WI EF

ICIN G EFF ECTS ON

A HORIZONTAL AXIS WIND TU R BI N E

BY

@RO NG,JIEQU N ,B.En g.

A thesi ssubmittedto theSchoolofGraduate Studiesin partialfulfillmentofthe degreeof

Masterof Engineering

Facultyof Engineer ingand Applied Science MemorialUniversityof Newfoundland

DECEMBER,1991

St.Joh n's Newfo undland

11+.

Na llona i llbraty of Canada

E1ibliolhOquonalioo;:llc duCaNKlJ

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ISBM0~ 3 15-7J2'J7-0

Canada

Abstract

freezingprecipitation hasex tremelyhighincidenceinpartsofAttanuc Can ada.and th iscondition isexpect ed toseverelyreducetheenergy out putfromaercgcnerator s.

Thisprojectwas aimed atthe evalu atio nofelfecu ofIreeeing precipitation condi- tions onthe outputof windturbinegenerators.Majorschievemeet shaveincluded the simula tionoffreezinSfainevents.in p.vticu lAf,glaze icingina.cold roomAnd in field applications;testing ofaNASA LS(1).0417wingsection in the windtunnel undersimu lat ed icingconditi ons; and theoreticalevaluati onof performancedegt il.' dationbyicingon bladesfor twohorizonta laxiswindturbines, IhM is, a 2.5III dia meter wind tur bineAnd a Cartcr·23windturbine.byll~inglifting-linelhro ry.

An experimentto modelthe formofice accumulat ion on... horizontalaxis rotor wasdoneinacoldroom.Iceprofiles on thebladesections wererecorded.Wind tunnelt~tsCoranairfoilusedtypicallyfotwindturbi nebladesweredonewit h various sim ulatedglaze andrime iceaccretionsattachedte theleading edgeof the airfoil. Li£t and drag coe fficient dat awere obtainedforanglesofatlack from -6·to 90°.Atheoretical methodwuused forestim at ionofdegradationof aerodynamic performanceof hcriecntal&Xiswindturbinesinicingcon ditions.The theoryused wasbasedonmarine-p ropell er lifting line theorythathad been adapt edfor wind turbineuse.Thismadeuse of airfoilsection data obtainedfromwind tunneltests.

Asimulat edicinltestonafullscalehorizontalaxi.•windtu rbine wasperformed attheAtlant icWind TestSite.

The cold roomicing testgave a betterunderstandingofthebluntshapedglaze iceaccretion on the leadingedgeofbladesectionswhere thewind speed was rela- tivelyhigh.The theoretica lesti mat ionsshowedthaticingeve nts,associated with

ambienttemperat uresclose tofreezing pointand highliquidwate rcontentin the air,coulddestroytheperformance of wind turbinescompletely.Thewindturbine field teet showedthataprogressive power reduction occurred duringasimulated freczingeventand a complete lossofpower fromthe wind turbinegene ratorwas encountered afterashorttime periodoffreezing precipitati on. Thewindtunnel testsfor the airfoil with simulatedice accretions onthe leadingedgerevealed that increaseofdrag coefficientanddecrease ofliftcoefficient onthe icedbladesections ofawindturbinewerethe main reasonsthatcaused the power ou tput from a wind turbineLadrop.

Acknowledgements

Ithankthe followingorganisations for providingfin...ncialsupport:Energy,Mines and Resources.Canad a;theNat ura l Sciencesand Engineering Hl'Sl'archCouncil ofCanada;Departmentof Mines&Energy,Governmen t of Newfoundl an dand Labr ador;MemorialUniver sityof Newfoundlan d;andthe AtlanticWilldTestSite.

lalsothank the techniciansin theThermallaboratory, FluidsLaboratory and machineshop,38well as allthe membersof the Centerfor Comput erAilledEn- gineeringofourfaculty,for their generous help.Thanksarealsodueto Mr.C.

Brot hers,Mr.M.Lodgeand all thetechniciansinthe Atlant icWindTestSitefor their instr ucti veadviceduring the wind turbinefieldtest. Finally, the aut horis inde btedtoDr.N.Bose.whohas actedassupervisor andprovided patientadvice andguidance throughoutthisst udy.

iii

Contents

Abstract Acknowledgem ent

TableofCont e nts

Listof Figures List aCTa bles

1 Introduction

2 IceAcc r etionProc essonaRot or

iii

iv

2.1 TypesofAtmospheric Icing 2.2 Nucleationof Water Droplets

2.3 WaterDropletImpingement. ... . ... 10

2.4 CriticalLiquid WaterContent II

2.5 Rate of Ice Accretion 15

3 The Theory of Propelle rTypeWindTurb in es 19

3.1 IdealPowerCoefficient for PropellerTypeWindTurbines 20 3.2 Lifti ng-linetheory. . ...•.. ..•,.. 22

3.2.1 Potenti..l Problemofa Prope llerType WindTurbine . :.!:l 3.2_2Calculatio nof Circ ulationDistr ibution . :.!rl

3.3 Applicationofthe Lifting-Line Theo ry 17

3.4 ComputationalMethodUsedfor Wind Tur binePerformance Evalu-

d~. ~

3.·1.1 NumericalProcess

3.4.2 CalculationsforWindTurbin eModels.

:\1 :1:\

4 Wind TunnelTest sfor Airfoilwit h SimulatedIceDeposi t s 43

·1.1 Calibration ofWind Tunne.Working Section. .\;, 4.1.1 Calibrat ionoftheHot- WireAnemomet er. I.';

4.1.2 WindTunnelCalib ration . -lf

4.2 Calibrat ionoftheStrainGauged BalanceTable. H

4.3 TestProced ure and Results ·1!)

4.4 TunnelInter fere nceEffect s andData Correction. :11

4.4.1 Blockage Correction III

4.4.2 Correctionfor Finite AspectRatio .';·1

5 IcingTest son Horizontal AxisWindTurbines 68

5.1 Model ScaleWind TurbineIcing Test. 69

5.2 FullScaleWindTurbine king Test 71

5.2.1 TestProcedu re 5.2.2 TestResults .

.5.2.3 ComparisonwithNat ural Icing

6 Discussion ofCu r r e nt Resea r ch

"

73 71

ss

6.1 Forrnarionof IceAccretion onthe Blades., 6.2 PerformanceDegradationofIced Airfoil 6.3 EvaluationorPowerLossesbyIcing . 7 Concl us io ns from theRes earch

vi

85 87 88 91

List of Figures

1.1 Glaaeice(ormatio n... 1.2 RimeiceCormation.•. 1.3 Mechanism ofglaze iceCormati on.

2.1 Collectionefficiencyofacylinder.

2.2 Rate oficing accretion..

3.1 Streamtubeformomentum theory.

3.2 Veloc ity diagra m&1bladesectionJr.

3.3 Coordinateof windturbinescrew surfacein the wake..

3.4 Forcediagramat blade sectiondr.. • • • ••.••. .. 3.5 Flowchu t forKI program. ..

3.6 Computedr~u l15ofpowerratio{or the2.5m diameter horizontaJ

axiswindturb ine .

3.7 Computedresults of powerratiofor the2.5m diamete rhorizontal axiswindturbine.. ...

17 16

:17

3.8 Computedresultsofpowerratio forthe 2.5mdiameter horizontal

axis windtur bine. . .19

3.9 Computedresultsofpowerre tio forCart~r·23wind turbine. 10 3.10Computedresull'ofpo....erratiofor Carter·23 windturbine. 41

vii

.1.1IComputedresultsor powerratio forCaner-zlwind turbine. 42

4.1 Layout of lowspeed wind tunnel. 56

4.2 Wind tunnelcrosssectionand distributionof calibration points, 56 ,1.:1 Dynamometerfor the airfoillest.

·IA Installationof airfoil on topo[ mountingbar..

·1.5 Instrumentationforthe windtunnel tests.

,1.6 Simulated glaze Iiceshape., 4.7 Simulated glaze2iceshape .. .

·1.8 Simulatedrimeiceshape.

4.9 Testresultsoflift coefficientforNASA LS(l)-0417 clean and glazel icedairfoil.

,1.10 Testresultsof liftcoefficient forNASA LS(I )·04Iicleanand glaze2 57 58 59 59 60 60

61

iced airfoil. .. " " . , .,. 62

4.11 Testresultsoi liftcoefficient for NASI.LS( I )-0417clean and rime icedelrfcil.:

·1.12Testresultsofdragcoefficientfor NASA LS(I)-0417clean andglaeet iced airfoil..

4.13Testresultsof dragcoefficient for NASALS(I)·0 417clean andglaze2 icedalrfcil.:,,, . , •...

