Master of Science in Product Design and ManufacturingJanuar 2012Torbjrn Kristian Nielsen, EPT

Submission date:Supervisor:

Norwegian University of Science and TechnologyDepartment of Energy and Process Engineering

Improvements of a Kaplan type smallturbineForbedre og vidreutvikle en Kaplan smturbin

Lars Fjrvold

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PrefaceDuring this thesis my knowledge about testing hydraulic machinery, erroranalysis and CFD has increased drastically. Also getting the opportunity ofhandsonexperiencehelpingTrygveOpland constructing the test rig in thelaboratoryhavebeen inspirationalandeyeopening.Therearea lotof thingsthat can be taught in theory but there are so many things that requireexperience in laboratorywork. Iwould like to thank Trygve for all help andguidanceduringthetestsandconstructionoftheturbine.The efficiency tests and a lot ofwork have been done in collaborationwithfellowstudentRemiAndreStople.Theend resultof thismaster thesiswouldprobablynothavebeenasgoodwithoutRemi.IwouldliketothankRemiforallthehoursspenttogetherworkingandsocializing.Next Iwould like to thank BjrnWither Solemslie for all the hours of helpreceivedon theMatlabprogramsdeveloped and guidance in calibration anduncertaintycalculation.TorbjrnK.NielsenhasbeenmyProfessorduringthisthesis.DuringtheweeklymeetingsinthebeginningofthesemesterhewasverygoodinguidingmeandRemi inwhattodonextandwhatweshould lookfor.Havingtheopportunityofalwaysbeingabletocomeintohisofficeandalwaysgethelpisfrommysideveryappreciated,thankyouTorbjrn.BrdBrandst,JoarGrilstadandHalvorHaukvikalsodeservethanksforhelpingthroughouttheproject.LastbutnotleastIwouldliketothankmyfamilyforsupportingmeduringtheentireprocess.LarsFjrvoldTrondheim,January20,2012

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AbstractThegoalwith thismaster thesiswas toestablishHilldiagramsand improveaKaplanturbineintendedforuseinAfghanistan.Theturbineefficiencyhasbeentested insetting1and2.Turbineefficiency insetting3and4couldnotbe testedbecause the runnerblades interferewiththe housing making it impossible to rotate the turbine. The efficiency wastested with an effective pressure head ranging from 2 to 8 meters. Bestefficiencypointwasnotreachedbecauseoflimitationsinthetestrigmakingitimpossibletoreacha lowereffectivehead.Thebestefficienciestested inthetwo different settings are presented in the table below together with theuncertainty in the actual test point. All tests are done according to the IECstandardformodeltestingofhydraulicturbines. Efficiency Rotationalspeed EffectiveheadSetting1 76.4 1.57% 552rpm 2.25mSetting2 83.8 1.59% 602rpm 2.72mThe computational fluid dynamics (CFD) simulations done on the inlet bendindicates that the bend should be rounded and flow controllers should beextendedovertheentirebend.Thisshouldbeconsideredtogetamoreevenvelocitydistributionattheinletoftheguidevane.Analternativeplacementof the lowerbearingwasdesignedbut isdiscardedbecauseofthedisadvantagesthemodificationleadsto.Highwearduetosanderosion on the seals causing highmaintenance and costly stopsmakes thesolutionnotoptimalforuseinwaterwithhighsandcontent.TherunnerbladedesignischeckedagainstthedesignprocedurepresentedbyProfessorHermodBrekkeinPumperogTurbinerandfoundtobesatisfying.Itisconcluded that time should rather be spent on optimizing the inlet of theturbine.Fluctuations inthemeasurementsmake itnecessarytochangethemeasuringequipmentor search forerror in theexistingequipmentbefore further testscanbe carriedout. Inorder tobe able to test in setting3 and4 the runnerneedstobeplacedwhilethebladesarefixedinsetting4.

