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An Experimental Investigation Of The Grazing Flow Impedance Duct At The University Of Florida For Acoustic Liner Applications

Permanent Link: http://ufdc.ufl.edu/UFE0044119/00001

Material Information

Title: An Experimental Investigation Of The Grazing Flow Impedance Duct At The University Of Florida For Acoustic Liner Applications
Physical Description: 1 online resource (217 p.)
Language: english
Creator: Bertolucci, Brandon L
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2012

Subjects

Subjects / Keywords: acoustic -- duct -- impedance -- liners
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: Acoustic liners remain the standard method for reducing environmental noiseemanating from aircraft engine nacelles. To aid in liner testing and development, facilitiescapable of accurately educing the acoustic impedance in the presence of mean flowanalogous to an aircraft engine are required. A facility was built to facilitate novel designapproaches and studies into fundamental acoustic liner flow physics. This thesis details the design, testing, and implementation of the Grazing FlowImpedance Duct (GFID) as an experimental test bench capable of educing the impedance of an acoustic liner. Each component of the facility is discussed detailing the specificfeatures applicable toward the facility as a grazing flow acoustic test bench. Characterizationof both the underlying fluid dynamics and acoustics are tested to determine the abilitiesand inherent limitations associated with the facility. Comparisons are made to similarfacilities. Finally, an acoustic liner provided by NASA is tested under grazing flow conditions and the impedance educed by applying the single mode method with favorableresults. The thesis ends with an exploratory investigation of the drag impact of anacoustic liner through three indirect velocity profile methods.
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 Brandon L Bertolucci.
Thesis: Thesis (Ph.D.)--University of Florida, 2012.
Local: Adviser: Cattafesta Iii, Louis N.
Local: Co-adviser: Sheplak, Mark.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2012
System ID: UFE0044119:00001

Permanent Link: http://ufdc.ufl.edu/UFE0044119/00001

Material Information

Title: An Experimental Investigation Of The Grazing Flow Impedance Duct At The University Of Florida For Acoustic Liner Applications
Physical Description: 1 online resource (217 p.)
Language: english
Creator: Bertolucci, Brandon L
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2012

Subjects

Subjects / Keywords: acoustic -- duct -- impedance -- liners
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: Acoustic liners remain the standard method for reducing environmental noiseemanating from aircraft engine nacelles. To aid in liner testing and development, facilitiescapable of accurately educing the acoustic impedance in the presence of mean flowanalogous to an aircraft engine are required. A facility was built to facilitate novel designapproaches and studies into fundamental acoustic liner flow physics. This thesis details the design, testing, and implementation of the Grazing FlowImpedance Duct (GFID) as an experimental test bench capable of educing the impedance of an acoustic liner. Each component of the facility is discussed detailing the specificfeatures applicable toward the facility as a grazing flow acoustic test bench. Characterizationof both the underlying fluid dynamics and acoustics are tested to determine the abilitiesand inherent limitations associated with the facility. Comparisons are made to similarfacilities. Finally, an acoustic liner provided by NASA is tested under grazing flow conditions and the impedance educed by applying the single mode method with favorableresults. The thesis ends with an exploratory investigation of the drag impact of anacoustic liner through three indirect velocity profile methods.
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 Brandon L Bertolucci.
Thesis: Thesis (Ph.D.)--University of Florida, 2012.
Local: Adviser: Cattafesta Iii, Louis N.
Local: Co-adviser: Sheplak, Mark.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2012
System ID: UFE0044119:00001


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ANEXPERIMENTALINVESTIGATIONOFTHEGRAZINGFLOWIMPEDANCE DUCTATTHEUNIVERSITYOFFLORIDAFORACOUSTICLINER APPLICATIONS By BRANDONL.BERTOLUCCI ADISSERTATIONPRESENTEDTOTHEGRADUATESCHOOL OFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENT OFTHEREQUIREMENTSFORTHEDEGREEOF DOCTOROFPHILOSOPHY UNIVERSITYOFFLORIDA 2012

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Indedicationtomyparents. 2

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ACKNOWLEDGMENTS Thisprojectisonlypossibleduetothehelpfulandcontinuingguidanceofmy advisors,Dr.LouisCattafestaandDr.MarkSheplakwhomprovidedmentorshipandlead meinthisprocess.Iwouldliketoextendmygratitudetotherestofmycommittee:Dr. Balachandar,Dr.DavidArnold(ECE),andMichaelJonesatNASALaRC.Thisproject wouldnotbepossiblewithoutthedonationoftheGITfacilityfromNASALaRC.Iwould specicallyliketothankMichaelJones,CarrollHarrison,andBrianHowertonfortheir continuedsupportoverthepastfouryears. Thephysicalconstructionandmachiningofthetunnelwasaccomplishedbyprimarily byRa ertyMachineandTool,TMREngineering,andMarkHurmandCo.Iwould liketothankWayneWillisforhisberglasswork.Muchofthedesignandconstruction wasaccomplishedbyaseriesofundergradswhoseassistancewasinvaluable;thankyou all.UniversityofFloridasta Je StudstilandMarkReidy'ssupportwaswellbeyond expectationandwereextremelyhelpful. Manywhiteboardmarkerscameandwentthroughthoughtfuldiscussionswithmy colleaguesastheyhelpedmeironoutthedetailsoftheprojectandsteermedownthe correctpath.IwouldliketospecicallythankDr.FeiLuiprovidingmanyhoursof discussion.Additionally,mypeersintheInterdisciplinaryMicrosystemsGroup(IMG) wereindispensable,including:Dr.RyanHolman,Dr.VijayChandrasekharan,Dr.Chris Bahr,Dr.DrewWetzel,Dr.JessicaMeloy,MiguelPalaviccini,MatiasOyarzun,Nik Zawodny,AshleyJones,andJohnGri n. Furthermore,IwouldliketoextendappreciationtoJasonJuneforthetremendous helpheprovidedinmynalyear.HewillbetakingtheprojectoverandIcannot imaginemorecapablehands.Also,aspecialthankstoKatieReed,herpatienceand supportwereaconstantsourceofstrengthandmotivationthroughouttheyears. 3

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TABLEOFCONTENTS page CHAPTER ACKNOWLEDGMENTS ................................. 3 LISTOFTABLES ..................................... 7 LISTOFFIGURES .................................... 8 ABSTRACT ........................................ 12 1BACKGROUNDANDMOTIVATION ....................... 13 1.1AircraftNoiseIssues .............................. 13 1.2TypesofAircraftNoise ............................. 15 1.3AcousticLinersWithinAircraftEngineNacelles ............... 19 1.4AerodynamicandAcousticPerformanceofLiners .............. 23 1.5AcousticLinerTestFacilities ......................... 24 1.6ThesisOutline .................................. 26 2THEPHYSICSOFAGRAZINGIMPEDANCEDUCTFACILITY ....... 30 2.1IntroductiontoGrazingDuctFlow ...................... 30 2.2Ductacoustics .................................. 31 2.2.1RigidWallAnalysisinaQuiescentMedium .............. 31 2.2.2ImpedanceBoundaryConditionsinaQuiescentMedium ...... 34 2.2.3TheConvectiveWaveEquationwithUniformVelocityProle .... 35 2.3FluidAnalysis .................................. 36 2.3.1TheBoundaryLayer .......................... 37 2.3.2TurbulentBoundaryLayers ...................... 40 2.3.3TurbulentChannelFlow ........................ 44 3LITERATUREREVIEW .............................. 51 3.1ChannelFlowStudies .............................. 51 3.1.1IdenticationandMeasurementofSecondaryFlowinChannels ... 52 3.1.2OriginsofSecondaryFlowandHighReynoldsNumberStudies ... 53 3.1.3ChannelFlowScalingArguments ................... 54 3.2ImpedanceEductionTechniques ........................ 56 3.2.1The In-situ Method ........................... 56 3.2.2InniteWaveguideMethodandSingleModeMethod ........ 58 3.2.3FiniteElementMethod ......................... 60 3.2.4FiniteElementMethodwithShear .................. 61 3.2.5InverseSemi-Analytical ......................... 62 3.2.6GrazingFlowDataAnalysis ...................... 63 3.2.7TheStraightforwardMethod ...................... 64 4

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3.2.8LaserDopplerVelocimetryImpedanceEduction ........... 65 3.2.9InsertionLossMethod ......................... 66 3.2.10FlowResistanceMethod ........................ 67 3.2.11ImpedanceEductionMethodSummary ................ 67 3.3ExperimentalAcousticLinerImpedanceTestFacilities ........... 68 3.3.1InternationalFacilities ......................... 68 3.3.2DomesticCorporateTestFacilities ................... 70 3.3.3DomesticUniversityTestFacilities ................... 73 3.3.4GovernmentFacilities .......................... 74 3.4Summary .................................... 76 4DESIGNANDIMPLEMENTATION ........................ 86 4.1AirHandling .................................. 86 4.1.1AirSupply,FlowValveandFlowSilencer ............... 86 4.1.2StagnationChamberandNozzle .................... 87 4.1.3DataAcquisition ............................ 88 4.2AcousticSource ................................. 89 4.3Ducting ..................................... 90 4.4TestSection ................................... 91 4.4.1OpticalWindow ............................. 92 4.4.2StaticPressureWall ........................... 92 4.4.3LinearMicrophoneArray ........................ 92 4.5Termination ................................... 93 4.6ExhaustDucting ................................ 94 4.7TheGFIDLayout ................................ 94 4.8DesignConclusion ............................... 95 5FACILITYCHARACTERIZATIONANDPROCESSVALIDATION ...... 102 5.1FluidTestingExperimentalSetup ....................... 102 5.1.1BasicPrincipalsofLaserDopplerVelocimetry(LDV) ........ 103 5.1.2LaserDopplerVelocimetryExperimentalSetup ............ 108 5.2FluidDynamicCharacterization ........................ 114 5.2.1Entranceregion ............................. 115 5.2.2Fullydevelopedregion ......................... 117 5.3AcousticCharacterization ........................... 121 5.3.1Near-AnechoicReectionExperiment ................. 121 5.3.2DescriptionoftheAcousticLiners ................... 124 5.4ImpedanceEductionUsingtheSingleModeMethod ............. 124 5.4.1ExperimentalSetupandApplicationoftheSingleModeMethod .. 125 5.4.2ValidationoftheSingleModeMethodViaNormalIncidenceUnder ZeroMeanVelocity ........................... 128 5.4.3ValidationoftheSingleModeMethodViaBenchmarkDataWith MeanFlow ................................ 129 5

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5.4.4ExperimentalImpedanceEductionofaWireMeshAcousticLiner intheGrazingFlowImpedanceDuct ................. 131 5.5DragContributionByAnAcousticLinerWithAcousticExcitation .... 132 5.5.1Two-DimensionalBoundarylayerapproximationusingSpaldingFit 133 5.5.2Momentum-Integral ........................... 133 5.5.3ControlVolumeAnalysis ........................ 134 5.5.4ConcludingRemarksofFluidDynamicResults ............ 137 6CONCLUSIONANDFUTUREWORK ...................... 167 6.1FacilityCharacterization ............................ 167 6.1.1FluidDynamicCharacterization .................... 167 6.1.2AcousticCharacterization ....................... 168 6.2ResearchImpact ................................ 168 6.3FutureWork ................................... 169 6.3.1FacilityImprovements .......................... 169 6.3.2AdvancedImpedanceEduction ..................... 171 6.3.3AcousticLinerShearStressTestings .................. 171 APPENDIX ADERIVATIONOFDUCTACOUSTICSINAQUIESCENTMEDIUMWITH SOUNDHARDWALLS ............................... 173 BDERIVATIONOFDUCTACOUSTICSINAQUIESCENTMEDIUMWITH PRESCRIBEDIMPEDANCEBOUNDARYCONDITION ............ 178 CDERIVATIONOFTHECONVECTIVEWAVEEQUATION .......... 182 DTECHNICALDRAWINGS ............................. 185 REFERENCES ....................................... 210 BIOGRAPHICALSKETCH ................................ 217 6

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LISTOFTABLES Table page 3-1Channelowstudies ................................. 77 3-2Grazingowimpedanceeductiontechniques .................... 78 3-3Acousticlinerimpedanceeductionfacilities ..................... 79 4-1Experimentalmassowrates ............................ 95 5-1VelocitylimitsoftheLDVprocessorfor120 mm lens ............... 137 5-2VelocitylimitsoftheLDVprocessorfor400 mm lens ............... 137 5-3SingleModeMethodeducedmeannormalizedimpedancevalues ......... 138 5-4Boundarylayervariableextraction ......................... 138 5-5Momentum-integralanalysisvariableextraction .................. 138 5-6Controlvolumeanalysisforestimationoffrictioncoe cient ........... 138 7

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LISTOFFIGURES Figure page 1-1Overallnoiselevelgoalsforfutureaircraftdesign ................. 27 1-2Standardpassengeraircraftnoisegeneratingsources ................ 28 1-3High-bypassratioenginenacellewithowandnoisesources ........... 28 1-4Acousticlinertypes .................................. 29 1-5Resistiveandreactiveacousticliners ........................ 29 2-1Waveguidewithhardwallandunknownimpedanceboundaryconditions .... 47 2-2Velocityproleswithinatwo-dimensionalboundarylayer ............. 47 2-3Theregionsofaturbulentboundarylayer ..................... 48 2-4Turbulentchannelowsymmetrylines ....................... 49 2-5Turbulentchannelowsecondaryvelocities .................... 50 3-1The in-situ methodexperimentalsetup ....................... 80 3-2Detailedviewofthe in-situ method ......................... 80 3-3Demonstrativecomplexpressuredecaydueanacousticliner ........... 81 3-4TheBFGoodrichtestfacility ............................ 81 3-5TheowductattheUniversityofMaine,France ................. 82 3-6TheONERAB2A .................................. 82 3-7TheGeneralElectricDCowduct ......................... 83 3-8TheGTRILinerFlowDuctFacility ......................... 83 3-9TheUTRCGrazingFlowFacility .......................... 84 3-10TheFITatNASALaRC ............................... 84 3-11TheGITatNASALaRC .............................. 85 3-12TheGFITatNASALaRC .............................. 85 3-13TheCDTRatNASALaRC ............................. 85 4-1TheGFIDairsupplysetup ............................. 96 4-2Inlineowsilencer .................................. 96 8

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4-3TheGFIDstagnationchamber ........................... 97 4-4TheGFIDstagnationtwo-stagenozzle ....................... 97 4-5Acousticsectionwithspeaker ............................ 98 4-6Testsectionphotographwithannotations ..................... 98 4-7Testsectionmicrophoneauxiliaryplug ....................... 99 4-8Testsectionwallinsertpieces ............................ 99 4-9Facilitysectionalignmentconnectors ........................ 100 4-10Near-anechoictermination .............................. 100 4-11Exhaustducting ................................... 101 4-12ThenalizedGFIDbysection ............................ 101 5-1BasicprincipaloflaserDopplervelocimetry .................... 139 5-2LaserDopplervelocimetryworkspace ........................ 139 5-3Laserbeamcombiner ................................. 140 5-4Beamcongurationoftheprimaryprobehead ................... 140 5-5Velocityrangefordi erentLDVprobecongurations ............... 141 5-6Cut-o frequencyasafunctionofparticlediameter ................ 141 5-7Beamalignmentwithtunneloor .......................... 142 5-8Beampathsthroughopticalwindow ........................ 143 5-9Calculatedbeamtracestoquantifyprobevolumeo setdistance ......... 144 5-10Focalpointo setasfunctionofwindowthickness ................. 145 5-11Fluiddynamicexperimentaltestsetup ....................... 146 5-12Entranceregioncrossductvelocityproleandintegratedbulkvelocity ..... 146 5-13Entranceregioncenterlinevelocity ......................... 147 5-14Non-dimensionalentranceregionvelocitygrowth ................. 147 5-15Centerlinevelocitymeasurementsinthefullydevelopedregion .......... 148 5-16Cross-ductvelocityproles .............................. 149 5-17Staticpressureexperimentalsetup ......................... 150 9

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5-18Pressurecoe cientasafunctionofMachnumber ................. 150 5-19Two-microphonemethodapplicationtoanechoictermination ........... 151 5-20Reectioncoe cientcomparisonofanechoicandhard-wallberglassdi user .. 151 5-21Acousticlinerstested ................................. 152 5-22Testsectionschematic ................................ 153 5-23Acousticlinerfacesheetcloseups ........................... 153 5-24SoundpressurelevelandphasedataforMach=0.0ow .............. 154 5-25SoundpressurelevelandphasedataforMach=0.1ow .............. 155 5-26SoundpressurelevelandphasedataforMach=0.3ow .............. 156 5-27SoundpressurelevelandphasedataforMach=0.5ow .............. 157 5-28Impedancetestinginthenormalincidencetube .................. 158 5-29Noowimpedanceresultscomparedtonormalincidence ............. 158 5-30Impedanceeductionofbenchmarkdatacomparison ................ 159 5-31SingleModeMethodresultsasafunctionofMachnumber ............ 160 5-32SingleModeMethodresultsasafunctionofMachnumbersans M =0 5 .... 161 5-33Coherenceofperforateliner ............................. 162 5-34Spaldingboundarylayerproleforhardwallandacousticlinerinstallation ... 163 5-35Pressurecoe cientwithliner ............................ 163 5-36Controlvolumeschematic .............................. 164 5-37Controlvolumegridpattern ............................. 164 5-38Controlvolumecontourmaps ............................ 165 5-39Controlvolumevelocitysurfacemap ........................ 166 D-1Nozzleoveralldimensions .............................. 186 D-2Nozzle-ductingadapterandalignmentplate .................... 187 D-3Nozzledownstreamange .............................. 188 D-4Nozzleupstreamange ................................ 189 D-5Secondstagenozzleassembly ............................ 190 10

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D-6Speakersectionisometricview ............................ 191 D-7Speakersectionexplodedisometricview ...................... 192 D-8Speakersectiontopview ............................... 193 D-9Speakersectionholeplacementdimensions ..................... 194 D-10Speakersectionsidealignmentholedimensions .................. 195 D-11Speakersectiontopdimensions ........................... 196 D-12Speakercoverplatedimensions ........................... 197 D-13Speakercoverplateisometricview ......................... 198 D-14Assembledtestsectioncutawayview ........................ 199 D-15Acousticlinerinstallationportinsert ........................ 200 D-16Testsectionsidewalldimensions .......................... 201 D-17Staticpressurewalldimensions ........................... 202 D-18Testsectionassemblyskeletonisometricview ................... 203 D-19Testsectiontopwallpermanentassembly ..................... 204 D-20Testsectionendcaps ................................. 205 D-21Testsectionauxiliaryplugs ............................. 206 D-22Near-anechoicdi userupstreamange ....................... 207 D-23Near-anechoicdi userupstreamangeholeplacement .............. 208 D-24Near-anechoicdi userupstreamassembly ..................... 209 11

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AbstractofDissertationPresentedtotheGraduateSchool oftheUniversityofFloridainPartialFulllmentofthe RequirementsfortheDegreeofDoctorofPhilosophy ANEXPERIMENTALINVESTIGATIONOFTHEGRAZINGFLOWIMPEDANCE DUCTATTHEUNIVERSITYOFFLORIDAFORACOUSTICLINER APPLICATIONS By BrandonL.Bertolucci December2012 Chair:LouisCattafestaIII Cochair:MarkSheplak Major:AerospaceEngineering Acousticlinersremainthestandardmethodforreducingenvironmentalnoise emanatingfromaircraftenginenacelles.Toaidinlinertestinganddevelopment,facilities capableofaccuratelyeducingtheacousticimpedanceinthepresenceofmeanow analogoustoanaircraftenginearerequired.Afacilitywasbuilttofacilitatenoveldesign approachesandstudiesintofundamentalacousticlinerowphysics. Thisthesisdetailsthedesign,testing,andimplementationoftheGrazingFlow ImpedanceDuct(GFID)asanexperimentaltestbenchcapableofeducingtheimpedance ofanacousticliner.Eachcomponentofthefacilityisdiscusseddetailingthespecic featuresapplicabletowardthefacilityasagrazingowacoustictestbench.Characterization ofboththeunderlyinguiddynamicsandacousticsaretestedtodeterminetheabilities andinherentlimitationsassociatedwiththefacility.Comparisonsaremadetosimilar facilities.Finally,anacousticlinerprovidedbyNASAistestedundergrazingow conditionsandtheimpedanceeducedbyapplyingthesinglemodemethodwithfavorable results.Thethesisendswithanexploratoryinvestigationofthedragimpactofan acousticlinerthroughthreeindirectvelocityprolemethods. 12

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CHAPTER1 BACKGROUNDANDMOTIVATION Concernsofhealthandgeneralpopulationannoyanceduetoaircraftnoisegrowas populationcentersexpandandairtra cbecomesalargerpartofdailylife,increasing environmentalnoisepollution.Aircraftnoiseispresentedanddiscussedinthecontext ofthenoisesourcesandcurrentabatementstrategiesdetailingimprovementsmade throughimplementationofacousticliners.Thee ectivenessofacousticlinersrequire detailedevaluationviaexperimentalfacilitiesnecessitatingafundamentalunderstanding ofbothacousticanduiddynamicphysicsaswellasthefacilitiesthemselves.Thechapter concludeswithanoutlineofthisthesisonthedevelopmentandtestingofoftheGrazing FlowImpedanceDuct(GFID)experimentalacousticlinerowfacilityforresearchon acousticlinersandlinertechnology. 1.1AircraftNoiseIssues Aircraftnoisehaslongbeenaproblemforcommunitiesnearairports.Aspopulation centerscontinuetoexpandandairportcommunitiesgrow,newrestrictionsandsubsequent abatementproceduresappliedtoaircraftnoisehaveincreasedsubstantially. Studieshavefoundthatasmanyas70%ofthepeoplelivingwithinightcorridors arebotheredbyaircraftgeneratednoise( Bronzaft&Ahern 1998 ).Theneedforaircraft noiseabatementhasalsobeenlinkedtoseveralcommunityhealthconcerns.Overthe lastthirtyyears,signicantresearchhasbeenconductedonpossiblesidee ectsofliving nearairports,includinglowbirthweights( Knipschild etal. 1981 ),increasedlevelsof unemployment( Kryter 1990 ),andchildhoodcognitionperformance( Stansfeld etal. 2005 ).Suchhazardshavepromptedbothregionalandnationalnestobeimplementedto airlineswhichdonotmeetrestrictions.Thereareinstances,suchasthecaseoftheBoeing 707,wherethecosttoretrotthedesigntoattainpropernoiselevelcerticationbecame costprohibitive,andoperationoftheaircraftwasdiscontinued( Smith 2004 ).Suchnes 13

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andrestrictionsnecessitateairlines,aircraftmanufacturers,andcomponentcontractorsto considernewtechnologiestodecreaseenvironmentalnoisepollution. AsillustratedinFigure 1-1 ,federalnoiserestrictionscurrentlyinStage4are periodicallyreviewedandalteredtomaintaincommunitynoisestandards.However, theserestrictionsdonotextendfarenoughintothefutureforadequateplanningof futureaircraftandadvancedtechnologies.NASA,inconjunctionwithaircraftandengine companies,hasdenedgoalsforaircraftnoisetoassistinfuturetechnologyandnoise testingdevelopment,where"N+1"referstomodelsbeingreleasedpriortotheconclusion oftheFAAStage4standards. Aircraftnoise,regardlessofitssource,hasthreepotentialobservergroups:aircraft passengersandcrew,airportsta includingmaintenanceandsupportpersonnel,and ight-pathcommunities.Thenoisemostpertinenttothepassengersandairport sta isthatgeneratedbythejetexhaust,internalcombustion,airframenoise,and structuralvibrationsofaircraftcomponents( Powell&Fields 1991 ).Generalaircraftnoise suppressionbenetsallpartiesinvolvedastotalnoiseisreducedovertimebyidentifying dominantnoisesourcesandapplyingappropriatereductionmeasures. Whilethereasonsforaircraftnoiseabatementarenumerous,themethodsfornoise levelreductionremainanongoingandcomplicatedendeavorforengineers.Overtheyears, issuesassociatedwithaircraftnoisehavehadalargeimpactonmanyaspectsofmodern life.Aircraftnoisehasinuencedcityplanningforightcorridorsandhasshapedaspects ofmodernaircraftdesign,suchasthenumber,size,andplacementofengines,aswell astheangleofdescentandtakeo ( Smith 2004 ).Tobetterunderstandthemechanisms behindaircraftnoise,theissueisapproachedontwofrontsbytheengineeringcommunity. Investigationsseparatethenoisegeneratedbytheairframefromthenoiseradiatedfrom thepropulsionsystem.Abreakdownofeachsourceanditsoriginsispresentedbelow alongwithsourcesofgeneratednoise. 14

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1.2TypesofAircraftNoise Separatingaircraftnoiseintodi erenttypesallowsthesourcesofeachtobe investigatedindependently,aswellastoestablishprioritiesforcurrentandfuture research.Theaircraftnoisesourcesoftheairframeandpropulsionsystemsareboth activelystudiedfornoiselevelreduction.Uniquesourcecharacteristicscontributetonoise sourceidenticationandfutureabatementprocedureswhilepresentingchallengesfor engineers.Abasicoverviewofthegenerationofeachnoisesourceisdiscussed,andcurrent noiseabatementproceduresaredescribed. Airframenoiseisaresultofthepassageofairinteractingwithphysicalstructureson theaircraft( Smith 2004 ).Anystructureinthepathoftheowwhichcausesasudden orabruptchangeinowdirectionhasthepotentialtocreatepressureuctuations.Due toexternalstructuresofvarioussizes,fromlandinggear,wings,andcontrolsurfaces,as wellasthefuselageitself,thegeneratedfrequenciesspanthefullrangeofhumansound perception;thusairframenoiseiscategorizedasbothtonalandbroadbandinnature ( Smith 2004 ). Thenoiseemanatingfromtheairframehasbeenexperimentallyfoundtobehighest forground-basedobserversduringapproachconditionswhenadditional,lessaerodynamic components,comeintoe ect( Motsinger&Kraft 1991 ).Figure 1-2 presentsanillustration ofanairplanewithlabeledsound-generatingsources.Componentsdesignedtoincrease drag,suchasapsandslats,provideanecessarystabilityconditionforcontrolduring landingbyreducingoverallspeed.However,thesecomponentsdirectlygenerateadditional aerodynamicsoundcapableofpropagatingtoanobserver( Smith 2004 ).Furthermore,the landinggeararealsodeployedatthistime,generatingadditionalnoise.Bydesign,landing geararegenerallynotstreamlinedforaerodynamicperformanceandincreasetheoverall noisesignatureoftheairframebyasmuchas10dB(ref20 Pa)( Smith 2004 ).Landing gearnoiseisgenerallycharacterizedbylowfrequencysoundpropagatingbothintothe passengercabinandexternallyoverlongdistances( Smith 2004 ). 15

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Whileairframenoiseisdominantduringapproachforlanding,propulsionnoise dominatesattakeo whenenginepowerismaximum( Smith 2004 ).Propulsionnoise isassociatedwithanypowersystemthatpropelstheaircraftforward.Thecurrent investigationwillfocusonthemodernhighbypassturbofanengine,housedinwhat iscommonlyreferredtoasanenginenacelle,whileforgoingexternalpropellordriven systems.Thus,thegeneratednoiseisacombinedresultofturbomachinerynoiseand resultantexhaustingjetaswellasthebypassfanandductingsystems.Theenginebypass ratio(BPR)denestherelationshipbetweenthemassofcoolerairdirectedaroundthe coreenginetothemassofairpassingthroughthecore( Mattingly 1996 ). Jetnoiseinmodernturbofanenginesisacombinationofturbulentmixingand, insomecases,shocksystemine ciencies( Smith 2004 ).Jetwakecharacteristicshave changeddramaticallyovertheyearsduetodesignmodicationstoengineconstruction. Thehighbypassratio,commonlyfoundinmodernaircraftenginesforaddedfuel e ciency,separatestheincomingairintotwoparts.Figure 1-3 illustratesahighbypass ratioenginewiththeowofairdisplayedinblueandtheacousticsourcesanddirection ofnoisepropagationindicatedinyellow.Aportionoftheincomingairisdirectedthrough theenginewhereitiscompressed,heated,andacceleratedrearward,generatingforward thrust.Surroundingthishotjet,theremainingmajorityoftheairissteeredaroundthe coreengineremainingrelativelycold,forminganouterconcentricshearow. Bypassratiosofpassengeraircraftshavesteadilyincreasedsincetheirintroduction, raisingfuele cienciesandloweringjetnoise( Smith 2004 ).TheRolls-RoyceTrent1000 enginerequisitionedfortheBoeing787hasabypassratioof11,doublingvaluesofonly 4-6typicallyfoundin1970'smodels( Nayfeh etal. 1975 ).Goalsforultra-highBPR's nearing20bytheyear2020areinview( Guynn etal. 2009 ). Withouttheinuenceofhighvelocityturbulentstructuresfoundinthehighspeed jet,thelargebypassairgenerateslowfrequencybroadbandnoise( Smith 2004 ).The airdirectedintothecoreenginereceivesatremendousvelocitygain(450 700 m/s ) 16

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generatingsmall-scaleturbulenteddiesproducingloud,higherfrequencybroadbandnoise ( Smith 2004 ).Thecold,slowerbypassairandhot,fasterturbineexhaustcombineand mixdownstreamoftheexhaustplane,generatingadditionalhighintensitysoundovera widefrequencyrange( Nayfeh etal. 1975 ).Althoughstillasourceofnoisegeneration,the bypasssystemhasbeenthehighestcontributortothedecreaseinjetenginenoise( Smith 2004 ).However,whilenoisewilldecreasewithincreasedBPR,tradeo sofincreased enginedrag,weight,andinstallationissuesbecomeapparent.OptimalBPRhavebeen estimatearound11-14( Daggett etal. 2003 ).Basicstepstowardnoiseabatementofjets arepresentedinsection 1.4 Whentherstjetenginewasintroducedonproductionscaleaircraft,jetnoise wasthedominantpropulsionnoisesourceinwhatisnowreferredtoasa"purejet" conguration,thatis,nobypasssystem.However,institutingabypasssystemleadto lowerspecicfuelconsumption,andfannoisewassubsequentlyidentiedasanoise source( Nayfeh etal. 1975 ).Sincethattime,theupstreamfanandcompressorstages havegarneredaconsiderableproportionofthefocusofaircraftnoiseabatementresearch foramultitudeofreasons.Theinclusionofthebypasssystemallowedforasignicant reductionofjetspeed,reducingthelevelsofjetnoise. Lighthill ( 1952 )proposedthat jetsoundintensityscalesas V 8 ,butthisrelationdropstoa V 3 relationforjetvelocities greaterthanapproximately400 m/s ( Dowling&Williams 1983 ).Thechangeinscaling comesfromabreakdownintheassumptionofthelowspeedjet;asthejetbecomes supersonictheratioofthesourcedimensiontoacousticwavelengthisnolongersmalland cannolongerbeconsideredcompact( Dowling&Williams 1983 ).Thee ectiveperceived noiselevel,inunitsofEPNdB,isasubjectivemeasureoftheperceivede ectofaircraft noiseonhumans( Smith 2004 ).Sincethe1960's,combinednoiselevelsfromtheengine havedroppedmorethan20EPNdBasaresultofthehighbypassratioenginecurrently usedinmodernaircraftdesign( Casalino etal. 2007 ).Thusitcanbestatedthatthe 17

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largestreductionsinjetnoiseareontheenginedesignswiththelargestbypassratios ( Marsh 1968 ). Theintroductionoftheengineairbypasssystemreducedoveralljetnoiselevels bydecreasingthejetspeed.However,thelargefanstagenecessaryforthebypassnow generatedadditionalnoiseatnon-negligiblelevels.Thefannoisewasdiscoveredto producemore"annoying"tonescomparedtothebroadbandhowlofthe"pure-jet", reminiscentofpastpropellor-driventransport( Smith 2004 ).Clinicalinvestigationshave demonstratedthathumansaremostsensitivetofrequenciesbetween2 4 kHz even thoughtheearisgenerallycapableofdiscerningfrequenciesbetween20 Hz 20 kHz ( Kryter 1959 ).Fansgeneratehigh-intensitytoneswithinthesensitivefrequencyrange capableofpropagatingtoexternalobserversduetoseveralinherentgeometricand installationreasonsdiscussedinthefollowingsections( Marsh 1968 ). Thenoisemeasuredwithinthefanstage,thatisanyregionpriortothecompressor asillustratedinFigure 1-3 ,isacombinationofbroadbandandhighintensitysound.The broadbandsourceisduetonoiseemanatingupstreamfromthecombustionchamber.In addition,jetnoisewillpropagateupstreamviathenacelleboundarylayerorifoperatedat subsonic"o -design"conditions.( Smith 2004 ). Thefrequenciesobservedinthefanstagearefoundtooriginatefromseveralsources. Thedominantnoisesourcestemsfromtheinteractionofthefanstageenduredswirlingair withtheexitguidevanesdownstream.Theappropriatelynamedbladepassagefrequency (BPF)isequaltotheproductoffanbladerotationfrequencyandthenumberofblades present( Motsinger&Kraft 1991 ).Theturbulentvorticesgeneratedfromthetrailing edgesandstando shockwavesatthetipsofthefanbladescanpropagatebothupstream (forwardoftheengine)anddownstream,incorporatinginwiththejetnoise( Smith 2004 ).Inthemultiplefanstagesofearlybypassenginedesigns,vorticalinteractions wouldcombinetogeneratenewtonesbasedonthesutmanddi erencefrequenciesofthe multiplestages,aswellasthecombinedharmonics( Nayfeh etal. 1975 ). 18

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WhiletheBPFmaybethedominantfrequencywithinthefanstage,severalsources relatedtotheenginedesignandmanufacturingalsoaddtotheoverallnoiseleveland soundsignature.Fanbladesthemselves,regardlessofinstallationuniformity,su erwear andaredeformedduetorain,hail,birds,anddebris.Eventually,notwofanbladesare identicalasminordi erencesalterowstructuresthatgeneratenoise.Whilethemeasured frequenciesmaybedominatedbytheBPF,theintensitiesofeachaswellasadditional noisespecictoaparticularblademaythereforechange( Smith 2004 ). Inletboundarylayersymmetryisalsoimportantfornoisegeneration.Ifthe developingboundarylayerhasanyazimuthaldependancesuchthatanytwobladesare subjecttodissimilarinletowconditions,additionalforcesareintroducedandpressure uctuationswillarise( Smith 2004 ).Currentpracticedictatesthattheinletowshould bebothaxisymmetricandas"clean"aspossible,accomplishedbyensuringthenacelle inletisfreeofanysupportstructuresorsharpcornerswhichmaycauseirregularow patterns( Nayfeh etal. 1975 ).Suchchangesindesignandtheawarenessofthetoneshas spurredinterestintheareaofengineinletnoisesuppression,nearlyuniversallythrough theimplementationofacousticliners. 1.3AcousticLinersWithinAircraftEngineNacelles Fannoisewithinenginenacelleshasgainedmuchattentionovertheyears.One particularareaofresearchfocusesonsuppressionofthefannoisethroughimplementation ofacousticlinerswithinthenacellewalls.Theacousticlinersreducenoisebyalteringthe boundarycontritionattheinteriorwalldecreasingtheamplitudeofanincidentsound wave( Motsinger&Kraft 1991 ). Thee ectivenessofanacousticlinerisdeterminedbymeasuringincomingand outgoingsoundwavesthroughanareawheretheacousticliningisusedatoneormore boundaries.Thisisgenerallyquantiedintheformofthespecicacousticimpedance, denedastheratioofthee ectivesoundpressureactingonasurface,totheparticle velocitythroughthesurfacearea( Beranek 1996 ). 19