63

64

65

·1.1,1Test resultsof drag coefficient forNASA LS(1)·0417cleanand rime

iced airfcil.: 66

5.1 Clock gauge table for measurementof ice profilein coldroomtests. 76 5.2 Glazeice profileat various blade sectionsfromcold room tests, (a)

5 minute!time duration, (b) 15 minutestime duration. .. 77 viii

5.3 Ice depositsonthe blades ofthewind turb inemodelafter 15minutes

icingtest,(a) Front view,(b} Sideview. is

5.4 Sceneoficing testin theAtlan ticWindTest SiteIuc.. 7!.!

5.5 Iceshaperecorde r. ;!)

5.6 A viewofice accre tiononthe windturbine'sbladesanda pieceof ice shedfrom oneblade (leftblade)afte r 40minutesicing test.. SO 5.7 Measured curves ofwindspeed and power outputduringthe icing

tes t.

'I

5.8 Eneetech-anpowe rcu rve forclea nrotor.

"

5.9 Glazeice profilerecordedfromtheicingtest , al 0.4301awayfrom the bladetipaftera 40 minuteicingtestduration.. 82 .1.10Ice accretion atthe radius fractio nrfR

=

0.75of a Windstreamsmall

windturb ine,aftera glazeicingevent ofseve ral hoursduratio n from

Bose {4l}. ... 82

List of Tables

4.1 Coordinat esoftheNASALS(l)-0417airfoilsect ion.. 67

S,I Cleanbladesection ofthe windturbi ne modelusedin cold room test s.The,.'( andZcoordina tesaregiven in mm. Section1:f/R=l, section2:r/1=4/5, section3:r/R=3/~,sect ion 4:fiR:1/5. 83 .'5.2 Iced blade sections with icing timedur ation: 5min,LWC: 1.67g/m³,

temperatu re:-SoC and windveloci ty:4m/ s.Section1:r/R=l, sec t ion2: f/R=" !;;, section3:r/R= 3/5,secti on4:r/R=1/5,(unit:

rom).. .. . . 84

Chapter 1 Introduction

As aform of renewab leenergy,wind energy offersma nyenvironmental.economi c andsocial benefits. The modernwindpower indust ryWi\.!Iborn in the chaosof theworldene rgycrisisof the1970's,though wind haa been generati ngpower for centuries. Among the developedcountries,theUnitedSlatesof Americais inthe lea ding positioninutilizationof windenergy; wind generatescloseto 2 TcrAWalt hou rsper yearin California ,whichis85%ofgenerated windpowerin theworld.

European countries,wherewind power technolouoriginated. have madetreme n- dous progressindevelopingDewwindenergy technology in recentyears. Canada..

whichiswellknownforitsrichnaturalresources,isaware oftheim po rtanceof exp loring such kind sofrenewableener~technolouinorderloconservenat ural energy resources.

Thewo rldenergy crisesandglobal warmingimpact thewholeworld.More a.n d morecount rieshavebeenmakingwind energy into utility-gradepower byimproving the efficiency of wind conversionsystems and reducing windenergy generation cost per kilowatt-hour.Increasing application ! of windturbinesoccur not only in regionswhere the windresourceisplenty,but alsoin cold regionswhere icin g eventsduringwinte rare prevalent.Thework ing prope rtiesof wind tu rbinescan

be alteredsubsta ntially underatmosphericicing co nditions[1,2,31.Thishas been emphasized bythe present research(4,5,6,7],

Freezingrain, whichis one of themain typesoficing event inparts ofCanada, can reduce totalenergyoutputfroma windturbine andthereforeincrease the cost of utilitypower generationdue to ice accretionon therotors.Rotoricingcanresult inserious degradationof aerodynamicperformance of a wind turbine by altering thegeometry of bladesect ions andthus, changingthe properties o( flow fieldaround each bladesect ion . Fromstatisticsforthe periodof1967·76 [Sj, ithas been shown that par ts of Atlantic,Arctic,sub-Arct ic and CoastalregionsofCanada have a high incidenceof freezing rainand freezingdrizzleevents during winter,and these conditions result in potential annualenergylosses fromwindconversion systems thatare operatingincoldregions(8],

Typically, the reexist two classesof iceaccretiononwind turbine blades[1,2];

these are knownasglaze andrimeice,as shownin figures1.1and1.2.Theicing formation ona rotor isgovernedbythe temperatureofthe water drople ts, theirsize, theliquid watercontent(LWC)of theair,as wellas the rate at whichtheystrike a surface. Rimeiceresults from a lowerair anddroplettemperatureand low liquid water contentin the air.Highlysupercooled water droplets freeze immediat elyon im pinging onabladeleadi ngto higherporositydeposits and hence lowerdensityof the ice.Theyform asoft milkycoveringof streamlinedsha p e[1,2]. Glaze ice forms attemperatures just below freezingpointinairwith a highliquid watercontent, largerdiameterof the waterdroplets as well as high relativeimpact speed.Under glazeicin g conditions,drop letsdonotfreezeimmed iately on impingement, dueto lower su percooling , butru n first alongthesurfacesomedistance [1,2], as illustrated infigure1.3.In thecaseofglazeicingor weticing, tbe eercdynemicpressureplays

an important rolein forming theice profile around theleadingedgeof ablade, Nearthestagnation point,thedropletsare (ar cedt.omove alongthesur faceof the bladeaway fromthestagnation pointorline,due tothe highpressure gradientnear the leading edge.Theresult isa depositofhigherdensi tytransparent ice with two protrusions whichareronsideredto degradeover allperformance ora wind turbine muchmoresignifican tlythan rimeicedeposits.

A seriesof experimental andtheoret icalstudiesweredone toshow the severity of bladeicingon horizontal axiswindtur bines.Based on a lifting-linetheory [9,10,111, a nu merical methodwas ada ptedtopredictthe degrada tion ofaerodynamic per- form ance for horizont al axis windturbinesdue to ice accretion. Thistheorywas developed for marinescrewpropellersand was adapted for windturbine usc by Sma lland Bose[12,13]and Bose(14J, and furt hermodifiedforwindturbines with an icedrotor.The performance calculatio n wasdone byusinglifting-linetheoryto- getherwith experimentaldata oflift and dragcoefficient s(ortheblade sect ionover awide range oranglesof attack.Thesedata.were provided bywind tun neltests ferwingsectio nswith severalsimulat ed ice shapesfor medunder glazeandrime icing doneunder this studyand alsodocumentedbyWilder/l5] and Bragg[16].

Tbecomput a t ional results showedtha ttypica lglaze icing cond itions completely dest royed the aerodynamicperformanc e of a Ca rter·23 wind tur bineand asmall wind turbinewith2.5mdiameterrotorovertip speedratiosfrom 0.5to12.The resultsalsoshowed thatrime ice hadlesseffect on the overallperformancewhen comparedwit h glaze ice; powerreductio nbyrimeicing was 30% for theCarter·23 windturbineand49% for the 2.5m diameter windturbine.

Windturbinemodel icin6testswere done undertypical freezingrain conditions whichweresimulatedinsidea.cold room atMemoria.lUniversity ofNewfoundland .

The ice profilesaroundthe rotor blades were documented forlater wind tunnel tests.Full scalewind turbine icing fieldtests wereconductedat theAtlantic Wind TestSitein Prince EdwardIsland, Canada . Full scalewind turbinetest results showedlhalfreezing precipi tation onthe rotorreduced theoutput of thewind turbineby 100%shortlyafterthefreezing eventandcould make the whole system go outofbalanceduetothe extraloads exertedontherotor by iceaccretion.

Although icing isa critical problemforawindconversionsystemoperatingin thecoldregionsduringwinter,insufficient attention has been paidtoit inthe pest. Thepurposeofthis projectwasto let expertsandplanners, who arein- volvedinthe utilizat ionof renewable energy,be awa reofthe severityof the wind turbineicing problem and alsoto obtain a methodologytopredictpreciselyand completelythe performance degradation ofhorizont al axis windturbinesfrom ic- ing.Recommendationswer ealso madefor possiblelater studies of windtur bine de-Icingtechnology.

\ 1'Glazeice formation . Figure..

Rime iceformation.

Figure1.2:

Mechanism of glazeice formalio n.

F'igure I.3:

Chapter 2

Ice Accretion Process on a Rotor

Wh en waterdrople ts impinge on thesurfaceofblades, theybegintospread ,are nucl eated andthenbeginto freeze.Duringthat process,th ey may coalescewith otherdrop letswhicharc onlypartia lly froze n; splash i ng also occurs ifthedroplets aresufficient lylu ge[111.

