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Effects of Turbulence on Fixed Wing Small Unmanned Aerial Systems

Permanent Link: http://ufdc.ufl.edu/UFE0045158/00001

Material Information

Title: Effects of Turbulence on Fixed Wing Small Unmanned Aerial Systems
Physical Description: 1 online resource (306 p.)
Language: english
Creator: Sytsma, Michael J
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2013

Subjects

Subjects / Keywords: dynamic -- flow -- free-stream -- image -- loads -- particle -- shear -- structure -- turbulence -- unmanned -- velocimetry
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: The stability of natural fliers would be an excellent trait to be designed into small unmanned aerial systems. However, there is a great deal of understanding that is missing regarding how turbulence affects flight loads. This is particularly important for low-speed aircraft in high levels of turbulence as would be experienced very near to the ground. The goal of this dissertation is to develop an increased understanding of how the presence of turbulence changes loads felt by an aircraft. This includes the development and characterization of a repeatable, variable, high intensity turbulent environment within a wind tunnel. The turbulent loads are examined to determine their relationship to turbulence statistics, and particle image velocimetry is used to better understand the flow characteristics that lead to such loads. An active turbulence grid has been constructed which allows for adjustable turbulent flow fields in the wind tunnel. These turbulent flows have been characterized using constant temperature anemometry to evaluate the statistical dependence on run mode, speed, and location. Mean load measurements performed on three composite flat plate wing models indicated that turbulence extended the stall behavior and modified the other loads. Dynamic loads were evaluated to develop an initial understanding of the spectral behavior of the loads behind turbulence. Particle image velocimetry on the flow field was measured to determine differences in the flow field. The baseline flows exhibited a detached shear layer from the leading edge that could reattach to form a separation bubble at lower angles of attack. The turbulent flows developed a thick and rapidly growing shear layer that was capable of maintaining attached flow to much higher angles of attack, and thereby extending stall and changing other loads. Differences in load behavior between low and higher aspect ratio wings was identified as being due to changes in the flow.
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 Michael J Sytsma.
Thesis: Thesis (Ph.D.)--University of Florida, 2013.
Local: Adviser: Ukeiley, Lawrence S.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2013
System ID: UFE0045158:00001

Permanent Link: http://ufdc.ufl.edu/UFE0045158/00001

Material Information

Title: Effects of Turbulence on Fixed Wing Small Unmanned Aerial Systems
Physical Description: 1 online resource (306 p.)
Language: english
Creator: Sytsma, Michael J
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2013

Subjects

Subjects / Keywords: dynamic -- flow -- free-stream -- image -- loads -- particle -- shear -- structure -- turbulence -- unmanned -- velocimetry
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: The stability of natural fliers would be an excellent trait to be designed into small unmanned aerial systems. However, there is a great deal of understanding that is missing regarding how turbulence affects flight loads. This is particularly important for low-speed aircraft in high levels of turbulence as would be experienced very near to the ground. The goal of this dissertation is to develop an increased understanding of how the presence of turbulence changes loads felt by an aircraft. This includes the development and characterization of a repeatable, variable, high intensity turbulent environment within a wind tunnel. The turbulent loads are examined to determine their relationship to turbulence statistics, and particle image velocimetry is used to better understand the flow characteristics that lead to such loads. An active turbulence grid has been constructed which allows for adjustable turbulent flow fields in the wind tunnel. These turbulent flows have been characterized using constant temperature anemometry to evaluate the statistical dependence on run mode, speed, and location. Mean load measurements performed on three composite flat plate wing models indicated that turbulence extended the stall behavior and modified the other loads. Dynamic loads were evaluated to develop an initial understanding of the spectral behavior of the loads behind turbulence. Particle image velocimetry on the flow field was measured to determine differences in the flow field. The baseline flows exhibited a detached shear layer from the leading edge that could reattach to form a separation bubble at lower angles of attack. The turbulent flows developed a thick and rapidly growing shear layer that was capable of maintaining attached flow to much higher angles of attack, and thereby extending stall and changing other loads. Differences in load behavior between low and higher aspect ratio wings was identified as being due to changes in the flow.
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 Michael J Sytsma.
Thesis: Thesis (Ph.D.)--University of Florida, 2013.
Local: Adviser: Ukeiley, Lawrence S.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2013
System ID: UFE0045158:00001


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EFFECTSOFTURBULENCEONFIXEDWINGSMALLUNMANNEDAERIAL SYSTEMS By MICHAELJ.SYTSMA ADISSERTATIONPRESENTEDTOTHEGRADUATESCHOOL OFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENT OFTHEREQUIREMENTSFORTHEDEGREEOF DOCTOROFPHILOSOPHY UNIVERSITYOFFLORIDA 2013

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c r 2013MichaelJ.Sytsma 2

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TomywifeRosalynandmyfamily 3

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ACKNOWLEDGMENTS IwouldrstliketothankmywifeforpatienceandsupportasI haveperformed countlesstestsandanalysisthroughtheyears.Shealwaysl istenedtomyrantswith patienceandlove.Iwouldliketoextendgreatthankstomyfa milyfortheircontinued supportinmyeducationalgoals.Iamindebtedtothemultitu decolleagueswhohave workedinandaroundtheResearchandEngineeringEducation Facility,astheyhave beenofgreathelpthroughouttheyears.Iwanttoacknowledg eDr.Ukeileyforbeingmy advisorandhelpingmethroughthisresearch,aswellasther estofmycommittee,Drs. PeterIfju,RickLind,ForrestMasters,andDavidBloomquis t.Agreatadditionalthanks totheAirForceSEEKEAGLEOfceandAirForceResearchLabor atoryforsupporting methroughthisresearch,bothintimeandtechnicalexperti se.Alastgratefulthanksto theAirForceOfceofScienticResearchforprovidingfund ingformetoperformthis research. 4

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TABLEOFCONTENTS page ACKNOWLEDGMENTS ..................................4 LISTOFTABLES ......................................8 LISTOFFIGURES .....................................10 ABSTRACT .........................................17 CHAPTER 1INTRODUCTION ...................................19 1.1BackgroundofTurbulenceEffectsonMannedAircraft ...........22 1.2TurbulenceonSmallUnmannedAircraft ...................31 1.3ResearchOutline ................................33 1.4ResearchPlan .................................33 1.5Contributions ..................................34 1.6DissertationOrganization ...........................35 2EXPERIMENTALFACILITIESANDTECHNIQUES ................36 2.1AerodynamicCharacterizationFacility ....................36 2.2TurbulenceGrids ................................37 2.2.1StaticTurbulenceGrid .........................37 2.2.2ActiveTurbulenceGrid .........................37 2.2.3Design ..................................38 2.2.4ComputerControl ............................42 2.2.5ForcingProtocol ............................43 2.3ConstantTemperatureAnemometry .....................44 2.4ModalTestingandStructuralDeconvolutionFiltering ............49 2.4.1StructuralDynamics ..........................49 2.4.2FrequencyResponseFunctionInverseFilteringTechn ique .....54 2.4.3LimitationsofDeconvolutionFilter ...................59 2.5ParticleImageVelocimetry ..........................60 2.5.1LaVisionSystemDetails ........................60 2.5.2BasicPIVTechnique ..........................61 2.5.3StereoPIV ................................62 2.5.4SourcesofError ............................64 2.5.5QuanticationofError .........................68 3CHARACTERIZATIONOFWINDTUNNELENVIRONMENT ..........86 3.1BaselineWindTunnelTesting .........................86 3.2CTADataSamplingandAnalysis .......................86 3.3SamplingErrorAnalysis ............................92 5

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3.4ActiveTurbulenceGridSinglePointStatistics ................93 3.5ActiveTurbulenceGridTransverseSurvey ..................95 3.6ActiveTurbulenceGridMultiplePointMeasurements ............97 3.7Summary ....................................99 4LOWORDERCOMPUTATIONALMODELING ..................114 4.1StatisticalRepresentationsofTurbulence ..................114 4.2FiniteImpulseResponseFilterTurbulenceSynthesis ............117 4.3Unsteady2-DVortexLatticeMethod .....................120 4.3.1BasicAlgorithm .............................120 4.3.2TurbulenceBoundaryConditions ...................122 4.42-DResults ...................................122 4.5Summary ....................................126 5EXPERIMENTALLOADRESULTS .........................137 5.1DesiredReynoldsNumbersandTurbulenceData ..............138 5.2MeanLoadsUncertaintyTreatments .....................139 5.2.1TypicalTreatment ............................140 5.2.2ModicationtoStandardErrorTreatment ...............141 5.3MeanLoadsinBaselineFlow .........................143 5.4MeanLoadsinthePresenceofTurbulence .................146 5.5UnsteadyLoadsinthePresenceofTurbulence ...............149 5.6Summary ....................................153 6EXPERIMENTALFLOWRESULTS .........................168 6.1ChordwiseExperiments ............................168 6.1.1CaseAData ..............................171 6.1.2CaseBData ..............................171 6.1.3CaseCData ..............................172 6.1.4CaseDData ..............................173 6.1.5ShearLayerScalingAnalysisandSimilaritySolution ........174 6.1.5.1Orderofmagnitudeandsimpliedshearequation ....174 6.1.5.2Similaritysolution ......................179 6.1.5.3ComparisonofanalyticalsolutiontoPIVdata .......180 6.2DownstreamExperiments ...........................181 6.2.1CaseA ..................................182 6.2.2CaseB ..................................183 6.2.3CaseC .................................183 6.2.4CaseD .................................184 6.2.5FittingVortexModelstoData .....................184 6.3Summary ....................................186 6

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7SUMMARYANDFUTUREWORK .........................207 7.1Summary ....................................207 7.2FutureWork ...................................209 APPENDIX AACTIVETURBULENCEGRIDCHARACTERIZATION ..............212 BTIMEVARYINGLOADSINTHEPRESENCEOFTURBULENCE ........244 CSIMILARITYSCALINGRESULTS .........................277 REFERENCES .......................................292 BIOGRAPHICALSKETCH ................................306 7

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LISTOFTABLES Table page 1-1Summaryofadverseturbulenceeffectsonaircraft ................22 2-1Frequencyresponsefunctionmodels .......................52 4-1SpectrafunctionformsofDrydenandVon-Karmanturbule ncemodels .....115 4-2TransferfunctionformsofDrydenandVon-Karmanturbul encemodels ....118 5-1ModelDimensions ..................................138 5-2ATGturbulencestatisticsatspeedstoyieldReynoldsnu mbersat X M =12 : 5 ..138 5-3Standarddeviationsofloadinvarioussituations .................140 6-1Chosen fordifferentA ..............................169 6-2Tableofrelevanttipvortexproperties ........................186 A-1ATGturbulencestatisticswithwindtunnelthrottleat1 4.5%andat X M =5 ...212 A-2ATGturbulencestatisticswithwindtunnelthrottleat1 4.5%andat X M =10 ...213 A-3ATGturbulencestatisticswithwindtunnelthrottleat1 4.5%andat X M =12 : 5 .214 A-4ATGturbulencestatisticswithwindtunnelthrottleat1 4.5%andat X M =15 ..215 A-5ATGturbulencestatisticswithwindtunnelthrottleat1 4.5%andat X M =20 ..216 A-6ATGturbulencestatisticswithwindtunnelthrottleat2 8.5%andat X M =5 ...217 A-7ATGturbulencestatisticswithwindtunnelthrottleat2 8.5%andat X M =10 ..218 A-8ATGturbulencestatisticswithwindtunnelthrottleat2 8.5%andat X M =12 : 5 .219 A-9ATGturbulencestatisticswithwindtunnelthrottleat2 8.5%andat X M =15 ..220 A-10ATGturbulencestatisticswithwindtunnelthrottleat 28.5%andat X M =20 ..221 A-11ATGturbulencestatisticswithwindtunnelthrottleat 43.5%andat X M =5 ...222 A-12ATGturbulencestatisticswithwindtunnelthrottleat 43.5%andat X M =10 ..223 A-13ATGturbulencestatisticswithwindtunnelthrottleat 43.5%andat X M =12 : 5 .224 A-14ATGturbulencestatisticswithwindtunnelthrottleat 43.5%andat X M =15 ..225 A-15ATGturbulencestatisticswithwindtunnelthrottleat 43.5%andat X M =20 ..226 A-16ATGturbulencestatisticswithwindtunnelthrottleat 58%andat X M =5 ....227 8

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A-17ATGturbulencestatisticswithwindtunnelthrottleat 58%andat X M =10 ...228 A-18ATGturbulencestatisticswithwindtunnelthrottleat 58%andat X M =12 : 5 ..229 A-19ATGturbulencestatisticswithwindtunnelthrottleat 58%andat X M =15 ...230 A-20ATGturbulencestatisticswithwindtunnelthrottleat 58%andat X M =20 ...231 9

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LISTOFFIGURES Figure page 2-1DiagramofAerodynamicCharacterizationFacilityatUF REEF .........70 2-2ATGafterarunwithrandomangulardisplacements ...............70 2-3DiagramofATGControlConnections .......................71 2-4X-wireprobeintunnelonrotarystage .......................71 2-5Asamplenormalcalibrationplot ..........................72 2-6X-wireprobegeometryindicatinggeometry ....................72 2-7Sampleanglecalibrationplot ............................73 2-8ForcedMass-Spring-DamperSystem .......................73 2-9MassspringdampersystemFRFmagnitudeandphase .............74 2-10PCBimpulsehammerusedinmodaltesting ....................75 2-11Frequencyresponsefunctionofloadcell ......................76 2-12Finaldeconvolutionlterfrequencyrepresentation ................77 2-13DeconvolutionlterFIRrepresentation .......................78 2-14Filtercorrectingvibrationfromsingleimpulseindif ferentaxes. .........79 2-15Comparisonofautospectraofhammer,unlteredloadan dlteredload ....80 2-16Comparisonoflters .................................80 2-17Filtercorrectingvibrationprecession. ........................81 2-18Filtercorrectingcontinuousforcing. .........................82 2-19DiagramindicatingbasicPIVprocedure ......................83 2-20StereoPIVsetupforchordwisemeasurements ..................83 2-21PIVpercentagedeviationfrom U 1 for500averagedimagesinbaselineow ..84 2-22PIVpercentagedeviationfrom U 1 inturbulentow ................84 3-1Baselineturbulenceintensitydownstreamontunnelcen terline .........100 3-2Variationof U 1 withrotationalparameter W ...................100 3-3Initialtestautospectraldensityplot .........................101 10

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3-4HotwireprobeplaceddownstreamfromATGinACF ...............101 3-5Activeturbulencegridturbulenceintensitydownstrea montunnelcenterline ..102 3-6Activeturbulencegridisotropydownstreamontunnelce nterline ........102 3-7Activeturbulencegridturbulenceintensitydownstrea m .............103 3-8Diagramoftraversedmeasurements ........................104 3-9Measuredpercentvariationfromcorefor U 1 withbaselineow .........105 3-10Measuredpercentvariationfromcorefor U 1 withrunmode n=2 : 5 ;! =0 ..106 3-11Measuredpercentvariationfromcorefor TI X withrunmode n=0 ;! =8 ...107 3-12Measuredpercentvariationfromcorefor I xz withrunmode n=0 ;! =3 ....108 3-13Measuredpercentvariationfromcorefor L 11 R withrunmode n=0 ;! =8 ...109 3-14Measuredpercentvariationfromcorefor U 1 withstaticgrid ...........110 3-15Lengthscaleswithrunmode n=2 : 5 ;! =0 ....................111 3-16Lengthscaleswithrunmode n=0 ;! =3 .....................112 3-17Lengthscaleswithrunmode n=0 ;! =8 .....................113 4-1DiagramofFilteringProcess ............................127 4-2PowerSpectralDensityPlotofSynthesizedTurbulencea ndTargetSpectra ..127 4-3Lengthwisesynthesizedvelocity ..........................128 4-4Basicstructureofa2-DairfoilrepresentedinUVLM ...............128 4-5 b u ^ { autospectraldensityplot .............................129 4-6 b u ^ | autospectraldensityplot .............................130 4-7 F ^ | autospectraldensityplot .............................131 4-8 M ^ { autospectraldensityplot .............................132 4-9 F ^ | and b u ^ { cross-spectraldensityplot ........................133 4-10 F ^ | and b u ^ | cross-spectraldensityplot ........................134 4-11 M ^ { and b u ^ { cross-spectraldensityplot ........................135 4-12 M ^ { and b u ^ | cross-spectraldensityplot ........................136 5-1Modelmountedformeanloadmeasurements ...................154 11

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5-2BaselinecoefcientdataforA=2model .....................155 5-3Baselinecoefcientdata ...............................156 5-4LiftandpitchingmomentcoefcientsforA=4 ..................157 5-5LiftandpitchingmomentcoefcientsforA=1andRe=200k .........158 5-6LiftandpitchingmomentcoefcientsforA=2andRe=100k .........159 5-7LiftandpitchingmomentcoefcientsforA=4andRe=100k .........160 5-8Standarddeviationofliftandpitchingmomentcoefcie nts ............161 5-9Averagedstandarddeviations ............................162 5-10Modelmountedwithhot-wireprobefordynamicloadmeas urements ......163 5-11Dynamicloadandturbulencedataat =0 n = 0 3 ...........164 5-12Dynamicloadandturbulencedataat =30 n = 0 3 ...........165 5-13Dynamicloadandturbulencedataat =0 n = 2 : 5 0 ...........166 5-14Frequencyresponsefunctionsofdynamicloadandturbu lence .........167 6-1Modelmountedonstingerwithlasershiningupwardtoill uminateachord ...188 6-2DiagramofchordwisePIVmeasurementlocation .................189 6-3Plotof U U 1 at =8 andA=1 ...........................190 6-4Plotof U U 1 at =8 andA=2 ...........................190 6-5Plotof U U 1 at =8 andA=4 ...........................191 6-6Plotof S 13 U 1 c at =8 andA=2 ...........................191 6-7Plotof U U 1 at =25 andA=2 ..........................192 6-8Plotof U U 1 at =15 andA=4 ..........................192 6-9Plotof S 13 U 1 c at =25 andA=2 ..........................193 6-10Plotof TKE U 1 2 at =25 andA=2 .........................193 6-11Plotof u 0 w 0 U 1 2 at =25 andA=2 ..........................194 6-12Plotof U U 1 at =45 andA=1 ..........................194 6-13Plotof U U 1 at =35 andA=2 ..........................195 12

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6-14Plotof U U 1 at =25 andA=4 ..........................195 6-15Plotof U U 1 at =25 andA=1 ..........................196 6-16Plotof U U 1 at =25 andA=2 ..........................197 6-17Plotof U u a scaledagainstsimilarityparameterforbaselineow ..........198 6-18Plotof U u a scaledagainstsimilarityparameterforturbulentow .........199 6-19StereoPIVsetupfordownstreammeasurements .................200 6-20Plotof U 1 ( Y;Z ) U 1 indownstreamexperimentsat =8 andA=1 .........200 6-21Plotof U 1 ( Y;Z ) U 1 indownstreamexperimentsat =8 andA=2 .........201 6-22Plotof U 1 ( Y;Z ) U 1 indownstreamexperimentsat =8 andA=4 .........201 6-23Plotof S 13 U 1 c indownstreamexperimentsat =8 andA=4 ...........202 6-24Plotof TKE U 1 2 indownstreamexperimentsat =8 andA=4 ..........202 6-25Plotof U 1 ( Y;Z ) U 1 indownstreamexperimentsat =25 andA=2 .........203 6-26Plotof U 1 ( Y;Z ) U 1 indownstreamexperimentsat =15 andA=4 .........203 6-27Plotof U 1 ( Y;Z ) U 1 indownstreamexperimentsat =45 andA=1 .........204 6-28Plotof U 1 ( Y;Z ) U 1 indownstreamexperimentsat =35 andA=2 .........204 6-29Plotof U 1 ( Y;Z ) U 1 indownstreamexperimentsat =25 andA=4 .........205 6-30Plotof U 1 ( Y;Z ) U 1 indownstreamexperimentsat =25 andA=1 .........205 6-31FittedLamb-Oseenvortexdata ...........................206 A-1Measuredpercentvariationfromcorefor U 1 withrunmode n=0 ;! =3 ...232 A-2Measuredpercentvariationfromcorefor U 1 withrunmode n=0 ;! =8 ...233 A-3Measuredpercentvariationfromcorefor TI X withbaselineow ........234 A-4Measuredpercentvariationfromcorefor TI X withrunmode n=2 : 5 ;! =0 ..235 A-5Measuredpercentvariationfromcorefor TI X withrunmode n=0 ;! =3 ...236 A-6Measuredpercentvariationfromcorefor TI X withstaticgrid ..........237 13

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A-7Measuredpercentvariationfromcorefor I xz withrunmode n=2 : 5 ;! =0 ...238 A-8Measuredpercentvariationfromcorefor I xz withrunmode n=0 ;! =8 ....239 A-9Measuredpercentvariationfromcorefor I xz withstaticgrid ...........240 A-10Measuredpercentvariationfromcorefor L 11 R withrunmode n=2 : 5 ;! =0 ..241 A-11Measuredpercentvariationfromcorefor L 11 R withrunmode n=0 ;! =3 ...242 A-12Measuredpercentvariationfromcorefor L 11 R withstaticgrid ..........243 B-1Dynamicdataat =0 n = 2 : 5 0 ,andRe=25,000 ............244 B-2Dynamicdataat =0 n = 2 : 5 0 ,andRe=50,000 ............245 B-3Dynamicdataat =0 n = 2 : 5 0 ,andRe=75,000 ............246 B-4Dynamicdataat =0 n = 0 3 ,andRe=25,000 .............247 B-5Dynamicdataat =0 n = 0 3 ,andRe=50,000 .............248 B-6Dynamicdataat =0 n = 0 3 ,andRe=75,000 .............249 B-7Dynamicdataat =0 n = 0 8 ,andRe=25,000 .............250 B-8Dynamicdataat =0 n = 0 8 ,andRe=50,000 .............251 B-9Dynamicdataat =0 n = 0 8 ,andRe=75,000 .............252 B-10Dynamicdataat =0 n = 0 8 ,andRe=100,000 ............253 B-11Dynamicdataat =30 n = 2 : 5 0 ,andRe=25,000 ............254 B-12Dynamicdataat =30 n = 2 : 5 0 ,andRe=50,000 ............255 B-13Dynamicdataat =30 n = 2 : 5 0 ,andRe=75,000 ............256 B-14Dynamicdataat =30 n = 2 : 5 0 ,andRe=100,000 ...........257 B-15Dynamicdataat =30 n = 0 3 ,andRe=25,000 .............258 B-16Dynamicdataat =30 n = 0 3 ,andRe=50,000 .............259 B-17Dynamicdataat =30 n = 0 3 ,andRe=75,000 .............260 B-18Dynamicdataat =30 n = 0 8 ,andRe=25,000 .............261 B-19Dynamicdataat =30 n = 0 8 ,andRe=50,000 .............262 B-20Dynamicdataat =30 n = 0 8 ,andRe=75,000 .............263 B-21Dynamicdataat =30 n = 0 8 ,andRe=100,000 ............264 14

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B-22FRFdataat =0 n = 2 : 5 0 ,andRe=25,000 ...............265 B-23FRFdataat =0 n = 2 : 5 0 ,andRe=50,000 ...............265 B-24FRFdataat =0 n = 2 : 5 0 ,andRe=75,000 ...............266 B-25FRFdataat =0 n = 0 3 ,andRe=25,000 ................266 B-26FRFdataat =0 n = 0 3 ,andRe=50,000 ................267 B-27FRFdataat =0 n = 0 3 ,andRe=75,000 ................268 B-28FRFdataat =0 n = 0 3 ,andRe=100,000 ...............268 B-29FRFdataat =0 n = 0 8 ,andRe=25,000 ................269 B-30FRFdataat =0 n = 0 8 ,andRe=50,000 ................269 B-31FRFdataat =0 n = 0 8 ,andRe=75,000 ................270 B-32FRFdataat =0 n = 0 8 ,andRe=100,000 ...............270 B-33FRFdataat =30 n = 2 : 5 0 ,andRe=25,000 ..............271 B-34FRFdataat =30 n = 2 : 5 0 ,andRe=50,000 ..............271 B-35FRFdataat =30 n = 2 : 5 0 ,andRe=75,000 ..............272 B-36FRFdataat =30 n = 2 : 5 0 ,andRe=100,000 .............272 B-37FRFdataat =30 n = 0 3 ,andRe=25,000 ...............273 B-38FRFdataat =30 n = 0 3 ,andRe=50,000 ...............273 B-39FRFdataat =30 n = 0 3 ,andRe=75,000 ...............274 B-40FRFdataat =30 n = 0 3 ,andRe=100,000 ..............274 B-41FRFdataat =30 n = 0 8 ,andRe=25,000 ...............275 B-42FRFdataat =30 n = 0 8 ,andRe=50,000 ...............275 B-43FRFdataat =30 n = 0 8 ,andRe=75,000 ...............276 B-44FRFdataat =30 n = 0 8 ,andRe=100,000 ..............276 C-1Plotof U U 1 at =8 andA=1 ...........................277 C-2Plotof U u a scaledagainstsimilarityparameter forbaselineow .........278 C-3Plotof U u a scaledagainstsimilarityparameter forturbulentow ........279 C-4Plotof U U 1 at =15 andA=4 ..........................280 15

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C-5Plotof U u a scaledagainstsimilarityparameter forbaselineow .........281 C-6Plotof U u a scaledagainstsimilarityparameter forturbulentow ........282 C-7Plotof U U 1 at =15 andA=4 ..........................283 C-8Plotof U u a scaledagainstsimilarityparameter forbaselineow .........284 C-9Plotof U u a scaledagainstsimilarityparameter forturbulentow ........285 C-10Plotof U U 1 at =35 andA=2 ..........................286 C-11Plotof U u a scaledagainstsimilarityparameter forbaselineow .........287 C-12Plotof U u a scaledagainstsimilarityparameter forturbulentow ........288 C-13Plotof U U 1 at =35 andA=2 ..........................289 C-14Plotof U u a scaledagainstsimilarityparameter forbaselineow .........290 C-15Plotof U u a scaledagainstsimilarityparameter forturbulentow ........291 16

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AbstractofDissertationPresentedtotheGraduateSchool oftheUniversityofFloridainPartialFulllmentofthe RequirementsfortheDegreeofDoctorofPhilosophy EFFECTSOFTURBULENCEONFIXEDWINGSMALLUNMANNEDAERIAL SYSTEMS By MichaelJ.Sytsma May2013 Chair:LawrenceUkeileyMajor:AerospaceEngineering Thestabilityofnaturalierswouldbeanexcellenttraitto bedesignedintosmall unmannedaerialsystems.However,thereisagreatdealofun derstandingthatis missingregardinghowturbulenceaffectsightloads.This isparticularlyimportant forlow-speedaircraftinhighlevelsofturbulenceaswould beexperiencedverynear totheground.Thegoalofthisdissertationistodevelopani ncreasedunderstanding ofhowthepresenceofturbulencechangesloadsfeltbyanair craft.Thisincludesthe developmentandcharacterizationofarepeatable,variabl e,highintensityturbulent environmentwithinawindtunnel.Theturbulentloadsareex aminedtodeterminetheir relationshiptoturbulencestatistics,andparticleimage velocimetryisusedtobetter understandtheowcharacteristicsthatleadtosuchloads. Anactiveturbulencegridhasbeenconstructedwhichallows foradjustableturbulent oweldsinthewindtunnel.Theseturbulentowshavebeenc haracterizedusing constanttemperatureanemometrytoevaluatethestatistic aldependenceonrunmode, speed,andlocation.Meanloadmeasurementsperformedonth reecompositeatplate wingmodelsindicatedthatturbulenceextendedthestallbe haviorandmodiedtheother loads.Dynamicloadswereevaluatedtodevelopaninitialun derstandingofthespectral behavioroftheloadsbehindturbulence.Particleimagevel ocimetryontheoweld wasmeasuredtodeterminedifferencesintheoweld.Theba selineowsexhibited adetachedshearlayerfromtheleadingedgethatcouldreatt achtoformaseparation 17

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bubbleatloweranglesofattack.Theturbulentowsdevelop edathickandrapidly growingshearlayerthatwascapableofmaintainingattache dowtomuchhigher anglesofattack,andtherebyextendingstallandchangingo therloads.Differencesin loadbehaviorbetweenlowandhigheraspectratiowingswasi dentiedasbeingdueto changesintheow. 18

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CHAPTER1 INTRODUCTION Bats,birdsandinsectsliveinageometricallyclutteredwo rldwithlargeamplitude unsteadyairowsyetexhibitrobust,agileandcontrolled ight.Theunsteadyairows consistofamixofdiscretegustsandcontinuousturbulence ,typicallywithadverse effectsonight;yetafusionofsensors,actuatorsandpass ivebehaviorallownatural yerstoachievecontrolledight.Smallunmannedaerialsy stems(SUAS)aretypically desiredtoylowerandslowerthanexistinglargeraircraft andatthesametimeexhibit manyoftheightcharacteristicsthatnaturalyersposses s.Flyingslowercausesmuch oftheatmosphericunsteadinesstobealargerproportionof theincomingvelocity vector.Thespatialscalesoftheturbulencearealsocloser tothatofthevehicleatlow altitudes,aparameterwhichnegativelyaffectsightstab ility.Additionallythedenition oflowextendsintogroundcluttermeaningthatthereareple ntyofobstacles,andany undesiredresponsecanquicklycauseacrash.Theprimarysc alingadvantageof aerodynamicresearchonSUASisthatfullscaleornearfulls caletestingispossible.In thepastdecadethishasbeenagreatadvantageforwindtunne ltestingwiththemajority ofresearchfocusingongoodowqualityformeanmeasuremen ts,butinterestinthe effectsofgustsandturbulenceontheseaircrafthaveledto researchbeingperformedin morerealisticenvironments. Theeffectsofgustsandturbulenceoncontrolledightwasr ecognizedasa problembeforethedaysofpoweredight,anditwastheseund esiredeffectsthat motivatedtheWrightbrotherstodevelopightcontrols[ 1 2 ].Theunpredictable natureofairdisturbancesanditssometimesdisastrouseff ectsforcedresearchinto thesubjectearlyon.Evidencedbythersttechnicalreport commissionedbyNACA [ 3 ],theeffectsofunsteadyaironightwereadifcultproble mthatneededtobe addressedforthesafetyofight.Aircraftofthaterawerer elativelyslowiers,and thepresenceofturbulenceandgustsposedamajorobstaclet ocontrolledight. 19

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Theincreasingprevalenceofaircraftledtomoreaccidents attributedtogusts,some withlargelossesoflife[ 4 ].Theseaccidentsmotivatedresearchintosensingand understandingatmosphericturbulencesothatsuchacciden tscouldbeavoidedthrough aircraftengineeringandightavoidance[ 5 ].Thelonglifespanofmanyoperatingaircraft hasalsocausedfatiguefromturbulencetobeamajorconside rationindesignand analysis[ 5 6 ]. SUASareaclassofaircraftsosmalltheyfalloutofthespect rumofresearch conductedontraditionalpilotedaircraft.Thisclassofai rcraftisofsignicantinterest tomanygroups,andtheintendedoperatingenvironmentrang eswidely[ 7 ].Thereis currentlyasignicantefforttodeterminetheeffectsoftu rbulenceonsuchsmallaircraft aswellasmethodstomitigatethoseeffects[ 8 – 11 ].TheincreasedinterestinSUAShas revealedmissingknowledgeoflowaltitudeturbulenceandi tseffectonsmallaircraft. Turbulenceveryneartotheground,aroundbuildingsandgro undclutter,hasrecently beenstudiedwithdirectapplicationtoSUAS[ 7 12 ].Thesestudiesindicatethatthe fullscaleaircraftstandardizedmodelsandtreatmentsmay nolongerbeadequateto representtheturbulentbehaviorinclutteredurbanenviro nments. OnegreatadvantagetothestudyofSUASisthattheycanoften betestedat fullscaleinawindtunnelfacility.Thishasbeenagreatboo ntoresearchinrecent yearsasithasalloweduniversityresearcherstoperformre searchutilizingrelatively lowcostwindtunnelfacilities.Howeverarecognizedprobl emofSUAStestingisan increasedaerodynamicsensitivitytoReynoldsnumbereffe cts[ 13 14 ].Thishasled tothedevelopmentofwindtunnelfacilitiesspecicallysu itedtothestudyofSUAS [ 15 16 ].SUAStendtobelightweight,resultinginightspeedswhi chareslowand wellwithinthesubsonicrange[ 17 ].Thesepropertiesmakethemverysusceptibleto theadverseeffectsofgustsandturbulence[ 18 ].ItisgreatlydesiredthatSUAScould operateinsuchenvironmentswithoutadversecontrollabil ityeffects,andmitigationis soughtthroughpassiveoractivemethods. 20

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Theeffectofunsteadyaerodynamicsonlargeaircrafthaveb eenextensively studiedoverthepast100years,resultingindetailedmodel sofaircraftbehaviorin thepresenceofgustsandturbulence[ 19 ].Furthermore,awiderangeofsensorsand controlmethodologieshavebeendevelopedforlargeaircra ft,andseveralaircrafthave beeneldedwithcompletegustsuppressionsystems.Thesem odelsmakesimplifying, linearizingassumptionswhichrelyontheaircraft'slarge massandrelativelysmall uctuationsincomparisontoightspeed[ 20 – 22 ].Theseassumptionsarepotentially invalidatedbythelargeturbulentperturbationspossible aswellassmallaircraftscales andinertia,butitisuncertainifandtowhatextentthesemo delsarestillapplicableto SUAS,motivatingthecurrentresearch.Additionally,thet hrustofmodelingforlarge aircraftisfocusedonaircraftstructuralloadsestimatio nsfordesignpurposes,whilstfor SUAStheightbehaviorandcontrollabilityaremajorconce rns. Thelargeaircraftmodelsarecapableofpredictiveloadses timation,andthis hasbeenusedingustmitigationsystems.Manygroups[ 17 23 24 ]areinvestigating turbulencesuppressionmethodsforsmallaircraft,andsom eareusingthesesame modelsdevelopedforlargeaircraftwithlimitedsuccess.I tisofinteresttodetermine whatcanactuallydescribetheresponseofsmall,lightairc rafttoturbulence.Thethrust ofthisresearchwillthereforeattempttodeterminetheeff ectsofturbulenceonthin,low aspectratio(A)wingsinrealisticsituationswheremanyoftheassumption susedon largeaircraftareinvalid. Inthefollowingsectionstheeffectsofturbulenceonaircr aftightwillbediscussed. Thiswillstartwithabriefmotivationforthestudyofturbu lenceasitpertainstoaircraft, anditisfollowedbyachronologicalmaturationofthestate oftheartforanalyzing turbulenceeffectsonlargeaircraft.Thiswillendinthecu rrentlyusedanalysismethods, andthenmorerecentworkpertainingSUASandUASwillbedisc ussed.Decitsin understandingwillthenbeaddressedtofurthermotivateth iswork. 21

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Table1-1.Summaryofadverseturbulenceeffectsonaircraf t Priority Problem 1 StructuralFailure 2 LossofControl 3 StructuralFatigue 4 DegradedHandlingQualities 5 CrewandPassengerComfort 1.1BackgroundofTurbulenceEffectsonMannedAircraft AtmosphericTurbulencehaslongbeenrecognizedascausing important,and oftenundesired,effectsonaircraftight[ 1 – 3 22 25 – 34 ].Theneedtoovercomegusts mayhavemotivatedtheWrightbrotherstodeveloprollcontr ol[ 1 2 ],andgustsand turbulencehaveproventobeproblematiconmanymorelevels .Ashortlistofthemajor adverseturbulenceeffectsonaircraftaresummarizedinta ble 1-1 inorderofperceived importance.Theearlierdaysofaviationwerelledwithig htmishapsprimarilyowing tothersttwoeffects,howeverasaviationmaturedtheothe reffectsstartedtobe dominantfactorsaswell. Structuralfailuresandlossofcontrolhavebeenmitigated throughregulation requiringrigorousengineeringdesign[ 5 6 35 ].Theseregulationsdictateasafetyfactor methodologybasedonempiricalaircraftloadenvelopesdep endingonaircrafttype. Theideabehindamandatedsafetyfactoristosetthebarfors tructuralfailureorloss ofcontrolhighenoughthatinpracticetheseeventsarevery infrequent.Fatigueistoan extentregulatedindesign,withdesignfatiguelivesbeing designedintoeachaircraft. Actualprogressionoffatigueisprimarilydeterminedthro ughperiodicinspectionsofthe aircraftstructureswithrepairsasnecessaryandultimate lyairframedecommissioning. Degradedhandlingqualitiescausesthepilottoworkharder makingpilotfatigueafactor. Pilotfatigueistypicallymitigatedbyincludingacopilot toshareresponsibilities,aswell asbymaximumsinglepilotdurations.Crewandpassengercom fortismitigatedby includingightsicknessbagsandaircraftwindows,howeve rtoalargeextentthedegree 22

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ofdiscomfortisaircraftandpassengerdependent.Allthes econsiderationsandmany morehavebeenstudiedscienticallyaslongasthehistoryo faviationitself. TheearliestpublishedscienticworkwasbyWilson[ 3 25 26 ]onrelating turbulencetoaircraftightbehaviorresultedinanalytic almodelsbasedonsimplications oflinearizedightmechanics[ 3 25 26 ].IntheseworksWilsonlinearizestheaircraft equationsofmotionandappliesadecomposedturbulentvelo cityvectoragainstthe aircraftightforces.TheseearlyinvestigationsbyNACAr esultedininsightsintothe basicwaysinwhichturbulenceandgustsaffectightcontro llability,andtheseresults arestillincludedinaircraftcontroltextstoday[ 4 ].Theuseoftheserelationsrequireda morecompleteunderstandingofhowtheunsteadyvelocityco mponentsaffectedaircraft loads. Thisgapinunderstandingwasbridgedwithlinearizedaerod ynamicmodelsfocused onthedynamicresponseofatwo-dimensionalairfoilinnonuniformow[ 34 ].Theworks ofWagner[ 36 ]andK¨ussner[ 37 ]developedexpressionsrelatingtheeffectsofanairfoil encounteringasuddenstepvariationinangleofattack.The odorsen[ 38 ]derivedan expressionrelatingverticalmotionofawingtodynamicloa ds,animportantfactorin utterconsiderations.Sears[ 39 40 ]shortlythereafterderivedanequationrelatingthe effectofasinusoidalverticalgustonloadsfromatwodimen sionalwing. Atthesametimetheseanalyticalaircraftdynamicsandload estimationmethods werebeingdeveloped,G.I.Taylor[ 41 ]wasdevelopingstatisticaltheoriesonturbulence whichhavebecomethestandardstoday.Thesepreviouslydev elopedtheoriesbased onexperimentalmeasurementswereshownvalidinmanycircu mstances.Taylor investigatedturbulentphenomenaneartheground,intheup peratmosphere,andin theoceansatthetimethatightscienceswerejustbeingdev eloped.Hisexperiments provedtheconceptsofastatisticalturbulentlengthscale ,behaviorofprobabilitydensity functions,decayofturbulence,turbulenceinteractingwi thsurfacesinopen(asina wing)orclosed(pipeorduct)ow.Theseexperimentsyields implifyingassumptions 23

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suchasTaylor'sFrozenFieldhypothesisandisotropyoftur bulenceatthesmallscales, aswellasobservationsonthefrequencycontentofturbulen ce[ 42 43 ]. TheodorevonK arm an[ 44 – 46 ]followedonTaylor'sworkanddevelopedafunctional representationofanatmosphericturbulencefrequencyspe ctrumwhichisself-similar acrossmultiplescales.Thissimplerepresentationofspec trahasbeenresearched andtestedsinceitwasformulated,butithasbeenfoundtobe remarkablyaccurate indescribingoverallturbulentspectra,evenatlowaltitu des[ 12 47 – 51 ].Combined withTaylor'swork,apurelystatisticaldescriptionofthe verycomplexphenomenaof turbulencehasbeendevelopedwhichinasimpliedwaydescr ibespertinentbehaviorof turbulentows. Theanalyticalworkdescribingatmosphericturbulenceand itseffectsonaircraft motivatedexperimentalendeavorsincludingwindtunnelan dighttesting.Initialight testingindicatedthewayforwardfordevelopingdesigncri teriabasedoffightmeasured data,howeverithighlightedthelackofknowledgeaboutatm osphericdisturbances[ 52 ]. Oneaspectofwindtunnelresearchofparticularrelevancet oSUASscaledresearch wasthecommissioningoftheLangleyPilotGustTunnelin193 7[ 53 ].Thisgusttunnel consistedofasledsystemcapableofacceleratinganapprox imately1meterspan modelaircrafttoightspeedsofapproximately25 ms 1 .Attheendofthesledthe aircraftmodelwasreleasedintofreeightafterwhichitwa sownoverafangenerating adiscreetgustofvariableshape.Themodelwasthencaughtw ithhangingnets.The Pilottunnelwasdecommissionedin1945andwasrebuiltinto themorecapableLangley GustTunnelwhichwascapableoflaunching2metermodelsupt o50 ms 1 .Thistunnel remainedinoperationuntil1956.Theresultsofthesetwotu nnelsaresignicanttothis workbecausetheytestedaircraftinthesmallUAVsizerange atcomparablespeedsand Reynoldsnumbers. TheinitialfocusoftheresearchinthePilotGustTunnelwas testingofsimple rectangularwingedmodels[ 53 ]andtheirreactiontogustsofvarioussizesinorderto 24

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comparetotheory.Comparisonswerereasonableexceptinth ecasesoflowA.The testsalsoevaluatedhowmonoplanetheorycomparedtobipla nes[ 54 ],andresults indicatedagreementforlonggusts,butthetheoryfailedfo rshort,sharpgusts.Further testsoncanardairplanemodelsindicatedthattheyaremore sensitivetoguststhana conventionalaircraftofthesamedimension[ 55 ].Inanefforttotestanalyticalmethods whichindicatedcompliantwingscouldbegustsuppressive, amodelwithtorsionally exiblewingswastestedwithsuccessinmitigatingtheeffe ctsofagust[ 56 ].Further gustmitigationwasobtainedbyinstallationofaleadinged gefence[ 57 ].Gusttunnel researchwasessentiallysuspendedduringWorldWarIIexce ptforsupportingthe designofanewaircraft[ 58 ]. AfterWWIIthePilotGustTunnelwasreplacedwiththenewLan gleyGustTunnel initsownfacility.Basicresearchcontinuedevaluatingth eeffectofforwardoraftsweep onaircraftgustbehavior[ 59 – 62 ],effectofairfoilselection[ 62 63 ]andtheeffectsof aircraftCG[ 64 ].Theexperimentsonsweepwereconductedbecauseatthetim eitwas uncertainhowsweepaffectedtheanalyticalgustloadsmode lsdevelopedforstraight wings,andacorrectionfactorwasdevelopedbymultiplying thestraight-wingmodels bythecosineofthesweepangle.Sweptwingedaircraftwerea lsoshowntosmooth outthenormalaccelerationfeltbygustwhichwaspartially attributedtothewaythese aircraftpitchdownmoreintothegustthatstraightwingsdi d.Changingtheairfoilsection thicknessandcamberdidnotappreciablyimpactgustrespon se,howevermodifyingthe leadingedgetobesharporroundedledtothesharperwingtoh aveamoreextreme gustresponse.Thiswasattributedtoleadingedgeseparati onandcorrespondingvortex lift,aphenomenonthatwasnotpredictedbyanalyticalmeth ods. Areviewofthestateofgustsciencesin1949byDonely[ 65 ]indicatedthatwhile manyrulesofthumbforaircraftdesignwithgustsinmindhad beendeveloped,none hadyetbeenofciallycodiedorappliedtoaircraftregula tion.Furthermore,hecited lackofknowledgeonhowgustsbehaveathigheraltitudesand howtheyreactwith 25

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fasteryingaircraft.Itwasalsoduringthiserathatthere wereadvancesintheory whichallowedcouplingofaircraftgustresponsetothestru cturaldynamicsofthe system.Thiswasfastbecominganimportantconsiderationa saircraftwereying faster,athigheraltitudesandwithhigherwingloadings.W iththeseneweraircraftitwas becomingincreasinglyimportanttoefcientlydesignthea ircrafttobestrongenoughfor anticipatedloadsyetaslightaspossible.Thephenomenaof utterduetoaeroelasticity becameofhighimportancetoaircraftdesignandanalysis[ 34 66 ].Thetransition tojetaircraftfrompropellerdrivenoneswasaccompaniedb yapushinthescience communitytoevaluatetheeffectsofgustsathigherMachnum bers,altitudesandwith muchlargeraircraft. Harmonicanalysiswasalsofastbecominganimportantaspec toftheevaluation ofunsteadyquantitiesassociatedwithaircraftingusts.V onK arm an's[ 44 ]earlywork onunderstandingthenatureofturbulencehadsinceextende dtotherealizationthat turbulenceconsistsofacascadeofscaleswhichcanbeinter pretedusingharmonic analysis[ 45 ].Thiswasnotlostontheaircraftgustresearchcommunityw honow understoodtheunsteadinessofaircraftinightresultedn otonlyfromdiscreetgustslike thosestudiedintheLangleyGustTunnel,buttheyalsoresul tedfromthecontinuous cascadeofturbulencescales[ 67 ].Theserealizationsledtoighttestssimultaneously measuringsomeowquantityaswellasaircraftinertialres ponse[ 33 68 – 72 ].The testresultsindicatedthatmostaircraftwereparticularl ysusceptibletoturbulenceof acertainwavenumber ,basedonightspeed U 1 andturbulencescale .These newrealizationswerequicktobeaddedtoaircraftdesigncr iterion[ 73 ].Therewasan increasingunderstandingthatwingexibilitynotonlyaff ectedgustloadresponse,but elasticvibrationscouldmagnifytheeffectonwingstrain[ 74 75 ].Effectsofgustswere ofprimaryimportancetostructuraldesigners,howeverthe ywerealsoimportantfor stabilityanalysis[ 76 77 ]. 26

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Aroundthistimesomeconfusioninterminologywasgenerate dwhichhaslargely remainedineffectuntiltodayregardinggustsandturbulen ce.InvestigationsbyTaylor andvonK arm anshowedaveryscienticaspectofturbulenceasaveryrand om process,whilemostresearchwastreatingunsteadinessin ightasduetodiscreetgusts whichhadadenedshape,whichaircraftwereanalyzedto.Th egrowingrealization thatwhatpilotsfeltasgustswerelargescaleturbulencean dwhatwasconsidered noiseorvibrationcouldbeattributedtosmallscaleturbul enceledtothesometimes interchangeablenatureofthetwowords[ 73 78 ].Additionally,theworldofaviation expandedrapidlyafterWorldWarII,leadingtomoreturbule nce-relatedightmishaps, andhencemoreresearcheffortwaspouredintothetopic. By1965theharmonicanalysisofturbulenceonaircraftfors tructuraldesign purposeswaswellentrenched,howeverthesimplicityofdis cretegustanalysis preventeditfrombeingreplacedentirely[ 77 79 – 82 ].Thiswasbeingpushedbythe increasingdatabaseofatmosphericturbulenceconditions [ 47 49 50 83 ].Furthermore, therewasanunderstandingofhowstaticallyderivedaircra ftstabilityderivatives couldbecombinedtodetermineanaircraft'sfrequencyresp onsetoturbulence[ 76 ]. Thismethodinmanycasesunder-predictedtheaircraftresp onsewhencompared againstighttestdata,indicatingwindtunnelmethodsto ndmoreaccuratefrequency responseinformationpriortoaircraftproduction.Thisag ainmotivatedwindtunnel facilitieswhichcouldexperimentallyinvestigatetheeff ectsofturbulenceonscaled aircraft[ 84 85 ].Thesewindtunnelsgeneratedunsteadyowssimilartoatm ospheric turbulencebyperturbingtheowupstreamofthetestmodel. Thebreadthofresearchhadatthispointdeterminedwhatwas mostimportant forgustloadsonaircraft[ 86 ].Averticalgustcausesanincreaseinwingloadingand acorrespondingnormalacceleration.Theaircraftfuselag eisalsocyclicallyloadedas thetailloadslagthewing,causingapitchdestabilization .Thisdestabilizationtendsto alleviategustloadsexceptwhenthegustscomeatanaircraf t-specicfrequencywhich 27

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cancausehigherloads.Sidegustsareimportantforstrengt hevaluationsonthevertical stabilizer,buttendtonotaffectthewingstrength.Incomi nggustshavelittleeffecton aircraftloads,andgustswhichvaryacrosstheaircraft,or haverotationalcomponents causeupsetstostability,butaslongastheturbulenceisno ttoolargearenotamajor contributortostructuralfailure. TheAirForcealsolookedintowaystoalleviategust-induce dloadsthroughan activecontrolsysteminthelate1960's.TheB-52EandC-5Aa ircraftwereselectedfor thestudyperformedbyBoeing,andoneB-52Eaircrafthadagu stalleviationsystem installed.Theanalysisportionoftheeffortindicatedtha ttheactivesystemwhichutilized existingcontrolsurfacescouldgreatlydecreasegust-ind ucedloadsaswellasthe fatiguedamagecausedbythem[ 87 ].Flighttestingofthesystematbothlowandhigh altitudesvalidatedtheanalysesandshowedthattheconcep twasviable,howeverthe systemwasneverintroducedtotheeetbecauseofprohibiti vecost[ 88 ]. The1970'sbroughtmoreanalysismethodswithincreasingly powerfulcomputers. Muchofpreviousworkonaircraftwasaccomplishedthroughe itheranalyticalmethods orthroughighttesting,butcomputertechnologyopenedth edoorsforincreasingly accuratesimulations.Muchworkfocusedonsimulationsoft urbulenceeffectson aircraft,particularlywheretheanalyticalmodelshadfai lings[ 89 – 92 ].Thesesimulations allowedforturbulencetobesynthesizedwhichwasmuchmore realisticthanpreviously used.Thespectralaircraftdesignprocesscontinuedtobeu pdatedasmorewind environmentswereexplored,andaircraftightdatawerelo gged[ 30 50 93 94 ].The conceptofmodelinganaircraftfrom4points,thewings,fus elageandtail,becamethe standardmethodwherebyturbulentloadsareappliedtothe ightdynamicsmodels,and thismethodisstillinusetoday. Thestateoftheartwastomodelturbulenceasarandomproces swithspecied statisticalandspectralpropertiesandapplyitagainstal umped-parameteraircraft modeltodetermineloadings.Theaircraftightdynamicsmo delwastypicallylinear, 28

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andturbulencewasoftentreatedasaGaussianprocess[ 4 ].Theloadsresultingfrom analysiswerethenstatisticallydecomposedtodeterminea ircraftdesignrequirements toavoidstructuralfailuresandspecifyfatiguelives.Thi sstatisticalanalyticmethod resultedinloadexceedancefrequencieswhichwereofcriti calimportancetofatigue engineers,anditalsoallowedstructuraldesignerstobuil dforaworstcasescenario. Forexample,MIL-STD-8785requiredallmilitaryaircraftt obecapableofwithstandinga gustthathasonlya 10 6 probabilityofoccurring.Interestinthiseldwaskeenfor many promotingaircraftsafety,astheconstantlyincreasingpr evalenceofaircraftledtomany turbulence-relatedaccidents.Thehighcostofthesedrove muchresearchtofocuson turbulenceasitappliestostructuralfatigueandfailure[ 27 ]. Thecomputersimulationsprovedtobeveryeffectiveateval uatingaircraftresponse toturbulence,andincreasingsimulationcomplexitypaido ffwithmoreaccurateresults [ 22 95 ].Advancesincomputingpowerallowedtheturbulencesimul ationtoevolve fromonedimensionaltimehistoriestoathreedimensional eld[ 31 32 ].Furthermore, thesesimulationscomparedwellwithighttestdata[ 29 ],andhencebecameagood candidatetechnologyforaircraftdesign.Theanalyticalm ethodshadincreasedin complexitybutstillreliedonalinearlumpedparametersys temtodescribetheaircraft [ 4 ].Thesemethodsalsotreattheaerodynamicsacrosstheairc raftasquasi-steady,an assumptionthatwassomewhatjustiedconsideringthehigh ightspeedsinrelation torelativelysmallturbulentperturbations,howeverthep ushforhigherdelityledto theinclusionofunsteadyaerodynamicmodelsintoaircraft .Furthermore,activegust alleviationproveditselfeffectiveformitigatinggustlo ads,makingactivecontrolsystems desirableforlargeexibleaircraft[ 20 21 ]. The1990'sbroughtcontinuedimprovementsincomputersimu lationcapabilities, howeverthematuringstateofthetechnologybroughtmuchof thisworkoutofacademic circlesandintotherealmofproprietaryownership.Amanua lonturbulenceanalysis preparedbyHouboltet.al.[ 21 ]discussedtheaircraftdesignprocesswithrespectto 29

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turbulence.First,astatisticaldatabaseispreparedoftu rbulencewhereintheskythe aircraftisintendedtoy.Next,thesevaluesareaugmented byregulationsasnecessary, intheUnitedStatestheseareMIL-STD-8593orFederalAviat ionRegulation(FAR)part 23and25.Thedataarethenappliedagainsttheaircrafttode terminebodyloadsusing boththediscretegustandthespectralmethod.Thediscrete gustisusuallythemore severeloadingcase,andittendstodrivethestructuraldes ign.Thespectralturbulence loadsarethenusedtodevelopfatiguelifeestimationswith redesignasnecessary.Allof thisanalysisisperformedundertheeyeofairworthinessce rticationpersonnelforight safety[ 19 21 ]. Turbulence,asitappliestolargeaircraft,hasbecomeanis suemostlyaffecting thestrengthandfatigueofthestructure.Theregulatorydo cumentsdirectanalyses utilizingtheaforementionedprocedures,howeveraircraf tmanufacturersmayutilize moreaccuratemethodsastheyhavebeendeveloped[ 19 ].Thiscanbeviewedas anincreasinglysuccessfulresearchareaasaircraftcrash esinvolvingturbulenceare incrediblyraredespitemoreandmoreaircraftintheskies. Forexample,themost recentairlinedeterminedtohavecrashedduetosevereturb ulencewasBOACairlines ight911in1966[ 96 ].Thisindicatesthatthedesignmethodshavebeensuccessf ul inmitigatingstructuralfailures.However,severeturbul encestillcausescostlyaviation accidentstoightattendantsandpassengers[ 28 ]. Whilelargeaircraftturbulenceresearchhasbeenfruitful ,therearecritical differencesthatmakeitnotwhollyapplicabletoSUAS.Thep rimarydifferencesare thesize,weightandspeeddisparities.Thesmallsizeandwe ightofSUAShavedriven downthewingloadingleadingtoamuchhighersusceptibilit ytoturbulentupsets.The Reynoldsnumberdifferenceistremendous,andSUASoperate inaReynoldsnumber regimewhichbehavesentirelydifferentlythanthelargely inviscidregimeoflarge aircraft.Partiallyowingtolowerightspeeds,butalsoto lowaltitudes,SUASythrough muchstrongerturbulencethanlargeaircraft.Thesediffer encesmeanthatdespiteyears 30