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Theuseoflinersfornoiselevelsuppressionisnotuniquetotheaerospaceindustry, andinfact,hasbeene ectivelyimplementedinseveralindustrieswherenoiserestrictions andsoundlevelsposeannoyance,health,and/orsafetyrisks.Acousticwalltreatmentand linershavebeenroutinelyusedsuccessfullyonturbomachinery( Smith 2004 ),automotive exhaustsystems( Dokumaci 2005 )andareprevalentinmanyarchitecturaldesigns( Egan 2007 ). However,unlikeindustrialorarchitecturalacousticlineruse,theaircraftengine maypresenttheharshestenvironmentofall.Suchlinersmustmaintaine ectiveness overabroadrangeofconditions.Theenginenacellecanbesubjectedtotemperature rangesof-50 Cto+500 Cleadingtoharshfreeze-thawcyclingofamassedwater.The potentialforreexistsiffueloroilmixturesbecomeentrainednearaheatsource.In additiontostringentenvironmentalconditions,thelinersmustmaintainstructuralrigidity ofthenacellewhileminimizingweight.Furthermore,linersshouldrequirelittleorno maintenanceoverthelifespanofthenacelle( Smith 2004 ). Dependingontheirphysicalconstruction,acousticlinerscanbebroadlydividedinto twomaincategories,locallyreactingandbulkreacting( Nayfeh etal. 1975 ).Figure 1-4 illustrateslinerscommonlyusedonmodernaircraft.Theconstructionofthelinerdenes thelinertypebyconstrainingparticlevelocitynormaltothesurfaceforlocallyreactive ( Motsinger&Kraft 1991 ).Theselinersaregenerallyahoneycombstructureofcellular separationswhereeachcellisorientednormaltothewalloftheduct.Aperforatedor wire-meshfacesheetrestsonthefaceofthecellwiththebaseofthecellattachedto arigidplatecreatingacellularsandwichofthethreecomponents( Motsinger&Kraft 1991 ).Abulkreactinglinerreplacesthecellularhoneycombstructurewithathick homogeneousberpanelbetweentheface-sheetandtherigidbackplate,allowingfor transverseprogressionofsound( Motsinger&Kraft 1991 ). Tounderstandhowanacousticlinersuppressesnoise,itisimportanttounderstand howacousticwavespropagatewithinanacelle.Asanacousticwaveadvancesawayfrom 20

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anoisegeneratingsourceinanenclosedduct,acousticenergystrikingaboundarycan resultinenergylossassociatedwitheitherthereectionorabsorptionoftheincident wave( Ingard 1994 ).Acousticreectionsariseasaresultofimpedancediscontinuities ( Blackstock 2001 ).Acousticabsorptionultimatelyconvertstheacousticenergyincidenton thenacellesurfacetoanotherdomain,suchasheatorstoredenergy( Ingard 1953 ). Modicationofalocalacousticeldonasurfaceismadepossiblethroughtwo potentialmechanisms.Therstisdestructiveinterferenceoftheincidentacousticwave bytuningthereactivephysicalcharacteristicsofthecavitytoaspecicfrequencytermed theresonantfrequency.Thisisaccomplishedbydesigningthecavitydepthtobe1 / 4the wavelength( )oftheincidentacousticwave.Thesubsequentreectiono thecavity basewillcausedestructiveinterferenceatthecavityopening( Nayfeh etal. 1975 ).The propagatingpressurewavethroughtheductisthenmetbyanacousticsinkatthe boundaryandsoundreectionisdrasticallyreduced( Nayfeh etal. 1975 ).Thesecond mechanismforsuppressionreducesincidentpressurebymeansofviscousresistancein whichacousticenergyisconvertedintoheatattheorice.Thisviscouse ectreducesthe particlevelocityattheentrancetothecavitythusweakeningtheacousticwave( Smith 2004 ).Thetwomechanismscancomplementoneanother,albeitatdisparatelevels dependingondesign,toformanarrayofcellsthatcoattheinteriorofanacelle. Alocallyreactivelineristypicallybestsuitedforaspecictoneoranarrowband offrequenciesnearthedesignfrequencyoftheresonator,generallycoveringoneoctave ( Motsinger&Kraft 1991 ).Thereactivemechanismforreducingthesoundintensity ismoste ectivewhenthecavitydepthisnear / 4oftheincidentpressurewavebut provesine ectivetothosefrequenciesofwhichlittletonodestructiveinterferenceoccurs. Frequencyandwavelengtharerelatedthrough = c 0 f (11) where c 0 isthelocalspeedofsound. 21

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Theperforate-sandwichconstructionofthelocallyreactivelinerdescribedearlier isdenotedasasingledegree-of-freedom(SDOF)linerwherethefacesheetandcavity aregenerallylumpedasasingledegree-of-freedom.Thisconceptcanbeexpandedto alargerrangeoffrequencysuppressionifaporousseptumsheetisusedintheplace oftheoriginalsoundhardbottomplateexposingasecondcavitytunedtoadissimilar frequency.Thelowercavitybecomesaseconddegree-of-freedomandthusthemoniker, 2DOF,iscommonlyused.Therangeofe ectivesuppressioncanbedesignedtocoverup totwooctavesincontrasttothecharacteristicsingleoctavecoverageoftypicalSDOF liners( Motsinger&Kraft 1991 ).Aschematicoftheresistiveandreactivemechanismis illustratedinFigure 1-5 Bulkreactinglinersareunconstrainedbythecellulardivisionsoflocallyreactive liners,consequentlyallowingfortransversewaveprogression( Nayfeh etal. 1975 ). Generallyisotropicmaterials,bulkreactinglinersaredesignedforgeneraluseapplications suchassuppressionofmultipleorbroadbandfrequencies.Incontrasttolocally-reactive linerssuppressingaspecictoneoranarrowfrequencyrange,bulkreactinglinerscan suppressuptothreeoctaves,howeverlesse ectivelythaneitherSDOFor2DOFliners ( Nayfeh etal. 1975 ).Bulkreactinglinersdissipateenergythroughviscousresistanceas kineticenergyislosttointra-matrixcollisions( Nayfeh etal. 1975 ).Althoughwidelyused inmanyindustries,adoptionofbulklinerswithintheaerospaceeldhasbeenhindered duetothelimitede ectiveness,inherentrisksassociatedwithfuelabsorption,andriskof failurethroughabrasion( Motsinger&Kraft 1991 ). Bothtypesoflinersrelyonasoundwaveinteractingwiththeboundariesasit propagatesthroughtheenginenacelleduct.Multiplereectionswithinaductincreasethe e ectivenessofalineraseachinteractionwithaductdissipatesadditionalacousticenergy. Forthisreason,longerregionsofliners,suchasinthebypassductsystems,arethemost e ectiveatsuppressingnoise,astherearemultipleopportunitiesforenergyconversion 22

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( Smith 2004 ).However,enhancednoisesuppressionvialengtheningtheinteriorducts necessitatesaweightpenalty,leadingtoexcessmaterialandfuelcosts( Smith 2004 ). 1.4AerodynamicandAcousticPerformanceofLiners Althoughlinershavegreatlyreducedthenoiselevelfromenginenacelles,additional researchisrequiredwithintheaerospaceandaeroacousticcommunities.Withanynew technology,widescaleimplementationshouldbeweighedagainstdisadvantagesassociated withitsapplication.Disadvantagesassociatedwithacousticlinersstemfromdesign constraintsonnacellesize,dragpenalty,andlinerpropertytesting. Aspreviouslymentioned,SDOFlocallyreactivelinersaremoste ectivewhenthe cavitydepthistunedtoagivenfrequency.However,the / 4 designoncavitydepth necessarilyincreasestheexternaldiameterofthenacelle.Thisadditionalthickness increaseoverunlinedductsincreasesmaterialcosts,drag,takeo weight,andreduces nacellegroundclearance( Motsinger&Kraft 1991 ).ForastandardBoeing777engine,the lowestBPFvalueliesinthe630and800Hz 1 / 3 octavebandrange( Bielak etal. 1999 ). Theoreticalsuppressionofthesefrequencieswouldaddoverafoottothenacellediameter ofanunlinedduct.Restrictionsonoverallsizerestrictfrequencysuppressiontothose frequenciesmostsensitivetohumanhearing,limitingfullnoisesuppression( Smith 2004 ). Inaddition,thedragpenaltyassociatedwithacousticlinershasbeeninvestigated inthepastbutstillremainsatopicofinterestduetoincreasingfuelcosts( Wolter 2005 ). Theoverallsizeofanaircraft'sengineisadirectfunctionofthebypassratio,amechanism designedtoincreasefuelperformance.Theviscousdragpenaltyassociatedwithacoustic linersduringightconditionsisafunctionofthewettedarea,thatisthelinermaterial indirectcontactwiththemovinguid.Thus,decreasedjetnoiseduetoincreased bypassratioscausesanon-trivialdragpenalty( Smith 2004 ).Facilityexperimentsare necessaryforperforminglinerdragstudiesaswellasdevelopmentofintelligentdesign toolsandnovelmeasurementtechniquestoreducethedragpenaltywhilemaintainingand enhancingacousticsuppressionperformance. 23

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1.5AcousticLinerTestFacilities Manyissuesofnacelleoweldsandnoisemechanismshavebeenpresentedto illustratecurrentchallengesamodernaircraftenginepresentstoengineers.Thisthesis coversthemathematicalmodels,design,andtestingproceduresforanaeroacousticwind tunnelfacilityforgrazingowacousticlinertesting.Thefollowingsectionwillpresent somemotivationforafacilityaswellassomeofthedesignconsiderationsnecessaryfor implementation. Full-scaleenginetesting,whilepossible,presentsnon-trivialissuesrelatedtocost andmaintenance,aswellasobvioussafetyandenvironmentalhazards.Noisesource identicationbecomesdi cultinfull-scalemodels,wherenoisereductionsfromliners nearthefanstagecanbecomeburiedbyuctuationsinjetnoise,possiblymaskingkey advancements( Motsinger&Kraft 1991 ).Whilefull-scaletestingisperformedatcertain facilities,themajorityoflinertestingisachievedinwellcontrolledacousticlaboratories forbettersourcecontrol( Smith 2004 ).Abriefoverviewoffacilitycomponentsanda reviewofpastandcurrentlinertestfacilitiesarepresentedinChapter 3 Afacilitydesignedfortheacquisitionofacousticlinerimpedancemeasurements, specicallythosepertainingtothesuppressionofaircraftenginenoise,shouldprovidea representativeenvironmentoftrueightconditionsaswellastheabilitytocontrolthe acousticanduidconditions.Thetestenvironmentcanbecharacterizedbythreeprimary components:theacousticsource,thetestsectionforsampleplacementandtesting,and theacoustictermination( Melling&Doak 1971 ). Achievingthehighintensityacousticeldoftheenginecanbeaccomplishedwith multiplesoundsources.Thesourcesshouldmatchboththeappropriately-scaledfrequency contentaswellasthesoundintensityofanacelleenvironment( Melling&Doak 1971 ). Soundpressurelevelsupto160; dB areideallyrequiredaslevelsofthismagnitudeare notuncommonwithinanacelleenvironment( Smith 2004 ).Theextremelyhighlevelsof acousticpowerpromoteanonlinearacousticresponsewithinanacelle,andcanbefound 24

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atlevelsaslowaslowas130 dB ( Smith 2004 ).Theabilitytowithstandsuchhighlevels withoutacousticleakageorothercomplications,suchassourceinterference,mustbe consideredduringthedesignofthetestsectionandalltestcomponents.Additionally,test Machnumbersabove M =0 5shouldbeattainedtomatchfull-scalecruiseconditions ( Smith 2004 ). Similartotheacousticeld,theoweldthroughoutthenacelle,excludingthe regionunderthedirectinuenceofthefan,canbeconsideredaslocallytwo-dimensional forsimplicity.Flowspeedisprimarilyrelatedtotheacousticconvectione ectdiscussed inChapter 2 .However,theowshouldbefedbyclean,dryairwithminimalturbulent uctuations( Smith 2004 ).Thefacilityconditionsmustbeestablishedinacontrolled mannersuchthatinformationregardingacousticlinerimpedanceundervariousowand acousticconditionscanbeextracted. Testsectionsforlinerimpedancetestingshouldbedesignedsuchthatalargerange oftestingcapabilities,includingmultiplesamplesizesandmaterials,canbeinvestigated withoutreplacingmultiplecomponents.Full-scalenacellescanbeseveralmetersin diameterandlength.Thesizeconstraintsimposedonalaboratorybyafull-scaleengine wouldbetoogreat,andthussmaller,moremanageable,windtunnelassembliesare generallyconsidered.However,thegeometryofthetunnelmustallowforthephysicsofa nacelleatightconditionstobeaccuratelycaptured( Melling&Doak 1971 ).Foreaseof manufacturingandinstallation,arectangularcrosssectioniscommonlyusedtoallowfor atwallinstallationandtestingprocedures. Usingawindtunnelincontrasttoafull-scaleenginedoespresentdrawbackson thetestedfrequencies,whicharerestrictedbythechosenexcitationsourceaswellasthe geometryofthetestfacility.Similarly,thetunnelwallsshouldbe"soundhard"asto notcauseundesirabledissipationofacousticenergy.Duringlinerimpedancetesting,new materialsandmethodsmayrequireoneormoretunnelwallstobereplaced.Ensuring theboundariesremainfreeofdiscontinuitiesrequiressamplesbeushmountedtothe 25

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wall,thusminimizingreectionsfromprotrudingcornersandmaintainingowuniformity. Assoundpropagatesandairowsdowntheductthereareopportunitiesforreections andnewnoisesourcestobegeneratedatjunctionsorareachanges.Downstreamnoise sourceshavethepotentialtopropagateupstream,contaminatingmeasurements.Upstream propagatingnoisecanbeminimizedbyterminatingintoananechoicoutlet,where reectionsareunabletopropagate( Melling&Doak 1971 ). Severalfacilitieshavebeenspecicallydesignedandusedforthegrazingow impedancetestingofacousticlinersallowingfornewtechnologiestobetestedand ultimatelyimplemented( Herkes etal. 2006 ).Inane orttoupgradecurrentcapabilities andsteerlinerdevelopment,NASALaRCdonatedportionsofsuchafacility,tothe UniversityofFlorida.SuchatestcapabilityinaU.S.universitylabisrareasmost facilitiesareoperatedbyprivatecompanies( Eversman&Gallman 2009 ),( Yu etal. 2008 ), governmentagencies( Watson&Jones 2009 ),orinforeigncountries( Auregan&Leroux 2008 ),( Thiele etal. 2008 ),( Jing etal. 2008 ).Universitycontainedfacilitiesallowforan openplatformforcollaborationandtheexibilityformultipleuses.Afullcomparisonof knownexperimentallinerfacilitiesispresentedinChapter 3 Acousticlinertestingisasmallsteptowardalargergoalofreducingaircraft generatednoise.Manyadvancementsarebeingmadetoreduceaircraftnoiseusing advancedmaterials,in-ighttrailingedgegeometrytreatment,andacoustictreatmentof landinggear( Herkes etal. 2006 ).Thefacilityproposedinthisworkisbutanothertoolto helpbetterunderstandandultimatelyreducefannoiseforpassengersandthecommunity atlarge. 1.6ThesisOutline Thecurrentchapterestablishedbasicaircraftnoisesources,noiseabatement technology,andhighlightedsomeadvantagesforauniversity-leveltestfacility.Chapter 2 presentsanalyticalmodelsforunderstandingtheacousticanduidicbehaviorwithin geometriespertainingtotheproposeddesign.AthoroughliteraturereviewinChapter 26

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3 describescurrentandpastfacilities.Anin-depthcomparisonatacousticimpedance measurementtechniquesarealsobecompared.Chapter 4 describesthedesignof theproposedfacility,contrastingthedi erencesbetweenitandtheoriginalGrazing ImpedanceTubeatNASALangleyResearchCenter.Chapter 5 laysoutaproposed experimentalinvestigationforcompletecharacterizationofthetunnel,establishing baselineowandacousticperformance. Figure1-1.Overallnoiselevelgoalsforfutureaircraftdesign.Databasedon EnvironmentallyResponsibleAviation(ERA)ProjectoftheNASAResearch OpportunitiesInAeronautics2010.AeronauticsResearchMission Directorate. 27

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Figure1-2.Aircraftnoisegeneratingsources. Figure1-3.High-bypassratioenginenacellesideview,adaptedfromVoutsinas,S.G. 2007.AeroacousticsresearchinEurope:TheCEAS-ASCReporton2005 highlights.TheJournalofSoundandVibration,Volume299,(Page426, Figure7). 28

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Figure1-4.Acousticlinertypes,adaptedfromRollsRoyce1996.TheJetEngine(Page 204,Figure19-6)Rolls-RoyceTechnicalPublications,England. Figure1-5.A2-Dsideviewofasinglelocallyreactivelinerwith(a)resistiveand(b) reactivefacesheetsforacousticenergyconversion,adaptedfromSmith(2004). AircraftNoise.CambridgeUniversityPress.(Page144,Figure4.26) 29

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CHAPTER2 THEPHYSICSOFAGRAZINGIMPEDANCEDUCTFACILITY Chapter1illustratedthenecessityforexperimentaltestfacilitiestostudyacoustic linersforaircraftnoisereduction.Thischapterwillpresenttheunderlyingphysics involvedwithagrazingowfacility,specicallyductacousticsandchannelow.The acousticanalysisconsistsofthreeidealizedexamples:acousticpropagationinahard-wall ductwithoutow,ductacousticswithanimpedanceboundaryconditionwithoutow, andnallytheacousticpropagationwithinaboundedmovinguid.Aconsideration oftheuidphysicsisaccomplishedbypresentingareviewoflaminarandturbulent boundarylayertheoryandscalinganalysis,aswellasanintroductiontoturbulentchannel ow.Suchphysicalinsightsareprerequisitestoanunderstandingoftheacousticandow eldsspecictothecurrentfacility. 2.1IntroductiontoGrazingDuctFlow Theproposedfacilityseekstoelucidatetheunderlyingphysicsregardingsuperimposed acousticandowelds.Laterchapterswillmakereferencetotopicsdiscussedultimately aidinginthedesign,implementation,andthoroughtestingoftheGFIDfacility. Theacousticeldwithinaclosedductishighlydependentuponsourceconditions, ductgeometry,andboundaryconditions.Initially,ahard-walledductisexaminedto establishabaselinesolution.Thehardwallsarethenreplacedwithacompleximpedance boundaryconditiontodemonstratetheimpactontheacousticeldbymodifyingthe boundaries,muchlikeanacousticliner.Finally,asteadyuniformowissuperimposed ontheacousticeldtoillustratethee ectofafreestreamMachnumberonacoustic properties.FullderivationsofselectequationsareworkedoutinAppendix A C Thelatterhalfofthischapterprovidesanin-depthlookattheoweldwithinan enclosedrectangularchannel.Theanalysisfocusesonthedevelopingboundarylayers withintheduct,beginningwithadiscussiononlaminarandturbulentboundarylayersas wellasturbulencescaling.Viscouse ectsspecictoturbulentchannelowwithin,suchas 30

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cornerowsandcross-axissecondarymotion,arediscussedviathegenerationanddecay ofvorticity. 2.2Ductacoustics 2.2.1RigidWallAnalysisinaQuiescentMedium Thepropagationofanacousticwavethroughatwo-dimensionalrigid-walledductof innitelengthandwidthisinvestigatedtoestablishabaselinesolutionforpropagation withoutenergylossattheboundaries,illustratedinFigure 2-1 a.Forsimplicity,the acousticeldisassumedtobegeneratedbyanupstreamtime-harmonicsourceofthe form e i t ,includingthesimplestcaseofasingletone.Thesourceisalsoassumedtobe su cientlyfarawaysuchthatthesolutioncanbeconsidereda"far-eld"approximation andthushydrodynamice ectsareassumedtobenegligible( Beranek 1996 ).Acoustic propagationislimitedtoonly"right-runningwaves",neglectingupstreampropagating reections.Thisassumptionsimpliesthesolutionandismoreapplicabletotheproposed facilitywherethepressurewaveswillterminateintoananechoicdi user.Theacoustic eldismodeledbyanassumedsolutionoftheform p ( x,y,t )= P ( x,y, ) e j t (21) wherethepressureeld, p ( x,y,t ),isexpressedastheproductofafrequencyandspatially dependentcomplexamplitude, P ( x,y, ),withacomplextime-harmonicexcitationterm, e j t ( Blackstock 2001 ). Assumingthegiventimeharmonicsourceandanisentropicspeedofsound,the pressurewaveequation, 2 P 1 c 0 # 2 p # t 2 =0 (22) canbeconvertedtothefrequencydomain 2 P + $ 2 P =0 (23) 31

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commonlyreferredtoastheHelmholtzequation( Blackstock 2001 ).Here, k = / c 0 representstheacousticwavenumber,denedastheratiooftheangularfrequencyand theisentropicspeedofsound.Theboundaryconditionsofzeroparticlevelocitynormalto thewallsareimposed.Separationofvariablesisanappropriateapproachtothesolution ofEquation 23 .Thesolutiontothelinear2 nd orderhomogeneouspartialdi erential equationreducestotranscendentalfunctionsinthetransversedirectionandthesumof complexexponentialsinthedirectionofpropagation( Blackstock 2001 ).Thenalresult representsthesuperpositionofaninnitenumberofright-runningacousticmodes, n presentedinEquation 24 .AfullderivationofthesolutionispresentedinAppendix A p = # n =0 cos n % y b # Ae $ j ( # x ) n x e j t (24) Theconstant A isafunctionofthesourceoperatingconditions,and b istheductheight. TheeigenvaluesofEquation 24 ,functionsofductgeometryandmodeofinterest,are representativeofthepropagatingwavenumbermode, $ y = n % b for n =0 1 2 ,... (25) Thetotalwavenumber, k ,canbedecomposedintodirectionaltracewavenumbers. Therelationshipbetweendirectionaltracewavenumbersandthetotalwavenumberis commonlyreferredtoasadispersionrelationship k = $ $ x 2 + $ y 2 (26) orsolvedfor $ x as $ x = % & c 0 2 n % b # 2 (27) Thewavenumberalignedwiththedirectionofpropagation, $ x ,isshowntobe dependentupontwoterms:theoverallacousticwavenumber,itselfafunctionofthe mediumandexcitationfrequency,and $ y ,aconstantdenedbyductgeometrythatis 32

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highlydependentupontheimposedboundaryconditions.Variousvaluesoftheseterms allowforthedispersionrelationshiptobepurelyreal,purelyimaginary,orcomplex. Viathedispersionrelationshipforhard-walledducts,modalwavepropagation occurswhenthevalueof $ x ispurelyreal.However,if $ x ispurelyimaginary,thewave isevanescentanddecayswithincreasingdownstreamdistance, x .Thethirdcasedictates that,fornitemodesassociatedwithcomplexvaluesof $ x ,thewavemaypropagatebut willeventuallyattenuate( Blackstock 2001 ). Forpropagatingmodes,wavenumbersdenedsuchthat k> $ y designatesthe frequencyvalueatwhichhigherordermodesaresupportedandareafunctionoftheduct geometryandsourceexcitationfrequency( Blackstock 2001 ), f n = nc 0 2 b (28) The0 th modeisaplanarwaveinarectangularduct,onedevoidoftransversepressure variations( Blackstock 2001 ).Ahigherorderpropagatingmodeisrstcut-onwhenthe transversedimensionoftheductisequaltoanintegernumberofhalf-wavelengths.Note thatalthoughonlytheplanarmodeissupportedtopropagateintheduct,socalled"soft modes"aregeneratedattheleadingandtrailingedgesofaninstalledacousticliner,but willevanescentlydecay( Watson etal. 2008 ). Fromapracticalstandpoint,thespatialdependanceofhigherordermodeswithina ductdenesthelocationofpossiblemicrophoneinstallationsitesforimpedanceeduction measurements.Duetothesizeofcurrentmicrophonesandductgeometry,testingisoften restrictedtofrequenciesassociatedwiththeplanarmode. Thecut-onfrequencydescribedinEquation 28 ,islimitedtoductswithidealized soundhardboundaries( Blackstock 2001 ).Thefollowinganalysisspecicallyinvestigates ductacousticsunderimpedanceboundaryconditions,suchasanacousticliner. 33

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2.2.2ImpedanceBoundaryConditionsinaQuiescentMedium Thevaluesof $ x determinewhichmodesarepermittedtopropagatewithinaduct. Ifthevalueof $ x canbealteredtoreducetheamplitudeofunwantedmodes,then undesirablenoiseresultingfromthesemodescanbeattenuatedinsidetheductpriorto propagatingtothesurroundingenvironment.Since $ x isafunctionofboth $ and $ y altering $ x requiresthateithertheductgeometryortheboundaryconditionsbemodied. Geometriesaregenerallydesignedforaerodynamice ciencyorstructuralintegrity, generallyleavingacousticmitigationasasecondaryconcern( Smith 2004 ).Thus,the boundaryconditionisusuallyaltered,mostcommonlythroughtheuseofacousticliners. Anewdispersionrelationshipcanbeobtainedfordi erentimpedanceboundaries. Whilezeroparticlevelocitynormaltothewallwasimposedforthehard-walledcase,the particlevelocityisnowgeneralizedasafunctionofthelocalimpedance.Akeyassumption appliedintheanalysisofimpedanceboundaryconditionsistheacousticlinersare "locallyreactive",thatisconstrainingparticlemotionnormaltothesurface( Nayfeh etal. 1975 ).Theboundaryconditionsmatchparticlevelocitynormaltothesurfacefromthe momentumequationtotheparticlevelocityimposedbythespecicacousticimpedance denedattheboundariesoftheimposedliner( Ingard 1999 ), 1 j "& 0 # p # y = P Z 1 y =0 (29) and 1 j "& 0 # p # y = P Z 2 y = b (210) Asolutionisdescribedfortwowallsseparatedbydistance b withspecicacoustic impedancevalues, Z 1 and Z 2 ,asshowninFigure 2-1 b.Itbecomesconvenienttointroduce theinverseofacousticimpedance,admittance,denedby i = & 0 c 0 Z i (211) 34

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Tosolvetheacousticeldwhenimpedanceboundariesarespecied,aseparationof variablestechnique,similartotherigid-walledcase,isemployed.Combiningliketerms, theratioof # y / k isobtainedasafunctionofthewavenumberandlineradmittance.Afull derivationofthisresultcanbefoundinAppendix B $ y $ # tan ( $ y b )= j 1 + 2 1+ 1 2 # # y # 2 (212) Theaboveexpressionisgenerallysolvednumericallyforthetransversewavenumber, $ y ,asafunctionofductgeometry,totalwavenumber,andthelinernormalizedspecic admittance( Ingard 1999 ).With $ and $ y known,valuesfor $ x canbecalculated, revealingwhichmodeswillpropagateandtheirattenuation.Morecomplexdesigns canfurtherattenuateundesirablemodesbyvaryinglineradmittancealongtheduct length. Thehard-walledandlocallyreactivelinercasesbothassumethatacousticpropagation issoleyafunctionofthegeometry,propagatingwavenumber,andimposedboundary conditions.However,inthee orttofurthermimicenginenacelleconditions,thee ectof theowofairpassingoveralinersurfacemustalsobeassessed. 2.2.3TheConvectiveWaveEquationwithUniformVelocityProle Bothofthepresentedsolutionshavebeensubjecttotherestrictionofzero-mean velocity,simplifyingthegoverningequationsnecessaryforsubsequentderivations. However,ifaknownmeanvelocityissuperimposedwithapropagatinglinearacoustic wave,theresultanteldisbestdescribedbytheconvectivepressure-waveequation. # 2 p # t 2 + c 2 0 # 2 p # x 2 ( Ma 2 1 ) = 2 u 0 # 2 p # x # t (213) where Ma isthelocalMachnumber,formedbynon-dimensionalizingthelocalmean velocitybytheisentropicspeedofsound, M = u 0 / c 0 .AfullderivationofEquation 213 isprovidedinAppendix C .NotethatinEquation 213 ,if Ma iszerotheclassic pressure-waveequationforaquiescentmediumisrecovered. 35

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Thedownstreammovinguidconvectstheacousticelddownstream,increasingthe speedatwhichpressurewavespropagate( Nayfeh etal. 1975 ).Foralinedduct,thee ect ofconvectiondecreasestheattenuationfordownstreamtravelingwaves( Eversman 1991 ). Forupstreamacousticpropagation,theoppositeistrue,andahigherattenuationrateis achieved( Tack&Lambert 1965 ).Inuniformow,theconvectionoftheacousticeldis theonlymechanismforalteringtheattenuationrate,theinuenceofwhichincreaseswith increasedfreestreamMachnumber( Eversman 1991 ). NotethatEquation 213 isonlyvalidforuniformow,butexperimentalresults havefoundasecondattenuationmechanism.Theinuenceofuidviscosityexhibitsa refractione ect,mostnotablynearwallswhereviscouse ectsdominateintheboundary layer( Nayfeh etal. 1975 ).Fordownstreamacousticpropagation,thevelocitygradient refractsthepropagatingacousticfronttowardtheboundaries,increasingtheattenuation rate.Forupstreampropagation,theattenuationratedecreasesasacousticwavesconverge towardthecenter( Nayfeh etal. 1975 ). Thetwocontradictorye ectsofconvectionandrefractionarestrongfunctionsof thewavenumber.Convectivee ectsarefoundtoinuencealargerangeoffrequencies ( Nayfeh etal. 1975 ).Conversely,refractione ectsareimportantathigherwavenumbers, andthushigherfrequencies,notablyfor $( > 1,wheretheboundarylayerthickness, ( ,is approximately 1 / 6 oftheacousticwavelength.Thus,refractione ectsbecomeincreasingly signicantatdownstreamlocationsduetoboundarylayergrowth( Tack&Lambert 1965 ). Theinuenceofrefractionhasbeendemonstratedbothexperimentallyand numerically( Mungur&Gladwell 1969 ; Tack&Lambert 1965 ).Therefractivee ects arebaseduponviscousdissipationinherenttotheboundarylayer.Thedevelopment, structure,andscalingofboundarylayersarediscussednext. 2.3FluidAnalysis Insection 2.2.1 ,theproblemofacousticpropagationthroughaductwasanalyzed subjecttozero-meanowtoestablisharelationshipbetweentheacousticwavenumber 36

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andtheimposedboundaryconditions.Auniformvelocityprolewasthensuperimposed insection 2.2.3 todescribetheimpactofaconvectivemediumonlinerattenuation. However,theuniformowproleviolatestheno-slipboundaryconditionimposedby viscousinteractionsofauidwithaboundary.Disregardingtheviscouse ectswithina xedareaductallowsforsomebasicphysicalinsight;however,thismethodofanalysis doesnotfullyrepresentthephysicsoftheproblem. Inordertobetterunderstandtheunderlyinguide ects,itisinstructivetoconsider thedevelopingboundarylayeronaatplateundertherestrictionsofanenclosedchannel. Specically,arectangularchannelisexaminedbecauseitisconsistentwiththeproposed facility.Thestudyofchannelowcanbeseparatedintotwodistincttopics:thenearwall developingboundarylayerandsecondaryowinuencednearthecornerregions,specic toenclosedrectangularchannelow. Thetwodeningtopicsofboundarylayersandchannelowarehighlydependent onviscousphenomena.Thesignicanceoftheviscousforcescanbequantiedviathe Reynoldsnumber Re = & U ) (214) TheReynoldsnumberisthedimensionlessratioofinertialtoviscousforces( Young 1989 ). Inequation 214 ) isalengthscaleofinterestsuchaschannelheightorlocalboundary layerthickness,while & and aretheuiddensityanddynamicviscosity,respectively. Alternatively,theuidpropertiescanbecombinedtoformthekinematicviscosity, = / $ .ThevalueoftheReynoldsnumberisindicativeofowregimecharacteristics. Section 2.3.1 discussestherangeofdi erentlengthscaleswithintheboundarylayerbased upontheReynoldsnumber. 2.3.1TheBoundaryLayer Theboundarylayerisathinregionofuidnearasurfacedominatedbyviscous forces.EvenforhighReynoldsnumberows,whereinertiale ectsdominate,the 37

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boundarylayerisresponsibleforviscousdragpenalties,vorticitygeneration,andpossible sheddinge ects( Batchelor 2000 ). Theboundarylayerwithinaowistheresultofinternalstressesinducedby intermolecularattractionsasuidparticlespassasurface( Schlichting&Gersten 1968 ).Theuidindirectcontactwiththesurfaceissubjecttothe"no-slipcondition", andconsequentlymustmatchthelocalsurfacevelocity.Thedynamicviscosity, ,is theuidpropertyresponsiblefordissipatingkineticenergy,thusreducingthelocal uidvelocitynearthewall.Atsomedistancefromthebody,theinuenceofviscosity becomesnegligible,andthefreestreamvelocityisreachedatadistance ( fromthewall. Mathematically, ( isdenedastheheightnormaltothesurfacewherethelocaluid reaches99%ofthefreestreamvelocity, U # ( White 2006 ). ForaNewtonianuidinasteady,two-dimensional,incompressibleboundarylayer, thelocalwallshearstress, + ji ,canbeestimatedastheproductofthedynamicviscosity andthelocalvelocitygradientatthewall( White 2006 ), + ji = & # u i # x j + # u j # x i (215) ApplyingEquation 215 totheboundarylayerinachannelcoordinatesystem,scaling analysisdemonstratesthatthesecondtermistwoordersofmagnitudesmallerthanthe rstterm, % v / % x # % u / % y .Thisleadstoanapproximationforwallshearstress + w $ # u # y * y =0 (216) Although ( itselfcanbeusefulingaugingtheinuenceofviscosity,thedisplacement thickness, ( % ,andmomentumthickness, ,provideadditionalinsight.Thedisplacement thicknessphysicallyrepresentsthedistanceastreamlineisdisplacedfromasurfaceto matchthemassowoftheboundarylayer( Panton 2006 ),andisdenedas ( % = # + 0 & 1 u ( y ) U # dy. (217) 38

