseparation. Figure1-5illustratestheseparationphenomenaoveratwo-dimensionalconvexcurved surfaceowisfromlefttoright.Upstreamoftheapex,afavorablepressuregradient @P=@s< 0acceleratestheow.Justdownstreamoftheapex,theuidparticlesnearthe wallaredeceleratedwhileencounteringbothanadversepressuregradient, @P=@s> 0, andwallskinfriction.Duetothenoslipconditionatthewall, v s n =0 =0,theownearest thesurfacetravelsslowestandthereforehasthelowestkineticenergy.Ifthemagnitudeof @P=@s> 0islargeenough,thenitekineticenergyofthetheuidparticlesisnotenough toovercometheresistiveforces,causingdecelerationandnallyseparation.Thisgives risetoapointwherethevelocitygradientbecomesidenticallyzero.Thispoint,termeda strongsingularitybyTobak&Peake1982,istheseparationpoint. Fromthediscussionabove,anadversepressuregradientisanecessary,butnot sucient,conditionforowseparationoveratwodimensionalcurvedsurface.Forsome mathematicalinsight,thenon-dimensionalizedstreamwise-directionmomentumboundary layerequationispresentedinEq.1{1.Thisequationisderivedundertheassumptionsof incompressible,steadylaminarowoverahighradiusofcurvaturesurface. v s @v s @s + v n @v s @n = )]TJ/F22 11.9552 Tf 10.494 8.088 Td [(@p @s + @ 2 v s @n 2 {1 FromFigure1-5,theboundarylayervelocityprolemusthaveapointofinection, @ 2 v s @n 2 =0,fortheowtofullyseparatefromthesurface.Applyingboundaryconditionsat thewall v n;n =0 =0, v s;n =0 =0,Eq1{1reducesto @p @s = @ 2 v s @n 2 n =0 : {2 27

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Interestingly,thecurvatureofthevelocityproleatthewallisstrictlyafunctionof thepressuregradient.Foranadversepressuregradient,thecurvatureatthewallwill bepositiveandthereforetherateofchangeofstreamwisevelocitywithrespecttothe wallnormal, @v s @n ,isincreasingoralternatively @ 2 v s @n 2 > 0.Thisindicatesthat @v s @n max is abovethewallandhencesoisthelocationoftheinectionpoint.Asthedownstream distanceincreases,theinectionpointmovesfurtherawayfromthewalluntileventually thevelocitygradient,andhencetheshearstress,attheboundaryiszero, @v s @n n =0 =0,and theowseparates. Inconclusion,two-dimensionalseparationcanbeassociatedwithcommon characteristicsintheowincludingtheonsetofowreversal,thevanishingofwall shearstress,andthesingularityoftheboundarylayersolution.Someofthem, eitherindividuallyorinconjunctionwitheachother,havebeenusedascriteriafor two-dimensionalseparation.However,three-dimensionalowsaremorecomplex,and thesecharacteristicsneednotdenetheonsetofowseparationDelery2001.Thenext sectiondealswiththesimilaritiesanddierencesbetweentwo-andthree-dimensionalow separation. 1.2.2.2Three-dimensionalFlowSeparation Forthree-dimensionalows,thethirddimensionnecessitatesamorecomplexanalysis ofseparation.Recallthatfortwodimensionalows,thevanishingofshearstresswas concomitantwithowseparation,andishencetermedastrongsingularity.However, inthree-dimensionalows,aweaksingularityoccurswhentheshearstress,avector quantityinthree-dimensionalow,vanishesinonlyaparticulardirection.Therefore,the conventionalconceptofowseparationdiscussedintheprevioussectioncannolongerbe appliedforthree-dimensionalows.Instead,aglobalviewoftheowpatternsandthe networkofsurfacestreamlinesmustbeobserved,seeFigure1-6. 28

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Consideraninitiallytwo-dimensionalboundarylayeratpoint A withapressure gradientthatactsonlyinthedirectionoftheowsothat P x;y;z A = P x : {3 Thevelocitydistributionoftheboundarylayeratpoint A x A ;y A ;z A hasnocrossow component, w x A ;y A ;z A =0,andcanthereforebewrittenas V x A ;y A ;z A =[ u x A ;y A ;z A ;v x A ;y A ;z A ; 0] : {4 Now,atpoint B ,introducethepresenceofapressuregradientwithanaddedtransverse directionsuchthat P x;y;z B = P x;z : {5 Thenewvelocitydistributionnowencompassesatransversedirectionandbecomes V x B ;y B ;z B =[ u x B ;y B ;z B ;v x B ;y B ;z B ;w x B ;y B ;z B ] : {6 Duetothenoslipcondition,theuidclosesttothewallhasthelowestvelocity. Therefore,whenthetransversepressuregradientisapplied,theuidnearthetopof theboundarylayerclosesttothefreestreamwilldeecttheleastwhiletheuidnearest thewallwilldeectthemost.Figure1-6Ashowsthreestreamtubestoillustratethis eect.Thisnon-uniformdeectionintheboundarylayerowgivesrisetocrossows. Therefore,evenunderastrongtransversepressuregradient,acrossowmayformwithout necessarilyproducingtheappearanceofasingularityLu2010. Unliketwodimensionalowswhereseparationisdenedatthelocationofvanishing skinfriction,thelocationofseparationforathree-dimensionalmodeldoesnotalways coincidewiththeshearstressatthewallbeingzeroGad-elHak2000.Furthermore, Tobak&Peake1982emphasizedthattheonsetofowreversalshouldnotbeusedto denethree-dimensionalseparation.Forthree-dimensionalows,theanalysisofseparation requiresanewapproach. 29

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In1948,Searsintroducedtheconceptoflimitingstreamlines.Hedenedthelimiting streamlinedirectionofthevelocityvectoras tan = w u y =0 ; {7 where isthelimitingstreamlineanglewithrespecttothefreestreamand y isdenedas thedirectionnormaltothesurface.Figure1-7depictsthelimitingstreamlineconcept.As owreachestheleadingedgeofathreedimensionalobject,thestreamlinesclosetothe surfacerstmeetintheformofanattachmentline.Searsshowedthatanetoflimiting streamlinesformsonthesurfacewitheverypointonthesurfacenetcorrespondingto thatofthevanishinguidvelocity.Heconcludedthatthelimitingstreamlinesareparallel totheskinfrictionlines.Thesestreamlinesthenconvergeandeventuallydivergeatthe separationline".Itisimportanttonotethatthesestreamlinescanonlycrossatthe locationofsingularpoints.Therefore,whenseparationoccursinathree-dimensional sense,theseparationlineisanenvelopeofconverginglimitingstreamlinesLu2010. AnotherinterestingresultcamefromtheworkofLighthill1963.Heproposedthat, neartheseparationline,skinfrictionandsurfacestreamlinesarenotidentical.Figure 1-8depictsthisfeature.Alimitingstreamtubeisformedbytwolimitingstreamlines ataheight h abovethesurfaceanddistance n apart.Asthelineofseparationis approached,thedistance h increases,whichmeansthatthelimitingstreamlinescan nolongerrepresentskinfrictionlines.Theincreasein h asthelimitingstreamlines convergetowardsthelineofseparationcanbeattributedtotwophenomenaTobak& Peake1982.Therstisthatthedistance n betweenadjacentlimitingstreamlinesquickly declines.Theseconddealswiththeresultantdropoftheskinfrictiontoalocalminimum atthelineofseparation. Thisinformationregardingskinfrictionlinesinthree-dimensionalowscanbe leveragedbytheuseofoilowvisualization.Thisoil-streaktechniquemakesvisible 30

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thepatternsofskin-frictionlines,allowingaqualitativeassessmentofattachmentand separationonthesurfacesofmodels. 1.2.2.3GeneralFlowFeaturesAroundaTurret Theshapeofmostturretmodelsisspecicallydesignedtohouseopticalsystemsand isthusnon-optimalinanaerodynamicsense.Thecomplexowaroundsuchmodelswas notonlystudiedbythoseinterestedinaero-opticaleects,butbythoseresearchingows overgenerichemisphericalarchitecturalshapes. Figure1-9isaschematicthatshowstherelevantowfeaturesinthecomplexow overaturret.Asthetwo-dimensionalboundarylayerconvectsdownstream,itreachesthe leadingedgeoftheturretandwrapsitselfaroundit,thuscreatingtwocounter-rotating streamwisevorticesoneateachspanwiseedge.Thishorseshoeshapedvortexismadeup ofseveralcounter-rotatingvorticeswhichareturnedandstretchedaroundtheturret.The vorticityoftheincomingboundarylayer,initiallyinthespanwisedirection,isredirected intostreamwisevorticity. Theowovertheturretisattachedintheforesection,butdetachesintheaftsection duetobothanadversepressuregradientandthree-dimensionaleects.Sincethesurface curvatureofthesemodelsareorientedinboththestreamwiseandthelateraldirection, thedevelopingspanwisevorticitylinesbecomedistortedandrendertheseparation lineintotheshapeofahorseshoe.Note,thatunlikemodelswithconformalwindows, modelswithatwindowsimposeageometricboundaryconditionthatcausestheowto prematurelyseparatealongitscenterlineandhencethehorseshoeshapedseparationline canbecomeelongated. Theseparationregionhaslargecomponentsofvelocityinallthreedirectionsand, forasurfacemountedmodel,interactswiththehorseshoevortexcreatingacomplexow inthewakeregion.Thisinteractionofthewakeandhorseshoevortexhasbeenshownto crosscommunicatewiththeupstreamvorticitycausingunsteadyvortexloopstobeshed Gordeyev etal. 2007. 31

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Toy etal. 1983studiedowoverdomessubmergedinboundarylayersandfound thatthewidthoftheshearlayerandthemaximumturbulenceintensityinthewake regionarebothhighlydependentontheturbulenceoftheincomingboundarylayer.Most notably,theyfoundthatthelocationofreattachmentofthewakeregionmeasuredin diametersdownstreamfromthecenterofthemodel, x reattach =D diereddramatically betweenasurfacemountedhemisphere x reattach =D =1 : 0,wheretheincomingboundary layerheightwasontheorderofthemodelheight,andahemispheremountedona cylinder x reattach =D =2 : 0.Thisstudyillustratesthatwhilecomparablesizedturret modelsmayexhibitsimilarowpatterns,theoverallquantitativemeasurementsmay diersignicantlybetweenthefourgenericmodelsdiscussedrefertoFigure1-3. Asdiscussedearlier,theinteractionofalltheintricateowfeaturesina three-dimensionalowcangreatlyaectopticaltransmission.Thefollowingsection introducestheseopticalaberrationsources. 1.2.3Aero-optics Thissectionisabriefintroductionintoaero-opticterminology,sources,andmethods ofmeasurement.Itbeginswithadescriptionofvarioussourcesofopticaldegradation. Thensomemetricsforquantifyingthesedistortionsareprovided.Lastly,adiscussionof variousmeasurementdevicesthatarecommonlyusedintheliteratureispresented. 1.2.3.1SourcesofOpticalDegradation Inordertofullycomprehendtheaero-opticproblem,itisimportanttorst understandtheunderlyingmechanismsthatcauseopticalaberrations.Theaero-optic degradationinalaserbeamcanbeattributedtoseveralsources,someofwhichare summarizedinVerho1979.Themainsourcesthatarefoundforlowsubsonicowover agenericturretareillustratedinFig1-10. Therstsourceofinterestistheinviscidoweldsurroundingtheaircraftoutside oftherelativelythinviscouslayerseeFigure1-11.Thepotentialowregionsare establishedoutsidetheboundarylayerwheretheowisassumedtobeinviscidand 32

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compressibilitycorrectionscanbeusedtoestimatethedensitychangesthroughthis region.Theglobaleectisthatofanaberratedlensthathasafocallengthgivenby f = R 1 1 )]TJ/F22 11.9552 Tf 11.955 0 Td [( 0 {8 where R isthecurvatureoftheowdictatedbytheradiusoftheaerodynamicbody, 1 isthelocaldensitywithintheowinthenear-eldoftheturret,and 0 isthefreestream density.Theopticaleectsofthistypeofoweldhavebeenfoundtodefocusthelaser Gilbert&Otten1982.Thesedefocusingeectscanbecorrectedwithcurrentadaptive optictechniques. Othersourcesofpropagationlossesaretheviscousboundarylayerandshearlayer. Theviscouseectsaremanifestedthroughtheboundarylayerandshearlayerwhichare typicallyfullyturbulentwithrandomuctuatingairdensity.Sincetheselayers'scalesare atleastanorderofmagnitudesmallerthanawavefrontbeamdiameterGilbert&Otten 1982,theenergypropagatedthroughthemisscatteredatwideanglescausinglargelosses inbothfar-eldpeakandaverageintensity. Whentheturbulentboundarylayerseparatesfromanaerodynamicbody,alarge wakeregionresultsandlongopticalpathsintheaftdirectioncansuerfromsevere opticaldegradation.Attheowspeedsofinterestinthisresearch,theseparatedwake owisalwaysturbulentandhaslengthscalesthatareontheorderoftheaerodynamic body.Althoughtheunsteadydensityuctuationsaresmallerthanthoseassociated withboundaryandshearlayers,thelargercoherencelengthsandlongerpathsforbeam propagationmaycauseanoticeablechangeinthepathandintensityofanopticallaser travelingthroughit. Analsourceofopticaldegradationcanbeattributedtotheformationofshocks, whichoccurwhenthelocalMachnumberexceedsunity.Dependingonthegeometryof theturret,localsonicspeedscanbereachedforfreestreamowswithrelativelylowMach numbers s 0 : 5.Thestrongdensitygradientsassociatedwithshocksandexpansionswill 33

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createathinregionwheretheopticalbeamisbothretractedanddispersed.Thiscauses largephaseaberrationsinthebeamandhencealargereductioninfar-eldlaserintensity. 1.2.3.2MeasureofOpticalAberrations Themeasureofperformanceforanopticalsystemwhosebeamtravelsthrough aturbulent,variantindex-of-refractionoweldisquantiedbyananalysisofthe far-eldirradiancepattern.Themeasureofopticalaberrationsinaoweldaretypically calculatedintermsofvariationsofthewavefront'sopticalpathlengthOPLoverthe lengthoftheopticalaperturewindow.TheOPListheproductofthegeometricpath lengthandtheindexofrefractionofthemediumthroughwhichitpropagatesPedrotti etal. 1987.Foraone-dimensionalopticalpath,theOPLisafunctionofbothspaceand timeandcanbedenedas OPL t;x = Z y 2 y 1 n t;x;y dy; {9 where n t;x;y istheindexofrefractioneldalongtheopticalbeampaththatthebeam travelsbetweentwopoints, y 1 and y 2 ,attime t .However,onlytherelativedierence inOPLalongtheintegrationpathisusedinpractice.Thisistermedtheopticalpath dierenceOPDandisdenedasthedierencebetweenthelocalOPLanditsspatial averageoverapredeterminedaperture OPD t;x =OPL t;x )]TJETq1 0 0 1 350.744 275.075 cm[]0 d 0 J 0.478 w 0 0 m 24.383 0 l SQBT/F15 11.9552 Tf 350.744 265.231 Td [(OPL t : {10 Thegureofmeritthatismostcommonlyusedtomeasurereductionsinoptical performanceofasystemistheStrehlratio, SR Eq1{11.Itisdenedastheratioofthe observedlightintensityfromapointsourceofanaberratedsystematagivendetection plane, I t ,tothetheoreticalmaximumpeakintensitywithoutaberrations, I 0 alsoknown asthediractionlimitedon-axisirradiance, SR t = I t I 0 : {11 34

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Theestimatedtime-averagedStrehlratio, SR ,asafunctionofthetime-averaged opticalphasevarianceacrossanaperture, 2 wasreportedbyMahajan1983,andis givenby SR =exp )]TJ/F22 11.9552 Tf 9.299 0 Td [( 2 : {12 Jumper&Fitzgerald2001notedthattheopticalphasevarianceisdirectlyrelated tothenormalized OPD varianceandwavelengthoftheoptimalbeam, 2 = 2 OPD rms 2 : {13 SubstitutingEq1{13intoEq1{12,thetemporallyaveragedStrehlratiocanbe calculatedwiththefollowingequation SR =exp )]TJ/F28 11.9552 Tf 11.291 16.857 Td [( 2 OPD rms 2 # : {14 Inparticular,notethatforaoweldwithanOPD rms ,theeciencyoftheopticalsystem isstrictlyafunctionofthewavelength,withsmallerwavelengthsproducingalessecient system. Foragivenow,arstinstinctmightbetousealargewavelengthopticalbeam suchthat SR approachesunity,i.e. I t approachesthediractionlimitedirradiance, I 0 However,itisimportanttorealizethatthemaximumintensityofanopticalbeamisalso inverselyproportionaltothesquareoftheopticalwavelength,Jumper&Fitzgerald2001 I 0 / Pd 2 Y 2 2 ; {15 where P isthelaseroutputpower, d istheaperturediameter,and Y isthefocallength oftheoptics.Eq.1{15showsthatforagivenopticalsystemconstant P d ,and Y ,the maximumdiractionlimitedon-axisintensityisinverselyproportionalto 2 .Therefore, drivenbythefactthatshorterwavelengthlasershavethepotentialtoproducemuch higherintensitywithminimalaberrations,recentresearchisleaningtowardthedesign ofopticalsystemswithsmallerwavelengths.Indeed,theUSAirForce'sairbornelaser 35

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systemusesachemicaloxygen-iodinelaser =1 : 3 m becauseofit'shighpeak intensityinun-aberratedconditionsKopp2008. 1.2.3.3ToolsforMeasuringAero-opticDistortion Someoftheearliestmeasurementtechniquestotakeadvantageofsmallrefractive indicesinowswereshadowgraphandschlierenphotography.Botharegenerally qualitativetechniquesthatrespondtothechangeinrefractiveindexofthemedium. Ingeneral,schlierentechniquesaremoresensitivetochangesinindexofrefractionand directlyrespondtotherstderivativeoftherefractiveindex, @n @x .Shadowgraph,onthe otherhand,respondstothesecondspatialderivativeoftherefractiveindex, @ 2 n @x 2 ,which makesitusefulinowswithshockwavesorturbulence,where @ 2 n @x 2 canbegreaterthan @n @x Settles2001providesadetaileddescriptionofthesetechniques.Bothtechniqueswere usedinearlystudiesforaero-opticalcharacterizationseeTrolinger1980forexamples andoeraqualitativemethodtodiscernthephasedierencescausedbychangeinindex ofdiractioninamedium. Asimilartechniquetothewell-knownschlierenmethodisbackgroundoriented schlieren.Foradetaileddescription,seeVenkatakrishnan&Meier2004andHargather &Settles2010.ThismethodusesGladstone-Dalerelationbetweendensityand refractiveindexoftheuid, n s G where n aretheindexofrefractionuctuations, aredensityuctuations,and G istheGladstone-Daleconstant,tocreateaow visualizationeldofdensitygradientsinuids.Itmakesuseofsimplerandomlygenerated dot-patternbackgroundpatterns,astrobelightsource,andacamerasensor.Thesensoris usedtostoretwoimages:areferenceimagewithoutthedensityeectandameasurement image,withdensityvariationscausedbytheow.Duetodensitygradientsintheow, themeasurementimagecontainsabackgroundpatternthat,whencorrelatedwiththe referenceimage,willgiveadisplacementpatternthatdirectlycorrespondstothechanges indensityoftheowKlinge etal. 2003.Itssimpleset-upeliminatestheneedofmirrors andlasers. 36

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Interferometry,anothermethodtomeasureaero-opticdistortion,hasbeenusedby deJonckheere etal. 1982toshowthecomplexinteractionoftheshearlayer,separated owregion,shockwave,andfreestreamowoveraturret.Interferometryworksonthe principlethatwhentwocoherentwavesofequalwavelengthcombine,theresultisa patternofthephasedierence.Specically,interferometryusesthephaseshiftoflight rayspassingthoughamediumtorecoverarefractiveindexeld.Thistechniqueobtains theopticalpathdierencebyrecordinganinterferencepatternfromthesuperpositionofa referencewaveandthewavepassingthroughthemediumofinterest. Whiletheseearliertechniquesprovidedmuchneededinsightintotheproblemof aero-optics,thereweremanydrawbacksthatincludedcomplexsetupsandlongdelaysto obtainresultsduetothepost-processingoflm.Morerecently,advancesinnewsensor technologyhaveresultedinhighframeratecameras.This,alongwithquicklyimproving dataacquisitionsystems,hasallowedresearcherstobuildupontheideasofshadowgraph, schlieren,andinterferometrytodevelopnewsensorswithhigherbandwidthandspatial resolutionthatcanbeusedinuiddynamicapplicationsforthedetectionofoptical degradation.Thetwomostcommonopticalsensingsystemsinrecentresearchincludethe Shack-HartmannsensorandMalleyprobe.Theyarebrieydiscussedbelow. ThetheorybehindtheShack-Hartmannsensorcanbeeasilydemonstratedwith Figure1-12.Whenawavefronttravelsthroughavariantindex-of-refractionmedium,the resultingwavefrontisdistorted.Thegureshowsasinglerayasittraversesthemedium. Huygen'sprinciplestatesthattheemergingraymustbenormaltotheassociatedresulting wavefrontTrolinger etal. 2002.Ifanopaqueplatewithanarrayofsmalldiameter aperturesisplacedatthepointwherethedistortedwavefrontemergesfromthevariant densityeld,thenanarrayofvectorsiscreated-allofwhicharelocallynormaltothe distortedwavefront.SuchaplateisknownasaHartmannplate.Aphotographicplate isthenplacedataknowndistance, d ,awayfromtheHartmannplate.Whentheplateis 37

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exposedtotheincomingraysforaveryshorttimeinterval,thedisplacementofeachray, ,fromtheun-aberratedcasecanberecorded. Theo-planarangleofthewavefront,denedas x ,canthenbecalculatedfromthe knowndistancebetweentheHartmannplateandthephotographicplate, d ,aswellasthe displacementoftheresultingaberratedray, asgivenby x =tan )]TJ/F21 7.9701 Tf 6.587 0 Td [(1 x d : {16 Notethatthetwootherdeectionangles, y and z ,arecomputedinasimilarfashion. Forsmalldeectionangles,thiscanbeapproximatedas x x =d .TherelativeOPLcan beapproximatelyconstructedasdescribedbyMalacara2007, OPL x j 1 d j +1 X n =2 x n )]TJ/F18 5.9776 Tf 5.756 0 Td [(1 + x n 2 x n )]TJ/F22 11.9552 Tf 11.955 0 Td [(x n )]TJ/F21 7.9701 Tf 6.587 0 Td [(1 ; {17 where x j isthelocationofthe j th sub-apertureintheHartmannplate.Ifthedistance betweentheholesissmallcomparedtothethechangeintheslopesinthewavefront,then Eq1{17isadiscretizedapproximationof OPL x j = Z x j 0 d OPL dx dx: {18 Similarly, z ,andhenceOPL z ,canbeobtainedfromthedisplacement z and thereforecompleteconstructionsofatwo-dimensionalwavefrontataninstantintime, OPL t;x;z ,canbedetermined. Now,iftheHartmannplateisinsteadreplacedwithanarrayoflensletsandthe photographicplatewithacharge-coupleddeviceCCDarray,thentheopticalsystem istermedaShack-Hartmannwavefrontsensor.Thesesensorshavebeenextensivelyused inrecentyearstoacquiretwo-dimensional,time-averagedwavefrontmeasurementsin variousoweldsGordeyev etal. 2004 a ;Land2000;Neal&Mansell2000.Typical CCDsensorscaptureframesfrom30-120HzNeal etal. 1998,andnewercommercially availablewavefrontsensorscancaptureframesatnearly500HzAmo2010.Whilethey 38

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provideimportant,two-dimensionalinsightintoatime-averagedwavefrontmeasurement, theyarenotsuitabletoobtaintime-resolveddata.Inordertoresolvethequickchanging wavefronts,temporalbandwidthsmustexceed50kHzGordeyev etal. 2004 a TheMalleyprobeisasimpleopticaldevicethat,unliketheHartmannsensor, providesonlyone-dimensionalslicesofopticalwavefrontsinthedirectionofthebeam propagationvector.Figure1-13showsaschematicofaMalleyprobeset-up.Abeam splitterisusedtosplitasinglebeamintotwobeamsinthestreamwisedirectionbya knowndistanceMalley etal. 1992.Generally,steeringmirrorsareusedtodirectthe beamsintothevariantindexofrefractionowandontoaatmirrorthatthenreects thebeamscoaxiallybacktoafocusinglens.Thereturningbeamsarealsoseparated fromtheincomingbeamswiththeuseofacubebeamsplitter,andeachbeamispassed toapositionsensingdevice.Thepositionsensingdevicemeasuresthebeam'scentroid positionasafunctionoftimeandthedeectionangleiscalculatedfromEq.1{16.The timedelaybetweenthetwobeamscanbecalculatedand,alongwiththeknowseparation distancebetweenthebeams,canbeusedtodeterminetheconvectivespeedoftheow structures, U c .KnowingthattheaberrationsconvectwiththeuidstructuresGordeyev etal. 2004 a ,theconvectionvelocityisthenusedtocalculatetheOPL, OPL x 0 ;t = Z t t 0 d OPL dx x 0 dx dt dt = Z t t 0 )]TJ/F22 11.9552 Tf 9.299 0 Td [( t U c dt: {19 OncetheOPLisknownatagiven x 0 ,Taylor'sfrozenowhypothesisisappliedtotrade spaceandtimeandthusprojecttheOPLtoadierent x i Hugo&Jumper1996, OPL x i ;t =OPL x 0 U c j x i )]TJ/F22 11.9552 Tf 11.955 0 Td [(x 0 j U c ;t : {20 Theratesofthesensingdevicesareusuallyseveralordersofmagnitudehigherthanthose fortheHartmannsensor O kHzvs O Hz. Insummary,thissectiondescribedseveralmethodsthathavebeenusedinthepast tobetterunderstandtheopticalenvironmentaroundvariousturretmodelgeometries. 39

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Shadowgraphandschlierenmethodsprovideagreatqualitativemethodforvisualizing changesindensityinagivenoweld,butcanbeverycomplexandtimeconsumingto setup.MostcommerciallyavailableShack-Hartmannsensorsarecapableofproviding quantitative,two-dimensional,highspatialresolutionwavefrontmeasurements.However, theyrelyonCCDsensorswhicharetypicallylimitedtoafewhundredframespersecond, andthusarenotabletotime-resolveopticalaberrations,whichforagivenoweld,may be O kHz.SomeworkaroundsincludetheimplementationofCMOSbasedsensorsthat havetheabilitytooperateathigherspeeds.MostMalleyprobeshaveasamplingrateof upto200kHzandallowfortime-resolvedone-dimensionalmeasurementsoftheOPD. Duetoitssplitbeammethod,thedataextractedcanbeusedtocalculatetheconvective speedoftheowstructures. 1.2.3.4OPD rms Non-DimensionalAnalysis Inordertoclearlyidentifytherelevantdimensionlessparametersthatgovernthe opticaldistortionmechanismforowoveraturret,itbecomesnecessarytorstrecognize theappropriatedimensionalparametersinvolved.Consideringtheturretparameter schematicinFigure1-4,itispossibletoidentifytwofundamentalgroupsofparameters whichareexpectedtoaectthebehavioroftheoweld.Thesetwogroupsareturret parametersincludingbothgeneralshapeandturretorientationandowparameters. Theturretparameterscanbebrokendownintothegeneralshapeparameters D a and H andorientationparameters and .Theseparametersarelistedbelow. :turretelevationangle :turretazimuthangle d :diameterofturretaperture D :diameterofturret H :heightofturret 40

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Theowparameters,however,arenotdirectlyfunctionsoftheturretshapeor orientationandinclude: :incomingboundarylayerheight :dynamicviscosityoftheuid :densityoftheuid SL :referencedensityatsealevel :typicalvorticalstructuresizewithinshearlayer c 0 :speedofsound U 1 :freestreamvelocity PerformingaBuckingham-Pianalysis,andchoosingprimarydimensionsMLt,yields Table1-1.Therearethreeprimarydimensions-massM,lengthL,andtimet-and thirteentotalparameters.Dimensionalanalysisrevealsthattherearetendimensionless pi-groups.Choosingthefreestreamdensity ,thefreestreamvelocity U 1 ,andtheturret diameter D astherepeatingparametersgivesthesetofpi-groupslistedbelow. Q 1 = a U 1 b D c OPD rms =OPD rms =D Q 2 = a U 1 b D c d = d=D Q 3 = a U 1 b D c H = H=D Q 4 = a U 1 b D c = Q 5 = a U 1 b D c = Q 6 = a U 1 b D c = =D Q 7 = a U 1 b D c = = U 1 D =1 = Re Q 8 = a U 1 b D c SL = SL = Q 9 = a U 1 b D c = =D Q 10 = a U 1 b D c c 0 = c 0 =U 1 =1 = Ma 41

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Thisleadstoafunctionalrelationshipoftheform OPD rms D = f d D ; H D ;;; D ; Re ; SL ; D ; Ma : {21 Thisrelationshipcanbefurtherdecomposed,sothatitiscomprisedofthreeseparate functions:theturretshape A ,turretorientation B ,andowparameters C OPD rms D = A d D ; H D ; type B ; C D ; Re ; SL ; D ; Ma {22 Therstparameter, A ,isrelatedtotheoverallturretgeometryandisheavily dependentontheaperturebeingeitheratorconformal. B issolelyafunctionofthe turret'sorientationwithrespecttothefreestreamow.Forsimplicity,andbecausethere havebeenveryfewexperimentswithanon-zeroazimuthorientationangle ,itwillbe assumedthat =0.However,theopticaldistortionshavebeenshowntobeastrong functionofelevationangle.Cress etal. 2008andDun2005havestudiedoptical aberrationsinturbulentboundarylayersandseparatedshearlayers,respectively,and furtherproposedthat-forelevationangleslargerthan90 o -opticalaberrationsscalewith 1/sin Thenalparameter C ,however,isafunctionoftheowparametersandcanbe furtherdecomposedtoaccommodatethepreviousexperiments.First,iftheincoming boundarylayer ismuchsmallerthantheturretheight H ,asisthecaseforallofthe previouswork,thentheboundarylayerdoesnotdirectlycontributetoanyaero-optical degradationGordeyev&Jumper2009.Also,forcaseswhereRe > Re c ,theseparation pointisxedatanelevationofapproximately120 o Vukasinovic etal. 2009 a ,oratthe locationofwheretheairowmeetstheatwindowdiscontinuity,ifpresent.Ithasalso beenshownthattheReynoldsnumberaectsonlysmallstructuresintheshearlayer, whicharenotasignicantcontributingfactorinopticalaberrationsGordeyev&Jumper 2009.Therefore,foraowswithaRe > Re c opticaldistortionsarenotastrongfunction ofRe.Furthermore,ithasbeenarguedthatforagiventurretshapeandorientation, 42

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thelargescalestructuresinsideoftheseparatedshearlayerareonlyfunctionsofthe incomingboundarylayerSavory&Toy1986;Toy etal. 1983,ifpresent,andturret shapeGordeyev&Jumper2009.Again,ifassuming <
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Thenextsetofexperimentsshownareforaconformal-windowedturretmounted onacylindricalbaserefertoFigure1-3A.Therstsetofexperimentsconsistofa 61mmdiameterspheremountedona49.9mmcylindricalbase.Forthesecases,the experimentaldatawasgatheredfromGordeyev etal. 2009,Vukasinovic etal. 2009 b Gordeyev etal. 2010 c ,Vukasinovic etal. 2010 b ,andVukasinovic etal. 2010 a .For moreinformationregardingthismodel,pleaserefertoSection2.2.3.Thesecondsetof experimentsconsistedofa30.4mmdiameterspheremountedona26.6mmcylindrical base.Forthesecases,theexperimentaldatawasgatheredfromGordeyev etal. 2006and Gordeyev etal. 2007.Formoreinformationregardingthesecondmodel,refertoSection 2.2.1.Thescalefactorusedinthescalingrelationshipis A =0 : 9 m/m.Notethatthe scalingrelationshiptagaindoesaveryreasonablejobofpredictingtheexperimental resultsforall andMa,evenforthedierentsizedmodels. Thenalsetofexperimentsshownareforatwo-dimensionalsurface-mounted at-windowedturretwasgatheredfromGordeyev etal. 2005andGordeyev etal. 2010 b .TheresultsareplottedinFigure1-16.Formoreinformationregardingthis model,referbacktoSection3.6.1andFigure2-3.Thescalefactorusedinthescaling relationshipwas A =1 : 7 m/m. Severalimportantobservationscanbedrawnfromthescalinganalysis: 1.Thescalefactor A dependssolelyontheturretgeometry: A =2.6 m/m forthesurfacemountedconformal-windowturrets, A =0.9 m/mforthe conformal-windowedturretsmountedonacylindricalbase,and A =1.7 m/m forthetwo-dimensionalsurfacemountedat-windowedturret. 2.Forconformaltypeturretswheretheincomingboundarylayerplaysarolei.e.the turretissurfacemountedtheresultsindicatetheworstopticalenvironment,orthe highestvalueof A .Inthescenariowheretheturretisxedtoacylindricalbase where 145 o sinceinbothcases,theaperturewouldbecompletelyimmersedintheseparated region. 44

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4.Therearenocurrentexperimentsthathaveshowntheeectoftheincoming boundarylayer.Earlyexperimentshowever,includingthoseofOkamoto1980, Toy etal. 1983,andSavory&Toy1986haveshownthattheincomingboundary layerplaysakeyroleinslowstructurespresentwithintherecirculationregion. 5.Thescalinganalysishereinisonlyaccurateforlowsubsonicows.Itwasshownthat athigherfreestreamMachnumbersMa > 0 : 5,theproposedscalingisnolonger valid,mostlikelyduetotheintroductionoflocaltransonicandsupersonicow features. 1.2.4FlowControl Inthesimplestterms,owcontrolcanbedenedasthemanipulationofowinan attempttoobtainfavorableresults-whethertheybereductionindragorenhancement inlift,transitionordelaytoturbulence,augmentingthemixingofmass,momentum,or energy,suppressingorenhancingturbulentlevels,reattachingordelayingseparatedow, orpossiblyevensuppressingowinducednoise.Thechallengeistoachievethedesired goalinanecientmanneratminimalcost. Thissectionintroducessomeofthemainconceptsofowcontrol,whilebriey highlightingsomepreviouswork.Anextensivereviewofpreviousresearchregardingow controlforaero-opticapplicationsisfoundinaliteraturereviewinChapter2. 1.2.4.1ApplicationstotheAero-opticProblem Inthecaseoftheaero-opticproblem,theinterestinthemodicationofowarounda turrethasbeenofgreatinterestsincethe1960's.However,itwasnotuntiltheearly90's thattheaero-opticcommunitystartedexploringtheuseofmodernowcontroltechniques tosuppressundesirableowfeaturesresponsibleforthedegradationofwavefronts.Inthis research,themaingoalistoexploremethodsofcontrolforlowspeedthree-dimensional owstodetermineitsrelationshipandapplicabilitytoaero-optics. Pastowcontroltechniqueshavebeendevelopedwithaneedtoaccommodatethe aerodynamicrequirementsofairplaneight.Earlymetricsfordeterminingthebenets ofseparationcontrolincludedqualitativeresultssuchasowvisualizationaswellas quantitativecalculationsusingbalancesandsteadypressuremeasurementstoobtain 45

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time-averagedliftcoecientsLachmann1961.However,themetricbecomesmorerigid whenowcontrolisforthepurposeofenhancingthetransmissionofopticalwavefronts throughregionsofhighlyturbulentowVukasinovic etal. 2008. Severalstudieshaveshownastrongcorrelationbetweenowfeaturesandaero-optic distortions.ArecentstudybyFitzgerald&Jumper2004examinedthemechanisms thatproduceavariable-densityeld.Theyinvestigatedweaklycompressibleshearlayers andshowedthatthepressureuctuationsassociatedwithstreamlinecurvaturewerea dominantinuenceontheinstantaneousdensityeld.In2004,Gordeyev etal. used ahot-wiredevicetomeasurevelocityuctuationsatseverallocationsneartheoptical atofaturretmodel.Correlatingthisdatawithaero-opticalmeasurements,theyfound thatopticaldistortionsoveraatwindowweregreatlygovernedbytheseparatedshear layerinanadversepressuregradient.Laterin2008,Wallace etal. focusedonreducing opticdistortionbyhomogenizingi.e.reducingturbulentuctuationsthewakeof theturretovertheapertureareausingactivecontroltechniques.Otherresearchers havealsoattemptedtoimprovetheopticalqualityofowbyusingunsteadypressure measurementsasametric.Theystatethatevenwhendirectmeasurementsofaero-optics arenotavailable,turbulenceintensitymeasurementsprovideastrongrelationshiptothe opticalqualityoftheowAndino&Glezer2010;Wallace etal. 2009,2010.Specically, Vukasinovic etal. 2010 a notedtheparticularlydestructivenatureoftheshearlayeron otherwiseaberration-freeowsduetothepresenceofthevorticalstructuresthatinduce strongpressuregradients. 1.2.4.2TerminologyandClassications Figure1-17showsaowcontrolcategorizationapproachthatisconsistentwiththe controlmethodologiesinrecentliteratureCattafesta etal. 2008 b .Thiscategorization isbasedonhowtheenergyistransferredintotheowandthecontrolstrategyinvolved. Thehierarchystartswithpassiveandactivecontrol,wherethelatterrequiresenergy expenditurefromanexternalsource.Furthermore,activecontrolcanbebrokendowninto 46

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eitheropen-orclosed-loop.Open-loopcontrolusesapre-determinedinputintothesystem andhencenosensingofowfeaturesisrequired.Closed-loopcontrol,however,requires sensingtodeterminetheoutputofanactuator,inturnaectingthesensorthroughthe dynamicsofthephysicalmodel.Closed-loopcontrolcanbebrokendownintoeither feedforwardorfeedback.WhileWilliams&Macmynowski2009haveillustratedthat feedforwardandfeedbackcanbeshowntobeequivalent,feedforwardcontrolspecically usesaprioriknowledgeofdisturbancestochangethecontrolsignalwhilefeedback controlrequiresthemeasurementofthecontrolvariabletobefedbacktothecontroller. Moreover,feedbackcontrolcanbebrokendownintostaticordynamiccontrol,wherethe timescalesoftheowareontheorderofthecontrolitselfforthelatter.Thissection focusesondescribingeachofthesemethods,alongwithpresentingsomepreviousresearch relevanttotheaero-opticcommunity. Passiveowcontrolisthesimplestandoldestofthesemethods.Thecontrolis passiveinthesensethatnoexternalactuationenergyisintroducedintotheow.Instead, energycanbetransferred-sayfromthefreestreamtotheboundarylayer-withtheuse ofgeometricmodicationsontheaerodynamicbody.Oneofthemostcommonpassive controldevicesisthevortexgeneratorVG.Figure1-18showstheuseofVGsonaircraft wingstosuppressseparation.VGsaresimpletoimplementandthereforehavegenerally beenusedasarstattempttocontroltheowoverthebodyofinterest.TheVGs'main functionistocreatestreamwisevorticesthatoverturnthemeanowandreenergizethe boundarylayer.Whilesimpletoimplement,theyhavealargeparametricspacethatneeds tobeoptimizedforidealeects.Theseparametersinclude,butarenotlimitedto:shape, sectionprole,orientation,size,andspacingGad-elHak2001.Also,sincemostpassive controldevicesareoptimizedforaspecicowcondition,theyhavebeenknowntocause detrimentaleectsattheo-designconditions. Asanexampleofpassivecontrolintheaero-opticcommunity,arecentstudyofow overahemisphericalmodelmountedonacylindricalbaseusedaft-mountedfairingsand 47

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splitterplates.Thistechniqueresultedindecouplingtheinteractionofthehemisphere andcylinderwakesandincreasedpressurerecoveryaftofturretSnyder etal. 2000; Vukasinovic&Glezer2007.In2005and2010,Gordeyevetal.usedbothVGplates andverticalpinstotoimproveaero-opticalenvironmentaroundatwo-dimensionalat windowedturretGordeyev etal. 2005,2010 c .Thesestudies,amongothers,aredetailed inChapter2. Open-loopcontroloersabalancebetweenthesimplicityofpassivecontrolandthe complexityofclosed-loopcontrol.Sinceapredeterminedsignalisusedastheinputto theactuator,thereisnoimplementationofacontrolalgorithmandthereforenofeedback sensorsareneeded.Becausethereisnocontroller-thecontrolsignalisestablished inadvance-thereisnometrictooptimizeandhence,noguaranteesthatthecontrol willhavefavorableeects.Sincethree-dimensionalowsaresocomplex,mostofthe literatureconcerningtheaero-opticproblemhavefocusedonthesimpler,open-loop controlmethods. Vukasinovicetal.haveusedhighfrequency,open-loopactuationonaconformal windowturrettodelayseparationalongthecenterplane,reduceopticaldistortionin excessof40%atMa=0.4Vukasinovic etal. 2008,regularizemotionsinthedownstream recirculationregionVukasinovic etal. 2009 a ,andreduceturbulentkineticenergywithin theshearlayerVukasinovic etal. 2009 b .Otherformsofopen-loopcontrolhasledtothe completeremovalofthehorseshoevortexusingsuctionWoszidlo etal. 2009andlarge reductionsinReynoldsstressAndino&Glezer2010. Whiletheresultsandconclusionsfrompassiveandopen-loopcontrolstudiesserve asasoundphysicalbasisforeectivecontrol,closed-loopcontrolhastheadvantage ofoeringgreatereciencyCattafesta etal. 2008 a .However,theschemesaremore complexandarethereforeimplementedlessincomplexthree-dimensionalows. Closed-loopcontrolcaneitherbemodel-based,ormodel-free.Asthenameimplies, model-basedtechniquesrequireasystemmodel.Themodelcanprovidesignicant 48

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physicalinsightintotheowtopologybothpre-andpost-control.Someofthemost popularmodel-basedschemesarebasedonProperOrthogonalDecompositionPOD wherelow-ordermodelsgiverelativelyhighresolutionandlowcomputationalintensity Pinier etal. 2007;Rowley2005.However,therearesomeshortcomingswhendeveloping amodelforanuncontrolledstatewhilenotexplicitlyincludingacontrolinput.Recently intheturretresearchcommunity,Wallace etal. 2008usedaPODapproachtoto reducepressureuctuationsby18%overthewakeofaatapertureturret.Other model-dependentmethodsincludeblackboxmodelsthatidentifytheuiddynamic systemusingausuallylinearinput-outputrelationshipbetweenactuationsignalsand sensorreadings.Mostofthesemethodsarecapableofrunningatthetimescalesofthe ow,andhencearetermeddynamicfeedbackcontrol.However,duetotheincrease intheircomplexity,thesemethodshaveonlybeenappliedtoverywellestablished benchmarkproblemsincludingowoveracylinder,aroundabackwardfacingramp,or overacavityPastoor etal. 2008. Ontheotherhand,closed-loopmodel-freeschemesusefeedbackschemeswhere adirectmodeloftheowneednotbeidentied.Instead,gradientbased,suchas extremum-andslope-seeking,approachesareusedtondadistinctminimaormaxima inasteady-statemapBecker etal. 2007;Press etal. 1986;Tian2007.Themethod usesauser-denedcostfunctiontosearchforoptimalactuationwaveformparameters. Forinstance,thedownhillsimplexalgorithmhasbeenusedsuccessfullytoincrease thelift-to-dragratioofowoveranairfoilbyafactoroftwoTian etal. 2006.The attractivenessofthealgorithmisitssimplicityandapplicabilitytomulti-parameter optimization.However,themaindrawbackofthetheseschemesisthattheydonot operateonthetimescalesoftheow,andarethereforeconsideredstaticorquasi-static. Inotherwords,theyworkontime-averagedobjectivefunctionssuchasachievingpressure recoveryandincreasinglift-to-dragratio. 49

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1.2.4.3FurtherDiscussiononFlowControlParameters Sofar,thissectionhasfocusedprimarilyontheclassicationofcontrolschemes.It hasnot,however,includeddetailedinformationontheapplicationofthesetechniques. Someotherparametersthatarepertinenttoowcontrolstudiesincludesensingand actuating,forcingtechnique,andowcontrolmethodology.Inthefollowingparagraphs, theseitemsarebrieydiscussed.Foramoredetailedreviewonrelevantowcontrol parametersandapplications,seeGad-elHak2001. Theselectionofsensorsandactuatorscanbeadauntingtask.Cattafesta&Sheplak 2011dealwithsomeoftheissuesregardingthebandwidth,sensitivity,dynamic response,linearity,robustness,andcostofselectingasuitablecombinationofsensorsand actuators.Eventhen,thelocationofthesedeviceswillalsodeterminetheeectivenessof thecontrolstrategy.AstudybyVukasinovic etal. 2005hasshowndramaticdierences intheeectofactuatorlocationwhenattemptingtosuppressofowseparationovera turret. Furthermore,actuationitselfcanbebrokendownintosteadyandunsteadyforcing. Forbothtypes,theuserstilldealswithlocationandrelativepositioningoftheactuators withrespecttocertainowfeatures.Unsteadyforcing,however,alsodealswithadditional parameters,includingtheamplitudesandfrequenciesoftheactuationsignalaswellasthe relativephasebetweenmultipleactuators.Greenblatt&Wygnanski2000presentsthe benetsofperiodicexcitation,andWygnanski2004discusseshighfrequencyforcingand itsbenets. Thetechniqueusedtomodifytheowcanbeeithertwo-orthree-dimensionalin nature.Three-dimensionalforcingvariestheactuationpropertyalongthespanwiseor azimuthaldirection,whiletwo-dimensionalforcingdoesnot.Severalstudieshaveshown thatthree-dimensionalforcingcanbeveryeectiveintwo-dimensionalowsduetotheir enhancedmixingeect.However,inanannualreviewofowoverblubodies,Choi etal. 2008notedthatthesameneednotbetrueforthree-dimensionalows. 50

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Finally,controlcaneitherbeappliedasboundarylayerordirectwakecontrol. Boundarylayercontroldealswiththemodicationoftheboundarylayerdirectlyby enhancingnearwallmomentum,usuallytopreventseparation.Tangentialblowing usingzero-netmass-uxactuatorshasbeenusedbyVukasinovic etal. 2005todelay separationby20 o overaturretmodel.Directwakecontrol,ontheotherhand,deals withanalreadyseparatedowandattemptstochangethewakeelddirectly.Anearly exampleistheresearchbyPurohit etal. 1983 a ,whereheusedsuctionatthebaseofa turretmodeltodirectlyaltertheowstructure. Tosummarize,severalcontrolmethodologieswereintroduced.Passivecontrolisthe easiesttoimplement,butbecausethesedevicesareoptimizedforaspecicowregime, theyoftencauseundesirableeectsattheo-designconditions.Hence,theyarethe leastecientformultipledesignconditions.Active,open-loopcontrolisbyfarthemost widelyusedmethodwhenattemptingtoreduceaero-opticaberrations.Ithasallowed researcherstoattemptowcontrolonthecomplexuidproblemwithoutmuchknowledge ofmoderncontroltheory.However,sincetheydonotoeranyfeedbacktotheactuators, thiscontroltechniqueisnotnecessarilyoptimalorecient.Albeitthemostcomplicated technique,closed-loopcontrolpotentiallyoersthemostecientapproach.However,the complexityoftheuiddynamicsofowaroundathree-dimensionalobjecthassteered mostresearcherstouseeitherpassive,open-loopcontrol,orevenacombinationofthetwo Gordeyev etal. 2010 c ;Vukasinovic etal. 2010 b 1.3Objectives Largelossesineectivenessareincurredinairborneopticalsystems.Forthecase oflaser-basedsystems,propagatingalightbeamthroughregionsofhighturbulence reducestheenergyandfocusofthebeam.Understandingthevariousthree-dimensional owfeaturesatlowspeedscanhelpbringfurtherunderstandingtotheowfeaturesthat contributetoaero-opticaldistortion. 51

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Themainobjectivesofthisresearchareasfollows.Therstistodesigna turretmodelthatisrepresentativeofaircraftdirectedenergyapplications.Thenthe three-dimensionalowwillbecharacterizedtoidentifypotentialsourcesofbothow separationandaero-opticdistortion,specicallyfocusingontheinteractionofthevarious owfeaturesthatarepresentinthelow-subsonicowregime.Onceaclearunderstanding isestablished,themaingoalwillshifttowardtheevaluationandimplementationofboth passiveandopen-loopactiveowcontrolmethods.Leveragingresearchintheowcontrol community,techniqueswillbedevelopedtosuppressunfavorableowdisturbancesand,in turn,mitigateaero-opticdistortion. 1.4Approach Aturretmodelwillrstbemadebasedonspecicationsgivenbythesponsor LockheedMartinCorporation.Tocharacterizethebaselinethree-dimensionalow aroundtheturret,severalexperimentswillbeconductedintheUniversityofFlorida low-speedwindtunnelfacility.First,theincomingboundarylayerwillbemeasured usinghot-wireanemometry.Then,thebaselineowovertheturretwillbecharacterized bysteadypressuremeasurementsoverthecenterlineofthemodel,unsteadypressure measurementsalongtheaperture,qualitativeoilowvisualizationalongthesurface, andstereoscopicparticleimagevelocimetryalongseveralplanesinthewakeregion.For aero-opticmeasurements,aMalleyprobeisusedtoobtaintime-resolveddataalong severallocationsalongtheatwindow.Conditionalspectralanalysiswillbeperformed usingtheaero-opticandunsteadypressuredatatodetermineasuitablecontrolmetric whenaero-opticmeasurementsarenotavailable.Finally,bothpassiveandactiveow controltechniqueswillbeimplementedtomitigateopticalaberrationsovertheaperture. 1.5Outline Theremainderofthedissertationisorganizedasfollows.Anin-depthliterature reviewcoveringearlyandrecentowoverturretsalongwithsomeoftheunresolved technicalissuesispresentedinChapter2.Adescriptionoftheexperimentalsetup, 52