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SammendragMlet med denne masteroppgaven var etablere Hill diagram for enKaplanturbin designet for bruk i Afghanistan og se p muligheten forforbedringer.Virkningsgradentilturbinenerblitttestetiinnstillingenogto.Turbinenharfireinnstillinger, innstillingtreog fire lotseg ikketestedaturbinenkilteseg fast iturbinhuset allerede ved innstilling tre. Virkningsgraden ble bestemt foreffektive fallhyder fra to til ttemeter. Best punktet til turbinen ble ikkefastsattdatestriggengjordedetumuligoppnlavenokfallhyder.Denbestevirkningsgraden testet i hver innstilling er presentert i tabellen under medusikkerheten i det aktuelle testpunktet. Alle testene gjennomfrt ergjennomfrt i henhold til IEC standarden for modelltesting avvannkraftturbiner. Virkningsgrad Omlpshastighet Effektiv

fallhydeInnstilling1 76.4 1.56% 552o/m 2.25mInnstilling2 83.8 1.60% 602o/m 2.72mComputational fluid dynamics (CFD) simuleringene utfrt antyder at innlpetbr avrundes og at strmningsforbedrende spenner seg over hele bendet.Dettebrvurderesforfenjevnerehastighetsfordelinginnpledeskovlene.Deterutarbeidetett forslag tilennyplasseringavdetnederste lageret,mendenne lsningenble forkastetgrunnetulempene forandringen frermedseg.Mye sand i vannet hvor turbinen skal benyttes vil slite ned pakningene ogdelegge lageret. Dette vil fre til kostbare stopp og hyevedlikeholdskostnader.Dermeder ikke lsningenoptimal iforvannmedhytsandinnhold.Lpehjuldesignet er kontrollert mot professor Hermod BrekkesfremgangsmetodefordesigneKaplanlpehjuliPumperogTurbiner.Designeter designet i samsvarmedmetoden beskrevet i Pumper og Turbiner, det erderforkonkludertmedattidhellerbrblibruktpoptimalisere innlpetpturbinen.

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Svingningerimlingenegjrdetndvendigskiftemleutstyretellerfinnehvasomskapersigningeneimlingenefrnyetesterkanutfres.Lpehjuletminstalleresmensskovleneersattiinnstillingfireforkunnetesteiinnstillingtreogfire.

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ContentsPreface..........................................................................................................................iAbstract......................................................................................................................iiiSammendrag...............................................................................................................vContents....................................................................................................................viiListofFigures..............................................................................................................xiListofTables.............................................................................................................xivListofsymbols...........................................................................................................xv1 Introduction.........................................................................................................12 Prefacestudy.......................................................................................................32.1 RelatedworkattheWaterpowerlaboratory.............................................62.2 DesignofaKaplanrunner...........................................................................62.3 Maindimensions.........................................................................................92.4 Potentialflow............................................................................................12

3 TestingofKaplanturbine..................................................................................153.1 Efficiencytest............................................................................................153.2 Cavitationtest...........................................................................................163.3 Runawayspeed.........................................................................................183.4 Calibration.................................................................................................183.5 Pressuregauge..........................................................................................193.6 Torquegauge.............................................................................................193.7 Tripmeter..................................................................................................213.8 Flowmeter................................................................................................223.9 Frequencyanalysis....................................................................................23

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3.10 LabViewprogram......................................................................................233.11 Clearancewatertest.................................................................................233.12 RiskAssessment........................................................................................23

4 Uncertaintiesinmeasuring...............................................................................254.1 Spuriouserror............................................................................................254.2 Randomerror............................................................................................254.3 Systematicerror........................................................................................254.4 Totaluncertainty.......................................................................................274.5 UncertaintiesintheCalibration................................................................274.5.1 Uncertaintiesinthecalibrationoftheflowmeter...........................274.5.2 Uncertaintiesinthecalibrationofthepressuregauge.....................294.5.3 Uncertaintiesinthecalibrationofthetorquegauge........................314.5.4 Uncertaintyincalibrationofthethermometer................................32

4.6 Uncertaintiesinthetests..........................................................................324.6.1 Generaluncertaintyinthetests........................................................324.6.2 Uncertaintyinthepressuremeasurements......................................344.6.3 Uncertaintyinthetorquemeasurements.........................................354.6.4 Uncertaintyinthevolumeflowmeasurements...............................364.6.5 Uncertaintyintherotationalspeedmeasurements.........................364.6.6 Uncertaintyinthecalculationofdensityofwater............................374.6.7 Totaluncertaintyinthehydraulicefficiency.....................................37