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Similartothedisplacementthickness,themomentumthicknessisalsodenedbyan integralrelation = # + 0 u ( y ) U # & 1 u ( y ) U # dy. (218) Themomentumthicknessphysicallyrepresentsthemomentumdecitperunitdepth causedbytheretardationoftheuidwithintheboundarylayer( Tennekes&Lumley 1999 ).Thenon-dimensionalshapefactor, H ,allowsforcomparisonofboundarylayersand isdenedastheratioofthetwopreceedingvariables, H = ( % (219) Alwaysgreaterthanunity,highershapefactorvaluesindicatenear-separationow. Blasius'ssolutionspeciesaconstantshapefactorvalueof2 59foranidealizedlaminar boundarylayer,higherthantheestimateofaturbulentboundarylayerof1 3basedona 1 / 7 th powerlaw( White 2003 ). DependinguponthelocalReynoldsnumber,theowiscategorizedaslaminar, transitional,orturbulent.Foragivengeometry,lowerReynoldsnumbervaluesindicate agreaterdependenceonviscouse ects.TheowregimeatlowReynoldsnumbersis designatedlaminartodescribethesmoothandorderedowstructure.Alaminarregime isfoundat Re D < 2 300forpipeowand Re x < 500 000forowoveraatplate ( White 2003 ).Here, x isthestreamwisedistancefromtheleadingedge.Theonsetof turbulencecanbedi culttopinpointasitisastrongfunctionofsurfaceroughnessand initialconditions.Conservativeestimatesare Re D > 4 000and Re x > 1 E 6forpipeand atplateows,respectively( White 2003 ).Thesubscriptonthe"Re"indicatesthelength orvelocityscaleusedforthespecicReynoldsnumbercalculation. Thegrowthofalaminarboundarylayerstemsfromacombinationoftheconvection ofmomentumandviscousdi usionawayfromthesurface( Mathieu&Scott 2000 ).The facilitybuiltforthisprojectwasdesignedforspeedsabove M =0 5tomodeltheow insideengineducts.TheseMachnumbersareachievedbyincreasingthefreestream 39

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speed,therebyestablishingaturbulentowregimebeyondacertainpoint.Duetotheir relevancetothepresentapplication,turbulentboundarylayersaregivenadditional discussion. 2.3.2TurbulentBoundaryLayers Asauidpropagatesdownstream,thesmoothandorderedowtransformstoone characterizedbythree-dimensionalrandomuctuations( Tennekes&Lumley 1999 ). Aturbulenteldishighlydependentonlocalvariablesincludingsurfaceroughness, pressuregradients,andevenexternale ectssuchaslocalenvironmentalnoise( Young 1989 ).Oncetheowbecomesunstableandtransitionstoaturbulentregime,thephysical characteristicsoftheow,andthustheboundarylayer,transform. Turbulentowexhibitsrandommotionwithawiderangeoflength,velocity,and timescales.Aturbulentowcontainsvorticalstructuresreferredtoas"turbulenteddies" thatconvectandentrainuid( Tennekes&Lumley 1999 ).Whilelaminarboundarylayer growthisdictatedbyviscousdi usion,thefasterturbulentboundarylayergrowth(i.e. increasein ( ( x )with x )stemsfromtheentrainmentofhighmomentumuidattributedto theturbulenteddies( Mathieu&Scott 2000 ). TermedtheReynoldsdecomposition,thelocalvelocity, u ( x,t ),ataparticularpointin spaceandtimecanbewrittenas u i = u i + u i .Moregenerally,theturbulentvelocityeld atanygivenpointisthesuperpositionofmean,(),anductuatingcomponents,() .On aatplate,theuctuatingvelocitycomponentcanbeashighas10%ofthefreestream velocityinaturbulentow,resultinginincreasedboundarylayermixing( Young 1989 ). Turbulentowenhancesthree-dimensionalmixing,whichincreasesthetransportof momentum,vorticity,andheatnearthesurfaceofabody,leadingtoaboundarylayer witha"fuller"meanvelocityprolethatentrainshighenergyuidfoundfurtherfrom thewall,illustratedinFigure 2-2 ( Tennekes&Lumley 1999 ).Afullerboundarylayeris quantiedbylower H values,denedinEquation 219 .Asaconsequenceoftheno-slip condition,largernearwallvelocitygradientsareformed,resultinginturbulentboundary 40

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layershavinghighermeanshearstressvaluesthanlaminarowsatsimilarconditions ( Mathieu&Scott 2000 ). Uptothispoint,boundarylayershaveonlybeendiscussedintermsofthedistance fromtheorigin, x ,theheight,suchasboundarylayerthickness, ( ,ormomentum thickness, ,whicharefunctionsofthenormaldistancefromthewall, y .Toquantifythe inuenceofviscouse ectswithinturbulentboundarylayers,thelengthscalespreviously presentedareinsu cient.Instead,anon-dimensionalviscouslengthscaleisdened, y + = yu % (220) theratioofwall-normaldistance, y ,toa"viscouswallunit".Thevariable u % denesthe frictionvelocity, u % = + w & (221) afunctionofthethelocalshearstressandlocaluiddensity.Similarly,anon-dimensional viscousvelocityscale, u + ,isformedbynormalizingthelocalmeanvelocitybythefriction velocity u + = u u % (222) Thequantitiespresentedcannowbeusedtoanalyzetheturbulentboundarylayerin termsofviscouslengthandvelocityscales. Oneparticularareaofinterestistheabilitytomeasureandextractthelocalshear stressvalues.Foralaminarboundarylayer,agoodapproximationtothelocalshearstress valueissimplyEquation 216 ( Young 1989 ).However,inaturbulentboundarylayer, highlyenergeticeddiesgiverisetoanadditionalimpartedstress,referredtoasturbulent Reynoldsstress, & u i u j .Thetotalstressthroughoutaturbulentboundarylayercanthen bewrittenas + ij = & # u i # x j + # u j # x i & u i u j (223) 41

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ItisevidentthatEquation 215 isasimplicationofEquation 223 forwhenReynolds stressesarenegligible,asisthecaseoflaminarboundarylayers. Theturbulentboundarylayercannowbesubdividedintoregionswherethelocal stressisdominatedbyeitherturbulentstressesorbyviscousstresses,termedtheinertial sublayerandviscoussublayer,respectively.Thetworegionsarebridgedbythebu er layer,whereboththeviscousandturbulentstressesplayapivotalrole( Schlichting& Gersten 1968 ). Denedwithintheapproximateregion y + % 5,theviscoussublayerisdominated byviscouse ectsandisalsostronglydependentonsurfaceroughness( Mathieu&Scott 2000 ).Assumingasmoothsurface,thenon-dimensionalvelocityinthisregionislinearly relatedtothedimensionlesswallunitlengthscale,i.e. u + $ y + ,leadingtothealternative designationof"linearsublayer".Strongviscousstresseswithinthisregiongeneratea momentumsinkasviscositysuppresseshighenergyuidentrainmenttowardthewall ( Tennekes&Lumley 1999 ). Thebu erlayerisgenerallydenedfor y + valueswithin5
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outto y / & $ 0 7( White 2006 ).ThevonKarmanconstant $ and B currentlyadhereto theexperimentalvaluesof0.41and5.0,respectively.However,valuesof0.38and4.08 havebeensuggestedforusewhen Re > 10 000( White 2006 ).Denotingtheformofthe equation,thisregionisoftenreferredtoasthe"loglayer",althoughothermathematical modelsexist( Kays etal. 2005 ). Asimilarformulathattakesintoaccountallthreeregionsoftheturbulentboundary layersimultaneouslywasdevelopedbySpalding( Spalding 1965 ), y + = u + + e $ # B e # u + 1 $ u + ( $ u + ) 2 2 ( $ u + ) 3 6 (225) Thewallshearstresscanthenbeextractedthroughthedenitionoftheviscouswallunit andthefrictionvelocityprovidedbyequations 220 and 221 ,respectively. Spalding'sequationbreaksdownathigh y + valuesnearthewakeregion,requiringa secondaryfunctionfortheouterregion. Musker ( 1979 )presentedanexplicitequationthat accountsforboththeinnerandouterregions, u + =5 424tan $ 1 2 y + 8 15 16 7 +log 10 / ( y + +10 6) 9 6 ( ( y + ) 2 8 15 y + +86 ) 2 0 ... 3 52+2 44 1 # 6 y ( # 2 4 y ( # 3 + y ( # 2 1 y ( # .2 (226) where # = # A / 2 ,ColesWakeparameter,and A isanouterlayervariablethatisa functionofthelocalpressuregradient.ExperimentaldatainChapter 4 willbettoboth Equations 225 and 226 forcomparison( White 2006 ). TherelationsforthethreeinnerlayerregionshavebeenplottedinFigure 2-3 .The horizontalaxis,representingthedistancefromthewallinviscouswallunits,iscommonly expressedonalogarithmicscale,illustratingthediscrepancyinsizesofthesublayers.The heightoftheviscoussublayercanbelessthan 1 / 100 th ofthetotalboundarylayerthickness ( Young 1989 ).Asanexample,anincompressibleowofairat100 m / s througha2 in. squaretunnelwouldhaveaviscoussublayerofapproximately2 9 m .Thelayer'ssmall sizehindersaccurateexperimentalsublayervelocitymeasurements. 43

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Manyoftheboundarylayerapproximationsandcomparisonsareapplicableto near-wallinternalowsaswell.However,theinuenceofmultipleconningwallsanda correspondingstreamwisepressuregradientinherenttointernalows,globallyimpacts theowstructureandboundarylayercharacteristics.Thefollowingsectionpresentssome generalchannelowfeaturesandtheirsignicancetothecurrentresearch. 2.3.3TurbulentChannelFlow TheGFIDfacilitycombinestheowandacousticpropagationthroughasquare channelinane orttomimicightconditionsforimpedanceeductionofacousticliner samples.Ductgeometryhasalreadybeenshowntoinuencetheacousticeldbylimiting therangeofsupportedfrequencies.Nearwallacousticrefractionbymeansofviscous e ectsalsoinuencesthepropagationandattenuationofacousticwaves,thusultimately a ectingimpedancemeasurements.Thissectionwillrevealsomeoftheimportant characteristicsassociatedwithturbulentchannelow.Notethatthissectionspecically dealswithowthroughchannelsofniteaspectratioslessthan(1:7),wherea2-D assumptionisnotapplicable( Dean 1978 ). Fluidowrestrictedtoanenclosedsectionsharessomecharacteristicswithexternal boundarylayersintermsofdevelopmentandstructure.Thepressurewithinthe developingregionisnonlinear,allowingthestreamwisevelocitytoonlybeafunction of x .However,unlikeboundarylayersofanexternalow,anenclosedchannelisstrongly inuencedbythenecessarydrivingpressuregradienttoovercomeviscouslosses.Oncethe owbecomesfullydeveloped,thestreamwisepressuregradientbecomesconstant,driving theow,andthecenterlinevelocityisnolongerafunctionofdownstreamdistance. Inordertodiscussinternalows,newscalingargumentsneedtobeestablished. Givenenoughstreamwisedistance,externalboundarylayerseventuallytransitiontoa turbulentregime( Young 1989 ).However,forinternalows,theboundarylayersfrom multiplewallsultimatelymerge,restrictingadditionalboundarylayergrowth.The inuenceofviscositypropagatesdownstreamandisdistributedtowardtheductcenterline. 44

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Thusductwidth(for2-Dows)isamoreappropriatelengthscaleforinternalows ( Gessner 1973 ; Hoagland 1960 ).Commonpracticeforturbulentchannelowscaling involvesusingacombinationofgeometricandviscousscales,generallyhydraulicdiameter andeitherthecenterlineorintegratedbulkvelocity( Anselmet etal. 2009 ).Thefollowing discussionisbasedontheGFIDsquareductgeometry. Channelowalsopresentsinterestingphysicsfromavorticityperspective.Inlaminar owsinvolvingincompressibleNewtonianuids,thevorticitytransportequationiswritten as D i Dt = j # u i # x j + # 2 i # x j # x j (227) wherethevorticityvector, i ,isthecurlofthevectorvelocityeld, "' !( V ( Panton 2006 ). Underfurtherassumptionsofsteady,fullydeveloped,three-dimensionalow,onlythe righthandsideofEquation 227 remains;representingvorticitystretchinganddi usionof vorticity,respectively( Panton 2006 ). HigherReynoldsnumbervaluesbasedonfrictionvelocity,( Re u > 180),areindicative offully-developed,three-dimensional,turbulentowinchannels.TheturbulentReynolds stressintroducesadditionalvorticityproductiontermsintoEquation 227 ( Brundrett& Baines 1964 ).Thetwoadditionaltermsaresimpliedforrectangulargeometryas, # 2 # x 2 # x 2 ( u 3 ) 2 ( u 2 ) 2 # & # 2 # x 2 2 # 2 # x 2 3 u 2 u 3 (228) Furthersimplicationscanbemadebylimitingthegeometrytoasquarecrosssection..In doingso,thersttermofEquation 228 dropsoutas u 2 and u 3 areequivalent( Brundrett &Baines 1964 ). Theremainingtermdescribesasourceofturbulentvorticityproductionstemming fromnonlinearReynoldsstress( Gessner&Jones 1965 ).Throughanalysisofthegeometry, theReynoldsstresstermcanbeshowntohavezeromagnitudealonganygeometriclines ofsymmetrywithintheduct,thusgeneratingeighttriangularregionsofnon-zerovorticity productionwithquadrantsymmetry,illustratedinFigure 2-4 ( Brundrett&Baines 1964 ). 45

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Theseadditionalproductiontermsgenerateaowwherethestreamwisevorticity, 1 ,isnon-zero.Restrictinganalysistothegeometrymentioned,thedenitionof 1 is expressedas 1 = # u 3 # x 2 # u 2 # x 3 (229) Thus,themeanstreamwisevorticity, 1 ,existsduetomeanlateralvelocitygradients ( Brundrett&Baines 1964 ).Similartotheturbulentlateralvelocities, u 2 and u 3 ,themean lateralvelocitiesarerestrictedtostaywithinthelinesofgeometricsymmetry( Brundrett &Baines 1964 ).Thisestablishessecondaryowpatternswithinthetriangularsymmetry regions.Aqualitativerepresentationofsecondaryvelocitystreamlines,orisovels,common tosymmetricturbulentductowareillustratedinFigure 2-5 ( Melling&Whitelaw 1976 ). Thesecondaryowpatternhasbeenexperimentallymeasuredandcanreacha maximumvalueof1 3%ofthecenterlinevelocity( Gessner etal. 1977 ; Melling& Whitelaw 1976 )butdemonstratesaglobalimpactontheowbyconvectingmomentum awayfromthewalls,ultimatelyimpactingthelocalboundarylayerstructure( Brundrett &Baines 1964 ).Alonglinesofsymmetry,therearenowallstoretardtheowandthus novorticityispresent( Melling&Whitelaw 1976 ).However,theconvectionofmomentum causeslargegradientsofcross-axisshearandvorticitytowardthecorners( Gessner 1973 ). Thesecondaryowactstomaintainstabilitybyconvectingmomentumfromregionsof vorticityproductiontowardregionsofvorticitydi usion,foundnearthewall( Brundrett& Baines 1964 ). Insummary,thischapterpresentedareviewoftheacousticpropagationandow patternsassociatedwithgeometrysimilartotheproposedfacility.Theanalysisofacoustic ductpropagationwithimpedanceboundaryconditionsdemonstratedtherelationshipof propagatingwavenumberandlinerimpedancevalues.Chapter 3 willdescribepublished methodsusedforlinerimpedanceeductiontesting.Chapter 3 willalsodiscusspast channelowexperimentstoestablishbaselinetestconditions.Suchexperimentswillbe outlinedinChapter 5 46

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Figure2-1.a)Two-dimensionalsoundhardboundarywaveguide,andb)Two-dimensional waveguidewithlocallyreactiveimpedanceboundaryconditions. Figure2-2.Laminarvs.turbulentboundarylayerproles. 47

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Figure2-3.Sublayerregionswithinturbulentboundarylayer. 48

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Figure2-4.Symmetrylines(dashes)separatingsecondaryvelocityestablishedby turbulentchannelow,adaptedfromGessner,F.B.1973.Theoriginof secondaryowinturbulentowalongacorner.JournalofFluidMechanics, Volume58.(Page8,Figure5b). 49

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Figure2-5.Isovelstreamlinesinducedbyturbulentchannelow,adaptedfrom Brundrett &Baines ( 1964 ). 50

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CHAPTER3 LITERATUREREVIEW Pastchannelandimpedanceeductionstudiesandalternativefacilitydetailsare reviewedwithanaimtodemonstratepriorachievementsandundertakingstoclearly establishthetandnecessityofthecurrentfacilitywithinthescienticcommunity.This reviewisdividedintothreesections:channelowstudies,acousticlinerimpedance eductiontechniques,andnallyareviewofknownfacilities.Section 3.1 outlines channelowstudiesandcomparesthemwithregardstoowphysicsandtestconditions. ImpedanceeductiontechniquesarereviewedinSection 3.2 comparingaccuracy,inherent assumptions,andthephysicalsetupofeachmethod.Section 3.3 concludesthechapter withasurveyofbothpastandcontemporaryfacilitiesusedforacousticlinerimpedance testing,includingacomparisonofsizes,achievablevelocityrange,andsoundexcitation pressurelevels. 3.1ChannelFlowStudies Duetotheinherentrectangularcrosssectiongeometryandthespeedrangeofthe GFID,athoroughinvestigationofpastturbulentchannelowstudiesispresented.The signicanceofturbulentchannelowstemsfromthedi erencesandpossiblechallenges forwhichowthroughanenclosedductmanifestsincontrasttotheowinafull-scale engineforwhichthefacilityaimstoreplicate.Thefacilitiesreviewedhereinarelimitedto tothosecapableofapplicableReynoldsandMachnumberswithrectangulargeometries similartotheproposedfacility. Considerableknowledgeofchannelowphysicshasbeenobtainedsincetheinception ofthedisciplineinthelate1920's.Channelowstudiescanbebroadlycategorizedby theindividualstudy'sendgoal.Emergingpatternsofthreechronologicalthemesappear inregardstoexperimentalchannelow:theidenticationandmeasurementofsecondary owpatterns,theinvestigationoftheoriginofthesecondaryowandashifttohigh 51

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Reynoldsnumberows,andnallyscalingargumentsapplicabletoturbulentchannelow. Acomparisonandreviewofeachstudyispresentedwithasummarizingtable. 3.1.1IdenticationandMeasurementofSecondaryFlowinChannels Initialexperimentsonchannelowbeganunknowinglyin1926byJ.Nikuradsewho observedthroughowvisualizationa"waviness"ofthelateralvelocityina(3 5:1)aspect ratiorectangularduct.Prandtl,Nikuradse'sadvisor,postulatedthewavinesswasdueto animbalanceofpressurestemmingfromthepresenceofthecornerswhichgenerateda cross-axissecondaryvelocitycomponent( Hoagland 1960 ). Fage ( 1936 )examinedthedi erenceinpressuredropbetweenrectangularandcircular ductsofequalhydraulicdiameter.Throughhisworkmeasuringstreamwisepressure gradients,Fageobservedthenon-isotropicnatureoftheturbulentelduniquetoowin rectangularducts( Howarth 1938 ). Laufer ( 1948 )performedfurtherchannelowinvestigationsthroughdetailedhot-wire experimentsatReynoldsnumbersofhydraulic O (10 4 ).Laufer'stestswerecarriedoutin (12:1)aspectratiochannel.Fluctuatingvelocitiesweremeasuredtoallowforcomparison ofturbulentenergyandlengthscalesacrossthechannel.Ashot-wireanemometrywas stillinitsinfancyatthistime,muchoftheauthor'sexperimentsweresimplytoprovethe e cacyofhot-wireasameasurementtool. Fromdiscoverytotheinitialmeasurementsofthesecondaryvelocityeld,Nikuradse, Fage,andLauferlaidtheinitialgroundworkforfutureuiddynamicexperimentsof channelow.Table 3-1 describesthecontributionsandspecicationsofeachexperimental e ort.Inane orttodirectlycomparethestudies,thetestReynoldsnumbersand measurementtechniqueareincluded.BecauseReynoldsnumbercanbebasedonseveral lengthandvelocityscales,valueswererecastbasedontheaverage,orbulk,velocity, U b andthehydraulicdiameter, D h Re D h = U av D h (31) 52

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Thehydraulicdiameterisdenedasafunctionofthecross-sectionalareaofthechannel, A ,andthewettedperimeter, P D h = 4 A P (32) Instudieswherethecenterlinevelocity, U CL ,wasspeciedinlieuoftheaveragevelocity, theapproximation U av =0 79 U CL proposedby Hoagland ( 1960 )wasapplied. 3.1.2OriginsofSecondaryFlowandHighReynoldsNumberStudies AfterLaufer,therewasaparadigmshiftfromsimplybeingabletomeasure secondaryowstoattemptingtoexplaintheoriginoftheowpatternsthroughaccurate experiments. Hoagland ( 1960 )and Brundrett&Baines ( 1964 )performedthorough experimentalinvestigationsusingacombinationofhot-wireanemometryandpitot tubes.Hoagland'sresultsveriedPrandtl'stheoryoftheshapeofsecondaryow contours,orisovelsasanoctetsetwithowtowardthecenterlinealongthediagonal symmetryplanes.Heconcludedthatthesecondaryowwasnotcausedbyanimbalance ofpressureandshear,asPrandtlhadtheorized,butinsteadbysheargradientsatthe walls.BrundrettandBainesdisagreedwithHoaglandonthesourceofthesecondaryow. Theirinvestigationledthemtoconcludethesourceofthesecondaryowvelocitywasdue toturbulentReynoldsstressneartheboundaries.AsturbulentReynoldsstressisinherent onlytoturbulentowregimes,sotoarethesecondaryowpatternstheygenerate.They demonstratedviahot-wireanemometrythatvorticityproductioniszeroalonggeometric symmetrylinesinacross-ductplane. Gessner&Jones ( 1965 )performedhot-wireexperimentsupto Re D h =3 E 5,the highestofanypreviousstudy.TheirresultssupportedthehypothesisofBrundrettand BainesthattheimbalanceofturbulentReynoldsstressandlateralstaticpressurewithin theductultimatelyinducedsecondaryowinrectangularchannels.Theauthorsalso foundthatshearstresscanbeconsideredconstantacrosstheductwalls,exceptinthe immediatevicinityofthecornerwhereskewnessishighest. 53

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Melling&Whitelaw ( 1976 )subsequentlyexperimentallyinvestigatehighReynolds numberchannelowphysics.Theuseofanon-intrusive2-DlaserDopplervelocimetry (LDV)systemenableductuatingvelocitymeasurementstobemadewithoutthe alignmentandinterferenceissuesassociatedwithhot-wireandpitottubeprobes.Their resultsconrmedthepriorexperimentalndingsof Gessner&Jones ( 1965 ).Theuse ofLDVallowedforsimilarsampleratesandbetternearwallresolutionthanhot-wire withoutthealignmentissuescommontoothermethods. 3.1.3ChannelFlowScalingArguments Thethirdmajorchronologicalthemerevolvesaroundscalingargumentsforchannel ow.Scalingargumentsareoftenappliedinuidmechanicsapplicationstoestablish universalequationsormodelsforpredictionofengineeringquantitiessuchasshearstress andheattransfer.TheCFDcommunityusesscalinglawsforfasterandmorerobust modelsandnumericalvalidation. Leutheusser ( 1984 )performedscalinganalysisinturbulentchannelowsbyapplying publisheddatato"LawoftheWall"curvetsforparameterextractionofEquation 224 previouslydiscussedinChapter 2 .Theauthornotedthattherelationdoesnotmatch experimentaldataatdistancesasfarfromthewallasthatofowunderazeropressure gradient.Similarpowerlawtswerenotabletobeappliedsuccessfully. Wei&Willmarth ( 1989 )useda2-DLDVsystemtoestablishReynoldsnumber scalingofturbulentquantitieswithinchannelow.Notingthatmostpreviousstudies assumedthatwithinthe"inner"region,upto y + < 100,thereexistedaReynolds numberindependentscaling.Theauthorsdemonstratesthisassumptionisinaccurate,and showedthatthemaximumvalueofturbulentintensityproleswasfoundtoincreasewith Reynoldsnumber.Theauthorsclaimthatinnerlawscalingcanbedemonstratedwithin y + < 15forstreamwisevelocityuctuations,althoughwall-normaluctuationscannotbe scaledusinginnervariables,whichwereattributedtothepresenceoftheneighboringwalls andvorticitystretching. 54

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BecausemanyofthenumericalchannelowstudiescenteronlowReynolds numberowsorinvestigatetransitionalowwithsecondaryowdevelopment,these arebeyondthescopeofthecurrentresearch.However, Anselmet etal. ( 2009 )numerically investigatedthedevelopmentoftheratioofcenterlinetobulkvelocity, U c /U b forturbulent channelowfrom Re Dh =5 E 3 3 E 4forrectangularductowofthreeaspectratios: (1 875:1),(1 43:1)and(1:1).Notingforthemajorityofinternalowresearchthat throughnon-dimensionalizationof U c /U b ,laminarowsthroughcircularpipesand high-aspectratio2-Dchannelows,thedatacouldcollapseviaasinglefunction;however asimilarcollapsingfunctionfornoncircularturbulentductowshadyettobedevised. Theauthorscomparedtheirnumericalresultswithexperimentaldataextractedfromthe literature,includingpreviouslydiscussed( Melling&Whitelaw 1976 ).Theywereable tocollapsealloftheavailabledatabyplotting U c /U b ,vs( x/D h ) / ( U b x/ ) 1 / 5 resulting inaslopeof0 185uptothepointofmaximum U c /U b .Whilenotonlydeningauseful comparisonfornewfacilities,theywerealsoabletobetterestablishedadenitionfor entrancelengthforaspectratioslessthan(13:1)basedonmeasurablequantitiesfor internalturbulentows.Additionally,theseresultswereestablishedintheabsenceof includingsecondaryowe ectsintheirnumericalsimulations,notingtheweakinuence ofsecondarymotiononthecenterlinevelocity. Table 3-1 summarizesturbulentchannelowstudies.Viatheevolutionofturbulent channelowinvestigations,anunderstandingoftheunderlyingassumptionsprovide checksandaidedinthetestinganddesignoftheGFIDinChapter 5 .Scalingarguments canbeusedfornon-dimensionalizingthechannel'sdevelopingboundarylayers,and streamwisepressuregradientsaremeasuredtoensurefullydevelopedow.Witha characterizedfacilityinplace,theimpedanceofanacousticlinerundergrazingowis measured.Areviewofthecurrenteductionmethodsaresummarizedbelow. 55

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3.2ImpedanceEductionTechniques Accurateimpedancemeasurementsofacousticlinersundergrazingowconditions arevitaltoe ectivelyreduceaircraftenginenoise.Severalmethodshavebeendeveloped todeterminelinerperformancecharacteristics.Thissectionwillinvestigatethetechniques usedforimpedanceeductionoflocallyreactiveliners.Manyofthetechniquesaretied closelytothefacilityinwhichtheyareused,asdetailedinSection 3.3 .Thetechniquesare presentedwithdetailsconcerningthespecicmethodforimpedanceeductionaswellas theunderlyingassumptionsassociatedwiththemethod. 3.2.1The In-situ Method Dean ( 1974 )presentedadirecttechniqueformeasuringtheimpedanceofalinerthat hasbecomewidelyusedduetotherelativeeaseofthemeasurement.Anillustrationof thismethod,designatedthe in-situ methodduetotheintrusivemannerofwhichthe microphonesareinstalled,isfoundinFigure 3-1 .Thistechniqueispopularduetothe relativeeaseoftheexperimentalsetuprequiringonlytwomicrophonestoaccuratelyeduce impedanceofalocallyreactiveacousticliner.Therstmicrophoneisush-mountedwith thesurfaceofthelinerwithinthechannelsubjecttograzingowconditions.Thesecond microphoneismountedwithinareactivecavitymeasuringthepressureofthespeciccell underanalysis. Themathematicalbackgroundofthemethodwillbeoutlinedandreliesonthebasics oflinearlyreactiveacousticssharedamongstmanyoftheimpedanceeductionmethods. Themethodisformulatedbyapplyingthedenitionofspecicacousticimpedanceasthe ratiooftheacousticpressure, P ,totheacousticparticlevelocity, u ,atapoint. Z = P A u A (33) P A denotesthemeasuredpressureoutsideofthecavityalongtheductwall,asillustrated inFigure 3-2 .Theparticlevelocity, u A ,isassumedtobeafunctionofthepressure measuredwithinthecavity, P B ,angularfrequency, ,andthecavitydepth, ) ,oftheform 56

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u A = P B & c ie i t sin ( $) ) (34) SubstitutingEquation 34 intoEquation 33 ,theimpedancecanbewrittenintermsof themeasuredSPLandphaseanglebetween P A and P B Z =10 SPL A SPL B 20 sin j cos sin ( $) ) (35) Theimpedancecanbedecomposedintorealandimaginarycomponents, Z = R + iX R =10 SPL A SPL B 20 sin sin ( $) ) (36) and X =10 SPL A SPL B 20 cos sin ( $) ) (37) Theimpedanceatapointonthelineristhecombinationofcavityreactance, Z c ,andthe surfaceimpedance, Z s .Asinglecavityisaclosedendtubeandthustheimpedance,sans resistivelosses,isexpressedas Z c = i cot( $) ) (38) Thesurfaceimpedancecannowbeexpressedasafunctionofthefacesheetresistance, R fs andfacesheetreactance(oftencalledmassreactance), X fs ,as Z s = Z fs + Z c = R fs + iX fs Z c (39) Thusthesurfaceimpedanceis Z s = R fs + i ( X fs +cot( $) )) (310) Hydrodynamicpressureuctuationscanbemuchlargerthantheacousticpressures andasaresultthe in-situ methodislimitedtograzingowspeedslessthan100 ft / s (30 m / s ).Anobviousdownsideofusingthismethodistheinherentdestructionofthe 57

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sampleundertestduetomicrophoneinstallation.Asdescribed,themethodisonly applicabletosingledegreeoffreedom(SDOF)liner. 3.2.2InniteWaveguideMethodandSingleModeMethod Armstrong ( 1974 )introducedthe"innitewaveguide"method,avoidinganydamage tothesamplebyush-mountingamicrophoneinatraversablesectionontheductwall oppositethesample.Theinnitewaveguidemethodassumesasingledominantmode planeprogressivewavewithintheductandthuslargeerrorsoccurifmultiplemodesare areofnear-equivalentmagnitude,includingreectionsfromanon-idealexittermination orevanescentmodesgeneratedattheleadingandtrailingedgesoftheinstalledliner. Theowisalsoassumedtobenon-turbulentanduniformacrosstheductandtheliner ofunknownuniformimpedance.Ifasingleacousticmodeispresentovertheliner,both themeasuredSPLandphaseatthecenterofthelinerwillbelinear,indicatingaconstant impedancevalue,asillustratedinFigure 3-3 Theinnitewaveguidemethodextractstheimpedanceofalinerbycomparingtwo microphones.Therstisastationarymicrophonemountedattheentranceplaneofthe linersleadingedge.Thesecondmicrophoneistraversedalongtheopposingwallfrom thereferencemicrophoneovertheliner.Theattenuationbetweenthetwomicrophones ismeasuredandthewavelengthisinferredfromthedataduringpost-processingasa functionofdownstreamdistance. Jones etal. ( 2001 )appliedthe"innitewaveguide"methodunderthename"Single ModeMethod"(SMM)todistinguishbetweenacomparisonmethodwithinthesame papercapableofhandlingmultiplemodescalledthetheFiniteElementMethod,discussed belowinSection 3.2.3 .TheyalsooutlineamethodinasimplerformthanArmstrong's thatismoreapplicabletoexperiments.Thismethodisoutlinedhere. Theaxialwavenumber, $ x ,canbedecomposedintoreal, $ xr ,andimaginaryparts, $ xi ,describedbyArmstrongasthephasevelocityparameterandattenuationparameter, 58

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respectively.Thedissipationofacousticwithinaductisdescribedby * P (0) P ( x ) * = e # x i x (311) andfurthercastasacousticpower, 20log & * P (0) P ( x ) * =20log( e # x i x ) (312) NotethattheleftsideofEquation 312 isalreadydenedinunitsofdBandthereforecan besimpliedandwrittenas dB = $ xi x 20log( e ) (313) Equation 313 issolvedfortheaxialwavenumberasafunctionofthedropinacoustic powerperunitdistance, $ xi = 1 8 68 dB x .. (314) Theanalysisoftheattenuationparameteriscastinmoregeneraltermsincombination withthephasevelocity $ x = d ( x ) dx + i 20log 10 ( e ) d SPL( x ) dx (315) Theaxialwavenumbercanbeassumedconstantoverthecenterofthelinerandbe extractedfromthemeasuredSPLandphasedecayasmeasuredatdiscretemicrophone locations.Themodelisonlyvalidforfrequenciesuptothecut-onfrequency,therefore fromEquation 25 both n and $ z =0.Theratiooftransversewavenumbertothedrive wavenumber, # y / # ,isafunctionofaxialwavenumber, $ x ,andthemeanMachnumber, M $ y $ = 3 1 4 (1 M ) 2 ( # x # ) + M 5 2 (1 M ) 2 6 1 / 2 (316) Equationeq:Ch 3 S MM k yisderivedinAppendix C .Notethatthe 1 / 2 powerwasabsentfrom Jonesetal. ( 2001 ) ,butisnecessaryinordertoreproduceacorrectdispersionrelationintheabsenceofflow.Theaveragenormalizedacousticimpedance, = Z / $ 0 c 0 measuredoverthecentralregionofalinerunderis = i & $ $ y 7 1 M $ x $ #8 2 cot 7 2 $ h $ y $ #8 (317) 59

