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Aeroacoustic Characterization of Scaled Canonical Nose Landing Gear Configurations

Permanent Link: http://ufdc.ufl.edu/UFE0045002/00001

Material Information

Title: Aeroacoustic Characterization of Scaled Canonical Nose Landing Gear Configurations
Physical Description: 1 online resource (383 p.)
Language: english
Creator: Zawodny, Nikolas Stephen
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2013

Subjects

Subjects / Keywords: aeroacoustics -- airframe -- beamforming -- cfd -- stereopiv -- turbulence -- vorticity
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: Aircraft noise is a critical issue in the commercial airline industry. Airframe noise is a sub-component of aircraft noise and is generally dominant over jet engine noise during approach conditions, which can lead to high community impact. Landing gears have been identified as major components of airframe noise during landing configurations for commercial aircraft. They are perhaps the least understood contributors to airframe noise due to complex flow patterns associated with intricate gear component geometries. Nose landing gear in particular have received much attention in recent years, exhibiting acoustic signatures on the order of the main landing gear assembly of an aircraft, while simultaneously being more amenable to scaled wind tunnel testing. In order to characterize the acoustic signature of a complex geometry such as a nose landing gear, it is important to isolate, study, and understand the acoustic contributions of individual component geometries. The purpose of this dissertation is to develop a correlation between the complex flow field nature and far-field acoustic signature of a nose landing gear sub-system. The model under investigation is a 1/2-scale shock-strut cylinder coupled with an adjustable torque link apparatus. This geometry was chosen due to its fundamental importance and implementation across a wide span of commercial aircraft. The fluid dynamic (surface pressure and stereoscopic particle image velocimety) and aeroacoustic (far-field microphone and phased array) experiments were performed in the University of Florida Aeroacoustic Flow Facility. The experimental data compare favorably with the results of a numerical simulation using PowerFLOW, a lattice-Boltzmann solver developed by the Exa Corporation. The far-field acoustic results of this dissertation have shown non-uniform scaling behavior as a function of frequency for the different model configurations tested. For frequencies that appropriately satisfied the condition of acoustic compactness (ka secondary noise contributors being the impingement of vortices shed from the cylinder on to the torque arm surface. The use of the phased microphone array for beamforming at frequencies above 1 kHz revealed that the torque arms also behave as broadband noise producers.
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 Nikolas Stephen Zawodny.
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: UFE0045002:00001

Permanent Link: http://ufdc.ufl.edu/UFE0045002/00001

Material Information

Title: Aeroacoustic Characterization of Scaled Canonical Nose Landing Gear Configurations
Physical Description: 1 online resource (383 p.)
Language: english
Creator: Zawodny, Nikolas Stephen
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2013

Subjects

Subjects / Keywords: aeroacoustics -- airframe -- beamforming -- cfd -- stereopiv -- turbulence -- vorticity
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: Aircraft noise is a critical issue in the commercial airline industry. Airframe noise is a sub-component of aircraft noise and is generally dominant over jet engine noise during approach conditions, which can lead to high community impact. Landing gears have been identified as major components of airframe noise during landing configurations for commercial aircraft. They are perhaps the least understood contributors to airframe noise due to complex flow patterns associated with intricate gear component geometries. Nose landing gear in particular have received much attention in recent years, exhibiting acoustic signatures on the order of the main landing gear assembly of an aircraft, while simultaneously being more amenable to scaled wind tunnel testing. In order to characterize the acoustic signature of a complex geometry such as a nose landing gear, it is important to isolate, study, and understand the acoustic contributions of individual component geometries. The purpose of this dissertation is to develop a correlation between the complex flow field nature and far-field acoustic signature of a nose landing gear sub-system. The model under investigation is a 1/2-scale shock-strut cylinder coupled with an adjustable torque link apparatus. This geometry was chosen due to its fundamental importance and implementation across a wide span of commercial aircraft. The fluid dynamic (surface pressure and stereoscopic particle image velocimety) and aeroacoustic (far-field microphone and phased array) experiments were performed in the University of Florida Aeroacoustic Flow Facility. The experimental data compare favorably with the results of a numerical simulation using PowerFLOW, a lattice-Boltzmann solver developed by the Exa Corporation. The far-field acoustic results of this dissertation have shown non-uniform scaling behavior as a function of frequency for the different model configurations tested. For frequencies that appropriately satisfied the condition of acoustic compactness (ka secondary noise contributors being the impingement of vortices shed from the cylinder on to the torque arm surface. The use of the phased microphone array for beamforming at frequencies above 1 kHz revealed that the torque arms also behave as broadband noise producers.
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 Nikolas Stephen Zawodny.
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: UFE0045002:00001


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AEROACOUSTICCHARACTERIZATIONOFSCALEDCANONICALNOSELANDINGGEARCONFIGURATIONSByNIKOLASS.ZAWODNYADISSERTATIONPRESENTEDTOTHEGRADUATESCHOOLOFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENTOFTHEREQUIREMENTSFORTHEDEGREEOFDOCTOROFPHILOSOPHYUNIVERSITYOFFLORIDA2013

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c2013NikolasS.Zawodny 2

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IdedicatethisdissertationtoCarlosRodriguezandErnestD'Angelo. 3

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ACKNOWLEDGMENTS Firstandforemost,Iwouldliketothankmyadvisorandcommitteechairman,Dr.LouisCattafesta.Hiscontinuingmentorshipandguidancehasmadethisresearchpossible.Iwouldalsoliketoextendmygratitudetotherestofmycommitteemembers:Dr.MarkSheplak,Dr.LawrenceUkeiley,Dr.JianLi(ECE),andDr.MehdiKhorramiofNASALaRC.Thanksalsogoestomycontactsinindustryfortheirprofessionaladviceandassistancewiththisandpreviousresearch:DanNeuhartofNASALaRCandThomasVandeVenoftheGulfstreamAerospaceCorporation.DevelopmentofmyacademicandexperimentalskillsetshasbeengreatlyassistedbymycolleaguesformerlyassociatedwithIMG.IwouldliketospecicallythankDrs.ChrisBahr,FeiLiu,andTarikYardibifortheirguidanceintheareasofacoustics,phasedmicrophonearrays,andsignalprocessing.BrandonBertolucciandJohnGrinhaveaidedmegreatlywithlearninghowtouselasermeasurementtoolsincludinglaserDopplervelocimetryandparticleimagevelocimetry.NumerousdiscussionswithMiguelPalaviccini,MatiasOyarzun,andAshleyJoneshavehelpedsteermedownthecorrectpathinthisresearchendeavor.ThewindtunnelexperimentsofthisdissertationwereperformedwiththeassistanceofgraduatestudentDerekDussault.IwouldalsoliketothankmylovelygirlfriendStacyLundstedtforherlovingsupportaswellasmycatDuncanforbeingthebestpetever.Lastbutcertainlynotleast,IwouldliketothankmyparentsJosephandYvonneZawodnyandmysisterEricaMacArthur.Theirendlesssupportandencouragementhasbeentrulyinspiringovertheyears. 4

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TABLEOFCONTENTS page ACKNOWLEDGMENTS ................................. 4 LISTOFTABLES ..................................... 9 LISTOFFIGURES .................................... 11 ABSTRACT ........................................ 21 CHAPTER 1INTRODUCTION .................................. 23 1.1Motivation .................................... 23 1.2LandingGearStructuralDynamics ...................... 25 1.2.1MainLandingGear ........................... 26 1.2.2NoseLandingGear ........................... 26 1.2.3TheShockStrutandTorqueArms .................. 27 1.3LandingGearNoise ............................... 28 1.3.1AerodynamicSound-GeneralTheory ................. 28 1.3.2AirframeNoiseGeneration ....................... 31 1.3.3TheVortexSoundAnalogy ....................... 32 1.3.4LandingGearNoiseSources ...................... 36 1.4UnresolvedTechnicalIssues .......................... 37 1.5ProposedResearch ............................... 37 2LITERATUREREVIEW .............................. 42 2.1TotalAirframeNoiseStudies .......................... 42 2.1.1EarlyNoisePredictionMethods .................... 42 2.1.2AirframePrimaryNoiseSourceIdenticationStudies ........ 45 2.2SimpleGeometryStudies ............................ 47 2.2.1FlowAroundaSingleCylinder ..................... 47 2.2.2FlowAroundTandemCylinders .................... 51 2.2.2.1FluidDynamicInteractions ................. 51 2.2.2.2Far-FieldAcoustics ...................... 53 2.3LandingGearExperimentalStudies ...................... 55 2.3.1SimpleLandingGearGeometryStudies ................ 55 2.3.2High-FidelityLandingGearGeometryStudies ............ 57 2.3.3ImplementationofNoiseReductionTechniques ............ 61 2.3.3.1PassiveNoiseReductionConcepts .............. 61 2.3.3.2ActiveNoiseReductionConcepts .............. 63 2.4LandingGearComputationalStudies ..................... 64 2.5UnresolvedTechnicalIssues .......................... 67 2.6ExperimentalandComputationalApproach ................. 68 5

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3EXPERIMENTALANDCOMPUTATIONALPROCEDURES ......... 79 3.1TorqueArmSub-systemModelDesign .................... 79 3.1.1TheCylinder .............................. 80 3.1.2TheTorqueArms ............................ 82 3.2ModelCongurations .............................. 82 3.3TestingFacility ................................. 82 3.4ModelSurfacePressureMeasurements .................... 83 3.4.1SteadyPressures ............................ 84 3.4.1.1ModelMeasurementLocations ............... 84 3.4.1.2DataAcquisitionandUncertainty .............. 85 3.4.2UnsteadySurfacePressureMeasurements ............... 87 3.4.2.1ModelSensorLocations ................... 87 3.4.2.2TransducerDesign ...................... 89 3.4.2.3SensorCharacterization ................... 95 3.4.2.4DataAcquisitionandUncertainty .............. 101 3.4.2.5TimeDomainReconstruction ................ 104 3.5AcousticInstrumentation ............................ 105 3.5.1LinearMicrophoneArray ........................ 106 3.5.2PhasedMicrophoneArray ....................... 107 3.5.2.1FrequencyDomainBeamforming .............. 107 3.5.2.2BeamformingAlgorithms ................... 110 3.5.2.3IntegratedAbsoluteLevels .................. 112 3.5.2.4PhasedArrayDesignandFabrication ............ 113 3.5.3DataAcquisitionandUncertainty ................... 114 3.6FlowFieldMeasurements ........................... 116 3.6.1SPIVSetup ............................... 117 3.6.2RegionsofAnalysis ........................... 118 3.6.3DataAcquisition ............................ 118 3.6.4SPIVUncertainty ............................ 120 3.6.5FlowFieldEstimation ......................... 120 3.6.5.1TheLambVector ....................... 121 3.6.5.2ProperOrthogonalDecomposition ............. 123 3.6.5.3ModiedStochasticEstimation ............... 124 3.7ComputationalFluidSimulations ....................... 127 3.7.1SimulationProcedure .......................... 127 3.7.2CaseandGeometryPreparation .................... 128 3.7.2.1NumericalSetup ....................... 128 3.7.2.2BoundaryConditions ..................... 130 3.7.2.3MeasurementWindows .................... 131 3.7.3SimulationDiagnostics ......................... 131 3.7.4MeanFlowMeasurements ....................... 132 6

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4SURFACEPRESSURESANDACOUSTICS ................... 168 4.1ModelSurfacePressures ............................ 168 4.1.1SteadySurfacePressures ........................ 168 4.1.1.1SingleCylinder ........................ 169 4.1.1.2TheTorqueArmModel ................... 170 4.1.2UnsteadySurfacePressures ....................... 176 4.1.2.1SingleCylinderMeasurements ................ 177 4.1.2.2ModelSurfacePressureSpectra ............... 179 4.1.2.3SimulatedModelPressureFluctuations ........... 184 4.1.2.4Near-FieldCoherence ..................... 185 4.1.2.5ComparisonwithSimulations ................ 187 4.2AcousticCharacterization ........................... 188 4.2.1AcousticSurveys ............................ 189 4.2.2DirectivityApproximations ....................... 191 4.2.3Near-toFar-FieldCoherence ...................... 193 4.2.4Far-FieldScalingBehavior ....................... 194 4.2.5CAAPrediction ............................. 197 4.2.6MotivationforHigh-FrequencyAnalysis ................ 199 4.2.7BeamformingResults .......................... 200 4.2.7.1NoteonLimitationsofBeamforming ............ 201 4.2.7.2ComparisonofAlgorithms .................. 201 4.2.7.3NoiseSourceLocalizationMaps ............... 205 4.2.8Summary ................................. 207 5FLOWFIELDMEASUREMENTS ......................... 249 5.1MeanFlowFieldandTurbulenceSurveys ................... 249 5.1.1SimulationComparisons ........................ 251 5.1.2VorticitySurveys ............................ 253 5.2FlowFieldEstimation ............................. 254 5.2.1PODResults ............................... 255 5.2.2TimeDelayAnalysis .......................... 258 5.2.3Low-OrderVelocityFieldReconstruction ............... 262 5.2.4PODAnalysisonPowerFLOWResults ................ 264 5.2.5Near-FieldAnalysisofAcousticSourceTerms ............ 266 5.2.5.1Low-OrderLambVectorTermRepresentations ...... 267 5.2.5.2LambVectorSpectralAnalysis ............... 270 5.3Summary .................................... 282 6CONCLUSIONSANDFUTUREWORK ...................... 333 6.1ResearchKeyFindings ............................. 333 6.1.1ConnectionsbetweenFluidDynamicsandAcoustics ......... 333 6.1.1.1SurfacePressureMeasurements ............... 333 6.1.1.2Far-FieldAcoustics ...................... 335 7

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6.1.1.3FlowFieldMeasurements .................. 337 6.1.2PowerFLOWasanaeroacousticsimulator .............. 338 6.2SuggestionsforFutureWork .......................... 339 APPENDIX AKULITEIN-LINEAMPLIFIERDESIGN ..................... 342 A.1AmplierBoardDesign ............................. 342 A.2Kulite-AmplierPerformance ......................... 344 BGROUPARRAYCALIBRATION ......................... 349 B.1MathematicalDescription ........................... 349 B.2WindTunnelCalibrationSetup ........................ 350 B.3CalibrationResults ............................... 351 B.3.1StaticCalibration ............................ 352 B.3.1.1LaserPulsePerformance ................... 352 B.3.1.2ArrayPointSpreadFunctionPerformance ......... 353 B.3.2FlowCalibration ............................ 354 CSPIVUNCERTAINTYANALYSIS ......................... 362 C.1BiasUncertainty ................................ 362 C.2SPIVBiasUncertaintiesforMeasuredRegions ................ 365 C.3RandomUncertainty .............................. 366 DPHASEDARRAYDIRECTIVITYPERFORMANCE .............. 370 REFERENCES ....................................... 373 BIOGRAPHICALSKETCH ................................ 383 8

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LISTOFTABLES Table page 1-1DimensionalParametersforAcousticSourceScaling ............... 41 2-1SummaryofTotalAirframeNoiseStudies ..................... 75 2-2FlowRegimesofaCircularCylinder[TableadaptedfromZdravkovich,M.M.1997FlowAroundCircularCylinders,Vol.1:Fundamentals.(Chapter1,page18,Table1.1).] .................................... 75 2-3EectsofSpacingonFlowBetweenTandemCylinders( Zdravkovich 1985 ) ... 76 2-4SummaryofSimpleGeometryStudies ....................... 76 2-5SummaryofLandingGearExperimentalStudies ................. 77 2-6AdvantagesanddisadvantagesofcommonCFDalgorithms ............ 78 2-7SummaryofLandingGearComputationalStudies ................. 78 3-1Far-eldSPLreductionsoftrippedcylinderwithhelicalwirewrapping. ..... 161 3-2Separationdistanceaspectratiosofthetorquearmhinge. ............ 161 3-3BiaserrorsoftheNetscannerpressuremodules. .................. 162 3-4Non-dimensionalverticallocationsofcylinderspanwiseelectretsrelativetomodelcenterline. ....................................... 162 3-5Non-dimensionalverticallocations(Z=D)oftorquearmelectretsandkulitesforprimarymodelcongurations .......................... 162 3-6MicrophonebranchdimensionsforFRFcalculation. ................ 163 3-7FrequencybandsusedformultisineandBLwhitenoisecalibrationinputsignals. 163 3-8Dataacquisitionparametersforrecessedelectretcharacterizations. ....... 163 3-9ShearlayercorrectionparametersforlineararraymicrophonesatafreestreamvelocityofM=0.167. ................................ 164 3-10Thermalnoiseandfrequencyresponsemagnitudeuncertaintiesofdierentfree-eldmicrophones. ..................................... 164 3-11StandarddeviationsofquantitiesinputintothebeamformingMonteCarlouncertaintyanalysis ........................................ 164 3-12SummaryofPIVimageacquisitionsetupincludingcameraopticsandowseederinformation ...................................... 165 9

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3-13SPIVmeasurementandprocessingparameters. .................. 165 3-14NominalspanwiselocationsofmodelsensorsusedinPIV-estimationruns .... 166 3-15TorquearmsurfacepressuresensorlocationsforPIV-estimationexperiments .. 167 3-16SimulationspecicationsforthePowerFLOWCFDsimulations. ......... 167 3-17MetricusedtodeterminenumberofvoxelsinosetVRregions. ......... 167 3-18MeasurementspecicationsofthetwoprimaryPowerFLOWsimulationruns .. 167 4-1PhaseITestingMatrix:Surfacepressureandfar-eldacoustictesting ...... 247 4-2ValuesofC0p;rmsforcylinderunsteadysurfacepressuresensors(U1=58m/s) 247 4-3ValuesofC0p;rmsfortorquearmunsteadysurfacepressuresensors(U1=58m/s) 248 4-4Advantagesanddisadvantagesofbeamformingalgorithms ............ 248 5-1SPIVmeasurementparametersfortorquearm=130congurationatU1=58m/s(M0.167) ................................... 332 A-1KuliteamplierPCBcomponents. ......................... 348 B-1Componentsofthelenstelescopeassembly. .................... 361 B-2Phasedarraycalibrationandexperimentaldataacquisitionparameters. ..... 361 C-1BiasuncertaintiesofallmeasuredSPIVregions .................. 368 C-2Randomuncertainty95%condenceintervalestimatesofcomputedvelocityterms ......................................... 369 10

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LISTOFFIGURES Figure page 1-1Potentialnoisesourcesonacommercialaircraft. .................. 39 1-2ProleandaftviewsoftheGulfstreamG550mainlandinggear(courtesyofGulfstreamAerospaceCorporation) ......................... 39 1-3ProleandforwardviewsoftheGulfstreamG550noselandinggear(courtesyofGulfstreamAerospaceCorporation) ....................... 40 1-4IllustrationofthepathofdeectionandresultingcompressionofagenericNLGshockstrutandtorquearmsduringaircraftlandingprocedure .......... 40 1-5Illustrationofpotentialnoisesourcesonagenericaircraftnoselandinggear. .. 41 2-1Illustrationofanaircraftyovernoisesourceidenticationexperiment. ..... 69 2-2Schematicofdisturbedowregionsaroundacircularcylinder .......... 69 2-3Schematicoftandemcylinderexperimentalconguration. ............. 70 2-4Representativesimplefour-wheellandinggeargeometry. ............. 70 2-5LaserlightsheetforPIVmeasurementsofwake-bodyinteractionsbetweentandemwheels. ......................................... 71 2-6Schematicofwindtunneltestsectioncongurationforyovermicrophonearraymeasurements. .................................... 71 2-7Schematicofacoustictestingcongurationinanopen-jetaeroacousticfacility. 72 2-8ComparisonofactualGulfstreamG550noselandinggearwiththehigh-delity1/4-scalereplica .................................... 72 2-9Scanningplanesfor2-dimensionalPIVmeasurementsonthe1/4-scaleGulfstreamG550noselandinggearmodel. ........................... 73 2-10Illustrationoflandinggearfairingnoisereductionconcepts. ........... 73 2-11Aircurtainblowingupstreamofasimulatedlandinggearcomponent. ...... 74 2-12Broadbandnoisereductionexperimentusingplasmaactuatorsonalandinggearsub-system(adaptedfrom Huangetal. ( 2010 )). .................. 74 3-1Close-upimageofGulfstreamG550noselandinggeartorquearmassembly. .. 133 3-2Illustrationsofthesimpliedshockstrut-torquearmdissertationmodel. .... 133 3-3Assembledandexplodedviewsofthemodelcylinder. ............... 134 11

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3-4Serratedtapeforcylinderboundarylayertripping. ................ 135 3-5Dimensionalparametersthatdenethemodelhelicalwirewrap. ......... 136 3-6Far-eldSPLresultsoftrippedcylinderhelicalwirewrapexperiments(lineararraymicrophoneL4). ................................ 136 3-7Assembledandexplodedviewsofthemodeltorquearm. ............. 137 3-8Pictorialrepresentationofthe4primarytestedmodelcongurations. ...... 137 3-9TheUniversityofFloridaAeroacousticFlowFacility. ............... 138 3-10VisualizationoftorquearmmountingassembliesintheUFAFFandphotographofUFAFFtestsectionconguredforacoustictesting. ............... 138 3-11Steadypressuretapcongurationforthemodelcylinderandtorquearm .... 139 3-12Close-upviewofmodelpressureportsdedicatedtounsteadysurfacemeasurementsonthemodelcylinderanduppertorquearm. ................... 139 3-13Illustrationofrecessedmicrophonehousingwithlabeleddimensionsandprimarycomponents. ...................................... 140 3-14EquivalentacousticductTMcomponentsforagradualareachangeandmicrophoneterminatedbranch. .................................. 141 3-15FRFcomparisonbetweenmicrophonebrancheswithopenandsealedterminationcongurations(parametersprovidedinTable 3-6 ). ................. 141 3-16Componentsofarecessedelectretmicrophonepackageandimagesoftheirinstallationwithinthemodelcylinderandtorquearm. ..................... 142 3-17SchematicandphotographofPWTsetupforrecessedmicrophonecalibration. 143 3-18IllustrationofMultisineoverlapperformanceviaFRFmeasurements. ...... 143 3-19FRFcomparisonbetweensealedandopenTygonRductterminationconditions(experimentallymeasured). ............................. 144 3-20ComparisonofexperimentallymeasuredFRFsusingMultisineandBLwhitenoiseinputcalibrationsignalswithsimulatedFRFviaTMestimation. ..... 144 3-21ComparisonofexperimentallymeasuredFRFsforthetwodierenttubulationlengthsusedwiththemodelrecessedelectretpackages. .............. 145 3-22RelativeTHDperformanceofasampleshortandlongstemrecessedelectretpackage. ........................................ 145 3-23Comparisonofmean-squarepressures(MSP)betweenreferencemicrophoneandDUT. ......................................... 146 12

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3-24(A)Comparisonofr[jHyx(f)j]forMultisineandBLwhitenoiseinputsignalsand(B)resultingr[Gyy(f)]usingBLwhitenoisesignal. ............. 147 3-25Illustrationoftimedomainreconstructionofrecessedelectretsensor. ...... 148 3-26Characteristicsofasamplerecessedelectrettransferfunction. .......... 148 3-27PhotographandschematicofUFAFFtestsectionouttwithfar-eldlinearmicrophonearray. ......................................... 149 3-28Two-dimensionalshearlayerrefractionprocessforthecaseofaplanethickshearlayer. .......................................... 149 3-29PlanararrayofMmicrophonesbeamformingtoascanningplaneofLgridpoints.[FigureadaptedwithpermissionfromauthorsofYardibi,T.,Zawodny,N.S.,Bahr,C.,Liu,F.,Cattafesta,L.,&Li,J.2010ComparisonofMicrophoneArrayProcessingTechniquesforAeroacousticMeasurements.(page736,Figure1),InternationalJournalofAeroacoustics,9(6),732-762.] .............. 150 3-30FFMAdesignparametersandillustrationofouterarraymicrophonespirallayout. 150 3-31Thefree-eldmicrophonearray(FFMA). ...................... 151 3-32ResolutionoftheouterFFMAasafunctionoffrequencyandtheoreticalPSFperformanceatoctavebandfrequencies. ...................... 152 3-33IllustrationoftraditionalPIVdataacquisition. .................. 153 3-34PhotographofSPIVsetupintheUFAFFandvirtualrenderingofSPIVsetupillustratinglightsheetdevelopment. ......................... 153 3-35ComponentbreakdownoftheLaVisionImagerproXPIVcamera. ....... 154 3-36SeederapparatususedforSPIVexperiments. ................... 154 3-37SPIVmeasurementplanesofthebaselinemodeloweld. ............ 155 3-38IllustrationofPIV-pressureprobedataacquisitionmethodformtdLSE-PODexperiments. ...................................... 155 3-39Flowchartillustratingthestaticestimationprocedure. .............. 156 3-40ModelsensorlocationsforPIV-estimationexperiments. .............. 156 3-41FlowchartofthePowerFLOWsimulationprocedure(adaptedfrom Exa ( 2011 )). 157 3-42ComputationalgridresolutionofthePowerFLOWtorquearmsimulations. ... 157 3-43VisualizationofthethreeosetVRregionsofoneofthetorquearms. ...... 158 3-44ProleandfrontviewsofthefourouterVRregions. ............... 158 13

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3-45VisualizationofthethreeosetVRregionsofoneofthetorquearms. ...... 159 3-46PowerFLOWsimulationenvironmentwithindicatedboundaryconditions. ... 159 3-47TimehistoryofPowerFLOW-simulatedliftanddragcoeentsexhibitedbythetorquearmmodel. .................................. 160 3-48MeanowresultsforthetorquearmPowerFLOWsimulation. .......... 160 4-1Illustrationofthesteadypressuremeasurementregionsonthetorquearmmodel. 209 4-2CircumferentialCpdistributionsofthebareandtrippedcylinderatthe4dierentspanwisemeasurementlocationsandacomparisonwiththeresultsof Roshko ( 1961 ). ......................................... 210 4-3TorquearmcylindersteadycircumferentialCpdistributionsatdierentspanwiselocations. ....................................... 211 4-4SteadyCpdistributionsofthetorquearmgapowsurfacefordierentmodelcongurations. .................................... 212 4-5ObservationoftorquearmtransientCpbehaviorfor=160. .......... 213 4-6Pressuresampledistributionsofuppercornerpressuremeasurementlocationsontorquearmgapowsurface. ........................... 214 4-7Steadypressuresofthetorquearminvertedbaselineconguration. ....... 215 4-8MeanmodelCpcomparisonsbetweenexperimentandsimulationruns. ..... 216 4-9Simulationresultsforthemeanmagnitudeofvelocityandxystreamlinesatselectplanesintheoweld. ............................ 217 4-10Comparisonofsurfacepressurepowerspectraldensitiesforthebareandtrippedmodelcylinderatthemodelcenterline(Z=0)andatacircumferentiallocationof=135. ...................................... 218 4-11Spanwisecoherenceoftrippedcylindersensorsrelativetocenterlinesensor. ... 218 4-12DemonstrationoffrequencyandpressurePSDamplitudescalingforacylinderandtorquearmsensor(=130). ......................... 219 4-13Powerspectraldensitiesofcylinderandtorquearmrecessedelectretsforthebaselinemodelconguration(=130,U1=58m/s). .............. 220 4-14Sampledistributionfunctionsofthe4torquearmrecessedsensorsfor=130,U1=58m/s. ..................................... 221 4-15SurfacePSDofselectcylinderandtorquearmpressuresensorsforprimarymodelcongurationsatafreestreamvelocityofU1=58m/s(M=0.167). ...... 222 14

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4-16EntiremodelsurfaceSPLmapspresentedin1/3octavefrequencybands. .... 223 4-17Coherencemeasurementsofcylinderunsteadypressuresensorsrelativetothecenterlinesensor,Z=0formodelprimarycongurations. ............ 224 4-18Coherencemeasurementsbetweencylinderandtorquearmelectretsensors,for=100conguration. ................................ 225 4-19Coherencemeasurementsbetweencylinderandtorquearmelectretsensors,for=130conguration. ................................ 226 4-20Coherencemeasurementsbetweencylinderandtorquearmelectretsensors,for=160conguration. ................................ 227 4-21Coherencemeasurementsbetweencylinderandtorquearmelectretsensors,for=130invertedconguration. ........................... 228 4-22SurfacepressureprobePSDcomparisonsbetweenexperimentandsimulation. 229 4-23Far-eldSPLcomparisonsofmodelcongurations(lineararraymicrophoneL4). 230 4-24Far-eldSPLcomparisonsofallstandardmodelcongurations(100f800Hz)atM0.167. .................................... 230 4-25OASPLasafunctionofshearlayer-correctedmicrophoneanglesforalltorquearmcongurationsatM0.167. ........................... 231 4-26CoherencebetweenmodelsensorsandlineararraymicrophoneL4. ........ 232 4-27ApplicationofStrouhalandpower-of-velocityscalingtofar-eldspectraofthe=100conguration. ................................ 233 4-28ApplicationofStrouhalandpower-of-velocityscalingtofar-eldspectraofthe=130conguration. ................................ 234 4-29ApplicationofStrouhalandpower-of-velocityscalingtofar-eldspectraofthe=160conguration. ................................ 235 4-30Illustrationofspectralscalingforselectmodelunsteadypressuresenorsforthe=160conguration. ................................ 235 4-31ApplicationofStrouhalandpower-of-velocityscalingtofar-eldspectraofthe=130invertedconguration. ........................... 236 4-32IllustrationoftheboundingboxfortheporousFW-Hcalculation. ........ 237 4-33Comparisonoffar-eldSPLfromsolidandporousFW-Hsolveroutputstothatoftheexperimentallineararraymicrophone. .................... 237 4-34Comparisonoffar-eldSPLfromsolidandporousFW-Hsolveroutputstothatoftheexperimentallineararraymicrophone. .................... 238 15

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4-35Comparisonofbeammapsforthedierentbeamformingalgorithmsatanarrowbandfrequencyof4kHzforthe=130congurationatM0.167. .......... 239 4-36Integratedlevel-spectraoftheDASandDAMASbeamformingalgorithmswithcomparisontoFFMAreferencemicrophone. .................... 240 4-37Comparisonoffar-eldSPLbetweenFFMAcenterreferencemicrophoneandfree-eldmicrophonepositionedonoppositesideoftestsection. ......... 241 4-38BeamformingmapsusingDASandRCBalgorithmsatoctavebandfrequenciesforthe=100congurationatM0.167. ..................... 242 4-39BeamformingmapsusingDASandRCBalgorithmsatoctavebandfrequenciesforthe=130congurationatM0.167. ..................... 243 4-40BeamformingmapsusingDASandRCBalgorithmsatoctavebandfrequenciesforthe=160congurationatM0.167. ..................... 244 4-41BeamformingmapsusingDASandRCBalgorithmsatoctavebandfrequenciesforthe=130invertedcongurationatM0.167. ................ 245 4-42NoisesourcemapsusingtheDAMASalgorithm(10,000iterations)ofprimarycongurationsatnarrowbandfrequenciesof1.008and2kHzatM0.167. .... 246 5-1Contoursofmeanvelocitymagnitude,TKE,andZ-vorticitywithgapowmeanvelocityandReynoldsstressprolesataheightofZ=0. ............. 285 5-2Contoursofmeanvelocitymagnitude,TKE,andZ-vorticitywithgapowmeanvelocityandReynoldsstressprolesataheightofZ=1.175D. ......... 286 5-3Contoursofmeanvelocitymagnitude,TKE,andZ-vorticitywithgapowmeanvelocityandReynoldsstressprolesataheightofZ=2.175D. ......... 287 5-4Contoursofmeanvelocitymagnitude,TKE,andZ-vorticitywithgapowmeanvelocityandReynoldsstressprolesataheightofZ=3D. ............ 288 5-5ComparisonsofnormalizedvelocitymagnitudeandTKEbetweenSPIVmeasurementsandPowerFLOWataheightofZ=0. ....................... 289 5-6ComparisonsofnormalizedvelocitymagnitudeandTKEbetweenSPIVmeasurementsandPowerFLOWataheightofZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(3D. ..................... 290 5-7ComparisonofReynoldsstressesatZ=0betweenSPIVandPowerFLOWatmid-wayslicebetweencylinderandtorquearm. .................. 291 5-8ComparisonofReynoldsstressesatZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(3DbetweenSPIVandPowerFLOWatmid-wayslicebetweencylinderandtorquearm. ................ 292 5-9InstantaneoussnapshotsofZ-vorticityinthegapowregionsforheightsofZ=0,-1.175D,-2.175D,and-3D. ............................ 293 16

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5-10ComparisonsofinstantaneoussnapshotsofZ-vorticitybetweenexperimentandPowerFLOWsimulationinthegapowregionsforheightsofZ=0and-3D. 294 5-11PODmodalenergybreakdownforgapowandnearwakeregionsofZ=0Dand)]TJ /F1 11.955 Tf 9.29 0 Td[(3D. ....................................... 295 5-12ContoursoftherstfourPODspatialmodesofuvelocity(u)forthegapowandnearwakeregionsatZ=0. ........................... 296 5-13ContoursoftherstfourPODspatialmodesofvvelocity(v)forthegapowandnearwakeregionsatZ=0. ........................... 297 5-14ContoursoftherstfourPODspatialmodesofuvelocity(u)forthegapowandnearwakeregionsatZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(3D. ......................... 298 5-15ContoursoftherstfourPODspatialmodesofvvelocity(v)forthegapowandnearwakeregionsatZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(3D. ......................... 299 5-16Meanestimationdierencesforgapowandnearwakemeasurementregions. 300 5-17Cross-correlationsbetweencylinderandtorquearmsensors. ........... 300 5-18Resultsofmtd-mLSEapplicationtoZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(3DgapowPODdatausingr=5,10,and20modesandmodalenergysummationsfortherst50modes. ..... 301 5-19SinglesnapshotcomparisonforthegapowregionatZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(3DbetweenoriginalSPIVvectoreld,low-orderrepresentationusing5PODmodes,andestimateusingmtdLSE-POD. ................................. 302 5-20SinglesnapshotcomparisonforthenearwakeregionatZ=)]TJ /F1 11.955 Tf 9.29 0 Td[(0:592DbetweenoriginalSPIVvectoreld,low-orderrepresentationusingvePODmodes,andestimateusingmtd-mLSE. .............................. 303 5-21ContoursofthesecondandtwelfthPODspatialmodesofuvelocity(u)forthegapowregionatZ=)]TJ /F1 11.955 Tf 9.29 0 Td[(3Dsubjectedto100,200,400,and800snapshotsinputintothePODsolver. .............................. 304 5-22Comparisonofinstantaneousvorticitysnapshotreproductionusingtherstve,ten,andacustomsetoftenPODmodes. ..................... 305 5-23ComparisonofPODmodalenergyfractionsbetweenSPIVandPowerFLOW. 306 5-24ComparisonoftherstvestreamwisePODmodesbetweenPowerFLOWandSPIVforZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(3Dgapowregion. ......................... 307 5-25ComparisonoftherstfourstreamwisePODmodesbetweenPowerFLOWandSPIVforZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(3Dnearwakeregion. ........................ 308 5-26ComparisonofinstantaneoussnapshotsofLx;1inthegapowregionatZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(3DbetweenexperimentalSPIVandPowerFLOW. ................ 308 17

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5-27ComparisonofsimulationsnapshotsatZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(3DbetweenLx;1andLx=Lx;1+Lx;2. .......................................... 309 5-28Visualizationofa5-modeestimationofaninstantaneoussnapshotoftheLambvectorpartialcomponents. .............................. 310 5-29PODmodalenergybreakdowncomparisonsbetweengapowregionsZ=)]TJ /F1 11.955 Tf 9.29 0 Td[(0:592D,)]TJ /F1 11.955 Tf 9.3 0 Td[(2:175Dand)]TJ /F1 11.955 Tf 9.3 0 Td[(3D. .................................. 311 5-30Resultsofa10-modeestimationofLx;1andLy;1fortheZ=)]TJ /F1 11.955 Tf 9.29 0 Td[(0:592Dgapowregion. ......................................... 311 5-31ComparisonofestimationresultsforLx;1andLy;1usingveandtwentymodesfortheZ=)]TJ /F1 11.955 Tf 9.29 0 Td[(0:592Dnearwakeregion. ....................... 312 5-32Band-limitedintegrationof~Lx;1and~Ly;1PSDsforthegapowregionataheightofZ=0fromPowerFLOWandSPIV. ....................... 313 5-33ComparisonbetweenrsttwouctuatingstreamwisePODmodesfromZ=0gapowregionfromSPIVandtherstmodefromPowerFLOW. ........ 314 5-34Band-limitedintegrationof~Lx;1and~Ly;1PSDsforthegapowregionattheheightsofZ=0:592D,)]TJ /F1 11.955 Tf 9.3 0 Td[(1:175D,and)]TJ /F1 11.955 Tf 9.3 0 Td[(2:175DfromexperimentalSPIVdata. 315 5-35Band-limitedintegrationof~Lx;1and~Ly;1PSDsforthenearwakeregionattheheightsofZ=0and)]TJ /F1 11.955 Tf 9.3 0 Td[(0:592DfromexperimentalSPIVdata. .......... 316 5-36Comparisonofband-limitedintegrationsof~Lx;1and~Ly;1PSDsforthegapowregionataheightofZ=)]TJ /F1 11.955 Tf 9.29 0 Td[(3DbetweenPowerFLOWsimulationandexperimentalSPIVdata. ...................................... 317 5-37GapowregionsinglepointPSDsofLambvectorpartialterms. ......... 318 5-38NearwakeregionsinglepointPSDsofLambvectorpartialterms. ........ 319 5-39Simulatedband-limitedmeansquarevaluecontoursofpartialandfullLambvectorcomponentsatZ=0. ............................. 320 5-40Non-dimensionalLambcomponentpowerspectraatselectpointsinZ=0regionindicatedinFigure 5-39 ........................... 321 5-41Simulatedband-limitedmeansquarevaluecontoursofpartialandfullLambvectorcomponentsatZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(1D. .......................... 322 5-42Non-dimensionalLambcomponentpowerspectraatselectpointsinregionZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(1DindicatedinFigure 5-41 ............................ 323 5-43Simulatedband-limitedmeansquarevaluecontoursofpartialandfullLambvectorcomponentsatZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(2D. .......................... 324 18

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5-44Non-dimensionalLambcomponentpowerspectraatselectpointsinregionZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(2DindicatedinFigure 5-43 ............................ 325 5-45Simulatedband-limitedmeansquarevaluecontoursofpartialandfullLambvectorcomponentsatZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(3D. .......................... 326 5-46Non-dimensionalLambcomponentpowerspectraatselectpointsinregionZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(3DindicatedinFigure 5-45 ............................ 327 5-47NormalizedeldpowerspectraofLxandLyatZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(3Dforfrequenciesof144,240,and336Hz. ................................. 328 5-48SimulatedeldpowerspectraofLxandLyatafrequencyof2kHz. ....... 329 5-49NormalizedeldpowerspectraofjrTijjatZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(3Dforfrequenciesof144,240,and336Hz. ................................... 330 5-50SimulatedeldpowerspectraofjrTijjatafrequencyof2kHz. ........ 331 6-1Illustrativecomparisonbetweensharpandroundededgesofthetorquearm. .. 341 6-2Illustrationoftheadditionofnoselandinggearwheelstothetorquearm. .... 341 A-1CircuitdiagramandPCBlayoutfortheKulitein-lineamplier. ......... 345 A-2AssembledKulite-amplierpackage. ........................ 345 A-3ComplexgainfrequencyresponseofKuliteamplierinterfacecircuits. ...... 346 A-4IllustrationofimprovedperformanceofKulitein-lineampliers. ......... 347 B-1Schematicoflenstelescopeassembly.Notethatthedimensionsareinmm. ... 355 B-2Illustrationoflaserpulsecalibrationsourcesetupandphotographofsparksourceoccurrence. ...................................... 356 B-3Phasedarraylocationsrelativetosparksourceforarraystaticcalibrationruns. 356 B-4TemporalandspectralperformanceoflaserpointsourcebasedonFFMAcenterreferencemicrophone. ................................ 356 B-5FFMAtheoreticalandexperimentalPSFperformancefordierentstaticcalibrationlocations. ....................................... 357 B-6Imageoflasertelescope,phasedarrayandtorquearmmodelinstalledwithintestsectionforphasedarrayin-situcalibration. .................. 358 B-7SpectralcontentofthelaserpulsesetupasmeasuredbytheFFMAcentermicrophoneforstaticandowcalibrationcases. ......................... 358 19

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B-8Eectofperformingin-situgrouparraycalibrationonbeamformingoflaserpointsourceatM0.167forafrequencyof4.992kHz. .................. 359 B-9Eectofperformingin-situgrouparraycalibrationonDASbeamformingoftorquearm=130congurationatM0.167forafrequencyof4.992kHz. ... 360 C-1IllustrationofcommonSPIVcamerasetupwithschematicsillustratingreconstructionof3-dimensionaldisplacementvector. ........................ 367 C-2ProleanddownstreamviewsoftheexperimentalSPIVcameraconguration. 368 D-1Thesoundpressureleveldistributionoverthearrayfaceatoctavebandfrequencies. 371 D-2Thephasedistributionoverthearrayfaceatoctavebandfrequencies. ...... 372 20

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AbstractofDissertationPresentedtotheGraduateSchooloftheUniversityofFloridainPartialFulllmentoftheRequirementsfortheDegreeofDoctorofPhilosophyAEROACOUSTICCHARACTERIZATIONOFSCALEDCANONICALNOSELANDINGGEARCONFIGURATIONSByNikolasS.ZawodnyMay2013Chair:LouisN.CattafestaIIIMajor:MechanicalandAerospaceEngineering Aircraftnoiseisacriticalissueinthecommercialairlineindustry.Airframenoiseisasubcomponentofaircraftnoiseandisgenerallydominantoverjetenginenoiseduringapproachconditions,whichcanleadtohighcommunityimpact.Landinggearshavebeenidentiedasmajorcomponentsofairframenoiseduringlandingcongurationsforcommercialaircraft.Theyareperhapstheleastunderstoodcontributorstoairframenoiseduetocomplexowpatternsassociatedwithintricategearcomponentgeometries.Noselandinggearinparticularhavereceivedmuchattentioninrecentyears,exhibitingacousticsignaturesontheorderofthemainlandinggearassemblyofanaircraft,whilesimultaneouslybeingmoreamenabletoscaledwindtunneltesting.Inordertocharacterizetheacousticsignatureofacomplexgeometrysuchasanoselandinggear,itisimportanttoisolate,study,andunderstandtheacousticcontributionsofindividualcomponentgeometries. Thepurposeofthisdissertationistodevelopacorrelationbetweenthecomplexoweldnatureandfar-eldacousticsignatureofanoselandinggearsub-system.Themodelunderinvestigationisa1/2-scaleshock-strutcylindercoupledwithanadjustabletorquelinkapparatus.Thisgeometrywaschosenduetoitsfundamentalimportanceandimplementationacrossawidespanofcommercialaircraft.Theuiddynamic(surfacepressureandstereoscopicparticleimagevelocimety)andaeroacoustic(far-eldmicrophoneandphasedarray)experimentswereperformedintheUniversityofFlorida 21

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AeroacousticFlowFacility.TheexperimentaldatacomparefavorablywiththeresultsofanumericalsimulationusingPowerFLOW,alattice-BoltzmannsolverdevelopedbytheExaCorporation. Thefar-eldacousticresultsofthisdissertationhaveshownnon-uniformscalingbehaviorasafunctionoffrequencyforthedierentmodelcongurationstested.Forfrequenciesthatappropriatelysatisedtheconditionofacousticcompactness(ka<<1),thetestedcongurationsdisplayedsoundpressurelevelsthatscalewitheitherafthorsixthpowerofvelocityversusnon-dimensionalfrequency(Strouhalnumber).Abovethisfrequencyrange,theyscalewithaseventhpowerofvelocityversusdimensionalfrequency.Alow-noisecongurationwasalsoidentiedthatconsistedofthetorquearmgeometrybeinginaninvertedorientation,whichiscommontomanyaircraftmainlandinggears.Low-orderestimatesoftheacousticsourcetermsofthevortexsoundanalogycomparedverywellwithsimilarlow-ordermodelsofthesimulatedoweld.Thesimulationalsoprovidedoweldinformationotherwiseunattainablethroughexperimentalmeans.Theseresultsindicatethattheprimaryvortexsoundsourcesatlowfrequenciesareunsteadyvorticity-velocityinteractionsalongthesharpedgesofthetorquearmswithsecondarynoisecontributorsbeingtheimpingementofvorticesshedfromthecylinderontothetorquearmsurface.Theuseofthephasedmicrophonearrayforbeamformingatfrequenciesabove1kHzrevealedthatthetorquearmsalsobehaveasbroadbandnoiseproducers. 22

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CHAPTER1INTRODUCTION Airframenoisegenerationofcommercialaircrafthasattractedmuchattentioninrecentyears.Withincreasedpopulationdensitiesinareaswithincloseproximitytocommercialairports,theFederalAviationAdministration(FAA)hasimposedincreasinglystrictregulationsonaircraftnoiselevels( FAA 2009 ).Whileaircraftengineshavebeenidentiedasanobviousculprit,advancesinhigh-bypassratioturbofanshavereducedtheircontributiontotheoverallaircraftnoise( Morgan&Hardin 1975 ).Inaddition,duringcommercialaircraftlandingprocedures,theenginesareinanidleconguration.Thiscausestheenginestocontributeonlyafractionofthetotalaircraftnoise,leavingthenoisegeneratedbytheairframeitself.AschematicoftheprimarynoisesourcesonamoderncommercialaircraftisshowninFigure 1-1 .Ofthenoisesourcesshown,landinggearshavebeenidentiedasadominantsourceformanycommercialaircraftduringapproachcongurations( Khorramietal. 2008 ; Micheletal. 1998 ; Pietetal. 1999 ). 1.1Motivation Thegeometriccomplexityofcommercialaircraftlandinggearspresentsinterestinghydrodynamicandaeroacoustictechnicalchallenges.Recentadvancesincomputationaluiddynamics(CFD)andcomputationalaeroacoustics(CAA)haveenabledpredictionsofthefar-eldacousticsignatureofcertainsimplecongurations,suchasthatduetoowoveracylinder( Orsellietal. 2009 )oroverthetrailingedgeofanairfoil( Winkleretal. 2009 ).Unfortunately,performingsuchcomputationsondetailedlandinggeargeometriesiscurrentlyinfeasible.Thisisbecauseahigh-speedowoveralandinggearcomposedofmultiplegeometriesofnumerouslengthscalesresultsinahighlythree-dimensionalturbulentoweldthatistoocomplexforcurrentCFDandCAAmethods( Spalartetal. 2010 ).Thus,theneedforexperimentalstudiesofsuchscenariosisrequired. Fundamentally,theindividualcomponentsthatmakeupalandinggearcanbeviewedasacollectionofblubodiesofdierentcharacteristiclengthscalessubjectedto 23

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afreestreamowU1.OneofthecharacteristicsofowoverablubodyisafrequencyfatwhichvorticesareshedfromthebodywithacharacteristiclengthscaleL,knownasthevortexsheddingfrequency( Howe 2003 ).ThissheddingfrequencyischaracterizedbythedimensionlessStrouhalnumberSt=fL U1,whichisconstantoverawiderangeofReynoldsnumbersRe=U1L ( Bearman 1969 ).Notethatandrepresentthemeandensityanddynamicviscosityofthefreestreamow,respectively.Despitethewell-knowntonalcontentassociatedwithvortexshedding,acoustictestsontypicallandinggeargeometrieshaverevealednocharacteristicsheddingtones.Instead,acousticsignaturesofthesegeometriesarecharacterizedasbeingmorebroadbandinnature,typicallytiedtoturbulentuiddynamics( Astleyetal. 2008 ).Onepossiblecauseofthisbehavioristhevorticalinteractionsbetweenclosely-spacedcomponentsinwhichtheproximityofthegeometriespreventsthefulldevelopmentofsheddingvortices.Suchnon-intuitiveacousticbehaviorprovidesevidencethattheisolationandanalysisofindividuallandinggearsub-systems,asopposedtoindividualcomponents,mustbeperformedinordertodeterminetheturbulentowdynamicsresponsibleforsuchdeviations. Thepresentresearchintendstocharacterizethenear-eldhydrodynamicsandfar-eldacousticsofascaledmodelofanoselandinggearsub-systemofvariablegeometry.Thissub-systemwaschosenforstudyduetoitsstructuralsignicanceandiscommontoawiderangeofcommercialaircraftlandinggears.Whiletheindividualgeometriesthatmakeupthecompletetestingmodelaresimpleandlackthenedetailsofanactualnoselandinggearsystem,theircombinationpresentsaneectiveexperimentalbaselinethatisstillrepresentativeofagearsub-assembly.Previousworkonsimilarmodelshasbeenperformedtoanextenteithertotesttheapplicationofanactivenoisereductiontechniqueonaxedgeometry( Huangetal. 2010 ),oramorecomplexmodelofanentirenoselandinggearwithsuchageometryasabuilt-insub-system( Neuhartetal. 2009b ; Zawodnyetal. 2009 ).Whilethesestudieshaveaidedinidentifyingcertainaerodynamicandacousticfeaturesofsuchgeometries,theydonotprovidein-depth 24

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informationconcerningtheconnectionbetweentheturbulentownatureandfar-eldacousticradiation.Datasetsofbothnear-eldhydrodynamicsandfar-eldacousticswillbeacquiredwiththegoalofdeterminingtheseconnections. Inthischapter,adiscussionofthestructuraldynamicscommontomanycommercialaircraftlandinggearswillrstbepresentedinordertoestablisharealisticframeworkforalandinggearmodel.Then,anoverviewofthephysicsofairframenoisegenerationisdiscussed.Thisisthenfollowedbyanoverviewofunresolvedtechnicalquestionsregardingaeroacousticcharacterizationoflanding-geargeometries.Finally,adiscussionoftheobjectivesandexpectedcontributionsofthisresearchwillbepresented. 1.2LandingGearStructuralDynamics Thelandinggearsareavitalaircraftsystem.Theprimaryfunctionsofanaircraftlandinggeararetoeectivelyabsorbthekineticenergyduetoaircrafttouchdown,attenuatethepropagationofimpactloadsexperiencedbytheaircraft,andminimizepassengerdiscomfort( Wei&Nie 2005 ).Duetothepurelystructuralnatureofthelandinggear,itisunderstandablethatithasthepotentialofproducingundesirableeectsontheaerodynamicperformanceofanaircraft.Forcommercialaircraftinparticular,landinggearsaregenerallyregardedasthemostaerodynamically\unfriendly"geometriespresentontheairframe,consistingofbulkyandcomplexstructuresthatcreateadditionalweightandinducedrag( Boorsmaetal. 2008 ).Consequently,thesegeometriestendtobecomeconsiderablenoiseproducerswhendeployedforlanding,especiallyforlargeaircraft.Tomitigatetheseadverseeectsduringaircraftcruiseconditions,retractablelandinggearsareimplemented.Unfortunately,theuseofretractablegearsusuallyimpliestheinclusionofadditionalelectricalandhydraulicequipment,thusincreasingtheweightoftheaircraft( Krugeretal. 1997 ).Thisisagreatexampleoftheconictingdesignrequirementsthatengineersandaerodynamicistsmustsatisfyinaircraftdesign. Formostcommercialaircraft,therearetwotypesoflandinggearspresentontheairframe:mainlandinggear(MLG)andnoselandinggear(NLG).Inadditiontothe 25

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primarygearfunctionsmentionedpreviously,MLGandNLGhavespecializedfunctionsoftheirown. 1.2.1MainLandingGear CommercialaircraftMLGaretypicallythelargerandheavierofthetwotypesduetotheircloserproximitytotheaircraftcenterofgravity(COG).Inaddition,theirnetweightincreasecanbeattributedtothepresenceofbrakingsystemswhicharegenerallynotpresentonNLG( Krugeretal. 1997 ).Figure 1-2 showsapairofimagesofaGulfstreamG550MLGwithkeystructuralcomponentslabeled.Oftheselabeledcomponents,theonesmostcommonacrosspracticallyallcommercialaircraftMLGarethetires,brakingsystem,andanoleo-pneumaticshockabsorberstrut(abbr.shockstrut).Theshockstrutistheprimarydampingmechanismresponsibleforverticalenergydissipationandisdiscussedinmoredetailinthenexttwosections. TheprimarystructuralissueassociatedwithMLGsisbrake-inducedvibration.Brake-inducedvibrationsaregearoscillationsthatoccurinthefore-aftdirectionofthegearandoccurduetothefrictiongeneratedbetweenthebrakesystem'srotatingandnon-rotatingpartsduringaircrafttouchdown( Pritchard 2001 ).Whilerecenttechnologicaladvancesingear-brakingtechnologyhaveledtothedevelopmentofsmallerbrakesandlightershockstrutsmadeofhigherstrengthmaterials,theseeortsincreasethelikelihoodoftheoccurrenceofMLGbrake-inducedvibrations.Thisisdemonstrativeofthetrade-obetweenreducingthesizeandweightofthegearstoimprovetheaerodynamicperformanceoftheaircraftattheexpenseofthestructuralreliabilityoftheMLGitself. 1.2.2NoseLandingGear WhilethespecializedfunctionofmostcommercialaircraftMLGisbraking,thatoftheNLGissteering( Pritchard 2001 ).ManyNLGhaveasteeringmechanismphysicallysecuredtotheprimaryshockstrut,allowingthepilottomanuallyrotatethestrutaboutitscentralaxis.Figure 1-3 showsapairofimagesofaG550NLGillustratingthissteering 26

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congurationalongwithotherprimarycomponentsindicated.Therotationaldegreeoffreedomassociatedwithasteerablelandinggeargivesrisetoanotherdynamicinstabilityproblemknownas\shimmy".Thefundamentalcauseofshimmyisatransferofenergyfromtheaircrafttothelateralandrotationalvibrationalmodesofthegearsystemduetolowstructuralstiness,wheelimbalances,freeplaybetweengearcomponents,and/orinsucientdamping( Pritchard 2001 ; Sateesh&Maiti 2009 ).Tomitigatetheoccurrenceofthisinstability,torsionalresistancemustbeprovidedwhichlinkstherotatingcomponentsoftheNLG(i.e.thewheelsandaxles)tothenon-rotatingones( Sateesh&Maiti 2009 ).Thisiscommonlyachievedwiththeuseofdevicesknownastorquearmsorlinks. 1.2.3TheShockStrutandTorqueArms Asidefromobviousrequiredcomponentssuchastiresandwheelaxles,thecomponentcommontobothMLGandNLGistheoleo-pneumaticshockstrut.Thetraditionalshockstrutisapassivepistondeviceinwhichanoilandagasarecombinedtoservetherespectivepurposesofdampingandstiening( Batterbeeetal. 2007 ).Anadditionalcomponenttocomplementthefunctionoftheshockstrutpresentonmoderate-tolarge-capacitycommercialaircraftNLGandMLGisthetorquelinkapparatus.Thisapparatusistypicallycomprisedoftwoarms-anupperandalowertorquearm-hingedtogetheratoneendwiththeotherendshingedtotheshockstrutandthewheelaxlerespectively(Figure 1-4A ).Thefunctionofthetorquearmsaretoprovidetorsionalrigiditybetweentheaxleandshockstruttoassistinattenuatingshimmyeects,whileallowingrelativemotionofthepistonwithintheshockstrut( Sateesh&Maiti 2009 ).Figure 1-4 presentsapictoralrepresentationofthedeectionexperiencedbytheshockstrutandtorquelinkapparatusofagenericNLGduringtheaircraft'slandingprocedure.Thisshockstrut-torquearmcongurationispresentacrossavastrangeofcommercialaircraftandistheprimarymotivationforthemodeldesignedforthisdissertation. 27

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1.3LandingGearNoise Inanunsteadyuidow,surfacepressureuctuationshavethepotentialofpropagatingtotheacousticfar-eldassoundwaves.Thepresenceofsolidsurfaceswithinsuchaowcanhavedrasticeectsonthisow-generatednoise.Flow-generatednoiseistypicallydividedintotwoprimarycategories:tonalandbroadband.Tonalnoiserepresentsthatgeneratedbyperiodiceventsintheow(suchasvortexshedding),whilebroadbandnoiseischaracterizedbyrandomeventsusuallyassociatedwithturbulence,orregionsofhighvelocityuctuationsacrossabroadrangeoffrequencies( Astleyetal. 2008 ).Whenconsideringowaroundcomplexgeometriessuchasalandinggear,itisreasonabletoassumethatthefar-eldacousticsignatureofsuchastructurewouldbeacombinationofthesetwosourcetypes( Smith 2008 ). 1.3.1AerodynamicSound-GeneralTheory Intheearly1950s,JamesLighthilldevelopedananalogythatwouldservetobethefoundationofmoderntheoryofaerodynamically-generatedsound,orrathersoundgeneratedbyturbulenceinanunboundeduid( Howe 2003 ).Hisworkstatesthataerodynamicsoundisweakrelativetotheoverallmotionoftheuidandthesoundgeneratedintheuidowisonlyimportantintheregionsofturbulentuctuations.ThisallowstheseregionstobeisolatedandanalyzedusingtheNavier-StokesEquationsandanisentropicequationofstate: @ @t+@(ui) @xi=0;(1{1) @(ui) @t+@(uiuj+Pij) @xj=0;(1{2) c2o=@p @js=const:=p0 0:(1{3) 28

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NotethatEquations 1{1 and 1{2 arepresentedinindicialnotation,wherePijisthetotalstresstensorincludingpressureandviscousterms(Pij=(p)]TJ /F3 11.955 Tf 12.33 0 Td[(p0)ij)]TJ /F3 11.955 Tf 12.32 0 Td[(ij),istheuiddensity,ui(oruj)isthelocalvelocityvector,pisthepressure,andcoisthelocalspeedofsound.Inaddition,0=)]TJ /F3 11.955 Tf 12.08 0 Td[(oandp0=p)]TJ /F3 11.955 Tf 12.09 0 Td[(porepresenttheperturbedvaluesofthelocaldensityandpressurerelativetothoseoftheinnitehomogeneousmedium,respectively.AfterseveralstepsofmanipulationofEquations 1{1 and 1{2 ,theclassicalLighthill'sequationmaybeobtainedas @2 @t2)]TJ /F3 11.955 Tf 11.95 0 Td[(c2or2=@2Tij @xi@xj:(1{4) Notethatthesourcetermontheright-handsideofequation 1{4 ,knownasLighthill'sturbulencestresstensor,isdenedas Tij=uiuj+Pij)]TJ /F3 11.955 Tf 11.95 0 Td[(c2o()]TJ /F3 11.955 Tf 11.95 0 Td[(0)ij;(1{5) where ij=8><>:1ifi=j0ifi6=j9>=>;(1{6) istheKroneckerdelta,ortheidentitytensor.ForthespecialcaseoflowMachnumber,highReynoldsnumberow,boththedensityuctuationsintheoweldandtheviscousstresstensormaybeconsiderednegligible.Therefore,theLighthillstresstensorreducesto Tij0uiuj:(1{7) Ageneralexpressionforthesolutionofequation 1{4 maythenbeformulatedintermsofpressurewiththeaidofequation 1{3 p0=c2o0=1 4@2 @xi@xjZ8Tij rd8;(1{8) 29

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where8representsthevolumeinwhichthetheacousticeldisbeingevaluated,andrrepresentsthedistancefromtheacousticsource. Toillustratethenatureoftheacousticsourcetermontherighthandsideof 1{8 ,anorder-of-magnitudescalinganalysismaybeperformed.Thegoalofthisprocessistodemonstratetheradiationpatternsofthehypotheticalacousticsourcewithrespecttoowspeedandpropagationdistance.Therststepistodeneaphysicalapplicationforwhichcharacteristiclength,velocity,frequency,andpressurescalesmaybedened.AgoodfoundationforthisisLighthill'sanalysisofasubsonic,turbulentisothermaljet( Lighthill 1954 ).ThepertinentcharacteristicscalesarelistedinTable 1-1 andtheresultingorder-of-magnitudeapproximationsforthecomponentsoftheacousticsourcetermarepresentedinEquations 1{9 through 1{11 ( Hirschberg&Rienstra 2004 ). Z8d8/D3(1{9) Tij/oU2o(1{10) @ @xi=@ co@t/f co/Uo coD(1{11) Notethatthisanalysisutilizestheassumptionoffar-eldacousticradiation,inwhichthesignalisapproximatedasauniformspherically-spreadingpressurewave.Therefore,theacousticwaveisconsideredtoradiateradiallyoutward(intherdirection).Anadditionalassumptionisthattheowofinterestisinthelowsubsonicrange,orratherthefreestreamMachnumberisconsiderablylessthanunity:M=Uo co<<1.Thescalinganalysisisperformedinequation 1{12 wherethesourceterminequation 1{8 isreplacedwiththescalingtermspresentedinEquations 1{9 through 1{11 p0/Uo coD2)]TJ /F3 11.955 Tf 5.48 -9.68 Td[(D3oU2o r/U4o r(1{12) 30

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Furthermore,onemaydenetheradiatedacousticpowerWofthesystem,whichisproportionaltothesquareofthepressureeld, W/p02/U8o r2:(1{13) Theresultsoftheabovescalinganalysisindicatethattheacousticpowerradiatedbyaturbulentowregionscalesproportionaltotheeighthpowerofvelocityandinverselyproportionaltothesquareofpropagationdistancer.Physically,thisradiationpatternisindicativeofavolumetricdistributionofquadrupolesources( Crighton 1975 ).Inotherwords,Lighthill'sacousticanalogystatesthatthefar-eldacousticpressureeldofaregionofturbulenceinanotherwisesteadyowisidenticaltothatofaregionofquadrupoleacousticsourceswithnoow( Lighthill 1952 1954 ). 1.3.2AirframeNoiseGeneration Lighthill'sanalogywaslaterextendedtoincludetheeectsofthepresenceofsolidboundarieswithintheturbulentowregion,whichisthefoundationofairframenoisegeneration( Curle 1955 ).Thepresenceofasolidboundaryintheowincreasesthecomplexityoftheresultantacousticradiationpatternduetothereectionanddiractionofsoundwavesattheboundaries.ThegeneralsolutiontoLighthill'sequationaccountingforthepresenceofsolidboundariesisshowninequation 1{14 p0=1 4@2 @xi@xjZVTij rdV| {z }I)]TJ /F1 11.955 Tf 16.02 8.09 Td[(1 4@ @xjZSPij+vivj rnidS| {z }II+1 4@ @tZShvi rinidS| {z }III;(1{14) whereSrepresentsthecontrolsurfaceboundingthevolumetricregionofinterest( Hirschberg&Rienstra 2004 ).BycomparingEquations 1{8 and 1{14 ,itcanbeseenthattwoadditionaltermsarepresentontheright-handsideofthelatter.Ascalinganalysis( Hirschberg&Rienstra 2004 )canbeperformedonthesenewtermsusingtheparametersdenedinEquations 1{9 through 1{11 : 31

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II:1 4@ @xjZSPij+vivj rnidS/Uo coDoU2o r)]TJ /F3 11.955 Tf 5.47 -9.68 Td[(D2/U3o r(1{15) III:1 4@ @tZShvi rinidS/Uo DoUo r)]TJ /F3 11.955 Tf 5.48 -9.68 Td[(D2/U2o r:(1{16) Finally,thesesourceapproximationsmaybeconvertedintotheirequivalentacousticpowers: II:W/p02/U6o r2;(1{17) III:W/p02/U4o r2:(1{18) Physically,termIItranslatestoasurfacedistributionofdipolesourcescausedbylocaluctuatingstressesexertedbythesurfaceontheuid,whiletermIIIrepresentsamonopolesoundeldgeneratedbymass-uxthroughtheboundingsurfaceS( Curle 1955 ; Hirschberg&Rienstra 2004 ).Sincethisscalinganalogyisbasedonowinthelowsubsonicrange(M<<1),observationofEquations 1{13 1{17 ,and 1{18 showsthatgoingfromaquadrupoletoadipoletoamonopolesourcerepresentsanincreaseinradiationeciency. Tosummarize,aseriesofscalinglawshavebeendenedthatassistwiththediscernmentofthepotentialacousticpowerradiationpatternswithrespecttomeanowspeedandpropagationdistanceinthecaseofthepresenceofasolidboundarywithinaregionofturbulentuidow.Thesetrendscanbeveryusefulindeterminingthenatureofacousticsourcespresentincomplexaerodynamicows,suchasthataroundlandinggears. 1.3.3TheVortexSoundAnalogy In1964,AlanPowellproposedanalternateapproachtotheacousticanalogythatshowshowaerodynamicsoundisgeneratedasaresultofthemovementofvorticesin 32

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anunsteadyuidow( Powell 1964 ).Itwaslaterre-iteratedby Howe ( 1975 )thatthe\...dynamicalsourceofsoundinlowMachnumberturbulencecanbeidentiedpreciselywiththoseregionsoftheowinwhichthevorticityvectorisnon-vanishing."ThisvortexsoundtheoryisdirectlycompatiblewiththatofLighthill'sinthatthesourcetermsofLighthill'sanalogyrepresentthetransferofvorticityandeddyformation.Thedierentialformofthevortexsoundequationisdenedas r2p)]TJ /F11 11.955 Tf 11.96 16.86 Td[(1 c20@2p @t2=r264(!u)| {z }I+r1 2u2| {z }II)]TJ /F9 11.955 Tf 11.29 0 Td[(u@ @t| {z }III)]TJ /F1 11.955 Tf 12.49 8.09 Td[(1 2u2r| {z }IV375:(1{19) wheretheacousticsourcetermsarelabelednumericallyontherightsideoftheequation.NotethatforsubsonicowsinwhichtheassumptionofM2<<1holdstrue,sourceterms(III)and(IV)areconsideredtobenegligible,leavingonlythesourceterms(I)and(II).Furthermore,term(II)endsupbeingconsiderablysmallerthanterm(I)inaturbulentowwhereM<<1andRe>>1.Therefore,thisleavesonlyterm(I),whichiscommonlyreferredtoastheLambvector: L=!u:(1{20) Now,withtheseassumptions,thesimpliedvortexsoundequationmaybere-writtenas r2p)]TJ /F11 11.955 Tf 11.96 16.86 Td[(1 c20@2p @t2=)]TJ /F3 11.955 Tf 9.3 0 Td[(0rL:(1{21) Decompositionofthevorticityandvelocitytermsintomeananductuatingcomponents,!i=i+!0iandui=Ui+u0irespectively,impliesthatthereareactuallyfourcomponentsofEqn. 1{20 .However,thecomponentthathasthemostdirectcompatibilitywiththeacousticsourcetermofLighthill'sanalogy( Casalino&Barbarino 2011 )istheunsteadycomponent L00=!0u0:(1{22) 33