5 Testrigsetup.....................................................................................................395.1 Detaileddescriptionoftherig...................................................................39

6 TheAfghaniKaplanturbine...............................................................................416.1 TheTurbinedesign....................................................................................41

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6.2 Specifications.............................................................................................426.3 Maindimensions.......................................................................................436.4 Runnerbladedesign..................................................................................43

7 Changesandlimitationsontherigandturbine................................................457.1 Pipedimensions........................................................................................457.2 Runnerbladefriction.................................................................................477.3 Upperbearing............................................................................................487.3.1 Bearingloadcalculation....................................................................51

7.4 Plexiglasscover..........................................................................................528 OptimisationsofinletbendusingCFD..............................................................558.1 CFDanalysisofinletbend.........................................................................558.2 Velocitymeasurementsininletbend........................................................588.3 Outlet.........................................................................................................61

9 Results...............................................................................................................639.1 Efficiencytests...........................................................................................639.1.1 Setting1.............................................................................................669.1.2 Setting2.............................................................................................68

9.2 Cavitationtests..........................................................................................709.3 Clearancewater.........................................................................................709.4 Mechanicalpower.....................................................................................719.5 Torque.......................................................................................................729.6 Fluctuationsinmeasurements..................................................................729.7 CFDofinletbend.......................................................................................73

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9.8 Velocitymeasurements.............................................................................7710 Discussionofresults......................................................................................7910.1 Efficiencytests...........................................................................................7910.2 Clearancewater.........................................................................................7910.3 Inletbend..................................................................................................7910.4 Outlet.........................................................................................................81

11 Conclusion.....................................................................................................8312 Furtherwork..................................................................................................8512.1 Rigsetup....................................................................................................85

13 Bibliography...................................................................................................87

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ListofFiguresFigure21CrosssectionofaKaplanturbine,Voithhydro...........................................3Figure22EfficiencycurvesforKaplanturbines.........................................................4Figure23Sturbine.....................................................................................................5Figure24Bulbturbine................................................................................................5Figure25Vectorcomponentsofforcesactingonarunnerblade............................8Figure26AxialcutofaKaplanturbinewithguidevanes..........................................9Figure27Speednumberplottedvs.axialspeed.....................................................10Figure28Relationbetweend/DandB0/Dplottedagainstns................................11Figure29Suctionheadandnumberofblades........................................................12Figure31Definitionofheights.................................................................................17Figure32EfficiencycurvewithchangingThomanumber.......................................17Figure33Thedeadweightcalibrationsetup...........................................................20Figure34Calibrationcurveforthetorquegauge....................................................21Figure35Tripmeterandreflexribbonreadytouse...............................................21Figure36Theflowmeteruseinthetest.................................................................22Figure41Calibrationcurvewitha95%confidenceinterval...................................29Figure 42 Calibration curve for the pressure gauge with a 95% confidenceinterval......................................................................................................................30Figure 43 Calibration curve for the torque gauge with a 95% confidenceinterval......................................................................................................................32Figure44Testfordriftinmeasurements300rpm,setting1...................................33Figure45Testfordriftinmeasurements300rpm,setting1...................................34Figure51Testrigsetup............................................................................................40Figure61Completeturbine,(Inventordrawing).....................................................41Figure71Originalpipesection................................................................................45Figure72Configuredpipesection...........................................................................46Figure73Runnerbladewithbrokenbladesection,seenfrombelow....................48Figure74Temperatureplottedvs.rpmat2.5meterpressurehead.Setting2......50Figure75Temperatureplottedvs.pressurehead.Setting1,800rpm....................50Figure76Temperatureplottedvs.pressurehead.Setting2,650rpm....................50Figure77FlowaftertheturbineoutsideBEP..........................................................53Figure81Velocityandpressuredistributioninpipebend......................................56Figure82Originalgeometry....................................................................................57Figure83Geometry1..............................................................................................57Figure84Geometry2..............................................................................................57