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ofresearch,theunderstandingofhowSUASareaffectedbytu rbulenceisstillinits infancy. 1.2TurbulenceonSmallUnmannedAircraft Theresearchconcerningmannedaircraftdivergedfromthat whichwouldbedirectly applicabletoSUAS,motivatingresearchonsuchsmallaircr aft.SUASaremuchsmaller, lighter,slowerying,andhavelowerwingloadingsthaneve nsmallpilotedaircraft. Additionally,thereisastructuralbenettoSUASthatallo wthemtobebuiltmuch strongerthanstrictlynecessarywhichalmosteliminatesm anyofthestructuralconcerns oflargermannedaircraft.Additionally,thesesmallaircr aftareenvisionedtoyvery closetothegroundandobstacles[ 7 ],aconcernthatmannedaircraftonlyencounter twiceperight,andusuallyforaveryshortduration. EarlymodelsofSUASusedasimilarlinearlumped-parameter systemtomodel theaircraft,howevertheagreementwithobservedighttes tdatawasnotverygood [ 18 97 98 ].Moderncompositefabricationmethodsbroughtthenewcap abilitytoform extremelyexiblewingswithoutstructuralfailure[ 99 ].Thisexibilitywasusedwithsome successtomitigatetheeffectsofturbulence,requiringle sscontroleffortforightpath correction[ 100 ].Theincreasedliftingsurfaceexibilityandhighturbul encelevelsfurther complicatedmodeling[ 101 ],andmucheffortwasspenttocomputationallymodelthe aero-structuralinteraction[ 102 – 104 ]. Muchresearchhasbeenperformedgatheringturbulencedata closetotheground, includingresearchfordesignofverticalorshorttakeoffa ndlandingaircraft[ 47 49 ], windturbines[ 105 ],andbuildings[ 106 107 ],andighttestresearchisstartingto becomeavailable[ 18 ].Akeydetrimentofthispreviousresearchwasthatonlyrel atively lowfrequencymeasurementswereperformed(order1Hz)whic hlimitedtheresolution ofthedatatolargerturbulentscales.Recentresearchinto thenear-groundight environmentthatSUASwouldhavetotraversebyWatkinsetal .[ 12 24 51 108 ] indicatesthattherearelargeuctuationsinallthreevelo citycomponentsrelativeto 31

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atypicalSUASightspeed.Thoseexperimentsgatheredhigh dataratemulti-point turbulencemeasurementsneartothegroundandbuildingsin anurbanenvironment forthepurposeofidentifyingtherealturbulentenvironme ntaSUASmustcontendwith. Ofparticularinterestwasanincreasinglystrongrollpert urbationeffectasthevehicle's spanbecamesmaller.Theexperimentsrevealedturbulences pectratendingstrongly towardstheuniversalKolmogorovlogarithmicslopeof-5/3 AsmorebecameunderstoodabouttheenvironmentSUASmustco pewith,it becameincreasinglyimportanttoconsidergustsandturbul enceinthedesignofa capablevehicle[ 7 109 ].Lissaman[ 17 ]highlightedcontroldifcultiesthatsmallerxed wingvehicleswouldhavetocontendwith,alsopinpointinga dequaterollcontrolasa shortcomingofmanyaircraftdesigns.Morerecentresearch inthecontrolcommunity hasfocusedonactivecontrolbasedmethodstomitigatethee ffectsofgustsand turbulenceonSUASight[ 23 98 ].Zarovyetal.[ 11 ]usedcontrolledrotorcraft tondthataccuratecontrolrequireshigherbandwidthanda uthoritythancurrent actuatorsexhibit.Thesecontrolschemesreduceinstabili ties,butthereismuchmore progresstobemadetowardsatrulygust-insensitiveaircra ft.Onebasicconcernis thatcontrolsystemsmakeassumptionsabouttheaircraftbe haviorinturbulence, howeververicationofthisbehaviorinhighturbulenceint ensitieshasyettobetested. Othercontrolschemesavoidspecicationoftheaircraftmo delaltogethertoavoid impropermodeling.Thisindicatesthataircraftgustrespo nsemodelsneedtobestudied, validated,andstandardizedbeforetheymaybeusedinasucc essfulgustmitigation algorithm. Cruzetal.[ 110 ]showedthemeanloadsfroma2-DlowReynoldsnumberat plateairfoilweremodiedbythepresenceofturbulence,wi thstallangleandmaximum liftcoefcientbothincreasingwiththepresenceofturbul ence.RaviandRavietal. [ 111 112 ]investigatedthedynamicpressureloadingeffectsonasim ilarmodeland foundthatthedynamicloadsgeneratedbytheturbulencecan easilyexceedmaximum 32

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staticvalues,andsmokevisualizationindicatedthatturb ulentperturbationscancause leadingedgeseparationandvorticesatangleofattacklowe rthanstall.Torreset.al [ 113 ]studieda2-DwindturbineairfoilatcomparableReynoldsn umbersandhadsimilar ndingstoCruzet.al.withthenuanceofatraditionallydes ignedairfoil.However, neitherofthesestudiesincludedlowAwingslikewhatmightbetypicalofaSUAS [ 100 ].LundstromandKrus[ 18 ]testedpropulsionsystemsandighttestedfullaircraft indifferentturbulentconditions,buttheyfoundthatturb ulencedidnotsignicantlyaffect overallaircraftperformance,indisagreementwithwindtu nnelwork. Thisresearchfocusesonbasicunderstandingofhowpropert iesofrealistically strongfreestreamturbulence,suchasintensityandlength scales,affectmean anddynamicloadsonniteA,xed-wingaircraftmodels.Additionalfundamental understandingissoughtonhowdifferencesinaircraftdesi gnparameterssuchasAaffectanaircraft'sresponseinturbulence.Insightintot heuidbehaviorisalsosought whichmayjustifydifferencesinloads. 1.3ResearchOutline Asisshownbytheprecedingtext,thereisaknowledgegapreg ardingmultiple aspectsofhowgustsandturbulenceaffectSUASwhichrequir efurtherstudybefore theycanbeeffectivelyusedasengineeredsystems.Thegoal ofthiseffortistherefore tostudytherelationshipsturbulencehaswithregardtoaer odynamicloads,andto determinecharacteristicphysicalowphenomenonwhichca usedestabilizingunsteady loads.Flowdiagnosticssuchasconstanttemperatureanemo metry(CTA)andparticle imagevelocimetry(PIV)wereutilizedtoevaluatehowtheu iddynamicseffectthe aerodynamicloads.Alowordercomputationalmodelwasdeve lopedtosimulatesome ofthemeasureddataandincreaseunderstandingbeyondthee xperiments. 1.4ResearchPlan Thestepsinvolvedincarryingoutthisresearchwere: 33

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Developandcharacterizeacontrolledenvironmentinthewi ndtunnelthatcan simulatethemulti-scaleturbulentenvironmentthatwould beobservedinaSUAS ight Developandcharacterizealow-ordercomputationalmethod ologyformodelingthe effectsofturbulenceonaliftingsurface Conductstudiestoestablishandunderstandtheeffectsoft urbulenceonthe averagedandtime-dependentaerodynamicloadsanddevelop relationships betweenthemodelloadsandturbulence Developafundamentalunderstandingofhowthefree-stream turbulencecouples withtheowoverawingtoeitheradverselyorpositivelyaff ecttheaerodynamic loads 1.5Contributions Thisresearchcontributesanincreasedknowledgeofhowrel ativelylargeintensity turbulenceaffectsloadgenerationonlowReynoldsnumberS UAS.Itwillbeshownthat meanloadsexhibitlargechangesinbehaviorascomparedaga instlowturbulenceows. AthigherAturbulencehastheeffectofsubstantiallyincreasingmaxi mumliftcoefcient andangleofattack,or .Turbulencealsosmoothsoutandoffsetsthepitching momentbehaviorresultingindifferentpitchstabilitybeh avior.Suchloadvariations haveasubstantialimpactondesignconsiderationsofSUASt hatoperateinturbulent environments,andthisworkhighlightstheneedforSUAStob etestedindifferent turbulencelevelstounderstandthefullspectrumofrespon se.ThelowerAmodels showedthatturbulencecaninterferewiththestrongtipvor texformationresulting inreducedliftcoefcientsandsimilarlyperturbedpitchi ngmoments.Thedynamic loadsareshowntomatchanexpectedturbulentpressurespec traldistribution,andthe variationsthemselvesareshowntobequitelarge.Simulati onsintendedtohighlight dynamicbehaviorshowthatthereisabandwidthofinterestf romroughlyanorderof magnitudelargerandsmallerthanthewing,outsideofwhich turbulencehasalessened effectondynamicloads.PIVmeasurementshighlightfundam entalowsdifferences whichcontributetochangesinmeanloads.Theshearlayeron thepressuresideof thewinggrowsmorequicklyinthepresenceofturbulence,an dthisenhancedgrowth 34

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isresponsiblefortheloadeffectsasitcausesearlierreat tachmentandpostponesstall tohigher .Thebehavioroftheshearlayerinfree-streamturbulencei salsosimilar acrossAhighlightingaphenomenonwhichimprovesperformanceofhi gherAwings andatthesametimedecreasesperformanceoflowAwings.PIVanalysisofthetip vorticesreinforcesthemeanloadsresults,andanalytical analysiscompareswellagainst measureddatawhichgivesinsightintopredictivecapabili ty. 1.6DissertationOrganization ThisDissertationaddressestheresearchplanbydescribin gexperimentalfacilities andtechniquesinchaptertwo.Inchapterthree,theturbule ntenvironmentgenerated inthewindtunnelischaracterized.Inchapterfour,thelow -ordercomputational methodologyisdescribedandresultsarepresented.Inchap terve,meananddynamic loadsinthepresenceofturbulenceareinvestigatedandcom paredagainstbaseline ow.Inchaptersix,PIVisutilizedtodevelopanunderstand ingofhowtheturbulence affectsairowpatternsaroundthewing.Inchapterseven,a summaryandenvisioned futureworkarepresented. 35

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CHAPTER2 EXPERIMENTALFACILITIESANDTECHNIQUES Properscaletestingrequiresthatallrelevantsimilarity variablesornon-dimensional groupsarematched[ 114 ].InthecaseofmuchofSUASwindtunneltesting,the actualaircraftistestedatactualightspeedandlocalalt itude,almostensuringfull similarity.However,ithasbeenshownthattheambientturb ulencelevelsgreatlyaffect theaveragedstaticloadsthatSUASexperience[ 13 14 ].Thiswouldtendtoindicate thattheresultofanystatictestshouldalsoincludeincomi ngturbulencestatisticsas avariableparameterwithanaccompanying group.Mostexistingwindtunnelsthat SUAShavebeentestedinonlyoperatewithasingleturbulenc ebehavior,andthe pushisusuallyforverylowturbulencelevels[ 15 ].Itwouldthereforemakesensethat thewindtunnelshouldbeabletogeneratevariablelevelsof turbulence.Thischapter willdescribethewindtunnelfacility,turbulencegenerat or,equipment,experimental techniques,anddataprocessingthatwillbeused. 2.1AerodynamicCharacterizationFacility Theaerodynamiccharacterizationfacility(ACF)locateda ttheUniversityof Florida(UF)ResearchandEngineeringEducationFacility( REEF)isalow-speed windtunnelwithanopenjettestsection[ 15 ],andisshownbyFigure 2-1 .Thetunnel wasspecicallydesignedtooperateatlowvelocitiesandwi thlowturbulencelevels.The tunnelentranceconsistsofaow-conditioningsectionand a8:1areacontractionratio thatresultsina1.07meter-squareentrancetotheopenjett estsection.Theenclosure surroundingthetestsectionhasavolumeofnearly57 m 3 withanaxiallengthof3m. Thefreestreamvelocitiesinthetunnelrangefromnominall y0.25to22 ms 1 byaltering thefrequencyonthevariablefrequencydrive.Previouslyp erformedowuniformity studiesforfreestreamvelocitiesof2and15m/swereconduc ted,demonstrating uniformcoreowthroughoutthetestsectionofatleast60%o fthe1.14 m 2 contraction exit.Experimentsusinghot-wireanemometrywerealsoperf ormedandtheturbulence 36

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intensitiesatthetestsectionentrancewerefoundtobeles sthan0.22%forfree-stream velocitiesgreaterthan1 ms 1 .Modelsinthewindtunnelaremountedonadynamic motionrigandloadscanbemeasuredusingeitheroftwosting balancesortwoload cells.FurtherdetailsontheACFcanbefoundinAlbertaniet .al.[ 15 ]. 2.2TurbulenceGrids Twodifferenttypesofturbulencegenerationgridshavebee nusedforthisstudy. Theseinvolveaconventionalstaticgridandanactivegrido fspinningvaneswhichwill bothbedescribedbelow.2.2.1StaticTurbulenceGrid Thestaticgridusedinthisstudyisanoffsetorthogonalgri dof21by21round woodendowels.Thedowelshaveadiameter,D,of1.85cmandha veacentertocenter spacing,M,of5cm.Theorthogonaldowelsareoffsetfromeac hotherbyonediameter suchthattheyaretouchingeachotherwheretheycross.Theg ridisafxedtoaframe thatisattachedtotheinletofthetestsectionwheninuse.T hesolidityofthisgrid, =100 D M 2 D M ; (2–1) is60%.Thisgridgeneratesarelativelylowturbulenceinte nsityof4%attheaxial locationstestedinthisstudy.2.2.2ActiveTurbulenceGrid Thegoaloftheactiveturbulencegrid(ATG)wastoexpandthe capabilitiesof theUFREEFACFtoenablehigherintensitygustandturbulenc eresearch.TheACF alreadyhadlimitedcapabilityforresearchoncoherentgus tsusingwindtunnelvelocity ramping,howeveritlackedthecapabilitytogenerateareal istic,continuousspectrumof turbulencescales.TheactualenvironmentSUASinhabitcan exhibitlargeturbulence intensityandlengthscales[ 12 24 51 108 ].Theseowpropertiesaredifculttoobtain inwindtunnelswithpassiveturbulencegrids,usuallyrequ iringlongfetchandlargertest sectionsizes[ 111 112 115 116 ].Activeturbulencegridsofferthecapabilitytogreatly 37

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increasebothintensityandlengthscaleinashortertunnel ,buttheyarestilllimitedin termsoflengthscaleofthetestsectionwhichmaybemuchsma llerthanatmospheric turbulence[ 117 – 120 ]. Itwasdesiredthattheturbulencehavecharacteristicleng thscalesaslarge aspossible,andturbulenceintensitiescouldbeadjustedi nasimplemanner.The maximumenvisionedightspeedwillbeontheorderof10m/ss othatmodels maybetestedwithReynoldsnumbersrangingfrom25,000to10 0,000.Itwasalso desirablethattheATGbeportablesoitcanberemovedfromth etestsectionwhilenot inuse.BaseduponaliteraturesurveyofexistingATGtypes, adesignverysimilarto Makita's[ 121 ]wasselectedasthemostsuitableforthecurrentstudy. 2.2.3Design TheATGintheACFisadesignsimilartothatdevelopedbyMaki ta[ 121 ]witha fewmodicationsleveragingonlessonslearnedsuchasinco rporationofcross-vane vibrationdampers[ 122 ],simplieddigitalcontrol[ 119 ],andunderstandingexpected differencesbetweenmotionproles[ 8 9 117 120 123 – 127 ].ThistypeofATGconsists oftwoorthogonalgridsofrotatingvanes.Eachvaneconsist sofashaftwithattached wingletswhicharedriventorotatebyacomputercontrolled motor.Thisapparatusis locatedinthewindtunnelattheupstreamendofthetestsect ion,andtheactionofthe spinningvanescausestheairowingthroughthedevicetobe comehighlyturbulent. Figure 2-2 isaphotooftheATGduringtestingoutsideofthewindtunnel ThedesignoftheATGwasaccomplishedbyrstconsideringst atisticalrequirements andcomparingthemagainstotherpublishedMakitastyleATG 's[ 8 9 117 120 123 – 127 ].Inordertoconductmeaningfulresearchonturbulence,th eATGwillgenerate variablelengthscalesaswellasvariableintensitiesoftu rbulence.Themaximum attainableintegrallengthscaleisontheorderofthetests ectiondimension,notionally 1m.Themaximumintensityshouldbeashighaspossible,anda pproximately20% rootmeansquare(RMS)intensityseemedpossibleaccording topreviousresearch 38

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[ 12 17 51 109 128 ].Sincethetestsectionis3mlong,theregionofinterestex tends fromtheverybeginningofthetestsectiontoapproximately 2.25mdownstream becausethecoreowisexpectedtospreadmuchmorethanitdo eswithouttheATG duetoenhancedmixing. Theturbulenceproducedmustdevelopquicklyinordertoach ievethedesired statistics,becausethetestsectionisrelativelyshort.A keynondimensionalparameter identiedbyotherresearchers[ 8 9 117 119 120 123 – 125 ]isthemeshratio,orratio ofdistancedownstream,X,tomeshsize,M, X M : (2–2) ReviewofotherATGdesignsindicatedthatacceptableturbu lentpropertiesexiststarting at 10 M downstream.Thedataavailableformeshdistanceslessthan 10 M indicatedthat theturbulenceisstillindevelopmentleadingtohighertur bulenceintensity,signicant anisotropy,andrapidlychangingconditionsdownstream.T heseconsiderationslead toanotionalmeshspacingof0.133meterswhichresultsinac ongurationwithseven verticalandsevenhorizontalvanes,witheightwingletsat tachedtoeachvane.This placesmosttestarticlesmountedonthedynamicmotionrigi naregionfrom10Mto 12Mdownstream. MostoftheexistingMakitaATG'swingletsaremountedonava neparalleltoeach other,resultinginthelargestturbulenceintensitiesand lengthscales[ 117 119 120 123 124 126 127 ].Thisisgenerallyattributedtotheentirevanecausingo wblockage. However,designssuchasthoseemployedbyPoorteandBieshe uvel[ 122 ],Kangand Meneveau[ 125 ],andRoadmanandMohseni[ 8 9 ]rotatedthewingletsontheshaft toobtainslightlydifferentresults.PoorteandBiesheuve lfoundthatalternatingthe winglets90degreesfromeachotherdowneachshaftcausedth eturbulencetobe moreisotropic,albeitwithadecreaseinmaximumlengthsca leandturbulenceintensity. RoadmanandMohsenirotatedthewinglets90degreesfromone endoftheshafttothe 39

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otherwithsimilarndings.Itisdesiredthatthetargettur bulencelevelsbeashighas possible,anditisforthisreasonthatthewingletsareinst alledinaparallelconguration. LarssenandDevenport[ 119 ]indicatedastrongcorrelationbetweenturbulent lengthscalesandintensitieswithvanerotationalrate.In terestingly,lowerrotational ratestendtoyieldlargerturbulenceintensitiesandlengt hscales.PoorteandBiesheuvel foundtheoppositeeffect,withhigherrotationratesresul tinginlargerintensitiesand lengthscales,althoughthesetestswereinwater[ 122 ].Giventhediscrepancy,it wasbesttoplanforahigherrotationrateandbeabletocontr ollower.Roadmanand Mohseni[ 8 9 ]introducedanondimensionaltip-speedratio, M = 0 : 5 Mf ATG U 1 ; (2–3) whichindicatedarationearunityyieldsmoreisotropictur bulence.Valuesof M larger thanunitydidnotappeartohavemucheffectonturbulentsta tistics,whilevaluessmaller thanunityhadstrongeffectsonisotropyandturbulenceint ensity.A M ofunityinthe ACFat10 ms 1 wouldrequireapproximatelya10Hzrotationalrate. AcontroldesignsimilartothatusedbyLarssenandDevenpor t[ 119 ]isused forthisdesignasitappearedcapableofratesupto20Hzandc ontrolofallmotors usingexistinghardware.AnaheimAutomation23MD206D-0000-00steppermotors withintegrateddriversmovethevanes.Digitalsignalsare sentthroughaNational InstrumentsPXIframewithaPXI-6533HighSpeedDigitalI/O card.Themotorsare wiredtoacceptdigitalsignalsforstepanddirectioncomma ndsataresolutionof200 stepsperrevolution.Thiscontrolmethodallowsforreliab leoperationofthemotorsby themselvesupto30Hz.Themotorsarecapableofspinningthe vanesupto18Hz, afterwhichthemotorsaresubjecttomalfunction.Starting at14Hz,howeverthevanes vibratestronglycausingthemtooccasionallycontacteach other.Maintaininga f ATG lessthan12Hzkeepsthevanesfromvibratingtoomuchandyie ldsa M of1.15at10 m/swhichissufcient. 40

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TheACFisusedbyotherresearcherswhorequirevarioustype sofequipment bemountedinthetestsectionatanytime.Therefore,itisde sirablethattheATGbe easilyremovedfromtheenclosedtestsection.Aprimarycon cernisthatthereareonly twoopposingstandardsizedoorstoallowaccesstotheinsid eofthetestsection,and theverytopofthetunnelinletis2.6mhigh.Theworkingport ionoftheATGtherefore hastoberaisedandloweredeachtimeitismovedinandoutoft hetestsection.The ATGisalsoonastand-aloneframetomountthevanes,motorsa ndwiringtoavoidany unnecessarymodicationtothetunnel.TheATGistherefore designedsothattheactual workingpartofthedeviceisraisedintopositionfortestin gandloweredsothatitcan beremovedfromthetestsection.Thebottomofthesupportin gframeemployslocking casterstofacilitatetransfers.TheATGisalsotiedsecure lytothetunneltoensurethatit doesnotmoveduringtesting. Thetestsectionisoutttedwithaninternalframingof80/2 0brand,T-slotaluminum, metric15seriesextrusions.Thisframingsystemprovidesa simpleandrigidattachment methodformountinginstrumentation,andtheATGisdesigne dusingthesameseries extrusioninordertobecompatiblewiththeremainderofthe tunnel.Onlyminor machiningwasnecessarytomountthemotors,bearingsandva nesintotheextrusions. ThemotorsarejoinedtothevaneswithLovejoyCP-Ltypeanti -backlashshaftcouplers, andthevaneshaftsterminateintoasealedbearing,pressed intoapocketmachined intheextrusion.Thevaneshaftsareconstructedof12.7mmo uterdiameter,10.7mm innerdiameter,316Lstainlesstubing.Theuseofstainless steelincreasedstiffness overothercandidatematerials,suchasaluminum,andmaint ainedacorrosionresistant nish.Thevanewingletsare1.5mmthick6061-T651aluminum sheetsfastenedto theshaftswithM6-1u-bolts.Theorthogonalvanesarejoine dtoeachotherincritical locationswithmachinedTeonblockstominimizevanevibra tionwhichallowhigher speedoperation. 41

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2.2.4ComputerControl Themotorsmustexhibitsmoothmotionthroughoutallpossib leratesettings, andalsothevelocitymustbecontinuouslyadjustableforma ximumoperational exibility.Steppermotorsareusedasaprecisewayofcontr ollingmotion,however thecostsassociatedwith14channelsoftypicalcontrolhar dwarewasprohibitive. Instead,motorswithintegrateddriversareusedsothatthe ycanbecontrolledwith digitaltransistor-transistorlogic(TTL)pulses[ 119 ].ThePXIchassisintheACFhasa PXI-6533digitalI/Ocardwhichoffersupto32channelsofhi gh-speeddigitalI/O.The motorsarewiredtooperateat200stepsperrevolutionandto acceptonedigitalTTL lineformotionandonefordirection.Eachofthemotorsisco nnectedtotherst14 digitallinesontherst2portsformotion.Theother2ports arewiredwiththe14digital linesforrotationaldirection.Thiscongurationallowse achmotortobeindependently controlledinrotationaldisplacement,rate,anddirectio n.Acontrolowdiagramisshown inFigure 2-3 ThePXI-6533iscapableofdigitaloutputonall32linesatup to20MHz,butthe motorcircuitrycanonlyacceptamaximumof500kHz[ 129 130 ].ThePXI-6533can not,however,senddifferentfrequenciestodifferentline s,soanalternativecontrol methodwasdeveloped.Themaximumenvisionedrotationalra teofthemotorswith attachedvanesis18Hz,whichat200stepsperrevolutionreq uires3,600signal uctuationspersecond;quiteshyof500kHz.Asufcientlyf astclockrateof f Ctrl =100 kHz,sendingwidelyseparatedsignalops,generatesamoti onthatisadequately smooththroughoutthedesiredraterange. Inordertoaccomplishthis,aMatlabscripttakesasinputst hestartingandending desiredrotationalrates,clockfrequency,andaxedaccel erationof 37 : 5 Hz sec 2 whichwas themaximumsustainableaccelerationwithoutmotorfailur e.Thescriptoutputsthe binarysignalwhichisthenfedthroughthePXI-6533tothemo tors.Thissignalconsists ofahighoronvaluetocommandastepfollowedbyanumberoflo woroffvalues.The 42

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timegapbetweenhighvaluesiscalculatedby S = d f Ctrl f ATG e (2–4) whichindicatestherelationbetweenthelowcounts,S,requ iredbetweeneachhighto obtainthedesiredrotationalrateinHz.Adividebyzeroerr orisavoidedbysettinga minimumrotationalrateat0.10Hz. Themotioncommandsarestoredinastreamof32-bit,unsigne dintegers,the rst14bitsofwhichcontainrotationalstepcommands,foll owedbytwounusedbits, andthenthenext14bitsaredirection.Therotationvectori screatedbyiteratively appendingaseriesoflows,followedbyasinglehigh,oftota llengthS.Thedirection vectorissettohighorlowbasedonthesignoftherotational rate,alsolengthS.These shortsegmentsareappendedtotheoutputcommandtimehisto ry,andanewtimeis calculatedresultinginanewdesiredspeedsetting.Althou gh,technically,thismethod onlyallowsforquantumrotationalratestobespecied,the resultisaverysmooth changeinmotion,especiallywhenverylargevaluesof f Ctrl areused. 2.2.5ForcingProtocol ThemethoddevelopedprovidesaexiblewaytocontroltheAT Grotationsina desiredmanneryetitisimplementedwithminimalequipment cost.Theforcingprotocol usedinpreviousstudies,whichprovidedthemostdesirable parametersofquickly developinglargelengthscalesandhighintensities,appea redtobethemethodwhere eachvane'srotationalrate,direction,andtimebetweenra te/directionchangewereall randomized;ratherthanothermodeswherethevaneswereope ratedsynchronously atthesamerate[ 117 120 122 – 126 ].Intherandomizedcasestheauthorsused algorithmswhichchosetheserandomnumbersfromauniformd istributionwithaset varianceandmean. Theforcingprotocolisimplementedwithaslightmodicati on,inthatthemotor ratesarequicklyacceleratedbetweentheselectedratesto avoidmotormalfunction. 43

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Afterthespeciedrateandtimedelayhavebeenrandomlysel ected,themotors acceleratetospinatthatconstantrateinonedirectionfor theselectedtimeperiodand thenramptothereverserateandholdthatforatimeperiod.A fterthesecondtime periodhaselapsedthemotorsramptothenextrandomlyselec tedrate,timeperiodand direction,andtheythenfollowthesamebehavior.Thismeth odcausesarandomization inrotationalrateanddirection,andasynchronousoperati onofallthemotors,andithas theaddedbenetofaddingzeronetvorticitytotheowovert wotimeperiods.Italso avoidsfrequencyspikesthatoccurinsynchronousoperatio n[ 121 ]andgeneratesa smoothfrequencydistributionwithdesired,adjustabletu rbulencestatistics[ 119 ]. 2.3ConstantTemperatureAnemometry Free-streamturbulenceisanimportantaspectofmanyuid owswhichis importanttotheunderlyingowphysics.Thereareseverals ensingtechniquesthathave beendevelopedfordifferenttypesofows.Constanttemper atureanemometry(CTA)is aowdiagnostictechniquewhichreliesonconvectiveheatt ransferfromaheatedwire orthinsurfacelmtodeterminecertainowcharacteristic s[ 42 49 78 131 132 ].The uid'svelocity,composition,temperature,orpressurema ybesensedthroughCTAas eachquantitymayaffecttheconvectiveprocess,butspecia lmethodsmustbeusedto separatetheeffectswhenmorethanoneparameterischangin g. TurbulencemeasurementshavetraditionallyusedCTAforla rgebandwidth measurementsofvelocitywitharelativelysimplesetup.CT Ausesanactivecontrol loopofthedrivevoltageacrosstheheatedelementtoprovid e”constanttemperature” whichhastheeffectofincreasingsensorbandwidthbeyondw hatwouldbepossible withasimplerpassivelyheatedelement.CTAmayuseaminiat urewire,acoated wire,athinorthicklmonaglassber,oralmonasurfaceas theheatedelement. Thesmallerelementsprovidebetterbandwidthbutaremoref ragile,andonlysome ofthelargerelementsmaybeusedinwater.Miniaturehot-wi reprobesforuseinair aretypicallyverysmallwires,ontheorderof5 mdiameter,thataresuspendedfrom 44

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electrodesspacedontheorderof1mmapart.Thisresultsins ensorswhichhavea verynespatialresolutionandlargebandwidth,causelowd isturbancetotheow,are inexpensiveandsimple,buttheyareinherentlyveryfragil eandmayonlybeusedin cleanows[ 131 132 ]. SingleelementCTAsetupswillsampleasinglequantity,and theyaremanufactured inmanycongurations.Multipleelementprobesarealsoava ilablewhichcanbe arrangedtoyieldadditionalinformationafteracalibrati on[ 131 132 ].Atwo-wiresetup withwiresorientednormaltoeachotherallowsfortheresol utionoftwo-components ofvelocitytobecalculatedafterarelativelysimplecalib rationhasbeenperformed.A three-wireprobecansimilarlydetermineathree-componen tvelocityvector,butthe calibrationismorecomplex. Fortheworkpresentedhere,asingleAuspexCorporation5 mdiameterX-wire hot-wireprobe(typeAHWX-100)wasconnectedtotwoDantec5 5M10CTAbridges. ThebridgeswereconnectedtoaPXI-4472dynamicsignalacqu isitionmoduleinstalled inthe8-slot,3UPXIchassis,whichwasusedforanalogtodig italconversion(ADC) oftheCTAsignals.ThisADCmoduleprovides8channelsofsim ultaneoussampling, with24bitsigma-deltaADC'sand110dBdynamicrange[ 133 ].AVelmextwo-axis traversewasconstructedandmatedwithtwoAnaheimAutomat ion23MDSI206S-00-00 steppermotorswithintegrateddriversandcontrollersfor precisecomputercontrolofthe hot-wireprobeduringowsurveys[ 134 ].Thetraversehasahorizontaltravelof0.45m andaverticaltravelof0.29mwhichwassufcienttomapthea reaofinterest. TheX-wireprobeswerecalibratedatthebeginningofeveryd ayoftesting,and voltageswereconvertedtovelocitycomponentsaccordingt otheeffectiveyawangle methodaspresentedbyBradshaw[ 135 ],whichimprovesuponthatpresentedbyHinze [ 78 ].Inthismethod,eachwireisrstcalibratedagainstveloc itywiththeownormal tothewire.Then,eachwire'slongitudinalsensitivityto owyawangleisdetermined byslewingtheprobethroughmultipleanglesatasinglevelo cityandcomparing 45

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againstacurvet.Theresultingcalibrationisusedtoconv ertthetwowirevoltages intolongitudinalandtransversevelocitycomponents.The probeisslewedacrossangles automaticallybyacomputercontrolledprecisionrotarytr averse.Figure 2-4 showsthe X-wireprobemountedontheautomaticprecisionrotatingta bleattheinletofthetest section,withthepitot-statictubemountednearby. ThenormalcalibrationoftheX-wireprobeisaccomplishedb ycantingtheprobe soeachwireisnormaltotheowandthenmeasuringthenormal wire'svoltageover arangeofvelocities,thusgatheringaseparatecalibratio nforeachwire.Apitot-static probeislocatedneartheX-wireprobetoaccuratelydetermi netheincomingow velocity.Thepitot-staticdifferentialpressureisreadb yaHeiseST-2Hpressure transducerwitharangeof0to250Pascal,andanaccuracyof0 .06%.Thisdynamic pressureisusedtocalculatevelocitywiththeinclusionof totalbarometricpressure readbyaDruckDP142witharesolutionof1Pa,andtemperatur eusinganOmega thermocoupleprobe.TheX-wireislocatedonthecenterofro tationofthestagewhich reduceserrorsduetoow-eldnon-uniformity.Thestageis slewedtopositiveor negative45degreeswhichcauseswiresAorBtobeperpendicu lartotheincoming ow,respectively.Thewindtunnelissettoaseriesofveloc itiesrangingfrom.5to20 ms 1 ,withastepevery.5 ms 1 .Ateachvelocitysettingtheowisallowedtostabilize forseveralseconds,andthenthenormalhotwirevoltageisa cquiredat2kHz,andpitot velocityisacquiredat4Hzfortwentyseconds.Theresultin gdataareaveragedand ttoafourthorderpolynomialforeachwirerelatingindivi dualvoltage, E A;B tonormal velocity, U A;B ,withtcoefcients, C 1 ; 2 ; 3 ; 4 U A;B = C 0 + C 1 E A;B + C 2 E 2 A;B + C 3 E 3 A;B + C 4 E 4 A;B : (2–5) Thepolynomialmethodtypicallydemonstratesaresidualer rorof1%orless,andan examplenormalcalibrationisshownbyFigure 2-5 46

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Thebasisoftheanglecalibrationisshownby U 2 A = U 2 1 cos 2 1 + k 2 A sin A U 2 B = U 2 1 cos 2 2 + k 2 B sin A ; (2–6) whichwasrstintroducedbyHinze[ 78 ].Theseequationsaccountforthesmallbut signicantlongitudinalcoolingeffectoneachindividual wirewhichresultfromthewire's anglefromnormal, 1 ; 2 ,atagivenfree-streamvelocity, U 1 .Thepurposeoftheangle calibrationistodeterminethelongitudinalcoolingcoef cients k A and k B .Thecalibration isaccomplishedbysettingthewindtunneltoamedianspeed, inthiscase5m s 1 andacquiringcalibrationdataatmultipleanglesbetween 45 .Thevoltageoutput fromthetwowiresisconvertedtovelocitythroughthenorma lcalibration,andthen plottedagainstthevelocityvaluepredictedbyEquation 2–6 .Thevaluesof k A and k B aremodiedfromastartingvalueof0.20untilthecurvesmat chcloselyintherangeof 35 .Figure 2-7 isanexampleplotoftheanglecalibrationwithcomparisonb etween measuredandcalculatedresults.AkeylimitationofX-wire sisthatthecalibration becomesunreliableoutsideaconeof 35 ,especiallyincasesofhighturbulence[ 136 ], henceanyresultsoutsidethisregionaretreatedasunrelia ble. Afterthenormalcalibrationpolynomialsandlongitudinal coolingcoefcientshave beendetermined,thevoltages E A and E B areconvertedtooutputatwocomponent velocityvectorwithonecomponentalignedlongitudinally alongtheX-wiresensorand theothercomponenttransverse.Figure 2-6 isadiagramoftherelevantgeometriesof theX-wireprobe.Bradshaw[ 135 ]thenmodiesthelongitudinalcoolingequation( 2–6 ) toyield U A U B 2 = cos 2 A + k 2 A sin A cos 2 B + k 2 B sin B ; (2–7) 47

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whichremovestheunknownvelocitymagnitude.Thisrelatio nisthenmodiedintoa quadraticformulawithnewconstants, C 0 ; 1 ; 2 ,about A by C 2 tan 2 A + C 1 tan A + C 0 =0 C 2 = Rk 2 2 cos 2 + R sin 2 k 2 1 C 1 =2 R 1 k 2 2 cossin C 0 = R cos 2 + Rk 2 2 sin 2 1 R = U A U B 2 ; (2–8) whichafterfurthermanipulationallowsfor A tobesolveddirectlyby tan A = C 1 + p C 2 1 4 C 2 C 0 2 C 2 : (2–9) Theidealvalueoftheanglebetweenthetwowires, ,is 2 ,howevermanufacturing allowsasmallerror .Thesevaluesareusedwiththecoolingequation( 2–6 )toresult infree-streamvelocitymagnitude U 1 = s U 2 A cos 2 A + k 2 A sin 2 A : (2–10) Thepositioningoftheprobeisnotexactintroducinganerro r ,yieldingarelation between A and ,whichisthenusedtosolveforlongitudinalandtransverse velocity components U x = U 1 cos U y = U 1 sin = A 2 + : (2–11) Thevaluesof k A k B and areadjustedwithinsmalllimitstoobtainabesttforthe calibrationdata. 48

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2.4ModalTestingandStructuralDeconvolutionFiltering AForceMeasurementSystemsMC-.10-.375-Astingbalancean daJR330E12A4-I40-EF loadcellareusedforthepurposeofaerodynamicloadmeasur ementinthisstudy.Both arestrain-gagedeviceswhicharecalibratedsothatthestr ainmeasurementsmay beusedtodeterminesixdegreeofmeasurement(6-DOM)loads .Theseloadsare ultimatelyexpressedasthreeorthogonalforcesandthreeo rthogonalmoments.These sensors,whileverysensitiveandaccurate,arestillimper fect,andmeasurements withthemaresubjecttomanysourcesoferror.Thecalibrati onforthesesensorsare onlyvalidoveradenedrange,andtheysufferfromtemperat uredependency,both ofwhichcanbecorrectedforusingstandardizedpractices[ 137 ].Theloadcellhasa lessinvolvedcalibrationmatrixthanthestingbalance,wh ichleadstoerrorsincases involvingcombinedloadings.Thereisatrade-offbetweent heloadcell'sdurabilityvs. thebalance'saccuracyandformfactor.Anotherimportants ourceofmeasurementerror whichdirectlyimpactsthisresearch,isanitefrequencyr esponsebandwidthdueto structuralvibrationwithinthebalanceandloadcellthems elves.Thissectionwillfocus onthecharacterizationofeachsensor'sfrequencyrespons ewithamodelattachedand developmentofafrequencyresponsefunction(FRF)deconvo lutionlteringtechniqueto removeunwantedvibrationaleffects.2.4.1StructuralDynamics Anyrealsensorwillhaveanitefrequencyresponsebandwid thduetomany factors,includingelectricalandstructuralconstraints [ 138 ].Thebandwidthmayhavea roll-offatacertaincutofffrequency,likealter,oritma ybecontaminatedbyresonant frequencieswithaccompanyingphaseshifts.Inthecaseoft hebalanceorloadcell connectedtoamodelandmountedtosomesupport,thefrequen cyresponseofthe electronicsisatouttoatleastonekilohertz,howeverthe wholesystemwillhave resonantfrequencieswhicharewellwithintheregionofint erest,namelylessthan100 Hz. 49

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Itisinstrumentaltodiscussasimplecaseofstructuraldyn amicsbeforedelving intothemorecomplicatedcaseofthebalanceorloadcell.Co nsidertheforced mass-spring-dampershowninFigure 2-8 [ 138 139 ].Thesystemisdescribedby theordinarydifferentialequation(ODE) m x + c x + kx = f ( t ) ; (2–12) withmassm,dampingparameterc,springconstantk,anddisp lacementx.The homogeneousportionoftheODEhasasolutionoftheform x ( t )= Ae n t cos p 1 2 n t ; (2–13) wherethedampingratiois = c 2 p km ; (2–14) andthenaturalfrequencyis n =2 f n = r k m : (2–15) Themagnitude,A,andphase, ,arebothdependentontheinitialconditions.Ifthe inhomogeneoustermisassumedtobeoftheform f 0 cos(2 ft ) ; (2–16) thenthesteady-statesolutionwillbeoftheform x ( t )= f 0 h cos(2 ft ) h = 1 k 1 q (1 r 2 ) 2 +(2 r ) 2 r = f f n =arctan 2 r 1 r 2 ; (2–17) where f n istheundampednaturalfrequency.ThesolutionwillhaveaF RFwhich consistsofamagnitude,H,andphase, ,(showninFigure 2-9 )whichwilldependon 50

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frequencyanddampingratio.Iftheresponseisformulatedi nthefrequencydomain, theforcingfunction, F ( ) ,actstocauseadisplacement, X ( ) ,throughthefrequency responsefunction, H ( ) ,or X ( )= H ( )_ F ( ) : (2–18) Realstructuresascomplexasthebalanceandloadcelldonot havesuchsimple FRFforms.Instead,theyaretypicallylledwithmultipler esonantfrequencies,which cansometimesbemodeledasasumofsingle-DOFsystems[ 138 139 ].Furthermore, eachfrequencydependsonthemassattached,asexempliedb yEq. 2–15 ,sothatthe FRFisdependentuponwhichmodelisattachedtothesensor.T hedenitionoftheFRF comesfromrearrangingEq. 2–18 into H ( )= X ( ) F ( ) : (2–19) Onasingle-inputsingle-outputsystem,determinationoft heFRFmaybeaccomplished byforcingthestructureandsimultaneouslymeasuringther esponse.Thefrequency datafrommeasurementsaretypicallyquitenoisyanddirect divisioncanamplify noise,sotheFRFistypicallydeterminedinseveralformula tionsdependinguponthe de-noisingrequired,called H 1 H 2 ,and H [ 139 140 ].Allmethodsuseauto-spectra P ( ) xx = X ( ) X ( ) ; (2–20) andcross-spectra P ( ) xf = X ( ) F ( ) ; (2–21) ofthesignalwhichcanleveragetheefciencyofafastFouri ertransform(FFT)to transformthetimeseries, x ( t ) ,intoitsfrequencyrepresentation, X ( ) .Table 2-1 indicateswheneachFRFdeterminationtechniqueshouldbeu sed,dependingon whethertheinputoroutputsignalcontainssignicantnois e. 51

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Table2-1.Frequencyresponsefunctionmodels Technique AssumedNoise Response Inputs H 1 nonoise noise H 2 noise nonoise H noise noise The H 1 formulation, H ( ) 1 = P ( ) xf P ( ) ff ; (2–22) ismostusefulwhenitisknownthattheresponseisnoisywhil etheinputforceiswell known.Dividingbytheautospectraoftheresponsetherebyd oesnotamplifynoise.The H 2 FRFformulationistheopposite, H ( ) 2 = P ( ) xx P ( ) xf ; (2–23) inthatitseekstominimizenoiseduetotheinputs.The H methodseekstooptimally averagethe H 1 and H 2 forminimumnoise.The H 1 methodisusedinthisworkasthe impulsehammerhasaverycleansignalwhiletheloadcelland balancehavesignicant noise. OnecommonwaytodeterminetheFRFonlight-weightstructur esistoperform animpulse-responsetest[ 139 141 142 ].Inthistestaforceisappliedtothestructure throughaninstrumentedhammer.Theimpulseforcecontains relativelyatdistribution ofenergyatfrequencieswithinitsbandwidth,whichislarg elydependentonthetypeof hammerandtipused.Theresponseparametermaybeinterpret eddifferently,asthe balanceandloadcelloutputvoltages,butbothuseacalibra tionmatrixtoconvertthese dataintoloads. Theimpulse-responsetestinthisworkusesaPCBPiezotroni cs86C02impulse hammershowninFigure 2-10 toexcitethebalanceorloadcellwithamodelattached. Thetestmustbeappliedwitheachmodelastheindividualmod el'smassandstiffness affectthesystem'sresponse.Theimpulsehammerandloadce llareconnectedto 52

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thePXI-4472dynamicsignalacquisitioncard,andthesting balanceisconnectedtoa SCXI-1520strainmeasurementmodule.ThePXI-4472hasthea bilitytotriggeronthe hammerandpre-recorddata,whiledataacquisitionfortheb alancemustbemanually triggeredwitha”pickle”switch. Figure 2-11 showsarepresentativeFRFforamodelontheloadcell.Inthi stest,a carbonberandbirchplywoodatplatemodelweighing117gi sattachedtotheJR3 loadcellwithstandardmodel-mountinghardware,andthelo adcellismountedrigidly toanopticaltable.Theimpulsehammerisusedwitharubbert ipwhichleadstoaat frequencyinputoutto100Hz.Boththehammerandtheloadcel lvoltagesareattached tothePXI4472cardpreviouslyusedfortheCTAcharacteriza tion,andtheinstrument issettotriggerontheforceinputwithapre-recordinginte rvalof0.1sec.Theinternal JR3electronicsemploysafourth-orderButterworthanalog low-passlterat926Hz,and thesamplingfrequencyis8192Hz.Twenty-veimpactsarere cordedinfourseparate experiments.Thedifferentexperimentsareintendedtodir ectlyexcitethe F Y and M Z F Z and M Y F X ,and M X axes. Thebalanceandloadcellarebothcomplexmulti-DOFstructu res,andtheir responsesconsistofcombinedbending,torsional,andmass -springtypeeffects. However,aswasdeterminedintheATGcharacterization[ 118 ],themajorityofthe turbulentenergyiscontainedinlowerfrequencies.Forexa mple90%oftheturbulent energyisinthespectrumlessthan100Hz,settingamaximumf requencyofinterest. Thefrequencycutoffisimportantasat2.5,5,7.5and10 ms 1 theminimumresolved turbulentlengthscaleisontheorderof2.5,5,7.5and10cm, respectively,which issmallerthanenvisionedmodels.Furthermore,thebridge hasprovisionsfora fourth-orderButterworthlowpasslterat100,1000or10,0 00Hz,whiletheload cellhasadjustableanalogltersat6.3,13,29,42,63,134, 190,and926Hz. TheaxeswhichwereintentionallyexcitedhadcleanFRFmagn itudeandphase, whileanyotheraxeshadsomewhatnoisyresultswhichstillf ollowedthebasictrend.It 53

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wasdifculttoexcitemultiplecomponentsofforcewithaa t-plategeometry,soinstead thethreeforceshadtobeexcitedseparately.The M X momentwassimilarlyexcited independentlywhiletheothermomentswerecombinedwithth eirprimarygenerating forces.ForceexcitationsalwaysresultedinaFRFmagnitud everynearunityatlow frequencies,howevermomentFRFmagnitudesweredependent onwherethemodel wastappedduetothemomentarm.Theimpulsetestimpactloca tionwasmoved everytapandthelocationrecordedsothatmomentFRF'scoul dbenormalizedin post-processing.Multipletestsindicatedaatresponseo utto40Hzformostmodels testedoutto0.5kg,butabovethisfrequencytheloadcellha daresonantpeak. Fortheloadcell,allsignalsdisplayedatleastsomecrosscouplingintheFRF. Thisisattributedtoboththeunknownbehavioroftheintern alelectronicsconverting 8strainmeasurementsinto6loadsignals,aswellasthecros s-couplednatureofthe calibrationmatrix.However,theindependentsignalsalld isplayedstrongpeaksfortheir mostcharacteristicvibrationmodes,andthesewereusedto determinehowtoexcitethe system. Inparticular,the F X axiswasthemoststiffandhaditsstrongestfrequencypast1 00 Hz.The M X axiswasthenextinlinewithitsstrongestfrequencyat100H z.The F Y and M Z channelswerecoupledtogetherandexhibitedmostenergyar ound68Hz.The F Z and M Y channelswerelikewisecoupledandconsistedofthreeequal lystrongmodes. Increasingthemassoftheatplatemodeldidnotaffecttheo verallshapeandbehavior oftheFRF,butitdidshiftthepeakfrequenciesdownward.2.4.2FrequencyResponseFunctionInverseFilteringTechn ique IfastructurehasaFRFinwhichthemodalfrequenciesarewel lseparated,or uncoupled,thentheFRFcanbemodeledasmultiplemass-spri ngdampersystems [ 139 ].TheFRFcanthenbeusedtodevelopaninverselter,alsokn ownasa deconvolver,whichseparatesouttheunwantedeffects.Con sideragaintheforced mass-spring-dampersystemwithafrequencyresponseshown byEqs. 2–17 [ 139 140 54

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143 ].Thegoalinconstructinganinverselteronthedatawould betoattentheFRF magnitudeandcorrectphaseshifts.Asthisisappliedacros sallfrequencies,itismost instructivetoworkinfrequencyspace.Thesimplestlterw hichcouldbeappliedagainst displacementdataistheinverseoftheFRF, G ( )= H ( ) 1 ,evaluatedinfrequency domain.Theforceislinearlymappedagainstdisplacementa sshownby F ( )= H ( ) 1 X ( )= H ( ) 1 H ( ) F ( ) : (2–24) Thisideallydeconvolvesthestructuraldynamics H ( ) from X ( ) toyieldtheoriginal forceswithphaselagscorrected. Inthemass-spring-damperandmanyotherphysicalsystems, thereisanet low-passlteringeffect[ 139 ].Inthepresenceofnoise,theinverseoftheFRFtherefore becomeslarge,amplifyingnoisearticially.Onemethodth athasbeenestablishedto dealwiththeproblemisWienerdeconvolution[ 140 ].Themethodisfrequentlyused todenoiseimagesbymakingtheassumptionthatboththenois eandthesignalare second-orderstationaryrandomprocesses[ 143 ].Animplicitassumptionisthatthe noiseandsignalareuncorrelated,whichmaybeincorrectco nsideringthatthesignal, inthiscaseunsteadyloads,mayaffectthenoisebyaddingex cessstructuralvibrations. Unfortunatelythemethodfailstoreconstructsignalsthat havebeencontaminatedby noise,soagoodsignaltonoiseratioisimportant.Themetho dcreatesessentiallytwo lters,therstofwhichistheinversesystemFRFwhichisco nvolvedwithaweighting functionbasedonsystemnoise,asshownby G ( )= H ( ) P ( ) xx k H ( ) k 2 P ( ) xx + N ( ) : (2–25) Thisrequiresanestimateofthenoise, N ( ) .Anestimateofelectronicnoisemay beperformedbysamplingthesystemwhileatrest,howeverit maybedifcultto estimatenoisewhenthesystemisdynamicallyloadedasitis likelystructuralnoise isdependentonthesignal.Anattempttocorrectthiswastog atherthenoisesignal 55

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whilethesensorwasrandomlyvibratedatalowlevel.TheWie nerlterdifferedfromthe simpleinverselteronlyathighfrequenciesandwherethes ignalwashighlyattenuated byananti-resonance. Anotherknownlowpasslteristhefourth-orderButterwort hlterwhichcanbe appliedtotheloadcellandstingbalanceelectronics.The lterisconvenientbecauseit closelyfollowsaroll-offmodeledby H ( )= 1 1+ f c f 2 n ; (2–26) andthecutofffrequency, f c ,andorder,n,areknown.Thisallowsacorrectiontobe appliedtothedeconvolutionlter, G ( ) ,toremovetheeffectsofthelow-passlterin theelectronicswhichwouldsimilarlyamplifyhighfrequen cynoiseintheoutput.The combinedinverselter, G ( )= H ( ) P ( ) xx k H ( ) k 2 P ( ) xx + N ( ) 1 1+ f c f 2 n ; (2–27) isthenreadytobeformedintoalter.Figure 2-12 isaresultingdeconvolutionlteras seeninthefrequencydomain. ThemathematicsperformedbyEquation 2–27 ontherawdatadoesnotyielddata thatisimmediatelysuitableforuseasalterbecausethel terisshifted,acausaland willcauseamplicationsofcertainfrequencycontent[ 140 ].Acustomltermustrst bedesignedsothatithasgoodbehavioracrossallfrequenci es.Thisworkusesthe windowingtechniquetodesignalterwhichconsistsofwork ingonthetimedomain representationof G ( ) g ( t ) whichisshowninFigure 2-13 (A).The g ( t ) signalisrst shiftedsothattheringingisstartedattimewhichishalfth eselectedlterwidth.The lteristhentruncatedtoacertainnumberofpoints,chosen tobeaftertheringingis substantiallydecreased(Figure 2-13 (B).Thepre-ringing,whichisanartifactofthe periodicnatureoftheDFTandFFT,isanunwantedacausalbeh aviorbutcannotbe 56

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truncatedtosatisfythecausalityrequirementofthistype oflterwithoutdamagingthe capabilityofthelter.Thiscausesagenerallysmallpre-r inginanysignal.Thelaststep isthatawindowisappliedagainstthelter,inthiscaseaBl ackmanwindow,tominimize unwantedamplicationsthatarecausedbythenon-inniten atureofthedata[ 140 ] (Figure 2-13 (C)). Theresultingtimetraceistheniteimpulseresponse(FIR) deconvolutionlter, oftenreferredtoasFIRtapsorFIRcomb[ 140 ].TheFIRlterisaccomplishedviaa circularconvolutionoftheJR3loadcellmeasuredloadagai nstthedeconvolutionlter toyieldacorrectedestimate, ~ F .Thisisquicklyaccomplishedinfrequencydomainas shownby ~ F = G X: (2–28) ConsideringtheimplementationofFIRwillleverageFFTalg orithmstoperformthe circularconvolution,itismostbenecialtochoosethesiz eofFFTtobeapowerof2in ordertoyieldanefciencyof N s log ( N s ) calculations[ 144 ].Thelterisdigitallyapplied againstthedatausingtheoverlap-addmethod[ 140 ]. Inthecaseoftheimpulse-responsetest,theforceandmomen toutputfromthe loadcellisdeconvolvedagainstthelterdevelopedfrom25 tests,andplotsofthe measuredhammerandloadcellforcesandcorrectedmomentsa replottedagainst thedeconvolvedloadcellforceinFigure 2-14 .Theimpactofthehammercauses themeasuredloadstoring,howeverthelterremovesmostof theringingandphase correctsthesignals.Thereisthepenaltyofalargerbaseno isesignalanderrorsinthe amplitudeandphasing,aswellasasmallpre-ringingbefore thehammerimpact. Thelteringhasasimilareffectontheauto-power-spectra ofthedeconvolvedload. Figure 2-15 showsautospectraofthehammerforce,loadcell F Z anddeconvolvedload cell ~ F Z .Thehammerhasaatfrequencyresponseouttoabout100Hzaf terwhichit graduallyrollsoff.The F Z autospectrashowspeaksatresonantfrequenciesandvalley s atanti-resonances.Thedeconvolved ~ F Z signalagreeswiththehammerautospectra 57

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quitewellexceptfortwocases.Therstcaseiswherecloser esonantmodessuch asbetween50-60Hzcausethecustomdesignedltertohavepo ort.TheFIRlter hasanitenumberoftaps,andincreasingthenumberoftapsw illleadtoabettert, howeverafteracertainpointthelterwillstarttofailbya mplifyingnoise.Thenumber oftapswasselectedbytrialanderrortoyieldthebestt.Th esecondcaseiswhere aparticularlystronganti-resonancesuchasat300Hzcause stheWienerlteringto attenuatethesignal.Thisisactuallybenecialasitpreve ntsthereconstructedsignal fromhavingsignicantnoiseat300Hz,howeveranyrealsign alinthatbandwillbelost asifitwerenotchlteredout.Theseinadequacieswerepres entinallcomponentsof theload.Theeffectiseasilyseeninthefrequencydomainre presentationoftheinverse transferfunction,theresultsfromWienerdeconvolution, andafterthewindowedcustom lterdesignprocess(Figure 2-16 ). Anotherissueinthissystemisthatthevibrationsduetoalo adinonedirectiontend tobleedintootherdirectionsduetoprecessionalvibratio n.Anexampleisthatvibrations fromanimpactintheZdirectionareshortlythereafterseen intheYdirectionandthen theyreturntotheZdirection.Theoscillatingloadeffecto ccursuntilthesignaldiesand ismostlikelyduetothestructuralsymmetryinthemounting aroundtheYandZaxes. Thelteringtechnique,althoughitassumesasingleinputsingleoutputtypeofbehavior, hasshownitselftofunctionwellinsuchcases.Figure 2-17 showshowanimpactinthe ZdirectionwithresultingmomentintheYdirectioncausesr inginginallfoursignals. ThedeconvolvedloadfromtheYforceandZmoment,whichshou ldnothavebeen affectedbyaZimpulse,areseentohaveasmallvibrationtha tessentiallydiestozero, wheretheunlteredsignalringscontinuously.Theresults indicatethatthetechniqueis capableofdecouplingthemeasuredloadsfromeachother. Thetechniquereconstructedtheimpulseload,soitwastest edagainstacontinuous loadtodetermineitseffectivenessinamorerealisticsitu ation.ALDSV203shaker unitwasconnectedtoaBr¨uelandKjr(B&K)dynamicloadcel lmodelnumber8230 58