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ThesimilaritybetweenthesourcetermsofLighthillandPowellcanbeclariedusingtheidentity div(!0u0)=@2u0iu0j @xi@xj:(1{23) Notethattheright-handsideofthisexpressionisequaltothatofLighthill'sequation,Eq. 1{4 ,usingthereducedLighthillstresstensordenedinEq. 1{5 (withthedensity0removed).NotethatwhiletheoriginalLighthillstresstensorwasnotdenedusingtheuctuatingvelocityterms,thevelocityuctuationsareactuallythetermsofinterest.ThisisbecausetheyrepresenttheuctuatingReynoldsstressesthataremostresponsibleforthefar-eldpressureuctuations(p0)inLighthill'sanalogy. InthecaseofthepresenceofaxedsolidbodywithasurfaceSinaturbulent,lowMachnumberow,Howe'sequationcanbere-structuredtoyieldthedipolecontributiontothefar-eldradiatedsound.ConsiderauiddomainisdenotedasallthatcontainsSasaninnerboundaryandextendsfarenoughtocontainallofthevorticity.Ifanobserverxisfarenoughfromthesourceregion,thenGreen'stheoremcanbeusedtogetanexpressionforthesoundpressureatx: p0(x;t)=)]TJ /F3 11.955 Tf 9.3 0 Td[(0Zall(!0u0)rG(x;y;t)]TJ /F3 11.955 Tf 11.96 0 Td[()dyd:(1{24) whereG(x;y;t)]TJ /F3 11.955 Tf 11.95 0 Td[()istheGreen'sfunctionthatsatises 1 c20@2G @t2)-222(r2G=(x)]TJ /F9 11.955 Tf 11.96 0 Td[(y)(t)]TJ /F3 11.955 Tf 11.95 0 Td[()(1{25) intheuiddomain,and @G @n=0(1{26) onthesolidboundaryS.Undertheassumptionthatthesizeofthesourceregionissmallcomparedtotheacousticwavelengths,thenthesourceregionissaidtobeacousticallycompact( Takaishietal. 2004 ).Inthiscase,thedierencesbetweentheretardedtimesof 34

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pointswithinthesourceregionarenegligible.Therefore,Eq. 1{24 maybere-writtenas p0(x;t)=)]TJ /F3 11.955 Tf 20.68 8.09 Td[(0xi 4c0jxj2Zall@ @t(!0u0)(y;t)-222(jxj=c0)rYidy;(1{27) whereYirepresentsthevelocitypotentialofanidealowaroundthesolidbodyofinterest.Thisexpressionwaslateradaptedandmodiedby Takaishietal. ( 2004 )toevaluatethevortexnoisefromacylinderinanitecomputationaldomain.Inotherwords,considerthattheuiddomainisbrokendownaccordingtoallint[ext,andonlyintiscapableofbeingmeasured.ThisregionencompassesSandaniteregionofvorticity.Inthiscase,itisusefultodeneasecondvelocitypotentialithatwouldbeproducedbyrigidbodymotionofbodySatunitspeedintheidirectionandisrelatedtoYiby Yi=yi)]TJ /F3 11.955 Tf 11.96 0 Td[(i;(1{28) whereyiiswithrespecttothesoundsource.Finally,thedipolecontributiontothefar-eldsoundcanbewrittenas p0(x;t)=)]TJ /F3 11.955 Tf 20.68 8.09 Td[(0xi 4c0jxj2Zint@ @t[(!0u0)(y;t)-221(jxj=c0)ri]dy:(1{29) Thismethodcanalsobeappliedtoexperimentaloweldmeasurements,suchasPIV,thatarealsolimitedbyanitespatialmeasurementregion.Suchanapplicationwasperformedby Udaetal. ( 2011 )onthecaseofthewakebehindacircularcylinder.Thenominaltwo-dimensionalowscenarioallowedforapproximationofthefar-eldsoundviaanalysisofthex)]TJ /F3 11.955 Tf 11.95 0 Td[(yplane. Itisimportanttonotethatthismethodhassomelimitations.Namely,thesimplestformofthefar-eldprediction,Eq. 1{29 ,isdependentontwoimportantconditions:(1)thatthevelocitypotentialimustrepresentthesolidbodyinquestion,and(2)thatthesoundofinterestisgovernedbydipoleradiation.Theimportanceof(1)isthatiistypicallyonlyavailableforsimplegeometriessuchasacircularcylinder( Udaetal. 2011 )andaatstrip( Howe 2003 ).Formorecomplexgeometries,thisvelocitypotentialwould 35

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mostlikelyhavetobenumericallycomputed.Asforthesecondcondition,itimpliesthatthismethodonlyappliesforthefrequencyrangeinwhichthesolidbodyisacousticallycompact.Abovethisfrequencyrange,thegeneralvortexsoundsolutionofEq. 1{24 isrequired,whichrequiresknowledgeoftheGreen'sfunction. 1.3.4LandingGearNoiseSources AscanbeseeninFigures 1-2 and 1-3 ,thestructuralmake-upsofbothmainandnoselandinggearsarequitecomplex,consistingofnumerousgeometriesofmultiplelengthscalesanddierentinter-componentspacings.Thisimpliesthatinadditiontothenoiseproducedduetothepresenceofthesolidsurfacesintheow,somecomponentsmayalsocontributetothetotalnoiseasreectivesources.Ingeneral,thefar-eldnoisepropagationfromowoverlandinggearsmaybedividedintothreeprimaryfrequencyregimescontributedtobythefollowingcomponentsbasedonacousticcompactness( Guoetal. 2006 ): Low-frequencies(f<1kHz).Largegeometriessuchaswheelsanddoors. Mid-frequencies(1f4kHz).Mainstrutsandlinkages. High-frequencies(f>4kHz).Smalldetailssuchassharpedges,hoses,andelectricalwiring. Notethatthenumericvaluesofthesefrequencyrangesvaryfromaircrafttoaircraft,andareshownhereasapproximationsbasedonthendingsof Guoetal. ( 2006 )forafull-scaleBoeing737mainlandinggear. Sincethewavelengthofanacousticwaveinamediumisgovernedbyco=f,itcanbeseenthatradiatedfrequencyandacousticwavelengthareinverselyproportionaltooneanother.Therefore,atlow-andmid-frequencies,theacousticwavelengthsarelargerelativetothelengthscalesofthegeometriesresponsibleforthenoisegenerationatthesefrequencies.Inotherwords,kL<<1,wherek=2 istheacousticwavenumberandListhecharacteristiclengthscale.Thismeansthatthesegeometriesmaybeconsideredtobeacousticallycompact,andtheacousticradiationbehaveslikeadistributionofdipoles 36

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( Guoetal. 2006 ).Athighfrequencies,however,thesewavelengthsmaybecomeontheorderoforevensmallerthanthedimensionsofthegeometriescausingtheacousticsourcestobecomenoncompact(kL1).Thismanifestsitselfintheformofphasevariationsinthesurfacepressuresonthebodies,whichcausesmutualcancellationoftheiracousticradiationandnallydegradationoftheradiationeciency(e.g.fromadipoletoaquadrupolebehavior).Asonemightimagine,thepresenceofbothacousticallycompactandnoncompactsourcesonalandinggearmakequantifyingtheacousticsignaturequitechallenging.AvisualrepresentationofsomepossiblenoisecontributionmechanismsduetoturbulentowaroundagenericnoselandinggearcanbeseeninFigure 1-5 .Thesephysicalphenomenaaretheprimarymotivationsforthereviewofliteraturepresentedin Chapter2 1.4UnresolvedTechnicalIssues Whiletherehavebeenmanystudiesdedicatedtonoiseproducedbylandinggears,theyhaveeitherbeenonverygeneralgeometricarrangements(suchastandemcylinders)orextremelycomplexhigh-delityreplicasofanentirelandinggear.Thestudiesonthemoregeneralgeometriessuchastandemcylindersarebenecialinthatextensivedocumentationonboththeuiddynamicandacousticbehaviorsofsuchcongurationshasbeenperformed.Unfortunately,ageometrysuchasthisistoosimpletobedirectlyapplicabletoalandinggearsystem.Conversely,studiesoffulllandinggearreplicascanbetoocomplex,makingitdiculttodevelopadetailedunderstandingoftheowphysicsresponsiblefornoisegeneration.Therefore,theisolationanddetailedacousticanalysisofrepresentativegearsub-systemsmustbeperformedinordertobetterquantifytheirindividualacousticcontributions.Thishypothesisisconsideredindetailintheremainderofthisdissertation. 1.5ProposedResearch Theobjectiveofthisdissertationistocharacterizetheaerodynamicandacousticsignatureofarepresentativemodelofanoselandinggearsub-system.Whilethere 37

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havebeennumerousstudiesontheacquisitionandattemptedreductionoflandinggearfar-eldnoiselevels,therehasbeenlittleworkdoneoncorrelatingthenear-eldhydrodynamicswiththefar-eldacousticsofalandinggearorgearsub-systemgeometry.Theturbulentownatureduetothecomplex,three-dimensionalinteractionsbetweenthecomponentswillbeanalyzedalongwiththefar-eldacousticbehaviorfordierentcongurations.Validityoftraditionalacousticscalingforowoverblubodieswillalsobedeterminedalongwiththeidenticationofdominantnoisesourcesonthemodelfordierentcongurations.Theresultsofthisstudywillbenettheaeroacousticcommunitybyprovidinganin-depthlookattheowmechanicsresponsibleforlandinggearnoisegeneration,allowingforthedevelopmentandimplementationofnoisereductionmethods. 38

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Figure1-1. Potentialnoisesourcesonacommercialaircraft. A B Figure1-2. (A)Proleand(B)aftviewsoftheGulfstreamG550mainlandinggear(courtesyofGulfstreamAerospaceCorporation). 39

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A B Figure1-3. (A)Proleand(B)forwardviewsoftheGulfstreamG550noselandinggear(courtesyofGulfstreamAerospaceCorporation). A B Figure1-4. Illustrationofthe(A)pathofdeectionand(B)resultingcompressionofagenericNLGshockstrutandtorquearmsduringaircraftlandingprocedure. 40

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Figure1-5. Illustrationofpotentialnoisesourcesonagenericaircraftnoselandinggear. Table1-1. DimensionalParametersforAcousticSourceScaling DimensionParameterDenition LengthDdiameterofjetnozzleVelocityUojetvelocityatnozzleexitFrequencyf/Uo=Ddominantacousticfrequency(assumed)Pressure,StressoU2odynamicpressureofturbulentjet 41

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CHAPTER2LITERATUREREVIEW Thischapterprovidesareviewofaeroacousticresearchonaircraft,landinggear,andlandinggear\type"geometries.First,anoverviewofacoustictestingonfull-scaleaircraftandnoisepredictionstudieswillbepresented.Areviewofstudiesonlandinggearandlandinggear-typegeometriesincludingexperimentalandcomputationalstudieswillfollow.Eachofthesesectionsisconcludedwithatablesummarizingthekeyndingsoftheresearchedliterature.Finally,asummaryofunresolvedtechnicalissuesbasedonpreviousresearchwillbediscussed. 2.1TotalAirframeNoiseStudies Therstattemptsatidentifyingthecontributionsofindividualairframecomponentstotheoverallacousticsignatureofcommercialaircraftbeganwiththeuseofsinglemicrophonemeasurementsoftheaircraftperformingayover.Empiricalpredictionschemesdependentonparameterssuchasaircraftvelocityandsurfaceareawerethendevelopedtoapproximatetheoverallsoundpressurelevel(OASPL)ofanaircraft.Technologicaladvancesandimprovedcomputingpowereventuallyledtotheutilizationofphasedmicrophonearraystocreatespatialvisualizationsofthenoisesourcesontheaircraft.Whileexperimentalndingsastowhatairframecomponentsaredominantnoiseproducershavebeenfoundtovaryonaper-aircraftbasis,aircraftlandinggearshavebeenevidencedtobeimportantairframenoiseproducersacrossavastspanofcommercialaircraft. 2.1.1EarlyNoisePredictionMethods Inthe1970s,theadventofhigherbypassratioenginesbegantoeectivelyreduceaircraftnoiseduetojetexhaust.Attentionthenfocusedonthenon-propulsiveaerodynamicnoiseproducedbytheairframeitself.Whiletherearenumerouspotentialsourcesofairframenoise(asdemonstratedinFigure 1-1 ),thatduetoturbulentowoverlandinggearsandwheelwellcavitieswerepostulatedearlyontobeveryimportantnoise 42

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contributors.ItwasthedesireofaerodynamicistsandacousticianstodevelopairframenoisepredictionschemesinordertoensurethataircraftmettheincreasinglystrictnoiseguidelinesenforcedbytheFAA.Oneofthemostwell-knowninitiationsofthesestudieswereperformedundertheNASAAircraftNoisePredictionProgram(ANOPP)( Fink 1979 ). Earlymethodsofairframenoisepredictionwerelargelyempiricalinnature.Flyovermeasurementsofmultipleaircraftwouldbetakeninwhichasinglemicrophonewouldbepositionedonarunwaywiththeaircraftyingoverhead.Theaircraftwouldtypicallybeina\clean"congurationinwhichtheengineswereidlingandlandinggearandcontrolsurfacesareretracted.Thisimpliesthatthedominantairframenoisewouldbeduetouctuatingliftanddragforcesontheaircraft'sliftingsurfaces( Morgan&Hardin 1975 ).Oneoftheearliestpredictionschemesutilizedanassumptionthatthedominantacousticsourcebehavedlikeadipoleandthatobservationoccurredinthefar-eldofthesource( Healy 1974 ).Thispredictionwasseentotthemeasuredairframenoisedataforseveraltestedaircraftfairlywell,exhibitingamaximumdeviationoflessthan3dBinoverallsoundpressurelevel(OASPL).ThepredictionisdenedinEquation 2{1 ,whereVistheaircraft'smeanvelocity,Sdenotesaircraftsurfacearea,Arepresentswingaspectratio,rdenotespropagationdistance,andK1isaconstantdeterminedfromexperimentaldata.NotethatOASPLisanintegratedSPLperformedoverapre-denedfrequencyrange.AsEquation 2{1 shows,thefar-elddipolesourceradiationassumptionisevidentwithdependencyonthesixthpowerofvelocityandinversesquareofpropagationdistance( Section1.3.2 ). OASPL=10log10V6S r2A4+K1(2{1) WhiletheairframenoisepredictionschemebyHealyyieldedreasonablepredictions,itwasverylimitedinthatitwasonlyapplicabletoaselectfewaircraftthatwereofverysimilarweightclassications.AnupdatedpredictiontoolwasdevisedbasedonrecordedOASPLmeasurementsof53dierentcommercialaircraft,spanningaweightvariationofsixorders 43

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ofmagnitude( Hardinetal. 1975 ).ThepredictioncanbeseeninEquation 2{2 OASPL=10log10V4:93S0:72 r1:62A2:06+K2(2{2) Itisinterestingtonotethatthispredictionexhibitsvelocityandpropagationdistancedependenciesdierentfromthoseofclassicdipoleradiation.ThepredictionofHardinalsoyieldedanaccuracysimilartothatofHealy,howeveroveramuchbroaderrangeofaircraftsizesandweights.ThedrawbackofthesepredictionmethodsisthatwhiletheydoprovidereasonableestimatesoftheOASPLduetotheaircraftyover,theyprovidenoinformationregardingthespectral,orfrequencycontentoftheradiatednoise. ThenextphaseoftheNASAANOPPinvolvedpredictionofthespectralcontentofairframenoiseforeithercleanordirtycongurations(thosewithlandinggearandcontrolsurfacesdeployed).Twowell-knownpredictionmethodsincludeadragelementmethodaswellasanoisecomponentmethod.Asthenameimplies,thedragelementmethoddeterminesthenoiseoftheprimaryairframecomponentsundertheassumptionthatthenoiseproducedisduetomechanicalenergydissipationbydragforces( Revelletal. 1976 ).Inadditiontotherequirementofadragcoecientforeachofthesecomponents,Revell'sdragelementmethodalsorequiredinputdataforliftcoecients,ightspeed,altitude,andairframegeometry.Thenoisecomponentmethod,ontheotherhand,considersthegenerationandpropagationofacousticenergyforindividualportionsoftheairframebasedoncomponentgeometriesandempiricalcorrelations( Fink 1979 ).Bothofthesemethodstreatthelandinggearsasindividualacousticcontributors.Anexampleempiricalformulationforthefar-eldacousticpowercontributionofalandinggearasafunctionoffrequencyusingthenoisecomponentmethodis SPL=10log10"V 194kt6D r2#+130+10log10(4:5)NfD V2"12:5+fD V2#)]TJ /F7 7.97 Tf 6.59 0 Td[(2:25;(2{3) 44

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where194kt(99.8m=s)isareferencevelocityinknots,Disthewheeldiameter,Nisthenumberofgearwheels(N=1or2forthisformulation)andfisthe1/3rdoctavespectralfrequency.ItisworthnotingthatthisequationutilizesthesourcedipoleassumptionandanempiricaldependencyontheStrouhalnumberrelativetothewheeldiameter,StD=fD V.ResultsofthepredictionmethodsproposedbyRevellandFinkshowthatwhilebothtechniquespredictthespectralnoiselevelseectivelyformultipleaircraftinacleanairframeconguration,onlythenoisecomponentmethodeectivelypredictedthespectrumshapesoftheyovernoisefordirtyaircraftcongurations. 2.1.2AirframePrimaryNoiseSourceIdenticationStudies Resultsofearlyairframenoisepredictionstudiesindicatedappreciablenoisecontributionsbycontrolsurfacessuchaswingapsandslatsaswellasthedrag-inducinglandinggears.Inthe1990s,thedevelopmentofphasedmicrophonearraysmadeitpossibletoconstructtwo-dimensionalacousticimagesofanaircraftoraircraftsub-systeminow,eectivelyhighlightingtheprimarynoisesources.Thisprocessisknownasacousticbeamforming( subsubsection3.5.2.1 ).Someresearchersduringthistimearguedthatitwasnecessarytoperformfull-scaleairframenoiseexperimentsduetothepotentiallackingofdetailedgeometriesandviolationofReynoldsnumbersimilaritieswithmodel-scalewindtunnelexperiments( Dobrzynski&Buchholz 1997 ).Thisbehaviorwaslaterobservedby Stokeretal. ( 2003 ),wherenoisesourceidenticationexperimentsyieldeddierentresultsbetweentwoscaledwindtunnelmodelsandafull-scaleighttest.ThediscrepancieswerepostulatedbytheauthorstobeduetoReynoldsnumbereectsandlackofdetailinthescaledmodels.Thetestingofentireaircraftexperiencingactualightconditionsrequiredyoverexperimentsinadedicatedairspaceutilizinglargemicrophonearrayplatformsonornearanairportrunway.Anillustrationofarepresentativefull-scaleaircraftyovernoisesourceidenticationexperimentalsetupcanbeseeninFigure 2-1 Oneoftheearlystudiesonfull-scaleaircraftnoisesourceidenticationwasdonein1986,inwhicha16-elementlinearmicrophonearraywasorientedtransversetotheight 45

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pathofaLockheedTriStaraircraftinacleanconguration( Howelletal. 1986 ).Theoutputofthelineararrayindicatedpositionsofmaximumacousticpowerresponsethatcorrespondedtothewing-mountedenginesoftheaircraft,whichwerepoweredonduringtheyover.Thisstudywasanimportantrststepinthedevelopmentofone-dimensionalacousticimagingaswellasintherequirementofremovaloftheDopplereectfrommicrophonetimeseriesdataformovingacousticsources. Furtherimprovementsinmicrophonearraydesignincludedtheimplementationoftwo-dimensionalmicrophonearraypatternswhichconsequentlyallowedtheviewingoftwo-dimensionalacousticimagingmaps.Theusageofarrayswithconstantmicrophonespacing,suchassquarelatticearraysofconstantmicrophonespacing,wereeventuallyreplacedwithcross-shapedandnon-redundantmicrophonedistributionstoassistwithremovalofspatialaliasingeectsathigherfrequencies( Underbrink 2002 ).In Micheletal. ( 1998 ),an8mby8mplateoflogarithmically-distributedspiralarmsof96and111microphoneswasutilizedinyovermeasurementsofaregionaljetinalandingcongurationwithslats,aps,andlandinggearsdeployed.Resultsshowedthemainlandinggearsandwingtrailingedgestobedominantnoisesourcesfordierent1/3rdoctavefrequencybands.Thiswasfurtherevidencedinalaterstudyby Michel&Qiao ( 1999 )inwhichtheacousticsignatureofadierentsingle-aisleaircraftrevealedthenoselandinggeartobeanimportantnoisesource,secondonlytotheengineexhaust. Full-scaleaircraftyoverexperimentshavealsotakenplaceinmorerecentyears.Advancementsinarrayprocessingandbeamformingtechniqueshaveyieldedacousticimagemapsofimprovedresolutioninshorterperiodsofrequiredprocessingtime.OnesuchstudywasperformedonaGulfstreamG550aircraftaspartoftheNASA-GulfstreamjointAirframeNoiseFlightTestprogram( Khorramietal. 2008 ).Inthisstudy,aseriesofexperimentswereperformedinwhichthetestmatrixwasstructuredaroundeitherapproachorlandingcongurations.Thestudiesallowednoisesourceidenticationofthecleanairframe,theairframewithisolatedcomponents(eitherapdeectionsor 46

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deployedlandinggears),andthatofadirtyairframeintendedtorepresentactualaircraftlandingconditions.Oneofthemostinterestingndingswasthatforthedirtyairframeconguration,thenoselandinggearwasastrongnoisecontributorbeingonly2-3dBbelowtheapandmainlandinggearsourcesatcertainfrequencies. 2.2SimpleGeometryStudies Asawhole,itissafetoconsideranaircraftlandinggearasacombinationofblu,ornon-streamlinedbodies.Ingeneral,owpastablubodyconsistsoftwoprimaryfeatures:(1)owseparationaheadofthedownstreamsideofthebody(rearstagnationpoint)and(2)theformationofalargewake( Roshko 1955 ).Oneofthemostcommonblubodiesstudiedinuidmechanicsisthecircularcylinder,whichisalsoarepresentativelandinggeargeometrysuchasashockstrutorwheelaxle.Whilethestudyofowaroundasinglecylinderisinadequatefromtheperspectiveofdevelopinganunderstandingoflandinggearuidmechanics,itisanimportantexperimentalbaselinethatrequiresreview. 2.2.1FlowAroundaSingleCylinder Flowaroundablubodysuchasacylindercanbecharacterizedbyregionsofdisturbedowinwhichthelocalvelocityandpressuredeviatefromthoseofthefreestreamconditions.TheseregionsaredepictedschematicallyinFigure 2-2 ,whereUorepresentsthefreestreamvelocityandDisthediameterofthecylinder.Thegureisdividedintofourdistinctowregions:(I)anupstreamretardedowregion,(II)aboundarylayerregionattachedtothecylindersurface,(III)aregionofdisplacedowbythepresenceofthecylinder,and(IV)thedownstreamwakeregion.Region(I)ischaracterizedbyhighvelocityuctuationsandtheformationofunsteadyowstructures.Region(II)representsviscousboundarylayerownearthesurfaceofthecylinderthateventuallyseparatesfromthesurfaceandpropagatesdownstreamintheformoffreeshearlayers.Thesefreeshearlayersalsodenetheouterbordersofthewakeregion(IV).Region(III)isanareaofdisplacedowinwhichthelocalstreamwisevelocityexceedsthatofthefreestream(UIII>Uo)whilethewakeregion(IV)ischaracterizedbythe 47

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formationandgradualdownstreamdecayoflargeowstructuresandlocalstreamwisevelocitylessthanthatofthefreestream(UIV
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foundexperimentallythatfortestedowconditionsof300
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circularcylindertothebluplate,dragforceincreasesandthevortexsheddingfrequencydecreases.Basedonthistrend,theplatewouldbethebluerbodyofthethree,followedbythewedgeandthenthecircularcylinder.Whilethelattertwoprovidegradualsurfacesalongwhichowmaybecomeattached,theatplatepresentsanearlydiscontinuouschangeingeometrycausingamuchgreaterdisturbanceofthefreestreamow,alargerwake,andgreaterdragforce.ThesendingsareimportantsincetheyhavedeterminedthatwhileStisanexcellentempiricaltooltoassistwithidentifyingtheperiodicityofvorticalstructuresinthewakeofablubody,itshouldnotbeconsideredtobeacertainvaluebasedonthefrontaldimensionsofthebody,butratheronthe\bluness"ofthebody. Thenaltopicofdiscussionforowovercylindersisowsimilarity.Inpractice,itcanbediculttoachieveexperimentallyreliablehighReowsoverblubodiesinacontrolledwindtunnelenvironment.AnexampleofsuchahighspeedowisthatexperiencedbythecylindricalshockstrutofaGulfstreamG550aircraftnoselandinggear.Withanominallandingspeedof75.6m/s,ashockstrutdiameterof3"(0.0762m),andassumingatmosphericpropertiesof=1.22kg=m3and=1:8310)]TJ /F7 7.97 Tf 6.58 0 Td[(5kg=(ms),thisequatestoReD3:8105.AscanbeseeninTable 2-2 ,thiscorrespondstotheTwoBubblecriticalowscenario.Foramoderatesizetunnel,thisRemaynotbeattainableduetomaximumtunnelspeedandmodelscalelimitations,particularlywhendealingwithacousticexperimentation. Inanattempttobypassthislackofdynamicsimilarity,windtunnelexperimentalistshaveimplementedsurfacetreatmentmechanismsto\trip"thecylinderboundarylayer,instigatinganearlieronsetoftransitiontoturbulence.Dependingonthemethodoftrippingused,theresultingowmaybemadetoresemblethatofthecritical,super-critical,andevenpost-criticalregimes.Theuseofthinwirespositionedinthevicinityof5060wasoneoftheearliesttestedtechniques( Igarashi 1986 ).Forarangeoftestedspeedsof1:3104Re9:6104,CDwasseentodecreasefromaround 50

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1.3to0.6andStwasseentoincreasefromaround0.2to0.3withinstallationofthewires.Thesetrendsareindicativeofahigherorderowregimeandareinagreementwithsimilarvaluespublishedby Roshko ( 1961 )and Bearman ( 1969 )foracriticalTr-BLstate.Morerecentstudieshavefoundthinwirestobetooobtrusiveandhaveimplementedmethodssuchasgritsandserratedtapesthataremoreushwiththecylindersurface.Forexample,inexperimentsperformedby Jenkinsetal. ( 2005 2006 ),aserratedtapewasusedtotripthecylinderboundarylayersatatestedspeedofRe=1:66105,andthecircumferentialCpvariationwasobservedtobehavesimilarlytoacylinderinthecriticalregime.TheimplementationoftrippingtechniquessuchasgritsandserratedtapestosimulatehigherReowsaroundblubodieshasthusenabledtheanalysisofmorecomplicatedturbulentowinteractions,suchasthosebetweenclosely-spacedcomponentscharacteristicoflandinggeargeometries. 2.2.2FlowAroundTandemCylinders Inmorerecentyears,applicationofowoverblubodieshasbeenexpandedtoincludeowinteractionsbetweenmultiplecomponents.Animportantsuchcongurationisthetandemcylinderarrangement.Inthisconguration,illustratedinFigure 2.6 ,twocylindersareplacedonebehindtheotherinthedownstreamdirection,orintandem.NotethattheseparationbetweencylindersisdenedintermsofanaspectratioL=D,whereListhedistancebetweencylindercenters. Zdravkovich ( 1985 )categorizedtheoverallowphenomenaoftandemcongurationsbasedonL=Daspectratio,whicharesummarizedinTable 2-3 .Eventhoughthiscongurationisfairlysimplegeometrically,itisimportantsinceitdemonstratestheowphenomenabetweenandinthevicinityofclosely-spacedgeometriesindicativeoflandinggears. 2.2.2.1FluidDynamicInteractions AninformativestudyontandemcylinderuiddynamicinteractionsisaseriesofexperimentsperformedattheNASALangleyAerospaceResearchCenter(LaRC)aspartoftheQuietAircraftTechnology(QAT)project( Jenkinsetal. 2005 2006 ; Neuhartetal. 51

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2009a ).Intheseexperiments,twocylindersofidenticaldiameterwerearrangedintandemwithaspectratiosofL=D=3.7and1.435toidentifytheowphenomenaassociatedwithdierentinter-componentspacings.ForanL=Dof3.7,bothcylindersshowedevidenceofvortexsheddingbasedonpressureandvelocityspectrafromunsteadysurfacepressuretransducersonbothcylindersandhot-wireanemometrymeasurementsinthewakeoftherearcylinder,respectively.ForL=D=1:435,however,therewasalackoftonalpeaksindicativeofvortexsheddinginthepressurespectra.Inaddition,onlyaslight\hump"waspresentinthevelocityspectraofthehot-wireprobe.Thishumpwasbelievedtobeduetouctuationsoftheshearlayersoftherearcylinderratherthanduetoanorganizedvorticalstructure( Jenkinsetal. 2006 ).Furthermore,useoftwo-dimensionalparticleimagevelocimetry(PIV)intheregionbetweenthecylinders(gapow)forL=D=3:7revealedasymmetricrecirculationpatternbehindthefrontcylinderverysimilartothatofasinglecylinderinow.PIVresultsinthegapregionforL=D=1:435revealedanasymmetricrecirculationpatternbetweenthetwocylinders,whichconsequentlyresultedinanasymmetricmeansurfacepressuredistributionaboutthecircumferenceoftherearcylinder. Oneoftheeventualgoalsofaerodynamicistsistobeabletodependoncomputationalsimulationsofcomplicatedowscenariosthatmaybediculttoanalyzeexperimentally.Duetothegeometricsimplicityandtwo-dimensionalownatureofthetandemcylinderconguration,itoersanexcellentopportunityforcomparisonofcomputationalsimulationswithexperimentalresults.Forexample,aseriesofparallelaeroacousticcomputationalstudieswereperformedonthetandemcongurationsatNASALaRCdiscussedpreviously( Khorramietal. 2007 ; Lockardetal. 2008 ).CFL3D,aNASA-developedCFDthree-dimensionalsolveroftheNavier-Stokesequationswithazonalturbulencemodelwasusedtoproducethepressureandvelocitynear-elddata.Thenear-eldpressureuctuationdatawerethenusedasinputsintoaCAAsolveroftheFfowcsWilliams-Hawkings(FW-H)equation( FfowcsWilliams&Hawkings 1969 )topredict 52

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thefar-eldacousticsignature.SpecialattentionwaspaidtothecaseofL=D=1:435sinceitwasconsideredtobemorerepresentativeofalandinggearconguration.ResultsoftheinitialCFDanalysisshoweddiscrepanciesinthesurfacepressuredistributionsandthemeanowpatternsdeterminedfromtheexperiments,particularlyintheRMSpressureuctuationlevelsaroundthecircumferenceofbothcylindersandtheobservedrecirculationphenomenoninthegapowregion.Itwasfoundthatthesimulationofaslightangleofattackoftheowdirection(0:51:5)resultedinmuchbettercomparisonbetweenthecomputedandexperimentalresults.Thisimpliesthattheremayhavebeenaslightskewnessintheexperimentalalignmentofthetandemcylinderswiththeowdirection( Lockardetal. 2008 ).ThisshowshowCFDsimulationscouldbeverybenecialinidentifyingpossibleexperimentalshortcomingsduetosensitivitytoparameterssuchasalignment. 2.2.2.2Far-FieldAcoustics Asdiscussedearlier,theperiodicsheddingofeddiesfromasinglecircularcylindermanifestsitselfintheacousticfar-eldasatone.Foratandemarrangementofcylindershowever,thefar-eldacousticsignaturecandeviatefromthisbehaviordependingontheirspacingandsizerelativetoeachother.Anexampleofthisisastudyby Fitzpatrick ( 2003 )wherenear-andfar-eldmeasurementsweretakenforatandemarrangementofcircularcylindersofthesamediameter.Specically,near-eldturbulencemeasurementsweretakenusingahotwireanemometerwhilenear-eldpressureuctuationsweretakenusingaBruel&Kjaerfree-eldmicrophone.Bothofthesetransducerswerepositionedalongthenominalshearlayerintheregionbetweenthetwocylinders,whileanadditionalmicrophonewaslocatedwithinthewallofthewindtunnel(far-eldmeasurement).WhileallthreetransducerswereabletoresolvevortexsheddingfrequenciesforseparationaspectratiosofL=D=4and5,novortexsheddingwasobservableforL=D=3.Althoughithasbeenreportedin Zdravkovich ( 1985 )thatthisseparationdistancecorresponds 53

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tointermittentsheddingbetweencylinders,broadbandturbulenceandothersourcesoftunnelnoisemaydominate. Inastudyconductedby Hutcheson&Brooks ( 2006 ),acousticmeasurementswereperformedonbothsingleandmultiplecylindercongurationstodetermineeectsofRe,surfaceroughness,andcylinderspacingonthefar-eldnoiseradiation.ForcylindersofthesamediameterandaspacingofL=D=1,asingletonewasobservedatafrequencyconsiderablyhigherthanthecharacteristicsheddingfrequencyforasinglecylinder.Thisisindicativeofthetrendsidentiedin Zdravkovich ( 1985 )asreportedinTable 2-3 .Conversely,anacoustictoneatafrequencylowerthanthecharacteristicsheddingfrequencywasobservedforspacingsofL=D=2and3,whileaspacingofL=D=4:5yieldedatonethatwasclosetothatofasinglecylinder.Atthisspacing,itisstatedthatpairingoftheeddiesfrombothupstreamanddownstreamrodstakesplace,yieldingvortexstreetsthataresynchronizedinfrequency( Hutcheson&Brooks 2006 ).Finally,sheddingfrequenciesofthecylinderswereseentoincreaseforL=D=2and3withtheapplicationofgritonthecylindersurfaces.Thismakessensesincetrippingoftheboundarylayerstobecomingfullyturbulenteectivelydelaysthepointofowseparationfromthecylindersurface,whichnarrowsthewakeofthecylinder.Asindicatedby Roshko ( 1955 ),thenarrowingofthewakeeectivelydecreasesthe\bluness"ofthebody,whichresultsinanincreaseinthevortexsheddingfrequency. Far-eldacousticsimulationsoftandemcylindercongurationshavealsobeenperformed.In Lockardetal. ( 2008 ),aFW-Hequationsolverwasusedtocomputeacousticspectraforselectfar-eldlocationsthatcoincidedwithexperimentaldatatakenintheNASAQuietFlowFacility(QFF)( Lockardetal. 2007 ).Far-eldsimulationsforthecaseofL=D=1:435showedoverallgoodagreementwiththeexperimentalresultsfromabroadbandperspective,howevernoticeabledierencesinthetonalcontentbetweenthemwereobserved.Vortexsheddingwasexperimentallyobservedtobegreatlysuppressedforthiscongurationduetothecloseproximityofthecylinders,whilethe 54

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simulationsofthefar-eldspectrashowedspectralpeaksinthevicinityofthecylindervortexsheddingfrequency.ForthecaseofL=D=3:7,however,vortexsheddingwasexperimentallyobservedtooccur,andthesimulationswereseentoshowmuchbetteragreement.ThissuggeststhatthisparticularCFD-CAAcombinationtechniquemayrequirerenementinordertomoreaccuratelycapturethefar-eldspectraldetailsexhibitedbyclosely-spacedgeometries. Theanalysisoftandemcylindercongurationsisanimportantrststepindevelopinganin-depthunderstandingoftheuidandacousticinteractionsofclosely-spacedgeometriesindicativeoflandinggears.Whiletheydoprovideexcellentphysicalinsightforsuchows,however,theirtwo-dimensionalownaturepreventsthemfrombeingdirectlycomparabletoowoverlandinggears,whichishighlythree-dimensional.Therefore,three-dimensionalstudiesofclosely-spacedcomponentsareessentialtomoreaccuratelyanalyzetheowphenomenaassociatedwiththataroundlandinggears. 2.3LandingGearExperimentalStudies Animportantdistinctionthatmustbemadebetweenowaroundlandinggearsandthataroundsimplebaselinegeometriessuchastandemcylinders,isthethree-dimensionalityofowaroundlandinggears.Whiletandemcylinderstudiesareusefulindemonstratingtheuiddynamicsandfar-eldacousticradiationpatternsofclosely-spacedcomponents,theiruniformgeometryresultsinalackofthree-dimensionalowfeaturesthatareindicativeoflandinggears.Therefore,experimentalattemptsatisolatingthree-dimensionallandinggeargeometriesisrequired,whetherfullsizeorscaled,andwhetherthecomplexityissimpliedorhighdelity.Bothtypesofstudiesaredocumentedinthefollowingsections. 2.3.1SimpleLandingGearGeometryStudies Simpliedlandinggeargeometriesarestudiedtoanalyzebulkowphenomenaand/orrepresentativeacousticradiationpatterns.Themodelwillusuallyconsistofaseriesofbasicgeometriessuchascylindricalstrutsandwheelsthatdemonstratetheoverallshape 55

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ofthelandinggear,howeverlackthedetailofsmallercomponents.Althoughthislackofdetailhasconsequentlybeenlinkedtotheabsenceofhigherfrequencynoisethatwouldexistonahigh-delitygeometry( Dobrzynski&Buchholz 1997 ),thestudyofsimplelandinggeargeometrieshaveassistedinidentifyingimportantnoisecontributionsduetowake-bodyinteractionsbetweenclosely-spacedcomponents( Quayleetal. 2008 ). Lazos ( 2002a b )conductedaseriesofexperimentsonagenericfour-wheellandinggearcorrespondingtoa31%scaleofaBoeing757mainlandinggear,whichisillustratedinFigure 2-4 .Intheformerofthesestudies,two-dimensionalPIVmeasurementsweretakenonthemid-planeoftwoinlinewheels,visualizedinFigure 2-5 .Resultsshowedanazimuthalasymmetryintheseparationoftheowfromtheaftsideofthefrontwheelandattachmentoftheowonthefrontfaceoftherearwheel.Anassumedresultofthisasymmetryisthepresenceofaslowly-oscillatingvortexinthegapowregionbetweenthetwowheels.Itisinterestingtonotethatthisasymmetricvortexcloselyresemblestheasymmetricrecirculationpatternobservedbetweenclosely-spacedtandemcylindersin Jenkinsetal. ( 2005 ).Thisvortexwashypothesizedtobeapossiblenoisesourceasaturbulenteddycarrierbetweenthewheels( Lazos 2002a ).Inaddition,thelatterofthesestudiesidentiedhighshearstressesalongthefrontfaceoftherearwheel,indicativeofthehighlyturbulentowinthisregion( Lazos 2002b ). Anacousticstudyonasimilargeometryofdierentscalewasperformedby Quayleetal. ( 2008 ).Inthisstudy,afour-wheellandinggearmodelwassuspendedinaclosed-walledwindtunneltestsection,withtwonestedmicrophoneco-arraysmountedintheoorofthetunneltestsectiondirectlybelowthemodel.TheexperimentalcongurationforthisstudyisillustratedinFigure 2-6 .Thisprovidedanoverhead,oryoverviewofacousticsourcesonthemodel.Resultsindicatethattheregionbetweenin-linewheelswasanimportantnoisecontributor,primarilyduetoscatteringofaerodynamicinstabilitiesontheforwardfaceoftherearwheels( Quayleetal. 2008 ).Inaddition,mosthighfrequencynoisewasfoundtoemanatefromthejunctionbetween 56

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theshockstrutandmainaxlebeamwhichisbelievedtobetheresultofincreasedowvelocitiesaroundthemainshockstrutduetogapowbetweenthewheels.Thisisanimportantstudysinceitconrmswake-bodyinteractionsofclosely-spacedcomponentstobeimportantairframenoisecontributors. 2.3.2High-FidelityLandingGearGeometryStudies Oneoftheearlierwindtunnelexperimentsonlandinggearswasafull-scalestudyonAirbus2-and4-wheelmainlandinggearswhichtookplaceintheDNWGerman-DutchWindTunnel( Dobrzynski&Buchholz 1997 ).Inthisstudy,far-eldmicrophoneswerepositionedatdierentlocationsoutsideoftheowregioncorrespondingtodierentstreamwisepolarradiationangles.Itwasfoundthatthenoiseproducedfrombothtypesofgearwerefundamentallybroadbandinnature,exhibitingnearlyconstantfar-eldnoiselevelsin1/3rdoctavebandsforthemajorityofthefrequencyrangeofinterest.Inaddition,thescalingoffar-eldnoisewiththe6thpowerofvelocity(dipoleradiation)wasconrmedformicrophonespositionedatradiationangles90o,where=180orepresentstheowdirection.Thiswasdeterminedbycollapsingdataacquiredfromthefar-eldmicrophonesforaseriesoftestedfreestreamvelocities,Uo,usingalevelcorrectionLbasedonareferencevelocityvrefandanexperimentalconstantC: SPLscaled=SPLm)]TJ /F3 11.955 Tf 11.95 0 Td[(L;(2{7) where L=10log10Uo vref6+C:(2{8) NotethatSPLmrepresentstherawmicrophonesignalpowerplottedin1/3rdoctavebands.Inaddition,powerlevelswereplottedversusnon-dimensionalfrequencySt=fs Uo,wheresisanarbitrarylengthscale.Whiletheresultsofthisshowedgoodcollapseofthedataforthefour-wheelgear,thecollapsewasobservedtodegradeatmiddlefrequenciesforthetwo-wheelgear.Thiswashypothesizedtobeduetothepresenceofnoise 57

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componentsinthevicinityofthewheelsthatoccurindependentofspeed( Dobrzynski&Buchholz 1997 ). Guoetal. ( 2006 )performedanextensiveseriesofacousticexperimentsonafull-scalereplicaofaBoeing737mainlandinggearfordierentlevelsofcomplexityandarangeofowspeedsrepresentativeoflandingconditions.ExperimentswereperformedintheBoeingLowSpeedAeroacousticFacility(LSAF),whichconsistsofanopen-jetwindtunnelwhosetestsectionrunsthroughananechoictestingchamber.Asthenameimplies,ananechoicchamberisonethatisnominallydevoidofacousticreectionsdowntoacertaincut-onfrequency.Thewalls,ceiling,andoorofthechamberaretypicallypopulatedwithtriangularacousticwedgesmeanttoprovideagradualacoustictermination,whichpreventsthepropagationofreectedacousticwavesthatcouldotherwisecontaminateacousticmeasurements.Typesofacousticmeasurementstakeninthestudyby Guoetal. ( 2006 )includedaphasedmicrophonearray-whichwaseitherinayoverorside-lineconguration-andalineararrayofpole-mountedmicrophonesthatspannedarangeofpropagationanglesalongtheoorofthetunneltestsection.AschematicoftheexperimentalsetupforthisstudycanbeseeninFigure 2-7 .Thistypeoftestingcongurationisdierentfromthatperformedby Quayleetal. ( 2008 ),sincetheopen-jettestsectionlackssolidwallsandallowsforacousticinstrumentationtobeplaceoutsideoftheowwithintheanechoicchamber.Asimilarcongurationwastestedby Dobrzynski&Buchholz ( 1997 ). Noisesourcelocalizationexperimentsperformedby Guoetal. ( 2006 )identieddominantacousticsourcesoncomponentslocateddownstreamofthefrontwheelsandmainstrut,namelyinthevicinityofthetorquelinkagesanddragbraces.Removalofsmallcomponentssuchashydraulichosesandelectricalwiringwereseentoyieldabroadbanddecreaseinacousticpower-mostnoticeableathighfrequencies-asevidencedbybothnoisesourcelocalizationmapsaswellasfar-eldmicrophonedata.Anotherinterestingndingwashowfar-eldmicrophonespectrawereseentoscaledierentlyfor 58

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dierentfrequencyranges.Scalingofmicrophonespectrawiththesixthpowerofvelocity(similartothatshowninEquation 2{7 )wasonlyseentoshowgoodcollapseofdataforlow-andmid-frequencies(100F1000Hz).Athighfrequencies(F1000Hz),microphonedatawereseentocollapsemuchbetterusingaseventhpowerofvelocityscaling,whichismorerepresentativeofturbulence-generatednoise( Guoetal. 2006 ).Asdiscussedin Chapter1.3.4 ,degradationofacousticradiationeciencyoccurswhentheacousticwavelengthbecomescomparablewiththedimensionsofgearcomponents,orkL1. Aeroacoustictestingofscaledhigh-delitylandinggearreplicashaveyieldedresultsthatinsomeinstancescomparewellwithtrendsobservedforfull-scaletestsandothersthatdonot.Forexample,scalingoffar-eldspectrawiththesixthpowerofvelocityhaveshownexcellentcollapseofdata( Humphreys&Brooks 2007 ; Zawodnyetal. 2009 ).Achangeinspectralscalingbehavior(i.e.fromsixthtoseventhpowerofvelocity)howeverwasnotobservedinthesestudies,nordidthespectraeectivelycollapsebasedonanon-dimensionalStrouhalfrequencyaswasperformedin Dobrzynski&Buchholz ( 1997 ).Instead,far-eldnoiselevelswereseentoonlyincreaseinamplitudewiththesixthpowerofvelocity,andnotchangeinoverallfrequencycontent. Guoetal. ( 2006 )alsoachievedaneectivecollapseofthespectraldatabasedondimensionalfrequency,ratherthananon-dimensionalStrouhalfrequency. Aerodynamicstudiesoncomplexlandinggeargeometrieshavealsobeenperformed. Ringshiaetal. ( 2006 )performedPIVstudiesonascaledmodelofasix-wheelmainlandinggearofaBoeing777aircraft.Theprimaryemphasisofthisstudywastogainanin-depthunderstandingoftheuidmechanicspresentinwake-bodyinteractionsonahigh-delitylandinggeargeometry.Particularregionsofinterestincludedthegapowbetweentwotandemwheelsandthatbetweenafrontandreardragbrace.Thegapowregionbetweenthewheelsrevealedthepresenceofavortexbetweenthetwowheels,whichissimilartotheresultsfoundin Lazos ( 2002a b ).Regionsofhighlevelsofturbulencewere 59

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alsoobservedinthewakeregionofthefrontdragbrace.Imagesofinstantaneousvelocityeldsinthegapowregionbetweendragbracesactuallyrevealedthepathtraveledbyavortexformedinthewakeofthefrontdragbrace,convectingdownstream,andimpingingonthefrontfaceofthereardragbrace.Thisuidinteractionwasevidencedtobeanimportantnoisesourceinanearlieracousticstudyonalargerscalemodelofthesamelandinggearby Ravettaetal. ( 2004 ),inwhicheliminationofthiswake-bodyinteractionbyphysicalremovalofthefrontdragbraceshowedareductioninnoiselevels. Inanaerodynamicstudyofahigh-delity1/4-scalereplicaofaGulfstreamG550noselandinggear,severalregionsinthewakeofthemodelwerescannedusingtwo-dimensionalPIVtechniquesinconjunctionwithsteadyandunsteadysurfacepressuremeasurementsatstrategiclocationsonthemodel( Neuhartetal. 2009b ).Thisisanimportantstudysinceitdemonstratesthepotentialofhighlightingtheaerodynamicandacousticsimilaritiesanddierencesbetweenmainandnoselandinggears.Figure 2-8 showsthelevelofdetailpresentonthemodelinitsfully-dressedcongurationrelativetotheactuallandinggearitself.Duetotherequirementofoptical\line-of-sight"accesstotheregionsthataretobescannedforPIV,thesemeasurementswerelimitedtoareasdownstreamofthemodeloralongitsouteredgesatselectplanes,whichcanbeseeninFigure 2-9 .Althoughtheinnerregionsbetweencomponentscouldnotbescanned,thefourplanesspecieddoprovideinformationonlevelsofturbulenceproducedbythemodelwhichcanhelpwithidentifyingregionsofprominentnoisegeneration.AscanbeseeninFigure 2-9 ,thefourplanesscannedcorrespondtothefollowing:(1)wakeofdoorandshockstrut,(2)wakeofuppertorquearmandshockstrutcylinder,(3)wakeofwheelandwheelaxle,and(4)outboardofstarboardwheel.Inaddition,thestrategicplacementofunsteadypressuretransducersthroughouttheseinnerregionsalsoaidedinidentifyingregionsofhighsurfacepressureuctuations.Aninterestingowphenomenonobservedinthisstudywasalackoftonalbehaviorintheunsteadysurfacepressurespectraassociatedwithsustainedvortexshedding.Thisobservationwasalsocomplimentedwithalackofobservablelarge-scale 60

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vorticalstructuresbeingshedfromthegearatanyofthePIVscanningplanes.Itisbelievedthattheprocessofvortexsheddingwaseitherpreventedorgreatlyinhibitedduetothecloseproximityofgearcomponentswithoneanother( Neuhartetal. 2009b ).Thehighestlevelsofturbulentkineticenergy(TKE)wereobservedinplane1,whilemaximumpressureuctuationswererecordedbyanunsteadypressuretransducerlocatedontheowsideoftheuppertorquearm.HighlevelsofTKEandrmspressureuctuationswerealsoobservedinplane3andaKulitepositionedontheaxle,respectively.Theseregionswerethusdeemedtobeimportantforconsiderationasimportantcontributorsofnoise.ThisstudywaslatercomplementedbyaseriesofaerodynamicandacousticexperimentsattheUniversityofFloridaaspartofacollaborativeGulfstream-NASA-UFlandinggearstudy( Zawodnyetal. 2009 ). 2.3.3ImplementationofNoiseReductionTechniques Sincethelate1990s,aeroacousticianshaveimplementednumerousmethodsofnoiseabatementonlandinggearandlandinggear-typegeometries,utilizingbothpassiveandactiveowcontroltechniques.Passiveowcontrolmechanismshaveincludeddevicessuchasspoilers,solidandperforatedfairings,andevenre-designorrelocationofgeometriesconsideredtoberesponsiblefornoisegeneration( Dobrzynskietal. 2009 ).Activecontrolmechanismshaveincludedactuatorsstrategicallyplacedonorneargeargeometriestoeitherdivertorreducethemagnitudeoftheowimpingingondownstreamcomponents.Whilesomeofthesemethodshaveshownpromiseingearnoisereduction,potentialdisadvantagesincludeincreasesinweightanddragloadingswiththeadditionofpassivereductions,aswellasadditionalhardwareandpowerrequirementsforactivemethods. 2.3.3.1PassiveNoiseReductionConcepts Thersttestedmethodsofpassivenoisereductiononlandinggearsweresolidfairings.Thefundamentalideabehindtheuseofsolidfairingsistostreamlinethegearstructure,mitigatingtheturbulentwake-bodyowinteractionsbetweencomponentsaswellasshieldingsharped-edgeandsmallergearcomponentsfromtheow.An 61

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exampleofasolidfairingappliedtoasimpliedlandinggeargeometryisshowninFigure 2-10B .Severalsuchfairingconceptswereutilizedin Dobrzynski&Buchholz ( 1997 )and Dobrzynskietal. ( 2005 ).Theseincludedaramp-typespoilerupstreamofthecavityofatwo-wheelnoselandinggeartodeecthigh-speedowfromthegearupperlegregionandtwostreamlinedfairingsthatcoveredthefrontlegandbrakesystemofafour-wheelmainlandinggear.Similarfairingideaswereimplementedby Quayleetal. ( 2007 )and Remillieuxetal. ( 2008 ). Whilethesesolidfairingconceptswereobservedtomitigatenoiseatmid-andhigh-frequencies,lowfrequencynoisewasseentoincreaseasaresultofhigh-speedowdeectionfromthefairingsontoneighboringcomponentsaswellaslowerfrequencyvortexsheddingfromtheeectively\bluer"geometry( Boorsmaetal. 2008 ; Dobrzynskietal. 2009 ).Theusageofporousfairingshavebeenimplementedtoassistwithcounteringtheseadverseeects.Figure 2-10C displaysanexampleofporousfairingsappliedtothemainstrutandforwardaxleofasimpliedgeargeometry.Allowingairtobebledthroughthesefairingsallowsaredistributionoftheairow,eectivelyreducinglarge-scaleturbulencestructuresandlowfrequencynoise( Boorsmaetal. 2008 ).Oneofthedrawbacksofporousfairingsisthepossiblepresenceofperforateself-noise.Thisnoiseistypicallyathighfrequenciesandisduetovortexsheddingfromowthroughtheperforationsinthefairing( Oerlemans&Sandu 2010 ).Astudyconductedby Boorsmaetal. ( 2009 )consistedofanextensiveseriesofexperimentswithperforatedfairingsofdierentporosities-porositybeingdenedastheratioofopentoclosedsurfaceareaonthefairing-onbothcylindricalandI-beamblubodygeometries.Hotwiremeasurementsmadeinthewakeofthebodiesevidencedadisappearanceofvortexsheddingphenomenonforporositiesgreaterthan20%.Theseporousfairingconceptswerealsoappliedtoasimplied1/4-scalereplicaofanAirbusA340mainlandinggear( Boorsmaetal. 2008 ).Itwasfoundthatlimitingthenumberofperforationsinthefairingtostagnationregions(i.e.regionsexperiencingmaximalpressureloadingsduetoincomingow)resultedinbroadbandnoisereductions, 62

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includingdrasticreductionofperforateself-noisepresentinthecaseofperforationsdistributedthroughouttheentirefairing.Suchndingsareveriedbyastudyconductedby Oerlemans&Sandu ( 2010 ),inwhichthecoveringofI-beamgeometrieswithmeshfairingswasseentoreducenoiseatlow-andmid-frequenciesfrom5-10dBatcertainfrequencies. 2.3.3.2ActiveNoiseReductionConcepts Unlikepassivenoisereductiondevices,activeonesrequireapowersourcethatactivatesanactuator(oractuators)tomodifytheincomingoweld.Whilethesemeasureshavethepotentialtoaddweightandcomplexitytothelandinggear,thepotentialnoisereductionbenetsmakethemworthconsideration.Onesuchideawaspresentedby Oerlemans&Bruin ( 2009 )inwhichtheyimplementedanupstream\aircurtain"todeecttheowaroundatwo-dimensionalbluobject.Figure 2-11 presentsaschematicoftheirtestingconguration.Notethatthejetthatproducedtheaircurtainspannedthewidthofthetunneltestsection(intothepageinFigure 2-11 ).Inthistestingconguration,theoorofthetunneltestsectionwasmeanttosimulatetheundersideofanaircraftfuselage.Theideaoftheaircurtainistominimizethehighspeedowslocaltothelandinggearitselftoreducenoisegeneration,whilenotaectingtheoverallaerodynamicperformanceoftheaircraft.Experimentalresultsshowedabroadbandnoisereductionpotentialbetween3and10dB,dependingontheorientationofthejetslotvelocityrelativetothefreestreamowdirectionandwhetherornotaowdeectorwaspresentjustupstreamoftheblowingslot.Theauthorsstatedthatfuturetestingwouldincludetheinstallationofamorecompleteaircraftlandinggearreplicainplaceofthesingleblubodyutilizedintheseexperiments. Anothernovelapproachofactiveowcontrolapplicabletoairframenoisereductionisplasmaactuators.InastudybyHuangetal.( Huangetal. 2010 ),arepresentativelandinggearsub-systemconsistingofanupstreamcylinderwithaconnecteddownstreamtorquelinkapparatuswasouttwithdielectricbarrierdischargeactuatorsthatinduce 63

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atangentialwalljetow.AschematicoftheexperimentalsetupcanbeseeninFigure 2-12 .Asthegureshows,theelectrodesoftheplasmaactuatorscouldbeorientedsuchthateitheranupstreamordownstream-directedowcouldbeproduced,andanear-eldmicrophonewasxedinthetorquearmjunctiontomeasurethedierencesinsurfacepressureuctuationsforthesedierentactuationdirections.TheseactuatorswereabletoproduceajetwithamaximumvelocityofUj;max8m/s.Inaddition,anarcoffree-eldmicrophoneswereorientedoutsideoftheowregionandcenteredaboutthetorquearmjunction.Theprimaryobjectiveofthisstudywastoreducethebroadbandnoisebelievedtobegeneratedduetotheimpingementofthewakefromthecylinderontothedownstreamtorquearms( Huangetal. 2010 ).Resultsoftheseexperimentsshowedaslightlylargerdecreaseinbroadbandnoiselevelsfortheupstreamactuationcase,howeverthisnoisereductionwasseentodeteriorateforspeedshigherthanthebaselinecaseofU1=30m/s. Whileactivenoisereductionconceptssuchastheonesdiscussedherehavethepotentialofexhibitingbroadbandnoiselevelreductions,thereareadditionalfactorstobeconsidered.Suchaswasthecaseforpassivenoisecontrolmechanismssuchasfairings,additionalweightforactivedevicessuchasplasmaactuatorsoranaircurtain(i.e.anexternalpowersourceand/orpressurizedairsupply,respectively)couldbeconsiderable.Inaddition,whilethewindtunnelexperimentsperformedby Oerlemans&Bruin ( 2009 )showedthattheactuationoftheaircurtaindidnotresultinincreasednoiselevels,itispossiblethatthismightnotbethecasewhenappliedtoafull-scaleaircraftatlandingspeeds.Thefactthattheeectivenessoftheplasmaactuatorsby Huangetal. ( 2010 )wasseentodeteriorateforspeedsgreaterthanU1=30m/s,whichisconsiderablylowerthanaircraftlandingspeeds,deemsthatthistechniquerequiresfurtheroptimization. 2.4LandingGearComputationalStudies Recentadvancesinhigh-performancecomputinghavegreatlyincreasedthecapabilitiesofCFDandCAAmethods.Whileitisstillinfeasibletocompletelymodel 64

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allthescalesofturbulencepresentonacomplexgeometrysuchasalandinggear,severalCFDapproacheshavebeenutilizedwiththeintentofelucidatingtheturbulentscalespertinenttotheresultingfar-eldnoisepropagation.Themoretraditionalofthesemethodsincludedirectnumericalsimulations(DNS),large-eddysimulations(LES),andReynoldsaveragedNavier-Stokes(RANS)solvers.AnoverviewoftheadvantagesanddisadvantagesofthesemethodsareoutlinedinTable 2-6 ( Tannehilletal. 1997 ). RecentadvancementstothetraditionalmethodslistedinTable 2-6 includedetached-eddysimulations(DES)andlatticeBoltzmannmethods(LBM).DESmaybeconsideredahybridizationofLESandRANSmethodsinwhichthelarge-scaleseparatedowregionsareaccountedforwithLESandboundarylayerturbulencemodelingisaccountedforwithRANS( Hedgesetal. 2002 ).LBMontheotherhand,departsfromthetraditionalCFDapproachesbasedondiscretizationoftheNavier-Stokesequationsandisbasedonsimpliedparticlekinetictheorymodels.ThemethodologybehindLBMistheutilizationofthesesimpliedmodelsonamesoscopicscalesuchthatthemacroscopicequations(i.e.Navier-Stokes)areobeyed( Chen&Doolen 1998 ). In Hedgesetal. ( 2002 ),owaroundagenericlandinggearofidenticalgeometrytothattestedin Lazos ( 2002a b )wascomparedbetweenDESandunsteadyRANS(URANS)simulationsaswellaswithexperimentaldata.ResultsshowedtheDEStoperformslightlybetterthanURANSatpredictingthesteadypressuredistributionaroundthefrontandrearwheelsaswellasatpredictingmorereasonableturbulencelevelsinthewakeofthegeometry.ThisisduetothefactthattheturbulencemodelutilizedintheURANSsimulationsactedasadampingmechanismforthesmaller-scaleturbulencestructures( Hedgesetal. 2002 ).Bothmethods,however,wereseentofailataccuratelypredictingoverallliftanddragforcesonthemodelincomparisonwithexperimentalresults.Thesesimulationswerelaterimproveduponby Noelting&Wessels ( 2008 ),inwhichaLBMwasutilizedforthesamelandinggeargeometry.Whilethesteadypressuredistributionsaroundthewheelswereseentobeverysimilarforallthreesimulationtechniques,the 65

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LBMsimulationstandsoutwithmuchmoreaccurateliftanddragcalculationsandgoodagreementwithexperimentalmeanowPIVdataofthemid-wheelplane. Computationalsimulationsonhigher-delitylandinggeargeometrieshavealsobeenperformed.In VandeVen&Louis ( 2009 ),adelayedDESsimulationwasperformedonapartially-dressedmodelofa1/4scalereplicaofaG550noselandinggear.Anunstructuredthree-dimensionalgridof58millioncellswasutilized,withthesmallesttestedsimulationtimestepbeing210)]TJ /F7 7.97 Tf 6.58 0 Td[(5secondsandasimulationdurationof0.05seconds.Thisallowedamaximumresolvablefrequencyof5kHzforanalysisofsimulatedsurfacepressurespectra,whichwasthencomparedwiththoseexperimentallymeasuredbyNASAandtheUniversityofFlorida( Neuhartetal. 2009b ; Zawodnyetal. 2009 ).Simulatedspectraforkeymodelsurfacelocationscorrespondingtophysicaltransducerlocationscomparedwellwithbothsetsofexperimentaldata,howeverthesmallsimulationtimesinducedsporadicuctuationsinthepowerspectraldensities.ThisstudywasusefulindemonstratingtheimprovedcapabilitiesofDESsimulationstoresolveowsaroundcomplexgeometriesgivenaneenoughcomputationalgridwithemphasisonregionsofdownstreamcomponentinteractions( VandeVen&Louis 2009 ). Noeltingetal. ( 2010 )conductedahybridCFD/CAAstudyonthesameG550geargeometryasdiscussedinthepreviousparagraph.TheoweldaroundthegearwascomputedusingaLBMsimulationwhoseunsteadysurfacepressureswerethenusedtocomputeafar-eldacousticsolutionwithaFW-Hsolver.ThecomputationalgridusedforthisanalysiswasCartesian(gridcellsarecubicinshape)withvariableresolutionandconsistedofatotalof32millioncells.Thenestlevelofresolutionwasreservedfortheregionsimmediatelysurroundingthemainstrutofthemodel,withresolutiondecreasingasdistancefrommodelgeometriesisincreased.Meanowandsurfacepressuredatawerereportedforeectivesimulationtimesof0.25and0.3seconds,respectively.ComparisonofsimulatedmodelwakevelocityandvorticitywithexperimentalPIVdatareportedin Neuhartetal. ( 2009b )showedexcellentagreement,withtheexceptionofaslightlylarger 66

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wakewidthpredictedbytheLBM.Thesurfacepressurespectrawerealsoseentoexhibitreasonableagreementwithexperimentalresultsuptofrequenciesaround3-4kHz. 2.5UnresolvedTechnicalIssues Itcanbeseeninthisliteraturereviewthatextensiveresearchhasbeendonetomitigatetheaerodynamicnoisegeneratedbylandinggearandlandinggear-typegeometries.Thecommontrendbetweentheuiddynamicstudiesistheidenticationofandfocusontheowinteractionsbetweenclosely-spacedgeometries.Unfortunately,themajorityoftheseexperimentalstudieshavebeenperformedondrasticallysimpliedgeometriessuchastwo-dimensionaltandemcylinderstudiesorgearmodelsconsistingofgenericandbulkygeometriesthatlackthenerstructuraldetailsindicativeofactuallandinggears.Fluiddynamicstudiesthathavebeenperformedonmoredetailedgeargeometrieshavecommonlylackedadirectacousticcomparisontocorrelatethehydrodynamicnear-eldwiththeacousticfar-eld.Studiesoffulllandinggearreplicascansometimesevenbetoocomplextodevelopadetailedunderstandingoftheowphysicsresponsiblefornoisegeneration. Veryrarelyhasasingleaeroacousticfacilityreportedbothdetailedaerodynamicandacousticresultsforagivenrepresentativelandinggeargeometry.Finally,whiletherehasbeenconsiderableadvancementsinthecapabilitiesofCFDandCAAmethods,therearestilldiscrepanciesbetweenthemandexperimentalresultsforthemtobesolelyreliedupon.Computationalmethodscanalsobeverylimiting,requiringextremelyhighandsometimesimpracticalgridresolutionsandcomputerresourcestobeabletocaptureallowfeaturesofinterest.Basedonthesetechnicalissues,itisthereforebelievedthattheisolationanddetailedaerodynamicandacousticanalysisofrepresentativegearsub-systemsmustbeperformedinordertobetterquantifytheirindividualacousticcontributions. 67

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2.6ExperimentalandComputationalApproach AscaledmodelofarepresentativenoselandinggearshockstrutsystemwillbedesignedandtestedwithintheUniversityofFloridaAeroacousticFlowFacility(UFAFF).Aerodynamicmeasurementswillconsistofsteadysurfacepressuremeasurementstodeterminethemeanpressureloadingsexperiencedbythemodel,unsteadysurfacepressuremeasurementsatstrategiclocationstoidentifyspectralfeaturesduetoeventssuchasowseparationandvortexshedding,andow-eldsurveysofwakeandinter-componentregionsusingstereoscopicparticleimagevelocimetry(SPIV).Acousticmeasurementswillincludeafar-eldlineararrayofmicrophonestodeterminethesoundlevelanddirectivityofthemodel,aswellasaphasedmicrophonearrayfornoisesourcelocalization.ComputationalsimulationsusingPowerFLOW,alattice-Boltzmannsolver,willalsobeutilizedtocomplementtheexperiments.InadditiontoCFD,thissoftwarehasCAAcapabilitiesthroughabuilt-inFfowcs-WilliamsandHawkings(FW-H)acousticsolver. 68

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Figure2-1. Illustrationofanaircraftyovernoisesourceidenticationexperiment.[FigureadaptedfromBrusniak,L.,Underbrink,J.R.,andStoker,R.W.2006AcousticImagingofAircraftNoiseSourcesusingLargeAperturePhasedArrays.(page12,Figure5),12thAIAA/CEASAeroacousticsConference,AIAAPaper2006-2715.] Figure2-2. Schematicofdisturbedowregionsaroundacircularcylinder.[FigureadaptedfromZdravkovich,M.M.1997FlowAroundCircularCylinders,Vol.1:Fundamentals.(Chapter1,page4,Figure1.1).] 69