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includingwindtunnel,turretmodelparameters,allmeasurementequipment,andvarious experimentaltechniquesisprovidedinChapter3.Baselineuiddynamicresultsincluding steadyandunsteadypressuremeasurements,oilowvisualization,hot-wireanemometry, particleimagevelocimetryandaero-opticmeasurementsarediscussedinChapter4. Controlexperiments,includingbothpassiveandactiveeortsaresummarizedinChapter 5.Finally,inChapter6,conclusionsfromcurrentexperimentsaresummarizedandthen futureworkisproposed. Figure1-1.Sourcesofopticaldegradationincludethedevicethatpowersthelaser,a beamcontrolsystem,aero-opticalinteractions,andatmosphericpropagation eects. 53

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Figure1-2.Eectofnear-eldowfeaturesonlaserintensity.Anyindexofrefraction uctuationcanleaddirectlytoascatteringoflaserbeamenergycausinga decreaseinfar-eldintensity. Figure1-3.Genericturretmodels.AHemispherewithconformalwindowmountedona cylindricalbase.BSurfacemountedhemispherewithconformalwindow.C Hemispherewithatwindowmountedonacylindricalbase.DSurface mountedhemispherewithatwindow. 54

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Figure1-4.Turretmodelgeometricparameters.Ahemisphericalcapwithdiameter D and agenerallyaft-facingaperturewindowofdiameter d ismountedona hemisphericalbaseofheight H .Thedirectionoftheaftfacingwindowis characterizedbyazimuthalandwindowangles, and ,respectively.The complimenttothewindowangleisdenedas =180 o )]TJ/F22 11.9552 Tf 11.955 0 Td [( Figure1-5.Separationovera2-Dcurvedsurface.Astheowencountersanadverse pressuregradient @P=@s ,thenitekineticenergyofthetheuidparticlesis notenoughtoovercometheresistiveforces,causingdecelerationandnally separation 55

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A B Figure1-6.Three-dimensionalseparationrequiresaglobalviewoftheowpatternsand wherethenetworkofsurfacestreamlinesmustbeobserved.A Three-dimensionalboundarylayerinacrossowwiththepresenceofa transversepressuregradient.AdaptedfromLu etal. 2010.BResulting unidirectionalskewingdiagramatpointB.AdaptedfromWhite2006. Figure1-7.Limitingstreamlinesalongayawedairfoil.Asowreachestheleadingedgeof athreedimensionalobject,thestreamlinesclosetothesurfacerstmeetin theformofanattachmentline.Thesestreamlinesthenconvergeand eventuallydivergeattheseparationline.Whenseparationoccursina three-dimensionalsense,theseparationlineisanenvelopeofconverging limitingstreamlines.AdaptedfromLu etal. 2010. 56

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Figure1-8.Limitingstreamlinesnearthree-dimensionalseparationline.Alimiting streamtubeisformedbytwolimitingstreamlinesataheight h abovethe surfaceanddistance n apart.Asthelineofseparationisapproached,the distance h increases,whichmeansthatthelimitingstreamlinescannolonger representskinfrictionlinesasproposedbyLighthill1963.Adaptedfrom Tobak&Peake1982. Figure1-9.Theowoverathree-dimensionalturretishighlycomplex.Athe two-dimensionalboundarylayerconvectsdownstream,wrapsitselfaroundthe leadingedgeoftheturret,andcreatescounter-rotatingstreamwisevortices. Theowdetachesintheaftsectionduetoboththepresenceofanadverse pressuregradientandthree-dimensionaleects.Theseparationregionhas largecomponentsofvelocityinallthreedirectionsand,forasurfacemounted model,interactswiththehorseshoevortexcreatingacomplexowinthewake region.AdaptedfromSavory&Toy1986. 57

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Figure1-10.Sourcesofaero-opticaldegradationatlowsubsonicowsinclude:1inviscid phenomenacausesdefocusingeectsthatcanbecorrectedwithcurrent adaptiveoptictechniques.2Boundaryandshearlayerswithscalesthatare atleastanorderofmagnitudesmallerthanawavefrontbeamdiameterand resultinscatteringthebeamenergyatwideangles.3Separatedregionwith lengthscalesontheorderoftheaerodynamicbodythatcauseanoticeable changeinthebeampathandintensity. Figure1-11.Interactionofwavefrontwithpotentialoweldaroundaturret.Theglobal eectisthatofanaberratedlensthathasafocallengthgivenby f = R 1 = 1 )]TJ/F22 11.9552 Tf 11.955 0 Td [( 0 where R isthecurvatureoftheow 1 isthelocaldensity, and 0 isthefreestreamdensity.Thesedefocusingeectscanbecorrected withcurrentadaptiveoptictechniques.AdaptedfromGilbert&Otten 1982. 58

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Figure1-12.Planarwavefrontandprobebeamdistortionmechanismthroughavariant indexofrefractionow.Ontheright,asampleofbothbothun-aberrated andaberratedoweldsasseenbythephotographicplateorposition sensingdevice.AdaptedfromJumper&Fitzgerald2001. Figure1-13.Malleyprobeschematicusedtoquantifyopticaldegradationinaoweld.A CWbeampassesthroughabeamsplitterandtheresultingbeamsare directedthroughtheowontoaatmirrorthatthenreectsthebeams coaxiallybacktoafocusinglens.Eachbeamispassedtoapositionsensing devicewhichmeasuresthebeam'scentroidpositionasafunctionoftime.. 59

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Figure1-14.OPD rms valuesforasurfacemountedconformal-windowedturret.All experimentalvalueswereextractedfromVukasinovic etal. 2008and Vukasinovic etal. 2009 b .Avalueof A =2 : 6 m/mwasusedfortheallts. Figure1-15.OPD rms valuesforaconformal-windowedturretmountedonacylindrical base.Theexperimentalvaluesmarkedwith wereextractedfromGordeyev etal. 2009,Vukasinovic etal. 2009 b ,Gordeyev etal. 2010 c ,Vukasinovic etal. 2010 b ,andVukasinovic etal. 2010 a whileexperimentalvalues markedwitha wereextractedfromGordeyev etal. 2006andGordeyev etal. 2007.Avalueof A =0 : 9 m/mwasusedfortheallts. 60

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Figure1-16.OPD rms valuesforatwo-dimensionalsurfacemountedcylinderwithat window.AllexperimentalvalueswereextractedfromGordeyev etal. 2005 andGordeyev etal. 2010 b .Avalueof A =1 : 7 m/mwasusedfortheall ts. Figure1-17.Thecategorizationofapproachestoowcontrolisbasedonhowtheenergy istransferredintotheow.Thehierarchystartswithpassiveandactive control,wherethelatterrequiresenergyexpenditurefromanexternalsource. Open-loopcontrolusesapre-determinedinputintothesystemandhenceno sensingofowfeaturesisrequired.Closed-loopcontrolrequiressensingto determinetheoutputofanactuator,inturnaectingthesensorthroughthe dynamicsofthephysicalmodel.AdaptedfromCattafesta etal. 2008 b 61

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Figure1-18.Theuseofvortexgeneratorscanbeusedtoentrainuidfromthefree-stream intotheboundarytodelayorsuppressseparationoveranitewing. AdaptedfromNorberg&Ulla2002. Table1-1.PrimarydimensionsofOPD rms dimensionalparameters ParameterMLt OPD rms 010 d 010 D 010 H 010 000 000 010 1-1-1 1-30 SL 1-30 010 c 0 01-1 U 1 01-1 62

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CHAPTER2 LITERATUREREVIEW Thischapterprovidesabackgroundliteraturereviewofpreviouswork.Therstpart ofthechapterdealswithearlyliteratureregardingtheowoveradome-likestructure. Then,researchonearlystudiesofowoveraturretprotuberanceandaero-optical distortionareaddressed.Next,somerecentworkconcerningthebaselineowover dierentturretmodelsarepresented.Thelastportionofthischapterreviewsvarious passiveandactiveowcontroltechniquesthathavebeenattemptedtobothsuppress owseparationandreduceopticaldistortions.Unlessotherwisestated,allReynolds numbersaredenedwithrespecttotheturretdiameter,D,andthefreestreamvelocity, U 1 .Forthoroughness,abriefsummaryofpertinentstudiesisalsosummarizedintables correspondingtoeachsectioninthischapter. 2.1OriginsofFlowoveraTurret Earlystudiesfocusedontheowoverahemisphericalobjectwiththemainattention placedonowfeatures.Thissectionfocusesonahandfulofexperimentsandsimulations thatsetthegroundworkforfuturethree-dimensionalowseparationandaero-optic distortionexperiments. 2.1.1EarlyLiteratureonFlowsoverHemisphericalObjects Someoftherstexperimentsinowoverahemispherewereconductedtostudythe eectoftheearth'sboundarylayerondome-likestructures.Albeitnotdirectlyrelated toaero-opticphenomena,thesestudiesprovidesignicantinsightonseveralowfeatures ofinterest.Thoseinvestigationsthataredirectlyrelatedtoatmosphericboundarylayers overgenerichemispheresaresummarizedinthissectionandarelistedinTable2-2. Toy etal. 1983wereoneofthersttostudytheeectofturbulentintensityin theboundarylayeronasubmergedhemisphere.Adomehemisphereof25 : 5cmwas immersedintwothickturbulentboundarylayersofdierentmeanvelocityandintensity proleslabeledasthin"andthick".SeeTable2-1fordetailsonthetwoboundary 63

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layerparameters.AllexperimentswereconductedataReynoldsnumberof1 : 6 10 5 Resultsfromstaticpressuremeasurementsrevealedthataroughturbulentboundary layerproducedlowerpressureintheforeregionandhigherpressureintheaftregionof thedome,indicatingadownstreammovementinseparationlocation.Amoreinteresting resultwasnotedwhencomparingthereattachmentpointofthereverseowbehindthe dome.Forthecasewherethedomewasentirelysubmergedwithintheboundarylayer, thereattachmentpointwaslocated1 : 0diametersdownstreamfromthecenterofthe model.However,resultsfromOkamoto1980showedthatthereattachmentpointfor adomeonasplitterplate,suchthattheboundarylayerismuchsmallerthanthedome height,waslocated2.0diametersdownstreamofthecenterofthemodel.Theseresults clearlyindicatetheinteractionoftheowaroundthehemisphereandtheturbulent boundarylayercauseaconsiderablereductioninthelengthoftherecirculationregion. In1986,Savory&Toywerethersttostudytheowdownstreamofahemisphere intheeldofindustrialaerodynamics.Theexperimentswereconductedwithboth surface-mountedhemisphereD=19cmandhemisphere-cylinderH=4cmmodelsin threedierentboundarylayers.Pressuredistributionsprovidedevidencethattheow developmentonahemispherewerecomplicatedbytheeectsofprolesofvaryingmean velocityandturbulenceintensity.SavoryandToyalsousedapulsed-wireanemometer systemtoacquirethree-dimensionalmeananductuatingvelocitycomponentsinthe near-wakeregion.TheyconcludedthattheupstreamboundarylayerconditionsseeTable 2-1forparametersdeterminedthesizeoftherecirculationregionaswellasthevolume oftherecirculatinguid.ResultsagreedwithpreviousndingsbyToy etal. 1983. Areattachmentlengthof1.1diametersdownstreamfromthecenterofthemodelwas foundforamodelsubjectedtoaturbulentboundarylayerwhilethereattachmentlength increasedto1.25diametersdownstreamwhenthemodelwassubjectedtoasmooth" boundarylayer.Itwasconjecturedthatamoreturbulentboundarylayerproduceda 64

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thickeningeectontheseparatedshearlayer,thuscausinggreatershearlayercurvature andareducedrecirculationregion. Someofthemorerevealingqualitativeresultsofthenear-wakeowstructuresalso camefromexperimentsbySavory&Toy1986onaD=40cmhemisphereinawater tunnelatRe D =1 : 6 10 3 .Fromtheanalysis,thecomplexowregimewasbrokendown intocontributionsfromthehorseshoevortex,boundarylayer,andshearlayer. Inthefollowingdecade,Taylor1992consideredtheuctuationsofstaticpressure createdbyowoveradome.Staticpressuresweremeasuredat7 : 5 o incrementsfordomes withheighttodiameterratiosof1,1 = 2,and1 = 3aswellasReynoldsnumbersbetween 1 : 1 10 5 and3 : 1 10 5 .SeeFigure2-1foraschematicofeachmodelinvestigated.Taylor foundthatforallthreedomeshapedmodels,iftheturbulenceintensitywasgreater than15%asisexperiencedinanaturalwindboundarylayer,thenthestaticpressure measurementsbecomerelativelyinsensitivetoReynoldsnumberforRe > 1 : 7 10 5 .More importantly,thestandarddeviationofthepressurecoecientattheseparationlocation recordedforthelargerheighttodiameterratiowaslargerinmagnitudethanthatofthe lowerheighttodiameterratiomodel. Thestudiessummarizedinthissectionwereonlyasmallportionoftheoverall literaturethatwascompiledinthe`80sandearly`90s.Althoughnoneofthepresented workdirectlyrelatedtotheaero-opticsproblem,ithasprovidedsignicantinsightinto thecharacteristicsofowoverdomeshapedobjectsubmergedinaboundarylayer.These studiesindicatethatthereisanimportantinteractionbetweentheupstreamboundary layerandtheoverallowfeatures.Specically,theworkshowedthatincomingturbulent boundarylayersresultedinareducedrecirculationregion.Moreimportantly,itwasfound thatthecomplexowregimecouldbeassessedasthecontributionsfromthreefactors: theincomingboundarylayer,theseparatedshearlayer,andthehorseshoevortex. 65

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2.1.2FlowoverTurretProtuberance Thissectiondescribestheexperimentsconductedintheearly1980'srelatedtothe aero-opticsproblemandaretherstsetofexperimentsthatattempttocharacterizeand controltheowaroundahemisphericalshapedturret.Thesestudiesaresummarizedin Table2-3. In1981,Craigpublishedasystematiclistdetailingvariousowcontrolmethodsfor owoveranairborneturret.InanalreviewfortheAirForceWeaponsLaboratory,he reportedbotharelevancebetweentheaerodynamicsandaero-opticsproblemsaswellasa simpliedobjectiveforturretowcontrol: Controlofowseparationfromtheoutermostpartoftheturret,and theresultantdevelopmentoftheturretwake,willresultinimprovedenergy propagationparticularlyforafttargets.Inaddition,theoveralldragandow instabilityresultingfromtheturretcanbereducedbythesamemethodswhich improvetheopticalcharacteristicsoftheow ::: Theowcontroldevice shouldimprovetheopticalqualityofturretow,particularlyforaft-loading turretangleswhereseparatedowisasevereproblem.Theopticalqualityof theturretowisdeterminedsimplybythemagnitudeandscaleofthedensity uctuationandthetotalpathlengthoftheturbulencealongthebeam.To improveopticalqualityinthemoststraightforwardmethodwouldbesimplyto reducethethicknessoftheturbulentregion. Craigalsoreportedpreviousowcontrolndingsregardingowoverairfoilsandtheir relevantapplicationtoowoveraturret.Heconcludedthathigh-liftairfoilowcontrol technologycanbeconceptuallyappliedtoowcontrolofowoveranairbornelaser. Table2-4summarizesthescreeningprocessproposedbyCraigforturretowcontrol conceptsinanearlyincompressibleMa < 0.4andcompressibleMa > 0.4ow. deJonckheere etal. 1982wereoneofthersttoprovideanin-depthanalysisof thecomplexowaroundaturret.Experimentaloweldinformationresultsincluded 66

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separationlinelocations,shearlayerlocation,andrmsdensityuctuations.Themodel consistedofaD=40cmhemispheremountedonaH=40cmcylindricalbase.Testing wasdoneoverarangeofMachnumbersfrom0.55to0.75.Inanattempttodescribe thequalitativeaspectsoftheseparatedowregion,deJonckheere etal. implemented adouble-pulsedholographicinterferometrytechnique.Theexperimentreliedontwo photographicsnapshotsmadeonthesamelminrapidsuccessiontodepictwavefront distortionanddynamiceectsoftheow.Totheauthor'sknowledge,thesearethe rstresultstoshowthecomplexinteractionoftheshearlayer,separatedowregion, shockwave,andfree-streamowoveraturret.Frombothintuitionandexperimental results,deJonckheere etal. concludedthattransitionfromlaminartoturbulentowin three-dimensionalboundarylayersisgovernedbybothamplicationofdisturbancesin themainowandthebehaviorofthecross-owcomponent.Anotherkeyresultwas illustratedbytheacquisitionofsteadypressuremeasurements.Thecoecientofpressure atMa=0.55,takenatthelocationwherethehemispheremeetsthecylindricalbase,did notmatchthetheoreticalpredictedvalue.Thisprovidedanindicationthatthislocation isnotastagnationpointandhenceitwasconcludedthatstrongthree-dimensionaleects werepresent. In1982,Schonberger etal. leveragedtheconceptofsuctionwithinthebaseow ofahemisphericalmodeltocreateafavorablepressuregradientontheaftportionofa turret.AturretwithD=42 : 7cmhemispherewasmountedonacylindricalbaseofH=24 : 4 cmandwastestedataReynoldsnumberof3 : 0 10 5 .Figure2-2showshowsteady suctionwasachievedthroughahollowfairingnosepiecelocateddownstreamoftheturret. Visualizationoftuftsontheturretshowedadelayinseparationfrom120 o nosuctionto 150 o m 3 = minsuction.Schonberger atal. alsonotedaattenedpressuredistribution ontheaftsectionoftheturretindicatingatransitionfromadversetoneutralpressure gradient.Similarresultswereobtainedwithdierentfairinggeometries. 67

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Purohit etal. 1983 a wereoneofthersttoconductnumericalinvestigations regardingowcontrolaroundaturret.UsingthecompressibleNavierStokesequations, theysolvedfortheoweldaroundasphericallycappedturretmountedonaat surfaceataMachnumberof0 : 6.Theanalysiswasperformedontwomodels.The rstwasaturrettreatedasasolidshell,whilethesecondconsistedofaporousshell withauniformsuctionrateof0 : 136kg/s.Spectralanalysisshowsadominantpeakat f =350Hz,correspondingtoaStrouhalnumberof0 : 23,similartowhatisexpectedof theseparatedowpastabluntobject.Thenumericalsolutionforthebaselinecasewas comparedtoexperimentalresultsfromRose etal. 1982whichprovidedvalidationfor thecomputationalprocedure.Hisresultsestablishedasignicantvariationinthewake structurecausedbyuniformsuctionattheturretsurface.Uniformsuctionwasnotonly showntoeliminatemostoftheretardeduidparticles,butitalsoreducedtheseparated andreverseowregionssubstantially. 2.2RecentAdvancesinFlowoveraHemisphericalTurret Inthepastdecade,manyresearchershaveconductedexperimentstomoreclosely examinetheaero-opticaldegradationcausedbyowseparationoverturretmodels.Flow andopticalperformancehavebeenassessedforalargecollectionofturretgeometries usingbothpassiveandactive,open-andclosed-loopcontrolmethodologies.Before discussingrecentowcontrolresults,therstsectionfocusesonstudiesthatsolely describethebaselineowi.e.nocontroloverahemisphericalturretmodel.Allstudies aresummarizedinTables2-5,2-6,2-8,and2-9. 2.2.1BaselineCharacterization Thissectionfocusesonexperimentsthatdescribethebaselineowovera hemisphericalturret.Table2-5summarizesallexperimentsdiscussedinthissection. Oneofthefewexperimentalinvestigationsthatfullycharacterizedthe three-dimensionalwakeregionbehindahemispherewasconductedbyLeder etal. 2003.Themodelconsistedofacylinder-mountedhemispherewithatotalheight 68

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H=218mmtodiameterD=109mmaspectratioof2.0.Thestudymeasuredallthree componentsofvelocityusingLaserDoppleranemometry.Allexperimentswerecarried outatRe D =2 : 0 10 5 Ma=0.08.Thescanningvolumewasspreadtothreediameters behindtheturretandonediameterabovetheapexandconsistedofapproximately20000 measurementpositions.Thetime-averagedvelocityeldshowedthattherecirculation regionenlargesastheyoumovefromtheapextothejunctionbetweenthemodel andsplitterplate.Furthermore,thewakeregionisshowntoextendinthestreamwise directiontoapproximatelyx/D=2.40.Thecalculationofturbulentkineticenergyshows thatuctuationsincreasedasthestreamwisedirectionincreased,withamaximumnear thebackendoftherecirculatingregion. Fewexperimentshavebeenconductedonturretmodelswithaatwindowas opposedtoaconformaltypewindow.Aninvestigationonsuchamodelwasconducted byGordeyev etal. 2004 b focusedonthebaselinecharacterizationusingbothhot-wire anemometryandaero-opticalmeasurements.Themodelconsistedofa30cmdiameter hemispheremountedona10cmtallcylindricalbasewithaslopediscontinuityof27 : 5 o betweenthehemisphereandtheatwindow.Aatmirrorofdiameter14cm,usedfor theaero-opticmeasurements,wasplacedintheatportionoftheturret.Themodelwas orientedatdierentazimuthanglessuchthattheatwindowwaseitherperpendicularto theoncomingow =90 o orslightlydownstream =100 o and110 o .Malleyprobe experimentsshowedthat,betweenthetestedMarangeof0.3-0.5,theopticaldistortion increasedwithincreasingazimuthangle.Resultsfromopticalmeasurementsshowed degradationofpeakintensityinthefareldthatscaledwithMa 2 .Hot-wiredataand opticalmeasurementresultsbothdemonstratedthattheconvectivespeedsoftheunsteady structureswereintherangeof0.6to0.8ofthefree-streamspeed.Mostimportantly,they concludedthatthemaincauseofopticaldistortionsaregovernedbytheseparatedshear layerintheadversepressuregradientregionoftheturret.Gordeyev etal. alsosuggested 69

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thatowcontrolstrategiesusedinowoverabackward-facingstepcouldbesuccessfulin reducingopticaldistortionsoveraturretmodel. Inamorerecentstudy,Gordeyev etal. 2007focusedontheowenvironment aroundaturretwithaconformal-typewindow.Theowarounda30 : 5cmhemispherical modelmountedona11 : 4cmbasewascharacterizedatMa=0 : 35 ; 0 : 40and0 : 45.They usedsurfaceoilowtechniquestovisualizethecomplexstructureofthewakelocated downstreamofthemodel.Thevisualizationofstreaklinesowingupstreamaftofthe modelrevealedtheformationofarecirculatingstructure.Anunsteadypressureport locatedonthecylindricalbaseatanazimuthangleof =135 o showedthevortex sheddingbehindtheturrettooccuratanon-dimensionalfrequencyofSt D =0 : 35. Gordeyev etal. alsousedaMalleyprobeandShack-Hartmannsensortoevaluate theaero-opticaldistortionsintheoweld.Deectionanglespectraresultsforlarge back-facingelevationanglesshowtheformationoftheshearlayeranditspeakataround 2kHz.AgreeingwithearlierndingsGordeyev etal. 2004 b ,theconvectivespeedofthe shearlayersstructureswerefoundtobe0 : 8ofthefree-streamspeed.BoththeMalley probeandShack-Hartmannsensorsshowedthat,forelevationanglesgreaterthan120 o =180 o )]TJ/F22 11.9552 Tf 10.238 0 Td [( fromFigure1-4,theshearlayerwasthedominantstructurerelevanttooptical distortions. Sluder etal. 2008wereoneoftheonlyrecentinvestigationstoresearchtheeect ofturretheighttodiameterratio H=D onbothaerodynamicloadsmeasuredwith abalanceandstaticpressurealongthemodel.A24cmdiameterhemisphere,ush mountedonavariableheightcylindricalbasewasusedasthemodel.Resultsfrom experimentsrunatRe D =9 : 5 10 5 showedthatthecoecientofliftdecreasedinan almostlinearfashionas H=D wasincreased.Also,bothaerodynamicloadsmeasured coecientofliftanddragwerenotReynoldsnumberdependentwithintheregion tested,3 : 5 10 5 < Re D < 1 : 1 10 6 .Aninterestingphenomenaregardingthepressure distributionasafunctionof H=D wascaptured.Whilethepressureattheapexofthe 70

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turretwasrecordedtobelowerforhigher H=D values,thepressurerecoveryalsooccurred soonerfurtherupstreamthanthatforthecasewheretherewasnocylindricalbase. Veryrecently,Porter etal. 2013publishedresultsforin-ighttestsofahemisphere oncylinderat-windowturretusingNotreDame'sAirborneAero-OpticsLaboratory AAOL.FormorespecicsontheAAOL,pleaserefertoJumper etal. 2012.In thisunprecedentedstudy,theAAOLprovidedtheuniquecapabilityofmeasuringthe fullrangeofbothazimuthandelevationangles,mostofwhicharenotavailableinthe windtunnelsetting.TwoCitationsewinformation,approximately50mapart.For allexperiments,themodelusedhadadiameterof30.5cm,10.2cmaperture,andwas mountedona10.2cmcylindricalbase.AlldatawasacquiredforMa=0.5.A10.1cm beamwasgeneratedinoneaircraftandsenttotheother,whereitpassedthroughthe aperturetoafaststeeringmirrorsystemthatremovedmechanicalvibrations,andthen theresultingbeamwasmeasuredbyahigh-speedShack-Hartmannsensorcapableof acquiringdataat25kHz.TheOPD rms wascalculatedforelevationanglesranging from60 o to125 o .AlocalmaximuminOPD rms wasobtainedforanelevationangleof approximately100 o withlargervaluesonlyoccurringforviewinganglesgreaterthan115 o Thisdatawasnon-dimensionalizedbyMa 2 D andthencomparedtolimitedwindtunnel teststakenatdiscreteviewingangles.Whilethetrendsaresimilar,itwasnotedthatthe localpeakinOPD rms shiftsupfrom100 o toapproximately110 o .Theauthorsattribute thistotunnelblockageeects s 10%,possiblycausingtheowtoseparateatadierent locationascomparedtotheighttests. 2.2.2PassiveControl Thissectionfocusesonexperimentsthatdescribecontrolmethodsinwhich onlypassivedeviceswereusedforowcontroloverahemisphericalturret.Table2-6 summarizesallexperimentsdiscussedinthissection. Someofthefewinvestigationscompletedinthelate1990sandearly2000sincluded passivecontroltoreducethedragcausedbythedominantvorticesshedoofaspherical 71

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turret.Similarapproachescanbeleveragedforaero-opticandthree-dimensionalow separationexperiments.In2000,Snyder etal. researchedtheeectofdierentsized splitterplatesandfairingsonahemispheremountedonacylindricalbase.Thepurpose oftheinvestigationwastocharacterizetheow-eldusingtuftsforowvisualization andsteadypressuretapsfordragandpressurerecoverymeasurements.Theturretmodel usedwasa23cmdiametersphereblendedtoa20cmdiametercylinder.Alltestswere ataReynoldsnumberbetween3 : 0 10 5 and9 : 0 10 5 ,correspondingtoamaximum Machnumberof0 : 19.Resultsfromthetuftsshowedthatthesplitterplatedidnotalter theseparationpointontheturret.Whilethesplitterplatedidnotproduceanypressure recoveryintheseparatedregion,itwasabletoreducethestrengthofthevorticesshed fromthesidesoftheturret,asnoticedfromowvisualization.Moreimportantly,afairing attachedtotherearsectionofthemodelwasabletocreatealargepressurerecoveryalong thetopandsideoftheturret. Insomerecentwork,Gordeyev etal. 2005andhiscolleaguesexploredtheeectof dierentpassivedevicesplacedupstreamofatwo-dimensionalturret-likemodelonthe optical-propagationenvironment.ThemodelshowninFigure2-3withdimensionswas asimplied,two-dimensional,at-windowedturretthatallowedthemtoinvestigate theseparatedowovertheturretwithoutintroducingthemorecomplicatedow patternspresentinthethree-dimensionalcase.Aseriesofexperimentswereconducted .4 < Ma < 0.8withthemodelatvaryingelevationangles =92 o )]TJ/F15 11.9552 Tf 9.298 0 Td [(150 o .Several passivecontroldevicesseeFigure2-3Bwereusedinanattempttoreducetheoptical degradationintheow.Thedevicesvariedinheightfrom h= =1to5,where isthe heightoftheincomingboundarylayer.Smallscalespanwisedisturbancescausedbypins andsmallvortexgeneratorsshowedpromisingresultsatlowelevationangles o )]TJ/F15 11.9552 Tf 12.072 0 Td [(105 o However,athigherangles,theywereunabletochangetheseparatedowdynamicsaftof themodelandhencetheopticalenvironmentdidnotimprove.Largervortexgenerators, 72

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ontheotherhand,producedcounter-rotatingstreamwisevorticesintheseparatedregion thatcreatedastrongerwakeresultinginanincreaseinopticalaberrations. In2007,Vukasinovic&Glezerfocusedonpassivemodicationofahemisphereon cylinderturretbytheadditionofapartitionplate.Allexperimentswereconductedwith a30 : 8cmhemispheremountedona9 : 5cmcylindricalbasewithanominalReynolds numberof8 10 5 ,correspondingtoaMachnumberof0.12.Aschematicofthemodel isshowninFigure2-4.Apartitionplatedividedthehemispheretopfromthecylindrical baseandwasusedtodecoupletheinteractionofthehemisphereandcylinderwakes. Staticpressureresultsforthemodiedturretalongthecentralplaneshowedthatwhile therewasnochangeinseparationlocation,theowalongthemodiedturretaccelerated moredownstreamoftheapexoftheturret.Also,asharpincreaseinpressurewasnoted atthejunctureofthehemisphereandsplitterplate.Theauthorssuggestedthatthis couldbeassociatedwitharecirculatingbubblethatformsatthejuncturebetweenthe hemisphereandsplitterplate. Inafollow-upstudytotheirownworkfrom2005Gordeyev etal. 2005, Gordeyev etal. 2010 b testedtheuseoflargecylindricalpinslocatedupstreamofa two-dimensionalturret-likemodelwithaatwindow.RefertoFigure2-3Aforadrawing oftheirexperimentalsetup.Themeasuredboundarylayerheightlocatedat1.25radii upstreamofthecenterofthemodelwasapproximatelyof =5mm.Intheparametric studyvariouspinswithdiametersrangingfrom d =0 : 1 )]TJ/F15 11.9552 Tf 12.294 0 Td [(0 : 4 ,spacingbetweenpinsof s =0 : 5 )]TJ/F15 11.9552 Tf 12.524 0 Td [(1 ,andheightrangingfrom h =1 : 2 )]TJ/F15 11.9552 Tf 12.524 0 Td [(3 : 2 wereconsidered.Resultsfrom velocityuctuationmeasurementsshowedthattheshorterpins h< 2 thickenedthe boundarylayerbutwereunabletoreducetheintensityofthemainshearlayercausedby theseparationovertheatwindow.Also,pinsthatweretoofarapart s> 0 : 7 formed aweaksecondaryshearlayerwhichdidnotaectthemainshearlayer.Aero-optical measurementswerethenmadetodeterminetheeectivenessofcloselyspaced,longpins. Theonlycongurationtoconsistentlyimprovetheaero-opticalenvironmentreduction 73

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in OPD rms by15-20%foralltestedelevationangleswasapinwiththefollowing parameters: d =0 : 1 s =0 : 5 ,and h =3 : 2 .Theimprovementinopticalenvironment, theymentioned,wasdirectlyrelatedtothereductioninturbulentintensityinthemain shearlayer.Theycontributedthisphenomenatotheinteractionofthemainshearlayer withthesecondaryshearlayercausedbypin. Mostrecently,Reynolds etal. 2012studiedtheeectofseveralgeometric modicationstoahemisphericalturretD=76.2mmwithaatwindow d =25.4 mmmountedonacylindricalbaseH=25.4mm.Allexperimentalmeasurements weretakenatRe D =1 : 93 10 5 ,correspondingtoMa=0.13.Elevencongurations, consistingofcombinationsofdierentturretandbasegeometries,werestudied.Each geometryislistedanddescribedinTable2-7.Oilowvisualizationwasrstusedto assesstheeectofthecontrolonvariouscharacteristiclengthscales.Theseincluded theforestagnationregion,themaximumandminimumwakethicknesses,aswellas theseparationline.Thisworkwassupplementedwithunsteadypressuremeasurements madeatcenteroftheaperturewindow.ResultsshowthatthecombinationofT1and B4alongwithT1andB5,bothproduceductuationsthatwerehigherthanthebaseline owT1andB1.Nocombinationofbaseandhemispheregeometriesshowedsignicant reductioninthermspressure.Particleimagevelocimetrywasthenusedtosupplement thepressurereadings.Thebaselinemodelshowedarecirculationregionthatextendedaa fulldiameterdownstreamfromthebaseoftheturret.Interestingresultswereobtainedfor thegeometricpairingbetweenT4andB1.Resultsshowsthatthismodelwassuccessful atincreasingthesizeoftherecirculationregion,whilebroadeningthewake.Fromthe PIVresults,theauthorshypothesizethatsmalleructuationswithinthelargerseparation regionmaycauseareductioninpossibleaero-opticaberrations. Asaconcludingnote,considerthatwhilemanypassiveowcontroldeviceshave showngreatpromiseinalteringtheow-eldinthewakeoftheturret,itisimportantto 74

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rememberthatanymodicationsmadetothemodelmustnotdiminishtheaft-viewing angle,andhencethefunctionality,oftheturret. 2.2.3Open-LoopControl Intheearly2000's,open-loopcontroldominatedtheaero-opticliterature.Some researchershaveevencombinedpassiveandopen-loopcontrolinanattempttoreducethe opticaldistortioninthenearwakeregion.Thissectioncoverstheworkregardingthese controlstrategiesandtheirresults.AllstudiesaresummarizedinTable2-8. Promisingresultshavebeenpublishedinthepastdecade.Particularly,Vukasinovic etal. 2005implementedhighfrequencyforcingtoreducetheextentoftherecirculating owdomaindownstreamoftheturret.AllexperimentsconsistedofaD=30 : 5cm hemisphericalmodel,ushmountedonthebottomwallofanopenreturntestsection. Themodelwasequippedwithtworowsofsyntheticjetactuatorsthatissuedownormal tothehemispheresurface.ThestudysummarizedresultsfromPIV,hot-wireanemometry, andstaticsurfacepressuremeasurements.AnalyzingPIVresults,theyfoundthatinthe uncontrolledcasethestrengthoftherecirculatingcoreoftheseparatedregionincreased withincreasingRe D .Theseresults,combinedwithstaticpressurereadingsalongthe surfaceofthemodel,indicatedthattheowrstseparatesontheouteredgesofthe turret.Separationinthecentralsymmetricplanewasfoundtooccuratanangular positionof5 o to10 o furtherthanthatinanouterplane.Highfrequencyforcingat St D =20 : 3forRe D =4 : 04 10 5 Ma=0.06andSt D =30 : 5forRe D =4 : 04 10 5 Ma=0.09wasimplemented.Bothcasesresultedinaphysicalforcingfrequencyof f =2075Hz.Theresultsshowedthattheowremainedattachedtothesurface forapproximatelytwentydegreesfurtherdownstreamcomparedtoseparationinthe absenceofcontrol.Resultsalsoshowedthattheeectofhighfrequencycontrolwasmost prominentalongthecentralplane. Twoyearslater,Vukasinovic&Glezer2007publishedworktosupplementearlier ndings.Thenewstudyusedahemispheremountedonacylinderbasemodelandall 75

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datawasobtainedatRe D =8 10 5 withactuationforcedatSt D =15 : 4,corresponding toaMachnumberof0.12andforcingfrequencyof2035Hz,respectively.SeeFigure2-5 foraschematic.Theirstudyfocusedondeterminingtheinuenceofseveralactuation parametersincludingjetmomentumcoecient,angulardistanceofactuatorarrayrelative toseparationpointinthecentralplane,andspanwiseextentoftheactuatorarray.The actuator'smomentumcoecientwasdenedas C = U 2 j A j = U 2 0 A 0 ,where A j and A 0 aretheareasofthejetoriceandturretfrontalcrosssection,while U j and U 0 denote themaximumjetandfreestreamvelocities,respectively.Severallevelsofmomentum coecientwereused, C 10 3 =2 : 8 ; 4 : 4 ; 6 : 1 ; 7 : 9 ; and9 : 8.Notsurprisingly,resultsshowed adirectrelationshipbetween C andtheextentofseparationdelayovertheturret.Next, theyinvestigatedtheactuationpositionrelativetotheseparationpointinthecentral plane.Theactuatorwasplacedat20 o and7 o upstreamand2 o downstreamofseparation. Thelargestseparationdelayresults o delayatcenterlinewereachievedwithactuation applieddownstreamfromseparation.Whilethisdoesnotdirectlyimplythatdownstream actuationyieldsthebestresultsforseparationdelay,itdoesshowthatthereisadirect relationshipbetweenseparationdelayandlocationoftheactuationrelativetothe separationregion.Lastly,theyfocusedonthespanwiseextentofactuationwiththearray located7 o upstreamoftheseparationpointinthecentralplane.Theactuatorarray spanninganangularcoverageof46 o resultedinaseparationdelayof8 o .However,when theangularcoveragewasincreasedto169 o theresultsshowednoseparationalongthe symmetryplaneoftheturretdowntothelevelofthejuncturebetweenthehemisphere andthecylinder. ArecentstudybyVukasinovic etal. 2008usedaD=25 : 4cmhemisphericalmodel mountedonasplitterplatewithowsatfourdierentMachnumbers:Ma=0.3,0.4,0.5, and0.64.Thesplitterplateprovidedtheexperimentalconditionthattheboundarylayer wasmuchsmallerthanthesphereradius.Open-loopowcontrolwasappliedusinga spanwisearrayofhigh-frequencysyntheticjetactuatorswithrectangularoricesoriented 76

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inthestreamwisedirection.Whenactuationwasplacedatanelevationangleof110 o staticpressuremeasurementsalongthecentralplaneshowedaseparationdelayof20 o at Ma=0 : 3whileonlya5 o delayatMa=0 : 5.Malleyprobemeasurements,however,showeda signicantreductionof40%intheopticaldistortionatMa=0 : 4.AtMa=0 : 5thedistortion reductiondroppedsignicantlywhichimpliedadecreaseincontroleectivenesswith increasingMachnumber. Oneofthemoreinterestingapproachestoreducingturbulentenergyinthenear wakeregioncameintheformofbothpassiveandopen-loopcontrol.RecentlyWoszidlo etal. 2009investigatedtheeectofvortexgenerators,triptape,andsuctiononthe turbulentintensityinthewakeregionoftheow.AspherewithD=21 : 6cmwasused intwocongurations.Therstwasacompletehemispherearcangleof180 o andthe otherasubmergedhemispherearclengthof120 o correspondingtohalftheheightof thehemisphereprotrudinginthetestsectionseeFigure2-6A,foraschematicofeach. AllexperimentswereconductedatRe D =2 : 5 10 5 Ma=0.06.Asuctionslotwas locatedalongtheentiretrailingedgeofthemodelatthejunctureofhemisphereand thetunneloorfromanazimuthalangleof =90 o through270 o .Theyfoundthat applyingsuctionaloneovertheentirespanoftheslotresultedinthecompleteremoval ofthehorseshoevortex.Byalsousingtriptapetothickentheincomingboundarylayer, theowstayedattached26 o furtherdownstream,therecirculationregioninthewake regionshrunk,andthehorseshoevortexwascompletelyeliminated.Furtherinvestigations usedvortexgeneratorsupstreamofthemodeltogeneratevorticesopposingthehorseshoe vortexseeFigure2-6B.Theseresultedinanoverallreductionofnormalizedturbulence intensityofroughly60%whencomparedtothebaselinecase.Totheauthor'sknowledge, Woszidlo etal. aretheonlypublishedstudyintherecentliteraturetoapplysuctioninan attempttoreducetheeectofthehorseshoevortexinthewakeowregion. AstudybyVukasinovic etal. 2009 b focusedondeterminingtheeectsofdirect small-scaleactuationontheaerodynamiccharacteristicswithinthenearwakeofaturret 77

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forRe D =4 : 46 10 6 Ma=0.3.Figure2-7showsaschematicofthe61cmhemisphere mountedona18 : 3cmcylindricalbase.Atotalof36syntheticjetactuatorswere distributedinthreerowsaroundtheconformal-typewindow.Thesinusoidalexcitation frequencywaskeptatSt D =3 : 9forallexperiments,correspondingtoaphysicalfrequency of1600Hz.Theactuationstrengthwasvariedover3 : 7 10 )]TJ/F21 7.9701 Tf 6.587 0 Td [(4
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modulatedwithasquarewaveat f AM =100Hzwitha50%dutycycle.Resultsshowed that,comparedtothebaselineow,themodulatedsignaldidnotaectthelocationof theseparationlocationinthecentralplane.However,duetothedissipativeeectsof thehigh-frequencyactuation,PIVresultsshowedadecreaseinthelevelsoftheturbulent kineticenergydistribution.Furthermore,hot-wireresultsinthewakeregionshowed acleardecreaseintheenergyalongallscales,exceptattheforcingandmodulating frequenciesandtheirharmonics. Oneofthelatestattemptsatregularizingtheturbulentowinthewakeregionof at-windowedhemisphericalturretwasmadebyAndino&Glezer2010.Thisstudy focusedonthelowspeedowMa=0 : 10,Re D =3 : 0 10 5 overa15 : 24cmdiameter hemispheremountedona10 : 16cmhighcylindricalbase.Theataperturemeasured7 : 11 cmindiameterandwasplacedatanelevationangleof120 o .Therewere11actuators radiallydistributedaroundtheupstreamportionoftheataperture.Twoactuation signalswereused:1apuresinewave,forcedataSt D =12 : 2 f =2480Hzand2an amplitudemodulatedsinewave,withmodulatingfrequencycorrespondingtoSt D =1 : 5 f =305Hz.CalculationofSt D wasbasedonturretdiameterandfree-streamspeed. Time-averagedPIVresultsalongthesymmetryplaneshowareductionintheReynolds stressof28%and10%whenusingamodulatedandsingletonesinewaveastheactuation signal,respectively. In2010,Vukasinovic etal. 2010 b combinedtheeectsofapassiveandopen-loop controlbyusingafrontmountedsplitterplatealongwithanarrayofactuators.They termedthismethodhybridcontrol".Themodelusedwasaslightlymodiedversion oftheoneusedinVukasinovic etal. 2009 b seeFigure2-8.Forallactivecontrol cases,theactuatorswererunattheirresonantfrequencyof1600Hzcorrespondingto St D =9 : 8atMa=0 : 3.Thesplitterplate'spurposewastoalterthetheinteraction betweentheoweldaroundthehemisphericalturretandthehorseshoevortexgenerated fromthecylindricalbase.Whentheplatewasusedwithoutactivecontrol,surface 79

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oilowvisualizationimagesshowedalargereductioninthewakerecirculatingregion downstreamoftheturretbyabout30%atMa=0 : 3aswellasaseparationdelayof 20 o atthesymmetryplane.Comparingseparationdelayresultsusingstaticpressure measurements,theynoticedthatthesplitterplatehadamoreprofoundeectthan activecontrolbyitself.However,hybridcontrolproducedthebestresults.Hot-wire anemometrywasconductedinseverallocationsinthewakeregionandfrequencyspectra wascalculated.Fromtheseresults,theyconcludedthatthethesplitterplateinduceda localeectthatvariesalongtheshearlayer,whiletheactivecontrolproducesaglobal reductionofthebroadbandenergyinthevelocityuctuations. Inafollow-uppapertoVukasinovic etal. 2010 b ,Gordeyev etal. 2010 c conducted experimentswithatwo-dimensionalShack-Hartmannsensortocharacterizetheoptical distortionsinthepresenceofactivecontrol.AlldatapresentedwasfortheMa=0 : 3case. Elevationanglesintherangeof129 o )]TJ/F15 11.9552 Tf 12.014 0 Td [(148 o weretested.Theuseofalargepartitionplate alonecausedareductioninthelevelsofopticaldistortionbyasmuchas33%.However, theyreportedthattheactivecontrolbyitselfonlyreducedtheopticaldistortionby22%, comparedtothebaseline.Hybridcontrolwasabletoreducetheopticaldistortionbyas muchas42%.Oneofthemorecompellingndingsfromthisreportwasthatwhenusing hybridcontrol,thelevelsofopticaldistortionbecameindependentoftheelevationangle. Thiswasmostlikelyduetothefactthathybridcontrolfullyattachedtheowaroundthe aperturefortheelevationanglerangethatwasstudied.Theresultsfromtheprevioustwo studieshaverecentlybeencombinedintoasinglejournalpaperVukasinovic etal. 2013. 2.2.4Closed-LoopControl Onlyrecentlyhastheturretcommunitystartedtoexploreclosed-loopcontrol techniques.Thissectionbrieydiscussessomeoftherecentexperimentswhichare summarizedinTable2-9. Recentlyin2008,Wallace etal. andhiscolleaguesinvestigatedtheeectof closed-loopcontroltoreducepressureuctuationsoverthewakeofaatwindowed 80

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turret.A30 : 48cmdiameterhemisphericalturretwitha12 : 7cmatapertureviewing angleof120 o wasmountedona12 : 7cmhighcylindricalbase.Alltestcaseswererun ataMachnumberbetween0.3and0.4,correspondingtoReynoldsnumberof2 : 0 10 6 and2 : 8 10 6 ,respectively.Anarrayof17syntheticjetsseeFigure2-9forlocations, withresonantfrequencyof2600Hzandmaximumvelocityoutputof50m/s,werealigned aroundtheataperture.AproperorthogonaldecompositionPODmethodwasusedin whichalargedatabaseofsurfacepressuresalongthewindowwasusedtocreateasystem modelforcontrolpurposes.Asimplefeedbackcontrollerwasusedinanattempttoreduce pressureuctuationsovertheaperture.Thecontrollersignalwasoftheform u t = )]TJ/F22 11.9552 Tf 9.298 0 Td [(K M X i =1 a i t # sin f 0 t )]TJ/F22 11.9552 Tf 11.955 0 Td [(t 0 {1 where K isaconstantfeedbackgain, a i M i =1 arethecoecientsfromthePODbasis, f 0 is thecharacteristicfrequencyoftheactuators,and t 0 isaphaseshiftusedtocompensate foranytimedelaybetweentheactuatorsandsensors.Comparingbaselineandcontrol pressureuctuations,an18 : 1%reductioninthermspressureontheataperturewas observed.Autocorrelationsofthepressureswereplottedandtheauthorsnotedthat theintegraltimescalesassociatedwiththeowovertheapertureweresmallerforthe controlledcasewhencomparedtothebaselineow,indicatingareductioninturbulent intensitynearthewindow. InanextensiontoWallace etal. 2008,Wallace etal. 2009usedbothopen-loop andaPODbasedclosed-loopcontrolmethodinaneorttoreducethepressure uctuationsoverthewindowaperture.Anon-dimensionalfrequencywaspresented, f + = f act x ref U 1 {2 where f act istheoscillationfrequency,x ref isthearc-lengthdistancebetweentheactuators andthebackoftheturret,and U 1 isthefreestreamvelocity.Althoughnoquantitative datawaspresented,itwasshownthatopen-loopcontrolat f + =2resultedinasmall 81

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reductionoftheunsteadypressureamplitude.Theyalsonoticedthatcertainactuation signalsresultedinincreasedunsteadypressureinthewakeregion.Forclosed-loopcontrol asnapshot-basedPODmethodproposedbyRowley2005wasappliedtotheunsteady pressuredata.Atotalof5,900snapshotsresultedfrombaselineandactuatedcases.A simpleproportionalfeedbackcontrollerseeEquation2{1wasimplemented,andresults showedanorderofmagnitudereductionintheintegraltimescalesoftheowoverthe aperture.Fromautocorrelationsofthepressuresignals,theauthorsconcludedthatthe theirclosed-loopstrategydrovetheowtohomogeneity,againimplyingareductionin turbulentintensityinthewakeregion. 2.3UnresolvedTechnicalIssues Thischaptersummarizedoverthirtystudiesthatdealtwiththecomplexowover variousthree-dimensionalturretmodels.Theliteraturefocusedontwogroupsofmodels: apartiallysubmergedsphereandahemispheremountedonacylindricalbase.Eachgroup ofmodelseitherhadaatorconformalaperture.Surprisingly,therewasnoworkdone onthecongurationofowoverasurface-mountedhemispherewithatwindowwhere thethicknessoftheupstreamboundarylayeriscomparabletothehemisphereradiusas expectedoveranaircraftturretforwhichtheoncomingboundarylayerthicknessisonthe orderoftheturretradius. Ofthepaperscited,overtwentyinvestigatedaturretwithconformal-typeaperture, whileonlyseveninvestigatedaturretwithaataperture.Oftheseventhatresearched theataperturedesign,notonedealtwiththecasewheretheturretwassurface mounted.Althoughthedatacollectedfromtheliteratureimpliesthatsurfacemounted modelswithatwindowsarelikelytoprovidethemostopticalaberrationsinthenear wakeoftheturret,thereisverylittlequantitativedataregardingthisconguration. Moreworkisneededinthisareatofullyunderstandthecomplexthree-dimensionalow characteristicsaroundsuchamodel. 82