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whichwasinturnconnectedtothemodelandJR3loadcellonth eopticaltable.Several analogvoltagesignalsweredevelopedandfedtotheshaker. TheB&Kloadcellwas connectedtothePXI-4472inplaceofthehammer.Theforcesa ndmomentsfromboth loadcellsweresimultaneouslymeasured.TheJR3signalswe rethendeconvolved usingtheimpulse-testdeterminedlterandcomparedagain stloadsmeasureddirectly fromtheB&Kdevice.Figure 2-18 showstheB&Kmeasuredforce,theJR3loadcell measuredforce,andthedeconvolvedforce.Thedataareoffs etfromeachother purposefullyforeasiervisualization,andthecutoffonth esweepcorrespondsto100Hz. Thedeconvolutionlterperformedquitewellonthecontinu oussinedataespeciallyby correctingthestrongresonancesoccurringat50and60Hzse enasthetwoamplitude humps.2.4.3LimitationsofDeconvolutionFilter Thedeconvolutiontechniqueusedisapplicabletowardsthe measurement ofturbulentloadsonawindtunnelmodel,butlikeanyinvers etechniqueithas limitations.Theinitiallyidentiedimperfectionsinthe techniquehavebeenthatthe windowedcustomlterisnotabletoexactlytthedesiredfr equencyresponse,and thatanti-resonancescausetheWeinerltertostronglyatt enuateatsuchfrequencies, therebylosingdata.Theseproblemscanbemitigatedthroug habetterunderstanding oftheircause,forexampleapoortcanbemadebetterbyincr easingthelengthofthe lterorbyafastersamplerate. Additionally,thereareotherissuesforwhichthecauseand effectarenotsoclear. Oneconcernisthatmodalcharacterizationisperformedwhe nthemodeldoesnothave airblowingoverit.Theaerodynamicloadingofthestructur eanddampingofvibration canpossiblychangetheFRF,andthelterwouldactatincorr ectfrequencies.Another possibleissueisthatvibrationsinducedintothesystemby turbulencemightinteractto raisethenoiseoorwhichmayadverselyaffecttheWeinerl terderivationandresults. 59

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Apossibleconcernisthatthesystemismultiple-input,mul tiple-outputwhilethelters treateverythingassingle-input,single-output. Althoughtherearemanylimitationstothedeconvolutionl tering,itshouldbe understoodthatthetechniqueisintendedtoincreasetheac curacyofthedata.Itwill beusefultowardsmakingresultingdynamicloadsdatamoreu nderstandableinlightof sensorimperfections. 2.5ParticleImageVelocimetry Digitalparticleimagevelocimetry(PIV)isusefulfornoni nvasivedeterminationof theowvelocityinaregionofinterest[ 145 – 147 ].MonoPIV,conductedwithasingle camera,isbestsuitedto2-Dowsasitcanonlyresolvetwoco mponentsofavelocity vectorinathinmeasurementplane,howevertheadditionofa nothercamera,forstereo PIV,allowsthetechniquetobeextendedto3-Dowsresolvin gathreecomponent velocitymap.Thissectionwilldiscussthemathematicsand algorithmsbehindPIVas wellasseveralsourcesoferror.2.5.1LaVisionSystemDetails ThisresearcheffortwillutilizeaLaVisionFlowMasterste reoscopicPIVsystem capableofgatheringimagesat7Hz.ItemploysadualcavityL itronNd:YAGpulselaser frequencydoubledtoemitlightat532nm.Thepulseduration isontheorderof4ns withadjustableenergyupto135mJperpulse.Thelasercavit iesareopticallycombined tobecollinearandaredirectedthroughadjustablesemicyl indricallensestogeneratea coplanarlasersheet.ThecamerasareLaVisionImagerProX2 Mwitharesolutionof 2048x2048pixelsanda14bitresolution.Thepixelsize, d c ,is7.4 m squareandthe minimumtimebetweenimages,dT,is110ns.TheLaVisionDaVi ssoftwareisusedto congurethesystem,gatherdata,andprocessimagesintove ctorelds. Thecamerascanbeconguredineithermonoorstereocongur ations.Mono congurationsareusedtodeterminevectoreldsperpendic ulartotheimaging direction.Theresultsareatwocomponentvelocityvector, andtheuseoftwocameras 60

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side-by-sideallowforalargerimagingareatobesimultane ouslygathered.Stereo focusesthetwocamerasonthesameregionwithScheimpugad apterstokeepthe lasersheetinfocusacrossbothfullframes.Thesoftwareis abletousea3-Dcalibration todevelopthreecomponentvectorsacrosstheentiremutual imagingeld. 2.5.2BasicPIVTechnique ThebasicsinglecameraPIVtechniqueemployedinthisstudy usesadoubleframe, doubleexposuremethod[ 145 ].Inthismethod,eachilluminationeventresultsina separatepicture.Thepicturesconsistofilluminatedseed particleseffectivelyfrozenata giveninstant,andthecamera'sCCDisideallycoplanarwith thelasersheet.Eachframe issubdividedintointerrogationwindowswhicharecross-c orrelatedagainsteachother. The2-Dmagnitudeofthecross-correlatedinterrogationwi ndowsresultsinanoiseeld withapeakthatisdisplacedfromcenter,assumingthatatle astsomeoftheparticles fromtherstwindowarestillpresentinthesecondwindow.A Gaussiankernelistto thelargestpeak,anditscentroiddescribesanoffsetfromt hecenteroftheinterrogation region.Aqualitymetric, Q = P 1 P min P 2 P min > 3 ; (2–29) isassessedwhichensuresthatthelargestpeak, P 1 issignicantlyabovesecondpeak, P 2 ,andthelowestvalue, P min .[ 145 ]Vectorsnotmeetingthiscriterionaredeleted andprocessingisstopped.Forthosethatpass,theoffsetin pixelsisthenconverted todistanceinmetersbyacalibration.Thespatialoffsetis thendividedbeatime difference,dT,betweentheimagestoyieldatwo-component velocityvector.Figure 2-19 showsthisprocess. Theapplicationofcross-correlationinsoftwareismostqu icklysolvedusinga 2-DFFTalgorithm,howevertheperiodicityrequirementred ucesacceptablespatial displacementtohalfoftheinterrogationwindow.Practica lconsiderationssuchas particlesleavingthelaserilluminationfurtherreducesm inimumoverlap.Methodshave beenestablishedinthesoftwaretoaccommodatetheserequi rementssuchasusing 61

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variablescaledinterrogationwindows,byoverlappingthe sewindows,andbyshiftingthe secondimage[ 145 – 147 ].ThisworkwillonlyusesoftwaredesignedaroundFFT's,an d alldatahavebeenprocessedwithmultipassadaptive(MA)in terrogationregionsanda 50%overlap. TheMAtechniquereduceserrorsassociatedwithowscontai ningdiversevelocities andincreasesspatialresolutionwhencomparedtoxedinte rrogationregions[ 145 ].The MAalgorithmrstcalculatesavectoreldwithaspeciedla rgewindow,forexample64 x64pixels.Ifthecross-correlationmeetsthequalitymetr ic,thecorrespondingpixelshift fromthisvectoreldisthenappliedtothefour32x32interr ogationregionscontained within,sothattheinterrogationregionfromthesecondfra meisshifted.Anewvector eldiscalculatedandresultsofthe32x32vectoroperation sarethenappliedtoa setof16x16interrogationregionsinasimilarmanner.Thes ubsequentlysmaller interrogationregionsexhibitlesserrorthanifthesingle smallinterrogationregionwere performeditselfbecausetheinterrogationregionfromthe secondframeisshiftedbased ondataandismuchmorelikelytocontainparticlesfromthe rstframe.Theoverlap chosenforavectoranalysiseffectivelyincreasesthespat ialresolutionatthecostof additionalcomputationaltime.Forexample,a50%overlapa ppliedagainsta16x16 interrogationregionwillyieldvectorresultsevery8pixe ls,howeverthetimetoperform thecross-correlationfortheentireeldwillhaveeffecti velydoubled[ 145 ]. 2.5.3StereoPIV StereoPIVtakesadvantageofthefactthatasinglecamerare solvesthe2-D velocityvectorsperpendiculartotheCCDandnotcoplanarw iththevectorsheet.The additionofasecondcameraorientedatananglefromtherst cameraallowsadifferent planeof2-Dvectorstobedetermined.Acalibrationdetermi nestheanglesbetween thecamerasaswellasthespatialmappingfromonecamera'si mageandvectoreld tothenext.Thesoftwarecanthencalculateouta3-Dvelocit yvectorusingthetwosets of2-Dvelocityvectorsatthepointsthatoverlapbothcamer as.Aknownlimitationis 62

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thatthevectorcomponentperpendiculartothelasersheetw illbelessaccuratethan thein-planecomponentsduetolimitedlasersheetthicknes s[ 146 147 ].Thestereo PIVcalculationmethodusedinthisworkisdescribedindeta ilbyCalluaudandDavid [ 145 148 ]. Thisworkmountedbothcamerasonthesamesideofthelasersh eet,withthelaser sheetbeingdirectedfrombelowsobothreceiveapproximate lythesameamountoflight fromside-scatter.Thecamerasareoffsetfromeachotherby nolessthan35 toobtain reasonable3-Dvectorswhileminimizingimagedistortion[ 145 ].Thecamerasarenotin generaldirectedperpendiculartothelasersheet,soaSche impugadapterisinstalled betweenlensandcamera.Theadapterallowsthelenstobeadj ustedatananglefrom thecamera'sCCDmakingitpossibletokeeptheentireimagin gregioninfocus.Figure 2-20 showsanotionalstereoPIVsetup. TheScheimpugadapteraswellassomelensescausetheimage tobedistorted, soacalibrationprocedureallowsfortherawimagecoordina tesystems,indicatedas X 1 ;Y 1 and X 2 ;Y 2 ,tobemappedtoaworldcoordinatesystem, X W ;Y W .Inthestereo vectorcalculationprocedureusedinthiswork,therawimag esarerstwarpedinto theworldcoordinatesystemviathecoordinatemapping.The warpingcauseseach interrogationregiontocontainapproximatelythesamepar ticlesonbothcameras, withdifferencescomingfrom3-Dperspectivechangesandth enon-zerothickness ofthelasersheet.Thecorrelationproceduredescribedfor MonoPIVisthenapplied separatelytoeachcamera,andtheresulting2-Dvectoreld sarecombinedintoa 3-Deld.Ifthecombinationreconstructionerrorislowert hanathresholddenedas 1pixel,theMAprocedureisappliedagainsttheindividual2 -Dvectorelds.Thisloop isrepeateduntilthetargetinterrogationregionsizeisre ached,andthelastsetof2-D eldsiscombinedintoa3-Deld.Thenal3-Deldthenunder goesalteringand smoothingprocess. 63

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Thecombinationofthe2-Dvectoreldsintoasingle3-Dvect oreldusesaset offourlinearequationswiththreeunknowns.Solutiontoth eseequationsattempts tominimizeandspreadtheerrorfromthe3componentsofvelo cityevenly.Recalling thecoordinatesystemsinFigure 2-20 ,the Z 1 Z 2 and Z W vectorcomponentsare approximatelyco-linear.The Z W valueshouldfallbetweentheothertwo,andtoolarge ofadeviationbetween Z 1 and Z 2 wouldconstituteareconstructionerror.The X 1 ; 2 and Y 1 ; 2 directionsmustgothroughacoordinaterotationtoyieldth eworldcoordinate system,butsimilarlytheirrotatedvaluesshouldmatchtow ithinanacceptable reconstructionerror.2.5.4SourcesofError Thereareseveralaspectswhichdirectlyaffecttheaccurac yofPIVmeasurements. Manyoftheseissuesrelatetothetracerparticles.Perhaps thesimplestconsiderations inPIVisthattheseedbeinsufcientquantityandevenlydis persedacrosstheimaging domainwithoutgapsorholes.Insufcientorabsentseeding willcausespuriousvectors tobecalculatedorsimplyholesinthedata.Theseedingmust becarefullyapplied toavoidthisproblem[ 145 149 ].Additionally,thelasersheetsfromeachlasercavity shouldbepreciselycoplanar,andthecamerasshouldbeprop erlyfocusedonthelaser planeorerrorswillresult[ 150 ].Theseedparticlesshouldbewellexposedinimagesso theyarewellabovethecamera'snoiseoor. Theseedusedinthisstudyisextravirginoliveoilthathasb eenatomizedbya LaVisionaerosolgenerator,andthemajorityofoliveoildr opletsgeneratedshould haveaparticlediameter, d p ,lessthan1 m [ 151 ]asthegeneratoremploystrapsto preventlargerparticlesfrompassingthrough.Theexpecte d d p modeis0.25 m ,with 92%ofparticlesbeingsmallerthan0.5 m [ 151 ].Aconcernisthattheseedparticle shouldcloselyfollowthesurroundinguid,asthePIVmetho dwillonlyreportwherethe particlesaremoving,nottheuid[ 146 147 149 ].Inair,mostparticlesaremoredense andhencewilltendtohaveanassociatedgravitationallyin ducedterminalvelocity.The 64

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terminalvelocityofasphericalparticleinambientuidma ybecalculatedby V t = gd 2 ( p m ) 18 ; (2–30) wheregisaccelerationduetogravity,disparticlediamete r, p and m arethedensityof particleanduidrespectively,and istheviscosityofair[ 152 ].Assumingadensityfor oliveoilof915 kg m 3 ,theterminalvelocityofthelargestparticlesinlaborato ryairwouldbe 3 10 5 ms 1 whichissignicantlysmallerthananyvelocityofinterest OneimportantconcerninPIVisthatthesizeofanaverageima gedparticleissuch thatitoccupiesmorethanawholepixelontheCCDarray,with twopixelsormorebeing preferable[ 145 146 149 150 153 ].Thisallowsforsub-pixelresolutiontobeobtained usingthestandardandwell-provenGaussiantpeakestimat orusedtoprocessalldata inthisstudy[ 145 147 149 ].Thispreventsaconditionknownaspixel-lockingwhere aparticleissensedononlyanindividualpixeldestroyinga nysub-pixelaccuracyand contaminatingtheprobabilitydistributionfunctiontobe lockedontoquantarepresented bythepixelatedvalues[ 150 153 ].Santiagoet.al.[ 154 ]estimatetheimagedparticle sizebyrstcalculatingacharacteristicdiameterofapoin tspreadfunction, d s =1 : 22(1+ M ) (2 f number ) ; (2–31) wheretheworstcasef-numberforallmeasurementsis2.8,Mi sthemagnication and isthewavelengthof532nm.Themajorityofthedataposition edthecameras approximately900mmfromtheimagingplane,and110mmlense swereused,resulting ina10xmagnication,whichinturnresultsin d s =40 m .IfGaussianbehavioris expectedwithatypical0.25 m particle,theimageddiameter, d e ,canbeexpressedas d e = M 2 d 2p + d 2s ( 0 : 5) ; (2–32) resultinginanimagedsizeof d e =40 m .Thisresultsina d e d c of5.4 pixels particle whichshould besufcienttoyieldaccuracyto 0 : 1 Md p ,or2.5 m [ 155 ],anditshouldeffectively 65

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reducepixellockingerrors[ 150 ].Particlesimagedtothissizesetsaneffectiveminimum interrogationregionof16x16pixels,asthereneedstobesp aceforseveralparticlesin eachinterrogationregiontoyieldgoodcorrelations. Anotherdensityratiorelatedissueisthatinhighvelocity gradientareaswithshear orvortices,thelocalcentripetalaccelerationscancause theseedtobemovedagainst theow,confoundingattemptstodetermineowvelocities. Thefactorisadequately denedbytheStokesnumber, Stk = 2 9 d L U 1 L m ; (2–33) where L isthesizeofobstaclebeingimpactedbytheair[ 146 147 156 ].Aparticle withaStokesnumbersignicantlylessthanunitywillclose lyfollowthemotionofthe uid.Thisisfrequentlyanissueinhigh-speedows[ 146 ].Awingwitha15cmlength inairowat7 ms 1 withthelargestparticleswillyieldaStokesnumberof 7 10 7 whichindicatesthemotionoftheseparticlesshouldbehigh lyrepresentativeoftheuid motion,evenatlowerspeeds. Anothercauseoferrorisparticleshavinginsufcientresi denceintheinterrogation regionandlasersheet,andthismaybeadjustedwiththedTch osenaswellaslaser sheetthicknessandbyusingMAprocessing[ 146 147 ].ThechosendTshouldcause themajorityoftheparticlestomoveapproximately5pixels [ 145 ],whilethefastest particlesshouldmovenofurtherthanhalftheintendedinte rrogationregion[ 146 ].The smallestwell-resolvedvelocitieswillcorrespondto 0 : 1 Md p asindicatedabove,andany particlesenteringorleavingimagingdomainsbetweenfram escausethecorrelationto havenoisewhichcanaffecttheGaussianpeaktalgorithm's accuracy[ 146 149 ]. ChoiceofdTisafundamentaltrade-offinPIVasthereareusu allyhighandlow speedregionswithoutofplaneowswhichcausedifculties inobtainingaperfectdT. ThedT'sselectedinthisworkwerechosensothatinthefaste stregionsoftheow, measurediteratively,theparticlesshouldnottraversemo rethanhalfthedistanceofan 66

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interrogationregionwhileattheslowendoftheowaminimu mvelocityofinterestwas setat0.05 ms 1 .ThisresultedinadTof50 s forthemajorityofdatapresentedinthis work. Backgroundlightingcanhaveunpredictableeffectsonresu ltsanderror,soin allcasesPIVwasperformedinadarkroom.Specialeffortswe retakentoensurea minimumofnon-laserlightenteredtheimages.Thelaserlig htitselfisquitepowerful, somatteblackbackstopswereinstalledonthewallsofthete stsectionsobackground laserreectionwasminimized,andallsurfacesvisibletot hecameraswerealsopainted matteblack.Testswithoutabackstopindicatedsimilarmea nmeasurementsbutyielded muchhigherRMSuctuationsinthesameow.Thiseffectissu spectedtobetheresult ofthebackgroundreectionchangingbetweenimagesresult inginthePIValgorithm occasionallymistakingsuchaneffectforparticlemovemen t.Thisalsolikelyaffects thequalitymetricofEquation 2–29 asoneofthepeaksmaybeduetobackground movement. Aprocessingbestpracticethatappearedtoreduceerrorswa sthesubtractionofthe averagefromeachimagebeforeprocessing.Thesubtract-av erageprocessremoved theeffectsoftheseveralburntoutpixelsonthecameras,an ditalsoreducedeffectsof modelsupportreection.Insomecaseseventhemattebackst opreectedsignicant laserlightcausinglocalizedRMSincreasesintheow,ands ubtractingtheaveragewas effectiveinreturningtheseareastoexpectedvalues.Alld atapresentedinthiswork havehadtherawimagessubtract-averagedbeforevectorcal culation. Alastcauseoferrorisduetotheimagewarpingthatoccursin stereoPIV.All rawimagesarewarpedtoaworldcoordinatesystem,hencethe reisasub-pixel interpolationschemethatcancauseerrorsbyskewingthepa rticles.Asanexample,in Figure 2-20 camera1isorientedperpindiculartothelasersheetsother eisnoskewing oftheimage,butcamera2isangled35 off.Thismeansthata32x32interrogation regionintherawcamera2imagegetswarpedto26x32pixels,l eavinglesspixelsto 67

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calculatevelocityinthe X W direction.Aninterestingeffectthishasonthedataisasma ll Moir e inaccuracythatshowsupincertainmeaneldsaswillbeshow nbelow. 2.5.5QuanticationofError Oncetheabovesourcesoferrorhavebeensufcientlymitiga tedandbest-case measurementsaresetup,considerationcanbegiventowards quantifyingtheexpected actualerrorinthemethod.PrasadandAdrian[ 157 ]developanerrorbasedonmotion ofaspeckledplateintheworldcoordinatesystem, X and Z ,appliedagainstmono PIVsetups.Theseerrorsareassumedtobeequalandaresimil arlyoutputbytheDaVis softwareasanoverallcalibrationerrorwhichindicatesho wfaroffcalibrationdotsare fromattedmodel.Thiserroriskepttolessthan0.3pixelsR MSforallmeasurements, with0.1pixelRMSbeingapracticalminimum.AsadTof50 s wasusedformuch ofthedatasampling,andataresolutionof75 m pixel ,thiswouldresultinamaximum standarddeviationof0.1m/s. ThiserrorimprovesinstereoPIVastherearetwoimages X stereo = X mono M p 2 ; (2–34) resultinginanexpectedstereoerrorof0.007 ms 1 intheXandZdirections.Prasad's methodwasusedtodeterminetherelativeerrorintheoutofp lanecomponent, Y ascomparedtothein-planecomponentsforstereocases.Pra sad'snalsimplied equation[ 158 ], Y X = Y Z = 1 tan ; (2–35) where istheanglebetweenthecameras,resultsinworstcaseoutof planecomponent havingastandarddeviationof0.02 ms 1 fortheallthemeasurementsinthiswork. Apracticallookaterrorintheow-eldrelatestothequali tyofthecorrelation whichisaffectedbyseedsize,uniformity,chosendT,andse edenteringandleaving interrogationregionsbetweenimages.Thisbaseerrorwasa ssessedinbaselineow andhighlyturbulentowsasitwasexpectedthatmeanowsof eachcasewouldbe 68

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uniformoverthemeasuredregionintheabsenceofawingorot herblockage.TheMA techniquewasusedgoingfroma64x64to16x16interrogation windowswitha50% overlap,andadTof50 mus BaselineowindividualPIVresultsgavea0.1m/svariancea crossmostindividual images.Averagesacross500imagesresultedinuniformityb etterthan1%asshownby Figure 2-21 ,andaslightMoir e errorisevidentasverticalroundedbands.Inturbulent owitwasdifculttodetermineerrorforindividualvector images,butover500images themeanresultswereconsistentwithin2%asshownbyFigure 2-22 .Themajorityof theturbulentintensitieswerealsoconsistenttowithin5% asshownbyFigure 2-23 Theseerrorsdidnotappeartobestronglyrelatedtothenumb erofsamples,butinstead werefoundtobemorestronglyrelatedtoseeding,backgroun dreection,calibration quality,andselecteddT. 69

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Figure2-1.DiagramofAerodynamicCharacterizationFacil ityatUFREEF.Photo courtesyofGreggAbate,AirForceOfceofScienticResear ch. Winglet StepperMotor Shaft CompleteVane Figure2-2.ATGafterarunwithrandomangulardisplacement s.Photocourtesyof MichaelSytsma. 70

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Figure2-3.DiagramofATGControlConnections Figure2-4.X-wireprobeintunnelonrotarystage.Photocou rtesyofMichaelSytsma. 71

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WireBPolynomialFit WireBCalibrationMeasurements WireAPolynomialFit WireACalibrationMeasurements HotwireOutputVoltageCalibratedVelocity m s 3 3 : 23 : 43 : 63 : 844 : 24 : 4 4 : 6 4 : 8 0 5 10 15 Figure2-5.Asamplenormalcalibrationplotwithdatapoint s(circles)andpolynomialt (lines). WireAWireB ProbeAxis WireANormal WireBNormal U 1 A B X Y Figure2-6.X-wireprobegeometryindicatinggeometryofwi resAandBwithrespectto incomingairvector U 1 andtheprobeaxis 72

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replacements Calculatedangleandvelocity Measuredangleandvelocity HotwireBMeasured HotwireBPredicted, k B =0.23 HotwireAMeasured HotwireAPredicted, k A =0.23U A;B m s Angle(deg) 40 30 20 10010203040 1 1 : 5 2 2 : 5 3 3 : 5 4 4 : 5 5 5 : 5 Figure2-7.Sampleanglecalibrationplot m c k F(t) x(t) Figure2-8.ForcedMass-Spring-DamperSystem 73

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=0 = : 1 = : 2 = : 3 = : 5 =1Phase FrequencyRatior= f f nMagnitudeH00 : 20 : 40 : 60 : 8 1 1 : 21 : 41 : 61 : 8 2 0 1 2 3 0 1 2 3 4 5 Figure2-9.MassspringdampersystemFRFmagnitudeandphas e 74

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Figure2-10.PCBimpulsehammerusedinmodaltesting.Photo courtesyofPCB Piezotronics. 75

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M Z M Y M X F Z F Y F X Frequency(Hz)FRFCoherence FRFgroupdelay(s) FRFMagnitude10 1 10 2 0 0 : 5 1 0 : 05 0 0 : 05 0 : 1 0 : 15 10 4 10 2 10 0 10 2 Figure2-11.Frequencyresponsefunctionofloadcelltappe dtoexcitepitching,bending, androllingmodes 76

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Frequency(Hz)DeconvolutionFiltergroupdelay(s)M Z M Y M X F Z F Y F XDeconvolutionFilterMagnitude10 1 10 2 0 : 2 0 : 15 0 : 1 0 : 05 0 0 : 05 0 : 1 0 : 15 10 3 10 2 10 1 10 0 10 1 10 2 Figure2-12.Finaldeconvolutionlterfrequencyrepresen tation 77

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CTime(s)BA00 : 05 0 : 1 0 : 150 : 20 : 250 : 30 : 350 : 40 : 45 0 : 5 0 : 1 0 0 : 1 0 : 1 0 0 : 1 0 : 1 0 0 : 1 Figure2-13.DeconvolutionlterFIRrepresentationA)Dat afromEquation 2–27 .B) Dataaftershiftingandtruncating.C)Dataaftershifting, truncatingand windowing 78

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XMoment(N-cm) ZMoment(N-cm)Time(s)YMoment(N-cm) XForce(N)Time(s)ZForce(N) YForce(N)00 : 10 : 20 : 30 : 40 : 5 00 : 1 0 : 2 0 : 30 : 40 : 5 1 0 1 2 4 2 0 2 3 2 1 0 1 6 4 2 0 2 30 20 10 0 5 0 5 10 15 Figure2-14.Filtercorrectingvibrationfromsingleimpul seindifferentaxes.Impulse hammerforce(black),loadcellmeasuredandmomentarmcorr ectedloads (cyan),anddeconvolvedloadcellsignal(red) 79

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Filtered F Z autospectra Unltered F Z autospectra Hammerforceautospectra 10 1 10 2 10 10 10 5 10 0 Figure2-15.Comparisonofautospectraofhammer,unltere dloadandlteredload G Z afterwindowedlterdesign G Z fromWienerdeconvolution 1 H ZF inversetransferfunction 10 1 10 2 10 2 10 0 Figure2-16.Comparisonofsimpleinversetransferfunctio nlter,Weinerlter,and windowedcustomlterresult 80

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replacements ZMoment(N-cm)Time(s)YMoment(N-cm)Time(s)ZForce(N) YForce(N)0 : 20 : 40 : 6 0 : 8 0 : 20 : 40 : 60 : 8 2 1 0 1 2 4 2 0 2 20 15 10 5 0 5 0 5 10 Figure2-17.Filtercorrectingvibrationprecession.Impu lsehammerforce(black),load cellmeasuredandmomentarmcorrectedloads(cyan),anddec onvolved loadcellsignal(red)foranimpulseappliedintheZdirecti on 81

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DeconvolvedJR3Loadcell F Z JR3Loadcell F Z B&KLoadCellXForce(N)Time(s) 00 : 5 1 1 : 5 20 15 10 5 0 5 10 15 Figure2-18.Filtercorrectingcontinuousforcing.Br¨uel andKjr(B&K)dynamicload cellforce(black),JR3loadcellforce(cyan),anddeconvol vedJR3loadcell force(red)forasinesweepappliedintheZdirection 82

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b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b bb b b bb b bb b bb bb b b b b bb b b b b b b b b b b b bb b b b b b b b b bb b b b b b b b b bb b b b b b b b b b b b b b bb b b b b b b b b b b bb b b b b b b b b bb b bb b b bbb b b b b b b bb b b b b b b b b b bb b b bbb b b b b b b b b b b b bb b b b b b b b bb b b b b b b b bb bb b b bbb b bbbbb bb b b b b b b bb b bbb bbb bb b bbb bb b b b b b b b b b b b bb b b b b b b b b b b b b b b bbbb b b bb b b b b bb b b b b b b b b bb b b b b b bb b b b b bbb b b b b bb b b b b b b b b b b b b b b b bb b b bb b b b bbb b b b bb b bbb b b b b b b b b b b b Image1 Image2MappedInterrogationRegions Cross-correlation ResultingVector Figure2-19.DiagramindicatingbasicPIVcross-correlati onproceduretoyielda two-componentvelocityvectoradaptedfromFlowMasterMan ual[ 145 ] LaserSheet WingTopView Camera1CCDCamera2CCD ScheimpugAngle X1Y1 X 2Y 2 X WY WFigure2-20.StereoPIVsetupforchordwisemeasurements 83

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Z cX c 0 : 3 0 : 2 0 : 100 : 10 : 20 : 3 1 0 : 5 0 0 : 5 1 0 0 : 1 0 : 2 0 : 3 0 : 4 Figure2-21.PIVpercentagedeviationfrom U 1 for500averagedimagesinbaseline ow Z cX c 0 : 3 0 : 2 0 : 100 : 10 : 20 : 3 2 1 0 1 2 0 0 : 1 0 : 2 0 : 3 0 : 4 Figure2-22.PIVpercentagedeviationfrom U 1 for500averagedimagesinhighly turbulentow 84

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Z cX c 0 : 3 0 : 2 0 : 100 : 10 : 20 : 3 5 0 5 0 0 : 1 0 : 2 0 : 3 0 : 4 Figure2-23.PIVpercentagedeviationfrommeanTKEinturbu lentow 85

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CHAPTER3 CHARACTERIZATIONOFWINDTUNNELENVIRONMENT InthischaptertheoperationalcapabilitiesoftheATGwill beinvestigatedto characterizetherepeatableturbulentoweldgeneratedb ytheATG.Thischaracterization willemploysingleandmulti-pointX-wireexperimentalcon gurationstogatherstatistical informationabouttheturbulencevelocitiesthroughoutth etestsection,forseveral free-streamvelocitiesandATGrunmodes. 3.1BaselineWindTunnelTesting TheACFwaspreviouslycharacterizedbyAlbertaniet.al[ 15 ].usingapitot-static rake,aswellasasinglewire,hot-wireprobe.Thepitot-sta ticrakewasusedto determinevelocitymagnitudecontoursatmultipledownstr eamlocations,whilethe wirewasusedtodetermineturbulenceintensityatthenozzl eexitplane.Thiswork isexpandedslightlyherebygatheringmoreturbulencedata inthedownstream direction.Thedataindicatesagrowthinturbulencelevels asthemeasurement locationprogressesdownstream,aswouldbeexpectedinaop enjettestsection. Theturbulencelevelsareverylow,frustratingattemptsto assessthedissipationrate andassociatedstatisticsofEquations 3–5 to 3–12 ,henceonlytheturbulentintensities arecalculated.Figure 3-1 showstheincreaseinturbulenceintensityastheprobeis moveddownstreamfromthetunnelinlet. 3.2CTADataSamplingandAnalysis Inthissectionthehot-wiredatasamplingprocedures,para metersandanalysis methodsaredescribed.Thebasicprocedurefordatagatheri ngutilizingtheATGisto rstrampthewindtunneluptoitsdesiredspeed.Thewindtun neliscontrolledviaan analogvoltage,0-10V,whichthevariablefrequencydrivei nterpretsasafrequency linearlymapped0-60Hz.Forconvenience,thewindtunnel's commandedthrottlewillbe speciedasapercentageofthis0-10Vrange.Themotionpro leoftheATGisstarted andseveralsecondsareallowedforthevanestorampuptothe irrotationalvelocity 86

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beforedatasamplingstarted.Themotionprolesareofnit elength,typically180 sec,andsamplingofthehot-wiresignalsonlyoccurswhilet hemotionproleisactive. Samplesaregatheredsimultaneouslyinblocksandthensave dtodisk. Experimentationshowedthatawindtunnelcommandedthrott leof14.5,28.5, 43.5,and58%issufcienttoyieldaroughly2.5,5,7.5,and1 0 ms 1 meanvelocity respectivelyatthecenterline X M =12 : 5 downstream,witharotationalparameter, W of0.6.Thisisincontrasttoawindtunnelcommandedthrottl eof10.5,21,32,and43% toyieldthesamevelocitywithouttheATG.Themeanfree-str eamvelocityisshownto varywithATGforcingfrequency.Figure 3-2 showsthevariationin U 1 asafunctionof rotationalparameter, W ,foracommandedthrottleof28.5%atseveraldownstream locations.Ingeneral,fastervanerotationalfrequencies decreasedvelocityforagiven windtunnelthrottlesetting.Thisisprimarilyattributed toincreasedpressureheadloss duetothevanesblockingtheow. Theexperimentsperformedinthischaptersetthewindtunne lcommandedthrottle toaspecicsetting,ratherthanadjustforadesiredspeed. Thesethrottlesettings resultedindifferentmeasuredmeanvelocitiesaccordingt odownstreamlocationand ATGrunmodewhichrepresentedthesimplestapproachtocont rollingtunnelspeed. Investigationsinchapter5tailoredthetunnelthrottlese ttingtoyieldaconsistentvelocity butrequiredtrialanderrorforeveryrunmodeandvelocity. Thisslightvariationhadlittle noticeableeffectontheturbulentstatisticsbutallowedf oraconstantReynoldsnumber betweenthedifferentATGrunmodes. ThedataissavedbyLabViewina*.lvmoatingpointtextform thatisreadbya Matlabscriptforfurtherprocessing.Theoatingpointfor matallowsfor120dBabove theminimumresolutiontobeexpressed.Therawvoltagedata isconvertedtovelocity vectorsusingthepreviouslydevelopedcalibration.AReyn oldsdecompositionisused toseparatetheuctuatingcomponentofvelocitycomponent s, u 0 ;v 0 ;w 0 ,fromthemean, 87

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u; v; w u = u 0 + u v = v 0 + v w = w 0 + w: (3–1) Inthecoordinatesystemchosenforthiswork,thevelocityc omponentuisoriented paralleltotheairfreestream,vishorizontalandparallel totheground,andwisaligned withthegravityvector.Thevelocitydataisusedtocalcula testatisticalinformationabout thevelocityeld[ 117 120 123 – 125 ]suchasmean U 1 = u (3–2) androotmeansquare(RMS)variation p u 0 2 p v 0 2 p w 0 2 : (3–3) Thepowerorenergyspectraldensities(PSD,ESD) uu ; vv and ww were alsocalculatedbyusingWelch'smethod[ 159 ]withaHannwindow.Thetemporal autocorrelationsofeachvelocitycomponent R uu R vv and R ww arecalculatedby performinganinverseFFTonthePSDs.Thedataissavedforea chblockofdataand thenaveragedwithallotherblockstoyieldanensembleaver ageasappropriate.The averagedPSDdataarethenusedtocalculateturbulentdissi pation[ 117 119 120 123 ] =15 Z 1 0 2 uu ( ) d; (3–4) whichdependsonthewavenumber = 2 f U 1 ; (3–5) 88

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thefrequency,f,andtheuidkinematicviscosity whichwasestimatedbasedoff ambienttemperature,pressureandhumidity[ 160 ].Equation 3–5 invokesTaylor'sfrozen eldhypothesistorelatelengthandtimescaleswhichisdis cussedinmoredetailbelow [ 41 43 161 ].Theturbulentdissipationisanimportantquantitydescr ibinganestimate ofdissipationofturbulentkineticenergy(TKE)whichoccu rsatthesmallestscales ofturbulence,knownastheKolmogorovScale.Itshouldalso beunderstoodthatthe formulationof isonlyanestimateasthehot-wiresensorisessentiallyinc apableoffully resolvingthesmallestscales.Thisisduetothenitesizeo ftheprobe,roughly1mmby 5 m,whichcannotresolveaKolmogorovscaleontheorderof0.2 mm.Theequation hasbeenshowntobereasonablyaccurateinsimilarsituatio ns[ 123 124 ]. Anotherimportantquantityinturbulenceistheintegralle ngthscale.Thislength scaleisanindicatorastothesizeofthelargestscalesoftu rbulenceinaow,and thereareseveralestimators.Anestimateofintegrallengt hscalebasedondissipation [ 117 119 120 123 ],isgivenby L uu =0 : 9 u 0 2 3 2 ; (3–6) whiletheonebasedontheautocorrelationintegrallengths caleisgivenby L 11 R = Z n c 0 R uu U 1 d: (3–7) Thesetwoformulationsgiveindependentvericationofthe magnitudeofthesame quantity.Thevalueof n c isthelocationatwhichtheautocorrelationcoefcientcro sses zeroforthersttimeafterazerolag[ 162 ].TheTaylormicroscale, = p u 0 2 r 15 ; (3–8) isanestimatorofthelargestlengthscaleinaturbulentow atwhichuidviscosity affectsthedynamicsofturbulenteddies.Itisanimportant scaledescribingtheend oftheinertialsubrangeandthebeginningofthedissipatio nrange.Anestimateofthe 89

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Kolmogorovscalefromdimensionalanalysis[ 117 119 120 123 ], = 3 1 4 ; (3–9) isthesmallestscaleinaturbulentow,anditisherethatth emajorityofviscous dissipationoccurs.Thevariouslengthscalesmaybeusedto calculateassociated Reynoldsnumbers, Re = p u 0 2 2 q 15 Re L uu = p u 0 2 L uu Re L uu R = p u 0 2 L uu R ; (3–10) whichareimportantindescribingthebehavioroftheturbul entow.Therelative turbulentintensities, TI X = p u 0 2 U 1 TI Y = p v 0 2 U 1 TI Z = p w 0 2 U 1 ; (3–11) areanindicatorofoverallstrengthofturbulenceinagiven ow.Anisotropyparameters, I xy;xz;yz = p u 0 2 p v 0 2 = p u 0 2 p w 0 2 = p v 0 2 p w 0 2 ; (3–12) giveanindicationofthelevelofanisotropyintheow.Stat isticssuchasEquation 3–4 assumeTaylor'sfrozeneldhypothesis[ 41 43 161 ]whichtreatstheturbulentow-eld asfrozen,i.e.notemporalvariation,duringthetimeanedd yconvectsacrossthexed owsensor.Thehypothesismakesthecalculationssimplerb ecause,forexample, lengthandfrequencyareeasilyinterchangeableusingamea nvelocityasinEquation 3–5 .Thehypothesis,howeverhasassumptionsthatareincreasi nglyviolatedbylarge turbulenceintensities[ 136 163 164 ].ItwasthisissuewhichmotivatedMydlarskiand Warhafttoinvestigatesucheffects[ 117 123 124 ],buttheyshowedthatthesesimple statisticsperformadequatelycomparedtomoreadvancedme thods[ 117 123 ]. ThesmallestTaylormicroscaleisexpectedtobeontheorder of5mmand Kolmogorovscaleshouldbe0.2mmbasedonpreviousstudies[ 119 120 124 ].Again 90

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invokingTaylor'shypothesiswith f max = U 1 = U 1 ; (3–13) maximumtemporalfrequenciesofinterestcanbecalculated .Assumingameanvelocity of5 ms 1 ,thefrequenciesare1000Hzand25kHz.Eachwire'slengthis onthe orderof1mm,henceitwouldnotaccuratelyresolveuctuati onsontheKolmogorov scale.Theturbulentdissipation isthereforenotintegratedouttotheKolmogorovtime scale(Equation 3–4 ),butinsteadtothemaximumfrequencyresolvablebytheX-w ire, calculatedbasedoffthefree-streamvelocityandlengthof thehot-wireis U 1 1 mm : (3–14) Forexample,inthecaseshownbyFigure 3-3 ,thiswouldbearound5kHz. Amaximumsamplingfrequencyof50kHzwasinitiallyselecte dtoyieldfrequency dataoutto25kHz[ 165 ]whichisfarbelowthebandwidthoftheX-wireprobe.Each ofthewireswereconnectedtotheDantecCTAbridgeswhichwe reconnectedtotwo channelsonthePXI-4472ADCmoduledescribedinChapter2.3 .Theseinputswere DC-coupledwitharangeof0-5Voltswhichissufcienttoavo idclippingerrorsatall speeds.Thenumberofsampleswassetat 10 6 ,whichisequivalentto20secondsof data.Thesamplelengthisselectedsothatapproximately50 0integrallengthscalesare recordedineachblockofdata. Thewindtunnelwascommandedtoathrottlesettingsof28.5w hichwasapproximately 5 ms 1 ,andtheATGforcingprotocolwassetwithamean n=4 ,avariance =2 andatimebetweenchanges 1 : 5 0 : 5 sec.Theprobewasinitiallylocated 10 M downstreamfromthecenterline.Datawasgatheredasasetof 64ensembles, andseparateexperimentswereconductedwiththeprobeorie ntedhorizontallyand verticallytoobtainthreecomponentsofvelocity.Theauto spectralenergydensitieswere calculated,assuminghomogeneityintheYandZdirections, asshowninFigure 3-3 91

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Theautospectralenergydensitiesareplottedagainstboth frequency,f,andaneddy turbulentlengthscale L = U 1 f ; (3–15) whichassumesTaylor'shypothesis. TheinitialdataindicatethattheATGaccomplishedthedesi gnedturbulence intensity(TI)ofapproximately20%,butthelengthscalewa sonlyontheorderof 0.20m,shyofthedesired1m.Furthersanitychecksshowthat thespectrumgreatly trendstowardstheuniversal 5 = 3 roll-off,andthecalculatedTaylormicroscale, ,is locatedcorrectlycomparedtothestrongenergyroll-offzo ne.Additionally,theX,Y andZdirectionsofturbulenceareverynearlyisotropicint hecasewith W = : 9 .The anisotropyappearedtobecontainedwithinthelargestleng thscalesofturbulence, aswouldbeexpectedfromturbulencetheory[ 42 ].Anintegrationoftheenergy densityindicatesthat 90% oftheenergyislocatedwithintherst100Hz,and 99 : 5% ofenergywaspresentwithintherst1kHz.Atestontheeffec tofsamplingfrequency ondissipationrateindicatedthat50kHzwasmorethanadequ ate.The64ensembles require21minutestogather,andpost-processingindicate sthattheturbulentstatistics donotchangesignicantlyafter6ensembles,or2minutesof data. 3.3SamplingErrorAnalysis Theremainderofthedatapresentedinthischapterwasgathe redat50kHzfor 20secin8ensembles.Thisvaluewaschosenbasedonanerrora nalysisassuminga maximumlengthscaleof0.3mandaminimumspeedof2.5ms 1 whichisconsidered theworst-caseasithastheleaststatisticalpowerresulti nginthelargestcondence intervals.Undertheseassumptionsthereshouldbestatist icallyindependentmeasurements atleastevery8.3s.Atthelowestspeedthisresultsinatlea st n =19 independent measurementsoverthemeasurementperiod.Furtherassumin gamaximum15% 92

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turbulenceintensitythisresultsinastandarderrorofthe samplemean[ 166 ], 0 : 15 U 1 p n ; (3–16) whichat95%condenceassuminganormaldistributionisrou ghly7%ofthemean value.Increasingspeeddoesnotsignicantlychangethisv alueasturbulenceintensity increasedwiththemeanfree-streamvelocity.InTables A-1 to A-20 the95%condence intervalwaspresentedasthestandarddeviationofthemean softheeightensembles multipliedby1.96whichagreeswellwiththeaboveanalysis Equation 3–4 dependsontheenergyspectraandEquation 3–7 dependsonthe autocorrelation,whichistheinverseFFTofthespectra.As pectralerroranalysis isthereforerelevant.Inthecaseofallcomputationsperfo rmed,thesamplerecord foraFFTwas 2 16 .Eachensembleconsistsof 10 6 measurementswhichyields15 independentbut29totalestimatesofenergyspectrausingW elch'speriodogrammethod witha50%overlap[ 159 166 ].Thisover8ensemblesyields n d =232 estimates ofenergyspectra.Theenergyspectra uu isexpectedtoliebetweenthecalculated spectra c uu accordingto[ 166 ] 1 2 p n d c uu uu 1+ 2 p n d c uu ; (3–17) withacondenceintervalof95%,assuminganormaldistribu tion.At n d =232 thisyields 13%whichshouldbeapplicabletothecalculationof andlengthscale. 3.4ActiveTurbulenceGridSinglePointStatistics AsinglepointCTAX-wireinvestigationisusedtodetermine thedependenceof turbulencestatisticsonATGrunmode,windtunnelspeedand downstreamlocation. ApictureofthesetupisshownbyFigure 3-4 .Thetunnelspeedwaschangedthrough throttlesettingsof14.5,28.5,43.5and58%.Runninghighe rspeedswiththeATGis potentiallydangerousasthevanesvibrateandimpacteacho ther,andthetestsection maysustaindamagefromimplosion.Fivedownstreamlocatio nsof X M areselected 93

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tobe5,10,12.5,15and20.Mostmodelswouldbemountedbetwe en X M of10to12, howeverthepitch-plungerigcanbemovedtoaccommodatemod elsfor X M from5to17 ifnecessary,justifyingtheextendedtestarea.TheATGrun modesconsistof15tests tobetterunderstandhowrunmodeaffectedstatisticsandar especiedbymeanand variancerotationalratepairs.Thefollowingmodesaretes ted: n =2 1 3 1 : 5 4 2 5 2 : 5 4 1 5 1 : 25 6 1 : 5 0 3 0 4 0 5 0 6 0 8 2 : 5 0 5 0 and 8 0 .Eachtestwascompletedwiththeprobeorientedhorizontal lyaswellasvertically toobtaindataforallthreecomponentsofthevelocityvecto r.Theresultsofthesetests areincludedinAppendixAintables A-1 through A-20 Theresultsshowinterestingtrendsinthedata.Theturbule nceintensityisseen torapidlydecayfrom X M =5 to X M =10 afterwhichthedecayismuchslower(Figure 3-5 ).Thismeansthatupstreamof X M =10 ,theturbulenceisinactivedevelopment, whilstdownstreamitisapproximatelywelldeveloped.This isconsistentwithndings byotherauthors[ 8 117 119 120 122 – 124 ].Partofthedecayprocessinvolvesthe transitionfromastronganisotropyat X M =5 toisotropynearingunitydownstream (Figure 3-6 ).The I yz parameterinFigure 3-6 trendsgreatlytowardsunityindicatingthat thecross-streamdirectionsarenearlyisotropicdownstre amofthedevelopmentregion. Thevariousstatisticswerealsoinvestigatedagainstthet ipspeedratiointroduced byRoadmanandMohseni,[ 8 9 ]howeverheretheredonotappeartobeanystrong relationsbetween W andthestatistics,otherthanthemeanasshownbyFigure 3-2 ThismaybeexplainedbecauseRoadmanandMohseniusedasync hronousmotion prolewhichwasquitedifferentfromthecurrentrandomize dprole.Thepowerspectral densitiesarealsoinvestigated,howevereachhasasimilar shapetothatinFigure 3-3 exceptforthe n =2 : 5 0 case.Thiscasehasastrongpeakcenteredat5Hzwith decayinghigherharmonics,ascanbeseeninFigure 5-13 .Theseresultsaresimilar tothatreportedbyMakita[ 121 ],howeverthestrongpeakisnotpresentforanyofthe 94

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other n 0 casesinvestigated.The n =2 : 5 0 effectalsodecreasesinintensity downstream. Threeseparaterunmodeswereselectedformoredetailedinv estigationsat the X M =12 : 5 location.Thislocationwasselectedbecausetheturbulenc eintensity slopehadleveledout,anditwasalikelymountingpositionf ormodelsattachedtothe dynamicmotionrig.Figure 3-7 showstheturbulenceintensityfortheserunmodes.The n =2 : 5 0 casewasnotonlyinterestingforitstonalspectra,butitex hibitedlow turbulenceintensities,smallintegrallengthscales,and anisotropyratiosverynearunity acrosstunnelthrottlesettings.The n =0 3 runmodewasoppositeandexhibited thelargestturbulenceintensityandlengthscales,andhig hlyanisotropicbehavior. n =0 8 wasalsoselectedasithadthehighestanisotropyratiosfor allthrottle settings. 3.5ActiveTurbulenceGridTransverseSurvey Single-pointX-wireCTAmeasurementstraversedacrossthe X M =12 : 5 planeinY andZdirectionswereusedtoindicatethedependenceofturb ulencestatisticsacross themeasurementplane.Thisinvestigationhighlightstheu niformityoftheturbulentow eld,particularlyintheregionwhereawindtunnelmodelwo uldbeplaced.Abaseline casewasalsoinvestigatedforcomparisonpurposes.Models tobetestedareexpected torangefrom15cminspanto60cminspan,andthechordmaybef rom15cmto30 cm,withanglesofattacklessthan30degrees.Thetraverses urveywasperformedto accommodateanyfuturemodelsbymovingthesingleX-wire 25 cminthevertical Zdirectionand 37 : 5 cminthehorizontalYdirectionat X M =12 : 5 .Figure 3-8 shows thetraversedareaoverlaidontestsectionsizewithanotio nalmaximummodelsize. Thedatawassampledat20kHzandusingthesameparametersan dperiodsusedto gatherthesinglepointstatistics,andtheX-wirewasorien tedtomeasurethevelocity componentsintheX-Zplane.Selectedguresareincludedin thischapter,whilethe remainderofthedataarepresentedinAppendixA,Figures A-1 to 3-17 .Thedataare 95

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presentedasapercentvariationfromameanofacoreregionw hichiscomprisedofthe innermost9points. Thesurveyindicatedageneraluniformityinthefree-strea mvelocityandother statisticswithinthecoreregionandextendingoutwardfor allcases.Thebaselinecase inFigure 3-9 showedveryslighthotspotswhicharearesuspectedtobeatt ributedto external,uncontrollableeventsoccurringwhilethosedat awerebeingtaken,forexample thebuilding'sairconditioningsystemcycling.Repeatede xperimentsyieldedsimilar results,withthehotspotsmovingsporadicallyacrossthe eld.Overallthebaselineow isveryuniformandtheshearlayerboundingthetestsection isnoteasilydetectedatthe extentofthesurvey. Theturbulentowsallexhibitedsimilaruniformitiesacro sstheregionofinterest, althoughtheshearlayerwasevidentintheYdirectionassho wnbyFigure 3-10 .The Zshearlayerindicatedanup-downnon-uniformitythatisat tributedtotheasymmetric shapeofthetestsectionenclosure.Theturbulentstatisti cssuchasintensityshown byFigure 3-11 ,anisotropyratioshownbyFigure 3-12 andautocorrelationlengthscale shownbyFigure 3-13 indicatethatamodelinsideofY=30cmandZ=12cmshould beawayfrommostoftheeffectsoftheshearlayerandbewithi nanessentiallyuniform ow.Thestaticgridfree-streamvelocityinFigure 3-14 showedthemostnon-uniformity thatwaspresentacrossallspeeds,andthisisattributedto thegridmembersnotbeing exactlycentered.Theeffectsaresmallandarenotexpected tobesignicant. Thenon-uniformityoftheshearlayerinZweredetectedbyan earlierexperiment andwereconsideredtobeduetotheeffectsofinterferenceo fthetraversingmechanism. Intheexperimentusedtogeneratethisdatatheeffectsofin terferencewereminimized bymountingthehot-wireonasting,sothereiscondencetha tthepresentedeffectsare real.Thepreviousexperimentalsoindicatedanon-uniform ityinmeanvelocityacrossY, andthiswasattributedtoanairgapbetweentheATGandtunne linletliponthatside. 96

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Thisgapwascoveredwithmaskingtapeandthedataindicatet hatthenon-uniformity waseliminated. Theanisotropyratioplotsappearslightlylessconsistent thantheturbulence intensities,butthisisexpectedtobeduethefactthatitis basedoffoftwoother turbulentstatistics.Increasedsamplingtimecouldpossi blyreducevariationin theseplots,butforthepurposesofthissurveyitisshownth attheanisotropyratiois essentiallyconsistentacrosstheregionoccupiedbymodel s.Theincomingintegral lengthscaleissimilarlynoisy,butshowslengthscaleswit hinaconsistentrange. Althoughnotstrictlyhomogeneous,theturbulentowelda smeasuredhasshownitself tobeacceptablyuniformforthepurposesofthisresearch. 3.6ActiveTurbulenceGridMultiplePointMeasurements Thesinglepointmeasurementsallowforaquantitativeasse ssmentofhow variablessuchasdownstreamlocation,windtunnelthrottl eandresultingvelocity,Y andZlocation,andATGrunmodeaffectedtheturbulentstati stics.Inparticular,the assumptionsofhomogeneityandTaylor'shypothesis[ 42 ]allowsforthecalculationof theincomingintegrallengthscale(Equation 3–7 ).Inordertodeterminetheintegral lengthscalesintheothertwoorthogonaldirectionswithou ttheassumptionofTaylor's hypothesis,multi-pointCTAmeasurementsaretakenandthe integralofthespatial cross-correlationcoefcientisusedtondlengthscale. TheprocedureutilizedherewastostarttheATGmotionprol ethathadbeen selectedandthensimultaneouslygatherdatafromtwocalib ratedX-wirehot-wire probes.Oneprobewasheldxedatthetunnelcenterlinewhil etheotherwasmoved byaknowndistanceineithertheYorZdirections.Theaxialm easurementplaneof bothprobeswereidenticalandco-linearwiththeaxisofmea surement.Oneprobe wasconnectedtothetwinDantec55M10bridgeswhiletheothe rprobewasconnected toDantec54T30MiniCTAbridgeswithastatedmaximumfreque ncyresolutionof10 97

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kHz.Datawasgatheredinaeightblocksof20secondsat10kHz .Theprobewasthen traversedaspecieddistanceandthedatasamplingprocess restarted. Thespatialcross-correlationcoefcientiscalculatedat eachdisplacementbytaking theinnerproductoftheYorZdirectionvelocitymeasuredfr ombothprobesanddividing itbythe L 2 normofeachsignalasshownby[ 166 ] CC y = h v 1 ;v 2 i k v 1 kk v 2 k CC z = h w 1 ;w 2 i k w 1 kk w 2 k : (3–18) Thecross-correlationcoefcientsarethennumericallyin tegratedusingtrapezoidalrule overdistancetoyieldtheintegrallengthscales, L 22 CC = 1 2 N X i =2 ( y i y i 1 ) CC y i + CC y i 1 L 33 CC = 1 2 N X i =2 ( z i z i 1 ) CC z i + CC z i 1 ; (3–19) whichmaythenbecomparedagainstthetemporalautocorrela tion-derivedlengthscales inEquation 3–7 Plotsoftheautoandcross-correlationcoefcientsvs.dis placementareshownby Figures 3-15 through 3-17 .TheYdisplacementswereabletobetraversedmuchfurther thantheZduetothepresenceofthetunnelceiling.Theprobe wastraversedupwards toavoidinterferencewiththesupportingmaterial.Themea suredcross-correlation coefcientscomparedtothethetemporalautocorrelationc oefcientsindicatesthe levelofanisotropyinlengthscale.Theautocorrelationle ngthscalewasdetermined byintegratingtothesamelimitsastheYtraverse,whilethe Zlengthscalewasonly integratedtoitsmaximumtraverselength. AninterestingresultisthattheYandZcross-correlationc oefcientsfallneatly ontopofeachotherindicatingthatsimilartothesingle-po intstatisticstheYandZ directionshaveagreatdealofisotropy.However,anunanti cipatedeffectisthatthe 98

