Understanding and controlling vorticity transport in unsteady, separated flows

296 Pages·2016·7.2 MB·English

University of Iowa
Iowa Research Online
Theses and Dissertations
Fall 2015
Understanding and controlling vorticity transport
in unsteady, separated flows
James Akkala
University of Iowa
Copyright 2015 James Akkala
This dissertation is available at Iowa Research Online: https://ir.uiowa.edu/etd/1947
Recommended Citation
Akkala, James. "Understanding and controlling vorticity transport in unsteady, separated flows." PhD (Doctor of Philosophy) thesis,
University of Iowa, 2015.
https://doi.org/10.17077/etd.8t9jvlnt
Follow this and additional works at:https://ir.uiowa.edu/etd
Part of theMechanical Engineering Commons
UNDERSTANDINGANDCONTROLLINGVORTICITYTRANSPORTIN
UNSTEADY,SEPARATEDFLOWS
by
JamesAkkala
Athesissubmittedinpartialfulfillmentofthe
requirementsfortheDoctorofPhilosophy
degreeinMechanicalEngineering
intheGraduateCollegeof
TheUniversityofIowa
December2015
ThesisSupervisor: JamesH.J.Buchholz
GraduateCollege
TheUniversityofIowa
IowaCity,Iowa
CERTIFICATEOFAPPROVAL
PH.D.THESIS
ThisistocertifythatthePh.D.thesisof
JamesAkkala
has been approved by the Examining Committee for the thesis requirement for the Doctor
ofPhilosophydegreeinMechanicalEngineeringattheDecember2015graduation.
ThesisCommittee:
JamesH.J.Buchholz,ThesisSupervisor
ChristophBeckermann
DonaldGurnett
Ching-longLin
FrederickStern
ACKNOWLEDGEMENTS
I would like to begin by thanking Professor James Buchholz for the tremendous
encouragement,guidanceandsupportthathehasprovidedtomethroughoutthisendeavor.
Without his inspiration, optimism and confidence in my abilities, this work could not have
been accomplished. I would also like to thank him for affording me the privilege of par-
ticipating in the Air Force Summer Faculty Fellowship Program and for giving me the
opportunitytopresentmyworkatseveralconferences.
Iwouldalsoliketothankmyesteemedcommitteemembers,Prof. ChristophBeck-
ermann, Prof. Donald Gurnett, Prof. Ching-Long Lin and Prof. Frederick Stern for their
valuabletime andinsightful discussion. My sincerethanks alsoextends tomyclose friend
KatieRadtkeforgenerouslyservingasmythesisreaderandprovidinginvaluablefeedback
forimprovingthequalityofthiswork.
It has been my pleasure to work with an amazing research team at the University
of Iowa. Azar Eslam Panah, Kevin Wabick and Craig Wojcik, in particular, have been
outstandingco-collaboratorsandIamfortunatetohavehadthechancetoworkwiththem.
Lastbutnotleast,Iwanttothankmyparentsfortheirsteadfast supportinallthatI
do, as well as my friends at the University of Iowa for providing me with some of the best
timesofmylife.
This work was supported in part by the Air Force Office of Scientific Research,
awardnumberFA9550-11-1-0019,andbyIIHR-Hydroscience&Engineering.
ii
ABSTRACT
Vortices interacting with the solid surface of aerodynamic bodies are prevalent
across a broad range of geometries and applications, such as dynamic stall on wind tur-
bine and helicopter rotors, the separated flows over flapping wings of insects, birds and
micro-air vehicles, formation of the vortex wakes of bluff bodies, and the lift-producing
vortices formed by aircraft leading-edge extensions and delta wings. This study provides
fundamental insights into the formation and evolution of such vortices by considering the
leading-edgevorticesformedinvariationsofacanonicalflappingwingproblem.
Specifically, the vorticity transport within three distinct experimental cases–2D
plunging airfoil, 3D plunging airfoil and 2D plunging airfoil with suction applied at the
leading edge–were analyzed in order to characterize the formation and evolution of the
leading-edgevortex(LEV).