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Sincetheinterestinopticaldegradationcausedbyowoverthree-dimensional modelshasonlybecomepopularlateinthepastdecade,itisnotsurprisingthat themajorityofinvestigationsattempttoleverageowcontrolstrategiesthathave previouslybeenusedfortwo-dimensionalows.Furthermore,evenwhencontrolisbeing implemented,aclearmetrictoassesstheeectivenessofcontrolontheaero-opticeld hasyettobedetermined.Infact,mostofthepreviousworkhasaggressivelytackled theproblemviaseparationcontroltechniques.Whilethismaybeaviablemethodto useforaconformal-windowturretmodel,thegeometricdiscontinuityimposedbya at-windowturretmaynotlenditselfwelltothisapproach.Instead,amorefundamental understandingoftheunderlyingowphysicsaroundaat-windowturretneedstobe tackled.Inparticular,theaero-opticcommunityisinneedofdetailedbaselineuid dynamicmeasurementsthatshowhowspecicowinteractionsrelatetoaero-optic aberrations.Onlythencanowcontrolbeimplementedinasuccessful,robust,and reliablemanner. 83

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Figure2-1.ModelsusedbyTaylortostudythelevelsofturbulenceovermodels submergedinaboundarylayer.AdaptedfromTaylor1992. Figure2-2.ModelusedbySchonbergertoresearchtheeectsofbothpassiveandactive controlontheowaroundaturretmodel.AdaptedfromSchonberger etal. 1982. 84

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A B Figure2-3.A2-DmodelusedbyGordeyev etal. .BTopviewofpassivecontroldevices lefttoright:largevortexgenerators,pins,andsmallvortexgenerators. AdaptedfromGordeyev etal. 2005. Figure2-4.Passivesplitterplatedesign.ASideview.BTopview.Adaptedfrom Vukasinovic&Glezer2007. 85

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Figure2-5.ModelusedbyVukasinovic.Notethethreestaticpressureportplanes:center, middle,andouter.Theactuationanglecanbechangedbyrotatingthe hemisphere.Allactuatorslotsareinthestreamwiseorientation.Adapted fromVukasinovic&Glezer2007. A B Figure2-6.AHemisphericalturretmodelsusedbyWoszidloforbothpassiveand open-loopcontrol.Ontheleftisacompletehemispherearcangleof180 o andontherightisasubmergedhemispherearclengthof120 o corresponding tohalftheheightofthehemisphereprotrudinginthetestsection.BLarge vortexgeneratorsareusedonediameterupstreamoftheturretmodelto disrupttheformationofthehorseshoevortex.AdaptedfromWoszidlo etal. 2009. 86

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Figure2-7.Turretmodelwithanarrayof36syntheticjetactuators.Allactuatorslotsare alignedwiththefreestreamvelocity.AdaptedfromVukasinovic etal. 2009 b Figure2-8.Hybridcontrolisimplementedbyaddingapartitionplatetotheupstream portionofthemodel.ASideview.BTopview.Allactuatorslotsare alignedwiththefreestreamvelocity.AdaptedfromVukasinovic etal. 2010 b Figure2-9.Turretmodelwithanarrayof17syntheticjetactuatorsaroundaatwindow aperture.ASideview.BAngledviewtobestshowthelocationofthe actuatorsrelativetotheatwindow.AdaptedfromWallace etal. 2008. 87

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Table2-1.BoundarylayerdetailsusedinstudybyToy etal. 1983. istheboundary layerheight, isthedisplacementthickness,and isthemomentum thickness. u 2 =U 2 1 denotestheturbulentintensity mm mm mmmin u 2 =U 2 1 max u 2 =U 2 1 Re Smooth26532.2622.450.000060.00701.81E4 Rough36064.7744.520.015500.00033.17E4 Table2-2.Summaryofearlystudiesonowsoverhemisphericalobjects AuthorYearRemarks Okamoto1980Studyreattachmentpointlocationofreverseowfor hemisphereswith R 1 Taniguchi etal. 1982Dimensionalanalysistonduniquefunctionsrelatingto C D Toy etal. 1983Comparisonofseparationlinebetweendomesubmergedin laminarandturbulentboundarylayers Savory&Toy1986Watertunnelmeasurementsdisplayedgenerationand developmentofvortexstructures Taylor1992Fluctuatingpressuremeasurementsovermodelswith dierentheighttodiameterratios Table2-3.Summaryofinitialowoveraturretprotuberancestudies AuthorYearRemarks Craig1981Summarizedscreeningprocessesforturretowcontrol deJonckheere etal. 1982Holographicinterferometrytechniqueprovidedin-depth analysisofowaroundturret Schonberger etal. 1982Appliedsteadysuctionthoughahollowfairingnosepiece withinbaseow Gilbert&Otten1982Summaryofaero-opticresearchandapplications Purohit etal. 1983Numericalsimulation:appliedsuctiontoalterwake structure 88

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Table2-4.FlowcontrolscreeningmethodologiesfromCraig1981 IncompressibleCompressible LaminarTurbulentLaminarTurbulent OnTurretConcepts SurfaceBlowing3221 SurfaceSuction3221 OTurretConcepts BaseBlowing3121 BaseSuction3121 BaseJetPump3121 TrappedVortexBaseFairing3121 Incompressible:Ma < 0 : 4,Compressible:Ma > 0 : 4 Laminar:Re < 2 10 5 ,Turbulent:Re > 2 10 5 Theratingsystemisasfollows:1desirable,2adequate,3undesirable Table2-5.Summaryofrecentbaselineowcharacterization AuthorYearRemarks Leder etal. 2003ExperimentallycharacterizedwakeregionusingLDV Gordeyev etal. 2004OpticaldistortionsscalewithMa 2 Gordeyev etal. 2007Surfaceoilowtechniquestovisualizecomplexthree dimensionalstructure Sluder etal. 2008Pressuredistributionsandaerodynamicloadsfordierent h=D ratioturrets Gordeyev&Jumper2009Developscalinglawsforlevelsofopticaldistortionsasa functionofturretgeometryandowconditions Porter etal. 2013FirstresearchtocompareighttestsusingAAOLto previouswindtunnelexperiments Table2-6.Summaryofrecentpassivecontrolstudies AuthorYearRemarks Snyder etal. 2000Aft-mountedfairingsandsplitterplatesincreasepressure recoveryaftofturret Gordeyev etal. 2005Passivevortexgeneratingvanesupstreamof'2D'turret withatapertureactuallyincreaseopticalaberrations Vukasinovic&Glezer2007Splitterplateusedtodecoupletheinteractionofthe hemisphereandcylinderwakes Gordeyev etal. 2010Usedpinstoimproveaero-opticalenvironmentaround atwo-dimensionalatwindowedturretmodelpin parameters: d =0 : 1 s =0 : 5 ,and h =3 : 2 Reynolds etal. 2012Wakeproleswerecharacterizedforelevenpassive modicationstohemisphericalturret. 89

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Table2-7.SummaryofReynolds etal. 2012passivecontrolmodels.Tcorrespondsto geometryofthehemisphericaltopwhileBcorrespondstogeometryofthe cylindricalbase. CaseDescription T1Baselinehemisphericaltop. T2Shortcylindricalpinswithheightof2.03mmanddiameterof1.52mmspacedat every30 o circumferentiallyand15 o azimuthally. T3Vortexgeneratingvaneswithheightof2.54mmlocatedalongthehalfportionof thedome. T4Longcylindricalpinswithheightof6.04mmanddiameterof1.52mmspacedat every30 o circumferentiallyand15 o azimuthally. T5Horizontalnswiththicknessof7.62mmandspaced6.04mmapartwrapped aroundmodelfromapextobase.Anaddedverticalnspanned180 o azimuthally. T6Horizontalnswiththicknessof7.62mmandspaced6.04mmapartwrapped aroundmodelfromapextobase.Noverticalnattached. B1Baselinecylindricalbase. B2Sawtoothcutswiththicknessof2.54mmaddedtocylindricalbaseatazimuth anglesof90 o and-90 o B3Crescentshapesplitterplateaddedataheightof5.38mmabovethetunneloor. B4Long.2mmandshort.4mmns,eachwith15.24mmheightare directedintheupstreamanddownstreamdirection,respectively. B5SameasB4,butturned180 o intheazimuthdirection. 90

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Table2-8.Summaryofrecentopen-loopcontrolstudies AuthorYearMachRemarks Vukasinovic etal. 20050.06-0.09Upto20 o separationdelayalongcenterplane usinghighfrequencyforcingSt D > 10 Vukasinovic&Glezer20070.12Studiedinuenceofjetmomentum coecient,angulardistanceofactuator array,andspanwiseextentoftheactuator array Vukasinovic etal. 20080.30-0.64ActuationatSt D > 1resultedinreductionof opticaldistortioninexcessof40%atMa=0.4 Woszidlo etal. 20090.06Suctionappliedattrailingedgeresultedin completeremovalofthehorseshoevortex Gordeyev etal. 20090.30OPDreductionofupto34%forowat Ma=0.3withinfrequencyband0 : 5
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CHAPTER3 EXPERIMENTALSETUP Thischaptersummarizestheexperimentalsetup.First,theturretmodelisdescribed anddetaileddrawingsareprovided.Then,anoverviewofthelow-speedwindtunnel facilityisgiven.Finally,experimentaltoolsandmethodsforbothbaselineandow controlcasesarediscussed. 3.1TurretModel Asubmergedsurface-mountedhemispherewithaatwindowisusedinthisstudy. ThecoordinateaxisandcorrespondingterminologyisshowninFigure3-1.Themodelhas adiameterof231mmwithaslopediscontinuityof42 o betweentheatwindowandthe hemisphere.Theatwindowmeasures110mmindiameterandisretrottedwithfour microphoneholdersalongthecenterline,spaced14 : 56mmapart.Thewindowcanrotate withrespecttothemodel,allowingacompleteunsteadypressuremapovertheaperture. Themodelissubmergedsuchthatitsheightprotrudingfromthesurfaceisonly 88 : 9mm,correspondingtoaheighttoradiusratioof H=R =0 : 77.Thebasecanbe rotatedthrough360 o ofazimuth,althoughforalltests,onlyanazimuthangleof180 o is investigated,correspondingtoanaft-lookingviewthroughthewindow.Acompletesetof technicaldrawingsofthemodelisprovidedinAppendixA. Theturretismounteddirectlyonthetunneloor,withitscenterlocated1 : 57m downstreamfromthebeginningofthetestsection.Theturretmodelencountersa boundarylayerthicknessofroughly29 : 5 0 : 3mm,thusprovidingtheexperimental conditionthattheratiooftheoncomingboundarylayertotheturretheightis i =H = 0 : 30.Thetunnelblockageimposedbytheturretislessthan4%. ThemodelismanufacturedbytheLockheedCompanyattheirstereolithography rapidprototypingcenterlocatedinOrlando,FL.Imagesoftheturretmodelfromseveral perspectivesareshowninFigure3-2.Anewtunneloorcapableofholdingthemodelwas machinedbyTMREngineeringinMicanopy,FLundermanagementofKenReed. 92

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ThebaselineowaroundtheturretisReynoldsnumberdependent.Toavoidchanges inseparationthatareassociatedwithowtransition,theboundarylayeristrippedusing a0 : 5mmthicksawtoothtapeGlasfaserFlugzeug-Servicezig-zagturbulatortapeplaced at S=R =0 : 80fromtheleadingedgeofthemodel.Figure3-3showsthelocationand specicdimensionsofthetriptapeused. 3.2UniversityofFloridaLowSpeedWindTunnelFacility TheEngineeringLaboratoryDesign407Bwindtunnelisarecirculatingtypetunnel withasquaretestsectionmeasuring0 : 61m 0 : 61mthatextends2 : 44mintheow direction.Forcompletetechnicaldrawingsofthetunnelandtestsection,seeELD2004. Therangeofcapablevelocitiesis3m/sto90m/scorrespondingtoamaximumMach numberof0.26atSTPandtheturbulentintensitylevelsarebelow0.1%Sytsma2006. Velocitymeasurementsaremadeusingapitot-staticprobelocated0 : 10mdownstream oftheleadingedgeofthetestsection.APIDcontrollerisimplementedviaaLabVIEW virtualinstrumenttoensureaconstantMachnumberduringanyexperimentalrun. Thewindtunnelisequippedwithanin-lineheatexchangerusedtomaintainthe testsectiontemperatureconstantduringexperiments.Theheatexchangerisinstalled downstreamofthemotorandupstreamofthetestsection.Coolantuidowratethrough theheatexchanger,providedfroma50-tonchillerunit,issetfromaservoactuated controlvalve.Thetemperaturemeasuredfromathermocouplelocatedjustdownstream oftheheatexchangerisfedtoathermalcontrolunit.Thecontrolunitautomatically opens/closesthecontrolvalvetoadjustthecoolantuidowratesuchthattheusers desiredtestsectiontemperatureismet.Thetestsectiontemperatureisusedtodirectly calculatetheMachnumber,Ma= V 1 = p RT Atwo-stageaxialfanisdrivenbyanin-line440Velectricmotor.Themotoris controlledbyaToshibaModelH7variablefrequencydrivethatoutputsaconstant frequencypowersignalbetween1.5and60Hz.Thewindtunneldisplacesafootprintof 93

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10 : 6m 3 : 5mandis2 : 4mhigh.Forthecharacterizedowqualityofthefacilityovera rangeofconditions,seeSytsma2006. Theinstalledtestsectionhastwo0.91mby0.46mopticalwindowsoneachsideand anopticallyclearceilingwhichallowsforwideopticalaccess.Thetestsectionisinstalled downstreamofowscreensandplenumandisupstreamofastraightwalleddiuser. Thewindtunnelhasanti-turbulencescreens,analuminumhoneycomb,anda25:4area contractionratio. 3.3WindTunnelCharacterization 3.3.1IncomingBoundaryLayer Incomingboundarylayerparametersareassessedusingconstanttemperature hot-wireanemometry.ADantecMiniCTAModule54T30isconnectedtoa5 m diameter,55P15miniatureboundarylayerprobeviaa55H22probesupport.The probeandsupportaremountedinacustom-madestreamlinedmountseeFigure3-4. Calibrationofthehot-wireiscarriedoutinthewindtunnelwithapitot-staticprobeas thevelocityreference.Thetemperatureisrecordedduringcalibration,allowingcorrections tothecalibrationcurvetobeappliedifthetemperaturevariesfromcalibrationto measurement.Theacquiredhot-wirevoltage, E a ,iscorrectedbymeansoftheknown valuesforthewiretemperature, T w ,thecalibrationtemperature, T 0 ,andthetemperature duringacquisition, T a ,by E corr = T w )]TJ/F22 11.9552 Tf 11.955 0 Td [(T 0 T w )]TJ/F22 11.9552 Tf 11.955 0 Td [(T a 0 : 5 E a : {1 Then,thegeneralrelationshipbetweenthecorrectedvoltageandtheowspeed, U ,is givenbyKing'spowerlaw, E 2 corr = A + BU n ; {2 wherethecoecients A B ,and n aredeterminedviaanonlinearleast-squarestofthe calibrationdata. Withthemodelabsentfromthetestsection,thewireisplacedat1.37mdownstream fromthestartofthetestsection,correspondingtoalocationthatisoneturretheight 94

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upstreamofthemodel.Therstmeasurementpointistakenat0.5mmabovethetest sectionoor.Athree-axisVelmextraversemodelPK266isusedtotraversetheprobeto 80locationsfromthetunneloorat0.5mmincrements.Measurementsareacquiredusing aNIcDAQ-9162chassiswitha4channelPXI-9234dataacquisitioncard.Eachchannel has24-bitresolutionwith114dBdynamicrangeandabuilt-inanti-aliasinglter.Ateach location,dataareacquiredforonesecondatasamplingrateof10kHz. Afterallmeasurementsarecompleted,thetime-averagedvelocity,standarddeviation, andasinglecomponentoftheReynoldsstressarecomputedateachlocation, U = 1 N N X i =1 U i ; {3 = v u u t 1 N )]TJ/F15 11.9552 Tf 11.955 0 Td [(1 N X i =1 U i )]TJETq1 0 0 1 355.094 450.416 cm[]0 d 0 J 0.478 w 0 0 m 9.199 0 l SQBT/F22 11.9552 Tf 355.094 440.573 Td [(U 2 ; {4 u 0 u 0 = 1 N )]TJ/F15 11.9552 Tf 11.955 0 Td [(1 N X i =1 U i )]TJETq1 0 0 1 354.701 396.125 cm[]0 d 0 J 0.478 w 0 0 m 9.199 0 l SQBT/F22 11.9552 Tf 354.701 386.282 Td [(U 2 : {5 The95%condenceintervalisthenusedtoensurethatthetotalnumberofsamples, N ,is sucientforconvergence, 95%condenceinterval= U t N; 95% p N : {6 TheuncertaintyformeanandsecondordermomentsarelistedinTable:PIVRandUnc. Theboundarylayerheightisthendenedasthedistancefromthewallwherethe velocityis99%ofthefreestreamvelocity, = y u =0 : 99 U 1 : {7 Twofrequentlyusedparametersusedtofurtherdescribetheboundarylayerarethe displacementandmomentumthicknesses, and .Thedisplacementthicknessisthe physicaldistancethattheinviscidowisdisplacedduetothepresenceoftheviscous 95

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boundarylayer.Similarly,themomentumthicknessistheamountofpotentialuidwhich containsthesameamountofmomentumthatislostthroughviscouseectsatthewall. Bothparametersarecalculatedasfollows, = Z 1 0 1 )]TJ/F22 11.9552 Tf 18.278 8.088 Td [(u U 1 ; {8 = Z 1 0 u U 1 1 )]TJ/F22 11.9552 Tf 18.278 8.088 Td [(u U 1 : {9 UncertaintyestimatesfortheboundarylayerparametersareobtainedviaMonte Carlosimulations.Theperturbationsrepresentingtherandomerrorinvelocityaredrawn fromaGaussiandistribution,witheachpointmeasurementperturbedindividually. Perturbationsassociatedwiththebiaserrorinmeasurementlocationaredrawnfrom auniformdistributionandareapplieduniformlytoeachscanpoint.Theintegration associatedwiththecalculationof and areperformedforeachperturbationtobuild statisticaldistributionsand95%condenceintervalsarecalculated. 3.3.2TunnelAcoustics Theacousticnoiseoorofthetunnelismeasuredforfreestreamvelocitiesranging from10-90m/s.AG.R.A.S.40BEfree-eldcartridgewithatype26CBpreamplieris usedforallmeasurements.Thesensorhasadynamicrangeof40 )]TJ/F15 11.9552 Tf 12.337 0 Td [(160dBre.20 Pa andafrequencyrangeof10Hz )]TJ/F15 11.9552 Tf 11.541 0 Td [(100kHz.AsshowninFigure3-5,thesensorisretrotted witha Br uel & Kjaer UA-0385nosecone,sothatideallyonlyacousticphenomenaare measured.Thesinglesensorismountedinthetestsection'smid-plane0 : 66mdownstream ofthetunnelleadingedge. TheG.R.A.S.sensoriscalibratedwitha Br uel & Kjaer pistonphonetype4228ata frequencyof250HzandSPLof124dBre.20 Pa. Theauto-spectraldensityiscomputedfromEquation3{10. P xx = 2 N 2 f [ X X ] ; {10 96

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where N isthenumberofsamplesperblock, f isthefrequencyresolution, X istheFast FourierTransformofthesensoroutputconvertedtoengineeringunitsPascals,and denotesthecomplexconjugate.Theacousticspectraldensityisthenconvertedtoasound pressurelevelSPLwithreferenceto20 Pa, SPL=20log 10 p P xx f 20 10 )]TJ/F21 7.9701 Tf 6.587 0 Td [(6 Pa : {11 TunnelacousticmeasurementsareacquiredsimultaneouslyusingaNIPXI-1024Q chassiswitha16channelPXI-4498dataacquisitioncard.Themodulesalsoprovide the4mAexcitationcurrentrequiredtopowerthetransducers.Eachchannelhas24-bit resolutionwith114dBdynamicrangeandabuilt-inanti-aliasinglter.Allmeasurements areaccoupledat0.5Hz.Dataareacquiredatvelocitiesfrom10-90m/sin10m/s intervalsatasamplingfrequencyof40,960Hzfor5seconds.Thedataaresplitinto100 blocksof2048sampleseach,resultingina20Hzbinwidth.Theblocksareaveragedusing aHanningwindowwitha75%overlap,resultingin206eectiveaverages.Thenormalized autospectralrandomuncertaintyis6.9%. 3.4BaselineFlowMeasurements 3.4.1SteadyPressure Steadysurfacepressuremeasurementsaremadealongthecenterlineoftheturret model.Atotalofthirty-eight0 : 711mminnerdiametertubulationsareinstalledin themodel.ThedistributionofthesepressureportsisshowninFigure3-6.Aneven distributionofeighteentapsspacedat S=R =0 : 0892intervals,arelocatedbetweenthe leadingedgeofthemodelandtheapex.Anotherseventapsareevenlydistributedspaced at S=R =0 : 0182intervalsbetweentheapexandtheatwindowdiscontinuity.The lasttwelvetapsarespacedat8 : 1mmalongtheatwindowseeFigure3-7.Foramore detaileddrawing,refertoAppendixA. Three16-channelEsterlinePressureSystemspressurescannersranges5psi,1psi, and10inH 2 Omeasurethestagnationpressuresatthediscretelocations.Foreachtest 97

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case,30samplesareacquiredatasamplingrateof2Hz.Allpressurereferenceportsare connectedtoapitot-staticprobelocated0 : 1mdownstreamofthetestsectionleading edge.Afterpressuremeasurementsaretaken,thestaticpressureandstandarddeviation arecalculated, p s = 1 N N X i =1 p i ; {12 = v u u t 1 N )]TJ/F15 11.9552 Tf 11.955 0 Td [(1 N X i =1 p i )]TJ/F15 11.9552 Tf 12.942 0 Td [( p s 2 : {13 Surfacepressurecoecientsarethencomputedbynormalizingthedierential pressure, p s )]TJ/F22 11.9552 Tf 11.955 0 Td [(p 1 ,bythedynamicpressure, C p = p s )]TJ/F22 11.9552 Tf 11.955 0 Td [(p 1 1 2 U 2 1 ; {14 C = 1 2 U 2 1 ; {15 where and U 1 arethefreestreamdensityandvelocity,respectively. 3.4.2UnsteadySurfacePressure Unsteadysurfacepressuremeasurementsalongtheatwindowofthemodelprovidea non-intrusivemeansofmeasuringthepressureuctuationfootprintleftbytheseparated oweldinthenearwakeregion. Unsteadysurfacepressuresaremeasuredusingthesamesensorusedforthetunnel acousticmeasurements.Foursensorsareush-mountedontheatwindowspaced14.56 mmapart,asshowninFigure3-7.Theatwindowcanberotatedthroughafull360 o Figure3-8showsimagestakenfromtherearofthemodelwiththewindowrotatedto discretelocations.Theunsteadypressurespectraldensity,calculatedfromEquation3{10, isthennon-dimensionalizedbythedynamicpressuretoyieldapercentage, p P xx f 1 2 U 2 1 100% : {16 98

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Dataareacquiredatasamplingfrequencyof10,240Hzfor10seconds.Thedataare splitinto100blocksof1024sampleseach,resultingina10Hzbinwidth.Theblocksare averagedusingaHanningwindowwitha75%overlap,resultingin206eectiveaverages. Thecalculatednormalizedautospectralrandomuncertaintyis6.9%. 3.4.3OilFlowVisualization Surfaceoilowvisualizationprovidesqualitativeinformationontheowtopology surroundingthemodel.Auorescentdyeisappliedtothemodelandthetunnelis allowedtoreachthedesiredspeed.Oncethedyehassettled,anultravioletlightisused tovisualizethestreaklinesmarkedoutbytheowonthesurfaceofthemodel.These resultingstreaklinescontaininformationregardingtheowseparation,vorticalstructures, andthesizeoftherecirculationregionbehindtheturret. Theuorescentdyeisamixtureofmotoroilanduorescentchalk.Motoroil W-50isusedforexperimentalrunsatvelocitiesof60m/sorlesswhilegearoil W-90isusedexclusivelyforthe90m/scase.Theratiois1gofchalkStrait-Line 65105per30mLofoil.Themixtureisappliedusinganeye-dropperatdiscretelocations spacedapproximately2 )]TJ/F15 11.9552 Tf 12.345 0 Td [(3cmapartoverthemodelanditsvicinityasshowninFigure 3-9.Approximately3mLofthemixtureisusedforeachexperimentalrun.Thehighly viscousoiltakesapproximatelyveminutesatthedesiredtunnelspeedtofullymarkthe surfaceowpattern.Notransientoweectsarecapturedinthetimethatittakesthe tunneltoreachfullspeed. Tocapturetheowfeatures,twosetsofimagesaretakensimultaneously.Thesetup isshowninFigure3-10.TwoSpectrolineultravioletlampsModelSB100Paremounted oneithersideofthetestsectiontoilluminatethesurfaceofthemodel.ANikonD300s dSLRcameraequippedwitha28mmf/2.8lensismountedoverheadwhileaNikonD70 dSLRcameraequippedwitha50mmf/1.8lensismountedonatripodatanangleto bettercapturetheowphenomenaovertheatwindow.Eachcameraismanuallyfocused 99

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onthemodelandsettoanexposureof10sec,f/8.0,andISO200.Bothcamerasare externallytriggeredsimultaneouslyusingNikonCameraControlProsoftware. 3.4.4Hot-wireAnemometry Theshearlayerdevelopmentisrstassessedalongtheturretstreamwisecenterline withvelocitymeasurementsmadebyaconstanttemperaturehot-wireanemometer.Note thatmeasurementswiththisproberesultinone-dimensionalslicesandcanthereforenot accountforthethree-dimensionaleectsencounteredwithintheshearlayerandwake region.However,itdoesprovideaqualitativefeelfortheenergywithintheshearlayer. Furtherexperimentsusingstereoparticleimagevelocimetry,discussedinthefollowing section,allowforafullcharacterizationofallthreevelocitycomponents.Fordetailson thecalibrationandusageofthehot-wireanemometer,refertoSection3.3.1. Theprobeistraversedusingathree-axisVelmextraverse,modelPK266.The traversehasaresolutionof6 : 35 minthestreamwiseandlongitudinaldirectionsanda resolutionof12 : 70 minthespanwisedirection.Allmeasurementsareacquiredusinga NIcDAQ-9162chassiswithafourchannelPXI-9234dataacquisitioncard.Eachchannel has24-bitresolutionwith114dBdynamicrangeandabuilt-inanti-aliasinglter. Velocityprolesaremeasuredatthe13streamwisemeasurementlocations,from x=H =0 : 45to3 : 76,ashighlightedinFigured3-11.Ateachlocation,theprobeis traversedin1mmincrementsinthelongitudinaldirection y=H foratotalof101 measurementpoints.Theonlyexceptionarethethreelocationsclosesttotheturret wheretheprobeonlytraversestowithin3mmofthewindow.Table3-2listsall streamwisemeasurementplanes,theextentoflongitudinalmeasurements,andthe totalnumberofmeasurementpoints.Ateachmeasurementpoint,dataarecapturedata samplingrateof10kHzforonesecond. Afterallmeasurementsarecompleted,thetime-averagedvelocityandin-plane uctuationsarecalculatedEqs.3{3and3{5,respectively.Foreachspanwiselocation, 100

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thepowerspectrumispresentedforthelongitudinalpositionthatcontainsthehighest uctuatingcomponent,ascalculatedbyEq.3{5. 3.4.5ParticleImageVelocimetry ParticleimagevelocimetryPIVallowsfornon-intrusivemeasurementsofthe localizedvelocityinaoweld.Figure3-12providesaschematicforageneral two-dimensionalPIVconguration.Smallseedingparticles,usuallyontheorderof microns,areusedastrackingparticlesoftheow.Adualpulselaserheademitsapair oflaserpulseswithapreciselycontrolledtimeseparation, t .Theemittedbeamspass throughacylindricallenstoformlasersheetsthatilluminatetheregionofinterestin aoweld.Thelaseristriggeredatauserdenedrate,andacameraispositioned perpendiculartothelasersheetcapturingasetofimages.Then,theimagepairis discretizedintointerrogationwindowsandthespatialcross-correlationiscomputed betweencorrespondinginterrogationwindowsoftheimagepairs.Fromthecorrelation, thex-andy-displacementsarecalculated.Finally,thein-planevelocitycomponents arecalculatedbydividingthesedisplacementsbytheknown t betweenlaserpulses. Theresultisasinglevelocityvectorassignedtoeachintegrationwindowbasedon theweightedaveragemotionofthemultipleparticlessharedbythecorresponding interrogationwindows.Theuserdened t isowdependentandisinitiallyadjustedby allowingtheparticlestomovealengthequalto25%ofaninterrogationwindowRael etal. 2007. AQuantelLaserEvergreen200Nd:YaglasermJ/pulse,locatedontopofthe testsection,isusedtoemitabeamthroughavariablefocallengthsphericallensand a-15mmfocallengthcylindricallens.Thisproducesalasersheetthatisredirectedby anopticallyatmirroralongtherequiredplaneofmeasurement.ALaVisionImager ProX4MPcamerawith2112by2072pixelresolutionisusedtocaptureallimagepairs. ThelaserandcameraaresynchronizedusingaLaVisionLaserPulseSynchronizer.For allcases,themodelandtunneloorinthenearwakeregionaretreatedwithDykem 101

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layoutuidtoreducesurfacereectionsandincreaseclaritynearthemodelsurface. FreestreamseedingisproducedbyaTSI9307-6whichusesanoilbaseduidinthiscase oliveoiltoproduce s 1 mdiameterparticles.Aschematicshowingthelasersheetand measurementsplanesisshowninFigure3-13. AllimagepairsareprocessedusingLaVisionDaVisv8.1softwareDaVis2010. Tospeedupprocessingandreduceerroneousvectors,amaskisdenedoveranyarea thatdoesnotcontainanyseedingi.e.overthesilhouetteofthemodel.Thevectorsare calculatedviaafour-passrecursivescheme:twopasseseachof64 64and32 32pixel interrogationwindows.A1:1circularGaussianweightingfunctionwith50%overlapis appliedtoeachinterrogationwindow.Oneachpass,outliersarerejectedbasedonthe valueofthecorrelationpeakratio.Finally,theinitialvectoreldsarecomputed,withno smoothingorinterpolationapplied.AdditionaloutliersarethenremovedinMATLABby usingmultivariateoutlierdetectionMVOD,asdescribedinGrin etal. 2010.The meanandturbulentquantitiesarethencomputed,usingEquations3{3and3{5foreach velocitycomponent.Finally,themagnitudeofvelocity j V j andturbulentkineticenergy k aredenedandcalculated, j V j = q U 2 i + U 2 j + U 2 z ; {17 k = 1 2 )]TJETq1 0 0 1 274.995 304.691 cm[]0 d 0 J 0.478 w 0 0 m 18.915 0 l SQBT/F22 11.9552 Tf 274.995 295.136 Td [(u 0 u 0 + v 0 v 0 + w 0 w 0 ; {18 where U z and w 0 w 0 arezerofortwo-dimensionalPIV. TwosetsofPIVexperimentsareperformedtoobtaintheowfeaturesaroundthe turret.Thespecicregionsofinterestincludetheboundarylayerattheapexoftheturret andseveralstreamwiseplanesinthenearwakeregion.Theexperimentalsetupforeachof thesecasesaredierentandthusaredescribedinthefollowingsections. 3.4.5.1TurretApexBoundaryLayer Theboundarylayerattheapexoftheturretisanimportantparametertoconsider whenperformingowcontrolexperiments.Thegeneralscalinganalysisofturbulentow overaatplateisrstusedtogetageneralideaoftherequiredmeasurementwindow. 102

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Basedon s Re )]TJ/F21 7.9701 Tf 6.587 0 Td [(1 = 5 x White2006,anddening x asthedistancebetweenthelocation oftheturbulentstripandtheapexoftheturret,theboundarylayerheightispredicted tobe O mm.Hence,ameasurementwindowofatmost O mmisrequiredtoobtain adequatespatialresolution.Withthegivenworkingdistancetothemodel,alonemacro lensisnotabletoobtaintherequiredmagnication.Therefore,aNikon200mmf/4 lensisretrottedwithaKenko1.4xteleconvertertoincreasemagnicationanda12 mmextensiontubetoreducetheminimumfocusdistance.Theaddedteleconverter andextensiontubeyieldameasurementwindowof22 22mmresultinginaspatial resolutionof16vectors/mm,asshowninFigure3-13B.Notethat,duetotheadditionof theteleconverter,theeectiveopticsarethatofa280mmf/5.6lens. 3.4.5.2StereoscopicWakeMeasurements StereoscopicPIVsPIVprovidesawaytoextractthethirdvelocitycomponent,a usefulmeasurementwhenassessingthethree-dimensionalowbehindaturretPrasad 2000.Ingeneral,twocamerasviewtheplaneofinterestatdierentangles.Sincethe sensorandmeasurementplanesarenolongerparalleltoeachother,thelensmustbe tiltedwithrespecttothesensorplane.TheangleoftiltisknownastheScheimpugangle andallowsthemeasurementplaneandimageplaneanglestooverlap,thusallowingfocus alongtheentiresensor.However,thisintroducesperspectivedistortionintheresulting images.Thesetofimagesarethentransformedviaasecondordermappingfunction tocorrectforthedistortionandapplythepropercoordinatesystem,asdescribedin Rael etal. 1998.Inpractice,theadjustingofboththeScheimpugangleandcamera positionisaniterativeprocess.Oncethecorrectlocationandlensanglesareachieved, theresultingviewwillyieldproperlyfocusedparticlesthroughouttheentireimage. Forcalibration,aTSIdualplane/dualsidedtargetplatemodel640010-4Pisused. Theplate'splanesareosetby1.00mmandeachhaveanarrayof120dotswhichare separatedby10.00mminboththestreamwiseandlongitudinaldirection. 103

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Figure3-14showsaschematicofthesetupforthewakemeasurements.TwoLaVision ImagerProX4MPcamerasarettedwithScheimpugmountswhereSigma105mm f/2.8lensesareattached.Theentiresetupisthenmountedonatraversesystemthatis rigidlyattachedtothelaser,butdecoupledfromthetunnel.Thissystemallowstheuser toeasilyadjustthetransverselocationofthemeasurementplaneswithouttheneedto recalibratebetweenruns. 3.4.5.3sPIVUncertainty BothbiasandrandomuncertaintyarecalculatedandpresentedinAppendixB.The randomuncertaintyiscalculatedusing95%condenceintervalsasdiscussedinBenedict &Gould1996.Thebiasuncertainty,however,ismorerigorousandisdescribedindetail AppendixB.Foramoregeneralunderstandingoftheuncertaintyanalysis,refertoHu 2009. 3.5Aero-OpticMeasurements Whiletheuiddynamicexperimentsyieldusefulinformationontheowstructures surroundingathree-dimensionalturret,aero-opticmeasurementsarerequiredtofully understandtheimpactoftheowstructuresontheopticalenvironment.Thissectionrst describesanimagingtechniquethatyieldsqualitativeinformationonopticaldegradation inthenearwakeregion.ThenaMalleyprobesetup,providingone-dimensionalslicesof opticalwavefrontsinthedirectionofthebeampropagationvector,isdetailed. 3.5.1Aero-OpticImaging Asaqualitativemeasureofpossibleaero-opticdistortion,asetofpreliminarytests areconducted.AsshowninFigure3-15,theexperimentconsistsofaUSAFResolution TestChartFigure3-16andaNikond300scamerawithaSigma150mmf/2.8lens attached.Astand-aloneapparatusisconstructedoutof80/20extrudedaluminumto rigidlyholdthetestchart.TheUSAFResolutionTestChartisaresolutiontestpattern thatiswidelyacceptedtotesttheresolvingpowerofopticalimagingsystemssuchas microscopes,camerasandimagescanners.Thecameraismountedonarigidtripodand 104

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isorientedsuchthattheeldofviewisparalleltothewindowturretangle.Thelensis manuallyfocusedontothetestchartandthecameraisexternallytriggeredviaNikon CameraControlProsoftware.Foralltests,theexposureissetto1.5sec.,f/16,andISO 200.ApairofCraftsmanWL500DPT-S500Wattspotlightsareusedtoevenlyilluminate thetarget.Thecamera,testchart,andspotlightsareallmountedonstand-aloneunits, thereforeisolatedfromtunnelvibrations. Threeseparateexperimentsareconducted.Therstcongurationconsistsofthe cameraorientedattheturretwindowangle,capturinganimageoftheisolatedtest chartwithnoowthroughthetunnel.Theimagesfromthisexperimentshowthe baselinetestchart,i.e.thetestchartwithnoow-inducedaero-opticdistortion.The secondcongurationissimilartotherst,butwithMa=0.26ow.Thisconguration qualitativelymeasureseectofaero-opticdistortioncausedbythetunnelboundarylayers. Thethirdandnalcongurationisidenticaltothesecond,butwiththeturretmodel installedinthetestsection. Foreachconguration,asetoftenimagesistaken.Eachimagerepresentsa one-and-a-halfsecondtimeaverageoftheeectofpossibleow-inducedaberrations.All tenimagesfromeachcongurationareaveragedtocreateasingleimagerepresentation oftheselectedcase.Theresultingimage,an8-bitjpegconsistingof256luminancelevels, isconvertedtogray-scaletoremoveanycolorcastcontaminationfromthespotlights orambientlight.Toqualitativelyassessanyaero-opticdistortion,theluminancevalues takenwithMa=0.26owaresubtracted,pixelbypixel,fromthebaselineimagenoow. Theresultisanimagethatalsocontains256luminancevalues,withzeropureblack correspondingtonodierencebetweenthetwoimages. 3.5.2MalleyProbe TheMalleyprobeisasimpleopticaldevicethatprovidesone-dimensionalslicesof opticalwavefrontsinthedirectionofthebeampropagationvectorMalley etal. 1992. Forageneraloverviewofthedevice,refertoSection1.2.3.3. 105

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3.5.2.1TunnelVibrations PriortoanyopticalaberrationmeasurementswiththeMalleyprobe,astudyusing PCBPiezotronics356A16triaxialaccelerometersisperformedtoquantitativelyassess tunnelvibrations.Calibrationoftheeachaccelerometeraxisiscarriedoutusinga PCB394C06shaker.TheaccelerationisrecordedusingaNIcDAQ-9162chassiswith afourchannelPXI-9234dataacquisitioncard.Eachchannelhas24-bitresolutionwith 114dBdynamicrangeandabuilt-inanti-aliasinglter.Thedataareacquiredata samplingfrequencyof640Hzfor100seconds.Tocalculatethesensitivity,thedataare splitinto100blocksof640sampleseach,resultingina1Hzbinwidth.Theblocksare averagedwithaFlatTopwindowwithnooverlap,resultingin395eectiveaverages withanormalizedautospectralrandomuncertaintyof5.03%.Theoverallpowerinthe fundamentalisthenintegratedtocalculatethesensitivity.Thisisrepeatedforeveryaxis ofeachaccelerometer. TheaccelerometersarexedatthreelocationsasillustratedinFigure3-17:oneon eachpositionsensingdeviceandoneontheundersideoftheturretmodel.Thetunnel vibrationspectraldensityiscomputed P aa = 2 4 N 2 f [ A A ]{19 where N isthenumberofsamplesperblock, f isthefrequencyresolution, isthe frequencyinradians, A istheFastFourierTransformoftheaccelerometeroutput convertedtoengineeringunitsm/s 2 ,and*denotesthecomplexconjugate.Theresultis thepowerspectraldensitywithunitsofm 2 /Hz. Forthemechanicalvibrationanalysis,allthreesensorsaresimultaneouslysampled usingaNIcDAQ-9162chassiswitha16channelPXI-4498dataacquisitioncard.Each channelhas24-bitresolutionwith114dBdynamicrangeandabuilt-inanti-aliasinglter. Allmeasurementsareaccoupledat0.5Hz.Dataareacquiredatasamplingfrequencyof 65kHzfor60seconds.Thedataaresplitinto600blocksof6500sampleseach,resulting 106

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ina10Hzbinwidth.TheblocksareaveragedusingaHanningwindowwitha75% overlap,resultingin1246eectiveaverages.Thecalculatednormalizedauto-spectral randomuncertaintyis2.83%. Aftermajorsourcesoftunnelvibrationsareassessed,beamdeectiondescribed inthefollowingsectionsandaccelerometerdataaretakensimultaneously.Conditional spectralanalysisCSAisthenimplementedtodecoupleanymechanicalvibrationeects. Formoreinformationonthisprocessingtechnique,refertoAppendixC. 3.5.2.2EquipmentandSetup Fortheexperimentsconductedherein,a10mW,532nmbeamisgeneratedwith aCoherentCWlaser.Thesinglebeamadvancesthroughabeamsplitter,generating twoparallelbeamsspaced10mmapart.Thesubsequentbeamspassthroughavariable neutraldensitylter,allowingtheusertoreducethemaximumbeampowerbyupto 8-stops.Thebeamsthenpassthroughanopticallyclearturretwindowandtravelthrough theturbulentowcreatedbythewakeandseparatedshearlayer.Thelocationsofthe beamswithrespecttotheturretwindowareshowninFigure3-18.Oncethroughthe ow,thebeamsareredirectedviasteeringmirrorstowardone-inchbi-convexspherical lenses,eachwithafocallengthof750mm.Theemergingbeamsareguidedtothecenter oftwoNewportOBP-A-4LpositionsensingdevicesPSDspecicationsareprovidedin Table3-3.Anadditional55mmhoodand532 10nmltersshowninFigure3-19 arettedonthesensortoensurethatambientlightisreduced,asthiscouldcausea non-linearinput/outputrelationship. 3.5.2.3DataAcquisitionandProcessing EachPSDmeasuresthebeamcentroidpositionandbeampowerasafunctionof time.AllmeasurementsusingthePSDsareacquiredusingaNIcDAQ-9162chassiswith a16channelPXI-4498dataacquisitioncard.Eachchannelhas24-bitresolutionwith114 dBdynamicrangeandabuilt-inanti-aliasinglter.Allmeasurementsareaccoupledat 0.5Hz.Thebeam'scentroiddisplacementsaredigitallyacquiredata65-kHzsampling 107

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ratefor60seconds.Thecoordinatesystemusedforthebeamdisplacementsasmeasured bythePSDsisshowninFigure3-20. Thebeamdisplacementsinthex-andy-directionarerstusedtocomputethebeam deectionangleinradians,denedas x t =tan )]TJ/F21 7.9701 Tf 6.587 0 Td [(1 x L {20 y t =tan )]TJ/F21 7.9701 Tf 6.587 0 Td [(1 y L ; {21 where L isthefocallengthofthelensand x y correspondtothebeamdisplacement fromthenullpositioninthex-andy-directionsonthePSD,respectively.Tocalculate thedeectionanglepowerspectrum,thedataaresplitinto600blocksof6500samples each,resultingina10Hzbinwidth.TheblocksareaveragedusingaHanningwindow with75%overlap,resultingin1246eectiveaverages.Thecalculatednormalized autospectralrandomuncertaintyis2.83%. Todeterminetheeectoftunnelvibrationsonthedisplacementmeasurements x and y ,thecoherencefunctionsbetweentheaccelerometerandPSDsignalsare computed, 2 a f = j P a j 2 P aa f P f ; {22 where P a f isthespectralcross-correlationfunctionand P aa f P f arethespectral auto-correlationfunctionsfortheaccelerationandbeamdisplacement,respectively.Then thecoherentoutputpowerbetweenthetunnelvibrationsandbeamdisplacementisgiven by 2 a f P f .Thisreal-valuedfunctiongivesanindicationofthefrequencieswhere tunnelvibrationsdominate.Then,conditionalspectralanalysisdescribedindetailin AppendixCisperformedtoremovethecoherentportionoftunnelvibrationsfromthe aero-opticsignal. 3.5.2.4CoherentStructureConvectiveSpeed Theconvectionspeedofaberrationstructurescanbecalculatedbyeithercomputing atimedelayedcorrelationfunctionorbyanalyzingthecross-correlationspectralfunction. 108

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Duetolowfrequencynoiseintroducedbytunnelvibrations,thelattermethodismore robustandisusedtocalculatestructureconvectivespeed.Theestimateofthefrequency function H 1 2 betweenthetwobeamdeectionsignalsiscomputed, H 1 2 = P 2 1 P 1 1 ; {23 where P 2 1 isthespectralcross-correlationbetweenthetwobeamsand P 1 1 isthe spectralauto-correlationfunctionoftherstbeam.Theargumentoftheestimated frequencyresponsefunctioncanthenbeusedtodeterminethephaselead/lagbetween thetwosignals.Sincetheelevationangle seeFigure3-1andthebeamseparation distance l arebothknown,thestreamwiseconvectivespeedcanbecalculated, U c = l= sin )]TJ/F21 7.9701 Tf 6.586 0 Td [(1 ,where istheslopeofthebestlinettotheargumentof H 1 2 3.6FlowControlImplementation Thissectionsummarizestheexperimentalsetupsthatareusedtoimplementboth passiveandactivecontrol.Passivecontrolisestablishedwithcylindricalpinsmounted alongthechord-wisecenterlineofthemodel.Activecontrolisaccomplishedviasteady tangentialblowingalongthetopportionoftheaperture. 3.6.1PassiveFlowControl Previouseortsusepassivedevicestobothsuppressowseparationorreduceoptical degradationcausedbytheformationofashearlayerGordeyev etal. 2010 b ,2005;Haynes etal. 2012;Reynolds etal. 2012;Vukasinovic etal. 2010 b .Thepurposeofthepassive devicesistoproducesmallscalespanwisedisturbancestodisruptthecoherentnature,and hencereducetheintensityofthemainshearlayer.Forthepurposeoftheseexperiments, equally-spacedcylindricalpinsarearrangedalongthechord-wisecenterline x=S =0of themodelinseveralcongurations. 3.6.1.1PinConguration Inordertoestablishanoptimalcongurationofpins,twelvedierentcasesare testedandresultscompared.Theheight,spacing,anddiameterofthepins,normalized 109

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bytheboundarylayerheightattheapexoftheturret =1.5mm-determinedfrom PIVmeasurements,areallvaried.ThegeometricparametersaredenedinFigure3-21 andalltestcasesarepresentedinTable3-4andFigure3-22.Notethatcongurations P1-P6usepinsthathaveadiameterthatissmallerthantheboundarylayerthickness d=< 1whilecongurationsP7-P12usepinsthathaveadiameterthatislargerthan theboundarylayerthickness d=< 1.Thesesetsofcongurationswillbereferredto as`thin'and`thick',respectively.Similarly,congurationsP1-P3andP7-P9allhavepins thatprotrudethroughtheboundarylayer h=> 1whilecongurationsP4-P6and P10-P12havepinsthatthatareembeddedintheboundarylayer h=< 1.Thesesetsof congurationswillbereferredtoas`tall'and`short',respectively.Finally,thespacingof thepinsissystematicallyvariedforagivenpindiameterandheight. 3.6.1.2AssessmentofControl Theeectofeachcongurationisassessedwithbothquantitativeandqualitative measurements.Unsteadypressuremeasurementsalongfourlocationsontheturret windowareusedtodeterminetheeectontheunsteadinessinthenearwakeregion. Qualitatively,surfaceoil-owvisualizationshowstheeectonboththeseparation lineandthelengthoftherecirculationregion.Asasupplementtounsteadypressure measurements,initialhot-wireanemometryisusedtotakesurveysoftheseparatedshear layer.Furthermore,theaero-opticimpactofeachpassivecontrolcaseisassessedwith Malleyprobemeasurements.Finally,themostinterestingcasesareselectedandsPIVis performedinthewakeregion. 3.6.2ActiveFlowControl Anewmodeliscreatedtoallowsteadyblowingalongthetopportionoftheturret aperture.Amodicationwasmadetolletthejuncturebetweenthecurvedportionofthe turretandtheatapertureandablowingslotisaddedtodischargeawalljettangentto theatwindowdetaileddiscussionofthemodelprovidedinthefollowingsection.As thejetisejectedfromtheslot,itentrainsuidfromthefreestream.Duetothebalance 110

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betweencentrifugalforceandtheradialpressuregradient,withaenoughblowing,the owmayreattachalongthecenteroftheaperture.TheEuler-nequationsummarizesthis phenomenon, V 2 R = 1 @P @n : {24 Notethatforagivenvelocityandcurvature,thepressureincreaseswithincreasedradial distance.Thisinturnallowsthejetandentraineduidtoadheretothesurface. 3.6.2.1TurretModel Anewturretmodelisdesignedandfabricatedtoallowforsteadyblowing,tangential totheatwindow.Thisactivecontrolmodelimplementsasmoothtransitionbetween theconformalportionandtheataperture,asshowninFigure3-24A.Thisalleviatesthe eectofthegeometricdiscontinuityand,withenoughsteadyblowing,mayallowtheow toreattachalongtheturretaperture.Axed-heightblowingslotof2.5mmiscreated alongthetopportionoftheaperturewindow.Theslotiscomprisedof17individual oricesorientedsuchthattheowtravelsdirectlydowntheatwindowasopposed totravelingtowardtheradialcenter.Eachoricehasadiameterof2.27mmandare spacedequidistantfromeachother.26mmapartalongtheupperportionofthe window,asshowninFigure3-23.Thecongurationofmultipleoriceswaschosenover theconventionalopenslotduetopreviousworkperformedbyDano etal. 2011.They foundthatanarearatioof75%providedthegreatestperformanceenhancementinterms ofowreattachmentalongahighangleofattackairfoil.Withthatinmind,theoriceto slotarearatiousedinthisstudyis0.20.Notethatforagivenmassowrate,decreasing theoricetooverallslotratio A j =A slot resultsinanincreaseinjetexitvelocitydue todecreasedjetexitarea.AnillustrationofthemodelisprovidedinFigure3-24and detailsregardingtheslotgeometryareprovidedviatechnicaldrawingsinAppendixA. Theairdeliverysystem,characterization,andassessmentofcontrolarealldiscussedin thefollowingsections. 111

