OCli .311

OCli .311

EFFECT OF FREESTREAM VORTICAL STRUCTURES AND VORTICITY ON STAGNATION REGION HEAT TRANSFER

by

CAung Naing O o

inpanialfulfillmentofthe requirements for the degree of

Doctor of Philosophy

Facultyof Engineeringand Applied Science Memorial Universityof Newfoundland

January2002

An experimentalstudywas perfonnedto investigatethe influenceoffreestream turbulence with coherentve rtical structuresonstagnationregion heat transfer.Aheat transfermodel with a cylindrical leading edge was testedin a lowspeedwindtunnelat Reynoldsnumbersrangingfrom 67.750 to142.250 based on leading edgediametero fthe model.Gridsof parallel rods withdiameters2.86em,1.59cm and0.95cm were usedto generate the freestrearnturbulence withwell-defined primaryvonexlines.The grids were placed atseveral locationsupstream of the heat transfermodel in orientations where the rods were perpendicular and parallel to the stagnationline.Hot-wire anemometry was

freestreamturbulence was characterized usingthe turbulenceintensity.integral lengrh scale.lateralvelocity and vonicityfluctuatingcomponent.Theturbulenceintensityand the ratio of integrallength scale to leading edge diameter were in the range of3.93to 11.78%and0.07 to 0.7.respectively.Characteristics of coherent vertical structures downstrearnofthe gridswereexaminedbyanalyzingthe isotropycf turbu lence.uateral velocityandvorticity fluctuating compo nentsand the wavelet energyspectra of the lateralfluctuating velocity components downstreamof the turbulencegrids.Heat transfer coefticients were estimatedbymeasuring thetemperaturedistribution and the heat flux.

Thegrids with rods perpendicularto thestagnationline. where the primary ve rtical structures are expecred to be perpendicular to the stagnation line.resultin higher heat transfertbanthose withrods parallelto the stagnation line.Thedifferenceberweenthe

two grid orientationswas more pronouncedfor the biggerrod-grids.The measured heat transfer data andfreestream turbulence characteristics werecomparedwith existing correlationmodels.Anattempt to predictthe heat transferaugmenrationatthestagnation line due to the turbulencewithcoherentvonical structures usinga neural network was made.A newcorrelation for the stagnationlineheat transfer.whichincludes the spanwisefluctualingvonicilycomponents,has been developed.

Acknowledgements

Iwould like to express mysincerestgratitude to Dr.Chan Chingfor hisexcellent advice, unfadingpatience,invaluable guidance.brotherlycareandcontinuous encouragement throughout the studyperiod.I also thank Dr.Neil Hookeyand Dr.

Michael Hincheyfor their usefulsuggestions and good-hearted help The financialsupport of the Natural Sciences and Engineering Research Council (NSERC) of Canada to conduetthisexperimental study is gratefullyacknowledged.

Specialthanksarealsogiventothetechnicians.staffmembersandfriendsat the FacultyofEngineeringandAppliedSciencefortheirkindassistanceo

Finally,I would like to mention myheartiest gratitudeto my beloved wife,Thi, and myfamilyfor their patienceand understanding.

Acknowledgments Table of Contents Lislo/Tabl.s List of Fignres List of Abbreviations and Symbols List of Appendices

1.1 ImponanceofStagnation Heat Transfer 1.2 lntluence of Freestream Von icity and Von ical Struetures

1.3 Objectives of the Study 1.4 Rational of the Study 1.5Methodology

2.1 Heat Transfer in the Stagnation Region

2.1.2 Empirical and Semi-Theoretical Correlation Models 2.1.3 Predietions by Computational Methods

2.2.1Wake Behind a Circular Cylinder

Page

2.2.2CoherentStructuresandTransponMechanismin Boundary Layers

2.3VonicityCharacteristicsandMeasurement 2.3.1Vorticity Dynamics in Turbulent Flows 2.3.2Measurement Techniques

2.3.2.\Thermal Anemometry 2.3.2.2Optical Anemometry 2.4Summary

III Experimental Set-up and Data Reduction 3.1Experimental Facilities

3.1.1 Wind Tunnel Configuration

3.1.3Turbulence Generating Grids

3.1.4Hot-wireAnemometers and Data Acquisition Systems 3.2Experimental Procedures,Data Reduction and Uncertainty Analysis 56

3.2.2.1Single Wire

3.2.2.3Vorticity Probe

4.1.1Turbulencelntensity 4.1.2IntegralLengthScale 4.1.3Fluctuating Velocity Components 4.1.4Spanwise Voni cityC omponem s andl sotropy

4.1.5 WaveletAnalysiso f Freestr eam Tu rbulence

Prediction of Stagnation Line HeatTransfer Augmentation 5.1Prediction UsingNeuralNetworks

Neural Computing

5.1.1.2Optimization oftheNeuralNetwork Model

5.2 Predictionby CorrelationModels 5.2.1Comparison withExistingCorrelation Models 5.2.2Correlat ionModellncorporatin g Voni calstnlClures

andtheVo rticity Field VI Conclusions,Contribution sand Recommendations

References

Appendix A AppendixB AppendixC

Experimental Uncertaintyof Parameters in EstimatingFr(%) ExperimentalUncertainty of TurbulenceParameters(%) The constantCy of'Eq.fc.Z)

Stagnation Line FrosslingNu mbers Variationoflnput and Output Parameters Neural Network Optimizat ionConfigurations

Page

UstofFlgures

Page

Figure I.! Illustrationof TurbineBlade Cooling Figure1.2 Variation of Turbine Inlet TemperatureoverRecent Years Figure1.3 Heat Transfer Distributionover a Turbine Blade Figure1.4 Vortex Filaments Stretched and Tilted byDivergenceof

Streamlines and Acceleration around Leading Edge Figure2.1 HeatTransferaroundaCylinderinCrossflow Figure2.2 Heat Transfer Distributionin the Stagnation Regionof

a Circular Cylinder

Figure2.3 Effect of Strouhal NumberbyVarying Reynolds Numberon the !7

Figure 2.4 VelocityProfile with Superimposed SinusoidalVariation Figure 2.5 Spatial Relation between Wires.Vortex Pairs and Heat Transfer 20 Figure2.6 ComparisonofPredictionb yEq.2 .6withothe rData Figure2.7 Predicted Stanton Number Distributionfor a Turbine Stator Figure 2.8 Heat TransferCoeflicient ona Vane

Figure2.9 Flow Regimes and Recirculation Regionin the Cylinder Wake 33 Figure2.10 Electrical Circuit ofa Constant-Temperature Anemometer Figure 2.11 Attenuation of MeasuredVelocity GradientDue

to Separation Distance

Figure 2.12 Dependence of Experimental(M)and DNS (0) Measured to True 43 Velocity Gradients on Wire Separation Distance Figure 2.13 (a) Kovasznay-Type Vorticity Probe and (b) Modified Version 44 Figure 2.14 Compact Four-Sensor Cross-Stream Vorticity Probe Figure 2.15 Schematic Diagramsof Multi-SensorProbes Figure3.1 Schematic Diagram of the Wind Tunnel Figure 3.2a Schematic Diagram of Heat Transfer Model Figure3.2b Photos of Heat Transfer Model Figure 3.3 Data Acquisitionfor Heat Transfer Model Figure3.4 C-ChannelsArrangement forParalleJ Rods Figure3.5 Arrangement of Rod-Grids Figure3.6 Four-Wire Vorticity Probe Figure 3.7 InstrumentationofVonicity Probe Figure 3.8 Spanwise Temperature Distributionsof Heated Stainless

Steel Strips

Figure 3.9 Distribution of FrosslingNumber in the Stagnation Region

Figure3.10 Curve Fitting for Autocorrelation Function Figure3.11 Instantaneous Velocityon a Slanted Sensor of X-wire

and Yaw Angle

Figure4.1 Streamwise Turbulence Intensity Downstream of the Grids Figure 4.2 Streamwise Integral Length Scale Downstream of the Grids

Figure 4.3 RMS Fluctuating VelocityComponents of Grids in Perpendicular Orientation

Figure 4.4 Streamwise Distribution of'Fluctuating VorticityComponents Figure 4.5 StreamwiseTrends of the Degree of Isotropy Figure 4.6 The Mexican Hat Wavelet Figure 4.7 PrimaryVorticesbehind the Grid-Rods in

Perpendicular Orientation

Figure 4.8 Temporal Plots of Wavelet Transform Coefficientsfor the 2.86cmRod-gridsatxd=25 Figure 4.9 Temporal Plots of Wavelet Transform Coefficients for

the 2.86cmRod-gridsat xd=125 Figure 4.10 Comparisonof Wavelet and Fourier Energy Spectra Figure 4.1I Wavelet Energy Spectra for 2.86 cm Grid (Perpendicular)