2. 1 T ypes of A tmospheric Icing

Icin g fromatmosphericsou rcescanf('Sullfromcontac twithsupercooledclouds or togdroplet s.fromfreezinsprecipitationorwe tSIlOW'.Eachofth~lypeaofki ngil associated with part ieulu meuor olog ial conditionsandC&I1resultin typicalLypc!!

and accumulationsoficeon awindturbine rotor.

Freezing pm:ipitationresultswhenliqu idprecip i t ation Catlin!fromwa.rmai, a.loftis cooledbelowthefree2ing po inta.sitfallsthro ugha.layerof co ldAirnearer the earth' , surface;this canbeinthe formoffree2in~rai n orIreeain gdrizz le.

Freezin gra i nisdefin eda.! havingdropsofmorethanO.S rom indiameterand ratesthatrangefrom lesethan 2.5mmperhourto grea te r than7.6mmper hour.Freezing drizzleieusually defined asfair lyunif orm precipit at ioncom posed exclusivelyof finedr opsofwa ter ofdiameterless than 0.5mm. Therate of dri7."le

falling range frumlessthan0.3mmper hour togreatertha n0,8mm perhourfl81. Thusaccumulatiomof icefromfreezingrain wou ldbe greaterthan from freezing drizzle.Both eventsareusuallyassociatedwithglazeiceaccretion.

Cloudandfogdrople t scan exist ina liquidst ate atte mperatureswellbelow freezingpoint.Whenthese dropletscome intocontactwith an object,the y freeze on impact,formingrime ice.Duetothe lowerliquidwate rcontentofthe air,this type of icing gene rallydoes not pose a problem fo r a windturbineexcept whenit occursin associatio nwith highwindsin whichlargeamou ntsof waterare brought intocont act withthe object,ice buildup is thenconsidera ble.

Wet snow,thatis blownagainstan object,maystick and change to ice with lo wer densitytha nthatfor med fromfreezingrain{181,Thesedifferentatmospheric icing conditionschange thebehaviourofthe wind turbinein differentways. The icingeffectson wind turbin esmainlyassociatedwith freezing raineventswillbedis- cussedin thefollowingchapters.Thistypeoficing event causesglaz e ice accretion on a windturbin e's rotor.

2 .2 Nucleation of Water Droplets

Theformationof an ice crystalfrom a water dropletwithinahomogeneousBuid demandstheexpenditu reof a certainquantityof energyillcreationof a solid surface. Therefore, the totalquantityof workrequired toform a stablecrystal nucleus is equalto theworkreq uired to formthesurface and thebulkof the particle,which is usuallycalled freeenergy,Accordingto Michel[19].thefree energydG.in the homoge neous fluidrequiredto formaspherical particleis given

by

(2.11 andtherate of nucleationofwater dropletsis

(2.2)

wheree.,isthe surfaceene rgyofthecrysta lincontactwith the liqui din_m.J/m~;

0;

isthe solid-liquidequili b rium tem peraturein Kelvin; UOisthe su percoolingor

theliquid in Kelvin;Lis thelatent heat inkJ/kg;kistheBoltzman n gas constant;

andAisa.consta nt.Inre a lity, the fluid is heterogeneous. Forthe same critical free energyrequired fornucleation and {ora similarcrysta l form, theamou ntof supercoolingforhomogeneous nuc leation,AOo•willthen bereduced[1!l1andthe valueof supercooling forheterogen eo usfluid .M" becomes

t1(J_,

=~nJ

_'.

I -C03"Y

_{2 •} (2.:I)

where 1 is usuallytaken as the angleof contact bet weenthe ice andthe nudeating material.At the limi t,whenthenucleation is initi ated with anice crystal,'1""0 an dthenthesupe rcoolingrequired for nu cleation,IiO~= O.Th isis expected because no superco olingisrequired to growicefrom anyex isting icenucleus.It is usually consideredthat usual inorganic nucleationinstatic conditionshasa temperaturethresholdofabout-3.S'ewhile, (orordinary tap water an average nucleating temperatureisfou nd tobe-2.,5' C [19J. Frr:1'!eq u ation2.2, the rateof water drople t nucle ationinc reases wit h the increase of degree of awater dro plet' sup ercooling,!:J.(),an dthere fore,det er minesthe icing processon wind turbineblades th atwillbe discusse din th enextsect ions.

2.3 Water Droplet Impingement

Whenwater droplets are movingtowardtheblades,theirmomentum affectsthe wayin which theyimpingeon the blades; the bigger the dropletsthe high erthe possibilitythatthe dropletwillimpingeon the bladesurface. Thebehaviourof the wate r droplets onimpingement attheleading edge ofthe bladecanbecon sidered to be similartomovementtowards a.nobject withacylindricalfront edge with localradius,r. Therate

or

thewater droplet's capturevariesalo ngthesu rface of the bla deatdifferentlocations . A detailedmathematicaldescript ionwaspresented byLoxowski [201. Theanalysisbegins byconside ringeachdrop letcate go ry,it s Reynoldsnumber,Re, anditsLa ngmuirinertiaparamete r, K,

Re=DUp.,

,.

^(2.4)

(2.5) whereP.andp",arethe densi t y of theair andwater,/J.istheviscosityofthe airstr ea m Deis the diameterofcylinder,Disthediameterofwat er dropletand U isthefreestream velocity,anda modifiedinertiaparameter,

(2.6) Withtheuse ofKo,valuesof thestagnation linecollisionefficiency, the total collectio n efficiency,E,on theprofile andthemaximumimpingementang le,6..., along the cylindricalsurface canbe deri ved[2OJ.

Figure2.1showsthe relation shipbetween the totalcollection efficiencyEand the Lan gmuirinertiaparamet er Kfor acylindr icalsurfacewithradiusRedoc- umentedfrom Mortimer

IiJ,

wh ere41 isa Langmuirand Blodgett impingement

10

parameterdefinedas

41

=

18p~V~ .

/14P", (2.7 )

Thecollectio n efficiency,E,in figure 2.1,isgoverned greatlybythe dropletSil l' , theradius ofthe cylinderor theleadingedge ofthe blade.The biggerthewater droplets andthesmallertherad iusofthe lead ing edge.themore water droplets imp inge orarecaptu redon theblade.Thisis due toincreasingLangmui rinertia param eter,K,andreducing Langmuir and Blodgettimpingeme ntparam eter.~. Resultantwindspeed,V,canaffect the collectionefficiency,E.ina negativeway by lncreeslng,41.

2.4 Critical Liquid Water Content

Ifwa t er isto freeze, thelatentheat of fusionmust bereleasedand11M tobe removed.In mostsit uat ions the rete of freezingislimited by theraleat which the heatcanbe dissipatedto the envi ronment.Thesteady-s tatehealbalance equation thatis assumedto describe thethermod ynamicsof accretionmay be written as [2 1)

where

q< is the convective heat loss between theaccretionandthe airstream by eonduc-

tion and convect ion;

q. is the evapora tive heat flux;

q~ is theheat flux duetoaerod ynamicheating ;

qK is theheatflux due to theconvers ionofdropletkinetic energ yinto heat;

q,

is thelat ent heat nuxto theaccretiondue to freezing of some,orall,ofthe direc tlyimpin ging wate r;

11

q",istheheat fluxbet ween thedireet:yimpinging waterandtheunderlying ac.

cretion;

q, istheheal flux belween theaccr etionand the underlyingsurface;

q. is the radiat ive heatfluxbetwee n the accretionand the airstream ; ,/",'andq(aresimilartoq...andq,butare forunfrozenwater.

Allofthe heatfluxesqare assumed to be positiveif theyadd heat tothe accre t ion, and negative in the oppositecase. Theterms of rilciationandinterna l condu ct ion, q.andq;are usually sm alland canbe ignoredcom pared withother terms.The heat/luxor heat convectionq.is givenby

q,=h(l.- '.), (2.9)

wheref ;andI.arerespect ivelythefreestreamairtemperature andthesteady-st ate accretion surfacetemperatu re.The quant ityhis theheat transfercoefficient and canhe written in termsofthe NusseltnumberN~.

h_k~Nu

- D, ' (2.10)

wherek~isthethermal conductiv ity ofthe airstream. Thevalueofthe Nusselt number,Nu,can be found byconsidering thespecific geometryofth e body[20] and maybe writ ten approximately,for asmooth surface,as

(2.11) andfora rough cylinder as

N.(O)=M"{2,4

+

1.2, ;n[3.6(0 - O.440)1l. (2.12)

In additiontothe heatconvection,thereisa transferof latent heatdue tothe evap- orationorsublimation of watervapourfromthesurface.According to Reynolds'

12

analogy[201, thisterm canbywrittenas

(2.1:1)

whereP,andSoare thePrandtl and Schmidt num ber; e isthe ratioofthe molecular weightof wat ervapour to dry air ;pisthestat ic pressurein thefreest ream; cpi911w specific heatcapacity atconstantpress ure for dryair;Ca ande. are thesaturation vapou rpressureof moistair at toandt. ;andI" isthelatentheatofevaporat ion.If the acc retionisdry,tha.tis, la<O·C.the latentheat of sublimation mightbemore approp riate,althougheven in thiscase,afilmof watermayexistonthe accretion surfa ce forthe finitetime requiredfor theimpinging waterto freez e com pletely.