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3.6.2.2AirDeliverySystem Pressurizedairisprovidedbya300HPSullariLS20Tcompressorcapableof800 SCFM,locatedinanisolatedstructureoutsideofthemainbuilding.Afterpassing througha1200CABblowergeneratedairdryer,theairislteredandnallystoredin two3800galloncapacityvessels.Thepressureissetto140psiforallexperimentsandan AllicatmassowcontrollerMFC,model2000SLPM,isusedtoregulatethemassow. ForspecicationsontheMFC,seeTable3-5.TheMFCusesalaminarowelementwhich allowsthevolumetricowrate Q tobecalculatedviatheHagen-Poiseuilleequation, Q = Pr 4 8 L ; {25 where P isthepressuredropacrossthedevice, r istheradiusofrestriction, L isthe lengthoftherestriction,and isthedynamicviscosityofthespeciedgas.Both L and r arexedwithintheunit,while P ismeasuredand iscalculatedbasedon thetemperatureoftheuid.TheMFCusesasimplePIDcontrollertokeeptheow ratemeasuredinstandardlitersperminute,SLPMxedatthedesiredset-point. Multiplyingthisvaluebythereferenceddensitybasedon25Cand101.32kPa,thetrue massow_ m canbecalculated.However,amoreusefulparameteristhecoecientof momentum, C = mV j 1 V 2 1 A 0 ; {26 where V j isthejetvelocity, 1 isthefreestreamdensity,and V 1 isthefreestreamvelocity. TostayconsistentwithpreviousworkGordeyev etal. 2009;Purohit etal. 1983 a ; Schonberger1980;Vukasinovic etal. 2009 a ,thereferencearea A 0 isdenedasthefrontal areaoftheturretmodel.Thefollowingsectiondescribesthemeasurementtechniqueused tocalculatethejetvelocitynearthevicinityoftheslot. 3.6.2.3JetVelocityMeasurement SincetheowfromtheMFCtotheslotexitcannotbeassumedtobeisentropic, thejetvelocitymustbemeasureddirectly.Ahot-wireanemometerisplacedatthemodel 112

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centerline,2.5mmoneslotheightawayfromtheslotexit.Thislocationisdetermined bytraversingtheprobeinthejetowdirectionuntilobtainingthepeakjetvelocity. Note,however,thejetvelocityproleisnotmeasured.Fordetailsonthecalibrationand usageofthehot-wireanemometer,refertoSection3.3.1. Theprobeiscarefullyplacedatthedesiredlocationusingathree-axistraverse, drivenbyaParkersteppermotormodelOS22B-SNL10.Thetraversehasaresolution of2.3 minalldirections.TheMFCissettothedesiredowrateandthesignalfrom thehot-wireisacquiredusingaNIcDAQ-9162chassiswithafourchannelPXI-9234 dataacquisitioncard.Eachchannelhas24-bitresolutionwith114dBdynamicrange andabuilt-inanti-aliasinglter.Atthegivenmeasurementpoint,dataarecapturedat asamplingrateof10kHzfortenseconds.Afterallmeasurementsarecompletedand therawdataisconvertedtounitsofvelocity,thetime-averagedjetvelocityEq.3{3is computed.Thehot-wireprobeisalsotraversedalongtheslot,alwaysequidistantfrom theslotexit,anddataisacquiredateachoriceexitlocation.Resultsshowthatthe meanjetvelocityvariesbylessthan8%alongtheentirespanofthewindow.Atotalof eightblowingcasesarecharacterizedalongthecenterlineandtheresults,includingthejet velocity,massowrate,andcalculatedmomentumcoecient,arelistedinTable3-6. 3.6.2.4AssessmentofControl Theeectofeachcongurationisassessedwithbothquantitativeandqualitative measurements.Unsteadypressuremeasurementsalongfourlocationsontheturret windowareusedtodeterminetheeectontheunsteadinessinthenearwakeregion. Qualitatively,surfaceoil-owvisualizationshowstheeectonboththeseparationline andthelengthoftherecirculationregion.Theaero-opticimpactofeachactivecontrol caseisassessedwithMalleyprobemeasurements.Finally,themostinterestingcasesare selectedandsPIVisperformedinthewakeregion. 113

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Figure3-1.Modeldimensionsandrelevantparameters.Themodelhasadiameterof231 mmwithaslopediscontinuityof42 o betweentheatwindowmmin diameterandthehemisphere.Themodelissubmergedsuchthatitsheight protrudingfromthesurfaceisonly88.9mm,correspondingtoaheightto radiusratioofH/R=0.77. A B C D Figure3-2.Turretmodelimagesfromseveralperspectives.Aangled,Brear,Cfront, andDtop. 114

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A B Figure3-3.Theboundarylayeristrippedusinga0 : 5mmthicksawtoothtapeGlasfaser Flugzeug-Servicezig-zagturbulatortapeplacedat S=R =0 : 80fromthe leadingedgeofthemodel.ACoordinatesusedforlocationoftriptape.B Thegeometryofthetriptape. Figure3-4.Setupusedtocalibratehot-wireinsidethetunnelwithapitot-staticprobe usedforvelocityreference. 115

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Figure3-5. Br uel & Kjaer UA-0385noseconemountedonG.R.A.S.microphoneusedfor tunnelacousticmeasurements. Figure3-6.Staticpressureportlocations.Atotalofthirty-eight0 : 711mminnerdiameter tubulationsareinstalledinthemodel.Anevendistributionofeighteentaps spacedat S=R =0 : 0892intervals,arelocatedbetweentheleadingedgeof themodelandtheapex.Anotherseventapsareevenlydistributedspacedat S=R =0 : 0182intervalsbetweentheapexandtheatwindowdiscontinuity. Thelasttwelvetapsarespacedat8 : 10mmalongtheatwindow.Foramore detaileddrawing,refertoAppendixA 116

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Figure3-7.Unsteadypressuresensorlocationsonatwindow.Foursensorsare ush-mountedontheatwindowspaced14.56mmapart.Theatwindow canberotatedthroughafull360 o A B C D E F Figure3-8.PhotosoftheturretaperturewithunsteadypressuresensorslocatedatA0 o B45 o ,C90 o ,D135 o ,E180 o ,andF270 o .Theatwindowcanberotated throughafull360 o 117

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A B Figure3-9.Surfaceoilowvisualizationprovidesqualitativeinformationontheow topologysurroundingthemodel.Theuorescentdyeisamixtureofmotoroil anduorescentchalkwitharatioof1gofchalkper30mLofoil.The mixtureisappliedusinganeye-dropperatdiscretelocationsspaced approximately2 )]TJ/F15 11.9552 Tf 11.955 0 Td [(3cmapartoverthemodelanditsvicinity.Approximately 3mLofdyeisusedforeachexperimentalrun.ATopview.BAngledview. Figure3-10.Oilowvisualizationset-up.aSpectrolineultravioletlamps:model SB100P,bturretmodel,cNikonD300sdSLRwitha28mmf/2.8lens, anddNikonD70dSLRwitha50mmf/1.8lens.Eachcameraismanually focusedonthemodelandsettoanexposureof10sec,f/8.0,andISO200. BothcamerasareexternallytriggeredsimultaneouslyusingNikonCamera ControlProsoftware. 118

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Figure3-11.Shearlayermeasurementlocationsusinghot-wireanemometry.Velocity prolesaremeasuredatthe15streamwisemeasurementlocations,from x=H =0 : 45to4 : 75.Ateachlocation,theprobeistraversedin1mm incrementsinthelongitudinaldirection y=H foratotalof101measurement points.Theonlyexceptionarethethreelocationsclosesttotheturretwhere theprobeonlytraversestowithin3mmofthewindow.Table3-2listsall streamwisemeasurementplanes,theextentoflongitudinalmeasurements, andthetotalnumberofmeasurementpoints. 119

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Figure3-12.Particleimagevelocimetryschematic.AdaptedfromDynamics2007. A B Figure3-13.AParticleimagevelocimetrysetupandBPIVmeasurementwindows. Separatelightsheetsandregionsofinterestcorrespondtotheboundarylayer attheapexblueoutlineandnear-wakeregionredoutline. 120

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Figure3-14.SetupforstereoscopicPIV.Allmeasurementplanesarealignedinthe streamwisedirectionandarelocatedat z=H =0, z=H = )]TJ/F15 11.9552 Tf 9.299 0 Td [(0 : 31, z=H = )]TJ/F15 11.9552 Tf 9.299 0 Td [(0 : 62. Figure3-15.Aero-opticimagingset-upusingaNikond300swithSigma150mmf/2.8lens andUSAFresolutiontestchart.Frontviewontheleft,sideviewonthe right. 121

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Figure3-16.USAFResolutionTestChartusedforpreliminaryqualitativeaero-opticimagingtests.Theoutlinedareais exclusivelyusedforallcomparisons. 122

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Figure3-17.MalleyProbewindtunnelset-upconsistsofaCWlaserpassedthrougha beamsplitter,redirectedbysteeringmirrorsthroughfocusinglensestoapair ofpositionsensingdevicesPSD,eachequippedwitha532nmlter.Red squaresdenoteaccelerometerlocationsa1,a2,a3. 123

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Figure3-18.Malleyprobebeamlocationsalongtheturretatwindow.SetsB1B2,B3B4, B5B6,andB7B8areacquiredsimultaneouslyandallowtheconvectivespeed tobemeasured,discussedinSection3.5.2.4. Figure3-19.ThepositionsensingdevicePSDisretrottedwithahoodand532nm bandpassltertoreducecontaminationfromambientlight. 124

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Figure3-20.Beamdisplacement.Theleftdiagramshowsahead-onviewofthePSDand illustratestheindividualbeamdisplacementinboththex-andy-directions. Therightillustrationshowsthegeometryusedtocalculatethebeam deectionangle, y x iscalculatedinasimilarfashion. A B Figure3-21.Passiveowcontrolsetup.ATopviewpinlocationsevenlydistributedat s= increments.BParametersusedtodenepingeometryincludethepin height h ,spacing s ,anddiameter d 125

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A B C D E F G H I J K L Figure3-22.PassivecontrolcongurationsaspresentedinTable3-4.Notethat congurationsP1-P6usepinsthathaveadiameterthatissmallerthanthe boundarylayerthickness d=< 1whilecongurationsP7-P12usepinsthat haveadiameterthatislargerthantheboundarylayerthickness d=> 1. Similarly,congurationsP1-P3andP7-P9allhavepinsthatprotrude throughtheboundarylayer h=> 1whilecongurationsP4-P6and P10-P12havepinsthatthatareembeddedintheboundarylayer h=< 1. 126

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Figure3-23.Steadyblowingslotcomprisedofaxed-heightblowingslot.50mmalong thetopportionoftheaperturewindow.Theslotiscomprisedof17 individualoricesorientedsuchthattheowtravelsdirectlydowntheat window.Theratiooftheareaoftheoricetothatoftheentireslotis0 : 20. Furtherdetailsregardingtheslotgeometryareprovidedviatechnical drawingsinAppendixA. A B Figure3-24.Thesteadyblowingmodelimplementsasmoothtransitionbetweenthe conformalportionandtheataperture,alleviatingtheeectofthe geometricdiscontinuity.Axed-heightblowingslotof2.5mmiscreated alongthetopportionoftheaperturewindow,allowingsteadyblowing tangentialtothewindowsurfacetobeusedforactiveowcontrol.Details regardingtheslotgeometryareprovidedviatechnicaldrawingsinAppendix A.SteadyblowingmodelshownfromaAproleandBstraightonview. 127

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Table3-1.Randomuncertainty95%condenceintervalestimatesofcomputedvelocity andReynoldsstressterms Quantity95%condenceinterval U i 1.96 r 1 N u 0 2 i u 0 2 i 1.96 r 1 N u 0 4 i )]TJ/F15 11.9552 Tf 11.955 0 Td [( u 0 2 i 2 u 0 i u 0 j i 6 = j 1.96 r 1 N u 0 2 i u 0 2 j )]TJ/F15 11.9552 Tf 11.955 0 Td [( u 0 i u 0 j 2 Table3-2.Shearlayermeasurementlocations x=Hy=H #pts 0.4500.932{1.46148 0.6530.626{1.46164 0.8550.562{1.46181 1.0580.337{1.461101 1.2610.337{1.461101 1.5100.337{1.461101 1.7600.337{1.461101 2.0010.337{1.461101 2.2590.337{1.461101 2.5090.337{1.461101 2.7590.337{1.461101 3.2580.337{1.461101 3.7580.337{1.461101 Table3-3.MalleyProbepositionsensingdeviceparameters OBP-A-4LSpecications Sensorsize4 4mm OutputVoltage 3Volts Responsetime < 20 s -3dBBandwidth300kHz Sensitivity.0 m/.0 V Resolution1.0 m Linearity 1%fullscale Maximumlightsensitivity1.5W/cm 2 128

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Table3-4.Passiveowcontrolcongurations d=s=h=d=s=h= P10.613.76.7P71.213.76.7 P20.66.86.7P81.26.86.7 P30.63.46.7P91.23.46.7 P40.613.70.7P101.213.70.7 P50.66.80.7P111.26.80.7 P60.63.40.7P121.23.40.7 Table3-5.Massowcontrollerdevicespecications Alicat2000SLPMMFCSpecications Accuracy .4%ofReading+0.2%ofFullScale Repeatability 0.2% OperatingRange0.5%to100% TypicalResponseTime100ms STPReferenceConditions25 o Cand14.696psia MaximumPressure145psig SupplyVoltage24-30Vdc SupplyCurrent0.750Amp PhysicalDimensions5.5H 8.1W 2.9D Table3-6.ActiveControlSteadyBlowingCases SLPM_ m kg/s V j m/s C 1000.197 10 )]TJ/F21 7.9701 Tf 6.587 0 Td [(2 67.50.023 2000.395 10 )]TJ/F21 7.9701 Tf 6.587 0 Td [(2 133.20.089 3000.593 10 )]TJ/F21 7.9701 Tf 6.587 0 Td [(2 167.40.139 4000.789 10 )]TJ/F21 7.9701 Tf 6.587 0 Td [(2 207.90.211 5000.987 10 )]TJ/F21 7.9701 Tf 6.587 0 Td [(2 233.10.260 6001.184 10 )]TJ/F21 7.9701 Tf 6.587 0 Td [(2 258.30.311 7001.381 10 )]TJ/F21 7.9701 Tf 6.587 0 Td [(2 287.90.375 8001.579 10 )]TJ/F21 7.9701 Tf 6.587 0 Td [(2 310.50.426 129

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CHAPTER4 BASELINERESULTS Thischapterwillsummarizetheexperimentalresultsforthebaselineow. Firstwindtunnelcharacterizationresultsarepresented.Then,steadyandunsteady pressuremeasurementsalongwithsurfaceoilowvisualizationareusedtoanalyzethe three-dimensionalowtopology.Wakeandshearlayermeasurementsaremadeusing particleimagevelocimetryandhot-wireanemometry.Finally,aero-opticmeasurementsare presented. 4.1WindTunnelCharacterization 4.1.1IncomingBoundaryLayer Previousexperimentalstudiesregardingowoverhemisphereshaveshownthat theincomingboundarylayerhasalargeeectonthedevelopmentnearwakeregime. Toy etal. 1983andSavory&Toy1986foundthatthevorticitywithintheincoming boundarylayerisdirectlyrelatedtothestrengthofthehorseshoevortices,andhencethe recirculationwithinthewake.Toassessthesignicance,boundary-layermeasurementsare carriedoutusingahot-wireprobe. UsingtheexperimentalmethoddescribedinSection3.3.1,incomingboundarylayer prolesaremeasuredinamodel-freetestsectionforfreestreamvelocitiesof40m/s and90m/s.Thehot-wireisplacedat1.37mdownstreamfromthestartofthetest section,correspondingtoalocationthatisoneturretheightupstreamofthemodel.The rstmeasurementpointistakenat0.5mmabovethetestsectionoorandistraversed in0.5mmincrementsforatotalof80locations.Forallcases,theowisallowedto developalongthesmoothtunnelwall.Figures4-1and4-2showtheresultsforfreestream velocitiesof40m/sand90m/s.Themeasuredvelocity,velocityuctuations,anddistance fromthewallarenormalizedbythefreestreamvelocity U 1 ,freestreamvelocitysquared U 2 1 ,andturretheight H ,respectively.Theboundarylayerheight ,displacement thickness ,momentumthickness ,formfactor = ,andReynoldsnumberbased 130

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onmomentumthicknessRe arecalculatedandpresentedinTable4-1.Toensurethat thetotalnumberofsamplesissucientforconvergence,themovingaverageateach y locationisplottedandisshowntoliewithinthecalculated95%condenceinterval. Notethatforbothfreestreamvelocities,theboundarylayermeasuresroughly 29 : 5 0 : 3mm,providingtheexperimentalconditionthattheratiooftheincoming boundarylayertotheturretheightis =H =0.30.Theshapefactor,denedasthe ratioofmomentumthicknesstodisplacementthickness,is1 : 4 0 : 1forbothboundary layersindicatingfullyturbulentprolesWhite2006.ThecalculatedReynoldsnumber basedonmomentumthicknessRe isgreaterthan6000,alsoindicatingturbulent prolesDeGraa etal. 1998.Themaximumturbulentintensity,denedas u 0 rms =U 1 ,is calculatedtobe0.05forbothcases. Theboundarylayerprolesarealsoplottedindimensionlessform,seeFigure4-3. Theinnervariablesconsistingofdimensionlesswallunits, y + = yu = ,anddimensionless velocity, u + = u=u ,arecalculatedfromtheexperimentaldata,where u = q w isthe frictionvelocity, isthekinematicviscosity.ASpaldingtWhite2006isappliedtothe experimentaldatatoextractthefrictionvelocity.Theexperimentalresultsarecompared toboththeSpaldingcurveEq.4{1andthelawofthewallEq.4{2, y + = u + + e )]TJ/F23 7.9701 Tf 6.586 0 Td [(B e u + )]TJ/F15 11.9552 Tf 11.955 0 Td [(1 )]TJ/F22 11.9552 Tf 11.955 0 Td [(u + )]TJ/F15 11.9552 Tf 13.151 8.087 Td [( u + 2 2 )]TJ/F15 11.9552 Tf 13.15 8.087 Td [( u + 3 6 ; {1 u + = 1 ln y + + B; {2 where and B aredimensionlessconstants.Foralargerangeofturbulentowsover smoothwalls,thedimensionlessconstantshavebeenfoundtobenear-universal: =0 : 41 and B =5 : 0White2006. 4.1.2AcousticNoiseFloor Spectraforthetunnelacousticcontaminationareobtainedatfreestreamvelocitiesof 0 )]TJ/F15 11.9552 Tf 12.318 0 Td [(90m/sinincrementsof10m/sinamodel-freetestsection.Theacousticsproduced bythetunnelarerstexaminedintheabsenceofamodel.Theresultsarepresentedin 131

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Figure4-4.ThetrendshowsincreasingSPLwithincreasingfreestreamvelocity.Thenoise generationisattributedtothein-line440VmotorcoupledwiththeToshibaModelH7 variablefrequencydrive. Whenthefrequencyisnon-dimensionalizedbythefreestreamvelocity U 1 andtest sectionheight L ,thetonalacousticpeakscollapse.ThisphenomenaisshowninFigure 4-5.Interestingly,thereappearstobetwonoisesources.Therstnoisesourcegenerates atoneatSt L =3 : 25andhasthreedominantharmonicsSt L =6 : 50 ; 9 : 75 ; 13 : 0.The secondisahigherfrequencytonethatappearsatSt L =37 : 4. Inordertodetermineifthereisanyacousticcontaminationfromthemodel,thetest isrepeatedwiththemodelinthetestsection.Theresultsforafreestreamvelocityof 90m/sareshowninFigure4-6.Thepresenceofthemodelhasnoeectontheacoustic signalmeasuredinthetestsection. Furthermore,theeectoftheacousticcontaminationontheunsteadypressure signalmeasuredbythesensorsontheatwindowofthemodelisinvestigated.Figure 4-7showstheacousticsignalmeasuredbythemicrophoneinthefreestreamalongwith theunsteadypressuresignalmeasuredbythesensoronthemodel.Thefrequencyisnow non-dimensionalizedbythemodelheight, H ,andfreestreamvelocity.Notethatforvalues greaterthanSt H =2 : 5,theunsteadypressuremeasurementsonthemodelaredrownedby acousticcontamination.Therefore,fortherestofthisstudy,datawillonlybeprocessed forvaluesofSt H < 2 : 5withanynoisecontaminationremovedfromthespectraatlower frequencies. 4.2FlowMeasurements 4.2.1StaticPressureDistribution Thestaticpressurealongthesurfaceofamodelcanbeusedasasimple,yeteective, wayoflocatingaseparationpoint.Whennormalizedbydynamicpressureandplotted versuslocationalongthecenterline,theycanqualitativelyindicateseparationbyshowing asuddendropinpressurerecovery.Themeanpressuredistributionsonthelongitudinal 132

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centerlineoftheturretareobtainedoverarangeofReynoldsnumbersfromRe H = 2 : 27 10 5 )]TJ/F15 11.9552 Tf 11.427 0 Td [(5 : 10 10 5 Ma=0.12-0.26.Whenthepressuredistributionsarenormalized bythedynamicpressuremeasuredwithapitot-staticprobewellupstreamofthemodel, thedatafromthethreeReynoldsnumberscollapseontoasinglecurve.Thevariationof surfacepressuredistributionareillustratedinFigure4-8A. Astheincomingboundarylayerinteractswiththeupstreamportionoftheturret,the owovertheturretbrieydecelerates,indicatedbythesmallpressurepeakatpressure taploc.3,andthenaccelerateswiththehelpofthefavorablepressuregradient.The owcontinuestoaccelerateuntilitreachesloc.16,justupstreamoftheturretapex. Thisobservationisconsistentwithpreviousdatareportedforowsoverhemispherical structuresSavory&Toy1986,wheretheowbeginstodeceleratebeforereachingthe adversepressuregradient.Whentheowapproachesthejuncturebetweenthesmooth turretcurvatureandtheabruptatwindow,thecoecientofpressureprolesindicate theonsetofowseparation,asnotedbythesuddendropinpressurerecoveryatloc.26. Itisinterestingtonotethatearlyexperimentsondome-likestructuresfoundthatfor incomingboundarylayerswithturbulentintensitieshigherthan15%,themeanpressure coecientswereinsensitivetochangesinReynoldsnumbersforRe >O 10 5 Cheung& Melbourne1983.Therefore,thecollapseofthecoecientofpressurecurveisindicative ofanincomingboundarylayerwithhighturbulentintensity,whichisconrmedwiththe directmeasurementoftheboundarylayer. Figure4-8Bshowsthestandarddeviationofthepressurecoecientasafunctionof locationforeachReynoldsnumbercase.NotethatthereisaReynoldsnumbereecton thestandarddeviation,oructuatingcomponent,ofthepressurecoecient.Thiseectis noticeableinregionsofhighturbulence,i.e.neartheincomingboundarylayerwithturret interactionandalongthewindowwheretheowisseparated.Interestingly, C islarger inmagnitudeforthelowerReynoldsnumberthanthatobtainedforthehigherReynolds 133

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numberow.TheseresultssupportthendingsofTaylor1992,whostudiedowsovera hemisphereforRe H =0 : 65 10 5 )]TJ/F15 11.9552 Tf 11.955 0 Td [(5 : 10 10 5 4.2.2UnsteadyPressure Unsteadysurfacepressuremeasurementsalongtheatwindowaretakentomeasure thepressureuctuationfootprintleftbytheseparatedoweldinthenearwakeregion. ThefollowingsectionsdescribemeasurementsacquiredforRe H =2 : 27 10 5 )]TJ/F15 11.9552 Tf 12.126 0 Td [(5 : 10 10 5 Ma=0.12toMa=0.26.Theatwindowisrotatedaboutitsaxisfromto0 o to180 o ; in15 o incrementsforeachtestrun.Forthepurposeoftheresultspresentedhere,Figure 4-9showsthenomenclatureestablishedforlocationofthepressuresensors.Notethat loc.4forallwindowangleorientationsisthesame,andisthereforeusedtoconrm repeatabilityoftheexperiments. 4.2.2.1SpatialAveragingEects Ithasbeenshownthatthenitesizeofatransducer-sensingelementlimitsitsspatial resolutionofapressureeldassociatedwithalocalturbulentowCorcos1963.Such pressureeldsaretranslatedataspeedcomparabletothecharacteristicvelocityofthe owandmayresultinalackofresolutioninspacecausinganapparentinabilitytoresolve intime.Theresultisanattenuationofthecalculatedspectraldensityacrosstheentire frequencyrange.Todetermineifthereisaspatialaveragingeectwiththeunsteady pressuremeasurementspresentedherein,threepressuretransducerswithvarioussensing elementsizesareusedtomeasuretheunsteadypressureatloc.1,0 o seeFigure4-9for reference.Thepressuresensorshavediaphragmsizesof6.45mmG.R.A.S.40BEwith type26CBpreamplier,3.18mm Br uel & Kjaer 4138-Awith2670preamplier, and0.91mmMEMSproprietary.FormoreinformationontheMEMSproprietary microphone,refertoWilliams2011.Theresults,plottedinFigure4-10,showno discernibledierencewithinuncertaintybetweenthethreemeasuredsignals,indicating thatforthefrequencyofinterestthereislittletonospatialaveragingeects. 134

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4.2.2.2ParameterNon-dimensionalization Figure4-11showsthebenecialeectsofnon-dimensionalizingthefrequencyand powerspectraldensity.Asmentionedinthepreviouschapteralow-passlterwitha cut-ofrequencyof2.5kHzisappliedtoallunsteadypressurespectratoremovethe eectsofacousticcontamination.Fortheplotsshown,thewindowwaskeptatthe0 o orientationandonlytheunsteadypressureatloc.1ispresented. Theunsteadypressureinthewakeexhibitabroadpeakatlowfrequenciesthat,with increasingReynoldsnumber,bothshiftstohigherfrequenciesandincreasesinmagnitude, ascanbeseeninFigure4-11A.Thislowfrequencypeakisbelievedtocorrespondtothe vortexsheddingfrequencyoftheowoverthecenteroftheturret.Inordertoconrm thesendings,thefrequencyisnon-dimensionalizedbyturretheight, H ,andfreestream velocity U 1 toproduceaStrouhalscaling, St H = fH U 1 : {3 WhenthespectraareplottedasafunctionoftheStrouhalnumber,thelowfrequency peakcollapsestoavalueofapproximatelySt H =0 : 1asseeninFigures4-11Band4-11D. Notingthatthisscalingiswithrespecttotheturretheightandnotdiameter,thisvalueis consistentwiththecommonlyknownblubodyStrouhalnumbersheddingof0.2Roshko 1955.AtSt H =0 : 3,thefrequencycontentbeginstoleveloandremainsconstant untilroughlySt H =1 : 0.ForSt H > 1 : 0,theunsteadypressureuctuationsrollowith increasingfrequency. Furthermore,thespectralpowerisconvertedtoengineeringunitsandisthen non-dimensionalizedbythedynamicpressure,viaEquation3{16.Whenboththe frequencyandspectralpowerarenon-dimensionalized,thespectracollapsefor Re > 3 : 4 10 5 135

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4.2.2.3TripTapeLocation Itisoftendesirabletolocateanoptimalpositionfortheplacementofatripping mechanismtocauseboundary-layertransitionfromlaminartoturbulentow.Ifthe triptapeisplacedneartheleadingedgeofthemodel,theowdisturbancemaynot besucienttotransitiontheowduetothefavorablepressuregradient.However, thereisanoptimallocationwherethetrippingmechanismcanbeplacedtoensurethat fulltransitionissuccessful.Withaxedtrip-tapecongurationseeFigure3-3for dimensions,adirectapproachproposedbyBraslow&Knox1958wasusedtocalculate apreliminarytriplocation. Fortheexperimentspresented,thetriptapeisplacedattwolocationsalongthe turretmodelcenterline, S=R =0 : 535and S=R =0 : 803.SeeFigure3-1forcoordinate system.Forbothcases,theunsteadypressurewasmeasuredatloc.1andloc.4withthe windowatthe0 o ,90 o ,and180 o orientations. TheeectoftriptapelocationforRe H =3 : 40 10 5 Ma=0.18isillustratedin Figure4-12forseverallocationsalongtheatwindow.Notethatforalllocations,the spectrashownarenoticeablydierent.Thisnon-collapseofthedataisindicativeofa dierentowregimeforeachtripconditionandisundesirable.Figure4-13showsthe resultsforRe H =5 : 10 10 5 Ma=0.26.Theseresultsshowacollapseofdataforboth tripconditions,stronglyindicatingfullyadevelopedturbulentowregime. However,inordertodeterminewhichtriplocationwillyieldfullyturbulentow atallReynoldsnumbersofinterest,thespectraforeachtripcaseisplottedforseveral ReynoldsnumbersandtheresultsareshowninFigure4-14.Theresultsfromawindow orientationof0 o atloc.1,illustratethatfortheowtobefullyturbulentattheat window,thetriptapemustbeplacedfurtherdownstreamthan S=R =0 : 535,with S=R =0 : 803beingasuitablelocation.Allsubsequentexperimentsareconductedwiththe triptapelocatedat S=R =0 : 803. 136

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4.2.2.4FluctuatingPressureSpectraAcrossTurretWindow Theuctuatingpressurespectraareplottedasafunctionoflocationalongtheat windowforRe H =5 : 10 10 5 Ma=0.26.Figure4-15illustratestheunsteadypressure forseveralwindoworientations o ,45 o ,and90 o .Spectralcontourplotsarecreatedfor allthreecongurations.Figures4-15A,Bshowtheunsteadypressurealongthesymmetric centerlineofthemodel.Asthelocationmovesfromtheturretapextothetunneloor loc.1toloc.7,theoverallunsteadypressurelevelsincreaseinabroadbandsenseand thedistinctsheddingfrequencyatSt H =0 : 1isdrowned".Thisincreaseinunsteady pressureisbelievedtobecausedbytheinteractionoftheincomingturbulentboundary layer,whichwrapsaroundthemodeltoformahorseshoevortex,withtheseparatedwake region.Figures4-15C,Dshowasimilartrend,havingthelargestunsteadypressureat thelocationnearestthetunneloor.Finally,Figure4-15E,Fareprovidedtoshowthe symmetryacrossthecenterlineoftheturretmodel. Thespectraarealsoplottedforlocationsaroundtheouterringofthewindow. Figure4-16Aillustratesthespectraatloc.1forwindoworientationsfrom0 o )]TJ/F15 11.9552 Tf 12.951 0 Td [(90 0 ForSt H < 1 : 0thespectrallevelincreasesasthewindowangleisincreased.For1 : 0 < St H < 2 : 5,however,thespectrallevelshowstheoppositetrend,withdecreasingunsteady pressurewithincreasingwindowangle.FocusingonFigure4-16B,asimilar,butmore pronouncedtrendisfoundforSt H < 1 : 0astheangularpositionchangesfrom90 o to180 o ForSt H > 1 : 0,theunsteadypressurecontinuestoincreaseasthewindowangleincreases. Thisincreaseinunsteadypressurecanbeaccreditedtotheinteractionoftheseparated wakeregionwiththerecirculatingow,whichisstrongestatthejuncturebetweenthe windowandthetunneloor.TheseowphysicsarefurtherdiscussedinSection4.2.3 withthehelpofoilowvisualization. Tohelpbetterunderstandthedistributionofunsteadypressurealongthewindow, measuredspectraareplottedassurfacecontoursforvariousfrequencyrangesforRe H = 5 : 10 10 5 Ma=0.26.Figures4-17-4-19showtheunsteadypressurecontouratseveral 137

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frequencies.Eachplotshowsthethirdoctavebandaboutthelistedcenterfrequency, f c Thelower f l andupperlimits f h oftheaveragearecalculatedby f l = f c = 1 = 6 and f h = f c 1 = 6 .AllfrequencyrangesarelistedinTable4-2.Forthelowfrequencyrange showninFigures4-17and4-18, : 25 < St H < 1.0,thedominantregionsofunsteady pressureareconcentratedalongtheportionofthewindowclosesttothebase.Thisis expected,asthemainsourceofunsteadypressureatthelowfrequenciesarethelarge coherentstructureswithintherecirculationregionthatmanifesttheirwayupfromthe bottomofthewindow.Figure4-19showstheunsteadypressuretrendsasthefrequency ofinterestisincreasedpast1000HzSt H =1.0.Thetop-mostregionsonthewindowsee anincreaseinunsteadypressure.Thisisduetothemuchsmallercoherentlengthscales high-frequencyembeddedwithintheseparatedshearlayer. 4.2.2.5CoherentStructureConvectionSpeed Thecrosscorrelationandcoherencefunctionsarecomputedfromuctuatingpressure signalsmeasuredfromtwoadjacentpressurelocationsalongthewindow.Thisanalysis providesinformationontheconvectivespeedofintegralscalesacrosstheatwindow. Phasedelayandcoherencebetweentwopressuretransducersloc.1andloc.2ata windoworientationsof0 o ,90 o ,and180 o arepresentedinFigure4-20. Thephaseplotsshowalineardependencewithincreasingfrequency,indicatingthe convectivenatureofcoherentstructures.Aftercalculatingthephaseslope,theaverage timedelay, ,betweenthetwounsteadypressuresignalscanbefound.Foragivensensor separationlength,theconvectivespeedsoftheowstructuresarethencalculatedby dividingthestreamwisedistancebetweenthesensorsbythecalculatedtimedelay. Forthe0 o windowrotationangletoprowinFigure4-20,wherethetwosensors arelocatedclosesttotheseparationline,theconstantphaseslopesuggestsacoherent structureconvectivespeedof0 : 81 U 1 .Thesendingsaresupportedbytheresultsfrom Gordeyev etal. 2004 b ,whofoundtheconvectivespeedoftheseparatedshearlayer inthenearwakeregiontobebetween0.6and0.8ofthefreestreamvelocity.Their 138

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resultswereobtainedforaat-windowturretmountedonacylindricalbase.Further investigationalongthelocationclosesttothejuncturebetweenthebaseofthemodeland theturretwindowbottomrowinFigure4-20showsaconvectionspeedofonly0 : 44 U 1 Furthermore,thephasedierencebetweentwosensorsthatareatthesamestreamwise locationbutdierentspanwiselocationalongthewindowmiddlerowinFigure4-20 indicatesthatthebulkofcoherentstructuresconvectinthestreamwisedirection. 4.2.3SurfaceOilFlowVisualization Theglobalbaselinetopologyisinvestigatedusingsurfaceoilowvisualizationfor Re h =2 : 27 10 5 andRe H =5 : 10 10 5 .Figure4-21showsthedevelopmentoftheoilasit travelsovertheturretatRe H =5 : 10 10 5 ,highlightingsomeofthekeysurfacefeatures. Upstreamoftheturret,theincomingboundarylayerhassignicantspanwisevorticity.As theboundarylayertravelsfurtherdownstream,itwrapsaroundtheturretandcreatesa horseshoeshapedvortex,givingrisetosymmetricbutopposingportionsofstreamwise vorticity.Astagnationpointisformedjustupstreamoftheturretleadingedge,and theouterowisdisplacedbytheturretblubody.Theowthenacceleratesalong thesurfaceandinitiallyseparatesalongthecenterlineoftheturret.Thisvisualization supportsthendingsfromthestaticpressuremeasurements,thattheowseparatesinthe centerlineduetothegeometricconstraintoftheatwindow. Alongthesidesoftheturret,theowcontinuestostayattacheduntilboth three-dimensionaleectsandanadversepressuregradientcausetheowtofullyseparate. Nearthejunctionoftheturretandthesupportingwall,however,theboundarylayer re-energizestheowcausingtheowtostayattachedfurtherdownstreambestvisualized inFigure4-21F.Theensuingseparatedowcreatesarecirculatingwakethatreattaches lessthanaturretheightdownstreamofthemodelandcausesowtotravelbackupthe atwindow.Thehorseshoevorticestravelalongthespanwiseedgesoftheturretandthen separate,continuingdownstream. 139

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Asmentionedearlier,thetrippedowshowssimilarunsteadypressuredistributions, andthereforesimilarowpatternsareexpectedbetweenalltheReynoldsnumbersstudied inthisexperiment.Tofurtherconrmthisnding,oilowvisualizationwasattempted forRe H =2 : 27 10 5 andRe H =5 : 10 10 5 .Figures4-22and4-23depictthedierences betweenthetrippedandun-trippedsurfacepatternsforthetwoReynoldsnumbercases. Themajordierencebetweenthetrippedandun-trippedsurfacepatternsforthe Re H =2 : 27 10 5 istheseparationline.Whentheowisnottripped,theseparation lineoccursfurtherdownstreamandappearstobeinuencedmostlybythegeometric constraintoftheatwindow.Amoresubtledierenceisthelocationoftheaftstagnation pointintheow.Thissuggestsalaminarseparationforthecasethatisnottripped.The trippedandun-trippedcaseshaveastagnationpointthatislocatedat0.5and0.3turret heightsfromthetrailingedgeofthemodel,respectively.Thesendingsareconsistent withtheunsteadypressureresultswhichshowthatatthelowReynoldsnumbercases,the owregimesaredrasticallydierentforalltripconditions. Figure4-23showsthattheseparationlineandoverallowpatternsarenearly identicalforthetrippedandun-trippedcasesatRe H =5 : 10 10 5 .Bothcaseshavethe rearstagnationpointlocatedat0.6turretheightsfromthetrailingedgeofthemodel. ComparingFigures4-22Aand4-23B,thelocationofthetwostagnationpointsmoveaway fromthemodelastheReynoldsnumberbecomeslarger.Thistrendisconsistentwith experimentsperformedonsurface-mountedhemisphericalturrets,wheretherecirculation regionspannedlessthanaturretdiameterawayfromatrailingedgeofthemodelToy etal. 1983.Ithasbeenshownthatturretsmountedonacylindricalbasehavemuch largerrecirculationregions,withsomecasesspanningalmost1.5radiifromthetrailing edgeofthemodelVukasinovic etal. 2009 b ,2010 b 4.2.4BoundaryLayeratTurretApex Inthesamefashionthattheincomingboundarylayerplaysalargeroleintheow overahemisphere,theboundarylayerattheapexoftheturretwillhelpdictatethe 140

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implementationofspecicowcontroltechniques.Theresultsofturbulentowovera atplateathighReynoldsnumbersserveasaguidetodetermineanapproximateviewing windowforPIVmeasurements. Forthecaseofaturbulentboundarylayeronaatplate,themomentumintegral equationcanbeusedtopredicttheboundarylayerheightasafunctionofdownstream location.Takenfromvariousexperimentsofowthroughapipe,itiswidelyacceptedto useaone-seventhpowerlawtoscaletheboundarylayerheightWhite2006.Substituting intothemomentumintegralequation,andassumingthattheboundarylayerheightiszero atapredetermined x =0,thescalinganalysisyields x = 0 : 16 Re 1 = 7 x : {4 Forthecaseoftheboundarylayergrowthontheturretmodel,theorigin x =0is locatedatthestagnationpointonthefrontportionofthemodel.Thispointisdirectly extractedfromstaticpressuremeasurementsseeFigure4-8A.Thedistancefromthis origintothedesiredmeasurementlocationturretapexiscalculatedtobe0.06m.For afreestreamvelocityof90m/s,theabovescalinganalysispredictsaboundarylayerwith anapproximateheightof1.9mm.Note,however,thattheanalysisassumednopressure gradientatplateandthuswilloverpredicttheboundarylayerheight. Motivatedbytheinitialcalculations,aPIVsetupdescribedinSection3.4.5.1is usedtomeasuretheboundarylayerheight.Figure4-24AshowstheresultsfromthePIV measurements.Asingleprolecorrespondingtothelocationattheapexoftheturretis plottedinFigure4-24B,showingaboundarylayerheightofapproximately1 : 5mm.As expected,themeasuredheightisslightlylessthanthepredictedheight,primarydueto theaccelerationoftheowcausedbythefavorablepressuregradient.Quantitatively,the localfreestreamvelocityoverthetopoftheturretismeasuredtoberoughly1.33 U 1 ThisresultsinalocalMa=0.35,whichintroducesthecompressibilityeectsnecessaryto measureaero-opticdistortions. 141

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4.2.5NearWakeRegionCharacterization SurfaceoilowvisualizationSection4.2.3andpressuremeasurements Section4.2.2presentedhereinhaveillustratedthecomplexnatureofowarounda three-dimensionalbody.AsshownbypreviousinvestigationsLeder etal. 2003;Manhart 1998;Savory&Toy1986;Tamai etal. 1987;Toy etal. 1983,thetransferofmassand momentumwithintherecirculationregionofahemisphereisaectedbyseveralprocesses. Astheowseparatesintheaftsectionofabody,theroll-upprocesscausesvortices toformwithintheshearlayerwhichleadstostrongstreamwiseuctuationsManhart 1998.Duetothehighthree-dimensionalityoftheow,additionaluctuationtermsare introduced.Specically,inthereattachmentregion,themomentumisdistributedfrom awall-normalcomponenttoastreamwiseandlateralcomponentSavory&Toy1986. Moreover,theseparationfromthehemispherealongthesidescausestheboundingshear layerstoleadtoperiodicsheddingofVon-Karmanvortices,introducingmoreunsteadiness inthelateralvelocitycomponents. Inthissection,theoveralloweldatMa=0.26isinvestigatedforaat-window turretbyinspectionofthespatialdistributionsofthemeanvelocityeldandsecond-order moments,alongwithtemporalspectraintheshearlayers.AsdescribedinSection3.4.5, thewakeregionischaracterizedusingsPIVwhichextractsallthreevelocitycomponents withintheplanareld.Then,bytraversingahot-wireanemometeralongseverallocations withinthecenterplane,spectrawithintheshearlayerarediagnosed.Themainregionof interestisthatdirectlydownstreamoftheturretwindow.Sincetheowhasbeenshown tobesymmetricaboutthecenterline,three x )]TJ/F22 11.9552 Tf 12.497 0 Td [(y planesononesideofthewindoware selectedcorrespondingto z=H =0 : 0symmetryplane,-0.31,and-0.62edgeofat window,asshowninFigure4-25. 4.2.5.1AccuracyofsPIVMeasurements Beforeanassessmentofthesecond-ordermomentsispresented,itisimportantto rstunderstandtheaccuracyofthesPIVmeasurementsinregardstoturbulentow.To 142

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dothis,thesub-pixelaccuracyofthecorrelationmustbecalculated.Inordertoassumea sub-pixelaccuracyofthedisplacementsmeasuredontheimageplane,themeandiameter oftheseedparticlesontheimageplanemustbegreaterthanonepixel.Ifthiscondition issatised,thentheresultingcorrelationsrepresentingthelightintensitydistributionon theimageplanecanbecharacterizedasobeyingaGaussianproleAdrian&Yao1985. Toverifythatthisconditionismet,thenominalparticlediameterasprojectedontothe imageplanecanbeestimatedby d e = q M 2 d 2 p + d 2 s {5 where d p isthenominalparticlediameterinphysicalunitsinthiscase1 m ,asquoted bytheseedermanufacturer,and d s isthediameterofthepointresponsefunctionofa lensattherstdarkringoftheAirydiskintensitydistributionAdrian&Yao1985. Themagnicationfactor M istheratiobetweenthesizeoftheprojectionontheimaging sensortothephysicalsizeinspace.Tocalculatethemagnicationfactor,thepixelpitch ofthecamerasensor.4 m/pxismultipliedbytheresolutionforeachtestcase 13 px/mm.Then,theAirydiskcanbecalculatedvia d s =2 : 44 M +1 f # {6 where f # isknownasthef-stopandisthefocallengthofthelensdividedbythecamera aperture,and =532 nm isthewavelengthofincidentlightsheet.InAppendixB,Tables B-2andB-3listthemagnicationfactors, f # ,computedAirydiscsize d s ,andcalculated nominalparticlesize d e forallsPIVcases.Sinceallresultsindicateanimageparticle diameterofgreaterthanonepixel,thecurrentsPIVset-upsatisesthesub-pixelaccuracy requirements. Then,toperformtheaccuracyanalysis,an rms sub-pixelerrormustbedened. Nobach etal. 2005investigatedtheaccuracyofdierentPIVinterpolationmethodson numericallygeneratedparticleimages.Theparticlesizeswerevariedtodeterminethe 143

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rms errorinsub-pixelaccuracywithsimulatedphotonnoisetoresembleexperimental conditions.Itwasfoundthatforthecaseofaparticlediameterof2.1pixelsresultedin anRMSerrorofapproximately0.02pixels.Thisresultisverysimilartothevalueof0.03 pxasquotedbyLaVisionDaVis2010.Basedonthesub-pixelerror,resolutionofthe image,and dt betweenimagecaptures,theaccuracyinthe rms velocitymeasurementsis calculatedtobe0.85m/s. 4.2.5.2MeanCharacteristics ThecontourplotsinFigures4-26showmeanvelocityandtheassociatedstreamlines alongthethreemeasurementplanes.Conrmingtheresultsfromsurfaceoilow visualization,thecross-sectionoftherecirculationregiondecreaseswithincreasing lateraldirection.Savory&Toy1986showedthatthatthelengthofthereattachment regionisdeterminedbytheturbulenceintensityandnotthemeanvelocityproleofthe incomingboundarylayer.Thestreamlinepatternsshowthatentrainmentofuidintothe recirculationregiontakesplacenearthetunneloorforeachlateralmeasurementplane. 4.2.5.3Second-orderMomentsandVorticity ThestrengthanddistributionoftheReynoldsstressesisdirectlyrelatedtothe individualmixingprocessofthestronguctuatingcomponents.Inordertoinvestigate thespatialdistributionsoftheReynoldsnormalandshearstresses,lledcontoursofthese quantitiesareplottedinthreeverticalplanesat z=H =0.0symmetryplane, z=H = )]TJ/F15 11.9552 Tf 9.298 0 Td [(0 : 31,and z=H = )]TJ/F15 11.9552 Tf 9.299 0 Td [(0 : 62normalstressesinFigure4-27andshearstressesinFigure 4-28.Intheinitialportionoftheseparatedshearlayer0 : 5 x=H 1 : 0thestreamwise uctuations =U 1 aresignicantlylargerthanboththespanwiseandvertical components,asshowninFigure4-27,indicatingtheformationofatwo-dimensional shearlayer.ThischaracteristicissupportedbyManhart1998whostudiedtheow overahemispherewithsimilarincomingboundarylayerconditions.Itisnotuntilfurther downstream x=H> 1 : 0thatsheddingfromthesidesoftheturretstarttointroducehigh 144

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three-dimensionalmixing,resultinginbothspanwiseandlongitudinaluctuationswithin theshearlayer. Asshowninpreviousinvestigations,therearesomefeaturesintheReynoldsstress contoursthatprovideevidenceofstrongthree-dimensionalow.First,thevertical Reynoldsshearstress =U 1 componentislowinthevicinityofthetunneloor Figure4-28A-C,whichwouldnotbeexpectedinatwo-dimensionalowwithastrong recirculationregion.InsteadthelateralReynoldsstressterm =U 1 ,highestalong theoutermostplane, z=H = )]TJ/F15 11.9552 Tf 9.298 0 Td [(0 : 62,showsregionsofhighuctuationswithinboththe shearlayerandnearthetunneloor4-28F.Inthesymmetryplane,themaximumof =U 1 occursdownstreamat x=H =1 : 5Figure4-28A,againcomparingwellwith previousworkManhart1998;Toy etal. 1983.Themostprominentofthree-dimensional eects,however,arethestrongspanwiseuctuations =U 1 nearthewallinthe reattachmentregionaround x=H =1 : 7Figure4-27G,whicharecomparableinstrength withthemaximaofthestreamwiseuctuationsintheverticalshearlayer.Asexplained inManhart1998thesestronguctuationscanbeattributedtoaredistributionof momentumfromthestreamwisevelocitycomponenttothespanwisecomponents.This isalsoevidencedfromtheoilowvisualizationresults,asshowninFigure4-23B.Again, thisphenomenaisaresultofthecurvedboundsthatcontaintherecirculationregion. Castro&Haque1987showthatcomparableeectsoccurinthereattachmentregionofa two-dimensionalfreeshearlayerboundedbyaseparationzone. Forcompleteness,theturbulentkineticenergycontourscomprisedofallthree normalReynoldsstresstermsareplottedinFigure4-29A,C,E.Theyshowthatthe highestkineticenergyisconcentratedalongthecenterlineofthemodelFigure4-29A, andreducedtoapproximately70%ofthemaximumasthemeasurementplaneismoved totheoutermostregionFigure4-29E.Furthermore,theoverallcharacteristicsofthe Reynoldsstressesintheshearlayercanberepresentedbyarapidgrowthwithincreasing energyfollowingthedownstreamevolution.Thespanwisevorticity z H=U 1 isalso 145