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Figure85Geometry3..............................................................................................58Figure86Pitottubemountedontheturbine..........................................................59Figure87HeightdifferenceinaknifePitotmeasurement......................................60Figure88Bearingwhenplacedinsidetheguidevanecentrepiece........................62Figure912ndorderpolyfit.....................................................................................63Figure923rdorderpolyfit......................................................................................64Figure934thorderpolyfit......................................................................................64Figure94Smoothingspline......................................................................................65Figure95Hilldiagram,efficiencyplottedagainsteffectiveheadandrotationalspeed.........................................................................................................................66Figure96Rawdatameasurements.EfficiencycurvesatconstantRPMplottedvs.effectivehead......................................................................................................68Figure97Hilldiagram,efficiencyplottedagainsteffectiveheadandrotationalspeed.........................................................................................................................69Figure98Rawdatameasurements.EfficiencycurvesatconstantRPMplottedvs.effectivehead......................................................................................................69Figure99Clearancewateratconstantrpm.............................................................70Figure910Clearancewateratconstantinletpressureheadinsetting2...............71Figure911Mechanicalpowerat500rpm................................................................72Figure912Torqueat500rpm..................................................................................72Figure913Originalgeometrywithinletvelocityof1.0814m/s..............................74Figure914Geometry1.Inletvelocity1.25m/s........................................................75Figure915Geometry2.Inletvelocity2.387m/s......................................................75Figure916Outlet velocityprofileswithoriginalgeometryanddifferent inletvelocities....................................................................................................................76Figur917Outletvelocityprofilesforgeometry3....................................................77Figure131Inflationalongwalloftheinlet...............................................................RFigure132Frontpanel...............................................................................................TFigure133Dataacquisitionandtranslationofvoltsignals.......................................TFigure134RPMsubVIforreadingsoftherotationalspeed.....................................UFigure135BlockdiagramfortheRPMsubVI...........................................................VFigure136Calculationnodeandfrontpanelvalues................................................VFigure137Storage..................................................................................................WFigure138Plottingofefficiencyheadgraph...........................................................W

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ListofTablesTable1Componenterrors........................................................................................27Table2Uncertaintiesinthecalibrationoftheflowmeter.......................................28Table3Uncertaintiesinthecalibrationofthepressuregauge................................30Table4Uncertaintiesinthecalibrationofthetorquegauge...................................31Table5Errorsinthetests..........................................................................................34Table6Uncertaintiesinthetorquemeasurements.................................................36Table7Uncertaintiesinthevolumeflowmeasurements........................................36Table8Volumeflow..................................................................................................42Table9Mainturbinecharacteristics.........................................................................43Table10Actualandscaledoutletvelocity................................................................77Table11Scaledvelocityvs.averagevelocity............................................................78Table12Velocitymeasurementsatconstantpressurehead...................................78Table13Weightcalibrationcalculation.....................................................................N

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ListofsymbolsSymbol Description UnitL Lift [N]CL Liftcoefficient [] Density [kg/m3]v Velocity [m/s]L Length [m]D Drag [N]CD Dragcoefficient []F Force [N]o Angle between angular

velocity and inletvelocity

[0]

Angle between lift anddragcomponent

[0]P Turbinepower [W]u Turbinevelocity [m/s]P Availablepowerinwater [W]g Gravityconstant [m/s2]Q Volumeflow [m3/s]H Head [m] Efficiency [%]Z Numberofrunnerblades []t Distance between

runnerblades[m]

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0 Speednumber [] Reducedangularvelocity [m1]cm Axialvelocityofwater [m/s]D Turbinediameter [m]h Hydraulicefficiency [%]Pm MechanicalPower [W]Ph HydraulicPower [W]m Mechanicalefficiency [%]Tm Torque [Nm]E Specificenergy [J]p Pressure [Pa]z Height [m] Thomanumber []qv Volumeflow [m3/s]m Massofwater [kg] Correction factor for air

buoyancy[]

f Relative error inmeasurements

[%]sy Standarddeviation [Varies]ey Absolut error in

measurements[Varies]

B Arclength [m]r Radius [m] Angle [0]

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c Measuredflowvelocity [m/s]c Scaledflowvelocity [m/s]h Heightdifference [m] Pitotcoefficient []Re Reynoldsnumber [] Dynamicviscosity [kg/(ms)]

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1 IntroductionRemote Hydrolight is a company designing turbines that aims to be costefficient and easy to produce. Remote Hydrolight represented by AndersAustegrwanted toestablishHilldiagrams for fourrunnervanesettingsonaKaplanturbinetheyhadproduced.Austegrdalsorequestedcavitationandrunawayspeedtests.Iftimeallowedithe also wanted suggestions on how the turbine could be improved. Theimprovementsshouldnotmaketheturbinemoredifficulttoproduce.