Figure4.12 Wavelet Energy Spectra for 1.59 cm Grid (Perpendicular) atReD=67,750

Figure 4.13 WaveletEnergy Spectra for 0.95cmGrid (Perpendicular)

Figure4.14 WaveletEnergy SpeClrafor2.86cmGrid (perpendicular)

Figure 4.15 Wavelet Energy Spectra for 1.59 cm Grid (Perpendicular)

Figure 4.16 Wavelet Energy Spectra for 0.95em Grid (perpendicular) at ReD=108.350

Figure 4.17 Wavelet Energy Spectra for 2.86em Grid (Perpendicular) at Reo=142 .250

Figure 4.18 Wavelet Energy Spectra for 1.59 em Grid (Perpendicular) at Reo=142.250

Figure 4.19 WaveletEnergy Spectra for 0.95em Grid (Perpendicular)

Figure 4.20 Distributionof Frossling Number in the StagnationRegion for 2.86em Rod-grid

Figure 4.21 DistributionofFrosslingNumberin the Stagnation Region for 1.59 em Rod-grid

Figure4.22 Distribution of Frossling Number in the Stagnation Region for 0.95 em Rod-grid

Figure 4.23 DislributionofNormalizedFrosslingNumberinlheStagnation Region for 2.86em Rod-grid

Figure 4.24 DislribulionofNormalizedFrosslingNumber intheStagnalion Region for 1.59 em Rod-grid

Figure 4.25 DislributionofNormalizedFrossling Number inlheSlagnalion Region for 0.95 em Rod-grid

Figure 4.26 SlagnationLineFrosslingNumber

Figure 4.27 Difference in Heat Transfer withGrid in Horizontal over Venical Orientationfor 2.86em Rod-grid Figure 4.28 Difference in Heat Transfer with Grid in Horizontal over

VerticalOrientation for 1.59 em Rod-grid Figure4.29 Difference in Heat Transfer with Grid in Horizontal over

VenicaIOrientationforO.95cmRod-grid Figure 5.1 Feed-forward ArtificialNeural Networks Figure5.2 Optimization of the Number of Hidden Neurons Figure5.3 Optimization of the Learning Rate Value Figure 5.4 Nusselt Number(Nil)vs.Integral Length Scale(A.,-D) Figure 5.5 Nusselt Number(Nil)vs. Streamwise Turbulence Intensity(IIU) Figure 5.6 Nusselt Number(Nil)vs.NormalTurbulence Intensity(vl.!) Figure 5.7 Nusselt Number(Nil)vs.Spanwise Turbulence Intensity(w l.!) Figure 5.8 Nusselt Number(Nil)vs.Normal Vorticity(aJ,D·l.!) Figure5.9 Nusselt Number(Nil)vs.SpanwiseVorticity(w,Dl.!) Figure 5.10 Relative Contribution (Strength) Factors of Input Variables Figure 5.11 Stagnation Line Frvs.Correlation Parameter proposed by

Vanfossen et al. (1995)

Figure 5.12 Stagnation Line Fr vs.Correlation Parameter with Spanwise VorticityandVelocity Fluctuationsfor both Grid Orientations

Ust of Abbreviations and Symbols

Waveletdilationparameter (s) Areaoftheheatedponionoftheleadingedge(m' ) Waveletlocationparameter(s ) Chord length ofa turhineblade(m )

c.

= Admissibilityconstant

Cla,b)= Wavelet transform usingwavelet scalea at locationb Diameterofarod(m)

Diameter of cylindrical leadingedge (m) E(f) Energy spectra (m' /s)

Frequency(Hz)

Frequency of the passband center of the wavelet (Hz) Kolmogorovfrequency(Hz) Sampling frequency(Hz) FrosslingNumber(NuI,[R£;;l

Heat transfer Coefficient(W/m'K) Current (Ampere) Degteeofisotropy

Thermal conductivity(W/m.K) Nusselt number(=hDlk)

Qco,",= Conductionheat 10ss( W) Qc~ ConvectionheatIransfer(W)

Q.. Heal inpul (W)

Q"", Radiationhe allo ss (W) R( r) AUlocorrelationfu netion forti me shiftt

Reynoldsnumbe rbasedond (=Ud'v) Reynoldsnumber based onD(=UD'v) S(I) Signal variable(hereinvelocity)

Distancebetween twowires(m)

Instantaneousvelocityof fluid flow overa hotwire(mls) Time(s)

StreamwiseTurbulencelnlensity( %)(=II IU <100) Tw( (J)= Temperatureofthelead ingedge atangl e8 (K)

Temperatureoffreeslream (K)

rmsoffl uetuating velocily component in streamwised irection (mls) Meanfreestreamvelocity (mls)

Uncen ainty(%)

rmsoffluetualing velocity component in spanwiseY direetion (parallelto stagnation line)(mls) Meanvelocityin spanwiseYditeetion (mls)

Voltage I'V)

rmsoffluetualingv elocilycomponent inspan wiseZ direclion (~ndicularlostagnalionline) ( mls) Meanvelocityinspanwise Z direetion Distancedownstreamof thegridIm)

Slreamwisedislancemeasuredalongalurbinebladerromlheslagnalion line(m)

Spanwisedirectionparallel to thestagnatio n line Spanwisedireetionperpendicularlolhe slagnal ion line Anglemeasured from the stagnationpoint (degree) Turbulent kinetic energy dissipationrate(m'/s') Kinematic viscosityo frreestream (m'/s) Timeshift(s )

Kolmogorovlengrhscale(m) Slreamwiseintegrallengrhscaleoflurbulence (m) Angular frequencyofthe passband center of the wavelet (radls) rmso ffluetuat ing von icity component inspan wiseYdirection ( l/s) 4 = InstantaneousvorticityinspanwiseYdirection(lis)

rms of'fluctuating von icityc omponentin spanwiseZdirection(li s) Instanlaneous von icily inspan wiseZdireclion ( lIs )

Ust of Appendices

AppendixA:EstimationofConduction Heat Lossesthrough the LeadingEdgeBody Using A Three-DimensionalFiniteElement Model AppendixB:EstimationofExperimen tal Uncenainties Appendix C:Calibration and Data Reduction Programs for Hot-wires

Chapter I Introduction

1.1Importanceof Stagnation Region Heat Transfer

Stagnationregion heat transfer in the presence of freestream turbulence is important in a number of common engineering applications.For example,in heal transfer devicessuchasboilersandlubularhealexchangers,thecross-flowover the lubes results in astagnation region.Heal transfer inthe stagnaticnregion is significantlyaugmented whenthefreestream becomesturbulent.The augmentation in heattransferdependson the flow characteristics,physicalp ropen ieso ftheflu id,shape,size and surfaceroughnessof Ihe stagnation region.Stagnationregionheal transfer is probablythernost critical in the blunt leading edgeregion ofgas turbineairfoilswhere the temperature of thecombustion gasesoftenexceeds the allowabletemperaturelimitof the bladematerials,Asaten percentincreasein the turbine inlet temperature from the current level of 1950K can resull inan approximale40%increase inspecificpoweroutpul,inkWlkgls,ofagas lurbine (Lakshminarayana,1996),modem gasturbine engineslend louse increasingly higherturbine inlet temperatures, Turbineinlet temperatures are,however,limitedbythe allowableturbine blade metaltemperature.While newerblade materials such as ceramic compositesandceramic coatingsare underdevelopment.the usualpracticeto achieve higher inlet temperaturesisthroughturbinebladecooling.The coolingisusually accomplishedbybleedingair from Ihe compressor outletand directing iI throughcooling channelsonlheblade(Figurel.l ).TheeffeCIivenessofthecoolinglechniqueis

important since a smaller cooling airflowrequirement would lead to a higher overall efficiencyof the turbine.A great deal of research on improvingboth blade cooling systemsand allowable metal temperatureshas been performed over the last few decades (Hannis and Smith.1982;LeGrives.1986).Significantimprovements in blade cooling techniqueshaveproduced greaterincreasesin turbine inlet temperaturethandevelopment ofbellermaterialtechnology (seeFigure1.2).While modem gas turbines operateat turbineinlettemperaturesofaboutI500°C.advancedbladecoolingtechniqueskeep the blade surface at temperatures lower than the allowablemetal temperature of about950°C (Bathie,1996;Lakshminarayana.1996;Satoetal..1997;Duffyet al.,1997).Astheexit temperature of a modem highenthalpyrise combustor can be greater than 2000°C. there is still significant potential to increase turbine inlet temperatures byfurther improving blade cooling techniques and allowable metal temperatures

Accurate prediction of turbine blade heat transfer (i.e.heat transfer from combustiongases to turbine blades) is essentialtoimprove blade cooling systemdesigns.