Theaerodynamicheatingtermisgivenby

(2.1-1) where"eis thelocal recoveryfactor on the cylindergiven by

r c

=

0.75+0.25cos28. (2.15)

Thislatter expressionis based on the work of Seban[22] and takes into account the adiabaticheating arisingfromcom pression of theairwhichisdeceleratedin passingaroundthe cylinder.as wellasfrictional heatingwithin theboundar ylayer.

which shouldbeconsideredwhen rotat ionalspeedof windturbine'srotorand the airspeed are high.Thekinetic energyfluxofthe dropletsq. isgiven approximatel y by

(2.16) whereR,., isdropletmass flux. Thedropletsareimpingingatthelrcesrreamair speed, and allof theirkineticenergyis convertedto heat.Thelatent heatflux due

13

to the impinging wateris

(2.17) whereI/o isthela tentheat offreezi ~gat the temperat ureoft•.Theheat flux between the accretionand impingingdropletsis thatrequired to warmthe droplet from thefree airstreamte mperat ure,t..,to thesteady statesurface temperatu reof the deposit,t.,that is,

(2.18) wherec'"istheaverage specific heatof waterbetweenthetemperat ures oft..andt••

The same algorithmcanheapplied toq",.andq(for unfrozenor run back water in whichR",is the run back water mass flux andt..is theincoming temperatureof the runback water.

Thecritica l value of theliquid water contentLWe. inthe air,below which allwater dropletsfreeze on impingemen t,can be obtained by consideringthe heat balanceinequa tion 2.8and setting thesurface temperature,tIljustatthe melting point,

(2.19) in which components of runbackwater are neglected. As the deposit temperature cannot exceedGoe,thereis,for givenambient temperature,air speed and droplet size,acriticalliquid water contentLWe.at whichallof the accreted droplets may be just frozen.IftheLWeislowerthan the criticalvalue all of thedroplets freeze and thedeposittemperatureis belowGoe.This isusuallyassociatedwith rimeice growthor dry growth.Ifthe liquidwater contentis abovethecrit ica l value,theresultofheat balancebetwee ntheair andsurfaceof ice accreti onis that the temperatureor the ice accretionis equalto themelting pointandthere ma ybe

14

11.portion ofunfrozen water onthesurfaceoftheaccretion movingaroundblade surface.Thisextraportionof waterwillbe drivenby theexternalforces,suchas theaerodynamicforcearoundbladesection, andcauses a formationof glaze icc withbluntshapesonthe blade surface. One can also assumelha!.theliquid water content iskeptata.certainvalueand let the ambienttemperat urechange.There should be acritical ambienttemperat uretcexistingat whichthe waterdroplets impinging on thebledee arc just froze n.Abosome specialicing eventsoccur,in whichglaze icest ill existsatlowerambienttemperaturedue to veryhighliquid water contentinthe air.

Experimenta lresults showthat higher liquidwatercontent in the airanti higher ambienttemperature willcause theoriginalbladesect ion profileto be distorted considerably duetothelarge pori,ion of unfrozenwaterrunningonthesurface of theice accretion.Figure 1.3 shows the mechanismofglazeiceformation.

2.5 Rate of Ice Accretion

The rate of iceaccret ionon the blades depends mainly onthe atmospheric con- ditions: the liquid water contentin theair; ambienttemperatur e;droplet' s size;

relativeairspeedtotheblade;andthe geometric size oftheblade.For11.blade wit h. radius,R,orthe cylindricalleading edge, the rate of theice accretion,R,I ,

wasexpressed by Mortimer [1],as

RR=3600VxLWCxE (2.20)

andthisisillustratedin figure 2.2.

The rate or accretion isst rongly governedby thedroplet's sizeand liquid water contentin the air in positiveways.The higherthe liquidwatercontentthehigher

15

thepossibility fortheblade to capt ure thewater droplets. Also,dropletswill deviate,due totheirmoment um, from thecurvat ure ofthe streamli nesinthe vicinity ofthele&dins edge:the larger thedropletsize, the highertheir momentum andthe moredroplets hitthe blade.Higher sensitivityofkinS growt hrateoccurs when waterdroplet size issma.ll .u sbown in figuM 2.2.Liquid watercontentin the airis also criticalforicing rate;higbersensitivitytoLWC occurs when droplet size islessthan20pm.The radiulofthe lead ingedge oftheblade andthe result ant relative wind velocitybothaffectthecollection efficiency,E,inanegative way.

Increasing windspeedcausesan increasein rateofwaterdroplet im pingementon the bladeandhencerateofaccretion.

However,therate ofice accretionreferred toaboveis tru e only ifitsatisfies the icing nucleatio n condit ionsdiscussed in section 2.4.Ifthe waterdroplets captured by the blades cannotfreezewithin acertaintime,the ::.::roJynamicforce,centripetal forceandeven gravityforcewill causethedropletsto beshedofffrom thewind turbine rotor andthereforetherewillbeno iceaccret ionon the wind turbine blades.

16

0.8 0.7

~

.,

0.6

E-

"' g-

^0.5

."

^0.4

E "' s

^0.3

~

^0.2

0.1

00

Langmuir ParameterK

Uppercurve:$

=

¹⁰⁰

Middle curve:<I'

=

1000 Lower curve:!II=10000

Figure 2.1:Collection.efficiencyofa cylinder.

17

as

05 10 15 W ~ 30 3S ~

Dropletdiameter (Microns)

4S

j

50

CurveI:R, ==15gJcm²/hr Curve 2:R,=109/cm¹/hr Curve3:R,

=

^5gJcm2/hr

Curve 4;R,""ltJcm²/hr Rt;:Rate orieing accretion

Figure2.2:Rate

o r

icing accretion.

IS

Chapter 3

The Theory of Propeller Type Wind Turbines

Propeller type wind turbiueecan be consideredto be airscrcws whichCltlfat~tenergy from the airandconvertitinto other formsofclI('rgy. This is incontrast to "- propellerwhichexpels energyinto the air orwater from anot herenergyS(lUTn'.

The similarityof thepropeller and the windturbineenables the snme theoretical developmentto be followed for performanceanalysis.

Propeller theory developed along two independentmethodsof approach,onc of which hasbeen calledmomentum thec-.and theother.blade clementtheo ry.The basisofthe theoryis thedetermin ation oftheforcesacting onthe rolortoproduce the motionof the fluid.The approach of bladeclementtheoryis concernedwith the for ces producedbythe bladesas a resultof the motionof thefluid.A more detailed modelwasdevelopedforpropellersandgeneralize dfor wind turbinesby Glauert{23].Thisutilized both the axial momentum andbladecleme nttheories andaseriesofrelationshi pswere developed to determine the performanceofawind turbine.

Modern propellertheory developedfrom the concept offree vorticesbeingshed

19

from therotating blades. These definea slipstream and generate induced velocities at theblades and inthe wake.This can be attributedto the work ofJoukowski [24], forinducedvelocity analysis; toBetz(25], for rotors with minimum energy loss; toGoldstein[9],for circulationdistribution,particularly foreffects ofafinite numberof bladesandto Eckhardtand Morgan[26J, for general improvementand applicat ion.This theory has beenreferredto byanumber ofnames, notably:

vortex theory, circulat ion theoryandlifting-linetheory.

3.1 Ideal Power Coefficient for Propeller Type Wind Turbines

To beginto understand the mechanismof rotorpowerabsorption fromwinds,the Rankine-Frondeactuat ordisc theory providesastart. Asaninitial approach, idealcondhions areconsideredfor windturbineoperation.Thefunction of a wind turbineis to extractenergy from the air andto produce mechanicalenergy.As a first approximation,to determinethe maximumpossibleoutput ofa.wind turbine frommomentumtheory,thefollowingassumptionsaremade,

1. bladesoperatewithoutfrictionaldrag;

2. a.slipstream separa testhe flowpassing through the rotordiscfrom that outside thedisc;

3. the staticpressureinside and outsideof theslipstream far ahead of and behind therotor are equalto the undisturbedfree-streamst atic pressure;

4. thrustloading is uniform overthe rotordisc;and 5. no rotationis impartedto the flow by the disc.