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Figure2-3. Schematicoftandemcylinderexperimentalconguration.[FigureadaptedfromJenkins,L.N.,Khorrami,M.R.,Choudhari,M.M.andMcGinley,C.B.2005MeasurementsofUnsteadyWakeInterferenceBetweenTandemCylinders.(page9,Figure3),11thAIAA/CEASAeroacousticsConference,AIAAPaper2005-2812.] A B Figure2-4. Representativesimplefour-wheellandinggeargeometry. 70

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Figure2-5. LaserlightsheetforPIVmeasurementsofwake-bodyinteractionsbetweentandemwheels. Figure2-6. Schematicofwindtunneltestsectioncongurationforyovermicrophonearraymeasurements.[FigureadaptedfromQuayle,A.R.,Dowling,A.P.,Babinsky,H.,Graham,W.R.,andLiu,Y.2008MechanismsforModelScaleLandingGearNoiseGeneration.(page4,Figure4),46thAIAAAerospaceSciencesMeetingandExhibit,AIAAPaper2008-16.] 71

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Figure2-7. Schematicofacoustictestingcongurationinanopen-jetaeroacousticfacility.[FigureadaptedfromGuo,Y.P.,Yamamoto,K.J.,andStoker,R.W.2006ExperimentalStudyonAircraftLandingGearNoise.(page308,Figure3),JournalofAircraft,43(2),306-317.] A B Figure2-8. Comparisonof(A)actualGulfstreamG550noselandinggearwiththe(B)high-delity1/4-scalereplica(image(A)courtesyofGulfstreamAerospaceCorporation). 72

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Figure2-9. Scanningplanesfor2-dimensionalPIVmeasurementsonthe1/4-scaleGulfstreamG550noselandinggearmodel. A B C Figure2-10. Illustrationoflandinggearfairingnoisereductionconcepts:(A)untreatedmodel,(B)modelwithasolidfairing,(C)modelouttwithporousfairings.[FigureadaptedfromQuayle,A.R.,Dowling,A.P.,Babinsky,H.,Graham,W.R.,andShin,H.2007LandingGearfora`Silent'Aircraft.(page2,Figure1),45thAIAAAerospaceSciencesMeetingandExhibit,AIAAPaper2007-231.] 73

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Figure2-11. Aircurtainblowingupstreamofasimulatedlandinggearcomponent.[FigureadaptedfromOerlemans,S.anddeBruin,A.2009ReductionofLandingGearNoiseUsinganAirCurtain.(page16,Figure9),15thAIAA/CEASAeroacousticsConference,AIAAPaper2009-3156.] A B Figure2-12. (A)Proleand(B)planviewsofbroadbandnoisereductionexperimentusingplasmaactuatorsonalandinggearsub-system.[FigureadaptedfromHuang,X.,Zhang,X.,andLi,Y.2010Broadbandow-inducedsoundcontrolusingplasmaactuators.(page2480,Figure3),JournalofSoundandVibration,329,2477-2489.] 74

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Table2-1. SummaryofTotalAirframeNoiseStudies Author(Year)Remarks Healy 1974OASPLairframenoisepredictionschemedevelopedutilizingassumptionofdipoleradiation Hardinetal. 1975ImprovedOASPLairframenoisepredictiontooldevelopedbasedonfty-threedierentcommercialaircraft Revelletal. 1976Dragelementmethoddevelopedforpredictionofspectralcontentofairframenoise Fink 1979Noisecomponentmethoddevelopedforpredictionofnoisefor\dirty"aircraftcongurations Howelletal. 1986Developmentofone-dimensionalacousticimagingandde-Dopplerizationtechniquesforaircraftyoverexperiments Micheletal. 1998Full-scaleaircraftyovernoisesourceidenticationusinglogarithmicspiralmicrophonearrays Michel&Qiao 1999Engineexhaustandnoselandinggearidentiedasdominantnoisesourcesonasingle-aisleaircraft Khorramietal. 2008FlyoverexperimentsofaGulfstreamG550aircraftrevealingnoselandinggearasastrongnoisecontributor Table2-2. FlowRegimesofaCircularCylinder[TableadaptedfromZdravkovich,M.M.1997FlowAroundCircularCylinders,Vol.1:Fundamentals.(Chapter1,page18,Table1.1).] StateRegimeReRangeDescription LNoSeparation0to4-5FlowrmlyattachedtoentiresurfaceClosedWake4-5to30-48Steady,symmetric,closednear-wakePeriodicWake30-48to180-200SinusoidaloscillationofshearlayersTr-WFarWake180-200to220-250TransitionoflaminareddiesNearWake220-250to350-400TransitionofirregulareddyTr-SLLower350-400to1k-2kDevelopmentoftransitionwavesIntermediate1k-2kto20k-40kFormationoftransitioneddiesUpper20k-40kto100k-200kEddiesbursttoturbulenceTr-BLPre-Critical100k-200kto300k-340kOnsetoftransitioninfreeshearlayersSingleBubble300k-340kto380k-400kAsymmetricturbulentseparationTwoBubble380k-400kto500k-1MSymmetricboundarylayerseparationSuper-Critical500k-1Mto3.5M-6MDisruptionofseparationbubblesPost-Critical3.5M-6Mto(?)Transitionregionadvancestowardsstagnationline 75

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Table2-3. EectsofSpacingonFlowBetweenTandemCylinders( Zdravkovich 1985 ) SpacingDescription L=D<1:1BothcylindersbehaveasasinglebodywithhighStvaluesFrontcylindershearlayersdonotreattachtorearcylinder1:13:8Vortexsheddingoccursatbothcylinders Table2-4. SummaryofSimpleGeometryStudies Author(Year)Remarks Roshko 1954IdenticationofnearlyconstantSt0:21forowaroundacylinderatlowRe Roshko 1955VariationofCDandStidentiedasafunctionofblunessofabody Bearman 1969IncreaseinStforowaroundacylinderdiscoveredforCriticalReDegradationofvortexsheddingfromtonaltobroadbandbehaviorforSuper-CriticalRe Zdravkovich 1985CategorizationofowphenomenaoftandemcylindercongurationsbasedonL=Daspectratio Fitzpatrick 2003Near-eldturbulenceandfar-eldacousticcharacterizationoftandemcylindersforseveralL=D Jenkinsetal. 2005,2006Detaileduiddynamiccharacterizationofgapowandwakeregionsoftandemcylinders Hutcheson&Brooks 2006Far-eldacousticanalysisofsingleandmultiplecylindercongurations Lockardetal. 2008Far-eldacousticsimulationsoftandemcylinderarrangementsshowreasonableagreementwithpreviousexperiments Neuhartetal. 2009Analysisofhighcircumferentialresolutionoftandemcylindersurfacepressureuctuations 76

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Table2-5. SummaryofLandingGearExperimentalStudies Author(Year)Remarks Dobrzynski&Buchholz 1997Far-eldacousticstudiesoffull-scaleAirbus2-and4-wheelmainlandinggears Lazos 2002Fluiddynamicsanalysesbetweentandemwheelsofagenericfour-wheellandinggeargeometry Ravettaetal. 2004Acousticstudyofa26%-scalereplicaofaBoeing777mainlandinggear;wake-bodyinteractionsconrmedtobeimportantnoisecontributors Dobrzynskietal. 2005Implementationofsolidfairingnoisereductionconceptsonfull-scalenoseandmainlandinggears Ringshiaetal. 2006PIVstudiesonregionsbetweentandemwheelsanddragbracesof13%-and26%-scale,high-delityreplicasofaBoeing777mainlandinggear Guoetal. 2006Far-eldacousticscalingandnoisesourceidenticationanalysesonfull-scalereplicaofaBoeing737mainlandinggear Humphreys&Brooks 2007NoisespectraanddirectivityanalysisofscaledreplicaofaBoeing777mainlandinggear Quayleetal. 2008Acousticanalysisofafour-wheellandinggearidentifyingregionbetweenin-linewheelstobeanimportantnoisecontributor Boorsmaetal. 2008Achievementofbroadbandnoisereductionswithutilizationofporousfairingsonasimplied1/4-scalereplicaofanAirbusA340mainlandinggear Neuhartetal. 2009Aerodynamicstudyofa1/4-scalehigh-delityreplicaofaGulfstreamG550noselandinggear Dobrzynskietal. 2009AssessmentonpassivenoisereductiondesignsforanA340\style"mainlandinggear Oerlemans&Bruin 2009Implementationofan\aircurtain"locatedupstreamofasimulatedlandinggearcomponenttoreducelocalhighspeedows Oerlemans&Sandu 2010Reductionoflow-andmid-frequencynoiseforowaroundI-beamgeometriesusingmeshfairings Huangetal. 2010Utilizationofplasmaactuatorsonalandinggeartorquelinksub-systemtoreducewakeimpingementnoise 77

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Table2-6. AdvantagesanddisadvantagesofcommonCFDalgorithms AlgorithmAdvantagesDisadvantages DNS-Capableofresolvingallscalesofturbulence-Computationallycostly-Canevaluatestatisticalquantitiesnotexperimentallymeasurable-LimitedtolowReLES-Capableofresolvinglargeandmediumscalesofturbulence-ProhibitiveforscenarioswithturbulentboundarylayersRANS-ManageablecomputingrequirementuptohighRe-Turbulenceassumptionsrequiredduetotimeaveraging-Utilizationofthetime-averagedNavier-Stokesequations-Solutiondoesnotfollowfromrstprinciples Table2-7. SummaryofLandingGearComputationalStudies Author(Year)Remarks Hedgesetal. 2002ComparisonofDESandURANSsimulationswithexperimentaldataforowaroundageneric4-wheellandinggear Noelting&Wessels 2008LBMsimulationofaforementionedlandinggeargeometrywithimprovedpredictionsforliftanddragforces VandeVen&Louis 2009DESsimulationof1/4-scalereplicaofaG550noselandinggeargeometryandcomparisonwithexperimentalresults Noeltingetal. 2010HybridCFD/CAAstudyonaforementionedG550geargeometryusingLBMsimulationtechniques 78

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CHAPTER3EXPERIMENTALANDCOMPUTATIONALPROCEDURES Inthischapter,theexperimentalsetupwillbedescribed.First,adetaileddescriptionofthelandinggeartorquearmassemblymodelwillbeprovided,followedbyadiscussionofthetoolsusedforaeroacousticdataacquisitionandanalysis. 3.1TorqueArmSub-systemModelDesign Themodeldesignedforthisstudyisacanonicalrepresentationofalandinggearshockstrutcoupledwithadownstreamtwo-armtorquelinkapparatus.ThegeometryofthiscongurationisadaptedfromthatofaGulfstreamG550noselandinggear.However,itisageometrythatiscommontomanycommercialaircraft.AnillustrationoftheG550shockstrut-torquelinkassemblycanbefoundinFigure 3-1 Themodelunderinvestigationisa1/2-scalefurthersimplicationoftheG550noselandinggeartorquelinkassemblyandisshowninFigure 3-2 .Astheseguresshow,theupperandlowertorquearmjunctionsattherespectivemainstrutandwheelaxlearebothreplacedwithsimpliedangejunctions.Inaddition,theshockpistonandmainstrutarereplacedwithauniformhollowcylinderthatextrudesaboveandbelowthetorquelinkassembly.ThediameterofthiscylinderisD=1.5"(38.1mm),basedonthe3"(76.2mm)diameterstrutpresentontheG550noselandinggear.ThetorquearmsthemselvesarealsosimpliedfromthetaperingI-beamprolesoftheG550noselandinggear,andareshapedastaperingatplatesofconstantthickness.Thelocationwherethetorquearmsarehingedtogetherisalsomodiedfromthetongue-in-groovehingeshowninFigure 3-1B toaside-by-sidehinge.Asaresult,thesesimpliedtorquearmsareofidenticalgeometry,yieldingamodelthatishorizontallysymmetricaboutthelocationwherethetorquearmsarehingedtogether.ThevariablenatureofthegeometryisdenedbythejunctionseparationdistanceHandthetorquearmseparationangle,whicharevisuallydenedinFigure 3-2B .Thesequantitiesarevariedinordertotestseveralgeartorque 79

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armcongurationsthatmayexhibitdierentfar-eldacousticlevelswhencomparedwiththosefortheG550noselandinggearbaselinecase. 3.1.1TheCylinder Thecylinderportionofthemodelisdividedintothreemainsections,allofwhicharemadeofAluminum6061material.Therstsectionisa\clamshell"piecethatissub-dividedintotwocylindricalhalvesthatmatetogether,allowingdirectaccesstothesurfacepressureinstrumentationfromtheinsideofthecylinder.Thesecylindricalhalvesareinstrumentedwithaseriesofsurfacepressuretapsconsistingofsmallsteeltubulationsthatareush-mountedwiththecylinderoutersurface.Thesepressuretapsservethedualpurposeofbothsteadyandunsteadysurfacepressuremeasurementcapabilities.Moredetailedexplanationsofthemodel'ssurfacepressuremeasurementcongurationarepresentedin Chapter3.4 .Theothertwosectionsofthecylinderareextensionpiecesthatextrudeoutofthewindtunneltestsectionandaresecuredtotheteststand.Eachsectionofthecylinderishollowforinternalroutingofpressureinstrumentationlinesoutofthetestsection.Figure 3-3 showsanexplodedillustrationoftheindividualcomponentsthatmakeupthemodelcylinder. SurfaceTreatments: .Toinitiateturbulentboundarylayerseparation,themodelcylinderisouttwithaserratedor\pinked"taperunningalongtheentirespanofthemodel.TheserrationpatternandcircumferentialplacementofthetriptapeareshowninFigure 3-4 .Thistapewasfabricatedmanuallybylayeringtwostripsofstore-boughtlabelingtapeandserratingbymeansofapinkedrotarycutter.Notethatthethicknessofthetapeusedwasmeasuredtobeapproximately0.2mm(0.008")andwascenteredbetween45and60.Alaserlinewasutilizedtoilluminatethecylinderpressuretapsat=60toserveasavirtualstraightedge(Figure 3-4C ).Thiswasdonetoensureasaccurateaplacementofthetapeaspossible.Whileseveralmethodsofboundarylayertrippingwereconsideredforthisstudy,thistechniquewaschosenbasedonsingleandtandemcylinderstudiesthatshowedtheuseofpinkedtapeinthisconguration( Jenkins 80

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etal. 2005 2006 ; Neuhartetal. 2009a )toyieldcircumferentialCpdistributionsthatcloselyresemblethoseofacylinderinsupercriticalow( Roshko 1961 ). Inadditiontoaboundarylayertrippingmechanism,themodelcylinderisalsoouttwithahollowaluminumhelicalwirewrapforthepurposeofmitigatingvortexsheddingfromthemodelsurfaceoutsideoftheregionofinterest(aboveandbelowtheregionoccupiedbythetorquearms).Thiswasimplementedinordertodampenthecontributionofthewell-knownAeoliantonebehaviorofabarecylinderincross-ow,toassistwithisolatingtheacousticcontributionofthetorquearmgeometryitself( Hutcheson&Brooks 2006 ).ThegenerallayoutofthehelicalwirewrapappliedtothemodelispresentedinFigure 3-2A ,andadescriptionofthewirewrapdimensionalparametersareshowninFigure 3-5 .Severalwirewrapsofdierentdiameterwereinitiallyslatedtobetestedonthecylindertoachieveoptimalvortexsheddingmitigation.Thesehavenon-dimensionaldiameters(relativetothecylinderdiameter)ofd=D=0.083,0.125,and0.167.Unfortunately,onlythewirewrapswiththetwosmallestdiameterscouldbetestedsincethelargestonewastoorigidtowraparoundthecylinder.Thefar-eldresultsofthetwotestedhelicalwirewrapsonatrippedaluminumcylinderareshowninFigure 3-6 .Astheresultsshow,appreciablereductioninspectrallevelsisachievedforbothtestedwirewrapdiameters.Thisismostobservableattheapparentsheddingfrequencyof352Hz,whereasindicatedinTable 3-1 ,a7dBreductionisevidentforbothcongurations.Inaddition,anOASPLreductionof4and3dBareobservedforthed=D=0.083and0.125cases,respectively.Therefore,thewirewrapofdiameterd=D=0.083,oradimensionalwirewrapdiameterofd=3.175mm(0.125in.),waschosentobeusedinthetorquearmexperiments.Finally,thehelicalwirewrappitchwasdenedtobes=D=1.67.Thiswasbasedonthendingsof Hutcheson&Brooks ( 2006 )thatahelicalwirewrapwithapitchlessthanthecoherentlengthofthecylinderwillassistinthedestructionofcoherentshedvortices.Inthissamestudy,thecoherentlengthwasfoundtobeontheorderof4-5cylinderdiameters. 81

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3.1.2TheTorqueArms Eachofthetwotorquearmsconsistofahollowframewithafrontandrearcoverplate,eachofwhichhastheabilitytobeinstrumentedwithsurfacepressuretransducers.AnillustrationofthetorquearmcomponentscanbeseeninFigure 3-7 .Asthisgureshows,eachtorquearmconsistsofatorquearmframeandafrontandbackcoverplate.TheframeswererapidprototypedoutofDuraformRmaterial,whilethecoverplatesweremachinedoutofDelrinR.Duetoalimitednumberofavailableinstrumentationchannels,onlyonetorquearmisusedtoacquiredataforasingletunnelrun.Therefore,theoverallmodelassemblyconsistsofaninstrumentedtorquearmaswellasanuninstrumentedone. 3.2ModelCongurations Thetorquearmgeometrywasvariedtoidentifyhowtheacousticsignaturechangedasafunctionoftorquearmseparationangle,andstreamwiseorientation.Thereare4primarymodelcongurationswhicharepictoriallypresentedinFigure 3-8 .Themotivationbehindtherst3ofthesecongurationsistoidentifyvariationsintheacousticsignatureofthemodelasafunctionoftorquearmspacing.Thenalconguration,ontheotherhand,istestedbasedonpreviousstudiesthatindicatehowtheplacementofthesharper-edgedgeometryofapairoftandemgeometriesupstreamoftheotherhasthepotentialtoyieldoveralllowerbroadbandfar-eldacousticlevels( Anglandetal. 2010 ; Dobrzynskietal. 2005 ).Anerresolutionschemeof=10wasalsotestedtoidentifynear-eldpressureandfar-eldacousticscalingtrends.Table 3-2 presentstheseparationdistanceaspectratiosbetweenthecenterlineofthemodelcylinderandthecentroidofthetorquearmhinge,aswellastheverticaldistanceofthejunctionfromthemodelcenterlineforalltestedcongurations.Thefulltestingmatrixforthesecongurationsispresentedin Section4.1 3.3TestingFacility AllexperimentswereperformedintheUniversityofFloridaAeroacousticFlowFacility(UFAFF).Theexperimentalworkwasdividedintotwophases:(1)modelsurface 82

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pressureandfar-eldacousticdatameasurementandanalysis,and(2)turbulentoweldmeasurementandanalysis.TheUFAFF,depictedinFigure 3-9 ,isalow-noise,open-jetacousticwindtunnelwithatestsectionmeasuring29"highby44"wideby120"long(0.737mby1.118mby3.048m)installedinanISO3745-certied100Hzanechoicchamber.Theinnerwalls,oor,andceilingoftheanechoicchamberarepopulatedwith36"(0.914m)-tallacousticwedges.Theoorofthetestsectionisalsopopulatedwithacousticwedgesmeasuring11.75"(0.298m)tall.Theopen-jettestsectionisboundedbyanaluminum-frameteststand,withinwhichaerodynamicmodelsandacousticfoamsidewallsmaybeinstalled.Themaximumemptytestsectionvelocityisapproximately72m/s. ThetorquearmmodelwasinstalledintheUFAFFinaverticalorientation,securedaboveandbelowthetestsection(Figure 3-10A ).Themodelwaspositioned18"(457.2mm)downstreamfromthetrailingedgeoftheinlet.Thisdownstreamdistancewasconsideredtobeadequatefromaowqualityperspectivebasedontheworkof Mathew ( 2006 )aswellasanacousticsperspective,ensuringadequatelineofsightbetweenthemodelandphasedandlineararraymicrophoneelements.Fortheacousticportionoftesting,theowoftheopenjetwaspartiallyboundedbymeansoftwoacousticfoamsidewalls,whichalsoservedasanacousticinsulatorforthemetaltestsectionhardwareaboveandbelowthetestsection.Additionalacoustictreatmentsaroundthetestsectionconsistedof3"(76.2mm)wedgefoamsheetsforcoveringbulktestsectioncomponentsaswellas0.5"(12.7mm)thickNomexbercloth.AphotographoftheUFAFFtestsectionwithmodelinstalledandouttforacoustictestingisshowninFigure 3-10B 3.4ModelSurfacePressureMeasurements Oneoftheprimarystrategiesimplementedinthedesignofthetorquearmmodelwastestingexibility.Thisincludedboththeabilitytomodifythetorquearmtodierentgeometriccongurationsaswellastohaveaninterchangeablesurfacepressuremeasuringsystem.Thismeasurementsystemisdesignedtobeabletobeeasilyconvertedbetweena 83

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steadyandunsteadymeasurementconguration.Thedesignofthissystemisdescribedinthefollowingsections. 3.4.1SteadyPressures Steadypressuremeasurementsareanimportantbaselinemeasurementtoolinaerodynamicows.Inparticular,theyprovideanimportantstartingpointforcomparisonsbetweenexperimentalandcomputationaldatasets.Thesteadysurfacepressurecoecient,Cp,isacquiredintwocrucialareasonthemodel:aroundthecircumferenceofthecylinderwithinthespanwiseregionenclosedbythetorquearms(denotedastheregionofinterest),aswellasonthefrontandrearsurfacesofoneofthetorquearms.NotethatCpisdenedas Cp= ps)]TJ /F3 11.955 Tf 11.95 0 Td[(p1 1 2U21=P q1;(3{1) wherep1,,andU1arethefreestreampressure,density,andvelocityrespectively,while psistheaveragemeasuredsurfacepressure.NotethatthequantityPrepresentsthesurfacepressuremeasurementrelativetothetunnelfreestreampressure,whichismeasuredviaapitotstaticprobe.Furthermore,thedynamicpressure,q1,isdirectlymeasuredfromthepressuredierencebetweenthestagnationandstaticpressureportsofadigitalgagepressuretransducer. 3.4.1.1ModelMeasurementLocations Cpmeasurementsonthemodelcylinderareacquiredalongfourcircumferentialringswith0.4064mm(0.016")innerdiameterpressureports.Thesepressuretapsconsistofsteelhypodermicneedletubulationsthatareush-mountedtothecylindersurfaceandarebentat90insideofthehollowcylinder.Thesetubulationsareconnectedtoaseriesofpressurescannersvia0.027"(0.686mm)innerdiameterurethanetubing.Anisometricviewoftheforward-facinghalfoftheinstrumentedcylinderisshowninFigure 3-11A ,wherethelocationsofthepressuretapringsareclearlyindicated.Notethatinadditiontoacenterplaneringofpressuretaps,therearetworingslocatedsymmetricallyat2D 84

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fromthecenterplaneandanotherat+3Dfromthecenterplane.ThetworingsatZ=0andZ=)]TJ /F1 11.955 Tf 9.29 0 Td[(2Darefullypopulatedwithtapsat15resolutionwhiletheonesatZ=2DandZ=3Darecoarselypopulatedwithtapsatevery30,yieldingatotalof72cylindersteadypressuremeasurementlocations.Thispressuretapcongurationwaschosenbasedonthenumberofpressuresensorchannelsavailablefortesting.ThesteadypressuretaplayoutforthetorquearmisshowninFigure 3-11B andconsistsofaseriesofrowsoftapsthatareequallyspacedadistanced=12.7mm(0.5")alongtheheightofthetorquearmplate.Asthetorquearmcoverplatetapers,theaspectratioofhorizontaltapspacingrelativetothetorquearmwidthremainsconstant.Inotherwords, wp(y) Wta(y)=0:345(3{2) Thereare11rowsof3tapseach,yieldingatotalof33steadypressurechannels.Inaddition,thisinstrumentedcoverplateisinterchangeablebetweenthefrontandbacksidesofthetorquearm.Thesesteadypressureports-bothonthecylinderandtorquearm-alsohavetheabilityofservingasunsteadyones.Thiscapabilityisdiscussedinthefollowingsection. 3.4.1.2DataAcquisitionandUncertainty Themodelsteadypressuresweremeasuredusingatotalof3EsterlineModel9116Netscannermodules,eachwith16availablepressurechannels.Sincethisonlytotals48channelsavailableforsimultaneousdataacquisitionandthereareatotalof105steadypressuremeasurementlocationsonthemodel,theyweredividedinto3separatescanningzones.Zone1isdedicatedtothecircumferentialtapslocatedatZ=0and3DwhileZone2includesthecircumferentialtapsatZ=2D,eachofwhichconsistof36taps.Finally,the33pressuretapslocatedonthetorquearmcoverplateareassignedtoZone3.Dataacquisitiononall3measurementzonesisperformedmanuallyforasingletunnelrun,inwhicheachzoneismanuallyattachedtotheNetscannersuponthecompletionofacquisitionofthepreviouszone. 85

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TheNetscannermoduleshavepressuremeasurementrangesof10in.H2O(2.49kPa),1PSID(6.895kPa),and5PSID(34.474kPa).Inordertopreventdataclipping,greatcarewastakenconcerningassignmentofspecicpressuretapstothedierentscannersbasedonavailablepressurerange.Forexample,asinglecylinderinpost-criticalowhasbeenevidencedtoexhibitasuctiontroughofCp)]TJ /F1 11.955 Tf 23.13 0 Td[(2:0( Roshko 1961 )inthevicinityof=75relativetotheoncomingowdirection.Forthetestingconditionsperformedinthisstudy,thiswouldexceed2.49kPaofsuction,thereforeexceedingtheacceptablerangeofthe10in.H2Omodule.Therefore,thistapaswellasthetapsoneithersideofit(=60;75;90),wereconnectedtothe1PSIDmodule.Pressuredataforeachzonewasacquiredforadurationof60secondsatasamplingrateof2Hz,yieldingatotalofN=120samples. Theroot-mean-square(rms)errorofanydatasetofconstantsamplingratecanbedenedas urms=q u2r+u2b;(3{3) whereu2rrepresentstherandomuncertaintycomponentofthesampledmeasurement,whereasu2brepresentsthebiasorsystematicerror.InthecaseofaCpmeasurement,urreducestothe95%condenceintervalforasamplemeasurementbasedonthecommonlyutilizedstudent-Tdistribution.ForN=120samples,thisrandomerrorbecomes ur=1:98 p N;(3{4) whererepresentsthestandarddeviationofthedataset.Thebiaserrorsontheotherhand,varydependingontherangeofthepressurescanner,andaredenedintermsofapercentageofthefull-scale(FS)rangeofthescanner.TheseerrorsaresummarizedinTable 3-3 86

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Thetotalpropagateduncertaintyforameasurementbasedonmultiplemeasuredparameterscanbeaccountedforusingtheroot-sum-squares(RSS)method: uX=s @X @y1uy12+@X @y2uy22;(3{5) whereX=f(y1;y2).Inthecaseofsteadypressuremeasurements,Cp=f(P;q1),makingtheRSS-generateduncertainty uCp=s @Cp @PuP2+@Cp @q1uq12=s 1 q1uP2+P q21uq12:(3{6) Therefore,allCpmeasurementswererecordedintheformofCpuCpandindicatedvisuallyintheformoferrorbarsin Section4 3.4.2UnsteadySurfacePressureMeasurements Unsteadysurfacepressuremeasurementsareanimportantmeasurementtechniquesincetheycancapturethehydrodynamicpressureuctuationsthatultimatelymanifestintheacousticfar-eldassound.Thiscoupledwithspacelimitationsduetothesmallscaleofthemodelrequiredagreatdealofcareconcerningthestrategicplacementofpressuresensorsthroughoutthemodel.Thetorquearmgeometryunderinvestigationposesaninterestingchallengeintermsoftakingunsteadysurfacepressuremeasurements.Studiesonowaroundclosely-spacedgeometries,suchastandemcylinders,haveshownRMSpressureuctuationsonthedownstreamcomponenttobemuchhigherthanthoseexperiencedbytheupstreamone( Jenkinsetal. 2005 2006 ).Thisisprimarilyduetotheimpingementoftheshearlayerfromtheupstreamcomponentontothedownstreamone.Therefore,itisimportantthatthetransducersusedinthisstudyhavetheabilitytowithstandthepressureamplitudesexperiencedbythedierentcomponents. 3.4.2.1ModelSensorLocations Inadditiontothepressureportsdiscussedintheprevioussection,thereareseveraladditionalsetsonthemodelthatarededicatedtounsteadypressuremeasurements.Theseincludeaspanwisearrangementofpressureoricesonthecylinderaswellasa 87

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customizedtorquearm.ThesearedetailedinFigure 3-12 .IfattentionisfocusedonthecylinderportionofthemodelinFigure 3-12A ,aspanwisedistributionofpressureportscanbeobserved.ThissensorlayoutwasemulatedfromthosepresentontheNASAtandemcylindersin Jenkinsetal. ( 2006 ); Neuhartetal. ( 2009a ).Theyrepresentanaperiodicdistributionthatprovideaspanwisesurveyofpressureuctuationswhileminimizingthechancesofspatialaliasinginthemeasurements.Thenon-dimensionalvertical(Z-direction)locationsofthesesensorsrelativetothemodelcenterlinearedetailedinTable 3-4 .Notethatthecircumferentiallocationofthisrowofsensorsisadjustable,howeverthetestedlocationforthisstudyisat=135relativetothefreestreamowdirection.Itisimportanttonotethatduetomodelinternalspacelimitations,notalloftheseportscanbepopulatedwithsensorsforagiventunnelrun.Specically,itwasdeterminedthatamaximumof7sensorscouldbeplacedwithinthecylinder.Therefore,asensorplacementschemewasdecideduponthatwouldmaximizespatialcoverageofthecylinder.TheselocationsareemphasizedinTable 3-4 Asforthetorquearm,anadditional7portswereutilizedforunsteadypressuremeasurements,thelocationsofwhicharepresentedinFigure 3-12B .Notethattwosensortypeswereusedinthetorquearm,4ofwhicharerecessedelectrets-thedesignofwhichispresentedinthefollowingsection-whilethenal3areLQ-125surfacemounttransducersmanufacturedbyKuliteSemiconductorInc.TheKulitetransducersaresealedgage(SG)deviceswitharatedpressurerangeof5PSISG.Boththesealednatureandhighpressurecapabilitiesofthesedevicesrequiredthedevelopmentofadditionalinterfacecircuitrytocomplementthem.Theywereouttwithanin-lineamplierpackagetoincreasethesensor'soverallsensitivityaswellasdampentheDCcomponentofmeasurement.Thedesignandperformanceofthisampliercircuitisdetailedin AppendixA 88

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3.4.2.2TransducerDesign Theunsteadypressuremeasurementmethoddesignedforthisstudyiscapableofbeingattachedtothesteadypressureportsalongwiththeadditionalonesdiscussedintheprevioussection.TheyconsistofPanasonictypeWM-61Aelectretmicrophoneshousedina\branch"cavitythatisrecessedawayfromtheowsideofthemodelsurface.Thepremisebehindthisconceptistoutilizethemicrophoneasanunsteadysurfacepressuresensorinamannerthatprotectsitfromharshenvironmentalconditionsandisnotlimitedbythepotentiallybulkysizeofthemicrophoneitself( Blackstock 2000a ).AnillustrationofthisconceptisshowninFigure 3-13 .Asthisgureshows,therecessedmicrophonesetupconsistsofasmall-diameterinlettubethatisush-mountedwiththeowsurface(sameasthoseusedforsteadypressuremeasurements),extrudedbelowthesurfaceandgraduallyincreasedinarea,andhasa90tubebranchthatmatesupwiththemicrophonediaphragm.ThebranchalsocontinuestoanoutletductconsistingofaconsiderablelengthofexibleTygonRtubingthatismeanttoserveasananechoictermination.Theoveralleectofthistransducerpackageistoyieldareduced-amplitudepressuresignalseenbythemicrophoneacrossabroadfrequencyrange. Thedesignoftherecessedpressuresensorwasbasedontherequiredsatisfactionofthreeobjectives: 1. Increasingtheonsetofresonancebeyondthefrequencyrangeofinterest 2. Reducingthepressureamplitudesexperiencedbythemicrophonetoensurelinearperformance 3. Minimizingthesizeofthetransducerpackagetoallowplacementofmultipletransducerswithincloseproximitytooneanother Asonemightexpect,thesethreeobjectivesrequireacompromiseinwhichtheimprovementofoneresultsinthedegradationoftheothers.Toquantifythis,themicrophonebranchsystemwasoptimizedusingatransfermatrix(TM)approach.Traditionallyutilizedinelectricalandmechanicalvibrationtheory( Lampton 1978 ),theTMapproachimplements 89

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matrixalgebratorelatetheinputsandoutputsofaphysicalsystem.Recentsuccessfulimplementationsofthisapproachincludethemodelingoftheperformanceofsyntheticjetactuators( Yangetal. 2011 ).AdetailedderivationofthestepsfollowedintheTMapproachforthisapplicationisdiscussedinthefollowingsection.SystemModeling Figure 3-13B displaysthepressure(p0i)andvolumeow(Q0i)interfacequantitiesusedtomodelthesystemperformance.Theprimarypurposeformodelingthissystemistoestimatethereductionofthepressuresignalexperiencedbythemicrophonerelativetothetubulationmountedushwiththemodelsurface.Thisisquantiedintermsofatransferfunction(TF)computedas TF=p0end p0in:(3{7) NotethatthepressureratioinEquation 3{7 isacomplexquantitycontainingamagnitudeandphase.TheTMequationforthetotalsystemisshowninEquation 3{8 : 264p0outQ0out375=[TM3][TMInt:][TM2][TMAC][TM1]264p0inQ0in375=264T11T12T21T22375264p0inQ0in375;(3{8) wheresubscripts`Int.'and`AC'representtheinterfaceandgradualareachangesectionsofthemicrophonebranch,respectively(Figure 3-13B ).AsEquation 3{8 shows,aTMiscomputedforeachsegmentoftheduct,thenmultipliedtogethertoyieldtheoverallsystemTM. TheTMforauniformductwithmeanowassumingplanewavepropagationcanbemodeledas 264p0Q0375x=l=ejM0kcl264cos(kcl))]TJ /F5 7.97 Tf 10.5 5.25 Td[(j0c0 Ssin(kcl))]TJ /F5 7.97 Tf 13.91 5.26 Td[(jS 0c0sin(kcl)cos(kcl)375264p0Q0375x=0;(3{9) whereM0representstheMachnumberoftheowenteringtheduct,kc=k0)]TJ /F5 7.97 Tf 6.59 0 Td[(j(+M0) (1)]TJ /F5 7.97 Tf 6.58 0 Td[(M20)istheconvectionwavenumber,listheductlength,andSistheductcross-sectionalarea 90

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( Blackstock 2000b ).Inaddition,k0=2f c0isthewavenumberandisafrictionfactor.Notethatthecaseathandisconcernedwithpressureperturbationswithinaductandhaszeromeanvelocity,thereforeimplyingthatM0=0.Thisfurthersimpliestheconvectionwavenumbertokc=k0)]TJ /F3 11.955 Tf 11.95 0 Td[(jandtheductTMbecomes 264p0Q0375x=l=264cos(kcl))]TJ /F5 7.97 Tf 10.5 5.26 Td[(j0c0 Ssin(kcl))]TJ /F5 7.97 Tf 13.91 5.26 Td[(jS 0c0sin(kcl)cos(kcl)375264p0Q0375x=0:(3{10) NotethatEquation 3{10 appliestoducts1,2,and3.Thisstillleavesthematricesforthegradualareachangeandinterfaceregions.Thegradualareachangeisasimpleconicalareaexpansionandistreatedasaseriescombinationofuniformductswithasmallstepincreaseindiameter,whichisvisualizedinFigure 3-14A .Inotherwords,eachsegmentwastreatedasauniformductofdiameterDi=1 2(Dx+Dx+x).Notethatthelengthofeachductsegment,x,waschosenbasedontheresolutionofthemachineusedtorapidprototypethebranchpieces,inordertomaketheTMmodelasaccurateaspossible.AnillustrationofthediscretizationofthegradualareachangecanbeseeninFigure 3-14A Todeterminethetheoreticalpressuremeasuredbythemicrophone,someboundaryconditionsaredened.Therstonesareattheinterface,whichcorrespondstothelocationofthemicrophonesidebranch,duct4.Thepressureandvolumetricowboundaryconditionsforthisare p02=p03=p04(3{11) and Q02=Q03+Q04:(3{12) Therefore,applyingtheseconditionsalongwiththedenitionofacousticimpedancefortheinletofduct4,Z4=p04=Q04,theTMfortheinterfacecanbedenedas 264p03Q03375=26410)]TJ /F7 7.97 Tf 13.33 4.71 Td[(1 Z41375264p02Q02375:(3{13) 91

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Theoutletoftheductalsorequiresaboundarycondition.Thetwopossibleboundaryconditionsforthesectionareeitheranopenorclosedtube,representingaradiationimpedanceandinniteimpedancecondition,respectively( Blackstock 2000b ).Theseconditionsmaybemathematicallydenedas Zout;open=p0out Q0out=Rrad+j!Mrad;(3{14) where Rrad=0c0k20 2;Mrad=0(4D=3) S;(3{15) and Zout;closed=p0out 0=1:(3{16) Bothterminationcongurationsareconsideredsincetheybothhavepotentialbenetsanddrawbacks.Asealedductmitigatesthepossibilityofacousticcontaminationfromtheambientenvironment,howeverrunstheriskofthereectionoflow-frequencyacousticwavesbackintotheduct.Conversely,anopenductmitigatesthepossibilityofback-reectionyetrunstheriskofambientacousticcontamination.Anunknownofthesetuppriortoperformingexperimentalcharacterizationistheviscousdissipationinducedbytheexittubing.Therefore,decisionastowhichoftheseterminationcongurationswouldbeusedinthetorquearmmodelisdeterminedthroughexperimentalcalibrationofthedevices. Thenalboundaryconditiontobedenedisthesidebranchwherethemicrophoneissecured,whichcanbetreatedasashort,closedendduct(Figure 3-14B ).Thismeansthatifthemicrophonediaphragmistreatedasasolidwall,thentheinniteimpedanceconditionresultsinapressuredoublingeect.Therefore,therelationshipbetweenthepressureexperiencedbythemicrophonediaphragmandthatattheductentrance-andhenceattheductinterfaceaccordingtoEquation 3{11 -isapproximatedas p0end=p04 cos(k0L4)=p02 cos(k0L4):(3{17) 92

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WenowhavethetoolsnecessarytocomputethetransferfunctionasdenedinEquation 3{7 .Todeterminep04,wemustbeabletocomputep02.ThismaybedonebyisolatingtheTMrepresentingthersthalfofthesystem,inotherwordsfromtheinlettotheinterface.Mathematically,thisisexpressedas 264p02Q02375=[TM2][TMAC][TM1]264p0inQ0in375:(3{18) Whiletheinputpressurep0inisknown,thevolumeowrateQ0inisnot.Fromthedenitionofacousticimpedanceitcanbedenedas Q0in=p0in Zin;(3{19) leavingthesysteminputimpedanceZinastheonlyunknown.ItmaybecomputedbyperforminganinversematrixoperationontheoverallsystemdenedinEquation 3{8 ,whichbecomes 264p0inQ0in375=264T11T12T21T22375)]TJ /F7 7.97 Tf 6.59 0 Td[(1264p0outQ0out375=264T11T12T21T22375264p0outQ0out375:(3{20) Therefore,theinputimpedancecanbecomputedas Zin=p0in Q0in=T11p0out+T12Q0out T21p0out+T22Q0out=T11Zout+T12 T21Zout+T22:(3{21) Finally,thepressureperturbationexperiencedbythemicrophone,p0end,iscomputedbyback-substitutingtheresultofEquation 3{21 intoEquation 3{19 togetQ0in,theninsertingthisresultintoEquation 3{18 tocomputep02,andnallyinsertingthisintoEquation 3{17 Asstatedpreviously,thedesiredoutputofthisprocessisthefrequencyresponsefunction(FRF)denedinEquation 3{7 ,whichisacomplexquantity.Therefore,bothamagnitudeandphasecorrectionmustbeappliedtothepressurerecordedbythemicrophoneintheperformedexperiment.AsampleFRFcomparisoncomputedusingtheTMapproachfortheopenandsealedterminationcasesdenedinEquations 3{14 and 93

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3{16 inthissectionispresentedinFigure 3-15 .ThephysicalparametersusedtogeneratethissystemoutputaredenedinTable 3-6 .Astheresultsshow,bothterminationcongurationsyieldnearlyidenticalresponsefunctionswiththeexceptionofthebehavioratlowerfrequencies,wherethesealedductexhibitslowerfrequency\ripples".Theseripplesareduetothereectionoflowfrequencyacousticwavesbackthroughthebranchsystemuponreachingthesealedendoftheduct.Furthermore,itcanbeseenthattheFRFmagnitudedisplaysagradualroll-oinrelativepoweruntilaresonanceoccursatapproximately8.5kHz,whichalsocoincideswithaphaseosetof-180.Fabrication Theactualmicrophonebranchesweremanufacturedviamicro-resolutionstereolithography,alayeredrapid-prototypingprocess.Thismethodoffabricationwaschoseninordertoensurereproducibilityofthesmall,intricatefeaturespresentwithinthebranch.Themicrophonesusedtopopulatethesehousingsare6-mm(0.236in.)diameterPanasonicWM-61aelectretcondensers,whichhavebeenusedinnumerousaeroacousticapplicationsincludingphasedmicrophonearrays( Brusniaketal. 2006 ; Zawodnyetal. 2009 ).Animageofafully-assembledrecessedmicrophonepackageisshowninFigure 3-16A .Notethatthetubulation,electret,andTygonRexittubingwereadheredtothemicrophonebranchviaRTVsiliconeadhesive.Thiswasdonetoprovidearelativelyrigidseal,whilealsoallowingeasyremovalofcomponentsintheeventofdamage.Figures 3-16B and 3-16C showinstallationoftherecessedsensorsinthemodelcylinderandtorquearm,respectively.IfattentionisdirectedtoFigure 3-16C ,thetorquearmsensorinstallationsetupisdividedintothreesub-images.ThersttwooftheseillustratethemountingofthethreeKulitesensors,whilethethirddisplaysthetorquearmwithallrecessedelectretsinstalled.Notethatthefthelectretinthisgurewasremovedpriortotestingduetocrowdingofinstrumentationlines(indicatedwitha $ symbol). Forthisstudy,twodierenttubulationlengthswereused;oneforthecylindersensorsandtheotherforthesensorslocatedinthetorquearm.Thiswasdonebecauseofthe 94

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expectedhigherpressureuctuationlevelsexpectedonthetorquearmduetoshearlayerimpingementfromthecylinder.Thelongerinlettubulation,thus,wasexpectedtoyieldalargerreductioninpressurelevelsexperiencedbythesensortoensurelinearperformance.Asaresultofthisincreasedinletlength,onsetofresonanceisexpectedtooccuratalowerfrequency.Comparisonsofthecomputedfrequencyresponsesforthetwotubulationsizesandarepresentedin Section3.4.2.3 3.4.2.3SensorCharacterizationExperimentalCharacterizationSetup Characterizationoftherecessedmicrophonestookplaceinanacousticplanewavetube(PWT)of0.335"(8.5mm)squarecross-section.Asthenameimplies,anacousticplanewavetubeisarigidductthatonlyallowsthepropagationofplanarwavesbelowacertaincut-onfrequency,fc.Belowthisfrequency,transducerslocatedanidenticaldistancefromanacousticdriverwillexperiencethesamepressureeld.Thecut-onfrequencyforasquarewaveguidewithanedgelengthacanbecomputedas( Blackstock 2000b ) fc=c0 2a;(3{22) wherec0isthespeedofsoundinthecalibrationmedium.Theplanewavetubeutilizedforthesecalibrationshasanedgelengthofa=8:5mm,yieldinganeectivecut-onfrequencyoffc20:3kHz,assuminganominalspeedofsoundofc0=345m/sinair.ThisPWTwaschosensinceit'sestimatedcut-onfrequencycoincideswiththeupper-endfrequencycapabilitiesoftheWM-61aelectretmicrophones.Thecalibrationwasperformedinaside-by-sidemannerinwhichboththerecessedelectret-referredtoasthedeviceundertest(DUT)-anda3.175-mmdiameterBruel&KjaerType4138referencemicrophoneareush-mountedwiththeinnerwallofaremovableendplate.Figure 3-17 presentsbothaschematicandaphotographofthePWTcalibrationsetup. Thegoalofthiscalibrationsetupistoobtainthefrequencyresponsefunction(FRF)oftherecessedelectretpackagerelativetotheush-mountedreferencemicrophone.The 95

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FRFoftherecessedtransduceriscomputedas H(f)=^Gyx(f) ^Gyy(f);(3{23) where^Gyx(f)representsthecross-spectraldensitybetweenthereferencetransduceryandtherecessedtransducerx,and^Gyy(f)representstheauto-spectraldensityofthereferencetransducer.Thesequantitiesarerespectivelydenedas ^Gyx(f)=1 f2 N2FFT[Y(f)X(f)]for0fFs=2[Hz];(3{24) and ^Gyy(f)=1 f2 N2FFT[Y(f)Y(f)]for0fFs=2[Hz];(3{25) whereYandXrepresentthefastFouriertransforms(FFTs)ofthetimeseriesofthereferenceandrecessedtransducers,respectivelyand()denotesthecomplexconjugate. Asdiscussedintheprevioussection,therecessednatureoftheelectretresultsinbothabroadbandreductioninpressureamplitudeandaphaseshiftascomparedtothatatthesurface.Therefore,abroadbandinputsignalschemewasdevisedusingtwomethodologies: Summationofsinewaves(\Multisines"), Band-limited(BL)whitenoise. Theformerofthesetwotechniquesisadeterministicapproachaccordingtothemethodsdevelopedby Schroeder ( 1970 ).AbroadbandspectrumofinputsignalswasbrokenupintovediscretebandsshowninTable 3-7 .Thesebandswerechosenbasedonlevelsexpectedtobeexperiencedbythetransducerinawindtunnelexperiment.Asthetableindicates,eachcalibrationfrequencybandcontainsoverlappingfrequencybins.ThisismeanttoensurethecomputationofasmoothFRFthattransitionsfromonefrequencybandtothenextwithnoconsiderablediscontinuities.AnillustrationoftheoverlappingregionsispresentedinFigure 3-18 ,presentedintheformofthecomputedFRFmagnitudejHyxjandphaseyx.Thesummedsinewavesweredenedin16Hzincrementsinordertocoincide 96

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withthedesiredbinwidthusedtoanalyzethespectralmeasurementsinthewindtunnelexperiments. AsfortheBLwhitenoisesignal,aStanfordResearchSystemsNetworkSignalAnalyzerwasusedtogeneraterandomnoiseovertwofrequencyrangesofappreciableoverlap,whicharealsoshowninTable 3-7 .ThepurposeoftestingthistypeofsignalwastoidentifythedierencesifanybetweenthecomputedFRFsbasedonadeterministicandrandominputsignal.ThedataacquisitionparametersforbothsetsofcalibrationwaveformsarepresentedinTable 3-8 .CharacterizationResults Therstitemtobedeterminedwasthepreferableductterminationconditionoftherecessedelectretbranch.Asstatedin Section3.4.2.2 ,twoterminationconditionsweresimulated:asealedTygonRduct,aswellasanopenone.Itwasassumedthatanyobserveddierencesintheperformanceoftherecessedelectretsforthesetwocongurationswouldbeinvariantoftheinputsourcewaveformtype.Therefore,theresultsofthesetwocongurationsweretestedusingmultisinewaveforms.AcomparisonbetweenthecomputedFRFsofasealedandopenductispresentedinFigure 3-19 .ItisinterestingtonotethequalitativedierencesbetweentheseresultsandthosepresentedinFigure 3-15 ,namelythedierencesinthelowfrequencyripplingbehavioratfrequenciesbelowapproximately400Hz.Thesimulationandexperimentalcasesdierinthesimulation'sover-predictionoftheamplitudeofthisripplingbehaviorforthesealedductcase.Instead,theexperimentalcomparisonshowscomparableamplitudesofoscillationbetweenthetwocongurations,withtheripplingpatternalternatingonabin-by-binbasis.Basedontheseresults,itwasdecidedthatasealedductwasthebetteroptiontobeusedinthewindtunnelexperimentssinceitwasexpectedtohelpinmitigatinganypossiblenoisecontaminationfromtheambienttunnelenvironment. ItthenneededtobedeterminedifanydierencesexistedbetweentheFRFcomputationsusingthemultisineandBLwhitenoisesignals.Whilethedeterministic 97

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signalshouldtheoreticallybeadequatetocharacterizethedevice,arandombroadbandsignalmaybeabetteroptionsinceitmorecloselyresemblesasignalexpectedtobeexperiencedbythesensorinthewindtunnelenvironment.Therefore,calibrationdatasetsforeachwaveformtypewereprepared,includingapplicablerandomuncertainties.AnexamplecomparisonbetweenthecomputedFRFsusingthesetwowaveformtypesforoneoftherecessedsensorsispresentedinFigure 3-20 .ThetheoreticalperformanceofthedeviceasdeterminedbyTMestimationisalsoprovided.NotethatthetwocalibrationwaveformtypesweresettohavenearlyidenticalRMSinputpressurestoensureaccuratecomparisonbetweenthetworesultingFRFs.BoththemultisineandBLwhitenoisewaveformsweresettohaveanRMScalibrationpressureof200Padistributedoverthefrequencyrangeof96F1;216Hz.ThisalsocorrespondstoanintegratedSPLoverthisfrequencyrangeof140dB. ItisworthnotingthattheonlynoticeabledierencesbetweentheexperimentalFRFsoccursagainatlowfrequencies,approximatelyintherangeof96F400Hz.TheFRFcalculatedusingtheMultisineinputsignalsappearstobemore\jagged"thanthatcomputedusingtheBLwhitenoisesignals.Furthermore,theoveralltrendsoftheTMpredictionmatchwellwiththosedeterminedexperimentally.OneofthemorenotablediscrepanciesbetweenthesimulatedandexperimentalFRFsisthefrequencywheretheelectretis180outofphasewiththereferencesignal.Fortheexperimentaldata,thislocationisseentooccur1kHzsoonerthantheresonancepeakobservedintheFRFmagnitude.Thisisunderstandablesincethediaphragmoftheelectretmicrophoneisitselfrecessedbeneaththeoutersurfaceofthemicrophonehousing,eectivelyinducinganadditionallinearphaseosetandthusasteeperphaseslope.NotethattheTMpredictionshowninFigure 3-20 isthatforasimulatedopenterminationduct.WhilethiscongurationconictswiththesealedTygonRtubingconditionoftheactualsensors,thesealedductTMpredictiongreatlyover-predictsthelow-frequencyoscillatorybehaviormakingitdiculttoperformalow-frequencycomparison.Fromthese 98

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results,itwasexpectedthattheFRFgeneratedusingtheBLwhitenoisesignalwouldyieldasmoothercorrectedautospectrum,particularlyatlowerfrequencies.Therefore,anuncertaintyanalysiswasperformedontheFRFgeneratedfromtheBLwhitenoisesignalstodetermineitspropagationintotheresultinguncertaintyofthecorrectedsignal'sautospectraldensity,Gyy(f).Beforethis,however,thelengthoftheinlettubulationwasvariedtoidentifyitseectsonthefrequencyresponseofthedevice.TubulationEectsonFRFPerformance Asstatedpreviously,therecessedelectretswereouttwithoneoftwotubulationlengths.Thelongerofthesewereutilizedwiththesensorstobeinstalledwithinthemodeltorquearm.Thiswasdoneinordertoensurelinearperformanceofthedeviceswhensubjectedtothepotentiallyhighpressureuctuationlevelsfromtheshearlayeroftheupstreamcylinder.Thenallengthsofthesetubulationsweredecideduponbasedonthecombinedobjectivesofmakingtheresonancefrequencyashighaspossible,ensuringalargeenoughpressureamplitudereduction,andensuringthatthesensorswilltintotheconnedinteriorspaceofthemodelcylinderandtorquearm.Basedontheseconstraints,inlettubulationlengthsofL1=16and20mmweredecideduponforthecylinderandtorquearmsensors,respectively.AcomparisonofthemeasuredrecessedelectretFRFsusingthesetwoinlettubulationlengthsispresentedinFigure 3-21 .Fromtheseresults,itcanbeseenthattheFRFsbehaveinverysimilarmannerswithsomenoticeabledierences.Specically,theresonancepeakofthelongertubulationoccursaround8kHz,whichisconsiderablylowerthanthatfortheshortertubulationatapproximately10kHz.Furthermore,thepackagewiththelongertubulationexhibitsamagnitudetrendsimilartotheshortertubulation,withanearlyconstantadditionalamplitudereductionof)]TJ /F1 11.955 Tf 22.32 0 Td[(1dBrelativetotheshortertubulationpackageuntilf3kHz.Thusthebenetofimprovedamplitudereductionwiththelongerinlettubulationiscounteredbytheearlieronsetofresonance.Tobetterquantifytheupperlimitofacceptablepressurelevelsforthetwo 99

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sensorpackages,distortionmeasurementsweretakenusingthesamePWTcalibrationsetup. Oneoftheprimarylimitationsthatexistwithusingelectretmicrophonesistheirtypicallyhighlevelsofdemonstratedtotalharmonicdistortion(THD).THDrepresentstheratiooftheroot-mean-square(RMS)outputvoltageofthedeviceatallhigherfrequencyharmonics,fnforn=2;3;:::;1,tothatatthefundamentalcalibrationfrequencyf1( Bollen&Yu-Hua 2006 ).Inthisdissertation,THDismathematicallydenedas THD=s P1n=2V2(fn) V2(f1)100%:(3{26) TheelectretschosenforthisstudyarequotedbythemanufacturertoexhibitaTHDof3%atanSPLof125dBat1kHz.Therefore,itisexpectedoftherecessedelectretstoperformwithintheirlinearoperatingrangeforOASPL125dB. Unfortunately,duetothepresenceofadditionalsourcesofdistortionintheclosedductofthePWT,theTHDofthesensorpackagecannotbedirectlydetermined( Williams 2011 ).AnalternativeistoobservethemeasuredTHDinarelativesensebetweentheDUTandthereferencetransducerasafunctionofincreasingSPL.ThiswasperformedinthePWTforthesensorsequippedwithbothinlettubulationlengthsalongwitha1/8"(3.75mm)Bruel&KjaerType4138referencemicrophone.Thisreferencetransducerisquotedbythemanufacturertoexhibita3%THDforanSPLof160dBata1kHzinputfrequency.SampleTHDcomparisonresultsforoneeachoftheshort-andlong-stemequippedrecessedelectretpackagesareshowninFigure 3-22 .NotethattheresultsareplottedasafunctionofSPLrecordedbythereferencetransduceratf1=1.008kHz(denotedasSPL1).Fromtheresults,itcanbeseenthatbothsensorpackagesperformverywellrelativetothereferencetransducer.Theshort-stempackageisseentoexhibitTHDlevelslessthanthereferencesensoruptoalevelofSPL1=153dB,whilethelong-stempackagepushesthislimitouttoatleastSPL1=156dB.Theseresultswereveryencouragingastotheacceptableperformancerangeoftherecessedelectrets 100

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forthetorquearmmodelapplication.ThisisbasedonrecordedmaximumintegratedlevelsofOASPL=150dBforasensorlocatedonthetorquearmcomponentofthenoselandinggearmodeltestedin Zawodnyetal. ( 2009 ).Itisalsoworthnotingthatthissensorexhibitedthehighestpressureuctuationlevelsoutofallsensorsonthemodelfortheseexperiments. Amoreaccuratemethodofquantifyingtheerrorsinducedbyharmonicdistortionintherecessedsensorsistocomputethedierencesbetweenthemean-squarepressures(MSPs)ofthereferencesensorandDUT.AnexampleofthisisillustratedinFigure 3-23 ,wheretheMSPoftheDUTisplottedversusthatofthereferencemicrophone.Uncertaintyboundsareillustratedfor3.2and10%randomuncertaintyinthereferencemeasurement,alsoincludingerrorbarsof3.2%randomuncertaintyfortheDUTmeasurements.Notethatthe3.2%uncertaintyboundsrepresenttheautospectralrandomuncertaintyrofthesensors.Astheseresultsshow,the3.2%uncertaintyboundsoftherecessedelectretoverlapwiththoseofthereferencetransduceruptoanMSPof2:4105Pa2,whichcorrespondstoanSPLof147.8dB.ForpressurelevelsabovethisanduptothemaximumtestedMSPof1.49105Pa2(anSPLof155.6dB),theautospectralrandomuncertaintyoftheDUTremainswithinthe10%uncertaintyboundsofthereferencemicrophone. 3.4.2.4DataAcquisitionandUncertainty Allunsteadysurfacepressuresandfree-eldmicrophonesweremeasuredusingaseriesofPXI-4462DAQcardswithinan18-slotNationalInstrumentsPXI-1045chassis.AllunsteadysurfacepressuremeasurementswereperformedatasamplingrateofFs=65.536kHzforadurationof30seconds,yieldingatotalnumberofN=1:966106samplesperdatarun,perchannel.Foradesiredfrequencyresolutionoff=16Hz,thedataaredividedintoNFFT=4;096samples/block,resultinginatotalofNblocks=480blocks.The 101

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totalnumberofaveragesiscomputedas( Bendat&Piersol 2000 ) nd=oor1+Nblocks)]TJ /F1 11.955 Tf 11.96 0 Td[(1 1)]TJ /F3 11.955 Tf 11.96 0 Td[(r;(3{27) whererrepresentstheblockoverlapratio.Duetotherandomnatureofthewindtunneldata,however,aHanningwindowisappliedtothedatatimeserieswithablockoverlapof75%(r=0.75).Thisresultsinacorrelationbetweensuccessivetimeblocks,thusreducingthetotalnumberofeectiveaverages,ndeff,accordingtoareductionfactor,.ForthecaseofaHanningwindowwith75%overlap,=0:52.Therefore,thetotalnumberofeectiveaveragesiscomputedtobe ndeff=nd=oor(0:521917)=996averages:(3{28) Duetotheobviouslynitenatureoftheacquireddata,bothrandomandbiaserrorsarepresentintheunsteadysurfacepressuremeasurements.Whenconsideringspectralquantities,thermserroristypicallynon-dimensionalizedas =q 2r+2b:(3{29) Ifwefocusourattentiononthemeasurementofasensor'scomputedautospectrum,^Gxx,thenthenormalizedrandomerrorriscomputedas r[^Gxx(f)]=[^Gxx(f)] Gxx(f)=1 p ndeff;(3{30) whilethenormalizedbiaserrorbisestimatedas( Bendat&Piersol 2000 ) b[^Gxx(f)]=b[^Gxx] Gxx(f)f2 24G00xx(f) Gxx(f):(3{31) NotethatEquation 3{31 istypicallyverydiculttoquantifyforarandomsystem.Furthermore,thesebiaserrorsareexpectedtobesmallrelativetotheirrandomcomponentsandarethusconsideredtobenegligible.Thisleavesrastheonlyerrorcontributionofconcernforthesemeasurements. 102

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Iftheuncertaintyanalysisistailoredtowardsdataacquiredbyarecessedelectret,thentheerrorscanbedividedintothoseoftheuncorrected(xi)andcorrected(yi)signals.FromEquation 3{30 ,theautospectralrandomerrorforanuncorrectedrecessedelectretdatasetisequaltor[^Gxx]=0:0317,or3.17%uncertainty.Theuncertaintyforthecorrectedautospectraldensity,however,requiresanadditionalcomputationalstepduetothedependenceonthecomputedFRF,Hyx(f),perEquation 3{23 .ApplyingtheRSSmethod,thetotalrandomuncertaintyofthecorrectedautospectraldensityiscomputedas ur[Gyy(f)]=s @Gyy @Gxxur[Gxx(f)]2+@Gyy @jHyxjur[jHyx(f)j]2:(3{32) SubstitutionoftheappropriatepartialderivativesofEquation 3{25 reducesto ur[Gyy(f)]=vuut 1 jHyx(f)j2ur[Gxx(f)]!2+ )]TJ /F1 11.955 Tf 9.3 0 Td[(2Gxx(f) jHyx(f)j3ur[jHyx(f)j]!2:(3{33) Deningtheintermediateuncertaintiesintermsoftheirnormalizedcounterpartsreducesthisexpressionfurtherto ur[Gyy(f)]=vuut Gxx(f) jHyxj2r[Gxx]!2+ )]TJ /F1 11.955 Tf 9.3 0 Td[(2Gxx(f)jHyx(f)j jHyx(f)j32r[jHyx(f)j]!2=q G2yy(f)r[Gxx]2+4G2yy(f)r[jHyx(f)j]2:(3{34) Thus,divisionofbothsidesofEquation 3{34 byGyy(f)producesthetotalnormalizedrandomuncertaintyforthecorrectedautospectraldensityas r[Gyy(f)]=q r[Gxx]2+4r[jHyx(f)j]2:(3{35) Notethatr[jHyx(f)j]iscomputedbasedonthecoherencefunction2yxas r[jHyx(f)j]=q 1)]TJ /F3 11.955 Tf 11.95 0 Td[(2yx(f) jxy(f)jp 2ndeff:(3{36) Withtherandomuncertaintyofthecorrectedautospectrumabletobequantied,itwasthenappliedtothecaseoftheBLwhitenoisecalibration.Thiswasdoneinorder 103

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todeterminewhetherornottheadditionaluncertaintiesimposedbytheBLwhitenoisesignalwouldexceedthatimposedbytheMultisinecase.Figure 3-24A showsacomparisonofr[jHyx(f)j]forarecessedelectretpackageusingthetwocalibrationwaveforms,whileFigure 3-24B showstheresultingr[Gyy(f)]usingtheBLwhitenoisecalibrationsignal.Astherstgureshows,theuncertaintyintheFRFmagnitudeisgreateracrossthemajorityofthetestfrequencyrangefortheBLwhitenoiseinputsignalcase.ThisisduetoareducedcoherencebetweenthereferencesensorandDUT.Furthermore,asFigure 3-24B shows,themaximumr[Gyy(f)]remainsbelow3.35%,whichislessthanthatoftherawautospectraldensitycomputedusingtheMultisineinputsignal,whichfromTable 3-8 isr[Gxx]=4:56%.Thisshowsthatoutofthetestedcalibrationmethods,usageoftheBLwhitenoisecalibrationsignaltocomputethesensorpackageFRFimposesaminimalchangeinuncertaintyofanuncorrectedautospectraldensitycomputedfromatimeseriesofrandomdataacquiredusingtheparametersoutlinedinTable 3-8 (worstcaseof3.35%comparedwithr[Gxx]=3:17%).Thisisimportantsincetheserandomdataacquisitionsettingsareutilizedforallunsteadypressureandfar-eldacousticdataacquiredforthisstudy. 3.4.2.5TimeDomainReconstruction Itisimportanttonotethatthetechniquesimplementedforcharacterizationoftherecessedelectrettransducersuptothispointareonlyvalidinthefrequencydomain.Therefore,asystemidenticationtechniquewasimplementedinordertoreconstructthetimeseriesoftherecessedelectretsasiftheywereush-mountedtothemodelsurface.Thisisbenecialforthecomputationofcorrelationsbetweensensorsforanalysisofconvectedowstructuresaswellasforstochasticestimationpurposes.ThiswasdoneusingtheSystemIdenticationtoolboxoftheMATLAB2012asoftware.ThesystemidenticationoftherecessedelectretswasperformedusingdataacquiredfromthesamePWTcalibrationsetupdiscussedin Chapter3.4.2.3 .Forthistestapplicationhowever,awiderrangeofinputcalibrationsignalsweretested,includingBLwhitenoise,periodic 104

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Schroedermultisines,squarewave,ramp,andsweptsinewaves.Thegoalofthistestistodevelopatransferfunctionthatwouldcorrecttheelectrettimeseriestoyieldtheush-mountedreferenceBruel&Kjaertimeseries. Priortoperformingsystemidentication,acut-ofrequencywasdened.Itwasbelievedthattherewouldbelittletonocoherencepresentbetweenmodelsensors,forfrequenciesabove1kHz.Inaddition,thesystemidenticationwasexpectedtobecomelessaccurateasthiscut-ofrequencybecameclosertotheresonancefrequencyofthedevice.Therefore,thecut-ofrequencyofinterestforthetimedomainreconstructionwassettotheupperlimitoftherstmultisinecalibrationbandof1.216kHz.Toensurethatthecalibrationsignalsanalyzedwerefreeofambientdistortion,adigital12th-orderButterworthlow-passlterwasappliedtothetimeseries.Then,thetimeserieswerefedintothesystemidenticationtoolkitforidenticationandvalidation. AnexampleoftheresultofthesignalcorrectionforoneoftheelectretsensorsisshowninFigure 3-25 .Fortheresultsofthisgure,arampcalibrationsignalwasusedforthereconstructionsinceitprovidedthesmallestRMSerror-t.Thetransferfunctionappliedtothissensorconsistedof12polesand11zeros,allofwhichliewithintheunitcircleandconsequentlysatisfythestabilitycriterion.TheFRFofthetransferfunctionwithitscomparisontotheexperimentallycomputedFRFoftherecessedelectretispresentedinFigure 3-26 alongwithanillustrationofthepolesandzerosofthetransferfunction. 3.5AcousticInstrumentation Fortheacousticportionoftesting,far-eldspectraisexaminedtoidentifyspectralfeaturesofthemodelforanarrayofgeometryandowconditions(testingmatrixprovidedin Section4.1 ).Scalingofthefar-eldspectraaidsindeterminingtheoverallbehaviorofthemodelasanacousticsource(e.g.dipole,quadrupole).Noisesourceidenticationviabeamformingisthenperformedtolocatethedominantnoisesourcesonthemodelandhowtheychangewithmodelconguration.Far-eldacousticandunsteady 105