A complete understanding of turbine blade heat transfer,however,may be d iffi cult. since gas turbine flows are complex with high turbulence, strong secondary flows.rotational effects,airfoil row interaction (rotor/statorand stator/rotor),local flow separation and shock-boundary layerinteractions (Blairet al.,1989).Thepredictionsofheattransferto the first stage blades and vanes ofa newlydesigned gas turbine can beinerrorbyafactor oftwoorthreeundercenainengineconditions(MaciejewskiandMoffat.1992;Larsson.

1997).However.a fundamental understanding of the isolated influence ofea ch of the aboveeffectsonheattransferwouldallowthemtobeincorporatedmore effectivelyinto cooling system designs

NewCooling Concept - - - . ."

~~~n~~~~on--//"'"

S O P h i S l i C 8 t e d A CoolingSySlems

FilmImpingement Convedion

~SimPleCOOling

~1:d'T:~:e~

^{- . :}

;1~~a~l;~etal

^Temp.

1000,9L....50-...I..-_....L..-_...l...-._~,...J Year

Figure 1.2VarialionofTurbine Inlet Temperature owrRecentYeal$ (Adop ted from Copyright@)RoUsRoyce,plc.)

The stagnationregion is of interest because heat transfer is usuaIlyamaximumat the blunt leading edge of the airfoils (see Figure1.3).The physics of stagnation region heat transfer in the presence offreestreamturbulenceis still poorlyunderstood despite the number of empirical correlations that have been developed

UNSTEADY WAKEFL!:NI STAGNATION

POINT

1.2Influence of Freestream Vorticity and Vortical Structures

Turbulence is characterized by fluctuating vorticity,and in a sens e. vorticiry can be viewed as the underlying characteristic of turbulence (Tennekes and Lumley.1972) Heat transfer augmentation in the stagnation regionis hypothesized to be caused by vo rticit y amplitication (Sutera et al..1963;Sutera.1965;Morkov in.1979).lfavonical filament. which is normal to the stagnation line and freestream flow direction.is considered.the filament is stretched and tilted:as it is advectedintothe stagnation region due to divergence and acceleration around the bluff body (see Figure1.4). This stretching causes the vorticity to be intensitied through conservation of angular momentum.The vortical filament with intensitied vorticity interacts with the boundary layer and induces

velocity gradients in the spanwise direction parallel to the stagnation line.The three- dimensional velocity gradients enhance the transpon mechanism within the boundary layer resulting in higher heat transfer.On the other hand,a vonical filament which is parallel to the stagnation line is not stretched.due to no apparent velocity divergence in this direction,asit approaches the stagnation region.Prior experimentaland numerical

Simoneau.1987;Rigby and Vanfossen.1991) show that this intensification of vorticity causes heat transfer to increase while the boundary layer remains laminar.A complete understandingof the transpon mechanisms of momentum and heat in turbulent flows has

turbulentflow play an imponantrole in momentum transponand heat transfer.

Manipulation of these vertical structures could result in a change in heat transfer (Jacobson and Reynolds.1993; HoandTai, 1996;Kasagiandlida.1999).

6

Vorticalfilamenl

Figure 1,4 Vortex Filamenls Stretched and Tilted by Divergence of StreamIinesand

Severalattempts havebeen made to understandthe relationshipbetween freestreamturbulence and stagnationregionheattransfer bystudyingtheisolated effect ofturbulent intensity,Reynoldsnumber,unsteady wake.stagnation point velocity gradient andintegral length scale(Smith and Kuethe,1966;Kestinand Wood . 1971;

Lowery andVachon.1975;0'BrienandVanf ossen,1985;Mehendale et al.,199 1;Han etal.•1993;Zhang and Han,1994;VanFossen er al.,1995;Ahmaed andYovanovich.

1997;Du et al.,1997).The studyof the effect of freestream vorticityonthestagnation regionheat transferis. however.verylimited,andno considerabIe effortstoinclude the

transfermechanism ingasturbineblades is considered.itis rational to studythe effect of freestreamvonicalstrua ures andvoni cityon the stagnation regio nheattransfer as the turbulenceatturbineinlet isexpectedtobehighlyan isotropic(Johnston,1974)andwell lacedwith coherent vortical strua ures( Lakshminarayana.1996).

1.3Ob]ectlves of the Study

Describinga turbulent flow withoutreferenceto thevorticity field andve rtical structuresisunlikely to provideacomplete picture oftheturbulence.Aknowledgeofthe effectoffreestrearnvorticity andvonicalstructures onstagnation regionheat transfer shouldlead toabetterunderstandingo f theph ysicalmechan ismoftheheattransfer. The goal ofthe current study is.therefore.toinvestigate the influence0ffreestreamvorticity andvonicalstructures on the stagnation region heat transfer.Thespecifie object ivesof the studyare:

(i) To generate turbulence withdifferentvon ical structures (one with primary von icessusceptible tostretching and anotherwith primary von ices not susceptibleto stretching as theyapproachthe stagnation region);

Iii) To quantifythefreestream turbulence bymeasuring the fluctuatingvelocity components.integrallengthscale and the vorticityfield and to analyzethe characteristicsof'vortical structures:

(iii ) To quantifythe heat transfer enhancement in thestagnation regionbythe two different turbulent flows in(i);

(iv) To examinethe nature ofheat transferaugmentationoverthe stagnation regionby differ entfree streamcoherentvonic a lstruct ures;

(v) Toinvestigatethe difference in stagnationregionheattransfer duetofreestream turbulencewith distinct ve rticalstructures and thatdue to turbulencegenerated usingsquare mesh grids;and

(vi) To examine the relationshipbetween the characteristics of the freestream turbulence,including information pertaining to the vonicalstructuresandthe voni city field.and stagnation region heat transfer.

1.4Rationale of the Study

Byincluding thevonical structures andvorticityfield to characterizethe freestreamturbulence,thisstudyshouldprovideabenerunderstanding ofthestagnation regionheat transfer.To the author' sknowledge.this isthe first studythat would incorporate freestream vonical structures and vonicitywhenformulatingmodelsforthe

heat transfer. Theconjecturethatvonicityamplificationinthestagnationregion plays an important role had not been experimentallyproven. and this study should produce quantitative experimental information on the relation between the freestreamvorticity and stagnationheat transfer,Most previous studies have focused on the effect of isotropic turbulence generated bysquare meshgrids on heat transfer augm entation.The influence offreestreamturbulencewithdifferentvonicalstruetures,i.e.turbulence witha specific directionofvo rticity,should be useful in manyengineering applications.Empirical models basedon a more complete description of the freestream turbulence should not only lead to more reliableestimates of heat transfer augmentation,but also provide further insight into the physical mechanismof stagnationregionheat transfer

1.5 Methodology

The experimental study included two major pans:(i)to generate andquantifythe characteristics offreestream turbulence with distinct cohere nt vortical structuresrand Iii) 10measure the heat transferin the stagnation region

(I)Turbulence Generation andMeasut8ments

The experiments were performedin a low speed wind tunnel,and passive turbulence gridswith parallel rods were used to generatethe freest ream turbulence with well-defined vortex lines.The characteristics of turbulence were measured using hot wire anemometry.A hot wirevonicity probe designed and builtin-house was used for the voni city measurements.The Reynolds number,velocity fluctuations, integral length scale

and spanwisefluctuating vc nic ity componentswere used tocharacterize the freestream turbulence.Thevertical structu reswere investiga ted usingthewavelettra nsform technique

(ii)HestTransferMessurementinthe SfagnstJonReglon

The stagnationregion was simulated using a heat transfer model with a cylindrical leadingedge.The cylindr icalleadingedge had a heatedmetal surface with a uniform heat flux.Anumbe rofthermocouples were embedded onthe leadingedge tomeasure surface temperatures in orderto estimate the heattransfer in the stagnat ion region

Chapter II Literature Review

2.1Heat Transfer in the Stagnation Region

Accurate predictionofstagnationregion heattransferin thepresenceof

freestreamturbulenceisimpon antin a numberof engineeringapplical ions.Theintluence ofturbulence intensity.integrallengthscale.Reynoldsnumber,surfaceroughness.