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n=2 : 5 ;! =0 runmodeshowedagreatdealofXYandXZanisotropyinlength scalesatallspeeds,withanaverageof1.2,eventhoughthet urbulenceintensity-based anisotropyparameterhasanaverageof1.05.Conversely,th e n=0 ;! =3 and n= 0 ;! =8 runmodesappeartohavelittleXYandXZanisotropyinlength scalesathigher speeds,averaging0.98and.97respectively,despitethefa ctthattheirintensity-based anisotropyratiosare1.13and1.12respectively.Thesedat athereforeindicatethat theintensity-basedanisotropyratioofEquation 3–12 isnotsufcienttoindicatetrue turbulenceisotropywhichrequiresalldirectionaldatato beequivalent[ 42 ]. 3.7Summary InthischaptertheATGwascharacterizedwithrespecttorun mode,downstream location,andcross-streamlocationusingsingleandtwo-p ointX-wireCTAmeasurements. Therunmodecharacterizationindicatedagreatdealofvari abilityinturbulence statistics,withturbulenceintensityrangingfrom10to35 %,anddown-streamdependence showingarapiddecaytoanearsteadystateat X M =12 : 5 ,andsuggestedthatthe verticalandhorizontalcross-streamstatisticsbehavedi nanisotropicmannerwitha meananisotropyratioof1.024averagedacrossallcases.Th ecross-streamsurvey indicatedthattheturbulentstatisticsareapproximately uniformacrossthetestregionof interest,withthemajorityofvariancebeinglessthan5%fr omacoreaverage,leaning towardsahomogeneousoweldaroundtestmodels.Themulti -pointmeasurements investigatedthecross-streamlengthscalesandcomparedt hemagainstthestreamwise lengthscales,indicatingagainthatthecross-streamstat isticsareisotropic,and highlightinganisotropydifferencesbetweenintensityan dlengthscalesacrossrun modes. 99

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U 1 = 18 U 1 = 15 U 1 = 10 U 1 = 7 U 1 = 5 U 1 = 3 X W100 v 0 U 1 100 u 0 U 10 : 480 : 710 : 951 : 191 : 43 1 : 67 1 : 92 : 142 : 48 0 0 : 5 1 1 : 5 0 0 : 5 1 1 : 5 Figure3-1.Baselineturbulenceintensitydownstreamontu nnelcenterline X M =20 X M =15 X M =12 : 5 X M =10 X M =5Free-streamvelocity U 1 ( ms 1)Rotationalparameter W 0 : 20 : 4 0 : 6 0 : 811 : 21 : 41 : 61 : 82 4 : 4 4 : 6 4 : 8 5 5 : 2 5 : 4 Figure3-2.Variationof U 1 withrotationalparameter W 100

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TurbulenceLengthScale(m) U zz Autospectra, TI z =16 : 16% U yy Autospectra, TI y =16 : 09% U xx Autospecrta, TI x =17 : 11% ,L=0.20meterEnergySpectralDensity U 2 Hz Frequency ( Hz ) k 5 = 3 10 3 10 2 10 1 10 0 10 0 10 1 10 2 10 3 10 4 10 10 10 5 Figure3-3.Initialtestautospectraldensityplot Figure3-4.HotwireprobeplaceddownstreamfromATGinACF. Photocourtesyof MichaelSytsma. 101

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Wintensity Vintensity UintensityTurbulenceintensity (%)X M locationdownstreamfromATG 5 101520 0 : 1 0 : 15 0 : 2 0 : 25 0 : 3 Figure3-5.Activeturbulencegridturbulenceintensitydo wnstreamontunnelcenterline I yz I xz I xyIsotropyparameterX M locationdownstreamfromATG 5101520 0 : 8 1 1 : 2 1 : 4 1 : 6 Figure3-6.Activeturbulencegridisotropydownstreamont unnelcenterline 102

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n=0 =8XoMlocationdownstreamn=0 =3n=2 : 5 =05101520 0 : 2 0 : 3 0 : 15 0 : 2 0 : 25 0 : 3 0 : 15 0 : 2 0 : 25 0 : 3 Figure3-7.Activeturbulencegridturbulenceintensitydo wnstreamontunnelcenterline fortheeselectedrunmodesandallspeeds. = TI X x = TI Y o = TI Z Black,blue,redandcyancorrespondto14.5,28.5,43.5,and 58%throttle respectively 103

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Z(cm)Y(cm) 60 40 200204060 60 40 20 0 20 40 60 Figure3-8.Diagramoftraversedarea(red)withmeasuremen tlocation(redsquares) comparedtotestsectionsize(black),largestexpectedmod el(blue)and coreaveragingregion(green) 104

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Meancorevelocity9.57ms 1 Y(cm)Z(cm)Meancorevelocity7.23ms 1Z(cm)Meancorevelocity4.86ms 1Z(cm)Meancorevelocity2.45ms 1Z(cm) 20020 0 : 5 1 1 : 5 20 10 0 10 20 0 : 5 1 1 : 5 20 10 0 10 20 0 : 5 1 1 : 5 2 20 10 0 10 20 0 : 5 1 1 : 5 20 10 0 10 20 Figure3-9.Measuredpercentvariationfromcorefor U 1 withbaselineow 105

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Meancorevelocity9.48ms 1 Y(cm)Z(cm)Meancorevelocity7.21ms 1Z(cm)Meancorevelocity4.87ms 1Z(cm)Meancorevelocity2.48ms 1Z(cm) 20 0 20 0 2 4 6 8 10 20 10 0 10 20 2 4 6 8 20 10 0 10 20 0 2 4 6 20 10 0 10 20 0 1 2 3 4 20 10 0 10 20 Figure3-10.Measuredpercentvariationfromcorefor U 1 withrunmode n=2 : 5 ;! =0 106

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MeancoreTI X =19.2%atmeancorevelocityof9.42ms 1 Y(cm)Z(cm)MeancoreTI X =18.4%atmeancorevelocityof6.90ms 1Z(cm)MeancoreTI X =17.5%atmeancorevelocityof4.46ms 1Z(cm)MeancoreTI X =16.2%atmeancorevelocityof2.22ms 1Z(cm) 20020 5 10 15 20 25 20 10 0 10 20 5 10 15 20 25 20 10 0 10 20 0 5 10 15 20 25 20 10 0 10 20 5 10 15 20 25 30 20 10 0 10 20 Figure3-11.Measuredpercentvariationfromcorefor TI X withrunmode n=0 ;! =8 107

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MeancoreI XZ =1.06atmeancorevelocityof9.54ms 1 Y(cm)Z(cm)MeancoreI XZ =1.03atmeancorevelocityof7.38ms 1Z(cm)MeancoreI XZ =1.02atmeancorevelocityof5.16ms 1Z(cm)MeancoreI XZ =1.04atmeancorevelocityof2.63ms 1Z(cm) 20 020 0 5 10 15 20 20 10 0 10 20 0 5 10 15 20 10 0 10 20 0 5 10 15 20 10 0 10 20 0 5 10 15 20 20 10 0 10 20 Figure3-12.Measuredpercentvariationfromcorefor I xz withrunmode n=0 ;! =3 108

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Meancore L 11 R =0.53matmeancorevelocityof9.42ms 1 Y(cm)Z(cm)Meancore L 11 R =0.53matmeancorevelocityof6.90ms 1Z(cm)Meancore L 11 R =0.58matmeancorevelocityof4.46ms 1Z(cm)Meancore L 11 R =0.59matmeancorevelocityof2.22ms 1Z(cm) 20 020 0 10 20 30 20 10 0 10 20 0 10 20 30 40 20 10 0 10 20 0 5 10 15 20 25 20 10 0 10 20 0 10 20 30 20 10 0 10 20 Figure3-13.Measuredpercentvariationfromcorefor L 11 R withrunmode n=0 ;! =8 109

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Meancorevelocity9.58ms 1 Y(cm)Z(cm)Meancorevelocity7.14ms 1Z(cm)Meancorevelocity4.75ms 1Z(cm)Meancorevelocity2.37ms 1Z(cm) 20 0 20 0 1 2 3 4 20 10 0 10 20 1 2 3 4 20 10 0 10 20 0 1 2 3 4 20 10 0 10 20 0 1 2 3 4 20 10 0 10 20 Figure3-14.Measuredpercentvariationfromcorefor U 1 withstaticgrid 110

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Verticalcrosscorrelationlengthscale=0.36(m) Horizontalcrosscorrelationlengthscale=0.44(m) Autocorrelationlengthscale=0.29(m) Tunnelthrottle14.5% Verticalcrosscorrelationlengthscale=0.38(m) Horizontalcrosscorrelationlengthscale=0.42(m) Autocorrelationlengthscale=0.34(m) Tunnelthrottle28.5% Verticalcrosscorrelationlengthscale=0.42(m) Horizontalcrosscorrelationlengthscale=0.45(m) Autocorrelationlengthscale=0.36(m) Tunnelthrottle43.5% Verticalcrosscorrelationlengthscale=0.44(m) Horizontalcrosscorrelationlengthscale=0.49(m) Autocorrelationlengthscale=0.39(m) Tunnelthrottle58% Distance(m) 00 : 10 : 20 : 30 : 4 0 : 5 0 : 60 : 70 : 8 0 0 : 2 0 : 4 0 : 6 0 : 8 1 0 0 : 2 0 : 4 0 : 6 0 : 8 1 0 0 : 2 0 : 4 0 : 6 0 : 8 10 0 : 2 0 : 4 0 : 6 0 : 8 1 Figure3-15.Autocorrelationincominglengthscalesandcr oss-correlationlengthscales withrunmode n=2 : 5 ;! =0 111

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Verticalcrosscorrelationlengthscale=0.40(m) Horizontalcrosscorrelationlengthscale=0.47(m) Autocorrelationlengthscale=0.48(m) Tunnelthrottle14.5% Verticalcrosscorrelationlengthscale=0.43(m) Horizontalcrosscorrelationlengthscale=0.50(m) Autocorrelationlengthscale=0.50(m) Tunnelthrottle28.5% Verticalcrosscorrelationlengthscale=0.45(m) Horizontalcrosscorrelationlengthscale=0.51(m) Autocorrelationlengthscale=0.52(m) Tunnelthrottle43.5% Verticalcrosscorrelationlengthscale=0.45(m) Horizontalcrosscorrelationlengthscale=0.53(m) Autocorrelationlengthscale=0.54(m) Tunnelthrottle58% Distance(m) 00 : 10 : 20 : 30 : 4 0 : 5 0 : 60 : 70 : 8 0 0 : 2 0 : 4 0 : 6 0 : 8 1 0 0 : 2 0 : 4 0 : 6 0 : 8 1 0 0 : 2 0 : 4 0 : 6 0 : 8 10 0 : 2 0 : 4 0 : 6 0 : 8 1 Figure3-16.Autocorrelationincominglengthscalesandcr oss-correlationlengthscales withrunmode n=0 ;! =3 112

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Verticalcrosscorrelationlengthscale=0.41(m) Horizontalcrosscorrelationlengthscale=0.52(m) Autocorrelationlengthscale=0.53(m) Tunnelthrottle14.5% Verticalcrosscorrelationlengthscale=0.39(m) Horizontalcrosscorrelationlengthscale=0.46(m) Autocorrelationlengthscale=0.49(m) Tunnelthrottle28.5% Verticalcrosscorrelationlengthscale=0.40(m) Horizontalcrosscorrelationlengthscale=0.47(m) Autocorrelationlengthscale=0.48(m) Tunnelthrottle43.5% Verticalcrosscorrelationlengthscale=0.41(m) Horizontalcrosscorrelationlengthscale=0.48(m) Autocorrelationlengthscale=0.49(m) Tunnelthrottle58% Distance(m) 00 : 10 : 20 : 30 : 4 0 : 5 0 : 60 : 70 : 8 0 0 : 2 0 : 4 0 : 6 0 : 8 1 0 0 : 2 0 : 4 0 : 6 0 : 8 1 0 0 : 2 0 : 4 0 : 6 0 : 8 10 0 : 2 0 : 4 0 : 6 0 : 8 1 Figure3-17.Autocorrelationincominglengthscalesandcr oss-correlationlengthscales withrunmode n=0 ;! =8 113

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CHAPTER4 LOWORDERCOMPUTATIONALMODELING Inthischaptersomeexistingspectralmodelsofturbulence willbeusedto synthesizeasignalthatisrepresentativeofatmospherict urbulence.Thissynthetic turbulenceisinjectedintoatwo-dimensionallow-orderco mputationalmodel.Some initialresultswillbepresentedindicatingtheeffectsof turbulenceonSUASwhichwill belooselycomparedtoexperimentalresultswhichisthemos tsignicantcontributionof thiseffort.Inwhatfollowsspectralmodelsofturbulencew illbediscussed,thenavortex latticemodelpresentedandnallysomeresultswillbedisc ussed. 4.1StatisticalRepresentationsofTurbulence Existingsyntheticaircraftturbulencemodelsaremostoft enappliedtostudyvehicle issuessuchasfatigue,strength,structuraldynamics,and stability.Theturbulence modelsprovideastatisticallyrepresentativerealizatio nofaturbulentoweldwith applicationtothespecictoolsusedtoanalyzetheirrespe ctiveissues.Theforms typicallyusedaretheVonKarmanandDrydenturbulencespec tramodels[ 5 6 19 31 32 35 167 ]whicharespeciedbythemilitarystandardsandFederalAv iation Regulations(FARs)fordesignandanalysisofaircraft.Int hesemodelsaunitvariance bandlimitedwhitenoisesignalispassedthroughaforming ltertogenerateasignal withthedesiredspectralproperties(Figure 4-1 ).Theformingltertraditionallyemploys aninniteimpulseresponse(IIR)typelterfor1-Ddatastr eamsbutcanbeexpandedto 3-Dbyinsteadusinganiteimpulseresponse(FIR)lter.Ho wever,aFIRlterwilllose frequencyresolutionasitisappliedoveranitebandwidth [ 31 32 ].Thissynthesisby digitallteringprocesshasbeenmodiedtoaccommodateth evaryingrequirementsof differenttypesofanalyses. Earlysynthesistechniquesreliedonanalogsignalmanipul ation.TheDryden spectralterisexactlysolvablebecausethesespectraare factorable,andhenceitwas mosteasilyusedinanalogsynthesispriortotheavailabili tyofdigitalcomputers[ 90 92 114

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95 ].However,theVon-Karmanspectraismorerealisticbecaus eitshigherfrequency termsrolloffintheexpected 5 3 logarithmicmannersoitismoredesirablefroma physicalstandpoint.Bothmodelsprescribedifferentspec tralformsforlongitudinal, lateral,andvertical(X,Y,Z)velocityperturbations.Int ypicalimplementations,each directionistreatedasstatisticallyindependentoftheot herdirections,althoughthe impositionofcross-correlationispossible[ 105 168 ]. Theshapingfunctionisthesquarerootofthepowerspectral density(PSD)function ofthemodelused,anditisnecessarythatthisfunctionbefa ctorableforuseineither ananalogordigitalIIRlter.Approximatefactorablefunc tionshavebeenfoundfor theVonKarmanspectrathatarevalidwithinacertainrange[ 6 167 ].AFIRlteronly requiresthatthevalueofthelterbeknownwithinitscomb, howeveritsimplementation suffersfrominherentlynitebandwidth.Theadvantageoft heFIRlteristhatthe discreteFourierTransforms(DFTs)requiredbythemethodc anleveragetheefciency ofFastFourierTransform(FFT)algorithmsforlargedatase ts[ 31 32 ].Additionally,FIR lteringwithaFFTiseasilyexpandedto3-Dallowingsynthe sisofallcomponentsofa volumetricoweld.Additionaltechniquesmaybeemployed toensurethatcontinuityis satised[ 168 169 ].TheDrydenandVon-Karmanspectralfunctionsformulated inradial frequency, ,aregivenby[ 6 ]Thedirectionallengthscales, L ^ { L ^ | L ^ k ,andturbulent Table4-1.SpectrafunctionformsofDrydenandVon-Karmant urbulencemodels Dryden Von-Karman ^ { ( ) 2 2 ^ { L i U 1 1 1+ ( L ^ { U 1 ) 2 2 2 ^ { L i U 1 1 h 1+ ( 1 : 339 L ^ { U 1 ) 2 i 5 6 ^ | ( ) 2 2^ | L ^ | U 1 1+12 ( L ^ | U 1 ) 2 h 1+4 ( L ^ | U 1 ) 2 i 2 2 2^ | L ^ | 1+ 8 3 ( 2 : 678 L ^ | U 1 ) 2 h 1+ ( 2 : 768 L ^ | U 1 ) 2 i 11 6 ^ k ( ) 2 2^ k L ^ k U 1 1+12 ( L ^ k U 1 ) 2 h 1+4 ( L ^ k U 1 ) 2 i 2 2 2^ k L ^ k 1+ 8 3 ( 2 : 678 L ^ k U 1 ) 2 h 1+ ( 2 : 768 L ^ k U 1 ) 2 i 11 6 intensities, ^ { ^ | ,and ^ k ,presentinthespectralformshavebeendenedforanaltitu de, 115

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h ,lessthan1000feetby L ^ { =2 L ^ | = h (0 : 177+0 : 000823 h ) 1 : 2 L ^ k = h 2 ; (4–1) and ^ { = ^ | = ^ k (0 : 177+0 : 000823 h ) 0 : 4 ^ k =0 : 1 u 20 : (4–2) Thewindspeedat20feetabovetheground, u 20 ,issetat15,30and45knotsforlight, moderateandsevereturbulenceconditions,respectively. Allthesemodelsarespecied inimperialunits[ 6 ]butareconvertedtometricforthisresearch. TheDrydenandVonKarmanarenottheonlyturbulencemodels, andlowaltitude modelssuchasthosebyKaimal[ 49 ]havebeenproposedtoaccountforturbulence producingvariablesotherthanonlyaltitudeandwindspeed .Recentlowaltitudestudies haveindicatedthatsuchturbulencetrendstowardsamodie dVonKarmanmodel, howeveritisdominatedbyhighintensityandlargelengthsc alegusts[ 12 24 51 ].This causesdifcultieswithdataanalysisasdiscretegusteven tsviolatetheassumptionsof stationarityandhomogenity.Historicalresearchsimilar lyindicatesvalidityofthebasic formoftheVonKarmanmodelwithmodicationsforspecicca ses[ 47 50 ].Thishas motivatedthedenitionofamoregeneralizedspectralfunc tionwhichmaintainsthe basicacceptedformyetallowsexibilityinmodelingturbu lenceatlowaltitudes,suchas ^ {; ^ |; ^ k ( )= 2 ^ {; ^ |; ^ k 1+ A 2 [1+ B n ] m 1 n 3 : 5 5 = 3 m 11 = 6 : (4–3) Additionally,forthepurposesofthisworkitisusefultowr itethemodelintermsof wavenumbers, ,asdenedbyEquation 3–5 116

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4.2FiniteImpulseResponseFilterTurbulenceSynthesis Theabilitytoeasilyimplementanarbitraryspectrallter motivatestheuseofa FIRdigitallteringtechniquetogenerateturbulentveloc itiesindimensionsfrom1-D to3-D[ 140 ].TheenvisionedFIRlterdoesnothavethecapabilitytoou tputallthe frequenciespresentintheturbulencemodels,soadecision mustbemadebeforehand ofthemaximumandminimumturbulentscalesofinteresttoth eanalysis.Thisdirectly inuencesthesamplingfrequencybytheNyquist-Shannoncr iterionandsetsanupper limitonthenumberofdiscretepointsusedinthelterascan beseenby f s = 2 L min = N s L max ; (4–4) and N s = 2 L max L min : (4–5) Aswiththespectralmodels,theFIRequationscanbederived ineitherradialfrequency, ,orwavenumber, EvenwiththeuseoftheexactIIRlters,itisunderstoodtha textremelylong wavelengthturbulentperturbationsdonotaffectthedynam icsofanaircraftbecause theyareviewedasslowchangestothemeanowwhichareatten uatedbythestability oftheaircraft.Similarly,theextremelyshortwavelength sareconsideredto'average out'acrossthebodyoftheaircraftleadingtononetaerodyn amiceffect[ 3 4 25 26 ]. Truncatingtheturbulencespectraatappropriatelocation sreducescomputational requirementsandwillminimizelossofdelitybetweentheF IRandIIRlters.Anotional conceptofminimumandmaximumlengthscalescanbetiedtoai rcraftgeometryand bodydynamics.Forexample,aminimumlengthscalecanbeset asafraction,A,ofa chordlength.Amaximumlengthscalecanbeamultipleofthel ongestperiodstability dynamicsofinterest(e.g.phugoidmode)[ 170 ]oftheairframemultipliedbytheight 117

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Table4-2.TransferfunctionformsofDrydenandVon-Karman turbulencemodels Dryden Von-Karman H ^ { ( ) ^ { q 2 L ^ { U 1 [ 1+( L ^ { ) 2 ] 1 2 ^ { q 2 L ^ { U 1 [ 1+(1 : 339 L ^ { ) 2 ] 5 12 H ^ | ( ) ^ | q 2 L ^ | U h 1+12 ( L ^ | ) 2 i 5 12 1+4 ( L ^ | ) 2 ^ | q 2 L ^ | U h 1+ 8 3 ( 2 : 678 L ^ | ) 2 i 1 2 h 1+ ( 2 : 768 L ^ | ) 2 i 11 12 H ^ k ( ) ^ k q 2 L ^ k U h 1+12 ( L ^ k ) 2 i 1 2 1+4 ( L ^ k ) 2 ^ k q 2 L ^ k U h 1+ 8 3 ( 2 : 678 L ^ k ) 2 i 1 2 h 1+ ( 2 : 768 L ^ k ) 2 i 11 12 speedby L min = C A L max = AT phugoid U 1 : (4–6) NowthattheboundsoftheFIRhavebeendetermined,anapprop riatenumberof discretizationscanbechosen.TheFIRlterisaccomplishe dviaacircularconvolution ofwhitenoiseseedagainstaspectralshapingfunctiontoyi eldtheturbulentperturbations asshownby d u ^ {; ^ |; ^ k x ^ {; ^ |; ^ k = R N s H ^ {; ^ |; ^ k ( ) : (4–7) ConsideringthisimplementationofFIRwillleverageFFTal gorithmstoperformthe circularconvolution,itismostbenecialtochoosethenum berofdiscretizationsto beapowerof2inordertoyieldanefciencyof N s log ( N s ) calculations[ 144 ].This isseldomanissuewhengenerating1-Dturbulencebutbecome simportantforlarge 3-Dgrids.AFIRlter'srepresentationofthespectralmode lsisnowsimplyasquare rootofthespectralenergydensityequation,anditdoesnot matterifthefunctionis spectrallyfactorableornotallowinganyarbitraryfuncti onalform.Table 4-2 presentsthe reformulationoftheDrydenverticalspectraandaccompany ingFIRtransferfunctionin termsofwavenumber. TurbulencesynthesisbyFFTlteringissetupbyrstgenera tingadataset, R N s ,of whitenoiserealnumbers N s sampleslong[ 6 140 167 ].Thewhitenoiseisgenerated fromarandomnumbergeneratorwhichensuresaGaussianprob abilitydistributionand 118

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statisticalstationarityandhomogeneity.TheFFTofthisd atasetgeneratesthespectral contentwhichisuniformintheFourierdomain.TheFIRspect ralshapingfunctionis thenmultipliedpointbypointagainstthemagnitudeofthes pectralcontent.Aninverse FFTisthenperformedonthisdatatoyieldtherealvaluedtur bulentvelocityasshownby d u ^ {; ^ |; ^ k x ^ {; ^ |; ^ k = r ifft h fft ( R N s )( ) H ^ {; ^ |; ^ k ( ) i : (4–8) Thepowerspectralestimatesforasample c u ^ {; ^ | usingWelch'speriodogrammethod[ 159 ] iscomparedagainstthetargetspectruminFigure 4-2 .Thewavenumbercanalsobe consideredintermsofaphysicalturbulencelengthscaleus ing = 1 2 : (4–9) Eachvectorofvelocityproducedbythismethodcanbetreate dseparatelyallowing anisotropyasitwaswiththeIIRlter.Eventhoughthesedat asetsrepresentanite lengthinspace,itisdesirablethatapotentiallyinnitel engthbeproduced.Thisis accomplishedeasilywiththeoverlap-addmethod[ 140 ],whichcreatescontinuingltered datawithnodiscontinuityattheboundariesaslongasthel terremainsthesame.If itissodesiredtheltermaybechangedbetweeneachoverlap -additerationatthe expenseofpossiblediscontinuitiesattheboundary.Inthe eldofdigitallteringthis canbesmoothedwithlittlefrequencycontenterror[ 140 ].InthiswaytheFIRmethod mayproduceinnitelengthdataofvaryingfrequencyconten t,henceallowingfor inhomogeneity,evenifthiscloudsthestatisticalinterpr etationoftheresults. Frequencycontentisnottheonlydescriptivestatisticrel evanttoturbulence simulation.ItistypicaltousewhitenoisewithaGaussianp robabilitydensityfunction (PDF)asseedforthelter[ 6 167 ].Thelteringprocessisalinearoperatorwhichwill yieldresultswithaPDFidenticaltotheinputs[ 140 ].Turbulencemeasurementsinwind tunnelsindicateaPDFthatissimilartoGaussian,butmayex hibitsignicantskewness andkurtosis[ 120 ].ResearchersinthepasthavereshapedtheinputnoisePDFb y 119

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combiningGaussianaswellasanotherdistributionfunctio nsuchasBesseltoyieldan approximatetargetPDF[ 90 ].ThismethodusedonIIRmethodsextendsperfectlytothe proposedFIRlterbecauseitisalinearlteralso[ 140 ]. Codewaswrittentogenerateturbulenceusingtheabovemeth odin1-D,2-D, and3-Delds.Anexampleeldof1-Dsynthesizedturbulence isshowninFigure 4-3 Theseturbulenceprolesexhibitthedesiredspectralcont ent(seeFigure 4-2 ),Gaussian PDFaswellasturbulentlengthscalesonthesameorderastha tspeciedbytheVon Karmanmodel.Theturbulentintensitywasalsodirectlycon trollablebyscalingthe spectrallters.Thismethodallowedfortherapidgenerati onofaturbulentsignalwith appropriatestatisticsforinjectionintotheunsteadyvor texlatticemethoddescribedin thenextsection. 4.3Unsteady2-DVortexLatticeMethod Aninviscid,unsteadyvortexlatticemethod(UVLM)withaco nvectingtrailingedge wakeisusedtodeterminetheunsteadyloadscausedbythesyn theticturbulence.This methodandassociatedcomputercodehasbeenpreviouslyuse dtosimulateapping wingaerodynamics[ 171 – 173 ],howeverthemethodisextensibletothetreatmentof turbulencewithsomemodications[ 174 ].Theimplementedunsteadyvortexmethod issimilartothatdescribedbyKatz[ 175 ]withamodicationtotheboundarycondition formulation.Ashortdescriptionofthemethodwillbeprese ntedtohighlightthesalient detailsofthemodications.4.3.1BasicAlgorithm TheUVLMusedinthisworkmodels2-Dinviscidpotentialowo veranairfoilof zerothickness.Theairfoilismodeledasdiscretizedvorte xpanels,eachwithadifferent butconstantcirculation.Eachpaneliscomprisedofarecta ngularboundhorseshoe vortexwithacontrolpointbetweenhorseshoes,eachwithci rculationvaluesof i and r i respectively.The N bv boundvorticesextendintothethirddimensioninnitely,h encethe trailinglegsofthehorseshoehavenoeffectontheowveloc ity.Aboundarycondition 120

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ofnoowthroughthesurfaceisspeciedat N cp controlpointslocatedbetweenvortex lamentscausingthesurfacetobeastreamline.TheKuttaco nditionisappliedtothe trailingedgebysettingthetrailingcontrolpointvortici tytozero.Wakevortexlaments ofvorticity G i areshedateachtimestepfromthetrailingboundvortex(Fig ure 4-4 ). Kelvin'scirculationtheoremisimplicitlysatisedasapp liedtotheentiresystemby i r i = G i ; (4–10) andbythelinearrelationship =[ A ] r + G: (4–11) Themappingmatrix [ A ] isanidentitymatrixwithanextraloweroffdiagonalsetto1, and G includesonlyvortexlamentsshedfromaboundvortex,inth ecaseofthiswork onlyfromthetrailingedge. Initiallythecirculationdistributions i and r i areunknownwithnovortexlaments shed.Theapplicationoftheowtangencyboundaryconditio nallows i tobesolved with [ B ] = N: (4–12) The [ B ] inuencematrixrelatesthevelocityinducedbyaunitstren gthboundvortexon acontrolpoint,andisonlyafunctionofpanelgeometry. r i canthenbesetto i anda wakevortexlamentisshedoffthetrailingedgewithcircul ationequalto N bv .Equation 4–12 and [ B ][ A ] r = [ B ] G N (4–13) arethenusedinaniterativeprocesstodetermine r i ateachtimestep. r i isthenusedto calculatepressureacrosseachpanel,andcombinedwithgeo metrytheliftandmoment arecalculated. 121

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4.3.2TurbulenceBoundaryConditions TheadditionofturbulenceintotheUVLMsimulationisaccom plishedinamanner similartopreviouswork[ 174 ],withsomeimprovements.Aninitialassumptionisthata generatedturbulenceelddoesnotchangeasitconvectsacr osstheairfoil.Thisisa combinationofTaylor'shypothesis[ 42 ]andthepossiblydecientassumptionthatthe airfoildoesnotalterthenatureoftheturbulence.Thevary ingturbulenceacrossthe chordoftheairfoilmotivatesthepreviousformulationoft heturbulencemodelsinterms ofwavenumber.Theturbulenceeldiseasilyreferencedaga instspatialdimensionsand isattachedtothefree-streamvelocityinaLagrangian-typ ecoordinatesystem. Thesynthesizedturbulenceisinjectedintotheboundaryco nditionthroughthe N vector.Withoutturbulence,thevelocityvectorswithin N arecalculatedbycomposing thedotproductofthefree-streamvelocity, U 1 ,angleofattack, ,pluslocalbody motion, !V cp i ,withthevortexpanelsurfacenormal, ^ n cp i ,with !N ^ {; ^ |; ^ k = U 1 cos ( )^ { + U 1 sin ( )^ | + !V cp i ^ n cp i : (4–14) Theturbulenceisinadditiontothefreestreamvalueofvelo city,anditisusedinthe samewaytogeneratetheboundaryconditionwith !N ^ {; ^ |; ^ k = d u ^ {; ^ |; ^ k + Ucos ( )^ { + Usin ( )^ | + !V cp i ^ n cp i : (4–15) Theturbulenceeldisconvectedacrosstheairfoilbytrans latingthe x ^ {; ^ |; ^ k coordinates accordingtothetimestepandfree-streamvelocityvector, andthevaluesarelinearly interpolatedtothecontrolpointlocationateachtimestep 4.42-DResults TheUVLMcodeimplementedbySnyderet.al.[ 171 – 173 ]wascombinedwith theFIRturbulencesynthesismodeltosimulatethedynamicl oadingonaSUAS airfoilina2-Dcomputation.SUASaremostdistinguishedfr omlargeraircraftbytheir ightspeedandsizeaswellasamissionwhichinvolvesasign icantdurationoflow 122

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altitudeight.Simulationsoftheeffectsofturbulenceon SUASwererunwithscaling similartothatwhichaSUASwouldexhibit.Spectralanalysi softheresultsindicated somequantitativeinsightsintotheeffectsofturbulenceo nSUASrevealinginteresting bandwidthcharacteristicsrelevanttoaircraftdesign,st ability,andcontrolcommunities. Multiplesimulationswererunonasingleprocessorcompute rtoyieldrelevant statisticaldata.Thesimulationswereallrunwithaatpla teairfoilof0.3meterchord xedatanangleofattackofvedegrees.Thetimestepwasset as0.002seconds basedonaconvergencestudyandthechordwascomprisedof25 0vortexpanels. TheVonK arm anturbulencemodelwasusedtogenerateturbulentvelocity historiesfor altitudesof3,30,and300meteraltitude,andthefree-stre amvelocitywassetat3,9 and18ms 1 yielding9simulations.Eachsimulationwasrunfor1millio niterationsor halfanhourofighttime,andeachsimulationrequiredtenh oursofcomputationaltime onasinglecore2.8GHzprocessor. Theinstantaneousverticalforceandpitchingmomentabout thequarterchordas wellasthevelocityincludingturbulenceevaluatedatthel eadingedgewereoutputat everytimestep.Theautoandcross-spectrawerecalculated viaWelch'smethodusing aHanningwindowwith50%overlap.TheinverseFFToftheauto spectradividedby thevarianceyieldedtheautocorrelationcoefcientfunct ionwhichwasthenusedto calculateturbulentlengthscales.ThesizeoftheFFTinWel ch'smethodwassetat 2 15 forthespectrasothattherewasadequateresolutioninthel owerfrequencies.Thelow wavenumberresolutionwasalsonecessarytoyieldcorrectt urbulentlengthscales. Theautospectraldensitiesfortheturbulentvelocitiesof allninesimulationsare showninFigures 4-5 and 4-6 .Theplotsarepreparedwithscalesofbothlinear frequenciesaswellasturbulentlengthscales.Asistobeex pected,thehighest frequenciesofturbulencefallwithintheinertialrangewh ichobeysthecanonical-5/3roll off[ 42 ].Thelargestscalesofturbulenceshownonthegureareana rtifactoftheFFT 123

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size f min = f s N FFT ; (4–16) aswellasthechoiceof150mfor L max intheturbulencesynthesis.Increasingaltitude causesalmosttheentirecalculatedspectrumtobeintheine rtialrangebecausethe lengthscaleincreasesaccordingtoEquation 4–1 .Increasingightspeedshiftsthe spectraifevaluatedagainstfrequencywhichisbestunders toodbylookingtoTable 4-1 howeverplottedagainstwavenumberthespectraateachalti tudelayontopofeach other. Theautospectraldensitiesforthetwoloadsgiveinsightin tothebandwidth ofturbulenceeffectsontheairfoil.Aswouldbeexpectedfr ompreviousresearch [ 4 31 32 ],thelargesteffectsonverticalforce F ^ | isduetothelargestscalesof turbulence(Figure 4-7 ).Furthermore,lengthscaleslessthantheunitchordhave ordersofmagnitudelesseffectthanlargerturbulentscale s.Thisismostlikelydueto the'averagingeffect'whichoccurswithsmallerscalesoft urbulence[ 4 ].Adifference regardinghowlowaltitudesaffectverticalforceisappare nt.Athighaltitudesthe lengthscalesofonemeterhaveanorderofmagnitudelessstr engththanthanlength scalesoftenmeter,howeveratlowaltitudesthestrengthof turbulentperturbationsis approximatelyconstantfromlengthscalesofonemeterandu p.Thisislikelyduetothe shapeoftheVonK arm anmodelatanaltitudeof3m. The M ^ { momentautospectraldensityhasaverydifferentbehaviorf rom F ^ | (Figure 4-8 ).Theverylargestscalesofturbulencehaveaninsignican teffectonthemoment, whilethereappearstobeadistinctmaximaofeffectparticu larlybetweentenandone hundredchordlengths.Atlowaltitudesthismaximaiscente redattenchordlengths. Thiscanbeexplainedthroughreasoninghowdynamiceventso ccur.Longwavelength turbulentperturbationsmaybestrongandhavealargeeffec tonlift,howeverthe momentwillonlyvarysimilartosteadystatebehavior.Cons ideringthatthemoment aboutthequarterchordofanuncamberedplateconsideredin potentialowshouldbe 124

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identicallyzeroandshouldnotvarywith ,thisisareasonableresult[ 156 ].Bysimilar reasoning,aturbulentperturbationontheorderofachordl engthwillcauseanuneven loadingacrossthechordresultinginasignicantchangein pitchingmoment. The F ^ | cross-spectrawithbothcomponentsofturbulentvelocitya reshownin Figures 4-9 and 4-10 .Thecontributionsdueto b u ^ { appeartobeuncorrelatedto F ^ | when consideringthecoherenceplot.Thephaseplotlikewisedoe snotseemtohaveany patternexceptatthelowestfrequencies.Thespectralanal ysispresupposesalinear relationshipbetween F ^ | and b u ^ { ,howeverthetruerelationshipisactuallybetween F ^ | and U + b u ^ { .Bernoulli'sequation p = 1 2 U 2 ; (4–17) speciesaquadraticrelationship,buttheturbulenceissm allcomparedtothefree-stream whichmeansthebehaviorofpressureshouldbelocallylinea r.Consideringthatthe turbulentperturbationsaresmallcomparedtothefree-str eamvelocity, b u ^ { isexpectedto haveonlyasmallcontributionto F ^ | andtheeffectsofsuchcanlikelybeconnedtothe largestlengthscales. Therelationshipbetween F ^ | and b u ^ | ismuchmorecoherentwithasharpdecrease incoherenceoccurringafteronechordlength.Thisisfurth erevidenceoftheaveraging effectofturbulenceacrossthechord.Atwavelengthslarge rthanachord,thephaseis nearzero,andthecross-spectralenergydensityincreases towardsaconstantvalue. Thisresultisconsistentwiththetheoreticalliftslopeof F ^ | =2 [ 156 ].Thenearly constantphasealsoindicatesthatturbulenceofdifferent scalesrequiresthesame convectiondistancetohaveaneffecton F ^ | .Thedecreasingcoherenceatthelargest wavelengthsofthelowaltituderunsistobeexpectedbecaus ethelargestlengthscales arenotpresentatsuchlowaltitudes. Therelationshipbetween M ^ { and b u ^ { seemstobealmostcompletelyuncorrelated asshowninFigure 4-11 .Thisextendstheargumentthatonlythelargestscalesof b u ^ { haveaneffectonaircraftloading.Figure 4-12 followsasimilartrendto F ^ | intermsof 125

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coherence,whilethepeakinenergydensityisstillapparen taroundonechordlength. Thisreinforcestheinterpretationofthe M ^ { autospectraanditsmaximaarecentered aroundonechord.Thephaseplotindicatesthattheeffecton M ^ { willbedelayeda differentconvectiondistancedependingonthewavelength of b u ^ | .Thiscansimilarlybe understoodthatthedifferentpartsofdifferentwavelengt hturbulenceaffectthemoment dependingonwheretheyareintheprocessofconvectingacro ss.Thelinearityofthe phaseindicatesthattheeffectson M ^ { areindeedcorrelated. 4.5Summary AFIRlteringmethodwasdevelopedforthepurposeofquickl ygenerating turbulentvelocitiesofdesiredintensity,arbitraryspec tra,variablePDF,inapotentially inhomogeneous,anisotropiceldrangingfrom1-Dto3-Dspa ce.Thismethodwas coupledwithaloworder2-DUVLMaerodynamicmodeltosimula tethetransient responsetoageneratedturbulenthistory.Thenumericalex perimentsevaluatedthe effectsoftwocomponentsofturbulentvelocityontheairfo illoads.Theresultsindicated thattheverticalcomponentoftheturbulentsignal b u ^ | hadthegreatesteffectonairfoil loads,andabandwidthofinterestwasidentiedforbothcom ponentsofairfoilload. Theverticalforce F ^ | appearedtobeaffectedfromlargeturbulencescalesuntilt he turbulencebecamesmallerthanthechordwhilethepitching moment M ^ { wasaffected mostbyturbulencearoundthesamelengthasthechord. 126

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Figure4-1.DiagramofFilteringProcess TurbulenceLengthScale (m) u j synthesizedturbulencepowerspectraldensity j VonKarmanpowerspectraldensity u i synthesizedturbulencepowerspectraldensity i VonKarmanpowerspectraldensityPowerSpectralDensity( m 2 rad sec )Wavenumber ( rad m ) 5 10 15 20 25 10 2 10 1 10 0 10 8 10 7 10 6 10 5 10 4 10 3 10 2 0 5 10 15 20 25 30 Figure4-2.PowerSpectralDensityPlotofSynthesizedTurb ulenceandTargetSpectra 127

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u j VelocityComponent u i VelocityComponentTurbulentVelocityPerturbation( m sec )Distance(m) 02040 60 80100 0 : 6 0 : 4 0 : 2 0 0 : 2 0 : 4 Figure4-3.Lengthwisesynthesizedvelocityforinputtoun steady2-Dvortexlattice method b b b b 1 b b b G 1 G 2 G 3 2 N bv 1 N bv r 1 r N cp =0 Figure4-4.Basicstructureofa2-DairfoilrepresentedinU VLM 128

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TurbulenceLengthScale (m) Alt:300m,U:18 ms 1 Alt:30m,U:18 ms 1 Alt:3m,U:18 ms 1 Alt:300m,U:9 ms 1 Alt:30m,U:9 ms 1 Alt:3m,U:9 ms 1 Alt:300m,U:3 ms 1 Alt:30m,U:3 ms 1 Alt:3m,U:3 ms 1U i AutospectralDensity( m 3 rads 2 )Wavenumber ( radm 1 ) 10 1 10 0 10 1 10 2 10 3 10 2 10 1 10 0 10 1 10 7 10 6 10 5 10 4 10 3 10 2 10 1 Figure4-5. b u ^ { autospectraldensityplot 129

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TurbulenceLengthScale (m) Alt:300m,U:18 ms 1 Alt:30m,U:18 ms 1 Alt:3m,U:18 ms 1 Alt:300m,U:9 ms 1 Alt:30m,U:9 ms 1 Alt:3m,U:9 ms 1 Alt:300m,U:3 ms 1 Alt:30m,U:3 ms 1 Alt:3m,U:3 ms 1U j AutospectralDensity( m 3 rads 2 )Wavenumber ( radm 1 ) 10 1 10 0 10 1 10 2 10 3 10 2 10 1 10 0 10 1 10 7 10 6 10 5 10 4 10 3 10 2 Figure4-6. b u ^ | autospectraldensityplot 130

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TurbulenceLengthScale (m) Alt:300m,U:18 ms 1 Alt:30m,U:18 ms 1 Alt:3m,U:18 ms 1 Alt:300m,U:9 ms 1 Alt:30m,U:9 ms 1 Alt:3m,U:9 ms 1 Alt:300m,U:3 ms 1 Alt:30m,U:3 ms 1 Alt:3m,U:3 ms 1F j AutospectralDensity( N 2 m rad )Wavenumber ( radm 1 ) 7 = 3 10 1 10 0 10 1 10 2 10 3 10 2 10 1 10 0 10 1 10 2 10 1 10 0 10 1 10 2 10 3 10 4 10 5 10 6 Figure4-7. F ^ | autospectraldensityplot 131

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TurbulenceLengthScale (m) Alt:300m,U:18 ms 1 Alt:30m,U:18 ms 1 Alt:3m,U:18 ms 1 Alt:300m,U:9 ms 1 Alt:30m,U:9 ms 1 Alt:3m,U:9 ms 1 Alt:300m,U:3 ms 1 Alt:30m,U:3 ms 1 Alt:3m,U:3 ms 1M i AutospectralDensity( N 2 m 3 rad )Wavenumber ( radm 1 ) 7 = 3 10 1 10 0 10 1 10 2 10 3 10 2 10 1 10 0 10 1 10 4 10 3 10 2 10 1 10 0 10 1 Figure4-8. M ^ { autospectraldensityplot 132

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TurbulenceLengthScale (m)CoherenceWavenumber ( radm 1 )Phase(rad) U i and F j CrossspectralDensity( Nm 2 rads )10 1 10 0 10 1 10 2 10 3 10 2 10 1 10 0 10 1 0 0 : 2 0 : 4 0 : 6 0 : 8 1 2 0 2 10 10 10 5 10 0 10 5 Figure4-9. F ^ | and b u ^ { cross-spectraldensityplot 133

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TurbulenceLengthScale (m)CoherenceWavenumber ( radm 1 )Phase(rad) U j and F j CrossspectralDensity( Nm 2 rads )10 1 10 0 10 1 10 2 10 3 10 2 10 1 10 0 10 1 0 0 : 2 0 : 4 0 : 6 0 : 8 1 2 0 2 10 10 10 5 10 0 10 5 Figure4-10. F ^ | and b u ^ | cross-spectraldensityplot 134

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TurbulenceLengthScale (m)CoherenceWavenumber ( radm 1 )Phase(rad) U i and M i CrossspectralDensity( Nm 3 rads )10 1 10 0 10 1 10 2 10 3 10 2 10 1 10 0 10 1 0 0 : 2 0 : 4 0 : 6 0 : 8 1 2 0 2 10 10 10 5 10 0 Figure4-11. M ^ { and b u ^ { cross-spectraldensityplot 135

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TurbulenceLengthScale (m)CoherenceWavenumber ( radm 1 )Phase(rad) U j and M i CrossspectralDensity( Nm 3 rads )10 1 10 0 10 1 10 2 10 3 10 2 10 1 10 0 10 1 0 0 : 2 0 : 4 0 : 6 0 : 8 1 2 0 2 10 10 10 5 10 0 Figure4-12. M ^ { and b u ^ | cross-spectraldensityplot 136

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CHAPTER5 EXPERIMENTALLOADRESULTS Inthischapterresultsofaerodynamicloadsgatheredfromt hin,rectangularat plateswillbepresented.Meanandtime-dependentaerodyna micloadswillbeevaluated toidentifyimportantdifferencesbetweenthelowturbulen cebaselineowandthe increasinglyturbulentowsbehindthestaticandactivegr ids.Specically,thevarious effectsoffree-streamturbulencegeneratedbythestaticg ridandATGwillbereported todemonstratehowitcanaffectstall,liftslope,andpitch ingmomentbehavior.The datafromthischapterindicateimportantdifferencesinlo adwhichhavetheirunderlying causeintheow-eldwhicharethenusedtodirectfurtherst udyinChapter6. Theatplatemodelsusedinthisworkareconstructedofbi-d irectionalcarbon laminatesbondedtoabirchplywoodcorewithroundededges. Threemodelswereused inthesetests,withdimensionsandchordReynoldsnumbers, Re = U 1 c ; (5–1) testedindicatedbyTable 5-1 .Airdensity, ,wascalculatedfrommeasuredtemperature, T,andatmosphericpressurep 1 from p 1 = RT: (5–2) Temperatureandatmospherictotalpressureweremeasuredi nsidethetestsectionfrom anOmegaDP-100thermocoupleandaDruckDPI-142absolutepr essuresensor.The viscosity wascalculatedusing[ 114 ] = 1 : 458 10 6 T 3 2 110 : 4+ T ; (5–3) wheretemperatureisinKelvins.Timeaveragedanddynamicl oadsaremeasuredand investigated. 137

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Table5-1.ModelDimensions A chord span thickness surfacearea ReynoldsNumber cm cm mm m 2 x1000 1 31.7 31.7 4.50 0.100 100,150,200 2 16.1 31.9 4.50 0.0512 50,75,100 4 16.1 62.7 4.50 0.101 50,75,100 5.1DesiredReynoldsNumbersandTurbulenceData Inordertofairlycompareexperimentaldata,themodelsnee dedtobetested atconsistentReynoldsnumbers.ExperienceinATGoperatio nindicatedthattunnel commandedthrottlesettingwouldhavetobecarefullysetfo reachturbulencecondition toobtainadesiredfree-streamvelocity.AcalibratedX-wi rehot-wireprobewasplaced onthetunnelcenterlineat X M =12 : 5 intheverticalorientation,andthethrottlesetting wasmanuallyadjustedtoobtainbestagreementinfree-stre amvelocity.Table 5-2 indicatesthefree-streamvelocityandrelatedturbulents tatisticsusedintheexperiments inthischapter.Experimentationshowedthatitwaspossibl etoyieldaReynoldsNumber variationoflessthan2%overa160smeasurementperiodfort heATGcases,and signicantlybetterforthestaticgrid.Thesestatisticso fferarangeofrelativeintensity, lengthscale,andanisotropyratiotoexperimentover.Table5-2.ATGturbulencestatisticsatspeedstoyieldReyn oldsnumbersat X M =12 : 5 X M n U 1 TI X TI Z L 11 R I xz Hz m s % % m 12.5 0 3 4 : 79 0 : 17 19.5 18.2 0.504 1.07 12.5 0 8 4 : 74 0 : 16 17.6 16.0 0.575 1.11 12.5 2 : 5 0 4 : 80 0 : 10 16.8 16.6 0.350 1.01 12.5 0 3 7 : 26 0 : 26 20.8 19.4 0.604 1.08 12.5 0 8 7 : 12 0 : 18 18.7 17.1 0.468 1.09 12.5 2 : 5 0 7 : 17 0 : 16 18.0 18.4 0.382 0.98 12.5 0 3 9 : 59 0 : 31 21.3 19.8 0.607 1.08 12.5 0 8 9 : 48 0 : 23 19.4 18.2 0.514 1.07 12.5 2 : 5 0 9 : 53 0 : 21 18.7 19.2 0.406 0.97 12.5 StaticGrid 4 : 77 0 : 02 4.0 3.7 0.091 1.07 12.5 StaticGrid 7 : 22 0 : 02 4.1 3.8 0.145 1.07 12.5 StaticGrid 9 : 62 0 : 02 4.1 3.9 0.201 1.07 138

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5.2MeanLoadsUncertaintyTreatments Experimentaluncertainty,asitappliestomeanaerodynami cloadssensedin awindtunnel,oftenfocusesonthecombineduncertaintyoft heinstrumentation, generallyassumingthatthesensedmeanloadsdonotvarysig nicantly[ 176 177 ]. Inmanycasesthisisanappropriateassumptionasuncertain tiesaretrulydrivenby instrumentation,inparticularthestrain-basedloadsens ors,howeverthisresearch hasbroughttolightproblemswiththisapproachintheprese nceofahighlyturbulent ow.Thechiefproblemisthatinthisworkthetime-varyinga erodynamicloadshave uncertaintiesthataredrivenbytheverystronguctuation s,andthesignalsarestrongly autocorrelated. Acharacteristicissuewithevaluatingstandarderrorisda tasamplingofsignals whichareautocorrelated.Classicalstatisticsassumesar andomlysampledquantity fromanitedatasethavingthesameprobability, x i ,toevaluatesamplemean, = P x i ni =1 n ; (5–4) samplestandarddeviation, = r 1 n 1 X ( x i ) 2 ; (5–5) andsamplestandarderrorofthemean, = p n ; (5–6) aswellasotherstatistics.Thesestatisticsareallestima torswhichdependonn,which isthenumberofsamples,andtheassumptionsrequirethatth esamplesberandom andhaveequalprobabilityofoccurrencetobeunbiasedesti mators.Thecaseofmany realdatameasurements,however,violatestheseassumptio nsleadingtothesesimple statisticsbeingbiased. 139

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Table5-3.Standarddeviationsofloadinvarioussituation s Load Electronic Trembling Aerodynamic F x 0.018 0.031 0.041 F y 0.028 0.050 0.134 F z 0.028 0.189 0.266 M x 0.000 0.002 0.002 M y 0.002 0.019 0.025 M z 0.004 0.005 0.024 5.2.1TypicalTreatment Astandarduncertaintytreatmentwillberstbeappliedaga insttheJR3loadcell inabaselineow[ 178 ].Inthissituationthereareseveralsourcesofuncertaint y,but thetwomajorsourcesofuncertaintyhavebeenfoundtobeloa dcellstrainvoltage standarddeviation,andangleofattack, ismeasuredwithadigitalinclinometer rigidlyattachedinlinewiththeloadcellandhasameasured accuracyof 0.07 with a95%condence.Theloadcellisexible,however,andatmax imumloadstheactual model maydifferasmuchas 0.2 leadingtoan uncertaintyof 0.21 with95% condence. Theloadcell'soutputhasastandarddeviationthatisdueto threemaincauses: internalelectronicnoise,dynamicmotionrigvibration,a ndow-inducedoscillations.The electronicnoisewasmeasuredtobeindependentof andmodel,andwasessentially aconstantparameter.Thevariationalloadwasmeasuredwit htheloadcellheldxed atan setbythepitch-plungerig,withtheA=2model.Thepitch-plungerighas aninherentvibration,ortrembling,duetoitsactivecontr olloop,whichintroduces uncertaintyintomeasurements.Thistremblingwassporadi cinnatureanditsresultsare calculatedforaworstcaseexperiencedinexperiments.Las t,thebaselineowinduces anunsteadycomponenttoloads,presumablyduetounsteady owstructures.Thiswas essentially independentatangleslessthanstall,butitwasdependento nfree-stream velocity.Thisiscalculatedforaworstcaselessthanstall .Thesevaluesareshownas standarddeviationsinTable 5-3 140

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Experimentationindicatedthatbaselinemeasurementssam pledat100Hz wereessentiallyuncorrelated,hencethenumberofsamples couldbeusedasnin determiningtherelativestandarderror R =100 p n 1 : (5–7) Samplingparameterswerethenselectedforbaselinerunsch osenwithsamplestandard deviationsinTable 5-3 andmeanaerodynamicloadsat valuesjustlessthanstallto yieldoverallrelativestandarderrorslessthan2%witha95 %condenceintervalfor baselineloadcases.Therelativeuncertaintynaturallyin creasesintermsofpercentage as,forexample,theaerodynamicloadgoestozeroatzero .Thismethodwas insufcientforturbulentcasesbecausetheloadsmeasurem entsweresignicantly autocorrelatedat100Hzandevenlowerfrequencies.5.2.2ModicationtoStandardErrorTreatment Theautocorrelationissueispartlyduetothecapabilityof moderndataacquisition hardwarewhichcangatherdataatahighrateforaverylongpe riodoftimewithout breakingthedatasetsintoindependentensembles.Inmeasu rementsofphysical phenomenathiscontinuouslysampleddataisfrequentlyaut o-correlatedacrosstime aswhatisbeingmeasuredishighlydependentonitspasthist oryanddynamicsofthe system.Theprobabilityofoccurrenceforthenextsampleis alsoaffectedbythephysics whichdrivethesystem.Akeysimplicationwhichisoftensp eciedisthatofstationarity, wheretheexpectedstatisticalpropertiesdonotvary.Weak stationarityisassumed inmostlaboratorysettingssothat and donotvary,andthisusefulassumptionis frequentlyvalid,leadingtounbiasedestimatorsforthese twoquantities. Thisleadstoaquestionofhowtoevaluatethestandarderror ofthemeanstatistic whenthenumberofsamplesisnotwhatprimarilydrivesthest andarderrorrelationship. Forexample,atemperaturesampledat1kHzfor10sandthesam etemperature sampledat10kHzfor1swillyieldthesamen.Thedatafromeac hdatasetwillbe 141

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verydependentonthedynamicsofthesystem,boththehighan dlowfrequency response.TheNyquist-Shannonsamplingtheoremindicates thattocaptureallrelevant dynamicsaquantityshouldbesampledattwicethefrequency ofinterestwithinasignal, hencethefastersampleddatawouldresultinfrequencyinfo rmationuptothehighest frequencyofinterest.Thedatawhichissampledlongerwoul dyieldbetterlowfrequency informationattheexpenseofhighfrequencydataforthesam en.Therequirement behindatotaltimespentsamplingatagivenfrequencyistha twhichyieldssufcient lowandhighfrequencyresults,buterrortreatmentinthepr esenceofautocorrelationis unclear,soamethodologyisdevelopedforthiswork. Andersonet.al.useamethodwhichincorporatestheautocor relationcoefcient function, ,toeffectivelyadjustthenumberofsamplesinameasuremen t.These correctioncoefcients r 1 =[1 2 X (1 k n ) z}|{ k n 1 k =1 ] r 2 =[1+2 X (1 k n ) z}|{ k n 1 k =1 ] ; (5–8) appliedtosequentialdatarequireanestimateofautocorre lationcoefcientfunction, z}|{ ,whichcanbebasedoffthemeasurementitself.However z}|{ isonlyknowwitha 95%condenceaccordingto 1 : 96 vuut (1+2 P 2 z}|{ k ) n ; (5–9) belowwhichvaluethevalueof z}|{ isindistinguishablefromzeroaccordingtothenull hypothesis.Thissetsalimit, n c ,tothesummationinEquation 5–8 ,whichisthelast indexthat z}|{ < 1 : 96 s (1+2 P 2 z}|{ k ) n .Additionally,when z}|{ iscalculatedwithFFTsthe autocorrelationissymmetric,anditmakeslittlesensetha tEquation 5–8 besummed above n 4 .Thissetsaminimumindexforsummation, n r = min [ n c ; n 4 ] ; (5–10) 142