Applyingthemomentum theoremtothe controlvolume in figure 3.1, thethrust,

20

T,canhe expressedas

whereV.is thefreestream velocityfar ahead ofthe rotor, V,isthewake velocity andUis thevelocitythroughtherotor disk. ByapplyingBernou lli's,-,qualioll to the flowupstream and downstreamofthe windturbine,and substitllti nginto equation3.1,oneobtai ns

u=

^Va

;V,.

(:1.2) Thisresult sta testhat the velocity throughthe turbi ne istheaVl'rageofthe wind velocityaheadofthe turbi neand wake velocitybehindthe turbine.By defining the axial induct ionfactor a as,

u=

VI(1-a) the wake velocitycanbe expressedas

and theinduced axialvelocityv, behindthe rotor disc can be expressedas (3.3)

(3..11

(3.5)

Fromtheexpressionforthe kineticenergy whichcanbeabsorbedbythewind turbine,theidealpowerout putfromwindturbine,P,becomes

(3.6)

whereAis the sweptarea of thewind turbine,andthereforethemaximumpower occurs whendP/ da=0 whichis

P",u=

~(PAVI3)

21

(3.7)

The power coeflkientofthewind tur bine,C"is definedas

(3.8) U~i ngthe valueofP",cor,theidea l powercoefficient reaches approximately 0.593.

In reality,wake rotationexistsduetoblade rot at ion. The inducedtangentia l velocitycom ponentin thewakcUlcan beexpressed as [121

Uj=2a'n r (3.9)

which is twicethe valueoftheind ucedvelocity at the rotordisk, wherea^fis an induced tangentialfactorandnis arot ational speed ofthe rotor .The resultant inducedvelocityatthe rot ordisk is perpe ndicul arto the result ant relativewind velocity110)as showninthe figure 3.2.

3.2 Lifting -line t heory

Thelifting-linetheoryusedforthe horizontalaxiswindtur bines analyzedhere was adapted from screwpropellercirculat ion theoryand providesa linkbetweena bladesection operatingintwo dimensional flow andthatcperati ngas apar t of a screw.The bladeisreplaced by a boundvortexline.This theo ryis based onthe conce pt that thelift developedbythe screwbladesis causedbya circulation flow with strength

r

that takesplace aroundeach blad e section.Theresu ltis decreased localvelocityacross theblade pressureside andincreasedlocal velocity across the suctionside.From everypoint of thisbound vortex spring free , trailing vort ices, whose strengt hper unitlength isar/8r,wherer is the distanc efromthe axis of the screwshown in figur e 3.3. When the inte rference flowofthis vort ex system is smallcompar edwith the velocityof the blades, thatis, the blades arelightly

22

loaded,the trailingvortices areapproximately helices,and togetherbuilda helical orscrewsurface.Whenthe clistribution of the circulation,r,is such that,fora giventhrust , theenergy lostperunit time is a minimum, the nowfarbehindthe screw is thesame as if the screw surface formedby the trailingvorticesisrigid, and movesbackwardsinthe direction of its axiswitha constantvelocity {91.TIll' flew away fromthebladesis assumed tobecont inuous and irrc tationel or without circulation.Thecirculat ion aroundanybladesection,insteady now,is then equal to thedisconti nuity in the velocitypotentialat the correspondingpointofthescrew surface{9J. Goldstein gave asolutionfor thevelocitypotential inthe nlli,ldomain around blades.

3.2.1 Pot e nt ial Probl e m ofaPro p ell er TypeWind Tur- bine

To solve this problem,assump tions are made that a wind turbinewith rotorradius, R,andone bladerotatingat speedofnoperates in a uniform airstream witha velocity V;oTheequatio nfor the trajecto ry of the screwsurface ,P,generatedby themotionofthe bladeand thewind is,[or0Sr

:s

R,

F(z,O)=8 - n~ =o, (:1.10)

whichis evaluatedin acylind rical polarcoordinatesystemmovingatlrecstrcem windspeedVIasshownin figure3.3;zison the rotational axiswhosepositive directionis downstreamfrom thewindturbinerotor disk and r isthe distance from the wind turbineaxis. According tothe assumptions of minimum energy lossmadeby Betz 125J.the screwsurfaceformedbythetrailing vorticesis rigid.

This screwsurface moves downstreaminthe directionofitsaxisrelative tothe undisturbed fluid with a constantinduced velocity,v,which cen be expressedas

23

v=±u.where the posit ivesignisforascrewpropellerand anegative signis for awind turbine.Byimposingthe impermeabilityboundaryconditionon the screw surfaceF,theactualvelocityof the screwsurface in the wakealongitsrotational axiscanbeexpressed interm sofavelocity poten t ial9,

(3.11) forthe conditionsor9 -wz/V,=0,05rSRand86/8r...0whenr_ 00.

Thisimpliesthatthenormalcom ponentoffluidspeedlocatedonthescrew surface isidenticalwiththatofthe screwsurface. As6isa functionof randP{9j, theboundaryconditionofequation3.11is hlanip ulatedby differentiating4-with respect10F,

(3.12)

(3.14) forP

=

0and0 ::::r SR.Forsimplicity,let the conslantvvi/n

=

1,and alsolet thelocal tipspeedrat io

(3.13) Equation 3.12 thenbecomes

86 fJl 8F= -~

forP

=

^0and0~r:fR.The velocity potential; shouldsati sfyLaplace'sequation V²6

=

0in the fluid domainandthisisgivenbyGoldstein [9] inthefonn of

a a'.

("8;; v» +

(IH')aF'=O. (3.15)

This equationshould satisfytheboundar y conditionsofequation3.11andalso must be a single-valuedfunctionof position ;itsderivativesmustvanishwhenris infiniteanditshould be continuous everywhereexcept at thescrewsurface. The Laplace equation3.15 was solved in conjunction withthe boundaryconditionsfor

thevelocity potenti al,q"at the discontinuitypointF

=

0 where thescrew surface isformed,by Goldstein [91to give

where

G(IJ)=

..L. _!. f

^F2m•1(11)

I+Jl² :zr2",=0(2m +IF ond

where,

{q,1is the velocitypotentialatdiscont inuitypoint;

!Iis thelocal tip speedratio;

Jloisthe tipspeed ratio;

a",isthe coefficientofthe circulation distrib ution;

A...is the approximation to thea",coefficients ;

t",is a correct ionfactor tothe approximationcoefficient ,A",;

2rn"+1'is an algorithmdefinedby Goldstein[9J [,,(x )is the modifiedBesselfunctionof the firstkind;

T1,,,(z)isa.modified {unctionof a seriesdefinedaa

3.2 .2 Calculationof CirculationDistribution

(:1.17)

(:I.ISI

(3.19)

Accordingto thedefinition insection3.2.1, thecirculation aroundany bladesection is equalto thediscontinuityof thevelocity potential,</I,at the correspondingpoint

25

on the screw surface. Following this definitionand restoringthe factornIt/Vb temporarily taken35oneinthe section 3.2,1.the circulation distributionrbecomes,

The equation 3.20 can alsobeexpressed35

(3.21)

where /( is known35theGoldsteinfactor whichwas solved by Goldstein[9] for a two bladedscrewpropellerand later solvedby Tachmindji

1271

for three,four,five and sixbladed propellers.The fador,K,is defined as

(3.22)

whereBis thenumber ofblades andr<lOis a circulation for a wind turbine with infinite number of blades.Goldstein'sanalysisincludes tip losseffects for thecircu- lat ion distributionalong thc blade span andallows for effectsof finiteblade number of a rotor.

For infinite number of blades, the circulation distributionrat eachbladesection

r_2ll"f U I

- B ' (3.23)

whereIIIis the tangentialcomponent of induced velocity in the wake and canbe expressed35

u,=2na'r (3.24)

Dy using Goldsteinfactor "', thecirculationdistribution at each bladesection for a windturbinewithfinitenumberof bladesbecomes

(3.25)

26

3.3 Application of the Lifting-L ine Theory

The circulationdistributionof equation3.25 in section3.2.2 fromthelifting-line theory can beadapt edto calculatetheperformanceof a windturb inewith given geometricalcharacteristics of machines.The windturbineperformanceevaluation with both a clean andan iced rotor wasdone byusing thismethodthat was developedbySmalland Bose [12,13]and Bose[loll.