Three-dimensionalrepresentationsofthevelocityandvorticityfieldswereobtained
via multi-plane particle image velocimetry (PIV) measurements and used to perform a
vorticity flux analysis that served to identify the sources and sinks of vorticity within the
flow. Time-resolved pressure measurements were obtained from the surface of the airfoil
andusedtocharacterizethefluxofvorticitydiffusingfromthesolidsurface,andamethod
forcorrectingdynamicpressuredatawasdevelopedandvalidatedfortheapplicationwithin
thecurrentstudy.
Upon characterizing all of the sources and sinks of vorticity, the circulation budget
wasfoundtobefullyaccountedfor. Interpretationoftheindividualvorticitybalanceterms
iii
demonstrated vorticity generation and transport characteristics that were consistent among
all three cases that were investigated. Three-dimensional vorticity fluxes were found to
be an almost negligible contributor to the overall circulation budget, mostly due to the
individual terms canceling each other out. In all cases, the diffusive flux of vorticity from
the surface of the airfoil was shown to act primarily as a sink of LEV vorticity, with a
magnitude roughly half that of the flux of vorticity emanating from the leading-edge shear
layer.
Inspection of the chordwise distribution of the diffusive flux within the 2D case
showed it to correlate very well with the evolution of the flow field. Specifically, the
diffusive flux experienced a major increase during the phase interval in which the LEV
remained attached to the downstream boundary layer. It was also noted that the accu-
mulation of secondary vorticity near the leading edge prevented the diffusive flux from
continuingtoincreaseaftertheroll-upoftheLEV.Thisresultwasvalidatedwithinthe3D
case, which demonstrated that maintaining an LEV that stays attached to the downstream
boundarylayerproducesalargerdiffusivefluxofvorticity–presumablyenhancingbothlift
andthrust.
Through the use of a spanwise array of suction ports, the suction case was able
to successfully alter the total circulation of the flow by removing positive vorticity from
the opposite-signed vortex (OSV) that formed beneath the LEV. This removal of positive
vorticityproducedameasuredincreaseinthetotallift,anditwasnotedthatweakeningthis
region of secondary vorticity allowed the LEV to impose more suction on the surface of
the airfoil. However, it was also noted that weakening the OSV resulted in a loss of thrust,
iv
which was attributed to the loss of suction that occurred near the leading edge when the
removal of secondary vorticity caused the energetic OSV to be reverted into a low energy
regionofseparatedflow.
Thephysicalinsightsprovidedbythisworkcanformthebasisofnovelflowcontrol
strategiesforenhancingtheaerodynamicloadsproducedinunsteady,separatedflows.
v
PUBLICABSTRACT
The interaction between vortices and the solid surface of an aerodynamic body is a
ubiquitous feature of high-angle-of-attack aerodynamics associated with a broad range of
aerospace structures, including maneuvering and flapping wings, blades on helicopter ro-
torsandgasturbineengines,theaerodynamicforebodesofmissilesandhigh-performance
aircraft. Thisstudyprovidesfundamentalinsightsintothedevelopmentofsuchvorticesby
consideringthevortexformedattheleadingedgeofaplungingairfoil.
The primary goal of this work was to rigorously characterize the formation and
evolution of the leading-edge vortex (LEV) based on the transport of vorticity both within
the bulk flow as well as near the surface of the airfoil. By performing a novel analysis
thatservedtoquantifythenear-walldynamicsoftheflow,thisstudydemonstratedthatthe
strength of the LEV was significantly reduced by its interaction with the solid surface. It
was further shown that the near-wall vorticity transport mechanisms associated with this
reduction also play a critical role in governing the formation and development of the LEV
priortoitsdetachment.
By explicitly characterizing how the vortex-airfoil interaction affects the evolution
of the LEV, the results of this study have significantly enhanced our understanding of why
the LEV develops the way it does. The physical insights provided by this work can form
the basis of novel flow control strategies for enhancing the aerodynamic loads produced in
unsteady,separatedflows.