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plottedinFigure4-29B,D,F.Atalllateralmeasurementplanes,theinitialvorticityis strong,butdiminishesinstrengthastheshearlayerconvectsandgrowsdownstream. Whiletheplotsindicatethatthespanwisecomponentofvorticitydominatesalongthe shearlayer,theverticalcomponentisexpectedtobegreatestnearthetunneloor.This conclusioncanbemadefromthe =U 1 uctuations,presentedinFigure4-27G. 4.2.5.4VelocitySpectra Duetothestrongtwo-dimensionalnatureoftheshearlayerneartheseparationpoint, velocityspectracanbecalculatedforMa=0.26fromhot-wireanemometerresultsalong severallocationsinthecenterplane z=H =0.Recallthatthehot-wireonlymeasures velocitymagnitudesandwillonlysupplyinformationregardingtheuctuationsinthe x )]TJ/F22 11.9552 Tf 12.577 0 Td [(y plane-withoutdistinguishingbetween u 0 and v 0 uctuatingcomponents.Figure 4-30showstheenergyspectrafromshorttimerecords,000samplescollectedover adimensionlessperiodofapproximately1000 tU 1 =H atthelocationofmaximum uctuationsfordierentlinecutsinthestreamwisedirection.Immediatelyafter separation x=H =0 : 45,theshearlayerspectraexhibitsa`hump'inenergycontentat approximatelySt H =0.1,conrmingunsteadypressuremeasurementsneartheseparation locationseeSection4.2.2.Furtherdownstream x=H> 0 : 65,thespectraindicatea broadbandincreaseintheenergycontentwithintheshearlayer,mostlikelyduetothe redistributionofenergyandspreadingoftheshearlayer.Figure4-31supplementsthis datawithadditionaldownstreammeasurements.Atnormalizedfrequencieshigherthan St H =1,anenergydecayproportionaltoSt )]TJ/F21 7.9701 Tf 6.586 0 Td [(5 = 3 isobserved,conrmingtheexpected energycascadeassociatedwithturbulentscales. 4.2.5.5NearWakeRegionRemarks Thediscussioninthissectionincludedanassessmentoftheextentofthemean recirculationregionandthecharacterizationoftheseparatedshearlayer,includingboth spatialevolutionandtemporalspectracalculations.Inaddition,whereapplicable,the resultswerecomparedtooilowvisualizationandunsteadypressureinadditionto 146

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previousinvestigationsregardingthewakeregionofahemisphericalmodels.Astudyof thenormalandshearReynoldsstressesindicatethattheshearlayeristwo-dimensional innatureneartheseparationlocation,withthemajorityoftheuctuationsoccurringin thestreamwisedirection.Thisresultjustiedtheuseofhot-wireanemometrytoextract temporalspectraatthelocationofmaximumturbulentintensitywithineachshearlayer prole.ResultsshowabroadpeakatSt H =1,withanenergydecayproportional to f )]TJ/F21 7.9701 Tf 6.586 0 Td [(5 = 3 forhigherfrequencies.Sinceitiswellknownthattheturbulentintensity withintheshearlayerisastrongindicatoroftheopticalenvironmentGordeyev etal. 2004 a ;Vukasinovic etal. 2010 a ,theuiddynamicresultsinthissectionhavestrong implications.Specically,thestrongtwo-dimensionalnatureoftheshearlayerinthenear wakeregionsuggeststhatthemajorityofaero-opticdistortionscanbecharacterizedusing onlythestreamwisecomponentoftheaero-opticsignal.Thiswillbeleveragedwhenusing theMalleyprobeforaero-opticmeasurements. 4.3Aero-OpticMeasurements Whiletheuiddynamicexperimentsyieldusefulinformationontheowstructures surroundingathree-dimensionalturret,aero-opticmeasurementsarerequiredtofully understandtheimpactoftheowstructuresontheopticalenvironment.Thissectionrst describesanimagingtechniquethatyieldsqualitativeinformationonopticaldegradation inthenearwakeregion.ThenmeasurementsaremadewithaMalleyprobe,providing one-dimensionalslicesofopticalwavefrontsinthedirectionofthebeampropagation vector.Themeasurementsarecontaminatedbystructuralvibrationsoftheexperimental setup.Thevibrationsareassessedandaportionofthemechanicaljitterisremovedfrom themeasurements.Arelationshipbetweenthespectraofthemeasureddeectionangle andtheOPD rms isdeveloped.Finally,conditionalspectralanalysisisusedtocorrelatethe aero-opticenvironmenttounsteadypressuremeasurements. 147

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4.3.1Aero-OpticImaging Asarstassessmentoftheaero-opticenvironmentinthenearwakeregionofthe turret,anaero-opticimagingtechniqueisimplemented.ThesetupisdiscussedinSection 3.5.1andshowninFigure3-15.Thisexperimentconsistsofatargetimageinthiscasea USAFResolutionTestChartandacamerathatmonitorstherelativedierencebetween imagesthataretakenwithandwithoutow.Toqualitativelyassessanyaero-optic distortion,theluminancevaluestakenwithMa=0.26owaresubtracted,pixelbypixel, fromthebaselineimagenoow.Theresultisanimagethatalsocontains256luminance values,withzeropureblackcorrespondingtonodierencebetweenthetwoimages. TheresultsofthetestareshowninFigure4-32A-C.Thersttestwastakenin anemptytestsectiontoverifythattheturbulent,butincompressible,boundarylayer hasnoeectontheaero-opticdistortion.ThisisillustratedbyFigure4-32B.Withthe modelinstalled,however,theowacceleratestoaMa=0.35asdiscussedinSection 4.2.4andcompressibilityeectscauseaero-opticdisturbancestoappear.Theeectsare showninFigure4-32C.Whiletheresultsarepurelyqualitativeandgivenoindicationof severeopticaldegradation,theydoindicatethattherearepossibleaero-opticaberrations withintheow.Furtherexamination,viatheformofasmallaperturebeamtechnique,is requiredtomakeanyrmconclusions.Theseexperimentsarediscussedinthefollowing sections. 4.3.2MalleyProbeMeasurements TheMalleyprobeisasimpleopticaldevicethatprovidesone-dimensionalslicesof opticalwavefrontsinthedirectionofthebeampropagationvector.Thereisanabundance ofpreviousworkthathasusedthisdevicetoquantifyaero-opticdistortionswithin compressibleboundarylayersGordeyev etal. 2012;Verho1979;Wittich etal. 2007, shearlayersHugo etal. 1997;Nightingale etal. 2006;Seidel etal. 2010;Siegenthaler etal. 2005;Volkov2010,andothercompressibleturbulentowsArunajatesan etal. 2006;Brown&Roshko1974;Sutton1969.However,itiswellknownthatcurrent 148

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windtunneltestresultsatmatchedightconditionsaresuspectbecauseofthe dicultyinseparatingthewindtunnelvibrationsfromtheaero-opticmeasurements ofinterest.Previousinvestigationshaveshownthattheopticaldistortionsduetothe structuralvibrationsofthetestapparatuscanbeasignicantsourceoferrorinoptical measurements,evenwhenthemagnitudeofthestructuralvibrationsislowCarroll etal. 2004. Aseriesofinitialtestsindicatethattunnelvibrationatlowfrequencies < 1kHz corruptthebeamdisplacementmeasurements.ConditionalspectralanalysisCSA techniquesareusedtoestimatetheaero-opticcontributionofavibration-corruptedsignal. ThedetailsaregiveninAppendixC.Figure4-34showstheresults,with O 2 tunnel vibrationreductionat f =500Hz.Thesepost-processingtechniquesprovedusefulin determiningproblematictunnelvibrations.Inafurtherattempttoreducethevibrations, theset-upwasrearrangedsuchthatoneofthesteeringmirrorswasremoved,resultingin anewset-upshowninFigure4-33.Still,morevibrationsignalsand/ormorecomplexi.e. higherorderand/ornonlinearmodelsarelikelyrequiredtoimprovemodelaccuracyfor allotherfrequencies. TheultimategoaloftheMalleyprobeexperimentsistousethemeasuredstreamwise deectionangletocalculatethe rms valueoftheopticalpathdierence,OPD rms .With thisinmind,theMalleyprobedataareprocessedwiththeroadmapshownbelow. 1.Usingtheset-upshowninFigure4-33,thestreamwisebeamdeectionangles aremeasured, 1 t and 2 t .Then,theautospectralandcross-spectraldensity functions, G 1 1 G 2 2 ,and G 1 2 arecalculated. 2.Thephaseofthecross-spectraldensityfunctioniscomputedandisusedto calculatetheconvectivespeedoftheaberratingstructures, U c .Thephaseplot alsoindicatesfrequencieswherestationarystructuresarepresent,knownasthe tip/tiltcomponent. 3.UsingHuygen'sprinciple,arelationshipbetweenOPD rms and G isdeveloped. 149

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4.Thetip/tiltcomponentof G isremovedbyapplyinganaperturelter AF A p ;f where A p = U c =f T=T and f T=T isthecut-ofrequencywherestationarystructures arenolongerpresent. 5.Residualvibrationcontaminationisremovedbyapplyingatto G f 0 : 23,thephaseplotshowsalineardependencewithincreasingfrequency,indicating theconvectivenatureofthestructures. 150

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AsshowninSection1.2.3.3,theopticaldistortionisbothafunctionofthedeection angleandtheconvectivespeedofthecoherentstructureswithintheow.First,the coherencebetweenthetwobeamsforeachpairingiscalculatedandshownintheleft columnofFigure4-36.Theresultsshowthatasthemeasurementlocationmovesfurther downtheturretwindow,thepeakcoherencedecreasesinmagnitudeandshiftstolower frequencies.Thissuggeststhegrowthofthecoherentstructureswithintheshearlayeras itconvectsdownstreamandincreaseinturbulencemixing,i.e.adecreaseinthestrength ofthecoherentstructures. Thephaseplotsatallmeasurementlocationsaredisplayedintherightcolumn ofFigure4-36.Theyindicateanear-lineardependencewithincreasingfrequency, showingevidenceoftheconvectivenatureofcoherentstructures.Tocalculatethe convectivespeed,theslopeofthephaseisdeterminedbycalculatingthebestlinetina least-squaressenseforSt H > 0 : 23,suchthatthetip/tiltcomponentofthesignalisnot included.Foraknownbeamseparationlength,theconvectivespeed U c isthencalculated bydividingthestreamwisedistancebetweenthebeamsbythecalculatedtimedelay. Physically,thisisindicativeofthespeedatwhichanoptically-activestructureconvects fromonebeamtothenext.Forthetwobeamslocatedclosesttothetopoftheaperture, andhencethemostupstreamportionoftheshearlayer,theconstantphaseslopesuggests acoherentstructureconvectivespeedof0.67 U 1 .Theresultsalsoshowthattheconvective speedofthecoherentstructuresincreaseswithdownstreambeamlocation.Thesendings aresupportedbypreviousinvestigationsGordeyev etal. 2010 b ,2004 b ,2006. 4.3.2.3DeectionAngleSpectra Recallthataero-opticdistortionisrelatedtothecombinationofdeectionangleand convectivespeedseeEq.1{19.Therefore,toestablishafaircomparisonofaero-optic degradationalongdierentwindowlocations,itisimportanttomultiplythebeam deectionspectrabythecalculatedcoherentstructurespeed U c .Furthermore,tokeepthe quantityinnon-dimensionalterms,thespectraisthendividedbythefreestreamvelocity 151

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U 1 .Thedeectionanglespectramultipliedbythecorrespondingconvectivetofreestream speedratio U c =U 1 isshowninFigure4-37.NotethatonlyoddbeamsB1,B3,B5,and B7areshown,sincetheevenbeamsB2,B4,B6,andB8aresolelyusedtocalculatethe convectivespeed.Themagnitudeofthenormalizedbeamdeectionspectramonotonically increasesasthemeasurementlocationsaremovedclosertothebase,indicatingthatthe uiddisturbanceshaveagreateraero-opticaleectastheyconvectdownstream.This isduetoboththelargershearlayerwidthandhigherconvectivespeeds.Forthebeam closesttothetopoftheapertureB1,thebroadbandpeakindicatesthepresenceofthe coherentstructureswithintheshearlayerVukasinovic etal. 2010 a .Asthemeasurement locationsaretakenfurtherdowntheaperture,thepeakshiftstolowerfrequencies whichisconsistentwiththeexpectedshearlayergrowthandhencelargercoherentow structures,asshowninFigure4-39. PreviousresearcheortsGordeyev etal. 2004 a ;Vukasinovic etal. 2010 a ;Wallace etal. 2008haveshowntheparticularlydestructivenatureoftheshearlayeronotherwise aberration-freeows.ItisthereforebenecialtoassessthesPIVturbulentkineticenergy prolesalongthebeampropagationpaths.Figure4-39plotsthecontourof k=U 2 1 while highlightingtheeachbeam'spropagationpath.Slicesoftheturbulentkineticenergyare plotted,withthereferenceframetransformedsuchthatthedataisplottedinthedirection normal^ n totheturretwindow,i.e.alongthebeampath.Asexpected,boththeenergy andthicknessoftheshearlayerincreaseswithdownstreamdistance,resultinginthe aforementionedincreaseinbeamdeectionspectra. 4.3.2.4RelationshipBetweenDeectionSpectraandOPD rms ThissectionprovidesameanstoextracttheOPD rms fromthecalculateddeection spectra.TheoperationoftheMalleyprobediscussedinSection1.2.3.3isbasedupon Huygen'sPrinciplewhichstatesthataraypassingthroughavariantindex-of-refraction mediummustemergenormaltotheassociatedresultingwavefront, W x;t .Recallingthat thedeectionangleisthespatialderivativeofthewavefrontandapplyingthefrozenow 152

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hypothesistotradetimeforspace x = U c t t;x = U c t = dW t;x = )]TJ/F22 11.9552 Tf 9.298 0 Td [(U c t dx = )]TJ/F15 11.9552 Tf 13.625 8.088 Td [(1 U c dW t dt : {7 SinceOPD rms istheconjugateofthewavefrontJumper&Fitzgerald2001, OPD 2 rms W 2 rms ,thenitcanberelatedtotheone-sidedone-dimensionalpower spectraldensityfunction G WW f via OPD 2 rms = Z 1 0 G WW f df: {8 Knowingtherelationshipbetweenthepowerspectraldensityandit'sderivative, thewavefrontpowerspectraldensitycanbecomputedfromthedeectionanglepower spectraldensityfunction, G WW f = U c 2 f 2 G f : SubstitutingthisintoEq.4{8gives OPD 2 rms = U 2 c Z 1 0 G f f 2 df {9 TheresultisanexpressionthatallowstheOPD rms tobecalculateddirectlyfromthe powerspectraldensityfunctionofthebeamdisplacement.However,thisrelationshipis onlyvalidforfrequencieswhereTaylor'sfrozenowhypothesisholdstrue,i.e.wherethe structuresarenon-stationary.Inotherwords,theextractedOPD rms isonlyvalidfornite apertures.Therefore,thetip/tiltcomponentmustberemovedfrom G beforecomputing thevalueofOPD rms .Amethodtoremovethetip/tiltcomponentisdiscussedinthe followingsection. 4.3.2.5One-DimensionalApertureFilter InpracticalapplicationsthestationarystructuresmeasuredatlowSt H aretypically removedbyafast-steeringmirroranddon'tcontributetotheoverall OPD rms .Therefore, inanexperimentalsetting,theyshouldbemitigatedbeforecalculatingOPD rms Siegenthaler etal. 2005hasshownthattheinclusionofaone-dimensionalaperture 153

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lter AF A p ;f servesasimilarpurposeasafast-steeringmirror.Dening)-348(= A p f=U c where A p isauserdenedaperturesize,theproposedlterisoftheform AF A p ;f = [ )]TJ/F15 11.9552 Tf 9.299 0 Td [(3 )]TJ/F15 11.9552 Tf 11.956 0 Td [( \051 2 + \051 4 + )]TJ/F15 11.9552 Tf 11.955 0 Td [(2 \051 2 cos 2 \051+6 sin cos ] \051 4 : {10 Formoreinformationontheaperturelter,includingthefullderivation,referto Siegenthaler2009. Fundamentally,thelterreducestheimpactofaberrationswithlengthscalesthatare largerthantheaperture.ThisisshowninFigure4-40Awherethegainof AF A p ;f is plottedasafunctionofthenon-dimensionalfrequency,)-362(= A p f=U c .Afterapplyingthe ltertothedeectionspectra,theOPD rms canbecalculatedby OPD 2 rms = U 2 c Z 1 0 AF A p ;f G f f 2 df = Z 1 0 P A p ;f G f df; where P A p ;f = U 2 c AF A p ;f = f 2 isthetransferfunctionbetweenthedeection anglespectraandtheOPD rms A p .Theaperture A p canbechosensuchthatthetip/tilt contributionisltered.BasedontheresultspresentedinSection4.3.2.2,acut-o frequencyof250HzSt H =0 : 23andaconvectivespeedof0 : 67 U 1 isused,corresponding toanaperturesizeof A p = U c =f =0.24m. Togainfurtherinsightintotheaperturelter,thecumulativesummationofthe transferfunctioncanbedenedas P cs = P f 0 P f = P 1 0 P f .Figure4-40Bplotsboth P A p ;f and P cs A p ;f asafunctionofSt H .Thetransferfunctionactslikeabandpass lter,with95%oftheenergycontainedforSt H > 0 : 2.Inessence,theltereddataiswhat wouldbeexpectedaftertheoriginalsignalpassesthroughafast-steeringmirrorGordeyev etal. 2012.Thismethoddictatesthat,foragivenaperturesize,band-passlteringthe deectionanglespectrumcanbeusedtocalculatetheoverallOPD rms Thesuggestedaperturelterisappliedtothedeectionspectra,andresultsare plottedinFigure4-41labeledas AF A p ;f G f .Theplotshowsthattunnelvibration eectsarestillpresentatlowfrequenciesinthespectra,asevidencedbynon-physical 154

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peaks,andmustberemovedinordertocomputeamoreaccuratemeasureofOPD rms Thefollowingsectiondescribesalow-frequencyttothespectraldatathateectively removesanyremainingmechanicalvibrations. 4.3.2.6DeectionSpectraLow-frequencyFit Whiletheprevioussectionshowedthatusinganapertureltercanreducestationary structuresi.e.thetip/tiltcomponent,Gordeyev&Jumper2009suggestthat non-physicalphenomena,includingtunnelvibrations,mustbesuppressedorremoved fromthedeectionspectrabeforeapplyingtheapertureltertothedata.Todothis,at isproposedforfrequencieswherevibrationsareproblematic, F f = 8 > < > : G f = f c f f c if f
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integratingthedeectionspectrawiththecut-onfrequencyasthelowerbound,therefore completelyremovinganycontributionbelow f c .TheOPD rms canthenbecalculatedusing thenewlowerboundwithoutanyltering,resultingin OPD 2 rms = U 2 c Z 1 f c G f f 2 df Theresultingeectivespectra,labeledas G f c ;f isplottedalongsidetheoriginal G andlteredspectra AF A p ;f F f c ;f and AF A p ;f G ,respectivelyinFigure 4-41.Ateachmeasurementlocation,theOPD rms iscalculatedbasedonthelow-frequency cut-olter,andtheresultsarepresentedinTable4-4. 4.3.2.8OPD rms CalculationRemarks Inthissection,twodistinctmethodsofcalculatingOPD rms werepresented.The rstusedaphysicalunderstandingoftheowtoremovetip/tilteectsbyapplying anaperturelterandthenmitigatedtunnelvibrationsviaalow-frequencyttothe deectionspectra.Asecondmethodtruncatedthedata,onlyusingthecontributionof deectionspectraaboveasetcut-onfrequency.TheresultsyieldedOPD rms valuesthat arewithin10%ofeachother,indicatingthatthelowfrequencydeectionanglesplayonly aminorroleintheoverallaero-opticenvironment. Recallingthatthisistherstworkthathasusedathree-dimensional, surface-mounted,at-windowedturret,thecalculatedOPD rms valuescanbecompared topreviousworkthatusedotherturrettypesseeSection1.2.1andFigure1-3for discussiononthefourturrettypes.Anon-dimensionalanalysisrefertoSection1.2.3.4 revealedthattheworstopticalenvironmentoccurredwhenaturretwassurfacemounted. Also,basedonstudiesaroundatwo-dimensionalcylinderwithaatwindow,itwas conjecturedthatowaroundathree-dimensionalat-windowedturretwouldresultin thehigheropticalaberrationswhencomparedtoaconformal-windowturret.Theresults presentedinthissectionconrmthispostulate.Infact,whennon-dimensionalizing thecalculatedOPD rms bythesuggestedscaling,sin = H Ma 2 ,theresultsfrom 156

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severalinvestigationsshowthatconformal-windowturretsmountedonacylindricalbase resultedintheleastaero-opticallyactiveenvironment.9 m/mwhilesurface-mounted conformal-windowturretsweremorethantwiceasactiveinanaero-opticsense.6 m/m.Theexperimentalresultshereinresultinanon-dimensionalizedOPD rms valueof 4.5 m/m,morethantwiceaslargeasthatexpectedforaconformal-typeturret. Thelargedierenceintheaero-opticenvironmentbetweentheconformal-and at-windowturretscanbeexplainedfromthemechanismthatcausesseparation.For theconformal-windowmodel,theowseparatesduetoanadversepressuregradient thatcausestheboundarylayertodecelerate,thuslosingthemomentumrequiredtostay attached.However,inthecaseoftheat-windowturret,theboundarylayerseparates, notduetolackofenergy/momentumtokeepitattached,butinsteadduetoanabrupt geometryconstraint.Therefore,anyextraenergythattheboundarylayerwouldhave bledtotheadversepressuregradientisnowbeingtransferredtotheseparatedshearlayer, directlyincreasingtheaero-opticaberrationswithin. 4.3.3CorrelatingAero-opticsandUnsteadyPressure Inmostsituations,real-timeaero-opticdatacannotbereadilymeasured.Therefore itisimperativetounderstandthecorrelationbetweentheaero-opticenvironmentand othermeasurableowquantities.Inaqualitativesense,itiswellknownthatevenwhen directmeasurementsofaero-opticsarenotavailable,turbulenceintensitymeasurements provideastrongindicatoroftheopticalqualityoftheow.Tothisregard,previous studieshaveassumedcorrelationbetweenowfeaturesandaero-opticdistortions. Vukasinovic etal. 2010 a notedtheparticularlydestructivenatureoftheshearlayer onotherwiseaberration-freeowsduetothepresenceofthevorticalstructuresthat inducestrongpressuregradients.Specically,Gordeyev etal. 2004 b foundthatoptical distortionsoveraatwindowweregreatlygovernedbytheseparatedshearlayerin anadversepressuregradient,Wallace etal. 2008reasonedthathomogenizingthe wakeoftheturretovertheapertureareamayreducetheaero-opticaberrations.Other 157

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researchersAndino&Glezer2010;Wallace etal. 2009,2010havealsoattemptedto improvetheopticalqualityoftheowbyusingunsteadypressuremeasurementsasa metric.However,nonehavedirectlycorrelatedtheaero-opticsignalwithanotherow quantity,e.g.pressureuctuations.Thissectionperformsconditionalspectralanalysis usingaero-opticandunsteadypressuredatatodetermineasuitablecontrolmetricwhen aero-opticmeasurementsarenotavailable. Thefollowinganalysisisaimedtodetermineacorrelationbetweentheunsteady pressureandthebeamdisplacementangle,whileremovingtheeectsoftunnelvibrations. Asingleaccelerometerismountedonthetestsectiontunneloor,asindicatedby Figure4-33.Althoughtheaccelerometeristriaxial,onlyasinglecomponentisused correspondingtothestreamwisecoordinatedirection.Similarly,onlythebeam displacementinthestreamwisedirectionisused.Figure4-42showsthepressureand beamlocationsfortheseexperiments.Duringthetests,threepressuretransducers P1,P2,andP3wereusedtocollectuctuatingpressuredata.Simultaneously,beam displacementdatawasacquiredattwolocations,eitherB3andB4orB5andB6. AsimilaranalysistothatconductedinAppendixCisappliedhere.Theoptical measurementsaremodeledasamultipleinput,singleoutputsystemasshowninFigure 4-43.Theoutputofthesystemisthestreamwisedeectionangleofthespeciedbeamas measuredbyapositionsensingdevicePSDaspartoftheoverallMalleyprobesetup. Thetwoinputsaretheunsteadypressureuctuationsandthemechanicaltestsection vibrations.Whileapossiblecontributiontotheoutputistheturbulentbutincompressible boundarylayerthatthebeampassesthroughontheupperportionofthetestsection, bothqualitativeaero-opticimagingdataSection4.3.1andpreviousinvestigationsCress etal. 2008;Gordeyev etal. 2003;Wittich etal. 2007,showthatatthisincompressible freestreamvelocityMa=0.26,theboundarylayerdoesnotdegradetheaero-optic environment.Foralltests,thefollowingsignalsareacquiredsimultaneously. x 1 t :inputpressuretimesignal 158

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X 1 f :inputpressurefrequencysignal= Ff x 1 t g x 2 t :inputvibrationtimesignalasmeasuredonthetunneloor X 2 f :inputvibrationfrequencysignal= Ff x 2 t g n t :inputnoisetimesignal N f :inputnoisefrequencysignal= Ff z t g y t :outputmeasuredopticaldisplacementsensortimesignal Y f :outputmeasuredopticaldisplacementsensorfrequencysignal= Ff y t g 4.3.3.1OrdinaryCoherenceFunction Todeterminethebestcandidatepairofunsteadypressure x 1 andaero-optic y signal touse,theordinarycoherencefunctionisplottedforallfourviablecombinationsP1B3, P2B4,P2B5,andP3B6.TheresultsareplottedinFigure4-44.Theordinarycoherence functionisstrongestwhenthecombinationofthepressureandaero-opticsignalisnear thetopoftheapertureP1B3.However,asthesignalsareacquiredatalocationlower ontheaperture,thecoherenceexperiencesasuddendrop,andiszeroforthecaseclosest totheturretbaseP4B6.Thelowcoherenceattheselocationscanbeattributedto therecirculationofow,whichmaycontributetotheunsteadypressure,butnottothe aero-optics.Instead,thelargemajorityoftheaero-opticdegradationcouldbecaused bytheseparatedshearlayer,whichismoreeasilymeasuredwiththeunsteadypressure portP1.TheresultsfromtheinitialvibrationtestsAppendixCindicatethatthe strongcorrelationatdiscretefrequenciesisrelatedtojointcontaminationfromstructural vibrations.Basedonthesetrends,theunsteadypressureandaero-opticsignalsclosestto theseparationpointP1andB1,respectivelyareusedforfurtheranalysis. TheconditionedordinarycoherencefunctionisplottedinFigure4-45toshowthe coherencebetweenthevariousthreesignals:unsteadypressuresignalmeasuredatlocation P1 x 1 ,mechanicalvibrationsasmeasuredonthetunneloor x 2 ,andthesignal measuredbythepositionsensingdevice y .Theresultsshowstrongcoherencebetween 159

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thevibrationsanddeectionangleatapproximately500Hz 2 =0 : 75and1000Hz 2 =0 : 18.Thetwoinputsignalsalsoshowstrongcoherenceatdiscretefrequencies.In ordertodetermineiftunnelvibrationsarecausingpressureuctuationsorviceversa,a simpleimpacttestisperformed.Withthetunnelturnedo,vibrationsareintroduced viamalletandboth x 1 and x 2 arerecorded.Theresults,notshown,indicatethatthe mechanicalvibrationsdonotcausesignicantoutputfromthepressuretransducer. 4.3.3.2ConditionedAutospectra Thecoherentoutputpower 2 xy G yy canbesubtractedfromtheoriginalautospectra G yy toobtaintheconditionedautospectra, G yy x 1 = G yy )]TJ/F22 11.9552 Tf 11.956 0 Td [( 2 x 1 y G yy G yy x 2 = G yy )]TJ/F22 11.9552 Tf 11.956 0 Td [( 2 x 2 y G yy : BothareplottedalongsidetheoriginalautospectrainFigure4-46. G yy x 2 corresponds totheoutputautospectrawhenthelineareectsoftunnelvibrationsareturned o.Similarly, G yy x 1 istheoutputautospectrawhenthelineareectsofunsteady pressurearereturnedo.Thissuggeststhatthecorrelatedeectbetweenthetwo inputsemanatesfromthesingleinputthatisturnedo.Notethatifthetwoinput signalswereuncorrelated,theconditionedautospectrawouldbetheonlynecessary calculation.Physically,however,pressureuctuationsfromtheowareexpectedto producemechanicaljitterinthetunnel.Therefore,thepartialcoherenceandpartial autospectramustalsobecalculated. 4.3.3.3PartialConditionedAutospectra Furtherinsightisacquiredbycalculatingthepartialcoherencefunctions, 2 x 2 y x 1 and 2 x 2 y x 1 seeAppendixC,Eq.C{19.Twosystemmodels,illustratedinFigure4-47,are createdtobetterunderstandthecontributionfromeachinput.ModelAdescribes... whileModelBdescribes. 160

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GA 1 = 2 x 1 y x 2 G yy x 2 :minimumcontributionfromunsteadypressure x 1 withall linearportionsofmechanicalvibrations x 2 removed. GA 2 = 2 x 2 y G yy :maximumcontributionfromtunnelvibrations x 2 directlythrough H 2 y orindirectlythrough L 21 GB 1 = 2 x 1 y G yy :maximumcontributionfromunsteadypressure x 1 directlythrough H 1 y orindirectlythrough L 12 GB 2 = 2 x 2 y x 1 G yy x 1 :minimumcontributionfromtunnelvibrations x 2 withall linearportionsofunsteadypressure x 1 removed. Itisassumedthatanycorrelationbetweentheunsteadypressureandtunnel vibrationsoriginatesfromtheunsteadypressurei.e.tunnelvibrationsdonotcause unsteadypressureuctuationsandthereforeonlythephysicallyrelevantcontributionsare plottedinFigure4-48.Notethat,asexpected,tunnelvibrationsareonlyaconcernfor lowfrequencies,withadominantpeakat f =500Hz.Thespectra GA 1 showsthatalarge portionoftheaero-opticdistortionisaccountedforbytheunsteadypressureuctuations. Futureworkcouldbedonetoextractthecomponentoftheaero-opticdegradationdue solelytopressureuctuations.Thiswouldbedonebycalculating H 1 y inFigure4-47Aand applyingittothepressuresignal, x 1 Itisimportanttonote,however,thatthisresultonlyholdsforthisspecic measurementlocationP1B1.Recallthatasthepressuremeasurementlocationmoved towardthebaseoftheturret,thecoherencebetweenitandthebeamsignaldiminished. Toobtainabetterestimate,itwouldbebenecialtoextendthistechniquetomultiple pressureinputs,measuringpressureuctuationsatdierentlocationsalongtheturret andnotlimitingthemtotheatwindow.Ideally,toachieveawelldenedmodel,the followingconditionsshouldbemetBendat&Piersol2000: Theordinarycoherencefunctionsbetweenanypairofuctuatingpressureinputs shouldnotbeunityatallfrequenciesofinterest.Physicallythiscorrespondsto redundantinformationfromtheinputs.Thisconsiderationallowsdistributedinput systemstobestudiedasdiscreteinputs. Themultiplecoherencefunctionbetweenanypressuresignalinputandthebeam displacementoutput,excludingthegiveninput,shouldnotequalunity.Ifthisis 161

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thecase,thenthisspecicinputisnotcontributinganynewinformationandcan beobtainedbylinearoperationsfromotherinputs.Furthermore,ifthemultiple coherencefunctionbetweenthemeasuredinputsandthemeasuredoutputisunity, theauto-spectrumofthenoiseisequaltozero.Thiscorrespondstoperfectlinearity betweenthesumoftheoutputsfromeachsourceandthemeasuredoutputofthe system. Ifafteranextensivestudyshowsthatimportantinputsarenotbeingomittedand themultiplecoherencefunctionbetweenthebeamdisplacementandtheunsteady pressuresignalsisnotsucientlyhigh,thenthemeasuredoutputdatadoesnot comefromlinearoperationsofthemeasuredinputs.Insuchacase,non-linear eectsshouldbeconsidered. 4.4BaselineFlowConcludingRemarks Thischapterexaminedthebaselineowaroundasurfacemountedthree-dimensional turretwithaataperture.Unsteadysurfacepressuremeasurementswerecollectedat variouswindowlocationsandtrendsweredetermined.Thelargerecirculationregion showedtobeamajorsourceofpressureuctuations,especiallyalongthelowerportion oftheturretwindow.Usinganoilowvisualizationtechnique,thecomplexnatureof theowwasvisualizedandseveralkeyowfeatureswerecaptured.StereoscopicPIV wasthenimplemented,andanassessmentoftheextentofmeanrecirculationregionand thecharacterizationoftheseparatedshearlayerwereundertaken.UsingaMalleyprobe, theaero-opticenvironmentwasdirectlymeasuredandtheshearlayerwasfoundtobe themainsourceofopticalaberrations.Finally,conditionalspectralanalysiswasusedto correlateaero-optictounsteadypressuremeasurements,indicatingameasurablecoherence onlyatlocationswherethemaincauseofunsteadypressureistheshearlayer. Recallthatamajorobjectiveofthepresentworkistoestablishowcontrol techniquesthatleadtothesuppressionoflargevelocityuctuationsformedinthe wakeregionastheowseparatesoaturret.AsdiscussedinChapter1,andthen laterevidencedwiththeresultsfromthischapter,previousresearchshowsthatthese uctuationsarecontributingfactorstoopticalaberrations.Thegoal,then,istosuppress theenergywithintheseparatedshearlayerbyeitheraddingenoughmomentumto theowtoreattachtheowoverthewindow,orintroducesmallscaledisturbancesto 162

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reducetheformationofcoherentstructureswithintheshearlayerthatresultinoptical distortions.Bothmethodsareinvestigatedinthefollowingchapter. 163

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Figure4-1.Incomingboundarycharacteristicsforafreestreamvelocityof40m/s.The topleftplotshowsthenormalizedfreestreamvelocity,thetoprightplotshows theturbulentintensity,andthebottomplotshowstheconvergenceforasingle locationwithintheboundarylayermarkedwitha 164

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Figure4-2.Incomingboundarycharacteristicsforafreestreamvelocityof90m/s.The topleftplotshowsthenormalizedfreestreamvelocity,thetoprightplotshows theturbulentintensity,andthebottomplotshowstheconvergenceforasingle locationwithintheboundarylayermarkedwitha 165

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Figure4-3.Dimensionlessboundarylayervelocityprolesfor40m/sand90m/s freestreamvelocities.Experimentaldataisplottedalongsidethelawofthe wallandtheSpaldingcurve. 166

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Figure4-4.SpectraHzbinwidthofwindtunnelacousticcontaminationasafunction offreestreamvelocityinamodel-freetestsection. 167

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Figure4-5.SpectraHzbinwidthofwindtunnelacousticcontamination.The frequencyisnormalizedbythefreestreamvelocity, U 1 ,andtestsectionheight L .ArstnoisesourcegeneratesatoneatSt L =3 : 25andhasthreedominant harmonicsSt L =6 : 50 ; 9 : 75 ; 13 : 0.Thesecondisahigherfrequencytonethat appearsatSt L =37 : 4. Figure4-6.SpectraHzbinwidthofacousticcontaminationwithandwithoutmodel installedintestsectionat U 1 =90m/sMa=0.26. 168

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Figure4-7.Eectofacousticcontaminationonunsteadypressurereadings.Thefrequency isnormalizedbythefreestreamvelocity, U 1 =90m/s,andturretmodelheight H .ForvaluesgreaterthanSt H =2 : 5,theunsteadypressuremeasurementson themodelaredrownedbyacousticcontamination. A B Figure4-8.ASurfacepressuredistribution, C p ,andBnormalizedstandarddeviation, C ,alongthecenterlineofthemodel.Theleftverticaldashedlinerepresents theboundarylayertrip,andtherightverticaldashedlinecorrespondsto locationoftheatwindow. 169

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Figure4-9.Unsteadypressuremeasurementlocations.Notethattheoutermostringis referredtoasloc.1,theinnermostringisreferredtoasloc.3,andthesole centerlocationisreferredtoasloc.4. Figure4-10.Eectsofspatialaveragingonunsteadypressuremeasurements.Unsteady pressuretakenatloc.1,0 o usingthreeunsteadypressuresensorswith dierentsensingelementsizes. \000 :G.R.A.S.40BEwithtype26CB preamplier.35mm, \000 : Br uel & Kjaer 4138-Awith2670preamplier .18mm,and \000 MEMSproprietarymicrophone.91mmWilliams 2011 170

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A B C D Figure4-11.Spectraofunsteadypressurespectranon-dimensionalizationforawindow orientationof0 o ,loc.1.Refertogure4-11formeasurementlocation.A DimensionalparametersHzbinwidth,Bfrequencynon-dimensionalized to St H bythefreestreamvelocity, U 1 ,andturretmodelheight H ,C pressurenon-dimensionalizedbydynamicpressure q 1 =0 : 5 U 2 1 ,Dboth pressureandfrequencynon-dimensionalized. 171

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Figure4-12.Non-dimensionalizedspectraofunsteadypressureasafunctionoftriptape locationforRe H =3.40 10 5 Ma=0.17atfourlocationsontheat windowasshowninwindowinsert. 172

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Figure4-13.Non-dimensionalizedspectraofunsteadypressureasafunctionoftriptape locationforRe H =5.10 10 5 Ma=0.26atfourlocationsontheat windowasshownininsert. A B Figure4-14.EectoftriptapelocationforseveralRe H at0 o windoworientationatloc.1 Refertogure4-11formeasurementlocation.TriptapelocatedatA S=R =0 : 535andB S=R =0 : 803.Frequencyresolution f is10Hz. 173

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Figure4-15.PressurespectraasafunctionofwindowlocationforRe H =5.10 10 5 Ma =0.26.Windowangleorientationsof0 o toprow,45 o middlerow,and 90 o bottomrow.Contourscaleis P=q 1 %. 174

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A B Figure4-16.Unsteadypressurespectraalongouterportionloc.1oftheatwindowfor Re H =5.10 10 5 Ma=0.26Refertogure4-11formeasurement location..Bothplotsshowtheunsteadypressuretrendsasafunctionof windowrotationangle.A0 o )]TJ/F15 11.9552 Tf 11.955 0 Td [(90 o B90 o )]TJ/F15 11.9552 Tf 11.955 0 Td [(180 o 175

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Figure4-17.Unsteadypressurecontours P=q 1 100%onturretwindowasafunctionof frequencyforRe H =5.10 10 5 Ma=0.26.Eachcontourisathirdoctave bandaverage,withthefrequencylistedbeingthecenterfrequency.Dotted linerepresentsedgeofturretwindow.Sensorlocationsareshownasblack circles. x and y locationsalongwindowarenormalizedbythewindowradius, a .Notethatthecontourbarsareinpercentandhavedierentscalesforeach frequencycase. 176

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Figure4-18.Unsteadypressurecontours P=q 1 100%onturretwindowasafunctionof frequencyforRe H =5.10 10 5 Ma=0.26.Eachcontourisathirdoctave bandaverage,withthefrequencylistedbeingthecenterfrequency.Dotted linerepresentsedgeofturretwindow.Sensorlocationsareshownasblack circles. x and y locationsalongwindowarenormalizedbythewindowradius, a .Notethatthecontourbarsareinpercentandhavedierentscalesforeach frequencycase. 177

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Figure4-19.Unsteadypressurecontours P=q 1 100%onturretwindowasafunctionof frequencyforRe H =5.10 10 5 Ma=0.26.Eachcontourisathirdoctave bandaverage,withthefrequencylistedbeingthecenterfrequency.Dotted linerepresentsedgeofturretwindow.Sensorlocationsareshownasblack circles. x and y locationsalongwindowarenormalizedbythewindowradius, a .Notethatthecontourbarsareinpercentandhavedierentscalesforeach frequencycase. 178

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Figure4-20.Phasedelayandcoherencebetweentwopressuretransducersloc.1andloc. 2atawindoworientationsof0 o ,90 o ,and180 o .Thisanalysisprovides informationonthespatialevolutionofintegralscalesacrosstheatwindow. 179

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A B C D E F Figure4-21.OilowdevelopmentoverthesurfaceoftheturretforRe H =5 : 10 10 5 Ma=0.26.A,C,Eshowthetopview,whileB,D,Fshowthe angledview.PairsA&B,C&D,andE&Faresynchronizedin time.Flowisfromrighttoleft. 180

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A B Figure4-22.ComparingglobalowstructuresbetweenAtrippedandBuntripped owusingoilowvisualizationforRe H =2 : 27 10 5 Ma=0.12.For trippedcondition,sawtoothtapeisplacedat S=R =0 : 80asshowninFigure 3-3.Flowisfromrighttoleft. 181

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A B Figure4-23.ComparingglobalowstructuresbetweenAtrippedandBuntripped owusingoilowvisualizationforRe H =5 : 10 10 5 Ma=0.26.For trippedcondition,sawtoothtapeisplacedat S=R =0 : 80asshowninFigure 3-3.Flowisfromrighttoleft. 182

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A B Figure4-24.BoundarylayerheightmeasurementsatdiscretelocationsusingPIVat Re H =5 : 10 10 5 Ma=0.26.ABoundarylayerprolesalongtheapexof theturretmodel.BProleextractedatapexofturret x =0mmincludes randomuncertaintyasmarkedbyhorizontalerrorbars. Figure4-25.sPIVmeasurementstreamwiseplaneslocatedat z=H =0.0,-0.31,and-0.62. Thesecorrespondtothesymmetryplane z=H =0 : 0,edgeofatwindow z=H = )]TJ/F15 11.9552 Tf 9.299 0 Td [(0 : 62,andhalfwaybetween z=H = )]TJ/F15 11.9552 Tf 9.299 0 Td [(0 : 31. 183

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A B C D E F Figure4-26.Meanspeed j U j =U 1 contoursA,C,EandstreamlinesB,D,Finthenear wakeregionoftheturretatseverallateralplanes z=H =0 : 0, z=H = )]TJ/F15 11.9552 Tf 9.299 0 Td [(0 : 31, and z=H = )]TJ/F15 11.9552 Tf 9.298 0 Td [(0 : 62.Turretmodeloutlineincludedforreference. 184

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A B C D E F G H I Figure4-27.NormalReynoldsstresscomponentsalongseverallateralplanes z=H =0 : 0, z=H = )]TJ/F15 11.9552 Tf 9.299 0 Td [(0 : 31,and z=H = )]TJ/F15 11.9552 Tf 9.299 0 Td [(0 : 62.A,B,Cstreamwiseuctuations =U 2 1 .D,E,Fverticaluctuations =U 2 1 .H,I,J spanwiseuctuations =U 2 1 .Resultsindicateatwo-dimensional shearlayernearseparation. 185

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A B C D E F G H I Figure4-28.NormalReynoldsstresscomponentsalongseverallateralplanes z=H =0 : 0, z=H = )]TJ/F15 11.9552 Tf 9.299 0 Td [(0 : 31,and z=H = )]TJ/F15 11.9552 Tf 9.299 0 Td [(0 : 62.A,B,C =U 2 1 .D,E,F =U 2 1 .H,I,J =U 2 1 186

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A B C D E F Figure4-29.A,C,ETurbulentkineticenergy k=U 2 1 andB,D,Flateralvorticity z H=U 1 extractedfromsPIVmeasurementsalongseverallateralplanes z=H =0 : 0, z=H = )]TJ/F15 11.9552 Tf 9.299 0 Td [(0 : 31,and z=H = )]TJ/F15 11.9552 Tf 9.299 0 Td [(0 : 62. 187

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Figure4-30.Hot-wireanemometryresultsinthenearwakeregion x=H< 1 : 5. Measurementplaneislistedonthetoprightofeachvelocityspectragure. Meanvelocityprole U=U 1 ,turbulentintensitycalculatedfromuctuating component =U 2 1 ,andspectraasmeasuredatthepointofhighest uctuationwithintheshearlayer,markedwitha \000 denotesa f )]TJ/F21 7.9701 Tf 6.587 0 Td [(5 = 3 trend.MeasurementlocationsareshowninFigure3-11. 188

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Figure4-31.Hot-wireanemometryresultsinthefarwake x=H> 1 : 5.Measurement planeislistedonthetoprightofeachvelocityspectragure.Meanvelocity prole U=U 1 ,turbulentintensitycalculatedfromuctuatingcomponent =U 2 1 ,andspectraasmeasuredatthepointofhighestuctuation withintheshearlayer,markedwitha \000 denotesa f )]TJ/F21 7.9701 Tf 6.586 0 Td [(5 = 3 trend. MeasurementlocationsareshowninFigure3-11. 189

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A B C Figure4-32.Aero-opticimagingresults.AReferenceUSAFResolutionTestChart.B DierenceimagebetweenreferenceandimagetakenatMa=0.26withno modelinstalled.CDierenceimagebetweenreferenceandimagetakenat Ma=0.26withmodelinstalled. 190

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Figure4-33.ModiedMalleyprobewindtunnelset-up.BasedontheCSAprocessing results,asinglesteeringmirrorisremovedtoimprovethemeasured aero-opticsignal. 191

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Figure4-34.Resultingdeectionautospectraafterusingconditionalspectralanalysisto removetheeectoftunnelvibrations. G yy denotestheoriginalsignal,while G z z denotesthelteredsignal.WhileimplementingCSAprovides O 2 reductionat500Hz,thebeamdeectionspectraisstillcontaminatedby noiseatlowerfrequencies. Figure4-35.Thephaseplotiscalculatedfromthecross-spectrumbetweenthedeection anglesasmeasuredatlocationsB1andB2.ForSt H < 0 : 23,thestructures arestationary,indicatingtip/tilteects.Thedataisusedtodeterminethe frequencyatwhichstructuresbegintoconvectdownstream. 192

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A B C D E F G H Figure4-36.CoherenceleftcolumnandphaserightcolumnofMalleyprobebeam pairs.BeampairsB1&B2,B3&B4,B5&B6,andB7&B8arerepresentedby rows1-4,respectively.Tocalculatetheconvectivespeed U c ,thetimedelayis determinedbycalculatingthebestlinetinaleast-squaressensetothe slopeofthephaseplot. 193

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A B Figure4-37.ABeamlocationsalongatwindow.BBeamdeectionspectraasa functionofwindowlocation.Thedeectionspectraismultipliedbythe convectivespeed U c andnormalizedbythefreestreamvelocity U 1 194

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A B Figure4-38.AContourplotofmeanvelocitymagnitude.Dottedlinesrepresentbeam locationsasshowninFigure4-37A.BSlicesalongbeampropagationpath ^ n -directionofmeanvelocityforeachbeamlocation.Upperandlowererror boundsarerepresentedbysolidlines. 195

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A B Figure4-39.AContourplotofturbulentkineticenergy.Dottedlinesrepresentbeam locationsasshowninFigure4-37A.BSlicesalongbeampropagationpath ^ n -directionofturbulentkineticenergyforeachbeamlocation.Upperand lowererrorboundsarerepresentedbysolidlines. 196

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A B Figure4-40.AnaperturelterisproposedbySiegenthaler etal. 2005toremovethe eectsofstationarystructuresfromthebeamdeectionspectra,AAperture lter AF A p ;f plottedasafunctionofnon-dimensionalfrequency A p f=U c BTransferfunction P A p ;f = U c 2 f 2 AF A p ;f betweenthedeection anglespectraandtheOPD rms A p ,plottedalongsidethecumulative summation P cs A p ;f = P f 0 P f = P 1 0 P f Figure4-41.Thedeectionspectraistreatedwithseverallterstoremovetip/tilteects andmitigatemechanicalvibrationcontaminationandareplottedasa functionofSt H G f denotestherawspectra. AF A p ;f isalterapplied toremovetip/tilt. F f c ;f correspondstothetappliedtoremovetunnel vibrations. G fc;f isthespectratruncatedataspecied f c 197

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A B Figure4-42.MalleyprobebeamlocationsshownfromAsideviewoftheturretandB head-onviewoftheturretwindow.Redcirclesindicatepressure measurementlocationswhilegreenlinesindicateMalleyprobebeamlocation. Figure4-43.Two-input,single-outputsystemrepresentingtheopticalmeasurements. Input X 1 =unsteadypressure, X 2 =accelerometerontunneloor, Y =laser positionsensingdevice,and N representsunmeasuredlineardynamics nonlinearities,andoutputsensorelectronicnoise. 198

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Figure4-44.Ordinarycoherencefunctionforvariousunsteadypressureandaero-optic measurements.Formeasurementlocations,seeFigure4-42. Figure4-45.Conditionedordinarycoherencefunctions. x 1 =unsteadypressureatlocation P1, x 2 =tunnelvibrationsmeasuredattunneloor, y =signalfromPSDat locationB1.Formeasurementlocations,seeFigure4-42. 199

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Figure4-46.Conditionedautospectrafor x 1 =unsteadypressureatlocationP1, x 2 =tunnel vibrationsmeasuredattunneloor, y =signalfromPSDatlocationB1.For measurementlocations,seeFigure4-42. A B Figure4-47.Twodistinctsystemmodelstodescribetheoutput y fromthetwo uncorrelatedinputs. GA 1 istheminimumcontributionfrom x 1 withalllinear portionsof x 2 removed. GA 2 isthemaximumcontributionfrom x 2 directly through H 2 y orindirectlythrough L 21 GB 1 isthemaximumcontribution from x 1 directlythrough H 1 y orindirectlythrough L 12 GB 2 istheminimum contributionfrom x 2 withalllinearportionsof x 1 removed. 200

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Figure4-48.Contributionstotheoutputautospectrafromtwodistinctsystemmodels. GA 1 correspondstotheminimumportionoftheoutputautospectrumthat comesfrom x 1 withalllinearportionsof x 2 removed. GB 2 correspondstothe minimumportionoftheoutputautospectrumthecomesfrom x 2 withall linearportionsof x 1 removed. 201