Figures 3.2illustr at es geometr icrelations between awindturbineblade secuon andtheairflow.The geometric pitchangle,¢.and advanceangle,P.are expressed

tantjJ= ; ; (3.26)

and

tanl3

= fi;

^(:1.27)

wherePhis the geometricalpitchand

n

is therctatlonalSI}CCc!

or

theblade. The aerodynamic pitchanglePi can be expressed interm ofadvance angleandind uced axialand tangentialfactorsas,

and

tanp; ^\'.(I-a) nr(l

+

^a') tanp f:

~:,l) tanP; = ~

(3.28)

(3.29) whereAi is an inducedadvanceratio. The resultantinducedvelocityshouhlbe normalto theincident air flowLerbs[lO]. ;mdthus

tanPi= ~'a'nT

21

(3.:10)

From the forcediagramin figure 3.4,the localthrust,dT"andtorque,dQ" at a blade cleme nt,dr, have thefollowing relation with theaerodynamicpitc hangle,

tanf3i =~'

^(3.31)

Theideal efficiency fora wind turbinebladeelement , neglecting the viscousdrag force, is

TN

=

~~

Vi dT, lanf3,

lanf3 (3.32)

By combiningequations3.27,3.28, 3.30 and 3.32,the expressionfor theinduced tangential factorisfound to be

(3.33) fly applyingtheKut ta-Joukowskicondit ionat each bladestat ionr,thelocal lifting force exertedontheblade elementdr is

dL

=

pV1rdr (3.34)

wheretiLis theliftforcelit.blade stat ion r,andristhecirculation distribution alongLitebladespan.Incorporati ng the Goldste incorrection factor,K,andusing equat ions 3.25 the liftcoefficient ateachblade element,dr, becomes

where thegep factorgis,

C 4gKO'

L=(l +ol)~ (3.35)

g=~. ^(3.36)

in whichCis the chordlength of thebl:..Je element andDis thediameterofthe rotor.

28

The non-d imensional thrustandtorquecoefficientsweredefinedas

KT

= p;n~

and

K

_-!L

Q - pD~n~

where,TandQarethetotalthrustandtorqueoftherot or.

The idealblade element thrustand torq ue coefficientskT"kQ,mayhecalculated as follows.Theideal thrustcoefficient was

~RdL pD4n' lf3x3Ka'(1+a') and thetorquecoefficientwas

kQ,

(:1.39)

(:lAO)

In realflow,drag exists dueto viscosityoftheair and theblade surfaceroughness.

Thebladeelementthrust and torquecoefficientsweremod ifiedby addingthedrag forceasshownin theforce diagramof figure3.4.This leads to the elementalthrust

dT=dTi

+

BdD3infii and thethrustcoefficientof each elementbecomes,

kT=(1

+

(/anPi)kT,

(:1.41)

(3A2)

where the drag-liftratioE=CoICr..Similarly, the torquecoefficientcan beme- pressedas

(3.'13) 29

finally,overallperformance,that is, totalthrust coefficient,KT ,torquecoefficient, KQ,efficiency,''It and powerratio,P" were found at each tip speedratio, f,lo, by integrating1I1e elementalvalues over blade span.He re rJis

(3.44) andPris

(3.45) illwhichPHthis themaximu mpossible powerabsorbedby a wind turbine:

which was referred to in section 3.1. This theory is strictly valid foronly lightly- loadedrotors where the slipstream expansion isneglected . Thisassumptionis reasonable for a wind turbineworkingunder the cut-outwindspeed.

3 .4 Computational Method Used for Wind Tur- bine Performance Evaluation

The performance calculationsfor horizontalaxiswindturbines withboth a clean andiced rotorwere done by usingthelift ing-line theory.To assess thewind turbine performance accurately,experimenta ldata forlift and drag coefficientsovera wide range of angles ofattackwereneeded. A theoreticalcurveof liftcoefficient was first calculatedby usingequation3.35.Thereal wind turbinecjererlcnel points werefoundby matchingthetheoretical curvewithsetsofexperiment aldataof lift coefficientandthenbyobtaining the correspondingdrag coefficient.The liftand drag coefficientsrequiredwere derivedfrom windtu nnel testsfor an airfoilused as windturbine blad es andwill be described inchapter4. A computerprogram that

30

had beenwritt enin FO RTRAN wasused for this task.Thisprogramwasinitially writtenby Sma ll and Bose(12,131for the performanc ecalculation of a windturhin(' with a cleanrot orand itWi\3adaptedforthe use ofawind turbine withaniced rotor.

3.4. 1 Nume rical Pro cess

This programconsistsofa ma in programKI together wit hsubrout ines L2,1.:1, 14,L5,Gold, and Gold3.L2ie a subrou tinefor initialbladesectiondatn input . Goldisasub routinecontaini ng Goldstein correctionfactor s,K,for two bladed windturbines; Gold3 pro videsGoldsteinfactorsforthree, four and sixhladed wind turbines. The main progr amKIintegrat esthesu broutines andthealgorit h mto calcula teawind turbine'soverallthr ustcoefficient,torque coefficient , effleiency andpowerratio over arangeoftipspeed rat io0.5to12 in 0.5 steps. Pareach tipspee d ratio,thewindturbine bladewasdivided in 11 radiusfractions, n.l to1in 0.1ste psexcept atthe 0.95 blade station, This programalso calc ulated the aerodynam ic properti esincludinginducedaxialand tangentialvelocity fadors, resultantangles of atta ckand Reynoldsnumberat eachblade clementsection. The performanceofa wind turb inewithtwo,three,fourand sixbladedrotorscanbe calc ulat edbyincorporating theappropriate Goldsteincoefficient for finitenumber of rotor blades andtip losses.

With inthemain program Kl ,calcula tionswer emadefirstfor atheo retical requiredlift coe fficient (equation 3.35)foreach bladesection over arange ofanglr.s ofattackfrom _6⁰to90⁰in 2⁰steps. Thisimplied that theinduced aerodynamic pitchangle/3;was

31

where ¢ is thegeome t ricpitch angle . The ope r ating pointof thebladesection was theinterscctio n of this calcu la ted lift coefficie ntcurve withthe actual section lift coefficientcur vefoun dfrom ex perimentalresults .These pointswere fou nd by using sub routine L3inwhic h theintersectionpoint s of the two curveswerederived by systematiccompariso nof twoadjace ntpoints oneach ofthe curves overangles of attackIrcm _6⁰to90⁰at twodegreeintervals.When one valueorthetheoret ical curvefell belowthe correspond ing valueon the expe r imenta l liftcurve,thetwo curveswere considered to becrossed. The2⁰was thensplit into10 andthe met hod repea tedtogeta clo serestimate. The intersecti on pointsgavetheactua lworking valueofliftcoefficient and ang leofatt ackforthebladesections.The actual angleor att ackfound by the iterativemethod wastheninput to the sub routine L4toderive thedragcoefficient fromtheexperimental curve.L5was a subroutine to recalculat e the new theoretical liftcoefficient pointby the samemethod usedinmainprogra m KIto gel a more prec ise resul t at theactualoperatin g angleof attack. Goldstein correctionfactors,11':,wereimposedbyusing subroutin esGOL D andGOLD3 fo r two,three, four andsixblad e dwindturbines. By usingtheequations 3.42,3.43, 3,44and 3.45 andSimpson' s numerical integr ationmethodoverbladespan, the overallperformance ofthe windturbineinclud ingthethrust coe fficient,KT, torq ue coe fficient,[(q,efficiency, 11,andpowerratio ,P" wer e obt ai ned forbothclean andiced rot ors. Theinitial paramet ers suchasbladegeome t ry,including rotor diamet er, geometricpitch angleanddistribu t ionofcho rdlengthalongtheblade span,and st a te ofrotor,i.e. cleanoriced bladewere requested bythe compu t er program.Alogical flow chart forthis computation al programis showninfigure 3.5.Thisprogramwas run in the VAX8530 mainframecomput er inthe Faculty of Engineering and Ap pliedScie nceattheMemor ial Un ive rsityofNewfoun dland.

32

3.4 .2 CalculationsforWindTurbine Models

Prediction ofaerodynamicperform ancedegradationfor windturbineswithiced rotors under rime and glaze icing conditions weredone byusing the theoryand numerical methoddescribe d above.Theprog ram com puted windturbinepcrfce- mance incl udingKT,Kq,J']andP;aswellas powerreduction over tipspeed ratio 0.5to 12, butforconciseness only the resultsof powerratio are displayed.

Twodesignsof windturbine we restudied .One was a two-bladedsmallwind turbine with2.5 m diamet er rotor,lineartwisted bla desand uniformblade cho rd length alongbladespan. Theother was a Ca rte r-23two-blad edwind turbine with 23m diameterrot or, non-linearblade twist andnon-linearbladechordlen g t h.

Both mach ines were assumedtoha ve thesameLS( 1).04l7airfoil blade section and operated at auniform wind speedof10 m/ sec.Windsh earcffectsand wind turbulence were neg lected in this computa tio n.