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where h ,istheducthalf-width. Armstrong ( 1974 )appliedhisversionofthemethodsuccessfullyoverafrequency rangeof1000 2500 Hz andspeedof M =0 5.Testsathigherspeedsproveddi cult toextracttheimpedanceastheuniformowassumptionwasinvalidatedbyhighshear gradients. 3.2.3FiniteElementMethod Inane orttodevelopatechniquethatislessrestrictivethantheinnitewaveguide methodandlessintrusivethanDean'smethod, Watson etal. ( 1995 )developedanite elementmodeling(FEM)method. Anassumedsolutiontotheconvectivewaveequation,Equation 213 ,isiteratively established.Thesolutionprocedurematchestheexperimentallyobtainedcomplexpressure amplitudeandphasedistributionalongtheductusingtheboundaryconditionsatfour ductplanes:thesourceplane,theexitplane,therigidwall,andtheacousticlinersurface. Thesourceplaneboundarycondition, p ( x =0 ,y )= p s ( y ) (318) isdenedattheleadingedgeplaneoftheacousticlinerundertestandismeasuredbya stationaryreferencemicrophone. Theexitplane,denedatthetrailingedgeplaneoftheacousticlinerundertest,isa functionofthetestMachnumber,wavenumber,andnormalizedexitimpedance, exit # p ( L,y ) # x = i $ p ( L,y ) M + exit (319) Thenormalizedexitimpedanceismeasuredbetweenthetestsectionandthenear-anechoic terminationduringtesting.Themethodwaslaterupdatedtorequireonlytheexit pressureinlieuoftheexitimpedance( Watson etal. 2008 ). 60

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Betweenthesourceandexitplanes,themethoditerativelysolvesfortheliner impedancebymatchingtheboundaryconditionsfortherigidwallofzeroparticlevelocity, # p # y =0 (320) andtheunknownacousticliner # p ( x, 0) # y = i $ p ( x, 0) +2 M # # x p ( x, 0) + M 2 i $ # 2 # x 2 p ( x, 0) (321) TheFEMcodeassumesauniformowprole(slugprole)andthuscanbelimited byhighshearregionsnearthewalls.Thismethodwasvalidatedagainstexperimental results( Watson etal. 1996 )andlateroptimized( Watson etal. 1998 ). Eversman& Gallman ( 2009 )usedasimilarFEMmodelbutextendthesearchparameterstoincludean e ectiveMachnumberandterminationimpedancetoaccountforshearingandreection e ects. Jones etal. ( 2005 )atNASALaRCreleasedbenchmarkdataforcomparisonof alternativeimpedanceeductionmethodologies. Jones etal. ( 2001 )foundthatunderthecorrectcircumstancesoflinearsound pressureandphasedecayratesacrossthelinerlength,theSMMmethodproduced impedancevaluesidenticaltotheFEMmodelandsuggestedwhenappropriatethatthe computationalcostbenetsoftheSMMmodelmakeitapreferablechoice. 3.2.4FiniteElementMethodwithShear Manyofthemodelspresentedinthisreviewassumeauniformow. Pridmore-Brown ( 2006 )notedthatforaccurateimpedanceeduction,thee ectofmeanshearshouldbe accountedforandneglectingthise ectcouldresultinimpedanceerrorsofupto10%.To suchanend,anewniteelementmethodwithshear(FEMS)codewasdevisedby Watson etal. ( 2001 )whichaccountedforsheare ectsbymeansofacrossductvelocityprole, dM / dy ,andsolvingthelinearizedconservationofenergy, i $ P = M # P # x + & 0 c 0 # U # x + # V # y =0 (322) 61

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thestreamwisemomentum, i $ U = M # U # x + 1 & 0 c 0 # P # x + dM dy V =0 (323) andtransversemomentumequations, i $ VM # V # x + 1 & 0 c 0 # P # y =0 (324) Intheaboveequations, U and V representthetime-averagedstreamwiseandtransverse velocities,respectively.Theseequationsaresolvedundersimilarboundaryconditionsto theFEMmodelwithanadditionalconstraintfordeningthevelocityproleatthesource plane.Theimpedanceofthelinerisattainedthroughiterativelymatchingthecalculated rigidwallpressuretothemeasuredpressureontherigidwallwhilematchingtheliner boundarycondition, & 0 c 0 V = & 1+ M ik # # x 'P (325) IntheFEMSmethod,itisassumedthatatransversevarianceinshearexistsduetothe noslipconditionandthuscrossductvelocitiesarerequiredasaninput( Jones etal. 2003 ). TheFEMSmodelwasdemonstratedtoworkespeciallywellforsinglemodetests.It wasshownthatforasinglefrequencyplaneprogressivewave,thesheare ectusedinthe FEMSmodelproducedhigherresistancevaluesthantheuniformassumptionoftheFEM model,thoughthereactancewasfoundtobevirtuallyidentical. 3.2.5InverseSemi-Analytical Elnady etal. ( 2009 )presentedasimplemodematchingschemereferredtoasthe "inversesemi-analyticaltechnique"(ISA).Themethodreliesonthemeasurementsoffour microphones,twoupstream( A and B )andtwodownstream( C and D )oftheacoustic linersection.Usingamultimodalapproach,thetestsectionisdividedintothreeregions: upstreamoftheliner,overtheliner,anddownstreamoftheliner. 62

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Anupstreamreectioncoe cientdenedasafunctionoftheupstreamtransfer function, H AB ,themicrophoneseparationdistance, s ,andtheaxialwavenumber, $ R B = & 1 H AB e j # (+) s H AB e $ j # ( ) s 1 (326) isusedtocalculatetheamplitudeofthedominantright-runningmode, a (1) + = & p B 1+ R B e $ j # (+) z B (327) adistance Z B fromtheleadingedgeoftheliner. Similarly,adownstreamreectioncoe cientisdenedasafunctionofthedownstream transferfunctionandtheindependentlymeasuredexitimpedance, z D R (1) e = & 1 H CD e j # (+) s H CD e $ j # ( ) s 1 e $ j ( # (+) # ( ) ) z D (328) a (1) + and R (1) e aretheonlyinputstoamatrixofamplitudesandmodeshapeatthe leadingandtrailingedgeplanesoftheliners.Theimpedanceisextractedoncetheeduced pressureelditerativelyconvergestomatchthemeasuredmodalcontentunderthe prescribedboundaryconditions.Themethodalsoassumesauniformowproleand thusincreasederrorisfoundwithhighshearows.Themethodcomparedfavorablywith NASAbenchmarkdataresults( Elnady etal. 2009 ). 3.2.6GrazingFlowDataAnalysis SimilartotheoriginalNASAmodel,athreepartFEMmodelforlinerimpedance eductionwasformulatedcalledtheGrazingFlowDataAnalysis(GFAZ)program,foruse attheformerBoeingWichitafacility,nowSpiritAeroSystems.Themethodisbasedon amicrophonetraversingalongthecenterlineoftheupperwall,oppositethelinerunder test.Assuminganon-reectiveterminationconditionandauniformowassumption, theGFAZmodelclaimstobecapableofsolvingforuptoeightsimultaneouspropagating modes.Initially,afrequencyresponsefunction(FRF)basedonapressureeldcalculated fromanassumedimpedancevalueisgenerated.Theimpedancevalueisiteratedand 63

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anewpressureeldiscalculateduntiltheiteratedFRFmatchesthemeasuredFRF fromthetraversingmicrophonetowithinasettolerance( Gallman&Kunze 2002 ).The methodsolvesthethreeregions,upstream,downstream,andacrosstheliner,separately andthenmatchesconditionsatthesharedboundaries.Thisprocesscomesataninherent computationalexpense. 3.2.7TheStraightforwardMethod Manyoftheeductionmethodspresentedhere,suchastheFEM,FEMS,GFAZ, andsimilarnumericalschemesareclassiedas"inversemethods",whichusemeasured pressureatknownlocationsandanassumedpressureeldtoconvergeonasolutionin ordertoextractcharacteristicsoftheboundaryconditions,suchasimpedance.These methodsarecomputationallyexpensivebutaregenerallymorerobustandlessrestrictive thanthealternatives,suchasthe in-situ orinnitewaveguidemethods( Jing etal. 2008 ). Incontrast,the"straightforward"method,presentedby Jing etal. ( 2008 ),extends the"innitewaveguide"byttingthemeasuredpressureeldoveranacousticlinerto aseriesofequations.Asanalternativetotherestrictiveassumptionoflinearphaseand SPLdecayofEquation 315 ,themeasuredpressureeld, p u ( x,y ),isassumedtoasum ofcomplexexponentials.Representingleftandrightrunningwavesasafunctionofthe axial, n ,andtransversewavenumbers, / n ,aswellascomplexmodelamplitudes, A n ,the pressureeldisdenedas p u ( x,y )= N i =1 A + n cos ( / + n y ) e $ i + n x + A $ n cos ( / $ n y ) e $ i n x (329) TheaxialwavenumberisextractedfromEquation 329 andthenEquations 316 and 317 areusedobtainthetotransversewavenumberandimpedance,respectively. Ideally,anyaxialwavenumberwillallowforimpedanceextraction,howeverin practice,asingledominantforwardtravelingmodeprovidedthehigheraccuracy.The authorsnotethatunlikeothermethodswhichmaybesensitiveto,orevenfailinthe presenceofupstreamreections,thestraightforwardmethodonlyreliesonthedominant 64

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modewavenumbers.Asaresult,themethodisindependentofreectedupstream propagatingwaves,relaxingtherequirementforcostlyanechoicterminations.This techniqueperformedwellcomparedtotheNASAbenchmarkdata( Jing etal. 2008 ). 3.2.8LaserDopplerVelocimetryImpedanceEduction Insteadofmeasuringtheacousticpressurewithinaductoratthesurfaceofalinerto inferthelinerimpedance, Minotti etal. ( 2008 )demonstratedalaserDopplervelocimetry (LDV)techniquetomeasureparticledisplacement. Theauthorsstatethatparticledisplacement,derivedfrominstantaneousvelocity measurements,reduceserrorwhenahighlyviscousowispresent.Measurementsof particlevelocityareusedtoextracttheparticledisplacementbysolvingasystemof equationsrelatingtheacousticvelocitytotheacousticdisplacementforeachcoordinate direction. V refx #0 x # x + i "0 z = V x + # V refx # y 0 y + # V refx # z 0 z (330) V refx #0 y # x + i "0 y = V y (331) V refx #0 z # x + i "0 z = V z (332) Theacousticimpedanceisthendescribedas Z n = p i "0 n (333) asafunctionofthetime-harmonicpressure, p ,andtheacousticdisplacementofa particle, 0 n ,where n =1:3representingthethreecartesiandirections. TheLDVsignalisreferencedtoanupstreamcone-mountedmicrophoneintheowto interpretphaseinformationduringpost-processing,discerningacousticuctuationsfrom similarrandomuctuationsoftheturbulentow.Theexperimentwaslimitedto25 m / s ImpedancevalueswerecomparedtomeasurementsmadeusingDean's in-situ method atthreestreamwiselocations.Similarly,powerspectrawascomparedbetweentheLDV 65

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methodandthoseofanembeddedmicrophone.Boththeimpedanceandspectraresults wereingoodagreement. Allofthepreviouslydescribedmethodshavefocusedonimpedanceeduction techniquesbymeasuringtheacousticpressureorparticledisplacementnearorwithin thelinersection.However,therearetwotechniquesthatusedi erentmethodologiesfor linerimpedance,usinginsertionlossandbiasow.Whileotherstudiesnotdescribedhere mayalsodemonstratesimilarstrategies,thetwopresented,utilizedbyB.F.Goodrichand GeneralElectricAircraftEngines,arespecicallygearedtowarddesignandtestingliners forenginenacelles. 3.2.9InsertionLossMethod TheInsertionlossmethod(ILM)usedbyB.F.Goodrichforlinerimpedanceeduction isinherentlytiedtothefacilityforwhichitisemployed( Syed etal. 2002 ).Thefacility, illustratedinFigure 3-4 ,isfurtherdescribedinSection 3.3 .Testingisaccomplishedby monitoringtheratioofsoundpressurelevelsinupstreamanddownstreamreverberation chambers.Loudspeakeracousticsourcesareplacedwithintheupstreamchamber.The assumeddi usedacousticeldsineachchamberallowforasinglemeasurementofthe frequencydependentsoundpressurelevel, SPL U ( f )and SPL D ( f )forupstreamand downstream,respectively.Thereductionofacousticpowerduetotheliner,,isdenedby thedi erenceinthehardwalled"calibration"caseandalinerofunknownimpedance. ILdB ( f )= SPL U ( f ) SPL D ( f )(334) $ PWLdB ( f )=[ ILdB ( f )] liner [ ILdB ( f )] hardwall (335) Thecalibrationcasedenesthecoe cientsofa2-Dmultimodalpropagationtechnique anditerativelysolvesforinsertionlossbasedonanassumedimpedance.Theliner impedanceiscorrectwhenthecalculatedILmatchesthemeasuredILtowithinaspecied tolerance. 66

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3.2.10FlowResistanceMethod Thedcowresistancemethod(FRM)utilizedatGeneralElectriciscapableof ndingtheresistanceofaperforateorwire-meshsheetwhichwouldnormallycovera locallyreactiveliner( Syed etal. 2002 ).Apositiveornegativepressuredi erentialis appliedacrossthematerialsectionwithasuperimposedgrazingowalongthesurface. Throughthismethodtheowresistanceiscalculatedastheratioofthepressuredrop acrossthesampletothebiasowvelocitythroughthesample Jones etal. ( 2003 ). Assumingthetestsheetisthin,theowresistanceofthelinercanbeassumedtobe equivalenttoacousticresistance.Whilethismethodprovidesfastresistancevalues,its doesnotprovideinsighttothereactancenoranyfrequencydependence,asnoacoustic sourceispresent.Thismethoddoeshoweverimplicitlyaccountforaboundarylayer inducedbythegrazingowovertheliner. 3.2.11ImpedanceEductionMethodSummary Theavailableimpedanceeductionmethodsdescribedabovecanbesortedintothree categories:waveguidemethods,inversetechniques,andnon-traditionalmethods.The waveguidemethodsincludetheinnitewaveguide,alsoknownastheSMM,andthe moreadvancedstraightforwardmethod.Bothassumeattingfunctionappliedtothe attenuatedcomplexpressurefromwhichimpedanceisextracted.Inversemethods,such astheFEM,FEMS,GFAZandinversesemi-analyticalarebecomingmorepopularduein parttoincreasedcomputationsspeeds.Theremainingnon-traditionaltechniquesexplore anddemonstratealternativemethodsforwhichimpedancecanbeeduced,butrestrictrun conditions.Basedontheprecedingreview,theSMMwaschosenforinitialapplication intheGFIDduetothebalanceofsimplicityinsetupandquicknessineducedsolution andrelativeaccuracy.Therestrictionsofthemethodareaccountedforthroughtheuse anear-anechoicterminationtominimizeupstreampropagatingacousticsandinitiallow runspeedstobetterapproximateauniformowassumption.Themodularnatureofthe facilityandtheactiveresearchinauniversitysettingallowforalternativemethodsto 67

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easilybeappliedforfutureresearch.Experimentalimpedanceeductionofanacousticliner underowisdemonstratedinSection 5.4.4 3.3ExperimentalAcousticLinerImpedanceTestFacilities Towardtheprojectgoalofdesigninganacousticlinergrazingowtestfacilityfor impedanceeductionmeasurements,alookattheunderlyingcomponentsthatmakeup thatfacilityhavebeeninvestigated.Section 3.1 outlinedexperimentalstudiesspecically relatingtothenatureoftheowinsideofrectangularchannels.Section 3.2 presentedthe availabletechniquesusedtodirectlyorindirectlyeducetheimpedanceofanacousticliner. Thesectionwillinvestigateallpastandpresentexperimentalowfacilitieswhichwere usedforlinerimpedancemeasurements. TheGFIDispartofauniversityenvironment,andthusthefundingsources, knowledgegained,andpublicationexpectationsaredi erentthanforaprivatecompany. Similarly,internationalfacilitiesareseparatedtohighlightwhatiscurrentlyavailable intheUS,whichisgenerallyeasierfromacollaborationstandpoint.Tosuche ect,the followingreviewedfacilities,categorizedbya liation,fallintooneoffourpossiblegroups: international,privateindustry,educationalinstitutions,andgovernmentresearchfacilities. Atotalof19facilitieswerefoundthroughathoroughliteraturesearch.However someareassumedtonolongerbeinworkingorderornolongerusedforimpedance measurements.Manyfacilitiessharecommonfeatures,sizes,andrunconditions.Some ofthefacilitieshavebeenillustratedattheendofthechapterforvisualizationpurposes todemonstratethewiderangeofpossibledesignimplementations.Table 3-3 listsallthe tunnels,organizedbya liation,listingcross-sectionsizesfordirectcomparison. 3.3.1InternationalFacilities TherstsetoffacilitiesinvestigatedarethosefoundoutsidetheUnitedStates. Atotalofveinternationalfacilitieswerefoundatboththeeducational(two)and governmentinstitutions(three). 68

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UniversityofMaine,France TheUniversityofMaineinLaMans,Franceoperatesaowduct,illustratedin Figure 3-5 .The15 100 mm (0 59 3 94 in. )cross-sectionductisfedbyanupstream compressorgeneratingowspeedsupto M =0 3andcontrolledviafeedbackfroman inlineowratemeter.Thetunnelhasananechoicterminationateachendoftheduct ( Auregan&Leroux 2008 ).Acousticexcitationupto140 dB between70 3000 Hz is generatedbytwoloudspeakers.Leadingedgemicrophonesarepositioned2 m downstream fromthecompressortoallowforowdevelopmentpriortotesting( Auregan etal. 2004 ). NationalAerospaceLaboratory,TheNetherlands TheNationalAerospaceLaboratory(NLR),anindependently-fundedtechnological instituteintheNetherlands,maintainstheAcousticFlowDuctfacilityforacousticliner impedancestudies.Thetunnelisareverberationstylefacility,similartothetunnelat Goodrich,bothusingtheinsertionlossmethodforglobalimpedanceeduction( Murray etal. 2005 ).LocalimpedancevaluesaremeasuredviaDean'smethod.Acousticexcitation viafourelectrodynamicspeakersgeneratesoundpressuresof150 dB upto6 kHz andtest speedsupto M =0 8areachievableoverthe1 05 m longductwitha150 mm 300 mm (5 9 in. 11 8 in )cross-section.Theowisdrivenbyadownstreamvacuumlinecapable ofdisplacing14 7 kg / s ofair( Murray etal. 2005 ). Frenchnationalaerospacecenter,ONERA,France TheFrenchnationalaerospacecenter,ONERA,operatestheAero-Thermo-Acoustic Bench(B2A)foracousticlinermeasurements,illustratedinFigure 3-6 .Theblowdown tunneliscapableof M =0 5owattemperaturesupto570 K withinthe4 m longtest sectionwitha50 mm 50 mm (1 97 in. 1 97 in. )cross-section.Thehightemperaturesare managedbyusingstainlesssteelwallsandsilicaopticalwindowsthroughoutthefacility. TheopticalaccessallowsforimpedancemeasurementsviaLDVthroughthedual-window setup.Apairofupstreamloudspeakersenclosedinpressuredchambersprovideshigh soundpressuresof140 dB inthefrequencyrangeof300 3000 Hz .Thetunnelterminates 69

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intoasoundproofroomviaanexponentialhornprovidingaquasi-anechoictermination withreectioncoe cientslessthan0 2upto M =0 3.Acousticlinerswithupto100 mm thickcanbetestedinthelowerwallwhile10staticpressureportsandtwothermocouples recordowconditions( Lavieille etal. 2006 ). GermanAerospaceCenter,DLR,Germany TheGermanAerospaceCenter(DLR)maintainstheColdAcousticTest-Rigforliner impedancetesting.Thetunnelcanrunineitheran80 mm (3 15 in. )squarecross-section ora140 mm (5 51 in. )diametercylinderconguration.Maximumspeedsof M =0 27 areobtainedonlyinthesquaresection.Twoloudspeakerspositionedonoppositeendsof thecentrallylocatedlinertestsectionprovideupto120 dB ofsoundpressureoverthe frequencyrangeof210 2110 Hz .Impedanceeductionisaccomplishedviatheinsertion lossmethod.Acrylicwindowsprovideopticallycleartestsectionaccessforopticalbased measurements.Bothendsofthetestrigareattachedtonear-anechoicterminations Richter etal. ( 2008 ). BeijingUniversityofAeronauticsandAstronautics,China BeijingUniversityofAerospaceandAeronautics(BUAA)maintainsa40 mm (1 57 in. )squareduct,2 1 m longandcapableofrelativelyslowrunatspeedsof30 m / s Twoupstreamloudspeakersprovideacousticexcitation.Uptotwo130 mm longlinerscan besimultaneouslytested Fung etal. ( 2009 ). 3.3.2DomesticCorporateTestFacilities TheremainingfacilitiesareallbasedintheUnitedStates.Facilitieswithinthe privatesectorarecapableoftestingin-houseorpatenteddesignsnotyetreleased,ornot intended,forthepublicdomain.Thepublicationshereinreferringtospecicationsof privatesectorfacilitiesaregenerallycomparisonstudiesofthethefacilityortheeduction techniquesperformedwithin. 70

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PrattandWhitney Marsh ( 1968 )performedseveraltestsonafullscaleJT3D-3turbofanengineto establishbaselinenumbers.Testsweremadeusingasingle 1 / 4 in. microphone3 in. downstreamoftheleadingedgealongwithfandischargeSPLlevelsof160 dB .SPLlevels werethenmatchedatthePratt&WhitneyAircraftFacilitywiththreecongurations: blow-downtypecompressedairdrivenwithupstreampulsedjetfornoiseexcitation, vacuumpull-downwithtwoelectrodynamicspeakers,andvacuumdrivenwithpulsed noise.Thefacilitycross-sectionalareawas80 in. 2 withmultipletestsectiongeometries includinga360 circularduct,180 semicircle,anda22 wedge.Velocitiesupto300 m/s weretestedbuttheprimaryfocuswasat91 m/s tomatchlandingconditionswherefan noisedominatesenginejetnoise. Boeing-Wichita/SpiritAerosystems SpiritAeroSystems,previouslyknownastheBoeingCommercialAirplaneGroup, Wichitadivision,operatestwoowducts.ThelargerofthetwoistheBoeingWichita 6 in. 6 in. FlowDuct,whichis23 5 ft. long.The48 in. longtestsectionislocated 9 ft. downstreamfromanycurves(18ductdiameters).Flowissuppliedbyeithera100 or300 psi sourcetoreachowspeedsupto M =0 5( Gallman&Kunze 2002 ).An exitnozzlewasdesignedtoreduceupstreamreections.Thefacilityisgenerallyusedfor testingacousticlinerboundarylayergrowth,includingapplyingapositionornegative pressuretothefacesheetcalledtranspiration( Drouin etal. 2006 ). TheSpiritAeroSystems2 in. 2 in. owductisanewertunneldesignedforacoustic linerimpedanceeduction.Broadbandtestingupto3000 Hz and150 dB isaccomplished viaelectropneumaticdrivers.Thetunneliscapableoftestingowspeedsupto M =0 5 ( Gallman etal. 2002 ).Linersuptoeightductdiameterslongcanbetestedwitha traversingmicrophonesushmountedinaTeonstriptoreduceleakageoppositetheliner at79evenlyspacedtraversepositions( Eversman&Gallman 2009 ). 71

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GeneralElectric TheAcousticLaboratoryatGeneralElectricAircraftEngines(GEAE)wasspecially designedtomeasuretheowresistanceofaperforateorlinearwiremeshacousticliner facesheet.Becauseonlythefacesheetofthelocallyreactivelineristested,noinformation regardingthelinerimpedancereactivecomponentcanbeassessed.IllustratedinFigure 3-7 ,theGEowductusedabiasowapproachwhereapositiveornegativepressure di erentialcanbeappliedtothelinerundertest,forcingtheairtobe"pushed"or "pulled"throughthefacesheet.Bycontrollingthevacuumpressurea2 5 m / s blowingor 1 5 m / s suctionvelocitycouldbeappliedtothesampleinthe5 5 5 5 in. testsection. Speedswerecontrolledviaanupstreamhighpressuresourceallowingforfreestreamrun conditionsof M =0 8tobeobtained.Thisfacilitycontainednoacousticsources,andthus onlymeasurestheDCowresistance( Syed etal. 2002 ).Thefacilityhassincebeenmoved totheUniversityofCincinnati. GoodrichCorporation Thepreviouslydescribedinsertionlossimpedanceeductiontechniqueintroducedthe owductapparatusatB.F.Goodrichasadouble-reverberatechamberdesign.Although notbuilt,thisdesignwasoriginallyconceptualizedby Melling&Doak ( 1971 ).Thedesign wastobeidealforacoustictestingbecausetheacousticeldinsidethechamberscanbe consider"di use"andthusonlyasinglemicrophoneisrequiredtomeasuretheacoustic power( Syed etal. 2002 ).IllustratedinFigure 3-4 thelinertestsectionhasa4 in. 5 5 in. cross-sectionallowingfortestingoflinerupto5 5 in. 24 in. .Theblowerdrivendesign allowsfortestingupto M =0 7. UnitedTechnologiesResearchCenter UnitedTechnologiesResearchCenter(UTRC)recentlybuiltandtestedtheirGrazing FlowFacility(GFF)( Simonich etal. 2006 ).TheGFFisa99 in. longductwitha 2 in. 5 in. cross-section.Speedsof M =0 65areachievedviatheUTRChighpressure system.Dualanechoicterminationsupstreamanddownstreammaintainlowreection 72

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coe cients.Acousticexcitationisaccomplishedviatwo150 W compressiondrivers capableofproducing140 dB ,andpositionedoneithersidesofthecentrallylocatedliner testsection.Acousticlinersupto12 in. inlengthweretestedviaDean'seductionmethod. Publishedbaselinenoisemeasurementsexhibitazerovelocitynoiseoorof45 dB and noiseoorsof105 dB and110 dB for M =0 36and0 64,respectively. 3.3.3DomesticUniversityTestFacilities AstheGFIDisinstalledusedinauniversityenvironment,specicbenetsassociated withsuchanenvironmentmakeitanattractivelocationforalinertestfacility.These benetsincludeaccesstojointresearchendeavorssuchascomputationalmodeling,ornew acousticlinertechnologiesaswellasadditionalfundingsourcesthatmaynotbeavailable totheprivatesectororgovernmentagencies.Atpresent,onlythreeuniversitieswere foundtopossesssimilarfacilities. UniversityofMinnesota TheUniversityofMinnesotabuiltagrazingowfacilitytotesttheattenuationof berglassoverarangeoffrequencies.Experimentswereperformeduptovelocitiesof 75 m/s andfrequencieswithin2060 Hz .Thefacilitywasbuiltwith1 5 in. thickPF615 berglassbondedtohardwoodpanelsonopposingwalls.Pressuremeasurementswere performedwithasmallcondensermicrophoneevery5 cm centeredoverthe1 m ofthetest section( Tack&Lambert 1965 ). UniversityofCincinnati TheUniversityofCincinnatimaintainstheAcousticLinerFlowDuct,butfewdetails areavailableintheliterature.Thetunnelhasa3 5 in. cross-sectionandiscapableto runupto M =0 7viaanupstreamhighpressuresource.Linersupto24 in. longwere testedononeorbothsidesofthe110 in. longowduct( Hillereau 2004 ). GeorgiaTechResearchInstitute TheGeorgiaTechResearchInstitute(GTRI)housesatestcenterdesignatedthe LinerFlowDuctFacility.Thefacility,showninFigure 3-8 ,iscapableofperforming 73

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impedanceeductionmeasurementsinits2 in. 4 7 in. cross-sectiontunnelwith temperaturesupto1200 F (922 K )andspeedsnear M =0 4( Ahuja etal. 2000 ).Four upstreamacousticdriverspositionednormaltotheowdirectionprovidesoundpressure levelsupto120 dB .Theowductiscapableofhousinglinersinanyofitsfourwallsfor maximumexibility.Combinationpitotprobeandthermocouplesmeasurevelocityand temperatureupstreamanddownstreamofthelinerinfourspeciedmeasurementplanes ( Ahuja etal. 2000 ). 3.3.4GovernmentFacilities TheFlowImpedanceTubeatNASALaRC Oneoftheoriginalfacilitiesdesignedspecicallyformeasurementsofacoustic linerimpedancewastheFlowImpedanceTube(FIT)atNASALaRC.Thetubewas constructedoffourmainstainlesssteelcomponentslistedindownstreamorder:the acousticsource,anairinletplenum,thetestductwithmicrophonetraversebar,and nallytheanechoictermination.Theacousticsourceusedfourtoveelectrodynamic speakerstogeneratesignalsupto140 dB ina2 in. diametercircularpipeatfrequencies upto3 4 kHz ( Parrott&Lester 1980 ).Thesoundwouldpropagatedownstreamthrough acirculartubewithhighlyresistiveperforatedwallsthatactedasawaveguide.The perforatepipewasencasedbyalargecylinderintowhichpressurizedairwasintroduced. Theairwouldthenbeforcedthroughthewallsoftheperforatepipeandowdownstream, superimposeduponthegeneratedacousticeld.Thetubegeometrywasconvertedto asquarecross-sectionfortheremainderoftheduct,2 in. 2 in. across.Theductwas constructedoffourductpiecesthatcouldbearrangedinanyorder,atotalof128 in. long, or64ductdiameters.Atraversebar,controlledbyasteppermotor,ranthelengthofthe fourpieceductsectionallowingamicrophonetotraverseoverthesampleliners.Theduct sectionterminatedintoananechoicterminationductofperforatedmetalwallsbacked bybulkabsorbingmaterialbehindperforatemetal.Theairlineemptiedtoavacuumfor maximumrunconditionsof M =0 5. 74

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TheGrazingIncidenceTubeatNASALaRC ThetraversebarintheFITwaspronetobothacousticandairleakage.Inane ort toupdatethefacility,newcomponentswereaddedincludinganewtestsection( Jones etal. 2004 a ).TheimprovementsledtothefacilitybeingrenamedtheGrazingIncidence Tube(GIT),illustratedinFigure 3-11 .Thenewtestsectionallowedforlinersamples tobeinstalledintheceilingoftheductforeasierinstallationandmicrophonecable strainrelief.Thetraversebarwasretainedbutpermanentlyattachedinplacetoreduce leakage.Thesingletraversingmicrophonewasreplaced,asthenewtestsectioncould holdupto95stationarymicrophoneswiththecapabilitytosimultaneoussample48 atatime.Theadditionalmicrophonesinstalledo -centerallowingfortestingpastthe rsthigher-ordermode(3 37 kHz ),upto10 kHz .Thecontinueduseofthetraverse barasastationarypiecehoweverrestrictedthetestsectioninstallationpositiontobe upstreamoftheducting,reducingcontroloverlinerplacementasafunctionofboundary layerdevelopment.Foradditionalcontrol,asuction/blowingdevicewasinstalledonall fourwallsupstreamofthetestsection.Thedevicewasattachedtoavacuumpumpthat wouldsiphonthenear-wallboundarylayeraway,establishingaknownstartingpointfor boundarylayerdevelopment( Jones etal. 2005 ). TheGrazingFlowImpedanceTubeatNASALaRC AnticipatingtheretirementoftheGIT,NASALaRCbuiltanewfacilitywithmany improvementsbasedonwhatwaslearnedthroughthreedecadesoftheFITandGIT. TheGFIT,illustratedinFigure 3-12 ,hasa50 8 63 5 mm crosssectionandcantest acousticlinersupto50 8 mm to609 6 mm long.Upto18side-mountedspeakerscan beusedtogethertogenerate150 dB singletone.Thesystemisrunbyanupstreamhigh pressuresourceincombinationwithadownstreamvacuumallowingfornearatmospheric conditionsatthetestsectionupto M =0 6.Adownstreamanechoicterminationwith locallyreactiveacousticlinerwallsminimizesupstreamreectionswhilesimultaneously slowingtheowbyincreasingthecrosssectionalareaoftheduct.Theductalsohas 75

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adual-axistraversepressureprobetomeasuretheinternalowproletofeedinto shear-basedeductionmodels( Jones 2011 ). TheCurvedDuctTestRigatNASALaRC NASALaRCalsoactivelymaintainstheCurvedDuctTestRig(CDTR),illustrated inFigure 3-13 ,demonstratingpotentialfutureaircraftenginedesignsbytestingliner impedancearoundabend.Inane orttoeliminatetheline-of-sightnoisesourcefrom theexternalenvironment,futureenginedesignsincorporateashortenedenginenacelle allowingforareductioninsizeandweight.TheCDTRhastwomainuniquecontributions tothelinertestingcommunity:thefacilityallowsformodalisolationandlinercurvature. Thefacilityiscapableofmeasuringupto3 kHz at140 dB viadualsourcelocationswithin a M =0 5ow( Jones etal. 2006 )withinatestcross-sectionof6 15 in. Thelevel ofcurvatureisadjustable,o settingtheincomingandoutgoingductbyuptooneduct diameter. 3.4Summary Thischapterhaspresentedareviewofthreeareasofresearchrelevanttothedesign andfuturetestingoftheproposedfacility.Section 3.1 presentedtheevolutionofturbulent channelowstudiespresentingnon-dimensionalscalinganalysis.Alookatacoustic linerimpedanceeductionmethodsandmathematicalmodelsinSection 3.2 presented severalavailablemethodsintheliteratureforexperimentallyeducingtheimpedanceofan acousticlinerunderow.Finally,Section 3.3 reviewedallknowngrazingowimpedance testfacilitiesforcomparison.Severalelementsofthefacilitiespresentedwereinstrumental inthedesignoftheGFIDpresentedinChapter 4 76

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Table3-1.Channelowstudies Author(s)Year Re D h Briefdescription Nikurdase1926Firsttonotesecondaryowe ects Fage 19366 9 E 4Founddi erenceinpressuredropbetween circularvs.non-circularducts Laufer 19483 1 E 4Directlymeasuredsecondaryowand turbulentenergy Hoagland 19606 3 E 4Experimentallyillustratedisovels Brundrett&Baines 19644 3 E 4Zerovorticityalongsymmetrylines Gessner&Jones 19653 0 E 5Secondaryowstemsfromrelationshipof Reynoldsandstaticpressure Melling&Whitelaw 19764 2 E 4UsedLDVtoverifypastresults Ahmed&Brundrett 19711 65 E 5Demonstratedthatwallshearstresswasbest indicatorforfullydevelopedchannelow Leutheusser 1984TurbulentFound"Lawofthewall"parametersfor channelow Wei&Willmarth 19894 E 4Innerlawscalingisvelocitycomponent specic Anselmet etal. 20093 E 4Collapseofentranceregionbasedoncenterline velocity 77

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Table3-2.Grazingowimpedanceeductiontechniques EductionmethodProsCons In-situ Simple,directIntrusive,damaging InniteWaveguide/SMMSimpleandfastAssumessingledominant progressivemode FEMAccurateuponconvergenceComputationallyexpensive FEMSAccountsforshearinge ectsComputationallyexpensive ISAFewinputsneededRelianceonconvergence decreasesspeed GFAZCansolveuptoeight propagatingmodes Maynotmatchsinglemode methodsfornonlinearliners StraightforwardIndependentofreectingwavesAssumesuniformow LDVNon-intrusivelymeasures acousticparticlevelocity Particlebasedowturbulence increasesuncertainly ILMSimpleandfastresultsafter propercalibration Broadbandonly,mustcalibrate sample FRMCanapplyasuctionorblowing toalterresistance Resistancevalueonly,must dismantlesample 78