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2 PrefacestudyThe Kaplan turbine was invented and developed by Austrian Victor Kaplanaround1913,andisdesignedtooperateatlowheadsandhighflowrates.Theturbine is an axial turbine,meaning that the direction of thewater flow isparalleltothebulbanddriveshaftthroughtherunnerblades.It iscommontocomparetheKaplanturbinewithapropellerduetoitsdistinctshape.

Figure21CrosssectionofaKaplanturbine,Voithhydro

VerticalaxisKaplanturbinesareinmanywayssimilartoFrancisturbinesaswellaspropellers.Besidestheshapeoftherunnerblades,theKaplanturbineusesthe same water way system andmethod to generate electricity as Francisturbines.Like theFrancis turbine theKaplanhaveaspiralcasing todistributethewater around the turbine.Guide vanes areused to regulate the volumeflowthroughtheturbine.Theguidevanesarealsousedtoinduceaswirlinthewater,so that thewaterhits the runnerblades in themostefficientangleaspossible.Therunnerbladescan inmanycasesalsobeadjustedtomaintainas

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optimal flow conditions as possible. With the opportunity to regulate twoparametersmakestheKaplanturbineefficientoverawidespectreofloadsandheads.ThismeansthatthehighefficiencyrangeofaKaplanturbine isgreaterthanefficiencyrangeofaFrancisturbinewhereyouonlymayadjusttheguidevanes.Kaplanturbinescanalsobeproducedwithfixedrunnerbladesandguidevanes.Bymountingfixedbladesor/andguidevanestheefficiencyrange isreduced.SeeFigure22 for theeffect fixedguidevanesand rotorbladeshaveon theefficiencyrangeofaKaplanturbine.

Figure22EfficiencycurvesforKaplanturbines

Kaplanturbineshavealsotheopportunitytobemountedwithahorizontalaxis.TheyarethenoftenreferredtoasSturbinesandBulbturbines.SturbinesareusedinthesamespectreofheadandflowratesasverticalaxisKaplans.PriceandavailablespacearefactorsthatgovernthechoicebetweenSturbinesandverticalaxisKaplans.VerticalaxisKaplansrequiresasmallerlandareathanSturbines.Sturbineshave smallerhydraulic losses compared toaverticalaxisKaplans, due to the fact that thewater does not have to change directionthroughtheturbine.

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Figure23Sturbine

The bulb turbine is only used in high energy sites with low head and highvolume flow.On the bulb turbine the generator and drive shaft ismountedinsidethebulbinfrontoftherunner.Afullgrownmanisabletostanduprightinsidethebulb.

Figure24Bulbturbine

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LiketheverticalaxisKaplan,Sturbinesandbulbturbineshaveguidevanesandrunnerbladeswiththepossibilitytobeadjustable.Theyallhaveadrafttubetoregainpressureaftertherunner.Itisnormalforallthesolutionstobedivedtopreventcavitationattheendoftherunnerblades.

2.1 RelatedworkattheWaterpowerlaboratoryThereareanumberofreportswrittenonsimilarcasesastheoneinthismasterthesisavailableattheWaterpowerlaboratory.BjrnWintherSolemsliemadeamasterthesisonhowtooptimizeadistributoronaPeltonturbine.Thereportcontainsarelativelygooduncertaintyanalysisthatisusedasguidanceinthisreport.Pl Tore Storlie performed extensive uncertainty calculations on equipmentusedinthetestperformedinthisthesisinhismasterthesis.Eve Walseth have performed and written a good report on tests andoptimization of a crossflow turbine.Walseths report is based on the samepointsas in this reportandmuchof theworkWalsethdid canbe correlatedwithtasksthatwillbeperformedinthisthesis.Anders Linde Holo have performed CFD calculations and written a shortintroductiononCFDmodelling.yvindAndresendidCFDanalysisaswellasestablishingHillchartsforaFrancisturbine.