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surfacepressuremeasurementsareacquiredsimultaneouslytohelpdeterminethepressureuctuationsaroundthemodelsurfacethatpropagateintotheacousticfar-eldassound.Thissectionpresentsthelinearandphasedmicrophonearraysthatareutilizedinthisstudyforacousticspectralanalysisandnoisesourceidentication,respectively. 3.5.1LinearMicrophoneArray Far-eldacousticspectraareacquiredusingalineararrayof10pole-mountedmicrophonesthatlinethesideoftheUFAFFtestsection.ThemicrophonesareG.R.A.S.SoundandVibrationtype40BEfree-eldcondensermicrophones.Thearrayisalignedwiththecenterlineofthemodelandorientedorthogonaltotheowdirection,providinganeective\sideline"acousticsurvey.ThisscenarioisillustratedinFigure 3-27 .Thearrayispositionedsuchthatthe4thmicrophonebackfromtheinlettrailingedgeispositionedcollinearwiththecenterlineofthemodelcylinder.Whilethismicrophoneistheoneprimarilyconsultedforspectralanalysis,theentirearrayisusedtomapoutpartialdirectivitypatternsforthedierentmodelcongurations.ThepartialdirectivityofthemodelisestimatedastheOASPLasafunctionofobservationangleC,whichistheshear-layer-correctedpropagationanglebetweenthetorquearmsandeachmicrophone( Amiet 1978 ).TheOASPLforamicrophoneatapropagationangleofCcanbedenedas OASPL(C)=10log10 1 p2refZfmaxfmin^Gyydf!;(3{37) wherepref=210)]TJ /F7 7.97 Tf 6.58 0 Td[(5Painair.Theupper-endfrequencyofinterestfmaxissettothatcorrespondingtoanegligiblechangein^Gyyofthemicrophones,whiletheeectivecut-onfrequency,fmin,oftheexperimentalsetupisbasedontheanechoicperformanceofthesetupaswellasthedistancebetweenthismicrophoneandthemodel.Asindicatedby Dowling&FfowcsWilliams ( 1983 ),thisdistancemustbelargerthananacousticwavelength(r>)toassumefar-eldpropagation.AsindicatedinFigure 3-27B ,theplaneofmicrophonesarepositionedr=1.219mawayfromthetorquearmmodel.Assuminganominalspeedofsoundofc=345m/s,thisyieldsanapproximatecut-on 106

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frequencyoffmin=280Hz.Thisservesasaninitialestimate,whichwillbene-tunedin Section4.1 viascalinganalysesoffar-eldspectra. Allofthefree-eldlineararraymicrophonesunderwentshearlayercorrectiontoaccountfortherefractiveeectsoftheUFAFF'sopenjetshearlayers.Thisincludedcorrectionofboththespatiallocationofandsoundpressurelevelexperiencedbyanobserverusingthemethodproposedby Amiet ( 1978 )undertheassumptionofaplanarshearlayer.AnillustrationofthegeneralizedshearlayercorrectionprocessisshowninFigure 3-28 .Inthisgure,theacousticsourceislocatedadistancehawayfromtheshearlayerwithinafreestreamow,andthemicrophoneislocatedanorthogonaldistancedfromtheshearlayerwithinthequiescentenvironment.Thequantitiesrmandrrrepresentthegeometricandrefractedsource-to-microphonedistancesrespectively,whilemandcrepresentthegeometricandcorrectedsource-to-microphonepropagationangles,respectively.TheresultsofapplyingAmiet'sshearlayercorrectiontothelineararrayelementsaresummarizedinTable 3-9 3.5.2PhasedMicrophoneArray Aphasedmicrophonearrayisusedtoidentifythedominantnoisesourcesonthemodelviaacousticbeamforming.Beamformingisaprocessbywhichtimeseriesdatafromanarrayofmicrophonesaretransformedintoasoundintensitymapoverapre-denedscanningregioninspace.Forthisdissertation,frequencydomainbeamformingwillbeutilized,abriefoverviewofwhichispresentedinthefollowingsection. 3.5.2.1FrequencyDomainBeamforming Inrecentyears,theuseofphasedmicrophonearrayshasbecomecommoninaeroacoustictestingforthepurposesofnoisesourcelocalizationandestimationofnoisesourcepowers.Beamformingisasignalprocessingtechniqueinwhichthesignalsfromeachmicrophoneinanarrayareappropriatelyweightedandshiftedbasedontheirdistancesfromaspatiallocationofinterest( Dougherty 2002 ).Theweightingandshiftingofthesesignalscanbedoneineithertimeorfrequencydomains.Inthisprocess,the 107

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focusofamicrophonearrayiselectronically\steered"toapre-denedgridofscanningpoints.Eachscanningpointistreatedasapotentialacousticsourcewhosepowerlevelandacousticintensityistobedetermined.Theoutputofthisprocessisamapoftheseacousticintensitiessuperimposedoverthescannedregion.Figure 3-29 providesavisualrepresentationofthisprocess.Notethatinthisgure,aplanarscanningregionofLscanpointsisdenedadistancezabovethefaceofanarrayofMmicrophones.Thevectorlabeledr1;mrepresentsthedistancefromthe1stscanningpointtothemthmicrophone.TheCrossSpectralMatrix Therststepinimplementingmanyfrequency-domainbeamformingalgorithmsisthecomputationofthecrossspectralmatrix(CSM).Thiscomplex-valuedmatrixisofsizeMMandcontainsboththeautospectraldensityvalueofeachmicrophonechannelaswellasanycombinationofcross-spectraldensitycomponentsbetweenallMchannelsandisformallydenedas G(f)=266666664G11G12G1MG21G22............GM1GMM377777775;(3{38) wherethediagonalelementsrepresentautospectraltermswhiletheo-diagonalelementsarethecross-spectralterms.Notethatthemathematicaldenitionsfortheautospectraldensityandcross-spectraldensityfunctionsweredenedatthebeginningofthissection. WhileEquation 3{38 isavalidtheoreticalexpression,adiscreterepresentationisrequiredsincethetimedatatowhichthebeamformingprocessistobeappliedisniteinnature.Therefore,assumingthatthetimepressurerecordforeachmicrophoneisdividedintob=1;2;:::;Bblocks,thenanN-pointFastFourierTransform(FFT)canbeappliedtoeachblockoftimedatatoobtainadiscretefrequencydomainrepresentationofthepressurerecordforeachmicrophone.TheresolutionoftheFFTisdenedasf=fs=N, 108

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wherefsisthesamplingfrequency.Ifweletyb[n]bebthblockofthetimerecordofpressuredataforamicrophone,thenthediscreteversionofthispressurerecordforblockbafterapplyingtheN-pointFFTisdenotedasYb.ThemathematicaldenitionofYbisshowninEquation 3{39 .( Arnold 2001 ) Yb=N)]TJ /F7 7.97 Tf 6.59 0 Td[(1Xn=0yb[n]e)]TJ /F12 5.978 Tf 7.78 4.62 Td[(j2fbn N;b=0;1;:::;B=N)]TJ /F1 11.955 Tf 11.95 0 Td[(1(3{39) Notethateachelementbdenotesanarrowbandfrequencyfb,eachofwhichisseparatedbytheresolutionoftheFFT(fb+1=fb+4f).OnceatotalofBcoecientsforeachmicrophonehavebeencalculated,eachelementoftheCSMiscomputedviasampleaveragingwhichisshowninEquation 3{40 ( Yardibietal. 2010a ).Notethat()*representsthecomplexconjugate. Gm;m0(fb)=1 BBXb=1Yb;m(f)Yb;m0(f);m;m0=1;2;:::;M(3{40) OncetheCSMhasbeencomputed,allmagnitudeandphaserelationsbetweenallpossiblepairingsofmicrophonesareknown.Theonlyadditionalrequirementtoestimatethesignallocationarethesteeringvectorsforeachmicrophone-scanningpointlocation.TheSteeringMatrix Thesteeringmatrixiscomposedofindividualsteeringor\microphoneweight"vectorsdenedforeachspatialpointtobescanned.Thesesteeringvectors,alsosynonymouswiththearraypropagationvectors,aredenedbythepredictednatureoftheacousticsourcesbeinginvestigated( Dougherty 2002 ).Typically,mostbeamformingalgorithmsutilizetheassumptionthatthesourcesunderinvestigationaremonopoleinnature,orradiatesphericallyinalldirections.ThefullsteeringmatrixitselfisofsizeML,andisdenedas A(fb)=[a1(fb);a2(fb);:::;aL(fb)];(3{41) 109

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and al(fb)=1 rl;1e)]TJ /F5 7.97 Tf 6.58 0 Td[(j2fb c0rl;1;;1 rl;Me)]TJ /F5 7.97 Tf 6.59 0 Td[(j2fb c0rl;M;(3{42) whereal(fb)representsthesteeringvectorcorrespondingtothelthmonopolesourceforthenarrowbandfrequencyfb.FromEquation 3{41 ,weseethataseparatesteeringmatrixexistsforeachnarrowbandfrequencyofinterest.ArrayPowerResponse Thenaloutputofthebeamformingprocessisamapofpowerlevelsdistributedacrossthescanningregion.TypicallypresentedinadBscale,thearraypowerresponseatthelthscanningpointofthespatialgridatafrequencyfbcanbedenedas ^Pl(fb)=al(fb)G(fb)al(fb):(3{43) Themapofpowerlevelsistypicallypresentedasacontourplotrelativetothepeakpowerlevel,ideallyrepresentativeofthedominantsourcelocationinthescannedregion. 3.5.2.2BeamformingAlgorithms Atotalofthreebeamformingalgorithmsweretestedinthisstudy.TheyaretheDelay-and-Sum(DAS)( Arnold 2001 ; Dougherty 2002 ; Humphreysetal. 1998 ),robustCaponbeamformer(RCB)( Lietal. 2003 ),andthedeconvolutionapproachforthemappingofacousticsources(DAMAS)( Brooks&Humphreys 2006 ).TheDASalgorithmisthemoreclassicalone,aderivationofwhichisprovidedin Chapter3.5.2.1 .Thebeamformeroutputisagridofpowerlevelscorrespondingtothespatialscanningregionofinterest.ThecalibratedDASpoweratanlthscanningpointis ^Pl=1 M2~aHl~DG~DH~al;l=1;:::;L;(3{44) whereMisthenumberofmicrophonesinthephasedmicrophonearray,~alisthearraysteeringvectorforthelthscanningpoint,Gisthecross-spectralmatrix,and~mathbfDrepresentsthegroupcalibrationmatrixdiscussedin AppendixB .Foragivenspatialregionofinterest,thistechniqueallowsforthestrengtheningofsignalscorrespondingto 110

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acousticsourcesandmitigationofsourcesfromotherareas.WhileDASisthefastestandsimplestofthemethodsutilizedhere,italsosuersfromhighsidelobelevelsandpoorresolutionatlowfrequencies.TheRCBmethodisanimprovementtotheDASmethod,oeringlowersidelobelevelsandimprovedlow-frequencyresolution.Morespecically,theRCBminimizestheoutputpowerofthearray,allowingthesignalofinterest(SOI)topassthroughundistorted.Itusesanuncertaintyestimateinthecalculationofthearraysteeringvectors,whichallowsadirectcomputationofamore\robust"estimateofthepowersofthesignalsreachingthearray.EstimationofthepoweroftheSOIsareperformedundertheassumptionthatthesteeringvectorsabelongtoanuncertaintyspheresubjecttojja)]TJ /F1 11.955 Tf 12.53 .17 Td[(^aljj,whererepresentsthesquareoftheradiusofuncertaintybasedonnormalizedsteeringvectors.Forthisstudy,anuncertaintyestimateof=0:1(10%)wasutilized.TheRCBpoweratanlthscanningpointiscomputedas ^Pl=1 ^aHlG)]TJ /F7 7.97 Tf 6.58 0 Td[(1^al;l=1;:::;L;(3{45) where^alrepresentstheuncertainty-incorporatedestimateofthearraysteeringvector.Thisestimateofthesteeringvectoriscomputedas ^al=al)]TJ /F1 11.955 Tf 11.95 0 Td[((I+G))]TJ /F7 7.97 Tf 6.59 0 Td[(1al:(3{46) ThisestimateisbasedontheLagrangianmultiplier0( Lietal. 2003 )thatsatisestheconstraintequation jj(I+G))]TJ /F7 7.97 Tf 6.59 0 Td[(1aljj2=:(3{47) Finally,theDAMASalgorithmutilizestheassumptionofstatisticallyindependentsourcestodeconvolvethephasedarraycharacteristicsfromthebeamformeroutputinordertoyieldthetrueacousticsourcesignature.Thisisperformedusinganinverseproblemformulationofthesystemofequations ^A^X=^P;(3{48) 111

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where^PisthebeamformeroutputoftheDASalgorithmdenedinEquation 3{44 ,^Arepresentsthereciprocalinuenceofthearraysteeringvectors,and^Xisthedeconvolved\noisesource"matrixofthescannedspatialregionforwhichmustbesolved.Whilethetraditionalsolutionofthesystemwouldbe^X=^A)]TJ /F7 7.97 Tf 6.58 0 Td[(1^P,howeverthelowrank(nearsingular)ofthe^Amatrixpreventsthis.Therefore,atailorediterativemethodisappliedthatimposesapositivityconstraintonthecomponentsof^Xundertheassumptionthatthesourcesareallstatisticallyindependent.Moredetailsareprovidedin Brooks&Humphreys ( 2006 2010 ). 3.5.2.3IntegratedAbsoluteLevels Anintegrationmethodisusedforthepurposeofcomputed\absolute"powerlevelsoftheacousticsources.ThisisinitiallyappliedtotheDASandDAMASalgorithms,withthegoalofidentifyingsimilaroutputsofthetwoandthusnegatingthecontinuingneedtoutilizetheDAMASalgorithm.ThisisbecauseofthetimeconsumingnatureoftheDAMASschemerepresentativeofthousandsofsolutioniterations.TheintegratedDASlevelsforascanninggridofLpointsisdenedas SPL(DAS)=Pl2L^P(DAS)l Pl2Lpsf(l):(3{49) ThelogicbehindEquation 3{49 isthatnormalizationofthesummedpowerlevelsinthescanninggridbythePSFofthearrayatthefrequencyofinterest,shouldeliminatethearrayresponsefromtheresults( Yardibietal. 2010b ).AsfortheDAMASalgorithm,normalizationofthearrayPSFisnotnecessarysincethesolutionhasalreadybeendeconvolvedfromthearraycharacteristics.Therefore,theintegratedlevelsoftheDAMASalgorithmcanbesimplystatedas SPL(DAMAS)=Xl2L^P(DAMAS)l:(3{50) 112

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3.5.2.4PhasedArrayDesignandFabrication Anaperiodicarraydesigntechniqueisimplementedusingthemethodologypresentedin Underbrink ( 2002 )whichprovidesimprovedspatialresolutionandarraysidelobereductiongiventhefrequencyrangeofinterestandnumberofavailablesensorchannels.Thearrayutilizedinthisworkispartofanestedmicrophonearray,consistingofanouterarrayforlowfrequencybeamforming(f32kHz)andaninnerarrayforhighfrequencybeamforming(f32kHz).Botharraysconsistofmicrophonesdividedintoarepeatedcircumferentialpatternoflogarithmicspirals.Themicrophonesthatcomposedeachofthesespiralswerespacedsuchthattheirproximitiesdecreaseasonemovesradiallyoutward,knownasa\reverselogarithmic"spiralpattern( Underbrink 2002 ).Duetotherelativelylowfrequencycontentexpectedtobegeneratedbythegeometryinquestion,onlytheoutermicrophonearraywasutilizedinthisstudy.Forreference,however,thedesignparametersofbothinnerandouterarraysareprovidedinFigure 3-30 .Thisarrayispopulatedwithatotalof55Bruel&KjaerType4958precisionarraymicrophones,whicharechosenduetotheirsmallsize,highsensitivity,andawideoperationalfrequencyrangeof20HzF20kHz.Inaddition,aBruel&KjaerType4954Bmicrophoneispositionedatthearraycenter.Thismicrophoneservesasareferencesensorwithwhichtoperformagrouparraycalibration.Thiscalibrationprocessisdetailedin AppendixB Thearraysupportframeisdesignedtomitigatetheeectsofstandingwavepatternsandpressuredoublingeectscommonlyassociatedwithsolidplatearrays.Specically,thearrayconsistsofasheetof3"(76.2mm)tallacousticwedgefoam,withthemicrophonesextruded5.5"(139.7mm)abovethewedgetips.Toensurestructuralstabilityofthearraywhilealsominimizingtheoverallweight,thearrayframewasfabricatedoutof3/8"(9.525mm)thickAluminum6061usingawaterjetmachine.Thismachiningprocessenabledtheremovalofexcessmaterial,yieldingaskeletalAluminumarrayframe.Apairofimagesofthefree-eldmicrophonearray(FFMA)isprovidedinFigure 3-31 113

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Theperformanceofaphasedarrayistypicallydenedbyit'sresolution.Thisismeasuredintermsofa3-dBbeamwidth,orthewidthofthearraymainloberepresentingamonopolesourceathalfthepowerofthemaximumsignalintensity.TheouterFFMAwasdesignedsuchthatthebeamwidthwouldbeminimizedusingthespirallayouttechniquesof Underbrink ( 2002 )andamaximumnumberof55availablemicrophonechannels.Theresolutionofthearrayisquantiedthroughcalculationofthearray'spointspreadfunction(PSF).ThePSFofthearrayforthelthpointina2-dimensionalscanninggridisdenedas psf(l)=~aHla0 M2;(3{51) wherea0representsthewavepropagationvectorofamonopolesourcelocatedatthecenterofthescanningregion.The3-dBbeamwidthfortheapplicablefrequencyrangeoftheouterFFMAisprovidedinFigure 3-32A .Inaddition,thePSFsforamonopolesourcelocatedinthecenterofascanningregionlocated53"(1.3462m)awayfromthearrayareplottedinarelativedBscaleforoctavebandfrequenciesupto16kHzinFigs. 3-32B 3-32F .InformationonthecomparisonsbetweenthetheoreticalandexperimentallymeasuredPSFsoftheFFMAisprovidedin AppendixB 3.5.3DataAcquisitionandUncertainty Linearandphasedarraymeasurementswereperformedusingidenticalsamplingparameterstothosepresentedin Chapter3.4.2.4 .Thecorrespondingrandomuncertaintyforthesesamplingparametersisr=3:21%,whichtranslatesto0:14dB.Inadditiontothisrandomcomponentuncertainty,eachtypeofmicrophonehasit'sownrespectivemanufacturer-quotedfrequencyresponsevariationaswellasthermal(self)noise.ThesearetabulatedinTable 3-10 .Thethermalnoisesigniesthemicrophonevoltageoutputduetothermalagitationofairmolecules,andrepresentsthelowerlimitatwhichacousticsignalscanbemeasured.Thefrequencyresponsemagnitudevariations,meanwhile,representacondencefactorofthemanufacturer-quotedFRFcalculations.Thesevalues,however,canbemisleadingrelativetothecurrentapplication.Forexample,theBruel 114

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&KjaerType4954B(whichisusedasthephasedarrayreferencemicrophone)hasaquotedfrequencyresponsemagnitudeuncertaintyof2dBforthefrequencyrangeof4Hzto80kHz.Foramaximalfrequencyofinterestof10kHz,however,theFRFplotprovidedbythemanufacturerindicatesthatthisismuchcloserto1dBforthecaseofamicrophoneouttwithit'sprotectiongrid.Therefore,sincethismicrophonealongwiththelineararrayG.R.A.S.microphonesareallusedinthisstudywiththeirprotectiongridsinstalled,afrequencyresponseuncertaintyof1dBisassumed.ThisresultsinatotalSPLuncertaintyof1.14dB. AnuncertaintyanalysiswasperformedontheDASbeamformingdatausingaMonteCarloanalysis Yardibietal. ( 2010b ).Perturbationquantitiesincludemicrophonelocationsinthree-dimensionalspace,ambiguityinthebeamformerscanningplane,facilitytemperatureuctuations,andmicrophonefrequencyresponses(ascomputedusingthegrouparraycalibrationtechniquedescribedin AppendixB ).ThesequantitiesareinputintotheMonteCarlosimulatorasstandarddeviationswhichweresubjecttorandomnumbergenerators.Atotalof1,000MonteCarloiterationswereperformed,asconvergencewasfoundtobesucientlyobtainedinthepreviousstudiesthatimplementedthistechnique( Bahretal. 2011 ; Wetzel 2009 ; Yardibietal. 2010b ).ValuesforthestandarddeviationsoftheuncertaintyperturbationquantitiesareprovidedinTable 3-11 .Notethatthevaluesusedforthefacilitytemperaturewerecomputedforeachexperiment,andthevalueindicatedinTable 3-11 representsthemeanstandarddeviationofalltheexperimentsperformed.Alsonotethatthex;yplaneisthatofthephasedarraymicrophonesandzistheout-of-planedistance.Theuncertaintiesforthemeasurementsofthex;yandzmicrophonepositionsrepresentthoseofthearrayframemanufacturingtolerances(0.08mm)0.003")andhalfofsmallestindexonthemeasurementtool(0.79mm)0.03125"),respectively. 115

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3.6FlowFieldMeasurements Floweldmeasurementswereperformedusingstereoscopicparticleimagevelocity(SPIV).PIVisanon-intrusivemethodofconductingspatially-resolvedvelocityeldmeasurements( Raeletal. 2007 ).Thismeasurementtechniquecapitalizesontheilluminationofseedparticlesinjectedintoaow,thereectionsofwhicharecapturedbyahigh-resolutioncamera.Thelocaldisplacementsoftheseedparticlesarethentrackedbetweentwoacquiredsnapshotsoftheilluminatedeldviaspatialcross-correlationsbetweenthesnapshotsusingFastFourierTransforms(FFTs).ApictorialrepresentationofPIVispresentedinFigure 3-33 SPIVutilizestwohigh-resolutioncamerasthatarepositionedaxeddistanceapartandangledtowardsacommonregionofinterestwithinaoweld.Alaserlightsheetisthencastintotheowregiontoillumuniateseedparticlesthatwereinjectedintotheowupstreamoftheareaunderinvestigation.Thismeasurementtechniqueisveryusefulinitsabilitiesto\see"aroundsolidsurfacesintheoweldthatwouldotherwisemaketraditional(2-dimensional)PIVimpossible,aswellasprovide3-dimensionalvelocityinformation.ThissectiondiscussestheSPIVexperimentalsetupintheUFAFF,dataacquisitionparameters,andastochasticestimationprocedureutilizedtoreconstructatime-resolvedestimateoftheoweld.Notethatduetotimeconstraints,onlythebaselinemodelcongurationwastestedwithSPIV. Theprimarypurposeofconductingoweldmeasurementsaroundthemodelistoquantifythenoisesourcegenerationtermsoftheacousticanalogyforsubsonic,turbulentowaroundthegeometryunderinvestigation.WhileSPIVprovidesameansformeasuringaspatially-resolvedsetofthree-dimensionalowelddata,thesystemusedinthisstudycanonlyacquirethedataatasamplingratethatisconsiderablylowcomparedtothecharacteristictimescalesoftheowelddynamics.Therefore,alow-dimensionaloweldreconstructiontechniquewasimplementedusingamodiedformofstochasticestimationsimilartothatdevelopedby Durgesh&Naughton ( 2010 ). 116

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3.6.1SPIVSetup TheexperimentalsetupforperformingSPIVmeasurementsonthetorquearmgeometryisillustratedinFigure 3-34 .AsFigure 3-34A shows,thetwocamerasaremountedatoppositeendsofa1.5mlongrailmountedverticallyvia8020hardware.ThelaserusedintheseexperimentswasanEvergreen200doublepulsedNd:YAGlasermanufacturedbyQuantelLaser.Thelaseremitsa6-mmdiameterbeamatawavelengthof532nm,withafull-widthathalf-maximum(FWHM)pulsewidthof7nsforanominalenergyoutputof200mJ/pulse.AsFigure 3-34B shows,thelaserisemittedasalightsheetthatilluminatesaplanarregionthroughtheoweld.Thelightsheetisapproximately2mmthickandisformedusingatwo-stagetelescopeattachedtothefrontofthelaseremissionorice.Thistelescopecontainsanadjustable2000mmfocallengthsphericallensfollowedbya-10mmfocallengthcylindricallens.Thepathofthelightsheetwaspartiallyblockedusinganobstructionpaintedaatblackenamel.Thiswasdonetopreventthelightsheetfromimpactingthesideofthemodelcylinderclosesttothelaser,astheintensityofthereectedlightishighenoughtoinducelong-termdamageonthecameras.AcomponentbreakdownofoneoftheLaVisioncamerasetupsisprovidedinFigure 3-35 andTable 3-12 TheseederapparatususedinthisstudywasdesignedtoprovideamaximumtestsectionsurfaceareacoveragetocompensatefortheopenjetshearlayeroftheUFAFF.Inotherwords,thelow-frequencyoscillationsoftheshearlayerstendtodisplacetheseedmaterial,thereforerequiringalargeareaofcoveragetoaccountforthisbehavior.ApictureoftheseederapparatusispresentedinFigure 3-36 .Astheimageshows,theseederconsistsofeightpipeextrusionsthataredistributedradiallyin45increments.Thelongerhorizontalpipeextrudesoutoftheinletthroughaholeinthewall,whereitconnectstotheseedgenerator.Theseederispositionedimmediatelydownstreamoftheinletprotectivescreensandapproximately12"(304.8mm)upstreamoftheinletcontraction.Seedmaterialistransferredtothefreestreamviaalineararrangementofholesinthe 117

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pipingwith1"(25.4mm)spacing.Thepipingis2"(50.8mm)inner-diameterSchedule40PVC.AdditionalspecicationsoftheseederusedintheseexperimentsareprovidedinTable 3-12 3.6.2RegionsofAnalysis WhendecidingonwhatregionsoftheoweldtoanalyzewithSPIV,amaximumareaofcoveragearoundthemodelwasdesiredaswellasmeasurementoftheoweldinareasthatappreciablycontributetotheacousticradiation.Itwasalsoimportanttoconsiderthelimitationsoftheexperimentalsetup.AsFigure 3-34 shows,thebeamthatholdsthelaserandcamerasislimitedverticallybythehorizontalsupportbeamslocatedaboveandbelowthecameras.ItwasdeterminedthatthePIVapparatuscouldonlybetraversedapproximatelyhalfofthemodelspan.Therefore,itwasdecidedthatonlythelowerhalfofthemodelspanwouldbeutilizedforoweldmeasurements.Thiswasconsideredtobeacceptable,however,duetothetop-to-bottomsymmetryofthemodel.ThesingleSPIVcameraarrangementofFigure 3-34A actuallyallowedforthemeasurementoftwoowregions:thegapow(areainbetweencylinderandtorquearm),andthenearwake(encompassesupto6Ddownstreamfromthetorquearm)regions.TheregionsofthemodeloweldthatwerescannedareshowninFigure 3-37 .Asthisimageshows,therearevemeasurementplanes,eachofwhichconsistofaninnergapowandanouternearwakeregion.Theseplaneswereselectedtoprovideasurveyoftheoweldatdierentheightsalongthemodel.Theywerealsosettocloselycoincidewiththemodelsurfacepressureprobestocorrelatetheobservedoweldbehaviorswiththemodelpressuresensors.Duetotimeandsetuprestrictions,SPIVisonlyperformedonthestandard=130conguration. 3.6.3DataAcquisition Thetorquearmgeometrypresentedinterestingchallengesfromadataacquisitionperspective.Itbecameincreasinglydiculttosupplyasucientamountofseedparticlesintheoweldastheregionofinterestbecameincreasinglyfartherfromthemodel 118

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centerplane.Asaresult,thenumberofattemptedPIVsnapshotswasadjustedperscannedregion,withtheobjectiveofobtainingsnapshotswithasfewinvalidvectorsaspossible.Twodierentdataacquisitioncriteriaweredened:oneforoweldmeanandturbulencestatistics,andanotherforoweldestimation.Theformercriterionwasmoreforgivinginthesensethatitwasnotnecessaryforanacquiredsnapshottocontainahighpercentageofvalidvectors,sincethestatisticsforeachvectorinthegridcouldbecomputedindependentlyofalltheothers.Thelattercriterion,ontheotherhand,ismuchmorerestrictive.Fortheestimationtoworkasaccuratelyaspossible,thesnapshotmustbeascompleteaspossible.Therefore,adefaultcriterionofnomorethan10%invalidvectorspersnapshotwasimposedforestimationpurposes.Itwasfoundthatthiscriterionhadtobeslightlyadjustedfortheregionsthatweremorechallengingtomeasure.Thecriteriaandresultingnumberofvalidsnapshotspermeasuredregionaredetailedin Section5 ThesnapshotdatawereacquiredusingDaVisv8.0software.AlthoughaPIVsnapshotsamplingfrequencyof4HzwasspeciedinDaVis,downloadingtheacquiredimagestothecomputerresultedinoccasionallaggingoftheimagecapture,thereforeresultinginacquisitionofPIVsnapshotsatrandomtimes.ItwasthereforedecidedthatthesurfacepressureprobedatabeacquiredsynchronouslywiththePIVdatausingatriggersignal.Moreinformationaboutthetriggeringschemeisdiscussedin Chapter3.6.5.3 .Thistriggersignaloriginatedfromtheprogrammabletimingunit(PTU)ofthePIVsystem,whichallowedthetriggeroutputtobedenedrelativetoareferencetimesignal.Thisreferencetimewassettotheoccurrenceoftheopeningoftherstlaser'smechanicalshutter,knownastheQ-switch,whichrepresentsthelaseremission.Thetriggersignalwasthendenedtooccuratatimet=2,wheretrepresentsthetimebetweentheringoftherstandsecondlightsheets.Thistimedelaywasdecideduponbasedonaconictingsetofcriteria.Fromaninterrogationwindowstandpoint,alongertimedelayiswantedtoensureadequatepixel-traversingofseedparticles,whilefroma 119

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three-dimensionalowperspective,ashortertimedelayiswantedtopreventparticlesthataresubjecttoastrongdownward(z)velocityfromleavingthelightsheet.Fortheseexperiments,atimedelayoft=8swasspecied.Thiswasfoundtobeareasonablebalancebetweenthetworequirements. TheSPIVdatawereprocessedusingafour-pass,interrogationwindowreductionscheme.Specically,thersttwoofthesepasseswereperformedusinga6464pixelinterrogationwindowusinga75%windowoverlap.Thenaltwopassesweredoneusinga3232pixelinterrogationwindowwitha50%windowoverlap.Auniversaloutlierdetectionspatiallterwasthenappliedtothenaloutputvectoreld.Asanalpass,amultivariateoutlierdetection(MVOD)algorithmtailoredtoasymmetricdatadistributionswasperformedonthevectorelddatasets( Grinetal. 2010 ).AdetailedbreakdownoftheSPIVprocessingstepsareshowninTable 3-13 3.6.4SPIVUncertainty ThebiasandrandomcomponentsofuncertaintywerecomputedforthetestedSPIVcongurations.Thebiasuncertaintieswerecomputedbasedonthephysicalgeometricalsetupofthetwocamerasrelativetotheoweldcoordinatesystem,aswellastheRMSdeviationsinthetsoftheconformalmappingfunctionstothecameraimages(generatedinDaVissoftware).Therandomcomponentsofuncertaintywerecomputedfortherstandsecondordermomentstatisticsofvelocity,whichrepresentthemeanandturbulenceterms,respectively.DetailsoftheSPIVbiasandrandomuncertaintycalculationsarepresentedin AppendixC 3.6.5FlowFieldEstimation Aswasstatedin Section1.3.3 ,thesolutiontothevortexsoundanalogyof Powell ( 1964 )and Howe ( 1975 )requiresthetime-resolvedquanticationoftheunsteadyvorticityanddissipationofturbulentmotionsintheoweldofinterest.Asimpledenitionofatime-resolvedmeasurementisonethathasasamplingfrequencyofatleasttwicethemaximumfrequencyofinterest.Unfortunately,thePIVsystemusedinthisstudydoes 120

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nothavethecapabilityofacquiringtime-resolvedmeasurements,havingamaximumpossiblesamplingrateofonly4Hz.Tocircumventthislimitation,astochasticestimationtechniqueisimplemented,inwhichtime-resolvedsurfacepressureuctuationsthataresynchronizedwiththelow-frequencysampledPIVdataareusedtogeneratealow-dimensionalestimateofthetime-resolvedoweld( Adrian&Moin 1988 ).Thistechniqueperformsamulti-time-delaylinearstochasticestimationtechniqueonamodalrepresentationoftheoweldcomputedusingproperorthogonaldecomposition(POD).ThisoverallprocessrepresentsamodiedformofLSE,commonlyreferredtoasmtdLSE-POD( Durgesh&Naughton 2010 ). 3.6.5.1TheLambVector Lighthill'sanalogydescribesthenoiseproducedbyturbulenceinaow-eld( Lighthill 1952 ).However,thismethodisnotveryusefulforthecaseofairframenoise.Alateradvancementofthisanalogyisthatof Curle ( 1955 ),whichstatesthatthesoundgenerationduetothepresenceofsolidsurfacesinasubsonicowmaybeestimatedbyaccountingforthescatteringofthepressurewavesonthesolidsurfaceofthebody.Fromanexperimentalstandpoint,however,thismethodcanbediculttoapplytoacomplexgeometry.Analternativetothisistheacousticanalogyof Powell ( 1964 ),whichcapitalizesontheconceptthatacousticgenerationcanbequantiedbyanalysisoftheunsteadinessofvorticityintheoweld.Thisformulationispresentedin Section1.3.3 ,whichundertheassumptionsofowwhereM<<1andRe>>1,indicatethattheprimaryacousticsourcetermofinterestistheunsteadyLambvector L00=!0u0:(3{52) Therefore,itwasdecidedthattheunsteadyLambvectorcomponentsweretobetheprimarysourcetermsofinterest. Sincetheexperimentalowelddataareacquiredintwo-dimensional(x;y)planes,therearelimitationsintowhatcomponentsoftheLambvectorcanbecalculated.To 121

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visualizethis,thecrossproductbetweenthevorticityandvelocitycanbeexpanded: !0u0=^i^j^k!0x!0y!0zu0xu0yu0z=(!0yu0z)]TJ /F3 11.955 Tf 11.96 0 Td[(!0zu0y )^i)]TJ /F1 11.955 Tf 11.96 0 Td[((!0xu0z)]TJ /F3 11.955 Tf 11.95 0 Td[(!0zu0x )^j+(!0xu0y)]TJ /F3 11.955 Tf 11.95 0 Td[(!0yu0x)^k; (3{53) wheretheunderlinedtermsrepresenttheonesthatcanbecomputedusingtheSPIVplanesmeasured.Asaresult,thisleavestwo\partial"Lambvectorcomponentsinthe^i)]TJ /F1 11.955 Tf 12.88 2.69 Td[(^jcoordinateplane.Itisthesetermsthataretheprimaryfocusoftheoweldestimation. Itisimportanttonotethatatime-resolvedestimateoftheLambvectorsourcetermsisdesirable.ThemostapplicableadaptationofHowe'svortexsoundformulationthathasbeeninvestigatedisthefar-elddipolesoundradiationequationforanite-measureduiddomain: p0(x;t)=)]TJ /F3 11.955 Tf 20.68 8.09 Td[(0xi 4c0jxj2Zint@ @t[(!0u0)(y;t)-221(jxj=c0)ri]dy;(3{54) wherexandyarethecoordinatesofthefar-eldobserverandsourceregion,respectively,andintrepresentsthenitedomain( Takaishietal. 2004 ).Furthermore,irepresentsthevelocitypotentialthatwouldbeproducedbyrigidbodymotionofthesolidgeometryatunitspeedintheidirection( Udaetal. 2011 ).Thisanalogyclearlyindicatesthatatime-resolvedmeasurementoftheoweldisnecessarytodeterminethesourcesintheeldthatareresponsibleforfar-eldradiation.Moreinformationaboutthisanalogyisprovidedin Section1.3.3 .Unfortunately,duetothecomplicatedandthree-dimensionalnatureofthetorquearmgeometry,thisvelocitypotentialwouldneedtobenumericallycomputed,whichisbeyondthescopeofthisdissertation.Asaresultofthis,calculationoftheLambvectortimederivativesisnotbenecial,andthereforetheLambvectortermsthemselveswillbeinvestigated. 122

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3.6.5.2ProperOrthogonalDecomposition Properorthogonaldecomposition(POD)identiescoherentstructuresinaspatially-resolvedowelddatasetanddistributesthekineticenergycontentoftheeldintoasetofcorrespondingmodes( Lumley 1967 ).PODalsoallowsfortheconstructionofareducedordermodelofahigh-dimensionalvelocityeld.Forthisstudy,thePODspatialmodeswerecomputedusingthemethodofsnapshots( Sirovich 1987 ).ForthecaseofPIV,thismethodisutilizedduetoitscomputationeciencyforthecasewhenthenumberofeldgridpointsaregreaterthanthenumberofsnapshots.WiththeuseofPOD,theentireowelddatasetisdecomposedintoasetofspatialmodesandtime-varyingexpansioncoecients u(x;y;t)=NXs=1a(s)(t)(s)(x;y);(3{55) wherea(s)(t)arethetime-dependentPODexpansioncoecientsand(s)(x;y)arethespatialvectorPODmodes.AsEquation 3{55 shows,thedecompositionisperformedforthevelocityvectoru.Therefore,theexpansioncoecientsarerepresentativeofallofthevelocitycomponentsinputintothePODsolver.ThePODmodesaretheeigenmodesoftheFredholmintegral ZX(x;y)=(x;y);(3{56) whereXisthespatialcorrelationmatrixcontainingmean-subtractedvelocitycomponentsataseriesofmPIVsnapshots.Thesingularvaluedecomposition(SVD)ofthecorrelationmatrixXTXiscalculatedas XTX=WWT;(3{57) whereisadiagonalmatrixofsingularvaluesinorderofdecreasingnumericvalue.Thismatrixrepresentsthekineticenergyofeachmode,withWcontainingthecorrespondingeigenvectors.SpatialPODmodes,(s)(x;y),arethencomputed,withthetotalnumberofmodesbeingequaltothenumberofacquiredPIVsnapshots: =XW)]TJ /F7 7.97 Tf 6.59 0 Td[(1=2:(3{58) 123

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Asanalstep,thetemporalPODcoecientsa(s)(t)arecomputedforeachmodeas a=W1=2:(3{59) TheoriginalvelocityeldrecordcanthenbereconstructedusingEquation 3{55 ,whichrepresentssummationoverallavailableNmodes(snapshots). Notethatinthisparticularapplication,PODisappliedtotheuctuatingvelocityeld.Thisisbecausethedesiredcomputedquantities(theLambvectorterms)areunsteadyinnature.Therefore,removalofthemeanoweldfromthePODcalculationsyieldsaspatialsetofmodeswhoseenergyisrepresentativeoftheuctuatingoweld.Therefore,Equation 3{55 isre-writtenas u0(x;y;t)=NXs=1a(s)(t)(s)(x;y);(3{60) andthusthereconstructionofaninstantaneousvelocityeldbecomes u(x;y;t)=U(x;y)+u0(x;y;t):(3{61) 3.6.5.3ModiedStochasticEstimation Amodiedformoflinearstochasticestimation(LSE-POD)wasutilizedontheacquiredSPIVdatasets.ThisestimationprocedurecouplestheoutputsofPODwithstandardLSE,inordertocreateatime-resolvedestimateoftheoweldmodesofhighestenergy( Bonnetetal. 1994 ).Thisisdonetoensuretheaccuracyoftheestimate,sinceinclusionofPODmodesoflowenergycouldpotentiallydegradetheaccuracyoftheresultingestimate.Thelow-orderestimateoftheoweldintermsofprimitive(velocity)variablesusingrPODmodessuchthatr
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areasetofunsteadysurfacepressureprobesp(m)onthetorquearmmodel.Notethatthesubscriptmrepresentsthepressuresensornumber.Theestimatedexpansioncoecientiscomputedas ~a(s)(t)=A(s)mpm(t);(3{63) whereA(s)maretheLSEcoecients.Minimizationofthemeansquareerrorintheestimateof~a(t)resultsinasystemofequationsallowsolvingfortheseLSEcoecients: AT=[PP])]TJ /F7 7.97 Tf 6.59 0 Td[(1[aP](s);(3{64) where AT(s)=266666664A1A2...ANp377777775(s);f[PP]g(s)=266666664 p1p1 p1p2 p1pNp p2p1 p2p2 p2pNp............ pNpp1 pNpp2 pNppNp377777775(s);f[aP]g(s)=266666664 A1p1 A2p2... ANppNp377777775(s);(3{65) andNprepresentsthenumberofsurfacepressureprobesinthemeasurement.InadditiontotheaboveformulationofLSE-POD,whichrepresentssingle-timeLSE,thereexistsafurthermodicationinwhichmultipletimedelaysareusedtosumthecorrelationsbetweenaandp( Durgesh&Naughton 2010 ; Tuetal. 2012 ). Theuseofpastandfuturedata,ornon-causaldata,canresultinstrongercorrelationsaswellasreduceerrorsassociatedwithsensornoise.Thismulti-timedelayformofLSE-POD(mtdLSE-POD)wasappliedinthisstudy,inwhichthetorquearmmodelsurfacepressureprobedatawasacquiredsynchronouslywiththeoccurrenceofthePIVsnapshot.AnillustrationofthisispresentedinFigure 3-38 .ThiswasdonesuchthatthetriggersignalapproximatelyrepresentedtheequivalentPIVsnapshotoccurrence( Section3.6.3 ).AsisdisplayedinFigure 3-38 ,anequivalentnumberofpre-andpost-triggersampleswereacquiredforeachoftheprobesignalstoallowmulti-timedelaycorrelationstobecomputedforequivalentnegativeandpositivetimedelays.AdetailedexplanationofthederivationandconstructionoftheLSEmatricesofEquation 125

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3{65 formulti-timedelayanalysisusingsymmetricnegativeandpositivetimedelayscanbefoundin Durgesh&Naughton ( 2010 ).EstimationProcessFlow TheestimationprocedureprocessowisillustratedinFigure 3-39 .Asitshows,anestimateoftheLambvectoriscomputedfromtheestimatedvelocityterms.Recallthatthisisnotmeanttobeafullreproductionoftheoweldparameters,butratheratime-resolvedreproductionofthehighestenergyterms.Moredetailsaboutthecalculationoftheintermediateestimationtermsarediscussedin Section5.2 ItisimportanttorecallthattheLambvectorincludesbothvorticityandvelocityinformation.AsitissummarizedinFigure 3-39 ,estimationisperformedontheexpansioncoecientsthatdescribethethree-dimensionaluctuatingvelocityeld(turbulencekineticenergy).Notethatinsteadofusingtheturbulencekineticenergyastheinputkernel,itcouldbepotentiallyreplacedbyvorticityortheLambvectoritself.However,thereareseveralreasonswhythisisnotperformed.First,settingvorticityasthekernelisnotasuitableselectionforthesimplereasonthatthevelocitydataisalsoneededtocomputetheLambvector.Whileestimationcanbeperformedonvorticityandvelocityseparately,combinationoftherespectivelow-orderestimatestoyieldanestimateoftheLambvectorisanarbitraryprocedure.Also,thereisanincreaseinuncertaintyassociatedwiththespatialgradientoftheeldtoyieldthevorticity,andthustheLambvector( Abrahamson&Lonnes 1995 ; Lourenco&Krothapalli 1995 ).Thiswould,ineect,introducealargeamountofnoiseintotheestimationprocess.Therefore,settingtheturbulencekineticenergyasthekernelofPODwasbelievedtobethemorereliablechoice.VariationofProbeLocations AtotalofninepressuretransducerswereutilizedinconjunctionwiththeSPIVrunsforthepurposeofprovidingsynchronized,time-resolvedunconditionalmeasurementsonwhichtobasetheoweldestimationprocess.Fiveofthesesensorswerepositionedalong 126

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thecylinderspanwhiletheotherfourwerepositionedonthetorquearminnergapowandedgesurfaces.Whilethecylindersensorsremainedstationaryforallmeasurementplanes,theonesonthetorquearmwerevariedsothattheywouldbewithincloseproximitytothelaserlightsheetforeachmeasurementplane.Thiswasdoneinordertoimprovethecorrelationsbetweentheunconditional(probe)andconditional(PODexpansioncoecients)measurementsintheestimationprocedure.ThespanwiselocationsofallsensorsusedinthePIVexperimentsandthepositionsofthetorquearmsensorsforthedierentmeasurementplanesaretabulatedinTables 3-14 and 3-15 ,respectively.IsometricimagesofthesensorlocationsofthemodelareprovidedinFigure 3-40 .NotethatcylindersensorsC1-C4arelocatedatacircumferentialangleof=)]TJ /F1 11.955 Tf 9.29 0 Td[(135whilesensorC5islocatedat=+135,positionedsymmetricallyfromsensorC4. 3.7ComputationalFluidSimulations Asapredecessorforwindtunnelexperimentation,aseriesofCFDsimulationswereperformedonthemodelgeometryinquestion.ThesesimulationswereconductedusingPowerFLOW,anovelsoftwarepackagethatutilizesalatticeBoltzmann-basedcomputationalalgorithm( Chen&Doolen 1998 ).Thistypeofsoftwarewaschosenbasedonreasonableagreementbetweensimulationandexperimentalresults-bothfromnear-elduiddynamicsandfar-eldacousticsperspectives-forcertainlandinggearandlandinggear-typegeometries( Bres 2011 ; Noeltingetal. 2010 ).Theprimarypurposeofconductingthesesimulationswastohighlightregionsofthemodelthatwouldbenetthemostfromplacementofunsteadypressuretransducersfortheeventualexperiments,aswellastoidentifytheow-eldvorticitydynamicsresponsiblefornoisegeneration. 3.7.1SimulationProcedure ThePowerFLOWsoftwareallowstheusertodeneanumberofdierenttypesofmeasurementsinasimulationenvironment.Thesemeasurement\stages"enabletheusertogaugetheperformanceofthesimulationincrementally,theoutputsofwhichincrease 127

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incomplexity.Forthisstudy,thesimulationmeasurementstagesweredividedintothreeprimarycategories: 1. Caseandgeometrypreparation 2. Simulationdiagnostics 3. Meanowmeasurements 4. Unsteadyowmeasurements 5. Far-eldacoustics AowchartsummarizingthesimulationprocedureispresentedinFigure 3-41 .Therstthreestagesofthesimulationprocedurearediscussedinthissection,whiledetaileddocumentationoftheresultsarediscussedinparallelwiththosefortheexperimentalmeasurementsin Chapter4 and Chapter5 3.7.2CaseandGeometryPreparation ThissectiondiscussesthestepsinvolvedwiththedevelopmentofthePowerFLOWsimulationenvironment.Thesestepsincludethenumericalsetupofthesimulationenvironment,deningtheoweldboundaryconditions,anddeningthemeasurementquantitiesandregionsofinterest. 3.7.2.1NumericalSetup AscanbeseeninFigure 3-42 ,thecomputationalgridconstructedforthisstudyisastructureddomainconsistingofcubicmeasurementcells,orvoxels,thatincreaseinsizeasonetravelsoutwardfromthemodelsurfaces.Specically,thecomputationalgridsizechangesbyafactoroftwoforadjacentresolutionregions.Eachgridregionisreferredtoasavariableresolution(VR)region.Thesmallestvoxelsizeconsistsofacharacteristicedgelengthknownasthelatticelength.Twodierentsimulationcaseswerecomputedfordierentmeasurementstolimitcomputationaltimeforeachcase.Therstofthesecaseswasdedicatedtomeanoweldmeasurementsandmeananductuatingsurfacepressures.Thesecondcasewasdedicatedtohigh-temporalresolutionoweld 128

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measurementsatselectplanes.AnoverviewofthegeneralsimulationspecicationsforthesecasesissummarizedinTable 3-16 AsFigure 3-42 shows,thenerVRregionsareconcentratednearthemodelsurfaces.Specically,foragivenmodelgeometry,aVRregionconsistingoflatticevoxelsisdenedbyextrudingthegeometryoutwardinalldirections,creatinganeective\oset"region.ThistrendcanthenberepeatedforVRregionsofincreasingcoarseness,witheachVRosetregionbeingextrudedfurtherfromthemodelsurfacethanthepreviousnerVRregion.Thisisdoneinpracticetolimitthetotalnumberofvoxelsinthesimulation,thusreducingcomputationtimeandoutputsimulationresultlesizes.ThesimulationsperformedinthisstudyconsistedofatotalofsevenVRregions.Therstthreeregionsweredenedasosetregions,whichtheentiresolidgeometrywouldhave.ThelastfourareeldVRregionsthatexpandoutwardfromthemodelgeometrytowardstheboundariesofthesimulationvolume.AnillustrationoftheosetVRregionsforoneofthetorquearmsisshowninFigure 3-43 .Asthisgureshows,theosetVRregionsexpandfromthesolidgeometrysurface.ThesizesoftheosetVRregionswasdenedsuchthateachregioncontainedeightlocalvoxels(Table 3-17 ).Thiswouldensureaccurateeldandsurfacecalculationsaswellaslimitthecomputationalcostsofthesimulation.ThefourouterVRregionsareshowninFigure 3-44 .NotethattheindicatedVR1regionrepresentsthetestsectionboundary.Theresolutionofthisregionisalsosharedwiththeoutersimulationvolume. ThetorquearmmodelwasdesignedinProEngineerWildre4.0andexportedasasimpliedparasolid.Inactuality,themodelconsistsofsixdierentcomponentsthatwereimportedorcreatedindividually:(1)cylinder,(2)torquearm,(3)junction,(4)junctionouterfairing,(5)junctioninnerfairing,and(6)helicalwirewrap.Exceptforthecylinder,allothercomponentswereimportedintothePointWisesoftwarewhereitunderwentmeshing.Themeshesappliedtothecomponentsconsistedofunstructuredtriangles.Simplersurfacessuchastheattorquearmsurfacewerepopulatedwithlarger 129

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triangleswhileroundedsurfacessuchasthejunctionwerepopulatedwithverysmallones.Thenumberofmeshelementsendedupvaryingbetween1,000and10,000elements.ThesecomponentswerethenimportedintoPowerCASE(thesimulationcaseandsetupsoftware)as.STLles.Thecylinder,meanwhilewascreatedinPowerCASEsinceitisasimplegeometry.Itwasdenedtohaveastructuredgridofsimpleangularrotationofrectangularelementswith1resolution.AnillustrationofthemeshedgeometryisprovidedinFigure 3-45 3.7.2.2BoundaryConditions AnillustrationoftheoveralllayoutofthesimulationenvironmentisshowninFigure 3-46 .Notethatthedimensionsofthesimulationuiddomainaredenedrelativetothediameterofthemodelcylinder,D=38:1mm(1.5"),withvaluesof19Dtallby140Dwideby116Dlong.Thesimulationswereinitiatedusingafreestreamvelocityconditioneverywhereintheuidregionofthecomputationaldomain.Thisinitialconditionresultedinatransienttimeperiodinwhichtheoweldbecamefully\aware"ofthepresenceofthetorquearmgeometry.AsFigure 3-46 shows,theuidregionofthesimulationvolumeisdividedintotwosub-regions:(1)acoreowregionrepresentingthedimensionsoftheUFAFFtestsectionand(2)ananechoicuidregionthatpreventsthereectionofacousticwavesbysimulatingaregionofhighviscosity.TheanechoicuidregionismeanttoserveasacruderepresentationoftheacousticabsorptioncapabilitiesoftheUFAFFanechoicchamber,whichisrateddowntoacut-onfrequencyof100Hz. Themodelsurfacesweredenedassolidviscoussurfacesthatobeytheno-slipboundarycondition,whilethesurfacesthatmakeuptheperipheryofthesimulationvolumeweresetasinviscidsidewalls.Themodelcylindersurfacewastreatedslightlydierent,however,inordertobetterrepresentaturbulentowscenario.Inordertoensureturbulentowseparationfromthecylindersurface,auniformsurfaceroughnessof0.05mmwasdenedtoserveasa\virtualtrip"device.Thenumericalvalueforthisparameterwaschosenbasedonaseriesofpreliminarysimulationrunsonowarounda 130

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singlecylindercoupledwithcomparisonstoexperimentalcircumferentialsteadypressuredistributionsmeasuredbyNASA( Jenkinsetal. 2005 ).ThistrippingtechniquewasadaptedfromthetandemcylinderLattice-Boltzmannsimulationsconductedby Bres ( 2011 ); Bresetal. ( 2010b ). 3.7.2.3MeasurementWindows Aconsiderablenumberofpreliminarysimulationrunswereperformedinordertoverifypropersimulationconvergenceandappropriateowbehavior.Asmentionedpreviously,thesolutionoutputoftwonalsimulationrunswereusedinthisdissertation.Thereasonforhavingtworunsisinordertolimittheresultingrequireddiskspaceforoutputles.Therstsimulationrunwasconsideredwithmeasuringsimulationconvergence,observingthemeanoweld,andcomputingsurfacepressurespectraatkeyregionsofinterest.Uponvericationoftheperformanceoftherstrun,thesecondonewasperformedwiththegoalofobtainingtime-resolvedoweldinformation.ThemeasurementsconductedinthesesimulationrunsareprovidedinTable 3-18 .Thesamplingperiodsaredenedintermsoflatticetimes,whereonelatticetimeistlattice=810)]TJ /F7 7.97 Tf 6.59 0 Td[(7seconds.Itisimportanttonotethattheindicatedsamplingratesdidnotrepresentsingleinstancesinthesimulation,butrathereachsampledtimeinstancerepresentsanaveragetakenacrossthesamplingwindow.Forexample,themeaneldwassampledwithaperiodof5,000latticetimesteps,whichtranslatestoaphysicaltimeperiodof0.004seconds(250Hz).Therefore,anygivensampleofthemeanoweldactuallyrepresentsanaverageofthedatafrom0.002secondsbeforethesampleto0.002secondsafterthesamplewastaken. 3.7.3SimulationDiagnostics AcommonwaytodiagnosetheperformanceofanunsteadyCFDsimulationistemporalconvergence.ThiscanbequantiedinPowerFLOWbymonitoringsurfacemeasurementtimehistoriessuchasaerodynamicloadsexperiencedbyabulksurfaceregionand/orpressuresatapointonthesurface.Theformeroftheseisanexcellentway 131

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todiagnosethegeometryasawholeandistypicallypresentedintheformofliftanddragcoeents,CLandCDrespectively( Bresetal. 2010b ).Forthesesimulations,theliftanddragforcesarethoseinthestreamwiseandtransversedirections,respectively(Figure 3-2A ).Theliftanddragforceswerecomputedandaveragedovertheentiresurfaceareaofthetorquearmgeometry,thetimehistoriesofwhichareshowninFigure 3-47 .Notethattheforcecoecientsarecomputedbynormalizingtheintegratedforcesbythecharacteristicforce1 21U21A,whereA= 4D2.Asthisgureshows,themodelforcesexhibitaninitialtransientperioduntilthecalculationsbegintoconverge,asevidencedbytheCDrunningaveragecalculation.Thegurefurthershowsthattheunsteadyproleofthemodelliftforcesoscillateaboutameanvalueofzero,whichisexpectedduetoitssymmetricgeometryrelativetotheoncomingowdirection.Notethatwhileatotalphysicaltimeof0.4secondswassimulated,aportionofthetimeperiodisrejectedtoeliminatethesetransienteects.Forthesesimulations,convergencewasconsideredtobeachievedwhentherunningaveragedragcalculationcametowithin3%ofthenalaveragedvalue.Thiswasfoundtooccurataphysicalsimulationtimeofapproximately0.08seconds,yieldingavalidsimulationtimeof0.32seconds. 3.7.4MeanFlowMeasurements Oncetemporalconvergencewasconrmed,resultsforthemeanoweldwereconsulted.Theprimarymetricforthisstageofsimulationvericationwasthatsymmetricowandsurfacetrendswereachieved.DemonstrationsofmeansurfaceandoweldmeasurementsarepresentedinFigure 3-48 .Asthisgureshows,slicesthroughseveralplanesoftheoweldshowsymmetricZ-vorticitydistributionsaswellasasymmetricsurfaceCpdistributionaroundtheentiretorquearmgeometry.Theseoweldvisualizationsrepresentaveragescomputedoverthesimulationtimerangeof0:080:4seconds,asdoallcomputationsdiscussedinlaterchapters. 132

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A B Figure3-1. (A)SimpliedmodelofaGulfstreamG550noselandinggear,(B)close-upimageofG550shockstrut-torquelinkassembly(wheelshiddenforclarity). A B Figure3-2. Illustrationsofthesimpliedshockstrut-torquelinkdissertationmodel:(A)renderedimageoftorquearmmodelgeometry,(B)primarygeometricmeasurementparameters(=torquearmseparationangle,H=junctionseparationdistance). 133

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A B Figure3-3. (A)Assembledviewand(B)explodedviewofthemodelcylinder. 134

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A B C Figure3-4. Serratedtapeforcylinderboundarylayertripping:(A)proleview,(B)cross-sectionalview,(C)experimentalpositioning. 135

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Figure3-5. Dimensionalparametersthatdenethemodelhelicalwirewrap. Figure3-6. Far-eldSPLresultsoftrippedcylinderhelicalwirewrapexperiments(lineararraymicrophoneL4). 136

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A B Figure3-7. (A)Assembledviewand(B)explodedviewofthemodeltorquearm. Figure3-8. Pictorialrepresentationofthe4primarytestedmodelcongurations. 137

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Figure3-9. TheUniversityofFloridaAeroacousticFlowFacility. A B Figure3-10. (A)VisualizationoftorquearmmountingassembliesintheUFAFFand(B)photographofUFAFFtestsectionconguredforacoustictesting. 138

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A B Figure3-11. Steadypressuretapcongurationforthemodel(A)cylinderand(B)torquearm. A B Figure3-12. Close-upviewofmodelpressureportsdedicatedtounsteadysurfacemeasurements(A)onthemodelcylinder,(B)ontheuppertorquearm. 139

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A B Figure3-13. Illustrationof(A)recessedmicrophonehousingwithlabeleddimensionsandprimarycomponents,and(B)systeminterfacequantitiesutilizedinTMcalculations. 140

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A B Figure3-14. EquivalentacousticductTMcomponentsfor(A)agradualareachangeand(B)microphone-terminatedbranch. Figure3-15. FRFcomparisonbetweenmicrophonebrancheswithopenandsealedterminationcongurations(parametersprovidedinTable 3-6 ). 141

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A B C Figure3-16. (A)Componentsofarecessedelectretmicrophonepackageandimagesoftheirinstallationwithinthemodel(B)cylinderand(C)torquearm(frontfaceofcoverplatejrearviewwithbackplateremovedandKulitesinstalledjrearviewwithelectretsensorsinstalled). 142

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A B Figure3-17. (A)Schematicand(B)photographofPWTsetupforrecessedmicrophonecalibration(schematicadaptedfrom Williams ( 2011 )). Figure3-18. IllustrationofMultisineoverlapperformanceviaFRFmeasurements(frequencybands: )]TJ ET 0 G 0 g BT /F1 11.955 Tf 172.11 -595.98 Td[(band1, band2, )]TJ ET 0 G 0 g BT /F1 11.955 Tf 281.89 -595.98 Td[(band3, band4, )]TJ ET 0 G 0 g BT /F1 11.955 Tf 391.67 -595.98 Td[(band5). 143

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Figure3-19. FRFcomparisonbetweensealedandopenTygonRductterminationconditions(experimentallymeasured). Figure3-20. ComparisonofexperimentallymeasuredFRFsusingMultisineandBLwhitenoiseinputcalibrationsignalswithsimulatedFRFviaTMestimation. 144

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Figure3-21. ComparisonofexperimentallymeasuredFRFsforthetwodierenttubulationlengthsusedwiththemodelrecessedelectretpackages.TheFRFsweregeneratedusingBLwhitenoiseinputcalibrationsignalswithinputRMSpressuresof224and40Pa(141and126dBre.20Pa)integratedovertherespectivefrequencyrangesof96HzF12:896kHzand7:2F20kHz. A B Figure3-22. RelativeTHDperformanceofasample(A)shortand(B)longstemrecessedelectretpackage. 145

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Figure3-23. Comparisonofmean-squarepressures(MSPs)betweenreferenceandDUTouttwithashorttubulationatatonalfrequencyof1.008kHz.NotethattheDUTisthesameastheoneinFigure 3-22A 146

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A B Figure3-24. (A)Comparisonofr[jHyx(f)j]forMultisineandBLwhitenoiseinputsignalsand(B)resultingr[Gyy(f)]usingBLwhitenoisesignal. 147

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A B Figure3-25. Illustrationoftimedomainreconstructionofrecessedelectretsensor:(A)comparisonbetweenlteredreferenceBruel&Kjaerandrecessedelectret,(B)comparisonbetweencorrectedrecessedelectretandreferencesensor.Atotalofonly0.0625secondsofdataareshownsincethisistheperiodofthedeterministicinputsignal. A B Figure3-26. Characteristicsofasamplerecessedelectrettransferfunction:(A)FRFwithcomparisontothatofexperimentalrecessedelectret,(B)unitcirclediagramofpolesandzeros. 148

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A B Figure3-27. (A)Photographand(B)schematicofUFAFFtestsectionouttwithfar-eldlinearmicrophonearray. Figure3-28. Generalshearlayerrefractionprocessforthecaseofaplanethickshearlayer.[FigureadaptedwithpermissionfromauthorsofBahr,C.,Zawodny,N.S.,Liu,F.,Wetzel,D.,Bertolucci,B.,&Cattafesta,L.2011Shearlayertime-delaycorrectionusinganon-intrusiveacousticpointsource.(page501,Figure3),InternationalJournalofAeroacoustics,10(5),497-530.] 149

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Figure3-29. PlanararrayofMmicrophonesbeamformingtoascanningplaneofLgridpoints.[FigureadaptedwithpermissionfromauthorsofYardibi,T.,Zawodny,N.S.,Bahr,C.,Liu,F.,Cattafesta,L.,&Li,J.2010ComparisonofMicrophoneArrayProcessingTechniquesforAeroacousticMeasurements.(page736,Figure1),InternationalJournalofAeroacoustics,9(6),732-762.] ParameterInnerArrayOuterArray OuterRadius,(mm)40.636.8InnerRadius,(mm)10.273.7#ofSpirals5.11.#ofCircles5.5.SpiralAngle()58.51.SensorCount25.55. Figure3-30. FFMAdesignparametersandillustrationofouterarraymicrophonespirallayout. 150

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A B Figure3-31. Thefree-eldmicrophonearray(FFMA):(A)frontfaceshowingfoamtreatmentandextrudedmicrophonerods,(B)rearimageofskeletalAluminumsupportframe. 151

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A B C D E F Figure3-32. (A)ResolutionoftheouterFFMAasafunctionoffrequencyandtheoreticalPSFperformanceatoctavebandfrequencies(B)1kHz,(C)2kHz,(D)4kHz,(E)8kHz,(F)16kHz. 152

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Figure3-33. IllustrationoftraditionalPIVdataacquisition.[FigureadaptedfromDantecDynamics,MeasurementPrinciplesofPIV,http://www.dantecdynamics.com/Default.aspx?ID=1049] A B Figure3-34. (A)PhotographofSPIVsetupintheUFAFFand(B)virtualrenderingofSPIVsetupillustratinglightsheetdevelopment. 153

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Figure3-35. ComponentbreakdownoftheLaVisionImagerproXPIVcamera. Figure3-36. SeederapparatususedforSPIVexperiments.Notethatowisoutofthepage. 154

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Figure3-37. SPIVmeasurementplanesofthebaselinemodeloweld. Figure3-38. IllustrationofPIV-pressureprobedataacquisitionmethodformtdLSE-PODexperiments.SurfacepressureprobedataareacquiredsynchronouslywithPIVdata.Staticestimatorsarecomputedandappliedtoasecondsetofcontinuousprobedatatocomputeatime-resolved,lowdimensionalestimateoftheoweld. 155

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Figure3-39. Flowchartillustratingthestaticestimationprocedure.[FigureadaptedfromMurray,N.,Ukeiley,L.,andRaspet,R.2007CalculatingSurfacePressureFluctuationsFromPIVDataUsingPoisson'sEquation.(page4,Figure3),45thAIAAAerospaceSciencesMeetingandExhibit,AIAAPaper2007-1306.] A B Figure3-40. (A)Cylinderand(B)torquearmsensorlocationsforPIV-estimationexperiments.Sensorsmarked representelectretswhile representKulites. 156

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Figure3-41. FlowchartofthePowerFLOWsimulationprocedure(adaptedfrom Exa ( 2011 )). A B Figure3-42. ComputationalgridresolutionofthePowerFLOWtorquearmsimulations. 157

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A B C D Figure3-43. VisualizationofthethreeosetVRregionsofoneofthetorquearms:(A)solidtorquearmonly,(B)torquearmwithosetVRregion7,(C)torquearmwithosetVRregion6,and(C)torquearmwithosetVRregion5. A B Figure3-44. ViewsofthefourouterVRregions:(A)proleview,(B)frontview. 158

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A B Figure3-45. VisualizationofthethreeosetVRregionsofoneofthetorquearms:(A)solidtorquearmonly,(B)torquearmwithosetVRregion7,(C)torquearmwithosetVRregion6,and(C)torquearmwithosetVRregion8. Figure3-46. PowerFLOWsimulationenvironmentwithindicatedboundaryconditions(notethatowisintothepage). 159

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A B Figure3-47. TimehistoryofPowerFLOW-simulatedliftanddragcoeentsexhibitedbythetorquearmmodel:(A)entiresimulationrecord,(B)therst0.1secondsofsimulationtime. A B Figure3-48. MeanowresultsforthetorquearmPowerFLOWsimulation:(A)meanZ-vorticityatseveralplanesalongupperspanwisehalfoftorquearm,(B)surfaceCpdistribution. 160

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Table3-1. Far-eldSPLreductionsoftrippedcylinderwithhelicalwirewrapping. SurfaceTreatmentSPLatf=352Hz(dB)OASPL(dB) Nowirewrap8494Wirewrap,d/D=0.0837790Wirewrap,d/D=0.1257791 Note:IndicatedSPLvaluesareinunitsofdBre.20Pa. Table3-2. Separationdistanceaspectratiosofthetorquearmhinge. ()L/DZ/D 1004.2243.7451103.8864.0081203.5274.2311303.1494.4281402.8454.5981502.5414.7171601.9324.812 161