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Table4-1.Incomingboundarylayerparametersforfreestreamvaluesof40and90m/s 40m/s90m/s mm31 : 3 0 : 329 : 5 0 : 3 mm4 : 7 0 : 24 : 3 0 : 2 mm3 : 3 0 : 13 : 1 0 : 1 = 1 : 4 0 : 11 : 4 0 : 1 Re 900018000 Table4-2.Thirdoctavebandfrequencylimitsusedtocreateunsteadypressurecontour plotsasshowninFigures4-17through4-19.St H isthenondimensionalized centerfrequency, f c f l isthelowerbandlimitand f h isthehigherbandlimit St H f c Hz f l Hz f h Hz 0.25250220280 0.32320280360 0.40400360450 0.50500450570 0.63630570710 0.80800710900 1.0010009001120 1.25125011201420 1.60160014201800 Table4-3.SensitivityvaluesmV/Gofaccelerometersusedintunnelvibrationstudies LocationXYZ PSD195.496.793.7 PSD290.692.397.7 Tunneloor96.894.099.4 Table4-4.ComputedOPDrms mand SRfortwodistinctcalculationmethods.The rst,denotedby AF A p ;f F f c ;f appliesalow-frequencyttothedeection spectraandthenappliesandaperturelter.Thesecond,denotedby G f c ;f onlyusesatruncatedportionofthedeectionspectra.Strehlratioisin parentheses. B1B3B5B7avg. AF A p ;f F f c ;f 0.022.930.050.710.122.130.152.040.087.35 G f c ;f 0.021.940.047.730.112.170.138.070.080.41 202

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CHAPTER5 FLOWCONTROLRESULTS Themainobjectiveofthischapteristoassesstheeectivenessofbothpassiveand activeowcontrolontheuiddynamicsandaero-opticenvironmentinthenearwake regionoftheturret.Passivecontrolisimplementedbyinstallingcylindricalpinsnormal tothesurfacealongthestreamwisecenterlinewhileactivecontrolisexecutedviasteady blowingalongtheatwindow.Theeectofeachcontrolcaseisassessedwithboth qualitativeandquantitativeexperiments.Unsteadypressuremeasurementsalongfour locationsontheturretwindowareusedtodeterminetheeectontheunsteadinessinthe nearwakeregion.Qualitatively,surfaceoil-owvisualizationshowstheeectonboththe separationlineandthelengthoftherecirculationregion.Theturbulentkineticenergy withintheshearlayerismeasuredviahot-wireanemometry.Theaero-opticimpactis assessedwithMalleyprobemeasurements.Finally,themostinterestingcasesareselected forsPIVmeasurementsinthewakeregion. 5.1Introduction Itiswellknowthatpreviousowcontroltechniqueshavebeenmainlydeveloped withaneedtoaccommodatethemeanaerodynamicrequirementsi.e.dragreductionand liftenhancement.However,themetricusedtoassesscontroleectivenessbecomesmore restrictivewhenowcontrolisforthepurposeofenhancingthetransmissionofoptical wavefrontsthroughregionsofhighlyturbulentowVukasinovic etal. 2008.Forow aroundaturretwithaconformalwindow,separationcontrolisaviableoptiontoreduce theeectsofthetheshearlayer,asisshownbyMorgan&Visbal2010;Vaithianathan etal. 2010;Vukasinovic etal. 2005;Vukasinovic&Glezer2007.However,itisyettobe determinedifseparationcontrolisanappropriatemetrictouseforowcontrolarounda submergedturretwithaatwindow.Sinceowseparationisduetotheabruptgeometric discontinuityassociatedwiththeatwindow,theintroductionofsmallscaledisturbances withintheowtodisrupttheformationofcoherentstructureswithintheshearlayermay 203

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beamoreviableandattractiveowcontroloptionasopposedtoforcedreattachmentof theseparatedow.Thepurposeoftheowcontrolexperimentsistwo-fold: 1.Assesstheeectofbothdirectwakevortexgeneratingpinsandseparation controlsteadyblowingontheaero-opticenvironmentviadirectMalleyprobe measurements. 2.Relatethesendingstouiddynamicmeasurementsinaneorttodetermine asuitablemetricwhenevaluationoftheaero-opticenvironmentisnotdirectly available.Fromaowcontrolpointofview,itisdesirabletousereadilyavailable measurementstodiscerntheaero-opticconditions,whiledevisingacontrollerto mitigatetheminrealtime. 5.2PassiveFlowControl Passivecontroldevicesintheformofcylindricalpinsareinstallednormaltothe surfacealongthechord-wisecenterline y )]TJ/F22 11.9552 Tf 12.345 0 Td [(z planeat x =0oftheturret,asdiscussed inSection3.6.1andshowninFigure3-21.Thepurposeofthepinsistointroducesmall scaledisturbancesthatpropagatedownstreamandeventuallyinteractwiththeseparated shearlayer.Theinteractionwiththeseparatedow,andhencetheeectontheuidic andaero-opticenvironmentishighlydependentonthedimensionsandcongurationof thepins.Withthisinmind,itisimportanttorstunderstandthecomplexowarounda niteaspectratiocylinder. Althoughthewakeproducedbyanitecylinderisnotaswellunderstoodastheless complextwo-dimensionalcase,thereissomeworkthathashelpedelucidatethevarious owfeaturesgeneratedbyowaroundathree-dimensionalcylinderPark&Lee2000; Pattenden etal. 2005;Sumner etal. 2004;Tanaka&Murata1999.Theseinvestigations extensivelystudiedthisowandshowthatitiscomplexinnaturewithnumerousow features,asillustratedinFigure5-1.Sumner etal. 2004showedthatthepresidingow featuresinclude:thehorseshoevortexthatiscreatedastheincomingowwrapsitself aroundthecylinder,thetipvortexwhichisformedduetoseparationalongthefreeend, thearcvortexthatisconstrainedwithintherecirculationregionwhichdoesnotpropagate 204

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downstream,andtrailingvorticesthatarecreatedastheowseparatesalongthesidesof structure. Inthecaseofpinsmountedalongthespanwisecenterlineoftheturret,the interactionofthenewlyformedstreamwisevortices,thetipvortices,andtheglobal topologyoftheowovertheturretisgovernedbythegeometriccongurationofthepins. Forthisstudy,atotalof12congurationsareimplemented.Thespacingbetweenpins s height h ,anddiameter d areallvaried.Allparametersarenormalizedby ,theboundary layerheightasmeasuredattheapexoftheturret.Formoreinformation,refertoSection 3.6.1,Table3-4andtheillustrationsinFigure3-22.Duetothesheeramountofdata collectedforallpassivecontrolcases,onlycertainresultsareshownwithinthefollowing sections.Toseethemeasurementresultsforallcases,pleaserefertoAppendixD.All ndingsaresummarizedinTables5-5and5-6. 5.2.1Aero-OpticMeasurements Recallthatoneoftheobjectivesofowcontrolimplementationistomitigate aero-opticaberrationsthatarenotamenabletocorrectionviacurrentadaptiveoptic techniques.Inpracticalapplications,anadaptiveopticsystemsensestheaberration andmodiestheshapeofdeformablemirrorstocompensatefortheslowtime-varying atmosphericpropagationeectsandlowfrequencyuiddynamicaberrations.Recent studiesattheAirborneAero-OpticsLaboratoryAAOLhaveshownthatanadaptive opticsystemusingafast-steeringmirrorcanreducethebeam'soveralljitteruptoa frequencyof f FSS =200HzJumper etal. 2012;Porter etal. 2013.Usingthiscut-on frequencyandrecallingthattheturretisa1/5 th scalemodel,ahigh-passlterwitha non-dimensionalcut-onfrequencyofSt H = f FSS H =U 1 =0 : 98 f =1kHzisusedonall presentedaero-opticdata. TheMalleyprobeisusedtotakeaero-opticmeasurementsatasinglelocationbeam pairsB3B4asshowninFigure3-18alongtheatwindow.TheOPD rms iscalculated fromthedeectionspectra,asdiscussedinSection4.3.2.7.Themetricusedtoassess 205

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controlisthenormalizeddierencein rms OPD,calculatedby OPD rms = OPD rms; control )]TJ/F15 11.9552 Tf 11.956 0 Td [(OPD rms; baseline OPD rms; baseline 100% ; {1 wherenegativevaluescorrespondtoadesirabledecreaseinOPD rms whencomparedto thebaselineow.Figure5-2showsthecalculatedOPD rms asafunctionof s= d= ,and h= .Filledmarkers N correspondtopinsthatprotrudethroughtheboundarylayer, whileallemptymarkers # 4 denotethepinsthatarecontainedwithintheboundary layer.Outofall12casesstudied,twoshowaprominentdecreaseinthecalculated aero-opticsignal,P3by21.4%andP9by15.8%.Bothcongurationshavepinsthat protrudethroughtheboundarylayer h> andarespacedcloselytogether s= =3 : 4. ForeachcontrolcasetheStehlratio SR,whichisindicativeofthequalityoftheemerging beam,isalsocomputedviaEq.1{14asdiscussedinSection1.2.3.2.Theresultsforall congurationsarelistedinTable5-1. Closerexaminationofthebeamdeectionspectramultipliedbythenormalized convectivespeedshowsthatonlyP3isfoundtoimprovetheaero-opticenvironmentalong theentirefrequencyrangeofinterestFigure5-3A.Infact,congurationP9onlyreduces thedeectionspectrafor1 : 0 < St H < 2 : 5,asshowninFigure5-3C.Thisisarelevantnd becauseastechnologypushesthebandwidthoffast-steeringmirrors,aresultlikethatof P9maynolongerbeattractiveduetheincreaseinspectralenergyathighfrequencies. Whilecasesthatreducetheaero-opticaberrationsareofprimaryimportance,itmayalso provefruitfultostudycasesthatresultinaworseopticalenvironment.CongurationP7 fallsintothiscategory,providinganincreaseofOPD rms of121%.Thedeectionspectra forthiscaseisplottedinFigure5-3B,showingabroadbandincreasealongtheentire frequencyrange. RecallthatOPD rms scalesbytheproductofbeamdeectionangleandconvective speedoftheaberratingstructuresOPD rms U c .Therefore,therearetwowaysto improvetheaero-opticenvironment:eitherreducethebeamdeectionangleorreduce 206

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theconvectivespeedoftheproblematicstructures.Aninvestigationoftheconstantphase plotsrevealthatallcontrolcasesresultedinahigherconvectivespeedwhencompared tothebaseline.Specically,congurationP3anP7resultedinaconvectivespeed increasefromthebaseline U c =U 1 =0 : 70to U c =U 1 =1 : 12and1.01,respectively.This suggeststhattheprimarymechanismforimprovementintheow'sopticalqualityisthe diminutionofthebeam'sdeection,andnotthedecreaseinconvectivespeed. 5.2.2UnsteadyPressureMeasurements Unsteadypressurewasfoundtocorrelatewellwithaero-opticmeasurementsalong thetopportionoftheturretwindowseeSection4.3.3fordiscussionandcantherefore helpinterprethowtheowunsteadinesstiesintoaero-optics.Theunsteadypressureis measuredatfourlocationsalongtheatwindow:0 o atloc.2,0 o atloc.4,180 o atloc.2, and90 o atloc.2refertoFigure4-9.Thebaselinespectraiscomparedtothecontrolled spectraandthepercentchangein rms pressureiscalculated, P rms .Table5-2shows theresultsof P rms ateachmeasurementlocationforallpassivecontrolcases.Figure 5-4illustratestheeectofvaryingeachparameterontheaverage P rms .Notethatall lledmarkers N correspondtopinsthatprotrudethroughtheboundarylayer,while allemptymarkers # 4 denotethepinsthatarecontainedwithintheboundarylayer. CongurationsthatresultedinareductioninOPD rms aremarkedwitha Ingeneral,forthecaseswherethepinprotrudesthroughtheboundarylayer h= = 6 : 7,asthespacingbetweenthepins s= decreases,the rms pressuredecreasesatall locationsmeasuredalongtheaperture.Theoppositetrendistrueforthecaseswhere theboundarylayerpinisfullysubmergedwithintheboundarylayer h= =0 : 7.This suggeststhattheconvectingstructuresincludingthestreamwiseandtipvorticescreated bythepinsmayattributetoenergyamplicationwhenthepinisimbeddedwithin theboundarylayer,causingtheuctuatingpressureinthewakeregiontoincrease. Intermsofseparation,theintroducedenergywouldbeexpectedtohelptheowstay attachedalongtheouteredgesoftheturret,butmayproduceamoreenergeticshear 207

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layerdevelopmentalongthecenterlinewhereseparationdelayisnotfeasibleduetothe geometricconstraintofthewindow. Ofspecialinterestisthechangeinunsteadypressureatthemeasurementposition nearestseparation,asitshowedtohavethehighestcorrelationwithaero-optic measurementsseeFigure4-44.TherstcolumnofTable5-2showsthecalculated P rms atthislocation.Notethatonlyasinglepassivecontrolcaseshowsareduction. Thiscase,P3,correspondstothecongurationwherethepinsprotrudethroughthe boundarylayer,arespacedonly3.4 apartandhaveadiameterthatisthinnerthanthe boundarylayerheight.Anothercaseofinterest,albeitfortheoppositereason,ispassive controlcaseP7.Thiscongurationresultsinadoublingofunsteadypressureatevery locationalongthewindow. Thetwocasesofinterest,P3andP7,wherethe rms pressureisaectedthemost .9%decreaseand97.4%increase,respectivelyarefurtherinvestigated.Thebaseline spectraateachwindowlocationisplottedalongwiththeselectedcontrolcasesandis presentedinFigures5-6A-D.ForcaseP3,thespectrasuggestthatthepingenerated vorticitycausesasuppressionofenergytransferintheseparatedshearlayerresultingin reducedspectralenergymeasuredacrossallwindowlocations.PreviousworkbyGordeyev etal. 2010 a onatwo-dimensionalturrethasshownthatthetipvortexproducedby thinpinsthatprotrudethroughtheboundarylayerpromotedaninteractionwiththe shearlayer,reducingitsturbulentintensity.Forthecongurationwherethepinsare placedfurthestapartP7,ahumpinthespectraisintroducedataroundSt H =0 : 1, correspondingtoanenergyamplicationofthestructuresembeddedwithintheshear layer,alsoevidencedfromthebaselinehot-wireresultsinSection4.2.5.4.Thissuggests thatthepassivedevicesaredirectlymodifyingthedynamicsofstructureswithinthe separatedshearlayer. Toillustratethecorrelationbetweenunsteadypressureandaero-opticmeasurements inamorequantitativemanner,Figure5-5plotsOPD rms against P rms .Theresults 208

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showalineartrendbetweenthetwometrics,suggestingthatanincreaseinoneis concomitantwithanincreasewiththeother.Todetermineifthereisalinearrelationship betweenthetwotostandard95%condencelevel,thelinearcorrelationcoecientis calculated, r xy = n P i =1 x i )]TJ/F15 11.9552 Tf 12.679 0 Td [( x y i )]TJ/F15 11.9552 Tf 12.747 0 Td [( y s n P i =1 x i )]TJ/F15 11.9552 Tf 12.68 0 Td [( x 2 n P i =1 y i )]TJ/F15 11.9552 Tf 12.747 0 Td [( y 2 ; {2 where x istheaverageofall P rms values, y istheaverageofallOPD rms values,and n isthetotalnumberofpoints.Sincethecalculatedcorrelationcoecient, r xy =0 : 91is largerthanthecriticalcorrelationcoecient =0 : 05, n =12, r t =0 : 578,thenthere isalinearrelationshipbetween P rms andOPD rms ,toa95%condencelevelWheeler etal. 1996.Thisencouragestheuseofunsteadypressuremeasurementsasafeasible metricinreal-worldapplications,wheredirectaero-opticdiagnosismaynotbereadily availableinrealtime. 5.2.3OilFlowVisualization Togainfurtherinsightintotheglobalowtopologyofthecontrolledow,oilow visualizationisconducted.Ofmaininterestistheeectofthecontrolonboththe separationlineandthelocationoftherearstagnationpoint, x R ,whichdenestheextent oftherecirculationregion.Previousinvestigationshaveproposedthatseparationdelay mayinherentlyimprovetheaero-opticenvironmentinthenearwakeregion.Infact, Vukasinovic etal. 2005suggestedthat delayinseparationandreductionintheextent oftherecirculatingdomainmayleadtothereductionoftheturbulentkineticenergy ."The resultsfromtheoilowvisualization,coupledwiththeunsteadypressuremeasurements, willprovidemoreinsightintothisconjecture. Theeectonseparationandrecirculationregionlengthforeachcongurationare listedinTable5-3.TheeectofcontroleitherpromotesPordelaysDseparation andeitherextends+ x R =H orcontracts )]TJ/F15 11.9552 Tf 9.299 0 Td [( x R =H thelengthoftherecirculation 209

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regionalongthemid-plane.AvisualrepresentationofthelistedvaluesisshowninFigure 5-7.Again,recallthatalllledmarkers N correspondtopinsthatprotrudethrough theboundarylayer,whileallemptymarkers # 4 denotethepinsthatarecontained withintheboundarylayer.TohelpvisualizethepincongurationsthatreduceOPD rms a issuperimposedonthosecases.Notethattheredoesnotseemtobeacorrelation betweentheextentoftherecirculationregionandthelocationoftheseparationlinewith respecttothebaselineow.Ingeneral,however,asthespacingbetweenadjacentpins increases,thechangeintheextentoftherecirculationregiondiminishes.Furthermore, theonlytwocasestopromoteseparationarecongurationsofpinsthatarethickerthan theboundarylayerandarespacedlessthan s= =6 : 8apart.Acloserlookattheoil owvisualizationresultsforthesetwocasesP8andP9showsthatthepinsactasa barrieratthestreamwisecenterlineoftheturret,causingmassiveseparationasshown inFigure5-8.Therecirculationregionisextendedforbothcasesaswell,resultingin x R =H =32 : 7%and x R =H =79 : 8%forcasesP8andP9,respectively.Eventhough congurationP9showedareductionof15.5%inOPD rms ,onewouldexpectalargedrag penaltyassociatedwiththepromotionofseparation,thusnotmakingthiscaseamenable topracticalimplementation. Resultsfrombothaero-opticandunsteadypressuremeasurementsshowedthat passivecontrolcasesP3OPD rms = )]TJ/F15 11.9552 Tf 9.299 0 Td [(21 : 4%, P rms = )]TJ/F15 11.9552 Tf 9.298 0 Td [(23 : 9%andP7OPD rms = 121 : 4%, P rms =97 : 4%wereofparticularinterest.Comparisonoftheglobalow topologybetweenthebaselineandthesepassivecontrolcongurationsisshowninFigures 5-9and5-10.NotefromFigure5-9thatforbothcases,separationisdelayed.Thiscan againbeattributedtotheenergizingoftheboundarylayercreatedbytheinteraction betweenthegeneratedstreamwisevorticityofthepinandthespanwisevorticityofthe boundarylayer,allowingtheowtoresistseparation.Furthermore,separationisdelayed furtherdownstreamforcongurationP7thanitisforcongurationP3.ForP7,theow 210

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ontheportionoftheturretneartheooractuallyremainsattacheduntilitreachesthe apertureatthejuncturebetweentheturretandtheoor. Takingalookattherearstagnationpoints,Figure5-10illustratesthatwhileboth passivecontrolcasesdelayseparation,P7reducestheextentoftherecirculationregion x R =H = )]TJ/F15 11.9552 Tf 9.298 0 Td [(2 : 3%whileP3bothwidensandextendsthelengthoftherecirculation region x R =H =27 : 7%.FromtheoilowalongtheapertureinFigure5-9F,itis noticeablethattherecirculatingwakeismuchstrongerinP7thanitisinP3.Thisresults intheenergizingofturbulentstructuresovertheaperture,increasingtheunsteadinessin nearwakeregion,therebyresultinginanincreaseinOPD rms Figure5-11plotstheOPD rms asafunctionof x R =H .Thegeneraltrendissuch thatanincreaseinrecirculationregionsizeresultsinadecreaseintheOPD rms .To determineifthereisalinearrelationshipbetweenthetwotostandard95%condence level,thelinearcorrelationcoecientiscalculatedviaEquation5{2.Thecalculated correlationcoecient, r xy = )]TJ/F15 11.9552 Tf 9.299 0 Td [(0 : 51islargerthanthecriticalcorrelationcoecient =0 : 10, n =12, r t =0 : 497,sothereisalinearrelationshipbetween x R =H and OPD rms ,toa90%condencelevelWheeler etal. 1996.Theseresultshavesignicant implicationsforcontrolofaero-opticdistortion,mainlyraisingthequestionofusing separationcontrolasametric.Thendingsinsteadsuggestthattherecirculationlength maybeofmoreimportance.Inordertomakeanyrmconclusions,furtheruiddynamic measurements{includingdirectshearlayermeasurements{needtobeassessedand relatedtotheowvisualizationndings. 5.2.4DirectShearLayerMeasurements Baselinemeasurementsusinghot-wireanemometryandsPIVshowthatboththe energyandshearlayerthicknessarecontributingfactorstotheaero-opticenvironment. Furthermore,resultsfromsPIVindicatethattheshearlayerisnominallytwo-dimensional inthenearwakeregion x=H< 1 : 5refertoSection4.2.5.3fordiscussion,whichallows 211

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theuseofhot-wireanemometrytoextracttheshearlayerprolesandprovideuseful informationofthevelocityuctuationsviatemporalspectra. 5.2.4.1Hot-wireAnemometry Theshearlayerdevelopmentisrstassessedalongtheturretcenterline z=H =0 withvelocitymeasurementsmadewithaconstanttemperaturehot-wireanemometer,as discussedinSection3.4.4.Fluctuatingvelocityprolesaremeasuredinthenear-wake regionatvestreamwisemeasurementlocations,from x=H =0.45to1.26,ashighlighted inFigured3-11.Thepercentchangeinvelocityuctuationswithintheshearlayerateach locationislistedinTable5-4.Inordertogetabettersenseoftheeectofcontrolalong theentirewakeregion,theaveragepercentchangeaboutallmeasurementlocationsis thencalculatedvia k U 2 1 = P x R y h U 2 1 i control )]TJ/F28 11.9552 Tf 11.955 8.966 Td [(P x R y h U 2 1 i baseline P x R y h U 2 1 i baseline ; {3 where R y correspondstotheintegrationalongtheverticalaxis y=H and P x isthe summationofall x=H linecuts.Notethatnegativevaluescorrespondtoadecreasein turbulentkineticenergywhencomparedtothebaselineow.Figure5-12showsthe computedndings.Notsurprisingly,thetwocongurations,P3andP9,thatresultin areductioninOPD rms alsoleadtoareductionoftheaverageturbulentkineticenergy withintheshearlayerby23.6%and40.9%,respectively.CongurationP7,whichresults inadoublingofthecalculatedOPD rms ,alsoleadstoanincreaseof93 : 4%intheaverage turbulentkineticenergy. Figure5-13plotstheOPD rms asafunctionof k=U 2 1 .Todetermineifthereisa linearrelationshipbetweenthetwotostandard95%condencelevel,thelinearcorrelation coecientiscalculatedviaEquation5{2.Thecalculatedcorrelationcoecient, r xy =0 : 88 islargerthanthecriticalcorrelationcoecient =0 : 05, n =12, r t =0 : 578,so thereisalinearrelationshipbetween k=U 2 1 andOPD rms ,toa95%condencelevel Wheeler etal. 1996.Theimplicationisthatthereisastrongcorrelationbetween 212

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turbulentintensityandaero-opticdegradation,i.e.thecongurationsthatresultinalarge increase/decreaseinaero-opticdistortionalsoresultinlargeincrease/decreaseinturbulent kineticenergy. Toobtainabetterfeelfortheevolutionoftheshearlayerforspeciccontrol cases,velocityuctuationsareplottedateachstreamwiselocation.Thendingsfor congurationsP8andP9,bothofwhichresultinadecreaseintheaverageturbulent kineticenergy )]TJ/F15 11.9552 Tf 9.298 0 Td [(4 : 1%and )]TJ/F15 11.9552 Tf 9.298 0 Td [(40 : 1%,respectively,areplottedinFigure5-14.Acloser lookattheuctuatingvelocityprolesshowsthatcongurationP9,whichalsoresulted inadecreaseinOPD rms ,illustratesthepropagationofthetipvortexshedfromthetop ofthepins.Attheclosestmeasurementlocationtoseparation x=H =0 : 45theshear layershowsevidenceoftwodistinctpeaks,thetoponebeingattributedtothetipvortex ofthepin.Asthetipvortexpropagatesdownstream,itmergeswiththemainshearlayer, increasingthewidthoftheshearlayer.Whilethisincreaseinwidthmayresultinan increaseinthebeampropagationpath,themaximumuctuationsarereduced,resulting inanoverallreductionintheOPD rms Figure5-15plotsthemeanvelocityproles,uctuatingcomponents,andspectraat thelocationofmaximum k=U 2 1 forcongurationsP3andP7.Resultsfromconguration P3showthattheshearlayerwidensonlyasmallamountwhilereducingthepeak intensitybyroughlyafactoroftwoateachmeasurementplane.Theuctuatingvelocity prolesatboth x=H =0 : 45and0.65showthepresenceofthetipvortexwhichmerges withtheseparatedshearlayerby x=H =0 : 85.Theimplicationisthenthatthetip vortexsuppressestheenergytransferfromthesmall-scale,high-frequencystructuresin themainshearlayer,reducingtheoverallenergy,andresultinginanimprovedaero-optic environment.Incontrast,congurationP7thickenstheshearlayermorerapidly,causing greatershearlayercurvatureandareducedrecirculationregionasevidencedfromtheoil owvisualizationFigure5-9C,F.Thisresultsinanincreaseinthepeakintensityandan increaseintheshearlayerthickness.ThispointstothefactthattheincreaseinOPD rms 213

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cannotbesolelyattributedtothemaximumuctuationswithintheshearlayer,but insteadalargerolecanbeassociatedwiththeintegratedturbulentkineticenergy,which includesthemodicationoftheshearlayerthickness. 5.2.4.2sPIV Althoughhot-wireanemometrysuppliestime-resolvedmeasurementsofthe uctuatingvelocitywithintheshearlayer,itdoesnotprovidethespatialresolution requiredtoassesstheturbulentkineticenergyalongthebeampropagationpaths.It isthereforebenecialtousesPIVtosupplementthepreviousresultsalongdierent spanwiseplanes.Figures5-16,5-18,and5-19showthecontoursof k=U 2 1 ateach z=H plane.Eachbeam'spropagationpathisdenotedwithdashedlines.Slicesofthe turbulentkineticenergyareplotted,withthereferenceframetransformedsuchthatthe dataisplottedinthedirectionnormal^ n totheturretwindow,i.e.alongthebeam propagationpath.Inotherwords,theyshowthedistributionofvelocityuctuations associatedwiththepaththatthebeammusttravel.Theresultsalongthecenter planeFigure5-16matchwellwiththeresultsfromtheprevioussection,showing thatcongurationP7Figure5-16Cresultsinawiderandmoreenergeticshearlayer.By contrast,congurationP3Figure5-16Bresultsinareductionoftheoverallturbulent kineticenergyintheshearlayer.Theseresultshelpvalidatethehot-wireanemometry measurements. Figure5-13plotstheOPD rms asafunctionof k=U 2 1 asmeasuredalongthe beampropagationpathforpincongurationsP3 4 andP7 .Notethatresults frombeamlocationB7arenotincluded,sincetheentiremeasurementdomainwasnot obtainedwithinthesPIVdata.Todetermineifthereisalinearrelationshipbetweenthe twomeasurementstostandard95%condencelevel,thelinearcorrelationcoecientis calculatedviaEquation5{2.Thecalculatedcorrelationcoecient, r xy =0 : 97islarger thanthecriticalcorrelationcoecient =0 : 05, n =12, r t =0 : 578,indicatingalinear 214

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relationshipbetween k=U 2 1 andOPD rms ,toa95%condencelevelWheeler etal. 1996. Sincethemeasurementsofturbulentkineticenergyhaveshowntoprovidea reasonableindicationofopticalaberrationswithintheow,theycanbeusedto betterunderstandtheaero-opticenvironmentalongtheo-centerstreamwiseplanes z=H = )]TJ/F15 11.9552 Tf 9.299 0 Td [(0 : 31and )]TJ/F15 11.9552 Tf 9.298 0 Td [(0 : 62,whereMalleyprobemeasurementsarenotavailable.The trendsaresimilaralongeachspanwiseplane,withP7showinganincreasein k=U 2 1 along allbeampropagationpaths.Again,whilethemaximumpeakintensityisn'taectedmuch forthedownstreambeamlocations,thewidthoftheshearlayerincreases,causingthe beamstotravelalongeraberratedpathandresultinginanincreaseinOPD rms .For allcasesbaselineandcontrol,theturbulentkineticenergyisreducedasmeasurement planesmoveawayfromthecenterlinesuggestingthatcontrolalongthecenterlineisof foremostimportance. Tofurtherunderstandtheinteractionofthepin-generatedowstructureswiththe separatedshearlayer,time-averagedspanwisevorticity z H=U 1 iscalculatedand contoursareplottedinFigure5-20.ForpincongurationP3Figure5-20C,D,thetip vortexisclearlyvisibleabovethevorticityfromtheseparatedshearlayer.Thetwomerge atapproximately x=H =0 : 70andtheoveralleectisareductioninthestreamwise vorticitywithintheresultingseparatedow.PincongurationP7resultsinawider spreadofvorticityovertheaperture,asevidencedinFigure5-20E,F. Whileonlyonecomponentofvorticitycanbecalculatedwiththepresentdata,these resultshelpelucidatetheinteractionbetweenthepin-inducedowstructuresandthe separatedow.Intheabsenceoftheothertwovorticitycomponents,previousresearch mayhelpclarifysomeofthendings.Roh&Park2003showedthattipvortexpairs areformedbytheinteractionoftheupwashfromtheseparationalongthesidesofthe pinanddownwashfromtheowoverthefreeendofthecylinder.Park&Lee2000 revealedthatthesetipvortices,whicharecounter-rotatinginnature,areresponsible 215

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forsteeringthevelocityeldinadownwarddirection,inthiscaseextendinginthe streamwisedirectionuntilitmergeswiththeseparatedshearlayer.Futureworkshould focusontheinteractionofthepinstructuresupstreamoftheseparationlocationandthen obtainabetterunderstandingofhowtheyinteractwiththemainshearlayer.Thenal goalistodiscovertheprecisemechanismthatthepinvorticesusetoaltertheshearlayer inafavorablemanner.Armedwiththisinformation,onecouldthendesignaclosed-loop controlmethodtomimicthismechanism. 5.3ActiveFlowControl Intheprevioussection,passivecontrolwasimplementedbyintroducingsmallscale disturbanceswithintheowtodisrupttheformationofcoherentstructuresembedded intheshearlayer.Inthissection,atangentialjetalongtheupperportionoftheturret windowisusedtoforcereattachmentalongtheatwindow.Detailsofthemodeland setuparegiveninSection3.6.2.ThemeansforcontrolstemsfromtheCoandaeect, wherethecurvatureofthemodelandhighspeedjetcreatesuction,entraininguid fromthefreestreamandinturndevelopingalateraltransportofenergy.Thisinduced energyfromthefreestreamenablestheowtoovercometheadversepressuregradient imposedbythewindowgeometricdiscontinuityallowingthereattachmentoftheow overthewindow.Ifsuccessful,theresultingowwillbeabsentofawakeandshearlayer, potentiallyresultinginamoreattractiveopticalenvironment.Forthisstudy,atotalof eightsteadyblowingcasesareimplemented.Formoreinformation,refertoSection3.6.2, Table3-6andtheillustrationsinFigure3-24. 5.3.1Aero-OpticMeasurements TheMalleyprobeisusedtoacquireaero-opticmeasurementsattwolocations B3andB5,asshowninFigure3-18alongtheatwindow.Forcomparison,two metricsareusedtoassesscontrol.Therst,whichiscommonlyusedintheliterature Gordeyev etal. 2009;Vukasinovic etal. 2008,2009 b ,2010 a isthenormalizeddierence indeectionspectravalues, .Thesecond,whichismoreappropriateforquantifying 216

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theaero-opticenvironment,isthenormalizedchangeinthe rms valueofOPDEq.5{1. TheOPD rms iscalculatedfromthedeectionspectra,asdiscussedinSection4.3.2.7.For bothcalculations,thesamehigh-passlterthatisappliedtothepassivecontroldatais appliedherecut-onfrequencyofSt H =0.98,seeSection5.2.1.Asummaryofresultsare giveninTables5-7andTable5-8. Figure5-21plotsboth andOPD rms asafunctionof C formeasurement locationB3.Lookingatthe ,therearenoactivecontrolcasesthatchangethe deectionbymorethan45%.Anincreaseinsteadyblowing,upto C =0 : 21causes adirectincreaseinthemeasuredintegrateddeectionspectra.Forlargervaluesof C thereisadecreaseinthevalueofdeectionangle,with C =0 : 38obtainingtheminimum )]TJ/F15 11.9552 Tf 9.298 0 Td [(41 : 7%.Anincreaseinsteadyblowingpast C =0 : 26doesnotresultinany appreciabledecreaseindeectionanglelessthan5%dierencebetweenallvaluesof C =0 : 26andgreater.Thissuggeststhatthereisanoptimumamountofsteadyblowing, withanyexcessresultinginminimal,ifany,gains.Now,consideringtheOPD rms ,which takesintoaccounttheconvectivespeedofthestructureswithintheow,thesametrends arevisible,buttheminimumoccursfor C =0 : 26.Furtherincreaseinsteadyblowing resultsinaworseningoftheaero-opticenvironment.Since didnotchangebymore than5%betweenthesecases,theincreaseinOPD rms isattributedtotheincreasein convectivespeedoftheaero-opticallyactivestructuresstructures. Threecasesofinterestarechosenforfurtherstudy: C =0 : 21resultsinboth themaximumOPD rms %and : 5%, C =0 : 26resultsintheminimum OPD rms )]TJ/F15 11.9552 Tf 9.298 0 Td [(40 : 8%,and C =0 : 38resultsintheminimum )]TJ/F15 11.9552 Tf 9.298 0 Td [(41 : 7%.Thedeection anglespectraareplottedfortwomeasurementlocations,B3andB5,inFigures5-22Aand 5-22B,respectively.ForthemeasurementlocationB3closesttothejetexita C =0 : 21 resultsinabroadbandincreaseinthespectrarelativetothebaseline,mostlikelydueto theadditionofenergyintotheowwithoutthebenetofowreattachment.Afurther increaseto C =0 : 26resultsinthelargestdecreaseintheoverall OPD rms whichscales 217

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with U c .Mostnotably,thereductionoccursforSt H < 3 : 5,indicatingthatthesteady blowingisreattachingtheowovertheatwindow,resultingintheremovalofthelarge scalestructuresthatwerepresentwithintherecirculatingregioninthebaselineow. Finally,for C =0 : 38,thespectravaluesarelowerthananyothercaseforSt H < 5, buttheadditionofextramomentumresultsinanincreaseinthecalculateddeection spectraathigherfrequencies.Similarresultsareseenfurtherdownstreamatmeasurement locationB5andareshowninFigure5-22B.However,since-forthecontrolcases-the convectivespeeddecreasesastheowmovesdownstream,thereisageneraldecreasein thebroadbandenergyinthemeasuredspectra. 5.3.2FlowVisualization Togainfurtherinsightintotheglobalowtopologyofthecontrolledow,bothwake andsurfaceowvisualizationareconducted.Ofmaininterestisthecontroleecton thereattachmentofowalongtheturretwindow.Theresultsfrombothvisualization techniqueswillprovidemoreinformationonthephysicalphenomenathatiscausingthe changeinOPD rms Therstsetofowvisualizationexperimentsareconductedinthenearwakeregion atthecenterlineplane z=H =0.TheresultsforallblowingcasesareshowninFigure 5-23.RecallthatthelargestOPD rms isachievedfora C =0 : 21,whichfromtheow visualizationFigure5-23Eshowsthatthisisthehighestblowingcasethatdoesn'tresult inaconsiderablechangeinthewakeregion.Althoughincreasingthejetmomentum to C =0 : 26doesnotresultinfullreattachmentoftheowovertheatwindow Figure5-23F,itdoesshowthemaximumimprovementinOPD rms .Thisindicates thatwhilesomeseparationdelayalongthewindowresultsinanimprovementinthe opticalenvironment,furtherinjectiontotrytofullyreattachtheowresultsinoptical degradation.Finally,theowvisualizationfor C =0 : 38,whichresultsintheminimum ,isplottedinFigure5-23H.Theinstantaneoussnapshotsuggeststhattheowisfully 218

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reattachedalongtheatwindow,whichcouldindicatewhythiscaseresultedinthelowest deectionanglespectra-albeitnotthelowestOPD rms : Resultsfromoilowvisualizationtopviewfortheselectactivecontrolcasesare showninFigure5-24.Notethatforallthreeactivecontrolcases,theowatthetunnel oorshowsthemostpronouncedeectoftheslotblowing-theownearthebaseno longerrecirculatesbackupthewindow,butinsteadcontinuestoextenddownstream.The meanseparationlinealongthesidesoftheturret,however,donotchangemuchfrom thebaseline.Thisisduetothefactthatthesteadyblowingistoofardownstreamof separationtohaveaneect.Whileallthreecontrolcasesshowsimilarbehavior,acloser lookattheatwindowindicatesatherecirculationzoneispresentonthewindowforthe C =0 : 21case.For C =0 : 26and0 : 38,theowontheatwindowisdirectedtoward thebase,withlittletonoowbeingrecirculatedbackupthewindow.Thesendings willbeconrmedwiththesPIVresultsinthefollowingsection.Theseresultsagreewell withtheMalleyprobemeasurements,whichshowedthatthe C =0 : 21casehasstrong low-frequencylargesizestructuresinthenearwakeregion,indicatingthepresenceofa recirculationregion. Bothowvisualizationtechniquesprovideagoodqualitativeunderstandingofthe eectofactivecontrolaroundaturret.However,toobtainabetterunderstandingofthe surroundingow,quantitativemeasurementsintheformofsPIVarerequired. 5.3.3DirectWakeMeasurements Inthissection,theoveralloweldatMa=0.26isinvestigatedforaat-window turretbyinspectionofthespatialdistributionsofthemeanvelocityeldandsecond-order moments.AsdescribedinSection3.4.5,thewakeregionischaracterizedusingsPIVwhich extractsallthreevelocitycomponentswithintheplanareld.Themainregionsofinterest arethosedirectlydownstreamoftheturretwindowatthreestreamwiseplanes, z=H =0 : 0 symmetryplane, )]TJ/F15 11.9552 Tf 9.299 0 Td [(0 : 31,and )]TJ/F15 11.9552 Tf 9.298 0 Td [(0 : 62edgeofatwindow,asshowninFigure4-25. 219

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ThecontourplotsinFigures5-25showmeanthree-dimensionalvelocityalongthe threemeasurementplanes.Alongthesymmetryplane z=H =0-rstrowofFigure 5-25,itisclearthatfor C =0 : 21,thereisstillasmallrecirculationregion,which explainsthelow-frequencycontentmeasuredwiththeMalleyprobeFigure5-22.With increasedblowingto C =0 : 26,moreambientuidisentrained,andthemeanow showsfurtherreattachmentalongthewindowFigure5-25D.Fullreattachmentisonly achievedfor C =0 : 38,conrmingresultsfromowvisualizationFigure5-23H.Along the z=H = )]TJ/F15 11.9552 Tf 9.299 0 Td [(0 : 31planesecondrowofFigure5-25,thejethaslessofaneectonthe separation.Allthreecontrolcasesshowaredirectionofthemeanow,butnoneshowfull reattachment.Recallthatatthislocation,theslotisfurtherfromthebaselineseparation point,thereforerequiringmoresteadyblowingtoachievesimilarresults.Finally,alongthe edgeofthewindow z=H = )]TJ/F15 11.9552 Tf 9.299 0 Td [(0 : 62wherethereisnolongeranyslotblowing,themean velocityprolesarenoteasilydistinguishableFigure5-25I-L.Whilethesendingmatch theresultsfromowvisualizationandprovideabettergeneralunderstandingofthemean ow,theydonotprovideaclearpictureoftheaero-opticenvironmentinthenearwake region.Instead,thecontoursofturbulentkineticenergyareusedtohelpelucidatethe turbulentoweld. Figure5-26showsthecontoursof k=U 2 1 atsymmetryplane, z=H =0.Eachbeam's propagationpathisdenotedwithdashedlines.Slicesoftheturbulentkineticenergy areplotted,withthereferenceframetransformedsuchthatthedataisplottedinthe directionnormal^ n totheturretwindow,i.e.alongthebeampropagationpath.Inother words,theyshowthedistributionofvelocityuctuationsassociatedwiththepaththat thebeammusttravel.Sincethemeasurementsofturbulentkineticenergyhaveshownto provideareasonableindicationofopticalaberrationswithintheowseeSection5.2.4 andFigure5-17,themetric k=U 1 iscalculatedalongthebeampropagationpathand resultssummarizedinTable5-9.TheresultsatbeamlocationB3alongthecenterplane Figure5-26,matchwelltheMalleyprobemeasurements.Specically,theyshowthatthe 220

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overallenergyisincreasedforcase C =0 : 21 k=U 2 1 =27 : 6%,OPD rms =104 : 5% andreducedforcases C =0 : 26 k=U 2 1 = )]TJ/F15 11.9552 Tf 9.299 0 Td [(81 : 1%,OPD rms = )]TJ/F15 11.9552 Tf 9.299 0 Td [(40 : 8and0 : 38 k=U 2 1 = )]TJ/F15 11.9552 Tf 9.299 0 Td [(93 : 1%,OPD rms = )]TJ/F15 11.9552 Tf 9.299 0 Td [(21 : 7%.Aswiththepassivecontrolcongurations, thecorrelationcoecientiscalculatedplotnotshownforbrevity.Thevalue, r xy =0 : 91, islargerthanthecriticalcorrelationcoecient =0 : 05, n =8, r t =0 : 707,indicating alinearrelationshipbetween k=U 2 1 andOPD rms ,toa95%condencelevelWheeler etal. 1996. Sincethemeasurementsofturbulentkineticenergyhaveshowntoprovidea reasonableindicationofopticalaberrationswithintheow,theycanbeusedto betterunderstandtheaero-opticenvironmentalongtheo-centerstreamwiseplanes z=H = )]TJ/F15 11.9552 Tf 9.298 0 Td [(0 : 31and )]TJ/F15 11.9552 Tf 9.299 0 Td [(0 : 62,whereMalleyprobemeasurementsarenotavailable.Figure 5-27plotsthecontoursofturbulentkineticenergyalongtheo-centerstreamwiseplanes forthebaselineandcontrolcases.AsillustratedwithsurfaceoilowvisualizationFigure 5-23andsPIVmeanvelocitycontoursFigure5-25,theeectoftheaddedmomentum diminishesforincreasing z=H .Again,thiscanbeattributedtothelocationofactuation beingtoofardownstreamofseparationtohaveadesirableeect.Theresultisanincrease inturbulentkineticenergyforallblowingcasesascomparedtothebaseline,inall likelihoodaectingtheaero-opticenvironmentinanadversemanner.Sincetheeectof steadyblowingvariesacrosstheentirewindow,theoverallconsequenceofsteadyblowing isyettobedetermined.Todoso,asissuggestedinthefollowingchapter,aspatially resolvedaero-opticmeasurementneedstobeconducted. 5.4FlowControlConcludingRemarks Passivecontrolwasimplementedbyinstallingcylindricalpinsnormaltothesurface alongthestreamwisecenterline,introducingsmallscaledisturbancesthatpropagate downstreamandinteractwiththeseparatedshearlayer.Itwasfoundthatforallpin congurations,therewasadirectcorrelationbetweenunsteadypressureandtheaero-optic environment.Surfaceoil-owvisualization,determinedthatforaat-windowturret, 221

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separationdelayshouldnotbeusedasametricwhenassessingaero-opticdistortions. Instead,thelengthoftherecirculationregionprovidedfurtherinsight.Finally,direct shearlayermeasurementsshowedthatthemaincausesoftheincreaseinOPD rms wastied toboththethickeningoftheshearlayerandincreaseinmaximumturbulentuctuations. Futureworkmayinvolvetheimplementationofanactivecontrolstrategythatuses unsteadymicrojetsthatpiercethroughtheboundarylayerandintroducesmallscale disturbancesinasimilarfashiontothepins. Activecontrolwasexecutedviasteadytangentialblowingalongtheatwindow, modifyingboththesmallscaleandlargescalestructureswithinthenearwake.Flow visualizationandsPIVshowedthatifreductioninOPD rms isthegoal,thenfull reattachmentoftheowoverthewindowisnotdesired.Instead,thereisanoptimal amountofsteadyblowingwillresultintheowbeingonlypartiallyattachedalongthe atwindow.Unlikepassivecontrol,activecontrolcomesatacost-i.e.themassow throughtheslotmustbesuppliedfromsomewherewithintheaircraft.Thisinvitesfuture worktodevelopaviablecostfunctionthatincludes C andOPD rms 222

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Figure5-1.Schematicofthetime-averagedowtopologyoveraverticallymounted cylindernotdrawntoscale.AdaptedfromPattenden etal. 2005. Figure5-2.OPD rms %measuredatbeamlocationB3,showninFigure3-18asa functionof s= ,forvariousvaluesof d= ,and h= .Filledmarkers N correspondtopinsthatprotrudethroughtheboundarylayer,whileallempty markers # 4 denotethepinsthatarecontainedwithintheboundarylayer. A B C Figure5-3.DeectionspectrameasuredatbeamlocationB3,showninFigure3-18asa functionofSt H forthreepassivecontrolcasesAP3OPD rms = )]TJ/F15 11.9552 Tf 9.299 0 Td [(21 : 4%, BP7OPD rms =121 : 4%,andCP9OPD rms = )]TJ/F15 11.9552 Tf 9.298 0 Td [(15 : 8%.Blacksolid line )]TJ/F15 11.9552 Tf 9.299 0 Td [(denotesbaselineandbluesolidline )]TJ/F15 11.9552 Tf 9.299 0 Td [(representscontrolcase. 223

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Figure5-4.Average P rms %acrossallwindowmeasurementlocationstrendsasa functionof s= d= ,and h= .Filledmarkers N correspondtopinsthat protrudethroughtheboundarylayer,whileallemptymarkers # 4 denote thepinsthatareembeddedwithintheboundarylayer.Congurationsthat resultinareductioninOPD rms aremarkedwitha .Congurationsof interestarelabeledaccordingly. Figure5-5.OPD rms asafunctionofaverage P rms %acrossallwindowmeasurement locations.Thecalculatedcorrelationcoecient, r xy =0 : 91suggestslinear correlation%condencelevel.Filledmarkers correspondtopinsthat protrudethroughtheboundarylayer,whileallemptymarkers # denotethe pinsthatareembeddedwithintheboundarylayer.Congurationsof particularinterestaremarkedwitha 4 224

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A B C D Figure5-6.Unsteadypressurespectraforbaseline|andselectedpassivecontrolcases P3---andP7-.-forMa=0.26.Pressuremeasurementlocationsalongthe windowareillustratedinthebottomleftcornerofeachplot. Figure5-7.Recirculationlength x R =H %trendsasafunctionof s= d= ,and h= Filledmarkers N correspondtopinsthatprotrudethroughtheboundary layer,whileallemptymarkers # 4 denotepinsthatareembeddedwithin theboundarylayer.CongurationsthatresultinareductioninOPD rms are markedwitha .CongurationsP8andP9promoteseparationseeFigure 5-8whileP3andP7delayseparationseeFigure5-9. 225

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A B C D E F Figure5-8.Oilowvisualizationforbaseline,P8,andP9casesforMa=0.26.Flowisfrom righttoleft.A-CaretopviewswhileD-Fareangledviews.AandDshow thebaselineow.BandEshowtheowforcaseP8.CandFshowthe owforcaseP9.Bothcontrolcasesshowanincreaseintheextentofthe recirculationregionwhilepromotingseparation. 226

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A B C D E F Figure5-9.Oilowvisualizationforbaseline,P3,andP7casesforMa=0.26.Flowisfrom righttoleft.A-CaretopviewswhileD-Fareangledviews.AandDshow thebaselineow.BandEshowtheowforcaseP3.CandFshowthe owforcaseP7. ATopview BAngledView Figure5-10.Oilowvisualizationforbaseline,P3,andP7casesforMa=0.26.ATop viewshowingtheseparationlineandtherearstagnationpoint x R that dividestherecirculatingregionfromthedownstreamow.BAngledview showingtheseparationlines. 227

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Figure5-11.OPD rms plottedasafunctionof x R =H .Thecalculatedcorrelation coecient, r xy = )]TJ/F15 11.9552 Tf 9.299 0 Td [(0 : 51suggestslinearcorrelation%condencelevel. Filledmarkers correspondtopinsthatprotrudethroughtheboundary layer,whileemptymarkers # denotethepinsthatareembeddedwithinthe boundarylayer.Congurationsthatresultinpromotionofseparationare markedwitha 4 Figure5-12.Turbulentkineticenergytrendsasafunctionof s= d= ,and h= .Filled markers N correspondtopinsthatprotrudethroughtheboundarylayer, whileemptymarkers # 4 denotethepinsthatareembeddedwithinthe boundarylayer.CongurationsthatresultinareductioninOPD rms are markedwitha 228

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Figure5-13.OPD rms plottedasafunctionof k=U 2 1 .Thecalculatedcorrelation coecient, r xy =0 : 88suggestslinearcorrelation%condencelevel. Filledmarkers correspondtopinsthatprotrudethroughtheboundary layer,whileemptymarkers # denotethepinsthatareembeddedwithinthe boundarylayer.Congurationsthatresultinpromotionofseparationare markedwitha 4 229