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Table3-3.Acousticlinerimpedanceeductionfacilities LinertestfacilityCross-sectionMaxowspeedSPL ( in. in. )( M )(dB) U.ofMaine(France)0 59 3 940.3140 NLR(Netherlands)5 9 11 80.8150 ONERA(France)1 97 1 970.3140 DLR(Germany)3 15 3 150.27120 BUAA(China)1 57 1 570.09P&W80 in. 2 0.87160 BoeingWichita6x66 60.5160 SpiritAeroSystems2x22 20.5150 GEAircraftEngine5 5 5 50.8N/A B.F.Goodrich4 5 50.7UTRC2 50.64140 U.ofMinnesota2 2 2 20.22U.ofCincinnati3 50.7N/A GTRI(GeorgiaTech)2 4 70.4120 FIT@NASALaRC2 20.5140 GIT@NASALaRC2 20.5140 GFIT@NASALaRC2 2 50.6150 CDTR@NASALaRC6 150.5140 79

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Figure3-1.Illustrationofthegeneralsetupforthe in-situ method,adaptedfromDean, P.D.1974.AnInSituMethodOfWallAcousticImpedanceMeasurementIn FlowDucts.JournalofSoundandVibration.Volume34.(Page101,Figure 5). Figure3-2.Closeupviewillustratingtheassumedpressureeldinalocallyreactive acousticlinercell. 80

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Figure3-3.LinearSPLandphasedecayinthepresenceofanacousticlinerdemonstrated byexperimentaldatafrom Jones etal. ( 2004 b ). Figure3-4.TheBFGoodrichtestfacility,adaptedfromSyed,A.A.etal,2002.The SteadyFlowResistanceofPerforatedSheetMaterialsinHighSpeedGrazing Flows.NASATechnicalReportNASA/CR-2002-211749.(Page31,Figure3). 81

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Figure3-5.TheowductattheUniversityofMaine,France,adaptedfromAureganetal. 2004.MeasurementofLinerImpedancewithFlowbyanInverseMethod.10 th AIAA/CEASAeroacousticsConference.AIAA2004-2838.(Page4,Figure5). Figure3-6.TheONERAB2A,adaptedfromLavielleetal.2006.Measurementofliner acousticimpedanceinashearlayerofasubsonicowbyLaserDoppler Velocimetry.SAPEM2005.(Page234,Figure1). 82

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Figure3-7.TheGeneralElectricDCowduct,adaptedfromSyed,A.A.etal,2002.The SteadyFlowResistanceofPerforatedSheetMaterialsinHighSpeedGrazing Flows.NASATechnicalReportNASA/CR-2002-211749.(Page34,Figure4c). Figure3-8.TheGTRILinerFlowDuctFacility,adaptedfromAhujaet.al.1997.A UniqueTestFacilitytoMeasureLinerPerformanceWithaSummaryofInitial TestResults.NASACR201667.(Page38,Figure2-1). 83

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Figure3-9.TheUTRCGrazingFlowFacility,adaptedfromSimonichetal.2006.12 th AIAA/CEASAeroacousticsConference.DevelopmentandQualicationofan In-SituGrazingFlowImpedanceMeasurementFacility.AIAA2006-2640. (Page2,Figure1). Figure3-10.TheFITatNASALaRC. 84

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Figure3-11.TheGITatNASALaRC. Figure3-12.TheGFITatNASALaRC. Figure3-13.TheCDTRatNASALaRC. 85

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CHAPTER4 DESIGNANDIMPLEMENTATION Chapter 3 reviewedcurrentandpastfacilitiesandrelevantstudiestotheGFID facilitydesign,withtopicsfocusingonturbulentchannelowinvestigations,impedance eductionmethods,andidenticationofacousticowfacilities.InSection 3.3 acomparison ofknownacousticlinertestfacilitiesservedtodevelopdesignconceptsforthecurrent facility.Fiveofthe17acousticlinertestfacilitiespresentedareatuniversities,andno currentUSuniversityfacilitiesareactive. Modernaircraftenginesconvectairacrossacousticlinersurfaceswithinthenacelle atspeedsnear M =0 7andproduceacousticsoundpressurelevelsinexcessof160 dB ( Smith 2004 ).TheeventualgoaloftheGFIDistomatchorexceedtheseconditions; howevertheinitialobjectiveistoreach M =0 5,andattainSPLvaluesat130 dB Themeanstoaccomplishthistaskweremadepossiblebythegenerousdonationof severalcomponentsoftheformerGITlinerfacilitybyNASALaRC(Section 3.3.4 )tothe UniversityofFlorida(UF)inDecemberof2008. TheGFIDfacilityisacombinationofahigh-speedwindtunnelandanacoustic planewavetestfacility.Duetooftendivergentdesignpaths,certaincompromiseswere madeduringthedesignphaseoneachfronttowardthecommongoalwithoutsacricing vitalmeasurementcapabilitiesrelatedtoeachtypeoffacility.Thischapterstrategically analyzestheindividualcomponentsthatmakeuptheGFIDinorderofdownstreamow: airsourceandpiping,stagnationchamber,acousticsourcesection,testsection,ducting, anechoictermination,andexhaustducting.Designchoicesweremadetoaccommodate existinggeometryandworkwithintheconstraintsofbudget. 4.1AirHandling 4.1.1AirSupply,FlowValveandFlowSilencer TheGFIDisablow-downfacilityforinitialtestingupto M =0 5.Thesystemis fedbya210 psig sourcecomposedoftwopressuretanksratedfor225 psig withatotal 86

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volumeof1016 ft 3 (28 77 m 3 ).ThetanksarelledbyaSullairLS-20Taircompressor outputting1760 ACFM (1 005 kg / s )at210 psig .Aschematicoftheairandelectrical connectionsisillustratedinFigure 4-1 AFisher667diaphragmactuatorregulatesthepressuretofunctionallevelsforthe facility.Thevalveitselfissettoallowamaximumof20 psig whenfullyopenandne adjustmentsaremadeviaaFisher3582stempositioner.Theregulatorvalvehadto behand-calibratedforthespecicapplication,loading,andpressuredropoftheentire system.Thevalvewascalibratedsuchthatthemaximumoutputwouldallowowupto M =0 7toaccommodatefuturetesting,bypassingfuturerecalibration.Allpipingfrom thecompressortothestagnationchamberis2 in. unlessstatedotherwise. Downstreamofthevalve,aUniversalSilencerU5C-4inlineowsilencer,illustrated inFigure 4-2 wasinstalledtoreduceinternalbroadbandnoiselevelsfromupstream contaminationincludingownoisefrompipebends,theowvalve,aswellasstructural noisefromthecompressororotherairhandingunits.The57 in. longsteel-casedunithas a4 in. internaldiameterlinedwithperforatedmetalcovering3 in. ofbroadbandacoustic insulation.Thepipingsetupwasdesignedtominimizeheadlossbyreducingtheuseof bendsandshortradiuscurves. 4.1.2StagnationChamberandNozzle Theinlinesilencerisconnecteddownstreamtoa12 in. steelschedule40T-junction viaa3 in. pipe.ThelargeinternalvolumeoftheT-junctionallowsforstagnation conditionstobemet.Across-sectionalviewofthestagnationchamberisillustratedin Figure 4-3 .Theinletpipeisorientedtoexpeltheowtowardtheaftwallwitha6 in. separationdistance.Thesensorsusedforstagnationpressure,OmegaPX303-100A5V pressuretransducer,andstagnationtemperature,OmegaRTD-8063-wireRTD,were screw-mountedintotherearwallformeasurementofstagnationproperties.Additionally, atomizedseedforopticalowmeasurementscanbeintroducedviaaportinthebackwall ofthestagnationchamberwhereitismixedwithintheincomingow. 87

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Atthefrontofthestagnationchamber,theowpassesthroughhoneycombow straightenersinstalled21 in. fromtherearwalland16 in. upstreamofthenozzleexit. Thestainlesssteelhoneycombstraightenersaremadeof0 25 in. hexagonalcells3 in. long.Thestraightenersreducelateralowmotionbyforcingstreamtubesthroughthe honeycombcellsstretchingthevorticity( Rae&Pope 1999 ).Axialturbulencereduction isgenerallyreducedthroughaseriesofowscreensandsettlingchamberswithina stagnationchamber.Duetotheheavyuseofoilbasedseedingintroducedwithinthe stagnationchamber,axialowscreeninstallationwaspostponed. Tomatethestagnationchamberwiththeexistingducting,atwo-stagenozzle wasimplemented,showninFigure 4-4 .Therststageisasteelschedule-40reducer, decreasingtheouterdiameterfrom12 in. to6 in. overan8 in. length.Thesecondstage nozzlebothreducesandchangesthegeometrybymodifyingtheinteriorwallsfroma6 in. diametercircletoa2 2 in. squareovera6 in. lengthforanarearatioof12.Thenozzle was"printed"viastereolithographyrapidprototypingusinghighstrengthAccura-60 polycarbonatetoaccommodatetheductgeometryandmaximizestrength. Thesecondarynozzlecontainsafour-portstaticpressurering1 in. fromwhere theareais2 2 in. ,equaltothereusedNASAductarea.Thefourpressureportsare connectedinparallelby0 040 in. vinyltubingtoaveragethepressuredistributionacross thefourwalls.AsingletubeconnectsthepressureringtoanOmegaPX409-005G10V pressuretransducer.Thenozzleexitwasoutttedwith"zig-zag"trip-tape, 3 / 8 in. wideby 1 / 64 in. thicktopromotetransitiontoaturbulentowregime( Rae&Pope 1999 ). 4.1.3DataAcquisition Allsensorsusedformeasurementandcontrolofgeneraltunneloperationwere acquiredbyaNationalInstruments(NI)cDAQ-9178eight-portUSBchassis.Inputuseda singlefour-portNI9129universalcDAQcardwhichacquiresthestagnationtemperature, stagnationpressure,andthestaticpressuresensorsignals.Thevarioussignalswere recordedinacustomNILabVIEW-basedinterfaceanddisplayedreal-timefortheuser. 88

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TheinterfacealsoperformsthetunnelMachnumbercontrolviaaproportionalintegral (PI)controllerbyadjustingtheoutputvoltagewithtypicalsettingsof P =1 4and I =0 4.A0 10 V incrementalvoltageoutputfromaNI9263cDAQcardadjustedthe pressureofaMarsh-BelloframT2000transducerfrom3 15 psi .Thevariablepressure linewasattachedtothepneumaticregulatorvalveontheFisherstem-positionertoadjust thevalveopeningtoachievethedesiredruncondition. Usingthesensorsformeasuringstagnationpressure, p 0 ,stagnationtemperature, T 0 andthecalculatedMachnumber, Ma ,themassowrate, m ,canbedeterminedfromthe isentropicrelationship m = p 0 ) RT 0 A ) 1 M & 1+ 1 1 2 M 2 $ +1 2( 1) (41) where R istheidealgasconstantforair, 1 theratioofspecicheats,and A isthe crosssectionalareaofthenozzle( John&Keith 2006 ).Themassowrateswithina 95%condencerangeweremeasuredforMachnumbersfrom M =0 1 0 5andare tabulatedinTable 4-1 .Notethattheuncertaintyvalueisstatisticalonlyastheisentropic calculationdisregardsviscouse ectsandthusEquation 41 overestimatesthemassow rate.Comparingthesevaluestothemaximumoutputofthecompressor,1 005 kg / s itisclearthatthecompressorisabletoproduceasu cientmassowratetosustain continuousowuptothetested M =0 5. 4.2AcousticSource Acousticexcitationwithintheductisusedinane orttomimicboththefrequency contentandamplitudeoftheBPFobservedwithinanaircraftnacelleentrancepreviously discussedinChapter 1 .AcousticexcitationwithintheGFIDwasgeneratedbyasingle BMS4592NDdual-compressiondriverwithanoutputrangefrom300 22 000 Hz drivenbyaCrown XLS 1500poweramplier( BMS 2010 ).Thedrivesignalwasdelivered totheamplierbyeitheradedicatedfunctiongeneratororaBruel&KjrPulsesystem, 89

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dependingontheexperiment.Fulldetailsofeachexperimentalsetupareincludedin Chapter 5 Thespeakerwasinstalledimmediatelydownstreamofthenozzlewithinaspecially designedductsection,showninFigure 4-5 .The10 in. longaluminumacousticductwas designedwitharemovablespeakerinterfaceplate,wherethespeakerismountednormal totheowwithinasidewall.Thespeakerfacewaso set0 25 in. fromtheow.Toll theresultingcavity,apieceofaluminumfoam0 249 in. thickwithdensity10 ppi (pores perinch)coveredbyanestainlesssteelmeshwasinstalled.Themeshguidestheow overthesurfaceyetallowstheacousticstopassthroughwithnegligibleacousticlosses assumed.Thealuminumfoamprovidesarigidpermeablestructureforthemesh. Theinitialgoaloftheacousticsetupwastoreachlevelsof130 dB atspecic frequenciestomatchexperimentsperformedintheliterature.Chapter 5 willdemonstrate thatthesingledriversetupwascapableofreachingthedesiredvalues.Howeverthe eventualgoalofattainingsoundpressurelevelsinexcessof160 dB willrequirearedesign withadditionalspeakersandampliers. 4.3Ducting TheoriginalGITductingremainedaspartoftheGFIDfacilityprovidingadditional owdevelopmentlengthandmultipleinstallationlocations.Theductingwasconstructed ofstainlesssteelwalls,withaminimumthicknessof1 in. Intotal,the105 in. (4 13 m ) longductisthecombinationofthreeindividualductpiecesoflength48 in. ,29 in. ,and 28 in. EachcomponentutilizesacommonjunctionconnectionsystemillustratedinFig. 4-9 ,allowingforthecomponentstobeinstalledinanyorder.Thisjunctionconnection wasreplicatedonallconnectionsoffabricatedsections.Steelalignmentpins,0 200 in. diameter,ensureasmoothtransitionbetweenfacilitycomponents. Theductingcamewithamicrophonetraversebarthatwasusedaspartofthe originalFITimplementationatNASA( Jones etal. 2001 ).Eventhoughtheupgradeto theGITreplacedthetraversebarwithstationarymicrophones,thetraversebarremained 90

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asastationarypiecetollthegap( Jones etal. 2004 a ).Toallowthetestsectiontobe installedin-betweenanytwoductpieces,thetraversebarwasremovedandeachduct pieceshasthetraversetrackpermanentlysealedwithacustomstainlesssteelllerpiece. Thefabricatedpiecesalsoeliminatedpotentialleakagethroughthetopoftheduct. 4.4TestSection Thetestsectionisamulti-usepieceabletobeinstalledbetweenanytwoduct pieces.AphotographofthetestsectionisshowninFigure 4-6 .Constructedofblack anodized6061aluminumtoreducesurfaceglareforopticalmeasurements,thetest sectionwasusedforbothuiddynamicandacousticmeasurements.Thetestsection designcontainstwosymmetryplanes,horizontalandvertical.Symmetricaboutthe horizontalsymmetryplane,thetopandbottomofthetestsectioneachhavethreeports, onecentrallylocatedacousticlinerinstallationport,andtwoouterauxiliaryports,each locatedoneductdiameter(2 in. )awayfromtheedgeofthecentrallinerport.The auxiliaryportsare0 076 0 076 in (3 3 in )squareholes.Thesimplegeometryallows forinstallationofindividualsensorsorquickaccesstothetunnelinterior.Thecentral acousticlinerinstallationportisdesignedtotacousticlinersofdimensions51 610 mm (16 36 2 51 in. ),overeightductdiametersinlength.Acrylicplugslledthespacewhen nolinerwaspresent.ThedimensionsmatchthoseusedbytheGFITfacilitydescribedin Section 3.3.4 atNASALaRCforcross-facilitycollaboration( Jones etal. 2010 ).Theliners usedfortestingaredescribedinChapter 5 Variousacoustictestswereperformednecessitatingtheauxiliaryportstohold microphones.Twoaluminuminserts,showninFigure 4-7 ,werefabricatedallowingfor two 1 / 4 in. microphonestobeinstalledwithinacircularrotationmountnecessaryforthe two-microphonetestinSection 5.3 .Anglemarkersof1 incrementswereinstalledonthe edgesofonequadrant. Thetwosidewalls,showninFigure 4-8 allowedforlarge29 in. lengthopeningfor measurementsupstream,downstream,andintheimmediatevicinityoftheacousticliner. 91

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Currently,threesidewallshavebeenfabricatedforspecicuses:astaticpressuretap insert,andopticallyclearwindow,andalinearmicrophonearraywall.Additionaldummy polycarbonatewallswerealsomadetoreduceunnecessaryuseandpotentialdamageto thespecializedwallsandinserts. 4.4.1OpticalWindow Themultipurposetestsectionwasdesignedtoallowforoptical-baseduiddynamic measurements,providingunrestrictedopticalaccessforeitheralaserorcameras. Whileplateglassisgenerallyrecommendedforwindtunnelapplications,thecostof manufacturingametalframewascostprohibitive;therefore,optical-grade1 125 in. thick MakrolonWGpolycarbonatewasused.Thepolycarbonateallowedforhighstrengthwhile maintainingopticalclarity.Thewindowthicknesswasfoundtobeanissueforlargeangles ofincidenceforLDVmeasurements.Ananalysisofthee ectsofthethickwindoware detailedinSection 5.1.2 4.4.2StaticPressureWall Staticpressurewithinthetestsectionwasmeasuredusing29centerlinepressuretaps with1 in. spacing.AphotographofthestaticpressureinsertisshowninthetopofFigure 4-8 .Thetapswerecounterboredintothealuminumplatesuchthata0 032 in. thru-hole ontheinsidefaceconnectedto0 040 in stainlesssteelpressuretappress-tandepoxiedin place.Apost-drill"facing"passofanendmillwasperformedtoremoveanydrillingburrs withouttheneedtoroundtheinternaltapcorners. 4.4.3LinearMicrophoneArray Alinearmicrophonearraywallinsertwasfabricatedfromaluminumwithten, 1 / 4 in. microphoneportswith0 85 in spacingalongthecenterlineoftheduct.Anillustration oftheinstalledmicrophonearrayisshowninFigure 5-22 andadditionallyphotographed withoutmicrophonesinFigure 4-8 .Centerlinemeasurementsassumeaplanemode; thereforetestingwiththisplateislimitedtofrequenciesbelowthehigher-ordermode cut-onat3 37 kHz .Microphoneholders,onloanfromTheBoeingCorporation,allowed 92

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forscreenless 1 / 4 "microphonestobeinstalledushwiththeinteriorsurfaceofthetunnel walltominimizeownoise. 4.5Termination ManyoftheimpedanceeductionmethodspresentedinSection 3.2 relyonan assumptionofprogressiveacousticswavesexclusivelypropagatinginthestreamwise direction.Inrealitythisconditionisimpracticaltophysicallyrealize,particularlyatlow frequencieswherelargewavelengthsrequireexcessivecelldepths.Breakdownsinthis assumptioncanleadtoincreasedcomputationaltimeforparameterconvergenceorfailure ineducingthedesiredparameteraltogether( Jing etal. 2008 ). Ananechoicterminationwasfabricatedthatbothreducesupstreamacoustic reectionswhilesimultaneouslydecreasingowvelocity.NASALaRCoriginallydesigned theterminationwhereitiscurrentlyimplementedaspartoftheGFITfacility.The internalcross-sectionoftheterminationlinearlyincreasesfromtheGFIDductgeometry of2 2 in. to8 125 9 125 in. overa120 in. length.Thegradualincreaseinthe cross-sectionalareadecreasestheowspeed.Inthecaseofthemaximumtestedow speedof M =0 5(171 5 m / s )atthenozzle,conservationofmasscalculationsrevealthat theowdecreasesto9 4 m / s attheterminationexit. IllustratedinFigure 4-10 ,thewallsareathree-piecelaminateconstructionofafelt metalfacesheet,honeycomb,andaluminumhard-wallbackplateformingahighlyresistive locallyreactiveacousticliner.Thewiremeshisa0 0625 in stainlesssteelsheetofwoven wires,cold-rolledtoanominalstaticresistanceof320 cgsrayls .Thestainlesssteel honeycombcellsare 3 / 8 in. withavaryingcavitydepthfrom0 125 in. to6 090 in .The honeycombisalignednormaltothewallsactingbothasacavityaswellasastructural component.Theendsofthehoneycombwereepoxiedtoa0 031 in. thickaluminum backplatesealingtheendofthecavity.Thisconstructionwasrepeatedonallfoursides andthestructurewaswrappedinseverallayersofberglass.Thenalstructurehasan octagonalexteriorshapewiththecornervolumeslledwithhigh-densitysprayfoamfor 93

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structuralintegrity.Section 5.3 presentstheresultsoftestsperformedontheanechoic termination. Allvelocity-basedtestinginChapter 5 requiredtheuseofanatomizedoilforow seeding.TheoilusedintheLDVexperimentsisaPhantomSmokeOil135fromPea SoupLtd,arenedmineraloil.Concernaroseovertheaccumulationofoilinthemetal meshoftheinteriorwallsoftheanechoicterminationandtheinabilitytocleanit,thereby reducingthelong-terme cacyoftheacousticreectionreductionproperties.Asecond hard-walldi userofidenticalinternaldimensionswasfabricatedof0 175 in. thick berglasslimitedonlytotestingwhenseedingwasnecessary,suchasLDV. 4.6ExhaustDucting Downstreamoftheterminationtheowissteeredoutofthetestroomandbuilding totheoutdoorenvironmentthroughaductofcross-sectionalareaequaltothetermination exit,asillustratedinFigure 4-11 .Theductwasfabricatedofsheetmetalwithentrance angesmatchingtheholepatternofthetermination.Theductisconstructedoftwo parts,wherethestraightdownstreamductslidesconcentricallyintothecurvedupstream duct,toallowforadjustmentsifnecessary.Acoarsemetalgratingwasinstalledatthe ductexitobstructingdebrisfromentering. 4.7TheGFIDLayout ThefulldrawingofallGFIDsectionsisillustratedinFigure 4-12 .Inall,theGFIDis 34 ft longfromtheinlinesilencertotheexhaustexitandextends4 ft o thewallfora totalfootprintof136 sq.ft .Additionalroomisnecessaryforcomputercontrol,storageof thealternatetermination,andvariousinstrumentation. Whilenotdiscussedineachsection,sealingleaksbetweenalladjacentsections, aswellasfromanyseemorjointisanontrivialissueforbothblowdownfacilitiesand acousticducts.Ifleftuntreatedthegapscouldleadtoadropinowvelocityand/or reductioninacousticenergypropagatingdowntheductaswellasundesiredacoustic scattering.Whenpossible,rubbero-ringswereinstalledonallcompressiontpiecessuch 94

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asopticalwindowsandinstallationports.AllexposedseamswerecoveredwithSilicone RTV.Additionalcoverageatoftenremovedinterfacesweresealedwitho -the-shelfSilly Putty. 4.8DesignConclusion ThischapterdescribedthelayoutanddetailedthecomponentsoftheGFIDin streamwiseorder.Section 4.1 describedtheairsource,pipingsystem,nozzle,andvelocity controlofthesystemusingLabVIEWforreal-timethermodynamicpropertymonitoring, recording,andtunnelcontrol.TheacousticsourcewasoutlinedinSection 4.2 .Accurate sourceexcitationmatchingtonalcontentandsoundpressurelevelsisvitalforacoustic linertestingandimprovementsshouldbemadeonthisstagetoincreaselevels.Section 4.3 detailedthethreepiecesofductingfromtheGITfacilitywhichwerereusedproviding addedlengthbetweenthenozzleandthetestsectionforincreaseowdevelopmentand multipletestsectioninstallationlocations.Section 4.4 describedthemodulartestsection andthecurrenttestingcapabilities,includingstaticpressure,opticalowmeasurements, andalinearmicrophonearray.Theanechoictermination,describedinSection 4.5 ,is vitalforacoustictestingbyreducingupstreampropagatingmodes.Duetothecurrent useofoil-basedseedingforLDV,theapplicationofanechoicterminationislimitedto acoustictestingwithoutowmeasurements.Chapter5describesthesetupandresults ofexperimentscharacterizingtheGFIDandthetestingofacousticlinerimpedance.Full technicaldrawingsofallUFdesignedpartsareincludedinAppendix D Table4-1.GFIDmassowratesasafunctionofMachnumber. SetMachNumberMassFlowRate[ kg / s ] 0.10.100-0.113 0.20.210-0.219 0.30.319-0.327 0.40.429-0.439 0.50.541-0.553 95

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Figure4-1.GFIDairsupplyschematicindicatingpneumaticlines,electricalconnections, andowpaths. Figure4-2.InternalviewoftheUniversalSilencerU5C-4owsilencerforreducingow noiseandstructurallinenoise. 96

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Figure4-3.TheGFIDplenumusesatwo-stagenozzle.Seedparticlesareintroducedfor homogeneousmixing. Figure4-4.DiagramoftheGFIDstagnationchamber.Theinletpipeisturnedtowardthe aftwallforcingstagnationconditionsandenhancinghomogeneousmixingof seedparticle.Thechamberusesatwo-stagenozzletomaintainowquality andmodifytheshape. 97

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Figure4-5.Acousticductsection(Left)withspeakermountedtospeakerplate(Right). Figure4-6.TheGFIDtestsectionhasacousticlinerinstallationportsontopandbottom andfourauxiliaryportsformicrophonesandadditionalsensors. 98

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Figure4-7.Photographofthetwomicrophonerotationalplugfortestsectionauxiliary portswithmicrophoneholders. Figure4-8.Staticpressuretapinsert(top)andlinearmicrophonearraywall(bottom). 99

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Figure4-9.CommonGFIDconnectorsjoiningeachadjacentsection. Figure4-10.GFIDnear-anechoicterminationcomposedoflinearreactiveacousticliner wallstomitigateupstreampropagatingnoise. 100

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Figure4-11.TheGFIDexhaustductingexpelstheowtothebuildingexterior. Figure4-12.AnillustrationoftheGFIDbysection,notdrawntoscale. 101

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CHAPTER5 FACILITYCHARACTERIZATIONANDPROCESSVALIDATION Thischapterwilllayoutthemethodologiesandresultsoftheuiddynamicand acousticinvestigationoftheGFIDasahighReynoldsnumberturbulentchannelowand agrazingowimpedancefacility.Theexperimentswerechosentospecicallyhighlight keyaspectsoftheowandacoustictesting,demonstratingtheperformanceoftheGFID comparedagainsttheavailableliterature.Section 5.1 outlinessetupforuiddynamic testingintheGFID,withaspecicfocusandbackgroundontheapplicationoflaser Dopplervelocimetryastheprimaryvelocitymeasurementtechnique.Section 5.2 presents theexperimentalresultsanddiscussionoftheuiddynamiccharacterizationoftheGFID. Thecharacterizationfocusesontwosectionsofthetunnel:theupstreamentranceregion fordevelopingowstudiesandthedownstreamfullydevelopedregion.Similarly,acoustic characterizationispresentedinSection 5.3 todeterminethetestinglimitationsimposed byupstreampropagatingreectionswithinthefacilitythatmayhindercertainimpedance eductiontechniques.Section 5.4 attemptstoeducetheimpedanceofanuntestedacoustic linerviatheapplicationofthesinglemodemethodthroughadata-processingvalidation processbasedonexperimentalresultstakenatbothUFandNASALaRC.Thechapter concludeswithSection 5.5 ,presentinganexperimentalanalysisofthedraginuenceof theacousticlinerusingthreeindirectvelocity-basedtechniques.Resultsanddiscussionare includedineachsection. 5.1FluidTestingExperimentalSetup Severaltechniquesareavailabletomeasurethevelocitiesofinterest.Compared tolargerwindtunnels,therelativelysmall2 in. 2 in. crosssectionoftheGFIDis moresensitivetoblockagefromintrusivemeasurementprobes.Asowdevelopmentis ofprimaryinterest,physicalprobeswouldneedtobetraversedtopredeterminedgrid locations.Traversablewallsectionsarepronetoleakageandincreasedcomplexity.Tothis end,non-intrusivemeasurementtechniques,suchasparticleimagevelocimetry(PIV)and 102

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laserDopplervelocimetry(LDV),arepreferredtointrusivetechniquessuchashot-wire anemometry,pitotprobes,andboundarylayerrake.UltimatelyLDVwaschosendueto ahigherspatialresolution,highdatarates,andarelativelysimplerexperimentalsetup comparedtoPIV. 5.1.1BasicPrincipalsofLaserDopplerVelocimetry(LDV) LaserDopplervelocimetry(LDV)isanon-intrusivepointmeasurementtechnique thatdirectlymeasurestheDopplershiftofatracerparticlepassingthroughthesmall intersectingvolumedenedattheintersectionofmultiplefocusedlaserbeams.The intersectingvolumedenesanopticalanemometerprobeofxedlocationinreference tothetransmittingandreceivingopticsandthusisreferredtoasthe"probevolume". TheprinciplebehindthemostcommonimplementationofLDV,illustratedinFigure 5-1 ,isbasedontwomonochromaticlaserbeamsofwavelength, 1 ,crossingatabeam separationangle, ,atthefocallengthofthetransmittingoptics.Aninterferencefringe patternisestablishedintheprobevolume,withfringespacing ( f ,duetoconstructiveand destructiveinterferenceoftheintersectingwavefronts( Albrecht etal. 2003 ) ( f = 1 2sin( / 2 ) (51) Theintensityoflightscatteredbyaparticlepassingthroughtheprobevolumeis dependentonthereceivingangleofthecollectorrelativetotheopticalaxis.AllLDV velocitydatainthisthesiswascapturedinback-scattermode,illustratedinFigure 5-1 wherethescatteredlightiscapturedalongthepathofthetransmittedbeam.Light collectedoppositethetransmissionpathiscalled"forwardscatter",possessingahigher reectedintensityattheexpenseofincreasedcomplexityduetoaseparatereceiverand intricatealignment( Albrecht etal. 2003 ).Thecollectedlightscatteredbytheparticleis directedviamulti-modeopticalbers(multi-modetoaccommodatemultiplecolors,one foreachvelocitycomponent)toaphoto-multipliertube(PMT)whereitisconvertedinto anelectriccurrent.ThesubsequentDopplershiftfrequency, f d ,fromthepassingparticle 103

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isrelatedtotheparticlevelocitycomponent, v p ,perpendiculartothebisectorofthetwo incidentbeams,( Dynamics 2000 ) v p = * 1 2sin( / 2 ) f d * (52) However,aparticlepassingthroughtheprobevolumewillgenerateaDopplershiftof f d foreitherapositiveornegativeparticledisplacement,illustratedinFigure 5-2 A. Inordertoeliminatethedirectionalambiguity,aconstantfrequencyshift, f 0 ,is addedtooneofthemonochromaticbeamsbyanopto-acousticmodulator,calledaBragg cell( Albrecht etal. 2003 ).WithoutaBraggcell,azerovelocityresultsinanullDoppler frequency.Theadditionoftheinducedfrequencyshiftresultsinazerovelocityequalto theo setfrequency,asillustratedinFigure 5-2 B,andanegativevelocitycanbeacquired f d = * 2sin( / 2 ) v p + f 0 * (53) Notingtheupperandlowerlimitsofasignalprocessor,Equation 54 canbeextendedto solveforthevelocitylimitsofaparticularsystem( Dynamics 2000 ) * ( f 0 f min ) 2sin( / 2 ) *
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leavingthetransmissionboxaresplitbetweentwoprobeheadswherethetransmitting opticsareheld. Theprimaryheadcontainsthefourbeamsofthetwoprimarywavelengths,514 nm and488 nm ,whilethesecondaryprobeheadoutputstwobeamsat476 nm .Illustratedin Figure 5-4 ,theprimaryprobeheadisgenerallyconguredwiththefourbeamsoutputting fromasquareorientationwithwavelengthpairsalignedoppositeeachother,commonly referredtoas"4-beammode".However,inordertoresolvewall-boundedowstheprobe canberecongured,asillustratedinFigure 5-3 B,toensureoneoftheincidentbeamsis notclippedbyawallorbody.Therecongured"3-beammode"probeheadhasthegreen andbluebeamsaligned180 apartandacombinationofthetwoislocated90 tothem both.Thereceivedscatteredlightisbandpasslteredandeachwavelengthisdirected towardanindividualPMT. Thebeamseparationangle, ,inFigure 5-1 isafunctionoftheseparationdistance betweentheexitpositionofthetwobeams,aswellasthefocallength, f ,ofthe transmittingoptics.Thereforethelenschoiceandbeamcongurationwilldetermine thevelocityrangeofaparticularsetupfromEquation 54 .TheUFsignalprocessorhasa reportedupperlimitof f max =180 MHz andaninferredlowerlimitof f min =15 85 MHz ( Jensen&Bertolucci 2012 ).Thesevaluesareusedtosolvefortheupperandlower velocitylimitoftheDantecsystemsignalprocessorusedandareshowninFigure 5-5 and tabulatedinTables 5-1 and 5-2 .Thelimitsarebasedontheavailablelensfocallengths availablefortheUFsystemof120 mm and400 mm ,howeveronlythe120 mm lenswas usedforthepresentexperimentsduetoimprovedspatialresolution. ProbeVolumeDimensions Thedetectionofparticleswithintheprobevolumehasseveralcontributingfactors includingwavelength,probevolumesize,particlesize,concentration,andtype,andoptical path,amongstothers.Severalofthesetopicsaretouchedintheremainderofthissection. Thesizeoftheprobevolumeitselfhasoneofthelargestinuencesondatarateatthe 105