pressure gradientand body shapeon stagnationregionheat transfer hasbeeninvestigated by several researchersusing avarietyofexperimentaland numericaltechniques.Inmost cases,theaugmentation of heattransferwith aspecificparameter ispresented.and models whichcorrelatecertain characteristicsof'freestream turbulence withstagnation regionheattransferhavebeenformulated.Despitethe extensiveamountof research,a completeunderstanding of the heat transferprocesshasnot yet been obtained.Thisis primarilybecause of the complexmanner in whicha largenumber of parametersaffect the heat transferprocess.

Heattransfer between thefreestream and the surface depends to a largeextent on the natureofthe boundarylayer at thesurface. The boundary layer,in lurn,depends on several parameters such as Reynolds number.freestreamturbulenceintensity.pressure gradient.surface roughness.etc.For the same temperaturedifference betweenthe freestream and thesurface. a thinnerboundarylayerleadsto higherheattransferratedue to agreater temperature gradientacrossthe thermal boundary layer.Heat transfer increases substantiallywhen the laminarboundary layerbecomesturbulent,because the

momentum transfer and heat transfer are closely coupled.However. the physical mechanism of heat transfer at the leading edge is quite unique.because heat transfer is significantlyaugmented by freestream turbulence while the boundary Iayeris believed to remain laminar in this region.Furthermore, heat transfer unsteadiness,defined asthe ratio of the rms to mean heat transfer rate,isamaximum at the stagnationpoint(Ching and O'Brien.1991).Although a complete understandingof the transport mechanisms of momentum and heat in turbulent flows has not been achieved.it is well establishedthat the coherent vertical structures in a turbulent flow play an important rolein momentum and heat transfer. A knowledge of the nature of heat transfer augmentation in the stagnation region due to the freestream turbulence with well definedvonical structures should.therefore,lead to better understanding of thephysicsin this region.

Characteristicsof' stagnation region hear transfer are reviewed from related previous studiesand briefly presented.followed by a review of the studies on turbulence with coherent vortical structures.The existing empirical correlationmodelsandpredictionsby computational methodsare also examinedandsummarizedin thissection.

Fora laminar freestream,heat transferin the stagnation region canbeestimatedif [he pressure distribution is known (Frossling, 1958).However. when the freestreamis turbulent.accurate prediction of heat transfer becomes very difficult.Several studies suggest that the therrnal boundary layer is more sensitive tofreestream turbulence than the hydrodynamicboundary layer.

(IJReynoldsNumber

Theboundary layer thickness aroundablutTbodydecreasesasIheR'oincreases.

resulting in anincreasein heat transfer.This effectcanbe seenclearlyin the experimentaldata ofAchenbach (1975).Heattransferdat aon a circular cylinder witha freestream turbulenceintensitylessthan0.5 percentover a wide range ofReynolds numbers areshown in Figure2.1and illustratethe boundary layereffects such as separation and transition on the heat transfer.In the Reynoldsnumber range hlO'to 4<10'.the flowpasses through four distinctflow regimes.The firstflow regime.which extends over the Reynolds number range upt03xI0'.isc haracterized byalaminar flow separation about 80°from thestagnationline.This isreflectedinthe heattransfer distribution wheredownstream oftheseparation point there is a continuousincreasein heat transferdue 10 theincreased transverseexchangeof fluid in the separatedflow region.Flow in the second regime is markedby separation ofthe boundary layeronthe rear surface ofthe cylinder and subsequentformationofaseparation bubble.The flow reanaches as a turbulent boundary layerwith a corresponding marked increasein the heat transferandfinally separates again further downstream.Two experimentalcurvesare presented for the criticalflowrange.atReD=3.!xI0'and4xl0'toillustrate the effectof Reynoldsnumber on the heat transferpeak due tothereanached boundary layer.The thirdflowregimeis distinguishedfrom the second one bythefact that the transition from laminarto turbulent is directwithout the occurrence of a separation bubble.No

critical and supercritical flow states.ForReo=1.9xlO'thetransitiontoturbulenceoccurs

on the frontsurface of the cylinder indicating that the fourth flow regimehas been established.Theheal Iransfer distributionsfor Reo=2.8xlO'and 4xlO'showtherapid shiftoflhelransilionpointlowardsthetronlSlagnalionpointwilh increas ingReynolds

When theReynoldsnumberincreases by 29percent.trom3.lxlO '104xl0'.heat transfer in the stagnation region increases by 13.6percent.ltshouldbe noted that Frosslingnumber.Fr= N/lI~.isusedtopresentlheheattransferdistribulionon the cylinder in Figure2.1.The use ofFrcollapsesthe heal transferdistribut ion10 asingle curve in the stagnation regionatallReosinceNilvan es linearl y wit

h..jR;; .

Figura 2.1 HeaITransferaroundeCylinderlnCrossflow(Achenbech,1975)

(lIjTurbulencelntenslty

For a given Reynoldsnumber.heat transferin thestagnation region increases significantlywith freestrearn turbulence intensity.Kestin (1966)determined that a relatively small turbulenceintensity of about 5 percent increasedtheaveragehe attransfer from a heatedcircularcylinder byabout50 percent.Fora giventurbulence intensity.the

remainalmost constant inlhelaminarboundarylayerre gionasshown inF igure2.2

o.,,"!;--~=-.L..-....::~~

Anql.f,OI'lnaqnotlOfl.B. CM1

In a studyof heat transfer on a turbineairfoil.Yehetal.,(l993)detenninedthat heat transfer in the stagnation regionincreased byabout 60percent when turbulence

intensity was increased from 1.8 to 5.9percent for Re=7x10⁶(based on the cascade inlet velocity and blade chord length).Freestreamturbulencewasfoundtopromoteearlierand broader boundary layer transition on the blade and increase the heat transfer in the stagnation region.The same phenomenon was observed in similar experiments at

moderate Reynolds numbers in the range 1xlO'to 3xIO'(Zhang and Han.1994:

Mehandale etal.,1991:Zhang and Han. 1995;VanFossenetal.,1995:0uetal.,1997).

(liIjIntegral LengthSca'e

The integral length scale describes the average eddy size associated with the turbulence.The size of turbulent eddies has considerable influenceonthestagnation region heat transfer as the augmentation is believed to be caused by vorticity amplification (see Figure 1.4).Turbulent eddies that are very large relative to the size of thebluffbodyarenotstrerchedand,thus. act only as mean flow variations.Eddies that are very small (approaching Kolmogorov scales) are destroyed by viscous dissipation before they can interact with the boundary layer.This leads to the hypothesis that somewhere between these two extremes there must be an optimum eddy size that causes the highest heat transfer augmentation

Yardi and Sukhatme(l978) found a systematic influence of the integral length scale on the stagnation region heat transfer by using a circular cylinderin crossflow.In their study, turbulence intensities were varied from I to 7 percent while the ratio of integral length scale to cylinder diameter ratio was varied from 0.03to 0.38.They found an increasing heat transfer with decreasing length scale and claimed that the optimum length scale was ten times the boundary layer thickness.VanFossenetal. (1995) used

differentturbulence gridsand model sto vary the ratioof integral lengthscale toleading edge diameterfrom0.05 to 0.30.Therewasanincreaseinstagnation regionbeattransfer withdecreasinglengthscale but nooptimumlengthscalewasfound.Wanger al.(1999) studiedthe effectof highfreestream turbulence with large length scaleon heatand mass lransferonaturbinebladewhichhad an effective cylindricalleadingedgediameter of9 mm.Inthelaminarboundarylayerregionaroundtheleadingedge.lowerheatlransfer rates were found for the highest freestream turbulence level with large length scale (turbulence intensityof18% andintegral length scaleof about 8cm) than for the moderateturbulence levels withrelativelysmall scales(turbulenceinlensity of8 .5% and integral lengthscaleofabout 2.6cm).

(/v)UnsteedyWeke

The unsteadywake from the upstream airfoil alsoinfluencesthe stagnation region heat transfer.Han et al.(1993) simulatedpassingwakes usingarotating spoked wheel and determined that a higherwake Strouhal number(S= 21lNdlll60U.whereNis the rod rotational speed in rpm.dis the rod diameter.IIis the numberof rods.andUis the main stream flowvelocity atthe cascadeinlet) greatlyenhanced the time-averagedheat transfer coetlicient overthestagnation region(Figure 2.3).

Zhangand Han (1995) studied the combinedeffect of freestream turbulence and unsteadywakeon heattransfer fromaturbineblade.Theydefined the mean turbulence intensity as the turbulence levelof the combined freestreamturbulenceand unstead y wake flow.The mean turbulenceintensity,regardless ofwhetherit wascaused bythe unsteady wake orthe turbulencegenerating grid or acombination of both,was an