The wind turbin es wereassumedto be operatingin typicalrime or1\la1.cicing conditions.Figures 3.6lo3.11 arecalculatedresults of powerratioforthe 2.5III

ro tor windturbineandtheCarler-23wind turbine atdifferentatmos phericicing con ditions.Results show that~heeffect of rime icingonthewind turbine'sbla des werenotassevereas that ofglazeicing; gleaeicingalmost completelydestroyed ba t hwind turbines'aerodynamicperformanc e.Rime icing reducedpower out put for the Carter-23 wind turb ineby 30%andforthe2.5 mrotordiameterwind tur bine by49% overa rangeoflipspeedratiosfrom 0.5 1012.

Figure3.1:Streamtube(or momentumtheory.

n» :

Figure3.2:Velo city diagramatblade sect iondr.

34

RohlioDal

Pla~

li ndlireclin!

Figure3.3:Coordinateof wind turbinescrewsurfacein lhe wake.

Bi : ,

dTiI : -=-dL

WB ; ••

~

L . /.Y

dD 4Q/ Blll/r l

Figure3.4:Forcedi~ram&1 blAdesectiontir,

Gte:Experimentalliftcoeffici ent Gde:Experimentaldragcoefficient

Figure3.5:Flowchartfor Klprog ram.

36

0.4

0.3

0.2

s e

l

^0.1

£

0 '

.

...

-0.1

\,.0 -0.20

Tipspeedratio

,.':Cle anwind turbine '0':Glazet iced windturbine

Figure3.6: Computed resultsofpower ratio for the2.5mdiameterhorizo ntalaxis windtu rbine.

37

0.4 0.35

0.3 0.25 .g_~ 0.2

~

0.15 R-

0.1 0.05

-0.05 0

...

"' . ...

. ... . ..

^,.

. , ..

^,

f'/

·10...•• ...0•••0•••0

Tipspeed ratio

10 12

....:Clean wind turbine '0 ':Glaze2icedwind turbine

Fi!lure3.;:Compu ted results of powerraliofor the 2.5mdiameterhoriw nlal axis wind turbi ne.

3S

~4

~35

0.3 ,I

!

~2S

l

. s /

e

^0.2 ;'

~

~15

,

of 0.1

Ii

0.05

..

^-

-<105 0

. \ ,

•

10 12

lipspeed rene

'.' :Cleanwind tur bine '0' :Rimeicedwind turbine

Figure 3.8:Computedresults

o r

powerratio forthe 2.5mdiame lerhorizontal axis win dturb ine.

39

/~

~~+--'*-_._ _ ._ _ - ^~ . .

^{_+.. +- _.••+ -}

o"..-'".,.. • O " f

0.4 0.3

.~ ^0.2

1

^0.1

-0.1

'

.. ...

-"'Il

\,.0:'

10 12 .0.20C-- - --:;-- - - -;-- - ---,, -- - -;c-- - - 7;:-- - ---!·

Tip speed ratio

"": Clean wind turbine '0':Glaze1iced windturbine

Figure3.9: Com putedresults ofpowerratiofor Cart.er·23 wind turbine.

40

-,

o ..

0.1 0.3

0.5,~---"---~--- .,

/~ , ¹

\ I

/ / \ 1

, • . . .•• 4 ·• •_. . . . . . ~

10 12

0.4

.~

• 0.2

~

Tipspeed ratio

'.':Cle a n wind turbine '0':Glaze2icedwind tur bine

Figure3.10 : Computed result s of po we rratio for Cartc r·2.1windturbine.

41

0.45 O.41~

0.35 0.3

Tipspeedratio

"":Clean windturbine '0':Rimeiced windturbine

10

Figure3.11:Comput ed results of powerrattc forCarler-23windturbine.

42

Chapter 4

Wind Tunnel Tests for Airfoil wi th Simulated Ice Deposits

Unt ilrecently, verylittl e experimenta ldata has been available011theperformance degrad atio nof airfoilsections resultingfrom rime orglozeicc accretionOWfwill(~

ranges ofangles of attack. Duringthepast10 ycara,most thl-'Ordicalami\' XIWt- iment alworkhas been focused ontwoaspects: the evaluationofdegrndatiou of aerodynamic performa nceforanairfoilin aircraftcruiseorclimbingcondluonsdue toice accretion;andthe conductoficing andde-icingtests for rotors ofhelicopters.

Bragg[28,291investigatedtheeffectsof simulatedicc shapes0111m,dragand pitchingmomentof anairfoil section in aircraftcruise conditions; thalisfor angles of attackinorbelowthestallregion.He also prov idedinformation onthe length of separationbubbles, reatt achment and trailing edge separation.Bragg andCoirier [30) simu latedglazeice accretionon a 21 inchchordmodel of a NACA0012 airfoil andreportedmeasurem ents ofsurfacepressure, Iirl,dragand momentcoelhc ieuts overa range ofangles ofattackinandbelow stall. Modelscale helicopt errotor icing tests weredonebyGulfondcral.[311.Icc shapesthalaccumulated011the rotor bladesduringicing tunneltestswere docu mentedandst udiedat dilrl:renl

43

Machnumberunder differen tatmosphericcondition saswell as theeffects of the performance ofthe rotorduetoicing,

Computational meanshavealso been developed to model the flow over an iced airfoil.Ceheci[32Jusedan interactive boundary layertechniqueto predict the aero- dynamiccharac te rist icsof an airfoilwithleadingedge ice accret ion.Potapczuk[33]

usedaparabolizedNavier-Stckeamodeltomake a similarcalculation.Bragg[16) predicted the performanceof aNACA 0012airfoil withsimulatedglaze ice ac- cretionand comparedthis withthat predictedby theNASA Lewice iceaccretion computercode for the sameicingcondit ions;resultsof boththe interacti vebound - ary layermodelandtheNevier-Stokesmethodwere compared with experiment al data, Numericalsimulationswerealsomade for helicopter bladeicing by Oleskiw [3<11to simulatetherime iceaccretionprocess onthe rotorblades.Potapczukand Berkowitz[35Jpresented experimental data for a Boeing737- 200AD Vwingsec- tionfor arange of angles of attackfrom_2⁰to 20⁰•These datawerecollected underglaze,rime and glaze-rimemixtureicing conditionsfor an airfoilof16inch chord.

Although considerable researchhas been done on atmosphericicing,per for - mancetests of aniced airfoilovera wide range of angles ofattack are rareand very littleexperimentaldata has beenfoundintheliterat ure on iced airfoilsover this widerange, thatis,anglesof attackfrom_6⁰to90⁰•This restrictstheapplica- t.ionof the theoretical method describedin chapter3for evaluationofperformance degradationofwindturbinesunder icing condit ionsasthemethod islargely de- pendent upon exper imentalsectiondataavec a rangeof anglesof attack from_6⁰ to 90·,

Thischapterdescribes tests onan airfoilina windtunnel,whosesection geom-

etrycorrespon dedto the airfoilsection used asthe bladesof aroto r.Testing was performe d in alow speedwind tunnel atMemor ialUniversityofNewfoundland.

The teste d airfoilmodelwas a NASALS{I) -0417wingsection. Varioussimulated icedsha pes that wererecorded from previoustests[51and from othe rdocuments [15,161weretested. The sim ulat ed ice sha pes weremadefrom woodinamodel shop in theFacul ty ofEngineeringand Applied ScienceatMemorialUniversity of New- foundland.AnAerolabbalance dynam ometertabl ewas usedto suppo rtthemodel andmeasurethe aerodynamicforces exertedonthe wing.A Keithley $5i5dat a acquisitionsystemandahot wireanemome te r wer e 1lSf'<1to measureIU'rodynam ic forcesexert ed ontheairfoilandthe wind velocityinside thewindtunnel.

4.1 Calibration of W ind Tunnel Worki ng Se c- tio n

The layoutof the low speedwind tunnel,which islocatedintheFluidsLaboratory intheFaculty ofEnginee ringand AppliedScience, is showninfigure.1.1.'l'h!s windtunnel is10m long;ithas a cross section of1mxlm. Section onl: isa boundarylayer testingsectionandsectio n2,which wasusedfor theairfoiltests,is upst reamof sectiononeandprovidesspace wherenon-bound arylayertests can he conducted.Themaxi mumwindspeed that could be providedby the windtunnel atthis locat ionwasabout 14.5m/ sec.

4.1.1 CalibrationoftheHot- Wi re Anemometer

ADisahot-wire consta nttem perat ureanemometer (CTA) was calib ra tedbefore the windtunn el testsweredone.Thehot-wireor hotfilm anemometer isatpresent themostwidely usedmeas uringsystem foranalys is of velocit iesin turbule nt now.