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whichmaybeusedby A = 2 n r 2 ; (5–11) toevaluatethestandarderrorofthemean. Typicalexperimentaltextslistatablewhichallowsonetoc hooseacoefcientof variation, c v = ; (5–12) andadesiredcondenceinterval(CI)andlookuparequisite numberofmeasurements whichwillmeettheCI.As c v increasesthenumberofsamplesincreases,justastighter CIboundsincreasenumberofsamples.Thesetablesalsoassu merandomlydistributed sampleswhichisviolatedbytheautocorrelationanddepend encedisplayedwithmany real-worldmeasurements.Usingtheabovecalculationmeth od,CIresultsmaybe tabulated,orinaniterativeprocedurethesamplingrequir ementscanbedeterminedto meetaspeciedCI.Thismethodwillprimarilybeappliedtoc alculate95%CIvaluesfor eachcomponentofload. 5.3MeanLoadsinBaselineFlow Themodelswereplacedintheowattachedtoeitherthesting balanceorthe JR3loadcellwithstandardmountingequipment.Thedynamic motionrigwasused tomovethemodelthroughseveralanglesofattack,or ,whileanautomatedVI gatheredloaddata.Figure 5-1 showsthemountingofthemodelontheJR3load cellinthetestsection.Themodelisverysimilartoonetest edbyMuellerandTorres [ 176 ],andthewindtunnelallowstestingatsimilarchordReynol dsnumbers.Themain differencesbetweenthemodelsistheshapeoftheedgesandt hemounting,whilethe measurementinstrumentationandtunnelthemselvesarequi tedifferent. Themodelswereplacedsothattheleadingedgewas1.67meter sdownstream fromthetestsectioninlet.Thiscorrespondstoa X M locationof12.5andabaseline streamwiseturbulenceintensityof0.5%.Loadsateachpoin tweregatheredfor 50secondsat4kHzwhichwasfoundtoyieldacceptable95%CIv aluesforhigher 143

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Reynoldsnumbercases.Theresultingloadswerecorrectedb yremovingtheaverage weightofthemodelthroughan'airoff'testandthennormali zedandrotatedintothe stabilityaxistoyieldaerodynamiccoefcients[ 176 ].Amean,standarddeviation,and 95%CIofthecoefcientdatawerecalculatedateachangleof attackpoint.Figure 5-2 showslift,dragandpitchingmomentmeanandstandarddevia tioncoefcientsfortheA=2 modelatthefourtestedReynoldsnumbersforboththebalanc e,markedasB, andloadcell,denotedLC.Themeasuredpitchingmomentisco rrectedusingparallel axistheorem[ 179 ], M Y = M Y o + F Z xR c 4 ; (5–13) wherethemeasuredmoment M Y o iscorrectedwiththenormalforce F Z andthedistance fromtheloadcellmomentreferencepointtothequarterchor d, R c 4 .Thiscausesthe pitchingmomenttobenoisy,asthealreadysmallsignalisco upledwiththenormalload componentmeasurement.Thedataisplottedwiththemeanval uesintheleftcolumn andstandarddeviationintherightcolumn.Theothermeanlo adcomponentswere effectivelyzeroduringthetestasexpected. Thesedataindicatethattheloadcellandstingbalancegive comparableresults. Bothsensorshavesimilarresolutionswhichresultsinthel owReynoldsnumbertests beingexcessivelynoisy.AtthisReynoldsnumberthedynami cpressureisapproximately 2Pa,sothesensedloadsarequiteneartheresolutionoorof thesensorsasis evidencedbytheirlargerelativestandarddeviations.Rep eatedexperimentswith longersamplingdidnotyieldbetterresults,asthediffere nceinloadsbeingdetected wasontheorderofthelevelsofdrift.ThelowReynoldsnumbe rdatadoesindicate thattheloadsfollowapproximatelythesametrend,however itispossiblestallhas beendelayed2degreeshigher.ThelowestReynoldsnumberte stsweresubsequently droppedbecauseofthis,andtheloadcellbecamethefavored sensorduetoitsinherent durabilityandstiffness.Furthermore,thedragwasinvest igatedanditwasseenthatthe axialforcewasconsistentlyontheorderofsensorresoluti on,aswouldbeexpectedbya 144

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thinatplate,henceanydragsignalwasprimarilyduetothe coordinatetransformation ofnormalforce.Theliftcurvesshowalluniquedataintheex periment,sodragcurves arenolongerplotted. Figure 5-3 showsliftandpitchingmomentcoefcientsgatheredatthet hree ReynoldsnumbersandcomparedagainstMullerandTorres'da ta[ 176 ].Alltests randomized inboththetareandwind-onteststominimizedrifterrorsan dtoeliminate stallhysteresiseffects,whichwerealsoshowntobesmall. Condenceintervalswere notincludedonthisplotbecauseforallbaselinecongurat ionstestedtheyweresmaller thanthesymbolsizes.ThedatashowaReynoldsnumberindepe ndenceforallthreeAmodelstested. Thereare3regimesofpitchingmoment:alowangleslightlyp ositiveslope,an intermediateanglewithanegativeslope,andapost-stall attenedslope.Thecutoff forthelowanglebehaviorappearstobe5-7 independentofAwhereasthecutoff fortheintermediateanglebehaviorappearstobe stall whichdoesdependonA.The < 5 casesindicateanapproximatelyzeropitchingmoment,aswo uldbeexpected fromaatplate.Above 5 thepitchingmomentshowsanegativeslope,possiblydue toformationofowstructuressuchasleadingedgeseparati onbubblesorstrongtip vortices.Theseoweffectswouldcauseaneffectivecamber withmovingcenterof pressureinthemeanow,therebycreatingaslopedmoment.T heslopepersists until stall afterwhichthepitchingmomentslopeisincreased,indicat ingthecenterof pressurehasmovedforward. MullerandTorres[ 176 ]reportedmaximumliftcoefcientsof0.84with stall at17.5 forasimilarwingataReynoldsnumberof100,000.Thiscompa resreasonablywith themeasuredmaximumliftcoefcientmeasuredbythebalanc eof0.89at17.9 and measuredbytheloadcellof0.80at18.1 .At10 MullerandTorresreportedalift coefcientof0.55whereasthebalancemeasured0.58andthe loadcellmeasured 0.52.MullerandTorressimilarlynotedthedeparturefroma parabolicdragcurveat 145

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stallasmeasuredinthisstudy.Asadirectquantitativecom parisontheymeasureda dragcoefcientof0.125at10 whilethebalanceregistered0.128andtheloadcell registered0.107.Thebalancereturnedamoreaccuratedrag gureasexpected.Muller andTorresalsonotedabehaviorinpitchingmomentsimilart othatexperiencedin thiswork,withtherstbreakpointa6 andthesecondbreakat stall .Thesedirect comparisonsindicatethattheresultsofthebalanceandloa dcellarecomparable, althoughtheloadcell'saccuracyislowerasexpected. Thestandarddeviationforallsignalsareapproximatelyco nstantacross except forincreasesafter stall .Atthelowestspeedsthesevaluesaredrivenbythenoiseint he sensorsaswellasatremblingvibrationpassedtothesensor sthroughthepitch-plunge rig.Thisiswhatcausesthesawtoothappearanceoftheloads tandarddeviationsin Figure 5-2 ,asthepitch-plungerigtremblesmoreatsome thanothers.Theeffectwas notconsistentinanyway,anditcouldnotbecontrolledwith theexistingpitch-plunge system. 5.4MeanLoadsinthePresenceofTurbulence MeanloadsforthethreecharacterizedATGrunmodesandstat icgrid,three Reynoldsnumbers,andthreeAweregatheredandprocessedsimilarlytothebaseline cases.ThedatafromdifferentReynoldsnumberswithturbul encedidnotindicate signicantdifferences,similartothebaselinecases,asi sshownbyFigure 5-4 fortwo turbulentcases.Figures 5-5 through 5-7 indicatedifferencesbetweenbaselineand turbulentrunmodesforthehighestReynoldsnumber.Furthe rmore,thedifferentATG runmodesdidnotsignicantlydifferfromeachother,indic atinganindependencefrom turbulentstatisticsovertherangetested.Thestaticgrid resultsindicateamiddleground betweenthebaselinecasesandtheATGcases. Thepresenceofturbulencehasaneffectonthemeanliftinal lAcases,withthe largesteffectsduetothehighturbulencelevelsforalloft heATGrunmodes.IntheA=1casedisplayedinFigure 5-5 ,turbulencehastheeffectofreducingtotalliftand 146

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smoothingoutthebehaviorofthecurve.Previouswork[ 177 ]indicatedthattheincrease inliftslopestartingaround =10 wasprimarilyduetoastronganddiscernibletip vortexformingoverthesuctionsurfaceofthewing.Thistip vortexishypothesized togeneratetheadditionalliftuntilitbreaksdownafterst all.Itwouldappearthatthe presenceofstrongturbulencepossiblyinhibitsthecohere ntformationofsuchavortex andthereforedecreasestotalliftgenerationsubstantial ly.Thisdecreaseinliftisevident althoughlesspronouncedinthestaticgridcase.Thiseffec tisalsoevidentinthe pitchingmomentastheaerodynamiccenterismovedlessfara ftthanbaselineow. TheA=2and4ATGcasesdisplayedinFigures 5-6 through 5-7 haveanopposite effectwhichincreases stall aswellasconsiderablyincreasesthemaximumlift coefcient.InthesecasestheATGrunmodeandcorrespondin gowstatisticsagain donotappeartobeimportant.Althoughnotincludedhere,ex aminationoftheother Reynoldsnumberstestedyieldedsimilarresults.Thesehig herAwingswouldbeless dominatedbythetipvortexeffectthatlikelyeffectedtheb ehavioroftheA=1wing, andbaselinestalloccursearlier.Thepresenceofturbulen cehadtheimmediateeffect ofextending stall beyondthebaselinecaseaswellassmoothingthetransition tostall. Thedataindicatethat stall fortheATGturbulencecasesmaybeashighas 30deg ,a considerableexpansionfromthebaselinecases,whilethes taticgridonlycreateda smallincreasein stall .Theroll-offofliftatstallwasverysmoothfortheATGcase s, whilethestaticgridappearedsimilartothebaselinecases .Thepitchingmomentof thestaticgridwassimilarinbehaviortothebaselinecase, buttheATGdatawerevery differentthanbaselineandfollowedbyextendingthetrend towardszerooutto < 7 afterwhichalesssteepslopeisobservedindicatingasimil arlocationofaerodynamic center. Thestandarddeviationwascalculatedincoefcientsforli ftandrollingmoment. Themeanofrollingmomentwasuniformlynearzeroforalltes ts,asexpected.Liftand pitchingmomentwereconfoundedwitheachotherduetothemo untingconguration, 147

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sopitchingmomentstandarddeviationdidnotrevealanynew trends.Thethreewing modelswereofdifferentmassandexhibiteddifferentstruc turaldynamicslimitingthe validityofanalysesacrossA.Thedatashowthatthestandarddeviationsofboth channelsareessentiallyconstantat valueslessthan stall asshownbyFigure 5-8 forA=1,sothesevalueswereaveragedacrossthepre-stallregio nforeachrunmode andReynoldsnumber.ThedatawerethencombinedintoFigure 5-9 toassesstrends inthemeanofthestandarddeviationaveragedupto stall ,fortheATGrunmodesonly. Thestaticgriddidnotgiveresultssignicantlydifferent fromthebaselinecase. TheA=1casebehavedoppositetotheothertwocases,withstandar ddeviation ofliftandrollingmomentincreasingslightlyasstallwasr eached.Thiscasealsohad lowoverallstandarddeviationofliftandrollingmoments, averaging0.35and0.045 respectively.BothA=2andA=4casesshowedessentiallyconstantliftandmoment standarddeviationsthatreducedslightlyafterstall.TheA=2casehadadecreased averageliftvarianceof0.42whiletherollingmomentincre asedsubstantiallyto0.06. TheA=4casecontinuedthistrendwithaverageliftdecreasingsl ightlyto0.40while themomentvarianceincreasedto0.1. The n =0 3 casehadconsistentlythehighest TI X;Z values,butthiswasnot reectedinconsistentlyhigherstandarddeviationsofbot hliftandrollingmoment.The owgeneratedfromtheothertwoATGrunmodesweresimilarin termsofthestandard deviations.ThedifferencesduetochangesinReynoldsnumb erwerealsosmalland withintheuncertaintyboundsofthemeasurements.Thetren dofincreasingvariance oftherollingmomentwithincreasingAwasveryclear,whilebothvarianceswere essentiallyconstantwithintheun-stalledightenvelope .Thiswouldtendtoindicate thathigherAaircraftwouldbemoreaffectedbyrollingdisturbances,al thoughthis maybeoffsetbyincreasedrollinginertia.Theinvarianceo fthestandarddeviation acrossunstalled regionsindicatethattheeffectsofturbulencecouldbesup pressedby intentionallyyingathigherliftcoefcients. 148

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5.5UnsteadyLoadsinthePresenceofTurbulence Thedynamicmotionrigwasnotusedwhenexperimentswerecon ductedto examinethetimedependentloadsbecausethelinearmotorsi nducealowlevel, non-stationaryvibration,ortrembling,intothedynamicl oadsofthemodelwhich wouldcontaminatetheltereddynamicloadsduetoturbulen ce.Thedynamicmotion rigpitchingmechanismisalsonotverystiffduetoplayinth elinkagesandmodel mountings.Inordertoyieldthebestresultstoassessthedy namicsoftheaerodynamic loads,theloadcellwasattachedtoan80/20framingsothati twasessentiallyrigidly mounted,andtheangleofattackwaschangedmanually.Twoid enticalsetsoftestswith andwithoutacross-wireprobeupstreamofthemodelwereper formed.Figure 5-10 showsthemountingofthemodelinthetestsectionwiththecr oss-wireprobeupstream. Thecross-wireprobewassupportedinarigidmannertoelimi nateexcessvibration whichwouldcontaminatethevelocityresults. TheA=2 modelwasmanuallychangedthrough valuesof0,10,20,and30 forthefourReynoldsnumbersandthreerunmodes,aswellasa nair-offtestwithATG runningtodetermineadynamictare.TheATGwasleftrunning toevaluatethelevel ofelectronicnoiseduetotheATGmotors,andthiswasevalua tedagainstATGoff samples.ItwasfoundthattheATGmotorsdidnotcauseobserv ablenoiseinthebase signal.ThesixJR3loadcelloutputvoltagesandtwoCTAvolt agesweresimultaneously recordedbythePXI-4472whentheprobewasinplace,andonly thesixJR3loadcell outputvoltageswererecordedwhentheCTAprobewasremoved .Ateach settinga modalcharacterizationwasperformedthroughimpulse-tes ting,andtheresultsofthe deconvolutionlterwerecheckedagainsttheimpulsetests foraccuracy.Theloadsare presentedinabody-xedcoordinatesystem,withXbeingfor ward,Youttherightwing andZbeingperpendiculartothewing. The F X F Y ,and M Z loadsdidnotappeartohaveanymeaningfuldatainthem, andtheywereobviouslycontaminatedstronglybyvibration precessionastheirPSDs 149

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showedstrongpeaksatthesameresonantfrequencyasthe F Z / M Y channel,even thoughtheirresonanceswereatotherfrequencies.Thedeco nvolutionlterdidnot performparticularlywellforthe F X F Y ,and M X channels,anditisappropriatetoomit theseaxesastheonlyloadingsdevelopedshouldbeduetoski nfrictionwhichwould beverysmallandlikelybelowthenoiseoorofthemeasureme nts.The F Z and M Y spectrawerequalitativelyidenticalineverycase,andthe yevenfollowedeachother verycloselywhenscaledcorrectly.Acalculationofthe M Y spectrawaspreparedwhich subtractedtheeffectsof F Z throughtheparallelaxistheorem,movingthemoment referencepointfromthecenteroftheloadcelltothequarte rchord.Thecorrectiondid notqualitativelychangethespectrainanyway,anditispos siblethatthecorrection onlyfurthercoupledthetwochannels.Theresultswerethat only F Z and M X contained uniquePSDdata. PSDplotsof F Z and M X varyingReynoldsNumber, ,andATGrunmodeforthe dynamictestswerepreparedwiththeX-wireupstreamoftheA=2 model.Thegures includethePSDoftheX-wirevelocitymagnitude(magenta)w ithadashedmagenta lineindicatingalogarithmicslopeof 5 3 .Theteallineisascaledfrequencyresponse functionforthemeasurementchannel.Theblacklineistheu nlteredload,andtheblue lineisthelteredload.Thedashedbluelineisacurvetto 8 3 whichtwelltothe lteredhigherfrequencydata.A 7 3 slopewasmoreappropriateforlowerfrequency data.Specicplotsareincludedinthischapter,andtherem ainderareshowninFigures B-1 through B-21 inAppendixB. ThePSDsoftheloadswerecomparedwithandwithouttheX-wir eprobemounted upstreamandtheywerefoundtobeidentical.Thishighlight snotonlythestationarity andrepeatabilityoftheturbulence,butalsothattheX-wir eprobe'saerodynamiceffect wasnegligiblecomparedtothegeneratedturbulence.The didnotappeartostrongly affectthePSDcurvesqualitativelyorquantitativelyassh ownbyFigures 5-11 and 5-12 similartothetimeaveragedloadsstandarddeviationcurve sindicated.Thisisfurther 150

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corroborationwiththestandarddeviationdataofFigures 5-9 ,asstandarddeviationis theintegralofthespectraldensity.Itisanimportantndi ngthat doesnotseemto affectdynamicloadseventhoughitdenitelyaffectsmeanl oads.Onlydatafor values of0and30 wereplottedforthisreason. Athoroughunderstandingofthewind-offloadcellnoise,sh owninredinFigure 5-13 ,wassoughtasthereweresignicantlystrongpeaksaround3 0,60,120,180, 240,etc.Hz.Thelinenoiseand30Hzpeakswereverydistingu ishableeverywhere. Thesepeaksdidnotchangewith orATGrunmode.Measurementsonadifferent PXIframewithadifferent4472cardinanotherlaboratoryin dicatedthesamepeaks, sothesenoisesourcesareprimarilyattributedtotheloadc ell'selectronics,although vibrationsimpartedthroughthegroundorventilationsyst emareanotherpossibility.The PSDcurvesfortheloadswereonlywellseparatedfromthesen oisetermsatthehigher 2velocities,althoughthetrendsarevisibleatthelower2v elocities.Thisnoisewas problematicforthe F Z casesastherewasastrongmodalpeakat61Hz,butitwaswell separatedfromthe M X naturalfrequencyat81Hz. Theloadspectraofboth F Z and M X bothexhibitedaroll-offthatwasfasterthan the 5 3 shownbytheturbulencevelocityPSDforallcases.Theunlt eredloadwas heavilycontaminatedintheregionsaroundtheresonances, butthelteredloadshowed adeniteconstantsloperoll-off.Atintermediatefrequen ciesontheorderof5-30Hzthe roll-offappearstobedevelopingbutmaybeapproximatedby a 7 3 slopeline.Higher frequenciesthanthistverywelltoaslopeof 8 3 .Thisroll-offwasconsistentacross bothloads,allrunmodes,Reynoldsnumbers,and valueswhichisaveryinteresting nd.Thelogarithmicslopeof 7 3 isrelevantbecausepreviousstudieshaveidentied thisvalueforturbulentpressuremeasurements[ 180 181 ].Thefactthatloadsappear totthisslope,orperhapsaslightlymoresteepslopeindic atethattheloadsarehighly correlatedwithuctuatingpressuresasonemightexpect.T heseresultsatleastinpart 151

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supportthoseobtainedbytheUVLMcodeinthepreviouschapt er,althoughtheexact structurewasnotduplicated. The n =2 : 5 0 runmodeshownbyFigure 5-13 exhibitsatonalvelocity spectrawithpeaksatharmonicsoftherotationalrate,i.e. 5,10,15,20Hz.The5Hz peakwasstrongest,andthehigherharmonicsdecayedinstre ngthduetotheinteracting turbulence.Aninterestingresultisthattheloadspickedu ponthetonalcomponentof theowwithanapproximatelysimilargainasthebroadbandc omponentsoftheload. Thetonaleffectwasfurtherinvestigatedbylookingatthe H 1 formulationoftheFRF betweenthevelocitycomponentsandtheloads, H F Z u 0 H F Z w 0 H M X u 0 and H M X w 0 .These areshowninFigures B-22 through B-44 .OnlythemagnitudeoftheFRFwasplottedas thephasewasnoisy,andnodeterminationscouldbemadeasto itsmeaning. TheFRFplotsreinforcethe 7 3 to 8 3 roll-offorthe F Z axis,anexampleofwhich isFigure 5-14 ,whichisevidentasalinewithaslopeof 2 3 to 1 .Theslopeismost steepatlowReynoldsnumbersandapproaches 2 3 atthehigherReynoldsnumbers, correspondingto 7 3 .The F Z axisalsoseemstogainastrongerboostingaindue tothetonalcomponentsofthe n =2 : 5 0 runmode.Thisiscontrastedbythe M X whichseemstobegaineddownwardatthesamefrequencies.Th eeffectsofthe higherharmonicsarenotveryvisibleabovethenoise.The M X FRFsdonotappearto decayinthesameway.Instead,theslopeistheleastatlowes tReynoldsnumbersand approachedzeroslopeatthehighestReynoldsnumber.Thest rongspikesinallthe FRFscanbetracedtoeitherelectronicnoiseoroneoftheres onantfrequencies.There appearstobeaslight'knee'inalltheFRFcurves,i.e.aloca tionatwhichthegainstarts decreasing.Thekneedecreasesfromaround10Hzatthehighe stReynoldsnumber almosttoDCatthelowestReynoldsnumber.TheFRFthatiscom parabletotheUVLM work, H F Z w 0 ,indicatessimilaritiesinbehavior.BothFRF'sareapprox imatelyatatlow frequenciesandrolloffasfrequencyincreases. 152

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5.6Summary InthischaptertheATGgeneratedturbulenceoverA=1,2and4atplatesat meanvelocitiescorrespondingtoReynoldsNumbersranging from25,000to200,000. Thecharacterizedturbulenceexhibitedintensitiesfrom1 3.7to21.3%,anisotropy ratiosfrom0.97to1.12,andintegrallengthscalesfrom0.3 5to0.61m.Mean loadsexperimentsperformedonbaselineandturbulentairi ndicatethatturbulence extendsstall,modiespitchingmoment,andgreatlyincrea sesthestrengthofthe oscillatingload.Turbulenceintensityiscorrelatedtoos cillatingloadintensity.Dynamic measurementsindicatethatthe F Z and M X loadcomponentsdecaywithalogarithmic 7 3 roll-offwhichissimilartotheroll-offofpressuremeasur ements.Themodel's did notseemtostronglyaffectthevariationsoftheloadswhenv iewedfromabody-xed perspective. 153

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Figure5-1.ModelmountedtoJR3loadcellonthepitch-plung erigformeanload measurements.PhotocourtesyofMichaelSytsma 154

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LCRe100k LCRe75k LCRe50k LCRe25k BRe100k BRe75k BRe50k BRe25kC M StandardDeviationAngleofAttackC D StandardDeviation C L StandardDeviationAngleofAttackC M C D C L 30 20 10 0102030 30 20 10 0 102030 0 1 2 3 4 5 0 0 : 2 0 : 4 0 : 6 0 : 8 0 0 : 5 1 1 : 5 2 2 : 5 3 0 : 4 0 : 2 0 0 : 2 0 : 4 0 : 6 0 : 2 0 0 : 2 0 : 4 0 : 6 0 : 8 1 : 5 1 0 : 5 0 0 : 5 1 Figure5-2.BaselinecoefcientdataforA=2model 155

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AR=4,Re=100k AR=4,Re=75k AR=4,Re=50k AngleofAttackC M C LMullerandTorresAR=2 AR=2,Re=100k AR=2,Re=75k AR=2,Re=50k AngleofAttackC M C LMullerandTorresAR=1 AR=1,Re=200k AR=1,Re=150k AR=1,Re=100k AngleofAttackC M C L0510152025 30 35404550 0 5101520253035 40 4550 0 : 2 0 : 15 0 : 1 0 : 05 0 0 : 05 0 : 5 0 0 : 5 1 0 : 3 0 : 2 0 : 1 0 0 : 1 0 : 5 0 0 : 5 1 0 : 3 0 : 2 0 : 1 0 0 : 1 0 : 5 0 0 : 5 1 1 : 5 Figure5-3.Baselinecoefcientdata 156

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AngleofAttackC M C L0 5101520253035404550 0 : 3 0 : 2 0 : 1 0 0 : 1 0 : 5 0 0 : 5 1 1 : 5 Figure5-4.LiftandpitchingmomentcoefcientsforA=4andRe=50k(+),Re=75k (o),Re=100k(*)forstaticgrid(black)and n =0 8 (blue) 157

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StaticGrid n =0 8 n =0 3 n =2 : 5 0 Baseline AngleofAttackC M C L05 10 15202530 35 404550 0 : 3 0 : 2 0 : 1 0 0 : 1 0 : 5 0 0 : 5 1 1 : 5 Figure5-5.LiftandpitchingmomentcoefcientsforA=1andRe=200k 158

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StaticGrid n =0 8 n =0 3 n =2 : 5 0 Baseline AngleofAttackC M C L05 10 15202530 35 404550 0 : 3 0 : 2 0 : 1 0 0 : 1 0 : 5 0 0 : 5 1 1 : 5 Figure5-6.LiftandpitchingmomentcoefcientsforA=2andRe=100k 159

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StaticGrid n =0 8 n =0 3 n =2 : 5 0 Baseline AngleofAttackC M C L05 10 15202530 35 404550 0 : 3 0 : 2 0 : 1 0 0 : 1 0 : 5 0 0 : 5 1 1 : 5 Figure5-7.LiftandpitchingmomentcoefcientsforA=4andRe=100k 160

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StaticGrid n =0 8 n =0 3 n =2 : 5 0 Baseline AngleofAttackC M StandardDeviation C L StandardDeviation0 5101520253035404550 0 0 : 02 0 : 04 0 : 06 0 0 : 1 0 : 2 0 : 3 0 : 4 0 : 5 Figure5-8.Standarddeviationofliftandpitchingmomentc oefcientsforA=1andRe =200k 161

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TI X (%) C R C L16 182022 0 0 : 05 0 : 1 0 0 : 5 1 Figure5-9.AveragedstandarddeviationsforA=1(black),A=2(darkgray)andA= 4(lightgray),with n =2 : 5 0 ,o n =0 3 and n =0 8 162

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Z X Y Figure5-10.ModelmountedtoJR3loadcellon80/20framingw ithhot-wireprobefor dynamicloadmeasurements.PhotocourtesyofMichaelSytsm a. 163

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Frequency(Hz)MxPSD ( N 2 cm 2 Hz ) FzPSD ( N 2 Hz )10 0 10 1 10 2 10 10 10 5 10 5 Figure5-11.Powerspectraldensitiesofdynamicloadandtu rbulencedataat =0 n = 0 3 ,andReynoldsNumberof100,000.Black:Measuredload, Red:Measuredloadnoiseoor,Cyan:LoadcomponentFRF,Blu e: Deconvolvedload,Magenta:Cross-wireverticalcomponent 164

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Frequency(Hz)MxPSD ( N 2 cm 2 Hz ) FzPSD ( N 2 Hz )10 0 10 1 10 2 10 10 10 5 10 5 Figure5-12.Powerspectraldensitiesofdynamicloadandtu rbulencedataat =30 n = 0 3 ,andReynoldsNumberof100,000.Black:Measuredload, Red:Measuredloadnoiseoor,Cyan:LoadcomponentFRF,Blu e: Deconvolvedload,Magenta:Cross-wireverticalcomponent 165

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Frequency(Hz)MxPSD ( N 2 cm 2 Hz ) FzPSD ( N 2 Hz )10 0 10 1 10 2 10 10 10 5 10 5 Figure5-13.Powerspectraldensitiesofdynamicloadandtu rbulencedataat =0 n = 2 : 5 0 ,andReynoldsNumberof100,000.Black:Measuredload, Red:Measuredloadnoiseoor,Cyan:LoadcomponentFRF,Blu e: Deconvolvedload,Magenta:Cross-wireverticalcomponent 166

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H M X w 0 H M X u 0 H F Z w 0 H F Z u 0 Wavenumber (radm 1 )Scaled H 1 frequencyresponsefunctionmagnitude10 0 10 1 10 2 10 2 10 1 10 0 10 1 Figure5-14.Frequencyresponsefunctionsofdynamicloada ndturbulencedataat =0 n = 2 : 5 0 ,andReynoldsNumberof100,000 167

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CHAPTER6 EXPERIMENTALFLOWRESULTS Thepreviouschapterhighlightedlargedifferencesbetwee nmeanloadsgenerated onwingsinthebaselineowvs.thoseofthehighlyturbulent ow.Itisofgreatinterest tounderstandwhatisthecauseofsuchbehavior,sothischap terusesvelocityelds measuredwithPIVtoillustrateandunderstandhowtheowha schangedbetween thebaselineandturbulentcases.Mathematicalreasoningi sthenappliedtobetter understandwhytheowsbehavesodifferently.Velocityel dmeasurementswere acquiredforthevaryinglevelsoffree-streamturbulencef romthebaselinecase,the staticgridandoneoftheATGrunmodes.Itshouldbenotedfor theseexperimentsthat adifferentA=1 modelwasusedsothataconstantReynoldsnumberof75,000wa s testedforallthreeAmodels. Severalexperimentswereperformedtounderstandtheowto pology.Intherst setofexperiments,hereafterreferredtoas”chordwise”,a stereocameraconguration wasusedtoimagealasersheetdirectedacrossthechordtobe onaconstantspan line.Twoimagesetswererecordedtogatherleadingtheedge (asshownbyFigure 6-1 )andtrailingedgeregions,thenthevectoreldswerestitc hedtogethertogeta morecompletepictureoftheoweldovertheentirewing.In thelastexperimentthe cameraswerefocusedinathreecomponentcongurationatal asersheetthatwas1/5 chorddownstreamofthetrailingedgeandperpendiculartot heincomingairow.These ”downstream”measurementswereaimedatunderstandingthe wingtipvortexbehavior. 6.1ChordwiseExperiments Thechordwiseexperimentsinvolvedacquiringthevelocity eldsatseveral measurementplanesacrossthreesemi-spanlocationstocov er y b =12.5%,25% and37.5%asshowninFigure 6-2 .The valueschosenfordiscussionofthevelocity measurementsweredeterminedbasedonspecicinteresting phenomenaidentied bytheloadsmeasurementsinChapter5.Interestingbehavio rsthatwerepresentin 168

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Table6-1.Chosen fordifferentA A CaseA CaseB CaseC CaseD 1 8 45 25 2 8 25 35 4 8 15 25 allAmodelswerebaselineandturbulenceinpre-stallwithnodif ferenceinlift(Case A),baselinestalledandturbulencepre-stall(CaseB)andb aselineandturbulence stalled(CaseC).AdditionallyfortheA=1 caseitwasinterestingtoseeany differencebetweenpre-stalledbehaviorathigher wheretherewasasignicant differenceinmeanlift(CaseD).The valueswereselectedsothattherewasmaximum commonalityincameraconguration,andthesevaluesaresh ownbyTable 6-1 Themodelswerelocatedsothattheirleadingedgeswereatad ownstreamlocation of X M =12 : 5 ,andthe n =0 8 ATGrunmodewasselectedwhichresultsinan18.7% TI X .The ofboththewingandcameraswerechangedmanuallysoastored ucelaser areswhichcouldpotentiallydamagethecamerasandskewda tanearthewing.The valuesweremeasuredwithadigitalinclinometerwithpartn umber21465A82from McMasterCarr.Thedevicehasaresolutionof 0 : 01 ,astatedaccuracyof 0 : 05 and theestimatedplacementaccuracyofthemodelandcameraswe relessthan 0 : 1 .All datapresentedshowthesuctionsideofthewingasthiswaswh ereinterestingow phenomenaoccurred.Datafromthepressuresideofthewingw erealsogathered forsomecasesbutdidnotshowsignicantdifferencesbetwe enbaselineandhighly turbulentow.ThebaselineandATGcasesweregatheredasth reecomponentdata. Thelargestdifferencesinowpatternsareapparentbetwee nbaselineandATG cases.Thethreecomponentdatawerevectorprocessedusing multipassadaptive (MA)processingfrom64x64toa16x16pixelinterrogationre gionwitha50%overlap. Thespatialresolutionwasapproximately75 m pixel ,theprocessingchoicesresulted inerroneousdatabelow1.2mmawayfromthewingsurface.Thi smeansthatvery 169

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near-wallowsareundetectablebyPIV,asareanyowstruct uressmallerthanafew mm. Modelsweremovedthroughseveral valuesand500imagesetswereacquired ateachlocation.Theimagesweresubtractedfromanaverage ofimages,andthe vectorgridswerethenprocessedintheDaVissoftware.Thev ectorgridswerefurther smoothedwitha9x9GaussianlterandaveragedinDaVistoyi eldasmoothed meaneldsuitedtocalculatingderivatives.Acomparisonb etweenasmoothedand un-smoothedmeanvectoreldshowedthatthedifferenceswe relessthantheother sourcesoferroridentiedinChapter2. ThedataarepresentedinthecoordinatesystemwithXco-lin earwiththe free-stream,Ypositiveouttherightwing,andZpositiveup ward.Inadditiontomean velocityelds,onecomponentofthemeanstresstensor, S uw =0 : 5( d u dz + d w dx ) ; (6–1) wascalculatedusingthesmoothedaverage,althoughthelt ercostinspatialresolution ofnefeatures.TheuctuatingturbulentquantitiesfromE quation 3–1 werecalculated foreachvectoreld,andfromthisdatatheReynoldsstresst ensor, u 0 u 0 u 0 v 0 u 0 w 0 v 0 u 0 v 0 v 0 v 0 w 0 w 0 u 0 w 0 v 0 w 0 w 0 (6–2) wascalculated.Turbulentkineticenergy(TKE)wasfurther calculatedfromtheReynolds stressesby TKE =0 : 5( u 0 u 0 + v 0 v 0 + w 0 w 0 ) : (6–3) Thedataarepresentedasoodedcontourplotsforthethrees panlocations,comparing baselineandturbulentows.Asparsevectorarroweldisov erlaidtogivethereader anideaofowdirectionality.Thesurfaceofthewingcaused erroneousdata,asdid 170

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themodelsupportincertainsituations.Thiscausedinterm ittenterrorsinthevector processingprocedurewhichaffectedotherstatisticssign icantlymorethanthemean values.Thedataaremaskedsothattheerroneousdataarenot displayed. 6.1.1CaseAData ThecaseAdataresultedinsimilarliftandpitchingmoments forallthreeAwings whencomparingthebaselinecasestothehighturbulenceint ensitylevels,soonemight thereforeexpectthemeanoweldstolookquitesimilar.In thiscasethebaselineand turbulentowsarenotstalled.Figure 6-3 through 6-5 showsimilar U 1 prolesacrossA,withasmallseparatedrecirculatingregionevidentforal lbaselinecasesbutabsent fromturbulencecasesatthesamplingresolution.Thebubbl egrowslargerwithAhoweveritisevidentthattheshearlayergrowsmuchmorequi cklyintheturbulentow atthesamespanstation.Thiseffectispresentacrossallth reeA.Figure 6-6 shows howthethinshearlayerformsattheleadingedgeandextends aboveaseparated regionbeforereattaching,whileturbulencecausestheshe arlayertoevolvesoquickly thatiteffectivelyeliminatestheseparatedregion.Thesp anwiseevolutionshowsthat theshearlayerisstrongesttowardsthecenterlineofthewi nganddecreasesinsizeand intensityoutboardforbothbaselineandturbulentcases.6.1.2CaseBData CaseB 'swereselectedbecausethebaselineowhadstalledwhilet heturbulent owremainedunstalled.TheA=1casewasmorecomplicatedasboththebaseline andturbulentcasesappearedtostallatthesame soitwasnotincludedinthis category.Inthesecasesthereweresignicantowdifferen cesbetweenbaselineand turbulence,withthebaselineowsexhibitingsignicant owdetachmentoveramajority ofthespan.Figure 6-7 showshowthebaselineowissignicantlydetachedwhilein turbulentowthereisaseparationbubblewhichreattaches overasignicantportion ofthewing.Figure 6-8 showsanevolvingthindetachedshearlayerinthebaseline case,buttheturbulencecaseshowsstrongforwardvelocity nearthesurfacewhich 171

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contributestotheowattachment.Theshearlayershighlig htedbytheplotsofmean shearinFigure 6-9 furtherreinforcesthedifferencesbetweenthestrong,thi nfreeshear layerofthebaselinecasescomparedagainsttheweaker,dif fusedshearlayerofthe turbulentcasewhichappearstobeattachedtothewall,with intheresolutionlimitations ofthemeasurements.Thisplotisrepresentativeofthebeha viorofbothAtested. TheTKEshownbyFigure 6-10 indicatesthemajorityofTKEforthebaselinecases existwithinthethinseparatedshearlayerwhichcoversthe detachedandrecirculating ow,whiletheturbulentcasehasverystrongTKEthroughout themuchthickershear layer.Thescalingoftheplotsobscuresthefactthatthenor malizedTKEoftheincoming turbulentow,ontheorderof0.30,issignicantlyhighert hanbaselineoforder0.05. The u 0 w 0 plotsshownbyFigure 6-11 showasimilartrendwithmarkeddifferences betweenbaselineandturbulentcases.TheBaselinecasesha veonlyaweakReynolds stresscomponentthatismostlyconnedtothefreeshearlay erwhiletheturbulentcase ismuchstrongerandisspreadoveramuchgreaterarea,highl ightingtheReynolds stress'roleinshearlayergrowth.SimilartotheCaseAdata ,thestrengthandsizeof theshearlayersarelargesttowardsthemodelcenterline,a ndtheydecreasefurtherout onthewing.TheA=2 wingalsoshowsthiseffectmuchmorestronglythantheA=4 wing.6.1.3CaseCData InCaseCboththebaselineandturbulentowsarefullystall ed,althoughthere aresignicantdifferencesinthepost-stallliftandpitch ingmomentcoefcients.TheA=1baselinecasegeneratessignicantlymoreliftaftersta llthanitdoesinturbulent ow,whileA=2and4casestheturbulentowgeneratesthegreatestlift. TheA=1wing's U 1 (Figure 6-12 )showsathinandcleandetachmentoftheowfromthe leadingedge,buttheeffectsofthetipvortexareevidentin the y b =0.25and0.375span stationsaslargeinectedregions.Comparedagainstturbu lencethisstrongtipvortex mustberesponsiblefortheincreasedlift,anditappearsth atinturbulentowthetip 172

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vortexeffectsaresuppressed.Thiseffectisfurtherinves tigatedwithdownstreamPIV measurementsintendedtoimagethetipvortex. TheturbulentA=1caselooksmorelikethatofA=2and4,showninFigures 6-13 and 6-14 .Inthesecasestheturbulentshearlayerappearstoreattac hatthewing tipsbutisfullyseparatedfurtherinwardalongthewing.Th eshearlayerisonceagain signicantlythickerthanthebaselinecase,andthebaseli neowisfullydetached.The partialattachmentofturbulentowcontributestohigherl ift,andthemannerinwhich theturbulentowbecomesdetachedstartingatthecentersp anandmovesoutward contributestothesmoothbehavioroftheliftandpitchingm omentcoefcientcurvesas theyapproachstall.AtrendisapparentonthehigherAwingswheretheturbulence casestillexhibitsarecirculatingregionsimilartobasel ine,howeverthisregionissmaller anddevelopslaterathigher .Bythetimethebaselineisstalledtherecirculating regionstillmaintainsreattachedownearthetrailingedg eastheexcitationfromthe free-streamturbulencemustalterthemomentumtransporti ntheshearlayer.As is increasedthatreattachmentnolongeroccursonthemiddles panandworksitsway outward.6.1.4CaseDData ThecasesBandCprovideanargumentforwhytheloadsfortheA=2and4 wingshavehigherliftandstall inturbulentow,butthecaseDdataareinteresting becausetheyindicatewhytheA=1winggeneratesmoreliftinbaselineow.Figure 6-15 showsthatthebaselineowhasaleadingedgeseparationbub blethatappears toreattachdown-chordacrossthewing'sspan.Thisbubblec ausesalargemean camberingeffectontotheairowjustbeyondtheshearlayer whichinturncausesthe highlift.Theturbulencecaseshowssignicantlymoreatta chedowandasmaller recirculatingregionwithacorrespondinglysmallereffec ttothemeanowfurtheraway fromthewing.Thustheturbulenceappearstocausetheowto bemoreattachedtothe detrimentofmeanliftgeneration. 173

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6.1.5ShearLayerScalingAnalysisandSimilaritySolution ItisevidentfromthepreviousPIVdatathatthepresenceofh ighlevelsof free-streamturbulencevastlychangestheowtopologyove rthewings,therefore changingtheloadsdeveloped.Thischangeseemscenteredar oundthebehaviorof theshearlayer,andagreaterunderstandingintothegrowth characteristicsofthe shearlayersinthebaselinevs.turbulentcasesissought.T hebaselinecaseappears todevelopathin,separatedfreeshearlayerattheleadinge dge,dependingon andA,whichmayormaynotreattachfurtherdownstream.Thisthin andfreeshearlayer isindirectcontrasttothethickandseeminglywallbounded shearlayerevidentinthe highlyturbulentcases.Thefollowinganalysisissimplest ifconsideredtobe2-DinX andZdirectionswhichcorrespondtostreamwiseandperpend iculardirections.This coordinatesystemallowstheinherentcurvatureoftheshea rlayersinbothowsto beremovedfromscalinganalysis,andinformationfromthei nboardwingsectionsto reinforcesa2-Dassumption,atleastfortheA=2and4cases.Indeeditisapparentfor theA=2and4casesthattheevolutionacrosstheYdirectionismuc hslowerthanthe othertwodirectionsjustifyingthisassumption.Constitu tiveequationswillbesimplied basedonascalinganalysiswhichidentiesimportantterms ,andasimilaritysolutionis presentedwhichdescribestheexperimentaldata.6.1.5.1Orderofmagnitudeandsimpliedshearequation ThisanalysisconsiderstheXcomponentoftheReynoldsAver agedNavier-Stokes (RANS)momentumequation,ignoringbodyforces[ 42 ] u @ u @x + w @ u @z = 1 @P @x @u 0 u 0 @x @u 0 w 0 @z + @ 2 u @x 2 + @ 2 u @z 2 : (6–4) Theowisincompressibleundertheconditionsbeingconsid eredresultinginamean continuityequationof @ u @x + @ w @z =0 : (6–5) 174

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Animportantconsiderationinthisanalysisisoftheordero fmagnitudeestimate chosenfordifferentterms.Thesechoiceswillbeguidedinp artbyobservationsofthe measuredows,excepttherewillbeabasicassumptionofath infreeshearlayer.For bothcases,itmakessensethattherelevantlengthscaleint hestreamwisedirectionis comparabletothelengthtraverseddownstream,or @ @x 1 L ; (6–6) anditmakessensetodeneanewlengthscale @ @z base = 1 ; (6–7) whichcanbeconsideredthethickness, ,oftheshearlayer.Akeyassumptionisthat theshearlayerthicknessisconsiderablysmallerthanthed istancedownstream,or L: (6–8) Fortheturbulentcase,however,thisassumptionappearsle ssvalidastheshearlayer growssoquicklythat 0 : 3 L; (6–9) anditmaynolongermakessensetodeneanewlengthscale.Th elackofasecond lengthscale ,however,makesthesolutionstothemomentumequationstri vialand removesmuchofthephysicsfromtheequations. Inbothcasestheowisforcedtodeceleratefromalocal U 1 velocitytozerowhen viewedovertheZdirection,althoughthebaselinecaseusua llyreacheszeroatthe interfaceoftherecirculatingregionascomparedtowhatap pearstobeazerovelocity nearthewallformanyturbulentcases.Theresolutionofthe PIVconductedforthis studymeansthatnoneofthedetailednearwallfeaturesofth eboundarylayercan beresolvedinanyofthiswork.Despitethedifferencesinth etwocases,bothliftand dragarecomparable,soitmakessensethatdownstreamofthe wingtherewillbea 175

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comparablevelocitydecitduetothedrageffects, U ,whichisunderstoodtobemuch lessthanthefree-stream,or U U 1 : (6–10) Howeveraninterestingconsiderationisthat U willbesmallerfortheturbulentcase thanforbaselineastheturbulentmomentummixingislikely toexpandthewakeata muchgreaterrateresultingin @U base U base @U turb U turb U turb U base : (6–11) Theuseofthisvelocityscalehasthesameeffectforbothcas es,namely @ u @x = U L : (6–12) Thecontinuityequationcanberewrittenas, @ u @x = @ w @z ; (6–13) andthescalingsdevelopedabovecanbecombinedtoyield U L = @ w ; (6–14) whichconsidering L indicatesthat w base U base .Thescalingsindicatethemean verticalvelocitycanbeconsideredbythefollowingexpres sion, w U L : (6–15) ThePIVdatashowthattheuctuatingturbulentcomponentsa reapproximatelyequally sizedso u 0 w 0 andonly u 0 willberetained.Thepressuredistributionswillsimilarl ybe treatedasunknown,andthesescalingscanthenbecombinedi ntotheRANSequations todetermineinformationabouttheow. 176

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TheXmomentumequationcanhavethescalingsinputtoyield u @ u @x + w @ u @z = 1 @P @x @u 0 u 0 @x @u 0 w 0 @z + @ 2 u @x 2 + @ 2 u @z 2 U 1 U L + U L U = 1 @P @x u 2 L u 2 2 + U L 2 + U 2 : (6–16) Arescalingoftheparametersby L=U 1 U makes 1+ U U 1 = 1 @P @x u 2 U 1 U base u 2 L U 1 U + U 1 L + L U 1 L : (6–17) TheseowsstillretainareasonablylargeReynoldsnumbero f75,000atendofchord, soanassumptionof LU 1 1 ; (6–18) isreasonable,however U 1 1 ; (6–19) requiresthemorerestrictingassumptionthat L .ConsideringthePIVmeasurements ofthebaselinecasewhichshowstheshearlayerthicknessis closerto 0 : 1 L ,thisis stillareasonableassumption,providedthatthisdoesnotc onsiderowsverycloseto thewingleadingedge.Withtheseassumptionsthesecondter mandviscoustermscan beremovedresultinginabalanceofpressureagainstturbul enceterms, 1 1 @P @x = u 0 u 0 1 U 1 U + L U 1 U ; (6–20) ofwhichthetermonthefarrightislargest.Inorderforthis termtohaveaneffectonthe owitshouldbeatleastO(1),indicatingthatthescalingfa ctorbetweentheshearlayer thicknessandLcanbestatedas L u 0 u 0 U 1 U ; (6–21) whichisaninterestingndingforthethinshearlayerwitha pplicationregardingits growth.Theconsiderationwithdirectapplicationtothetu rbulentcaseisthatanincrease inthefree-streamturbulentintensity u 0 u 0 willsimilarlylikewiseincreasetheshearlayer 177

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thickness .However,asnotedbeforethe U turb shouldbedecreasedfrom U base at thesamelocationdownstreamduetoenhancedmomentummixin gandspreadingofthe wake.Thisindicatestheremaybeabehaviorlike ( u 0 ) n ; (6–22) wheretheexponent,n,islessthantwoasfree-streamturbul enceisincreased. However,thisstilldoesnotresultinasolutionthatcanbea ppliedagainstthedata. Anotherthoughtisthattheshearlayerintheturbulentcase iscomparabletothe lengthscaleasstatedbeforeas L .AddingthisconstraintintoEquation 6–22 yields U u 0 u 0 U 1 ; (6–23) whichindicatesthevelocitydecit,andinturntotaldrag, isafunctionofturbulence intensityandmeanvelocity.Thisresulthassomevalidityi nthatincreasedturbulence willresultinenhancedmomentummixing.Theenhancedmixin gwilltendtoslowmore uidfasterandresultinalargerdecit. TheresultingRANSequationapplicabletoshearlayersafte rsmalltermshavebeen removedis[ 42 ] u @ u @x + w @ u @z = 1 @P @x @u 0 w 0 @z ; (6–24) whichstillretainsaproblemofclosure.Acommonlyapplied closuremodelistheeddy viscosity[ 42 ], u 0 w 0 = T @ u @z ; (6–25) whichtreatstheReynoldsstresscomponent u 0 w 0 asamomentumtransporttermwith T astheeddyviscosity.ApplicationtoEquation 6–24 yields u @ u @x + w @ u @z = 1 @P @x + @ @z T @ u @z ; (6–26) whichlendsitselftoasimilaritysolution. 178

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6.1.5.2Similaritysolution Inordertocollapsethedataasimilaritysolutionputforth byKorstet.al.isused [ 182 ].Thissimilaritysolutionrstintroducesthestreamfunc tion, @ @z = u @ @x = w; (6–27) whichcanbecombinedwithvariablesthatarenon-dimension alizedsimilartothe scalinganalysis, = u u a = x L = u a L : (6–28) Amaindifferenceisthatthevelocity u a isnotthefree-stream,butratheralocal maximumthatexistsononeendoftheshearlayer.Combiningt heseintoequation 6–26 andneglectingthepressurechangealongastreamlineyield s @ @ = @ @ T Lu a @ @ ; (6–29) inwhichthefollowingsimilarityvariables,[ 182 ] f ( )= g ( ) f ( ) 0 = = y x ; (6–30) canbeusedtobringtheresultstoasolvableform.Thenewter m indicatesthe spreadoftheshearlayerandalsoincludestheReynoldsnumb erderivedfromthe eddyviscosity,withtheassumptionthateddyviscosityisa constantalongastreamline 179

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accordingtotheG o ertlerformulation[ 183 ].Equation 6–30 bringsabouttherelations, @ @ = fg 0 f 0 g @ @ = 1 gf 0 ; (6–31) andtheassumptionofsimilaritysets gg 0 =1 g ( )= p 2 ; (6–32) whichwhencombinedintoEquation 6–29 andsimpliedtorstorderwillyield[ 182 ] 00 +2 =0 : (6–33) Thisordinarydifferentialequationnowhasasimplesoluti on.Assumingboundary conditionsof u a asamaximumvelocityononesideandzerovelocityontheothe r,anda coordinatesystemwhere =0 attheshearlayercenterline,or u =0 : 5 u a ,thesolutionis = u u a =0 : 5(1+ erf ( )) : (6–34) Itshouldbenotedthatseveralassumptionsweremadetobrin gthesolutiontothispoint. First,pressureeffectsareignored.Second,theeddyvisco sitytermisassumedconstant alongastreamline,andthirdthehigherordertermsaredrop pedtoyieldEquation 6–33 whichwouldhaveotherwiserendereditunsolvableandrequi rednumericalmethods. 6.1.5.3ComparisonofanalyticalsolutiontoPIVdata Thesimilaritysolutiondevelopedabovewasthenusedtocol lapsethemeanshear prolesofthebaselineandturbulentdata.The u datawereextractedalongseveral verticallinesatconstantchord.Figure 6-16 showsanexampleofhowthedatawere gathered.Thedataateachchordstationwerethennormalize dandmappedtothe coordinatesystemwhere u a wasfoundasthemaximaofeachproleand wassetto zeroattheverticallocationcorrespondingto 0 : 5 u a 180

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Thedatacollapsedreasonablywellwith =9 forthebaselinecaseand =3 : 5 for theATGcaseasareshownbyFigures 6-17 and 6-18 respectively.Infact,thesimilarity scalingcollapsedandcomparedwelltoEquation 6–34 wellacrossallspanstations,Aand indicatingtheoverallvalidityofthismethod.Variations fromEquation 6–34 are likelytheresultsofviolationoftheassumptionsbehindit sderivation,howeverthese deviationsaresmalloverthemajorityoftheshearlayer.Fi gures C-1 through C-15 in AppendixCfurtherdemonstratethevalidityofthisdataove rthetestedvariables.The abilityofthe valuestotthedataindicatetheabilityofturbulencetoin creasethe growthrateoftheshearlayerinaconsistentmanner,andits howsthatthemeanshear layersareself-similaracrossdifferentconditions. 6.2DownstreamExperiments InthissectionthePIVcamerasweredirectedinastereocon gurationtoimagea laserplaneperpendiculartotheincomingvelocityvectorw iththeaimofunderstanding thedifferencesinwingtipvortexthatwerealludedtobythe chordwiseexperiments. ThecamerasetupfortheseexperimentsisshowninFigure 6-19 .Theowwasmoving directlythroughthelasersheetwithathicknessontheorde rof1mm,andthedTwas setaccordingtothepreviouslydescribedprinciplesat50 s .Thelasersheetwas0.2 chordlengthsdownstreamofthetrailingedgeofthewings.T hislocationwasnecessary asfurtherdownstreamthemeanvorticesoftheturbulentcas ediffusedveryrapidly, confoundinganalysis.Thecamerasetuprequiredthatthele adingedgeofthewings bemovedto X M =9 : 5 whichhadanegligibleeffectonbaselineowbutincreasedt he ATGrunmode n =0 8 case TI X to20.5%whichshouldhavenegligibleeffect onmeanloadsasasimilarcasewastestedinChapter5.Atleas t2500imagessets weregatheredforeveryexperiment,andaftersubtractinga naveragefromtheimages, thedatawerevectorprocessedusingMAfrom64x64toa16x16p ixelinterrogation regionwitha50%overlap.Theresultingvectorlesweresmo othedandaveragedto developameaneld,whilethesameturbulentandshearelds werealsodetermined. 181

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Forthediscussioninthissection,thecoordinatesystemha sbeensetsothatthe outboardtipofthetrailingedgeistheorigin,andtheYandZ dimensionsarenormalized againstchord.Itisacommonbehaviorthatwingtipvortices will”wander”frommoment tomomentintheYandZdirectionasmeasuredfrommorethanac horddownstream [ 184 – 188 ],howeverthebaselinecasedidnotshowanyappreciablewan deringwithin theresolutionofPIVprocessingforun-stalledcasesbecau sethemeasurementswere soclosetothetrailingedge.Itisthereforeacceptabletos implyaveragethebaseline dataasanywanderingwillhaveanegligibleimpactonthedat a[ 185 ].Thehighly turbulentcase,however,didnotexhibitrecognizabletipv orticesonanindividualvector eldbasis.Infact,thestrengthoftheturbulencewassufc ienttoobliteratethesignature ofatipvortexonthemajorityoftheindividualvectorelds .Onlyafterlongaveraging doesthetipvortexbecomeapparentandwellformed.Thiscau sedagreatspreadingof theeffectsinameansenseacrossthevectoreld,sotheresu ltsshouldbeinterpreted withcaution.DevenportandIgarashishowedthatevensmall amplitudewandering causesalargeeffectonmeanandRMS[ 185 187 ]. 6.2.1CaseA Thelow caseswhichexhibitedacompletelyun-stalledbehaviorind icatean organizedmeantipvortexwithlargedifferencesbetweenba selineandturbulence,but notmuchdifferenceacrossA.Figures 6-20 through 6-22 showanormalized U 1 with avectoreldinYandZoverlaid.Thebaselinecasesallappea rsimilarwithavortex thatfollowsanearlyirrotationalpatternasisexpectedfo ratipvortex[ 186 187 ].The strengthandsizeofthevortexincreasesslightlywithincr easingA,anditshowsacore regionwithinected U 1 whichisconsistentwiththebehaviordiscussedinliteratu re [ 186 187 ]. Theturbulentcase,howeverexhibitsagreatdealofspreadi ngacrosstheentire imagingdomainduetoenhancedturbulentmomentumdiffusio n.Thevortexitselfalso appearstobehaveinamorerotationalmanner.Themeanshear showninFigure 6-23 182