important parameter on the heat transferrate.A higherStrouhal number alsoinduces earlier andbroader boundarylayertransit ion (Han et al.•1993;ZhangandHan.1995:0 u etal..I997 )

o

-l---.--...----4-~-...--__._-J -1.2

Figure 2.3ElfeetofStrouhal Number by Varying Reynolds Number on the Lo. .I Heat Transfer Distribution on a Gas TUrbine Blade (Han etal .. 1993)

(vjVott/ea/StrucfUresllndVott/clty

Vorticity amplificat ion isbelievedto be animportant physicalmechan ismfor heat transfer augmentation in the stagnationregion.Although the intera etionbetweena lUrbulent lTeestreamandthelaminarboundarylayer inthestagnationregion is still not fullyunderstood,amplified vorticityfluctuaticns seem to excite and induce substantial

three-dimensionaleffects intheboundary layer.therebyenhanci ngthe heat transfer.

Furtherm ore,differentcoherentve rticalstructuresof freestream turbulence interact differently with the laminarboundarylayerresult ingin dissimilarheattransfer augmentation

Suteraetal.(1963. 1964 )presenteda mathematicalmodelfor theinteraction of vorticityin the oncomingflow with the two-dimensional stagnation-point boundary layer The physical situationconsidered was that ofasteadyflow.witha sinusoidal variatio n of velocitysuperimposed in the norma ldirection. intoaplanestagnation pointasshown in Figur e 2.4.Vorticny with thisorientationis suscepti ble10stretch ing in the stagnat ion- pointflow.Theequations ofv o ni city and energytran sport weresolved to detenn inethe effect ofthe addedvorticity.Theircalculations revea led that thethermalboundary layer was muchmoresensitiveto the external vorticity thanthe hydrod ynam icboundary layer.

Thetheory alsopredicted the existenceofa neutral scale.which isabout 2.6 timesthe Hiemenzboundarylayerthickness. whereamplificalionbystretchingis exactlybalanced by viscousdissipat ion.Onlyvonic ityof larger scale woul dexperiencenetamplificat io n whiles mallersc alevonic ity would be au enuated.

Rigb y andVanfo ssen(1991) investiga tedtheeffectofasimilarspanwi se sinusoidalvariation invelocity on acylindrica l leadingedgeofa semi-infiniteflat plate Theyhypothesized that a minimum level of von icit ymust be supplied tothe leading edge foravortextofonn.It was foundthattheintro~uctionof a spanwisevariatio nlnto the freestrea m alwayscaused anincreasein thespanwise avera ged heal transfer coefficienl The percentage increase in theheat transfer coefficient was found10besubsta ntially

greater than the freestream disturbance expressed asa percentageoffreestreamvelocity For example.a0.04 disturbance with a wavelengthof 0.4timesthe leadingedge radius located 9radiiupstream of the leadingedge resulted inan increasein heat transfer coefliciento fl8percemabovethetwo-dimensionalca se.

Vanf ossen and Simoneau (1985) employeda combinationof flow visualization using the smoke-wire technique and thermal visualizationusing liquidcrystals to demonstratetherelation between vortex pairsand thespanwise heattransferdistribution Anarrayofparallelwires wasinstalled upstream ofthe model leading edge to generate vortexpairs.The simultaneousflow and thermalvisualization showed that theregionsof

higheslh ealtransfe r werebe lWeenlhevonexpa irsa s shown schemalicallyinFigure2.5.

Inlhisregion.theinducedvelocityfrom adjacentvortexpairs isdirectedtoward sthe cylindersurface

Figure2.5 Spatial R...tion be_n Wlres.Vorlex Pairs and HutTr"nsf.r (V"nFossen"ndSlmon",u.1915)

Van Fossen etat.(1995) used five different turbulence generating grids (four were square mesh. biplane grids made from square bars and the fifth grid was an array of fine parallel wires perpendicular to the model spanwise direction) in an attempt10 correlate turbulence parameters and stagnation region hear transfer.The correlation developedbythestudyfitlhedataofthefoursquaremeshgrids.butunder-predictedthe heat transfer augmentation caused by the grid of parallel wires.Itwas conciuded that the augmentation was also a function of' the isotropy of the turbulent flow field as the turbulence generated by parallel wires had vortex lines dominating in one direction in comparison with grids of square mesh.The results indicate thai turbulence with the majority of its vorticity oriented normal to the freestrearn andnorrnal to the axis of the leading edge could have better interaction with lheboundary layerto increase the heat

2.1.2Empirical andSemi· Theoretical Correlation Models Several empirical and semi-theoretical correlation models have been developed to predict stagnation region heat transfer in the presenceoffreestream turbulence. With increasing knowledge of turbulence and the physical mechanism of stagnation region heat transfer,the existing models need to be modified for more accurate prediction of heal transfer enhancement due to freestream turbulence.Heat transfer at the stagnation line is usually correlated with Reynolds number,freestream turbulence intensity and integral length scale.Since characterizing turbu!ence with these three parameters seems

to beinsufficient,the currentcorrelation models are foundtobe experimentspecific,not perforrningwe llwithdatafromotherr esearchers.

Frossling (1958) obtained a semi-theoreticalsolution forheattransferin the stagnation regionofacylinderforalaminarfreestream,The solutionis validin the laminarboundarylayer regionup to theseparation point.Usingan experimentall y deterrninedvelocity distribution givenby

Frossling obtainedasolutionforNII!,f&;,theFrossling number,asa functionof the

angularposition from thestagnation point:

...!!!!..-=O.9-1-19 _0.510fJ ,_O.5956fJ '

,f&;

-I 16

Smith and Kuethe (1966)suggested a semi-empiricaltheory for the augmentation of heat transfer at the stagnationpointofa circularcylinder.Byassumingthe eddy viscosity to be proportional tothe freestream turbulence and to the distance from the wall,theysolved the two dimensionalboundary layer equationsto obtainan approximate linear relationbetweenNII!,f&;andTII,f&;.Experimental dataforTII,f&;<20

agreedsatisfactorilywiththe theory,butdeviatedsignificantly athighervalues of TII,f&;.The data alsoindicated an additionalReynoldsnumber effect. especiallyat

!ow valueswhichthey expressed as:

(2.3a)

1(Reo )=0.0277[I- erp(-2.9xI0·sReo)l

It must also be noted that atTII=O,the theory predictedNil,j"&;=1.00 rather than Frossling'svalue of 0.945.Equation 2.3implies a linear relation between the stagnationpoint FrandthefreeslreamturbulencelevelforaconslanlReynoldsnumber However,experimental data from later studies showed thatFrwas not a linear function ofturbulent intensityat higherturbulence intensities.Theincorrectassumptionofa linear relationcould be due to the limitedrangeofTII,uplO6 percent,consideredbySmithand

Kestin and Wood (1971)and Lowery andVachon (1975)also usedthe parameter TII,j"&;to ccrrelate the stagnationlineheat transfer data.Kestin and Wood obtained a

correlation for the Frossling number at the stagnation pointin the range 0<TII,j"&;

<40 byforcing thecurve to pass throughNil.

-/&;

=0.945 atTII,j"&; =0:

.»:

=0.945+3AiTII,[Re⁰"J-3.99[TII-/&;l' (2.4)

-/&;

L100 100J

Loweryand Vachon(1975) extended therange ofTil-/&;to 64 and didnot force theircurve 10 pass through IheFr=O.945forTII=O.Theyfound that the maximum

deviation of any data point from their curve was 10.5 percent and that 87 percent of the data points were within 6.1percent of the curve.Theircorrelation is given by:

~=I.OJO

...].6]{TII,JRe;;] _ j.0 7JTII,JRe;;]:

,JRe;; 100 ~L 100

Lowery and Vachon concluded lhat disagreementbetween Equalions2.4 and2.5 couldbe due 10 the difference inthe test range of Reynolds number. The correlationof Equation 2.4signiticantlyover-predicts NllwhenTII,JRe;;becomes greater than 20.

Daniels and SchullZ(1982) found that heat transfer at the leading edge ofa turbineblade was within10''/0of the value predicted byEquation 2.5.However.experimental data from otherstudiesshowlhatEquation2.5isonlyvalidforTII,JRe;;from010 40.but under-

predictsNllwhenTII,JRe;;becomes grearer than eo

VanFossen et al. (1995) developed a correlation model for the stagnation point heat transfer by incorporating theintegral length scale in addit ion to Reynolds number and turbulence intensity:

(2.6)

where the co nstanlC is F r al zero lUrb ulence intensity.

Yeh et 31.(1993) proposeda correlation modelfor the heat transfer at the stagnation point ofa gas turbine blade based on the parameter developed byVanfossen

et al. (1995).They modified the correlation model by changing the constants and exponents in order to best fittheirexperimemal data.The correlation is given by:

; ; =

0.0073]{TIIReD·"'(~r·" · 1" '

+0.94;