2.2 DesignofaKaplanrunnerTheKaplanrunnerconsistsofavariablenumberofblades,dependingonheadandvolumeflow,andahubthebladesareattachedto.Therunnerbladesareusually designed as curved hydrofoils using pressure differences to createtorquewhichistransferredtoelectricalpower.Designingtherunnerbladestoperformoptimalwiththegivenflowconditions isextremely importanttogainhighefficiency.Forces from thewateractingon the runnerblades canbebrokendown intotwomainforces,liftanddragforce.

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[ ]2LvL C l dr N (2.1)

Equation(2.1)andequation(2.2)givesusthe liftanddrag force.Tobeabletocalculate the forces the lift anddrag coefficientshave tobe known. Lift anddrag coefficients can be found using certain programs, such as xfoil or it ispossibletofindliftanddragcurvesforcertainNACAandGttingenfoils.Togetasaccuratecoefficientsaspossiblemodeltestsarenecessary.Especiallywhenthebladesaremounted inacascade,which is thecase foraKaplan turbine,model tests are important to calculate lift and drag coefficients. It is on theotherhandpossibletousexfoilandcorrecttheresultsfromtheprogramwithtestdoneonothercascadesectionstogetreasonablecoefficients.Athickairfoilhaveagoodpeakperformancewhileamoreslenderair foilhaveawiderspectrewithhighperformance,butpeakperformance fora slenderair foil isnotasgoodcomparedwitha thickerair foil.Sincea thickair foilhaveahighpeak performance they are also have a larger risk for cavitation and theefficiencyfallsdrasticallyoutsidebestangleofattack.

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[ ]2DvD C l dr N (2.2)

When lift and drag is found,we can find the force acting in the rotationaldirection.

cos( ) sin( ) [ ]2u

F F F N (2.3)

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Figure25Vectorcomponentsofforcesactingonarunnerblade

F is found by using equation(2.4). It is important to evaluate the force F incorrelationwiththethicknessandstrengthoftherunnerblade.IfFislargeandthebladeprofileisthin,thebladecanbreakordeform.

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[ ]cos 2 cos

LC vLF l dr N (2.4)

AfterFuis found the energy output from the turbine can be determined. Bytaking the sumofall forcesactingoneach small sectiononeachblade,andmultiplythesumwiththerotationalspeedoftheturbine,theenergyoutputisdetermined.

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sin( ) W2 cosL

uC vP F u u dr

(2.5)

Theenergytheturbineproducescannotbehigherthantheavailableenergyinthewaterpassingtheturbine.Asimplewaytocalculatetheavailableenergyinthewater isbyusingequation(2.6).Hererepresent losses inthewaterway,valvesandotherfactorsthatreducetheeffectivehead.

1

' 2 [ ]zcP g Q H g r dr H Wz

(2.6)

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Figure26AxialcutofaKaplanturbinewithguidevanes

Z1 is the number of runner blades on the turbine, while t is the distancebetweeneachblade(1).

1

2 [ ]rt mz (2.7)

22 cos [ ]

sin( )n z

Lg H clC

t v u

(2.8)

2.3 MaindimensionsWhendesigningaKaplan turbinemanyparametersarechosenandbasedonexperienced data. The speed number is an important parameter. The speednumberforKaplanturbinesspansfrom1.5to3andcanbeusedtodetermineifaKaplanorFrancisturbineshouldbeused.Ifthespeednumber is lowerthan1.5aFrancisturbinemightbethebestchoice,buttherearegreyareaswhereotherparametershave tobe considered tobe able to choosewhich turbinethat isoptimalforthesite.Thespeednumber isafunctionofangularvelocityandthevolumeflow.

0 nQ (2.9)

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Theaxialflow isdependentonhowfasttheturbine isrotating,socm isfoundfrom if experienced values ifminor simplifications and linear relations areaccepted.InFigure27thelineardependenceandequationisshown.