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highlightsthisdifference.Thebaselinecaseshowsstrong meanshearnearthevortex coreaswouldbeexpectedinirrotationalow,whiletheturb ulentcaseshowsanear zeroshearacrosstheeld.Similartothechordwiseexperim ents,turbulencehasthe effectofrapidmomentumdiffusionwhichdecreasesthemean shear.TheTKEshown byFigure 6-24 hasthemajorityofenergyconnedtothetipvortexandwing' sshear layers.TheturbulentcasehasamuchhigherbackgroundTKEa sistobeexpected,but theTKEgenerationisspreadoveramuchlargerregioninthet ipvortexaswellasthe wing'sshearlayer.6.2.2CaseB InCaseBthebaselinecaseshowsinFigure 6-25 someeffectsofstallontheow fortheA=2 wing.Thetipvortexisdisorganizedandtheinnerspanowha salarge separatedshearlayerthatisshownbyalargevelocitydeci tregion.Theun-stalled turbulentcase,howevershowsanorganizedtipvortexwitha velocitydecitregion thatismuchlessintense,andagainthemeanturbulentvorte xappearstobehighly rotationalinnature.TheA=4 casetellsadifferentstory,asthebaselineandturbulent vorticesarebothwell-denedasshownbyFigure 6-26 .Thisisaconsequenceof thenearlyre-attachedbaselinetipowshownintheoutboar dwingsectionofFigure 6-8 ,showingthatlocalattachmentoftheowhasastrongeffect onwingtipvortex formation.6.2.3CaseC TheCaseCdatashownbyFigures 6-27 to 6-29 showasimilarlargeow detachmentanddisorganizationofthetipvortexforthebas elinecasesasseenin Figure 6-25 .Itisapparentthatwingtipvortexowbehaviorismoreofaf unctionof thanitisofAasFigures 6-25 and 6-29 arenearlyidentical.Theturbulentcasesshow evidenceofanorganizedmeantipvortexindicatingthatexi stenceofatipvortexisnot necessarilyanindicatorofun-stalledloads. 183

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6.2.4CaseD Thesedatashowremarkabledifferencesinthebaselinefrom theA=2and4data atthesame .Inthiscasethebaselinevortexisverystrong,organized, andslightly misshapedcomparedagainstthebrokenvortexofFigures 6-25 and 6-29 .Thebaseline owalsoappearstobemuchmorerotationalthanlower cases,buttheturbulent owlooksverysimilartotheothertwoAcases.Theseresultsareconsistentwith thechordwisePIVdataaswellaswiththehypothesisputfort hinChapter5regarding differencesinloadsforthiscase.Itdoesappearthatturbu lenceweakensthetipvortex thatisresponsibleforthesuper-linearliftfortheA=1wing,aswellascausesallAwingstoactsimilartoeachotherastheyapproachturbulent stall. 6.2.5FittingVortexModelstoData Itwasofinteresttodeterminequantitativedifferencesin thetipvortexesandtot themeasureddatatoacceptedmodelstolearnmoreaboutthe ow.Thevortexcenters, Y c and Z c ,arerstidentiedineachvectoreldbyndingthelocatio nswheretheVand Wcomponentsofvelocitycrosszeroinsidethevortexcoresi milartothatperformed byRokhsazet.al.andIgarashi[ 186 187 ].Theowvelocitiesaretheninterpolated ontoapolarcoordinatesystemwhoseoriginisplacedatthev ortexcenter.Theangular velocity, V ,isaveragedalongtheradius, r ,aroundtheentirepolarvectoreldforall caseswheretheowexhibitsacoherentvortex. TheLamb-Oseenvortexdistribution, V = V max 1+ : 5 1 : 25643 r core r 1 e 1 : 25643 r 2 r 2 core (6–35) asdescribedbyDevenport[ 185 ]isthetheoreticalvelocitydistributionofafree axisymmetricvortexlamentthathasdecayedduetoviscous effects. V max isthe maximumvelocity,while r core istheradiusat V max .Thisderivationisbasedontheone 184

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presentedbyBatchelor[ 189 ], V = 2 r core 1 e r 2 r 2 core (6–36) whichisadirectsolutiontotheNavier-Stokesequationsin polarcoordinates.The circulation, ,canbesolvedgiven r core and V max by = 2 V max r core 1 e 1 ; (6–37) whichisrelatedtotheliftgeneratedonthewing[ 156 ].Equation 6–35 hasbeenshown tobeaccurateatdescribingthevelocityofthewingtipvort exonceithasprogressed severalchordlengthdownstream,butitshowserrorscloset othewingduetothe non-zeropressuregradientsinvolved[ 184 187 188 ].Thiswouldleadthecirculation foundbyEquation 6–37 tobeinaccurate,howeveracorrectedvortexstrengthmaybe calculatedaccordingto 0 = R V dr R 2 r core 1 e r 2 r 2 core dr 2 V max r core 1 e 1 ; (6–38) whichisaratioofintegratedstrengthmultipliedbyEquati on 6–37 Figure 6-31 showshowwelltheLamb-Oseenvortexproletsthemeasured datafortheun-stalledcases.Ingeneralforbaselineowth etisgoodoutto r core but under-predictsafterthat,andthetisalsogenerallygood forATGcases.Thevortex center, V max r core and 0 arecombinedintoTable 6-2 forallcasesthatexhibited denedvortices. Theturbulenceconsistentlyhadtheeffectofraisingthevo rtexcoreandbringingit muchclosertothewingtiporiginintheYdirection.Asexpec tedthewanderingofthe vortexcorecausedtheturbulentcasetohaveamuchlarger r core andasmaller V max Thebaselinecasesexhibitedtypicalbehaviorofarotation alcorewithinanirrotational vortex,howeverintheturbulentcasestherotationalcoreh addiffusedsomuchthat itdominatedtheimagingdomain.Theturbulentcaseexhibit edconsistentlystronger 185

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Table6-2.Tableofrelevanttipvortexproperties BaselineorATG A Y c Z c V max U 1 r core c cU 1 C cU 1 Baseline 1 8 0.04025 0.06721 -0.348 0.03547 -0.123 -0.151 ATG 1 8 0.02493 0.117 -0.123 0.1659 -0.202 -0.208 Baseline 2 8 0.06906 0.07627 -0.431 0.03706 -0.159 -0.195 ATG 2 8 0.04772 0.1254 -0.141 0.1798 -0.253 -0.26 Baseline 4 8 0.06705 0.06944 -0.409 0.04201 -0.171 -0.215 ATG 4 8 0.03931 0.1173 -0.156 0.173 -0.268 -0.275 ATG 2 25 0.0009444 0.1669 -0.318 0.2082 -0.659 -0.648 Baseline 4 15 0.06939 0.09037 -0.598 0.05745 -0.342 -0.408 ATG 4 15 0.02031 0.137 -0.258 0.1804 -0.463 -0.473 ATG 1 45 0.05111 0.2622 -0.355 0.2755 -0.972 -0.903 ATG 2 35 -0.004917 0.1341 -0.268 0.2551 -0.678 -0.633 ATG 4 25 0.007068 0.1808 -0.333 0.2242 -0.742 -0.734 Baseline 1 25 0.1069 0.1714 -0.61 0.1526 -0.926 -0.834 ATG 1 25 0.03688 0.1878 -0.326 0.1862 -0.603 -0.59 0 thandidthebaselinecasewiththeexceptionoftheA=1 ; =25 case.Inthis case,thebaselineliftissignicantlygreaterthanthetur bulentlift,sothe 0 difference isexplained.Furthermore 0 increaseswithAindicatingtheextenttowhichthe measuredvortexisweakenedbyitsinteractionwithitsoppo singvortexontheotherside ofthewing,andalsoexplainingtosomeextentwhytheliftsl opeofhigherAisgreater [ 156 ]. 6.3Summary InthischaptertheresultsobservedfromPIVmeasurementso fthevelocityeld wereusedtoinvestigatetheeffectsoffreestreamturbulen ceontheowoverlowAat platewingsandrelatetotheaerodynamicloadsdiscussedin Chapter5.Theprimary effectofhighlevelsoffree-streamturbulencewasshownto beaquicklydeveloping shearlayerwhichmaintainedowattachmenttomuchhigher andacrossagreater spanthanoccurredinbaselineow.Thebaselinecases,inco ntrast,exhibitedverythin separatedshearlayerswhichcouldreattachatlower leadingtoun-stalledbehavior, buttheyfailedtoreattachathigher leadingtostall.Thedataalsoshowthatthe superlinearliftoftheA=1wingwasduetoastrongtipvortexformedinconjunction 186

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withalargeseparatedandreattachedregion.Turbulencewa sshowntocauseow attachmentovermuchoftheA=1wingresultinginaweakertipvortex,bothofwhich contributedtolowerlift. 187

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Figure6-1.[Modelmountedonstinger,stereocameras,andlasershining upwardtoilluminatea chordatconstantspan]Modelmountedonstinger,stereocam eras,andlasershining upwardtoilluminateachordatconstantspan.Photocourtes yofMichaelSytsma. 188

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Figure6-2.DiagramofchordwisePIVmeasurementlocationo nthreeAwings. y b = 12.5% y b =25% y b =37.5% 189

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y b =0 : 125 y b =0 : 25 y b =0 : 375 0 0 : 2 0 : 4 0 : 6 0 : 8 1 Baseline Z cX c 00 : 51 0 : 1 0 0 : 1 0 : 2 Z cX c 00 : 51 0 : 1 0 0 : 1 0 : 2 Z cX c 00 : 51 0 : 1 0 0 : 1 0 : 2 Turbulence Z cX c 00 : 51 0 : 1 0 0 : 1 0 : 2 Z cX c 00 : 51 0 : 1 0 0 : 1 0 : 2 Z cX c 00 : 51 0 : 1 0 0 : 1 0 : 2 Figure6-3.Plotof U U 1 at =8 andA=1 y b =0 : 125 y b =0 : 25 y b =0 : 375 0 0 : 2 0 : 4 0 : 6 0 : 8 1 1 : 2 Baseline Z cX c 00 : 51 0 : 1 0 0 : 1 0 : 2 Z cX c 00 : 51 0 : 1 0 0 : 1 0 : 2 Z cX c 00 : 51 0 : 1 0 0 : 1 0 : 2 Turbulence Z cX c 00 : 51 0 : 1 0 0 : 1 0 : 2 Z cX c 00 : 51 0 : 1 0 0 : 1 0 : 2 Z cX c 00 : 51 0 : 1 0 0 : 1 0 : 2 Figure6-4.Plotof U U 1 at =8 andA=2 190

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y b =0 : 125 y b =0 : 25 y b =0 : 375 0 0 : 2 0 : 4 0 : 6 0 : 8 1 1 : 2 Baseline Z cX c 00 : 51 0 : 1 0 0 : 1 0 : 2 Z cX c 00 : 51 0 : 1 0 0 : 1 0 : 2 Z cX c 00 : 51 0 : 1 0 0 : 1 0 : 2 Turbulence Z cX c 00 : 51 0 : 1 0 0 : 1 0 : 2 Z cX c 00 : 51 0 : 1 0 0 : 1 0 : 2 Z cX c 00 : 51 0 : 1 0 0 : 1 0 : 2 Figure6-5.Plotof U U 1 at =8 andA=4 y b =0 : 125 y b =0 : 25 y b =0 : 375 0 2 4 6 8 10 Baseline Z cX c 00 : 51 0 : 1 0 0 : 1 0 : 2 Z cX c 00 : 51 0 : 1 0 0 : 1 0 : 2 Z cX c 00 : 51 0 : 1 0 0 : 1 0 : 2 Turbulence Z cX c 00 : 51 0 : 1 0 0 : 1 0 : 2 Z cX c 00 : 51 0 : 1 0 0 : 1 0 : 2 Z cX c 00 : 51 0 : 1 0 0 : 1 0 : 2 Figure6-6.Plotof S 13 U 1 c at =8 andA=2 191

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y b =0 : 125 y b =0 : 25 y b =0 : 375 0 : 4 0 : 2 0 0 : 2 0 : 4 0 : 6 0 : 8 1 1 : 2 Baseline Z cX c 00 : 51 0 : 4 0 : 2 0 0 : 2 Z cX c 00 : 51 0 : 4 0 : 2 0 0 : 2 Z cX c 00 : 51 0 : 4 0 : 2 0 0 : 2 Turbulence Z cX c 00 : 51 0 : 4 0 : 2 0 0 : 2 Z cX c 00 : 51 0 : 4 0 : 2 0 0 : 2 Z cX c 00 : 51 0 : 4 0 : 2 0 0 : 2 Figure6-7.Plotof U U 1 at =25 andA=2 y b =0 : 125 y b =0 : 25 y b =0 : 375 0 : 2 0 0 : 2 0 : 4 0 : 6 0 : 8 1 1 : 2 Baseline Z cX c 00 : 51 0 : 2 0 0 : 2 Z cX c 00 : 51 0 : 2 0 0 : 2 Z cX c 00 : 51 0 : 2 0 0 : 2 Turbulence Z cX c 00 : 51 0 : 2 0 0 : 2 Z cX c 00 : 51 0 : 2 0 0 : 2 Z cX c 00 : 51 0 : 2 0 0 : 2 Figure6-8.Plotof U U 1 at =15 andA=4 192

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y b =0 : 125 y b =0 : 25 y b =0 : 375 0 2 4 6 8 Baseline Z cX c 00 : 51 0 : 4 0 : 2 0 0 : 2 Z cX c 00 : 51 0 : 4 0 : 2 0 0 : 2 Z cX c 00 : 51 0 : 4 0 : 2 0 0 : 2 Turbulence Z cX c 00 : 51 0 : 4 0 : 2 0 0 : 2 Z cX c 00 : 51 0 : 4 0 : 2 0 0 : 2 Z cX c 00 : 51 0 : 4 0 : 2 0 0 : 2 Figure6-9.Plotof S 13 U 1 c at =25 andA=2 y b =0 : 125 y b =0 : 25 y b =0 : 375 0 0 : 5 1 1 : 5 2 2 : 5 3 3 : 5 Baseline Z cX c 00 : 51 0 : 4 0 : 2 0 0 : 2 Z cX c 00 : 51 0 : 4 0 : 2 0 0 : 2 Z cX c 00 : 51 0 : 4 0 : 2 0 0 : 2 Turbulence Z cX c 00 : 51 0 : 4 0 : 2 0 0 : 2 Z cX c 00 : 51 0 : 4 0 : 2 0 0 : 2 Z cX c 00 : 51 0 : 4 0 : 2 0 0 : 2 Figure6-10.Plotof TKE U 1 2 at =25 andA=2 193

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y b =0 : 125 y b =0 : 25 y b =0 : 375 1 0 : 8 0 : 6 0 : 4 0 : 2 0 Baseline Z cX c 00 : 51 0 : 4 0 : 2 0 0 : 2 Z cX c 00 : 51 0 : 4 0 : 2 0 0 : 2 Z cX c 00 : 51 0 : 4 0 : 2 0 0 : 2 Turbulence Z cX c 00 : 51 0 : 4 0 : 2 0 0 : 2 Z cX c 00 : 51 0 : 4 0 : 2 0 0 : 2 Z cX c 00 : 51 0 : 4 0 : 2 0 0 : 2 Figure6-11.Plotof u 0 w 0 U 1 2 at =25 andA=2 y b =0 : 125 y b =0 : 25 y b =0 : 375 0 : 2 0 0 : 2 0 : 4 0 : 6 0 : 8 1 1 : 2 Baseline Z cX c 00 : 20 : 40 : 60 : 8 0 : 6 0 : 4 0 : 2 0 0 : 2 0 : 4 Z cX c 00 : 20 : 40 : 60 : 8 0 : 6 0 : 4 0 : 2 0 0 : 2 0 : 4 Z cX c 00 : 20 : 40 : 60 : 8 0 : 6 0 : 4 0 : 2 0 0 : 2 0 : 4 Turbulence Z cX c 00 : 20 : 40 : 60 : 8 0 : 6 0 : 4 0 : 2 0 0 : 2 0 : 4 Z cX c 00 : 20 : 40 : 60 : 8 0 : 6 0 : 4 0 : 2 0 0 : 2 0 : 4 Z cX c 00 : 20 : 40 : 60 : 8 0 : 6 0 : 4 0 : 2 0 0 : 2 0 : 4 Figure6-12.Plotof U U 1 at =45 andA=1 194

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y b =0 : 125 y b =0 : 25 y b =0 : 375 0 : 2 0 0 : 2 0 : 4 0 : 6 0 : 8 1 1 : 2 Baseline replacements Z cX c 00 : 20 : 40 : 6 0 : 8 0 : 6 0 : 4 0 : 2 0 0 : 2 0 : 4 Z cX c 00 : 20 : 40 : 6 0 : 8 0 : 6 0 : 4 0 : 2 0 0 : 2 0 : 4 Z cX c 00 : 20 : 40 : 6 0 : 8 0 : 6 0 : 4 0 : 2 0 0 : 2 0 : 4 Turbulence Z cX c 00 : 20 : 40 : 60 : 8 0 : 6 0 : 4 0 : 2 0 0 : 2 0 : 4 Z cX c 00 : 20 : 40 : 60 : 8 0 : 6 0 : 4 0 : 2 0 0 : 2 0 : 4 Z cX c 00 : 20 : 40 : 60 : 8 0 : 6 0 : 4 0 : 2 0 0 : 2 0 : 4 Figure6-13.Plotof U U 1 at =35 andA=2 y b =0 : 125 y b =0 : 25 y b =0 : 375 0 : 2 0 0 : 2 0 : 4 0 : 6 0 : 8 1 1 : 2 Baseline Z cX c 00 : 51 0 : 4 0 : 2 0 0 : 2 Z cX c 00 : 51 0 : 4 0 : 2 0 0 : 2 Z cX c 00 : 51 0 : 4 0 : 2 0 0 : 2 Turbulence Z cX c 00 : 51 0 : 4 0 : 2 0 0 : 2 Z cX c 00 : 51 0 : 4 0 : 2 0 0 : 2 Z cX c 00 : 51 0 : 4 0 : 2 0 0 : 2 Figure6-14.Plotof U U 1 at =25 andA=4 195

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y b =0 : 125 y b =0 : 25 y b =0 : 375 0 : 4 0 : 2 0 0 : 2 0 : 4 0 : 6 0 : 8 1 1 : 2 Baseline Z cX c 00 : 51 0 : 4 0 : 2 0 0 : 2 Z cX c 00 : 51 0 : 4 0 : 2 0 0 : 2 Z cX c 00 : 51 0 : 4 0 : 2 0 0 : 2 Turbulence Z cX c 00 : 51 0 : 4 0 : 2 0 0 : 2 Z cX c 00 : 51 0 : 4 0 : 2 0 0 : 2 Z cX c 00 : 51 0 : 4 0 : 2 0 0 : 2 Figure6-15.Plotof U U 1 at =25 andA=1 196

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VelocityeldandprolelocationVelocityprolesBaseline Z cX c 00 : 51 0 : 6 0 : 4 0 : 2 0 0 : 2 0 : 4 0 : 6 Z c u U 1 0 : 500 : 511 : 5 0 : 5 0 0 : 5 Turbulence Z cX c 00 : 51 0 : 5 0 0 : 5 Z c u U 1 0 : 500 : 511 : 5 0 : 5 0 0 : 5 Figure6-16.Plotof U U 1 at =25 andA=2 197

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u u a 00 : 20 : 40 : 60 : 81 1 : 5 1 0 : 5 0 0 : 5 1 1 : 5 Figure6-17.Plotof U u a at =25 Y b =0 : 25 andA=2 scaledagainstsimilarity parameter forbaselineowat X c = 0.2, 0.3 0.4 0.5 0.6 0.7 ,and Equation 6–34 asdashedlinewith =9 198

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u u a 00 : 20 : 40 : 6 0 : 8 1 1 : 5 1 0 : 5 0 0 : 5 1 1 : 5 Figure6-18.Plotof U u a scaledagainstsimilarityparameter forturbulentowat X c = 0.2, 0.3 0.4 0.5 0.6 0.7 ,andEquation 6–34 asdashedlinewith =3 : 5 199

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U 1 Camera1CCDCamera2CCDWingTopView LaserSheet X WY W Figure6-19.StereoPIVsetupfordownstreammeasurements BaselineTurbulence Z cY c 0 : 4 0 : 200 : 20 : 4 0 : 2 0 0 : 2 0 : 4 Z cY c 0 : 4 0 : 200 : 20 : 4 0 : 2 0 0 : 2 0 : 4 0 : 6 0 : 7 0 : 8 0 : 9 1 Figure6-20.Plotof U 1 ( Y;Z ) U 1 indownstreamexperimentsat =8 andA=1 200

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BaselineTurbulence Z cY c 0 : 4 0 : 200 : 20 : 4 0 : 2 0 0 : 2 0 : 4 Z cY c 0 : 4 0 : 200 : 20 : 4 0 : 2 0 0 : 2 0 : 4 0 : 6 0 : 7 0 : 8 0 : 9 1 Figure6-21.Plotof U 1 ( Y;Z ) U 1 indownstreamexperimentsat =8 andA=2 BaselineTurbulence Z cY c 0 : 20 0 : 20 : 4 0 : 2 0 : 1 0 0 : 1 0 : 2 0 : 3 0 : 4 Z cY c 0 : 20 0 : 20 : 4 0 : 2 0 : 1 0 0 : 1 0 : 2 0 : 3 0 : 4 0 : 6 0 : 7 0 : 8 0 : 9 1 Figure6-22.Plotof U 1 ( Y;Z ) U 1 indownstreamexperimentsat =8 andA=4 201

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BaselineTurbulence Z cY c 0 : 200 : 20 : 4 0 : 2 0 : 1 0 0 : 1 0 : 2 0 : 3 0 : 4 Z cY c 0 : 200 : 20 : 4 0 : 2 0 : 1 0 0 : 1 0 : 2 0 : 3 0 : 4 10 5 0 5 10 Figure6-23.Plotof S 13 U 1 c indownstreamexperimentsat =8 andA=4 BaselineTurbulence Z cY c 0 : 200 : 20 : 4 0 : 2 0 : 1 0 0 : 1 0 : 2 0 : 3 0 : 4 Z cY c 0 : 200 : 20 : 4 0 : 2 0 : 1 0 0 : 1 0 : 2 0 : 3 0 : 4 0 0 : 05 0 : 1 Figure6-24.Plotof TKE U 1 2 indownstreamexperimentsat =8 andA=4 202

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BaselineTurbulence Z cY c 0 : 4 0 : 200 : 20 : 4 0 : 2 0 : 1 0 0 : 1 0 : 2 0 : 3 0 : 4 Z cY c 0 : 4 0 : 200 : 20 : 4 0 : 2 0 : 1 0 0 : 1 0 : 2 0 : 3 0 : 4 0 0 : 2 0 : 4 0 : 6 0 : 8 1 1 : 2 Figure6-25.Plotof U 1 ( Y;Z ) U 1 indownstreamexperimentsat =25 andA=2 BaselineTurbulence Z cY c 0 : 4 0 : 20 0 : 20 : 4 0 : 2 0 : 1 0 0 : 1 0 : 2 0 : 3 0 : 4 Z cY c 0 : 4 0 : 20 0 : 20 : 4 0 : 2 0 : 1 0 0 : 1 0 : 2 0 : 3 0 : 4 0 : 5 0 : 6 0 : 7 0 : 8 0 : 9 1 1 : 1 Figure6-26.Plotof U 1 ( Y;Z ) U 1 indownstreamexperimentsat =15 andA=4 203

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BaselineTurbulence Z cY c 0 : 4 0 : 200 : 20 : 4 0 0 : 2 0 : 4 0 : 6 Z cY c 0 : 4 0 : 200 : 20 : 4 0 0 : 2 0 : 4 0 : 6 0 0 : 2 0 : 4 0 : 6 0 : 8 1 1 : 2 Figure6-27.Plotof U 1 ( Y;Z ) U 1 indownstreamexperimentsat =45 andA=1 BaselineTurbulence Z cY c 0 : 4 0 : 200 : 20 : 4 0 0 : 2 0 : 4 0 : 6 Z cY c 0 : 4 0 : 200 : 20 : 4 0 0 : 2 0 : 4 0 : 6 0 0 : 2 0 : 4 0 : 6 0 : 8 1 1 : 2 Figure6-28.Plotof U 1 ( Y;Z ) U 1 indownstreamexperimentsat =35 andA=2 204

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BaselineTurbulence Z cY c 0 : 4 0 : 200 : 20 : 4 0 : 2 0 0 : 2 0 : 4 Z cY c 0 : 4 0 : 200 : 20 : 4 0 : 2 0 0 : 2 0 : 4 0 0 : 2 0 : 4 0 : 6 0 : 8 1 1 : 2 Figure6-29.Plotof U 1 ( Y;Z ) U 1 indownstreamexperimentsat =25 andA=4 BaselineTurbulence Z cY c 0 : 4 0 : 200 : 20 : 4 0 : 2 0 0 : 2 0 : 4 Z cY c 0 : 4 0 : 200 : 20 : 4 0 : 2 0 0 : 2 0 : 4 0 0 : 2 0 : 4 0 : 6 0 : 8 1 1 : 2 Figure6-30.Plotof U 1 ( Y;Z ) U 1 indownstreamexperimentsat =25 andA=1 205

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V U 1r c 0 0 : 050 : 10 : 150 : 20 : 250 : 30 : 35 0 : 7 0 : 6 0 : 5 0 : 4 0 : 3 0 : 2 0 : 1 0 0 : 1 Figure6-31.Measured V distributionsforbaseline(solidlines)andturbulence(d ashed lines)andttedLamb-Oseenvortexforbaseline(dottedlin es)and turbulence(dashdottedlines)forA=1 ; =8 A=2 ; =8 A=4 ; =8 A=4 ; =15 A=1 ; =25 A=2 ; =25 206

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CHAPTER7 SUMMARYANDFUTUREWORK 7.1Summary Thisstudypresentsanexaminationoftheeffectsoffree-st reamturbulenceon lowReynoldsnumberowover,thin,rectangularatplateso fvariableA.Themain goalsofthisstudyweretodevelopanincreasedunderstandi ngofhowthefreestream turbulenceinteractswiththeowfeaturesoverthesewings toalteraerodynamicloads. Therelevantoutcomesofthisworkare: Acontrolledandcharacterizedturbulentenvironmentwasd eveloped Alowordercomputationalsimulationwasusedtoassessdyna micloadingeffects ofturbulenceandthiswascomparedagainstcorrectedmeasu rements Themeanloadswereshowntobestronglyaffectedbytheprese nceoffree-stream turbulence Theoweldwasshowntovaryduetothepresenceoffree-stre amturbulence, resultinginloadchanges Anactiveturbulencegrid(ATG)wasdevelopedtogeneratetu rbulencewithhigh intensityandlargeintegrallengthscaleswithintheREEFA CFwindtunnel.Thisgridis computercontrolledsothatitcangenerateturbulencewith differentstatisticalproperties dependingonrunmodeanddownstreamlocation.Theturbulen cestatisticswere assessedusingX-wireconstanttemperatureanemometry,an dturbulencestatistics wereevaluatedtounderstandhowtheseevolveddownstream, cross-streamandwith varyingtunnelspeedsandrunmodes.TheATGwasshowncapabl eofgenerating free-streamturbulenceintensities(TI)from15to35%,wit hlengthscalesontheorder of0.6m,andwithspectraapproximatingthevonK arm an[ 6 ]modelthatshoweda possibilityfortonalorsmoothbehaviordependingonrunmo de. Asignalprocessingtechniquewasalsodevelopedtopartial lyreconstructthe spectralcharacteristicsofaerodynamicloadsfrommeasur ementstakenfromeitherthe stingbalanceorloadcell.Thistechniqueutilizesamodie dWienerdeconvolutionwhich 207

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isdesignedintoaFIRlterwiththewindowingtechnique.It wasshowntobeeffective atcorrectingtimeandfrequencydatafromanimpulse,andmo deratelyeffectiveata correctingacontinuousforcingfunction. Asimilarsignalprocessingtechniquewasusedtogeneratea syntheticturbulence signalthatwasinjectedintoalow-order2-Dcomputational aerodynamicscode.The codewasrunwithseveralsettingstoassesstheeffectsofth eturbulentsignalona 2-Datplateairfoil.Theresultsindicatedbandwidthsofi nterestandcharacteristic behaviorsofthecalculatedloadsinthepresenceofturbule nce.Theverticalcomponent ofturbulencehadthegreatesteffectontime-varyingloads ,andtheseeffectsbecame smallerasthesizeoftheturbulentperturbationsapproach edthechordofthewing. Loadsfromthreeatplatewingswereevaluatedinbaselinea ndturbulentowsin thewindtunnel.Meanandcondenceintervalsof6-DOMloads weremeasured.The presenceoffree-streamturbulencehaddifferenteffectso ntheloadsoftheA=1 wingcomparedtotheA=2 and 4 wings.OntheA=1 wingthemaximumliftwas decreasedbyturbulence,andstallbehaviorwasnotsignic antlyaffected,howeveron theotherwingsthehighfree-streamTIgreatlyincreasedth estallrangeofthemodels andsmoothedoutthepitchingmomentbehavior.Inadditiont othemeaneffects,the loadvariancewasgreatlyincreased,butthemagnitudeoflo advariationwasfoundto notbeastrongfunctionofangleofattack.Thedynamicloadm easurementstestedthe signalprocessingtechniqueandindicateda 7 3 roll-offoftwoaxes,butunfortunately thetechniquedidnotyieldvaluableresultsfortheotherax es.Themeasureddynamic loadsfrequencyresponsecomparedfavorablyinaqualitati vesensetothesimulated frequencyresponse. Particleimagevelocimetrywasusedtomeasureowpatterns inthebaseline andturbulentowsinordertoexplainthedifferencesinloa ds.Thebaselineandlow turbulenceowsexhibitedthinseparatedshearlayersthat formedattheleadingedge andcouldreattachdownstreamatun-stalledanglesofattac k.Stalledcasesexhibited 208

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detachedfreeshearowneartothecenterofthewingsandext endingoutward. Highintensityturbulencechangedtheoweldstoexhibita thickshearlayerformed attheleadingedgethatappearedattachedatmuchhigherang lesofattackthan baselinecases.Theenhancedspreadingoftheturbulentshe arlayergavetheowthe appearanceofreattachingtothewingresultinginthechang esinloads.Downstream measurementscorroboratedtheseresultsandalsoshowedwh ylowandhighaspect ratiowingsexhibiteddisparateloadbehaviors. 7.2FutureWork Thisdissertationbroughttolightthelargevariabilityof loadsinthepresenceof turbulenceinthefree-stream,andthedrasticchangesinth emeanow-eldthatcause theseloads.Likemuchexperimentalresearch,thisworkwas unabletomeasureall quantitiesofinterestatthesametime.Computationalreso urcesareeverincreasingin capability,anditwouldbeadvantageoustoonedaybecapabl eofsimulatingtheeffects ofturbulenceinahighdelitycomputationaldomainasanex tensionofthepresented work.Afullowsimulationwouldallowtruedynamicloadsto bedeterminedin6-DOM, andtheowwouldbeknownatalllocationsandtimesopeningu panalysiscapabilities thatwerenotpossibleinthePIVdata,forexamplewithFouri eranalysis.Furthermore, thefree-streamturbulencecanbemodiedacrossawiderran geallowingforamore completespectrumofresultstobepresented.However,thec omputationsneedto resolvetheowdowntotheverysmallscalesforadequaterep resentationofturbulence, andthesimulationrunsneedtobelongenoughtoyieldstatis ticswithacceptable condenceintervals.Theserequirementswilllikelydelay highresolutioncomputational researcheffortsforsometime. Thisresearchwaslimitedtotestingcertainturbulenceint ensity,lengthscales, L 11 ,andotherstatisticsbasedonfacilityanddesignconstrai nts,butthesevariables areimportanttotheunderstandingofthefullspectrumofef fects.Forexample,Ravi et.al.indicatedadependenceof L 11 ontime-varyingliftanddrag[ 112 ].Futurework 209

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wouldbenetfromtheabilitytovaryTIand L 11 independentlyandsmoothlyovera widerange,butthisisacharacteristicdifcultyofwindtu nnelgeneratedfree-stream turbulence.Amorereasonablegoalwouldbetotestintermed iateTIturbulentowsto determinetheeffectsonloadandow-eld.Itwasshownthat theeffectsofturbulence appearedsaturatedforthemeanloadsintheATGows,andtha tthestaticgridcreated anincrementinloadsfromthebaselinecase.Itwouldbeinte restingtoexplorethe spacebetweentodevelopamorecompletemapofhowTIaffects loads. Thesignalprocessingtechniqueusedinthisworkwasanatte mpttomeasure thetimevaryingloadsinanundistortedmannertobetterund erstandtheproblems associatedwithightinturbulence,butthiswasshowntobe adifcultthingtodo.Ravi et.al.utilizedadifferenttacticofmeasuringtime-depen dentpressures[ 112 ],butas theywereoveraverynitemeasurementslicethismethodisl ackingalso.Itwould benetunderstandingifthetime-varyingloadscouldaccur atelybedetermined,for examplewithapressuresensitivepaintmethodoraverystif floadsensingtechnique. Bettertime-varyingloadmeasurementscombinedwiththeen hancedtestingcapability previouslymentionedwouldbeusefulinexpandingtherealm ofanalysistechniques available. Amostimportantndingfromthisresearchisthatwindtunne ltestsatlowReynolds numberwithverylowfree-streamTIwillgiveresultsthatar enotinlinewiththerealityof ightconditionsexperiencedbySUAS.Itisalsoclearthatg eneratingvariablelevelsof turbulenceexperimentallyisnotasimpletask,anditmaybe infeasibleformanyfacilities toimplement.Theinterestingdiscoveryinwhichthehighly turbulentshearlayergrows muchfasterthanthebaselineshearlayer,leadingtoamuchh igherdegreeofattached ow,givesinsightintohowasolutionmaybedeveloped.Test satadditionalTIwould resolvethedependenceoftheshearlayergrowthrate, ,aswellastheloadbehavior onindividualwings.Furthertestswithtraditionalcamber edairfoilswouldshowhowthey differfromatplatesinturbulence.Thisisusefuldata,bu ttherealitemofinterestwould 210

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beabehavioralmodelwhichindicateswhatsortofgeometrya ndadversepressure gradientistheturbulentowcapableofovercoming.Amored etailedunderstandingof theowseparationandattachmentphenomenoninvaryinglev elsofTIcanbeused tounderstandhowarbitrarygeometrieswilldifferintheir loadingascomparedtolow turbulenceows.Thisunderstandingcanthenbeusedtoincr ementallyaugment baselineloadsdataofarbitrarygeometriesasafunctionof TI,withminimumnecessity oftesting.Amodelcapableofdoingsocouldbeusedtocorrec texistingdata,collected inasimilarregime,tobevalidforcasesofhigherTI. 211

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APPENDIXA ACTIVETURBULENCEGRIDCHARACTERIZATION TableA-1.ATGturbulencestatisticswithwindtunnelthrot tleat14.5%andat X M =5 X M n U 1 95% CI TI X TI Y TI Z Re L 11 Re L 11 L 11 R Re L 11 R I xy I xz I yz Hz m s % % % m 2 s 3 mm mm m m 5 2 1 2 : 46 0 : 10 25.9 23.5 18.6 4.69 0.16 4.4 187 0.049 2097 0.293 12430 1.10 1.39 1.27 5 3 1 : 5 2 : 35 0 : 10 24.0 21.8 17.5 4.04 0.17 4.2 159 0.040 1515 0.354 13351 1.10 1.38 1.25 5 4 2 2 : 29 0 : 15 23.9 21.0 16.2 3.58 0.18 4.3 158 0.041 1500 0.584 21287 1.14 1.47 1.29 5 5 2 : 5 2 : 21 0 : 13 22.9 20.6 16.1 3.17 0.18 4.3 143 0.037 1234 0.442 14893 1.11 1.42 1.28 5 4 1 2 : 28 0 : 13 23.4 20.6 16.4 3.41 0.18 4.3 154 0.040 1427 0.439 15625 1.14 1.43 1.26 5 5 1 : 25 2 : 22 0 : 13 22.7 20.0 16.0 2.97 0.18 4.4 147 0.039 1305 0.437 14680 1.14 1.42 1.25 5 6 1 : 5 2 : 15 0 : 14 23.1 19.6 15.7 2.76 0.19 4.5 149 0.040 1324 0.466 15443 1.18 1.47 1.25 5 0 3 2 : 54 0 : 13 28.4 22.8 19.7 4.72 0.16 5.0 239 0.071 3424 0.390 18721 1.24 1.44 1.16 5 0 4 2 : 52 0 : 14 27.5 21.9 19.1 4.45 0.17 4.9 229 0.068 3133 0.439 20309 1.26 1.44 1.15 5 0 5 2 : 46 0 : 13 26.2 21.9 18.3 4.15 0.17 4.7 203 0.058 2483 0.393 16890 1.20 1.43 1.19 5 0 6 2 : 38 0 : 15 26.9 21.8 18.5 4.06 0.17 4.8 204 0.058 2498 0.485 20748 1.24 1.45 1.17 5 0 8 2 : 34 0 : 15 25.7 21.3 17.7 3.66 0.17 4.7 189 0.054 2148 0.505 20250 1.21 1.45 1.20 5 2 : 5 0 2 : 44 0 : 11 24.6 22.0 18.4 4.33 0.17 4.3 173 0.045 1795 0.391 15654 1.12 1.34 1.20 5 5 0 2 : 20 0 : 14 23.2 19.3 16.1 2.98 0.18 4.4 152 0.040 1377 0.500 17043 1.20 1.44 1.20 5 8 0 2 : 09 0 : 15 23.6 20.1 16.3 2.59 0.19 4.6 151 0.042 1364 0.476 15641 1.17 1.45 1.23 212

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TableA-2.ATGturbulencestatisticswithwindtunnelthrot tleat14.5%andat X M =10 X M n U 1 95% CI TI X TI Y TI Z Re L 11 Re L 11 L 11 R Re L 11 R I xy I xz I yz Hz m s % % % m 2 s 3 mm mm m m 10 2 1 2 : 36 0 : 09 17.2 16.7 13.9 0.84 0.25 6.6 179 0.072 1933 0.393 10619 1.03 1.23 1.20 10 3 1 : 5 2 : 24 0 : 10 16.1 15.2 12.5 0.64 0.27 6.7 161 0.065 1564 0.465 11139 1.06 1.28 1.21 10 4 2 2 : 16 0 : 11 15.3 15.1 11.8 0.51 0.29 6.9 152 0.063 1388 0.521 11447 1.01 1.30 1.28 10 5 2 : 5 2 : 10 0 : 12 15.9 14.9 11.5 0.46 0.29 7.4 164 0.073 1618 0.591 13144 1.07 1.37 1.29 10 4 1 2 : 15 0 : 12 15.5 14.3 11.7 0.49 0.29 7.1 159 0.068 1514 0.553 12306 1.08 1.33 1.22 10 5 1 : 25 2 : 08 0 : 13 15.4 14.7 11.6 0.42 0.30 7.4 159 0.071 1510 0.604 12881 1.05 1.33 1.27 10 6 1 : 5 2 : 02 0 : 13 15.6 15.5 11.6 0.40 0.30 7.4 156 0.070 1458 0.606 12707 1.00 1.34 1.34 10 0 3 2 : 42 0 : 12 20.1 17.7 15.0 0.93 0.25 7.6 245 0.111 3608 0.501 16275 1.14 1.34 1.18 10 0 4 2 : 36 0 : 12 19.3 17.2 14.3 0.83 0.25 7.5 228 0.103 3126 0.531 16129 1.12 1.35 1.20 10 0 5 2 : 30 0 : 12 18.0 16.6 14.2 0.72 0.26 7.3 201 0.088 2435 0.530 14621 1.08 1.26 1.17 10 0 6 2 : 28 0 : 12 18.2 16.6 13.7 0.70 0.26 7.5 207 0.092 2565 0.494 13704 1.10 1.33 1.21 10 0 8 2 : 18 0 : 14 18.1 16.4 13.4 0.62 0.27 7.5 197 0.088 2319 0.609 16007 1.11 1.35 1.22 10 2 : 5 0 2 : 30 0 : 10 15.6 15.1 12.9 0.72 0.26 6.4 152 0.058 1390 0.473 11326 1.04 1.21 1.17 10 5 0 2 : 14 0 : 13 15.4 14.2 11.5 0.41 0.30 7.7 169 0.078 1716 0.622 13605 1.08 1.34 1.24 10 8 0 2 : 05 0 : 14 16.0 15.5 12.2 0.39 0.31 7.9 172 0.081 1773 0.590 12842 1.03 1.30 1.27 213

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TableA-3.ATGturbulencestatisticswithwindtunnelthrot tleat14.5%andat X M =12 : 5 X M n U 1 95% CI TI X TI Y TI Z Re L 11 Re L 11 L 11 R Re L 11 R I xy I xz I yz Hz m s % % % m 2 s 3 mm mm m m 12.5 2 1 2 : 48 0 : 09 15.2 15.0 13.0 0.50 0.29 8.0 203 0.098 2462 0.418 10557 1.02 1.17 1.15 12.5 3 1 : 5 2 : 36 0 : 10 14.2 13.2 12.4 0.37 0.31 8.3 184 0.091 2040 0.480 10725 1.07 1.14 1.07 12.5 4 2 2 : 29 0 : 12 13.8 13.3 11.9 0.30 0.33 8.7 183 0.095 2003 0.556 11696 1.04 1.16 1.11 12.5 5 2 : 5 2 : 22 0 : 13 14.1 13.0 12.2 0.27 0.34 9.1 190 0.104 2164 0.611 12741 1.09 1.15 1.06 12.5 4 1 2 : 25 0 : 13 14.0 13.2 11.5 0.27 0.33 9.2 193 0.106 2242 0.604 12747 1.06 1.22 1.15 12.5 5 1 : 25 2 : 18 0 : 14 14.5 13.6 12.3 0.25 0.34 9.6 202 0.116 2443 0.639 13497 1.06 1.18 1.10 12.5 6 1 : 5 2 : 16 0 : 13 14.3 14.0 12.0 0.25 0.34 9.4 194 0.109 2249 0.584 12049 1.03 1.20 1.17 12.5 0 3 2 : 55 0 : 12 17.2 15.6 14.7 0.56 0.28 8.7 255 0.134 3911 0.488 14233 1.10 1.17 1.06 12.5 0 4 2 : 49 0 : 12 17.2 15.0 13.5 0.51 0.28 9.0 255 0.137 3901 0.534 15202 1.14 1.27 1.11 12.5 0 5 2 : 42 0 : 13 16.0 14.3 13.6 0.43 0.30 8.9 229 0.122 3138 0.582 15002 1.12 1.17 1.05 12.5 0 6 2 : 42 0 : 12 16.2 14.9 13.2 0.43 0.30 9.0 235 0.127 3313 0.525 13694 1.08 1.22 1.13 12.5 0 8 2 : 34 0 : 14 15.8 14.7 13.1 0.37 0.31 9.1 225 0.123 3026 0.580 14263 1.08 1.21 1.12 12.5 2 : 5 0 2 : 41 0 : 10 13.8 12.9 12.0 0.41 0.30 7.8 174 0.082 1814 0.507 11279 1.07 1.15 1.08 12.5 5 0 2 : 21 0 : 13 14.3 13.2 11.6 0.24 0.34 9.6 203 0.117 2466 0.633 13357 1.09 1.23 1.13 12.5 8 0 2 : 14 0 : 15 14.8 14.9 13.1 0.25 0.34 9.4 198 0.112 2355 0.559 11760 0.99 1.12 1.13 214

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TableA-4.ATGturbulencestatisticswithwindtunnelthrot tleat14.5%andat X M =15 X M n U 1 95% CI TI X TI Y TI Z Re L 11 Re L 11 L 11 R Re L 11 R I xy I xz I yz Hz m s % % % m 2 s 3 mm mm m m 15 2 1 2 : 43 0 : 10 14.4 13.2 13.1 0.34 0.31 9.0 209 0.112 2620 0.468 10920 1.09 1.10 1.01 15 3 1 : 5 2 : 33 0 : 10 13.0 12.2 12.1 0.25 0.34 9.1 183 0.100 2019 0.489 9873 1.07 1.08 1.01 15 4 2 2 : 23 0 : 12 13.4 12.5 12.1 0.21 0.35 9.8 196 0.115 2294 0.555 11114 1.07 1.11 1.04 15 5 2 : 5 2 : 20 0 : 13 14.2 12.8 12.5 0.20 0.36 10.5 219 0.138 2865 0.581 12102 1.11 1.13 1.02 15 4 1 2 : 23 0 : 13 13.9 12.5 11.8 0.19 0.36 10.6 219 0.139 2876 0.609 12587 1.11 1.18 1.06 15 5 1 : 25 2 : 19 0 : 13 14.0 12.8 12.2 0.19 0.36 10.5 215 0.136 2782 0.585 11995 1.09 1.15 1.05 15 6 1 : 5 2 : 14 0 : 14 14.2 13.8 12.5 0.19 0.37 10.5 213 0.135 2723 0.587 11886 1.03 1.14 1.11 15 0 3 2 : 51 0 : 13 16.7 15.2 14.2 0.41 0.30 9.8 274 0.162 4503 0.545 15196 1.09 1.17 1.07 15 0 4 2 : 45 0 : 12 15.8 14.6 13.9 0.36 0.31 9.6 249 0.144 3710 0.569 14686 1.09 1.14 1.05 15 0 5 2 : 35 0 : 12 15.6 13.9 13.2 0.32 0.32 9.7 236 0.137 3354 0.537 13128 1.12 1.18 1.05 15 0 6 2 : 36 0 : 12 15.2 14.5 13.5 0.32 0.32 9.6 229 0.132 3149 0.536 12822 1.05 1.13 1.08 15 0 8 2 : 29 0 : 14 15.5 14.3 12.7 0.27 0.33 10.2 240 0.146 3462 0.593 14023 1.08 1.22 1.13 15 2 : 5 0 2 : 35 0 : 10 12.8 11.8 11.7 0.27 0.33 8.7 175 0.092 1848 0.493 9927 1.09 1.10 1.01 15 5 0 2 : 18 0 : 13 14.5 13.1 12.1 0.19 0.37 11.0 233 0.154 3261 0.593 12543 1.11 1.20 1.08 15 8 0 2 : 12 0 : 15 15.2 14.1 13.7 0.21 0.36 10.6 229 0.146 3139 0.587 12608 1.08 1.11 1.03 215

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TableA-5.ATGturbulencestatisticswithwindtunnelthrot tleat14.5%andat X M =20 X M n U 1 95% CI TI X TI Y TI Z Re L 11 Re L 11 L 11 R Re L 11 R I xy I xz I yz Hz m s % % % m 2 s 3 mm mm m m 20 2 1 2 : 29 0 : 08 12.2 11.3 12.1 0.24 0.35 8.6 160 0.082 1528 0.424 7872 1.08 1.00 0.93 20 3 1 : 5 2 : 18 0 : 10 11.9 10.6 12.2 0.18 0.37 9.3 161 0.089 1549 0.504 8752 1.12 0.98 0.87 20 4 2 2 : 12 0 : 11 12.2 11.4 12.2 0.16 0.38 9.8 168 0.098 1691 0.539 9275 1.07 1.00 0.93 20 5 2 : 5 2 : 08 0 : 12 13.3 12.0 12.3 0.15 0.39 10.6 195 0.125 2289 0.603 11056 1.10 1.08 0.98 20 4 1 2 : 13 0 : 11 12.4 11.4 11.6 0.15 0.39 10.3 181 0.111 1956 0.595 10460 1.09 1.07 0.98 20 5 1 : 25 2 : 08 0 : 12 13.3 12.7 12.7 0.15 0.39 10.6 196 0.125 2315 0.598 11028 1.05 1.05 1.00 20 6 1 : 5 2 : 06 0 : 12 13.3 12.6 12.6 0.17 0.38 10.0 184 0.111 2039 0.564 10347 1.05 1.06 1.01 20 0 3 2 : 35 0 : 12 15.0 13.1 13.4 0.31 0.32 9.5 224 0.128 3003 0.552 12949 1.14 1.11 0.97 20 0 4 2 : 30 0 : 12 14.7 12.6 13.5 0.28 0.33 9.6 217 0.126 2831 0.580 13059 1.17 1.09 0.93 20 0 5 2 : 24 0 : 11 14.2 12.5 12.6 0.23 0.35 9.9 208 0.123 2601 0.561 11861 1.13 1.12 0.99 20 0 6 2 : 22 0 : 11 14.3 13.0 12.7 0.24 0.34 9.7 206 0.120 2542 0.550 11681 1.10 1.13 1.03 20 0 8 2 : 16 0 : 13 14.4 12.7 12.9 0.21 0.35 10.0 207 0.124 2567 0.656 13524 1.13 1.11 0.98 20 2 : 5 0 2 : 22 0 : 09 11.3 10.0 11.1 0.18 0.37 9.0 151 0.081 1359 0.496 8333 1.13 1.02 0.90 20 5 0 2 : 09 0 : 12 13.1 12.5 12.6 0.15 0.39 10.6 194 0.124 2256 0.589 10741 1.04 1.04 0.99 20 8 0 2 : 00 0 : 13 14.2 13.6 13.9 0.17 0.37 10.2 194 0.119 2265 0.561 10666 1.05 1.02 0.98 216

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TableA-6.ATGturbulencestatisticswithwindtunnelthrot tleat28.5%andat X M =5 X M n U 1 95% CI TI X TI Y TI Z Re L 11 Re L 11 L 11 R Re L 11 R I xy I xz I yz Hz m s % % % m 2 s 3 mm mm m m 5 2 1 5 : 55 0 : 20 28.8 23.3 22.2 16.25 0.12 5.9 633 0.226 24022 0.363 38596 1.24 1.30 1.05 5 3 1 : 5 5 : 44 0 : 18 27.7 23.3 22.5 16.30 0.12 5.6 564 0.190 19086 0.322 32441 1.19 1.23 1.03 5 4 2 5 : 28 0 : 15 26.3 22.9 21.7 15.74 0.12 5.3 488 0.154 14285 0.299 27743 1.15 1.22 1.06 5 5 2 : 5 5 : 17 0 : 18 25.7 22.6 21.6 15.14 0.12 5.1 454 0.140 12384 0.407 36094 1.14 1.19 1.05 5 4 1 5 : 27 0 : 16 26.5 23.0 21.9 16.17 0.12 5.2 484 0.151 14044 0.332 30834 1.15 1.21 1.05 5 5 1 : 25 5 : 15 0 : 16 25.4 22.4 21.2 15.30 0.12 5.0 438 0.132 11493 0.347 30308 1.13 1.20 1.06 5 6 1 : 5 5 : 00 0 : 20 25.2 22.0 20.8 14.44 0.12 5.0 418 0.125 10505 0.412 34595 1.15 1.21 1.05 5 0 3 5 : 49 0 : 24 30.4 23.5 21.8 16.61 0.12 6.1 683 0.252 28011 0.431 47984 1.29 1.39 1.07 5 0 4 5 : 48 0 : 23 29.5 23.1 22.1 16.78 0.12 5.9 639 0.227 24494 0.451 48648 1.28 1.34 1.04 5 0 5 5 : 43 0 : 20 28.8 23.2 21.7 16.42 0.12 5.8 602 0.209 21779 0.396 41272 1.24 1.33 1.07 5 0 6 5 : 32 0 : 21 28.8 23.0 22.2 16.52 0.12 5.7 579 0.197 20122 0.432 44204 1.26 1.30 1.03 5 0 8 5 : 20 0 : 21 27.9 23.0 21.5 15.91 0.12 5.5 530 0.174 16846 0.456 44160 1.21 1.30 1.07 5 2 : 5 0 5 : 50 0 : 19 28.3 23.6 22.9 16.80 0.12 5.7 590 0.202 20920 0.319 33124 1.20 1.23 1.03 5 5 0 5 : 13 0 : 19 25.7 22.3 21.2 15.57 0.12 5.0 441 0.133 11692 0.476 41867 1.15 1.21 1.05 5 8 0 4 : 83 0 : 26 24.0 20.9 19.8 12.80 0.13 4.9 377 0.110 8507 0.553 42819 1.15 1.22 1.06 217

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TableA-7.ATGturbulencestatisticswithwindtunnelthrot tleat28.5%andat X M =10 X M n U 1 95% CI TI X TI Y TI Z Re L 11 Re L 11 L 11 R Re L 11 R I xy I xz I yz Hz m s % % % m 2 s 3 mm mm m m 10 2 1 5 : 42 0 : 18 20.5 18.9 18.3 4.10 0.17 8.2 608 0.300 22195 0.394 29161 1.08 1.12 1.03 10 3 1 : 5 5 : 19 0 : 15 19.6 17.8 17.3 3.79 0.17 7.8 530 0.249 16837 0.372 25170 1.10 1.13 1.02 10 4 2 4 : 97 0 : 16 18.5 17.0 16.4 3.46 0.18 7.4 454 0.202 12351 0.405 24788 1.08 1.13 1.04 10 5 2 : 5 4 : 87 0 : 18 17.7 16.4 15.5 3.11 0.18 7.3 422 0.186 10689 0.513 29488 1.08 1.15 1.06 10 4 1 4 : 97 0 : 16 18.3 16.6 16.3 3.48 0.18 7.3 442 0.194 11720 0.458 27740 1.10 1.12 1.02 10 5 1 : 25 4 : 82 0 : 18 17.5 15.8 15.6 3.09 0.18 7.2 407 0.176 9923 0.501 28253 1.11 1.13 1.02 10 6 1 : 5 4 : 71 0 : 20 16.9 15.5 14.6 2.74 0.19 7.2 384 0.166 8840 0.524 27824 1.09 1.16 1.06 10 0 3 5 : 44 0 : 22 21.5 19.3 18.5 4.10 0.17 8.6 672 0.348 27095 0.488 37937 1.11 1.16 1.04 10 0 4 5 : 30 0 : 20 21.1 18.7 18.4 4.03 0.17 8.4 626 0.315 23537 0.488 36488 1.13 1.15 1.02 10 0 5 5 : 14 0 : 18 20.2 17.6 17.9 3.92 0.17 7.9 548 0.259 18000 0.456 31681 1.15 1.13 0.98 10 0 6 5 : 10 0 : 20 20.8 18.2 17.6 3.79 0.17 8.2 576 0.282 19909 0.487 34400 1.14 1.18 1.03 10 0 8 4 : 96 0 : 22 20.0 17.5 16.6 3.42 0.18 8.0 531 0.256 16939 0.578 38192 1.14 1.20 1.05 10 2 : 5 0 5 : 30 0 : 15 19.7 18.4 18.0 4.08 0.17 7.7 539 0.250 17403 0.353 24582 1.07 1.09 1.02 10 5 0 4 : 80 0 : 19 17.6 15.5 15.2 3.09 0.18 7.2 407 0.176 9918 0.611 34432 1.14 1.16 1.02 10 8 0 4 : 57 0 : 24 16.5 14.8 13.8 2.24 0.20 7.5 378 0.171 8587 0.674 33797 1.11 1.19 1.07 218