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TABLEOFCONTENTS
LISTOFTABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x
LISTOFFIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi
NOMENCLATURE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xix
CHAPTER
1 INTRODUCTIONANDBACKGROUND . . . . . . . . . . . . . . . . . . 1
1.1 MotivationandGoals . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 LiteratureReview: TheLeading-EdgeVortex . . . . . . . . . . . . . . 2
1.2.1 LEVFormationProcess . . . . . . . . . . . . . . . . . . . . . 4
1.2.2 LEVScaling . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.2.3 EvolutionoftheLEV . . . . . . . . . . . . . . . . . . . . . . 9
1.2.4 EffectofCross-SectionalShapeofanAirfoil . . . . . . . . . . 14
1.2.5 Three-DimensionalVortexStructure . . . . . . . . . . . . . . 16
1.3 LiteratureReview: BoundaryVorticityDynamics . . . . . . . . . . . 19
1.3.1 VorticityTransportatBoundaries . . . . . . . . . . . . . . . . 20
1.3.2 FlowControlandBoundaryVorticityManipulation . . . . . . 30
1.4 Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
1.5 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2 DEVELOPMENTOFTHEVORTICITYFLUXANALYSIS . . . . . . . . 37
2.1 DerivationofVorticityFluxEquation . . . . . . . . . . . . . . . . . . 37
2.2 CharacterizationoftheDiffusiveFluxofVorticity . . . . . . . . . . . 43
2.3 ModelImplementation . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3 METHODOLOGY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.2 ModelGeometriesandExperimentalTechniques . . . . . . . . . . . . 56
3.3 Suction System and Internal Fluid Transmission Lines of the AR4
Airfoil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
3.4 DigitalParticleImageVelocimetry . . . . . . . . . . . . . . . . . . . 70
3.4.1 StereoParticleImageVelocimetry: BaselineandSuctionCases 70
3.4.2 2DParticleImageVelocimetry: AR2Case . . . . . . . . . . . 76
3.5 ForceMeasurements . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
3.6 TransientPressureMeasurements . . . . . . . . . . . . . . . . . . . . 80
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3.6.1 BaselineandSuctionCases . . . . . . . . . . . . . . . . . . . 80
3.6.2 Finite-ARCase . . . . . . . . . . . . . . . . . . . . . . . . . 82
3.6.3 PressureDataAcquisition . . . . . . . . . . . . . . . . . . . . 85
4 CORRECTIONOFDYNAMICPRESSUREMEASUREMENTS . . . . . . 86
4.1 Methods for Assessment and Correction of Transient Pressure Mea-
surements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
4.2 TestCase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
4.3 DynamicCalibration . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
4.4 InverseIdentificationMethods . . . . . . . . . . . . . . . . . . . . . 95
4.4.1 Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
4.5 ModelImplementationandCorrectionofPlungingAirfoilData . . . . 98
5 RESULTSFORTHEBASELINECASE . . . . . . . . . . . . . . . . . . . 100
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
5.2 GlobalFlowDynamicsandLEVEvolution . . . . . . . . . . . . . . . 100
5.3 CharacterizationoftheVorticityBudget . . . . . . . . . . . . . . . . 103
5.3.1 Region A: AttachedFlow . . . . . . . . . . . . . . . . . . . . 113
5.3.2 Region B: SeparationattheLeadingEdge . . . . . . . . . . . 115
5.3.3 RegionC: LEVDetachment . . . . . . . . . . . . . . . . . . 118
5.3.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
6 CHARACTERIZATION OF THE FLOW PHYSICS GOVERNING THE
FORMATIONOFTHELEV . . . . . . . . . . . . . . . . . . . . . . . . . 123
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
6.2 FormationoftheLEV . . . . . . . . . . . . . . . . . . . . . . . . . . 123
6.3 DevelopmentoftheOSV . . . . . . . . . . . . . . . . . . . . . . . . 129
6.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
7 FORCESONA2DPLUNGINGPLATE . . . . . . . . . . . . . . . . . . . 139
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
7.2 LiftDecomposition: ContributionsfromUpperandLowerSurfaces . . 142
7.3 LiftDecomposition: Viscous/InviscidContributions . . . . . . . . . . 146
7.4 AerodynamicsoftheLEV . . . . . . . . . . . . . . . . . . . . . . . . 149
7.5 OverviewofSubsequentChapters . . . . . . . . . . . . . . . . . . . . 154
8 RESULTSFORTHEFINITEASPECT-RATIOCASE . . . . . . . . . . . 155
8.1 GlobalFlowDynamicsandEvolution . . . . . . . . . . . . . . . . . . 155
8.2 FluxAnalysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
viii