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Figure5-14.Meanvelocityprole U=U 1 ,turbulentkineticenergy =U 2 1 ,and spectraasmeasuredatthepointofhighestuctuationwithintheshearlayer, markedwitha .Baseline|,P8|,andP9|. \000 denotesa f )]TJ/F21 7.9701 Tf 6.587 0 Td [(5 = 3 trend. 230

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Figure5-15.Meanvelocityprole U=U 1 ,turbulentkineticenergy =U 2 1 ,and spectraasmeasuredatthepointofhighestuctuationwithintheshearlayer, markedwitha .Baseline|,P3|,andP7|. \000 denotesa f )]TJ/F21 7.9701 Tf 6.587 0 Td [(5 = 3 trend. 231

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A B C D B1B3B5B7 Figure5-16.ContourplotsandlinecutsofturbulentkineticenergyextractedfromsPIV measurementsat z=H =0.Dottedlinesincontourplotsrepresentbeam locationsasshowninFigure4-37A.A,B,andCcorrespondtothe baseline,P3,andP7congurations,respectively.Dshowsslicesalongbeam propagationpath^ n -directionofturbulentkineticenergyforeachbeam locationforbaseline ,P3 4 ,andP7 .Upperandlowererrorbounds arerepresentedbysolidlinesofmatchingcolor. 232

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Figure5-17.OPD rms plottedasafunctionof k=U 2 1 asmeasuredwithsPIValongthe z=H =0plane.Thecalculatedcorrelationcoecient, r xy =0 : 97suggests linearcorrelation%condencelevel. 4 correspondcongurationP3, while denotecongurationP7.Beammeasurementlocationsaremarked accordingly. 233

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A B C D B1B3B5B7 Figure5-18.ContourplotsandlinecutsofturbulentkineticenergyextractedfromsPIV measurementsat z=H = )]TJ/F15 11.9552 Tf 9.299 0 Td [(0 : 31.Dottedlinesincontourplotsrepresentbeam locationsasshowninFigure4-37A.A,B,andCcorrespondtothe baseline,P3,andP7congurations,respectively.Dshowsslicesalongbeam propagationpath^ n -directionofturbulentkineticenergyforeachbeam locationforbaseline ,P3 4 ,andP7 .Upperandlowererrorbounds arerepresentedbysolidlinesofmatchingcolor. 234

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A B C D B1B3B5B7 Figure5-19.ContourplotsandlinecutsofturbulentkineticenergyextractedfromsPIV measurementsat z=H = )]TJ/F15 11.9552 Tf 9.299 0 Td [(0 : 62.Dottedlinesincontourplotsrepresentbeam locationsasshowninFigure4-37A.A,B,andCcorrespondtothe baseline,P3,andP7congurations,respectively.Dshowsslicesalongbeam propagationpath^ n -directionofturbulentkineticenergyforeachbeam locationforbaseline ,P3 4 ,andP7 .Upperandlowererrorbounds arerepresentedbysolidlinesofmatchingcolor. 235

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A B C D E F Figure5-20.ContourplotsandlinecutsofturbulentkineticenergyextractedfromsPIV measurementsat z=H =0and )]TJ/F15 11.9552 Tf 9.299 0 Td [(0 : 31.A,Bcorrespondtothebaseline, C,DtocongurationP3,andE,FtocongurationP7. 236

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Figure5-21.OPD rms and asafunctionof C foractiveowcontrolcases. MeasurementstakenatlocationB3asshowninFigure4-37A.Resultsare listedinTable5-7.Filledmarkers correspondtoOPD rms ,whileempty markers # denote .Congurationsofinterestaremarkedwitha A B Figure5-22.Deectionangletimesconvectivespeedspectraforbaseline )]TJ/F15 11.9552 Tf 9.298 0 Td [(andselected activecontrolcasesshowninFigure5-21: C =0 : 211 )]TJ/F15 11.9552 Tf 9.299 0 Td [(, C =0 : 260 )]TJ/F15 11.9552 Tf 9.299 0 Td [(, and C =0 : 375 )]TJ/F15 11.9552 Tf 9.298 0 Td [(forMa=0.26.Malleyprobemeasurementstakenat locationAB3andBB5asshowninFigure4-37A. 237

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A B C D E F G H I Figure5-23.Instantaneousowvisualizationimagesforallactivecontrolcases:A C =0 : 0,B C =0 : 02,C C =0 : 09,D C =0 : 14,E C =0 : 21,F C =0 : 26,G C =0 : 31,H C =0 : 38,I C =0 : 43.Imagestakenatthe centerplane z=H =0withaNikon60mmf/2.8lensattachedtoaNikon D300scamerasetto1",f/5.6,andISO500.Flowisfromlefttoright. 238

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A B C D Figure5-24.OilowvisualizationforAbaselineandselectedactivecontrolcases showninFigure5-21:B C =0 : 21,C C =0 : 26,andD C =0 : 38for Ma=0.26.Flowisfromlefttoright. 239

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A B C D E F G H I J K L Figure5-25.Contourplotofmeanvelocityforselectactivecontrolcaseatallthree measurementplanes z=H =0A-D, z=H = )]TJ/F15 11.9552 Tf 9.298 0 Td [(0 : 31E-H,and z=H = )]TJ/F15 11.9552 Tf 9.299 0 Td [(0 : 62 I-L.BaselineA,E,I, C =0 : 211B,F,J, C =0 : 260C,G,K,and C =0 : 375D,H,L. 240

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A B C D E B3B5 Figure5-26.ContourplotsandlinecutsofturbulentkineticenergyextractedfromsPIV measurementsat z=H =0 : 0.Dottedlinesincontourplotsrepresentbeam locationsB3andB5asshowninFigure4-37A.A,B,C,andD correspondto C =0,0.21,0.26,and0.38,respectively.Eshowsslicesalong beampropagationpath^ n -directionofturbulentkineticenergyforeach beamlocationB3ontheleft,B5ontheright.Upperandlowererror boundsarerepresentedbysolidlinesofmatchingcolor. 241

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A B C D E F G H Figure5-27.ContourplotsandlinecutsofturbulentkineticenergyextractedfromsPIV measurementsat z=H = )]TJ/F15 11.9552 Tf 9.299 0 Td [(0 : 31toprowand )]TJ/F15 11.9552 Tf 9.298 0 Td [(0 : 62bottomrow.A,E baseline.B,F C =0,0.21.C,G C =0,0.26.D,H C =0.38. 242

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Table5-1.PercentchangeinOPD rms forbeamlocationB3forallpassivecontrolcasesfor Ma=0.26.Negativenumberssignifyareductioncomparedtothebaseline. ResultsareplottedinFigure5-2.RefertoFigure3-18forMalleyprobe measurementlocationsandtoTable3-4orFigure3-22forpinconguration cases. CaseOPD rms SR U c =U 1 Figure Baseline{0.930.70{ P16.8%0.920.74D-5 P24.7%0.921.04D-9 P3-21.4%0.961.12D-13 P410.3%0.910.79D-17 P546.2%0.850.80D-21 P614.2%0.911.01D-25 P7121.4%0.691.01D-29 P813.2%0.911.09D-33 P9-15.8%0.951.00D-37 P1047.0%0.850.97D-41 P11102.1%0.730.82D-45 P1211.9%0.911.07D-49 Table5-2.Percentchangein rms pressureforallpassivecontrolcasesforMa=0.26. Negativenumberssignifyareductionin rms pressureascomparedtothe baseline.Theaveragechangein rms pressureacrossallwindowlocationsis plottedinFigure5-4.RefertoFigure4-9forpressuremeasurementlocations andtoTable3-4orFigure3-22forpincongurationcases. Avg.Figure P130.633.618.626.527.3D-3 P27.713.52.65.87.4D-7 P3-15.3-20.7-33.3-26.1-23.9D-11 P48.817.514.210.812.8D-15 P532.037.028.322.730.0D-19 P619.842.936.521.930.3D-23 P790.7102.396.3100.497.4D-27 P837.833.3-8.820.915.8D-31 P934.917.4-6.314.915.2D-35 P1030.647.237.047.340.5D-39 P1175.9101.275.291.686.0D-43 P1231.966.551.251.950.4D-47 243

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Table5-3.Oilowvisualizationresultsforpassivecontrolcasesshowingtheeecton boththeseparationlineandthelocationoftherearstagnationpoint x R =H The x R =H areplottedinFigure5-7.Forspecicpincongurations,referto Table3-4andFigure3-22. CaseSeparation x R =H x R =H Figure Baseline{2.380.0%{ P1D2.33-2.1%D-2 P2D2.24-5.9%D-6 P3D3.0427.7%D-10 P4D2.26-5.0%D-14 P5D2.11-11.3%D-18 P6D2.12-10.9%D-22 P7D2.31-2.9%D-26 P8P3.1632.7%D-30 P9P4.2879.8%D-34 P10D2.08-12.6%D-38 P11D2.12-10.9%D-42 P12D2.70-13.4%D-46 D:delayinseparation.P:promoteseparation. Table5-4.Integratedchangeinturbulentkineticenergy k=U 1 fromshearlayer measurementresultsforpassivecontrolcases.Theaveragevaluescalculated viaEq.5{3areplottedinFigure5-12.Forspecicpincongurations,referto Table3-4andFigure3-22. Case x=H =0.450.650.851.061.26Avg.Figure P140.1%70.1%49.8%37.4%24.4%36.2%D-4 P257.6%22.8%5.9%-2.1%-7.6%2.4%D-8 P332.2%-7.2%-18.9%-24.1%-30%-23.6%D-12 P492.1%46.9%21.1%11.5%8.7%15.9%D-16 P5137.1%81.0%44.2%26.8%19.3%32.4%D-20 P6116.5%55.7%29.2%16.5%8.6%19.8%D-24 P7503.8%226.2%140.1%83.9%43.2%93.4%D-28 P8248.3%52.3%11.6%-12.3%-23.9%-4.1%D-32 P9163.9%-10.2%-33.9%-46.7%-52.9%-40.9%D-36 P10148.6%68.2%19.9%7.3%-2.4%12.2%D-40 P11361.7%169.3%79.7%42.1%23.0%55.1%D-44 P12106.1%46.8%23.5%19.8%9.5%19.4%D-48 244

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Table5-5.Summaryofpassiveowcontrolresultsfortallpincongurations h> .P1, P2,P3 d< andP7,P8,P9 d> CaseSeparation x R =H P rms k=U 2 1 OPD rms P1-2.1%27.3%36.2%6.8% P2-5.9%7.4%2.4%4.7% P327.7%-23.9%-23.6%-21.4% P7-2.9%97.4%93.4%121.4% P832.7%15.8%-4.1%13.2% P979.8%15.2%-40.9%-15.8% Pincongurationsarenotdrawntoscale.Forspecicdimensions,refertoTable3-4and Figure3-22.Forseparationline, )]TJ/F15 11.9552 Tf 9.298 0 Td [(:baselineand )]TJ0 g 0 G/F15 11.9552 Tf 9.298 0 Td [(:control. 245

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Table5-6.Summaryofpassiveowcontrolresultsforshortpincongurations h< P4,P5,P6 d< andP10,P11,P12 d> CaseSeparation x R =H P rms k=U 2 1 OPD rms P4-5.0%12.8%15.9%10.3% P5-11.3%30.0%32.4%46.2% P6-10.9%30.3%19.8%14.2% P10-12.6%40.5%12.2%47.0% P11-10.9%86.0%55.1%102.1% P12-13.4%50.4%19.4%11.9% Pincongurationsarenotdrawntoscale.Forspecicdimensions,refertoTable3-4and Figure3-22.Forseparationline, )]TJ/F15 11.9552 Tf 9.298 0 Td [(:baselineand )]TJ0 g 0 G/F15 11.9552 Tf 9.298 0 Td [(:control. 246

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Table5-7.PercentchangeindeectionangleandOPD rms forbeamlocationB3forall activecontrolcasesforMa=0.26.Negativenumberssignifyareduction comparedtothebaseline.ResultsareplottedinFigure5-21.RefertoFigure 4-37AforMalleyprobemeasurementlocations. C U c =U 1 OPD rms SR Baseline{0.73{0.89 0.021.6%0.7510.0%0.87 0.0914.3%0.7732.1%0.81 0.1414.6%0.9343.1%0.78 0.2128.5%1.18104.8%0.61 0.26-21.2%1.36-40.8%0.96 0.31-24.6%1.50-38.3%0.96 0.38-38.3%1.84-21.7%0.96 0.43-19.8%2.39-6.9%0.90 Table5-8.PercentchangeindeectionangleandOPD rms forbeamlocationB5forall activecontrolcasesforMa=0.26.Negativenumberssignifyareduction comparedtothebaseline.RefertoFigure4-37AforMalleyprobemeasurement locations. C U c =U 1 OPD rms SR Baseline{0.93{0.74 0.02-1.7%1.1527.5%0.61 0.09-1.3%1.1826.2%0.62 0.14-14.1%1.192.0%0.73 0.21-16.3%1.250.5%0.74 0.26-45.0%1.39-55.9%0.94 0.31-44.1%1.25-67.1%0.97 0.38-40.2%1.50-59.2%0.95 0.43-33.8%1.66-41.2%0.91 Table5-9.PercentchangeinintegratedturbulentkineticenergyforbeamlocationsB3 andB5at z=H =0forallactivecontrolcasesatMa=0.26.Negativenumbers signifyareductioncomparedtothebaseline.ResultsareplottedinFigure 5-26.RefertoFigure4-37AforMalleyprobemeasurementlocations. C B3B5 0.21127.6%-6.5% 0.260-81.1%-84.4% 0.375-93.1%-91.6% 247

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CHAPTER6 SUMMARYANDFUTUREWORK Itiswellknownthatunsteadyowcausedbytheseparationoveraturrethasan adverseeectonaero-opticapplications.Understandingthevariousthree-dimensional owfeaturesandtheireectsonboththeuiddynamicsandaero-opticsisakey challengethatneededtobeaddressed.Themaintasksofthisresearchareasfollows. Therstistodesignaturretmodelrepresentativeofaircraftdirectedenergyapplications. Thenthethree-dimensionalowischaracterized,identifyingpotentialsourcesofthe turbulentwakeandaero-opticdistortion,specicallyfocusingontheinteractionof thevariousowfeaturesthatarepresentinthelow-subsonicowregime.Oncea clearunderstandingisestablished,themaingoalshiftstowardtheevaluationand implementationofowcontrolstrategies.Leveragingresearchintheowcontrol community,bothpassiveandactivecontrolareimplementedtosuppressunfavorable owdisturbancesand,inturn,mitigateaero-opticdistortion. Thisclosingchaptersummarizesthekeyndingsoftheinvestigation,discusseskey impactstotheaero-opticsowcontrolcommunity,andprovidessuggestionsforfuture work. 6.1ResearchSummary 6.1.1BaselineFlow Ithasbeenestablishedthattheincomingboundarylayercharacteristicsaredirectly relatedtothedevelopmentofowoverathree-dimensionalhemisphereSavory& Toy1986;Toy etal. 1983; ? .Aspartofthebaselinecharacterization,boundary-layer measurementsdeterminedthattheratiooftheincomingboundarylayertothe turretheightis =H =0.30,matchinganapplicableightcondition.Toobtainan understandingoftheuctuatingnatureoftheowinthenear-wakeregion,unsteady pressuremeasurementsareconductedatseverallocationsalongtheatwindow.Spectral contourplots,plottedinthird-octavebands,revealthatthereweretwodominantregions 248

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contributingtotheunsteadinessoftheow.Therstisconcentratedalongtheportionof thewindowclosesttothebase,wherelargecoherentstructureswithintherecirculation regionaredominant.Thesecondislocatedalongtheupperportionoftheatwindow, withthesourcebeingtheseparatedshearlayer.Themeasuredconvectivespeedof coherentstructures,whichisavitalmetricwhendeterminingtheaero-opticenvironment, showsthatthebulkofcoherentstructuresconvectedinthestreamwisedirection. Oilowvisualizationprovedtobeanadvantageoustooltoextractphysicalmeaning fromsomeofthequantitativemeasurements.Theresultsillustratedtheinteraction betweentheincomingboundarylayerandturretwhichresultsinthecreationofa horseshoeshapedvortex.Thevisualizationsupportsthendingsfromthestatic pressuremeasurements,mainlythattheowseparatesinthecenterlineduetothe geometricconstraintoftheatwindow.Theresultoftheseparatedowisahighlythree dimensionalwake,containingcoherentlengthscalesofvarioussizes,allpossiblesourcesto thedegradationoftheaero-opticconditions. Thenaluiddynamicmeasurementsinvolvecharacterizingtheseparatedshear layer,andincludebothspatialevolutionandtemporalspectracalculations.Where applicable,theresultsarecomparedtooilowvisualizationandunsteadypressurein additiontopreviousinvestigationsregardingthewakeregionofahemisphericalmodels. AstudyoftheReynoldsstressesindicatesthattheshearlayeristwo-dimensionalin natureneartheseparationlocation,withthemajorityoftheuctuationsoccurringin thestreamwisedirection.Thisresultjustiestheuseofhot-wireanemometrytoextract temporalspectraatthelocationofmaximumturbulentintensitywithineachshear layerprole.Sinceitiswellknownthattheturbulentintensitywithintheshearlayer isastrongindicatoroftheopticalenvironmentGordeyev etal. 2004 a ;Vukasinovic etal. 2010 a ,theuiddynamicresultshavestrongimplications.Mostnotably,the strongtwo-dimensionalnatureoftheshearlayerinthenearwakeregionsuggeststhat themajorityofaero-opticdistortionscouldbecharacterizedusingonlythestreamwise 249

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componentoftheaero-opticsignal-andingthatisleveragedwhenusingtheMalley probeforaero-opticmeasurements. Whiletheuiddynamicexperimentsyieldusefulinformationontheowstructures surroundingathree-dimensionalturret,aero-opticmeasurementsarerequiredtofully understandtheimpactoftheowstructuresontheopticalconditions.First,an imagingtechniqueprovidesqualitativeinformationfortheopticaldegradationinthe nearwakeregion.Resultsindicatedthattheowisindeedopticallyactive,evenforan incompressiblefreestreamofMa=0.26.Basedonthisnding,measurementsaremade withaMalleyprobeatseverallocationsalongtheatwindow,providingone-dimensional slicesofopticalwavefrontsinthedirectionofthebeampropagationvector.Dueto mechanicaljittercontamination,conditionalspectralanalysisisimplementedtoboth removeaportionofthevibrationsfromthemeasurementsandsuggestimprovementsin theMalleyprobesetup. Whileithasbeenconjecturedthatowaroundathree-dimensionalat-windowed turretresultsinhigheropticalaberrationswhencomparedtoaconformal-window turret,noquantitativeresultswereavailable,untilnow.Sincethiswastherstsetof experimentsthatusesasurface-mounted,at-windowedturret,thecalculatedOPD rms valuesarecomparedtopreviousworkthatutilizesotherturretmodeltypes.When non-dimensionalizingthecalculatedOPD rms bythesuggestedscaling,sin = H Ma 2 theresultsshowthattheowaroundasurface-mounted,at-windowturretismorethan twiceasopticallyactiveastheowsurroundingasurface-mountedconformal-window turret. Inmostsituations,real-timeaero-opticdatacannotbereadilymeasured.Therefore itisdeemedimperativetounderstandthecorrelationbetweentheaero-opticenvironment andothermeasurableowquantities.Conditionalspectralanalysisisimplementedby usingaero-opticandunsteadypressuredatatodetermineasuitablecontrolmetricwhen aero-opticmeasurementsarenotavailable.Theconditionedspectrashowedthatalarge 250

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portionoftheaero-opticdistortionisaccountedforbytheunsteadypressureuctuations. Toobtainabetterestimate,however,futureworkshouldextendthistechniquetomultiple pressureinputs,takingpressuremeasurementsatdierentlocationsalongtheturretand notlimitingthemtotheatwindow. 6.1.2FlowControl Basedonthebaselineowexperimentsandpreviousresearch,thepurposeofthe owcontrolexperimentsistwo-fold.First,anassessmentoftheeectofbothdirect wakevortexgeneratingpinsandseparationcontrolsteadyblowingontheaero-optic environmentviaMalleyprobemeasurementsisneeded.Ideallytheimplementationofow controlwouldproduceamitigationoftheaero-opticaberrationsthatarenotamenableto correctionviacurrentadaptiveoptictechniques.Thesecondpurpose,fromaowcontrol pointofview,istotorelatethesendingstouiddynamicmeasurementsinaneortto determineasuitablemetricwhenevaluationoftheaero-opticenvironmentisnotdirectly available.Thesereadilyavailablemeasurementscanbeusedtodeviseacontrollerto enhancetheopticalqualityoftheowinrealtime. 6.1.2.1PassiveFlowControl Amajorobjectiveofthepresentworkistoestablishowcontroltechniquesthatlead tothesuppressionofaero-opticallyactivestructuresformedinthewakeregionastheow separatesoaturret.Asshownfromthebaselineowexperiments,thelargepressureand velocityuctuationsareshowntobecontributingfactorstoopticalaberrations. Passivecontrolisimplementedbyinstallingcylindricalpinsnormaltothesurface alongthestreamwisecenterline.Forcongurationswherepinsareembeddedwithin theboundarylayer,thepin-generatedtipvortexenergizedtheboundarylayer,always resultinginseparationdelay,anincreaseinunsteadypressureontheatwindow,and concomitantincreaseinaero-opticdistortion.Amorecompellingresultinvolvedthepins thatprotrudedthroughtheboundarylayer.Inthesecases,thepin-inducedtipvortex interactedwiththeseparatedshearlayer,withthepins'congurationgeometricand 251

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spacingparametersgoverningtheintegrationwiththeseparatedshearlayer.Itisfound thatasthespacingbetweenthepinsdecreases,the rms pressuredecreasesatalllocations measuredalongtheaperture.AsummaryofallndingsislistedinTable5-5andTable 5-6. OPD rms measurementsrevealedthattwocongurationsresultinimprovementofthe aero-opticenvironment.Unsteadypressuremeasurementsalongdierentwindowlocations areusedtodeterminetheeectontheunsteadinessinthenearwakeregion.Anincrease inunsteadypressureresultsinadirectincreaseintheaero-opticbeamdeectionangle, whichisquantiedbycalculatingthelinearcorrelationcoecient.Then,akeynding camefromthesurfaceoil-owvisualization,whichshowsthatallbuttwocongurations delayseparation.Fromthis,itwasdeterminedthatforaat-windowturret, separation delayshouldnotbeusedasametricwhenassessingaero-opticdistortions .Instead,the lengthoftherecirculationregionshowsadirectcorrelationwiththemeasuredaero-optics. Finally,theseparatedshearlayerischaracterizedusinghot-wireanemometry.Theresults showthatthemaincauseoftheincreaseinOPD rms istiedtoboththethickeningofthe shearlayerandincreaseinmaximumturbulentuctuations.Finally,sPIVisconducted forthetwocongurationsthatshowthemostdeviationfromthebaselinecasebestand worseperformancebasedonOPD rms .Thehighspatialresolutionallowsfortheplotting oftheturbulentkineticenergyalongthebeampropagationpath,helpingtodemonstrate theconnectionbetweenthevelocityuctuationsandtheaero-opticbeamdeection angles. 6.1.2.2ActiveFlowControl Activeowcontrolisimplementedusingtangentialblowingalongtheupperportion oftheturretwindow,withthemainobjectivebeingtoforcereattachmentalongtheat window.Thishasthepotentialtoresultinamoreattractiveaero-opticalenvironmentby removingboththerecirculatingwakeintheimmediateregionbehindthewindowand highlyturbulentshearlayer. 252

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Malleyprobemeasurementsaremadetoassesstheaero-opticowqualityattwo beamlocations.Calculationsof showthatforsteadyblowingupto C 0 : 21,there isamonotonicincreaseinthedeectionspectra.Furtherblowingresultsinadecreasein thecalculated ,withtheminimumoccurringfor C =0 : 38.Applyingtheconvective speedofthestructuresandcalculatingOPD rms showsthattheminimumoccursfor C =0 : 26,andnot C =0 : 38.Thissuggeststhat thereisanoptimumamountofsteady blowing,withanyexcessresultinginadegradationoftheopticalenvironment .Then, basedonthe C =0 : 26case,bothowvisualizationandmeanvelocityprolesfromsPIV demonstratethat fullreattachmentalongthewindowneednotbenecessarytoachieve areductioninOPD rms .Furthermore,oilowvisualizationshowsthatsignicantwake modicationisonlypossiblenearthecenterlineofthemodel,indicatingthatthelocation oftheslotistoofardownstreamtoreattachtheowalongtheouterconformalportions oftheturret.Thisgivesrisetofutureworkfocusingonrelocatingtheslotcloserto, andperhapsupstreamof,thethree-dimensionalseparationlineandperhapsextending itbeyondthesidesofthewindow.Finally,thehighspatialresolutionofsPIVallowfor theplottingcontoursoftheturbulentkineticenergy,helpingtoobtainbetterjudgement oftheaero-opticenvironmentatlocationswhereMalleyprobemeasurementsarenot acquired. 6.2ResearchImpact Aliteraturereviewofpreviousworkshowsthattheaero-opticcommunityisinneed ofdetailedbaselineuiddynamicmeasurementsthatshowhowspecicowinteractions relatetoaero-opticaberrationsforasurface-mountedat-windowturret.Although thedatacollectedfromtheliteratureimpliesthatsuchmodelsarelikelytoprovidethe highestopticalaberrationsinthenearwakeoftheturret,thereisverylittlequantitative dataregardingthisconguration.Moreresearchisneededwiththismodeltypetofully understandthecomplexthree-dimensionalowcharacteristics,andhowtheydierfrom theconformalwindowturret.Basedontheneedsofthecommunity,thenear-wake 253

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three-dimensionalowischaracterized,identifyingpotentialsourcesoftheturbulent wakeandaero-opticdistortion,specicallyfocusingontheinteractionofthevariousow featuresthatarepresentinthelow-subsonicowregime.Thisdatabaseofresultswill serveasastrongreferenceforfuturework,inboththeexperimentalandcomputational domains.Infact,aftertherstreleasedpublicationofthisworkPalaviccini etal. 2011, theinvestigationusingahighdelityimplicitLESsimulationonthismodelgeometry wasconductedbyMorgan&Visbal2012,albeitatamuchlowerfreestreamMa=0.10 Re H =50k. Throughouttheliterature,separationdelayisusedtoassesstheaero-opticconditions forowaroundaconformalwindowturret.Thus,theinitialgoalofthisresearchplaced anemphasisonthecontrolofowseparationtoreduceaero-opticdistortioninthenear wakeofathreedimensionalat-windowturret.However,afterpreliminarypassiveow controleortsindicatedthattheowseparationandaero-opticdistortionweren'twell correlated,furtheruiddynamicmeasurementswerewarranted.Theprimarygoalthen shiftedtowardndingasuitablemetrictousewhenaero-opticmeasurementsaren't available.Asetofmetricsthatcorrelatewellwithaero-opticdistortionunsteadypressure alongthewindow,lengthoftherecirculationregion,andturbulentkineticenergyinthe wakeareproposedforusewhentheassessmentofopticaldegradationisnotavailable. Thisisrelevantfortworeasons.First,fromaowcontrolpointofview,thisisacrucial ndingasitallowstheuseofreadilyavailablemeasurementstodiscerntheaero-optic conditions,whichcanbeusedtodeviseacontrollertomitigatetheminrealtime.Second, forthedevelopingstagesofresearch,theresultshereinprovidetheaero-opticcommunity withothermetricstouseforsituationswhereaero-opticdegradationmaynotbeavailable duetoeitherlowsubsonicoworlackofinstrumentation. Withknowledgeoftheaero-opticsources,alongwithanecientowcontrolfeedback metricandscheme,researcherswillbeabletointelligentlydesignandimplement futureairborneopticalsystems.Ultimately,iftheaero-opticdistortionisreducedto 254

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acceptablelevels,theuseofopticalsystemscouldbeimplementedonaircraft.Inthenext section,recommendationsaregivenforfutureworkrelatedtobothextendedbaseline characterizationandowcontrolmethodologies. 6.3RecommendationsforFutureWork Extensiveuiddynamicssurroundingahemisphericalturrethavebeeninvestigated byveryfew,withmostoftheworkdoneintheearlytomid1980'sdeJonckheere etal. 1982;Okamoto1980;Purohit etal. 1983 b ;Rose etal. 1982;Savory&Toy1986,?;Toy etal. 1983.Furthermore,theresearchhereinisoneoftherstconcerningthenatureof theowproducedbyasurfacemountedat-windowturret.Whileitwasasignicant stepforwardinbuildingafoundationforfuturecomputationalmeasurements,athorough understandingofthehighlythree-dimensionalowaroundtheturretisessentialifow controlistobeattemptedwithsuccessfulresults.Withtheguidanceoftheresults presentedinthisdocument,futureexperimentsareproposed. Oneofthemajorndingsinthisresearchwastiedtousingconditionalspectral analysistoshowthatalargeportionoftheaero-opticdistortionwasaccountedforby theunsteadypressureuctuationsalongthewindow.However,inapracticalapplication unsteadypressuremeasurementswillnotbeavailableontheturretwindow,asthat wouldobstructthelineofsightofanybeam.Leveragingthefactthatthesizeof therecirculationregionwaslinearlycorrelatedwiththedegradationoftheaero-optic environment,futureworkshouldextendthetherangeofmeasurementlocationstoinclude thetunneloorinthewakeregion. ModicationsshouldbemadetotheMalleyprobeexperimentalsetuptofurther reducecontaminationfromtunnelvibrations.Althoughconditionalspectralanalysiswas utilizedtoestablishtheimpactofmechanicaljitterontheaero-opticsignal,littleeort wasmadetosystematicallyidentifythemainsourcesofvibration.Astudyinvolving multiplesensorsisnecessarytodevelopamethodologyfordirectedenergysystemtesting inwindtunnelsthatdecouplesmechanicalvibrationeectsfromaero-opticaberrations 255

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duetodensitygradientsinthewakeregionofaturret.Thismethodologywouldbe directlyapplicabletoawidevarietyoftestfacilitieswhereaero-opticmeasurementsare made. Thepassivecontrolschemeutilizedinthisstudywasdesignedspecicallyfora singleazimuthandelevationangleandcouldhaveadverseeectsatodesignconditions. Movingtoanaircraftapplicationrequiresdevelopmentofarobustcontrolschemethat canadapttoreal-timechangesintheow.Oneoptiontoremedythisistousethecurrent passivecontrolresultstocreateanarrayofpinswithaxedthicknessrelativetothe nominalboundarylayerthickness.Inareal-timeorattheveryleast,quasi-dynamic sense,thepinheightcanbevariedinanadaptivefashionuntilthedesiredcontroleectis optimized.Theresultsmayshowavariationofbothpinheightandspacingasafunction ofthedistancefromtheturretapex.Anotherlogicalstepistoimplementsteadyjetsas asubstitutetopassivecontrol.Inthepast,steadymicrojetshavebeensuccessfullyused tosuppressowseparationand/orreduceturbulentuctuationsoverabackwardfacing rampAubrun etal. 2010;Kumar&Alvi2009.Asimilaroptimizationtothatofthe passivecontroleortscanbeimplementedwhere,insteadofvaryingtheheightofthepins, thevelocityratio,andhencethemomentumcoecient C ,isvaried. Modicationscouldalsobemadetotheactivecontrolimplementationtoimprove resultsandreducecost.Theresultsfromsteadyblowingsuggestedthatthereisan optimumamountofsteadyblowing,withanyexcessresultinginadegradationofthe opticalenvironment.Thisapparentstaticmaplendsitselftosimplemodel-freeow controlstrategies,suchasextremum/slopeseekingordownhillsimplexBecker etal. 2007;King etal. 2007wherealocaloptimumcanbesearchedforinaquasi-dynamic sense.Furthermore,inanlaboratoryfacilitysettingthemassowisgenerallyobtained fromhighcapacitytanksthatareconstantlychargedbyacompressor.Inanaircraft application,however,thesourceofpressurizedairwouldneedtoeithercomefromthe enginesorseparatededicatedpump.Forthisreason,theimplementedcontrolalgorithm 256

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wouldneedtotakeintoaccountthe C expenditureintheformofapenaltyfunction withintheoptimizedcontrollaw. 257

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APPENDIXA TURRETMODELTECHNICALDRAWINGS Thisappendixincludesallofthetechnicaldrawingsfortheturretmodelusedin thisstudy.Thisappendixdescribesallmanufacturedpartsincludingmodicationstothe existinglow-speedwindtunnelfacility.Allfourturretmodelsbaseline,passivecontrol, steadyblowing,andZNMFmodelaredescribedandtechnicaldrawingsofeachalong withrelevantaccessoriesareprovided. A.1TunnelModications Inordertoperformtheprescribedexperiments,somemodicationsweremadetothe existingUniversityofFloridaLow-SpeedWindTunnelFacility.Theprimaryrenements includedtheimplementationofanewtunneloortohousetheturretmodel,FigureA-1, andanewsetofclearpanelstomaketheceilinganopticallyaccessibleportionofthetest section.BothweremanufacturedbyTMREngineering. A.2BaselineModel ThebaselineturretmodelwasmanufacturedbyLockheedMartin,usinga stereolithographyprinter.Themodelissecuredtothetunneloorviathree1/4"-20 bolts.Byloosening,butnotremovingthebolts,themodelcanberotatedthroughafull 360 o rangeofazimuthangles.Modelingclayisappliedtothejuncturebetweenthemodel andtunneloorsealinganygapsthatwerepresentduetomanufacturingtolerances. FigureA-2showsthetechnicaldrawingsforthismodel,includingthelocationofall steadypressureportsalongthecenterline. Twowindows,eachwithdistinctpurposes,weremanufactured.Therstallowed bothsteadyandunsteadypressuremeasurementstobesimultaneouslycollectedalong theat,whilethesecondwascreatedfromopticallyclearacrylictoallowforaero-optic measurements.BothtechnicaldrawingsareseeninFiguresA-3andA-4.Thewindows areattachedtothemodelviaasafetycross-barFigureA-5,allowingtheapertureto berotatedafull360 o withouttheneedofremovingthewindow.Foranon-permanent 258

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sealalongthecontactingsurfacesofthewindowandtheturretmodel,ahardening silicone-basedsealantisused. A.3PassiveControlModel Themodelusedforpassivecontrolmeasurementsisthebaselinemodelretrottedto taninsertforcylindricalpins.Twoinsertsweremanufactured,oneforthin d= =0 : 6 andoneforthick d= =1 : 2pins.TheyareshowninFiguresA-6andA-7.Eachinsertis loadedintothechordwisecenterlineofthemodelandsecuredvia1/2"long4-40machine screws.Thejunctionbetweentheinsertandthemodelislledwithlightweightspackle and,afteritdries,islightlysandedtoleaveauniformsurface.AnewwindowFigure A-8wasmanufacturedoutofopticallyclearmaterial,allowingsimultaneousunsteady pressureandaero-opticmeasurementstobeperformed. A.4SteadyBlowingModel Anewmodelwiththesamegeneraldimensionswasmanufacturedforthe steady-blowing,activecontrolcases.TechnicaldrawingsareprovidedinFiguresA-9, A-10,andA-11.Themodeldiersfromthepassivecontrolmodelinthatithasalet appliedatthejuncturebetweentheconformalportionoftheturretandtheatportionof thewindow.ThisisillustratedindetailBofFigureA-10.Themodelcontainsindividual oricesforbothblowingtopofwindowandsuctionbottomofwindow,althoughonly theblowingsectionisusedintheexperimentspresentedinthisthesis. 259

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FigureA-1.Schematicoftunneloorforturretmodels. 260

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FigureA-2.Baselineturretmodelshowinglocationsofsteadypressureports. 261

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FigureA-3.Turretwindowusedforsteadyandunsteadypressuremeasurementsonallbaselinecases. 262

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FigureA-4.Opticallyclearturretwindowusedtomakeaero-opticmeasurements. 263

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FigureA-5.Safetybarusedtosecurewindowtoturretmodel. 264

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FigureA-6.Passiveowcontrolinsertforthinpins d= =0 : 6. 265

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FigureA-7.Passiveowcontrolinsertforthickpins d= =1 : 2. 266

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FigureA-8.Turretwindowusedforunsteadypressuremeasurements. 267

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FigureA-9.Steadyblowingturretmodel. 268

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FigureA-10.Steadyblowingturretmodel,alternateview1. 269

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FigureA-11.Steadyblowingturretmodel,alternateview2. 270

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APPENDIXB SPIVUNCERTAINTY B.1SampleCountandConvergence Toensurethatthetotalnumberofsnapshotsacquiredissucientforconvergence, thetotalnumberofthemovingaverageiscalculatedforeachReynoldsstresscomponent ofvelocityatthelocationwithhighestturbulentkineticenergy.FigureB-1showsthe locationofhighestturbulentkineticenergyandthecalculatedmovingaverageasa functionofsampleswiththecomputed95%condenceintervalbounds.TheReynolds stressisobservedtoconvergewithinthecondenceintervalafterapproximately150 sampleimagepairs.Thissuggeststhatthe500imagestakenwerehighenoughtocompute turbulentquantities. B.2RandomUncertainty Therandomuncertaintyiscalculatedusing95%condenceintervalsasdiscussedin Benedict&Gould1996.The95%condenceintervalsforbothrstandsecondorder statisticsarelistedinTableB-1. B.3BiasUncertainty ThebiasuncertaintiesofsPIVdataareestimatedbyrelatingthedisplacements measuredbyeachcamerasensor x; y tothoseoftheactualparticlesinspace X; Y; Z Hu2009.Thisuncertaintyformulationisbasedonthepinholelens assumption,wheremeasureddisplacementsofathree-dimensionaldisplacementin physicalspacehaveunitsofmmandaredenotedas X Y ,and Z .Thesephysical displacementsarebasedonthedisplacementintheimageplanesofthetwocameras x 1 ; y 1 and x 2 ; y 2 ,whichhaveunitsofpx.FigureB-2illustratesadisplacement vectorinphysicalspace,alongwiththecorrespondingdisplacementasmeasuredbythe camerasensorsandtheanglesthatrelatethetwo.Theseanglesrelatethelightsheet totheviewingraysinthe xz -plane 1 2 andthe yz -plane 1 2 .Basedonthese schematics,thethreecomponentsofdisplacementareextracted: 271

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x = x 2 tan 1 )]TJ/F15 11.9552 Tf 11.955 0 Td [( x 1 tan 2 tan 1 )]TJ/F15 11.9552 Tf 11.955 0 Td [(tan 2 B{1 y = y 2 tan 1 )]TJ/F15 11.9552 Tf 11.955 0 Td [( y 1 tan 2 tan 1 )]TJ/F15 11.9552 Tf 11.955 0 Td [(tan 2 = 1 2 y 1 + y 2 + 1 2 x 1 )]TJ/F15 11.9552 Tf 11.955 0 Td [( x 2 tan 2 )]TJ/F15 11.9552 Tf 11.955 0 Td [(tan 1 tan 1 )]TJ/F15 11.9552 Tf 11.956 0 Td [(tan 2 B{2 z = x 2 )]TJ/F15 11.9552 Tf 11.955 0 Td [( x 1 tan 1 )]TJ/F15 11.9552 Tf 11.955 0 Td [(tan 2 = y 2 )]TJ/F15 11.9552 Tf 11.955 0 Td [( y 1 tan 1 )]TJ/F15 11.9552 Tf 11.955 0 Td [(tan 2 B{3 Sincethecomponentsmeasuredarestillinunitsofpx,theresolutionpx/mm, R ,is usedtoextractthephysicalunits,resultingin X = R x Y = R y Z = R z DaVissoftwareprovidestheresolutionforeachtestcase. B.3.1SatisfyingSub-pixelAccuracy Thebiasuncertaintyanalysisperformedassumesasub-pixelaccuracyofthe measurement.Inordertoassumeasub-pixelaccuracyofthedisplacementsmeasured ontheimageplane,themeandiameteroftheseedparticlesontheimageplanemust begreaterthanonepixel.Ifthisconditionissatised,thentheresultingcorrelations representingthelightintensitydistributionontheimageplanecanbecharacterizedas obeyingaGaussianproleAdrian&Yao1985.Toverifythatthisconditionismet,the nominalparticlediameterasprojectedontotheimageplanecanbeestimatedby d e = q M 2 d 2 p + d 2 s B{4 where d p isthenominalparticlediameterinphysicalunitsinthiscase1 m ,as quotedbytheseedermanufacturer,and d s isthediameterofthepointresponsefunction ofalensattherstdarkringoftheAirydiskintensitydistributionAdrian&Yao1985. Themagnicationfactor M istheratiobetweenthesizeoftheprojectionontheimaging sensortothephysicalsizeinspace.Tocalculatethemagnicationfactor,thepixelpitch ofthecamerasensor.4 mu m/pxismultipliedbytheresolutionforeachtestcase. 272

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Then,theAirydiskcanbecalculatedvia d s =2 : 44 M +1 f # B{5 where f # isknownasthef-stopandisthefocallengthofthelensdividedbythecamera aperture,and =532 nm isthewavelengthofincidentlightsheet.TablesB-2and B-3liststhemagnicationfactors, f # ,computedAirydiscsize d s ,andcalculated nominalparticlesize d e forallsPIVcases.Sinceallresultsindicateanimageparticle diameterofgreaterthanonepixel,thecurrentsPIVset-upsatisesthesub-pixelaccuracy requirements. B.3.2Root-Sum-SquareAnalysis Aroot-sum-squareanalysisisperformedonEqs.B{1,B{2,andB{3,accountingfor theresolutiontoconverttophysicalunits.Thisyieldstheanalyticaluncertaintiesofthe physicalparticledisplacements: X bias = s 1 @ X @ x 1 2 + 2 @ X @ x 2 2 + X 2 sp B{6 Y bias = s 1 @ Y @ x 1 2 + 2 @ Y @ x 2 2 + 1 @ Y @ y 1 2 + 2 @ Y @ y 2 2 + Y 2 sp B{7 Z bias = s 1 @ Z @ x 1 2 + 2 @ Z @ x 2 2 + Z 2 sp B{8 wherethesubscript sp representthedisplacementcalculationsusingasub-pixel rms error.Toperformtheuncertaintyanalysisabove,an rms sub-pixelerrormustbedened. Nobach etal. 2005investigatedtheaccuracyofdierentPIVinterpolationmethodson numericallygeneratedparticleimages.Theparticlesizeswerevariedtodeterminethe rms errorinsub-pixelaccuracywithsimulatedphotonnoisetoresembleexperimental conditions.Itwasfoundthatforthecaseofaparticlediameterof1.5pixelsresultedin anRMSerrorofapproximately0.06pixels.ThebiasuncertaintyanalysisfortheSPIV experimentsinthisstudyisthencomputedusingEqs.B{6,B{7,andB{8.Notethatthe particledisplacementsmeasuredbyeachcamera, x 1 ; y 1 and x 2 ; y 2 ,aresetto 273

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anappropriate rms sub-pixelaccuracybasedontheestimatedparticleimagesizeforeach case.EachpartialderivativeofEqs.B{6,B{7,andB{8iscomputednumericallyusinga centereddierencemethod: @ X @ x 1 = R x 2 tan 1 )]TJ/F21 7.9701 Tf 6.587 0 Td [( x 1 + 1 tan 2 tan 1 )]TJ/F21 7.9701 Tf 6.587 0 Td [(tan 2 )]TJ/F21 7.9701 Tf 13.151 5.699 Td [( x 2 tan 1 )]TJ/F21 7.9701 Tf 6.587 0 Td [( x 1 )]TJ/F23 7.9701 Tf 6.586 0 Td [( 1 tan 2 tan 1 )]TJ/F21 7.9701 Tf 6.586 0 Td [(tan 2 x 1 + 1 )]TJ/F15 11.9552 Tf 11.955 0 Td [( x 1 )]TJ/F22 11.9552 Tf 11.955 0 Td [( 1 # B{9 where i isthermspixelerrorinthetofthesPIVconformalmappingfunctionforthe i th camera.ThesevaluesaresuppliedbyDaVissoftwareforeachcameraandarelistedin TablesB-4andB-5. Thenalstepincomputingthebiasuncertaintyofthevelocitycomponentsissimple divisionofthedisplacementuncertaintiesbytheuserdened t betweenlightpulses. ThisisacceptablebecauseofthehightemporalresolutionofthesPIVsystemstimingunit O ns,whichprovidesanegligiblecontributiontotheuncertainty.ForallsPIVcases, the t waschosenas8 s. u bias = X bias t ;v bias = Y bias t ; and w bias = Z bias t B{10 ThecalculatedbiasuncertaintyresultsaregiveninTablesB-6andB-7. 274

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A B FigureB-1.AContourplotofturbulentkineticenergyandBrunningaverageof Reynoldsstresstermswith95%condenceintervalbounds---evaluatedat thelocationdenotedby inA.TakenatMa=0.26forthebaselinemodelat thecenterlineplane z=a =0. 275

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A B C D FigureB-2.A,BIllustrationofageneralsPIVcamerasetupshowingthe reconstructionofathree-dimensionaldisplacementvector;Cschematicof xz-planeandDschematicofyz-plane.AdaptedfromHu2009. TableB-1.Randomuncertainty95%condenceintervalestimatesofcomputedvelocity andReynoldsstressterms Quantity95%condenceinterval U i 1.96 r 1 N u 0 2 i u 0 2 i 1.96 r 1 N u 0 4 i )]TJ/F15 11.9552 Tf 11.955 0 Td [( u 0 2 i 2 u 0 i u 0 j i 6 = j 1.96 r 1 N u 0 2 i u 0 2 j )]TJ/F15 11.9552 Tf 11.955 0 Td [( u 0 i u 0 j 2 276

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TableB-2.Relevantparametersusedtoestimatetheprojectednominalparticlediameter forthebaselineandpassivecontrolcases z=a =0 z=a = )]TJ/F15 11.9552 Tf 9.298 0 Td [(0 : 25 z=a = )]TJ/F15 11.9552 Tf 9.298 0 Td [(0 : 50 ParameterCam1Cam2Cam1Cam2Cam1Cam2 FocalLengthmm99.291108.21195.528110.10097.526110.724 f #811811811 M0.1000.1000.1020.1020.1010.101 d s m11.42315.70711.44415.73511.43415.721 d e px1.5442.1231.5472.1271.5452.125 TableB-3.Relevantparametersusedtoestimatetheprojectednominalparticlediameter fortheactivecontrolcases z=a =0 z=a = )]TJ/F15 11.9552 Tf 9.298 0 Td [(0 : 25 z=a = )]TJ/F15 11.9552 Tf 9.298 0 Td [(0 : 50 ParameterCam1Cam2Cam1Cam2Cam1Cam2 FocalLengthmm98.818109.08997.409109.41898.901107.758 f #811811811 M0.1000.1000.1020.1020.1010.101 d s mm11.42315.70711.44415.73511.43415.721 d e px1.5442.1231.5472.1271.5452.125 TableB-4.Relevantparametersusedtodeterminethebiasuncertaintyforthebaseline andpassivecases z=a =0 z=a = )]TJ/F15 11.9552 Tf 9.299 0 Td [(0 : 25 z=a = )]TJ/F15 11.9552 Tf 9.299 0 Td [(0 : 50 ParameterCam1Cam2Cam1Cam2Cam1Cam2 x i;rms = y i;rms px0.1000.1220.0970.1210.1040.130 FocalLengthmm99.291108.21195.528110.10097.526110.724 deg30.881-10.04329.711-8.73629.975-8.834 deg2.7920.2662.4080.7472.5990.686 Resolutionpx/mm13.46513.46513.66113.66113.66413.664 TableB-5.Relevantparametersusedtodeterminethebiasuncertaintyfortheactive controlcases z=a =0 z=a = )]TJ/F15 11.9552 Tf 9.299 0 Td [(0 : 25 z=a = )]TJ/F15 11.9552 Tf 9.299 0 Td [(0 : 50 ParameterCam1Cam2Cam1Cam2Cam1Cam2 x i;rms = y i;rms px0.0960.1160.1270.1570.1000.125 FocalLengthmm98.818109.08997.409109.41898.901107.758 deg30.011-9.52029.558-9.14829.978-9.223 deg-1.8420.7792.8600.2491.8570.3473 Resolutionpx/mm13.53113.53113.78513.78513.59513.595 277

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TableB-6.Biasuncertaintiesinm/sateachmeasuredsPIVplaneforthebaselineand passivecases z=a plane u bias v bias w bias z=a =00.9231.0601.897 z=a = )]TJ/F15 11.9552 Tf 9.299 0 Td [(0 : 250.8991.0501.965 z=a = )]TJ/F15 11.9552 Tf 9.299 0 Td [(0 : 500.9431.0692.091 TableB-7.Biasuncertaintiesinm/sateachmeasuredsPIVplanefortheactivecontrol cases z=a plane u bias v bias w bias z=a =00.8931.0201.875 z=a = )]TJ/F15 11.9552 Tf 9.299 0 Td [(0 : 251.0681.2622.519 z=a = )]TJ/F15 11.9552 Tf 9.299 0 Td [(0 : 500.9241.0772.005 278