Dullenkopfand Mayle (1995) also proposed a correlation model(Eq,::.8)in whichtheycalculated the effectiveturbulence levelbased on theturbul enceimensityand integrallengrhscaleofthefreesrream.TheheatrransferNusseltnumberwaslhengiven asafunclionofReynoldsnumber ,Prandllnumberandeffectiveturbulencelevel.

Til,

= (1 +;~~~::'>' t:

NII..=NIID/~

n,,,:;;:TII~

Q,is a constant which mayvary from 2.4 to4 depending on the strainrate of freestream approaching the leading edge.

The abovemodels are found lobe experimentspecificto varying degrees.While onecancorrelaledatafromthesameexperimenttoasatisfaClorylevelofaccuracy,there are significant discrepancies when compared with other experimental data (see Figure

2.6).Wanget al,(1999)also showed that current correlationmodels did not fit well for turbulencew ithextremel ylargescales,i.e.}."Dofaboutone.

V Smith and Kuethe(1966) t> Lowery and V.chon(197S)

o

Mehendaleetal.11991)

o Vehetal.(19931 - E o - C U )

Furthermore,previousattempts to formulate correlationmodels are basedon isotropic turbulencegenerated bymeshgrids.These modelsunder-predictthestagnation lineheat transferfor freestream turbulence with vortex lines inspecific orientation (Vanf ossen eta1..1995).Therefore,the parametersused in current modelsare found to beinsufficienttocharacterizethefreestreamturbulence.Ve rtical struetureandvonicity characteristics are believedto play important roles in stagnationregion heattransfer,and inclusion oftheseparameters incorrelation modelsshould leadto more robustand

2.1.3 Predictions by Computational Methods

Computational techniques havebeenincreasinglyemployedto estimateheat transferonabluffbodyinaneXlemalflo w.Therehavebeen severalnumericalstudieson gas turbineblade heat transfer usingboth DirectNumerical Simulations CDNS) and turbulencemodeling.Since DNS isstill a research tool and the Reynoldsnumbers handled by DNSare well below that of most applications (Kasagi and lida,1999).this section onlyreviews computationalmethodswhichuse turbulence modeling.In most earlyattempts,heat transfer wasestimatedusinga boundarylayeranalysis. wherethe flowfieldoutside the boundarylayeris approximatedfrominviscid codes and the momentumand energyequationsare solvedfor theboundarylayer.However.the inabilitytocalculate heattransfer beyond the separation point prevented the boundary layerequation techniquesfrom beingwidelyused.For thecase ofsta gnation region heat transfer.the boundarylayeranalysis cannot prediet heat transfer at the leadingedgewell due to poor grid resolutionin thevery thin boundarylayer at the leadingedge.ln addition.the heat transfer predictionin the leadingedge regionwith boundary layer analysesmaybe in error.beeause of the necessityof modeling freestream turbulence (Boyle.1991). Alternatively.theheat transfer ean be ealculatedusingaNavier-Stokes analysis.which solvesthe entireflow field.TheNavier-Stokesanalysis.however,needs morecomputational resources than boundary layeranalysis.Thisiscurrentlythe most widelyused analysisby industries and researchers due to the rapid increase of computing power.Accuracyof heattransfer predictionbycomputationaltechniquesgenerally depends on:

(i) governing equations (simplified Navier-Stokes, thin-layeror parabolized.orfull Navier-Stokes);

(ii) choice of turbulence and heat flux models;

(iii) computational techniques (different methods of finite volume.finiteelement and finite difference);and

(iv) grid resolution

Boyle (1991) computed the heat transfer distributionson seven turbinevaneand bladegeometriesusingaquasi·threedimensionalthin·layerNavier·Stokesanalysis.The turbulent Prandtl number model proposed byKays and Moffat (1975) and modified Baldwin-Lomax turbulent eddy viscosity model were used in the study.The predicted results for a turbine stator are givenin Figure 2.7for a laminar freestream and a freestream turbulenceintensity ofS.3percent. When freestream turbulence was imposed.

significant errors arose in the stagnation region,and this was found to be true for other blade geometries,In order to improve the heat transfer prediction in the leading edge region,the calculations were repeated using turbulence models proposed bySmith and Kuethe(1966) and Forrest (1977).Boyle (1991) concluded that the Forrest modelgave the best results for the stagnation region

Amerietal.(1992)computedheattransferratesontwoturbinebladesbysolving the two-dimensional,compressible,thin-layerNavier-Stokes and energyequations.The Baldwin-Lomax algebraic model and theq •OJlow Reynoldsnumber two-equation

the heat flux calculations.There is a significantdiscrepancy between the experimental

and predictedheal transfer in the stagnationregion (Figure 2.8).implyingthatthe present turbulence modelsare not suitablefor stagnation point heat Iransfer

Larsson(1997)used a two-dimensionalfull Navier-Stokes solver tocalculate the

low-Reynoldsk-sand twok- t» turbulence models assumingturbulent Prandtl number of 0.9.Atfourpercentfr eestream turbulence level,thepredictionofs tagnationregionheat transferbyall turbulencemodelswas significantly higherthan experimentaldata.

Estimation ofstagnation regionheat transferdidnot improveevenafter turbulence modelswere modified as suggested byKato and Launder (1993)

With increasing computingpower,analysis with full Navier-Stokes and energy equationsolvers is expectedto dominatecurrent and future computationalstudieson turbomachinery heattransfer.However, prediction of stagnation regionheat transfer

better understanding of the stagnation region heat transfer and turbulencecharacteristics is essential for the development of appropriate turbulence and heat flux models

While momentum and heat transport mechanisms in turbulent flows have been studiedformanydecades,thedynamicsofturbulentflowsarestillnotfuIlyunderstood Recent advancesin DNS have provided an excellentinsightinto turbulence dynamics and transpon mechanisms for turbulent flows,especially at low Reynoldsnumbers (Kasagi and lida, 1999).Animportant contribution of DNS has been to provide a better understandingoftheroleofcoherentvonicalstrueturesonturbulentflowsin momentum and heattranspon mechanisms.A coherent motion ora coherent structureisdefinedasa three-dimensional region of the flow over which at least one fundamental flowvariable (velocity component, density, temperature, etc.)exhibits significant correlation with itself. or with another variable,over a range of space and/or time that is significantly larger than the smallest local scales of the flow (Robinson. 1991).While energy dissipationof a turbulent flowis associated with the smallest scalesof the flow,larger coherent eddiesare responsible fortransponing momentum and heat across the flow (TennekesandLumley, 1972;Souza et al.,1999).Several boundary layer studies have shown that breaking the large scale coherent motion close to the wall using various meanscouldresultinaskinfrictionreduetionOacobsonandReynolds,I993;Moinand

Bewley.1994;Ho and Tai,1996).Knowledgeof turbulentcoherent structures and their roles intransponmechanismsi sessential inthestudyofturbulentheattransfer.

The kinematicsof coherent structures hasbeeninvestigated using several techniques:flowvisualization.statistical analysistechniques.e.g.wavelet analysis and conditional-sampling.and numerical simulation.e.g.DNS and large-eddysimulation (LES).Thestudies of turbulence with coherent structures arereviewedinthis section.

focusingon theturbulent wake behinda circular cylinderandcoherent motionsin the boundary layer.because of substantialresearchworkin these areas.Sincethe current studyhad anintention to use turbulencegenerating grids of paralieIrods. the characteristicsof vonicalstructures inthewakeofacircular cylinderandtheir evolution with downstreamdistancewould be useful for this study.Areview ofcoherent structures in boundary layers.andtheir roleintransponmechanisms andinteractionwith uniforrn freestream.should give certainknowledge onthe physicsof the effeaof the turbulent freestream on the laminar boundary layerof thecurrent study.

2.2.1 Wake BehindaCircular Cylinder

Von exshedding and the wakecharacteristicso f acircular cylinder aredependent on Reynoldsnumber.and differentflowregimes can be defined(Roshko, 1992;

Williamson.1996b;Zdravkovich.1997).Thevarious vortexdynamics phenomenaofthe wake for each regimewithincreasing Reynoldsnumber are brieflydiscussed below.

(I)Stelldy umlnll' Wilke(Re. <49)

Up to aReynolds numberof about five. thereis no flowseparation.Flow separationinitiates at Re.ofaroundfive.and up to ReJaround49.thewake comprises a steady recirculation region of twosy mmetrically placedvonices on eachside ofthewake (Figure2.9.a).The recirculationregiongrows with the Reynoldsnumber.and the flow remainslaminar in both near wake and far wake in this flow regime (Williamson.1996b).