PAGE 219

TableA-8.ATGturbulencestatisticswithwindtunnelthrot tleat28.5%andat X M =12 : 5 X M n U 1 95% CI TI X TI Y TI Z Re L 11 Re L 11 L 11 R Re L 11 R I xy I xz I yz Hz m s % % % m 2 s 3 mm mm m m 12.5 2 1 5 : 58 0 : 17 18.0 17.8 16.5 2.80 0.19 9.0 604 0.326 21853 0.402 26942 1.01 1.09 1.08 12.5 3 1 : 5 5 : 30 0 : 18 17.7 16.4 15.8 2.59 0.19 8.7 544 0.284 17745 0.588 36657 1.08 1.12 1.04 12.5 4 2 5 : 07 0 : 18 16.4 15.6 14.8 2.33 0.20 8.2 452 0.222 12285 0.518 28708 1.05 1.10 1.05 12.5 5 2 : 5 4 : 88 0 : 18 15.8 14.7 14.5 2.06 0.20 8.1 414 0.200 10278 0.527 27090 1.07 1.09 1.01 12.5 4 1 5 : 00 0 : 16 16.4 15.1 14.8 2.35 0.19 8.0 436 0.210 11426 0.448 24419 1.09 1.11 1.02 12.5 5 1 : 25 4 : 87 0 : 18 15.6 14.4 14.1 2.03 0.20 8.0 406 0.195 9909 0.542 27481 1.09 1.11 1.02 12.5 6 1 : 5 4 : 74 0 : 19 14.9 14.0 13.6 1.76 0.21 8.0 376 0.180 8466 0.520 24470 1.06 1.09 1.03 12.5 0 3 5 : 48 0 : 21 19.5 18.2 17.9 3.00 0.18 9.3 662 0.368 26273 0.487 34734 1.08 1.09 1.02 12.5 0 4 5 : 36 0 : 21 19.0 17.8 17.2 2.85 0.19 9.0 612 0.332 22498 0.505 34221 1.06 1.10 1.03 12.5 0 5 5 : 27 0 : 19 18.1 16.9 16.7 2.64 0.19 8.8 563 0.298 19018 0.505 32217 1.07 1.08 1.01 12.5 0 6 5 : 31 0 : 21 18.3 17.0 16.1 2.52 0.19 9.2 596 0.329 21309 0.568 36838 1.08 1.14 1.05 12.5 0 8 5 : 14 0 : 22 17.7 16.0 14.9 2.26 0.20 9.1 550 0.300 18165 0.623 37748 1.10 1.18 1.07 12.5 2 : 5 0 5 : 43 0 : 14 17.3 17.0 16.1 2.72 0.19 8.6 538 0.277 17368 0.365 22886 1.02 1.08 1.06 12.5 5 0 4 : 95 0 : 19 15.4 14.2 13.7 1.95 0.20 8.2 415 0.204 10346 0.625 31706 1.08 1.13 1.04 12.5 8 0 4 : 69 0 : 24 14.6 13.8 12.8 1.40 0.22 8.7 397 0.207 9445 0.688 31438 1.06 1.14 1.07 219

PAGE 220

TableA-9.ATGturbulencestatisticswithwindtunnelthrot tleat28.5%andat X M =15 X M n U 1 95% CI TI X TI Y TI Z Re L 11 Re L 11 L 11 R Re L 11 R I xy I xz I yz Hz m s % % % m 2 s 3 mm mm m m 15 2 1 5 : 50 0 : 16 16.6 16.4 16.0 2.11 0.20 9.4 573 0.324 19721 0.424 25822 1.01 1.04 1.03 15 3 1 : 5 5 : 19 0 : 14 15.6 14.8 14.9 1.81 0.21 9.0 488 0.265 14308 0.405 21879 1.05 1.05 1.00 15 4 2 4 : 94 0 : 16 15.0 14.2 13.7 1.57 0.22 8.8 436 0.232 11425 0.500 24657 1.05 1.09 1.04 15 5 2 : 5 4 : 87 0 : 16 14.3 13.4 13.3 1.34 0.22 9.0 417 0.225 10436 0.472 21835 1.07 1.07 1.00 15 4 1 5 : 01 0 : 16 14.8 13.7 13.6 1.50 0.22 9.1 447 0.243 11970 0.477 23515 1.08 1.08 1.01 15 5 1 : 25 4 : 73 0 : 21 14.8 13.5 13.2 1.35 0.22 9.0 420 0.227 10584 0.850 39559 1.09 1.12 1.02 15 6 1 : 5 4 : 65 0 : 17 13.7 12.9 12.4 1.15 0.23 8.9 381 0.204 8694 0.487 20743 1.06 1.11 1.05 15 0 3 5 : 34 0 : 21 18.7 17.7 16.7 2.24 0.20 10.0 666 0.400 26627 0.529 35250 1.06 1.12 1.06 15 0 4 5 : 24 0 : 20 18.2 17.1 16.0 2.14 0.20 9.8 620 0.364 23090 0.523 33196 1.06 1.14 1.07 15 0 5 5 : 27 0 : 19 16.9 15.9 15.5 1.90 0.21 9.7 573 0.333 19693 0.514 30416 1.06 1.08 1.02 15 0 6 5 : 16 0 : 19 17.2 15.3 15.4 1.80 0.21 9.9 588 0.350 20753 0.528 31237 1.13 1.12 0.99 15 0 8 5 : 04 0 : 21 16.6 14.9 14.3 1.56 0.22 10.1 561 0.338 18854 0.650 36248 1.11 1.16 1.04 15 2 : 5 0 5 : 31 0 : 16 15.9 15.1 14.8 1.97 0.20 9.1 512 0.278 15710 0.552 31145 1.05 1.08 1.02 15 5 0 4 : 79 0 : 18 14.3 13.0 12.8 1.28 0.23 9.1 415 0.226 10324 0.651 29758 1.10 1.12 1.02 15 8 0 4 : 54 0 : 23 14.2 13.3 12.5 0.96 0.24 9.9 426 0.252 10870 0.716 30843 1.07 1.14 1.07 220

PAGE 221

TableA-10.ATGturbulencestatisticswithwindtunnelthro ttleat28.5%andat X M =20 X M n U 1 95% CI TI X TI Y TI Z Re L 11 Re L 11 L 11 R Re L 11 R I xy I xz I yz Hz m s % % % m 2 s 3 mm mm m m 20 2 1 5 : 29 0 : 16 15.9 15.2 15.9 1.69 0.21 9.7 543 0.316 17717 0.435 24362 1.04 1.00 0.95 20 3 1 : 5 5 : 10 0 : 14 14.3 13.2 14.4 1.32 0.22 9.5 463 0.264 12850 0.447 21724 1.08 0.99 0.92 20 4 2 4 : 91 0 : 15 13.6 12.6 13.8 1.08 0.24 9.6 429 0.248 11035 0.476 21155 1.08 0.99 0.91 20 5 2 : 5 4 : 79 0 : 16 13.5 12.3 13.3 0.95 0.24 9.9 428 0.256 11013 0.583 25126 1.10 1.01 0.92 20 4 1 4 : 88 0 : 15 13.5 12.7 13.7 1.08 0.24 9.5 417 0.238 10450 0.470 20661 1.06 0.98 0.93 20 5 1 : 25 4 : 73 0 : 17 13.6 12.7 13.3 0.93 0.25 10.0 430 0.258 11092 0.585 25141 1.07 1.02 0.95 20 6 1 : 5 4 : 67 0 : 16 13.3 12.3 13.0 0.82 0.25 10.3 425 0.262 10835 0.524 21689 1.08 1.02 0.95 20 0 3 5 : 17 0 : 22 18.1 17.0 17.0 1.83 0.21 10.4 651 0.406 25419 0.573 35827 1.07 1.07 1.00 20 0 4 5 : 13 0 : 20 17.5 15.6 16.1 1.63 0.21 10.5 627 0.395 23551 0.573 34178 1.12 1.08 0.97 20 0 5 5 : 06 0 : 19 16.5 15.2 15.9 1.49 0.22 10.3 571 0.351 19532 0.568 31601 1.09 1.04 0.96 20 0 6 5 : 03 0 : 21 16.4 15.2 15.5 1.41 0.22 10.4 574 0.359 19761 0.686 37741 1.08 1.06 0.98 20 0 8 4 : 90 0 : 19 15.2 14.0 14.4 1.19 0.23 10.3 509 0.313 15541 0.635 31532 1.09 1.05 0.97 20 2 : 5 0 5 : 16 0 : 14 14.7 13.6 14.7 1.50 0.22 9.3 469 0.261 13201 0.455 22991 1.08 1.00 0.92 20 5 0 4 : 74 0 : 19 13.7 12.3 13.2 0.88 0.25 10.3 445 0.276 11891 0.689 29712 1.11 1.03 0.93 20 8 0 4 : 52 0 : 21 14.0 13.0 13.2 0.75 0.26 11.0 466 0.308 13037 0.711 30105 1.08 1.06 0.98 221

PAGE 222

TableA-11.ATGturbulencestatisticswithwindtunnelthro ttleat43.5%andat X M =5 X M n U 1 95% CI TI X TI Y TI Z Re L 11 Re L 11 L 11 R Re L 11 R I xy I xz I yz Hz m s % % % m 2 s 3 mm mm m m 5 2 1 8 : 42 0 : 31 31.4 23.4 22.6 32.34 0.10 7.0 1230 0.515 90793 0.428 75415 1.34 1.39 1.04 5 3 1 : 5 8 : 41 0 : 26 29.7 23.9 22.7 32.16 0.10 6.6 1098 0.435 72353 0.366 60860 1.24 1.31 1.05 5 4 2 8 : 26 0 : 24 28.7 23.9 23.1 32.67 0.10 6.2 986 0.369 58360 0.336 53125 1.20 1.25 1.04 5 5 2 : 5 8 : 22 0 : 22 27.6 23.8 22.8 32.08 0.10 6.0 909 0.328 49594 0.316 47863 1.16 1.21 1.05 5 4 1 8 : 32 0 : 23 28.5 24.1 22.8 32.41 0.10 6.2 987 0.370 58436 0.327 51622 1.18 1.25 1.05 5 5 1 : 25 8 : 20 0 : 21 27.6 23.8 22.8 32.42 0.10 6.0 898 0.321 48385 0.308 46446 1.16 1.21 1.04 5 6 1 : 5 8 : 05 0 : 22 27.3 23.6 22.5 32.26 0.10 5.8 849 0.295 43215 0.362 53040 1.15 1.21 1.05 5 0 3 8 : 30 0 : 36 32.8 23.5 22.1 32.64 0.10 7.1 1295 0.555 100619 0.502 91102 1.39 1.49 1.07 5 0 4 8 : 36 0 : 35 31.6 23.5 22.1 32.50 0.10 6.9 1222 0.509 89648 0.517 90915 1.34 1.43 1.07 5 0 5 8 : 39 0 : 30 30.5 23.5 22.3 32.29 0.10 6.8 1154 0.468 79864 0.444 75755 1.30 1.37 1.06 5 0 6 8 : 39 0 : 30 29.9 23.4 22.3 31.91 0.10 6.7 1113 0.445 74367 0.466 77907 1.28 1.34 1.05 5 0 8 8 : 23 0 : 29 29.5 23.8 22.2 32.34 0.10 6.4 1034 0.397 64144 0.475 76865 1.24 1.33 1.07 5 2 : 5 0 8 : 48 0 : 28 30.6 23.3 22.7 32.08 0.10 6.9 1185 0.488 84321 0.386 66727 1.31 1.35 1.03 5 5 0 8 : 23 0 : 21 27.7 24.3 22.7 32.60 0.10 6.0 908 0.326 49482 0.303 45933 1.14 1.22 1.07 5 8 0 7 : 53 0 : 44 28.9 22.8 21.8 31.16 0.10 5.8 847 0.297 43065 0.873 126580 1.27 1.32 1.04 222

PAGE 223

TableA-12.ATGturbulencestatisticswithwindtunnelthro ttleat43.5%andat X M =10 X M n U 1 95% CI TI X TI Y TI Z Re L 11 Re L 11 L 11 R Re L 11 R I xy I xz I yz Hz m s % % % m 2 s 3 mm mm m m 10 2 1 8 : 53 0 : 27 21.4 20.0 19.2 8.18 0.14 9.6 1170 0.673 82085 0.446 54384 1.07 1.11 1.04 10 3 1 : 5 8 : 34 0 : 23 20.6 19.1 19.0 8.19 0.14 9.0 1029 0.555 63503 0.403 46135 1.08 1.08 1.00 10 4 2 8 : 11 0 : 20 20.0 18.2 18.3 7.99 0.14 8.6 936 0.485 52524 0.382 41402 1.10 1.09 0.99 10 5 2 : 5 7 : 93 0 : 19 19.5 17.7 17.5 7.63 0.15 8.4 861 0.433 44496 0.402 41298 1.10 1.11 1.01 10 4 1 8 : 07 0 : 19 19.9 18.4 18.1 8.06 0.14 8.5 907 0.462 49381 0.371 39641 1.08 1.10 1.02 10 5 1 : 25 7 : 86 0 : 19 19.5 17.6 17.7 7.80 0.14 8.2 842 0.416 42494 0.436 44585 1.11 1.10 1.00 10 6 1 : 5 7 : 70 0 : 22 18.5 16.9 16.9 7.40 0.15 7.9 751 0.355 33821 0.416 39632 1.10 1.09 1.00 10 0 3 8 : 40 0 : 31 22.6 19.6 19.5 8.22 0.14 9.9 1256 0.748 94683 0.531 67135 1.15 1.16 1.01 10 0 4 8 : 39 0 : 29 21.9 19.5 19.0 8.38 0.14 9.5 1172 0.671 82458 0.524 64336 1.12 1.15 1.02 10 0 5 8 : 25 0 : 26 21.5 19.2 18.9 8.26 0.14 9.3 1099 0.612 72463 0.482 57115 1.12 1.14 1.01 10 0 6 8 : 22 0 : 27 21.5 18.9 18.7 8.22 0.14 9.2 1085 0.601 70630 0.502 59002 1.14 1.15 1.01 10 0 8 8 : 03 0 : 28 21.0 18.5 17.8 7.88 0.14 9.0 1014 0.549 61706 0.540 60716 1.14 1.18 1.04 10 2 : 5 0 8 : 41 0 : 24 20.8 19.6 19.3 8.37 0.14 9.1 1062 0.579 67648 0.393 45898 1.06 1.08 1.01 10 5 0 7 : 82 0 : 20 19.0 17.8 17.6 7.71 0.14 8.0 798 0.385 38219 0.487 48338 1.07 1.08 1.01 10 8 0 7 : 28 0 : 39 19.9 16.0 16.2 6.61 0.15 8.5 819 0.416 40247 0.968 93594 1.25 1.23 0.99 223

PAGE 224

TableA-13.ATGturbulencestatisticswithwindtunnelthro ttleat43.5%andat X M =12 : 5 X M n U 1 95% CI TI X TI Y TI Z Re L 11 Re L 11 L 11 R Re L 11 R I xy I xz I yz Hz m s % % % m 2 s 3 mm mm m m 12.5 2 1 8 : 68 0 : 26 19.1 18.5 18.0 5.68 0.16 10.5 1158 0.726 80464 0.456 50488 1.04 1.06 1.02 12.5 3 1 : 5 8 : 46 0 : 21 18.2 17.7 17.3 5.59 0.16 9.8 1002 0.587 60203 0.409 41943 1.03 1.05 1.02 12.5 4 2 8 : 25 0 : 19 17.6 16.5 16.4 5.23 0.16 9.5 921 0.526 50918 0.399 38574 1.07 1.07 1.01 12.5 5 2 : 5 8 : 04 0 : 18 17.1 16.1 15.8 4.91 0.16 9.3 858 0.481 44175 0.429 39474 1.07 1.08 1.02 12.5 4 1 8 : 24 0 : 19 17.4 16.4 16.5 5.28 0.16 9.4 897 0.504 48273 0.415 39681 1.06 1.06 1.00 12.5 5 1 : 25 7 : 99 0 : 18 16.8 15.8 15.8 4.91 0.16 9.1 808 0.440 39215 0.428 38217 1.06 1.06 1.00 12.5 6 1 : 5 7 : 84 0 : 22 16.2 15.1 14.9 4.55 0.17 8.9 759 0.408 34602 0.495 42014 1.07 1.09 1.02 12.5 0 3 8 : 47 0 : 31 20.7 19.0 18.5 5.84 0.16 10.9 1275 0.833 97462 0.557 65169 1.09 1.12 1.02 12.5 0 4 8 : 25 0 : 27 20.2 18.3 18.0 6.02 0.15 10.2 1134 0.694 77140 0.527 58650 1.11 1.12 1.02 12.5 0 5 7 : 95 0 : 25 19.3 17.4 18.2 6.09 0.15 9.3 956 0.535 54811 0.492 50349 1.11 1.06 0.96 12.5 0 6 7 : 87 0 : 25 19.4 17.3 18.1 6.08 0.15 9.3 945 0.527 53589 0.511 51998 1.12 1.07 0.95 12.5 0 8 7 : 60 0 : 25 18.6 16.5 17.2 5.79 0.16 8.8 833 0.441 41622 0.573 54107 1.13 1.09 0.96 12.5 2 : 5 0 7 : 96 0 : 20 18.4 17.3 18.3 6.33 0.15 8.7 852 0.446 43560 0.388 37822 1.06 1.01 0.95 12.5 5 0 7 : 32 0 : 20 17.1 15.2 16.5 5.65 0.16 7.9 661 0.314 26195 0.571 47724 1.13 1.04 0.92 12.5 8 0 6 : 73 0 : 31 17.2 14.2 15.2 4.50 0.17 8.2 631 0.310 23861 0.816 62940 1.21 1.13 0.93 224

PAGE 225

TableA-14.ATGturbulencestatisticswithwindtunnelthro ttleat43.5%andat X M =15 X M n U 1 95% CI TI X TI Y TI Z Re L 11 Re L 11 L 11 R Re L 11 R I xy I xz I yz Hz m s % % % m 2 s 3 mm mm m m 15 2 1 8 : 51 0 : 26 18.6 18.5 17.6 4.81 0.16 10.8 1148 0.747 79019 0.466 49314 1.01 1.06 1.05 15 3 1 : 5 8 : 33 0 : 20 17.2 16.8 16.4 4.56 0.16 10.1 966 0.585 56033 0.419 40102 1.03 1.05 1.02 15 4 2 8 : 10 0 : 18 16.3 15.6 15.5 4.14 0.17 9.7 856 0.500 43983 0.405 35609 1.05 1.05 1.00 15 5 2 : 5 7 : 86 0 : 19 16.0 15.3 14.8 3.86 0.17 9.6 800 0.459 38375 0.430 35909 1.04 1.08 1.03 15 4 1 8 : 06 0 : 18 16.2 15.6 15.4 4.23 0.17 9.5 826 0.471 40930 0.442 38389 1.04 1.05 1.02 15 5 1 : 25 7 : 82 0 : 21 15.8 15.1 14.9 3.87 0.17 9.4 774 0.437 35952 0.445 36611 1.05 1.06 1.01 15 6 1 : 5 7 : 49 0 : 21 15.4 14.7 13.8 3.55 0.18 9.2 703 0.386 29623 0.474 36351 1.04 1.12 1.07 15 0 3 8 : 25 0 : 30 20.1 18.5 17.7 4.94 0.16 11.2 1240 0.833 92232 0.567 62745 1.09 1.14 1.05 15 0 4 8 : 21 0 : 30 19.6 18.0 17.5 4.86 0.16 11.0 1176 0.773 82960 0.624 66969 1.09 1.12 1.03 15 0 5 8 : 18 0 : 25 18.3 17.4 17.0 4.65 0.16 10.4 1040 0.650 64849 0.500 49874 1.05 1.08 1.02 15 0 6 8 : 13 0 : 26 18.3 17.2 16.6 4.50 0.17 10.5 1041 0.657 65077 0.531 52586 1.06 1.10 1.04 15 0 8 7 : 94 0 : 25 17.3 16.3 15.8 4.10 0.17 10.2 927 0.565 51601 0.588 53723 1.06 1.09 1.03 15 2 : 5 0 8 : 40 0 : 20 17.1 17.3 16.6 4.80 0.16 9.8 937 0.551 52638 0.404 38563 0.98 1.03 1.05 15 5 0 7 : 75 0 : 22 15.8 14.9 15.0 3.93 0.17 9.3 759 0.423 34571 0.574 46964 1.06 1.06 0.99 15 8 0 7 : 20 0 : 30 15.8 13.6 13.4 2.96 0.18 9.9 754 0.449 34077 0.852 64679 1.16 1.18 1.02 225

PAGE 226

TableA-15.ATGturbulencestatisticswithwindtunnelthro ttleat43.5%andat X M =20 X M n U 1 95% CI TI X TI Y TI Z Re L 11 Re L 11 L 11 R Re L 11 R I xy I xz I yz Hz m s % % % m 2 s 3 mm mm m m 20 2 1 8 : 35 0 : 24 17.5 17.0 17.5 3.93 0.17 11.1 1080 0.718 70046 0.481 46942 1.03 1.00 0.97 20 3 1 : 5 8 : 04 0 : 19 15.8 14.7 16.5 3.59 0.18 10.0 851 0.513 43422 0.431 36471 1.07 0.96 0.89 20 4 2 7 : 79 0 : 17 14.8 13.6 15.4 3.09 0.18 9.9 760 0.450 34635 0.427 32886 1.09 0.96 0.88 20 5 2 : 5 7 : 62 0 : 18 14.3 13.0 15.1 2.82 0.19 9.7 707 0.412 29953 0.446 32383 1.10 0.94 0.86 20 4 1 7 : 74 0 : 17 14.8 13.6 15.2 3.17 0.18 9.6 736 0.426 32516 0.431 32860 1.08 0.97 0.90 20 5 1 : 25 7 : 55 0 : 18 14.3 13.1 14.7 2.80 0.19 9.7 693 0.401 28823 0.448 32190 1.09 0.97 0.89 20 6 1 : 5 7 : 40 0 : 18 13.9 12.5 14.3 2.47 0.19 9.9 677 0.400 27515 0.479 32919 1.12 0.97 0.87 20 0 3 7 : 69 0 : 29 20.0 17.8 19.0 4.37 0.17 11.0 1128 0.745 76285 0.569 58225 1.12 1.05 0.94 20 0 4 7 : 75 0 : 26 19.0 16.7 18.2 4.14 0.17 10.8 1064 0.692 67939 0.545 53432 1.14 1.05 0.92 20 0 5 7 : 77 0 : 25 17.9 15.9 17.6 3.85 0.17 10.6 982 0.625 57816 0.527 48708 1.12 1.02 0.91 20 0 6 7 : 65 0 : 25 17.6 16.0 17.2 3.75 0.17 10.4 939 0.589 52898 0.552 49623 1.10 1.02 0.93 20 0 8 7 : 60 0 : 21 16.0 14.7 15.8 3.22 0.18 10.2 827 0.505 41016 0.512 41550 1.09 1.02 0.93 20 2 : 5 0 8 : 15 0 : 18 15.8 15.1 16.1 3.89 0.17 9.8 839 0.493 42260 0.413 35427 1.04 0.98 0.94 20 5 0 7 : 68 0 : 22 14.2 13.1 14.0 2.67 0.19 10.0 731 0.440 32060 0.642 46794 1.09 1.02 0.94 20 8 0 7 : 23 0 : 27 14.5 12.5 13.3 2.07 0.20 10.9 762 0.499 34855 0.888 62033 1.16 1.09 0.93 226

PAGE 227

TableA-16.ATGturbulencestatisticswithwindtunnelthro ttleat58%andat X M =5 X M n U 1 95% CI TI X TI Y TI Z Re L 11 Re L 11 L 11 R Re L 11 R I xy I xz I yz Hz m s % % % m 2 s 3 mm mm m m 5 2 1 11 : 05 0 : 42 33.4 23.6 22.1 48.31 0.09 8.0 1963 0.939 231102 0.487 120001 1.42 1.51 1.07 5 3 1 : 5 11 : 13 0 : 35 31.3 24.1 22.5 48.62 0.09 7.5 1742 0.784 182146 0.413 95877 1.30 1.39 1.07 5 4 2 11 : 11 0 : 31 30.1 24.5 22.8 48.81 0.09 7.2 1603 0.691 154095 0.369 82271 1.23 1.32 1.07 5 5 2 : 5 10 : 83 0 : 29 29.9 25.1 23.2 49.19 0.09 6.9 1496 0.622 134236 0.351 75775 1.19 1.29 1.08 5 4 1 11 : 08 0 : 30 30.1 24.5 22.9 48.85 0.09 7.2 1592 0.684 151989 0.360 79972 1.23 1.32 1.07 5 5 1 : 25 11 : 04 0 : 28 29.0 25.0 23.1 49.15 0.09 6.9 1463 0.601 128360 0.331 70741 1.16 1.26 1.08 5 6 1 : 5 10 : 51 0 : 40 30.2 25.2 23.5 50.40 0.09 6.7 1422 0.573 121296 0.591 125163 1.20 1.28 1.07 5 0 3 10 : 96 0 : 47 33.9 23.3 21.8 48.74 0.09 8.0 1977 0.947 234475 0.559 138512 1.45 1.56 1.07 5 0 4 10 : 95 0 : 43 33.1 24.1 22.1 48.86 0.09 7.8 1876 0.875 211251 0.529 127783 1.37 1.50 1.09 5 0 5 10 : 97 0 : 37 31.7 24.2 22.6 48.59 0.09 7.5 1734 0.779 180479 0.444 103019 1.31 1.40 1.07 5 0 6 10 : 87 0 : 38 31.8 24.3 23.0 49.55 0.09 7.4 1692 0.747 171821 0.486 111734 1.30 1.38 1.06 5 0 8 10 : 87 0 : 38 30.9 24.2 23.0 49.02 0.09 7.2 1614 0.697 156249 0.515 115436 1.28 1.35 1.05 5 2 : 5 0 11 : 07 0 : 37 32.2 23.9 22.2 49.09 0.09 7.6 1813 0.830 197233 0.427 101403 1.35 1.45 1.08 5 5 0 10 : 97 0 : 28 29.1 24.9 23.4 49.55 0.09 6.8 1446 0.590 125374 0.327 69628 1.17 1.24 1.07 5 8 0 9 : 52 0 : 53 31.9 25.5 23.3 51.17 0.09 6.4 1288 0.492 99553 0.834 168783 1.25 1.37 1.09 227

PAGE 228

TableA-17.ATGturbulencestatisticswithwindtunnelthro ttleat58%andat X M =10 X M n U 1 95% CI TI X TI Y TI Z Re L 11 Re L 11 L 11 R Re L 11 R I xy I xz I yz Hz m s % % % m 2 s 3 mm mm m m 10 2 1 11 : 23 0 : 36 22.4 20.9 19.6 12.84 0.13 10.5 1764 1.113 186608 0.486 81410 1.07 1.14 1.07 10 3 1 : 5 11 : 19 0 : 31 21.4 20.2 19.7 12.90 0.13 10.0 1592 0.954 152068 0.435 69343 1.06 1.09 1.02 10 4 2 10 : 98 0 : 26 20.9 19.1 19.0 12.94 0.13 9.6 1465 0.841 128702 0.398 60916 1.10 1.10 1.01 10 5 2 : 5 10 : 69 0 : 24 20.6 19.0 18.8 12.77 0.13 9.3 1360 0.755 110931 0.396 58147 1.09 1.09 1.01 10 4 1 11 : 01 0 : 25 20.8 19.2 19.0 12.95 0.13 9.5 1456 0.834 127201 0.390 59498 1.08 1.10 1.01 10 5 1 : 25 10 : 70 0 : 25 20.4 18.9 18.4 12.80 0.13 9.1 1331 0.730 106243 0.439 63828 1.08 1.11 1.03 10 6 1 : 5 10 : 29 0 : 34 21.0 18.8 18.5 12.70 0.13 9.1 1306 0.712 102413 0.711 102205 1.12 1.14 1.02 10 0 3 11 : 12 0 : 41 23.4 19.8 19.1 12.77 0.13 10.9 1894 1.241 215179 0.614 106526 1.18 1.23 1.04 10 0 4 11 : 14 0 : 37 22.6 19.8 19.3 12.76 0.13 10.6 1775 1.126 189119 0.571 95854 1.14 1.17 1.02 10 0 5 11 : 10 0 : 33 22.2 20.0 19.3 12.94 0.13 10.3 1685 1.038 170402 0.492 80800 1.11 1.15 1.04 10 0 6 11 : 09 0 : 35 22.1 19.7 19.0 12.83 0.13 10.3 1681 1.036 169506 0.562 91940 1.12 1.16 1.03 10 0 8 10 : 82 0 : 36 21.9 19.5 18.8 12.79 0.13 10.0 1574 0.940 148607 0.648 102435 1.12 1.17 1.04 10 2 : 5 0 11 : 23 0 : 31 21.4 20.2 19.8 12.93 0.13 10.0 1606 0.966 154710 0.432 69185 1.06 1.08 1.02 10 5 0 10 : 80 0 : 23 20.2 18.8 18.6 12.74 0.13 9.2 1339 0.738 107636 0.368 53593 1.08 1.09 1.01 10 8 0 9 : 41 0 : 47 21.9 17.9 18.4 12.11 0.13 8.9 1225 0.654 90012 0.895 123188 1.23 1.20 0.97 228

PAGE 229

TableA-18.ATGturbulencestatisticswithwindtunnelthro ttleat58%andat X M =12 : 5 X M n U 1 95% CI TI X TI Y TI Z Re L 11 Re L 11 L 11 R Re L 11 R I xy I xz I yz Hz m s % % % m 2 s 3 mm mm m m 12.5 2 1 11 : 49 0 : 35 20.2 19.3 18.7 9.22 0.14 11.5 1773 1.219 188649 0.504 77946 1.05 1.08 1.03 12.5 3 1 : 5 11 : 48 0 : 28 18.8 18.6 18.1 9.15 0.14 10.7 1547 0.995 143528 0.439 63282 1.01 1.04 1.03 12.5 4 2 11 : 31 0 : 25 18.4 17.8 17.6 9.05 0.14 10.4 1442 0.898 124757 0.413 57378 1.03 1.05 1.01 12.5 5 2 : 5 10 : 96 0 : 25 18.4 17.5 17.2 8.84 0.14 10.2 1366 0.833 111981 0.469 63073 1.05 1.07 1.02 12.5 4 1 11 : 25 0 : 24 18.4 17.5 17.7 9.09 0.14 10.3 1417 0.875 120529 0.400 55167 1.05 1.04 0.99 12.5 5 1 : 25 10 : 96 0 : 23 18.0 17.0 17.0 8.86 0.14 9.9 1303 0.775 101806 0.442 58036 1.06 1.05 1.00 12.5 6 1 : 5 10 : 42 0 : 34 18.6 16.7 17.2 8.70 0.14 9.8 1271 0.751 96928 0.701 90512 1.11 1.08 0.98 12.5 0 3 11 : 15 0 : 40 21.8 19.4 18.7 9.45 0.14 11.9 1921 1.367 221457 0.608 98559 1.12 1.16 1.04 12.5 0 4 11 : 20 0 : 36 20.6 19.5 18.5 9.32 0.14 11.4 1750 1.192 183706 0.549 84613 1.06 1.12 1.05 12.5 0 5 11 : 20 0 : 32 19.9 19.1 18.3 9.26 0.14 11.0 1633 1.077 159986 0.507 75375 1.04 1.08 1.04 12.5 0 6 11 : 12 0 : 34 20.2 18.9 18.1 9.33 0.14 11.0 1656 1.097 164483 0.584 87540 1.07 1.12 1.04 12.5 0 8 10 : 96 0 : 32 19.3 18.0 17.5 8.93 0.14 10.6 1496 0.952 134264 0.614 86618 1.07 1.11 1.03 12.5 2 : 5 0 11 : 45 0 : 30 18.9 19.6 18.4 9.32 0.14 10.6 1535 0.979 141317 0.427 61616 0.97 1.03 1.06 12.5 5 0 10 : 93 0 : 24 18.1 17.1 17.2 8.87 0.14 9.9 1310 0.781 102892 0.479 63049 1.06 1.05 0.99 12.5 8 0 9 : 56 0 : 42 19.3 16.4 16.7 7.85 0.14 9.9 1212 0.718 88208 0.860 105627 1.18 1.16 0.98 229

PAGE 230

TableA-19.ATGturbulencestatisticswithwindtunnelthro ttleat58%andat X M =15 X M n U 1 95% CI TI X TI Y TI Z Re L 11 Re L 11 L 11 R Re L 11 R I xy I xz I yz Hz m s % % % m 2 s 3 mm mm m m 15 2 1 11 : 14 0 : 33 19.6 19.4 18.1 7.86 0.14 11.7 1702 1.194 173795 0.500 72784 1.01 1.08 1.07 15 3 1 : 5 11 : 15 0 : 27 18.1 17.9 17.0 7.56 0.15 11.0 1488 0.985 132812 0.447 60223 1.01 1.07 1.05 15 4 2 10 : 97 0 : 24 17.3 17.1 16.7 7.27 0.15 10.5 1331 0.842 106342 0.435 54898 1.01 1.03 1.02 15 5 2 : 5 10 : 69 0 : 23 17.2 16.3 16.1 6.95 0.15 10.4 1275 0.798 97572 0.456 55743 1.06 1.07 1.01 15 4 1 10 : 99 0 : 23 17.1 16.5 16.7 7.27 0.15 10.4 1304 0.816 102040 0.415 51946 1.03 1.02 0.99 15 5 1 : 25 10 : 72 0 : 21 16.5 15.8 15.8 6.82 0.15 10.2 1206 0.737 87208 0.428 50652 1.05 1.05 1.00 15 6 1 : 5 10 : 28 0 : 29 16.9 15.6 15.8 6.66 0.15 10.1 1173 0.712 82519 0.648 75174 1.08 1.07 0.99 15 0 3 10 : 76 0 : 40 21.5 19.2 18.4 7.96 0.14 12.3 1900 1.404 216691 0.655 101089 1.12 1.17 1.05 15 0 4 10 : 91 0 : 35 20.3 18.6 17.8 7.77 0.14 11.9 1764 1.263 186757 0.574 84910 1.09 1.14 1.04 15 0 5 10 : 89 0 : 32 19.6 18.4 17.7 7.69 0.14 11.6 1651 1.147 163621 0.531 75726 1.06 1.11 1.04 15 0 6 10 : 87 0 : 32 19.2 17.8 17.5 7.57 0.15 11.4 1583 1.081 150383 0.547 76054 1.08 1.10 1.02 15 0 8 10 : 68 0 : 33 18.4 17.3 16.9 7.21 0.15 11.0 1435 0.944 123587 0.653 85440 1.06 1.09 1.02 15 2 : 5 0 11 : 04 0 : 28 18.1 18.5 17.9 7.86 0.14 10.7 1420 0.910 121038 0.436 57958 0.97 1.01 1.04 15 5 0 10 : 52 0 : 22 16.8 15.7 16.1 7.06 0.15 10.0 1178 0.706 83205 0.476 56128 1.07 1.04 0.98 15 8 0 9 : 28 0 : 39 17.8 15.7 15.9 6.03 0.15 10.1 1113 0.674 74296 0.853 94017 1.14 1.12 0.99 230

PAGE 231

TableA-20.ATGturbulencestatisticswithwindtunnelthro ttleat58%andat X M =20 X M n U 1 95% CI TI X TI Y TI Z Re L 11 Re L 11 L 11 R Re L 11 R I xy I xz I yz Hz m s % % % m 2 s 3 mm mm m m 20 2 1 11 : 05 0 : 33 18.9 18.7 18.1 6.48 0.15 12.3 1706 1.258 174710 0.515 71598 1.01 1.04 1.03 20 3 1 : 5 11 : 22 0 : 27 16.8 16.5 16.8 5.88 0.15 11.7 1464 1.023 128514 0.465 58451 1.01 1.00 0.99 20 4 2 11 : 10 0 : 24 15.8 15.2 15.6 5.33 0.16 11.4 1329 0.908 106005 0.460 53770 1.04 1.01 0.97 20 5 2 : 5 10 : 83 0 : 25 15.7 14.9 15.1 4.96 0.16 11.4 1293 0.886 100279 0.547 61925 1.05 1.04 0.99 20 4 1 11 : 13 0 : 23 15.5 15.0 15.4 5.26 0.16 11.3 1296 0.877 100738 0.445 51174 1.03 1.01 0.97 20 5 1 : 25 10 : 88 0 : 23 15.0 14.3 14.6 4.83 0.16 11.1 1206 0.804 87283 0.460 49915 1.04 1.02 0.98 20 6 1 : 5 10 : 47 0 : 29 15.4 14.1 14.7 4.52 0.17 11.4 1222 0.834 89590 0.751 80708 1.09 1.05 0.96 20 0 3 10 : 64 0 : 38 20.6 19.3 18.6 6.52 0.15 12.9 1885 1.458 213222 0.616 90138 1.07 1.11 1.04 20 0 4 10 : 72 0 : 37 19.7 18.4 18.0 6.31 0.15 12.6 1775 1.343 189044 0.670 94384 1.07 1.09 1.02 20 0 5 10 : 86 0 : 32 18.5 17.8 17.3 6.05 0.15 12.3 1644 1.210 162203 0.566 75823 1.04 1.07 1.03 20 0 6 10 : 83 0 : 34 18.4 17.2 17.0 5.86 0.15 12.3 1639 1.214 161269 0.639 84830 1.07 1.08 1.01 20 0 8 10 : 77 0 : 30 17.1 16.4 16.1 5.37 0.16 11.9 1465 1.049 128791 0.608 74654 1.05 1.06 1.02 20 2 : 5 0 11 : 25 0 : 26 17.1 17.2 16.9 6.34 0.15 11.4 1465 1.006 128811 0.446 57114 0.99 1.01 1.02 20 5 0 10 : 83 0 : 26 15.1 14.3 14.6 4.85 0.16 11.1 1208 0.805 87562 0.620 67405 1.05 1.03 0.98 20 8 0 9 : 70 0 : 34 16.1 14.7 14.4 3.98 0.17 11.7 1221 0.860 89479 0.817 85001 1.10 1.12 1.02 231

PAGE 232

Meancorevelocity9.54ms 1 Y(cm)Z(cm)Meancorevelocity7.38ms 1Z(cm)Meancorevelocity5.16ms 1Z(cm)Meancorevelocity2.63ms 1Z(cm) 20 0 20 0 2 4 6 8 20 10 0 10 20 0 2 4 6 8 10 20 10 0 10 20 2 4 6 8 20 10 0 10 20 0 2 4 6 20 10 0 10 20 FigureA-1.Measuredpercentvariationfromcorefor U 1 withrunmode n=0 ;! =3 232

PAGE 233

Meancorevelocity9.42ms 1 Y(cm)Z(cm)Meancorevelocity6.90ms 1Z(cm)Meancorevelocity4.46ms 1Z(cm)Meancorevelocity2.22ms 1Z(cm) 20 0 20 0 2 4 6 20 10 0 10 20 0 2 4 6 20 10 0 10 20 0 1 2 3 4 20 10 0 10 20 0 1 2 3 4 5 20 10 0 10 20 FigureA-2.Measuredpercentvariationfromcorefor U 1 withrunmode n=0 ;! =8 233

PAGE 234

MeancoreTI X =1.7%atmeancorevelocityof9.57ms 1 Y(cm)Z(cm)MeancoreTI X =2.3%atmeancorevelocityof7.23ms 1Z(cm)MeancoreTI X =1.6%atmeancorevelocityof4.86ms 1Z(cm)MeancoreTI X =1.7%atmeancorevelocityof2.45ms 1Z(cm) 20 020 0 50 100 150 200 20 10 0 10 20 50 100 150 200 20 10 0 10 20 0 50 100 150 200 20 10 0 10 20 50 100 150 200 20 10 0 10 20 FigureA-3.Measuredpercentvariationfromcorefor TI X withbaselineow 234

PAGE 235

MeancoreTI X =18.8%atmeancorevelocityof9.48ms 1 Y(cm)Z(cm)MeancoreTI X =17.9%atmeancorevelocityof7.21ms 1Z(cm)MeancoreTI X =16.9%atmeancorevelocityof4.87ms 1Z(cm)MeancoreTI X =14.2%atmeancorevelocityof2.48ms 1Z(cm) 200 20 5 10 15 20 25 20 10 0 10 20 0 5 10 15 20 20 10 0 10 20 0 5 10 15 20 25 20 10 0 10 20 0 10 20 30 20 10 0 10 20 FigureA-4.Measuredpercentvariationfromcorefor TI X withrunmode n=2 : 5 ;! =0 235

PAGE 236

MeancoreTI X =21.8%atmeancorevelocityof9.54ms 1 Y(cm)Z(cm)MeancoreTI X =20.7%atmeancorevelocityof7.38ms 1Z(cm)MeancoreTI X =19.6%atmeancorevelocityof5.16ms 1Z(cm)MeancoreTI X =17.7%atmeancorevelocityof2.63ms 1Z(cm) 20020 0 10 20 30 20 10 0 10 20 5 10 15 20 25 30 20 10 0 10 20 0 5 10 15 20 25 20 10 0 10 20 5 10 15 20 25 20 10 0 10 20 FigureA-5.Measuredpercentvariationfromcorefor TI X withrunmode n=0 ;! =3 236

PAGE 237

MeancoreTI X =3.9%atmeancorevelocityof9.58ms 1 Y(cm)Z(cm)MeancoreTI X =3.9%atmeancorevelocityof7.14ms 1Z(cm)MeancoreTI X =3.8%atmeancorevelocityof4.75ms 1Z(cm)MeancoreTI X =3.7%atmeancorevelocityof2.37ms 1Z(cm) 20020 20 40 60 80 100 20 10 0 10 20 20 40 60 80 100 20 10 0 10 20 20 40 60 80 100 20 10 0 10 20 0 20 40 60 80 100 20 10 0 10 20 FigureA-6.Measuredpercentvariationfromcorefor TI X withstaticgrid 237

PAGE 238

MeancoreI XZ =0.95atmeancorevelocityof9.48ms 1 Y(cm)Z(cm)MeancoreI XZ =0.94atmeancorevelocityof7.21ms 1Z(cm)MeancoreI XZ =0.97atmeancorevelocityof4.87ms 1Z(cm)MeancoreI XZ =0.99atmeancorevelocityof2.48ms 1Z(cm) 20020 5 10 15 20 10 0 10 20 0 5 10 15 20 20 10 0 10 20 5 10 15 20 10 0 10 20 5 10 15 20 20 10 0 10 20 FigureA-7.Measuredpercentvariationfromcorefor I xz withrunmode n=2 : 5 ;! =0 238

PAGE 239

MeancoreI XZ =1.01atmeancorevelocityof9.42ms 1 Y(cm)Z(cm)MeancoreI XZ =1.02atmeancorevelocityof6.90ms 1Z(cm)MeancoreI XZ =1.05atmeancorevelocityof4.46ms 1Z(cm)MeancoreI XZ =1.10atmeancorevelocityof2.22ms 1Z(cm) 20020 5 10 15 20 10 0 10 20 0 5 10 15 20 10 0 10 20 5 10 15 20 10 0 10 20 0 5 10 15 20 20 10 0 10 20 FigureA-8.Measuredpercentvariationfromcorefor I xz withrunmode n=0 ;! =8 239

PAGE 240

MeancoreI XZ =1.03atmeancorevelocityof9.58ms 1 Y(cm)Z(cm)MeancoreI XZ =1.04atmeancorevelocityof7.14ms 1Z(cm)MeancoreI XZ =1.04atmeancorevelocityof4.75ms 1Z(cm)MeancoreI XZ =1.06atmeancorevelocityof2.37ms 1Z(cm) 20020 0 5 10 15 20 10 0 10 20 5 10 15 20 10 0 10 20 5 10 15 20 20 10 0 10 20 0 10 20 30 20 10 0 10 20 FigureA-9.Measuredpercentvariationfromcorefor I xz withstaticgrid 240

PAGE 241

Meancore L 11 R =0.40matmeancorevelocityof9.48ms 1 Y(cm)Z(cm)Meancore L 11 R =0.37matmeancorevelocityof7.21ms 1Z(cm)Meancore L 11 R =0.40matmeancorevelocityof4.87ms 1Z(cm)Meancore L 11 R =0.46matmeancorevelocityof2.48ms 1Z(cm) 20 0 20 0 10 20 30 40 20 10 0 10 20 10 20 30 40 50 20 10 0 10 20 10 20 30 40 50 20 10 0 10 20 0 10 20 30 40 20 10 0 10 20 FigureA-10.Measuredpercentvariationfromcorefor L 11 R withrunmode n=2 : 5 ;! =0 241

PAGE 242

Meancore L 11 R =0.57matmeancorevelocityof9.54ms 1 Y(cm)Z(cm)Meancore L 11 R =0.53matmeancorevelocityof7.38ms 1Z(cm)Meancore L 11 R =0.50matmeancorevelocityof5.16ms 1Z(cm)Meancore L 11 R =0.48matmeancorevelocityof2.63ms 1Z(cm) 20020 0 10 20 30 20 10 0 10 20 0 10 20 30 20 10 0 10 20 0 10 20 30 20 10 0 10 20 0 10 20 30 20 10 0 10 20 FigureA-11.Measuredpercentvariationfromcorefor L 11 R withrunmode n=0 ;! =3 242

PAGE 243

Meancore L 11 R =0.27matmeancorevelocityof9.58ms 1 Y(cm)Z(cm)Meancore L 11 R =0.27matmeancorevelocityof7.14ms 1Z(cm)Meancore L 11 R =0.27matmeancorevelocityof4.75ms 1Z(cm)Meancore L 11 R =0.28matmeancorevelocityof2.37ms 1Z(cm) 20 020 0 10 20 30 40 20 10 0 10 20 10 20 30 40 20 10 0 10 20 0 10 20 30 40 50 20 10 0 10 20 10 20 30 40 20 10 0 10 20 FigureA-12.Measuredpercentvariationfromcorefor L 11 R withstaticgrid 243

PAGE 244

APPENDIXB TIMEVARYINGLOADSINTHEPRESENCEOFTURBULENCE Frequency(Hz)MxPSD ( N 2 cm 2 Hz ) FzPSD ( N 2 Hz )10 0 10 1 10 2 10 10 10 5 10 5 FigureB-1.Powerspectraldensitiesofdynamicloadandtur bulencedataat =0 n = 2 : 5 0 ,andReynoldsNumberof25,000.Black:Measuredload, Red:Measuredloadnoiseoor,Cyan:LoadcomponentFRF,Blu e: Deconvolvedload,Magenta,Cross-wireverticalcomponent 244

PAGE 245

Frequency(Hz)MxPSD ( N 2 cm 2 Hz ) FzPSD ( N 2 Hz )10 0 10 1 10 2 10 10 10 5 10 5 FigureB-2.Powerspectraldensitiesofdynamicloadandtur bulencedataat =0 n = 2 : 5 0 ,andReynoldsNumberof50,000.Black:Measuredload, Red:Measuredloadnoiseoor,Cyan:LoadcomponentFRF,Blu e: Deconvolvedload,Magenta,Cross-wireverticalcomponent 245

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Frequency(Hz)MxPSD ( N 2 cm 2 Hz ) FzPSD ( N 2 Hz )10 0 10 1 10 2 10 10 10 5 10 5 FigureB-3.Powerspectraldensitiesofdynamicloadandtur bulencedataat =0 n = 2 : 5 0 ,andReynoldsNumberof75,000.Black:Measuredload, Red:Measuredloadnoiseoor,Cyan:LoadcomponentFRF,Blu e: Deconvolvedload,Magenta,Cross-wireverticalcomponent 246

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Frequency(Hz)MxPSD ( N 2 cm 2 Hz ) FzPSD ( N 2 Hz )10 0 10 1 10 2 10 10 10 5 10 5 FigureB-4.Powerspectraldensitiesofdynamicloadandtur bulencedataat =0 n = 0 3 ,andReynoldsNumberof25,000.Black:Measuredload,Red: Measuredloadnoiseoor,Cyan:LoadcomponentFRF,Blue:De convolved load,Magenta,Cross-wireverticalcomponent 247

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Frequency(Hz)MxPSD ( N 2 cm 2 Hz ) FzPSD ( N 2 Hz )10 0 10 1 10 2 10 10 10 5 10 5 FigureB-5.Powerspectraldensitiesofdynamicloadandtur bulencedataat =0 n = 0 3 ,andReynoldsNumberof50,000.Black:Measuredload,Red: Measuredloadnoiseoor,Cyan:LoadcomponentFRF,Blue:De convolved load,Magenta,Cross-wireverticalcomponent 248

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Frequency(Hz)MxPSD ( N 2 cm 2 Hz ) FzPSD ( N 2 Hz )10 0 10 1 10 2 10 10 10 5 10 5 FigureB-6.Powerspectraldensitiesofdynamicloadandtur bulencedataat =0 n = 0 3 ,andReynoldsNumberof75,000.Black:Measuredload,Red: Measuredloadnoiseoor,Cyan:LoadcomponentFRF,Blue:De convolved load,Magenta,Cross-wireverticalcomponent 249

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Frequency(Hz)MxPSD ( N 2 cm 2 Hz ) FzPSD ( N 2 Hz )10 0 10 1 10 2 10 10 10 5 10 5 FigureB-7.Powerspectraldensitiesofdynamicloadandtur bulencedataat =0 n = 0 8 ,andReynoldsNumberof25,000.Black:Measuredload,Red: Measuredloadnoiseoor,Cyan:LoadcomponentFRF,Blue:De convolved load,Magenta,Cross-wireverticalcomponent 250

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Frequency(Hz)MxPSD ( N 2 cm 2 Hz ) FzPSD ( N 2 Hz )10 0 10 1 10 2 10 10 10 5 10 5 FigureB-8.Powerspectraldensitiesofdynamicloadandtur bulencedataat =0 n = 0 8 ,andReynoldsNumberof50,000.Black:Measuredload,Red: Measuredloadnoiseoor,Cyan:LoadcomponentFRF,Blue:De convolved load,Magenta,Cross-wireverticalcomponent 251

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Frequency(Hz)MxPSD ( N 2 cm 2 Hz ) FzPSD ( N 2 Hz )10 0 10 1 10 2 10 10 10 5 10 5 FigureB-9.Powerspectraldensitiesofdynamicloadandtur bulencedataat =0 n = 0 8 ,andReynoldsNumberof75,000.Black:Measuredload,Red: Measuredloadnoiseoor,Cyan:LoadcomponentFRF,Blue:De convolved load,Magenta,Cross-wireverticalcomponent 252

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Frequency(Hz)MxPSD ( N 2 cm 2 Hz ) FzPSD ( N 2 Hz )10 0 10 1 10 2 10 10 10 5 10 5 FigureB-10.Powerspectraldensitiesofdynamicloadandtu rbulencedataat =0 n = 0 8 ,andReynoldsNumberof100,000.Black:Measuredload, Red:Measuredloadnoiseoor,Cyan:LoadcomponentFRF,Blu e: Deconvolvedload,Magenta,Cross-wireverticalcomponent 253

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Frequency(Hz)MxPSD ( N 2 cm 2 Hz ) FzPSD ( N 2 Hz )10 0 10 1 10 2 10 10 10 5 10 5 FigureB-11.Powerspectraldensitiesofdynamicloadandtu rbulencedataat =30 n = 2 : 5 0 ,andReynoldsNumberof25,000.Black:Measuredload, Red:Measuredloadnoiseoor,Cyan:LoadcomponentFRF,Blu e: Deconvolvedload,Magenta,Cross-wireverticalcomponent 254

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Frequency(Hz)MxPSD ( N 2 cm 2 Hz ) FzPSD ( N 2 Hz )10 0 10 1 10 2 10 10 10 5 10 5 FigureB-12.Powerspectraldensitiesofdynamicloadandtu rbulencedataat =30 n = 2 : 5 0 ,andReynoldsNumberof50,000.Black:Measuredload, Red:Measuredloadnoiseoor,Cyan:LoadcomponentFRF,Blu e: Deconvolvedload,Magenta,Cross-wireverticalcomponent 255

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Frequency(Hz)MxPSD ( N 2 cm 2 Hz ) FzPSD ( N 2 Hz )10 0 10 1 10 2 10 10 10 5 10 5 FigureB-13.Powerspectraldensitiesofdynamicloadandtu rbulencedataat =30 n = 2 : 5 0 ,andReynoldsNumberof75,000.Black:Measuredload, Red:Measuredloadnoiseoor,Cyan:LoadcomponentFRF,Blu e: Deconvolvedload,Magenta,Cross-wireverticalcomponent 256

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Frequency(Hz)MxPSD ( N 2 cm 2 Hz ) FzPSD ( N 2 Hz )10 0 10 1 10 2 10 10 10 5 10 5 FigureB-14.Powerspectraldensitiesofdynamicloadandtu rbulencedataat =30 n = 2 : 5 0 ,andReynoldsNumberof100,000.Black:Measuredload, Red:Measuredloadnoiseoor,Cyan:LoadcomponentFRF,Blu e: Deconvolvedload,Magenta,Cross-wireverticalcomponent 257

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Frequency(Hz)MxPSD ( N 2 cm 2 Hz ) FzPSD ( N 2 Hz )10 0 10 1 10 2 10 10 10 5 10 5 FigureB-15.Powerspectraldensitiesofdynamicloadandtu rbulencedataat =30 n = 0 3 ,andReynoldsNumberof25,000.Black:Measuredload, Red:Measuredloadnoiseoor,Cyan:LoadcomponentFRF,Blu e: Deconvolvedload,Magenta,Cross-wireverticalcomponent 258

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Frequency(Hz)MxPSD ( N 2 cm 2 Hz ) FzPSD ( N 2 Hz )10 0 10 1 10 2 10 10 10 5 10 5 FigureB-16.Powerspectraldensitiesofdynamicloadandtu rbulencedataat =30 n = 0 3 ,andReynoldsNumberof50,000.Black:Measuredload, Red:Measuredloadnoiseoor,Cyan:LoadcomponentFRF,Blu e: Deconvolvedload,Magenta,Cross-wireverticalcomponent 259

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Frequency(Hz)MxPSD ( N 2 cm 2 Hz ) FzPSD ( N 2 Hz )10 0 10 1 10 2 10 10 10 5 10 5 FigureB-17.Powerspectraldensitiesofdynamicloadandtu rbulencedataat =30 n = 0 3 ,andReynoldsNumberof75,000.Black:Measuredload, Red:Measuredloadnoiseoor,Cyan:LoadcomponentFRF,Blu e: Deconvolvedload,Magenta,Cross-wireverticalcomponent 260

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Frequency(Hz)MxPSD ( N 2 cm 2 Hz ) FzPSD ( N 2 Hz )10 0 10 1 10 2 10 10 10 5 10 5 FigureB-18.Powerspectraldensitiesofdynamicloadandtu rbulencedataat =30 n = 0 8 ,andReynoldsNumberof25,000.Black:Measuredload, Red:Measuredloadnoiseoor,Cyan:LoadcomponentFRF,Blu e: Deconvolvedload,Magenta,Cross-wireverticalcomponent 261

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Frequency(Hz)MxPSD ( N 2 cm 2 Hz ) FzPSD ( N 2 Hz )10 0 10 1 10 2 10 10 10 5 10 5 FigureB-19.Powerspectraldensitiesofdynamicloadandtu rbulencedataat =30 n = 0 8 ,andReynoldsNumberof50,000.Black:Measuredload, Red:Measuredloadnoiseoor,Cyan:LoadcomponentFRF,Blu e: Deconvolvedload,Magenta,Cross-wireverticalcomponent 262

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Frequency(Hz)MxPSD ( N 2 cm 2 Hz ) FzPSD ( N 2 Hz )10 0 10 1 10 2 10 10 10 5 10 5 FigureB-20.Powerspectraldensitiesofdynamicloadandtu rbulencedataat =30 n = 0 8 ,andReynoldsNumberof75,000.Black:Measuredload, Red:Measuredloadnoiseoor,Cyan:LoadcomponentFRF,Blu e: Deconvolvedload,Magenta,Cross-wireverticalcomponent 263