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Table3-3. BiaserrorsoftheNetscannerpressuremodules. Scanner#PressureRange(PSID)ub(%FS) 10.3610.1521.00.0535.00.05 Table3-4. Non-dimensionalverticallocationsofcylinderspanwiseelectretsrelativetomodelcenterline(testedsensorlocationsindicatedinbold). Sensor#Z/D 10.0-0.07-0.17520.42-0.7-0.89231.0-1.07-1.17541.42-1.7-1.89252.0-2.07-2.17562.42-2.7-2.89273.0 Table3-5. Non-dimensionalverticallocations(Z=D)oftorquearmelectretsandkulitesforprimarymodelcongurations Sensor#=100=130=160SensorType T10.5080.5920.969WM-61AT21.5271.7911.956WM-61AT31.4691.8332.072WM-61AT42.4913.0423.385WM-61AT52.4913.0423.385LQ-125T63.0013.6464.042LQ-125T73.0013.6464.042LQ-125 162

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Table3-6. MicrophonebranchdimensionsforFRFcalculation(resultsshowninFigure 3-15 ). ParameterDimension(mm) L120.0D10.4L20.5D2;33.0L31.5Lout4000.0 Table3-7. FrequencybandsusedformultisineandBLwhitenoisecalibrationinputsignals. WaveformBand#Frequencyrange(Hz) Multisine 1 96 F 1,216 2 832 F 5,184 3 4,800 F 10,176 49,792F15,200 5 14,816 F 20,192 BLwhitenoise196F12,89627,200F20,000 Table3-8. Dataacquisitionparametersforrecessedelectretcharacterizations. WaveformFs[kHz]Tacq[s]NFFTWindowOverlap[%]r[Gxx][%] Multisine65.536304,096Rectangular04.56BLwhitenoise65.536304,096Hanning753.17 163

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Table3-9. ShearlayercorrectionparametersforlineararraymicrophonesatafreestreamvelocityofM=0.167. Microphonerm=Dm()h=rm()c()rc=rmP(dB) L134.93113.630.42118.65107.170.941.41L233.33106.260.44111.02100.330.961.04L333.3498.300.45102.8592.780.980.63L432.0090.000.4694.4284.791.000.20L532.3481.700.4586.0776.671.03-0.23L633.3373.740.4478.1568.771.05-0.63L734.9366.370.4270.9461.361.07-0.99L837.0559.740.4064.5654.611.09-1.29L939.6053.900.3759.0548.581.10-1.53L1042.5248.810.3454.3943.261.12-1.71 Table3-10. Thermalnoiseandfrequencyresponsemagnitudeuncertaintiesofdierentfree-eldmicrophones. MicrophoneThermalnoiseFrequencyResponseFreq.Range G.R.A.S.Type40BE36dB1dB10Hzto40kHzBruel&KjaerType495828dB2dB50Hzto10kHzBruel&KjaerType4954B40dB2dB4Hzto80kHz Note:Thermalnoisere.20Pa,frequencyresponsesre.250Hz(primarycalibrationfrequency) Table3-11. StandarddeviationsofquantitiesinputintothebeamformingMonteCarlouncertaintyanalysis Quantity Microphonelocation:x;y(mm)0.08z(mm)0.79Scanningplane:z(mm)1.59Facilitytemperature:(C)0.070Microphoneresponses:Magnitude(%ofnominal)15.0Phase(deg.)10.0 164

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Table3-12. SummaryofPIVimageacquisitionsetupincludingcameraopticsandowseederinformation OpticsCameraLaVisionProX4MResolution(pixels)20482048Focallens(mm)105Teleconverter1.4X SeedingSeederModelTSI9307-6Particlediam.(m)1Seedermatl.Oliveoil Table3-13. SPIVmeasurementandprocessingparameters. ProcessingStepMethod Imagepre-processingSlidingmin-maxlter,lterlength=3pxApplygeometricmaskingsVectorprocessing(passes1and2)SPIVcorrelationIW=6464pxWindowoverlap75%VectorvalidationAccept(u;v;w)ifstereoreconstructionerror<5pxInterpolationofmissingvectorsNoneFiltervectorelds33smoothingVectorprocessing(passes3and4)SPIVcorrelationIW=3232pxWindowoverlap50%VectorvalidationSeersttwopassesInterpolationofmissingvectorsSeersttwopassesFiltervectoreldsSeersttwopassesUniversaloutlierdetectionFilterregion=33pxVectorremovalifresidual>2.5Vectorpost-processingMVOD( Grinetal. 2010 )Algorithm:Skewness-adjustedoutlyingnessFinalinterpolationofmissingvectorsMeanvalue-padding 165

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Table3-14. NominalspanwiselocationsofmodelsensorsusedinPIV-estimationruns LabelSpanwiseLocation(Z=D) C1-0.42C2-1.175C3-2.175C4,C5-3.0E1-0.592E2-1.196E3-2.405E4-3.009K1-0.625K2-1.229K3,K4,K5-2.135K6,K7,K8-3.042 166

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Table3-15. TorquearmsurfacepressuresensorlocationsforPIV-estimationexperiments MeasurementPlane(Z=D)ElectretLocationKuliteLocations 0.0E1K1,K2,K4-0.592E1K1,K2,K4-1.175E2K2,K4,K5-2.175E3K3,K4,K5-3.0E4K6,K7,K8 Table3-16. SimulationspecicationsforthePowerFLOWCFDsimulations. Parameter[units]Value Modelcong.[;]130.SimulationMach#0.17Latticelength[mm]0.5Voxelcount[106]22.0Timestep[10)]TJ /F7 7.97 Tf 6.58 0 Td[(7sec.]8.1Sim.time[sec.]0.4 Table3-17. MetricusedtodeterminenumberofvoxelsinosetVRregions. 1LatticeLength2LatticeLengths4LatticeLengths VR788+(8*2)=248+24+(8*4)=64VR68*2=1616+(8*4)=48VR58*4=32 Table3-18. MeasurementspecicationsofthetwoprimaryPowerFLOWsimulationruns Run#MeasurementTypeMeasuredRegionsPeriod(#LatticeTimes) 1MeaneldSimulationvolume,5000modelsurfacesSurfaceloadingsModelsurfaces1SurfacepressuresModelsurfaces16SampledfacesFW-Hporousbox162Time-resolvedZ=0,1D,14eldplanes2D,3D 167

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CHAPTER4SURFACEPRESSURESANDACOUSTICS Acombinationofaerodynamicandacousticexperimentswereperformedonthetorquearmgeometriesinordertoascertainthefundamentalcausesofairframenoisegeneration.Thiswasdoneintwoexperimentaltunnelentries,oneutilizingmodelsurfacepressureandfar-eldacousticmeasurements(PhaseI),andanotherperformingoweldvelocitymeasurements(PhaseII).ThischaptercoversthePhaseIresults.Asaprecursortoexperimentsonthecompletedmodel,aseriesoftrialsurfacepressureexperimentswereperformedonthemodelcylinderitself.Thiswasdoneinordertovalidatethesteadyandunsteadypressuremeasurementtechniquesviacomparisonwithdocumentedsinglecylinderstudies.Oncethiswasdone,theentiretorquearmgeometrywasanalyzed.Far-eldacousticmeasurementswereperformedwiththeuseofalinearmicrophonearrayforspectralanddirectivityanalysis,andaphasedmicrophonearrayfornoisesourcelocalization.PowerFLOWsimulationsofthemodelbaselineconguration(=130)wereconsultedforcomparisonwiththeexperimentalmeasurementsaswellasforphysicalinsightintotheobservedphenomena. 4.1ModelSurfacePressures Therstphaseoftestingwasdedicatedtomeasurementofmodelsurfacepressuresandfar-eldacoustics.TheexperimentalmatrixoftestrunsissummarizedinTable 4-1 ,withtheprimarytestingvariablebeingthetorquearmseparationangle.Notethatthissectiondiscussesthenear-eldpressureandfar-eldacousticmeasurements,whiletheoweldmeasurementsviaSPIVarediscussedin Chapter5 4.1.1SteadySurfacePressures Steadypressureswereacquiredatstrategiclocationsonboththemodelcylinderandoneofthetorquearms.ThesearesummarizedinFigure 4-1 .Steadypressuremeasurementsweretakenforfourmodelcongurations,whicharedenedintermsof 168

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thetorquearmseparationangle,( Section3.2 ).AllsteadypressuremeasurementsweretakenforafreestreamvelocityofU1=58m/s. 4.1.1.1SingleCylinder Asaprecursortofullmodelexperiments,themodelcylinderwastestedbyitselfinbothsteadyandunsteadysurfacepressuremeasurementcongurations.Duetotheopen-jetnatureoftheUFAFF,optimalalignmentofthemodelwiththenominalowdirectionisachallengingtaskduetoalackofcoordinatesystemreferences.Therefore,thecylinderwasrsttesteduntrippedwiththegoalofattainingasymmetriccircumferentialCpdistributionasanalignmenttool.AsFigure 4-2A shows,symmetricpressuredistributionswereobtainedforthebarecylinderatall4spanwisemeasurementlocations.ThisgurealsoshowsthatnearlyidenticalCpdistributionswereobtainedforZ=0,2D,and3D,whilethatatZ=-2Ddisplaysaslightlyosetpressurerecoverytrendintheregion60330. Thenextstepwastotripthemodelcylinder.Asstatedin Section3.1.1 ,thecylinderwastrippedwithaserratedtapeatcircumferentiallocationscenteredbetween45-60and300-315.Figure 4-2B showstheresultingCpdistributionsatthe4spanwiselocationsalongthetrippedcylinder.Asthisgureshows,thedistributionsoverlapverywellwitheachother,withthelargestdiscrepanciesoccurringintheimmediatevicinityoftheserratedtriptape.Thisbehaviorwasexpectedsincethesmallradiusofcurvatureofthecylindermakesitsensitivetoanyslightinconsistenciesintheserrationpattern(i.e.tapewidth,placementonthecylinder).Thisisespeciallyunderstandablesincethetriptapewaspreparedandappliedtothecylindermanually.Todevelopaclearerunderstandingofthetriptape'seectonthecylinderpressuredistribution,andthustheresultingwakeoweld,thisCpdistributionwascomparedwithexperimentsperformedby Roshko ( 1961 ).Roshko'sexperimentsareveryimportantsincetheyencompassoneofthelargestdatasetsofcylindercircumferentialpressuredistributionssubjectedtoawiderangeofowconditions.ThiscomparisonisshowninFigure 4-2C forthepressuretapslocated 169

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atZ=0.ThiscomparisonshowsthattheCpresultsforthecurrentexperimentverycloselyresemblethoseofacylinderinpost-criticalow,andthusshouldrepresentatransitiontoturbulenceinthecylinderboundarylayers( Zdravkovich 1997 ).Furthermore,separationoftheowfromthesurfaceofthecylinderisobservedtooccurinthevicinityof=105,whichisindicatedbyarecoveryofpressuredownstreamofthesuctiontroughatapproximately75. 4.1.1.2TheTorqueArmModel SteadypressureswereacquiredatthethreeregionsofthemodelshowninFigure 4-1 forthefourprimarymodelcongurationspresentedinFigure 3-8 .Notethattheresultsfortheinvertedmodelcongurationarekeptseparatefromthepreviousonesduetothedrasticallydierentoverallmodellayoutforthisconguration.Therefore,therstthreecongurationsarereferredtoasstandardcongurations,whilethefourthoneisreferredtoastheinvertedconguration.StandardCongurations Thecylinderwasfocusedonrstinanattempttoidentifytheinuenceoftheproximityofthedownstreamtorquearmstothecylinderasafunctionofverticalspan.Theresultsforthecongurations=130;100;and160areshowninFigure 4-3 .NotethattheresultsforZ=2DarenotshownduetoitscoarserresolutionascomparedtoitssymmetriccounterpartatZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(2D.Furthermore,symmetrictrendswereveriedbetweenZ=2Dforalltestedcongurations.Astheresultsshow,thereisvirtuallynodierenceinthecylinderCpdistributionatZ=0betweenthedierentcongurations.Thistrendagreeswellwiththetandemcylinderstudiesperformedby Jenkinsetal. ( 2005 ); Neuhartetal. ( 2009a ),whofocusedonacylinderseparationdistanceaspectratiointherangeof1:435L=D3:7.Theseseparationdistancescomparewellwiththoseofthecongurationstestedhere,namelyL=D=1.932,3.149,and4.224for=100;130;and160,respectively.NotethattheseparationdistanceLispictoriallydenedinFigure 4-1A .AsforaspanwiselocationofZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(2D,whiletheoveralltrendsremainthesame 170

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forthedierenttorquearmangles,aslightasymmetryisobservedinthepressurerecoveryregion105255foratorquearmseparationangleof=160.ThistrendisfurtherrepeatedforthesametorquearmangleatZ=3D,whichisobservableinFigure 4-3C .Itwasinitiallybelievedthattheseasymmetrieswereduetoslightmisalignmentofthetorquearmsrelativetothefreestream,howevercarefulne-tuningofthetorquearmorientationdidnotremedythisbehaviorfor=160.Furtherinvestigationintothecausesoftheseasymmetriesisdiscussedinthenextsection.AnotherobservationforZ=3Dishowthesuctionlevelthedownstreamsurfaceofthecylinderappearstodecreaseastheproximitybetweenthecylinderandtorquearmdecreases. Pressuresonthetorquearmitselfweremonitoredonboththeinnergapowandrear(wake)surfacesbymeansofthetap-instrumentedcoverplate,whichwasswitchedbetweenthetwosurfacesforeachconguration.TheresultsforthegapowsurfacearepresentedinFigure 4-4 asafunctionofsensornumber.Notethatincreasingsensornumberrepresentsincreasingheight,wheresensor#1isclosesttothecylindercenterlineand#11isclosesttothetorquearmjunction.IfattentionisdirectedtoFigure 4-4B ,itcanbeseenthatthecenterlinepressuresfor=130and=100aresimilarinshape,withthecaseof=160beinginsharpcontrast.Itisalsointerestingtoobservehowthelocationofpeakpressuremovesfromsensor#8to9betweenthesetwocongurations.Duetothedierenttorquearmangles,thesesensorsarelocatedatbothadierentspanwiseheightanddownstreamlocationrelativetothecylinder.Observationofthecenterlinepressuresforthecaseof=160revealsasteadyincreaseinpressureupthroughsensor#6,withasharpdropafterthissensor.Itispossiblethatthistransitionrepresentspassingthethresholdatwhichtheshearlayerinteractswiththetorquearmgapowface.Unfortunately,itisunclearfromthisinformationastowhetherthisbehaviorisdominatedbycylinder-torquearmproximity,torquearmwidth,oracombinationofboth. 171

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Figures 4-4C and 4-4D showtheCpprolesoftherightandleftsidesofthetorquearmgapowface,respectively.Theseshowthatreasonableside-to-sidesymmetryisobtainedforthecasesof=130and=100,withtheexceptionofsensors10and11forthelatterofthesetwocases.Whilethemodelunderwentcarefulalignment,itisbelievedthatthisbehavioristheresultoftherotationofthetorquearmsforthe=100casesuchthattheyareorientedmorecloselywiththestreamwisedirectionoftheow.Thisinturncouldincreasethechanceofslightdeviationsfromsymmetryinsurfacepressuresonthegeometry.Anotherinterestingobservationisforthe=160case,whichshowsheighteneduncertaintylevelsinsensors6-11ascomparedtotheformercases.Thisbehaviorwasanalyzedinmoredetailbysamplingthepressuredataatahigherrateandforalongertimedurationtoobtainmoreofatime-resolveddepictionofthebehavior. Pressureswererecordedonthegapowtorquearmsurfaceforthe=160caseagainat50Hzforadurationof20seconds,yieldingatotalof1,000samplesperpressuretaplocation.Thissamplingratewaschosensinceitwasthemaximumallowablewithoutexceedingthebandwidthoftheacquisitioncomputer,thusensuringthatconsecutivesampleswerenotrepeated.Thissamplingratewasalsofoundtobeslowenoughsuchthatcouplingofthelengthofpressuretubingwiththetransducerscouldrespondtothepressureuctuations.ThemeanCpprolesofthetorquearmforthistestrunareshowninFigure 4-5A .Fromtheresults,itcanbeseenthattheleftandrightsideproleslineupmuchbetterwithoneanotherascomparedwiththeresultspresentedinFigure 4-4 ,withthereduceduncertaintiesbeingadirectresultoftheincreasednumberofsamples.Furthermore,Figures 4-5B and 4-5C showtheinstantaneoustorquearmCpprolesattwosamplesspaced100samples-or2seconds-apartfromoneanother.Thisimpliesthattheremayexistanoscillatoryowstructurewithinthegapowregioninducedbythecloseproximityofthecylinderandtorquearm.ThisoscillatorybehaviorwasalsoobservedinthecylindercircumferentialCpdistributionsatheightsofZ=2Dand3D.Inaddition,repeatedsurfacepressureacquisitionrunsfortheothertwotorquearm 172

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congurationsdidnotrevealanysuchoscillatorytrends,thusmakingthisbehavioruniquetothe=160case. Itisworthnotingthatthelocationsofthepressuresensorsonthetorquearmgapowfaceforthiscongurationspanacylinder-to-torquearmseparationaspectratioof1:790L=D1:215.TheseseparationdistancesareeithercomparabletoorlessthanthesmallesttestedtandemcylinderspacingofL=D=1:435by Jenkinsetal. ( 2005 2006 ); Neuhartetal. ( 2009a ),inwhichanasymmetricmeanrecirculationpatternwasobservedinthegapowregionbetweentheupstreamanddownstreamcylinders.Thisrecirculationpatterntooktheformofasinglerecirculationvortexthatfavoredonesideofthegapowregion,asopposedtothetraditionaldouble-vortexrecirculationpatternpresentinthecaseofasinglecylinder( Zdravkovich 1997 ).Itisalsoimportanttonotethatthelocationofthissinglevortexmanifestedondierentsidesofthegapowregionbetweenthetwowindtunnelentriesperformedby Jenkinsetal. ( 2006 )and Neuhartetal. ( 2009a ).Thisimpliesthatthepresenceandlocationofthisrecirculationpatternwasverysensitivetothealignmentofthetandemgeometrywiththeow.Theimplicationsofthisbehavioronthecurrentexperimentareunknown,however,duetothecontrastindownstreamgeometriesfromacircularcylindertothesharp-edgedrectangularshapeofthetorquearm. Asanalnoteonthistopic,thesampledistributionsofthepressuredatarecordedatthesensorlocationsindicatedinFigure 4-5A werecomputedandarepresentedinFigure 4-6 .ThedatainthisgurerepresentatunnelrunwherethepressuredatawereacquiredataslowerrateofFs=5Hzforadurationof300seconds,yieldingatotalof1,500samplesperpoint.Asthedatashows,anearlyequalandoppositetrendisobservedbetweenthetwochannels.Thisshowsthatthehypotheticalowstructurefavorsonesideofthetorquearmovertheother,howeverexhibitsaquasi-periodictendencytoswitchsides.Moresimply,thesedistributionsfurtheremphasizethepresenceofabi-modalbehaviorindicativeoftwodierentowstates. 173

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InvertedConguration Theinvertedbaselinecongurationrepresentsadrasticchangefromthestandardcongurations,wherethetorquearmisessentiallyippedaroundtobecometheupstreamcomponentofthetandemgeometry.Thiswastestedbasedonindicationsthatsuchacongurationwillyieldoveralllowerfar-eldacousticlevels( Anglandetal. 2010 ; Dobrzynskietal. 2005 ),supportingthehypothesisthatplacementoftheblueroftwobodiesupstreamoftheothercouldpotentiallyreducethenoiseassociatedwiththeowinteractionsinthegapowregionbetweenthem. ThesteadyCpresultsfortheinvertedbaselinecongurationareshowninFigure 4-7 .IfattentionisdirectedtoFigure 4-7C ,itcanbeseenthatexcellentside-to-sidesymmetryisobtained,withallpressureprolesexhibitinglargeamplitudepositivepressures.Thegeneralobservabletrendisthatpressuregraduallydecreasesasonetravelsupwardalongthetorquearmface.Thehighpressuresatsensor#1areunderstandablesincethesepressuretapsareclosesttothehingebetweenthetwotorquearms,whichessentiallyservesasastagnationpointinthisconguration.Thetorquearmgapowsurfacepressures,showninFigure 4-7D ,showagradualdecreaseinsuctionasonemovesupwardalongthetorquearmface,untilaplateauisreachedaftersensor#8.TheCpdistributionsforthefourcylindricalringsofthedownstreamcylinderareshowninFigure 4-7B .TheresultsforZ=0closelyresemblethoseofthereartandemcylinderstudiesconductedby Jenkinsetal. ( 2005 )foraseparationaspectratioofL=D=3:7,withsomeslightexceptions.Theseincludepeakpressureoccurringinthevicinityof=15,ratherthanatthestagnationlocation(=0),aswellasaconsiderablyhigheramplitudesuctiontrough(Cp=)]TJ /F1 11.955 Tf 9.3 0 Td[(2:3ascomparedtoCp)]TJ /F1 11.955 Tf 22.97 0 Td[(1:5).ItisalsoimportanttonotehowtheCpprolesforheightsofZ=2D;3Dshowalmostnovariationinsuctionalongtheentirecylindercircumference.Thisimpliesthatthelargewakeimposedbytheincreasedwidthoftheupstreamtorquearmattheseheightspreventsanyowfromre-attachingtothecylindersurface. 174

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SimulationResults:MeanFlowField TogainphysicalinsightintotheobservedmodelCpbehavior,thePowerFLOWsimulationsofthebaselinecasewereconsulted.First,theCpdistributionswerecomparedbetweentheexperimentalmeasurementandsimulation,whicharepresentedinFigure 4-8 .Forthecylindercomparisons-showninFigures 4-8A 4-8C -reasonableagreementisobserved,withtheonlyappreciablediscrepanciesoccurringinthevicinityofthesuctiontroughsintherangesof6090and270300.Thisisexpectedduetothedierenceintrippingtechniquesimplementedbetweenthesimulationandexperimentalcases,namelytheserratedtapefortheexperimentsandauniformsurfaceroughnessof0.05mmforthesimulation.Thelargestdierenceinbehaviorasafunctionofspanalongthemodelisthebehaviorofthepressurerecoveryregion.AtZ=0,itcanbeseenthattherearsideofthecylinderattainsaconstantCpvalueofapproximately-0.3,whereasthoseatZ=)]TJ /F1 11.955 Tf 9.29 0 Td[(2DandZ=3Ddisplayaslight\dip"inpressure. Asforthetorquearmgapowpressures,theexperimentalandsimulationcomparisonsareshowninFigures 4-8D 4-8F .Theseresultsshowagreementinthegeneralpressuretrends,howeverwithanearlyconsistentosetinpressurelevelsbetweenthetwodatasets.Whiletheexactcauseofthisosetisnotknown,itispossiblytheresultofthefreestreamvelocityboundaryconditiondenedinthePowerFLOWsimulations.Asstatedin Section3.7.1 ,thecomputationaloweldwasdenedforalateral(y)lengthof140cylinderdiameters,whichisinstarkcontrasttotheinletoftheopenjettestsectionwidthof29cylinderdiameters.Thesimulation,thereforedoesnotaccountforthepresenceoftheshearlayersthatresultfromtheopenjetofthetestsection.Despitethesesubtledierences,however,itwasbelievedthatconsultingthePowerFLOWsimulationmeanoweldresultscouldbemoreinformativeastothereasonbehindtheobservedmodelsurfacepressurebehaviors. Althoughthesimulationswereonlyperformedforthebaselinecaseof=130,themeanoweldresultscanstillprovidephysicalinsightintothemodelsurfacepressures. 175

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Figure 4-9 showscontourplotsandxystreamlinesofthemagnitudeofvelocityatverticallocationsofZ=0,2D,and3D.NotethatthevelocitydataarenormalizedbythefreestreamvelocityandaremathematicallydenedinEquation 4{1 jVj U1=p U2+V2+W2 U1:(4{1) AtaheightofZ=0,itcanbeseeninFigure 4-9B thatanearlyuniformvelocitydecitispresentintheimmediatewakeofthecylinder.ThisiscomplementedbytheuniformpressurerecoveryregionobservableinFigure 4-8A .Conversely,Figure 4-9C showsaregionofincreasedvelocityalongtherearcylindersurface,whichexplainsthedipinthepressurerecoveryregiondisplayedinFigure 4-8B .Furthermore,thestreamlinesofFigure 4-9C showthepresenceofaslightlyasymmetricmeanrecirculationpatterninthegapowregionofthemodel.Furthermore,themeanrecirculationpatternataheightofZ=3DdisplaysstationaryvorticesofsmallerscalethanthoseatZ=2D,duetothesmallerspacingbetweenthecylinderandtorquearm.CarefulexaminationofthevelocitycontoursinFigure 4-9D showsavariationinthevelocitydecitimmediatelybehindthecylinder,whichiscomplementedbythevariationinthepressurerecoveryCpdistributionshowninFigure 4-8C 4.1.2UnsteadySurfacePressures UnsteadysurfacepressuremeasurementswereacquiredonthemodelatthelocationsindicatedinFigure 3-12 andTable 3-4 .Therewereatotalof14sensorlocations:7alongthecylinderspanatacircumferentiallocationof=135relativetotheoncomingowdirection,and7atvariouslocationsonthetorquearm.Notethattheselocationswerestrategicallychoseninanattempttoidentifythepresence(orlackthere-of)ofcoherentowstructureinteractionsbetweenthecylinderandtorquearm.Thedatapresentedinthissectionbeginwithvalidationoftheperformanceoftherecessedelectretsensorsbytestmeasurementsonthemodelcylinder.ThisisfollowedbyasurveyofPSDsandintegratedpressurelevelsfromthemodelsensorsasafunctionoftorquearmseparation 176

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angle.Followingthis,thedeterminationofanycoherenteventsbetweencylinderandtorquearmsensorsisinvestigated,followedbyacomparisonofthemodelbaselineresultstothosecomputedfromthePowerFLOWsimulations.Allpressuresensordatashowninthischapterwerefoundtodisplaystationarityaccordingtotheapplicationofareversearrangementtest( Bendat&Piersol 2000 ). 4.1.2.1SingleCylinderMeasurements Similarlyasforthesteadypressureexperiments,theunsteadyoneswereperformedaftervericationofthefunctionalperformanceoftherecessedelectrettransducersviasinglecylindertests.ThemodelcylinderwasinstalledintheUFAFFtestsectionwithrecessedsensorsatthe7locationsdenedinTable 3-4 atacircumferentiallocationof=135relativetothefreestreamdirection.Itwasrstdecidedtotesttheeectoftrippingthecylinderonthesurfacepressurespectra.Notethatthedataarepresentedhereintermsofpressurepowerspectraldensity(PSD)andnon-dimensionalfrequency(StD).NotethatStDwaspreviouslydenedinEquation 2{5 .AcomparisonofPSDsforthebareandtrippedmodelcylinderasafunctionofStDisshowninFigure 4-10 forafreestreamvelocityofU1=58m/s,oraReynoldsnumberbasedoncylinderdiameterofReD=1:5105.Themostnotablecontrastbetweentheseresultsistheoccurrenceofthetonalpeakindicativeofthevortexsheddingfrequencyofthecylinder.Forthebarecylindercase,thissheddingpeakoccursintherangeof0:19StD0:20,whichagreeswithdocumentedresultsforacylinderinthepre-criticalowregime( Zdravkovich 1997 ).Forthisowregime,thecylinderisundergoingtransitiontoturbulenceintheshearlayers.Forthetrippedcaseontheotherhand,thesheddingfrequencyisobservedtooccurinthevicinityofStD0:28,whichagreesverywellwiththeStD=0:285forthesingletrippedcylinderdocumentedin Jenkinsetal. ( 2006 )forReD=1:66105.Inadditiontothedierentsheddingfrequencies,itisalsoworthnotingthedierentspectraltrendsbetweenthetwocongurations.Thebarecylindercaseappearstoexhibitanearlyconstantroll-otrend,whilethetrippedcasedisplaysaatbandofenergyinthe 177

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rangeof0:4StD2untilitbeginstoroll-oatafasterrateofdecaythanthebarecase.Thefrequencyatwhichthespectrumtransitionsfromtheatbandtotheroll-odecayisbelievedtocorrespondtotheformationofshearlayer,orKelvin-Helmholtz(KH)instabilities( Brunetal. 2008 ),whichisindicativeoftheearlieronsetoftransitiontoturbulenceinthecylinderboundarylayers.NotethatthisdoesnotimplythatKHinstabilitiesarenotpresentforthebarecylinder,butratheroccurfurtherawayfromthecylindersurfaceduetothefurtherupstreamlocationofowseparation. Theothermeasurementusedtovalidatetherecessedsensorperformancewasspanwisecoherencebetweenthecylindersensors.Spanwisecoherenceofanominally2-dimensionalowscenarioisusefulinidentifyingthepresenceofcoherentowevents,suchasvortexshedding.Thepurposeofthisanalysisistohavearelativebasisforwhichtocomparewiththeresultsforthetorquearmmodel.Morespecically,itisdesiredtoidentifytheeectthedownstream(orupstream)torquearmshaveontheformationofcoherentspanwisevorticesfromthecylinder.TheresultsofthespanwisecoherenceforthetrippedcylinderatU1=58m/sareshowninFigure 4-11 .Notethattheordinarycoherencefunctionisutilized: 2xy(f)=^Gxy(f)2 ^Gxx(f)^Gyy(f);(4{2) wherexandydenotethereferenceandtestsensor,respectively.ForthedatashowninFigure 4-11 ,thesensorlocatedatZ=0issetasthereferencemeasurementwhileeachoftheotherspanwisesensorsaretreatedasthetestmeasurements.Fromtheresults,aspikeincoherenceispresentforallsensorsrelativetothecenterlineoneataStrouhalnumberofStD0:28,whichlinesupwiththetonalpeakobservableinFigure 4-10 .Thisisfurtherconrmationthatthistonalpeakisindicativeofthevortexsheddingfrequencyofthecylinder.Itcanalsobeseenthatthepeakcoherencevaluedegradesasdistancefromthereferencesensorincreases.Thisisbelievedtobeduetothepresenceofsmall-scale3-dimensionalshearlayerinstabilities( Williamson 1996 ). 178

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4.1.2.2ModelSurfacePressureSpectra Spectralsurveyswereperformedonthemodelcylinderfortorquearmseparationsintherangeof=100-160in10increments,aswellasfortheinvertedconguration.ThesewereperformedfortheprimarytestingspeedofU1=58m/s.Asforthetorquearm,spectralsurveyswerelimitedtotheprimarycongurationsasdescribedin Section3.2 ,duetothenitenumberoflocationsatwhichthetorquearminstrumentationlinescouldberoutedthroughthemodelcylinder. TheprimarymodelcongurationsweretestedforfreestreamvelocitiesofU1=35,45,52,58,and65m/stoidentifywhatspeeds,ifany,deviatedfromdynamicpressurescalingbehavior.Thespectraldatawerealsofrequency-shiftedaccordingtoStD.AnexamplesetofresultsforthisscalingprocessareshowninFigure 4-12 forthecylindersensoratZ=3DandtorquearmsensorT4.NotethatnormalizedpowerspectraldensityisplottedasPSDf=q21,wherefissetasthebasisforStrouhalscaling,orf=U1=D.Fromtheseresults,itcanbeclearlyseenthatthespectraldataforthethreeupperspeedscollapseverywellinabothamplitudeandfrequencymanner,whilethedataforthetwolowerspeedsdonot.Thesetrendswereveriedforalloftheothermodelsensors.ThisimpliesthataowregimethresholdiscrossedbetweenthespeedsofU1=52and45m/s.Therefore,allunsteadydata-includingthoseoffar-eldmicrophones-areconsideredforthethreeuppertestedspeeds.Ofthesespeeds,U1=58m/sistheoneprimarilyconsultedsinceitrepresentsamiddlerangeofthethreeaswellasbeingthespeedatwhichthePowerFLOWsimulationswereperformed. Aspectralsurveywasinitiallyperformedforthebaselinecongurationof=130,theresultsofwhichareshowninFigure 4-13 .Notethatthecylinderandtorquearmdataaredisplayedonseparategraphsforimageclarity.InitialobservationofFigure 4-13A revealsageneraltrendinincreasingbroadbandlevelsasonetravelsupwardalongthecylinder,withnoobservabletonalpeaksindicativeofvortexshedding.Itisimportanttonotethatincreasingverticaldistancefromthemodelcenterlinealsoindicatesdecreasing 179

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proximitybetweenthecylinderandtorquearm.Itisalsointerestingtoseehowthespectralshapechangesasonemovesupwardsalongthecylinder.ThePSDsatheightsofZ=0;0:42DdisplaybroadbandbehaviorverysimilartothatofthesingletrippedcylindershowninFigure 4-10 ,withtheobviousexceptionofthelackoftonalpeaks.Thisimpliesthatwhilethedevelopmentoforganizedvorticalstructuresisinhibited,shearlayerinstabilitiessimilartothatofasinglecylinderarestillpresentattheselocations.Thisbehaviorrapidlydecays,however,markedbythedevelopmentoftwobroadspectralhumpsatlowfrequenciesfollowedbyasteadycascadeofspectralenergywithincreasingfrequency.Thisimpliesthattheeverdecreasingproximitybetweenthetwocomponentsdisruptsthedevelopmentofthecylindershearlayer. IfattentionisdirectedtoFigure 4-13B ,thePSDsoftorquearmsensorsT1-T4canbeseen.Asdiscussedin Section3.4.2 ,thersttwoofthesesensors(T1andT2)arelocatedalongtheedgesofthetorquearm,whiletheothertwo(T3andT4)arelocatedonthegapowcoverplate.ThespectraofsensorsT1andT2displayasinglespectralhumpinthevicinityof220Hz,withaslightincreaseinspectralenergyinsensorT2around128Hz.SensorT3alsodisplaysthisincreaseinspectralenergyaround128Hzwhilealsolackingtheonearound220Hz.Finally,sensorT4exhibitsbothofthesespectralhumpspriortoagradualdecayinspectralenergy.ItisinterestingtonotehowthepressurePSDoftorquearmsensorT4displayslow-frequencyspectraltrendsthatcloselyresemblethoseofthecylindersensorlocatedatZ=3D.Thisisnotsurprisingsincethetorquearmgapowsurfaceandcylinderareinsuchcloseproximitytooneanotheratthisheight.Thedoublespectralhumpwasbelievedtobeanindicatorofabi-modaltypebehavior.Itwasbelievedthatobservationofthesensor'ssampledistributionfunctionwouldprovideadditionalinsightintothisbehavior.Asasidenote,itisworthmentioningthatthespectraofthetorquearmsensorsexhibita\rippling"behaviorforfrequenciesabove5kHz.Itwasconcludedthatthisbehaviorwasnotduetotheowmechanics,butrathertoslightcompressionoftheTygonexittubingasitwasroutedbetweenthetorquearm 180

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andcylinder,priortoexitingthemodel.Forthisreason,aswellastheearlieronsetofresonanceofthesedevicescomparedwiththeonesinthecylinder,alltorquearmspectraareconsidereduptoafrequencyof5kHz. ThesampledistributionfunctionsforthefourtorquearmsensorsareshowninFigure 4-14 .TheskewnessandkurtosisforeachsampledistributionarealsopresentedanddenotedasthequantitiesSandK,respectively.Whiletheyarenotdisplayedhere,thesampledistributionfunctionsofthecylinderelectretswerecomputedandfoundtoexhibitapproximatelyGaussiandistributions.ThesampledistributionsforsensorsT1andT2areseentoexhibitGaussianbehavior,evidencedalsobytheskewnessandkurtosisquantities,whilethoseofT3andT4deviatefromthisbehaviorgreatly.MostnoteworthyissensorT4,whichdisplaysalargepeakinnumberofsamplesforpositivepressuresaswellasaplateauinthesampledistributionfornegativepressures.Thisisfurtherevidenceofthepresenceofabi-modalbehaviorbetweenthetwocomponentsatthisheight.Similarsampledistributionshavebeenfoundforunsteadypressuresensorslocatedonthegapowsurfaceofareartandemcylinder( Neuhartetal. 2009a ). Ofthesevencylindersensors,theoneslocatedatintegerheightmultiplesofthecylinderdiameterwereselectedtodisplaythesurfacepressuresasafunctionofthetorquearmconguration.ThisisduetotheirrelativelysimilarverticallocationstothetorquearmsensorsT1-T4.ThePSDsfortheseeightsensorsareshowninFigure 4-15 forU1=58m/s.ThePSDdatawerethenintegratedandnormalizedbythedynamicpressuretoyieldanrmspressureuctuationcoecientC0p;rmsaccordingtoEquation 4{3 .Theintegrationboundsforthiscalculationweresettof0=96Hzandf1=4:992kHz.TheC0p;rmsresultsforthecylinderandtorquearmsensorsforalltestedcongurationsarepresentedinTables 4-2 and 4-3 ,respectively.Likethepressureautospectrathemselves,theseintegratedvalueshavearandomuncertaintyofr3:35%.ThisuncertaintyisapproximatedfromtheincorporationoftheuncertaintiesoftheelectretFRFs. 181

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C0p;rms=Prms q1=q Rf1f0Gyy(f)df q1(4{3) StartingwithFigure 4-15A ,itcanbeseenthatthepressurespectraforZ=0areverysimilarforthestandardcongurations.Thisisingoodagreementwiththecircumferentialsteadypressuresmeasuredatthislocationforthesecongurations,whichwereshowntobenearlyidentical.ItisnotedthatnotonalpeaksnormallyindicativeofvortexsheddingarepresentinthesePSDplots.Instead,thereisabroadincreaseinspectralenergydistributedintherangeof100F400Hz,withhigherbroadbandfrequencycontentcloselyresemblingthatofthesingletrippedcylinder(Figure 4-10 ). AsforthecylindersensorlocatedatZ=1D,itcanbeseenthatthePSDs,showninFigure 4-15B ,exhibitslightbroadbandvariationswithchangingtorquearmseparationangle.Oneofthemorenoticeabledierencesisthepresenceofaspectralplateauinthevicinityof2kHzfor=130,againrepresentativeofthesingletrippedcylinderbehavior.Thisbehaviordisappearsfortheothertwostandardcongurations,conceivablyforsimilarreasons.Theabsenceofthisspectraltrendforthe=160casemakesphysicalsense,sincethecloserproximityofthetorquearmtothecylinder'srearsurfaceimpedesthedevelopmentofthecylindershearlayer.Animportantfeaturetonoteaboutthe=100case,generallyspeaking,isthatwhilethetorquearmsthemselvesareslightlyfurtherdownstreamofthecylinder,thejunctions(thecomponentsthatconnectthetorquearmstothecylinder)areclosertogether.Thiscouldeectivelyincreasethepresenceofspanwiseinconsistencies,suchastheshearlayerdevelopmentatsensorslocatednearthecylindercenterline.Thiscouldhelpexplainthelackofthespectralplateauforthiscase.AsfocusisshiftedupwardstoZ=2D;3Dalongthecylinderspan,thespectraltrendsfor=100and130areseentobeverysimilarwithaslightincreaseinlevelsforthelattercase.For=160,however,thereisaconsiderableincreaseinbroadbandlevelsforthetwosensors,aswellasaspectralhumpnear370HzforthesensorlocatedatZ=3D. 182

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ThetorquearmsensorsT1andT2wereexpectedtodisplaysimilarspectralbehaviorsincetheywerebothlocatedontheframesofthetorquearm,despitethefactthattheywereonoppositesidesofthemodel.AsFigures 4-15E and 4-15F show,bothsensorsdisplaysimilarspectralhumpsnear250and200Hzfortherespectivecasesof=100and130.Wherethesetwosensorsdierconsiderablyisfor=160,wheresensorT1showsanearlyatspectrumuptoapproximately1kHzuntilitrollsowithatrendsimilartotheothertwocongurations.Thisisattributedtothetorquearmbeingconsiderablyclosertothecylinderandthusallowingthecylindershearlayertodeveloparoundandmissthetorquearmatthisheight.SensorT3,meanwhileshowslittlevariationwithtorquearmangle,withtheexceptionofslightlyhigherlevelsforthe=100and160cases.Finally,sensorT4showsconsiderablevariationbetweenthecongurations.Asdiscussedpreviously,thecaseof=130showsthedoublespectralhumpindicativeofabi-modalbehavior.Thisdisappearsfor=100,wherethespectrumdisplaysasinglespectralhumpnear220Hz,withslightlylowerlevelsthanthepreviouscase.Thegreatestdierencebetweenthesestandardcongurationsisforthe=160case,whichexhibitsrelativelylowspectrallevelsuntilalargespectralhumpisencounteredatapproximately380Hz.SimilarspectralhumpsatornearthisfrequencyarealsovisibleintorquearmsensorT3aswellasthecylindersensoratZ=3Dforthisconguration. Themodelsensorswereexpectedtoexhibitconsiderablydierentspectralbehaviorfortheinvertedbaseline(=130)conguration.Inthisconguration,thetorquearmsareupstreamofthecylinder,thusresultinginanupstreamcomponentofvariablecross-sectionimpartingawakeofvariablewidthalongthespanofthemodel.The180rotationofthemodelalsoresultedinthecylindersensorsbeingpositionedatacircumferentialangleof)]TJ /F1 11.955 Tf 9.3 0 Td[(45ratherthan+135.Notethatforthistorquearmseparation,thecross-sectionsofthetorquearmandcylinderareofcomparablesizeforZ1:23D.Thisimpliesthattheresultingshearlayersofthetorquearmattheseheightshavea 183

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greaterchanceofimpingingonthesurfaceofthecylinder,andthusthecylindersensorsinthisregionwereexpectedtodisplayconsiderablyhigherpressureuctuationsthanforthepreviouslydiscussedstandardcongurations.ObservationofFigures 4-15A and 4-15B conrmthisassumption.Comparisonbetweenthe=130andtheinvertedcasesshowsthatthesetwosensorsexhibitbroadbandlevelsapproximatelytwoordersofmagnitudehigherfortheinvertedcaseforfrequenciesabove400Hz.Thistrendowesitselftothesmallscalesofturbulencecontainedwithintheshearlayerfromthesharpedgesofthetorquearm.Furthermore,thelattertwocylindersensorsinFigures 4-15C and 4-15D displaypressureuctuationlevelsfortheinvertedcongurationthatarecomparabletoandlessthanthoseforthestandardbaselineconguration,respectively.Thisfurtherre-enforcestheassumptionthatthewidercross-sectionofthetorquearmattheseheightsresultinalargerwakewhoseshearlayersdonotcomeintofullcontactwiththedownstreamcylinder. Finally,torquearmsensorsT1,T2,andT4allshowreducedbroadbandPSDlevelsfortheinvertedconguration.ThisisinterestingtonotesinceT1andT2,beinglocatedalongtheframeedgesofthetorquearm,showlowerlevelswhenthetorquearmislocatedupstreamofthecylinder.Thisimpliesthatthepressureuctuationsalongthetorquearmframeduetoowseparationarounditareconsiderablylowerinamplitudethanduetotheimpactingofthecylindershearlayerfromthestandardbaselineconguration.NotethatthereisnoPSDdataforsensorT3intheinvertedcongurationsinceitwasnotfunctioningforthesetunnelruns. 4.1.2.3SimulatedModelPressureFluctuations AnexcellentbenetofthePowerFLOWsoftwareistheabilitytovisualizesurfacepressureuctuationsontheentiremodelsurface.AnillustrationofthiscapabilityisprovidedinFigure 4-16 .Theseplotsrepresentthepressureuctuationsexperiencedbythemodelin1/3rdoctavefrequencybands.Notethattheselevelsdonotrepresentactual\sound",butratheraconvenientwaytoviewthepressureuctuationsonalogscale.As 184

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theresultsshow,thehighestspectralpowerlieswithinthelowerfrequencybandsandisconcentratedneartheverticalextremaoftheinsidefaceandalongtheedgesofthetorquearms.Asthefrequencyincreases,inadditiontothedecreaseinuctuationpowerlevelsonthemodel,itcanbeseenthattheregionsofhighestpressuredeviateawayfromtheinsidetorquearmsurfaceandbecomemorecentralizedalongthetorquearmedges.Thisimpliesthatthehigherfrequencyacousticsofthemodelcouldbeprimarilyduetotheowaroundthesharpedges. 4.1.2.4Near-FieldCoherence UponobservationofthemodelsurfacepressurePSDs,theidenticationofcommonspectralfeaturesbetweencertainprobeswarrantedtheneedtoanalyzewhichofthesefeaturesrepresentedcoherentevents.Initially,thecoherenceanalysiswaslimitedtothecylindersensorsreferencedtothecentersensoratZ=0.Thiswasdonetoserveasaquanticationofthespanwisecoherencealongthecylindersurface.Duetothepresenceofthetorquearmsdownstreamofthecylinder,thespanwisecoherencewasexpectedtodeteriorateataconsiderablyshorterspan(atalowerverticallocation)thanforthecaseofthesingletrippedcylinder,theresultsofwhichareshowninFigure 4-11 .Asalltestedcongurationsshow,thereisadrasticdropinthebroadbandcylinderspanwisecoherenceforsensorsabovetheonelocatedatZ=0:42D.Furthermore,Figures 4-17A 4-17C showthatthestandardcongurationsof=100and130displayapeakinthecoherencebetweenZ=0and0:42Dintherangeof200-220Hz.Ontheotherhand,the=160congurationdisplaysadualcoherencehumpat150and220Hzofloweramplitudesthanthepreviouscongurations.Theseareincontrasttotheinvertedconguration,whichexhibitsconsiderablylowercoherencebetweenthesetwosensorsforessentiallyallfrequencies.Fromtheseresults,itcanbeimpliedthattheupstreampresenceofthesharp-edgedtorquearmsfortheinvertedcongurationdeterioratetheformationofanylarge-scalevorticalstructures. 185

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Fromthecylinderspanwisecoherenceresults,itwasbelievedtobeareasonableassumptionthattherewouldbehigherlevelsofcoherencebetweentorquearmandcylindersensorswithinrelativelyclosespanwiseproximitiesofoneanother.Toquantifythespatialrangesoverwhichcoherentowstructuresarepresent,coherencecalculationswereperformedfortorquearm-cylindersensorpairings,whicharepresentedinFigure 4-18 4-21 .Itwasbelievedthatidenticationofcoherenteventsbetweenthecylinderandtorquearmcouldassistinidentifyingnoisegenerationmechanisms.ThetorquearmsensorsT1-T4wereselectedasthereferencetransducers,andtheordinarycoherencefunctionwasestimatedbetweenthesesensorsandtheonesinthecylinder.Forreference,thetorquearmsensornon-dimensionalverticallocationsrelativetothemodelcenterplaneareprovidedinTable 3-5 AsFigure 4-18 shows,certaincylindersensorsshowlargerlevelsofcoherencecomparedtoothersforthedierenttorquearmreferencesensors.ForT1,cylinderelectretsatZ=0.42,1.00,and1.42Dexhibitmaximumcoherencevaluesofabout0.33inthevicinityof256-272Hz.Thelevelsofmaximumcoherencebetweensensorsareseentoincreaseasthetorquearmsensornumbersincrease,whichalsohappenstocoincidewithregionswherethetorquearmcomesintocloserproximitywiththecylinder.ThecylindersensorsthatdisplaythehighestlevelsofcoherencealsohappentoresidewithinaspanwiselocationrelativetothereferencetorquearmsensorofZ=D<1.Itisalsoworthnotingthepresenceoftwopeaksinthecoherenceat96and240HzinFigures 4-18B and 4-18D forthecylindersensorsatZ=2.00and2.42D.Thisfurtherenforcesthenotionthatabi-modalowbehaviorexistsintheinnergapowregion. IfattentionisshiftedtoFigure 4-19 ,itcanbeseenthatsimilartrendsareobservedbetweenthe=100and130cases.Theprimarydierencesareaslightshiftincylindersensornumbersthatdisplaymaximumcoherencewiththetorquearmsensors.Forexample,Figure 4-19C showsmaximumcoherencebetweensensorT3andthecylindersensoratZ=2:00D,whereasfor=100,thiswassoforthecylindersensorat 186

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Z=1:42D.ThischangeinsensornumberisduetothetorquearmsensorshiftinginverticallocationclosertoaheightofZ=2:00DfromZ=1:42Dbetweenthetwocongurations.Furthermore,theonlysensorpairingsdisplayingprominentbi-modalcoherencebehaviorareT4andthecylindersensoratZ=3:00D,whichareatnearlyidenticalverticallocations(Table 3-5 ). Thecoherenceresultsfor=160congurationshowsomeslightdierencesfromtheotherstandardcongurations.Firstly,thehighestlevelsofcoherencewithsensorT2occurwiththecylindersensoratZ=1:00D,whichisnearlyafulldiameterverticallyawayfromsensorT2.Finally,thecoherenceresultsfortheinvertedcongurationpresentedinFigure 4-21 showdrasticallyreducedlevelswhencomparedtothestandardcongurations.Thisisbelievedtobeduetotheincreasedblunessoftheinvertedgeometry.Theeectofthisincludesanincreasedwakewidth,earlyowseparationduetotheupstreamsharpedgesofthetorquearm,andpossiblyareductionincoherentowinteractionswithinthegapowregionofthetorquearmgeometry.Analysisoftheimpactofthisobservednear-eldbehavioronthefar-eldacousticsisdiscussedin Section4.2 4.1.2.5ComparisonwithSimulations Theunsteadypressurespectrawerecomparedforthebaselinemodelcongurationbetweentheexperimentalandsimulationresults.Thiswasbelievedtobeimportantsinceithelpstodeterminethereliabilityofthesimulationsforobservationofunsteady,inadditiontosteadyquantities.Therefore,asetofvirtualsurfacepressureprobesweredenedinthePowerFLOWsimulationcasetocorrespondwithselectsensorsontheactualmodel.Thesimulatedprobepressurespectrawereprocessedinamannerverysimilartotheexperimentalones,deningafrequencyresolutionof16HzandutilizingaHanningwindowwitha75%blockoverlap.Duetotheshortdurationofthesimulation(0.32s),thevarianceandhencetheprobespectraluncertaintywerequitelarge.Specically,thevirtualprobesweredownsampledtoasamplingfrequencyofFs=26.172kHz,yieldingamereveblocksoverwhichtoperformthespectralaveraging,thusresultinginan 187

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autospectralrandomuncertaintyofr=35%.Nevertheless,thesimulatedspectrawerebelievedtobeusefulforextractinginformationpertainingtospectraltrendsandlevels. TheresultsofthesurfaceprobespectralcomparisonsarepresentedinFigure 4-22 .Generallyspeaking,thereisexcellentagreementbetweensimulationandexperimentforallshownprobes.Morespecically,thesimulatedcylindersensorsatheightsofZ=0and1Dshowgoodoverlapatfrequenciesbelow2kHzandbegintodivergefromtheexperimentalresultsafterthis.Conversely,thespectraofFigures 4-22C and 4-22D showexcellentagreementuptoapproximately5kHz,includingthelowfrequencybi-modalhumpsdiscussedpreviously.IfattentionisshiftedtothespectrashowninFigures 4-22E 4-22H ,againexcellentbroadbandagreementisobtainedupto5kHzforallsensors.Furthermore,thetwospectralhumpsofsensorsT2andT4areevidencedinthesimulatedspectra.Theonlyconsiderabledierenceinthespectralcomparisonsisthepresenceoftwolow-frequencyspectralhumpsinthesimulatedspectrumofsensorT1inFigure 4-22E ,whichisnotpresentintheexperimentaldata.Itshouldbenoted,however,thatduetotheshortdurationofphysicaltimethesimulationrepresents,thelowfrequencyfeaturescontainaconsiderableamountofuncertainty.Therefore,someofthespectralhumpsatlowfrequenciescouldbeaberrantandpotentiallydiminishgivenmoresimulationtime.Despitethis,thereisexcellentagreementinthespectrallevelsandtrends. 4.2AcousticCharacterization Far-eldacousticmeasurementswereperformedtoprovideafundamentalacousticcharacterizationofthenumerousmodelgeometries.Bothlinearandphasedmicrophonearrayswereutilizedforobtainingfar-eldspectrallevelsandidentifyingthedominantregionsofnoisegenerationviabeamforming,respectively.Duetothelimitationsofbeamformingtohigherfrequencies(f1kHz),insightintothenoisegenerationatlowerfrequenciesisaccomplishedthroughcoherencemeasurementsbetweenfar-eldmicrophonesandsurfacepressuresensors,aswellasestimationofthevortexsoundsourcetermsintheoweldusingtheSPIVdatasetsin Section5 188

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4.2.1AcousticSurveys AsTable 4-1 shows,far-eldspectrallevelswereobtainedforatotalofeightcongurationsforvedierentfreestreamtunnelvelocities.ItwasfoundintheunsteadysurfacepressureresultsthatonlythethreehighestspeedscorrespondingtoMachnumbersof0.15,0.17,0.19yieldedspectrallevelsthatportrayedscalingwithdynamicpressure.Therefore,itisreasonabletoassumethatthefar-eldlevelsforthesethreespeedsmaybereferredtoforobtainingspectralscalingtrendsasafunctionofowspeed.Thissectionpresentsthefar-eldspectrallevelsobtainedforthedierentmodelcongurations,theirscalingbehaviors,andpartialdirectivitypatterns. ComparisonofModelCongurations: .Thefar-eldspectraltrendsandpartialdirectivitypatternswerecomparedforthedierentmodelcongurationsatatunnelvelocityofU1=58m/s.TheacousticspectrawerecomparedbyanalysisofthedatarecordedbylineararraymicrophoneL4.Thismicrophonewaschosensinceitislocateddirectlyacrossfromthemodelcylinder(m=90).Thedirectivitypatterns,meanwhile,werecomputedusingallmicrophonesinthelineararrayandnormalizingtheirspectrallevelstoacommonmicrophonedistancefromthemodelundertheassumptionoffar-eldacousticradiation.Thisnormalizationwasperformedafterapplyingashearlayercorrectionproposedby Amiet ( 1978 ).Moreinformationonthisispresentedin Section4.2.2 Figure 4-23 displaysaspectralcomparisonofthefar-eldacousticsignatureofthefourprimarymodelcongurations.Forthe=100and130congurations,abroadspectralhumpcenteredaround240Hzcanbeobserved.Inaddition,the=130congurationdisplayshigherspectrallevelsacrosstheentirefrequencyrangeoutofthesetwocongurations.Ifattentionisshiftedtothe=160conguration,thepoweratlowfrequenciesisseentonearlyplateauwithaslighthumppriortoasteepdropoaroundf=400Hz.Forfrequenciesabove400Hz,thiscongurationexhibitsspectrallevelscomparabletothoseofthe=130conguration.Itisreasonabletoassumethat 189

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theresultingcloseproximitybetweentorquearmsandcylinderfor=160eliminatesanyappreciablevortexsheddingfromeithercomponent.Theinvertedconguration,meanwhile,displaysaspectralhumpat400Hzthatisapproximately5dBbelowthatofthestandard=130conguration.Thiscongurationalsoexhibitsspectrallevelsthatareconsiderablylowerthanthoseoftheothercongurationsforthefrequencyrangeof144f352Hz. ItisworthrecallingthatthesheddingfrequencyofthesingletrippedcylinderunderthesameowconditionsoccurredaroundaStrouhalnumberofStD=0:28,whichtranslatestoadimensionalfrequencyoff420Hz.Thespectralhumpsobservedforthe=100and130congurationsoccuratamuchlowercentralfrequencyof240Hz.Thebroadnessofthisspectralhumpwasinitiallybelievedtobeduetovortexsheddingoofthetorquearms,whichhaveanever-changingcross-sectionalwidth.Thismayexplainthedistributionofenergyinthespectrum,sincethevariablecross-sectiondenotesachangingStrouhalcharacteristiclengthscale. Tobetterunderstandthevariationofthelow-frequencybehaviorofthemodelasafunctionof,thespectralresultsforallstandardmodelcongurationsarepresentedinFigure 4-24 foratruncatedfrequencyrangeof100f800Hz.Fromthisgure,itcanbeseenthatanglesintherangeof=100)]TJ /F1 11.955 Tf 12.64 0 Td[(130displayspectralhumpswithpeakvaluesoccurringineitherthe240or256Hzfrequencybins.Thishumpincreasestoacenteredfrequencyof272HzatahigherSPLforthe=140conguration.Itisafterthiscongurationthatthisspectralhumpisseentodisappear,withthe=150congurationexhibitinganenergyplateauandthe=160congurationdisplayingaconsiderableenergydropinthefrequencyrangeof100f400Hz.Thisgradualdisappearanceofthespectralhumpcoincideswellwiththeoutlinedbehavioroftandemcylindersofdierentseparationdistanceaspectratiosintermsofvortexsheddingbehavior( Zdravkovich 1985 ),whichareoverviewedinTable 2-3 .Furthermore,itisinterestingtoobservehowthedisappearanceofthespectralhumparound256Hzforthe 190

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=160congurationinFigure 4-23 coincidesverywellwithasimilarspectraltrendexhibitedbyrecessedtorquearmelectretT1inFigure 4-15E ,whichislocatedalongthetorquearmedge.Thisimpliesacorrelationbetweenthepressureuctuationsonthetorquearmedgewiththeacousticradiation.Thisispursuedin Section4.2.3 throughtheestimationofthecoherencebetweenthemodelpressuresensorsandthereferencelineararraymicrophoneL4.Thefollowingsectionpresentsthedirectivityresultsforallcongurationstodetermineifanydisplayaquieteracousticsignaturecomparedtotheprimary=130conguration. 4.2.2DirectivityApproximations Thefree-eldmicrophonesthatmakeupthelineararraywereusedtoconstructapartialdirectivitypatternforallofthetestedmodelcongurations.Duetothe\linear"congurationofthemicrophones,aradialcorrectionfactorrc=rrefwasappliedtoeachmicrophoneasiftheywerelocatedinaradialarcaroundthemodel.Thiscorrectionfactorrepresentsthepressureradiationtrendofp1=rindicativeoffar-eldradiation.Therefore,thenormalizedSPLaccountingforthisradialadjustmentwasdenedas SPLnorm=SPLsc+20log10(rc=rref):(4{4) Forthesecalculations,thereferencedistancewassettothegeometricdistancermfromthemodelcylindertolineararraymicrophoneL4,whichwassetto48"(1.219m).Thecorrectedradiationanglescandcorrectedmicrophonedistanceratiosrc=rmaredenedin Section3.5 TheresultsofthedirectivitycalculationsareshowninFigure 4-25 .Notethattheseresultswerecomputedoverafrequencyrangeoffmin=160Hztofmax=5kHz.ThelowerfrequencyboundwaschosensinceitcorrespondedtothelowerlimitatwhichthespectraforalllineararraymicrophonesweresuccessfullycollapsedusingEquation 4{4 .Theupperfrequencylimit,meanwhilewassomewhatarbitrarysincethefar-eldspectrawereseentoexhibitarapidroll-oafter1kHz,andthereforewouldnotimpact 191

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theOASPLcalculationconsiderably.However,sincethetorquearmmodelpressuresensorswerelimitedtoa5kHzupperfrequencyofanalysis,thisseemedtobeasuitablecut-ofrequencyforthiscase.ThisupperlimitalsoexhibitedaSNRofatleast10dBforallcongurations.Notethatthelowerfrequencyboundof160HzalsoexhibitedaSNRofatleast10dBforallcongurations.ItisalsoworthnotingthatonadBscale,thepreviouslycomputedautospectralrandomuncertaintyofr=3:21%andthemanufacturer-quotedfrequencyresponseuncertaintyof1dBresultsinanOASPLuncertaintyofr;OASPL1:14dBforthevaluesshown. AstheresultsofFigure 4-25 show,thereisconsiderablevariationinthelevelsbetweenthedierentmodelcongurations.Ofthestandardcongurations,the=100congurationshowsthelowestlevelsacrossallradiationangles,howeverthisisonlybyafractionofadBfromthe=160congurationfor50C80.ThelargestdiscrepancyinOASPLcomparedwiththeothercongurationsoccursforradiationanglesC84:8,wherethiscongurationisatleast1dBbelowtheothercongurations.Thecongurationswiththehighestintegratedlevelsarethe=140and=150congurationsforC70. Meanwhile,the=130invertedconguration,showsthelowestOASPLsoverallmeasuredradiationangles.Itislowerthanthe=100congurationbyapproximately2dBacrossallmeasureddirectivityangles.Furthermore,sincethe=130congurationrepresentstheonebasedonanactuallandinggear,itwarrantscomparisonwiththeinvertedone.Acrosstheentirerangeofmeasuredradiationangles,theinvertedcongurationhasanOASPLofapproximately4dBbelowthestandard=130conguration.Thisfurtherreinforcesthenotionproposedby Dobrzynskietal. ( 2005 )and Anglandetal. ( 2010 )thatplacementofasharp-edgedgeometryupstreamofaroundedoneofcomparablecross-sectionwillresultinanearliershearlayerformationthatwill\miss"thedownstreamcomponent.Asaresult,theradiatednoiseisreducedduetoadrasticreductioninwakeimpingementonthedownstreamcomponent. 192

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Aninterestingobservation,inadditiontothelevelsthemselves,isthepropagationanglesatwhichthemaximumlevelsareobservedtooccur.Forexample,the=100congurationdisplaysamaximumOASPLoccurrencebetweenC=76:7and68:8.Thisrangeisseentograduallyincreaseto84:8C100:3betweenthe=130and=160congurations.Thisincreaseinpropagationangle(furtherupstream)appearstocoincidewellwiththemovementofthetorquearmhingeclosertotheupstreamcylinder. 4.2.3Near-toFar-FieldCoherence Thecoherencefunctionwasestimatedbetweenthereferencemicrophoneofthelineararray(L4)andthemodelsurfacepressuresensorstoidentifycorrelationsbetweenthesurfacepressureuctuationsandtheresultingradiatedacoustics.TheresultsofthesecalculationsfortheprimarymodelcongurationsarepresentedinFigure 4-26 .Ifattentionisfocusedonthecylindersensorsforthe=100congurationinFigure 4-26A ,itcanbeseenthatallsensorsexhibitacoherencerelativetolineararraymicrophoneL4above0.1inthefrequencyrangeof200f300Hz.ThistrendissimilartothetorquearmsensorsinFigure 4-26E ,withthehighestlevelsofcoherenceoccurringforthetorquearmsensorT1.Similaroverallbehaviorisobservedforthe=130conguration,howeverwithanadditionalelevationincoherencearoundalowerfrequencyof120Hz.Oneofthemostnotablesimilaritiesbetweenthesetwocongurationsisthepresenceofthelocalcoherencemaximaat224and256Hz,respectivelyfortorquearmsensorT1.Thisimpliestheformationandsheddingofcoherentvorticalstructuresfromthesharpedgesofthetorquearm.Itisalsoveryinterestingtonotehowthecoherencespikeat120Hz,namelywiththecylindersensoratZ=3D,correspondswellwithasimilarcoherencespikebetweenthissamesensorandthetorquearmsensorT4inFigure 4-19D Thenear-tofar-eldcoherencebehaviorsofthe=100and130congurationsisseentoallbutdisappearforthe=160congurationinFigures 4-26C and 4-26G ,thereforeattributingthecloseproximitiesofthecylinderandtorquearmstothepreventionofcoherentvorticalstructuresfromdevelopingandconvectingdownstream. 193

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Thisappearstochangeslightlyfortheresultsof=130invertedcongurationshowninFigures 4-26D and 4-26H ,wherecoherencevaluesofatleast0.2areobtained.TheseoccurforthecylindersensorsatZ=0and0:42DaswellasforthetorquearmsensorT1atafrequencyof400Hz.ThesealsocoincidewellwiththecoherenceelevationsobservedbetweenthecylindersensoratZ=0:42DandtorquearmsensorT1inFigure 4-21A .Thisimpliesthepresenceofatleastintermittentvortexsheddingbetweenthetwocomponentsintheinvertedconguration,atleastintheregionswherethetorquearmwidthiscomparabletothecylinderdiameter.Thegeneralobservedtrendofthesedataarethatcoherencebetweenthesurfacepressuresandfar-eldacousticsdegradeasthedistancebetweencylinderandtorquearmdecreases. 4.2.4Far-FieldScalingBehavior Scalingofthefar-eldspectrawasperformedforthefourprimarymodelcongurationsusingtraditionalfrequencyandspectralamplitudetechniques.Theseconsistedofnon-dimensionalfrequencyscalingusingtheStrouhalnumber,StD=fD=U1,whereDwassettothecylinderdiameter.Forspectralamplitudes,atechniquedependentonthepoweroffreestreamvelocitywasusedtoidentifytheapproximateacousticsourcebehaviorofthetorquearmmodelfordierentfrequencyranges.Thisamplitudescalingtechniqueisdenedas SPLsc(f)=10log10PSDf(1=Mn) (2010)]TJ /F7 7.97 Tf 6.58 0 Td[(6)2;(4{5) wherenrepresentsthevelocity,ormorespecicallytheMachnumber,powerscalingfactor.Thismethodisalsodependentonaffactorwhichistraditionallysettothefrequencyresolutionofthemeasurement,orf=16Hzinthiscase.However,inthecaseofscalingbasedonStrouhalnumber,itismoreaccuratetousef=U1=D( Spalart 2013 ).Theexpectedvalueofnforoptimalfar-eldspectradatacollapseisasubjectofconsiderabledebateintheliterature.AswasdocumentedinSections 2.1.1 and 2.3.2 ,landinggearnoisehasbeenbroadlycharacterizedasexhibitingdipole-likeacousticscalingbehavior.Thisevidencewouldmakeavelocitypowerscalingfactorofn=6seemtobe 194