(II)Periodicumlnll' Regime(Re.

=

4910140-194)

Theelongated recirculationregionin the near-wake becomes unstable asReJ increases.The shear layers.which are separated from the cylinder.roll up and the final produet isa staggered arrayoflaminareddies known as Karman vortex street or Karman-

Bemard eddystreet(Zdravkovich. 1997)asgiven in Figure2.9(b).The flowin the wake inthis regimeisstill laminarwithprimary vortices parallel tothe cylinder.Taneda(1959) and Matsuiand Okude(1980 ) claimedfromtheirexperimentaldata the formationof secondaryeddystreet beyondxd = 50waspresentin thisflow regime apart fromthe

(III) W. k....Tr.nsltlonReg lme(Re . -190-260)

Transitiontoturbulence commencesinthe wake in thisregimedue toincreasing instability of the Karman vortices.The transitionregime is associatedwithtwo discon tinuouschangesin the wake formation(Williamson. 1996b).AtRed" 180- 194.the inception of von exloops can be seen along with the formation of streamwisevortex pairs due to the deformationof primary vortices as theyare shed.at awavelength of around 3- 4 diameter s (Williamso n.1988;Zhang et al.,1995).The seconddiscontinuity.which occurs overa rangeofRedfrom230to250,comprisesfiner-scalestreamwisevort ices, witha spanwise length scale of aroundone diameter.The prominentcharacteristicof this flowregime is theevidenceof streamwise vortex structuresalong with theprimary vortices, Thelarge intermittentlow-frequencywake velocit yfluctuationsarepresentdue to the vortexdislocations in thistransitionregime (Williamson. 1992).AtRed"260.the three-dimensionalstreamwisevort exstructuresin the near wakebecomeincreasingly disordered (Williamson. I996a;Prasad and Williamson.199 5).

(Iv) Sheer-LeyerTransitionRegime(Re.=1.000to200,000)

In this flow regime.transitionoccursin the free shearlayer separatedfrom the cylinder.andthe wakeis turbulent.The transition regionmoves withincreasi ngRed

alongthetreeshear layerstowards the separation.Three-dimensionalstructureson the scale of shear layer thickness areexpected to develop in thisregimeaswell asthree- dimensionality on thescale of the Karmanvonices(Weiand Smith.1986;Williarnson et al.•1995;Williamson.1996b ).Thechangesincharacter ofthevortexshedding are relatively small overa large rangeofRed.and the streamwise vortex scalesare almost independent ofReynolds number within this regime (Williamson.1996b)

The presence of primaryvortices are stronglyevidentup tord= 50.and the primary vonices become dislocatedand cannot be preciselytraced beyond rd>50 in this flow regime (Zdravkovich. 1997).However.coherentlarge scalestructureswere repon edin the farw akei n a fewstudies(Antonia etal.,1987.Bissetetal..I990.Zho uet al..I999).Funhermore.large scalese condary voni cal slructures.calieddoublerollers in theliterature (PayneandLumley.1967;Corkeetal..1 992).arefoundinthefar wake (rd

>IOO)of the circular cylinder.

(v) Boundary.L4ye, Transnlon Regime (Re.>200,000)

The transition region in the shear layertransitionregime moves towards the

separationpoint with an increasein Reynoldsnumberas mentionedearfier.and finally.

the boundarylayer on thesurfaceof the cylinderitself become sturbulent.his generally assumedthaithe downstream wake wouldbe fully turbulent.anditis not expectedthat coherentvo rticeswould be observed (Williamson.1996b).Roshko(1961).however.

claimed that periodic vortex sheddingwas strongly in evidenceeven inthisflow regime.

2.2.2 Coherent Structures and Transport Mechanismin Boundary Layers

In aturbulent boundary layer,kineticenergy fromthe freestreamis conven edinto turbulent fluctuations and then into intemal energy by viscousaction.Thisprocessisself- sustainingin the absence of strong stabilizing effects.The coherent structures in a turbulentboundary layer are believed to be responsible for this self-sa staining (production and dissipation)of turbulence and transpon mechanismin theboundarylayer (Kline and Robinson,1989;Robinson.1991).

A turbulent boundary layercan be dividedinto different regionsstartingfrorn the wall:thesublayer,buffer region, log region and wake or intermittentregion.Thesublayer and buffer regions are referred to as theinner region,and the combinedlog and wake regions are known as the outer region.The most dominant coherent structuresina turbulent boundary layerare horseshoe,hairpin and streamwise vortices (Head and Bandyopadhyay, 1981;Jeongetal.,1997) ,andthesestruCluresplaydifferentrolesin the transpons of momentum and heat.The quasi-streamwise vorticesnear the wall could 'pump-out'mass and momentumfrom the wall (Robinson,1991).The majorit yof the turbulence production in the entireboundary layer occursin the buffer regionduring intermittent,violentoutward ejectionoflow-speedfluid and duringinrushes of high- speed fluidat a shallow angle toward the wall.Thisphenomenon is knownasbursting.

Outward movement,away from the wall.of the heads of horseshoe and hairpinvonices is closely associated with bursting (Smith and Walker.1997;Carpenter.1997).

In the outer region. three-dimensionalbulges on the scale of the boundary layer thicknessform in the turbulentlnon-turbulent interface.Deepirrotationalvalleysoccuron

the edges of the bulges,through which freestrearn fluidis entrainedinto the turbulent region (Robinson.1991).Theinlerminenlregionoflheboundarylayerisdominatedby large-scalemotions(also called entrainmenteddies).Entrainment of porentiaIfluid occursinvalleysin the lurbulentlnon-Iurbulenl interface that exitat the edges ofbulges (Spinaand Smits,1987;Antonia etal.•1989;Robinson,1990;Robinson.1991).Based ontheknowledge of' turbulentboundary layer.it may be concludedthat the motionof largescale eddies.or eddieswith integrallength scale, could play an imponam role in the transponmechanisms at the turbulent/non-turbulentimerface of a turbulent freestream and laminar boundary layer of the stagnationregion.Usingtheimegrallengrh scaleof turbulence (Yardi andSukhatme,1978;Yeh et al.,1993;VanFossen et al.,1995; Wanget al.,1999) incorrelat ionmodelslodererminethe intluenceoffreeslreamonlhestagnalion healtransfer seems 10bejustified

2.3VorticityCharacterist icsand Measurements 2.3.1VorticityDyna mics in TurbulentFlows

Von icily can be considered lhe organizing princip1e of lurbulentmolion(Wallace.

1986)and iSlhefealurelhaldislinguishesturbulencefromolherrandomfluid motions like ocean waves and atmospheric gravitywaves (Tennekes and Lumley,1972).Vorticity

n,=&,,~

where&'Jkislheallemalinglensorand~ islhevelocilyinthejdirection.

(2.9)

At eachpoim in the flow field,lhemotion ofasphericalfluid paniclecanbe decomposed into translation,expansionand rotation,Thevorticitycan be interpretedas twicetheinstantaneous solid body-like rotation rateof' the fluid paniclesor,more precisely,twice the rotation rate ofpaniclesalong principal axesinthefluidwherethere exists no sheardeformationIl'anton, 1984 ).Alternatively, vorticity canbe defined asthe circulation per unitarea of surface perpendicularto thevorticity field.

Vorticity playsanimportant rolein the dynamicsofturbulence.Thereare some dislinetadvantagestodescribingthedynamicsofturbulentmolion interms of vonic ily.

The equation of motionin termsofvonicity is:

The total rale ofchange ofvonicily,local ptus ccnvecrlcn,isdue to the deformationofthevortex lines andviscous diffusionof vonicily(two termson the right hand sideofEq.2.10).Since the diffusionof von icity isa relativelyslow process,it is possibleto ignore thelast term ofEquation (2.10)inmanyapplications.Therefore,a changein the vorticity ofa panicle isprimarilydue to the distortion caused bythe strainingofthevortex lines.Vorticity dynamicsmUSIplayaprominentroleinheat transferalthe leadingedge because of thevonic ity amplificationduet ovortexstretching,

2.3.2Measurement Techniques

There have been significant advances in the measurement of von icityin turbulent flows over the last fewyears(Wallace and Foss.1995).The techniques can be generally classifiedinto thermal anemometryand optical anemometry.

2.3.2.1Thermal Anemometry

A hot-wire anemometer is a transducer that senses the changes in heat transfer from asmall.electrically heated sensor exposed to fluid motion.There aretwo modes of operationofa hot-wire anemometer depending on the waythe sensor heatingcurrent is controlled.lntheconstant-currentmode.thecurrenttothesensor iskeptconstantand variations in sensor resistancecaused bythe flow are measured bymonitori ng thevoltage dropvariations across the sensor. In the constant-temperature mode. the wire is placed in

temperature.Fluctuationsinthecoolingofthewireareseenasvariations in wire current.

A simpleconstant temperature anemometer is shown in Figure 2.10.The constant- temperature mode is used for velocitymeasurementsalmostexclusively.because it exhibitsconsiderablyhigher frequencyresponse than the constant-current mode(Lekakis,