Figure27Speednumberplottedvs.axialspeed

Fromthespeednumberthelargestrunnerdiameterisfoundthrough

0 2

2 2 0

4 [ ]0.12 0.18

D m (2.10)

SmallKaplanturbinescanbemadewithacylindricalhousingtoreducethecostof manufacturing, but cylindrical housing lead to increased clearance lossbetweentherunnerbladesandthehousing.Whenasphericalhousingisusedthe narrowest part on the draft tube is produced with a diameter 35%narrowerthanD2.

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Figure28Relationbetweend/DandB0/Dplottedagainstns

The diameter of the hub d and the height of the intake B0 also need to becalculated.BothofthesetwoparameterscanbereaddirectlyofFigure28.B0anddaredependentonthespecificrevolutionnumberns.Number of runner blades and suction head is dependent on the pressuredistribution around the runner blade.Numberof blades and suctionhead ischosensothatthepressurearoundthebladeforawiderangeaspossiblenotfalls under the boiling pressure or under the critical cavitation number. Thepressure distribution around blades changes when blades are placed in acascade like inarunner.Suctionheadandnumberofbladescanbe foundbyusingFigure29Suctionheadandnumberofbladesand isa functionof thespecificrevolutionnumber(1).

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Figure29Suctionheadandnumberofblades

2.4 PotentialflowThe two previous chapters describe how themain dimensions of a runnershouldbewhenabladeprofileisalreadychosen.Standardfoilscouldbeusedwithknown liftanddragbuttheoptimal istodesignaprofilethat isdesignedfor the intended flow conditions. To be able to create such a profilefundamental equations like the continuity, NavierStokes and the Eulerequationhavetobesolvedwithageometryprofile.Thisisaniteratingprocesswhere theequationsareusedon thegeometry, thegeometry ischanged foreverytimetheequationsareapplieduntildesiredvelocityandpressurefieldsareobtainedforthegivengeometry.Thecontinuityequationinfluiddynamicsstatesthatinasteadystateprocess,therateatwhichmassentersasystemisequaltotherateatwhichmassleavesthesystem.Continuityequationingeneralform:

0D divVDt (2.11)

TheNavierStokesequationdescribesthemotionofafluidsubstance. Itgivesthevelocityofafluidparticleatagivenpoint inaflowatagiventime.When

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NavierStokesisappliedtoaseriesofpointsinaflowoneobtainaflowvelocityfield.Afterthevelocityfieldisfoundthedragforcemaybefound.NavierStokesequation:

jiij

j j i

DV g p divVDt x x x

(2.12)

Iftheflowisincompressibleandviscosityanddensityisconstantweget:

2DV g p VDt

(2.13)

Whenfutherassumingthattheviscoustermsarenegligibleequation(2.13) isreducedtotheEulerequationforinviscidflow.Eulerequationforinviscidflow:

DV g pDt

(2.14)

The Euler equation for steady, incompressible and frictionless flow along astreamlinebetweentwopoints1and2becomestheBernoulliequation.

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3 TestingofKaplanturbineThestandardIEC60193containrulesandguidelinesforhowtoperformmodelacceptancetestsinlaboratories.TheKaplanturbinethatwillbetestedisnotamodel turbinebuta full scaleprototype.This implies that the testingwillbeperformedasonamodelturbineaccordingtotheIEC60193standard,butthescalingtoprototypeisnotnecessary.

3.1 EfficiencytestTotalefficiency(3.3)isdefinedastheamountofmechanicalpowerdeliveredbythe turbine shaft relative to the total available hydraulic power. The totalefficiency can be divided in hydraulic efficiency(3.1) and mechanicalefficiency(3.2), where hydraulic efficiency is defined as mechanical powertransmitted from the runner through bearings and couplings to the shaftrelativetotheavailablehydraulicpower. Themechanicalefficiency isdefinedaspowerdeliveredbytheshaftrelativetothemechanicalpower.Hydraulicefficiency:

mhh

PP

(3.1)

Mechanicalefficiency:

mm

PP

(3.2)

Efficiency:

h mh

PP

(3.3)

To calculate the efficiency of the turbine torque (Tm), rotational speed (n),volumeflow(Q)andpressurehastobemeasured.Alsothegravityconstant(g)and the density () of thewater have to be calculated in order to find theefficiency.Themechanicalpoweriscalculatedwithequation(3.4). 2 [ ]m mP n T W (3.4)

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Thehydraulicpower is calculatedwithequation(3.5)where index1 indicatesthat thedensityandvolume flow ismeasuredat thehighpressureand inletsideoftheturbine.Eisthespecificenergycalculatedwithequation(3.6).