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anattractiveoption.However,thesimpliednatureofthetorquearmgeometrymightresultinmodicationstothistraditionalscalingbehavior.Therefore,integernvalueswereappliedtothedataintherangeof5n8.Thesevalueswerechosenbasedonobserveddeviationsfromthetraditionaln=6trendsintheliterature,aswellastheworkof Kambe ( 1986 ),whichfoundsucharangeofacousticpressurescalingbehaviorrelativetovelocityforvorticesconvectinginthevicinitiesofdierentblubodygeometries.Notethatonlythescalingfactorsthatyieldedthemostaccuratedatacollapses(specicallytowithin1dB)areshowninthefollowingresults. Accordingto Dowling&FfowcsWilliams ( 1983 ),amicrophonemeasurementisconsideredtobeinthefar-eldifitislocatedgreaterthanoneacousticwavelengthawayfromthesource.Therefore,acut-onfrequencycanbedenedbasedonthecurrentmicrophonelocations.Asstatedin Section3.5 ,thelinearmicrophonearrayislocated48"(1.22m)fromthemodelcenterplane.Ifthisdistanceisdenedasoneacousticwavelength,thenthecorrespondingcut-onfrequencyisf280Hz.Unfortunately,thebaselinemodelexhibitsaprimaryspectralhumpatacenteredfrequencyof256HzattheprimarytestingspeedofM0.167.Asaresult,thespectrabelowthecut-onfrequencyareexpectedtoexhibitdeviationsfromfar-eldpoweramplitudescalingbehavior.Despitethis,however,thespectraareplotteddowntoaminimumfrequencyof96HzinordertoidentifythepresenceofStrouhalscaling. Thefar-eldscalingresultsforthe=100congurationareshowninFigure 4-27 .Interestingly,theresultsshowthreedistinctspectralregionsthatexhibitdierentscalingbehaviors.Therstoftheseoccursoveranon-dimensionalfrequencyrangeof0:1StD0:25.InadditiontoexhibitingStrouhalscaling,thespectraareseentocollapseverywellusingafthpowerofvelocityscaling.Notethatthispowerofvelocityissmallerthanevidencedinthemajorityofliteraturepertainingtodipoleradiation,howeveradditionalconsiderationsmakethisanexplainablescalingbehavior,suchasedgescatteringoofasharp-edgedacousticallycompactsurface( Williams&Hall 1970 ). 195

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Thesecondregionofspectralcollapseoccursoverthedimensionalfrequencyrangeof416f720Hzforafthpowerofvelocityscaling.Similarscalingwasfoundby Kambe ( 1986 )forthecaseofinjectingvorticesatasemi-innite,sharp-edgedplate.Thiseecthasbeenevidencedtobetheresultofacousticdiractioninthepresenceofowstructuresimpactingthesharpedgesofthegeometry.Thenalspectralregionisforfrequenciesabove720Hz,inwhichthespectraareseentocollapseverywellwiththeseventhpowerofvelocitywithoutStrouhalscaling.Thisscalingbehaviorhasbeenevidencedinliterature,particularlyforthefulllandinggearstudiesof Guoetal. ( 2006 ),whichshowedasimilareectiveseventhpowerofvelocityscalingfordimensionalfrequenciesabove1kHz.Therehasalsobeenspeculationoftheearlyworksof Phillips ( 1956 ),whoconcludedthattheAeoliantoneradiationsduetocross-owaroundcylindersdisplayedasixthpowerofvelocitytrend.Aftercloserobservation,however,recentauthorshaveobservedthatthetrendofthisdatasetcorrespondsmorecloselytoaseventhpowerofvelocitytrendratherthanasixthpowerofvelocity. Ifattentionisshiftedtothespectralresultsofthe=130congurationinFigure 4-28 ,similarspectralfeaturesareobservedascomparedtothepreviouscase,withsomedeviations.Forexample,asimilarStrouhalscalingbehaviorisobservedatlownon-dimensionalfrequencies,althoughthiscaseshowsawiderspectralhumpoverarangeof0:1StD0:26andabest-casespectralamplitudescalingfactorofn=6ratherthan5.Furthermore,therewasnoevidenceofamiddlefrequencyrangeforthe=130congurationthatscaledwiththefthpowerofvelocity.Instead,thespectracollapseforavelocitypowerfactorofn=7aboveafrequencyof416Hz. AscanbeseeninFigure 4-29B ,the=160congurationexhibitsamarginallygoodcollapseofthespectrausingaStrouhalandfthpowerofvelocityamplitudescaling,howeverwithonlyasubtlespectralhumpatStD=0.25.Thiscouldpossiblytieinwiththenear-absenceofcoherencebetweenthemodelsensorsandthefar-eldmicrophone.Itisinterestingtonote,however,thatStrouhalscalingwasevidencedto 196

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eectivelycollapsethelow-frequencybehaviorsofthemodelunsteadypressuresensorsforthisconguration.AnillustrationofthisisprovidedinFigure 4-30 ,whichshowsthepowerspectraofacylinderandtorquearmrecessedsensornormalizedbythefreestreamdynamicpressurewithStrouhalscaling.Itispossiblethatanytypeofvortexsheddingbehaviorisintermittentanddoesnotoccurreliablyenoughtopropagatetothefar-eld.Apossiblediagnosisofthiswouldbeanysurfacepressuresensorsthatwouldindicatenon-stationarity,howeverthiswasfoundtonotbethecase.Instead,themajorityofthesurfacepressureprobesonthemodeldisplayedabroadbandspectralbehavior,withtheexceptionofT4,whichexhibitedaslightspectralhumpcenteredaround400Hz(Figure 4-15 ).Finally,theinvertedcongurationinFigure 4-31 recoverstheStrouhalbehavioraswellasavelocitypowerscalingofn=5foranapproximatenon-dimensionalfrequencyrangeof0:1StD0:26.AtM0.167,thepeakamplitudeofthespectrumatStD0:26correspondstoadimensionalfrequencyoff432Hz.Itisatthisfrequencythatacoherenceofatleast0.2wasmeasuredbetweenlineararraymicrophoneL4andthemodelcylindersensorsatZ=0and0.42DaswellasthetorquearmsensorT1.Thisimpliesthatthereisacombinedsheddingbehaviorexhibitedbyboththetorquearmandcylinder.Thismakessensesincethenominalsheddingfrequencyofthesingletrippedcylinderatthisfreestreamvelocitywaspreviouslyidentiedtobeintheimmediatevicinityof400Hz.Fordimensionalfrequenciesabove416Hz,themodelfar-eldspectrawasseentodisplayaseventhpowerofMachnumberscalingindependentofStrouhalbehavior.Thisupperfrequencybehavior,therefore,isseentobecommonbetweenallofthemodelcongurations. 4.2.5CAAPrediction Thecomputationalaeroacoustic(CAA)capabilityofthePowerFLOWsoftwarewastestedusingitsbuilt-inFW-Hsolver.Thiswascomputedusingbothasolidandporousformulation.Thesolidsurfaceformulationwascomputedbasedonstrictlythesurfacepressureuctuationsofthesurfacemeshesofthemodelcomponents,whilethe 197

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porousformulationwascomputedusingthepressure,density,andvelocityuctuationsthrougharectangularprismboundingthetorquearmmodel.AnillustrationoftheFW-HporousboundingboxaroundthemodelisprovidedinFigure 4-32 .Notethatthedimensionsoftheboxwereselectedsuchthattheheightcoincidedwiththetestsectionbounds(sidewalls),thewidthwaswideenoughtoencompassthemodelwakeandshearlayers,andlongenoughtoencompassapproximately6.5cylinderdiametersofdownstreamconvection.Thesignicanceofthesetwocomputationmethodsisthatthesolidformulationaccountsfordipoleradiation,whiletheporousonealsoaccountsforquadrupoleradiation( Bresetal. 2010a ).Itwasexpectedinitiallythatthedierencesbetweentheoutputsofthesetwowouldbesmall,sincetheblubody-natureofthemodelwasbelievedtoexhibitprimarilydipolenoise. TheCAApredictionofthesolverwasimplementedforasinglemicrophonetest,whichwasdonebysimulatingavirtualmicrophoneatthenominallocationoflineararraymicrophoneL4fromthetunnelexperiments.RecallthattheuiddomainwassimulatedsuchthatthefreestreamvelocityboundaryconditionwaspresentwellpasttheactualboundsoftheUFAFFtestsection.Therefore,consequently,thesimulatedmicrophoneislocated\intheow".Thisisnotaproblem,however,sincetheuiddomainwassettobeananechoicuidlayerimmediatelyoutsideofthetestsectiondimensions.Thispreventsthesimulatedmicrophonefrombeingcontaminatedbynoiseduetothefreestreamow.Asaresultofthis,noshearlayercorrectionwasapplied. TheresultsofthesinglesimulatedmicrophoneforbothsolidandporousformulationsandtheircomparisonswiththeexperimentaldataareprovidedinFigure 4-33 .Aspredicted,thereisverylittledierencebetweenthesolidandporoussolutions,withtheexceptionofslightlyhigherpowerlevelsfortheporousonethroughouttheentirefrequencyrange.Thecomputeddierenceinintegratedpowerlevelsbetweenthetwocongurationswasfoundtobeonly1.2dBOASPL.Furthermore,bothoftheexperimentalresultsforthecasesofwithandwithoutthehelicalwirewrappresenton 198

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thecylinderextensionrodsarealsoprovided.Theonlydierencebetweenthetwospectraoccursat400Hz,whichwaspreviouslymeasuredtobethenominalsheddingfrequencyofthesingletrippedcylinderatthisvelocity.Itisimportanttorecallthatthespectrawerecomputedgivenonly0.32secondsofsimulationdata.Therefore,forthesimulationsamplingfrequencyof78.5kHzandmatchingthefrequencyresolutionoftheexperimentaldata,only6FFTblockswereavailableforaveraging.Thisexplainsthehighvarianceinthesimulatedspectra.Itisconceivablethatthespectralpeaksbetween200and320Hzcouldsettletosomethingmorecloselyresemblingtheexperimentaldatawithadditionalsimulationtime.Despitethis,however,thefar-eldpredictionslineupverywellwiththeexperimentaldatauptoafrequencyofapproximately3.5kHz. ThemostimportantconclusionthatcanbedrawnfromtheCAApredictionisthatthesolidformulationcapturesthemajorityoftheacousticpower,whiletheporousformulationonlycontributedafractionofthetotalpower.Thisveriesthatthetorquearmmodelgeometrycanbeconsideredtobegovernedprimarilybyadipoleradiationbehavior. 4.2.6MotivationforHigh-FrequencyAnalysis Itisworthrecallingthatthisstudyisonthephysicalsourcesofnoisegenerationonthetorquearmgeometry.Whiletheloweracousticfrequenciesthathavedisplayedhighspectrallevels,Strouhalscalingbehavior,andappreciablecoherencewiththefar-eld(f500Hz),higherfrequenciesalsowarrantanalysis.ThisisbasedonthefactthathigherfrequenciesareweightedbytheFAAonthegroundsthathumanhearingismostsensitivetofrequencieswithintheapproximaterangeof1f5kHz( Kryter&Pearsons 1963 ).Therehavebeenanumberofweightingschemesdevelopedtoemphasizethisfrequencyrange,whilereducingthecontributionofpowerlevelsoutsideofthisfrequencyrange. TwoofthemorecommonSPLweightingschemesappliedtofar-eldspectraofaircraftnoiseareknownasA-andD-weightingschemes.Anillustrationofthese 199

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weightingsintermsofpoweramplitudegainonadBscaleispresentedinFigure 4-34 .Asthegureshows,bothweightingschemesdisplayazerogain,indicatedby0dB,atafrequencyof1kHz.TheA-weightingschemeistheolderofthetwo,andhadoriginallybeenformulatedbasedonhumanresponsestopuretonesatrelativelyquietSPLs( Fletcher&Munson 1933 ).Thisweightingwaslaterimproveduponby( Kryter&Pearsons 1963 )toaccountforhumanresponsestoband-limitedwhitenoise,whichisaccountedforwiththehigher-amplitudegainsoftheD-weightingschemeoverthesamefrequencyrange.Inasense,theD-weightingmaybemoreapplicabletoaircraftnoiseduetothebroadbandnatureofthenoisesignature.Inaddition,theD-weightingalsodisplaysa0dBgainbetween500Hzand1kHz,potentiallydecreasingthelowendofthefrequencyrangeofinterestto500Hz. Sincethetorquearmgeometryunderinvestigationrepresentsa1/2-scalelandinggearsub-system,thehighfrequenciesofinterestneedtobescaledbyafactoroftwo.ThisresultsinaD-weightingbasedfrequencyrangeofinterestof1f10kHz.However,basedonthelimitationsoftheUFAFFwindtunnelbackgroundnoise,thereliableupperfrequencylimitofthetorquearmmodelisreducedto8kHz.Thisisthefrequencyatwhichthequietesttorquearmcongurationisatleast6dBabovethewindtunnelbackgroundnoise.WhilethisSNRisbelowthetypicallypreferred10dBforaeroacousticwindtunnelmeasurements,theusageofaphasedmicrophonearrayisanexcellenttoolforeectivelyisolatingthesignalofinterest.Therefore,thefrequencyrangeof1f8kHzrepresentsaneectivefrequencyrangeforbeamforminganalysis. 4.2.7BeamformingResults BeamformingwasperformedforthemodelprimarycongurationsatfreestreamMachnumbersof0.13,0.15,and0.17.Unfortunately,thelowerofthesethreespeedswasfoundtobeoutsideoftheregionofecientdynamicpressurescalingduetotransitionoftheowregimearoundthemodel.Therefore,sinceonlytwospeedscannot 200

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demonstrateeectivescalingbehaviors,onlytheowcaseofM0.17forthedierentmodelcongurationsarepresented. 4.2.7.1NoteonLimitationsofBeamforming ItisimportanttorecallthattheouterFFMAwasdesignedtohaveacut-onfrequencyofapproximately1kHz.Basedonthenear-andfar-eldspectralresultsoftheprevioussections,thehighestacousticenergycontentexistsforfrequencieswellbelowthisforallcongurations.However,thislowfrequencyrangewasalsoevidencedtobetheonlyrangewherecoherentacousticsourcesarepresent.Thisisfurthersupportedbythefactthatthisfrequencyrangelieswithinaregionwherethesourcescanbeclassiedasacousticallycompact,orka<<1.Forexample,thehighestfrequencyatwhichthemodelsurfacepressuresensorsshowedappreciablecoherencewiththefar-eldis416Hz,whichwasfoundforthe=130invertedconguration.SubstitutingthisfrequencyintotheHelmholtznumberyieldska0:287,withabeingsettothediameterofthecylinder.Therefore,beamformingonfrequenciesabovethisshouldsatisfythecriterionofmostbeamformingalgorithmsthatmultipleacousticsourcesinascanningregionmustbeuncorrelatedwithoneanother.Unfortunately,thenon-compactnessofthesourcesisnotbenecialsincethesourcewaveformbehaviordeviatesfromthemonopolemodelinputintothebeamformer.Whilethiswillnotaecttheperformanceofthebeamformerfromanoisesourcelocalizationstandpoint,ithasthepotentialofyieldingincorrectpowerlevels.Therefore,analysisoftheFFMA'sabilitytocomputeabsolutepowerlevelstookplacethroughintegrationofthebeamformeroutput( Yardibietal. 2010b ). 4.2.7.2ComparisonofAlgorithms Aswasstatedin Chapter3.5.2.1 ,theDAS,RCB,andDAMASalgorithmswereavailableforthisstudy.However,itwasdecidedthatusingallthreealgorithmstopresentalloftheresultswouldbetoooverwhelming.Therefore,aweighingoftheadvantagesanddisadvantagesaswellasacomparisonofthebeamformeroutputsofthealgorithmswereperformed.Asummaryoftheprimaryadvantagesanddisadvantagesofthealgorithms 201

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areshowninTable 4-4 .Furthermore,ademonstrationofthethreebeamformeroutputsatanarrowbandfrequencyof4kHzonthe=130congurationareprovidedinFigure 4-35 .Thesebeammapsweregeneratedbydeningascanningregiontocorrespondtoaplanethatslicedthroughthecenterplaneofthetestsection,whichwasmeasuredtobe53"(1.346m)fromtheplaneofarraymicrophones.Initially,theentirestreamwiselengthoftheopen-jettestsectionwasscannedtoidentifypossiblenoisecontaminants.TheDASandRCBbeammapsweregeneratedusinga1cmresolution,whileDAMASwascomputedusinga3cmresolutiontoreducecomputationtime.Astheresultsshow,DASandRCBdisplayagreementinthetrendsofthenoisesourcedistributions,focusingalongthemid-regionofbothtorquearms.Theybothalsoidentifythemaximumpowerlevelinthescanninggridtowithin1cmofeachotherontheinsidesurfaceofthetorquearm.Furthermore,theRCBbeammapofFigure 4-39G displaysamuchnerresolutionthanDAS.ThedrawbackofRCB,asindicatedinTable 4-4 ,isthattheoutputpowerlevelsarenotreliable,andarethusonlypresentedinarelativedBscale.TheDAMASresultofFigure 4-35D ,meanwhile,presentsa\noise"mapratherthanabeammapwithahigherdynamicrangeof20dB.Thismapdiersfromtheprevioustwo,sincetheconvolutioneectsassociatedwiththearraypointspreadfunctionaretheoreticallyremoved.Thisnoisemapagreeswiththeprevioustwobeammapsinthesensethatthemaximumpowerlevelsareinsimilarlocations.Ratherthanthesourcesbeingcontainedwithinasingledistribution,however,theDAMASresultshowsdistinctgridpointsofhighacousticpower.Notethatunlessindicatedotherwise,atotalof10,000DAMASiterationswereperformed.Itwasfoundthat2,000iterationsyieldedconvergedintegratedlevels,howeverwithdeviationsinthenoisesourcemapresults.Increasingthisto10,000iterationswasfoundtoprovideconvergenceinbothcategories. Anotherimportantfactortoconsideristhevalidityoftheabsolutelevelspredictedbythebeamformer.Thereareanumberofreasonsastowhyincorrectabsolutelevelscouldbeproduced,includinginter-microphonescatteringeects,microphoneposition 202

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error,errorinthenominaldepthlocationofthescanninggrid,errorsinthespeedofsoundduetofacilitytemperaturevariations,andmicrophonefrequencyresponsevariations.Therefore,thiswasinitiallydiagnosedfortheDASandDAMASalgorithmsbyreconstructingtheentirefar-eldspectrumofthebaseline=130congurationusingthebeamformerscanninggridintegrationmethodsofEqs. 3{49 and 3{50 ,respectively.Theresultsoftheseintegrationsforafrequencyof4kHzarepresentedinFigures 4-35B and 4-35D .Notethatbothoftheseresultsareinitiallyveryencouragingbasedontheiridenticalcomputedintegratedlevelsof57.0dBfortheintegrationboxesshowninthegures.Thenextstep,however,wastoidentifythesimilarityoftheseintegratedbeamforminglevelswiththoseofthecenterreferencemicrophoneacrosstheentirefrequencyrangeofinterest.Therefore,duetothedecreasingresolutionoftheDASbeamformeratlowfrequencies,theintegrationregionwasexpandedtobetheentiretestsectiondimensionsofFigure 4-35 .NotethatintegratedlevelsfortheRCBalgorithmwerenotcomputedbasedonitsinabilitytocomputeaccurateabsolutelevels( Chapter3.5.2.2 ). TheresultsoftheintegratedbeamformerspectrawithacomparisontotheFFMAcenterreferencemicrophoneareshowninFigure 4-36 .TheresultsoftheMonteCarlo(MC)uncertaintyanalysisarealsoshown,includingthemeanintegratedlevelsandthe95%errorbounds.Again,theseintegratedlevelswerecomputedbysettingthescanninggridtotheentiretestsectiondimensions.Astheresultsshow,thereisexcellentoverlapbetweenthenominalDASandDAMASintegrationsinthefrequencyrangeof1f5kHz.Surprisinglybothalgorithmslineupwellwiththecentermicrophoneoverthelowfrequencyrangeof256f450Hz,withDAMASoverlappingslightlybetter.Abovethisfrequencyrange,thereisreasonableagreementinthespectraltrendsbetweenallthree,howeverwithoccasionalgapsbetweenspectrallevelsthroughoutthefrequencyrange.Furthermore,above5kHztheDASisseentounder-predictthereferencemicrophonelevels,whileDAMASremainstowithin1dBupto10kHz.Meanwhile,theMCmeanresultsareseentoslightlyover-predictthenominalintegratedDASthroughout 203

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theentirespectrum.Thisdiscrepancybeginstowidenforfrequencyiesabove7kHz,whereitreachesamaximumdierenceofapproximately5dBat10kHz.TheMCupperandlowererrorboundswerefoundtospanapproximately1dB.Unfortunately,therequiredcomputationaltimeforimplementingtheMCuncertaintyanalysisforDAMASacrosstheentirefrequencyrangemadeitinfeasible. TheFFMAreferencemicrophonewasthencomparedtoafree-eldmicrophonepositionedontheoppositesideofthetestsection,approximatelyacrossfromtheFFMAcenter.Thepurposeofthisistodiagnosethepresenceofscatteringeectsalongthearrayface.TheresultsofthisarepresentedinFigure 4-37 .Duetoaslightdierencebetweendistancesofthesetwomicrophonesfromthemodelsourceregion,thedistancecorrectionofEquation 4{4 wasappliedtotheoppositemicrophonetomatchthatoftheFFMA.Theresultsindicateaverysimilarbroadbandbehaviorbetweenthem,withanexceptionatseveralfrequenciesintheFFMAspectrum.Thelargestdiscrepancyoccursat512Hz,wheretheFFMAreferencemicrophonedisplaysafrequency\null"behavior.Thisfrequencycorrespondstoanacousticwavelengthof0.68m(26.7"),whichisveryclosetothedistancebetweentheFFMAmicrophonesandtheedgeofthetestsectionsidewalls.Furthermore,thereisanSPLelevationabovethebroadbandlevelsatharmonicfrequenciesof750Hz,1.5kHz,and3kHz.Thelowerofthesefrequenciescorrespondstoahalf-wavelengthof0.23m(9.1"),whichrepresentstheapproximatedistancebetweentheFFMAplaneofmicrophonediaphragmsandthemetalbaseofthearrayframe.Therefore,thisappearstohaveresultedina\semi"soundhardreectionfromtheframebacktothemicrophones.ThespectraofmicrophonesfromeachcircularringoftheFFMAwerecheckedandalsofoundtodisplaysimilarbehavior,thusverifyingthattheentirearrayisaectedbythis.Despitethesesmallenergyelevations,thearrayseemstofunctionreliablyforfrequenciesatandabove1kHz.Inaddition,theFFMAwasfoundtobepositionedwithinthemainlobeofthetorquearmdirectivitypatternforallbeamformingfrequenciesofinterest.Thedetailsofhowthiswasdeterminedarediscussedin AppendixD 204

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Basedontheperformancesofthedierentbeamformingalgorithms,itwasdecidedthatDASwasconsultedforabsolutelevelestimatesandnoisesourcelocation,whileRCBwasutilizedforprovidingnerresolutionnoisesourcelocalizations.ItwasalsobelievedthatDAMAScouldoersomeinsightatcertainlowerfrequencieswheretheDASandRCBalgorithmsexhibitpoorresolution. 4.2.7.3NoiseSourceLocalizationMaps SincethespectraoftheprimarymodelcongurationsshowninFigure 4-23 displayneithertonalorStrouhal-scalingspectralfeaturesatfrequenciesattheFFMA'snominalbeamformingfrequencyrangeof1f20kHz,thebeamformingmapsweredecidedtoservemoreasasurveytoolandtorelatethespectrallevelsbetweencongurationswiththeirnoisesourcelocations.Therefore,theinitialsurveyswereperformedfortheoctavebandfrequenciesof1,2,4,and8kHz.ThebeammapsarepresentedusingbothDASandRCBmethodsforquanticationofpowerlevelsandrenednoisesourceidentication,respectively.TheDASandRCBbeammapsfortheseoctavefrequenciesarepresentedfortheprimarymodelcongurationsinFigures 4-38 4-41 Therstfeaturetoobserveintheseguresisthatthetorquearmmodelisseentobethenoiseproducerforallthefrequenciestested.Thiswasagoodrststepidentication,sinceitprovesthatthefar-eldmicrophonespectrarepresentthatduetothemodel,ratherthanduetocontaminantssuchassidewalland/ordiusernoise.Ifattentionisfocusedonthestandardcongurations,verysimilargeneraltrendscanbeobservedbetweenthem.At1.008kHz,allcongurationsdisplayapeakvalueatorinthevicinityofthetorquearmhinge,ontheinside(gapow)regionofthemodel.Asimilarbehaviorisobservedbetweenthemodelcongurationsfor2kHz,howeverwithanexceptionforthe=160conguration,whichdisplaysthepeakvaluedriftingalongthelowertorquearminnergapowsurface.Despitethisshiftinpeaklocation,themainlobeofboththeDASandRCBbeamformersareclearlyfocusedaroundthemiddleofthegapowregion.Forfrequenciesof4and8kHz,theresultsofbothDASandRCBbeamformersdisplayalmost 205

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perfectlysymmetricbeamdistributions,highlightingtheupperandlowertorquearmsasthenoisesources.InadditiontodisplayingnerresolutionthanDAS,theRCBisalsoseentoportraythetorquearmsourcesasmoredistributedalongthetorquearminnersurface,ratherthanasnearlycircularsources.Verysimilarbehaviorwasobservedforthenoselandinggearbeamformingexperimentsof Zawodnyetal. ( 2009 ). Whilethebeammapsdisplayfocalregionsofnoisegeneration,theydonotgivemuchinformationregardingnoisesourcedistributions.Therefore,theDAMASalgorithmwasappliedtoallcongurationsforfrequenciesof1.008and2kHz,whicharepresentedinFigure 4-42 .Notethattheseplotshaveadynamicrangeof20dB,andweregeneratedusing10,000DAMASiterations.Ingeneral,thesourcedistributionsarecloselyclusteredforthenoisemapsat1.008kHzforallcongurations.Thischangesfor2kHz,wheretheapparentnoisesourcesaremuchmoredistributedandisolatedtoalmostindividualpixels.Ifattentionisfocusedonthe=100congurationresultsofFigures 4-42A and 4-42E ,thereareprominentsourceregionsaroundthetwojunctionsandthetorquearmhinge.Thereisanadditionalsource,however,at2kHzintheimmediatewakeregionofthecylinderatthemodelcenterline.Sincenosensorpairingsonthemodelwereseentodisplayappreciablecoherenceatthisfrequency(oranyfrequencyabove720Hz),thisisbelievedtobeduetoincoherentacousticscattering.Thisideaisfurtherre-enforcedbytheseventhpowerofvelocityscalingtrendsindependentofStrouhalscalingobservedinthefar-eldspectrareportedin Section4.2.4 TheDAMASresultsat1.008kHzforthe=130and=160congurationsshowverysimilarbehavior.Thisconsistsofaclusterofacousticsourcesthatconnectthecylindertothetorquearmhingeregion.Thisisbelievedtorepresentashearlayerinteractionbetweenthetwocomponents.Themapsat2kHzforthesetwocongurationsalsocompareverywell,withprimarysourcesexistingnearthecenterlinebetweenthecylinderandtorquearmandnearthejunctions.Meanwhile,the=130invertedcongurationdisplaysasomewhatpeculiarnoisemapat1.008kHz.Inadditionto 206

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displayingprominentsourcesnearbothjunctions,asourcecluster\trail"existsthatemanatesfromthelowerjunctionandpropagatesverticallyupwardanddownstreamwhereitterminatesapproximately20cm(5D)fromthecylinder.Thisbehaviorisdiculttoclassify,howevercouldbeduetonoisegenerationfromthejunctionshearlayerthatconvectsdownstreamandupwards.However,apeculiarobservationisthatthisbehaviorisnotrepeatedfortheupperjunction,especiallysincethisisasymmetricgeometry.At2kHz,thepeakpowerlevelsoccursalmostexactlyatthecentroidofthecylinder,withsecondarysourcesintheupstreamanddownstreamvicinitiesofthetorquearmjunctions.ThelocationofthepeakvalueatthecylindercenteragreeswiththeresultsoftheDASandRCBmapsinFigure 4-41 .Thisisbelievedtobeduetoimpingementoftheupstreamtorquearmshearlayerontothecylinder. 4.2.8Summary Asdiscussedpreviously,themodelcongurationshavedisplayedeectivefar-eldspectralamplitudescalingatlowfrequenciesusingafthorsixthpowerofMachnumberscalingfactorwithStrouhalscaling.TheformerofthesescalingshasbeenpreviouslyshowntobetheresultofacousticscatteringoofsharpedgesinaturbulentowatlowMachnumbers( Williams&Hall 1970 ),whilethelattercorrespondstotraditionaldipoleradiationfromowaroundblubodies( Curle 1955 ; FfowcsWilliams&Hawkings 1969 ).Thepresenceofafthpowerofvelocityscalingintheacousticallycompactfrequencyrangeofthemodelisencouragingduetothepresenceofsharpedgesonthetorquearm.Furthermore,pastthisacousticallycompactfrequencyrange,theStrouhalscalingbehaviorappearstovanishandthespectralamplitudescollapsebasedonaseventhpowerofMachnumber.Thisbehaviorisseentobeincommonwiththendingsof Guoetal. ( 2006 ),whichappearstobetheresultofacousticscatteringanddiractionofvorticesimpactingthegeometriesfornon-compactfrequencies.Fortorquearmseparationangles140,includingtheinvertedconguration,themodeldisplaysindicationsofvortexshedding 207

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acrossasmallrangeoffrequencies,whichisattributedtothevariablewidthofthetorquearmcross-section. ThethreebeamformingalgorithmstestedwiththeFFMAdataeachhadtheircontributionstothisstudy.InadditiontotestingtheclassicalDASalgorithm,improvedresolutionbeammapswereprovidedbytheRCBalgorithm.Comparisonofbeammapsforidenticalfrequenciesandmodelcongurationsyieldedexcellentagreementinapparentsourceregionandpeakpowerlevellocationsinthescanninggrid.TheDAMASalgorithmwasalsoappliedinanattempttoobservetheactualnoisesourcedistributionsaroundthemodelgeometry,aswellastocomputeintegratedabsolutelevelsforcomparisonwiththoseofDAS.TheDAMASalgorithmwasseentoyieldabsolutelevelsthatmatchedverywellwithDASoverabroadfrequencyrange,howeverwithslightlybettermatchingwiththeFFMAreferencemicrophoneforfrequenciesbelow600Hzandabove5kHz.Recallthatwhiletheseintegratedlevelsyieldedreasonableresults,thenoisesourcelocalizationabilityoftheFFMAisnotreliablebelow1kHz.Thishasbeenevidencedbythepresenceofafrequencynullandslightspectralelevationsduetoscatteringandreectionsforfrequenciesbelowthis.Therefore,identicationofnoisesourcesbelowthisfrequencymustbeperformedvianear-eldanalyses. AnotherinterestingobservationisthatwhileDASandRCBhaveconsistentlyshownthatthetorquearmsarethebroadbandnoiseproducersforthestandardcongurations,DAMAShasindicatedthattherearesecondarysourceswithinthegapowregionaswell(Figures 4-35D 4-42 ).Thisisaninterestingresultsinceitshowsthattherearenoisesourcesduetocylinder-torquearminteractionsinadditiontonoiseduetoowshearingoofthetorquearmsharpedgesatthesehighfrequencies.Therefore,near-eldanalysisofthePowerFLOWsimulationsmayhelpassistwithvisualizingthenoisesourcesathigherfrequenciesinadditiontothoseatlowerones. 208

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A B C Figure4-1. Illustrationofthesteadypressuremeasurementregionsonthetorquearmmodel:(A)cylindercircumferentialCpmeasurementlocationsat Z=0 Z=2D ,and Z=3D ,(B)torquearminnergapowsurfaceand(C)torquearmwakesurface. 209

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A B C Figure4-2. CircumferentialCpdistributionsofthe(A)barecylinderand(B)trippedcylinderatthe4dierentspanwisemeasurementlocations,and(C)comparisonwiththeresultsof Roshko ( 1961 ).Thedashedlinesin(B)and(C)indicatethetriptapelocationsdescribedin Section3.1.1 210

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A B C D E F Figure4-3. TorquearmcylindersteadycircumferentialCpdistributionsat(A),(D):Z=0,(B),(E):Z=)]TJ /F1 11.955 Tf 9.3 0 Td[(2D,(C),(F):Z=3D. 211

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A B C D Figure4-4. SteadyCpdistributionsofthetorquearmgapowsurfacefordierentmodelcongurations:(A)illustrationofmeasurementlocations,(B)centerline,(C)rightside,(D)leftside.(Key:,=130;,=100;4,=160).MeasurementsareforafreestreamvelocityofU1=58m/s(M0.167). 212

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A B C Figure4-5. ObservationoftorquearmtransientCpbehaviorfor=160:(A)meanresults,(B)dataforsample#200,(C)dataforsample#300(Fs=50Hz,Tacq=20seconds).Thesampledistributionsofthesensorscircledin(A)arepresentedinFigure 4-6 213

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A B Figure4-6. Pressuresampledistributionsofuppercornerpressuremeasurementlocationsontorquearmgapowsurface:(A)leftside,(B)rightside.ThedistributionsrepresentthoseoftheprobescircledinFigure 4-5A .Theyrepresentatotalof1,500samplesacquiredat5Hzforadurationof300seconds. 214

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A B C D Figure4-7. Steadypressuresofthetorquearminvertedbaselineconguration:(A)upstreamviewoftorquearmgeometry,(B)downstreamcylinderrings,(C)torquearmupstreamsurface,(D)torquearmgapowsurface.Theclose-upviewof(A)indicatesthatthetorquearmwidthbeginstoexceedthatofthecylinderslightlyaboveaheightofonecylinderdiameter. 215

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A B C D E F Figure4-8. MeanmodelCpcomparisonsbetweenexperimentandsimulationruns:cylinderat(A)Z=0,(B)Z=)]TJ /F1 11.955 Tf 9.3 0 Td[(2D,(C)Z=3D,andgapowtorquearm(D)centerline,(E)leftside,and(F)rightsideproles.Theresultsrepresentthe=130congurationatM0.167. 216

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A B C D Figure4-9. Simulationresultsforthemeanmagnitudeofvelocityatselectplanesintheoweld:(A)illustrationofmeasurementplanes;oweldresultsat(B)Z=0,(C)Z=2D,and(D)Z=3D. 217

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Figure4-10. Comparisonofsurfacepressurepowerspectraldensitiesforthebareandtrippedmodelcylinderatthemodelcenterline(Z=0)andatacircumferentiallocationof=135. Figure4-11. Spanwisecoherenceoftrippedcylindersensorsrelativetocenterlinesensor(spectraofreferencesensorshowninFigure 4-10 ). 218

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A B C D Figure4-12. DemonstrationoffrequencyandpressurePSDamplitudescalingforacylinderandtorquearmsensorfor=130(Left,unscaled;Right,scaled);(A),(B)cylindersensoratZ=3D,(C),(D)torquearmsensorT4. 219

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A B Figure4-13. Powerspectraldensitiesof(A)cylinderand(B)torquearmrecessedelectretsforthebaselinemodelconguration(=130,U1=58m/s). 220

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Figure4-14. Sampledistributionfunctionsofthe4torquearmrecessedsensorsfor=130,U1=58m/s. 221

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A B C D E F G H Figure4-15. SurfacePSDofselectcylinderandtorquearmpressuresensorsforprimarymodelcongurationsatafreestreamvelocityofU1=58m/s(M=0.167).Cylinder:(A)Z=0,(B)Z=1D,(C)Z=2D,(D)Z=3D.Torquearm:(E)T1,(F)T2,(G)T3,(H)T4. 222

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A B C D E F G H Figure4-16. EntiremodelsurfaceSPLmapspresentedin1/3octavefrequencybands.Centerfrequencies:(A)200Hz,(B)250Hz,(C)315Hz,(D)400Hz,(E)500Hz,(F)630Hz,(G)800Hz,(H)1000Hz.Theresultsareforthebaseline=130conguration. 223

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A B C D Figure4-17. Coherencemeasurementsofcylinderunsteadypressuresensorsrelativetothecenterlinesensor,Z=0forthecongurationsof(A)=100,(B)=130,(C)=160,(D)=130inverted. 224

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A B C D Figure4-18. Coherencemeasurementsbetweencylinderandtorquearmelectretsensorsfor=100conguration.Torquearmreferencesensors:(A)T1,(B)T2,(C)T3,(D)T4. 225

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A B C D Figure4-19. Coherencemeasurementsbetweencylinderandtorquearmelectretsensorsfor=130conguration.Torquearmreferencesensors:(A)T1,(B)T2,(C)T3,(D)T4. 226

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A B C D Figure4-20. Coherencemeasurementsbetweencylinderandtorquearmelectretsensorsfor=160conguration.Torquearmreferencesensors:(A)T1,(B)T2,(C)T3,(D)T4. 227

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A B C Figure4-21. Coherencemeasurementsbetweencylinderandtorquearmelectretsensorsfor=130invertedconguration.Torquearmreferencesensors:(A)T1,(B)T2,(C)T4. 228

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A B C D E F G H Figure4-22. SurfacepressureprobePSDcomparisonsbetweenexperimentandsimulation.Cylindersensors:(A)Z=0,(B)Z=1D,(C)Z=2D,(D)Z=3D.Torquearmsensors:(E)T1,(F)T2,(G)T3,(H)T4. 229

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Figure4-23. Far-eldSPLcomparisonsofmodelcongurations(lineararraymicrophoneL4). Figure4-24. Far-eldSPLcomparisonsofallstandardmodelcongurations(100f800Hz)atM0.167. 230

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Symbol 100 MMM 110 120 130 + 140 150 160 / 130invtd. Figure4-25. OASPLasafunctionofshearlayer-correctedmicrophoneanglesforalltorquearmcongurationsatM0.167. 231

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A B C D E F G H Figure4-26. CoherencebetweenmodelsensorsandlineararraymicrophoneL4;(A),(E)=100,(B),(F)=130,(C),(G)=160,(D),(H)=130inverted.Cylinder:(A)-(D).Torquearm:(E)-(H). 232

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A B C D Figure4-27. ApplicationofStrouhalandMachnumberscalingtofar-eldspectraofthe=100conguration:(A)rawSPLvs.dimensionalfrequency,(B)M5-scaledSPLvs.StD,(C)M5-scaledSPLvs.dimensionalfrequency,and(D)M7-scaledSPLvs.dimensionalfrequency. 233

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A B C Figure4-28. ApplicationofStrouhalandMachnumberscalingtofar-eldspectraofthe=130conguration:(A)rawSPLvs.dimensionalfrequency,(B)M6-scaledSPLvs.StD,and(C)M7-scaledSPLvs.dimensionalfrequency. 234

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A B C Figure4-29. ApplicationofStrouhalandMachnumberscalingtofar-eldspectraofthe=160conguration:(A)rawSPLvs.dimensionalfrequency,(B)M5-scaledSPLvs.StD,and(C)M7-scaledSPLvs.dimensionalfrequency. Figure4-30. Illustrationofspectralscalingforselectmodelunsteadypressuresenorsforthe=160conguration:(A)cylindersensoratZ=3D(B)torquearmsensorT4. 235

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A B C Figure4-31. ApplicationofStrouhalandMachnumberscalingtofar-eldspectraofthe=130invertedconguration:(A)rawSPLvs.dimensionalfrequency,(B)M4-scaledSPLvs.StD,and(C)M7-scaledSPLvs.dimensionalfrequency. 236

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A B C Figure4-32. IllustrationoftheboundingboxfortheporousFW-Hcalculation:(A)frontview,(B)proleview,(C)isometricview. Figure4-33. Comparisonoffar-eldSPLfromsolidandporousFW-Hsolveroutputstothatoftheexperimentallineararraymicrophone.Resultsareforthe=130congurationatafreestreamvelocityofM0.167. 237

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Figure4-34. Comparisonoffar-eldSPLfromsolidandporousFW-Hsolveroutputstothatoftheexperimentallineararraymicrophone.Resultsareforthe=130congurationatafreestreamvelocityofM0.167. 238

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A B C D Figure4-35. Comparisonofbeammapsforthedierentbeamformingalgorithmsatanarrowbandfrequencyof4kHzforthe=130congurationatM0.167:(A)experimentalPSFusingDAS(torquearmmodelnotpresent),(B)DASwithmaximumpowerlocationindicatedby\"symbol,(C)RCBinnormalizeddB,and(D)DAMASinabsolutedB.Flowisfromrighttoleft. 239

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Figure4-36. Integratedlevel-spectraoftheDASandDAMASbeamformingalgorithmswithcomparisontoFFMAreferencemicrophone.Spectraplotteddowntoacut-onfrequencyof256Hzsinceitcorrespondstoanacousticwavelengthof53"(1.346m),whichisthedistancebetweentheFFMAandscanningplane. 240

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Figure4-37. Comparisonoffar-eldSPLbetweenFFMAcenterreferencemicrophoneandfree-eldmicrophonepositionedonoppositesideoftestsection.OppositemicrophonescaledtomatchFFMAdistancefromsourceregionusingEquation 4{4 .Theuncertaintyboundsforeachmicrophoneare1.14dB,ascomputedin Section3.5.3 241

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A B C D E F G H Figure4-38. Beamformingmapsusing(A)-(D)DASand(E)-(H)RCBalgorithmsatoctavebandfrequenciesforthe=100congurationatM0.167:(A),(E)1.008kHz,(B),(F)2kHz,(C),(G)4kHz,(D),(H)8kHz.PeakSPLinscanninggridindicatedby\"symbol. 242

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A B C D E F G H Figure4-39. Beamformingmapsusing(A)-(D)DASand(E)-(H)RCBalgorithmsatoctavebandfrequenciesforthe=130congurationatM0.167:(A),(E)1.008kHz,(B),(F)2kHz,(C),(G)4kHz,(D),(H)8kHz.PeakSPLinscanninggridindicatedby\"symbol. 243

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A B C D E F G H Figure4-40. Beamformingmapsusing(A)-(D)DASand(E)-(H)RCBalgorithmsatoctavebandfrequenciesforthe=160congurationatM0.167:(A),(E)1.008kHz,(B),(F)2kHz,(C),(G)4kHz,(D),(H)8kHz.PeakSPLinscanninggridindicatedby\"symbol. 244

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A B C D E F G H Figure4-41. Beamformingmapsusing(A)-(D)DASand(E)-(H)RCBalgorithmsatoctavebandfrequenciesforthe=130invertedcongurationatM0.167:(A),(E)1.008kHz,(B),(F)2kHz,(C),(G)4kHz,(D),(H)8kHz.PeakSPLinscanninggridindicatedby\"symbol. 245

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A B C D E F G H Figure4-42. NoisesourcemapsusingtheDAMASalgorithm(10,000iterations)ofprimarycongurationsatnarrowbandfrequenciesof(A)-(D)1.008and(E)-(H)2kHzatM0.167:(A),(E)=100,(B),(F)=130,(C),(G)=160,(D),(H)=130inverted.A20dBdynamicrangeispresentedinallplots. 246

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Table4-1. PhaseITestingMatrix:Surfacepressureandfar-eldacoustictesting FlowSpeedMeanSurfaceUnsteadySurfaceFar-eldBeamforming()(M)(Cp)(C0p;rms,PSD)(SPL) 1000.10y X-0.13y XX0.15y XX0.17 y y XX0.19y X-1100.17X-1200.17X-1300.10y X-0.13y XX0.15y XX0.17 y y XX0.19y X-1400.17X-1500.17X-1600.10y X-0.13y XX0.15y XX0.17 y y XX0.19y X-1300.10y X-Inverted0.13y XX0.15y XX0.17 y y XX0.19y XMeasurementKey:cylinder(circumferential), cylinder(spanwise), y torquearm(gapowsurface), torquearm(rearwakesurface) Table4-2. ValuesofC0p;rmsforcylinderunsteadysurfacepressuresensors(U1=58m/s) ()Z=0Z=0:42DZ=1DZ=1:42DZ=2DZ=2:42DZ=3D 1000.01800.02570.03470.04350.06020.05610.06001100.01850.02840.04020.05410.09150.09270.12071200.01780.02950.04380.05840.09810.10610.13271300.01900.03390.05610.07260.11580.12470.16281400.01720.02910.04860.06280.10000.10570.14671500.01770.02900.04460.05910.10120.10350.15151600.02160.03330.05190.07810.12880.13000.1711130Inv.0.09720.17290.25910.16120.10440.06820.0387 247

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Table4-3. ValuesofC0p;rmsfortorquearmunsteadysurfacepressuresensors(U1=58m/s) ()T1T2T3T4 1000.15220.14850.17160.17931300.15290.20820.21800.25241600.08630.18500.25430.2378130Inv.0.02000.0353-0.0616 Table4-4. Advantagesanddisadvantagesofbeamformingalgorithms AlgorithmAdvantagesDisadvantages DAS-Computationallycheap-Lowresolution-Integratedabsolutelevels-HighsidelobelevelsRCB-Excellentresolution-Yieldsincorrectpowerlevels-Lowsidelobelevels-LimitedtosourcesofhighSNRDAMAS-Deconvolvedacousticoutput-Computationallyexpensive-Integratedabsolutelevels-Visualizationdiersfromotheralgorithms 248

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CHAPTER5FLOWFIELDMEASUREMENTS Theprimaryreasonsforperformingoweldmeasurementsaroundthetorquearmmodelweretomeasurethemeanoweldbehavior,quantifythree-dimensionalturbulencestatistics,andattempttoobtaintime-resolvedestimatesofthevortexsourcetermsofhighestenergythatareresponsiblefornoisegeneration.ThemeasurementparametersforthedierentSPIVregionsaresummarizedinTable 5-1 .AnillustrationoftheseplanesisalsoprovidedinFigure 3-37 .Notethatsnapshotswereremovedfortheestimationprocessingiftheydisplayedaninvalidvectorpercentagegreaterthan10%. 5.1MeanFlowFieldandTurbulenceSurveys Themeanoweldwasrstanalyzedforallmeasurementplanes.Thiswasdonetoprovideatraditionalstatisticalanalysisoftheoweldtoidentifyregionsthatwarrantfurtheranalysis.Inadditiontothemeanvelocitycomponents,thevorticityandtotalturbulencekineticenergy(TKE,k)werecalculated.Sincethevelocitydatawasacquiredwithinasinglesheetinthexyplane,onlytheout-of-planecomponentofvorticitycouldbecomputed.TheTKE,however,consistsofallthreecomponentsofnormalReynoldsstressandisdenedas k=1 2)]TJ ET q .478 w 203.37 -399.89 m 222.29 -399.89 l S Q BT /F3 11.955 Tf 203.37 -409.44 Td[(u0u0+ v0v0+ w0w0:(5{1) IdentifyingowregionsofhighTKEandshearReynoldsstresscomponentscouldbeindicatorsofnoisegeneration.Regionsofhighvorticitycanalsohighlightregionsofnoisegenerationduetovorticalinteractions.Theresultspresentedinthissectionconsistofspatialeldspresentedaslledcontourimagesandprolecuts.Thecontourimagesareplottedwithinthemaximumandminimumboundsoftheelddata,andallprolecutsareplottedwithRMSuncertaintybounds(consistingofbothbiasandrandomcontributions). Themeanvelocitymagnitude,TKE,andZ-vorticityareplottedfortheprolesatZ=0,-1.175,-2.175,and-3DinFigures 5-1 5-4 .Ifattentionisfocusedonthemean 249

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velocitymagnitudecontours,itcanalsobeseenthatthemeanstreamlinepatternsaresuperimposed.Thesestreamlinepatternsareinteresting,particularlyfortheZ=0height.Asthegureshows,thetorquearmhingeislocatedapproximatelythreecylinderdiametersfromthecylindercenteraxis.Thisisadistancethathasbeenshowntoyieldatraditionalsinglecylinderrecirculationpatternforthecaseoftandemcylindersatanequivalentspacing( Neuhartetal. 2009a ).Theobservedbehavior,however,isseentodeviatefromthis,displayinginsteadasingularityatapproximatelyx=D=2.Thisnon-traditionalrecirculationpatternisbelievedtobeduetothelackofspanwiseuniformityasopposedtowhatwouldbethecaseforatandemcylindersetup.Meanwhile,therecirculationsdonotbecomestronglyapparentuntiltheheightofZ=3D.Thisisduetotheowimpingingonthetorquearm(whichisofwidercross-sectionthanthecylinderatthisheight),andcirculatingbacktowardsthecylinder. IfattentionisfocusedontheTKEresults,itcanbeseenthatthereisagradualincreaseinmeanTKElevelsasthedistancebetweenthecylinderandtorquearmdecreases.Inparticular,thisincreaseisseentotakeplaceinthegapowregion,withthewakeexhibitingpeaknormalizedTKElevelsaround0.1.ThepeakTKElevelsinthegapowregionareseentoincreasebyafactorof2.5ingoingfromthecenterlinetoZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(3D.Furthermore,themeanvelocityprolesinthegapowdisplaysimilaritiesbetweentheheights,withthelargestdierencesoccurringfortheWcomponent.Thepeakamplitude,whichisseentooccuratthemodelcenterline(y=D=0),increasestoabout0:2U1forthemeasuredplanesbelowZ=0.Thisproleisalsoseentobecomebroaderasheightdecreases,whichcoincideswiththetorquearm'sincreasingthickness.Fortheturbulenceproles,someinterestingobservationscanbemade.First,thecylindershearlayersareclearlymadevisiblebythetwinpeaksinthe u0u0and u0v0plots,whichremainfocusedaroundy=D0:5forthetestedproles.Oneveryinterestingtrendishowthe w0w0prolesarehigherthanthe v0v0neary=D=0atZ=0,butisthendominatedby v0v0asthemodelheightdecreases.Thismeansthatwhiletheout-of-plane 250

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componentofvelocitydoesincreasewithclosercylinder-to-torquearmproximity,thelateralvelocityuctuationsbecomedominantinthecoregapowregions. TheincreaseinTKEandindividualReynoldsstresslevelsattheheightsofcloseproximitybetweenthecylinderandtorquearmarepreliminaryindicatorsthattheseregionsmaybethemostresponsiblefornoisegeneration.Furtheranalysisisrequired,however,sincethestatisticsoftheoweldprovideonlypartialinsight.Asthemajorityoftherestofthischapterwilldiscuss,analysisofinstantaneousvectoreldsisimportantforbothcomparativepurposesbetweenSPIVandPowerFLOWsimulations,aswellasfortime-resolvedestimationoftheoweld.First,itisimportanttoidentifytheowfeaturesincommonbetweentheexperimentalmeasurementsandsimulationresults. 5.1.1SimulationComparisons TheexperimentalmeanandturbulentoweldstatisticswerecomparedwiththoseofthePowerFLOWsimulationstojustifytheircomparisonsoftheestimatedLambvectorcalculations.ThemeanvelocitymagnitudeandTKEcontoursatheightsofZ=0andZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(3DareshowninFigures 5-5 and 5-6 .AstheresultsforZ=0show,thevelocitymagnitudecontoursareinexcellentagreement,particularlyregardingtheinnergapowstreamlinebehavior.Asthestreamlinesshow,boththeSPIVandsimulationresultsshowanearlyidenticalrecirculationsingularityatapproximatelyx=D2.Whilethereisaslightdierenceinthelaterallocationofthesingularity,thisappearstobeanearlysymmetriclateraldierencebetweenthem.Anadditionaldierenceisthewidthofthecylinderwake,whichisslightlywiderinthesimulationresults.Thisismostlikelyduetoearlierowseparationfromthecylinder,whichcanbeconrmedbythefar-eldpredictionofFigure 4-33 .Thisgureshowsasecondarypeakat336Hz,whichisbelievedtobeduetointermittentsheddingfromthecylinder.ThisfrequencyislowerthanthatexperimentallymeasuredforasingletrippedcylinderataowspeedofM0.17,whichhappenedtobearound416Hz.Theearlierseparationisthereforeduetothesurfaceroughnessboundaryconditionimposedonthecylinder.Theslightlywiderwakeisalso 251

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visibleintheTKEcontourlevelsofFigure 5-5D .ThesimulatedlevelsofTKElevelsarealsoconsistentlylowerthanthoseexperimentallymeasured. ThemeanoweldandTKEbehaviorsatZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(3DforboththeSPIVandPowerFLOWsimulationsareshowninFigure 5-6 .Whilethestreamlinepatternsforthegapowandnearwakeregionsaresimilar,theyhaverecirculationpatternsofslightlydierentshape.Thisisbelievedtobeduetoasymmetricowbehavioratthisheightfortheexperiments,whichwasnotfullycapturedbythesimulation.ThepresenceofexperimentalasymmetryisalsoevidentintheTKEcontoursinFigure 5-6B .Whilethelevelsareverysimilarinthegapowregionsbetweenthetwo,theenergyismuchmoredistributedalongthelowerportionofthegapowregionfortheexperiment,whilethesimulationshowsasymmetricenergydistributionwithafocalregionofintensityatthecenterofthetorquearmface. Aswasdenedin Section1.3.1 ,thereducedLighthillstresstensorofEquation 1{7 containsthesixcomponentsofReynoldsstress,whichincludethenormalandshearcomponents.ThesearethefundamentaltermsofLighthill'sacousticanalogythatrepresentnoisegenerationofaturbulentow.Sincethegapowregionisbelievedtobetheprimaryregionsofnoisegeneration,ReynoldsstresscomparisonsbetweenPowerFLOWandSPIVareperformed.Figures 5-7 and 5-8 showtheresultsoftheexperimentalandsimulationReynoldsstressesalongaslicelocatedmid-waybetweenthecylinderandtorquearmatheightsofZ=0and)]TJ /F1 11.955 Tf 9.3 0 Td[(3D,respectively.Theseplotsshowmixedresults.Again,thereisevidenceoftheslightlywiderwakepredictedbyPowerFLOWbyobservingthepeaksinRSuu,whicharerepresentativeofthecylindershearlayer.Inadditiontobeingoveralllowerinamplitude,thepeakvaluesareclosertoy=D0:7ratherthanthe0.5indicatedbytheexperimentalresults.Furthermore,levelsofRSvvaresignicantlyunder-predicted.Interestingly,however,theRSwwlevelsareveryclosetotheexperimentalvaluesforbothmeasurementplanes.Anotherinteresting 252

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featuretoobserveisthatthepredictedshearReynoldsstressesshowmuchbetteroverallagreementwiththeSPIVresultsforbothplanes. 5.1.2VorticitySurveys Surveysofvorticitycanassistwithidentifyingtheowstructuresresponsiblefornoisegeneration.Aswasfoundin( Chapter4.1.2.2 ),broadspectralhumpswereobserved,whichareincontrasttothehigh-amplitudesinglespectralpeaktypicalofblubodyvortexshedding.Thiswasbelievedtobetheresultofthevaryingtorquearmwidth.Therefore,itwasbelievedthatobservationofthedierentvorticitydistributionsatdierentheightscouldhelpidentifywhichregionswereresponsibleforthenoiseatdierentfrequencies.Sinceverylittleoftheuctuatingbehaviorcanbeinferredfromtime-averagedvorticityelds,instantaneoussnapshotsareconsideredinstead. InstantaneoussnapshotsofZ-vorticityforthegapowmeasurementplanesatZ=0,-1.175D,-2.175D,and-3DareshowninFigure 5-9 .Thebehaviorisseentovarygreatlyatthedierentmeasurementplanes.ForZ=0and-1.175D,individualvorticesareclearlyseentoshedfromthecylindersurface.However,atZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(1:175D,thevorticesareactuallyseentoconvergeontothetorquearmsurface,ratherthandispersinglaterallyoutwardasisthecaseforZ=0.Thetwolowestheights,however,showamuchdierentbehavior.Ratherthantherebeinganobservablepresenceofindividualvortices,therearetwoprimaryvorticalregionsofoppositesense.Thisoccursasaresultofthecloseproximityofthetorquearmandlargerwidthascomparedtothecylinder,andcanhelpexplainthemeanrecirculationpatternsobservableinFigures 5-3A and 5-4A ItwasalsodesirabletoensurethatthePowerFLOWsimulationexhibitedsimilarbehaviorandtrendsinZ-vorticity.ThePowerFLOWoweldresultsarefromahigh-frequencyowmeasurementofselectplanesthroughtheoweld.ThesemeasurementplanesoccurredatheightsofZ=0,1D2Dand)]TJ /F1 11.955 Tf 21.3 0 Td[(3D.SamplesnapshotcomparisonsatheightsofZ=0andZ=)]TJ /F1 11.955 Tf 9.29 0 Td[(3DarepresentedinFigure 5-10 .Theseheightswerechosenforcomparisonsincetheyaretheonesthatarenominallyidenticalbetweenexperimental 253

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measurementsandsimulation.NotethatthePowerFLOWimagesarepresentedwithamplitudescalesidenticaltothosepresentedintheexperimentalones.Bothexperimentalandsimulationdataagreewell,exhibitingbothsimilarvortexdistributionsandintensities.BothsnapshotsforZ=0showverysimilarlateraldispersionofvortices,whilethoseforZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(3Dshowacommongapregionoftwinlargevortexrecirculations. ThecomparisonsofmeanandturbulencestatisticsbetweentheSPIVandPowerFLOWdatasetshavebeenshowntobeinreasonableagreement.Tofurthertestthiscomparison,observationofinstantaneousvorticitysnapshotswasalsoperformed.Thevorticitydistributiontrendsandintensitieswerefoundtoagreewellwithoneanother.Basedonthesesimilarities,thePowerFLOWresultsaretobeusedasreferencedatatotheexperimentaldataforestimationoftheoweld.Thefollowingsectiondiscussestheoweldestimationprocedure,results,andtheapplicationoftheestimatestocomputealow-orderrepresentationofthesourcetermsofthevortexsoundanalogy. 5.2FlowFieldEstimation Linearstochasticestimationwasperformedonthelowtime-sampledSPIVdatatodevelopalow-ordertime-resolvedestimateoftheoweld.ThealgorithmimplementedinthisstudyismtdLSE-POD,inwhichstochasticestimationofPODexpansioncoecientswasperformed.TheestimatedPODexpansioncoecientsarecomputedas~a(s)(t)=A(s)mpm(t),whereA(s)maretheLSEcoecientscomputedfromatime-delayanalysisgiventheactualPODcoecientswiththesynchronizedpressureprobetimeseries,andpm(t)representacontinuoussetofpressureprobetimedatathatwereacquiredimmediatelypriortotheSPIV/synchronizedprobetrial.Thenewestimatedcoecients,alongwiththepreviouslycomputedPODspatialmodes,allowforatime-resolvedlow-ordervelocityeldreconstruction.Multipletimedelaysinthepressureprobecross-correlationsweretestedontheestimationuntilameanoptimizedtimedelaywasidentiedonwhichtobasetheestimation.Theoweldestimatewasthenusedtocomputelow-orderestimatesoftermsattributedtoacousticnoisegeneration,includinguctuatingz-vorticityandthe 254

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Lambvectorterms.TherststepthatwasperformedwasPODonallthreecomponentsofvelocity. Aswasstatedin Chapter3.6.5.3 ,theestimatedPODexpansioncoecientsarecomputedas~a(s)(t)=A(s)mpm(t),whereA(s)marecomputedfromatime-delayanalysisgiventheactualPODcoecientswiththesynchronizedpressureprobetimeseries,andpm(t)representacontinuoussetofpressureprobetimedatathatwereacquiredimmediatelypriortotheSPIV/synchronizedprobetrial.Thesenewestimatedcoecients,alongwiththepreviouslycomputedPODspatialmodes,allowforatime-resolvedlow-ordervelocityeldreconstruction.Oncethislow-ordervelocityeldestimatewasdeveloped,itwasusedtocomputetheLambvectorsourcetermsofthevortexsoundanalogy.Morespecically,thesourcetermcomponentcontributionsthatcouldbeextractedfromthetwo-dimensionalPIVplanewerecomputedandcomparedtoasimilarlow-orderrepresentationofthesamesourcetermscomputedfromthePowerFLOWsimulations.Thesimulationresultswerethenusedtocomputeandanalyzethecontributionsofthethree-dimensionalvorticityandvelocitytermstothecompleteLambvectorsourceterms. 5.2.1PODResults Priortoperformingstochasticestimation,thePODmodesofthethree-dimensionaluctuatingvelocityeldwereanalyzed.Thiswasforavarietyofreasons:visualizationofthespatialmodalbehaviorofthedierentscannedregions,identicationofenergycontentwithinthesemodes,andwhichofthesemodesmightbesuitablewithwhichtoperformestimation.Thelatteritemwasdeterminedbytheprevioustwo.Inotherwords,itwasdesirablethatthemodesselectedtoconstructthelow-orderowestimateswouldcaptureaconsiderableamountofowenergyandtheowdynamics.Therefore,thePODspatialmodesandtheirenergybreakdownwereanalyzed. Considertheextremesofthemeasurementregions,Z=0DandZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(3D.Theseregionshaveverydierentcross-sectionsinthexyplane,withthetorquearmcross-sectiongoingfrom33%narrowerto25%widerthanthecylinderandbeinglocatedoverthree 255

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cylinderdiametersawaytowithinonediameter.Therefore,itwasbelievedthatanalysisofthemodesofthesedierentheightscouldprovideinsightintothedierentowmechanicsalongthemodelheight.Inaddition,observationoftheenergydierencesbetweensuccessivemodesprovidesanadditionalmetriccomparison. TherelativeamountofenergywithinaPODmodesiscomputedas(s)=PNs=1(s),where(s)istheeigenvalueofthesthPODmode.ThemodalenergyfractionsforthersttwentymodesareshownforthesetwoheightsinFigure 5-11A and 5-11B .Astheresultsforthegapowshow,thereisconsiderablymoreenergyinthersttwomodesofthegapowatZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(3DthanatZ=0D.Thereisalsoachangeinenergyfractionofapproximately0.14(14%)betweenthesersttwomodesforZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(3D,withlessthan2%dierenceforZ=0.ThisshowsthatthemodalenergyismuchmoredistributedacrossthemodesfortheZ=0gapowregion.Ifattentionisshiftedtothenearwakemodes,similartrendsareobserved,howeverreversedbetweenthetwoheights. ThewakeofZ=0Dshowsthersttwomodeswithenergyfractionsof12and10%respectively,withadropof6%energytothenextmode.TheZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(3Ddatashowsadierenttrendinwhichtheenergyismoredistributedinthelowermodes,showingamuchmoregradualenergydecay.Theseresultsareveryinformativeastothepresenceofcoherentstructuresaswellaslevelsofturbulence.Thewakeresultsarereasonableinthattandemgeometriesoflargerdownstreamspacingareexpectedtohavehigherlikelihoodofvortexshedding.However,thisbehaviorwouldalsobeexpectedtoapplyfortheinnergapowregion.However,thenon-uniformspanwisegeometryofthegapowregionisbelievedtodisrupttheformationofcoherentvortices.ItisalsoworthrecallingthecontourimagesinFigures 5-1 and 5-4 .WhilethegapowregionofZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(3DhashigherlevelsofTKE,thereisalsoarecognizablerecirculationregionbehindthecylinder.Asforthewakeregions,thelargewidthofthetorquearmatZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(3Danditscloseproximitytothecylindermostlikelyinhibitstheconvectionofdownstreamvorticesshedfromthe 256

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cylinder.ThetorquearmhingeatZ=0Dhowever,issmallerthanandfurtherawayfromthecylinder,andthusismorelikelytoshedcoherentvortices. TherstfourPODmodesofstreamwiseandtransversevelocitycomponents(u,v)forthegapowandnearwakeregionsfortheheightsatZ=0andZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(3DareshowninFigures 5-12 5-15 .ForZ=0,thePODmodesshowanorganizedpattern,forthemostpart.Therstandsecondmodesofuinthegapowshowanearlyperfectlysymmetricpatternconsistingofasinglehigh-energystructurerepresentativeofthecylindershearlayer.Thethirdmode,however,isabitambiguous.Itappearstoportrayasimilarcylindershearlayerstructurewithanenergybuild-upnearthetorquearm.Thefourthmodemeanwhileshowsanasymmetricpatternwithprimarystructureshighlightingtheshearlayerregionsandsecondarystructuresthatappeartobeoriginatingfromthetorquearm.Meanwhile,thenearwakeregionshowsmodesthataremoretypicalofthoseofablubody.Therstandsecondasymmetricmodesarenearlyidenticaltothosecomputedby Durgesh&Naughton ( 2010 )forthewakebehindawedgewithanellipticalleadingedge.Thethirdandfourthmodesarenearlysymmetricpairsthatbeararesemblancetothefourthmodeof Durgesh&Naughton ( 2010 ).Ifattentionisfocusedonthersttwovmodesforthegapowregion,itcanbeseenthattheymakeupapairofstructuresthatappeartorepresentthehighlevelsoftransversevelocitynearthetorquearmsurface.Thersttwomodesforthenearwakeareagainnearlyidenticaltothoseof Durgesh&Naughton ( 2010 ),withthethirdandfourthmodesbeingasymmetricpairs.Finally,thefourthmodeofthegapowshowstwohigh-energystructuresinacongurationverysimilartotherstmodeofthewakeregion.Thismakessensesincethelargespacingbetweenthecylinderandtorquearmatthisheightwouldpermitthewaketodevelopinamannersimilartothatofasinglecylinder( Neuhartetal. 2009a ). IfattentionisfocusedonthePODmodesofZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(3DinFigure 5-14 and 5-15 ,someinterestingobservationscanbemade.TherstuandvmodesofthegapowregionareconsiderablydierentfromthoseofZ=0.(1)uportraystwolargestructuresinthe 257

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vicinitiesoftheshearlayers,and(1)vshowstwostructurescenteredabouty=D=0.Recallthatthismodecontainsmorethan26%ofthetotalmodalenergy(Figure 5-11A ).Furthermore,thersttwoumodesforthenearwakeregionshowverysimilarstructurestothoseofZ=0,howeverappeartobedistortedandasymmetric.ThisisbelievedtobeduetothemuchclosertandemspacingatthisheightascomparedtoZ=0.Thersttwovmodesshowatrendsimilartothoseofu.Thesecondandthirdumodesforthegapowappeartoshowasymmetricpatterninwhichtwomodalstructuresipfromside-to-sidealongthetorquearmsurface.Finally,thefourthvmodeofthenearwakeregionisverysimilartothethirdmodeof Durgesh&Naughton ( 2010 ). 5.2.2TimeDelayAnalysis Aswasstatedin Chapter3.6.5.3 ,theestimationwasattemptedonaselectsetofthePODexpansioncoecients,ratherthanontherawSPIVvelocitydata.However,itisimportanttorecallfrom Chapter3.6.5.2 thatthesePODexpansioncoecientswerecomputedfromthenon-time-resolvedSPIVdatasetsandapplytoallthreeuctuatingvelocitycomponents.PerformingestimationonthePODcoecientswasexpectedtoimprovetheaccuracy,sincethesmallerturbulentfeatures(thatproducepoorcorrelations)wouldbeleftout.Thus,onlythecoherentstructuresshouldremain.Ofcourse,owaroundthetorquearmmodelunderinvestigationposesinterestingchallenges,sinceitisahighlyturbulentowscenario.Despitethis,however,theredoappeartobecoherentstructures(atleastwithinthegapowregion)asevidencedbytheinter-sensorcoherencemeasurementspresentedin Chapter4.1.2.4 .Themulti-timedelaycapabilitywasexpectedtoalsoimprovetheestimationaccuracy,sincetheresultingcross-correlationsbetweenthevariousmodelprobecombinationswouldbeunlikelytoyieldhighcorrelationsatazerotime-delay.Therefore,estimationwasperformedoverarangeoftimedelays =U1 D;(5{2) 258