Thechoice of the sensor diameter involvesa compromise between a smallvatue toimprove the signal-to-noiseratio at high frequencies.10increase frequencyresponse andspatial resolution, and10reduce flow interference and end conduc tionlosses.and a large value to increase wire strength andreduceits contamination due to paniclesin the

fluid.Anoptimum diameter is usually considered to bein the range z-sum(Lekakis, 1996).Thesensor length should beshonto ma.ximize spatial resolutionand to minimize aerodynamicloadingand longto minimizeendconduetionlossesandtoprovideamore uniformtemperaturedistribution.The bestcompromiseis usuallyobtainedwhenthe length-to-diameter ratiois approximately200 (Ligraani and Bradshaw. 1987;Turana nd Azad.1 989).

BridgeVoltage~~R :R)

a, ~-=

Control Resistance R.(Sensor)

A vorticity probe musthavethe capabilityto measuretwovelocitygradients simultaneously,ideally at a point.However. with multi-sensorprobes.thermal anemometry can provideonlyan approximation.Forexample.

a,

4'ata pointin the flowisobtained from 4/1Avbyusing two parallel wiresseparated by4y.Therefore, spatialresolutioncons iderationsare imponant since wires spaced far apan willnotrefleet the requiredpointpropeny, and wiresspaced tooclose couldlead to inaccura cydue to aerodynamicdisturbancesbetween wires.ln addition,the temporal resolution has to be carefullyconsideredto obtaingood measurements

SpatlslsndTemporslResolutions

Wyngaard(1% 9) analyzedthe responseofavo rticity probe byanalyticall y subject ing it to the three-dimensional velocity spectrum given byPao (1965)and assuming isotropy.He recommended that sensorlength should not be more than 3.31/

(where 1/isthe Kolmogorovlength scale),and foundthat separationof twoparallelwires by SI/,,3.3couldmeasureabout 85%o fthe varianceoftrue velocitygradien l.

Antonia et al,(l993) teSled Wyngaard's parallel sensors analysisbyusingdata from two directnumerical simulations (DNS) at thecenter lineof a turbulent channel flow (Kim et al.,1987;Kim,1989).The finitedifferenceapproximation .111.1y was defined asmeasured fluctuating velocitygradient and the truegradient6'0'was obtained by spectral differentiationusing Chebychevpolynomials.The ratioof the variance of the measured gradient to the true gradientdecreaseswithincreasingsensor separationas shownin Figure2.11,whereLly·is the separationbetween two wires normalized by1/

Ideallythe separation between the twoparallelwires should be assmall as possible;however,there is a trade-off to minimizeaerodynamicdisturbance between the wires.Experimentaldata of measured to truevelocitygradients are compared withDNS data in Figure 2.12,where the solidline represents Wyngaard'sanalysiswithDNS spectrum, against .1.1'*.It is clear from Figure 2.12that the wire separation must be greater than Zn to avcid interference.

1

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~oe

°0~...w...-...L....6...r...L...J I1Y*

DNSalR,=ISO DNS a,R,:~OO

\Vyngarrd'sana1~'siswit h Pac' s spectrum Wyn garrd'sanalysiswith DNSspccuum - TruncatedwithPac's spcctrum

Wallaceand Foss(199 5) concludedthat the optimum sensor separation for determin ingvelocitygradientswas about2-4'7 when both resolution and accuracy constraints were considered.Zhuand Antonia (1995) studied the spatial resolut ion o fa four X-wirevorticityprobe,where the X-wiresform sidesofabox.They determined that streamwise velocityderivativeswere moreanenuated with separation betweenwiresthan the lateral derivatives,and the streamwisevo n icitywas less attenuated than the lateral vorticity compo nent.Miand Antonia (1996)measured thelateralvo rticity components

usingtwo X· wiresseparated in the appropriate directionin the turbulentinte rmedi ate wake.They determined that theseparation between the twoXvwiresshould not be smallerthanJn.

Figure 2.12Dependenclof Experimlnlal ([J)and DNS(01 Mlasured to Trul Vllocity Gradilnts on Wire SlparationDiSUInCI(Antonia Ital., 19931

Ideally.sampling of the sensorsignalsofprobesdesignedto measurevorticity componentsshould temporallyresolvea frequency, f,'"U/13TJ),whereVis the local mean velocity.Thisrequires that the sampling frequencyoff,be at leasttwice the Kolmogoro vfrequency fi in order tosatisfytheNyquist criterion(Wallace and Foss, 1995).

PerlormllnceofVorflcltyProbes

Kovasznay (1950,1954) proposed ageometrical configurationofhotwires formingthelegs ofa Wheatstonebridge (Figure2.13) andlater modifiedbyKasrrinakis etal.(1979) to measurevorticity.The probe consistsoffourslanred wires forming two X-wires.Whilea pairof slanted wireswas used as an X-wire¹⁰measure a lateral velocitycomponent(VorIf),the other twoslanted wiresmeasuredthesrreamwise velocity (U) toesri mate the lateralv elocity derivatives(c(r% rcUe: ).However,the optimum sensor length to diameter ratio and the geometry of this typeofvorticityprobe leadtoalargedistancebetweenXswire s.andvorticity components measured withthis type of probe can be in serious error (Wallace and Foss,1995).

• I

I 0\'.1.

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(a' r (bl

Figure 2.13(al Kovasznay-Type Vor1icity Probe and (bl ModilledVersion (Parkand

Foss(Foss.1981. 1994;Fosseta1..1987;Foss and Haw.1990ll.I990b) developed and refined an arrayof four hot-wire sensors to measure the cross-stream vonicitycomponents,.q and fJ,( Figure2.14).Antonia & Rajagopalan (l990) and Zhou and Antonia(2 000) used asi milarv onicity probe to measurea;.and""in thewake of a circularcylinderandasquaremeshgrid.respectively.Thespatialseparationbetween the pairofparallel wireswas about 3.5'1andthat between the two wiresintbe X-arraywas

aboutS.I".Rajagopalan and Antonia (1993) used a compact version of the vorticity probe in a turbulent boundary layer.The separations between the parallel wires ranged from I.S" to 6" and separationbetween the X-wires was 1.8" to7.4".The measured rms vorticity "" was in reasonable agreement with the DNS results of SpaIan(1988)

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^y

^.J

A vonicity probe of four sensors can only measure a single component of vorticity at a given time.Several attempts have been made to measure two and three componentsofvonicity simultaneously with multi-sensors probes:a five-sensor probe for two vorticity components (Eckelmann et al.,1977).a six-sensor probe for two vorticity components (Kim.1989:Kim and Fiedler.1989).a nine-sensorprobeforthree vorticity components (Wassman and Wallace.1979:Balint etaI.•1991:Vukoslaveevie et al.,1991:Hokan,1993).and a twelve-sensor probe (Tsinober etaI.•1992;Maraslietal.•

1993;Vukoslaveevie and Wallace.1996).Configurations of some multi-sensor probes

are given in Figure 2.15.Although these multi-sensor probes can measuremorethanone vorticity component simultaneously. they have the followingdisad vantages (i) The greater number of hot-wires need more data acquisition resourcesand lead to

higher level of uncertainty in signal interpretation;

(ii) Complex data reduction programs are required and agreements on computing procedures for a certain probe geometry. especially the nine and twelve-sensors probes,hasnotbeenobtained;

(iii) The more complex geometry and greater number of hot-wires widen the probe sensing volume leading to poor spatial resolution:unlike the four-sensor probes, the spatial resolution has not been studied satisfactorily

2.3.2.2OpticalAnemometl}'

Two of the most widely used optical anemometry techniques are Laser Doppler Anemometry (LDA) and Particle Imaging Velocimetry (PIV).Both techniques measure the velocity of seeding particles.which must adequately follow the lluid motion.Apart from the spatial and temporal resolution constraints as in thermal anemometry, the constraints of density and size of particles are encountered inoptical anemometry.The primary advantage of optical techniques is its non-intrusiveness to thellow

Foss and Haw (I990b) found agreement between the thermal and optical anemometry methods for a mixing layer. Wallace and Foss (I995) compared thermal and optical anemometry measurements with DNS for a boundary layer and a mixing layer. In the boundary layer measurements.LDA and PIV data agreed better with DNS data than

data from the hot-wires.The deviation of hot-wire data becomes larger close10the wall where the resolution problems of thermal anemornetry are most severe.However. there was good agreement in the vorticity data with optical and thermal anemometry in the mixing layer where the spatial resolution problem is not as severe as in the near-wall region of a boundary layer.

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Figure 2.15Schematic Diagrams of Multi.sensorProbes (Wallace and Foss, 1996)