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APPENDIXC CONDITIONALSPECTRALANALYSIS ThepurposeofthissectionistointroduceconditionalspectralanalysisCSA techniquestoestimatetheaero-opticcontributionofavibrationcorruptedMalleyprobe signal.Theproblemarisesinthatcontaminatingnoisesourcesfromtestapparatus,such astunnelvibrations,cancontaminatethemeasuredaero-opticdata.Amultiple-input, single-outputMISOmodelisdevelopedtoaccountforseveralpossiblecontaminating noisesourcesalongwiththetotalnoisesignalofthesystem.Fourieranalysisisperformed. Itisshownthattheaccuracyofthemodelisdependentuponthecoherencesbetween theinputsandtheoutputspectra.CSAtechniquescanthenbeusedtoremovethe coherentoutputduetothemeasuredvibrationinputsinanattempttoobtainabetter estimateofthedesiredaero-opticspectrum.Thismethodologycanbeusedtocorrect aero-opticmeasurementsoutputforanymeasuredadversestructuralmotioninput. C.1Multiple-input,Single-outputNoise-freeModel Themodelforasingle-input,single-outputSISOsystemisshowninFigure FigureC-1A,wherextistheinputtimeseriesdata,andytisthetimeseriesdata fortheoutput,andhtistheimpulseresponsefunction,andtheoutputisgivenbythe convolutionintegral y t = Z 1 h t )]TJ/F22 11.9552 Tf 11.955 0 Td [( x d: C{1 Then,takingtheFourierTransformofeachsideanddening = t )]TJ/F22 11.9552 Tf 11.956 0 Td [( yields Y = Z 1 Z 1 h t )]TJ/F22 11.9552 Tf 11.955 0 Td [( x d e )]TJ/F23 7.9701 Tf 6.586 0 Td [(j!t dt = Z 1 x e )]TJ/F23 7.9701 Tf 6.587 0 Td [(j!t d Z 1 h e )]TJ/F23 7.9701 Tf 6.586 0 Td [(j! + d = X H where =2 f istheradianfrequency.ThisequationrepresentstheFouriertransform oftheSISOmodel.Similarly,foraMISOmodel,asshowninFigureC-1B,theoutputis 279

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simplyaweightedlinearcombinationofeachinput Y f = n X i =1 X i f H i f : C{2 C.2Auto-spectralandCross-spectralAnalysis Todeterminetherelationshipsbetweentheinputsandbetweeneachinputandthe output,auto-spectralandcross-spectralanalysisisperformed.Theequationforthe one-sided,auto-spectraldensityforthemeasuredoutputis G yy = 2 T E [ Y Y ] : C{3 where E [ Y Y ]istheexpectedvalueoftheproductof Y withitscomplexconjugate, Y Takingtheexpectedvalueisnecessarybecause Y isarandomvariable,soastatistical estimateofthevariableovermultipleblocksofadatasetmustbeconstructed. Recallingthatthefrequencyresponsefunctionisnotrandomandsubstitutingthe MISOmodelequationintotheaboveyields G yy = n X i =1 H i G yx i : C{4 Theauto-spectraldensityisareal,positivefunctionoffrequency.Thisvalue representsthemeasuredpowerspectraldensityofthesignaloverafrequencyrange. Intheelectricaldomain,itiscomputedasV 2 /Hz.Thermsdisplacementmeasurement fromapositionsensingdeviceasiscommonlyusedtomakeaero-opticmeasurements maybecomputedas x PSD = p G yy .Similarly,thermsdisplacementcalculatedfrom anaccelerometerinputsignalasiscommonlyusedtomakemechanicalvibration measurementsiscomputedfrom x PSD = q G xx = f 4 where G xx istheautospectraof theaccelerometersignal. Asimilaranalysiscanbemadetoderivethecross-spectraldensityforeachinput signalwithrespecttotheoutput.Thecross-spectrumisastatementofthecorrelation betweentwosignals,performedinthefrequencydomain.Cross-spectraltermscanbe 280

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positiveornegativecomplexvalues.Apositivenumberindicatesconstructiveinterference, whereasanegativenumberindicatesdestructiveinterferencebetweentworespective references.Thevaluesarecomplexbecausetherecanbephaseleadsandlagsbetweentwo signals,indicativeofdelaysinthetimedomain.Thesolutionisshownbelow. G x i y = n X i =1 H i G x i x i ; C{5 where G x i y isthecross-spectrumbetween i th inputandtheoutput y ,and G x i x i isthe auto-spectrumofthe i th referenceinput. C.3NoiseConsiderations Inallexperimentalenvironments,thereneedstobeconsiderationforanyadditive noisethatpresentsitselfinthenalmeasuredsignal.Inthiscase,thenoiseencompasses anyun-modeledlineardynamics,nonlinearities,andoutputsensorelectronicnoise.The additionofnoisetotheMISOmodelresultsinanewschematic,illustratedinFigureC-2. Theoutputofthismodelisgivenby Y f = n X i =1 X i f H i f + N f ; C{6 whereeach X f and Y f arecomputedusingthediscreteFouriertransformofthe measured x t and y t Thedenitionoftheordinarycoherencefunctionisgivenby 2 x i y = j G x i y j 2 G x i x i G yy : C{7 Themultiplecoherencefunctionisadirectextensionoftheordinarycoherence function.Bydenition,itistheratiooftheidealoutputspectrumduetothemeasured inputsintheabsenceofnoisetothetotaloutputspectrumwhichinherentlyincludes noise.Inequationform,themultiplecoherencefunctionisgivenby 2 y : x = G yy )]TJ/F22 11.9552 Tf 11.955 0 Td [(G nn G yy =1 )]TJ/F22 11.9552 Tf 13.15 8.088 Td [(G nn G yy : C{8 281

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TovalidatetheMISOmodel,theordinaryandmultiplecoherenceofthemodelwillbe used.ReferringtotheMISOmodelinFigureC-2,fourconditionsmustbemetforthis modeltobewelldenedBendat&Piersol2000: Theordinarycoherencefunctionsbetweenanypairofinputsshouldnotbeunity atallfrequenciesofinterest.Physicallythiscorrespondstoredundantinformation fromthetwoinputs.Thisconsiderationallowsdistributedinputsystemstobe studiedasdiscreteinputs. Theordinarycoherencefunctionsbetweenanyinputandtheoutputshouldnot equalunity.Ifthisisthecase,thenotherinputsarenotcontributingtotheoutput andthemodelshouldbereducedtosimplyaSISOcase. Themultiplecoherencefunctiondenedabovebetweenanyinputandother inputs,excludingthegiveninput,shouldnotequalunity.Ifthisisthecase,then thisinputisnotcontributinganynewinformationandcanbeobtainedbylinear operationsfromotherinputs.Furthermore,ifthemultiplecoherencefunction betweenthemeasuredinputsandthemeasuredoutputisunity,theauto-spectrum ofthenoiseisequaltozero.Thiscorrespondstoperfectlinearitybetweenthesum oftheoutputsfromeachsourceandthemeasuredoutputofthesystem. Themultiplecoherencefunctionbetweentheoutputandthegiveninputsshouldbe sucientlyhigh.Otherwise,eithersomeimportantinputsarebeingomitted,orthe measuredoutputdatadoesnotcomefromlinearoperationsofthemeasuredinputs andnon-lineareectsshouldbeconsidered. Ifallinputsandthenoiseareuncorrelated,thesystemcanbede-noisedby calculating G nn = G yy )]TJ/F22 11.9552 Tf 12.132 0 Td [( 2 y : x G yy ,wherethemultiplecoherencefunctionisthesummation oftheordinarycoherencefunctionsbetweenallinputsandtheoutput, 2 y : x = P n i =1 2 x i y However,inmostpracticalcases,theinputsareusuallysomewhatcorrelated.Therefore, CSAtechniquesdescribedinthefollowingsectionarerequiredtoremovethecorrelated partsoftheinputs. C.4ConditionalSpectralAnalysis TheMISOmodelprovesinsucientinestimatingtheoutputspectraproduced whentheinputsarecorrelated.Becauseofthehighcoherencevaluesexpectedbetween measuredinputsinthewindtunnelenvironment,anaturalextensiontotheMISOmodel istheCSA.Physically,theCSAconditionstheinputsourcessuchthatifaninputsource 282

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wereturnedo,thecorrelatedportionoftheoutputspectraduetotheturnedoinput willberemoved.Specically,thecorrelatedcomponentofaninputisremovedfromall otherinputs.Thiscanbeappliediterativelytoanarbitrarilysizedsequenceofinputs. ThiseliminationprocesseectivelyleavesaMISOsystemwithuncorrelatedinputsand newsetsofeectivetransferfunctions.Forsimplicity,theanalysiswillbedemonstrated onatwo-input,single-outputsystem,butthesametechniquescanbeextendedtosystems withmorethantwoinputs. FigureC-3representsatwo-input,single-outputmodel,wheretheoutput y t and thenoise n t arethesameasinFigureC-2.Theinputsarenowmutuallyuncorrelated, suchthatthenewmodelcanbedescribedasthesumoftwoseparateSISOmodels.The constantparameterlinearsystem L 1 y istheoptimumlinearsystemtopredict y t from x 1 t .Similarly, L 2 y istheoptimumlinearsystemtopredict y t from x 2 1 t i.e.,the portionof x 2 t with x 1 t removed. Inequationform,thebasicfrequencydomainrelationisgivenby Y f = L 1 y f X 1 f + L 2 y f X 2 1 f + N f ; C{9 where L 1 y f = G 1 y f G 11 f and L 2 y f = G 2 y 1 f G 22 1 f : C{10 Computationoftheseconditionedspectraldensityfunctionscanbeachievedusing algebraicexpressionsonpreviouslydenedspectraldensityfunctionsfromtheoriginal 283

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recordsandaregivenby G 2 y 1 f = G 2 y f )]TJ/F15 11.9552 Tf 11.955 0 Td [([ G 21 f =G 11 f ] G 1 y f C{11 G 1 y 2 f = G 1 y f )]TJ/F15 11.9552 Tf 11.955 0 Td [([ G 12 f =G 22 f ] G 2 y f C{12 G 22 1 f = 1 )]TJ/F22 11.9552 Tf 11.956 0 Td [( 2 12 f G 22 f C{13 G 11 2 f = 1 )]TJ/F22 11.9552 Tf 11.956 0 Td [( 2 12 f G 11 f C{14 G yy 1 f = 1 )]TJ/F22 11.9552 Tf 11.956 0 Td [( 2 1 y f G yy f C{15 G yy 2 f = 1 )]TJ/F22 11.9552 Tf 11.955 0 Td [( 2 2 y f G yy f : C{16 Thisdecomposes y t intothesumoftwouncorrelatedtermsrepresentingthe partof y t dueto x 1 t viaoptimumlinearoperationsandthepartof y t notdueto x 1 t .Also,sincetheoutputterms v 1 t v 2 t ,andthenoiseterm n t aremutually uncorrelated,themeasuredoutputautospectrum G yy f isthesumofthethree autospectraterms G yy f = G v 1 v 1 f + G v 2 v 2 f + G nn f .Therstautospectrumterm, G v 1 v 1 f ,istheordinarycoherentoutputspectrumassociatedwithaSISOmodelwith x 1 t astheinputand y t astheoutput.Thesecondautospectrumterm, G v 2 v 2 f ,isthe partialcoherentoutputspectrumassociatedwithaconditioned-input,conditioned-output modelwith x 2 1 astheinputand y y 1 astheoutput.Theuncorrelatednoiseterm, G nn f canbedenotedas y y ; 2 ,orastheoutputnotduetoeither x 1 t or x 2 t Thepartialcoherencefunctionbetweentheuncorrelatedsignalsisgivenby 2 2 y 1 f = j G 2 y 1 f j 2 G 22 1 f G yy 1 f ; C{17 2 1 y 2 f = j G 1 y 2 f j 2 G 11 2 f G yy 2 f C{18 andplaysassimilarroletotheordinarycoherencefunction,exceptthatitusesthe conditionedrecordsinsteadoftheoriginalrecords.Itisbenecialtofurthersimplifythe partialcoherencefunctiontocontainonlyinformationfromthemeasuredsignals.Todo so,allpartialcomponentswithinEqs.C{17,C{18arereplacedwithEqs.C{11through 284

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C{16.Then,multiplyingeachpartialcoherencefunctionby G 11 / G 11 2 and G 22 / G 22 2 respectively,yields 2 2 y 1 = j G 2 y 1 j 2 G 22 1 G yy 1 = j G 2 y G 11 )]TJ/F22 11.9552 Tf 11.955 0 Td [(G 1 y G 21 j 2 G 2 11 G 22 G yy )]TJ/F22 11.9552 Tf 11.955 0 Td [( 2 12 )]TJ/F15 11.9552 Tf 5.479 -9.684 Td [(1 )]TJ/F22 11.9552 Tf 11.955 0 Td [( 2 1 y C{19 2 1 y 2 = j G 1 y 2 j 2 G 11 2 G yy 2 = j G 1 y G 22 )]TJ/F22 11.9552 Tf 11.955 0 Td [(G 2 y G 12 j 2 G 2 22 G 11 G yy )]TJ/F22 11.9552 Tf 11.955 0 Td [( 2 21 )]TJ/F15 11.9552 Tf 5.479 -9.684 Td [(1 )]TJ/F22 11.9552 Tf 11.955 0 Td [( 2 2 y : C{20 Theresultisthatthetwo-input,single-outputmodelwithmutuallyuncorrelated inputsFigureC-3canbetransformedintotwoseparatesingle-input,single-output modelsasshowninFigureC-4. Thesemethodswillprovideinformationonthesensitivityofthelaseroutputto eachvibrationinput,thusallowingustorstmakeinformeddecisionsonpossiblesetup modicationstoreducemechanicaljitter.Thiswillresultinremovingnoisespectraat theoutputthatisduetothemeasuredmechanicalvibrations,leavingonlythedesired aero-opticmeasurement.Thefollowingsectionsdetailtheimplementationofthismethod toreducemechanicalvibrations. C.5RemovingTunnelVibrationEects C.5.1AccelerometerCalibration Tunnelvibrationsareassessedbyattachingthreetriaxialaccelerometersatdierent locationsdenotedbya1,a2,anda3alongtheexperimentalset-upasshowninFigure 3-17.Eachaccelerometeraxisiscalibratedasdetailedin3.5.2.1.FiguresC-5A-Cshow thespectraofallaccelerometersusedforcalibrationundera1GloadingandTable4-3 liststhecalculatedsensitivities.Forallcases,dataareacquiredforafreestreamMa=0.26 U 1 =90m/s.Simultaneoustotheaccelerometersignalacquisition,beamdisplacement dataaretakenattwolocationsasindicatedbyB1andB2inFigure3-18. C.5.2EectonAero-opticSignal Theautospectraforeachaccelerometer P a 1 ;P a 2 ;P a 3 andbeamdisplacement signal P B 1 ;P B 2 arerstcomputedforthestreamwisedirections.FigureC-6shows that,forfrequencieslargerthan1kHz,thebeamdisplacementmeasurementsareorders 285

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ofmagnitudelargerthananymechanicalvibrationdisplacementasmeasuredbythe accelerometers.Furthermore,thereisatleastanorderofmagnitudedierencebetween thevibrationsmeasuredonthetestsectionoora3andthosemeasuredonthePSD a1,a2.Anotherpossiblesourceofmechanicalvibrationsincludesthelasersource.The signalfromanaccelerometerattachedtothelasershowedthat,atthefrequenciesof interest,thecalculated rms displacementisminimalwhencomparedtothemagnitudeas thosemeasuredatlocationsa1,a2,anda3.Fromthis,itisconcludedthatthenegligible mechanicalvibrationofthelaserdoesnotcontributetothebeamdisplacementsignals, andhenceisnotincludedinanyfurtheranalysis. Inaneorttodeterminetheeectoftunnelvibrationsontheestimateofaero-optic distortion,whichiscalculateddirectlyfromthebeamdisplacement,ordinarycoherent functionsarecalculated.FigureC-7showsastrongcoherenceatdiscretefrequencies betweenthebeamdisplacementandaccelerometersignals.Thecoherencebetween allaccelerometersignalsandB1droptozeroforfrequenciesabove500Hz,whilethe coherencewithB2doesnotdosountilfrequenciesreach1kHz.Thiscanbeattributed tothepossiblevibrationoftheextrasteeringmirrorsthatareusedtoredirectB2toits correspondingPSDseeFigure3-17. Inanattempttoremovethecoherentportionofthemechanicaljitterfromthe measuredPSDmeasurements,thefollowingsignalsareacquiredsimultaneously. x 1 t :inputvibrationtimesignalasmeasuredonthePSDa1 X 1 f :inputvibrationfrequencysignal= Ff x 1 t g x 2 t :inputvibrationtimesignalasmeasuredonthetunneloora2 X 2 f :inputvibrationfrequencysignal= Ff x 2 t g z t :inputaero-optictimesignal Z f :inputaero-opticfrequencysignal= Ff z t g y t :outputmeasuredopticaldisplacementsensortimesignal 286

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Y f :outputmeasuredopticaldisplacementsensorfrequencysignal= Ff y t g FigureC-8illustratesamultipleinput,singleoutputmodelofthecurrentsetup. H 1 f and H 2 f aretheoptimalfrequencyresponsefunctionsforeachinputsignalsuch thattheyareuncorrelatedwiththeunknown Z f signal.Notethat Z f represents unmeasuredlineardynamicsoftheaero-opticinputassumingminimalnonlinearitiesand outputsensorelectronicnoise. C.5.3OrdinaryCoherenceFunction Tondthefrequencieswheretunnelvibrationsaredominant,boththeautoG 11 G 22 G yy ,andcross-spectra G 12 G 1 y G 2 y arecomputedandplottedinFiguresC-9 andC-10,respectively.Variouscorrelationsbetweenchannelsareobserved,buttheexact causeofeachcanonlybeinterpretedcorrectlywithfurtheranalysis.Itisclear,however, thatthesignalfromthepositionsensingdevice, y ,hassignicantenergyat500Hzthatis mostlikelyduetooneorbothofthemeasuredvibrationsignals. TheordinarycoherencefunctionsareplottedinFigureC-11andareusedtoestimate thecomponentoftheoutputsignalthatisduetomechanicalvibrations.Astrong coherence, 2 =0 : 95,isobservedatapproximately500Hzbetweenallcombinationsof input-outputsignals.Atdiscretefrequencies,between200and340Hz,thereisstrong coherencebetweeninput1accelerometeronthePSDandtheoutput, 2 1 y ,withthe coherencebetweeninput2accelerometerontunneloorandtheoutput, 2 2 y ,being considerablyweaker.Althoughnotshown,thetwoinputsarecorrelatedwitheachother, 2 12 6 =0,whichindicatesthatthemechanicalvibrationsfromthetunnelareinducing vibrationsonthePSD,sincethealternativeisnotphysicallypossible. Thecoherentoutputpoweristhencomputedbymultiplyingordinarycoherence functionwiththeoutputautospectra, G yy 1 = 2 1 y G yy and G yy 2 = 2 2 y G yy .Sincethetwo inputsarecorrelated,eachcoherentautospectraistheportionoftheoutputautospectrum duetoitsinputthroughbothH 1 andH 2 .Then,theconditionedoutputautospectrais 287

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calculatedbysubtractingthecoherentoutputpowerfromtheoutputautospectra: G yy 1 = G yy )]TJ/F22 11.9552 Tf 11.955 0 Td [( 2 1 y G yy G yy 2 = G yy )]TJ/F22 11.9552 Tf 11.955 0 Td [( 2 2 y G yy : Theconditionedautospectra,plottedinFigureC-12representtheoutputwhenthelinear eectsofbothinputsareremoved.Itisimportanttonotetheimplications:allcorrelated eectsbetweenthetwoinputsoriginatefromtheinputthatisturnedo.Thismeansthat G yy 2 istheoutputspectrafromthePSDthatwouldoccurifthetunneloorvibrations x 2 wereturnedo,assumingthatthevibrationasmeasuredonthetunneloorcan inducevibrationsonthePSD,butthattheoppositeisnottrue. Ifthetwoinputsignalsareuncorrelated,thenthedesiredsignal G zz iscalculated bysubtractingthecoherentoutputpowerof x 1 and x 2 fromthemeasuredoutput, G yy However,sincethisisnotthecase,thepartialcoherenceandpartialoutputpowermust bedened.Thesearedescribedinthenextsection. C.5.4PartialCoherenceFunction Asanextensionoftheordinarycoherencefunction,thepartialcoherencefunction indicatesthelineardependenceoftheoutputtooneinputwiththeotherinputturned o.WhilestructuralvibrationsonthePSDcontributetotheoutputautospectrum,they arecorrelatedtothevibrationsasmeasuredonthetunneloor,i.e.theonlyimportant structuralvibrationsinthemeasurementarethosethatoriginateduetothemechanical vibrationofthetunneloor.Therefore,theautospectraofthedesiredsignal G zz canbe computedbysubtractingthepartialcoherentoutputpowerbetween x 1 and y withthe lineareectsof x 2 removedandtheordinarycoherentoutputpowerbetween x 2 and y fromthemeasuredsignal.Thisresultsin: G zz = G yy )]TJ/F22 11.9552 Tf 11.955 0 Td [( 2 1 y 2 G yy 2 )]TJ/F22 11.9552 Tf 11.955 0 Td [( 2 2 y G yy ; C{21 288

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wherethepartialcoherencefunctionisdenedas 2 1 y 2 = j G 1 y 2 j 2 G 11 2 G yy 2 = j G 1 y G 22 )]TJ/F22 11.9552 Tf 11.955 0 Td [(G 2 y G 12 j 2 G 2 22 G 11 G yy )]TJ/F22 11.9552 Tf 11.955 0 Td [( 2 21 )]TJ/F15 11.9552 Tf 5.479 -9.684 Td [(1 )]TJ/F22 11.9552 Tf 11.955 0 Td [( 2 2 y : C{22 Notethatthepartialcoherencefunctionisacombinationofpreviouslycalculated quantities,suchthatnonewmeasurementsareneeded.FigureC-13showstheresults, with O 2 tunnelvibrationreductionat f =500Hz.Conditionalspectraltechniques provedusefulindeterminingproblematictunnelvibrations.Aseriesofinitialtestsshowed thattunnelvibrationatlowfrequencies < 1kHzcorruptedthebeamdisplacement measurements,seeFigureC-7C-D.Still,morevibrationsignalsand/ormorecomplexi.e. higherorderand/ornonlinearmodelsarelikelyrequiredtoimprovemodelaccuracyfor allotherfrequencies. A B FigureC-1.LinearAsingle-input,single-ouputSISOmodelandBmultiple-input, single-outputmodels. FigureC-2.SchematicofaMISOmodelincludinganoisecomponent. 289

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FigureC-3.Conditionedmodelequivalenttoadual-inputversionofFigureC-2. A B FigureC-4.TwoSISOmodelsreplacethetwo-input,single-outputmodelshowninFigure C-3.ADecompositionof y t from x 1 t .BConditioned-input, conditioned-outputmodel. 290

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A B C FigureC-5.Accelerometercalibrationforeveryaxisofeachaccelerometer.AandB correspondtotheaccelerometersplacedoneachpositionsensingdevicea1 anda2,respectivelywhileCcorrespondstotheaccelerometerplacedonthe tunneloora3.ReferenceFigure3-17fordetailedlocations. 291

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A B FigureC-6.Autospectraofoutputsignalsfroma1=accelerometeronPSD1,a2= accelerometeronPSD2,a3=accelerometerontunneloor,B1=beam deectionasmeasuredbyPSD1,andB2=beamdeectionasmeasuredby PSD2. A B FigureC-7.Ordinarycoherencefunctionsfroma1=accelerometeronPSD1,a2= accelerometeronPSD2,a3=accelerometerontunneloor,B1=beam deectionasmeasuredbyPSD1,andB2=beamdeectionasmeasuredby PSD2. 292

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FigureC-8.Two-input,single-outputsystemrepresentingtheopticalmeasurements. Input X 1 =accelerometeronPSD, X 2 =accelerometerontunneloor, Y = laserpositionsensingdevice,and Z representsunmeasuredlineardynamics i.e.,theaero-opticinput,nonlinearities,andoutputsensorelectronicnoise. FigureC-9.Autospectraofoutputsignalsfrom1=accelerometeronPSD,2= accelerometerontunneloor, y =laserpositionsensingdevice. G 11 and G 22 haveunitsofm/s 2 2 while G yy hasunitsofm 2 FigureC-10.Cross-spectramagnitudeofoutputsignalsfrom1=accelerometeronPSD,2 =accelerometerontunneloor, y =laserpositionsensingdevice. 293

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FigureC-11.Ordinarycoherencefunctionsfrom1=accelerometeronPSD,2= accelerometerontunneloor, y =laserpositionsensingdevice. FigureC-12.Conditionedautospectrafrom1=accelerometeronPSD,2=accelerometer ontunneloor, y =laserpositionsensingdevice. 294

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FigureC-13.Resultingoutputautospectraafterremovingpartialcoherentoutputpower between x 1 and y withthelineareectsof x 2 removedandtheordinary coherentoutputpowerbetween x 2 and y fromthemeasuredsignal. 295

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APPENDIXD EXTENDEDPASSIVECONTROLRESULTS Thepurposeofthisappendixistosupplementtheresultsfromthepassivecontrol congurationsSection5.2withthedatathatwasnotofdirectimportancetothe discussion.TheguresareorganizedbypincongurationsallshowninFigureD-1and consistofoilowvisualizationresults,unsteadypressurespectra,turbulentuctuating wakeprolesandspectra,andaero-opticmeasurements. A B C D E F G H I J K L FigureD-1.Illustrationofallpassivecontrolcongurationsnotdrawntoscale.All relevantparametersarelistedinTable3-4. 296

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A B FigureD-2.Resultsfromoilowvisualizationforbaseline )]TJ/F15 11.9552 Tf 9.298 0 Td [(andpassivecontrolcaseP1 )]TJ/F15 11.9552 Tf 9.298 0 Td [(.ATopviewshowingtheseparationlineandtherearstagnationpoint x R =H = )]TJ/F15 11.9552 Tf 9.299 0 Td [(2 : 1%thatdividestherecirculatingregionfromthedownstream ow.BAngledviewshowingtheseparationlines. A B C D FigureD-3.Unsteadypressurespectraforbaseline )]TJ/F15 11.9552 Tf 9.299 0 Td [(andpassivecontrolcaseP1 \000 Pressuremeasurementlocationsalongthewindowareillustratedinthe bottomleftcornerofeachplotandresulting P rms arelistedatthetopright. 297

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FigureD-4.Meanvelocityprole U=U 1 ,turbulentintensity =U 2 1 ,and spectraasmeasuredatthepointofhighestuctuationwithintheshearlayer, markedwitha .Baseline )]TJ/F15 11.9552 Tf 9.298 0 Td [(,andcontrolcaseP1 )]TJ/F15 11.9552 Tf 9.299 0 Td [(. I 2 denotesthe percentchangeoftheintegratedturbulentkineticenergywithintheshear layer.Forthespectra, \000 denotesa f )]TJ/F21 7.9701 Tf 6.587 0 Td [(5 = 3 trend. 298

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A B FigureD-5.MalleyproberesultsforpassivecontrolcaseP1asmeasuredatB3see Figure4-37forlocation.ABeamdeectionspectramultipliedbythe convectivespeed U c andnormalizedbythefreestreamvelocity U 1 .Baseline )]TJ/F15 11.9552 Tf 9.298 0 Td [(,andcontrolcaseP1 \000 .BPhasebetweenMalleyprobebeams.To calculatetheconvectivespeed U c ,thetimedelayisdeterminedbycalculating thebestlinetinaleast-squaressenseshownby \000 totheslopeofthe phaseplot. 299

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A B FigureD-6.Resultsfromoilowvisualizationforbaseline )]TJ/F15 11.9552 Tf 9.298 0 Td [(andpassivecontrolcaseP2 )]TJ/F15 11.9552 Tf 9.298 0 Td [(.ATopviewshowingtheseparationlineandtherearstagnationpoint x R =H = )]TJ/F15 11.9552 Tf 9.299 0 Td [(5 : 9%thatdividestherecirculatingregionfromthedownstream ow.BAngledviewshowingtheseparationlines. A B C D FigureD-7.Unsteadypressurespectraforbaseline )]TJ/F15 11.9552 Tf 9.299 0 Td [(andpassivecontrolcaseP2 \000 Pressuremeasurementlocationsalongthewindowareillustratedinthe bottomleftcornerofeachplotandresulting P rms arelistedatthetopright. 300

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FigureD-8.Meanvelocityprole U=U 1 ,turbulentintensity =U 2 1 ,and spectraasmeasuredatthepointofhighestuctuationwithintheshearlayer, markedwitha .Baseline )]TJ/F15 11.9552 Tf 9.298 0 Td [(,andcontrolcaseP2 )]TJ/F15 11.9552 Tf 9.299 0 Td [(. I 2 denotesthe percentchangeoftheintegratedturbulentkineticenergywithintheshear layer.Forthespectra, \000 denotesa f )]TJ/F21 7.9701 Tf 6.587 0 Td [(5 = 3 trend. 301

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A B FigureD-9.MalleyproberesultsforpassivecontrolcaseP2asmeasuredatB3see Figure4-37forlocation.ABeamdeectionspectramultipliedbythe convectivespeed U c andnormalizedbythefreestreamvelocity U 1 .Baseline )]TJ/F15 11.9552 Tf 9.298 0 Td [(,andcontrolcaseP2 \000 .BPhasebetweenMalleyprobebeams.To calculatetheconvectivespeed U c ,thetimedelayisdeterminedbycalculating thebestlinetinaleast-squaressenseshownby \000 totheslopeofthe phaseplot. 302

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A B FigureD-10.Resultsfromoilowvisualizationforbaseline )]TJ/F15 11.9552 Tf 9.298 0 Td [(andpassivecontrolcase P3 )]TJ/F15 11.9552 Tf 9.299 0 Td [(.ATopviewshowingtheseparationlineandtherearstagnation point x R =H =27 : 7%thatdividestherecirculatingregionfromthe downstreamow.BAngledviewshowingtheseparationlines. A B C D FigureD-11.Unsteadypressurespectraforbaseline )]TJ/F15 11.9552 Tf 9.299 0 Td [(andpassivecontrolcaseP3 \000 .Pressuremeasurementlocationsalongthewindowareillustratedin thebottomleftcornerofeachplotandresulting P rms arelistedatthetop right. 303

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FigureD-12.Meanvelocityprole U=U 1 ,turbulentintensity =U 2 1 ,and spectraasmeasuredatthepointofhighestuctuationwithintheshear layer,markedwitha .Baseline )]TJ/F15 11.9552 Tf 9.298 0 Td [(,andcontrolcaseP3 )]TJ/F15 11.9552 Tf 9.299 0 Td [(. I 2 denotes thepercentchangeoftheintegratedturbulentkineticenergywithinthe shearlayer.Forthespectra, \000 denotesa f )]TJ/F21 7.9701 Tf 6.586 0 Td [(5 = 3 trend. 304

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A B FigureD-13.MalleyproberesultsforpassivecontrolcaseP3asmeasuredatB3see Figure4-37forlocation.ABeamdeectionspectramultipliedbythe convectivespeed U c andnormalizedbythefreestreamvelocity U 1 .Baseline )]TJ/F15 11.9552 Tf 9.298 0 Td [(,andcontrolcaseP3 \000 .BPhasebetweenMalleyprobebeams.To calculatetheconvectivespeed U c ,thetimedelayisdeterminedby calculatingthebestlinetinaleast-squaressenseshownby \000 tothe slopeofthephaseplot. 305

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A B FigureD-14.Resultsfromoilowvisualizationforbaseline )]TJ/F15 11.9552 Tf 9.298 0 Td [(andpassivecontrolcase P4 )]TJ/F15 11.9552 Tf 9.299 0 Td [(.ATopviewshowingtheseparationlineandtherearstagnation point x R =H = )]TJ/F15 11.9552 Tf 9.299 0 Td [(5 : 0%thatdividestherecirculatingregionfromthe downstreamow.BAngledviewshowingtheseparationlines. A B C D FigureD-15.Unsteadypressurespectraforbaseline )]TJ/F15 11.9552 Tf 9.299 0 Td [(andpassivecontrolcaseP4 \000 .Pressuremeasurementlocationsalongthewindowareillustratedin thebottomleftcornerofeachplotandresulting P rms arelistedatthetop right. 306

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FigureD-16.Meanvelocityprole U=U 1 ,turbulentintensity =U 2 1 ,and spectraasmeasuredatthepointofhighestuctuationwithintheshear layer,markedwitha .Baseline )]TJ/F15 11.9552 Tf 9.298 0 Td [(,andcontrolcaseP4 )]TJ/F15 11.9552 Tf 9.299 0 Td [(. I 2 denotes thepercentchangeoftheintegratedturbulentkineticenergywithinthe shearlayer.Forthespectra, \000 denotesa f )]TJ/F21 7.9701 Tf 6.586 0 Td [(5 = 3 trend. 307

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A B FigureD-17.MalleyproberesultsforpassivecontrolcaseP4asmeasuredatB3see Figure4-37forlocation.ABeamdeectionspectramultipliedbythe convectivespeed U c andnormalizedbythefreestreamvelocity U 1 .Baseline )]TJ/F15 11.9552 Tf 9.298 0 Td [(,andcontrolcaseP4 \000 .BPhasebetweenMalleyprobebeams.To calculatetheconvectivespeed U c ,thetimedelayisdeterminedby calculatingthebestlinetinaleast-squaressenseshownby \000 tothe slopeofthephaseplot. 308

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A B FigureD-18.Resultsfromoilowvisualizationforbaseline )]TJ/F15 11.9552 Tf 9.298 0 Td [(andpassivecontrolcase P5 )]TJ/F15 11.9552 Tf 9.299 0 Td [(.ATopviewshowingtheseparationlineandtherearstagnation point x R =H = )]TJ/F15 11.9552 Tf 9.299 0 Td [(11 : 3%thatdividestherecirculatingregionfromthe downstreamow.BAngledviewshowingtheseparationlines. A B C D FigureD-19.Unsteadypressurespectraforbaseline )]TJ/F15 11.9552 Tf 9.299 0 Td [(andpassivecontrolcaseP5 \000 .Pressuremeasurementlocationsalongthewindowareillustratedin thebottomleftcornerofeachplotandresulting P rms arelistedatthetop right. 309

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FigureD-20.Meanvelocityprole U=U 1 ,turbulentintensity =U 2 1 ,and spectraasmeasuredatthepointofhighestuctuationwithintheshear layer,markedwitha .Baseline )]TJ/F15 11.9552 Tf 9.298 0 Td [(,andcontrolcaseP5 )]TJ/F15 11.9552 Tf 9.299 0 Td [(. I 2 denotes thepercentchangeoftheintegratedturbulentkineticenergywithinthe shearlayer.Forthespectra, \000 denotesa f )]TJ/F21 7.9701 Tf 6.586 0 Td [(5 = 3 trend. 310

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A B FigureD-21.MalleyproberesultsforpassivecontrolcaseP5asmeasuredatB3see Figure4-37forlocation.ABeamdeectionspectramultipliedbythe convectivespeed U c andnormalizedbythefreestreamvelocity U 1 .Baseline )]TJ/F15 11.9552 Tf 9.298 0 Td [(,andcontrolcaseP5 \000 .BPhasebetweenMalleyprobebeams.To calculatetheconvectivespeed U c ,thetimedelayisdeterminedby calculatingthebestlinetinaleast-squaressenseshownby \000 tothe slopeofthephaseplot. 311

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A B FigureD-22.Resultsfromoilowvisualizationforbaseline )]TJ/F15 11.9552 Tf 9.298 0 Td [(andpassivecontrolcase P6 )]TJ/F15 11.9552 Tf 9.299 0 Td [(.ATopviewshowingtheseparationlineandtherearstagnation point x R =H = )]TJ/F15 11.9552 Tf 9.299 0 Td [(10 : 9%thatdividestherecirculatingregionfromthe downstreamow.BAngledviewshowingtheseparationlines. A B C D FigureD-23.Unsteadypressurespectraforbaseline )]TJ/F15 11.9552 Tf 9.299 0 Td [(andpassivecontrolcaseP6 \000 .Pressuremeasurementlocationsalongthewindowareillustratedin thebottomleftcornerofeachplotandresulting P rms arelistedatthetop right. 312

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FigureD-24.Meanvelocityprole U=U 1 ,turbulentintensity =U 2 1 ,and spectraasmeasuredatthepointofhighestuctuationwithintheshear layer,markedwitha .Baseline )]TJ/F15 11.9552 Tf 9.298 0 Td [(,andcontrolcaseP6 )]TJ/F15 11.9552 Tf 9.299 0 Td [(. I 2 denotes thepercentchangeoftheintegratedturbulentkineticenergywithinthe shearlayer.Forthespectra, \000 denotesa f )]TJ/F21 7.9701 Tf 6.586 0 Td [(5 = 3 trend. 313

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A B FigureD-25.MalleyproberesultsforpassivecontrolcaseP6asmeasuredatB3see Figure4-37forlocation.ABeamdeectionspectramultipliedbythe convectivespeed U c andnormalizedbythefreestreamvelocity U 1 .Baseline )]TJ/F15 11.9552 Tf 9.298 0 Td [(,andcontrolcaseP6 \000 .BPhasebetweenMalleyprobebeams.To calculatetheconvectivespeed U c ,thetimedelayisdeterminedby calculatingthebestlinetinaleast-squaressenseshownby \000 tothe slopeofthephaseplot. 314

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A B FigureD-26.Resultsfromoilowvisualizationforbaseline )]TJ/F15 11.9552 Tf 9.298 0 Td [(andpassivecontrolcase P7 )]TJ/F15 11.9552 Tf 9.299 0 Td [(.ATopviewshowingtheseparationlineandtherearstagnation point x R =H = )]TJ/F15 11.9552 Tf 9.299 0 Td [(2 : 9%thatdividestherecirculatingregionfromthe downstreamow.BAngledviewshowingtheseparationlines. A B C D FigureD-27.Unsteadypressurespectraforbaseline )]TJ/F15 11.9552 Tf 9.299 0 Td [(andpassivecontrolcaseP7 \000 .Pressuremeasurementlocationsalongthewindowareillustratedin thebottomleftcornerofeachplotandresulting P rms arelistedatthetop right. 315

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FigureD-28.Meanvelocityprole U=U 1 ,turbulentintensity =U 2 1 ,and spectraasmeasuredatthepointofhighestuctuationwithintheshear layer,markedwitha .Baseline )]TJ/F15 11.9552 Tf 9.298 0 Td [(,andcontrolcaseP7 )]TJ/F15 11.9552 Tf 9.299 0 Td [(. I 2 denotes thepercentchangeoftheintegratedturbulentkineticenergywithinthe shearlayer.Forthespectra, \000 denotesa f )]TJ/F21 7.9701 Tf 6.586 0 Td [(5 = 3 trend. 316

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A B FigureD-29.MalleyproberesultsforpassivecontrolcaseP7asmeasuredatB3see Figure4-37forlocation.ABeamdeectionspectramultipliedbythe convectivespeed U c andnormalizedbythefreestreamvelocity U 1 .Baseline )]TJ/F15 11.9552 Tf 9.298 0 Td [(,andcontrolcaseP7 \000 .BPhasebetweenMalleyprobebeams.To calculatetheconvectivespeed U c ,thetimedelayisdeterminedby calculatingthebestlinetinaleast-squaressenseshownby \000 tothe slopeofthephaseplot. 317

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A B FigureD-30.Resultsfromoilowvisualizationforbaseline )]TJ/F15 11.9552 Tf 9.298 0 Td [(andpassivecontrolcase P8 )]TJ/F15 11.9552 Tf 9.299 0 Td [(.ATopviewshowingtheseparationlineandtherearstagnation point x R =H =32 : 7%thatdividestherecirculatingregionfromthe downstreamow.BAngledviewshowingtheseparationlines. A B C D FigureD-31.Unsteadypressurespectraforbaseline )]TJ/F15 11.9552 Tf 9.299 0 Td [(andpassivecontrolcaseP8 \000 .Pressuremeasurementlocationsalongthewindowareillustratedin thebottomleftcornerofeachplotandresulting P rms arelistedatthetop right. 318

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FigureD-32.Meanvelocityprole U=U 1 ,turbulentintensity =U 2 1 ,and spectraasmeasuredatthepointofhighestuctuationwithintheshear layer,markedwitha .Baseline )]TJ/F15 11.9552 Tf 9.298 0 Td [(,andcontrolcaseP8 )]TJ/F15 11.9552 Tf 9.299 0 Td [(. I 2 denotes thepercentchangeoftheintegratedturbulentkineticenergywithinthe shearlayer.Forthespectra, \000 denotesa f )]TJ/F21 7.9701 Tf 6.586 0 Td [(5 = 3 trend. 319

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A B FigureD-33.MalleyproberesultsforpassivecontrolcaseP8asmeasuredatB3see Figure4-37forlocation.ABeamdeectionspectramultipliedbythe convectivespeed U c andnormalizedbythefreestreamvelocity U 1 .Baseline )]TJ/F15 11.9552 Tf 9.298 0 Td [(,andcontrolcaseP8 \000 .BPhasebetweenMalleyprobebeams.To calculatetheconvectivespeed U c ,thetimedelayisdeterminedby calculatingthebestlinetinaleast-squaressenseshownby \000 tothe slopeofthephaseplot. 320

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A B FigureD-34.Resultsfromoilowvisualizationforbaseline )]TJ/F15 11.9552 Tf 9.298 0 Td [(andpassivecontrolcase P9 )]TJ/F15 11.9552 Tf 9.299 0 Td [(.ATopviewshowingtheseparationlineandtherearstagnation point x R =H =79 : 8%thatdividestherecirculatingregionfromthe downstreamow.BAngledviewshowingtheseparationlines. A B C D FigureD-35.Unsteadypressurespectraforbaseline )]TJ/F15 11.9552 Tf 9.299 0 Td [(andpassivecontrolcaseP9 \000 .Pressuremeasurementlocationsalongthewindowareillustratedin thebottomleftcornerofeachplotandresulting P rms arelistedatthetop right. 321

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FigureD-36.Meanvelocityprole U=U 1 ,turbulentintensity =U 2 1 ,and spectraasmeasuredatthepointofhighestuctuationwithintheshear layer,markedwitha .Baseline )]TJ/F15 11.9552 Tf 9.298 0 Td [(,andcontrolcaseP9 )]TJ/F15 11.9552 Tf 9.299 0 Td [(. I 2 denotes thepercentchangeoftheintegratedturbulentkineticenergywithinthe shearlayer.Forthespectra, \000 denotesa f )]TJ/F21 7.9701 Tf 6.586 0 Td [(5 = 3 trend. 322

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A B FigureD-37.MalleyproberesultsforpassivecontrolcaseP9asmeasuredatB3see Figure4-37forlocation.ABeamdeectionspectramultipliedbythe convectivespeed U c andnormalizedbythefreestreamvelocity U 1 .Baseline )]TJ/F15 11.9552 Tf 9.298 0 Td [(,andcontrolcaseP9 \000 .BPhasebetweenMalleyprobebeams.To calculatetheconvectivespeed U c ,thetimedelayisdeterminedby calculatingthebestlinetinaleast-squaressenseshownby \000 tothe slopeofthephaseplot. 323

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A B FigureD-38.Resultsfromoilowvisualizationforbaseline )]TJ/F15 11.9552 Tf 9.298 0 Td [(andpassivecontrolcase P10 )]TJ/F15 11.9552 Tf 9.299 0 Td [(.ATopviewshowingtheseparationlineandtherearstagnation point x R =H = )]TJ/F15 11.9552 Tf 9.299 0 Td [(12 : 6%thatdividestherecirculatingregionfromthe downstreamow.BAngledviewshowingtheseparationlines. A B C D FigureD-39.Unsteadypressurespectraforbaseline )]TJ/F15 11.9552 Tf 9.299 0 Td [(andpassivecontrolcaseP10 \000 .Pressuremeasurementlocationsalongthewindowareillustratedin thebottomleftcornerofeachplotandresulting P rms arelistedatthetop right. 324

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FigureD-40.Meanvelocityprole U=U 1 ,turbulentintensity =U 2 1 ,and spectraasmeasuredatthepointofhighestuctuationwithintheshear layer,markedwitha .Baseline )]TJ/F15 11.9552 Tf 9.298 0 Td [(,andcontrolcaseP10 )]TJ/F15 11.9552 Tf 9.299 0 Td [(. I 2 denotesthepercentchangeoftheintegratedturbulentkineticenergywithin theshearlayer.Forthespectra, \000 denotesa f )]TJ/F21 7.9701 Tf 6.587 0 Td [(5 = 3 trend. 325

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A B FigureD-41.MalleyproberesultsforpassivecontrolcaseP10asmeasuredatB3see Figure4-37forlocation.ABeamdeectionspectramultipliedbythe convectivespeed U c andnormalizedbythefreestreamvelocity U 1 .Baseline )]TJ/F15 11.9552 Tf 9.298 0 Td [(,andcontrolcaseP10 \000 .BPhasebetweenMalleyprobebeams. Tocalculatetheconvectivespeed U c ,thetimedelayisdeterminedby calculatingthebestlinetinaleast-squaressenseshownby \000 tothe slopeofthephaseplot. 326

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A B FigureD-42.Resultsfromoilowvisualizationforbaseline )]TJ/F15 11.9552 Tf 9.298 0 Td [(andpassivecontrolcase P11 )]TJ/F15 11.9552 Tf 9.299 0 Td [(.ATopviewshowingtheseparationlineandtherearstagnation point x R =H = )]TJ/F15 11.9552 Tf 9.299 0 Td [(10 : 9%thatdividestherecirculatingregionfromthe downstreamow.BAngledviewshowingtheseparationlines. A B C D FigureD-43.Unsteadypressurespectraforbaseline )]TJ/F15 11.9552 Tf 9.299 0 Td [(andpassivecontrolcaseP11 \000 .Pressuremeasurementlocationsalongthewindowareillustratedin thebottomleftcornerofeachplotandresulting P rms arelistedatthetop right. 327

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FigureD-44.Meanvelocityprole U=U 1 ,turbulentintensity =U 2 1 ,and spectraasmeasuredatthepointofhighestuctuationwithintheshear layer,markedwitha .Baseline )]TJ/F15 11.9552 Tf 9.298 0 Td [(,andcontrolcaseP11 )]TJ/F15 11.9552 Tf 9.299 0 Td [(. I 2 denotesthepercentchangeoftheintegratedturbulentkineticenergywithin theshearlayer.Forthespectra, \000 denotesa f )]TJ/F21 7.9701 Tf 6.587 0 Td [(5 = 3 trend. 328

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A B FigureD-45.MalleyproberesultsforpassivecontrolcaseP11asmeasuredatB3see Figure4-37forlocation.ABeamdeectionspectramultipliedbythe convectivespeed U c andnormalizedbythefreestreamvelocity U 1 .Baseline )]TJ/F15 11.9552 Tf 9.298 0 Td [(,andcontrolcaseP11 \000 .BPhasebetweenMalleyprobebeams. Tocalculatetheconvectivespeed U c ,thetimedelayisdeterminedby calculatingthebestlinetinaleast-squaressenseshownby \000 tothe slopeofthephaseplot. 329

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A B FigureD-46.Resultsfromoilowvisualizationforbaseline )]TJ/F15 11.9552 Tf 9.298 0 Td [(andpassivecontrolcase P12 )]TJ/F15 11.9552 Tf 9.299 0 Td [(.ATopviewshowingtheseparationlineandtherearstagnation point x R =H = )]TJ/F15 11.9552 Tf 9.299 0 Td [(13 : 4%thatdividestherecirculatingregionfromthe downstreamow.BAngledviewshowingtheseparationlines. A B C D FigureD-47.Unsteadypressurespectraforbaseline )]TJ/F15 11.9552 Tf 9.299 0 Td [(andpassivecontrolcaseP12 \000 .Pressuremeasurementlocationsalongthewindowareillustratedin thebottomleftcornerofeachplotandresulting P rms arelistedatthetop right. 330

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FigureD-48.Meanvelocityprole U=U 1 ,turbulentintensity =U 2 1 ,and spectraasmeasuredatthepointofhighestuctuationwithintheshear layer,markedwitha .Baseline )]TJ/F15 11.9552 Tf 9.298 0 Td [(,andcontrolcaseP12 )]TJ/F15 11.9552 Tf 9.299 0 Td [(. I 2 denotesthepercentchangeoftheintegratedturbulentkineticenergywithin theshearlayer.Forthespectra, \000 denotesa f )]TJ/F21 7.9701 Tf 6.587 0 Td [(5 = 3 trend. 331

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A B FigureD-49.MalleyproberesultsforpassivecontrolcaseP12asmeasuredatB3see Figure4-37forlocation.ABeamdeectionspectramultipliedbythe convectivespeed U c andnormalizedbythefreestreamvelocity U 1 .Baseline )]TJ/F15 11.9552 Tf 9.298 0 Td [(,andcontrolcaseP12 \000 .BPhasebetweenMalleyprobebeams. Tocalculatetheconvectivespeed U c ,thetimedelayisdeterminedby calculatingthebestlinetinaleast-squaressenseshownby \000 tothe slopeofthephaseplot. 332

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BIOGRAPHICALSKETCH MiguelPalavicciniwasborninCaracas,Venezuelain1984.HelivedinVenezuela untiltheageof5,whenhisparentsmovedtotheUnitedStates.Afterlivinginfour dierentstatesinveyears,hisfamilynallysettleddowninPembrokePines,FLforall ofhismiddleandhighschoolyears.MiguelgraduatedfromCharlesW.FlanaganHigh Schoolin2002andenrolledattheUniversityofFlorida.UponreceivingaBachelorof ScienceinAerospaceEngineeringfromin2006,heimmediatelybegangraduatestudies attheUniversityofFloridaundertheguidanceofDr.LouisCattafesta.Miguelreceived hisMasterofScienceinMechanicalEngineeringin2008andhisPh.D.inAerospace Engineeringin2013. 343