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expenseofspatialresolutionassociatedwithlargerprobevolumes.Theprobevolume sizeisdenedbythreedimensions,thewidth, dx ,theheight, dy ,andthelength, dz .The widthandheightoftheprobevolumearenearlyalwaysequal( Dynamics 2000 ).Eachof thedimensionsisdependentuponthebeamwaistdiameter, a 0 ,denedas a 0 = 4 f % Ed I (55) where f isthetransmittingopticsfocallength, d I and aretheincidentbeamdiameter andwavelength,respectively( Dynamics 2000 ).Althoughnotapplicabletothisstudy,the beamexpansionratio E ,isunityunlessabeamexpanderforlargeropticsisinstalled. Forthe120 mm and400 mm lensesavailable,thebeamwaistsare56 6 m and189 m Assumingequalheightandwidth,thedimensionsoftheprobevolumearedenedby dx = dy = a 0 cos( / 2 ) (56) and, dz = a 0 sin( / 2 ) (57) ApplyingEquations 56 and 57 forthe120 mm in2/4-beammoderesultsin dx = dy = 57 3 m and dz =361 9 m Estimationofmoments LDVmeasurementsareinherentlytiedtotherandomsamplingofseedparticles passingthroughtheprobevolume.Therateatwhichtheparticlespassthroughthe probevolumeisafunctionofthevolumeuxofseedparticles.Ashigherspeedows havealargervolumeuxforaxedregion,LDVmeasurementsofaveragedquantitiesare inherentlybiasedtowardhighspeedows;thisisreferredtoasa"velocitybias".Inorder tocompareowsofunequalsamplerates,themeasuredquantitiesneedtobeweighted. Whilethereareseveralpossibleexpressionsfortheweightingfactor, g i ,newerLDV systemsallowforaccuratemeasurementsofthetransittime, + i ,thelengthofthetime 106

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requiredforeachparticlemeasuredtopassthroughtheprobevolume,whichisinversely proportionaltothemagnitudeofthevectorvelocity( Albrecht etal. 2003 ). Usingthetransittimeastheweightingfactor,eachvelocitysample, u i ,isweighted andthemeanowvelocityandstandarddeviationarerespectivelyexpressedas u = N 9 i =1 u i g i N 9 i =1 g i (58) and 2 u = : ; ; ; ; ; < N 9 i =1 ( u i u ) 2 g i N 9 i =1 g i (59) The ( ) symbolindicatesthattheequationexpressesanestimationofthecalculated quantity( Albrecht etal. 2003 ). SeedingandLimits DetectionofaparticlebythePMTswithinthesystemisafunctionofincidentlaser intensity,particlesize,relativerefractiveindicesoftheparticlematerialandowmedium, particleshape,andreceivingangle( Albrecht etal. 2003 ).Theparticlesizedictatesthe e ectivenessoftheparticletoscatterlight,andthusthebenetoftheseedingparticle forusewithLDV.Theparticlesizeisrelatedtotheincidentwavelength, ,throughthe non-dimensionalMieparameter,whichinaircanbesimpliedto 3 = % d p (510) where d p istheparticlediameter( Albrecht etal. 2003 ).AllLDVmeasurementsinthis thesisuseaPeaSoupPS31oil-basedseedertoproduceadryatomizedoilsmokeparticle. TheseederrequiresaproprietaryPhantomSmokeOil135,ahighlyrenedmineraloil withareportedparticlediameterof d p =0 3 m ,andthushasaMeiparameterbetween 107

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1 83 1 98fortheoutputwavelengthsofthelaser.Theparticlesgeneratedareassumedto beofequalsize,ormonodisperse,spherical,andnon-absorptive. Theseedparticlescanbethoughtofassmallspheresthatideallymovewiththeow. However,asthesizeoftheparticlesincreases,arelativeslipvelocitybetweenthetrue uidmotionandthemotionoftheparticleoccurs.Theslipbetweentheseedingparticles andthesurroundinguid, s ,isdenedas s = u f u p u f (511) where u f and u p aretheuidandparticlevelocities,respectively.Thisisespecially importantwhendealingwithhighspeedturbulentowsastheparticlesizeactsasa low-passlterforbothturbulentandspectralanalysis( Albrecht etal. 2003 ).Theparticle diameterandmaterialpropertiesdenethecut-o frequencyforwhichtheparticlescan accuratelyfollowtheow.Ifthedensityoftheparticles, & p ,ismuchlargerthanthatof thesurroundinguid,theparticlediameter, d p ,canberelatedtothecut-o frequency, f c through d p < : ; ; < 18 & p f c 1 2 % % 1 (1 s ) 2 1 (512) where isthekinematicviscosityofair( Albrecht etal. 2003 ).Figure 5-6 illustrates Equation 512 overarangeofsizesapplicabletotheproposedexperimentshowingtwo commonseedingmaterialsandallowingfora1%sliperror.Theverticallineindicates thecut-onfrequencyofhigherorderacousticmodesdictatedbythetunnelgeometryof 3 37 kHz for M =0,denedbyEquation 28 .BasedonFigure 5-6 ,theparticleproduced bythemineraloilbasedPeaSoupseedercanbeaccuratelyusedforfrequenciesabove 10 kHz 5.1.2LaserDopplerVelocimetryExperimentalSetup ThissectionwilloutlinehowLDVmeasurementswereusedforGFIDuiddynamic characterization.ThealignmentoftheLDVsystemtotheGFIDisdescribed.The 108

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limitationsofthesystemandthoseimposedbytheGFIDareoutlinedspecicallyfor applicationtothisthesisandingeneraltoapplytofutureexperiments. TheLDVprobeheadwaspositionedbya3-axisParkertraverseallowingforprecise movementswith3 m repeatability,controlledviaacustomLabVIEWuserinterface capableofcommunicatingwiththeprovidedLDVsoftware,DantecBSA.Thethree axeswerealignedwiththetunnelcoordinatesystemateachtestsectioninstallation location.Thelongestaxis,aParker406XR-1250,had1250 mm oftravelandwasaligned streamwisewiththex-direction.Theothertwoaxes,bothaParker404XR-300with 300 mm oftraveland3 m resolution,werealignedwiththecross-tunneldirections.The traversewasrigidlyattachedtotheGFIDstandtomaintainalignment. WhilecarewastakenwhenattachingthetraversetotheGFIDstandforalignment, aniteo setangleisunavoidable.Preciseknowledgeofprobelocationforbothnear-wall andcenterlinemeasuresrequiresthetraversemotiontotrackthecoordinatesystemof thetunneldenedbytheinherentgeometry.Alaserdisplacementsensor(LDS),Keyence LK-G97,wasattachedtothetraverseandthedistancetoaattunnelsurfacewas measuredasthetraversewasmovedalongasingleaxis.Theanalogdatawasrecordedvia LabVIEWandtheseparationdistanceplotted.Theresultantanglewasfoundthrough alineartofthedata.Thetestswererepeatedforallthreeaxesandtheresultant slopeswereusedasatranslationofallmotionrequeststothetraverse,bothmanualand automatedthroughtheBSAsoftware. UsingtheLDSallowedforthetraversemotiontobealignedtothetunnelcoordinate system,however,theprobeheaditselfisnot.Theprobelaseremittersarefactoryaligned suchthatallbeamscrossataxedlocationdenedbythelensfocallength.Asaresult, alignmentoftheprobe'sindividualbeamsareunnecessary.However,alignmentofthe probeheadtothetunnelcoordinatesystemisessentialformeasuringthetruevelocity. Severalstepsareinvolvedinaligningtheprobeheadtothetestsection.Aligningtothe tunneloorensuresthattheplaneoftwolaserbeamsisequaltothetunneloorplane. 109

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IllustratedinFigure 5-7 ,analignmentprocedurewasimplementedwheretwobeams emanatingfromtheprobeheadaresetatlowpoweranddirectedattheinterfaceofathin opaqueshimrestingonthetunneloor.Theprobeheadiscarefullyrotateduntilthelight passingunderneaththeshimatbothpointsisofequalintensity. Thereectionofthebeamso ofthefrontofthewindowareusedforadditional alignmenttoensurethatprobeheadisnormaltothetestsection.Beamreectionso of thewindowsurfacewillfallonthefrontlensoftheprobeandindependentpitchandyaw adjustmentsweremadetotheprobeheaduntilthesecondaryandtertiaryreectionswere alignedwiththeprimaryemittingbeams. Finally,withtheprobeheadalignedtothetunnelitwasnecessarytodenethezero locationofthetraverserelativetothetunnelcoordinatesystem.Thisrequiresthatthree locationsareaccuratelyknown,theoor,thesidewall,andtheupstreamverticaledgeof thetestsection.Thetunneloorwaspreviouslyalignedusingtheopaqueshim.Tolocate theinteriorsurfaceofthetestsectionatechniqueoutlinedby Dynamics ( 2000 )isapplied. Withthelaseroutputtingatlowpower,theprobevolumeisincrementallysteppedinthe z-directionuntilthemonitoredanodecurrentismaximized,withcaretonotoverloadthe PMT.Justastheprocessorwillhavethehighestsignalwhenaparticlepassesthrough thecenteroftheprobevolume,sotoowillasolidobject,andthustheinteriorsurfaceof thewindowwillreectthemostlight.Thisprocesswasabletodeterminethetunneledge to 10 m .Withlocationofthesidewall,oor,andtestsectionentranceknowntothe traverse,thecenterlineofthetunnelcanbedenedasnumerico setsofthesefeatures. Experimentalsetup AswillbediscussedinSection 5.2 ,twotypesofexperimentswereperformed: centerlinemeasurements,andcross-ductmeasurements.Allcenterlinedatauseda4-beam congurationformeasuring2Dvelocitydataorientedsuchthatboththegreenandblue overlappingprobevolumesmeasuredapositivevelocity,asillustratedinFigure 5-4 A. 110

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Thecross-ductprolesrequirednear-wallmeasurementsonboththetopandbottom wall.Generally,near-wallmeasurementsaremadeusinga3-beamprobeconguration, illustratedinFigure 5-4 B.However,asa3-beamcongurationisalignedtoasurface suchthatnobeamsarecropped,thebenetsofthesecondvelocitycomponentfrom 3-beamcongurationarenegatedontheupperwallunlessthetheprobeheadwasrotated 180 .Thenecessaryrotationstepcouldundotheintricatealignmentoftheprobehead. Additionally,duetothenatureofthe3-beamconrmation,onevectormustalways measureanegativevelocity.AslistedinlistedinTable 5-1 ,thelowvelocitylimitof 54 26 m / s wouldbelimitingformanyoftheowstestedinthisthesis.Toutilizethe spatialresolutionofthe120 mm lensfornearwallmeasurementswhenperforming cross-ductproles,1-Dvelocitymeasurementsofthestreamwisevelocitycomponentwere madeusingjustthe514 nm beam. Thecrossductprolesonlymeasurethelocalvelocityvaluebutwerenota ectedby uctuationsinfreestreamconditions.ThestationarysecondaryLDVprobeheadwith wavelength476 nm wassetupoppositetheprimaryheadandalignedtomeasuredthe centerlinevelocity.Velocitycanonlybesampledwhenbothprobesregisteredasignal withina250 s window.Thereferencevelocity, u ref isthenusedtosmoothoutthetunnel uctuationsofthemeanow u i = u i,t & u ref i u ref i (513) wherethesubscript i referstoanindividualsample. E ectofwindowthickness Originally,allthreecomponentsofvelocityweretobemeasuredsimultaneouslyby usingbothprobeheadsandaligningtoapinhole.However,initialexperimentsthrough thetestsectionopticalwindowpresentedinSection 4.4 demonstratedverylowandoften nulldatarates.Whilelowerdataratesareexpectedfor3DLDVduetothesmallregion ofoverlappingprobevolumes,thewindowwasdeterminedtobeaprimaryfactor.To 111

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betterunderstandtheissueandtheinuenceofthewindowonthemeasurements,an opticalmodelwassetupbasedonSnell'slaw. Themodelwasbasedontracingtwobeamsemanatingfromtheprobehead, illustratedinFigure 5-8 ,andaccountedfortheangleshiftsattheincidentandtransmitting interfacesofthewindowofnitethicknessaccordingtoSnell'sLaw, n 2 sin 3 2 = n 1 sin 3 1 (514) Snell'sLawisasimpleequationbasedontheindexofrefractionoftwomediums,inthis caseair( n =1 00)andthepolycarbonatewindow( n =1 59).Thebeams,showninsolid bluelineinFigure 5-8 ,aretraceduntiltheycross.Similarly,athirdbeampathfromthe centerofthelens,illustratedasadashedline,wascalculatedtoindicatethepathoflight reectedbyaparticletothereceivingopticsandthustheo setdistance, d Asampleraydiagramforthecaseof2-/4-beam120 mm lenscongurationwith an 3 =60 o setangleisshowninFigure 5-9 .Themodelwasusedtoanalyzeboththe 120 mm and400 mm lensesforallanglesfrom 3 =45 90 asmeasuredfromthewindow suchthat90 correspondstonormalincidence.TheresultsareshowninFigures 5-10 A-D. Thereexistsamaximumangle 3 ,beyondwhichthetwoprobeheadswouldphysically interferewitheachother.Thisvalueisindicatedbytheverticalreddottedline.Theangle atwhichtheseparationdistance, d ,overlapswiththeprobevolumewidthbyatleast50% togenerateapotentialmeasurementisindicatedbythehorizontalblackline( Jensen& Bertolucci 2012 ). BasedonFigures 5-10 A-D,itisevidentthatthe120 mm lensisunabletobeusedin a3Dmeasurementsetupwiththecurrentwindow.Theo setanglesrequiredforeithera 4-beamor3-beamconguration,86 and82 respectively,arebothbeyondthemaximum anglewithoutprobeheadinterference.Incontrast,theuseofthe400 mm focallength lensisapplicableforallangles,duetothesmallerassociatedbeamseparationangle resultingfromlongerfocallengths. 112

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The400 mm lenswouldalwaysbeamoreappropriatechoiceforperforming3D velocitymeasurementsthroughthecurrentwindow.However,thisthesiswasmore concernedwiththecharacterizationofthefacilitytowardtheapplicationtoacoustic liners,includingdevelopmentofthecenterlinevelocityaswellascross-ductvelocity proles,specicallywiththeaimofnear-wallvelocityprolebasedshearmeasurements, discussedinSection 5.5 .AspreviouslydemonstratedthroughEquation 55 ,theassociated probevolumesofthe120 mm and400 mm lensesare56 6 m and189 m respectively, andthusthebetterspatialresolutionachievedwiththe120 mm wasmoreapplicableto thecurrentgoal. VelocityDataReduction AsdepictedbythedirectionofthearrowsinFigure 5-4 ,theLDVprocessorrecords apositivevelocityinthedirectionofthefrequencyshiftappliedbytheBraggcelland outputsavelocitywithoutreferencetotheactualcoordinatesystem.Acoordinate transformationmustbeappliedtothedatatotransformittovelocitywithinthecorrect coordinatesystem.Forcenterlinevelocitymeasurements,theprobeheadwasorientedas showninFigure 5-4 A,permittingboththegreenandblueprobetomeasureapositive velocityofequalmagnitude.Therawdataisrecordedastwochannels,correspondingto thetwoprobecolors.Thegreenisrecordedas"LDA1"andtheblueas"LDA2".The rawchannelsaretransformedtotunnelcoordinatesystemviathegenerictransformation matrix = > ? U V @ A B = = > ? sin cos cos sin @ A B = > ? LDA 1 LDA 2 @ A B (515) The1Dbulkvelocityandcontrolvolumemeasurementusedthesinglegreenprobeand wasalignedwiththetunneloor,discussedinSection 5.1.2 ,thereforenotransformation matrixwasnecessary. Outlierrejectionwasexecutedviaamultivariate"adjustedoutlyingness"approach proposedby Hubert&VanderVeeken ( 2008 ).Forthe1Dvelocitydata,boththelocal 113

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andreferencevelocitieswereusedasinputs.Thecleandataissubjectedtotransittime weightingpreviouslydescribedinEquations 58 and 59 toaccountforthevelocitybiasof themeanandstandarddeviationofthemeasuredvelocities. ThecontrolvolumeapproachtocalculatingdragpresentedinSection 5.5.3 required thatthedensitybeknown.Thedensityisbasedonthemeasuredisentropicproperties & = & 0 & 1+ 1 1 2 M 2 ( $ 1 (516) Thestagnationdensity, & 0 ,iscalculatedfromtheidealgasequation.Unlikeafandriven tunnel,theowpropertiesofablowdownfacilitycanbetimedependentduetoupstream compressorsandairholdingtanksoutofthecontrolofthetunnel.Toaccurately accountforthetruevalueofdensityandotherowproperties,aLabVIEWcodewas writtentosamplethetunnelrunconditionsalongwithatimestamp.Thecodewasrun simultaneouslytotheLDVmeasurementstoguaranteethatthetwotimesrecordedfor eachmeasurementwerefromthesameinternalcomputerclock.Afteroutlierrejection wasappliedtothevelocitydata,theremainingdatawastimematchedtothenearest setofowproperties.Thetunnelcontrolonlysamplesataconstant5 Hz ,however LDVsamplingisdependentonseedingdensityandcanreachseveralthousandsamples persecond.Asaresult,theremaybeseveralvelocitysamplesthatmatchtothesame sampledowproperty. 5.2FluidDynamicCharacterization Thefrontofanaircraft'senginenacellegenerallyaccommodatesacousticlinersto attenuatetheforwardpropagatingnoisefromtheengine'sfanandcompressionstages. UnliketheboundedowwithintheGFID,full-scaleenginenacelleacousticlinersare subjecttodevelopingowoverthelinerfacethatcontinuesuptothefanstageandmay neverreachafullydevelopedconditions.Thedevelopingowwithinthisregiongives risetoamodicationoftheboundaryconditionandthusisanimportantowfeatureof acousticlinerresearch.However,establishingandtestingacousticlinerimpedanceunder 114

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fullydevelopedconditionswithintheGFIDallowsforaknownenvironmenttoreduce measurementinconsistenciesandprovidecommonowcharacteristicsthatcanbeeasily replicatedbyalternatefacilitiesandnumericalstudies. TheuiddynamicassessmenttocharacterizetheGFIDwassplitbetweentwo locations,illustratedinFigure 5-11 ,eachdedicatedtoaspecicowregime:theentrance regionandthefullydevelopedregion.Thetestsectionwasinstalledat x / D h =0 19for entranceregiontestswithopticalaccessbetween x / D h =2 5 16 5andmoveddownstream to x / D h =58 5 77 5,withaviewablerangefrom x / D h =60 74,forfullydevelopedregion testing. AtestReynoldsnumberbasedonbulkvelocityof Re D h =2 25 E 5waschosento meetthreerequirements.ThisregimeallowsfordirectcomparisonwithhighReynolds numberturbulencechannelowstudiesandcomparisonstootherfacilitiesfoundinthe literature.Additionally,tominimizee ectsduetocompressibility,thespeedwaschosen suchthatthelocalMachnumberwaslessthan0 3atallductlocations( John&Keith 2006 ).Finally,inanticipationofacousticlinerdragassessmentinSection 5.5 ,thevelocity neededtobeashighaspossibletomaximizetheshearinuence. 5.2.1Entranceregion TheowwithintheentranceregionoftheGFIDwasexperimentallyassessedfrom x / D h =2 5 16 5at Re D h =2 25 E 5.Twoseparateexperimentswereperformedinthe entranceregionanalyzingtherelationoftunnelbulkvelocityandthecenterlinevelocityas comparedtosimilarfacilitiesandrunconditions. Thebulkvelocity,alsoreferredtoastheaveragevelocity,istheresultofintegrating thelocalstreamwisevelocityoverthecross-sectionalarea.Thebulkvelocityinincompressible owisconstantforallaxialdistancesandthusisconvenienttouseasavelocityscale forcomparingReynoldsnumbersofthevariouschannelows.Thebulkvelocitywas measuredusinga2DLDVprobeat x / D h =2 5asshowninFigure 5-4 ,corresponding tothefurthestupstreampositionthatisopticallyaccessiblewithoutblockingoneofthe 115

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incidentlaserbeamswiththewindow'sedge.A30-pointverticalprolewasmeasuredat thecenterlineofthetunnelwith20 000velocitysamplesateachmeasurementposition. Thevelocitymeasurementswerelimitedtotherangeof y / D h =0 09 0 91duetocropping ofincidentlaserbeamsbythetunneloorand/orceiling.Measurementpositionspacing wasdenedbytworegions,aninnercorewhichspannedthemajorityofthesampled spaceat 18 mm aboutthecenterlinein2 mm incrementsandtheouterregionwith 0 5 mm incrementsfrom 18 5 21 mm ThemeanvelocitypointsareshowninFigure 5-12 overlaidbythebulkvelocityvalue of66 63 0 37 m / s ,thewidthofwhichindicatesthe95%condenceinterval.Thebulk velocityoverlapsthemajorityofthevelocitypointmeasurementsdemonstratingtheow ismostlyuniformwiththetaperinge ectsofaboundarylayerneartheouteredges. Centerlinevelocitywassampledalongthecentralaxisofthetunnel,at y = z = 25 4 mm ,from x / D h =2 5 16 5with25 4 mm betweenmeasurementlocations.Thedata areshowninFigure 5-13 withthemeasuredcenterlinevelocitynormalizedbythebulk velocityasafunctiondownstreamdistanceintermsofductdiameter.Forcomparison, themeasureddataisdisplayedalongwithdataextractedfromtwoexperimentalhigh Reynoldsnumberturbulentchannelowstudiesfrom Gessner etal. ( 1977 )and Melling &Whitelaw ( 1976 )withbulkvelocityReynoldsnumbersof Re D h =2 5 E 5and Re D h = 4 2 E 4,respectively. EventhoughthethreedatasetsinFigure 5-13 haveturbulentReynoldsnumbers, directcomparisonisdi cultbecauseeachsethasauniqueaxialstartinglocationand allthreedisplaydissimilarcenterlinevelocityaxialgrowthrates.RecallfromChapter 3 Anselmet etal. ( 2009 )postulatedhigh-Reynoldsnumberturbulentchannelowentrance regiondatawillcollapsewhenplottedas U c U b = X / D h ( U b x / ) ) 1 / 5 (517) 116

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Equation 517 wasappliedtothethreedatasetsandtheresultsareshowninFigure 5-14 .Allthreedatasetsdisplayalinearincreasewithdistance;thetwocomparisonsets maintainthelineartrendupto ( X / D h ) / ( U b x / ) 1 / 5 =1 5which Anselmet etal. ( 2009 )described asthelimitoftheentranceregion.Basedonthisvalue,theentranceregionoftheGFID wouldextendto x / D h =36 2. Anselmet etal. ( 2009 )reportedaslopeof0 185tobesttthedata,displayedby thedashedblacklineinFigure 5-14 .Representedbythesolidblackline,thedatafrom Gessner etal. ( 1977 )wasindependentlytinaleast-squaressensetoEquation 517 with aresultantslopeof0 167 0 05.Similarly,theGFIDentranceregiondataresultedin attedslopeof0 145 0 039.Linearregressionwasonlyappliedtothe Gessner etal. ( 1977 )comparativedataduetothefarupstreamstartingpositioncomparedto Melling& Whitelaw ( 1976 ). TheMonte-Carlosimulationgeneratesadistributionofpotentialvaluesdependenton thedistributionofinputvariables,asdescribedby Coleman&Steele ( 2009 ).Variable distributionsaregeneratedasanassumednormaloruniformdistributionsabout theprovidedmeanvalue.Thebulkandcenterlinevelocitieswereassumednormally distributedwithmatchingstandarddeviations.Theuniformlydistributedpositionwas accountedforasthesumofthreepotentialuncertainties:the y =0positionoftheoor vialaseralignment,therepeatabilityintraversemotion,andtheductheight. ThevelocitymeasurementswithintheentranceregionoftheGFIDreasonably matchedtheconditionsofsimilarfacilities.Bymatchingtheproperdimensionless parameterssetforthby Anselmet etal. ( 2009 ),whichareassociatedwiththegrowth ofthecenterlinevelocity,thetestsectionwithaninstalledacousticlinercanbe appropriatelyplacedforaspecicowcharacteristic. 5.2.2Fullydevelopedregion Thedeterminationofthefullydevelopedconditionsinthestrictestsenserequires thatallowvariablesareunchangingwithadditionalstreamwisedistance.Forturbulent 117

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Reynoldsnumberowsinpipesandchannelsoforder Re D h =10 5 ,thisvaluecanbeas highas x / D h =70 100forhigher-orderturbulencequantities.Althoughsheare ects, suchasboundarylayers,generallyconvergenear x / D h =30,mostmeanquantitiesare essentiallyconsideredfullydevelopedbeyondthispoint( Zagarola&Smits 1998 ).This isinagreementwiththecalculatedentrancelengthvalueof x / D h =36 2determinedin Section 5.2.1 Allmeasurementsweremadewithaplexiglassinsertinstalledintheacousticliner installationport,referredtohereasa"clean"testsection.Thecleantestsectionallowed foraclearerassessmentofthefacilityinuenceontheow.Flowassessmentwasbased onthreemeasuredquantitiestoestablishbaselinefullydevelopedconditions.First,the centerlinevelocityismeasuredtodemonstratethattheboundarylayersontheenclosing wallshaveconvergedandtheowisnolongeraccelerating.Second,crossductvelocity prolesweresampledatmultiplestreamwisedistancesfordirectcomparison.Lastly,the staticpressurewithinthetestsectionisexaminedatmultiplerunconditions. AsillustratedinFigure 5-11 ,thetestsectionwasinstalledwiththeupstreamedge at x / D h =58 5,thefurthestdownstreaminstallationavailable,allowingformaximum owdevelopment.Velocitymeasurementsweremadeviaa1DLDVprobewitha120mm lensallowingfornearwallmeasurementstobetterresolvethehighervelocitygradients comparedtotheentranceregion.TheresultspresentedherearealsousedinSection 5.5 forquantifyingthesheare ectoftheacousticlinerinstallation. Thecenterlinevelocitywasmeasuredwiththeprobealignedat y = z =25 4 mm with 25 4 mm spacingbetweenpoints.Replicatingtheentrancelengthtest,28spatiallocation weresampledwith20,000samplesperlocation.ThemeasureddataareshowninFigure 5-15 witherrorboundsdisplayinganearconstantvalueof U c / U b =1 25.Thevalueagrees withthereportedrangeof U c / U b =1 1 1 3forhighReynoldsnumberturbulentchannel ows( Anselmet etal. 2009 ).Therefore,thedevelopingboundarylayershaveconverged andarenolongeracceleratinganinviscidcore. 118

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Sheare ects,includingboundarylayers,aresubjecttothee ectsofturbulenceand consequentiallytakelongerthanmeancenterlinevelocitytoreachasteadystatevalue. Mean1Dvelocityprolesweremeasuredattwostreamwiselocationsof x / D h =63and 72,chosentomeasuretheowoneductdiameterupstreamanddownstreamoftheliner wherethee ectofthelinerontheboundarylayermaybeevident.Thistestwasrepeated withanacousticlinerinstalledforacomparativestudy,includedinSection 5.5 .The cross-ductproleswerecomposedof63samplelocationsovertworegions:thesparse centralcoreandadensenear-wallregionwith1 mm and0 5 mm spacing,respectively. Thefullcross-ductprolesareshowninFigure 5-16 Awithuncertaintybounds representedbythelinesofequivalentcolor.Thetwoprolesmatchwithinexperimental uncertaintydemonstratingthatviscouse ectshavedi usedcompletelyandtheproles arenolongerdevelopingwithincreaseddistance. Additionally,thesamedatawascomparedtotwoturbulentchannelowcasesfrom Gessner ( 1964 )withReynoldsnumbers Re D h =1 5 E 5and Re D h =3 0 E 5bounding thevaluetestedinthisthesisof Re D h =2 25 E 5,showninFigure 5-16 B. Gessner ( 1964 ) onlypresentedahalfductproleforeach,hencetheGFIDdatawasrescaledtothesame dimensionsfordirectcomparison.Again,thedatamatchwithinexperimentaluncertainty atboththelowerandhigherReynoldsnumbercases. TheuncertaintyboundsillustratedinFigure 5-16 stemfromaMonte-Carloanalysis ofthemeasuredvelocity.TheMonte-Carloapproachisbasedonthatpresentedby ( Coleman&Steele 2009 )accountingforthebiaserrorofandthemeasuredvelocities. WhiletherecanbeseveralsourcesofbiaserrorinLDVmeasurements,includingparticle response,probevolumesize,residencetime,andgeometricerrors( Semaan 2010 ).Onthe geometricerrorhasyettobeacknowledgedinthischapter.Thegeometricerroraccounts fortheassumedmeasuredlocationtotheactuallocation.Thedi erenceinthesetwo pointsisafunctionofthetraverse,machiningtolerances,andmethodofalignment.The traversehasareportedrepeatabilityof3 m ,machiningtoleranceswere 0 005 in. ,and 119

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thealignmentoftheprobevolumetothesurfaceaccountforanuncertaintyofhalfthe probevolumethickness.Thesumoftheseerrorsarethebiaserrorsusedforuncertainty calculationsandareassumeduniformlydistributed.TheMonte-Carlomethodusesthe meanandstandarddeviationofeachmeasuredquantitytobuildadistribution,uniform forbiaserrorandnormalforLDVvelocitysamples.Thedistributionisthensampled randomlytocalculatedesiredquantities;thevelocityprolesinthiscase. Finally,thestaticpressurewasmeasuredalongthetestsectionlength.Forinternal ows,aconstantpressuredropacrossanitedistanceisindicativeoffullydeveloped ow.Inaddition,staticpressuremeasurementscanbehelpfulinassessingleakageand smalldisturbancesthatmayotherwisebehiddenwithinturbulentstreamwisevelocity. Duetotherelativesimplicityandspeedofthetest,measurementsweremadeatnotonly thetestReynoldsnumber, Re D h =2 25 E 5correspondingtoa M =0 22ow,butalso M =0 3 0 4and0 5asthesevaluescouldprovideinsightforfuturetestingathigher speeds. MeasurementsweremadeusingthestaticpressurewallinsertdescribedinSection 4.4 andareshowninFigure 4-8 .Duetolimitedmeasurementcapabilities,the29static pressuretapsweresampledintwosetsforeachrunconditionillustratedinFigure 5-17 ; taps2 15and16 29measuringset1(upstream)andset2(downstream),respectively. Thesetupwasswitchedtotheothersetwithoutturningo thetunneltomaintainsettled runconditions.Themostupstreampressuretap,port1,wasreservedforbothsetsasa referenceportforeachdi erentialmeasurement.Eachstaticpressuresetwassampled viaa1 psi di erentialPressureSystemsInc.(PSI)pressurescanner.Inturn,port1is measuredviaaPSI5 psi di erentialpressurescannerreferencingthetunnelstaticpressure ringatthenozzle.Pressuresweresampledat5 Hz syncedtotheGFIDtunnelcontroller forsimultaneousrecordingoftunnelconditions. Thelocalmeasuredpressureateachport, p i wasconvertedtoacoe cientof pressure, C p ,throughtheratioofthepressuredropfromthestaticringatthenozzle 120

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tolocalport,bythedynamicpressure C p = ( P i P # ) ( 2 P # M 2 (518) Thecompressibleversionofthedynamicpressurewasusedtoaccountforpotential compressibilitye ectsfromthehigherMachnumbertestsandisequivalenttothe traditionaldenition q = 1 2 & V 2 atincompressiblerunconditions( John&Keith 2006 ). TheresultsareshowninFigure 5-18 displayingthe29measuredvaluesasafunction ofdownstreamdistancewithcalculateduncertaintiesdisplayingaseeminglylinear downwardtrend.Thedatashowasmalldeviationfromthetrendnear x / D h =71 5,which increasesathigherMachnumbers.Thislocationcorrespondstothedownstreamacoustic linerinstallationportedge.LinearregressionofeachofthefourMachnumberswas appliedandtheresultant R 2 valueisdisplayedinthelegendoftheFigure 5-18 .Allthe datasetsarewelltbythelinearregressionwith R 2 valuesof0.96orgreater,indicating thepressuredropislinear,andthepressureandshearhavereachedanequilibrium. Theowmeasuredatatestsectioninstallationat x / D h =58 5wasdemonstratedto befullydeveloped.Threeexperimentsexaminedthestreamwisedevelopmentofcenterline velocity,comparativevelocityproles,andalinearpressuregradientwithinthetest section.Withthefullydevelopedassumptionconrmed,acoustictestingatthislocation canbeperformedunderaknownowenvironment. 5.3AcousticCharacterization 5.3.1Near-AnechoicReectionExperiment AcousticcharacterizationoftheGFIDcentersontheevaluationoftheprimary assumptioninmanyoftheimpedanceeductionmethodspresentedinSection 3.2 ,that thepressureeldintheductiscomposedofaplaneprogressivewave.Theassumption iscriticalforseveraleductionmethods,althoughdi culttophysicallyrealizedueto potentialimpedancemismatchesattheboundariesandareachangesintheduct.The windtunnelandacousticwaveguidecombinationinherenttotheGFIDdesignnecessitates 121

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adi usertoslowthehighspeedow,requiringanexpansionofthecross-sectional area.Similarly,turnsintheexhaustductingandothernon-idealitiesallpresent potentialreectionsourcesthatcanpropagateupstream,increasingthenoiseoor andcontaminatingmeasurements. Theanechoicdi userintroducedinSection 4.5 wasfabricatedtoreducetheupstream acousticpropagationgeneratedbydownstreamreectionsources.Thee ectivenessof theterminationwasexperimentallydeterminedbymeasuringthereectioncoe cientof theanechoicdi user,essentiallyarelativemeasureofthereectedacousticenergy.For comparisonthehardwallberglassdi user,exclusivelyutilizedforallLDVmeasurements, wasalsotested. RecallfromSection 4.5 andillustratedinFigure 4-10 ,thattheinternalboundaries oftheanechoicdi userarethemselveslocallyreactiveacousticliners.Thevariable honeycombdepthincreaseswithdownstreamdistanceandthushigherfrequencies areattenuatedrst.Lowfrequencyattenuationcorrespondingwithlargehoneycomb depthsincreasesfurtherdownstream.Eventhoughattenuationisafunctionoffrequency andaxialdistance,nomicrophonescanbeinstalledinthedi useritself.Instead,all measurementsaremadeupstreamwithinthetestsection,andthedi userislumped asasingleunknownimpedanceatthesampleplaneindicatedinFigure 5-19 .The e ectivenessoftheterminationwillbequantiedbymeasuringthereectedacoustic energy,determinedbythereectioncoe cientusingthetwo-microphonemethod(TMM) ( E1055-98 1998 ). Themeasurementwascarriedoutwithacleantestsection,i.e.noacousticliner installed,andthetestsectionwasinstalledatthefurthestdownstreampositionofthe GFID.TwoBruel&Kjr4938 1 / 4 in. microphoneswereinstalledinthedownstream auxiliaryportandaportableBruel&KjrPulseAnalyzerSystemwasusedforboth dataacquisitionaswellasacousticsignalgenerationviaaCrown XLS 1500amplier. Aperiodic-randomsignalwasgeneratedbetween300 3500 Hz with8 Hz bin 122