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whererepresentsthesymmetriccorrelationtimedelay.Recallfrom Chapter3.4.2.5 thattheelectretsensorsweresubjectedtoatime-domainreconstructionusingsystemidenticationinordertoaccountfortheirrecessedconguration.ThiswasnotnecessaryfortheKulitesensorssincetheywereush-mountedwiththemodelsurfaceanddisplayedaatfrequencyresponseupto6kHz.Allsensorswerelow-passlteredwithacut-ofrequencyof1.216kHzsincethecoherenteventswereobservedtooccurbelowthisfrequency( Chapter4.1.2.4 ).Inaddition,thepressuredataweredownsampledbyafactorof16toyieldanestimationsamplingrateof4.096kHz.ThepressuredatawereacquiredsynchronouslywiththePIVsnapshots,withatwo-sidedtimedelayof0.03125sec.(max48).Thisleavesatotalof256pressuresamplespersnapshot,with127priortothesnapshot,oneattheapproximatesnapshotoccurrence,andanother128afterthesnapshotoccurred. Theestimationaccuracywasdeterminedusingameansquaredierencemethod.AsquareddierencebetweentheestimatesofthePODexpansioncoecients~a(s)(t)andtheactualcoecientsa(s)(t)wascomputedfors=f1;2;;rgmodesandsummed.Thisresultingsumwasthennormalizedbythesumofthesquarevaluesoftheactualexpansioncoecients.ThisresultsinatotalofNestimationdierences,oneforeachsnapshot.Mathematically,thisdierencecalculationisdenedas ~a(t)=Prs=1~a(s)(t))]TJ /F3 11.955 Tf 11.96 0 Td[(a(s)(t)2 Prs=1a(s)(t)2;(5{3) wherer
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achievetheminimummeanestimationdierence.Initially,theestimationaccuracywascomputedforuptotwentytimedelays,ormax=11:15.However,someofthemeasuredregions,namelythewakeregionsofthethreelowestmeasuredheights,didnotreachaminimizedestimationdierence.Therefore,thisnumberoftestedtimelagswasincreasedbyafactoroftwo.NotethatwhilethePODexpansioncoecientsremainunaectedbychangingthenumberoftimedelays(havingasizeof[Nr]),theLSEcoecientmatricesincreaseinsizewithincreasingtimedelay.Specically,thesizeoftheLSEcoecientmatrixAisofsize[(2Fs+1)Npr],whereNp=9representsthetotalnumberofprobes. TheresultingmeanestimationdierencesforthesetimedelayrangesarepresentedinFigure 5-16 .ThegapowresultsofFigure 5-16A showaninterestingtrendofdecreasingmeanestimationdierenceasthemeasurementheightchangesfromZ=0toZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(3D.Ingeneral,theoptimaltimedelayalsoappearstodecreaseastheheightdecreases,withanexceptionforthecaseofZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(2:175D,whereitdisplaysanominaltimedelayofnom=3:72justslightlylargerthanthatforZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(1:175D(nom=2:97).Furthermore,themeanestimationdierencesforthewakeregionsinFigure 5-16B showanearlycompletelyoppositetrend,wheretheregionsofZ=0and)]TJ /F1 11.955 Tf 9.3 0 Td[(0:592Dhavethelowestmeanestimationdierences.Unfortunately,theseestimationdierencesarestillfairlylarge,beinggreaterthan0.5.Thisisbelievedtobemostlikelyduetonon-idealprobeplacementsforthewakemeasurements,thusresultinginpoorcorrelationsbetweentheprobesandPODexpansioncoecients. Someinsightastowhytheestimationsperformedbetterinthegapowregionsthanthewakeregionscanbeobtainedbyobservingthesensorcross-correlations.AsetofthesearepresentedinFigure 5-17 .Figure 5-17A displayscross-correlationsbetweenthecylinderelectretsandtheKuliteslocatedonthetorquearmgapowsurfaceclosesttotheedge(Figure 3-40 forreference).Thesesensorswereselectedinordertorepresenttheconvectionofowstructuresfromthecylindertothetorquearm.Astheresults 260

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show,thereisanobservabletrendofanincreaseinthepeakcorrelationvalueasthemeasurementregionisdecreasedfromZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(0:592DtoZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(3D.Thisseemsreasonablesincethereisahigherlikelihoodofcoherentstructuresconvectingfromthecylindertothetorquearmasthedistancebetweenthecylinderandtorquearmdecreases.Furthermore,thecross-correlationswerecomputedbetweenthetorquearmKulitesthatwereclosesttothetorquearmedgeandtheedgeelectrets,theresultsofwhichareshowninFigure 5-17B .Ratherthandisplayingasinglehigh-amplitudecorrelationpeakcharacteristicofstreamwiseconvection,therearetwopeaks,oneeachforpositiveandnegativetimedelays.ItisalsoimportanttonotethatthepeakcorrelationamplitudesforthesesensorpairsareapproximatelyhalftheamplitudeofthoseinFigure 5-17A ,withanexceptionforthesensorsapplicabletotheZ=)]TJ /F1 11.955 Tf 9.29 0 Td[(0:592Dcase.Thesecorrelationshelpprovideinsightastowhythegapowregionsatlowerheightsperformedbetterwiththeestimation,aswellaswhythetorquearmwakeregionperformedsopoorly. Thequestionofhowmanymodestofactorintotheestimationmustbeaddressed.Itisimportanttounderstandthatthegoaloftheestimationisnottoreproducetheentireoweld,butrathertheoweldmodesofhighestenergy.Attemptingtoreproducetheentireoweldwouldresultinextremelylargeestimationdierences.Therefore,aseriesofestimationtrialswereperformedontheZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(3Ddatawiththenumberofmodessettor=5,10,and20.TheresultsofthistestareshowninFigure 5-18A .Astheresultsshow,thereisanevidenttrendofincreasingmeanestimationdierenceasthenumberofmodesinputintotheestimatorincreases.Itisstillunclear,however,astowhetherornotthemeanestimationdierenceisthenominalindicatorofestimationperformance.Thisisbecausetheturbulentnatureoftheoweldinquestionmayresultinlackofcorrelationswiththetime-resolvedprobes.AdditionalinsightcanbegainedbyobservingthemodalenergysummationsforthesamecaseinFigure 5-18B .Astheseresultsshow,therstvemodescontainapproximately51%ofthetotalenergyinthePODdataset.Increasingthistotenmodesyieldsanincreaseinenergyto59%,thento67.5%usingtwentymodes.The 261

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asymptoticbehaviorofthemodalenergysummationssupportsthenotionthatlimitingtheanalysistoasmallernumberofmodescouldpotentiallycapturethemoreimportant\bulk"owfeaturesresponsiblefornoiseatfrequenciesbelow1kHz. 5.2.3Low-OrderVelocityFieldReconstruction ThevelocityeldswerereconstructedinitiallyusingtherstvePODmodesofeachdataset.However,asitwillbecomeevident,thiswasnotadequateforcapturinganacceptablelow-orderbehaviorofthehigherlevelcalculations,suchasvorticityandtheLambvectorcomponents.Therefore,thisnumberofmodesincorporatedintotheestimation,aswellasthesequencewasvaried.Thismeansthattraditionally,LSE-PODand/orQSE-PODhavebeenperformedwiththemodesinconsecutiveorder.Whilethishasbeenshowntobesucientformoregeometricallysimpleand/orlowerspeedapplications,thehigherleveltermssoughtafterherewarrantdierentmodecombinationstocapturetheowbehavior.BasedonthemeanestimationdierencesinFigure 5-16 ,thevelocityeldreconstructionwasrsttestedonthegapowdataofZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(3DandthenearwakedataofZ=)]TJ /F1 11.955 Tf 9.29 0 Td[(0:592D. Ademonstrationofthelow-orderestimationofthevelocityeldsforthegapowatZ=)]TJ /F1 11.955 Tf 9.29 0 Td[(3DandthenearwakeofZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(0:592D,areshowninFigures 5-19 and 5-20 ,respectively.Theseguresshowthestreamwisecomponentofvelocitynormalizedbythefreestreamvelocity(58m/s).Tobeclear,Figure 5-19A istheoriginalSPIVsnapshot,Figure 5-19B isthelow-ordermodelrepresentationofthissnapshotusingtherstvePODmodes,andFigure 5-19C istheestimateofthelow-ordermodelforthissnapshot.ThesamerationalityappliestoFigure 5-20 .AsFigure 5-19B shows,thelow-orderrepresentationcompareswellwiththebulkowbehavioroftheoriginalSPIVvectoreldofFigure 5-19A .Theprimaryowfeaturesthatarenotretainedarethehighlevelsofowreversalandtheextentofthediversionofthecylindershearlayerduetoit'simpactonthetorquearm.Inotherwords,theshearlayerisseentodivertdowntobelow-1D,whilethelow-orderrepresentationoftheshearlayeronlyextendsdownto 262

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about-0.65D.Finally,Figure 5-19C showstheresultingestimateofthevelocityeldusingthelow-ordermodel.Theonlydiscernibledierencebetweenthisandthenominallow-orderrepresentationofthesnapshotisthatthevelocitydecitintheshearlayercoreregionisslightlymoreelongatedthanthenominalone.Theestimationdierenceforthisspecicsnapshotwascomputedtobeonly=0:019(1.9%).VerysimilarfeaturesareobservedinFigure 5-20C ,withboththenominallow-orderreproductionandthelow-orderestimateeectivelyportrayingthebulkowfeaturesofthevelocityeld.Again,theonlyappreciableowfeaturesnotcapturedbythelow-ordermodelarethehighamplitudenegativevelocityregions.Forthiscase,theestimationdierencewascomputedtobe=0:004(0.4%),whichisconsiderablylessthantheoneshowninFigure 5-19C .Eventhoughthisparticularsnapshothasamuchlowerestimationdierence,however,themeandierencefortheentiredatasetwasconsiderablyhigherthanthatforthegapowdataatZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(3D. WhiletheinitialestimationresultswiththeuseofvePODmodesseemtocapturetheprimaryowfeaturesfromavelocitystandpoint,thisdoesnotnecessarilyapplyforthecaseofthevorticityandLambvectorterms.Therefore,aqualitativetestofconvergencewasperformedonthersttwentyPODmodes.ThisconsistedofsimpleobservationofthemodesforcommonfeaturesusingadierentnumberofvelocitysnapshotsinputintothePODsolver.ThenumberofsnapshotsinputintothePODsolverwasvariedbetween100,200,400,and800.ThePODmodesofuvelocitywereobservedforthistest.TheresultsshowedthatthersteightPODmodesconvergedwell,howevertheninthandtenthdidnot.Thenextmodesfoundtoconvergewereelevenandfourteen.Therestofthersttwentymodesshowedconsiderableuctuationsforthedierentsnapshotsets.Ademonstrationofbothaconvergentandanon-convergentsetofPODmodesispresentedinFigure 5-21 .ThecontourimagesinFigures 5-21A 5-21D showaclearconvergencetoanalsmoothedrepresentationofthemodalshapes. 263

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Theperformanceofaten-modemodeloftheoweldwasthentestedbetweenamodelconsistingofthersttenPODmodes,andoneconsistingofmodess=[1,...,8,11,14].Thesemodeswereselectedbecausetheywerefoundtopasstheconvergencetestoutofthersttwentypossiblemodes.Figure 5-22 presentstheresultsofestimationusingveandtenPODmodes.Fundamentally,thenerfeaturessuchasindividualvorticesbecomereplacedwithasmoothmodalrepresentationofvorticity.Theresultsshowsimilarbehaviorbetweenthedierentmodecombinations,howevertherearesomeminordierencesintheshapesandintensitiesofthemodestructures.Theestimationdierencesforthisparticularsnapshotare=0.018,0.048,and0.042forthe5-mode,10-mode,andcustom10-moderepresentations,respectively.Bothofthe10-modecasesexhibithigherdierencesthanthe5-modeone,howeveronlyfractionsofapercentdierencebetweeneachother.Furthermore,theoptimizedmeanestimationdierencesoftheentiresnapshotrecordforthethreecasesare =0.351,0.415,and0.411.Therefore,inameaneldsense,thereisverylittleimprovementwiththeuseofthecustomized10-modesetascomparedtothersttenmodes,andapoorermeanestimationwhencomparedtothe5-modeset.Itisimportanttorealize,however,thattheinclusionofadditionalmodesintotheestimationwillinevitablyresultinincreasedmeanestimationdierences.InsteadoffocusingontheestimationperformanceofanarbitrarysetofPODmodesinameansense,thesimulationresultscanbeusedtoidentifyPODmodesincommonwiththeSPIVmeasurements. 5.2.4PODAnalysisonPowerFLOWResults ThePowerFLOWsimulationresultswerethenconsultedforPODanalysis.Thepurposeofthiswastodeterminemodesthatbothsimulationandexperimenthaveincommon,andtotesttheresultingLambvectorestimationusingthesecommonmodes.AsinglemodeestimationtestwasthenconductedwiththeSPIVdataandcomparedtothesinglemoderepresentationsoftheLambvectorpartialterms.ThepurposeofthissinglemodetestwastodeterminethemodesfromtheSPIVdatasetsthatagreedthebestwiththosefromPowerFLOW.SimilartotheSPIVdata,PODofuctuatingu;v;andw 264

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velocitycomponentswasperformedonthesimulatedoweld.ThePODwasperformedonatotalof1,193snapshotsthatspannedtheconvergedsimulationtimeof0.32seconds.Thisowelddatasetwaslow-passlteredatacut-ofrequencyof1.216kHzanddownsampledbyafactoroffourfromtheoriginal4,773snapshotsetsampledatarateof14.916kHz.Asaresult,theeectivesimulatedoweldwassampledatapproximately3.56kHz.Asaresultofthis,estimationisnotrequired,sincetheoweldmeasurementsarealreadytime-resolved. TomoreaccuratelyrepresentthemeasuredSPIVregions,thePowerFLOWdataweredividedintoappropriategapowandnearwakeregions.Asbefore,thedataareconsideredherefortheheightsofZ=0and)]TJ /F1 11.955 Tf 9.3 0 Td[(3DsincetheyaretheonesthatcoincidemostcloselywiththeSPIVdata.Figure 5-23 displaysacomparisonofthemodalenergybreakdownsbetweensimulationandexperimentforthegapowandnearwakeregionsfortheseheights.Whiletheseresultsshowverysimilarenergyfractiontrends,insomecasesthereareconsiderabledierencesintheenergiescontainedintherstseveralmodes.Therefore,alow-orderreconstructionoftheeldusingthesamenumberofmodesforsimulationandexperimentaldata,couldresultindierenteldenergycontentsbetweenthem.Anadditionalcomplicationistheestimationprocedureitself.Sincethebest-casecomputedestimationerrorwasonly35%,whichwasfora5-modeestimateoftheZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(3Dgapowregion.Therefore,35%oftheestimatedsnapshotswouldbetheresultofpoorcorrelations,andthushaveincorrecteldintensities. ItisalsousefultolookatindividualmodesinordertoensurethattheenergycomparisonsofFigure 5-23 arebetweenmodesofthesamecharacter.Forexample,doesmode1oftheSPIVdatasetrepresentmode1ofthePowerFLOWdataset?ThegapowandnearwakeregionsofZ=)]TJ /F1 11.955 Tf 9.29 0 Td[(3Dwereselectedtoillustratethis.ThePowerFLOWPODmodeswerevisuallyobservedtondwhichonesmatchedtheSPIVmodes.AcomparisonoftherstvestreamwisePODmodesbetweenthePowerFLOWandSPIVgapowregiondatasetsareshowninFigures 5-24 ,whiletherstfourmodesofthewake 265

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regionareshowninFigure 5-25 .ItisworthnotingthatsomeofthemodalimagesdisplaystructuresthathaveippedsignscomparedtotheSPIVmodes.Astheguresindicate,thePowerFLOWmodesarenotintheexactsamenumericalsequenceastheSPIVmodes.Forexample,thegapowPODmodesfromPowerFLOWthatmatchtherstvemodesoftheSPIVdatasetaremodes1,3,2,5,and4.Asimilartrendisobservedforthenearwakemodes,whichhaveamatchingsequenceofmodes1,3,2,and4.Asaresultofthismodenumbermismatchbetweenexperimentandsimulation,theenergiesdonotcompareaswellasiftheywereinconsecutiveorder.ThiscouldpotentiallyresultindierencesinintensitiesoftheresultingLambvectoreldcalculationsbetweenexperimentandsimulation.Anotherinterestingfeaturetoobservewiththewakeresultsishowsomeofthemodesareippedaboutthey=DaxisbetweenPowerFLOWandSPIV.Specically,thisisseentooccurforSPIVmodes1and4betweenFigures 5-25A () 5-25E and 5-25D () 5-25H .Thisisadditionalevidenceofhowthesimulationdisplayssymmetricowbehavioratthisheight,whiletheexperimentalSPIVresultshaveindicatedowasymmetry. 5.2.5Near-FieldAnalysisofAcousticSourceTerms ThepartialLambvectortermsarecomputedfromtheestimatedoweld.ThesearealsocomparedwiththeoutputsofthePowerFLOWsimulation,aswellasLambvectorpartialtermsthatcouldnotbemeasuredexperimentally.Thecomparisonstobemadewiththesimulationsareconsideredtobewarrantedbasedonexcellentagreementsbetweenthesurfacepressuremeasurements(bothsteadyandunsteady),far-eldacoustics,andreasonableagreementbetweentheoweldstatistics.Theprimarygoalofthissectionistoidentifythephysicalowmechanismsresponsiblefornoisegeneration,whichcanbedividedintothreesub-goalsofthissection:(1)toidentifytheregionsofprominentLambvectorsourcetermintensities,(2)identifysimilaritiesbetweenthelow-orderrepresentationsoftheexperimentalLambvectortermsandthesimulationresults,and(3) 266

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determinethecontributionsofthemeasuredLambvectortermstothecompleteacousticsourcetermsascomputedinPowerFLOW. 5.2.5.1Low-OrderLambVectorTermRepresentations TherststepincharacterizingtheexperimentalLambvectorsourcetermsistoanalyzethelow-orderestimatesofthequantities.Sinceonlypartialcomponentscanbecomputedfromtheexperimentaldata,itisimportanttoindicatethepropernotationforalloftheterms.First,thecompleteuctuatingLambvectorequationmaybewrittenas L=!0u0=()]TJ /F3 11.955 Tf 9.29 0 Td[(!0zu0y+!0yu0z)^i+(!0zu0x)]TJ /F3 11.955 Tf 11.95 0 Td[(!0xu0z)^j+(!0xu0y)]TJ /F3 11.955 Tf 11.96 0 Td[(!0yu0x)^k: (5{5) NotethatEquation 5{5 istheunsteadycomponentoftheLambvectorwhichwasdenotedasL00in Chapter3.6.5.1 .Forthesakeofconvenience,thecomponentsaredenotedasLfortheremainderofthischapter.Withthis,allpartialcomponentsarelabeledaccordingly Lx;1 = )]TJ /F3 11.955 Tf 9.3 0 Td[(!0z u0y Lx;2=!0yu0z Ly;1 = !0z u0x Ly;2=)]TJ /F3 11.955 Tf 9.3 0 Td[(!0xu0z (5{6) Lz;1=!0xu0yLz;2=)]TJ /F3 11.955 Tf 9.3 0 Td[(!0yu0x: Thetermshighlightedin blue representtheonesexperimentallycalculated.Finally,the\pseudo"-divergenceisalsocalculatedas r^L=rhLx;1^i+Ly;1^ji:(5{7) 267

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ThePowerFLOWvisualizationsoftwareisalsoabletocomputetheindividualLambvectorpartialcomponentsofEquation 5{7 .ThisisusefulinthatitallowsforbothcomparisonbetweenexperimentalandsimulatedsnapshotsandforobservingtheenergycontentdierencesbetweenthepartialandfullLambvectorcomponents.Figure 5-26 showsacomparisonofinstantaneoussnapshotsofLx;1betweenSPIVandPowerFLOW.Theresultsshowreasonableagreement,withsimilarfeaturesofnearlyidenticalintensities.BothimagesshowtheLambvectorsourcesbeingdivertedinthepositiveydirectionduetothetorquearm'scloseproximitytothecylinder.Furthermore,thedierencesinenergycontentbetweenLx;1andLxforasinglesnapshotinPowerFLOWisillustratedinFigure 5-27 .Whiletherearenoticeabledierencesbetweenthepartialandcompleterepresentations,thepartialLx;1doesseemtocapturethemajorityoftheLambvectorsources.Awaytoquantifythedierencesbetweenthecomponentsisthroughspectralanalysis,whichisconductedinthenextsection. Basedontheverylittledierencebetweena5-and10-modeestimateofthevorticityfortheZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(3Dgapow,the5-modemodelwasusedtocomputeestimatesoftheLambvectorpartialtermsandpseudo-divergence.TheresultsofthisarepresentedinFigure 5-28 .Theseresultsareveryencouraging,particularlyforthepartialtermsthemselves.Inadditiontothe~Lx;1and~Ly;1estimatesbeingverysimilartothenominallow-orderrepresentation,theyalsoexhibitmodalstructuresthatarerepresentativeofthehighestenergytermsintheoriginalsnapshot.Asforthepseudo-divergence,whiletheestimatedoesdisplaystructuresthatappeartorepresenttheoriginalsnapshot,thePIVsnapshotitselfappearstobenoisy.ThiscouldbepossiblyduetothenumberofspatialgradientsperformedonthePIVdatawiththiscalculation,orpossiblybecausethemeasurementregiondoesnotcovertheareasofhighestnoisegeneration.Sincethecurrentinterestliesinthedipolecharacteristicsofthesoundeld,thenthedivergenceisnotofvitalimportancesinceitrelatesmoretoaquadrupoleterm(Equation 1{23 ).Therefore,thecontinuingfocusisontheLambpartialtermsthemselves. 268

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ItisworthinvestigatingthepossiblecausesastowhytheestimatesofthegapowregionsperformedbetteratthelowerheightswhiletheyperformedbetterinthenearwakeregionsnearZ=0.AsFigure 5-29 shows,thePODmodalbreakdownsforZ=)]TJ /F1 11.955 Tf 9.29 0 Td[(2:175Dand)]TJ /F1 11.955 Tf 9.29 0 Td[(3Dareverysimilar,withosetsintheenergiesatthersttwomodes.ThemodalbreakdownforZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(0:592D,however,ismuchmoresimilartothatofZ=0inFigure 5-11A .However,bymode10,allthreeoftheseregionsexhibitverysimilarenergybreakdowns.Thisisfurtherjusticationthattheprimarydierencesintheowbehaviorbetweenthedierentheightscanbeexplainedbytheselowermodes.Thisisalsobelievedtorepresentwhichregionsonthemodelaremoreresponsibleforthenoisegeneration.Thisisfurthertestedbyobservingtheestimator'sabilitytocapturethedominantLambvectorsourceswithintheZ=0:592Dgapowregion. Singlesnapshotestimationsof~Lx;1and~Ly;1attheZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(0:592DgapowregionareshowninFigure 5-30 .Theresultsinthisgureweregeneratedusinga10-modeestimate.Thisnumberofmodeswaschoseninordertoachieveanenergycontentaround50%.AninterestingrstobservationishowthelevelsoftheLambvectortermsareconsiderablylowerthanthoseobservedatZ=)]TJ /F1 11.955 Tf 9.29 0 Td[(3D.ThisagreeswiththetrendofthesurfacepressureprobesfromPhase1,wheretherewasagradualincreaseinspectrallevels,particularlybetween100and300Hz,astheheightofinterestmovesawayfromZ=0(Figure 4-13 ).Inaddition,therewerealsolowerlevelsofcoherencebetweencylinder-torquearmprobesnearZ=0comparedtothosenearZ=2and3D(Figure 4-19 ).Furthermore,the~Lx;1estimateinFigure 5-31B isclearlyseentofallshortwithpredictingtheLambvectorsourcetermsoriginatingfromthecylindertopshearlayer(y=D=0:5).Averysimilarbehaviorisobservedfor~Ly;1,wherethesourcesalongtheuppershearlayerarenotaccountedforintheestimate.Asaresult,theestimateofthisregiondoesnotappeartobereliablemostlikelyduetoacombinationofthemajorityofthemodelsurfaceprobesnotbeingwellpositionedtocapturethecoherentowbehaviorinthisregionaswellasoveralllowerlevelsoftheLambvectorsources. 269

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TheestimationofthenearwakeregionatZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(0:592Dwastheonethatperformedthebestoutofallofthenearwakeregions.AnillustrationoftheestimationperformanceonasnapshotoftheLx;1andLy;1termsispresentedinFigure 5-31 .Thisgureshowsacomparisonoftheoutputsusinga5-modeanda20-modeestimation.Forthe~Lx;1results,boththe5-and20-moderesultshavestructuresinsimilarspatiallocations,howeverthe20-modeestimatestructuresareofdierentoverallshapeandenergydistribution.Thereisalsooverallhigherenergycontentwiththe20-modeestimate,whichisexpected.Similarresultsareobtainedforthe~Ly;1estimates,howeverthemodalstructuresforthe5-modeestimateactuallyseemmorerepresentativeoftheoriginalsnapshotthanthe20-modeestimate.Theseresultsdisplayaconictbetweenthedierentmodenumberestimations.Whilethe20-modeestimatecontainsnearly20%moreenergythanthe5-modeestimate(50.8%comparedto31.7%),verylittleisgainedintermsofthelow-orderrepresentationsoftheLambvectorterms.Therefore,a20-modeestimatedoesnotappeartobeoverlybenecialcomparedtoa5-modeone. 5.2.5.2LambVectorSpectralAnalysis DuetothelimitedeldofviewoftheexperimentalSPIVdata,itwashopedthatthesimulationresultscouldberelieduponforllinginthemissingLambvectorinformation.Uptothispoint,thesimulationandexperimentalresultshavebeeninreasonableagreementwithoneanother,andthereforethesimulationresultsarecontinuedtobeusedasareferenceregardingthecalculationofthespectralcontentoftheLambvectorpartialterms.Now,itisimportanttodenethefrequenciesofinterest.Sincethegoalistoidentifytheoweldsourcesresponsibleforfar-eldacousticpropagation,therearespecicfrequenciesofinterest.Recallfrom Section4.2.1 thataprimaryspectralhumpwasevidentinthefar-eldacousticmeasurements,whichwasalsofoundtoexhibitStrouhalscalingin Section4.2.4 .Thiswasfoundtooccurovertherangeof0:1StD0:27,whichtranslatestodimensionalfrequencyas144F416Hz,basedonafreestreamvelocityof58m/s.Furthermore,coherencemeasurementsbetweenthemodelpressure 270

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sensorsandtheprimarylineararraymicrophonein Section4.2.3 displayeddistinctcoherencepeaksatorimmediatelynearthe128and240Hzfrequencybinsinnearlyallofthesensors.Theserepresentspecicfrequenciesthatwillbeinvestigatedforspectralanalysis,withanoverallbroadbandfrequencyrangeof96HzF1.216kHz.EstimationStrategy Uptothispoint,theLambvectorpartialtermshavebeenestimatedusingsomewhatarbitrarymodelimits.Therefore,itwasdesirabletodevelopamorewell-denedmethodofmodeselectionfortheLambvectortermestimations.Itwasthereforedecidedthatatwo-stepmodevalidationsetofcriteriabeapplied:(1)themodesmustdisplayavisualconvergencetest(aspresentedinFigure 5-21 )and(2)themodesmustbeincloseagreementwiththosefromPowerFLOW.Oncethesemodeswereselected,theiraccompanyingPODexpansioncoecientswerethencoupledwiththetriggeredprobedatatoyieldasetofLSEcoecients.Thesecoecientswerethenappliedtoasecondcontinuoussetofdatafromthesameprobes.ThisprovidedaseriesofestimatedPODexpansioncoecientsthatcouldbeappliedtothePODmodestoyieldatime-resolvedestimateofthevelocityeld.ThisdatawasthenusedtocomputetheLambvectorpartialterms.ThenalstepwastothenperformanFFTandanalyzethespectralcontentoftheLambvectorterms.NotethatduetothelargenumberofFFTsthatmustbeperformed(oneforeachspatialgridlocation),onlytensecondsofcontinuousprobedatacouldbeusedfortheestimatesofLambspectra.Also,duetotheapparentlynoisycontentoftheLambvectorpseudodivergencecalculation,onlytheLambtermsthemselvesundergofurtheranalyses.AsforthePowerFLOWdata,sinceitonlyrepresentsapproximately0.32secondsofphysicaltimeandonly1,193snapshotswereusedinthissection,itwillbeusedprimarilyforspatialgridvisualizationsinsteadofsinglepointPSDs. Itisimportanttonote,however,thatonlytwoofthetime-resolvedplanesmeasuredwithPowerFLOWmatchupnominallywiththeSPIVregions.TheseareattheheightsofZ=0andZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(3D.TheotherplanesmeasuredinPowerFLOWareatZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(1D 271

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andZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(2D,whichdon'texactlycomparewiththeplanesatZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(0:592D,)]TJ /F1 11.955 Tf 9.3 0 Td[(1:175D,and)]TJ /F1 11.955 Tf 9.3 0 Td[(2:175DthatwerealsomeasuredwithSPIV.Asaresultofthis,theexperimentalcomparisontosimulationcouldonlybereliablydonewithZ=0andZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(3D.Asfortheotherregionsthatcannotbedirectlycompared,thePODmodesthatpassedtheconvergencetestwouldbeusedintheestimationcalculation.Low-OrderLambVectorSpectra Low-ordereldrepresentationsofthespectralpoweroftheLambpartialcomponentsarepresentedinthissection.Insteadofpresentingeldimagesofindividualfrequencies,however,theyareintegratedoveradenedfrequencyrange.Thereasonforthisisbecausetheeldimageschangeverylittlewithfrequency.Instead,theeldprimarilychangesinintensity.Therefore,individualprobesofhighintegratedintensityfromtheeldwereselectedforviewingspectra. ThePowerFLOWandSPIVresultsofthenon-dimensionalized,integrated~Lx;1and~Ly;1PSDsfortheZ=0gapowregionarepresentedinFigure 5-32 .Inessence,theseeldimagesrepresentaband-limitedvariancecalculationoverthefrequencyrangeof96HzF1.216kHz.BothsetsofresultsweregeneratedusingtwelvePODmodesthatpassedthecommonalityandconvergencetests.Bothsetsofresultscompareverywellintermsofthespatialdistributionsofthespectralpower.Someinterestinginsightcanbegainedfromthesedistributionsaswell.First,itappearsthatthe~Lx;1sourcetermsareprimarilyfocusednearthegapowsurfaceofthetorquearm.ThisimpliesthatthestreamwisepartialcomponentoftheLambvectorisprimarilyduetothebuild-upofTKEnearthetorquearmsurface.Furthermore,the~Ly;1termsareofgreatestintensityalongthecylindershearlayers.Itisalsointerestingtonotethattheeldintensitiesaredierentbetweensimulationandexperiment.Specically,theexperimentalestimatesof~Lx;1areafactorofapproximatelyfourtimeslowerthanthesimulation,while~Ly;1estimatesarelowerbyafactorofapproximatelyeight.Thereareseveralpossibilitiesthatcanexplainthesedierences.Itcouldbesimplytheresultofthecouplingofslightlyloweructuating 272

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velocitiesandvorticitylevelsascomparedtothesimulationand/ortheoccasionalpoorcorrelationsbetweenthepressureprobesandLSEcoecients.Thisisbelievedtobealikelycausesincethesmallestmeanestimationdierencethatcouldbeobtainedforthisregionwas =0:67.Anotherinterestingobservationishowtheestimateof~Ly;1isofmuchhigherintensityalongthelowershearlayer,whereasthePowerFLOWpredictionindicatescomparableintensitiesonbothsides.ThiscanbeexplainedbythePODmodes.RecallthatthersttwoPODmodesofstreamwisevelocityuctuationsfortheSPIVdatawerefoundtobepairsthatconsistedofhigh-intensitymodestructuresalongeachcylindershearlayer.Theoneofhigherintensityhappenedtobealongthelowershearlayer.ThispropagatedintotheformulationfortheestimateofthetransversepartialLambvectortermsince~Ly;1=~!0z~u0x.AcomparisonbetweenthersttwostreamwisePODmodesfromSPIVtotherstmodefromPowerFLOWispresentedinFigure 5-33 .Astheseguresshow,themodalstructuresofthersttwomodesfromtheSPIVdatasetaremodalpairs,whiletherstmodefromthePowerFLOWdataseemstocontainbothofthesemodalfeatures. Theband-limitedintegratedspectralgapoweldsattheheightsofZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(0:592D,)]TJ /F1 11.955 Tf 9.3 0 Td[(1:175D,and)]TJ /F1 11.955 Tf 9.3 0 Td[(2:175DareshowninFigure 5-34 .Astheseresultsshow,the~Lx;1resultsremainconcentratedinthecoregapowregionwiththe~Ly;1componentalongthecylindershearlayers.ItshouldbenotedthatwhiletheintegratedLambenergycontentisseentoincreasewithdecreasingmodelspanwiseheight,thisispartiallytheresultofincreasedenergycontentcontainedwithintherstseveralPODmodesasthemodelheightdecreases.Therefore,thismakesitdiculttodirectlycomparetheLambenergylevelsbetweenthedierentheights.Despitethis,however,theincreaseinLambspectrallevelsdoesfollowthesamebasictrendoftheincreaseinlevelsofTKEwithdecreasingheightalongthemodelspan. ThenearwakeregionsatZ=0and)]TJ /F1 11.955 Tf 9.3 0 Td[(0:592Darealsointerestingtoobservesincethetorquearmcrosssectionsattheseheightsarebotheitherthesamesizeoforsmaller 273

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thantheupstreamcylinderandareontheorderofthreediametersdownstreamfromit.Fromthendingsof Zdravkovich ( 1985 ),tandemcylinderswiththisspacingresultinintermittentsheddingfrombothcylinders.Whileithasalreadybeenobservedinthesurfacepressurespectrain Chapter4.1.2.2 thatthecylinderdoesnotappeartoexhibitcoherentvortexshedding,thereisapossibilityofintermittentfromthedownstreamtorquearm.The~Lx;1and~Ly;1integratedPSDsforthenearwakeregionsatZ=0and)]TJ /F1 11.955 Tf 9.3 0 Td[(0:592DareshowninFigure 5-35 .Inadditiontodisplayingsimilareldpowerdistributions,theintegratedlevelsareverysimilartooneanother.ThisisattributedtosimilarPODmodalenergybreakdownsandsimilarestimationtimedelayperformance.Themostintensepowerlevelsareseentoallbewithinonecylinderdiameterofthetorquearmtrailingedge. Finally,theintegratedLambspectraforthegapowregionataheightofZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(3DispresentedinFigure 5-36 .ThePowerFLOW~Lx;1resultsshowtwoprimaryregionsofhighintensitynear(x=D;y=D)=(1:25;0:3).Thesetworegionsarebelievedtobeindicativeoftheextremelyhighuctuationsoftransversevelocityintheseregionsduetotheblunessofthetorquearmatsurface.Itisinterestingtonotethatthesestructuresdonotdirectlyimpingeonthetorquearmitself.Thisisbelieved,however,tobetheresultofthelow-orderrepresentation.Furthermore,thePowerFLOW~Ly;1resultsalsodisplaytwoprimaryhigh-intensitystructures,howeverinthevicinityofthecylindershearlayers.TheSPIVresultsarepresentedinFigures 5-36C and 5-36D .TheseresultsagaincomparereasonablywellwiththosefromPowerFLOW.Outofallofthemeasuredgapregions,thisheightistheonlyonewithpeak~Lx;1integratedPSDsthatexceedthoseofthe~Ly;1values.The~Lx;1resultsshowahigh-energystructurefocusednear(x=D;y=D)=(1:25;)]TJ /F1 11.955 Tf 9.3 0 Td[(0:3),whichisverysimilartothatshowninFigure 5-36A .Sincethevectoreldisunfortunatelycroppedduetotheviewinglimitations,itisunknownwhetherornottherewouldbeasimilarstructureinasymmetricallyoppositeposition.Therearealsosomeadditionalsecondarystructuresclosertox=D0:9,whicharenot 274

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presentinthePowerFLOWresult.Thisisinherentlyduetotheasymmetricbehaviorintheexperimentalresults.Meanwhile,the~Ly;1resultsshowahigh-energyregionalongthelowercylindershearlayer,whiletheuppershearlayerisnotheavilyemphasized.Again,thiscouldbeduetoPODmodesofhigherintensityalongy=D<0,examplesofwhichareillustratedinFigure 5-24 .ThesemodalimagesapplysincethetenmodesusedinboththePowerFLOWlow-orderspectralrepresentationsandSPIVlow-orderestimatesincludethemodesshowninthisgure. IndividualpointswereselectedfromtheLambeldsforobservingPSDs.ThelocationsoftheseeldprobescorrespondtoregionsofpeakintensityoftheLambpartialtermsandareindicatedby\"intheeldimages.ThePSDsoftheselocationsarepresentedinFigure 5-37 .Notethattheyaredividedaccordingtoregion,sincedirectcomparisonbetweenregionscannotbereliablydoneduetodierentmodalenergycontentbetweenthem.TwoofthemoreinterestingcasesarefortheZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(2:175Dand)]TJ /F1 11.955 Tf 9.3 0 Td[(3Dregions,providedinFigures 5-37D and 5-37E ,respectively.ForZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(2:175D,bothLambpartialcomponentPSDsdisplayhighpoweratfrequenciesintherangeof96HzF160Hz,afterwhichthereisaspectralroll-o.AtZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(3D,however,thereisabroadspectralhumpinthe~Lx;1PSDcenteredbetween240and256Hz,andhasaroll-oafter368Hz.ItisworthnotingthatthisPSDbearsastrikingresemblancetothelow-frequencybehaviorofthemodelasmeasuredbythefar-eldlineararraymicrophoneL4(Figure 4-24 ).ThesePSDsalsodisplaysimilaritieswiththemodelsurfacepressures.Forexample,highlevelsofcoherenceweremeasuredbetweencylindersensorsatZ=1:42D,2D,and2:42D,andthetorquearmsensorT3inthefrequencyrangeof128Hz-160Hz(Figure 4-19C ).SensorT3,whichislocatedataspanwiselocationofZ=D=1:833,displayedasinglespectralhumpcenteredaround128Hz(Figure 4-13B ).Furthermore,thecylindersensoratZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(3DandtorquearmsensorT4displayedtwospectralhumpscenteredat128and224HzinFigures 4-13A and 4-13B .Interestingly,the~Lx;1spectrumatZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(3Donlydisplaysalargespectralhumpcenteredat240Hz. 275

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Therefore,itispossiblethatthelow-orderestimationdoesnotcapturethisbi-modalbehavior,and/orthatthelowerfrequencyspectralhumpcouldbetheresultofconvectionofowstructuresalongthetorquearmsurface. TheselectedpointPSDsofthenearwakeregionsatZ=0andZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(0:592DareshowninFigure 5-38 .Astheresultsshow,thereareindicationsofvortexsheddingatbothheights.Thespectralhumpsarecenteredatrespectivefrequenciesof400and320Hz.Thesehumpsaremostnoticeableinthe~Lx;1component,whichisexpectedsinceitcontainsthetransversecomponentofvelocity.Ifweusethelocaltorquearmcross-sectionwidthstonon-dimensionalizethesefrequencies,onegetsStW;Z=0=(4000:0213)=58=0:147andStW;Z=)]TJ /F7 7.97 Tf 6.59 0 Td[(0:592D=(3200:0307)=58=0:169,whichcomparereasonablywelltothesinglerectangularcylinderStnumbersrecordedby Shimada&Ishihara ( 2002 ).Thesefrequencieshadbeenpreviouslyfoundin Section4.2.4 toliewithinthespectralhumpportionofthemodelfar-eldacousticSPLthatobeyedStrouhalandsixthpowerofMachnumberscaling.Whilethesefrequenciescannotbeclaimedtobetheultimatecauseofnoiseatthesefrequencies,theycanbeidentiedasprominentcontributors.Full-OrderLambVectorTermVisualizations Uptothispoint,thelow-orderestimatesoftheexperimentally-measuredLambvectorpartialtermshavebeenobservedinthefrequencydomain,withcomparisonstothePowerFLOWresultsatselectplanes.Thesecomparisonshavedemonstratedreasonableagreement,aswellashaveunsteadysurfacepressuresandthepredictedfar-eldacousticsignaturereportedinthepreviouschapter.Therefore,itisconsideredacceptabletousethesimulationresultstocomputethefull-orderLambvectoreldandcomparethepartialtermsthatcouldonlybemeasuredintheexperimentswiththefullLambvectorterms.ThesetermswerecomputedandexportedsothatanFFTcouldbeperformed.Theresultingimageswillthusprovideinsightastowhatregionsaremostresponsiblefornoisegeneration,andatwhatfrequencies.Theintegratedandspectrallevelsinthissectionwerecomputedinasimilarmannerastheintegratedlevelsintheprevioussection, 276

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however,thespectraofthissectionwerecomputedinPowerACOUSTICS,aprocessingsoftwareadd-ontoPowerFLOW.Atotalnumberof4,460snapshotswereutilizedforeachofthefourplanesofmeasurement(atmodelspanwiseheightsofZ=0;)]TJ /F1 11.955 Tf 9.3 0 Td[(1D;)]TJ /F1 11.955 Tf 9.3 0 Td[(2Dand)]TJ /F1 11.955 Tf 9.3 0 Td[(3D),thatspanthefull0.32secondsofvalidsimulationtime.Thisresultsinaneectivesamplingfrequencyof14.275kHz.Thespectrawerecalculatedusingafrequencyresolutionofapproximately16Hz(actually16.0038Hz),with892samplesperblock,andvetotalFFTblocks.WiththeincreasednumberofsnapshotsusedintheLambspectralcalculations(ascomparedtotheprevioussection),pointsofhighintensityareselectedfromtheeldtoviewpowerspectra.Notethatonlytheresultsforthein-planeLambvectorcomponentsLxandLyarepresented,becausethelevelsoftheout-of-planeLzwerefoundtoconsiderablysmallerthanthein-planeones. Figure 5-39 displayscontoursoftheband-limitedmeansquarevalues(MSV),ofboththepartialandcompletestreamwiseandtransverseLambvectorcomponents,forthemodelcenterline(Z=0).Aswiththeprevioussection,theMSVwascomputedinaband-limitedmanneracrossthefrequencyrangeof96HzF1:216kHz.IfattentionisfocusedonthestreamwisepartialandcompleteLambcomponentinFigures 5-39A and 5-39B ,respectively,itcanbeseenthatthegapowsurfaceofthetorquearmhingeistheregionofhighestintensity.Thiscanbeattributedtothehighlevelsoftransversevelocityofuidparticlesuponcontactoftheblutorquearmsurface.ThetransverseLambcomponent,however,highlightsthecylindershearlayersandthetorquearmedges.Thiscanbephysicallyexplainedbytheconvectionofvorticesbytheacceleratedowpastthetorquearm.Ingeneral,theinclusionoftheadditionaltermsintoeachcomponentisseentoincreasetheoverallpowerlevelswithintheeld.Tobetterquantifythisincrease,pointsofhighLambintensityareselectedtoobservespectrallevels. ThepointsselectedforobservingpowerspectraataheightofZ=0areshowninFigure 5-40 .Notethatduetotheshortphysicalsimulationtime,thevarianceoftheprobescanbequitelarge.Therefore,thefocushereisidentifyingfrequenciesthat 277

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displaythehighestspectralpower.ThehighestLxspectralpeakof144Hzoccursatpoint3,whichislocatedveryclosetothelowerleadingcornerofthetorquearmhinge.Meanwhile,thehighestLyspectralpeakoccursatafrequencyof336Hzforprobe5,whichisalsoveryclosetothelowerleadingedgecornerofthetorquearmhinge.Thisprobealsodisplayssecondarypeaksat144,240,and400Hz.Thesignicanceofthe336Hzpeakisthatitisthefrequencyofthesecondhigh-amplitudepeakinthesimulatedfar-eldSPLofthemodelinFigure 4-33 .Ingeneral,theadditionofLx;2andLy;2totherespectivestreamwiseandtransverseLambcomponentsaddsaconsiderableamountofenergy.Forthepeakfrequenciesofprobes3and5,forexample,thisinclusionyieldedanincreaseinPSDbyafactorof2,or3dB. Figure 5-41 displaystheband-limitedintegratedLambeldspectraforZ=)]TJ /F1 11.955 Tf 9.29 0 Td[(1D.Overall,theresultsarequalitativelysimilartotheresultsatZ=0,withpeakLxintensitiesalongthetorquearmgapowsurfaceandpeakLylevelsalongthetorquearmedges.Thecylindershearlayers,however,displayslightlyhigherLylevelsatZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(1D.AsFigure 5-42C shows,probe(3)inthecylindershearlayercontainsfairlybroadbandLypowerbetween128Hzand416Hz.Theselevels,however,areconsiderablysmallerthanthoseinFigure 5-42D ,whichrepresentpoint(4)locatednearthetorquearmlowerleadingedgecorner.Thisprobedisplaysasinglelarge-amplitudepeakat240Hz.Thereisalsoanadditionalhigh-amplitudepeakinLxlevelsinFigure 5-42A at192Hz.AtaheightofZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(2D,theLambintensitiesareseentoincrease.AscanbeseeninFigure 5-43B thereisaconsiderableincreaseinLxspectrallevelsinthegapowregionclosertothecylinder.ItisalsoseenthatthelocationofboundarylayerseparationfromthecylinderexhibitsoneofthehighestintegratedlevelsofLyinFigure 5-43E .ThespectrumatthispointofhighintensityisprovidedinFigure 5-44D ,whichdisplaystwohigh-amplitudepeaksat144and192Hz. Finally,theZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(3DregionisconsideredinFigure 5-45 .Overall,theinclusionofLx;2andLy;2partialtermsintothefullLxandLyexpressionsdoesnotseemtoadd 278

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muchpowertotheeldatthisplane.However,thereareseveraldistinctregionswherethisisnotthecase.ComparisonbetweenFigures 5-45A and 5-45B showveryhighLambpowerlevelsatbothleadingedgecornersofthetorquearmforLx,howeverthereisnearlyacompletelackofappreciablepowerattheselocationswhenonlyconsideringLx;1.Figure 5-45B alsoindicatesthatthereareincreaseductuationsinthegapowregionatZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(3Dascomparedtothepreviousregions.Furthermore,whiletheLyresultsaresimilartothepreviousregions,thepeakintensitiesnearthetorquearmleadingedgecornersareconsiderablyhigherthananyofthepreviousheights.Theseresultsfurtherenforcethatthesharptorquearmedgesareprominentnoisecontributors.AtaheightofZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(3D,forexample,thetorquearmsedgesarecompletelyexposedtotheoncomingow.Inasense,Ly;1=!0zu0xatthislocationcanbeconsideredtobeduetothecouplingoftheshearlayervelocityuctuationswiththevorticesshedfromthetorquearmleadingedge,whileLx;1=)]TJ /F3 11.955 Tf 9.3 0 Td[(!0zu0ycanberegardedasthecouplingbetweenthevorticesshedfromthecylinderwiththelargetransversevelocityuctuationsinthegapowregionasuidparticlesstagnateanddivertaroundtheblutorquearmsurface. TheselectedeldpointpowerspectraatZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(3DareshowninFigure 5-46 .TheLxprobesindicateadrasticincreaseinlevelswiththeinclusionofLx;2=!0yu0zintothestreamwiseLambcomponent.Figure 5-46B indicatesthatthereisagradualincreaseinspectrallevelsfrom144Hzto240Hzatthetorquearmedgealmostsolelyduetotheout-of-planeterms.InthecaseoftheLypoints,therearemixedresults.Forthecaseoftheprobenearthecylinderowseparationpoint,thespectraisseentobenearlyexclusivelyduetoLy;1,withspectralpeaksat240and304Hz.Figure 5-46D ,however,revealsthatLy;1byitselfcontainsmisleadinghighspectrallevelsforfrequenciesbelow200Hzattheuppertorquearmedge.Fortheprobeatthelowertorquearm,however,inclusionofLy;2=Lx;2=)]TJ /F3 11.955 Tf 9.3 0 Td[(!0xu0zcontributesgreatlytothepowerspectra,particularlyatfrequenciesof144,208,352,and464Hz. 279

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Boththeexperimentalandsimulatedsurfacepressureprobeshavedisplayedevidenceofabi-modalbehavior,particularlyinthevicinitiesofZ=2Dand3D.ThishasbeenobservedbothinthepressurePSDsinFigure 4-22 andinsampledistributionsofexperimentalprobeT4(Figure 4-14 ).Therefore,itwasbelievedthattheZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(3Dfull-orderLambspectralcalculationscouldhighlightthis.Thisbehaviorhasbeenobservedtooccuratorwithinonefrequencybinof144Hzand240Hz.Inaddition,multiplesimulatedprobesextractedfromtheeldimagesatthedierentmeasuredheightshavedisplayedprominentenergyat352Hz.Therefore,theLambspectraldataatthesespecicfrequenciesareplottedfortheseindividualfrequenciesinFigure 5-47 foraheightofZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(3D.IfattentionisfocusedonFigures 5-47A and 5-47B ,theimagesdisplayasingleprimarystructureinthegapowregion.Thisstructureisseentoipbetweendierentsidesofy=D=0forthedierentfrequencies.AsimilarbehaviorisobservedfortheLyeldimagesinthattheregionofhighestintensityalsoswitchesbetweenthetorquearmsides.Thisisbelievedtobeanindicatorofthebi-modalbehavioroftheoweld,sinceitshowsthatratherthandisplayingsymmetricbehavioratindividualfrequencies,thecloseproximityofthegeometriesresultsintheowstructuresoscillatingwithinthegapowregion.Thedierentfrequenciessignifythatthisisnotasingleperiodicprocess,butratherthattheowswitches\states"atdierentfrequencies. ItisalsoimportanttoobservethebehavioroftheLambvectortermsathigherfrequencies(1kHzf8kHz).Thisisthefrequencyrangeatwhichhumanhearingismostsensitivetobroadbandnoise( Section4.2.6 ).Astheacousticresultsofthetorquearmmodelshowedin Section4.2 ,thereisanappreciablebroadbandnoisesignatureofthemodeluptoapproximately10kHz.Therefore,itwasdecidedtovisualizetheLambvectorcomponentsatafrequencyof2kHzforthedierentsimulatedheights.ThisfrequencywaschosenbecauseitrepresentstheonsetatwhichA-andD-weightingsaccountforprimaryhumanhearingsensitivity(basedonafrequencyscalingfactoroftwo),andalsobecausetheLambspatialdistributiontrendswereseentochangeverylittleabove2kHz. 280

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Furthermore,thisisalsoafocalfrequencyatwhichtheDAMASbeamformingalgorithmwasperformedonthetorquearmprimarycongurations(Figure 4-42 ). TheLxandLyPSDresultsatafrequencyof2kHzarepresentedinFigure 5-48 forthesimulatedplanes.Fromageneralstandpoint,theLylevelsarehigherthanLx.Asseenpreviously,thehighestLylevelsoccuralongthecylinderandtorquearmshearlayers.AnothergeneraltrendisthatthelevelsforbothLambcomponentsincreasewithdecreasingheightawayfromZ=0.ThereisalsoanabruptincreaseinLxandLyspatialdistributionswithinthegapowregionbetweenZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(1DandZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(2D.ThelargestlevelsofLxareseentooccuralongthetorquearmgapowsurfaceatZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(2DwhilethoseofLyoccuralongthetorquearmshearlayersatZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(3D.Theseresultsareindicatorsthatwhilethetorquearmsharpedgesareaprominentbroadbandnoisecontributor,theinnergapowinteractionsarealsoimportantathigherfrequencies,particularlyformodelheightsatandabove/belowtwocylinderdiametersfromthecenterline.AnalysisoftheLighthillStressTensorDivergence Aswasstatedin Section1.3.3 ,therearesimilaritiesbetweenthesourcetermsofPowell'svortexsoundanalogyandtheacousticanalogyofLighthill.Therefore,itwasbelievedthatadditionalinsightintotheowbehaviorcouldbegainedbycomparingthesimulatedspectraloutputsofboththeLambvectorandthemagnitudeofthedivergenceofLighthill'sstresstensor,jrTijj.ThemaingoalofanalyzingLighthill'sstresstensoristoidentifythecausesofnoisegenerationfordierentfrequencyranges. AstheLambvectorspectralresultsoftheprevioussectionindicated,severalprimarynoisesourceswereidentied.Theseincludecylindershearlayerimpingementontothetorquearmsurface,owshearingoofthesharptorquearmedges,andabi-modallow-frequencycouplingofthesebehaviors.Therefore,thePSDofjrTijjwascomputedandplottedforthesamenarrowbandfrequenciesshownintheprevioussection. 281

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Specicallytheseareatlow(acousticallycompact)frequenciesof144,240,and336Hz,andahigh(acousticallynon-compact)frequencyof2kHz. Figure 5-49 displaysthenon-dimensionaleldPSDsofjrTijjataheightofZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(3Dforfrequenciesof144,240,and336Hz.Again,theresultsshowthattheregionsofhighestintensityarethecylinderandtorquearmshearlayers.Forthetwolowerfrequenciesof144and240Hz,itcanbeseenthatthemostintensespotsipbetweenthelowerandtheuppertorquearmshearlayers.ThisisaverysimilartrendtothatobservedintheLxandLyresultsatthesesamefrequenciesinFigure 5-47 .Furthermore,theeldimageat336HzalsosharessomecommonfeatureswiththeLyimageinFigure 5-47F ,whereboththeuppercylinderandtorquearmshearlayerareofhighestintensity.TheimageinFigure 5-49C alsoclearlyshowsinteractionsbetweentheshearlayersofthecylinderandthetorquearmedgesat336Hz.TheseresultsoftheLighthillstresstensordivergencemagnitudeareinapproximateagreementwiththetrendsoftheLambvectorcomponents,howeverwithgreateremphasisbeingplacedonthecylinderandtorquearmshearlayernoisesources. ThemagnitudeoftheLighthillstresstensordivergenceisnallyconsideredatafrequencyof2kHzforallsimulatedheights,theresultsofwhicharepresentedinFigure 5-50 .TheresultsagainshowagradualincreaseinspectrallevelsastheheightdecreasesfromZ=0.TheheightsofZ=0,-1D,and)]TJ /F1 11.955 Tf 9.3 0 Td[(2Dshowacombinationofsourcesbothinthecylinderandtorquearmshearlayers,aswellasduetoowimpingementontothetorquearmsurface.However,theimpingementsourcesareofconsiderablysmallerintensitythantheshearlayersofthetorquearmsharpedges.Forexample,thepeaklevelsoftorquearmowimpingementoccuratZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(2D,andareapproximately3-4dBbelowthepeaklevelsinthetorquearmshearlayeratZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(3D. 5.3Summary Aseriesofpost-processingtechniqueswereperformedontheowelddatabothfromexperimentallymeasuredSPIVdatasetsandselectoweldplanesfromaPowerFLOW 282

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CFDsimulation.Theseprocessingtechniquesbeganwithmoretraditionalstatisticalcalculationssuchasthemeanvelocityeld,three-dimensionalReynoldsstressesandTKE,andvorticity.Thecalculationsthenbecamemorecomplexwithalinearstochasticestimationproceduretodevelopatime-resolved,low-orderestimateoftheuctuatingvelocityeld.Theestimatedoweldwasthenusedtocomputetheacousticsourcetermsofthevortexsoundanalogytoidentifytheregionsoftheoweldthatareresponsiblefornoisegeneration.Themeanoweldstatisticsrevealedanon-traditionalrecirculationpatterninthewakeofthecylinderthatconsistedofasingularityvortex.Thisndingissignicantsinceitwasfoundtodiergreatlyfromthetandemcylinderwakebehaviorofsimilardownstreamspacing,whichisanindicatoroftheinuenceofthecurrentthree-dimensionalgeometry.AgradualincreaseinTKElevelswasfoundingoingfromthemodelcenterlinetoaplanelocatedthreediametersbelowthecenterline.Atthislowestmeasuredheight,theturbulencelevelswerefoundtobeprimarilyduetothetransversevelocityuctuationsduetoparticlesattemptingtotraversearoundtheblutorquearm,ratherthanthestreamwisecomponent.ThetorquearmwakerevealedcharacteristicsoftypicalblubodysheddingforheightsofZ=0andZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(0:592Dbasedonhigh-energyPODmodesthatcloselyresemblethoseof Durgesh&Naughton ( 2010 )andindicationsofatleastintermittentvortexsheddingfromestimationresults.Asthetorquearmbecamewiderandclosertothecylinder,however,theTKElevelsbecamemoreconcentratedinthegapowregionswhicharewhereattentionwasfocused. ThePowerFLOWresultsofthein-planeLambvectortermcalculationshaveprovidedevidencetoindicatethattheprimarysourceofnoiseisthevortex-shearlayercouplingoftheowaroundthesharpleadingedgesofthetorquearm.Thereisalsoasecondarysourceregionofhighintensitywithintheinnergapowregionatthetwolowestheightsmeasured.Furthermore,theseresultswereconrmedbyanalyzingthespectralcontentofthemagnitudeoftheLighthillstresstensordivergence,orjrTijj.TheLambvectorcomponentsdisplaythehighestband-limitedintegratedpowersataheightofZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(3D, 283

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whichisinterestingforseveralreasons.First,theverycloseproximityofthetandemgeometrywouldtraditionallyimplythatthenoisewouldbelowerbasedonprevioustandemcylinderexperiments( Lockardetal. 2008 ; Neuhartetal. 2009a ).Thisisbecausethereisnochanceforthevorticesshedfromeachsideofthecylindersurfacetocommunicatewithoneanother.Thisrationality,however,hasalwaysappliedforcircularcylindersofidenticaldiameter.Thetorquearmgeometryinquestionisconsiderablydierentfromsuchasimpliedcase,havingavaryingspanwisecross-sectionandthedownstreamcomponentconsistingofsharpedges.Thelargetorquearmwidthattheseheightsappearstopromoteabi-modalfeedbackbehaviorbetweenthetorquearmandcylinder,whichappearstoassistintransferringenergytothevortex-shearlayercouplingbehaviormentionedpreviously.Thisisevidencedbytheippingofprimarysourceregionsaboutthey=D=0axisinboththegapowandtorquearmedgeregions. 284

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A B C D E F Figure5-1. Contoursofmean(A)velocitymagnitude,(B)TKE,and(C)Z-vorticitywithlinecutprolesofgapow(D)meanvelocity,(E)normalcomponentsofReynoldsstress,and(F)shearcomponentsofReynoldsstressataheightofZ=0.Thevelocityprolesarethoselocatedhalfwaybetweenthecylinderandtorquearmhinge(indicatedbytheverticallinein(A)). 285

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A B C D E F Figure5-2. Contoursofmean(A)velocitymagnitude,(B)TKE,and(C)Z-vorticitywithlinecutprolesofgapow(D)meanvelocity,(E)normalcomponentsofReynoldsstress,and(F)shearcomponentsofReynoldsstressataheightofZ=1.175D.Thevelocityprolesarethoselocatedhalfwaybetweenthecylinderandtorquearmcross-section(indicatedbytheverticallinein(A)). 286

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A B C D E F Figure5-3. Contoursofmean(A)velocitymagnitude,(B)TKE,and(C)Z-vorticitywithlinecutprolesofgapow(D)meanvelocity,(E)normalcomponentsofReynoldsstress,and(F)shearcomponentsofReynoldsstressataheightofZ=2.175D.Thevelocityprolesarethoselocatedhalfwaybetweenthecylinderandtorquearmcross-section(indicatedbytheverticallinein(A)). 287

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A B C D E F Figure5-4. Contoursofmean(A)velocitymagnitude,(B)TKE,and(C)Z-vorticitywithlinecutprolesofgapow(D)meanvelocity,(E)normalcomponentsofReynoldsstress,and(F)shearcomponentsofReynoldsstressataheightofZ=3D.Thevelocityprolesarethoselocatedhalfwaybetweenthecylinderandtorquearmcross-section(indicatedbytheverticallinein(A)). 288

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A B C D Figure5-5. Comparisonsofnormalized(A),(C)velocitymagnitudeand(B),(D)TKEbetweenSPIVmeasurementsandPowerFLOWataheightofZ=0:(A)and(B)aretheSPIVmeasurements,(C)and(D)arethesimulationresults. 289

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A B C D Figure5-6. Comparisonsofnormalized(A),(C)velocitymagnitudeand(B),(D)TKEbetweenSPIVmeasurementsandPowerFLOWataheightofZ=)]TJ /F1 11.955 Tf 9.29 0 Td[(3D:(A)and(B)aretheSPIVmeasurements,(C)and(D)arethesimulationresults. 290

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A B C D E F Figure5-7. ComparisonofReynoldsstressesatZ=0betweenSPIVandPowerFLOWatmid-wayslicebetweencylinderandtorquearm:(A)RSuu,(B)RSvv,(C)RSww,(D)RSuv,(E)RSuw,(F)RSvw.LocationoflinecutindicatedinFigure 5-5A .The\---"linesrepresentsimulationresults. 291

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A B C D E F Figure5-8. ComparisonofReynoldsstressesatZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(3DbetweenSPIVandPowerFLOWatmid-wayslicebetweencylinderandtorquearm:(A)RSuu,(B)RSvv,(C)RSww,(D)RSuv,(E)RSuw,(F)RSvw.LocationoflinecutindicatedinFigure 5-6A .The\---"linesrepresentsimulationresults. 292

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A B C D Figure5-9. Instantaneoussnapshotsofvorticityinthegapowregionsforheightsof(A)Z=0,(B)-1.175D,(C)-2.175D,and(D)-3D.Flowisfromlefttoright. 293

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A B C D Figure5-10. ComparisonsofinstantaneoussnapshotsofZ-vorticitybetween(A),(C)experimentand(B),(D)PowerFLOWsimulationinthegapowregionsforheightsof(A),(B)Z=0and(C),(D)Z=)]TJ /F1 11.955 Tf 9.3 0 Td[(3D.Flowisfromlefttoright.Identicalcontourlevelsforallimages. 294

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A B Figure5-11. PODmodalenergybreakdownfor(A)gapowand(B)nearwakeregionsofZ=0Dand)]TJ /F1 11.955 Tf 9.3 0 Td[(3D. 295

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A B C D E F G H Figure5-12. ContoursoftherstfourPODspatialmodesofuvelocity(u)forthe(A)-(D)gapowand(E)-(H)nearwakeregionsatZ=0.(A),(E)(1)u,(B),(F)(2)u,(C),(G)(3)u,(D),(H)(4)u. 296

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A B C D E F G H Figure5-13. ContoursoftherstfourPODspatialmodesofvvelocity(v)forthe(A)-(D)gapowand(E)-(H)nearwakeregionsatZ=0.(A),(E)(1)v,(B),(F)(2)v,(C),(G)(3)v,(D),(H)(4)v. 297

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A B C D E F G H Figure5-14. ContoursoftherstfourPODspatialmodesofuvelocity(u)forthe(A)-(D)gapowand(E)-(H)nearwakeregionsatZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(3D.(A),(E)(1)u,(B),(F)(2)u,(C),(G)(3)u,(D),(H)(4)u. 298

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A B C D E F G H Figure5-15. ContoursoftherstfourPODspatialmodesofvvelocity(v)forthe(A)-(D)gapowand(E)-(H)nearwakeregionsatZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(3D.(A),(E)(1)v,(B),(F)(2)v,(C),(G)(3)v,(D),(H)(4)v. 299

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A B Figure5-16. Meanestimationdierencesfor(A)gapowand(B)nearwakemeasurementregions.Resultsareforr=5modes. A B Figure5-17. Cross-correlationsbetween(A)cylinderelectretsandtorquearmgapowsurfaceKulites,and(B)torquearmsurfaceKuliteswithtorquearmedgeelectrets.Eachplotrepresentsthecorrelationbetweensensorsthataretheclosesttothelightsheetforeachmeasurementplane.SensornumbersaredenedinFigure 3-40 andarecolor-codedtomatchthemeanestimationdierencesofFigure 5-16 300

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A B Figure5-18. Resultsof(A)mtd-mLSEapplicationtoZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(3DgapowPODdatausingr=5,10,and20modesand(B)modalenergysummationsfortherstftymodes. 301

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A B C Figure5-19. SinglesnapshotcomparisonforthegapowregionatZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(3Dbetween(A)originalSPIVvectoreld,(B)low-ordermodelrepresentationusingtherstvePODmodes,and(C)estimateusingmtdLSE-PODonrstvePODmodes. 302

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A B C Figure5-20. SinglesnapshotcomparisonforthenearwakeregionatZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(0:592Dbetween(A)originalSPIVvectoreld,(B)low-orderrepresentationusingtherstvePODmodes,and(C)estimateusingmtd-mLSE. 303

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A B C D E F G H Figure5-21. Contoursofthe(A)-(D)secondand(A)-(D)twelfthPODspatialmodesofuvelocity((2)u,(12)u)forthegapowregionatZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(3D.ThePODmodeswerecomputedbasedonaninputof(A),(E)100,(B),(F)200,(C),(G)400,and(D),(H)800snapshots.Mode(2)uisseentoconvergetoasmoothrepresentationfor800snapshots,whilemode(12)udisplaysalargevariationforallinputsnapshots. 304

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A B C D E Figure5-22. Comparisonofinstantaneousvorticitysnapshotreproductionusingtherstve,ten,andacustomsetoftenPODmodes:(A)instantaneoussnapshotofZ-vorticity,(B)low-orderrepresentationofZ-vorticityusingthersttenPODmodes,(C)estimateusingtherstvemodes,(D)estimateusingthersttenmodes,(E)estimateusingtheten-modesets=[1,2,...,8,11,14]. 305