TheDisa55MOIanemometer isa multipurposeinstrumentprimarily usedfor mea- surements of theinstantaneousmass flowofa gas orliquid;it uses as atransducer either a hot-wireor a hot-filmprobe. Theinstrumentbas a build-inDC meter for measure mentofprobe coldresistance and for indicationofmeanflow. Based on measuringtheconvective heat lossfrom the electricallyheated hot-wire/filmsensor ca used bythe now ofgasorliquidsurroundingthesensor, the fluidvelocitycan bemeasured. A PHsinglehot-wire sensorfrom Dantec was used;thisconsisted of a 5,um diameter platinum-platedtungstenwire. Wires are suspendedbetweentwo prongs,to whichtheyare welded .The probewasplacedatthecentre of the tunnel working section.The anemometerwas adjustedto haveoptimumfrequencyre- sponseby using abuilt in square wave generator with different frequencies.Values of standardnow velocitie sat the workingsection of the wind tunnelwereobtained byusing a pitot-tube. Aset of 20 pointsof wind velocitysampleswere collected by controlling air now at the inletofthe windtunnel fan. Dantec Acqwiredata acquisitionsoftwarewasused to processthecalibration data.

4.1. 2 WindTunnelCalibration

The ideal flowfieldprovided bya windtunnel for an airfoil test shouldbe uniform with low turbulenceintensityacrossthetunnelworking section. Non-uniformflow can causedistort ionof the loadsexertedon thetestedbody.Flowwith higher turbulenceintensitycan change the positionof transitionto turbulentflowonthe suct ionsideof the model and,therefore,change the dragand maximum lift.The qualityof the flowfieldin the workingsection had tobe examined before tests proceeded.

Atwo degreeof freedom motiontraverse wasdesigned to supportthe probe so

46

thatthesensorcouldbepositioned everywhere acrossthe tunnel working sect ion through acantilever. Figure4.2 showspoints measuredacrosswind tunnel section.

Thewindspeed and turbulence intensity ateachpoint weremeasuredand are shown inappendixinpage100.Theresults show thatbeyondlitewall boundarylayer, the maximum turbulen ceappear edatpointG7and was about 4%; theturbulence wasmuchlower towa rds thecentreof theworkingsect ion. The definition of the ftowturbulence inten sity,U,;,usedwas,

1I,i

=

u~:.^{x 100, (,1.11}

whereU'"is themeanvalue ofthewindspeedandu'''u isthe rootmean square or the standard deviation defined as

1N

u. ..=

N

?;(U(nl-U.I' ^(·1.2)

inwhichUiswindvelocitymeasuredandNis thenumber ofsam ples.Thelow turbulence intensityand lowmean velocity variationsacrosstheworking section providedgoodcondit ions for the airfoiltest s.

4.2 Ca li brat io n of the St rain Gauged Bal an ce Table

AnAerolabPyramidalStrainGaugedBalance SystemWiL.'lusedtosupport the model in thewind tunnel. Thisdeviceis shownin figure 4.3,Itsangles ofatt ack could be adjust ed over a rangeor±:25":egrccand its angle ofyawover a range of360 degrees. Itwas possible10meas ure six force and moment r:omponcn1s whichfully determinedtheresultant forceexertedby the airstreamon the airfoil.

A mountingadaptor was fixed onthe mountin gplateatthe lop ofthe balance 47

tableto cbange the range of angles ofattack fromprevious±2~degreeto -10to 36 degrees.Theranges of angleofattack wereextendedfurther to 90degreeat a lower tunnelvelocity of6m/sccj thisrestrictionenwind speedwas duetothe capacity limitationof thebalancetable.The forcecomponentswere separat edmechanically andmeasuredthrough individualstrain gaugedload cells.The signalfrom each straingaugewas amp lifiedbyastrain gauge amplifierand thensent toamicro computer.A Keithley5575 dataacquisition unit was used toprocess the signals.

The average value of each componentwasfoundby usc of aprogram whichtook the meanof thedata points corrected.

Fromthefigure4.3,the basic linkageon the balance tablemay be termed a pyramidallinkage.The centralspider which carriedthe spindlewas supportedon fourdiagonalstrutswhich, ifextended, would meet ata point known as the balance centre.The balance table was calibrated before set up beneath the windtunnel.

Forcecalibration was done by using a 10 inchdiameterpulley thatcouldturn freely on a ball bearing withoutmuch resistance. Loadsof 0.5,I, 5,to, 20,40 lbs were appliedtocheck the linearity of thestrain gaugesand0.5 up to 90 lbs.lnfor the moment. The calibrateddata of forceandmomentwere sentto the computerto get polynomialforce andmoment funct ions for the calibrat ions.As all thecalibrations ofthe componentswereaboutthe balance centreandthe stemused to support the model had a 0.4 m differenceinheightfromthebalance:centreto thepoint at whichthe airfoilWMattached anda.samounting adapterwasused to change therange of angles of att ack from ±25 degree to therangeof-10to 90 degree, correction was madefor thecomponentof pitch moment from theforce balanceby addingtheextramoment resultingfromthe displacementbetweenthe mounti ng centreandtherotationa lcentre.

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4.3 Tes t Pro cedure a n d Re sult s

The airfoiltestedwas a NASA LS(I)·O·.n7wing sectionwith a0.2IIIchordlength and a 0.8 m span:l.c.an aspect ratiooffour .Thisbladesectionwas the samcfamily astheblade sectionsused for theCarter WEC-23windturbine.The offset softhe profileof thisairfoilareshowninta ble 4.1.ThismodelWi\.,made from aluminium alloy (H6061) anditwas manufacturedon aeNCmachin eat the [Inivcrsityof Victoria.

The airfoilwasmo unted on thelopofthemountingbar ofthe(lyna11loolf't"r inside thewindtunnelasshownin figure4.4.Each channelsigna lfrom til ..st rain gauges wassetto zerobefore eachtestto reduce theeffects ofzerodriftfrom theamplifiers.Signalsfrom thest ra in gauges onthe dynamometerfor eachIorru componentweresentto a multichannelstrain gauge signalamp lifier.FigureU·) showsthe instrumentationfor the windtunnel lest .

Severaltests wereperformedforthe clean airfoilandfor the airfoil withVl\riOll~

simulatedice profiles.Three iceaccretion shapes were simulated.The gla70C Iicc deposit shown in the figure4.6 was obtainedfrom a 5 minutedurationicingtest on a windturbinemodel that isdescribedin thenextchapter; the g!;w.c2ice profileshown in figure4.7was from the NASA Lewis research centre(161 under icingcondit ionsoftem pe rat ure_7°C,liquidwater conte nt2.IBgJm³,windspeed 57 mJsecand dropletdiameter20Jlffiitherime iceprofileshowninfigure 4.8 was from Wilder[151.The ice profilesweretracedandsimulatedby using aspecially shaped wood strip.Eachsimulatedice profile was attached to the leading edge or the airfoilbyusing double-sidedstickytape so that thesecould be faste nedand removed easily.Plasticinewas usedto seal gapsbetween the airfoiland simulated

"9

iceaccretion. A hotwire sensor,which wasfixed ona cant ile ver, wasplaced upstr eamofthemodel. The windveloc it ywithin the chamberwasset to6

miser.

forrange of angleofattac kof-6-to 90-.

Figures 4.9to4.14showthetestresultsof lift anddr,,! coefficientsforthe clean airfoil andairfoil withgla~I,glaze2and rime iceshapes.Testswere donefor steps ofT anglesofatt ackexceptatangle of att ack ofIS-forthe cleanairfoil, wherethe maxi mum lift coefficient appeared.

Duetothecapacity limitati onof thedynam omet.er,thewind velocitywas set to6mlsccforthe full rangeairfoiltestsi.e.the rangesof angleofattackfrom-6 to 90degree.

In theclean airfoilteet, the model wasstableuntilan angleofattackof16-

WI\.!Ireached where the airfoil sta lledwithanabrupt drop in the liftcoefficient and increasein the drag coefficient.Duetoalack ofrigidityof thesupport bar, mount ing plateand the balancetableitself, theseparatedturb ulent flowonthe back ofthe airfoilforced the model tovibrate.This vibration couldinduceadditional now turbulencearoundthe airfoil andaffected the test resultsbeyondthe staU Iqiontosomeextent.Thesimulated glazeIice profile test showed that even atlowangles ofattack , for example0-,flow separatio noccurred behindthetwo 'horns' oftheiceshapeandthe flow aroundthe surfaceof the airfoilwas turb ulent, and thisindu ced somevibrationofthe model.Thesignificantlyalteredshape of theairfoilas aresultof theicing causedthestrea mlined flow aroundthesurfaceof theairfoil10 breakdowneven atlow angles of attack.Thiswas associated witha decreaseoflift and increasein pressure drag.Therime iceaccretiontest showed that no significantchangeofthe airfoil performance tookplace,exceptaroundthe point ofmaximum Hrtcoefficient, where therewasaIlightdropof liftcoefficient.

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