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Frequency(Hz)MxPSD ( N 2 cm 2 Hz ) FzPSD ( N 2 Hz )10 0 10 1 10 2 10 10 10 5 10 5 FigureB-21.Powerspectraldensitiesofdynamicloadandtu rbulencedataat =30 n = 0 8 ,andReynoldsNumberof100,000.Black:Measuredload, Red:Measuredloadnoiseoor,Cyan:LoadcomponentFRF,Blu e: Deconvolvedload,Magenta,Cross-wireverticalcomponent 264

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H M X w 0 H M X u 0 H F Z w 0 H F Z u 0 Wavenumber (radm 1 )Scaled H 1 frequencyresponsefunctionmagnitude10 1 10 2 10 2 10 1 10 0 10 1 FigureB-22.Frequencyresponsefunctionsofdynamicloada ndturbulencedataat =0 n = 2 : 5 0 ,andReynoldsNumberof25,000 H M X w 0 H M X u 0 H F Z w 0 H F Z u 0 Wavenumber (radm 1 )Scaled H 1 frequencyresponsefunctionmagnitude10 0 10 1 10 2 10 2 10 1 10 0 10 1 FigureB-23.Frequencyresponsefunctionsofdynamicloada ndturbulencedataat =0 n = 2 : 5 0 ,andReynoldsNumberof50,000 265

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H M X w 0 H M X u 0 H F Z w 0 H F Z u 0 Wavenumber (radm 1 )Scaled H 1 frequencyresponsefunctionmagnitude10 0 10 1 10 2 10 2 10 1 10 0 10 1 FigureB-24.Frequencyresponsefunctionsofdynamicloada ndturbulencedataat =0 n = 2 : 5 0 ,andReynoldsNumberof75,000 H M X w 0 H M X u 0 H F Z w 0 H F Z u 0 Wavenumber (radm 1 )Scaled H 1 frequencyresponsefunctionmagnitude10 1 10 2 10 2 10 1 10 0 10 1 FigureB-25.Frequencyresponsefunctionsofdynamicloada ndturbulencedataat =0 n = 0 3 ,andReynoldsNumberof25,000 266

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H M X w 0 H M X u 0 H F Z w 0 H F Z u 0 Wavenumber (radm 1 )Scaled H 1 frequencyresponsefunctionmagnitude10 0 10 1 10 2 10 2 10 1 10 0 10 1 FigureB-26.Frequencyresponsefunctionsofdynamicloada ndturbulencedataat =0 n = 0 3 ,andReynoldsNumberof50,000 267

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H M X w 0 H M X u 0 H F Z w 0 H F Z u 0 Wavenumber (radm 1 )Scaled H 1 frequencyresponsefunctionmagnitude10 0 10 1 10 2 10 2 10 1 10 0 10 1 FigureB-27.Frequencyresponsefunctionsofdynamicloada ndturbulencedataat =0 n = 0 3 ,andReynoldsNumberof75,000 H M X w 0 H M X u 0 H F Z w 0 H F Z u 0 Wavenumber (radm 1 )Scaled H 1 frequencyresponsefunctionmagnitude10 0 10 1 10 2 10 2 10 1 10 0 10 1 FigureB-28.Frequencyresponsefunctionsofdynamicloada ndturbulencedataat =0 n = 0 3 ,andReynoldsNumberof100,000 268

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H M X w 0 H M X u 0 H F Z w 0 H F Z u 0 Wavenumber (radm 1 )Scaled H 1 frequencyresponsefunctionmagnitude10 1 10 2 10 2 10 1 10 0 10 1 FigureB-29.Frequencyresponsefunctionsofdynamicloada ndturbulencedataat =0 n = 0 8 ,andReynoldsNumberof25,000 H M X w 0 H M X u 0 H F Z w 0 H F Z u 0 Wavenumber (radm 1 )Scaled H 1 frequencyresponsefunctionmagnitude10 0 10 1 10 2 10 2 10 1 10 0 10 1 FigureB-30.Frequencyresponsefunctionsofdynamicloada ndturbulencedataat =0 n = 0 8 ,andReynoldsNumberof50,000 269

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H M X w 0 H M X u 0 H F Z w 0 H F Z u 0 Wavenumber (radm 1 )Scaled H 1 frequencyresponsefunctionmagnitude10 0 10 1 10 2 10 2 10 1 10 0 10 1 FigureB-31.Frequencyresponsefunctionsofdynamicloada ndturbulencedataat =0 n = 0 8 ,andReynoldsNumberof75,000 H M X w 0 H M X u 0 H F Z w 0 H F Z u 0 Wavenumber (radm 1 )Scaled H 1 frequencyresponsefunctionmagnitude10 0 10 1 10 2 10 2 10 1 10 0 10 1 FigureB-32.Frequencyresponsefunctionsofdynamicloada ndturbulencedataat =0 n = 0 8 ,andReynoldsNumberof100,000 270

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H M X w 0 H M X u 0 H F Z w 0 H F Z u 0 Wavenumber (radm 1 )Scaled H 1 frequencyresponsefunctionmagnitude10 1 10 2 10 2 10 1 10 0 10 1 FigureB-33.Frequencyresponsefunctionsofdynamicloada ndturbulencedataat =30 n = 2 : 5 0 ,andReynoldsNumberof25,000 H M X w 0 H M X u 0 H F Z w 0 H F Z u 0 Wavenumber (radm 1 )Scaled H 1 frequencyresponsefunctionmagnitude10 0 10 1 10 2 10 2 10 1 10 0 10 1 FigureB-34.Frequencyresponsefunctionsofdynamicloada ndturbulencedataat =30 n = 2 : 5 0 ,andReynoldsNumberof50,000 271

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H M X w 0 H M X u 0 H F Z w 0 H F Z u 0 Wavenumber (radm 1 )Scaled H 1 frequencyresponsefunctionmagnitude10 0 10 1 10 2 10 2 10 1 10 0 10 1 FigureB-35.Frequencyresponsefunctionsofdynamicloada ndturbulencedataat =30 n = 2 : 5 0 ,andReynoldsNumberof75,000 H M X w 0 H M X u 0 H F Z w 0 H F Z u 0 Wavenumber (radm 1 )Scaled H 1 frequencyresponsefunctionmagnitude10 0 10 1 10 2 10 2 10 1 10 0 10 1 FigureB-36.Frequencyresponsefunctionsofdynamicloada ndturbulencedataat =30 n = 2 : 5 0 ,andReynoldsNumberof100,000 272

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H M X w 0 H M X u 0 H F Z w 0 H F Z u 0 Wavenumber (radm 1 )Scaled H 1 frequencyresponsefunctionmagnitude10 1 10 2 10 2 10 1 10 0 10 1 FigureB-37.Frequencyresponsefunctionsofdynamicloada ndturbulencedataat =30 n = 0 3 ,andReynoldsNumberof25,000 H M X w 0 H M X u 0 H F Z w 0 H F Z u 0 Wavenumber (radm 1 )Scaled H 1 frequencyresponsefunctionmagnitude10 0 10 1 10 2 10 2 10 1 10 0 10 1 FigureB-38.Frequencyresponsefunctionsofdynamicloada ndturbulencedataat =30 n = 0 3 ,andReynoldsNumberof50,000 273

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H M X w 0 H M X u 0 H F Z w 0 H F Z u 0 Wavenumber (radm 1 )Scaled H 1 frequencyresponsefunctionmagnitude10 0 10 1 10 2 10 2 10 1 10 0 10 1 FigureB-39.Frequencyresponsefunctionsofdynamicloada ndturbulencedataat =30 n = 0 3 ,andReynoldsNumberof75,000 H M X w 0 H M X u 0 H F Z w 0 H F Z u 0 Wavenumber (radm 1 )Scaled H 1 frequencyresponsefunctionmagnitude10 0 10 1 10 2 10 2 10 1 10 0 10 1 FigureB-40.Frequencyresponsefunctionsofdynamicloada ndturbulencedataat =30 n = 0 3 ,andReynoldsNumberof100,000 274

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H M X w 0 H M X u 0 H F Z w 0 H F Z u 0 Wavenumber (radm 1 )Scaled H 1 frequencyresponsefunctionmagnitude10 1 10 2 10 2 10 1 10 0 10 1 FigureB-41.Frequencyresponsefunctionsofdynamicloada ndturbulencedataat =30 n = 0 8 ,andReynoldsNumberof25,000 H M X w 0 H M X u 0 H F Z w 0 H F Z u 0 Wavenumber (radm 1 )Scaled H 1 frequencyresponsefunctionmagnitude10 0 10 1 10 2 10 2 10 1 10 0 10 1 FigureB-42.Frequencyresponsefunctionsofdynamicloada ndturbulencedataat =30 n = 0 8 ,andReynoldsNumberof50,000 275

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H M X w 0 H M X u 0 H F Z w 0 H F Z u 0 Wavenumber (radm 1 )Scaled H 1 frequencyresponsefunctionmagnitude10 0 10 1 10 2 10 2 10 1 10 0 10 1 FigureB-43.Frequencyresponsefunctionsofdynamicloada ndturbulencedataat =30 n = 0 8 ,andReynoldsNumberof75,000 H M X w 0 H M X u 0 H F Z w 0 H F Z u 0 Wavenumber (radm 1 )Scaled H 1 frequencyresponsefunctionmagnitude10 0 10 1 10 2 10 2 10 1 10 0 10 1 FigureB-44.Frequencyresponsefunctionsofdynamicloada ndturbulencedataat =30 n = 0 8 ,andReynoldsNumberof100,000 276

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APPENDIXC SIMILARITYSCALINGRESULTS VelocityeldandprolelocationVelocityprolesBaseline Z cX c 00 : 5 1 0 : 6 0 : 4 0 : 2 0 0 : 2 0 : 4 0 : 6 Z c u U 1 00 : 511 : 5 0 : 5 0 0 : 5 Turbulence Z cX c 00 : 51 0 : 6 0 : 4 0 : 2 0 0 : 2 0 : 4 0 : 6 Z c u U 1 00 : 511 : 5 0 : 5 0 0 : 5 FigureC-1.Plotof U U 1 at =8 andA=1 277

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u u a 00 : 20 : 40 : 60 : 81 1 : 5 1 0 : 5 0 0 : 5 1 1 : 5 FigureC-2.Plotof U u a at =8 Y b =0 : 1 25 andA=1 scaledagainstsimilarity parameter forbaselineowat X c = 0.2, 0.3 0.4 0.5 0.6 0.7 ,andEquation 6–34 asdashedlinewith =9 278

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u u a 00 : 20 : 40 : 60 : 81 1 : 5 1 0 : 5 0 0 : 5 1 1 : 5 FigureC-3.Plotof U u a at =8 Y b =0 : 1 25 andA=1 scaledagainstsimilarity parameter forturbulentowat X c = 0.2, 0.3 0.4 0.5 0.6 0.7 ,andEquation 6–34 asdashedlinewith =3 : 5 279

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VelocityeldandprolelocationVelocityprolesBaseline Z cX c 00 : 51 0 : 6 0 : 4 0 : 2 0 0 : 2 0 : 4 0 : 6 Z c u U 1 0 : 500 : 511 : 5 0 : 6 0 : 4 0 : 2 0 0 : 2 0 : 4 0 : 6 Turbulence Z cX c 00 : 51 0 : 6 0 : 4 0 : 2 0 0 : 2 0 : 4 0 : 6 Z c u U 1 00 : 511 : 5 0 : 6 0 : 4 0 : 2 0 0 : 2 0 : 4 0 : 6 FigureC-4.Plotof U U 1 at =15 andA=4 280

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u u a 00 : 20 : 40 : 60 : 81 1 : 5 1 0 : 5 0 0 : 5 1 1 : 5 FigureC-5.Plotof U u a at =15 Y b =0 : 1 25 andA=4 scaledagainstsimilarity parameter forbaselineowat X c = 0.2, 0.3 0.4 0.5 0.6 0.7 ,andEquation 6–34 asdashedlinewith =9 281

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u u a 00 : 20 : 40 : 60 : 81 1 : 5 1 0 : 5 0 0 : 5 1 1 : 5 FigureC-6.Plotof U u a at =15 Y b =0 : 1 25 andA=4 scaledagainstsimilarity parameter forturbulentowat X c = 0.2, 0.3 0.4 0.5 0.6 0.7 ,andEquation 6–34 asdashedlinewith =3 : 5 282

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VelocityeldandprolelocationVelocityprolesBaseline Z cX c 00 : 51 0 : 6 0 : 4 0 : 2 0 0 : 2 0 : 4 0 : 6 Z c u U 1 0 : 500 : 511 : 5 0 : 5 0 0 : 5 Turbulence Z cX c 00 : 51 0 : 6 0 : 4 0 : 2 0 0 : 2 0 : 4 0 : 6 Z c u U 1 00 : 511 : 5 0 : 5 0 0 : 5 FigureC-7.Plotof U U 1 at =15 andA=4 283

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u u a 00 : 20 : 40 : 60 : 81 1 : 5 1 0 : 5 0 0 : 5 1 1 : 5 FigureC-8.Plotof U u a at =15 Y b =0 : 3 75 andA=4 scaledagainstsimilarity parameter forbaselineowat X c = 0.2, 0.3 0.4 0.5 0.6 0.7 ,andEquation 6–34 asdashedlinewith =9 284

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u u a 00 : 20 : 40 : 60 : 81 1 : 5 1 0 : 5 0 0 : 5 1 1 : 5 FigureC-9.Plotof U u a at =15 Y b =0 : 3 75 andA=4 scaledagainstsimilarity parameter forturbulentowat X c = 0.2, 0.3 0.4 0.5 0.6 0.7 ,andEquation 6–34 asdashedlinewith =3 : 5 285

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VelocityeldandprolelocationVelocityprolesBaseline Z cX c 00 : 51 0 : 5 0 0 : 5 Z c u U 1 0 : 500 : 511 : 5 0 : 5 0 0 : 5 Turbulence Z cX c 00 : 51 0 : 5 0 0 : 5 Z c u U 1 0 : 500 : 511 : 5 1 0 : 5 0 0 : 5 FigureC-10.Plotof U U 1 at =35 andA=2 286

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u u a 00 : 20 : 40 : 60 : 81 1 : 5 1 0 : 5 0 0 : 5 1 1 : 5 FigureC-11.Plotof U u a at =35 Y b =0 : 1 25 andA=2 scaledagainstsimilarity parameter forbaselineowat X c = 0.2, 0.3 0.4 0.5 0.6 0.7 ,and Equation 6–34 asdashedlinewith =9 287

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u u a 00 : 20 : 40 : 60 : 81 1 : 5 1 0 : 5 0 0 : 5 1 1 : 5 FigureC-12.Plotof U u a at =35 Y b =0 : 1 25 andA=2 scaledagainstsimilarity parameter forturbulentowat X c = 0.2, 0.3 0.4 0.5 0.6 0.7 ,and Equation 6–34 asdashedlinewith =3 : 5 288

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VelocityeldandprolelocationVelocityprolesBaseline Z cX c 00 : 51 0 : 5 0 0 : 5 Z c u U 1 0 : 500 : 511 : 5 1 0 : 5 0 0 : 5 Turbulence Z cX c 00 : 51 0 : 5 0 0 : 5 Z c u U 1 0 : 500 : 511 : 5 1 0 : 5 0 0 : 5 FigureC-13.Plotof U U 1 at =35 andA=2 289

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u u a 00 : 20 : 40 : 60 : 81 1 : 5 1 0 : 5 0 0 : 5 1 1 : 5 FigureC-14.Plotof U u a at =35 Y b =0 : 3 75 andA=2 scaledagainstsimilarity parameter forbaselineowat X c = 0.2, 0.3 0.4 0.5 0.6 0.7 ,and Equation 6–34 asdashedlinewith =9 290

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u u a 00 : 20 : 40 : 60 : 81 1 : 5 1 0 : 5 0 0 : 5 1 1 : 5 FigureC-15.Plotof U u a at =35 Y b =0 : 3 75 andA=2 scaledagainstsimilarity parameter forturbulentowat X c = 0.2, 0.3 0.4 0.5 0.6 0.7 ,and Equation 6–34 asdashedlinewith =3 : 5 291

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REFERENCES [1]Wright,O.andWright,W.,“TheWrightBrothers'Aeropla ne,” TheCentury Magazine ,Vol.5,1908. [2]Padeld,G.D.andLawrence,B.,“Thebirthofightcontr ol:Anengineering analysisoftheWrightbrothers'1902glider,” TheAeronauticalJournalofAircraft Vol.December,2003,pp.697–718. [3]Hunsaker,J.C.andWilson,E.B.,“ReportonBehaviorofA eroplanesinGusts,” Tech.Rep.NACATR-1,NACA,1915. [4]Etkin,B.,“TurbulentWindandItsEffectonFlight,” JournalofAircraft ,Vol.18, No.5,1981,pp.327–345. [5] CodeofFederalRegulations,FederalAviationRegulations Parts23and25 ,2009. [6]“FlyingQualitiesofPilotedAircraft,”Tech.Rep.MILHDBK-1797,UnitedStatesAir Force,19December1997. [7]Ol,M.,Parker,G.,Abate,G.,andEvers,J.,“FlightCont rolsandPerformance ChallengesforMAVsinComplexEnvironments,” AIAAGuidance,Navigationand ControlConferenceandExhibit ,No.AIAA2008-6508,Honolulu,Hawaii,August 2008. [8]Roadman,J.M.andMohseni,K.,“GustCharacterizationa ndGenerationforWind TunnelTestingofMicroAerialVehicles,” 47thAIAAAerospaceSciencesMeeting No.AIAA2009-1290,Orlando,Florida,January2009. [9]Roadman,J.M.andMohseni,K.,“LargeScaleGustGenerat ionforSmallScale WindTunnelTestingofAtmosphericTurbulence,” 39thAIAAFluidDynamics Conference ,No.AIAA2009-4166,SanAntonio,Texas,June2009. [10]Johnson,E.andJacob,J.D.,“DevelopmentandTestingo faGustandShear TunnelforNAVsandMAVs,” 47thAIAAAerospaceSciencesMeetingIncluding TheNewHorizonsForumandAerospaceExposition ,No.AIAA2009-64,Orlando, Florida,January2009. [11]Zarovy,S.,Costello,M.,Mehta,A.,Gremillion,G.,Mi ller,D.,Ranganathan,B., Humbert,J.S.,andSamuel,P.,“ExperimentalStudyofGustE ffectsonMicro AirVehicles,” AIAAGuidance,Navigation,andControlConference ,No.AIAA 2010-7818,Toronto,OntarioCanada,August2010. [12]Watkins,S.,Loxton,B.J.,Abdulrahim,M.,andMilbank ,J.,“FlowFieldsin ComplexTerrainandTheirChallengestoMicroFlight,” AIAAGuidance,NavigationandControlConferenceandExhibit ,No.AIAA2008-6509,Honolulu,Hawaii, August2008. 292

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[13]Carmichael,B.H.,“LowReynoldsNumberAirfoilSurvey ,”Tech.Rep.NASA CR-165803,LowEnergyTransportSystems,1981. [14]Mueller,T.J.,“TheInuenceofLaminarSeparationand TransitiononLow ReynoldsNumberAirfoilHysteresis,” JournalofAircraft ,Vol.22,No.9,1985, pp.763–770. [15]Albertani,R.,Khambatta,P.,Hart,A.,Ukeiley,L.,Oy arzun,M.,Cattafesta,L.,and Abate,G.,“ValidationofaLowReynoldsNumberAerodynamic Characterization Facility,” 47thAIAAAerospaceSciencesMeeting ,No.AIAA2009-880,Orlando, FL,January2009. [16]Thipyopas,C.andMoschetta,J.-M.,“DevelopmentofEx perimentalFacilitiesfor Multi-MissionMAVs,” InternationalJournalofMicroAirVehicles ,Vol.2,No.3, 2010,pp.141–156. [17]Lissaman,P.,“EffectsofTurbulenceonBankUpsetsofS mallFlightVehicles,” 47thAIAAAerospaceSciencesMeeting ,No.AIAA2009-65,Orlando,FL,January 2009. [18]Lundstrom,D.andKrus,P.,“TestingofAtmosphericTur bulenceEffectsonthe PerformanceofMicroAirVehicles,” InternationalJournalofMicroAirVehicles Vol.4,No.2,June2012,pp.133–150. [19]Lomax,T.L., StructuralLoadsAnalysisforCommercialTransportAircra ft:Theory andPractice ,AIAA,1995. [20]Hoblit,F.M., GustLoadsonAircraft:ConceptsandApplications ,AIAAEducation Series,1988. [21]Houbolt,J.C.,“ManualontheFlightofFlexibleAircra ftinTurbulence,”Tech.Rep. AD-A237-949,AdvisoryGroupforResearchandDevelopment, 1991. [22]Authors,V.,“[TheFlightofFlexibleAircraftinTurbu lence]State-of-the-Artinthe DescriptionandModellingofAtmosphericTurbulence,”Tec h.Rep.734,Advisory GroupforAerospaceResearchandDevelopment,1986. [23]Pisano,W.J.andLawrence,D.,“AutonomousGustInsens itiveAircraft,” AIAA Guidance,NavigationandControlConferenceandExhibit ,No.AIAA2008-6510, Honolulu,Hawaii,August2008. [24]Milbank,J.,Loxton,B.,Watkins,S.,andMelbourne,W. H.,“Replicationof AtmosphericConditionsforthePurposeofTestingMAVsMAVF lightEnvironment Project:FinalReport,”Tech.Rep.AOARD-054075,Schoolof Aerospace, Mechanical&ManufacturingEngineering,RMITUniversity, 2005. [25]Wilson,E.B.,“TheoryofanAirplaneEncounteringGust s,II,”Tech.Rep.TR21, NACA,1917. 293

PAGE 294

[26]Wilson,E.B.,“TheoryofanAirplaneEncounteringGust s,III,”Tech.Rep.TR27, NACA,1918. [27]Brunstein,A.I.,“ClearAirTurbulenceAccidents,” SAFEJournal ,Vol.8,January 1978,pp.17–19. [28]Kaplan,M.L.,Huffman,A.W.,Lux,K.M.,Charney,J.J., Riordan,A.J.,and Lin,Y.-L.,“Characterizingthesevereturbulenceenviron mentsassociatedwith commercialaviationaccidents.” MeterologyandAtmosphericPhysics ,Vol.88, 2005,pp.129–152. [29]Frost,W.,Chang,H.-P.,andRingnes,E.A.,“Analysesa ndAssessmentsof SpanwiseGustGradientDatafromNASAB-57BAircraft,”Tech .Rep.NASA CR-178288,FWGAssociates,Inc.,1987. [30]Turner,E.W.,“AnExpositiononAircraftResponsetoAt mosphericTurbulence UsingPowerSpectralDensityAnalysisTechniques,”Techni calReportAFFDL TR-76-162,AirForceFlightDynamicsLaboratory,1977. [31]Campbell,C.W.,“AddingComputationallyEfcientRea lismtoMonteCarlo TurbulenceSimulation,”NASATechnicalPaperNASATP-2469 ,NASAGeorgeC. MarshallSpaceFlightCenter,1985. [32]Campbell,C.W., ASpatialModelofWindShearandTurbulenceforFlight Simulation ,Ph.d.thesis,ColoradoStateUniversity,1984. [33]Eggleston,J.M.andDiedrich,F.W.,“TheoreticalCalc ulationofthePowerSpectra oftheRollingandYawingMomentsonaWinginRandomTurbulen ce,”Tech.Rep. TN3864,NACA,1956. [34]Bisplinghoff,A.L.,Ashley,H.,andHalfman,R.L., Aeroelasticity ,Dover,1955. [35]“FlyingQualitiesofPilotedAirplanes,”Tech.Rep.MI L-F-8785C,UnitedStatesAir Force,5November1990. [36]Wagner,H.,“UberdieEntstehungdesdynamischenAuftr iebesvonTragugen,” Z angewMathematicalMechanics ,Vol.5,February1925. [37]K¨ussner,H.G.,“SchwingungenvonFlugzeugugeln,” Luftfahrtforschung ,Vol.4, June1929. [38]Theodoreson,T.,“GeneralTheoryofAerodynamicInsta bilityandtheMechanisms ofFlutter,”Tech.Rep.496,NACA,1934. [39]Sears,W.R., Asystematicpresentationofthetheoryofthinairfoilsinn on-uniform motion ,Ph.D.thesis,CaliforniaInstituteofTechnology,1938. [40]Sears,W.R.,“SomeAspectsofNon-StationaryAirfoilT heoryandItsPractical Application,” JournaloftheAeronauticalSciences ,Vol.8,1941,pp.104–108. 294

PAGE 295

[41]Taylor,G.I.,“StatisticalTheoryofTurbulence,” ProceedingsoftheRoyalSocietyof London ,Vol.151,1935,pp.421–444,455–464. [42]Mathieu,J.andScott,J., AnIntroductiontoTurbulentFlow ,CambridgeUniversity Press,2000. [43]Taylor,G.I., TheScienticPapersofSirGeoffreyIngramTaylor ,Cambridge UniversityPress,1960. [44]vonK arm an,T.,“TheFundamentalsoftheStatisticalTheoryofTurbu lence,” JournalofAeronauticalSciences ,Vol.4,1937,pp.131–138. [45]vonK arm an,T.,“ProgressintheStatisticalTheoryofTurbulence,” Proceedingsof theNationalAcademyofSciences ,Vol.34,1948,pp.530–539. [46]vonK arm an,T.andLin,C.C.,“OntheConceptofSimilarityintheTheo ryof IsotropicTurbulence,” ReviewsofModernPhysics ,Vol.21,1949,pp.516–519. [47]Jones,J.W.,Mielke,R.H.,andJones,G.W.,“LowAltitu deAtmospheric TurbulenceLO-LOCATPhaseIII,”Tech.rep.,TheBoeingComp any,1970. [48]Comte-Bellot,G.andCorrsin,S.,“SimpleEularianTim eCorrelationofFull-and Narrow-BandVelocitySignalsinGrid-GeneratedIsotropic Turbulence,” Journalof FluidMechanics ,Vol.48,1971,pp.273–337. [49]Kaimal,J.C.,Izumi,Y.,Wyngaard,J.C.,andCote,O.R. ,“Spectral CharacteristicsofSurface-LayerTurbulence,”Tech.rep. ,AirForceCambridge ResearchLaboratories,1972. [50]Ramsdell,J.V.,“WindandTurbulenceInformationforV erticalandShortTakeoff andLandingOperationinBuilt-upUrbanAreas,”Tech.rep., PacicNorthwest Laboratories,1975. [51]Watkins,S.,Milbank,J.,andLoxton,B.J.,“Atmospher icWindsandTheir ImplicationsforMicroairVehicles,” AIAAJournal ,Vol.44,2006,pp.2591–2600. [52]Rhode,R.V.andLundquist,E.E.,“PreliminaryStudyof AppliedLoadFactorsin BumpyAir,”Tech.Rep.TN374,NACA,1931. [53]Donely,P.,“AnExperimentalInvestigationoftheNorm alAccelerationofan AirplaneModelinaGust,”Tech.Rep.TN706,NACA,1939. [54]Donely,P.andShufebarger,C.C.,“TestsintheGustTu nnelofaModelofthe XBM-1Airplane,”Tech.Rep.TN-731,NACA,1939. [55]Donely,P.,Pierce,H.B.,andPepoon,P.W.,“Measureme ntsandAnalysisofthe MotionofaCanardAirplaneModelinGusts,”Tech.Rep.TN758 ,NACA,1940. [56]Shufebarger,C.,“TestsofaGust-AlleviatingWingin theGustTunnel,”Tech.Rep. TN802,LangleyMemorialAeronauticalLaboratory,1941. 295

PAGE 296

[57]Donely,P.andShufebarger,C.C.,“TestsofaGust-All eviatingFlapintheGust Tunnel,”Tech.Rep.TN745,NACA,1940. [58]Reisert,T.D.,“Testsofa 1 17 -ScaleModeloftheXBDR-1AirplaneintheNACA GustTunnel,”Tech.Rep.WRL539,NACA,1944. [59]Pierce,H.B.,“Testsofa45 Sweptback-WingModelintheLangleyGustTunnel,” Tech.Rep.TN1528,NACA,1948. [60]Pierce,H.B.,“Gust-TunnelInvestigationofa45 Sweptforward-WingModel,” Tech.Rep.TN1717,NACA,1948. [61]Reisert,T.D.,“Gust-TunnelInvestigationofaWingMo delwithSemichordLine SweptBack30 ,”Tech.Rep.TN1794,NACA,1949. [62]Cahen,G.L.,“Gust-TunnelInvestigationoftheEffect sofLeading-Edge SeparationontheNormalAccelerationsExperiencedbya45 Sweptback-Wing ModelinGusts,”Tech.Rep.RML53J07,NACA,1953. [63]Pierce,H.B.andTrauring,M.,“Gust-TunnelTeststoDe termineInuenceofAirfoil SectionCharacteristicsonGust-LoadFactors,”Tech.Rep. TN1632,NACA,1948. [64]Funk,J.andBinckley,E.T.,“AFlightInvestigationof theEffectsof Center-of-GravityLocationonGustLoads,”Tech.Rep.TN25 75,NACA,1951. [65]Donely,P.,“SummaryofInformationRelatingtoGustLo adsonAirplanes,”Tech. Rep.997,NACA,1949. [66]Theodorsen,T.,“Generaltheoryofaerodynamicinstab ilityandthemechanismof utter,”Tech.Rep.TR496,NACA,1949. [67]Liepmann,H.W.,“OntheApplicationofStatisticalCon ceptstotheBuffeting Problem,” JournalofAeronauticalSciences ,Vol.19,1952,pp.793–800. [68]Press,H.andMazelsky,B.,“AStudyoftheApplicationo fPower-Spectral MethodsofGeneralizedHarmonicAnalysistoGustLoadsonAi rplanes,”Tech. Rep.TN2853,NACA,1953. [69]Liepmann,H.W.,“ExtensionoftheStatisticalApproac htoBuffetingandGust ResponsetoWingsofFiniteSpan,” JournalofAeronauticalSciences ,Vol.22, No.3,1955. [70]Press,H.andHoubolt,J.C.,“SomeApplicationsofGene ralizedHarmonic AnalysistoGustLoadsofAirplanes,” JournalofAeronauticalSciences ,Vol.22, No.1,1955. [71]Press,H.,Meadows,M.T.,andHadlock,I.,“Estimateso fProbabilityDistribution ofRoot-Mean-SquareGustVelocityofAtmosphericTurbulen cefromOperational Gust-LoadDatabyRandom-ProcessTheory,”Tech.Rep.TN336 2,NACA,1955. 296

PAGE 297

[72]Diedrich,F.W.,“TheDynamicResponseofaLargeAirpla netoContinuous RandomAtmosphericDisturbances,” JournalofAeronauticalSciences ,Vol.23, No.10,1956,pp.917–930. [73]Press,H.andMeadows,M.T.,“ARe-evaluationofGust-L oadStatisticsfor ApplicationsinSpectralCalculations,”Tech.Rep.TN3540 ,NACA,1955. [74]Rhyne,R.H.andMurrow,H.N.,“EffectsofAirplaneFlex ibilityonWingStrains inRoughAirat5,000FeetasDeterminedbyFlightTestsofaLa rgeSwept-Wing Airplane,”Tech.Rep.TN-4107,NACA,1957. [75]Shufebarger,C.C.,Payne,C.B.,andCahen,G.L.,“Aco rrelationofresultsof ightinvestigationwithresultsofananalyticalstudyofe ffectsofwingexibilityon wingstrainsduetogusts,”Tech.Rep.TR1365,NACA,1958. [76]Eggleston,J.M.andPhillips,W.H.,“TheLateralRespo nseofAircrafttoRandom AtmosphericTurbulence,”Tech.Rep.TRR-74,NASA,1960. [77]George,D.,Smedfjeld,J.B.,andSchriro,G.R.,“AnEng ineeringEvaluationof AirplaneGustLoadAnalysisMethods,”Tech.Rep.ADR06-1463-1,Grumman AircraftEngineeringCorporation,1963. [78]Hinze,J.O., Turbulence ,McGraw-Hill,1959. [79]Houbolt,J.C.,Steiner,R.,andPratt,K.G.,“DynamicR esponseofAirplanesto AtmosphericTurbulenceIncludingFlightDatainInputandR esponse,”Tech.Rep. TRR-199,NASA,1964. [80]Pritchard,F.E.,EasterBrook,C.C.,andMcVehil,G.E. ,“Spectraland ExceedanceProbabilityModelsofAtmosphericTurbulencef oruseinAircraft DesignandOperation,”Tech.Rep.AFFDL-TR-65-122,Cornel lAeronautical Laboratory,1965. [81]WilliamH.Austin,J.,“DevelopmentofImprovedGustLo adCriteriaforUnited StatesAirForceAircraft,”Tech.Rep.SEG-TR-67-28,AirFo rceSystems Command,1967. [82]Houbolt,J.C.,“GustDesignProceduresBasedonPowerS pectralTechniques,” Tech.Rep.TR-67-74,AirForceFlightDynamicsLaboratory, 1967. [83]Burns,A.,“PowerSpectraofLowLevelAtmosphericTurb ulenceMeasuredfrom anAircraft,”Tech.Rep.CP733,AeronauticalResearchCoun cil,1964. [84]Gilman,J.andBennett,R.M.,“AWind-TunnelTechnique forMeasuring FrequencyResponseFunctionsforGustLoadAnalysis,” AircraftDesignand TechnologyMeeting ,No.AIAA65-787,LosAngeles,California,November1965, pp.1–12. 297

PAGE 298

[85]Buell,D.A.,“AnExperimentalInvestigationoftheVel ocityFluctuationsBehind OscillatingVanes,”Tech.Rep.TND-5543,NASA,1969. [86]Dutton,J.A.,“EffectsofTurbulenceonAeronauticalS ystems,”Tech.rep., PennsylvaniaStateUniversity,1970. [87]Burris,P.M.andBender,M.A.,“AircraftModeAlleviat ionandModeStabilization (LAMS),”Tech.Rep.AFFDL-TR-68-161,AirForceFlightDyna micsLaboratory, 1968. [88]Burris,P.M.andBender,M.A.,“AircraftLoadAlleviat ionandModeStabilization (LAMS)FlightDemonstrationTestAnalysis,”Tech.Rep.AFF DL-TR-68-164,Air ForceFlightDynamicsLaboratory,1968. [89]Reeves,P.M., ANon-GaussianModelofContinuousAtmosphericTurbulence for UseinAircraftDesign ,Ph.D.thesis,UniversityofWashington,1974. [90]Reeves,P.M.,Campbell,G.S.,Ganzer,V.M.,andJoppa, R.G.,“Development andApplicationofaNon-GaussianAtmosphericTurbulenceM odelforUse inFlightSimulators,”NASAContractorReportNASACR-2451 ,Universityof Washington,1974. [91]Dutton,J.A.,Kerman,B.R.,andPetersen,E.L.,“Contr ibutionstotheSimulation ofTurbulence,”NASAContractorReportNASACR-2762,ThePe nnsylvaniaState University,1976. [92]Fichtl,G.H.,“ATechniqueforSimulatingTurbulencef orAerospaceVehicleFlight SimulationStudies,”NASATechnicalMemorandumNASATM-78 141,GeorgeC. MarshallSpaceFlightCenter,1977. [93]Houbolt,J.C.,“UpdatedGustDesignValuesforUseWith AFFDL-70-106,”Tech. Rep.AD-778821,AirForceFlightDynamicsLaboratories,19 73. [94]Houbolt,J.C.andWilliamson,G.G.,“SpectralGustRes ponseforanAirplane withVerticalMotionandPitch,”Tech.Rep.TR-75-121,AirF orceFlightDynamics Laboratory,1975. [95]Wang,S.-T.andFrost,W.,“AtmosphericTurbulenceSim ulationTechniqueswith ApplicationtoFlightAnalysis,”NASAContractorReportNA SACR-3309,The UniversityofTennesseeSpaceInstitute,1980. [96]Krause,S.S., AircraftSafetyAccidentInvestigations,AnalysesandApp lications McGraw-Hill,2003. [97]Waszak,M.R.,Davidson,J.B.,andIfju,P.G.,“Simulat ionandFlightControlofan AeroelasticFixedWingMicroAerialVehicle,” AIAAAtmosphericFlightMechanics Conference ,No.AIAA2002-4875,August2002. 298

PAGE 299

[98]Etele,J.,“OverviewofWindGustModellingwithApplic ationtoAutonomous Low-LevelUAVControl,”Tech.Rep.DRDCOttowaCR2006-221, DefenceR&D Canada,2006. [99]Jagdale,V.,Ifju,P.,Stanford,B.,andAlbertani,R., “ABendableLoadStiffened WingforSmallUAVs,” InternationalJournalofMicroAirVehicles ,Vol.2,No.4, December2010,pp.239–253. [100]Ifju,P.G.,Jenkins,D.A.,Ettinger,S.,Lian,Y.,Shy y,W.,andWazak,M., “Flexible-Wing-BasedMicroAirVehicles,” AIAAAtmosphericFlightMechanics Conference ,No.AIAA2007-0705,Reno,NV,August2002. [101]Waszak,M.R.,Jenkins,L.N.,andIfju,P.,“Stability andControlPropertiesofan AeroelasticFixedWingMicroAerialVehicle,” AIAAAtmospherivFlightMechanics Conference ,No.AIAA2001-4005,Montreal,Canada,August2001. [102]Lian,Y.andShyy,W.,“Three-DimensionalFluid-Stru ctureInteractionsofa MembraneWingforMicroAirVehicleApplication,” AIAAStructuralDynamics Conference ,No.AIAA2003-1762,Norfolk,Virginia,April2003. [103]Stanford,B., AeroelasticAnalysisandOptimizationofMembraneMicroAi rVehicle Wings ,Ph.D.thesis,UniversityofFlorida,2008. [104]Golubev,V.V.andVisbal,M.R.,“ModelingMAVRespons einGustyUrban Environment,” InternationalJournalofMicroAirVehicles ,Vol.4,No.1,March 2012,pp.79–92. [105]Veers,P.S.,“Three-DimensionalWindSimulation,”S andiaReportSAND88-0152, SandiaNationalLaboratories,1988. [106]Grimmond,C.S.B.andOke,T.R.,“AerodynamicPropert iesofUrbanAreas DerivedfromAnalysisofSurfaceForm,” JournalofAppliedMeteorology ,Vol.38, 1998,pp.1262–1292. [107]MacDonald,R.W.,“ModellingtheMeanVelocityProle intheUrbanCanopy Layer,” Boundary-LayerMeteorology ,Vol.97,2000,pp.24–45. [108]Watkins,S.,Thompson,M.,Loxton,B.,andAbdulrahim ,M.,“OnLowAltitude FlightThroughtheAtmosphericBoundaryLayer,” InternationalJournalofMicro AirVehicles ,Vol.2,2010,pp.55–68. [109]Combes,S.A.andDudley,R.,“Turbulence-driveninst abilitieslimitinsectight performance,” ProceedingsoftheNationalAcademyofSciences ,Vol.106, No.22,2009,pp.9105–9108. [110]Cruz,E.G.,Watkins,S.,Loxton,B.,andWatmuff,J.,“ AFlatPlateRectangular WingSubjectedToGrid-GeneratedTurbulence,” AIAAAppliedAerodynamics Conference ,No.AIAA2008-6247,Honolulu,Hawaii,August2008. 299

PAGE 300

[111]Ravi,S., TheInuenceofTurbulenceonaFlatPlateAirfoilatReynold sNumbers RelevanttoMAVs ,Ph.D.thesis,RMITUniversity,2011. [112]Ravi,S.,Watkins,S.,Watmuff,J.,Massey,K.,Peters en,P.,Marino,M.,and Ravi,A.,“Theowoverathinairfoilsubjectedtoelevatedl evelsoffreestream turbulenceatlowReynoldsnumbers,” ExperimentsinFluids ,2012. [113]Torres-Nieves,S.,Maldonado,V.,Lebron,J.,Kang,H .-S.,Meneveau,C.,and Castillo,L.,“Free-StreamTurbulenceEffectsontheFlowa roundanS809 WindTurbineAirfoil,” ProgressinTurbulenceandWindEnergy ,Vol.IV,2012, pp.275–279. [114]Fox,R.W.andMcDonald,A.T., IntroductiontoFluidMechanics ,JohnWiley& Sons,ftheditioned.,1998. [115]Seoud,R.E.andVassilicos,J.C.,“Dissipationandde cayoffractal-generated turbulence,” PhysicsofFluids ,Vol.19,No.105108,2007. [116]Liu,R.andTing,D.S.-K.,“TurbulentFlowDownstream ofaPerforatedPlate: Sharp-EdgedOriceVersusFinite-ThicknessHoles,” TransactionsofASME Vol.129,2007,pp.1164–1171. [117]Mydlarski,L.andWarhaft,Z.,“Ontheonsetofhigh-Re ynolds-number grid-generatedwindtunnelturbulence,” JournalofFluidMechanics ,Vol.320, August1996,pp.331–368. [118]Sytsma,M.andUkeiley,L.,“WindTunnelGeneratedTur bulence,” 49thAIAA AerospaceSciencesMeetingincludingtheNewHorizonsForu mandAerospace Exposition ,No.AIAA2011-1159,Orlando,FL,January20112011. [119]Larssen,J.V.andDevenport,W.J.,“TheGenerationof HighReynoldsNumber HomogeneousTurbulence,” 32ndAIAAFluidDynamicsConferenceandExhibit No.AIAA2002-2861,St.Louis,Missouri,June2002. [120]Kang,H.S.,Chester,S.,andMeneveau,C.,“Decayingt urbulenceinan active-grid-generatedowandcomparisonswithlarge-edd ysimulation,” JournalofFluidMechanics ,Vol.480,2003,pp.129–160. [121]Makita,H.,“Realizationofalarge-scaleturbulence eldinasmallwindtunnel,” FluidDynamicsResearch ,Vol.8,1991,pp.53–94. [122]Poorte,R.E.G.andBiesheuvel,A.,“Experimentsonth emotionofgasbubbles inturbulencegeneratedbyanactivegrid,” JournalofFluidMechanics ,Vol.461, June2002,pp.127–154. [123]Mydlarski,L.andZ.Warhaft,Z.,“Three-pointstatis ticsandtheanisotropyofa turbulentpassivescalar,” PhysicsofFluids ,Vol.10,1998,pp.2885–2894. 300

PAGE 301

[124]Mydlarski,L.andWarhaft,Z.,“Passivescalarstatis ticsinhigh-Peclet-numbergrid turbulence,” JournalofFluidMechanics ,Vol.358,1998,pp.135–175. [125]Kang,H.S.andMeneveau,C.,“Experimentalstudyofan activegrid-generated shearlessmixinglayerandcomparisonswithlarge-eddysim ulation,” Physicsof Fluids ,Vol.125102,2008. [126]Mordant,N.,“ExperimentalhighReynoldsnumberturb ulencewithanactivegrid,” AmericanAssociationofPhysicsTeachers ,Vol.76,2008,pp.1092–1098. [127]Hattori,Y.,Moeng,C.-H.,andNobukazuTanaka,H.S., andHirakuchi,H., “Wind-TunnelExperimentonLogarithmic-LayerTurbulence undertheInuence ofOverlyingDetachedEddies,” BoundaryLayerMeterologyandAtmospheric Physics ,Vol.134,2010,pp.269–283. [128]Lissaman,P.B.S.andPatel,C.K.,“NeutralEnergyCyc lesforaVehiclein SinusoidalandTurbulentVerticalGusts,” 5thAIAAAerospaceSciencesMeeting andExhibit ,No.AIAA2007-863,Reno,Nevada,2007. [129]AnaheimAutomation,910EastOrangefairLane,Anahei m,CA92801, 23MD SeriesMotor/DriverCombinationUsersManual ,January2010. [130]NationalInstruments, NI653XUserManualforTraditionalNI-DAQ ,February 2005. [131]TSICorporation, TSIThermalAnemometryProbes [132]Jorgensen,F.E., Howtomeasureturbulencewithhot-wireanemometers-a practicalguide ,DantecDynamics,2002. [133]NationalInstruments, NI447xSpecications ,February2005. [134]AnaheimAutomation,910EastOrangefairLane,Anahei m,CA92801, 23MDSI SeriesMotor/Driver/ControllerCombinationUsersManual ,January2010. [135]Bradshaw,P., Anintroductiontoturbulenceanditsmeasurements ,Pergamom Press,NewYork,1971. [136]Tutu,N.K.andChavray,R.,“Cross-wireanemometryin highintensityturbulence,” JournalofFluidMechanics ,Vol.71,1975,pp.785–800. [137]Gilbertson,L.G.,Doehring,T.C.,Livesay,G.A.,Rud y,T.W.,Kang,J.D., andWoo,S.L.-Y.,“ImprovementofAccuracyinaHigh-Capaci ty,Six Degree-of-freedomLoadCell:ApplicationtoRoboticTesti ngofMusculoskeletal Joints,” AnnalsofBiomedicalEngineering ,Vol.27,1999,pp.839–843. [138]Meirovitch,L., FundamentalsofVibrations ,McGraw-Hill,2001. [139]Maia,N.andSilva,J., TheoreticalandExperimentalModalAnalysis ,Research StudiesPressLtd.,1997. 301

PAGE 302

[140]Smith,S., TheScientistandEngineer'sGuidetoDigitalSignalProces sing www.dspguide.com,1997. [141]Mee,D.J.,“DynamicCalibrationofForceBalances,”T ech.rep.,TheUniversityof Queensland,2002. [142]Shreve,J.A., ModicationofaLongitudinalWindTunnelBalanceforIdent icationofMicroAirVehicleInstabilities ,Master'sthesis,RochesterInstituteof Technology,2005. [143]Gonzalez,R.,Woods,R.,andEddins,S., DigitalImageProcessingUsingMatlab PrenticeHall,2003. [144]http://www.fftw.org, FastestFourierTransformintheWestManualforversion 3.2.2 [145]LaVision, FlowMasterProductManual ,ItemNumber1105011-4. [146]Raffert,M.,Willert,C.,Werely,S.,andKompenhans, J., ParticleImageVelocimetryaPracticalGuide ,SpringerBerlinHeidelberg,2007. [147]Adrian,R.J.,“TwentyYearsofParticleImageVelocim etry,” ExperimentsinFluids Vol.39,2005,pp.159–169. [148]Calluaud,D.andDavid,L.,“Stereoscopicparticleim agevelocimetry measurementsofaowaroundasurface-mountedblock,” ExperimentsinFluids Vol.36,2004,pp.33–61. [149]Westerweel,J., Digitalparticleimagevelocimetry:theoryandapplicatio n ,Delft UniversityPress,1993. [150]Overmars,E.,Warncke,N.,Poelma,C.,andWesterweel ,J.,“BiaserrorsinPIV: thepixellockingeffectrevisited,” 15thInternationalSymposiumonApplicationsof LaserTechniquestoFluidMechanics ,Lisbon,Portugal,July2010. [151]“LaVisionAerosolGeneratorDataSheet,”.[152]Lamb,S.H., Hydrodynamics ,Dover,NewYork,1945. [153]Christensen,K.T.,“Theinuenceofpeak-lockingerr orsonturbulence statisticscomputedfromPIVensembles,” ExperimentsinFluids ,Vol.36,2004, pp.484–497. [154]Santiago,J.G.,Wereley,S.T.,Meinhart,C.D.,Beebe ,D.J.,andAdrian,R.J., “Aparticleimagevelocimetrysystemformicrouidics,” ExperimentsinFluids Vol.25,1998,pp.316–319. [155]Prasad,A.,Adrian,R.J.,Landreth,C.,andOffutt,P. ,“Effectofresolutiononthe speedandaccuracyofparticleimagevelocimetryinterroga tion,” Experimentsin Fluids ,Vol.13,1992,pp.105–116. 302

PAGE 303

[156]Anderson,J.D., FundamentalsofAerodynamics ,McGraw-Hill,3rded.,2001. [157]Prasad,A.K.andAdrian,R.J.,“Stereoscopicparticl eimagevelocimetryapplied toliquidows,” ExperimentsinFluids ,Vol.15,1993,pp.49–60. [158]Prasad,A.K.,“Stereoscopicparticleimagevelocime try,” ExperimentsinFluids Vol.29,2000,pp.103–116. [159]Welch,P.D.,“TheUseofFastFourierTransformforthe Estimationof PowerSpectra:AmethodBasedonTimeAveragingOverShort,M odied Periodograms,” IEEETransmissionAudioandElectroacoustics ,Vol.AU-15,1967, pp.70–73. [160]White,F.M., ViscousFluidFlow ,McGraw-Hill,3rded.,2006. [161]Taylor,G.I.,“DiffusionbyContinuousMovements,” ProceedingsoftheLondon MathematicalSociety ,Vol.xx,1921,pp.196–212. [162]O'Neill,P.L.,Nicolaides,D.,Honnery,D.,andSoria ,J.,“AutocorrelationFunctions andtheDeterminationofIntegralLengthwithReferencetoE xperimentaland NumericalData,” 15thAustralasianFluidMechanicsConference ,TheUniversityof Sydney,Sydney,Australia,December2004. [163]Shabbir,A.,Beuther,P.D.,andGeorge,W.K.,“X-Wire ResponseinTurbulent FlowsofHigh-IntensityTurbulenceandLowMeanVelocities ,” Experimental ThermalandFluidScience ,Vol.12,1996,pp.52–56. [164]Abdel-Rahman,A.A.,Hitchman,G.J.,Slawson,P.R.,a ndStrong,A.B.,“An X-arrayhot-wiretechniqueforheatedturbulentowsoflow velocity,” Journalof PhysicsE:ScienticInstrumentation ,Vol.22,1989. [165]NationalInstruments, NIDynamicSignalAcquisitionUserManual ,February 2005. [166]Bendat,J.andPiersol,A.G., RandomDataAnalysisandMeasurementProcedures ,JohnWiley&Sons,2nded.,1986. [167]Gage,S.,“CreatingaUniedGraphicalWindTurbulenc eModelfromMultiple Specications,” AIAAModelingandSimulationTechnologiesConferenceand Exhibit ,No.AIAA2003-5529,Austin,Texas,2003,p.10. [168]Frelich,R.,Cornman,L.,andSharman,R.,“Simulatio nofThree-Dimensional TurbulentVelocityFields,” JournalofAppliedMetrology ,Vol.40,2001, pp.246–258. [169]Sidin,R.S.R.,IJzermans,R.H.A.,andReeks,M.W.,“A Lagrangianapproach todropletcondensationinatmosphericclouds,” PhysicsofFluids ,Vol.21,No. 106603,2009. 303

PAGE 304

[170]Yechout,T.R.,Morris,S.L.,Bossert,D.E.,andHallg ren,W.F., Introductionto AircraftFlightMechanics ,AIAAEducationSeries,2003. [171]Bryson,D.E.,Weisshaar,T.A.,Snyder,R.D.,andBera n,P.S., “AeroelasticOptimizationofaTwo-DimensionalFlappingM echanism,” 51st AIAA/ASME/ASCE/AHS/ASCStructures,StructuralDynamics ,andMaterials Conference ,No.AIAA2010-2961,Orlando,Fl,April2010. [172]Chabalko,C.C.,Snyder,R.D.,Beran,P.S.,andOl,M.V .,“Studyof DeectedWakePhenomenaby2DUnsteadyVortexLattice,” 50th AIAA/ASME/ASCE/AHS/ASCStructures,StructuralDynamics ,andMaterials Conference ,No.AIAA2009-2475,May2009. [173]Chabalko,C.C.,Snyder,R.D.,Beran,P.S.,andParker ,G.H.,“ThePhysicsof anOptimizedFlappingWingMicroAirVehicle,” 47thAIAAAerospaceSciences MeetingIncludingTheNewHorizonsForumandAerospaceExpo sition ,No.AIAA 2009-801,Orlando,Florida,January2009. [174]Pettit,C.L.,Hajj,M.R.,andBeran,P.S.,“GustLoads withUncertaintyDueto ImpreciseGustVelocitySpectra,” 48thAIAA/ASME/ASCE/AHS/ASCStructures, StructuralDynamics,andMaterialsConference ,No.AIAA2007-1965,Honolulu, Hawaii,April2007. [175]Katz,J.andPlotkin,A., LowSpeedAerodynamics ,CambridgeUniversityPress, 2001. [176]Mueller,T.J.andTorres,G.E.,“AerodynamicsofLowA spectRatioWings atLowReynoldsNumberswithApplicationstoMicroAirVehic leDesignand Optimization,”Tech.Rep.UNDAS-FR-2025,UniversityofNo treDame,November 2001. [177]Mizoguchi,M.andItoh,H.,“EffectofAspectRatioonA erodynamic CharacteristicsofRectangularWingsatLowReynoldsNumbe rs,” 50thAIAA AerospaceSciencesMeetingincludingtheNewHorizonsForu mandAerospace Exposition ,No.AIAA2012-0052,Nashville,Tennessee,January2012. [178]Moffat,R.J.,“DescribingtheUncertaintiesinExper imentalResults,” Experimental ThermalandFluidSciences ,Vol.1,1988,pp.3–17. [179]Hibbeler,R.C., EngineeringMechanicsStatics ,Prentice-Hall,ninthed.,2001. [180]Tsuji,Y.andIshihara,T.,“Similarityscalingofpre ssureuctuationinturbulence,” PhysicalReviewsofModernPhysics ,Vol.68,2003,pp.026309–1to026309–5. [181]Gotoh,T.andFukayama,D.,“PressureSpectruminHomo geneousTurbulence,” PhysicalReviewLetters ,Vol.86,No.17,2000,pp.3775–3778. 304

PAGE 305

[182]Korst,H.H.,Chow,W.L.,Hurt,R.F.,White,R.A.,andA ddy,A.L.,“Analysisof FreeTurbulentShearFlowsbyNumericalMethods,” Proceedingsofconference onfreeturbulentshearows ,Vol.1,NASA,1973,pp.185–232. [183]Schlichting,H.andGersten,K., Boundary-LayerTheory ,Springer,2000. [184]Elsayed,O.A.,Asrar,W.,Omar,A.A.,andKwon,K.,“Ev olutionofNACA23012 WakeVorticesStructureUsingPIV,” JournalofAerospaceEngineering ,Vol.25, 2012,pp.10–20. [185]Devenport,W.J.,Rife,M.C.,Liapis,S.I.,andFollin ,G.,“Thestructureand developmentofawing-tipvortex,” JournalofFluidMechanics ,Vol.312,1996, pp.67–106. [186]Rokhsaz,K.,Foster,S.R.,andMiller,L.S.,“Explora toryStudyofAircraft WakeVortexFilamentsinaWaterTunnel,” JournalofAircraft ,Vol.37,2000, pp.1022–1027. [187]Igarashi,H., AstereoscopicPIVstudyonthebehaviorofnear-eldwingti pvortex structures ,Master'sthesis,IowaStateUniversity,2011. [188]Sohn,M.H.andChang,J.W.,“VisualizationandPIVstu dyofwing-tipvortices forthreedifferenttipcongurations,” AerospaceScienceandTechnology ,Vol.16, 2012,pp.40–46. [189]Batchelor,G.K.,“Axialowintrailinglinevortices ,” JounralofFluidMechanics Vol.20,1964,pp.645–658. 305

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BIOGRAPHICALSKETCH MikeSytsmawasbornafarmerinaportionofSouthernAmerica calledHomestead, whichistechnicallypartofFlorida.Therehelearnedtolob ster,sh,anddealwith CategoryVhurricanes.ThirteenyearsinschoolatUniversi tyofFloridataughthim nothingmorethanthatsailingisthemostimportantthingin life,andhencehemust devotehislifetoit.Afternishinghismaster'sdegreeheh atchedaplanwhereaftera fewyearsofworkingheshallcastofftheworldofworkinfavo roftheworldofsailing. Hejusthappenedtogetmarried,buyandsellacoupleofsailb oatsandcompletehis Ph.D.inthattime,butthathasnotchangedhisplans. 306