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width.Outputgainwasadjustedsuchthatthemeasuredpressureatthetestfrequency wasaminimumof10 dB abovethenoiseoor,asperthetestprotocoldescribedin ( E1055-98 1998 ).Themicrophoneswerethenrotated180 andthetestwasrepeatedin this"switched"conguration,eliminatingtheneedformicrophonephasecalibration. Theacousticpressuresatthetwomicrophones, P 1 and P 2 ,weresampledasafunction offrequency, =2 % f ,andareexpressedas P 1 ( ) + s, )= P + ( e j # ( + s ) + Re $ j # ( + s ) ) (519) and P 2 ( ) )= P + ( e j #* + Re $ j #* ) (520) respectively.Thereectioncoe cient, R ,iswrittenintermsofthetransferfunction, H 12 between P 1 and P 2 R = H 12 ( ) e $ j # s e j # s H 12 ( ) e j 2 # ( s + ) (521) Figure 5-20 showsthereectioncoe cient, R ,versusfrequencyforboththeberglass di userandtheanechoicdi user.Theverticalthicknessofeachcolorillustratesthe95% condenceintervalofthemeasurementasdeterminedbyaMonte-Carlosimulationbased ongeometricandambientthermodynamicconditionsdescribedin Schultz ( 2006 ).The anechoicdi userdemonstratesareectioncoe cientnearlyhalfthatofthehardwall berglassdi userwiththehighestreectioncoe cientsatlowfrequencies.Thefrequency dependentreectioncoe cientdemonstratesamaximumof0 19at300 Hz decreasing tolessthan0 13forhigherfrequencies.Incontrasttotheanechoicdi user,thehardwall berglassdi userdisplaysmuchlargerreectioncoe cients,upwardsof0 40at324 Hz Additionally,thehardwalldi userishighlyfrequencydependentdemonstratinglarge spikesinthedata,potentiallyduetoastructuralresonanceoftherelativelythin-wall berglassof0 175 in. Inbothcases,thecut-onfrequencyofthersthigher-ordermodeof thefacilityisevidentnear3400 Hz 123

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5.3.2DescriptionoftheAcousticLiners Allacousticexperimentsusedoneoftwolocallyreactiveacousticliners,shownin Figure 5-21 ,borrowedfromtheNASALaRCLinerPhysicsGroup.Duringtesting,the linersareinstalledinthetopacousticlinerinstallationportofthetestsection,described inSection 4.4 ,andheldinplacebyacustomfabricatedlinerholdersecuredonthetop byeightscrews.Anillustrationoftheinstallationandprimarydimensionsareshownin Figure 5-22 Therstlinerisaconventionalperforateacousticlinercomposedofathreestacked layers.Thetoplayerisaperforatefacesheet,shownindetailinFigure 5-23 A.The aluminumfacesheetis0 20 in. thick,with0 045 in. diameterholesinastaggeredhole patternwith0 125 in. hole-to-holespacing.Bothlinershaveexteriordimensionsof 2 50 16 36 in. ,overlappingthewallsofthetestsectionby0 25 in. oneachsidetoreduce edgee ectsontheow. Thesecondlinerhasidenticalouterdimensionsastheperforateliner,butusesa densewovenstainlesssteelwiremeshfacesheet,showninclose-upviewinFigure 5-23 B. Unliketheperforateliner,thewiremeshfacesheetisnotpermanentlybondedtothe honeycombcells.Duringtesting,thewiremeshwasheldinplacebyapplyingaspray adhesivetothesmalltopsurfaceofthehoneycombcellstokeepthefacesheetinplace. Tapewasappliedtotheleadingandtrailingedgesofthelinertoeliminatethepossibility ofairpenetratingunderneaththeliner. 5.4ImpedanceEductionUsingtheSingleModeMethod AsdescribedinChapter 3 ,therearemanymodelsandalgorithmsavailablefor impedanceeduction.The"innitewaveguidemethod"developedby Armstrong ( 1974 ), andlaterusedunderthenameofthesinglemodemethod(SMM)in Jones etal. ( 2004 b ) byNASAwaschosenandusedforimpedanceeductioninthisinvestigationduetothe simplicityandaccuracyinthepresenceofaplaneprogressivewave( Jones etal. 2004 b ). 124

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Theanechoictermination,testedinSection 5.3 ,minimizesupstreamacousticpropagation, aidingtheassumptionofasinglemodebyrestrictingupstreamreections. TheSMMisthesoleimpedanceeductiontechniqueusedinthisthesis.Additionally, thisthesisistherststudytousetheparticularwiremeshacousticlinerandthusno otherpublishedresultsareavailableforcomparison.Thereforeadditionalstepswereput inplacetovalidatethemethodandbuildcondenceintheresults.Theprocessisbased ontwocomparativeevaluationsusingexperimentaldatafrombothUFandNASALaRC facilitiespriortoapplyingthemethodtotheGFID.First,educedimpedanceofthewire meshwithzeromeanowintheGFIDusingtheSMMiscomparedtotestingthesame linerundernormalincidenceconditions.Thenormalincidencetestwasperformedin aseparatenormalincidencewaveguideusingthetwo-microphonemethod(TMM),an impedancetestingstandard E1055-98 ( 1998 ).Therefore,itwasdeemedimportantthat thepresentdatabecomparedtodatawithtrustedresultseventhoughthisrepresents alimitedcasebynegatingtheMachnumberdependanceoftheSMM.Forthesecond step,theSMMisappliedtopublishedbenchmarkgrazingowdatafrom Jones etal. ( 2005 )andtheresultsarecomparedwiththepaper'stwoadvancedFEM-basedmethods forimpedanceeduction.Withthecondencethatthedatareductionprocessprovided accurateresultsfromtheprocessvalidationsteps,theimpedanceofthewiremeshsample iseducedasafunctionoftestfrequency.Thewiremeshlinerexperimentaldataisshown forallfrequenciesandMachnumbersfollowedbythestepsusedtovalidatetheprocessing method.Eachevaluationmethodisdescribedwithresultsfollowing. 5.4.1ExperimentalSetupandApplicationoftheSingleModeMethod TheSMMeducestheimpedanceofanacousticlinerbymeasuringthecrossspectrum overthelinerrelativetoanupstreamreferencemicrophone.Thestudiespublishedby Armstrong ( 1974 )and Jones etal. ( 2004 b ),presentedinSection 3.2.2 ,bothusedtwo microphonesfortheirexperiments,astationarymicrophoneupstreamoftheliner,anda secondmicrophoneinstalledinatraversablesectionofthewalloppositetheliner.The 125

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GFIDtestsectionwasdesignedwithdiscretemicrophonelocationsinlieuofatraverse bartoreduceairleakageinherenttoaslidingtraverse( Jones etal. 2004 a ).Whilea traversebarhasmoreexibilityovermicrophonesamplelocations,theGFID'smultiple microphoneshavetheadvantageofallowingshorterruntimesthroughsimultaneous sampling,maintainingmoreconsistentrunconditionsoverthecourseoftheexperiment. Tenush-mountedmicrophoneswereinstalledinthealuminummicrophonewallof theGFID,positioningthemicrophonesalongthehorizontalmid-planeofthetunnelof thewallspanningthecentral8 5 in. ofthe16 36 in. longlinerwith0 85 in. spacing betweenmicrophones,asdepictedinFigure 5-22 .Measurementsweremadealong thecentralportionoftheacousticlinertominimizecontaminationfromevanescent modesgeneratedattheleadingandtrailingedgesduetoimpedancemismatches.A referencemicrophonewasinstalledattheupstreamsideoftherotationaltwo-microphone holderwithintheupstreamauxiliaryport,fourhydraulicductdiametersupstreamof theleadingedgeoftheliner.Includingthereferencemicrophone,atotalof11 1 / 4 in. microphoneswereused:nineGRAS40 BE andtwoBruel&Kjr4939.Allmicrophones wereindividuallycalibratedoutsideofthetunnelusinga94 dB 1000 Hz signalgenerated byaBruel&Kjr4231pistonphonesoundcalibratorandwerewithin1%ofmanufacturer calibratedspecications.Thepistonphoneonlyallowsforamplitudecalibration. DataacquisitionwasperformedbyLabVIEWrunningonaNationalInstruments(NI) PXI 1042 Q chassisviaa16channelNIPXI 4498DAQcard,simultaneouslysampling allmicrophones.AnAgilent33220 A functiongeneratorprovidedthewaveformtothe amplierandspeakerforacousticexcitationatdiscretefrequenciesfromf=500 3000 Hz in500 Hz increments.Thefunctiongeneratoramplitudewasadjusteduntil130 dB was measuredbythereferencemicrophone,recreatingtheconditionsdescribedby Jones etal. ( 2005 ).AllfrequenciesweretestedatfourbulkMachnumbers: M =0 0 0 1 0 3 0 5. Dataareacquiredatasamplingfrequencyof10,000Hzfor30seconds.Thedataare 126

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splitinto300blocksof1000sampleseach,resultingina10Hzbinwidth.Theblocksare averagedusingaHanningwindowwitha75%overlap. Figures 5-24 5-27 showthemeasuredcomplexpressureforalltestedMachnumbers, respectivelyascombinedplotsofunwrappedrelativephaseinblueandthesoundpressure level(ref.20 Pa )ingreen,versusthedistancefromtheleadingedgeoftheliner.Recall fromEquation 315 ,thattheSMMassumesasingledominantmodepropagatinginthe positivex-direction.Iftheseconditionsaremet,boththerelativephaseandSPLwill exhibitalineardecaydemonstratingalossofacousticenergy,whereinthe e j t system chosenmanifestsasanegativeslopeofbothvalueswithincreaseddistance. Themeasureddatapredominantlyfollowstheexpecteddownwardtrendexcluding afewcasesinwhichtheSPLdemonstratesadeviationfromalineartrend.Whileeach casewillbediscussedwiththeappliedlineartsandresultanteducedimpedancein Section 5.4.4 ,the f =500 Hz casemeritsnote.Qualitatively,itisevidentthatacross allrunconditions,includingquiescent,the f =500 Hz casedisplaysareasonablylinear relativephasewhereastheSPLvaluesareerraticwithnodiscernibledownwardtrends; evenintensifyingatsomelocations.IncreasedSPLvaluesimplyabreakdownofnecessary modelassumptions,includingthepresenceofupstreampropagatingwaves.However, similarresultsat f =500 Hz wereobservedanddiscussedintheliteratureby Jones etal. ( 2005 )andwereattributedtopossiblelongitudinalstandingwaves.Withtheinabilityof themodeltohandlesuchcases,the f =500 Hz casesareabsentfromsubsequentplots anddiscussions. Asthepressurewassampledatdiscretelocations,thetwotermswhichmakeup theaxialwavenumber, $ x ,areeasilycalculatedfromEquation 315 .Thetwoterms inEquation 315 assumeaconstantslopeandthusthedatawerettoalineina least-squaressense.AfewofthecasesdemonstratedariseinSPLnearthedownstream endoftheinstalledlinerandsoonlythelinearregionwasusedforlinearregression. Unlikethe f =500 Hz case,thesecasesareconsideredlimitedbutnotfailuresas 127

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theyallcontainaportionofthedatademonstratingthedownwardtrendindicativeof theexpectedattenuation.Uponcalculatingtheaxialwavenumberforeachcase,the impedancevaluewasthenextractedfromEquations 316 and 317 .Bothimpedance resultspresentedandtheimplementationoftheSMMperformedherewillbereferred toas"UFSMM"fortheremainderofthisthesis.Table 5-3 providesthemeaneduced impedancevalues,theresultsareplottingwithuncertaintyforeachmethodintheir respectivesections. 5.4.2ValidationoftheSingleModeMethodViaNormalIncidenceUnder ZeroMeanVelocity Therstmethodcomparestheeducedimpedanceforthecaseofzeromeanow againstanASTMstandardforimpedanceeductioninanormalincidenceimpedance tube.Thetwo-microphonemethodhastheadvantageofcomputationalspeedand simplicity,howeverthemethodinherentlyassumesaquiescentenvironmentandthusany comparisonsmustbeperformedwithoutow. Thewiremeshacousticlinerwassecuredtotheendofanormalincidencetube(NIT) atUF,asillustratedinFigure 5-28 .TheNITisafullyenclosedhard-walledacoustic waveguidesealedononeendbyaspeakerandtheotherbythesampleundertest.The NIThasasquare25 4 25 4 mm crosssectionandis96 cm inlengthwith1 in. thick aluminumwalls.ExcitationwasprovidedbyaBMS4590 P speakeruptotherstcut-on modeofthewaveguideat6 7 kHz .Signalgenerationanddataacquisitionwereperformed byaCrown XLS 1500amplierandaBruel&KjrPulseAnalyzerSystem.Inputwas periodic-randomnoisewith ( f =8overthefrequencyrangeof300 Hz to6 7 kHz FollowingASTMstandard E1055-98 ( 1998 ),twoBruel&Kjr4138 1 / 8 in. microphonesareinstalledinamicrophonerotationplug,spaced s =20 7 mm apart and ) =32 1 mm fromthesample.Thetestwasrepeatedwiththetwomicrophones rotated180 toaverageoutsmallamplitudeandphasedi erencesandthegeometricmean ofthetwocasesisused.ThemethodologybehindtheTMMwasdetailedinSection 5.3 128

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Thecomplexspecicacousticimpedanceoftheunknownsample, Z N ,isrelatedtothe characteristicimpedanceofthemedium, Z 0 ,andthereectioncoe cient R = Z N Z 0 Z N + Z 0 (522) Theunknownspecicacousticimpedanceofthesampleisnormalizedbythecharacteristic impedanceofair, & 0 c 0 ,andcanbesplitintothetherealandimaginarycomponents, = Z N & 0 c 0 = + i 0 (523) where isthenormalizedspecicacousticresistanceand 0 isthenormalizedspecic acousticreactance.ThenormalizedacousticimpedancevaluesusingtheTMMare comparedtothe M =0 0UFSMMcaseinFigure 5-29 TheplotsdemonstratethattheUFSMMmatchesthenormalizedimpedancevalues oftheTMMwithinexperimentaluncertainty.Bothmethodsagreeontheresonant frequency, f res ,ofthelinerundernoowconditionsdenedwherethenormalizereactance displaysapositivezero-crossingatapproximately f res =2500 Hz .Thecomparisontothe NITprovidesinitialcondenceofthefacilityanddatareductionprocessforaspecialcase withnograzingow. 5.4.3ValidationoftheSingleModeMethodViaBenchmarkDataWith MeanFlow ThesecondmethodemploysthefullSMMalgorithmtestingtheMachnumber dependencyatmultiplefrequenciesversuspublishedbenchmarkdatafrom Jones etal. ( 2005 ).Thedataarepresentedin Jones etal. ( 2005 )asrelativephaseandSPLvalues measuredwithcorrespondingdistancefromtheliner'sleadingedge. Theacousticlinertestedin Jones etal. ( 2005 )wasahigh-resistanceliner,designated theCT57.Insteadofeitherawiremeshorperforatefacesheetatophoneycombcells, thelinerwascomposedofnarrow0 06 mm diameterceramictubes85 6 mm deep, rigidlyterminatedbyahardwallbackplateprovidingsupportandenablingalocally 129

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reactiveboundaryconditionbyacousticallyisolatingeachcell.Theceramictubes, whilenotdirectlyapplicabletoreal-worldenginenacelleapplications,providealinear responseforarangeofMachnumbersandsoundpressurelevels,whichisusefulforfacility benchmarkingandcomparisons.Thereaderisdirectedto Jones etal. ( 2005 )foradditional detailsanddiscussionregardingtheCT57. ThebenchmarkdatawastakenintheGITfacilitydetailedinSection 3.3.4 Jones etal. ( 2005 )includeddatafromtheCT57forthreeSPLvalues,sixMachnumbers,and overthefrequencyrangefrom500 3000 Hz .Inthisthesis,onlythe M =0 255caseat 130 dB wasusedastheMachnumberisnearesttothetestconditionspresentedinSection 5.4.4 .TheresultsfromthebenchmarkdatausingtheUFSMMcodewerecompared againstthepublishedimpedanceresultsgeneratedbytwoFEMbasedapproaches, the"2D-FEM",andthe"Q3D-FEM".Theresultswithcorrespondingmeasurement uncertaintyoftheUFSMMdataareshowninFigure 5-30 .Notethattheuncertainty estimatesshownaresolelybasedonthe95%condenceofthelinearregressionasno informationregardingrunconditionswasavailableforthebenchmarkcase. SimilartotheGFIDdata,the f =500 Hz casefailedtoproduceareasonabletand wasexcludedfromFigure 5-30 andensuingdiscussion.TheUFSMMcodecapturesthe overalltrendsofboththenormalizedresistanceandreactance,althoughthenormalized resistanceisslightlyover-predicted.TheUFSMMdoescaptureboththeresonanceand anti-resonanceofthelineratthepositiveandnegativezero-crossingofthenormalized reactance,respectivelyatapproximately f =1000 Hz and f =2000 Hz .Thelargest discrepancybetweenallthemethodsoccursneartheanti-resonance. Jones etal. ( 2005 ) notedthatthetwoFEM-basedmodelsdemonstratedadisparityatanti-resonancein contrasttotheotherwiseexcellentmatching. Thebenchmarkdataprovidedagoodcomparisontopublisheddatatakeninawell documentedandtrustedfacility.Thecomparisonprovidescondenceinthemethodology 130

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andimplementationoftheSMMalgorithmandtheGFIDtomoveforwardtoeducean untestedacousticliner. 5.4.4ExperimentalImpedanceEductionofaWireMeshAcousticLinerin theGrazingFlowImpedanceDuct AftervalidatingtheGFIDdataanalysisprocess,thesamemethodwasappliedtothe remainingdatatakenintheGFIDforthepreviouslyuntestedwiremeshliner.Theresults ofthe M =0 0casearerepeatedalongwiththeowcasesof M =0 1 0 3and0 5, showninFigure 5-31 .Theuncertaintyestimatesindicatethe95%condenceboundsof theextractednormalizedcompleximpedancevaluesincludingtunnelrunconditions. InFigure 5-31 thelargestuncertaintyacrossallMachnumbersoccursat f = 1000 Hz ,thelowestfrequencycasedemonstratingalineart.However,thedisparity betweenthe f =1000 Hz caseandtheremainingfrequenciesdecreaseswithhigherMach number.Qualitatively,theraw f =1000 Hz SPLtrendsshownininsertBofFigures 5-24 5-27 demonstratethelargestdeviationfromalineartrendwithincreasedMachnumber andthustheerrorinlinearregressionwashigher.The M =0 5caseacrossallfrequencies demonstratesthelargesterror,althoughthenormalizedresistancestaywithinthepositive domain. InspectionoftherawdataplottedinFigures 5-27 A-Fdemonstrateanincrease inSPLtowardthedownstreamendofthelinerforallcasesindicativeofupstream propagatingwaves.Additionally,thehighersheare ectsassociatedwithlargerelative Machnumbermaybeinvalidatingthestrictuniformowassumptioninherenttothe modelbyintroducingrefractione ectsnearthewalls( Nayfeh etal. 1975 ).Toallowfor additionalinsightanddiscussionofthetrendsandunderlyingphysicsofthenormalized impedanceresults,thevaluesarerepeatedinFigure 5-32 excludingthequestionable M =0 5case. Theexclusionofthe M =0 5inFigure 5-32 allowsforrescalingofthedatato moreclearlyemphasizetrends.Thenormalizedreactancedecreaseswithincreased 131

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Machnumberpushingthezero-crossingandimplicativelinerresonance, f res ,tohigher frequenciesfromapproximately f res =2500for M =0 0topast f res =3000 Hz for M =0 3.Incontrast,thenormalizedresistanceincreasedwithhigherMachnumber, howeverwasrelativelyinsensitivetoexcitationfrequency.Thepressureeldmeasured withthewiremeshlinerinstalledprovidedalinearslopeindicativeofamorestrongly dominantacousticmodecomparedtotheperforatelinerandthusmoreapplicableforthe applicationoftheSMM.UnliketheCT57lineroftheNASAbenchmarkdatainSection 5.4.3 ,theanti-resonancewasbeyondthecut-onfrequencyoftheGFID. 5.5DragContributionByAnAcousticLinerWithAcousticExcitation Withthetunnelcharacterizedandshowntobecapableofeducingtheimpedanceof anacousticlinerunderow,ane ortwasmadetoquantifytheinuenceofanacoustic linersubjecttoacousticexcitationontheshearstressofthesurroundingow.This inuencewasstudiedthroughthreeindirectvelocityproletechniquesusingLDVvelocity measurements:acenterlineboundarylayercurvettingtechnique,momentumintegral analysisofcenterlinecross-ductproles,andahalf-ductcontrolvolumeanalysis.Eachof theexperimentswasperformedbothwithandwithoutanacousticlinerinstalledfordirect comparison.Allvelocitymeasurementswereperformedat x / D h =63and72. TheLDVvelocitymeasurementsrequiredoilbasedseedingandasaresultneitherthe anechoicdi usernorthewiremeshlinerusedfortheacousticimpedanceeductiontests wereabletobeused.Insteadthepreviouslydescribedperforateacousticliner,introduced inSection 5.3.2 wasinstalled. Itwasassumedthatthelargestinuenceofthelinerwouldbedeterminedthrough acousticexcitationatthelinerresonantfrequency.Asthelinerhadnotbeentested inow,theresonantfrequencywasunknown.TwoGRAS40 BE 1 / 4 in. microphones wereinstalled,oneineachoftheauxiliaryports,upstreamanddownstreamofthe installedacousticliner.Acousticexcitationanddataacquisitionwereprovidedbya Bruel&KjrPulseAnalyzerSystemandaCrown XLS 1500amplierwithinputof 132

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periodic-randomnoiseof800discretefrequenciesfrom300 Hz to3 5 kHz .Thetestwas operatedat Re D h =2 25 E 5.Thecoherencebetweenthetwomicrophonesisplottedin Figure 5-33 .Thecoherencedisplaysa500 Hz dropsurrounding1750 Hz .Thelackof coherencebetweenthetwomicrophonesindicatesthatthethisfrequencygapissubject tothemostlossinacousticenergy.Thevalueof f =1750 Hz wasassumedtobethe resonantfrequencyandtheallsheartestingwasperformedatthisvaluewitha130 dB (ref.20 Pa )signalasmeasuredbytheupstreammicrophone. 5.5.1Two-DimensionalBoundarylayerapproximationusingSpaldingFit Thedownstreamboundarylayerproleonthesamplesidewasextractedfromthe cross-ductvelocityprolesupto y = D h / 2 .Theextractedvelocityvaluesandassociated wall-normalpositionswereinputtoacodethatiterativelyappliedthemtotheSpalding turbulentboundarylayert,Equation 225 ,solvingforthefrictionvelocity, u % = $ + w / $ andwallo setdistance.TheprocesswasaddedintoaMonte-Carlosimulationtobuild upadistributionoffrictionvelocitiesadjustingthenormallydistributedvelocityand uniformlydistributedpositionateachacquisitionlocation( Coleman&Steele 2009 ). TheSpaldingtisnotapplicabletotheouterlayerandthusonlywall-normalpositions correspondingto y + valueslessthan1000wereusedforparameterextraction( White 2006 ). Thenon-dimensionalboundarylayerprolesareshowninFigure 5-34 ,wherethe shadedregionsindicatestheuncertaintyboundsfromtheMonte-Carlosimulation.Table 5-4 providesthevaluesforvariablesextractedfromthe2Dboundarylayert.The skinfrictioncoe cientresultsforthehardwallandacousticlineroverlapwithinthe experimentaluncertainty. 5.5.2Momentum-Integral Thesecondmethodusesthefullcross-ductproletoapproximatetheskinfriction coe cientwithavariantoftheclassicmomentumintegralequation.Originallyproposed byKarman,themethodisgenerallyappliedtoatplateboundarylayers,howevercanbe 133

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usedwithinternalowswhenwrittenas( Anselmet etal. 2009 ) C f =2 d dx H +2 & U 2 c dp dx (524) notingthat and H aretheboundarylayermomentumthicknessandshapefactor, respectively.Unliketheboundarylayercurvet,thismethodtakesintoaccountthe pressuredropacrosstheliner. Thestaticpressureinthetestsectionwasmeasured,followingthestepsdescribedin Section 5.2.2 .TheresultsareshowninFigure 5-35 overlaidwiththedataofFigure 5-18 whennolinerwasinstalled.Theverticaldashedlinesindicatethelocationoftheleading andtrailingedgeoftheacousticliner.Thestaticpressuremeasuredbothupstreamand downstreamofthelinerappeartomatchthenolinercase.However,acrosstheliner thereisanotablepressuredi erencebetweenthetwocases.Thevaluesof and H for Equation 524 areextractedfromthedownstreamvelocityproleunderthesubstantiated assumptionthattheowisfullydeveloped. TheresultsfromthemomentumintegralmethodarelistedinTable 5-5 .Theskin frictionvalueswithintheuncertaintyrangearelargelymeaninglessastheencompass theynon-realnegativeskinfrictionimplyingowreversalaswellasskinfrictionvalues indicativeofamuchhigherspeedow.Theresultsindicatethatthemethodismore sensitivetolargeuncertaintiesintheinputvariables. 5.5.3ControlVolumeAnalysis Thenalmethodtoquantifythesheare ectappliedacontrolvolumeapproachand integratedthemomentumuxthroughtwocontrolsurfacesboundingtheacousticliner, illustratedinFigure 5-36 .Theapplicationofacontrolvolumeanalysiswaslessdependent onnear-wallinuencecomparedtothecross-ductprolemethods,asthemajorityofthe momentumislocatedinthecentralcoreoftheduct. Thecontrolsurfacesweredenedbyagridpatternwithspacingbasedon Gessner etal. ( 1977 ),illustratedinFigure 5-37 ,emphasizingthecentralcoreoftheow.Due 134

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tothestablesymmetryplanesimposedfromsecondaryowpatternsinaturbulent channelowpreviouslydiscussedinChapter 2 ,onlyasingleoctetwouldbenecessaryto measure.However,astheinuenceoftheacousticlinerononewallisspecicallyunder investigationnosuchassumptioncouldbemadeandonlytheverticalsymmetryplane whichbisectsthelinerwasassumedaccurate. Theintegralformoftheconservationofmomentuminthestreamwisedirectionunder asteadyowassumptioncanbeexpressedas, F x = + w A + + P 1 A 1 P 2 A 2 = cs 1 u x 1 & 1 v 1 dA 1 + cs 2 u x 2 & 2 v 2 dA 2 (525) where A + isthewettedareatheshearstressactsupon.Thenumberedsubscriptsrefer tothecontrolsurfacesillustratedinFigure 5-36 .Equation 525 indicatesthattheshear forceappliedattheboundariesisbalancedbythesumofthepressuredropandlossto momentum. Inapurelyincompressiblefullydevelopedow,themomentumtermswouldcancel outandpressurewouldbalanceshearstressdirectly.However,themeasurement determinesiftheacousticlinerimposesanadditionallossmechanismimposedbythe acousticlinerunderexcitation.Thepressureandmomentumatthestreamwisecontrol surfacesactonareas A 1 and A 2 ofdimensions H H ,where H isthewallheightand widthofthesquareduct.Theshearstressactsonallfourwallsoveradistance L .Writing outtheareasandnotingthatthevelocitynormaltothecontrolsurfaceandtherelative velocityareequalateachlocation, F x = + w (4 HL )+( P 1 P 2 ) H 2 =2 + H / 2 0 + H 0 & 2 u 2 2 dzdy 2 + H / 2 0 + H 0 & 1 u 2 1 dzdy. (526) Theassumedverticalsymmetryplaneat y = H / 2 allowsforintegrationononlyhalfthe ductwidth;thisvalueisdoubledtoencompassthefullductcross-section.Equation 526 135

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canberewrittentoisolate + w ,andnotingthat $ p = P 1 P 2 + w = H 2 4 HL $ p + 2 4 HL 3 + H / 2 0 + H 0 & 2 u 2 2 dzdy + H / 2 0 + H 0 & 1 u 2 1 dzdy 6 (527) Theshearstressiscastintermsofthenon-dimensionalcoe cientoffriction, C f ,by divingeachtermofEquation 527 bythedynamicpressure.Thenalsimpliedequation isthenwrittenas C f = H 4 L $ p ( 2 p # M 2 + 1 2 HL 1 ( ( 2 p # M 2 ) 3 + H / 2 0 + H 0 & 2 v 2 2 dzdy + H / 2 0 + H 0 & 1 v 2 1 dzdy 6 (528) ThemeasuredvelocitycontoursaredisplayedinFigure 5-38 .Theimagesillustrate thesymmetrichigh-velocitycentralcorewithslightbulgingouttowardtheduct cornersindicativeofsecondaryvelocityowe ects.Thesamedataispresentedfrom analternativeperspectiveinFigure 5-39 withhighervelocitiesbothshownincolor gradientandincreasedelevation.Thisviewmoreclearlyillustratesthesecondaryvelocity e ectsat z / D h =0 5andthecentralcorevelocity. Similartothe2Dcenterlineprole,eachpositionandvelocitywereperturbedto generateadistributionofsamples.Ano-slipvelocityconditionwasimposedontunnel boundariesandlinearlyttothenearestsampledlocation.Unlikethecenterline,asthe LDVprobevolumewastranslatedinboththe y and z plane,thenon-symmetricsize ofthe1Dprobevolumehadtobetakeintoaccountbyallowingthez-dimensiontobe perturbedtothefull372 m lengthoftheprobevolumewhilethey-dimensionwasonly perturbedwith58 m ,asdeterminedbyEquations 57 and 56 ,respectively. TheresultsofthenumericalintegrationareincludedinTable 5-6 .Similartothe momentum-integralandboundarylayercurvetapproaches,theskinfrictionvaluesof theacousticlinercontrolvolumeandthehardwalldonotdemonstrateadiscernible di erence. 136

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5.5.4ConcludingRemarksofFluidDynamicResults Thesheare ectofanacousticlinerwithresonantacousticexcitationwasdetermined throughthreevelocityprole-basedtechniques:a)curvettinga1Dboundarylayer prole,b)applyingamomentum-integralanalysistoacrossductprolesupand downstreamoftheacousticliner,andc)viaacontrolvolumeanalysisthroughahalf-duct plane.TheresultsofallshearexperimentsarelistedinTables 5-4 5-5 ,and 5-6 .Theskin frictionresultsofthethreeexperimentswiththeacousticlinerinstalledandexcitedatthe liner'sresonantfrequencyoverlapthoseofthehard-wallcasewithinexperimentalerror. Theindirectvelocityprolemethodsappliedwereunabletodemonstratethatthe installationandexcitationoftheacousticlinerhadanydiscerniblee ectstotheshear contribution.Astheshearinuenceoftheacousticlinerisafunctionofthewettedarea, alongerlinermayhavealargerimpact.Thefutureapplicationofadirectorquasi-direct measurementoftheshearstressbyimplementingaMEMSoatingelementsensoror oil-lminterferometrymayprovebenecial. Table5-1.Maximumnegativevelocityusingthe120 mm lens ProbecongurationLowVelocity[ m / s ]HighVelocity[ m / s ] 3-beam-54.26314.6 4-beam-38.61223.8 Table5-2.Maximumnegativevelocityusingthe400 mm lens ProbecongurationLowVelocity[ m / s ]HighVelocity[ m / s ] 3-beam-179.91043 4-beam-127.2737.7 137

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Table5-3.UFSMMeducedimpedancevaluesofawiremeshlinershowninFigure 5-31 M =0 0 M =0 1 M =0 3 M =0 5 Freq.[ Hz ] -0-0-0-0 10001.29-1.111.07-0.541.61-1.357.52-1.64 15000.88-0.951.10-1.461.86-2.874.52-3.31 20000.81-0.481.06-0.791.83-1.712.21-1.31 25000.79-0.031.19-0.092.02-0.661.93-1.41 30000.930.271.650.402.32-0.142.60-1.13 Table5-4.2Dboundarylayerapproximationoffrictionvelocityandshearstress WallcongurationFrictionVelocity[m/s]Shearstress[Pa]C f 10 $ 3 HardWall3.08-3.3211.22-13.043.30-3.92 Acousticliner3.05-3.2511.37-12.253.36-3.91 Table5-5.Momentum-integralanalysisvariableapproximations WallcongurationC f 10 $ 3 HardWall-1.20-4.50 Acousticliner-1.04-5.76 Table5-6.Controlvolumeanalysisforestimationoffrictioncoe cient WallcongurationC f 10 $ 3 HardWall4.59-6.57 Acousticliner3.51-5.24 138

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Figure5-1.BasicprincipalandsetupoflaserDopplervelocimetry(LDV),adaptedfrom DantecDynamics.IntegratedSolutionsinLaserDopplerAnemometry. Publication318 v 1 ( Page 3 ,Figure 1 A B Figure5-2.Dopplerfrequencyworkspacewithresultantvelocity. 139

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A B Figure5-3.Beamcombinercomparisonandworkings. A B Figure5-4.3-beamand4-beamcongurationoftheprimaryprobehead. 140

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Figure5-5.Velocityrangefordi erentprobecongurations 0 2 4 6 8 10 2 4 6 8 10 Frequency [kHz] Particle diameter [ m] First higher order mode Mineral Oil Olive Oil / H 2 O Figure5-6.Cut-o frequencyasafunctionofparticlediameter. 141

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Figure5-7.LDValignmenttunnelprocedureusingmatchedintensitiesoftwolaserbeams athinopaqueshimtoaligntheprobeheadplanetothetestsectionoor. 142

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Figure5-8.IllustrationoftheLDVbeampathsthroughtheopticalwindowforan arbitraryo setangle, 3 .Eachlabeledangleanddistancearecalculatedbythe modeltodeterminetheo setdistanceoftheo -axisprobevolumetothe expectedprobelocationasdeterminedbythereceivingoptics. 143

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A B Figure5-9.A)Thecalculatedbeampathswith38 mm spacingmodelingthe2-beamor 4-beamprobeheadthrougha120 mm focallengthtransmittinglenswitha 3 =60 o setangle.Thesimulated27 94 mm thickwindowisdisplayedasthe blueboxmatchingthethicknessoftheGFIDopticalwindow.B)Thecropped viewofcalculatedbeampathsshowingtheo setbeamcrossingtothe expectedlocationdictatedbythefocusofthereceivingoptics.Alldimensions arebasedonreferencelocationofthetransmittingbeamnearesttothe window. 144

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A B C D Figure5-10.Theseparationdistancebetweenthetrueprobevolumeandtheassume locationbasedonreceivingopticfocuspoint.Theverticalredlineindicates themaximumangle,measuredfromthewallbeforethetwoprobeheads couldinteract.Thehorizontalblacklinesindicateswheretheseparationisat least50%probevolumeandthisasignalispossible.Eachplotisfora di erenttransmittinglensfocallengthandprobeheadconguration combinationofthefollowing:A)120 mm ,4-beam,B)120 mm ,3-beamC) 400 mm ,4-beam,D)400 mm ,3-beam. 145