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A B C D Figure5-23. ComparisonofPODmodalenergyfractionsbetweenSPIVandPowerFLOWfor(A),(B)Z=0and(C),(D)-3Dgapowandnearwakeregions:(A)and(C)arethegapowcomparisonsand(B)and(D)arethenearwakecomparisons. 306

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A B C D E F G H I J Figure5-24. ComparisonoftherstvestreamwisePODmodesbetweenPowerFLOWandSPIVforZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(3Dgapowregion.(A)(1)u,(B)(2)u,(C)(3)u,(D)(4)u,(E)(5)u.ThestreamwisePODmodesoftheSPIVdatasetarerepeatedhereforconvenience:(F)(1)u;SPIV,(G)(2)u;SPIV,(H)(3)u;SPIV,(I)(4)u;SPIV,(J)(5)u;SPIV. 307

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A B C D E F G H Figure5-25. ComparisonoftherstfourstreamwisePODmodesbetweenPowerFLOWandSPIVforZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(3Dnearwakeregion.(A)(1)u,(B)(2)u,(C)(3)u,(D)(4)u.ThestreamwisePODmodesoftheSPIVdatasetarerepeatedhereforconvenience:(E)(1)u;SPIV,(F)(2)u;SPIV,(G)(3)u;SPIV,(H)(4)u;SPIV. A B Figure5-26. ComparisonofinstantaneoussnapshotsofLx;1inthegapowregionatZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(3Dbetween(A)experimentalSPIVand(B)PowerFLOW.Bothimageshaveidenticalcontourlevelbounds. 308

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A B Figure5-27. ComparisonofsimulationsnapshotsatZ=)]TJ /F1 11.955 Tf 9.29 0 Td[(3Dbetween(A)Lx;1and(B)Lx=Lx;1+Lx;2. 309

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A B C D E F G H I Figure5-28. Visualizationofa5-modeestimateofaninstantaneoussnapshotoftheLambvectorpartialcomponents.TheoriginalsnapshotsofLx;1,Ly;1,andr^Lin(A),(D),and(G),respectively.The5-moderepresentationsarein(B),(E)and(H).Theestimatesofthe5-modesnapshotsarein(C),(F),and(I). 310

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Figure5-29. PODmodalenergybreakdowncomparisonsbetweengapowregionsZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(0:592D,)]TJ /F1 11.955 Tf 9.3 0 Td[(2:175Dand)]TJ /F1 11.955 Tf 9.3 0 Td[(3D. A B C D Figure5-30. Resultsofa10-modeestimationof(A),(B),Lx;1and(C),(D)Ly;1fortheZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(0:592Dgapowregion:(A),(C)LambvectorSPIVsnapshots,(B),(D)10-modeestimates. 311

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A B C D E F Figure5-31. ComparisonofestimationresultsforLx;1andLy;1usingveandtwentymodesfortheZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(0:592Dnearwakeregion:(A),(D)originalSPIVsnapshotsofLx;1andLy;1respectively,(B),(E)5-modeestimates,(C),(F)20-modeestimates. 312

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A B C D Figure5-32. Band-limitedintegrationof(A),(C)~Lx;1and(B),(D)~Ly;1PSDsforthegapowregionataheightofZ=0from(A),(B)PowerFLOWand(C),(D)SPIV.Thelow-orderrepresentationsforsimulationandexperimentwerecomputedusingtwelvePODmodesthatwereinagreementwithoneanother.TheintegrationofthePSDswereperformedoverthefrequencyrangeof96HzF1.216kHz. 313

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A B C Figure5-33. ComparisonbetweenrsttwouctuatingstreamwisePODmodesfromZ=0gapowregionfromSPIVandtherstmodefromPowerFLOW:(A)(1)u;SPIV,(B)(2)u;SPIV,(C)(1)u;PF. 314

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A B C D E F Figure5-34. Band-limitedintegrationof(A),(C),(E)~Lx;1and(B),(D),(F)~Ly;1PSDsforthegapowregionatheightsof(A),(B)Z=0:592D,(C),(D))]TJ /F1 11.955 Tf 9.3 0 Td[(1:175D,and(E),(F))]TJ /F1 11.955 Tf 9.3 0 Td[(2:175DfromexperimentalSPIVdata.Thelow-orderrepresentationsoftheelddataforeachheightwerecomputedusingtenPODmodesthatdemonstratedconvergence.TheintegrationofthePSDswereperformedoverthefrequencyrangeof96HzF1.216kHz. 315

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A B C D Figure5-35. Band-limitedintegrationof(A),(C)~Lx;1and(B),(D)~Ly;1PSDsforthenearwakeregionatheightsof(A),(B)Z=0and(C),(D))]TJ /F1 11.955 Tf 9.3 0 Td[(0:592DfromexperimentalSPIVdata.Thelow-orderrepresentationsoftheelddataforeachheightwerecomputedusingelevenandninePODmodesthatdemonstratedconvergencefortherespectiveheights.TheintegrationofthePSDswereperformedoverthefrequencyrangeof96HzF1.216kHz. 316

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A B C D Figure5-36. Comparisonofband-limitedintegrationsof(A),(C)~Lx;1and(B),(D)~Ly;1PSDsforthegapowregionataheightofZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(3Dbetween(A),(B)PowerFLOWsimulationand(C),(D)experimentalSPIVdata.Thelow-orderrepresentationsforbothsimulationandexperimentwerecomputedusingtenPODmodesthattheysharedincommonanddemonstratedconvergence.TheintegrationofthePSDswereperformedoverthefrequencyrangeof96HzF1.216kHz. 317

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A B C D E Figure5-37. GapowregionsinglepointPSDsofLambvectorpartialterms:(A)Z=0D,(B)Z=)]TJ /F1 11.955 Tf 9.3 0 Td[(0:592D,(C)Z=)]TJ /F1 11.955 Tf 9.3 0 Td[(1:175D,(D)Z=)]TJ /F1 11.955 Tf 9.3 0 Td[(2:175D,(E)Z=)]TJ /F1 11.955 Tf 9.3 0 Td[(3D. 318

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A B Figure5-38. NearwakeregionsinglepointPSDsofLambvectorpartialterms:(A)Z=0D,(B)Z=)]TJ /F1 11.955 Tf 9.3 0 Td[(0:592D.ThePSDswerecomputedusingtensecondsofcontinuousprobedata. 319

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A B (1)(2)(3)C D E (4)(5)(6)F Figure5-39. Simulatedband-limitedmeansquarevaluecontoursofpartialandfullLambvectorcomponentsatZ=0:(A)Lx;1,(B)Lx,(D)Ly;1,(E)Ly.PointsselectedforviewingLambspectraindicatedin(C)forLxand(F)forLy. 320

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A B C D E F Figure5-40. Non-dimensionalLambcomponentpowerspectraatselectpointsinZ=0regionindicatedinFigure 5-39 .Lxpoints:(A)point1,(B)point2,(C)point3.Lypoints:(D)point4,(E)point5,(F)point6. 321

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A B (1)(2)C D E (3)(4)F Figure5-41. Simulatedband-limitedmeansquarevaluecontoursofpartialandfullLambvectorcomponentsatZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(1D:(A)Lx;1,(B)Lx,(D)Ly;1,(E)Ly.PointsselectedforviewingLambspectraindicatedin(C)forLxand(F)forLy. 322

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A B C D Figure5-42. Non-dimensionalLambcomponentpowerspectraatselectpointsinregionZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(1DindicatedinFigure 5-41 .Lxpoints:(A)point1,(B)point2.Lypoints:(C)point4,(D)point5. 323

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A B (2)(1)(3)C D E (4)(5)F Figure5-43. Simulatedband-limitedmeansquarevaluecontoursofpartialandfullLambvectorcomponentsatZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(2D:(A)Lx;1,(B)Lx,(D)Ly;1,(D)Ly.PointsselectedforviewingLambspectraindicatedin(C)forLxand(F)forLy. 324

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A B C D E Figure5-44. Non-dimensionalLambcomponentpowerspectraatselectpointsinregionZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(2DindicatedinFigure 5-43 .Lxpoints:(A)point1,(B)point2,(C)point3.Lypoints:(D)point4,(E)point5,(F)point6. 325

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A B (1)(2)C D E (3)(4)(5)F Figure5-45. Simulatedband-limitedmeansquarevaluecontoursofpartialandfullLambvectorcomponentsatZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(3D:(A)Lx;1,(B)Lx,(D)Ly;1,(E)Ly.PointsselectedforviewingLambspectraindicatedin(C)forLxand(F)forLy. 326

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A B C D E Figure5-46. Non-dimensionalLambcomponentpowerspectraatselectpointsinregionZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(3DindicatedinFigure 5-45 .Lxpoints:(A)point1,(B)point2.Lypoints:(C)point3,(D)point4,(E)point5. 327

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A B C D E F Figure5-47. Normalizedeldpowerspectraof(A)-(C)Lxand(D)-(F)LyatZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(3Dforfrequenciesof(A),(D)144Hz,(B),(E)240Hz,and(C),(F)336Hz. 328

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A B C D E F G H Figure5-48. SimulatedeldpowerspectraofLxandLyatafrequencyof2kHzat(A),(E)Z=0,(B),(F)Z=)]TJ /F1 11.955 Tf 9.29 0 Td[(1D,(C),(G)Z=)]TJ /F1 11.955 Tf 9.29 0 Td[(2D,(D),(H)Z=)]TJ /F1 11.955 Tf 9.3 0 Td[(3D.LxPSDsshownin(A)-(D),LyPSDsshownin(E)-(H). 329

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A B C Figure5-49. NormalizedeldpowerspectraofjrTijjatZ=)]TJ /F1 11.955 Tf 9.3 0 Td[(3Dforfrequenciesof(A)144,(B)240,and(C)336Hz. 330

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A B C D Figure5-50. SimulatedeldpowerspectraofjrTijjatafrequencyof2kHzat(A)Z=0,(B)Z=)]TJ /F1 11.955 Tf 9.3 0 Td[(1D,(C)Z=)]TJ /F1 11.955 Tf 9.3 0 Td[(2D,(D)Z=)]TJ /F1 11.955 Tf 9.3 0 Td[(3D. 331

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Table5-1. SPIVmeasurementparametersfortorquearm=130congurationatU1=58m/s(M0.167) RegionN(Stats.)N(Est.)VectorcountRes.FieldImage Z=0 GapFlow100096552301.493NearWake1000944114031.493Z=0:592D GapFlow100089566541.495NearWake1000871130671.502Z=1:175D GapFlow100083855021.502NearWake1000893133681.502Z=2:175D GapFlow1500125719261.476NearWake1500136086361.479Z=3D GapFlow150083311481.476NearWake150099885691.484 Resolutioninmm/vec. 332

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CHAPTER6CONCLUSIONSANDFUTUREWORK Thisnalchaptersummarizestheprimaryndingsofthisdissertationandprovidesfutureworksuggestions.Theresearchndingspertaintohowtheexperimentaluiddynamicmeasurementshaveassistedfar-eldacousticmeasurementswiththeidenticationofphysicalsourcesofnoisegeneration.Inaddition,theroleofthePowerFLOWsimulationsasatoolforaeroacousticpredictionsandhowtheyhavecomparedtotheexperimentalresultsarealsodiscussed. 6.1ResearchKeyFindings 6.1.1ConnectionsbetweenFluidDynamicsandAcoustics Thestudyofaerodynamicnoisegenerationfromlandinggearorlandinggear\type"geometrieshasbeenatopicofincreasinginterestoverthepastdecadeorso.Thesestudieshaveprogressedfromsinglemicrophoneanddirectivitymicrophonearraystophasedarraysfornoisesourceidentication,andmorerecentlytoanalysisoftheoweldsurroundingthegearcomponents.Thisdissertationwasaimedatperformingallofthesemeasurementtypestoprovideascompleteofapictureaspossibleofthecausesofnoisegeneration. 6.1.1.1SurfacePressureMeasurements Steadysurfacepressuremeasurementsofboththecylindercircumferenceandthetorquearmatdierentmodelheightsrevealconsiderablevariationsinthegapowregionbehavioralongthemodelspan(Figure 4-1 ).Onaccountofthethree-dimensionalgeometryofthetorquearm,thespacebetweenthetandemcomponentsaswellasthesizeofthedownstreamcomponentchangeconsiderably.Thesevariationsareevidentinthebehaviorsofthepressurerecoveryregionsofthecylinderatthedierentheightsalongthemodelspan,wheretheychangefromastandarduniform(constantvalue)behavioratthemodelcenterlinetoaparabolicbehaviorataheightoftwocylinderdiameters,andnallytoanoscillatorytrendalongtherearcylindersurfaceataheightofthree 333

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cylinderdiameters.Meanwhile,thesteadypressuresonthetorquearmrevealedageneraltrendofincreasingpressurewithincreasingheightalongtheouteredgesofthegapowtorquearmsurface.Forthemostpart,thesteadymodelpressuresweresimilarbetweenthestandardmodelcongurations,withanexceptionforthe=160conguration.Thiscongurationdisplayedaprominentbi-modal(i.e.,twostates)behaviorevidentinthesteadypressuredata,whichindicatedthatthetransitionbetweenthesestateswasatverylowfrequency.Theinvertedconguration,meanwhile,portrayedaclearlydierentbehavior.Thecylinder,whichnowbecamethedownstreamcomponent,displayedacircumferentialpressuretrendverysimilartothatofadownstreamtandemcylinderatthemodelcenterline( Jenkinsetal. 2005 ).Forheightsaboveonecylinderdiameter,thetorquearmwidthexceedsthatofthecylinderandthusresultsinanearlyinvariantsteadypressuretrendaroundthecylindercircumference.Thisisduetothetorquearmwakeexpandingaroundthecylinderandpreventingwakeimpingementontothecylindersurface. Theuseofunsteadypressuretransducersprovidedinsightastothespectralcontentofthepressureuctuationsatkeylocationsonthemodel.Sensorslocatedonthecylinderindicatedagradualincreaseinspectrallevelsastheheightincreasesabovethemodelcenterline.Asimilartrendisobservedforthetorquearmsensors,howeverprimarilyatlowfrequencies.Fortheprimary=130conguration,allofthesensorsclearlyindicatethegradualemergenceofabi-modalbehaviorwithincreasingheightabovethemodelcenterline.Thebi-modalbehaviorofthiscongurationwasathigherfrequenciesthanthe=160onesinceitwasevidentintheunsteadypressurespectra.Theinvertedconguration,meanwhile,displaysconsiderablyhigherspectrallevelsonthecylinderforheightsatandbelowonecylinderdiameter,whiletheybecomecomparabletoandlowerthanthoseofthestandardcongurationsforheightsabovethis.Thisisfurtherevidencethatthetorquearm\shields"thecylinderfromtheoncomingowatheightswherethetorquearmiswiderthanthecylinder. 334

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6.1.1.2Far-FieldAcoustics Thesinglemicrophonemeasurementsrevealedinterestingdierencesbetweenthecongurationsintermsofspectralcontentandfar-eldscaling.Thelow-frequencyspectralcontentofthemodelwasseentoremainsimilarinshapeforarangeoftorquearmseparationanglesupuntilapointwheretheprimaryspectralhumpwasseentodegradeanddisappear.Thisbehaviorcoincideswellwiththefar-eldradiationstudiesoftandemcylindersina\sub-critical"spacingofL=D=1.435( Lockardetal. 2008 ),whichisverysimilartothemodelspacingsforthe=160conguration.Thistandemcylindercongurationresultedinanabsenceofavortexsheddingpeakinfar-eldmicrophonespectra.Whilethe=160congurationdiddisplayalowerfrequencyrangethatcollapsedbasedonStrouhalscaling,aspectralhumpwasabsent. The=100and130congurationsbothdisplayedspectralhumpsthatscaledwithStrouhalnumberandthefthandsixthpowersofvelocity,respectively.However,basedontheuncertaintiesofthemicrophonemeasurementsthemselves,thesepowersareessentiallyinterchangeable.Nevertheless,itisappropriatethatthesepowerscalingsrespectivelyrepresentacousticallycompactscatteringoofanitesharpedge( Williams&Hall 1970 )anddipoleradiation( Curle 1955 ).Allmodelcongurationsbegantodeviatefromthisscalingbehaviorabove416-432Hz,anddisplayaseventhpowerofMachnumberscalingwithdimensionalfrequency.ThefactthattheyareseentoscaleindependentofStrouhalnumberimpliesthatthesoundistheresultofHelmholtz,oredgescattering.Sincethisfrequencyrangeisabovethatofacousticcompactness,itisdiculttoquantify.However,thepresenceofthesharptorquearmedgesmakesthishigher-frequencyscalingaplausibleexplanation. Directivitymeasurementsweretakenforatotalofeightmodelcongurations,denedbasedontheseparationanglesbetweenthetorquearmcomponents( Section4.2.2 ).Therewasanincreaseinlevelswithincreasingtorquearmanglesbetween=100and140.Afterthis,theOASPLsdroppedslightlyforthe150congurationandthen 335

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considerablyforthe160conguration.Thelowestcongurationtested,however,wastheinverted=130conguration.ThiscongurationdisplayedOASPLsapproximately4dBbelowtheprimary=130congurationacrossallradiationangles.Thisisduetotheowseparatingfromthesharpleadingedgesofthetorquearmcomponentsandtheresultingwakeexpandingaroundthecylinder.Thisisevidencefromunsteadycylindersurfacepressurespectratooccurformodelheightsonecylinderdiameteraboveandbelowthemodelcenterline,wherethetorquearmwidthbecomescomparabletothecylinderdiameterandcontinuestowiden.Asaresult,thereisadrasticreductioninblubodyinteractionforthisconguration( Anglandetal. 2010 ). Thebeamformingresultswereverysimilarforthestandardcongurations,withtheDASandRCBalgorithmsindicatingthetorquearmtobeabroadbandnoiseproducer.Thiswasanexpectedby-productofthetorquearm'ssharpedges.Theinvertedconguration,however,deviatedfromthisbehaviorconsiderably,withthejunctionsbeinghighlightedastheprimarynoiseproduceratmid-tohighfrequencies.However,sincethemodeljunctionsweredesignedtobeorientedintheoppositestreamwisedirection,theyactedmorelikenoisecontaminantsforthisconguration.Asecondarysourceregionwasapparentonthedownstreamcylindernearthemodelcenterline,indicatingadditionalnoiseduetoshearlayerimpingementfromthetorquearmontothecylinderinthisregion.Thiswasbelievedtohaveoccurredsincethetorquearmwidthatthisheightisslightlylessthanthatofthecylinder.Applicationofadeconvolution(DAMAS)beamformingalgorithm( Brooks&Humphreys 2006 )atfrequenciesof1and2kHzhelpedtobetterunderstandtheapparentnoisesourcedistributionsofthemodel,sincetheprevioustwoalgorithmsdisplaypoorresolutionatthesefrequencies( Chapter4.2.7.3 ).Thestandardcongurationsdisplayeddominantnoisesourcesnearthetorquearmhingeandthetorquearmjunctionsatbothofthesefrequencies.Theinvertedcongurationalsodisplaysprominentnoisesourcesnearthejunctionsaswellasnearthecenterlineofthedownstreamcylinder.Thislatterobservationconrmsthatthetorquearmshearlayers 336

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stillimpingeonthecylinder,howeveritappearstobelocalizedwithintheregionwherethetorquearmhingewidthissmallerthanthecylinderdiameter. 6.1.1.3FlowFieldMeasurements Measurementsofselectoweldplanesatdierentheightsofthe=130congurationprovidedinsightintothemodel'sthree-dimensionalowdynamics.Surveysofvorticitywithinthegapowregionsatthesedierentheightsrevealedconsiderablechangesinthebehaviorofvorticesshedfromthemodelcylinder.Atthemodelcenterline,wherethespacingbetweencomponentsislargest,individualvorticesareseentoshedinamannersimilartothatofasinglecylinderoranupstreamtandemcylinderina\super-critical"conguration( Jenkinsetal. 2006 ).Atthelowestheightsmeasured,however,thevorticesbecamelessdistinctandwereconnedbythelarger-widthtorquearmcross-section.Turbulencestatisticsrevealedgradualincreasesofturbulencekineticenergywithinthegapowregionwithdecreasingheightfromthemodelcenterline.Thesegapowturbulencelevelsendupconsiderablyovertakingthoseinthewakeregion,particularlyattwoandthreecylinderdiametersbelowthemodelcenterline. OneoftheprimaryobjectivesofusingSPIVinthisstudywastocomputethemeasurablecomponentsoftheLambvector(L00=!0u0).Thisvectorwasidentiedby Powell ( 1964 )tobetheprimarysourceterminthevortexsoundanalogy.Sinceatime-resolvedcalculationofthissourcetermisrequiredbydenitionofthevortexsoundanalogy,alinearstochasticestimationtechnique(mtdLSE-POD)wasappliedtodevelopalow-ordertime-resolvedestimateoftheLambvectorsourceterms.ThemtdLSE-PODresultsendedupdisplayingexcellentagreementinband-limitedlevelsofthelow-orderLambvectorpartialtermestimatesbetweenexperimentalSPIVdataandPowerFLOWsimulations.TheseagreementspromptedtheuseofthePowerFLOWsimulationstoextractthefull-orderLambvectorterms.VisualizationofthesimulatedLambvectorintensitydistributionsovertheeldplanesrevealedthatthetorquearmedgesareaprominentandbroadbandsourceofnoise.Thehighestspectrallevelsoftheseterms 337

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occurredatthelowestrecordedheightofthreediametersbelowthemodelcenterline.Inadditiontothetorquearmedges,however,thisheightalsodisplayedhighsourceintensitieswithinthegapowregionitself.Observationofnarrowbandfrequencymapsofthisregionclearlydisplayedevidenceofthebi-modalbehaviordisplayedintheunsteadysurfacepressurespectra.Inaddition,thewakeregionswereobservedtocontainverylittleoverallLambvectorspectralintensitieswithaslightexceptionatthemodelcenterline.Atthisregion,thenearwakeregiondidshowintensitiescomparabletothoseinthegapowregion.However,thepeakLambintensitiesatthislocationwereapproximatelyafactorofthreetimeslowerthanthoseatthreediametersdown,whichtranslatesintoapowerdecitofnearly5dB.Despitethis,however,theexperimentallow-orderestimatesofthestreamwiseLambvectorpartialterminthewakeatthemodelcenterlinedisplayedahigh-energypeaknear400Hz.ThisfrequencyalsohappenstobetowardstheupperrangeofStrouhalnumbersthatdisplayedeectivefar-eldspectralcollapsingbasedonStrouhalnumber. 6.1.2PowerFLOWasanaeroacousticsimulator ThePowerFLOWsimulationsdisplayedexcellentagreementwiththeexperimentalmeasurementsintermsofsteadyandunsteadypressures,oweldmeanandturbulentfeatures,andafar-eldacousticprediction.Basedontheseagreements,theadditionalfeaturesofPowerFLOW,namelytheonesthatcannotbeexperimentallymeasured,werealsoconsideredtobereliable.Theseincludethepressureuctuationsoftheentiremodelaswellasthefull-eldplanarspectralmeasurementsoftheLambvectorcomponents(discussedintheprevioussection).Theformeroftheseitemswaspresentedin Chapter4.1.2.3 ,whichclearlyshowedthatmodelpressureuctuationswerethemostintenseontheinnergapowsurfaceofthetorquearmsfurthestfromthemodelcenterlineaswellalongthecylinderneartheregionofowseparation.Thiswasseentooccurforthirdoctavebandcenterfrequenciesof200and250Hz.Abovethesefrequencies,theregionsofhighestintensitygraduallymoveupwardsalongthetorquearmedges.Atthe 338

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highestreportedcenteredfrequencyof1kHz,essentiallythetorquearmedgesalongtheirentireheightaretheregionsofhighestspectralintensity. 6.2SuggestionsforFutureWork Thisdissertationreportedonthecharacterizationofthecausesofaerodynamicnoisegenerationforturbulentowaroundatorquearmgeometrypresentonnumerouscommercialaircraftnoselandinggears.Whilereasonableprogresswasmadeonthisfront,continuedworkiswarranted. Itisimportanttorecallthattheoweldmeasurementsperformedinthisstudywerelimitedtoaplanareld.Asaresultofthis,onlypartialcomponentsofthevortexsoundsourcetermscouldbecalculated.Therefore,itissuggestedthatfutureworksonthree-dimensionalblubodyinteractionsbeconductedwithvolumetricoweldmethods.Theseincludedual-planeSPIV( Huetal. 2001 ),plenopticvelocimetry( Nonnetal. 2012 ),andtomographicPIV( Violato&Scarano 2013 ).ThelatterofthesereferencedstudiesisparticularlyapplicablesincetheresearchersusedtomographicPIVtoinvestigatethebehaviorofajetcorebreakdownandtocomputethethree-dimensionalcomponentsoftheLambvectorforacousticcharacterization. Anextstepoftestingthistypeofgeometryistoperformaoweldstudyonaquieterconguration,namelytheinvertedone.ThiscongurationwasfoundtodisplayanOASPLapproximately4dBquieterthantheprimarycongurationtestedinthisdissertationforallmeasuredradiationangles.Therefore,itwouldbeinterestingtoidentifythefundamentalowfeaturesthataredierentbetweentheinvertedandstandardcongurations. Anothertestingpossibilityistoroundthetorquearmedges.Theresultofthiscouldbetopotentiallydecreasethebroadbandlevelsthatwouldtypicallybeassociatedwithowaroundsharpedges.ThiscouldpotentiallyresultinreductionofA-weightedOASPL,sincefrequenciesbetween1and5kHzareweightedthehighest.Anillustrationofthe 339

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comparisonbetweenthesharp-edgedtorquearmtestedinthisstudyandaroundedtorquearmedgeconceptispresentedinFigure 6-1 Othermodicationsthatmaybeappliedtothebaselinetorquearmgeometryareowcontroldevices.Passivedevicesthathaveshowngreatpromiseinrecentyearswithlandinggeargeometriesareporousmeshes( Boorsmaetal. 2009 ; Oerlemans&Sandu 2010 ).Thesemeshescanbetestedinapplicationaroundentirelandinggearcomponents,orportionsofthelandinggeartotestreductionofnoiseatlowand/orhighfrequencies.Anotherowcontrolmethodthathasshowngreatpromiseistheusageofsteadyblowingtoreduceblubodyinteractionnoise.Anapplicationofthiswassuccessfullyappliedtoatwo-dimensionaltandemcongurationconsistingofanupstreamcylinderandadownstreamH-beam( Anglandetal. 2010 ).Theresultsofinducingsteadyblowingalongthespanofthecylinderresultedinapeakfar-eldSPLreductionof9.3dBataStrouhalnumberof0.2,andabroadbandreductionof3.2dB.Therefore,thesimilaritybetweenthetwo-dimensionaltandemcongurationandthegeometryofthisdissertationmakesteadyblowinganattractiveowcontrolmethod. Finally,thetorquearmgeometryisafundamentallandinggearcomponentthatcanbeaddedtoinordertobecomemorecomplex.Themodularnatureofthetorquearmmakesitamenabletotheadditionofothercomponents,suchaswheels.AnillustrationoftheadditionofwheelstothecurrenttorquearmgeometryisshowninFigure 6-2 .NotethatthewheelsshowninthisgurearereplicasoftheGulfstreamG550noselandinggear( Zawodnyetal. 2009 ),andaresizedtomatchthescaleofthetorquearmgeometry.Theadditionofthesewheelstothetorquearmresultsinanobviousincreaseinwindtunnelblockage.ConsideringtheUFAFFtestsectiondimensions,thetorquearmgeometrywiththewheelsshowninFigure 6-2B resultsina10.9%blockagebyfrontalarea.Thisrepresentsatestsectionblockageincreaseof6.9%fromthe4%ofthetorquearmmodelitself.Asaresult,thisisslightlylargerthantherecommendedmaximumof10%.Therefore,afacilitywithaslightlylargertestsectionmaybewarranted. 340

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A B Figure6-1. Illustrativecomparisonbetween(A)sharpand(B)roundededgesofthetorquearmcomponent. A B Figure6-2. Illustrationoftheadditionofnoselandinggearwheelstothetorquearmgeometry:(A)currenttorquearmgeometry,(B)torquearmgeometrywithaddedwheels. 341

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APPENDIXAKULITEIN-LINEAMPLIFIERDESIGN TheKulitesensorsusedinthisstudyareLQ-125stylesensors,withapressureratingof5PSIsealedgage.Thesesensorswerechosenbecauseoftheiratpackaging,whichmakethemidealforushmountingonaatsurfacewithinaconnedvolume,suchastheinsideofthetorquearmframe.Unfortunately,thesealedcavitynatureandhighratedpressurerangeofthesedevicesmakethemunsuitableforrecordingpressureperturbationsinthecurrentapplicationwithoutappropriateinterfacecircuitry.Therefore,anampliercircuitpackagewasdesignedandimplementedtoaccompanyunsteadysurfacepressuremeasurementsmadewiththeKulitesensorsonthemodeltorquearm.Thisin-lineamplierwasadaptedfromoneoriginallydesignedforapiesoresistivemicrophone.ThisoriginaldesignwasprovidedcourtesyofDylanAlexanderoftheInterdisciplinaryMicrosystemsGroupattheUniversityofFlorida. A.1AmplierBoardDesign Thethreeprimaryreasonsfordevelopingthisin-lineamplierweretoimprovethemeasurementsensitivityofthedevice,workasahigh-passltertoremovetheDCcomponentofthesignal,andminimizeelectronicnoisecontaminations.Therstoftheseisdirectlyattributedtothehighratedpressureofthefactory-issueddeviceascomparedtotheexpectedpressureuctuationlevelsforthecurrentapplication.ThiscalledforanamplicationoftherawsignalfromthesensordenedintermsofagainfactorGas G=Xamp Xraw;(A{1) whereXrawrepresentstherawvoltageoutputofthedevicewhileXampistheampliedsignal.Furthermore,sealedgagesensorsaretypicallyknownforhavingahighamplitudeDCsignalcomponent.Sincetheprimarymeasurementobjectiveofthesedevicesispressureuctuations,itwasdesirabletoincorporateahigh-passlterintotheampliercircuit.ThiswasaccomplishedviainsertionofanRCcircuitintotheamplierpackage. 342

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Finally,itwasdesirablethattheampliercontributeminimalnoisetothemeasurementsaswellasreducetheelectronicnoisecontaminationimposedbytheUFAFFtestingfacility.Theformerofthesetypesofnoisegenerationisrelatedtotheamplieritself,whilethelatterisafunctionofthepositionoftheamplierrelativetothetransducer.Previousmeasurementsmadewiththesesensorsusinganexternalamplierboardlocatedapproximately5feetfromthesensorshaveyieldedsignalscontaminatedbyelectromagneticmagneticinterference(EMI)inducedbythewindtunnel'svariablefrequencydrive(VFD).Thiswaslaterattributedtothelonglengthofthesensor'swiringactingasanantennafortheEMIcontaminationpriortoreachingtheampliercircuitry.Thus,insertionoftheampliercircuittobe\in-line"withthesensorwasexpectedtoremedythisproblem. TheamplierchosenforthisapplicationistheAD8429lownoiseinstrumentationamplier,manufacturedbyAnalogDevices.Thisamplierwaschosenbecauseofitsexcellentlownoiseperformanceof1nV=p Hzforgainfactorsintherangeof100G10;000.ThegainwassetusingasinglegainresistorRGaccordingtotherelation G=1+6k RG:(A{2) Themanufacturer-quotedsensitivitiesfortheKulitesusedinthisstudywerereportedtobeapproximately10mV/PSI(1.45V/Pa),whichwasdeterminedtobeverylowfortheexpectedpressuresinthecurrentapplication.Therefore,againofG=100wasselectedasasuitableamplicationfactor.Thehigh-passlterforthecircuitwasdesignedtoexhibitacornerfrequency,f)]TJ /F7 7.97 Tf 6.59 0 Td[(3dB,thatwouldbecomparabletothatofthedataacquisitionsystemutilized.Thisfrequencycorrespondstotherelation f)]TJ /F7 7.97 Tf 6.59 0 Td[(3dB=1 2RfCf:(A{3) NotethatthecornerfrequencyoftheNI-PXI4462dataacquisitioncardsusedinthisstudyisf)]TJ /F7 7.97 Tf 6.58 0 Td[(3dB=3.4Hz.Figure A-1 providesacircuitdiagramoftheampliercircuit,as 343

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wellasavisualizationofthelayoutoftheeventualprintedcircuitboard(PCB).AlistoftheboardcomponentsandtheircorrespondingvaluesarealsoprovidedinTable A-1 .ThenalKulite-amplierpackageispresentedinFigure A-2 .Notethatthelengthofelectricalwiringbetweenthesensorandampliercircuitwassettoapproximately12"(304.8mm),whichallowedexibilityinthepositioningofthesensortomultiplepotentiallocationswithinthemodeltorquearm. A.2Kulite-AmplierPerformance TheperformanceoftheamplierswerequantiedpriortoconnectiontotheKulitesensors.ThiswasdonebysupplyingBLwhitenoise(0F12:8kHz,f=16Hz)asaninputsignaltotheamplier,andtheinputandoutputsignalswererecorded.ComputingtheFRFbetweenthetwosignalswasperformedtoyieldacomplexrepresentationoftheampliergainasafunctionoffrequency.Thecomplexgainresponsesforthe3ampliersusedintheexperimentsareprovidedinFigure A-3 .Astheseresultsshow,excellentrepeatabilitywasobtainedforthecircuits,withallamplierpackagesexhibitingatampliergainmagnitudesofjGj98forfrequenciesabove48Hz.Furthermore,thephaseresponsesarealsoverysimilarforthethreeamplierpackages,exhibitinganearlyatresponseforfrequenciesatandabove96Hz. Asavericationoftheimprovedperformanceofthein-lineamplier,twooftheKuliteswereplacedinthetorquearmmodelandsubjectedtotheowspeedsofinterest.ThesesensorplacementsareillustratedinFigure A-4A .Oneofthesetransducerswasouttwiththein-lineamplier,whiletheotherwasconnectedtotheoriginalexternalamplierboard.ItwasfoundpreviouslythatthesimplepoweringontheUFAFF'svariablefrequencydrive(VFD)wouldseverelycontaminatetheKulitesignalwhenconnectedtotheexternalamplierboard.Therefore,noiseoorsofthetwosensorsetupsweretakenpriortotestingtheminowcases.TherawPSDsofthetwodierentKulite-amplierpackages(inunitsofV2=Hz)inquiescentandowcasesarepresented 344

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inFigs. A-4B and A-4C ,respectively.Fromtheseresults,itcanbeclearlyseenthatthein-lineamplierprovidesadrasticreductioninelectronicnoise. A B FigureA-1. (A)Circuitdiagramand(B)PCBlayoutfortheKulitein-lineamplier. A B FigureA-2. (A)CompleteKulite-amplierpackageand(B)close-upimageofampliercircuit. 345

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FigureA-3. ComplexgainfrequencyresponseofKuliteamplierinterfacecircuits. 346

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A B C FigureA-4. IllustrationofimprovedperformanceofKulitein-lineampliers:(A)Modelinstallation,(B)comparisonofnoiseoorsbetweendierentKuliteampliercongurations,(C)comparisonofKulite-amplierPSDsintorquearmmodelatafreestreamvelocityofU1=58m/s. 347

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TableA-1. KuliteamplierPCBcomponents. ComponentValueDescription AD8429N/ALownoiseinstrumentationamplierRG60.4GainresistorRf;1,Rf;250.0kResistorforhigh-passlterCf;1,Cf;21.0FCapacitorforhigh-passlterC1,C210.0FTantalumcapacitorC7,C80.1FCeramiccapacitor 348

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APPENDIXBGROUPARRAYCALIBRATION Inordertoensurethatfrequencydomainbeamformingusingaphasedarrayoutputsaccuratesourcelocationandstrengthestimates,thecomputedsteeringvectorsmustbeclosetotheactualones.Tomitigatetheissuesofsourcesofuncertaintysuchasmicrophonepositionerrors,awidely-usedcalibrationproceduredevelopedby Dougherty ( 2002 )isimplemented.Inthisprocedure,microphonearraydataiscollectedonanominallyacoustic\point"sourcethatexhibitsmonopolebehavioroverthefrequencyrangeofinterest.Additionally,thiscalibrationsourceshouldbepositionedascloseaspossibletothelocationoftheregiontobeanalyzedduringexperimentationtominimizelobedistortioneects.Fromtheacquiredmicrophonearraydata,aCSMisconstructedandfrequency-dependentcomplexcorrectionfactors(magnitudeandphase)areobtainedforandappliedtoallmicrophones.Thistechniquewasappliedforbothstaticandowconditions,theformerofwhichwasmeanttodiagnosetheexperimentalperformanceofthearrayascomparedtothetheoretical,andthelatterofwhichwastoprovideanin-situcalibrationtocorrecttheexperimentaldatasetsforshearlayerrefraction.Thisappendixoutlinesthearraycalibrationcalculations,physicalsetup,andademonstrationoftheresults. B.1MathematicalDescription Asdiscussedin Chapter3.5.2.1 ,thebthfrequencyblockofapressurerecordforthemthmicrophonecanbedenotedasYm(fb).Thispressurerecordcanbefurtherdenedinthepresenceofasinglecalibrationsource: Ym(fb)=am;calscal(fb);(B{1) wheream;calisthenominalsteeringvectorandscalisthesignalwaveformofthecalibrationsource,bothofwhichareunknown.Thegoalistocomputeacomplex 349

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correctionfactor~Dmforthemeasurementofthemthmicrophone: Ym;cal(fb)=~DmYm(fb):(B{2) ThiscomplexcoecientisdeterminedbyredeningtheCSM,G,intermsofthesquaredforceofthesignalfromthecalibrationsourceF2calandthecorrectsteeringmatrixAcal: Gcal=F2calAcalAHcal;(B{3) and ~Dm=m;th m;cal;form=1;:::;M(B{4) wherem;cal=am;calej kam;calkisthenon-zeroeigenvectorofthesolutionofEquation B{3 andm;th=am;th kam;thkisthatbasedonthesteeringvectordenitionspresentedinEquations 3{41 and 3{42 .Therefore,utilizingtheassumptionthatkam;calkkam;thk,thenEquation B{2 reducesto Ym;cal(fb)=am;thscal(fb):(B{5) Thisinturn,yieldsacorrectedcross-spectralmatrixcalculatedas Gcal=~DG~DH:(B{6) Notethatthissectionhasbeenanoverviewofthearraygroupcalibrationprocess.Moredetailofthisprocesscanbefoundin Yardibietal. ( 2010a ). B.2WindTunnelCalibrationSetup CalibrationofthephasedarraytookplacewithintheUFAFFtestsectionusinganon-intrusive,laser-inducedacousticpointsource.ThissourcewasgeneratedusingtheEvergreen200Nd:YAGpulsedlasersystem,whichiscapableofoutputtingamaximumenergyof200mJ/pulsewithapulsewidthof10ns(FWHM).Theincidentlaserbeamwaspassedthroughamulti-stagetelescopeassemblyforthepurposeofexpandingandre-convergingthebeamtoanearlyinnitesimalpoint,thuscausingaplasmaformation,or 350

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a\spark"inair.ThecomponentsofthistelescopeassemblyaredetailedinFigure B-1 andTable B-1 .Ascanbeseen,atotaloffourlensesarepresentinthetelescope,thersttwoofwhichareplano-concavelensesthatservethepurposeofexpandingthelaserbeam.Thenaltwolensesareachromaticdoubletsthatre-focusthebeam.Thelensesarehousedinaseriesof3"(76.2mm)diameterblack-anodizedaluminumtubes.Theeectivefocallengthoftheassembly(asmeasuredfromtheexitplaneofthetelescope)isapproximately14.57"(370mm),whichisalmostexactlyequaltothehalf-heightoftheUFAFFtestsection.Thelasersparklocationwaspositionedtobeasclosetothedownstreamsurfaceofthemodeltorquearmaspossible.This,coupledwiththeverticallocationofthesourceendedupbeing1.5"(38.1mm),oronecylinderdiameterfromthehingeofthetwotorquearms. Figure B-2 providesanillustrationofthelaserpulseassemblywithintheemptyUFAFFtestsectionaswellasaphotographofasparkoccurrence.Theseimagesrepresentthestaticcalibrationconguration.Inadditiontohavingtwoupperandloweracousticfoamsidewalls,boththeinletanddiuserwereinsulatedwith3"(76.2mm)tallwedgefoamsheetstoprovideasclosetoananechoicenvironmentaspossible.Thetelescopewasinstalledwithinthelowersidewallsuchthattheedgeofthetelescopewasushwiththeowsurfaceofthesidewall.Notethattheendofthetelescopewassealedbyatransparentwindowwithananti-reectivecoating,whichallowedbothacleanushmountingofthetelescopeaswellasminimizationofenergylossesofthetransmittedlightthatwouldoccurwithanuncoatedwindow. B.3CalibrationResults Sampleresultsofthetwocalibrationproceduresarepresentedinthissection.Therstonedetailsthestaticcalibrationcase,inwhichtheexperimentally-computedpointspreadfunction(PSF)iscomparedwiththetheoreticaloneforvarioussourcelocationsrelativetothearrayposition.Thiswasmeanttoserveasavalidationoftheperformancesofboththephasedarrayaswellasthelaserplasmaformationasanacousticcalibration 351

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source.Thesecondcalibrationsetupconsistsofthephasedmicrophonearraypositionedinitsoriginalstaticcalibrationlocationwiththemodelinstalled,andundergoingowconditions.MicrophonecalibrationdatablockswererecordedsynchronouslywiththelaserpulseusingtheQ-switchoftheEvergreenlaserasatriggersignal.Thisensuredthattheincidenceofthelaserpulsewouldtakeplaceatthesamesamplenumberforeachblock,thuspreservingthe\deterministic"contentofthelaserpulse.ThesamplingparametersaredetailedinTable B-2 B.3.1StaticCalibration Aseriesofstaticcalibrationrunswereperformedonthephasedmicrophonearrayforavariationofsourcelocations.ThiswasdoneinordertoexperimentallydeterminethearrayPSFandidentifyitssimilaritytotheory,aswellascharacterizethesourcedistortioneectsofshiftingthearrayrelativetothesourcelocation.Thisisimportantsincevericationthatthearrayperformancematchesthatpredictedbytheoryprovidesassuranceofaccurateabsolutespectrallevelscomputedbythearray.Therefore,thePSFofthearraywasestimatedexperimentallyforarangeofsourcelocations.Duetothecomplexityofthelasersourcesetup,thearraylocationwasshiftedwithintheUFAFFrelativetothestationarylasertelescope.ThesesourcelocationsareshowninFigure B-3 B.3.1.1LaserPulsePerformance Theperformanceofthelaserpointsourcewasdiagnosedinitiallywiththeuseofthephasedarraycenterreferencemicrophoneinbothtimeandfrequencydomains.Thiswasdoneinordertodeterminethepresenceandcausesoffacilityreectionsaswellasthebroadbandcontentofthelaserpulse.TobetterquantifythenominalperformanceoftheFFMA,thetimeseriesofthecentermicrophonewaslteredtoremovecontaminantsduetounwantedfacilityreections.Thiswasdonebyzero-padding,or\gating"thesignaloutsideofaspeciednumberofsamples.Thissamplecut-oissetsuchthatthetimescalescorrespondingtoarrayinter-microphonereectionswouldbepreserved,whilethosecorrespondingtoreectionsduetothefacilitywouldberemoved. 352

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ForthecaseoftheFFMAcenteredwiththelaserpulselocation(Figure B-3A ),thetemporalandspectralperformanceoftheplasmaformationisshowninFigure B-4 .Notethatforthiscase,theinnerarraymicrophoneswereinstalledsincetheentirearraywasbeingcharacterized.AsFigure B-4A shows,thereisaclearoccurrenceoftheincidentpressurewavefromthelaserpulseat4.2ms.Thereisalsoanoticeablesecondaryclusterofpeaksinthetimeseriescenteredaround5.5ms.Thiswasdeterminedtobeduetoasecondaryreectedwaveofthelaserpulsewaveoofthetestsectionsidewalls.Inaddition,thereasonforthepresenceofmultiplepeaksisduetothescatteringofthissecondarywaveooftheinnerarraymicrophones,whichareincloseproximitytooneanotherandthereferencemicrophone.Furthermore,scatteringoftheincidentpressurewaveooftheinnerarraymicrophonescanbeseeninatimerangeof4:2
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forthelocationstested,withsomeslightdierencesinthelevelsofcertainsidelobes.Inaddition,distortionofthemainlobeisobservedforthetwoshiftedarraypositions.Thisprovidesproofthatcenteringthearrayasclosetothesourceregionaspossiblesoastomakethesourcelocalizationasaccurateaspossible. B.3.2FlowCalibration Themostappealingfeatureofthelaserpointsourcesetup,isthepossibilityofperformingthecalibration\in-situ",orduringawindtunneltestofinterest.Thisallowsforthecalculationofagroupcalibrationmatrixforthecaseofowaroundthegeometryofinterest.Thismatrixcanthenbeappliedtophasedmicrophonearraydataforanidenticalowcasetoaccountforshearlayerrefractioneects,thuseliminatingtheneedforapplyingatraditionalshearlayercorrection.Thisisausefulbenetsinceperformingbeamformingonacomplexoweldhasshownphaseresponsesbetweenarraymicrophonestobehighlynon-linear,thusnegatingtheapplicabilityoftraditionalshearlayercorrectionposedby Amiet ( 1978 ).Thetelescopesetupforin-situtestingwiththetorquearmmodelisshowninFigure B-6 .Asthegureshows,thetelescopewindowismountedushwiththesidewallsurfaceandthesparksourceislocatedapproximatedhalfwayupalongtheheightofthetestsection.Thetelescopewindowwaspositionedatadownstreamlocationsuchthatthesparkwouldbeasclosetothetorquearmhingeaspossible,namelywithin1"(25.4mm)ofthehingeforthecongurationwiththesmallestseparationangleof=100. Theperformanceofthelaserpointsourceforthecaseswithowwerefoundtobeverysimilartothestaticcalibrationcaseforfrequencieswithintheaudiblerange.However,theinducedfacilityeectssuchasvibrationofthefoamsidewallsresultedinreducedperformanceofthelaserpulseathigherfrequencies.AnillustrationofthisisshowninFigure B-7 .Asthisgureshows,thereisconsiderablylesspowerinthepointsourceforfrequenciesabove25kHz.Thiscouldposeconsiderablelimitationsforotherexperimentalsetupsthatwouldutilizethislaserpointsourceconcept,especiallythoseof 354

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smaller-scalethathavehighercharacteristicfrequenciesofinterest.Thisdoesnotposeaprobleminthisapplication,however,sincetheupperfrequencyofinterestis10kHz. Thearrayperformancewasthendiagnosedusingthelaserpulsetocomputegroupcalibrationmatricesforcaseswithow.ThiswasdonebyrunningtheUFAFFatseveralspeedswhileringthelaserandsynchronouslyacquiringdatafromtheFFMAmicrophones.Withthesourcelocationknownfromthestaticcalibrationexperiments,agroupcalibrationmatrixwasconstructedforeachcaseandappliedtotheCSMofthedata.Theresultofthisprocess,againusingthestandardDASalgorithmisshowninFigure B-8 .Notethatfortheseplots,adynamicrangeof10dBisshown,whichisstandardforthepresentationofexperimentalbeamformingresultsusingtheDASalgorithm.Asthisgureshows,applicationofthegrouparraycalibrationmatrixresultsinasuccessfulupstreamshiftofthemainlobetocoincidewiththemeasuredsourcelocation.ThisisrepeatedinFigure B-9 forthecaseofawindtunnelexperimentofthetorquearmmodelinthe=130conguration.ThegrouparraycalibrationmatrixappliedtothisdatawastakenimmediatelypriortotheFFMAcontinuousdatasetusedtogeneratethebeamformingmap. FigureB-1. Schematicoflenstelescopeassembly.Notethatthedimensionsareinmm. 355

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A B FigureB-2. (A)Illustrationoflaserpulsecalibrationsourcesetupand(B)photographofsparksourceoccurrence. A B C FigureB-3. Phasedarraylocationsrelativetosparksourceforarraystaticcalibrationruns:(A)arraycenteredwithsource,(B)arrayshifted0.28mdownstream,(C)arrayshifted0.56mdownstream. A B FigureB-4. (A)Temporaland(B)spectralperformanceoflaserpointsourcebasedonFFMAcenterreferencemicrophone(representsthenoiseoorofthemicrophoneusingHanningwindowwith75%overlap). 356

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A B C D E F FigureB-5. FFMAtheoreticalandexperimentalPSFperformancefordierentstaticcalibrationlocations:(A),(D)arraycenteredwithsource,(B),(E)arrayshifted0.28mdownstream,(C),(F)arrayshifted0.56mdownstream(leftcolumn-simulated,rightcolumn-measured). 357

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FigureB-6. Imageoflasertelescope,phasedarrayandtorquearmmodelinstalledwithintestsectionforphasedarrayin-situcalibration. FigureB-7. SpectralcontentofthelaserpulsesetupasmeasuredbytheFFMAcentermicrophoneforstaticandowcalibrationcases. 358

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A B FigureB-8. Eectofperformingin-situgrouparraycalibrationonbeamformingoflaserpointsourceatM0.167forafrequencyof4.992kHz:(A)nocalibrationapplied,(B)grouparrayin-situowcalibrationmatrixapplied.The\+"symbolrepresentsthepeakamplitudefortheuncalibrateddataandthe\"symbolrepresentstheactualmeasuredsourcelocation.Resultsareforanemptytestsection,withowfromrighttoleft. 359

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A B FigureB-9. Eectofperformingin-situgrouparraycalibrationonDASbeamformingoftorquearm=130congurationatM0.167forafrequencyof4.992kHz:(A)nocalibrationapplied,(B)grouparrayin-situowcalibrationmatrixapplied.The\+"symbolrepresentsthepeakamplitudefortheuncalibrateddataandthe\"symbolrepresentsthepeakamplitudeforthecalibrationone.Flowisfromrighttoleft. 360

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TableB-1. Componentsofthelenstelescopeassembly. Lens#LensTypeFocalLength(mm)Diameter(mm) L1Plano-Concave-5025.4L2Plano-Concave-5025.4L3DoubletAchromatic25076.2L4DoubletAchromatic50076.2 TableB-2. Phasedarraycalibrationandexperimentaldataacquisitionparameters. ParameterCalibration(Pulsed)RunsTunnelExperiments SamplingFreq.(kHz)20480065536PulseRate(Hz)2N/ABlockLength(Nsamples)64004096AveragingMethodEnsembleFFTSamplingTechniqueDiscreteContinuousNblocks500480WindowingRectangularHanningBlockOverlap(%)075 361

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APPENDIXCSPIVUNCERTAINTYANALYSIS C.1BiasUncertainty ThebiasuncertaintiesofSPIVdatawereestimatedbyrelatingthedisplacementsmeasuredbyeachcameratothoseoftheactualparticlesinspace( Hu 2013 ).Thisuncertaintyformulationisbasedonthepinholelensassumption,inwhichthemeasureddisplacementsofathree-dimensionaldisplacementinphysicalspace(X;Y;Z),are(x1;y1)and(x2;y2)intheimageplanesofthetwocameras,respectively.Theanglesoftheviewingraysrelativetothelightsheetnormalaredenotedas1and2inthexz-planeand1and2intheyz-plane.AnillustrationofthisdisplacementcomponentbreakdownappliedtoacommonSPIVcongurationisprovidedinFigure C-1 .Withtheuseoftrigonometry,allthreecomponentsofdisplacementarecomputedas x=x2tan1)]TJ /F1 11.955 Tf 11.96 0 Td[(x1tan2 tan1)]TJ /F1 11.955 Tf 11.96 0 Td[(tan2;(C{1) y=y2tan1)]TJ /F1 11.955 Tf 11.95 0 Td[(y1tan2 tan1)]TJ /F1 11.955 Tf 11.95 0 Td[(tan2=y1+y2 2+x2)]TJ /F1 11.955 Tf 11.95 0 Td[(x1 2tan2)]TJ /F1 11.955 Tf 11.95 0 Td[(tan1 tan1)]TJ /F1 11.955 Tf 11.95 0 Td[(tan2;(C{2) and z=x2)]TJ /F1 11.955 Tf 11.95 0 Td[(x1 tan1)]TJ /F1 11.955 Tf 11.95 0 Td[(tan2=y2)]TJ /F1 11.955 Tf 11.96 0 Td[(y1 tan1)]TJ /F1 11.955 Tf 11.96 0 Td[(tan2:(C{3) Animportantquantitytofactorintoconsiderationistheresolutionassociatedwiththeconversionofthedisplacementsinthecameraimage(CCD)planetothoseintheobject(lightsheet)plane.ThisisgovernedbytheresolutionfactorR,avaluelessthanunityinunitsofmm/pixelthatrepresentstherelativescalingbetweenthedewarpedphysicalplaneandtheimageplane(providedbytheDaVissoftware).Therefore,thedisplacementcomponentsinphysicalspacecanberewrittenas X=R(x2tan1)]TJ /F1 11.955 Tf 11.96 0 Td[(x1tan2) tan1)]TJ /F1 11.955 Tf 11.96 0 Td[(tan2;(C{4) Y=R(y1+y2) 2+R(x2)]TJ /F1 11.955 Tf 11.96 0 Td[(x1) 2tan2)]TJ /F1 11.955 Tf 11.95 0 Td[(tan1 tan1)]TJ /F1 11.955 Tf 11.95 0 Td[(tan2;(C{5) 362

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and Z=R(y2)]TJ /F1 11.955 Tf 11.96 0 Td[(y1) tan1)]TJ /F1 11.955 Tf 11.96 0 Td[(tan2:(C{6) Therefore,abiasuncertaintyanalysisisperformedthataccountsfortheRMSpixeldeviations()inthetsoftheconformalmappingfunctionsappliedtothecameraimagesaswellasfortheassumptionofsub-pixelaccuracyofthemeasurement.Inordertoassumeasub-pixelaccuracyofthedisplacementsmeasuredontheimageplane,themeandiameteroftheseedparticlesontheimageplanemustbegreaterthanonepixel.Ifthisconditionissatised,thentheresultingcorrelationsrepresentingthelightintensitydistributionontheimageplanecanbecharacterizedasobeyingaGaussianprole( Adrian&Yao 1985 ).Toverifythatthisconditionissatised,thenominalparticlediameterasprojectedontotheimageplanecanbeestimatedby de=q M2d2p+d2s;(C{7) wheredpisthenominalparticlediameterinphysicalunits(inthiscase,asquotedbytheseedermanufacturer),anddsisthediameterofthepointresponsefunctionofalensattherstdarkringoftheAirydiskintensitydistribution( Adrian&Yao 1985 ).Thisdiameterisfurtherdenedas ds=2:44(M+1)f#;(C{8) wheref#isthefocallengthofthelensdividedbythecameraaperture,andisthewavelengthofincidentlight.Inthisapplication,theincidentlightisthatofthePIVlaserlightsheet,=532nm.Inaddition,Misthemagnicationfactor,whichisequaltothephysicalsizeofonepixel(mm/pixel)dividedbytheresolutionR.Forexample,foramagnicationofM=0:1andf#=8,theAirydiskdiameteriscomputedtobe0.0114mm.SubstitutionofthisintoEquation C{7 andassuminganominalseedparticlediameterof1mresultsinanimageparticlediameterofde1:54pixels.Therefore,suchanSPIVmeasurementsetupwouldsatisfytherequirementsforsub-pixelaccuracy. 363

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PerformingRSSontheexpressionsinEquations C{4 C{6 yieldstheanalyticaluncertaintiesofthephysicalparticledisplacements: uX="@X @x112+@X @x222+X2sp#1 2;(C{9) uY="@Y @x112+@Y @x222+@Y @y112+@Y @y222+Y2sp#1 2;(C{10) and uZ="@Z @x112+@Z @x222+Z2sp#1 2:(C{11) Notethatthesubscripts\sp"representthedisplacementcalculationsusingasub-pixelRMSerror. Toperformtheuncertaintyanalysisabove,anRMSsub-pixelerrormustbedened.Theauthorsof Nobachetal. ( 2005 )investigatedtheaccuracyofdierentPIVinterpolationmethodsonnumericallygeneratedparticleimages.TheparticlesizeswerevariedtodeterminetheRMSerrorinsub-pixelaccuracywithsimulatedphotonnoisetoresembleexperimentalconditions.Itwasfoundthatthecaseofaparticlediameterof1.5pixelsresultedinanRMSerrorof0.06pixels.Therefore,thebiasuncertaintiesfortheSPIVsetupshowninFigure C-1 maybecomputedusingEquations C{9 C{11 ,withtheparticledisplacementsmeasuredbyeachcamera,(x1;y1)and(x2;y2),settoanappropriateRMSsub-pixelaccuracybasedontheestimatedparticleimagesizeforeachcase. EachpartialderivativeofEquations C{9 C{11 maybecomputeddiscretelyusingacentereddierencemethod.Forexample,thepartialderivative@X @x1inEquation C{9 wouldbecomputedas @X @x1=R[x2tan1)]TJ /F7 7.97 Tf 6.59 0 Td[((x1+1)tan2] tan1)]TJ /F7 7.97 Tf 6.59 0 Td[(tan2)]TJ /F5 7.97 Tf 13.15 5.7 Td[(R[x2tan1)]TJ /F7 7.97 Tf 6.59 0 Td[((x1)]TJ /F5 7.97 Tf 6.58 0 Td[(1)tan2] tan1)]TJ /F7 7.97 Tf 6.59 0 Td[(tan2 (x1+1))]TJ /F1 11.955 Tf 11.96 0 Td[((x1)]TJ /F3 11.955 Tf 11.96 0 Td[(1);(C{12) 364

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whereiistheRMSpixelerrorinthetoftheSPIVconformalmappingfunctionfortheithcamera.ThesevaluesarealsoprovidedbytheDaVissoftwareforeachcamera,eachofwhichappliestobothxandydirectionsforthatcamera.Foragoodcalibration,thisvalueistypicallylessthan0.5pixel. Thenalstepincomputingthebiasuncertaintyofthevelocitycomponentsissimpledivisionofthedisplacementuncertaintiesbythetimebetweenlightsheets.ThisisacceptablebecauseofthehightemporalresolutionofthePIVsystem'sPTU(1ns),whichprovidesanegligiblecontributiontotheuncertainty. C.2SPIVBiasUncertaintiesforMeasuredRegions TheprevioussectionderivedthebiasuncertaintiesforatypicalSPIVcamerasetupinwhichbothcamerasarelookingatthesamesideofthelightsheet.Thecongurationsforthisstudy,however,weredierentinthateachcamerasawdierentsidesofthelightsheet.Adiagramofthissetup,withappropriateanglesanddisplacementslabeledisshowninFigure C-2 .Asaresultofthisconguration,thexandycomponentsofdisplacementare\ipped"relativetothepreviously-discussedconguration.Therefore,thedisplacementsbecome X=R(x1+x2) 2+R(y2)]TJ /F1 11.955 Tf 11.95 0 Td[(y1) 2tan2)]TJ /F1 11.955 Tf 11.95 0 Td[(tan1 tan1)]TJ /F1 11.955 Tf 11.95 0 Td[(tan2;(C{13) Y=R(y2tan1)]TJ /F1 11.955 Tf 11.96 0 Td[(y1tan2) tan1)]TJ /F1 11.955 Tf 11.96 0 Td[(tan2;(C{14) and Z=R(x2)]TJ /F1 11.955 Tf 11.96 0 Td[(x1) tan1)]TJ /F1 11.955 Tf 11.96 0 Td[(tan2:(C{15) Conversely,thedisplacementuncertaintyfortheexperimentalsetupalsoswitchesbetweenxandy: uX="@X @y112+@X @y222+@X @x112+@X @x222+X2sp#1 2;(C{16) 365

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uY="@Y @y112+@Y @y222+Y2sp#1 2;(C{17) and uZ="@Z @y112+@Z @y222+Z2sp#1 2:(C{18) Finally,thebiasvelocityuncertaintiesarecomputedas ubu=uX t;vbu=uY t;andwbu=uZ t:(C{19) Thebiasuncertaintieswerecomputedforeachmeasuredregionbasedonthemagnicationfactorsandcameraanglesforeachconguration.SinceDaVisreportedthatallcongurationshadcamerainverseresolutionfactorsintherangeof9:81=R10:6pixels/mmandthesizeofeachcamerapixelis7.4m,thisresultsinarangeofmagnicationfactors:072M:078.Basedonthesevalues,theapproximatenominalparticlediameterintheimageplaneisde1:5pixels,asdiscussedintheprevioussection.Therefore,thesub-pixelaccuraciesforallmeasurementsweresettox1=x2=y1=y2=0:06pixelsbasedonthendingsof Nobachetal. ( 2005 ).TheresultingbiasuncertaintiesforallmeasuredregionsarepresentedinTable C-1 C.3RandomUncertainty Therandomuncertaintiesofthevelocitydatawerecomputedusingthe95%condenceintervalestimatespresentedby Benedict&Gould ( 1996 ).ThesearepresentedfortherstandsecondordermomentsofvelocityinTable C-2 366

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A B C D FigureC-1. (A),(B)IllustrationofcommonSPIVcamerasetupwithschematicsillustratingreconstructionof3-dimensionaldisplacementvector;(C)schematicofxz-planeand(D)schematicofyz-plane.[FigureadaptedfromHu,H.2013StereoParticleImagingVelocimetryTechniques:TechnicalBasis,SystemSetup,andApplication(page75,Figure4.2),Handbookof3DMachineVision:OpticalMetrologyandImaging.] 367

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A B FigureC-2. (A)Proleand(B)downstreamviewsoftheexperimentalSPIVcameraconguration.(Drawingsarenottoscale.) TableC-1. BiasuncertaintiesofallmeasuredSPIVregions Regionubuvbuwbu Z=0GapFlow2.4902.5431.488NearWake1.9451.9451.042Z=0:592DGapFlow2.8682.8681.605NearWake4.2284.2292.405Z=1:175DGapFlow2.4512.4521.356NearWake2.7992.7991.564Z=2:175DGapFlow1.0421.0420.445NearWake1.7451.7450.923Z=3DGapFlow2.7862.7851.558NearWake2.2082.2071.209 Note:unitsareinm/s 368

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TableC-2. Randomuncertainty95%condenceintervalestimatesofcomputedvelocityterms Quantity95%condenceinterval ui1:96q u02i N u02i1:96r u04i)]TJ /F1 11.955 Tf 6.59 -.99 Td[(( u02i)2 N u0iu0j(i6=j)1:96r u02iu02j)]TJ /F1 11.955 Tf 6.59 -.99 Td[(( u0iu0j)2 N 369

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APPENDIXDPHASEDARRAYDIRECTIVITYPERFORMANCE Themagnitudesandphasesofthephasedarraymicrophoneswerecomputedinordertodeterminetheimpactofthedirectivityofthetorquearmmodel.Therationalitybehindthisisthathigherfrequenciesofinterestimposelimitationsontheusageofphasedarrays.Asthefrequencyradiatedbyanacousticsourceincreases,thesourcebecomesmoredirective,andthusthemainlobeofthepressurewavebecomesnarrower.Athighenoughfrequency,thesourcebecomesdirectiveenoughthatthephasedarrayexceedsthewidthofthemainlobeandradiated\sidelobes"reachthearraymicrophones.Theresultofthiswouldbetocreatepressurenullsalongthesurfaceofthearray,thuscontaminatingthenoisesourcelocalizationcapabilitiesofthearray.Therefore,themagnitudeandphasedistributionsonthearrayplaneofmicrophonesarecomputedforarangeoffrequenciestoverifythatallmicrophonesliewithinthemainlobeofthepressurewave. Thephasedarraymicrophonedatawerecomputedforthe=130conguration.Thesedataweretheninterpolatedusingacubicsplineoverthevirtual\face"ofthearray.TheresultsforthephasedarrayamplitudesareshowninFig. D-1 ,whilethephasesareshowninFig. D-2 .Notethattheresultswerecomputedfortheoctavebandfrequenciesof1.008,2,4,and8kHz.ThemagnitudelevelsforeachfrequencywereextractedfromthecalibratedCSM,GandplottedintheformofSPLindB.Theseresultsshowanapproximatevariationof4-5dBacrossthearrayface.Thephaseresults,meanwhile,werecomputedfromthecomputedfrequencyresponsesofthearraymicrophonesrelativetothecenterreferencemicrophone.Thephaseresultsshowadecreaseinminimumphaseexperiencedbythearrayasthefocalfrequencyincreases.Thephasecontoursdisplaythephasedecreasingradiallyoutward.Theregionofpositivephaseappearstooccurintherighthalfofthearrayface,whichcorrespondstothetorquearmmodelbeingpositionedforwardfromthearraycenter.Therefore,theregionsofpositivephase,whichrepresent 370

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negativetimedelaysrelativetothecenterreferencemicrophone,areindicativeofwherethewavefrontimpactstheplaneofmicrophones. A B C D FigureD-1. Thesoundpressureleveldistributionoverthearrayfaceatoctavebandfrequenciesof(A)1kHz,(B)2kHz,(C)4kHz,and(D)8kHz.LevelsareplottedinabsoltedBandthemicrophonesareindicatedbytheblackcircles. 371

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A B C D FigureD-2. Thephasedistributionoverthearrayfaceatoctavebandfrequenciesof(A)1kHz,(B)2kHz,(C)4kHz,and(D)8kHz.Levelswerecomputedrelativetothearraycenterreferencemicrophoneandareplottedindegrees.Themicrophonesareindicatedbytheblackcircles. 372

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BIOGRAPHICALSKETCH NikolasZawodnywasborn1983inMiami,FL.AftergraduatinghighschoolfromtheMASTAcademyin2002,heenrolledattheUniversityofFlorida.UponreceivingdualBachelorofSciencedegreesinbothMechanicalandAerospaceEngineeringin2007,hedecidedtofurtherhiseducationintheeldofAerospaceEngineeringattheUniversityofFlorida.NikolasreceivedhisMasterofSciencedegreeinAerospaceEngineeringin2009andhisPh.D.inthespringof2013.BothdegreeswereachievedundertheguidanceofDr.LouCattafesta.Asofthesummerof2013,NikolaswillbeginworkingintheAeroacousticsBranchattheNASALangleyResearchCenter. 383