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Figure5-11.Testsectioninstallationlocationforentranceregionmeasurementsfully developedmeasurementsdownstream.Thecoordinatesystemisplacedon thetunnelooratthelocationmarkedas x/D h =0. Figure5-12.Crossductvelocityandintegratedbulkvelocitywithcorrespondingerrors measuredat x / D h =2 5. 146

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Figure5-13.Centerlinevelocitynormalizedbybulkvelocityasafunctionofdownstream distanceinoftheentranceregionoftheGFIDcomparedagainstsimilardata from Gessner etal. ( 1977 )and Melling&Whitelaw ( 1976 ). Figure5-14.TheGFIDentranceregionexperimentalvelocitydataexpressedasratioof centerlinetobulkvelocityasafunctionoffunctionfrom Anselmet etal. ( 2009 ).Dataandtarecomparedtothesimilarexperimentaldatafrom Gessner etal. ( 1977 )and Melling&Whitelaw ( 1976 ). 147

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Figure5-15.Normalizedcenterlinevelocitymeasurementsinthefullydevelopedregion. Shadedregionindicatesthe95%condenceintervalofthedata. 148

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0.5 0.6 0.7 0.8 0.9 1 1.1 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 U/U CL y/h GFID x/Dh = 63 95% Confidence GFID x/Dh = 72 95% Confidence AB Figure5-16.(A)Fullcross-ductvelocityprolesat x / D h =63and72demonstrating matchedproleswithinexperimentaluncertaintyand(B)Half-ductvelocity prolesat x / D h =63and72comparedtoreferencedataoftwohigh-Reynolds numberfullydevelopedchannelowfrom Gessner ( 1964 ). 149

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Figure5-17.Experimentalsetupofthestaticpressureexperimentwherethepressureport windowissampledintwosets Figure5-18.CpasafunctionofMachnumberwitherrorbars. 150

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Figure5-19.Experimentalsetupofthetwo-microphonemethodapplicationformeasuring thereectioncoe cientoftheanechoicdi user. 500 1000 1500 2000 2500 3000 3500 0 0.1 0.2 0.3 0.4 0.5 Frequency [Hz] R Fiberglass Diffuser Anechoic Diffuser Figure5-20.Reectioncoe cientoftheanechoicdi userascomparedtothehardwalled berglassdi userusingthetwo-microphonemethodwithperiodic-random noiseinput. 151

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Figure5-21.Photographofthetwoacousticlinerstested,aresistivelinerwithhighly resistivefacesheet(background)andaperforatedfacesheetresonantliner (foreground).Bothacousticlinersare2 5 16 36 in. 152

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Figure5-22.GFIDtestsectionwithremovablewallsandreplacementwindowsallowfor fullopticalandsensoraccess. A B Figure5-23.Closeupviewofperforate(A)andwiremeshfacesheet(B) 153

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0.1 0.15 0.2 0.25 0.3 6 4 2 Liner distance [m] [rad] 0.1 0.15 0.2 0.25 0.3 126 127 128 SPL A 0.1 0.15 0.2 0.25 0.3 5 0 5 Liner distance [m] [rad] 0.1 0.15 0.2 0.25 0.3 120 125 130 SPL B 0.1 0.15 0.2 0.25 0.3 10 5 0 5 Liner distance [m] [rad] 0.1 0.15 0.2 0.25 0.3 110 115 120 125 SPL C 0.1 0.15 0.2 0.25 0.3 10 5 0 Liner distance [m] [rad] 0.1 0.15 0.2 0.25 0.3 80 100 120 SPL D 0.1 0.15 0.2 0.25 0.3 10 5 0 Liner distance [m] [rad] 0.1 0.15 0.2 0.25 0.3 110 120 130 SPL E 0.1 0.15 0.2 0.25 0.3 10 0 10 Liner distance [m] [rad] 0.1 0.15 0.2 0.25 0.3 120 125 130 SPL F Figure5-24.Thephase(leftaxisandbluecircles)andSPL(rightaxisandgreen diamonds)(ref.20 Pa )for M =0 0:(A) f =500 Hz ,(B) f =1000 Hz ,(C) f =1500 Hz ,(D) f =2000 Hz ,(E) f =2500 Hz ,(F) f =3000 Hz 154

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0.1 0.15 0.2 0.25 0.3 4 3 2 Liner distance [m] [rad] 0.1 0.15 0.2 0.25 0.3 126 127 128 SPL A 0.1 0.15 0.2 0.25 0.3 2 0 2 4 Liner distance [m] [rad] 0.1 0.15 0.2 0.25 0.3 122 124 126 128 SPL B 0.1 0.15 0.2 0.25 0.3 6 5 4 3 2 1 0 1 2 Liner distance [m] [rad] 0.1 0.15 0.2 0.25 0.3 114 116 118 120 122 124 126 128 130 SPL C 0.1 0.15 0.2 0.25 0.3 10 5 0 Liner distance [m] [rad] 0.1 0.15 0.2 0.25 0.3 80 100 120 SPL D 0.1 0.15 0.2 0.25 0.3 10 5 0 Liner distance [m] [rad] 0.1 0.15 0.2 0.25 0.3 110 120 130 SPL E 0.1 0.15 0.2 0.25 0.3 10 0 10 Liner distance [m] [rad] 0.1 0.15 0.2 0.25 0.3 120 125 130 SPL F Figure5-25.Thephase(leftaxisandbluecircles)andSPL(rightaxisandgreen diamonds)(ref.20 Pa )for M =0 1:(A) f =500 Hz ,(B) f =1000 Hz ,(C) f =1500 Hz ,(D) f =2000 Hz ,(E) f =2500 Hz ,(F) f =3000 Hz 155

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0.1 0.15 0.2 0.25 0.3 4 3 2 1 Liner distance [m] [rad] 0.1 0.15 0.2 0.25 0.3 126 127 128 SPL A 0.1 0.15 0.2 0.25 0.3 8 6 4 2 Liner distance [m] [rad] 0.1 0.15 0.2 0.25 0.3 124 125 126 127 SPL B 0.1 0.15 0.2 0.25 0.3 4 3 2 1 0 1 2 Liner distance [m] [rad] 0.1 0.15 0.2 0.25 0.3 121 122 123 124 125 126 127 SPL C 0.1 0.15 0.2 0.25 0.3 6 5 4 3 2 1 0 1 Liner distance [m] [rad] 0.1 0.15 0.2 0.25 0.3 108 110 112 114 116 118 120 122 SPL D 0.1 0.15 0.2 0.25 0.3 8 6 4 2 0 Liner distance [m] [rad] 0.1 0.15 0.2 0.25 0.3 110 115 120 125 130 SPL E 0.1 0.15 0.2 0.25 0.3 10 5 0 Liner distance [m] [rad] 0.1 0.15 0.2 0.25 0.3 120 125 130 SPL F Figure5-26.Thephase(leftaxisandbluecircles)andSPL(rightaxisandgreen diamonds)(ref.20 Pa )for M =0 3:(A) f =500 Hz ,(B) f =1000 Hz ,(C) f =1500 Hz ,(D) f =2000 Hz ,(E) f =2500 Hz ,(F) f =3000 Hz 156

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0.1 0.15 0.2 0.25 0.3 3 2.5 2 1.5 1 Liner distance [m] [rad] 0.1 0.15 0.2 0.25 0.3 124 126 128 130 132 SPL A 0.1 0.15 0.2 0.25 0.3 6 4 2 Liner distance [m] [rad] 0.1 0.15 0.2 0.25 0.3 125 130 135 SPL B 0.1 0.15 0.2 0.25 0.3 2 0 2 4 Liner distance [m] [rad] 0.1 0.15 0.2 0.25 0.3 122 123 124 125 SPL C 0.1 0.15 0.2 0.25 0.3 4 3 2 1 0 1 2 Liner distance [m] [rad] 0.1 0.15 0.2 0.25 0.3 121 122 123 124 125 126 127 SPL D 0.1 0.15 0.2 0.25 0.3 10 5 0 5 Liner distance [m] [rad] 0.1 0.15 0.2 0.25 0.3 120 122 124 126 SPL E 0.1 0.15 0.2 0.25 0.3 10 8 6 4 2 Liner distance [m] [rad] 0.1 0.15 0.2 0.25 0.3 110 112 114 116 118 SPL F Figure5-27.Thephase(leftaxisandbluecircles)andSPL(rightaxisandgreen diamonds)(ref.20 Pa )for M =0 5:(A) f =500 Hz ,(B) f =1000 Hz ,(C) f =1500 Hz ,(D) f =2000 Hz ,(E) f =2500 Hz ,(F) f =3000 Hz 157

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Figure5-28.Experimentalsetupofthenormalincidencetube(NIT)illustratingthe two-microphonemethodofimpedanceeduction. 0 1000 2000 3000 4000 0 2 4 Frequency [Hz] TMM UF SMM 0 1000 2000 3000 4000 4 2 0 Frequency [Hz] Figure5-29.Normalizedresistance(top)andreactance(bottom)ofwiremeshacoustic linerresultscomparingthetwo-microphonemethodoftheNITtotheGFID usingtheSMM. 158

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500 1000 1500 2000 2500 3000 0 5 10 15 Frequency [Hz] 2D FEM Q3D FEM UF SMM 500 1000 1500 2000 2500 3000 5 0 5 Frequency [Hz] Figure5-30.Comparisonresultsofeducednormalizedspecicacousticimpedanceviathe UFSMM,the2D-FEM,andtheQ3D-FEMimpedanceeductiontechniques appliedtobenchmarkdatafrom Jones etal. ( 2005 )ofatubularceramic resistivelinertestedat M =0 255. 159

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500 1000 1500 2000 2500 3000 3500 5 0 5 10 Frequency [Hz] Ma=0.0 Ma=0.1 Ma=0.3 Ma=0.5 500 1000 1500 2000 2500 3000 3500 6 4 2 0 2 Frequency [Hz] Figure5-31.Normalizedspecicacousticimpedanceofthewiremeshacousticlinertested intheGFIDat M =0 0 0 1 0 3 and0 5.Impedanceeductionperformed viaUFSMM. 160

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500 1000 1500 2000 2500 3000 3500 2 0 2 4 Frequency [Hz] Ma=0.0 Ma=0.1 Ma=0.3 500 1000 1500 2000 2500 3000 3500 4 3 2 1 0 1 Frequency [Hz] Figure5-32.Normalizedspecicacousticimpedanceofthewiremeshacousticlinertested intheGFIDat M =0 0 0 1 and0 3.ImpedanceeductionperformedviaUF SMM. 161

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0 500 1000 1500 2000 2500 3000 3500 0 0.2 0.4 0.6 0.8 1 Frequency [Hz] Coherence 1750 Hz Figure5-33.CoherenceofperforatelineratM=0.22. 162

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Figure5-34.Spalding2Dboundarylayerproletforhardwallandacousticliner installation. Figure5-35.Pressurecoe cientwithliner. 163

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Figure5-36.Schematicofthe2Dcontrolvolumeandphysicalsetup. Figure5-37.Gridpatternindicating1DLDVmeasurementlocationsinthehalf-duct plane.Measurementsweremadeat x / D h =63and72.Dashedlinesindicate expectedsymmetryplanes. 164

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Figure5-38.Controlvolumevelocity[m/s]contourmaps,A)Upstreamhardwall,B) Upstreamacousticliner,C)Downstreamhardwall,D)DownstreamAcoustic liner. 165

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Figure5-39.Controlvolumesurfacemapvelocityin[m/s],A)Upstreamhardwall,B) Upstreamacousticliner,C)Downstreamhardwall,D)DownstreamAcoustic liner. 166

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CHAPTER6 CONCLUSIONANDFUTUREWORK Concludingthisthesis,thischapterrecapsthekeypointsofthefacilitycharacterization, demonstrationofabilitytoeduceacousticimpedanceofanacousticliner,anddetailing suggestionsforfuturework.Improvementstofacilitydesignalongwithsuggested implementationsaredescribed. 6.1FacilityCharacterization 6.1.1FluidDynamicCharacterization Experimentswereperformedtohighlighttheowintwodistinctregionsofthe tunnel,theentranceregionimmediatelydownstreamofthenozzle,andalocationfar enoughdownstreamtoassumefullydevelopedconditions.Bothregionsweretestedand comparedtopublishedwork. Thecharacterizationoftheentranceregioncenteredonmatchingthegrowthof theacceleratedcentralcoreowtofacilitiesofsimilargeometriesandrunconditions. Anselmet etal. ( 2009 )proposedanon-dimensionalscalingofentranceshowninEquation 517 .TheGFIDdataappliedtoEquation 517 yieldedaslopeof0 145 0 039,slightly under-predictingthereportedvalueof Anselmet etal. ( 2009 )of0.185.However, independentanalysisofthedatafrom Gessner etal. ( 1977 )resultedinaslopeof 0 167 0 05,inagreementwiththeGFIDresults.Thesendingsindicatethatthe growthintheGFIDentranceregioniswithintheexpectedrangeforahighReynolds numberturbulentchannelowfacility.Equation 517 canthenbeextendedtoestimate theentrancelengthoftheGFIDto x / D h =36 2. Vericationofdownstreamfullydevelopedconditionswereevaluatedwiththeleading edgeofthetestsectioninstalledat x / D h =58 5.Analysisofthecenterlineandbulk velocity,aswellasthestreamwisestaticpressureallindicatedthatthemeanowwas fullydeveloped.Theresultsallowforacousticlinertestingunderknownconditions 167

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andsimplerinputsforadvancedimpedanceeducationanalyseswheretheowproleis considered. 6.1.2AcousticCharacterization Anear-anechoicdi userwasfabricatedtoreduceupstreamacousticpropagation. Thereectioncoe cientwasdemonstratedtobelessthan13%overthefrequencyrange ofinterest.Incontrast,thehard-walldi userusedforuiddynamicstudieswasfound tohavereectioncoe cientsabove40%overthesamerange.Utilizationoftheanechoic di userhowevershouldbelimitedtoacoustictestingwhennoowseedispresent,thereby reducingthepotentialofoilaccumulationonthefacesheet. 6.2ResearchImpact Theprimarygoalofthisthesiswastodesign,construct,aacoustic-owbenchand educetheimpedanceofanacousticlinerundergrazingow.Thechosenimpedance eductionmethod,thesinglemodemethod(SMM),aswellastheabilitytoaccurately extractimpedance,werevalidatedthroughatwostepprocessusingawiremeshacoustic liner. First,thewiremeshlinerwastestedintwofacilities,theGFIDwithzeromean grazingowusingtheSMMtoeducetheimpedance,andinanormalincidencetube usingthetwomicrophonemethod.Theimpedancewasmatchedbetweenthetwofacilities acrossthefrequencyrangetested. ThesecondstepappliedtheSMMtopublisheddatafromNASAwithcorresponding impedanceresultsusingtwoFEM-basedeductionapproaches.TheSMMwasableto matchgeneraltrendsoftheFEM-resultsatthetestedfrequenciesbutyieldedlargeerrors neartheanti-resonanceoftheacousticliner. Finally,thevalidatedmodelwasappliedtoexperimentaldatafromtheGFIDofthe wiremeshlineroverfourMachnumbersandvediscretefrequencies.Impedanceresults fortheacousticlinerdemonstratedbothhigherresistancevaluesandincreasedresonant frequencywithincreasingMachnumber.Impedancewasunabletobedeterminedfrom 168

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thetestdataforafrequencyof500 Hz ,regardlessofMachnumber.Theexperiment demonstratedtheGFIDcapableofeducingtheimpedanceofanacousticlinerallowingfor alternatemethodstobeappliedtothedata. 6.3FutureWork Duringthedesign,fabrication,andtestingwithintheGFID,potentialareasof improvementswerenoted.Thefollowingsectionswilldiscusspotentialimprovements thatcouldbemadetothefacilityinSection 6.3.1 andimprovementstowardimpedance educationcapabilitieswithintheGFIDinSection 6.3.2 6.3.1FacilityImprovements Stagnationchamber ThestagnationchamberisthemostupstreamcomponentoftheGFIDandthus playsalargeroleindownstreamowinuence.Additionally,thestagnationchamber housesstagnationpropertymeasurementsensorsandintroducesowseeding.Tohelp smoothoutsmalluctuationsfromtheupstreamowvalve,thestagnationchamber volumecouldbeincreased.Anincreasedvolumewouldreducetheinitialowspeedand couldbeaccomplishedwithpipeextensionofequaldiametertothecurrentstagnation chamber.Thiswouldalsoallowfortheintroductionofowtreatmentsuchasowscreen andsettlingchambersforturbulencereduction. Thesecondstagenozzleiscurrentlytheonlylinkbetweenthelargestagnation chamberandthemassiveGFIDducting.Carehasbeenappliedtoreduceloadingon thenozzlebutimprovementcouldbemadethroughoutttingthenozzlewithinametal cagestructuretodecoupletheplasticnozzlefromadownstreamload,therebyreducing potentialcrackingorbreakageofthenozzle. Flowseeding Flowseedingforopticalbaseduiddynamicmeasuredareintroducedattheaftend ofthestagnationchamber.Extendedrunperiodsdemonstratedthatoilwouldpoolatthe baseofthestagnationchamber,causingstreaksdownstream.Asimpledrainpipewould 169

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allowfortheremovalofoilbuild-upwithouttheneedtodismantlethechamber,thereby reducingthepotentialformisalignment. Additionally,thecurrentseederprovidedexcellentparticlesizeforLDVmeasurements, howeverlimitedmeasurementtimeduetowindowoil-accumulation.Futuretestsshould exploretheuseofnon-oilbasedseedingincludingdryseeding,whichmayrequireexternal collection,orwater-basedoiluidsforeasyclean-up.Alternativeseedapproachescould eliminatethenecessityofthehard-walldi user. Acousticexcitation Thespeakerusedforexcitationwasabletogeneratediscretetonesupto130 dB (ref.20 Pa )underspeedsupto M =0 5.Additionaldriversandamplierswillallow forhigherSPLtestconditions.Throughinter-facilitycollaborationwiththeGFITat NASALaRC,SPLvaluesmaybeabletoreachandsurpassvaluesfoundinaircraftengine nacellesof160 dB Testsection Thetestsectionwasdesignedonalimitedbudgetandthroughlessonslearnedseveral improvementsarerecommended.Allwindowsweremountedtothetestsectionthrough holeswithinthewindowmaterialitself.Themountingholesareastressconcentration thatissubjecttocracking.Newwindowsshouldutilizemetalframesandoatglassfor improvedopticalperformanceandreducedwindowstress.Themetalframeswouldallow forathinnerwindowmaterial,therebypotentiallyreducingtherestrictionsimposedon3D LDVmeasurementsasnotedinSection 5.1.2 Asthetestsectionwasusedforalltestingdemonstratedthroughoutthisthesis,the windows,auxiliaryports,andlinerportsweremountedandunmountedmanytimes.The excessivewearhasworndownmanyofthetappedholesanditisrecommendedthateach holebeoutttedwithreplaceable,stainlesssteelheli-coils. 170

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Hard-walldi user Thelargeoscillationsinthereectioncoe cientofthehard-walldi userindicate apotentialstructuralmodewhichmaybeduetotherelativelythinwallsandminimal massofthedi user.Itisrecommendedthatadditionalberglasswrappingbeapplied tothecurrentdi useroraninexpensivereplacementhardwalldi userbefabricated withadditionalsti ness.Thehardwalldi usershouldonlybeuseduntilasuitable replacementowseedcanbeacquiredanddemonstratedappropriateforuidstesting. 6.3.2AdvancedImpedanceEduction Aswasdemonstratedbythisthesis,theGFIDwasusedasatestbedformaking acousticmeasurementsandeducingtheimpedanceofanacousticlinerundergrazing owconditions.TheSMMwaschosenduetotheinherentsimplicity,allowingforthe GFIDitselftobetheforefrontoftheresearchandnotamorecomplicatedmethod.With thefacilitycharacterizedthefocusshouldshifttowardadvancedmethodsandincreased accuracyoveralargerrangeofrunconditions.Alternateeductionmethodsshouldbe exploredincludingtheStraightforwardmethodandtheSemi-directmethodoutlinein Section 3.2 .Bothofthesemodelsarelesssensitivetoupstreamacousticpropagation thantheSMMandthuscouldbeusedathigherspeeds.Inaddition,theyhavebothbeen demonstratedtoprovideimpedanceresultsmatchingthoseofmoreadvancedFEMbased approaches. 6.3.3AcousticLinerShearStressTestings Thegrowingdemandforaircraftnoisereductionwillplaceagreaternecessityonthe applicationofacousticliners.Theimpactofanacousticlineronthepassingowremains atopicofincreasinginterest.Thereareseveralmethodsformeasuringshearstressofa owandthereaderisdirectedto Naughton&Sheplak ( 2002 )forathoroughreview. Inthisthesis,threeindirectmeasurementtechniquesusingvelocityproleswere exploredbutwereunabletodetermineameasurableshearimpactduetotheacoustic liner.Indirectmethods,suchasvelocityproletechniques,areattractiveduetothe 171

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non-intrusivenatureandeaseofuse.Futuretestingusingvelocityprolebasedtechniques couldemploymulti-componentvelocitymeasurementsandadvancedcontrolofthe freestreamvelocity.AlternativemethodssuchasPIVcouldbeemployedtoreduce experimentalacquisitiontime. Futuresheartestingshouldalsoexploretheuseofbothbothquasi-directanddirect methods.Thefamilyofquasi-directmethods,suchasoil-lminterferometry(OFI)and micropillararrays,allowforshearstressofaowtobeinferredfromtheimpactofshear onanothermeasurablequantity.Bothmethodsareappliedattheboundaryandthushave agreaterpotentialtodeterminetheactualimpactfromanacousticliner.Similarly,direct methodssuchasforcebalances,andmorerecentlyMEMSbasedshearstresssensorscould playarollforaverageandpointshearvalueassessmentrespectively. TheGFIDhastheabilitytoplayauniqueroletowardadvancingtheresearchand applicationofacousticlinersthroughinvestigatingtheunderlyingphysicsandimproved measurementmethodology.Pastandfuturecollaborationwithbothcorporatepartners andgovernmentlaboratorieswillallowtheGFIDtohelpdesignthenextgenerationof acousticlinersandtestingtechnology. 172

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APPENDIXA DERIVATIONOFDUCTACOUSTICSINAQUIESCENTMEDIUMWITHSOUND HARDWALLS Assumptions Linear Isentropic Homogeneous two-dimensional Schematic Analysis Let p ( x,y,t )= P ( x,y, ) e j t (A1) Giventhepressurewaveequation 1 c 0 # 2 p # t 2 !" 2 p =0(A2) Plugging A1 into A2 resultsin 1 c 2 0 # 2 # t 2 ( Pe j t ) !" 2 ( Pe j t ) =0 173

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( j ) 2 c 2 0 Pe j t e j t 2 P =0(A3) Note: j = ) 1 j 2 = 1 k = c 0 c 0 # 2 = k 2 Eq. A3 isrewrittenas k 2 Pe j t e j t 2 P =0 Divideout e j t frombothsides 2 P + k 2 P =0(A4) Where k 2 isthedispersionrelationshipgivenby k 2 = & c 0 2 = k 2 x + k 2 y Assumeaworkingformforthepressuretobetheproductofthreeunivariable functions, p ( x,y,t )= Y ( y ) X ( x ) e j t (A5) ApplyingaSeparationofVariablesapproach, A5 canbesubstitutedinto A4 Y d 2 X dx 2 + X d 2 Y dy 2 + k 2 XY =0 Let X "" denoteasecondderivative,rewrittenas YX "" + XY "" = k 2 XY Dividebytheproduct XY 1 X X "" + 1 Y Y "" = k 2 (A6) Notethatthetransversey-directionishomogeneousandconversely,thepropagating x-directionisnon-homogeneouswithboundaryconditionsappliedatinnity 174

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Firstsolvingthehomogeneousdirection 1 Y Y "" = k 2 X "" X = k 2 y =constant Rewrittenas Y "" + k 2 y Y =0(A7) Equation A7 underhomogeneousboundaryconditionsresultsinthebasisfunctionto thesolutionofthesumoftranscendentalfunctions Y ( y )= C 1 cos( k y y )+ C 2 sin( k y y )(A8) Where C 1 and C 2 areconstants.Acknowledgingthattransverseboundaryconditionsare expressedintermsofthederivativeofpressure,takethederivativeof A8 Y ( y )= k y C 1 sin( k y y )+ k y C 2 cos( k y y ) Applythersttransverseboundaryconditionofnoslipatthewall, Y ( y =0)=0= k y C 1 ! sin(0)+ k y C 2 cos(0) k y C 2 =0 k y + =0 C 2 =0 Applythesecondtransverseboundarycondition Y ( y = b )=0= k y C 1 sin( k y b ) k y or C + =0 sin( k y b )=0 175

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k y b = n % k y = n % b forn=0,1,2,3... Notethat n =0isatrivialsolutionforthevelocityeldbutdoesdescribean importantuniformpressureeld. Theboxedresultarethetransverseeigenvalues,thetransverseeigenfunctionsare sin n % y b # Recall, k = c 0 = 2 % f c 0 fn = nkc 0 2 % = nc 0 2 b deneseigenfrequencies Heretheintegervalueof n describesthepressuremodeswithintheduct.Therst eigenfrequencydenesthecut-onfrequencyofthersthigherordermode. ToconcludethetransversedirectionfortheSeparationofVariables,thebasisfunction isrewritten Y ( y )= C 1 cos n % y b # (A9) Solve A6 intheprogressivex-direction X "" + k 2 x X =0 yieldsthesolutionofasumofexponentialfunctionsduetotheprescribedboundary conditionsatinnity. X ( x )= C 3 e $ jk x x + C 4 e jk x x (A10) Thetermsofeq. A10 representtheprogressionofacousticwavesbothawayfrom thesourceandthoseprogressingtowardthesource.Theone-dimensionalpropagation assumptionimpliesthereisnotasecondsourcenorareectivesurface,thereforethat C 4 goestozero. 176

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Notethat ( k x ) n = C k 2 k 2 y = % & c 0 2 n % b forn=0,1,2,3... Becausetheprogressivex-directionhasnon-homogeneousboundaryconditions,theX andYindividualsolutionsmustbecombinedrst. Combiningthetwoindependentbasisfunctions,recallingthat p ( x,y,t )= X ( x ) Y ( y ) e j t p = # n =0 cos n % y b # C 5 e $ j ( k x ) n x e j t Where C 5 = C 1 C 3 Forsimplicity, C 5 isrecastastheconstant A .Thenalanswernow becomesasfollowswiththechangeofvariables. p = # n =0 cos n % y b # Ae $ j ( k x ) n x e j t (A11) 177

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APPENDIXB DERIVATIONOFDUCTACOUSTICSINAQUIESCENTMEDIUMWITH PRESCRIBEDIMPEDANCEBOUNDARYCONDITION Assumptions Linearpressurepropagation Isentropicow Homogeneousmedium Two-dimensional Schematic Analysis Given Arectangularductwithgeneralizedacousticlinersattheboundaries,prescribedat y=0andy=b.Similarly,thez-direction Thez-directionisneglectedinthisanalysisbutthetheorycanbeextendedorbe superimposedwiththehardwalledcaseinAppendix A Thelocallyreactinglinerspossestwodi erenceimpedancevalues, Z y 1 at y =0and Z y 2 at y = b Thesolutionfollows Ingard ( 1999 )DuctAcousticsnotes. BoundaryConditions Theboundaryconditionsrepresentmatchingparticlevelocityatthesurface. 178

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BC1: 1 j "& 0 # p # y = P Z 1 y =0 BC2: 1 j "& 0 # p # y = P Z 2 y = b Notethattheright-handsideofBC2containsanegativesigndenotingthatthe velocityisinthenegativey-direction,outwardnormalfromthewall. GeneralizedSolution Usingaseparationofvariablesapproach,theproblemcanbedecomposedintothe productoftwofunctions. p = Y ( y ) X ( x ) e j t Where, Y(y)isafunctiondescribingthetransversespatialvariationintheacousticeld. X(x)isafunctiondescribingthespatialvariationinthedirectionofpropagation. e j t describesthetimeharmonictemporalvariationoftheacousticeld.Eitherthe realortheimaginarycomponentisusedforanalysis. TransverseDirection,Y(y) Becausetheproblemisboundedatnitevalues,thesolutioncanbewrittenasthe sumoftranscendentalfunctions. Y ( y )= A sin( k y y )+ B cos( k y y ) or Y ( y )= A [ cos ( k y y )+ Rsin ( k y y )] .Where A and B areconstants,and R = B / A Atthistimeitisusefultointroducethereciprocalofimpedance,theadmittanceis denedby i = & 0 c 0 Z i 179

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. ApplyBoundaryConditions ApplyBC1 & 0 c 0 u y 1 = p 1 y =0 & 0 c 0 # # A k y j & 0 [ Rcos ( k y 0) D EF G 1 " sin ( k y 0) D EF G 0 ]= # # A [ cos ( k y 0) D EF G 1 + R " sin ( k y 0) D EF G 0 ] 1 c 0 k y j R = 1 Usingthedenitionofthewavenumberand 1 / j = j j & k y k R = 1 SolveforR, R = 1 j & k k y (B1) ApplyBC2 & 0 c 0 u y 2 = p 2 y = b & 0 c 0 # # A k y j & 0 [ Rcos ( k y b ) sin ( k y b )]= # # A [ cos ( k y b )+ Rsin ( k y b )] 2 c 0 j k y Rcos ( k y b ) sin ( k y b ) cos ( k y b )+ Rsin ( k y b ) = 2 & k y jk sin ( k y b )+ Rcos ( k y b ) cos ( k y b )+ Rsin ( k y b ) = 2 (B2) PluginR, & k y jk sin ( k y b )+ 1 j k k y # cos ( k y b ) cos ( k y b )+ 1 j k k y # sin ( k y b ) = 2 Divideeachtermby cos ( k y b ),andusingthetangentfunctionand 1 / j = j & k y jk tan ( k y b ) j 1 k k y # 1 j 1 k k y # tan ( k y b ) = 2 180

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! & k y jk tan ( k y b ) 1 = 2 j 1 2 & k k y tan ( k y b ) 1 + 2 = & k y jk tan ( k y b )+ j 1 2 & k k y tan ( k y b ) 1 + 2 = j & k y k tan ( k y b ) / 1 2 & k k y 2 +1 0 & k y k tan ( k y b )= j 1 + 2 1+ 1 2 k k y # 2 181

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APPENDIXC DERIVATIONOFTHECONVECTIVEWAVEEQUATION Assumptions Linear Isentropicow Homogeneousmedium Incompressible Negligiblebodyforces Irrotational 1-Dpropagation Equations Continuity: & 0 4 V + D & Dt =0(C1) Momentum: & 0 D 4 V Dt + P (C2) Equationofstate: c 2 0 = #& # p s (C3) PlugEquation C3 intoEquation C1 toget & 0 4 V + 1 c 2 0 DP Dt =0 (C4) TakethespatialderivativeofEquation C2 & 0 D 4 V ) Dt + 2 P =0 (C5) ApplyatotaltimederivativetoEquation C4 toget, & 0 D Dt 4 V # + 1 c 2 0 D 2 P Dt 2 =0(C6) 182

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SubtractEquation C6 fromEquation C5 resultsintheconvectivewaveequation, 1 c 2 0 D 2 P Dt !" 2 P =0 (C7) Equation C7 canberewrittenas D 2 P Dt 2 c 2 0 2 P =0 whichcanbefurtherexpanded, & # # t + 4 V '& # # t + 4 V P c 2 0 2 P =0 # 2 P # t 2 +2 4 V # P # t + 4 V #" 4 V # P c 2 0 2 P =0 (C8) IfaCartesiancoordinatesystemisassumedwiththex-directioninthestreamwise direction,Equation C8 canbesimpliedas # 2 P # t 2 +2 V # # x & # P # t + U 2 # 2 P # x 2 c 2 0 2 P =0 (C9) Applyaseparationofvariablesapproachtothetimefunctionrepresentinganacoustic sourcedenotedbyacomplexexponential P = X ( x ) Y ( y ) Z ( z ) e j t (C10) PlugEquation C10 intoEquation C9 andnotingthedenitionofthewavenumber andMachnumberyeilds $ 2 +2 Mj $ X X + M 2 X "" X Z "" Z Y "" Y X "" X =0 (C11) SolvingEquation C11 forthetransversez-directionresultsin Z "" + $ 2 z Z (C12) withsolution Z ( z )= A 1 cos $ z z + A 2 sin k z z, (C13) 183

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andsimilarly, Y "" + $ 2 y Y (C14) Y ( y )= B 1 cos $ y y + B 2 sin k y y. (C15) SubstituteEquations C12 and C14 intoEquation C11 yields X "" X ( 1 M 2 ) 2 M ( j $ ) X "" X + ( $ $ 2 z $ 2 y ) (C16) Thepropagationofaxialacousticenergyisassumedtoaprogressivewave,theitcan beassumedtoberepresentedby X = e j # x x (C17) ApplyEquation C17 toEquation C16 4 $ 2 x ( 1 M 2 ) +2 M $ x $ + ( $ $ 2 z $ 2 y )5 e j # x x =0 (C18) ThesolutiontoEquation C19 is $ x = M $ + C $ 2 ( 1 M 2 ) $ 2 y (1 M ) 2 (C19) Rearrangingandsolvingfortheratioof # y / # yields $ y $ = 3 1 4 (1 M ) 2 ( # x # ) + M 5 2 (1 M ) 2 6 1 / 2 (C20) 184

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APPENDIXD TECHNICALDRAWINGS ThisappendixcontainsallthetechnicaldrawingsmadeatUFfortheGFID. Partssuchasthenear-anechoicdi userweredesignedbyNASAandthusonlythe specicpartsadaptedfortheGFIDareshown.Thetechnicaldrawingsarepresentedin downstreamorderstartingwiththesecondstagenozzle.Furtherdetailsaboutthedesign andimplantationofeachpiecearefoundinChapter 4 185

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BIOGRAPHICALSKETCH BrandonBertolucciwasborninSpokane,Wa.HegraduatedfromJoelE.Ferris HighSchoolin2001.BrandonreceivedhisBachelorofScienceinMechanicalEngineering fromOregonStateUniversityin2005.Throughhisengineeringstudieshefoundadraw towardaerospaceengineeringandjoinedtheIMGresearchgroupattheUniversityof FloridaundertheadvisementofDr.LouisCattafesta.Afteraseriesofsmallprojects anopportunitytoworkcloselywithNASAonafacilitydevelopmentprojectaroseand withnewlyappointedco-chairDr.Sheplakheacceptedthenewprojectinhisthird yearofgraduateschool.CompletinghisdoctorateintheFallof2012,heacceptedan aeroacousticspositionatTheBoeingCompanyinSeattle,Wa. 217