1( ) [ ]hP E Q W (3.5)

2 2

1 2 1 21 2( ) [ ]2

abs absp p v vE z z g J (3.6)

Index2referstotheoutletandlowpressuresideoftheturbine(2),(3).

3.2 CavitationtestCavitation is formation ofwater vapour bubbles inwaterwith low pressurewhichimplodesandcondensateswhenthebobblesenteraregionwithhigherpressure.Thecreationofwatervapourbobbleshappenswhenthepressureinthewaterdropsbelow thevapourpressure.When thepressure in thewaterrises above the vapour pressure again the vapour bubbles condensates infractionsofasecond.Whenthishappensasmall jetofwater iscreated fromthebubbles.Ifthebubblescondensatesandcollapsenearasurfaceandthejetfromthewaterhitsthesurface,smallfractionsofthesurfacemaybedestroyedleavingsmallcraters.Thistypeofcavitationiscallederosioncavitation.Thomanumber:

NPSEE

(3.7)

In hydro power cavitation can be a big problem and lower the efficiency byseveralpercent.Lowpressurezonesarecreatedintheoutletofturbineswithdrafttubesandthatusepressuredifferencestoproduceenergy.The Net Positive Suction specific Energy is defined according to the IECstandard(3)asfollows:

2

2 22 [ ]2

vref

pp C JNPSE gZ gZkg

(3.8)

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WhereC2 isdefinedas themeanvelocityatpoint2 foundbyQ/A2.Pv is thevapourpressureatZref.

Figure31Definitionofheights

Bystudyingequation(3.8)and(3.6)itbecomesclearthattheThomanumberissimplyrelatedtotheheightdifferencehsalsoreferredtoasthedivingoftheturbine.Whentestingforcavitationthe IECstandardsuggeststhatthespecificenergycoefficient, see equation(3.9), is kept constant while the Thoma number isslowlyreducedwhiletheefficiencyislogged.

Figure32EfficiencycurvewithchangingThomanumber

When lowering the Thoma number the efficiencywill keep constant until itreaches 0 is reached. Here the efficiency will increase because of the

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lubricationeffectthecavitationbubbleshaveontherunnerbladesbeforetheefficiencyfallsdrastically.

2 22

cNPSER

(3.9)

3.3 RunawayspeedRunawayspeedisdefinedaswhenh=0andPED=PnD=0(3).Therunawayspeedis the highest achievable rotational speed the turbine can reach.When theefficiency is equal to zero all the available energy in the water is used toovercome centrifugal and friction forces in bearings and other components.Duetothefrictiontorqueinbearingstherealrunawayspeedcannotbetested.Tofindthemaximumrunawayspeedthetestsshouldbedoneundertheworstsetting combinations for the turbine. If the tests are not tested under plantconditionscavitationhavetobeevaluated.Runaway speed is found by increasing the RPM until hydraulic efficiencybecomeszero.Because of heat generation in the upper bearing runaway test could not becarriedoutinthisthesis.Discussionoftheheatgenerationintheupperbearingisfoundinchapter7.3.

3.4 CalibrationCalibration of measuring equipment is done to minimize error inmeasurements.Calibrationofmeasuringequipment isdoneaccording to theIEC(3).Whencalibratingequipmentthemeasuringrangeoftheequipmenthastobeknownandtheoperatingrangeoftheturbinehastobeknown.The equipment is calibrated bymeasuring a number of values outside andinside the range the actual testing will be carried out in against a knownquantity. The values measured are given as a Volt signal that has to becorrelatedwith theactualunitmeasured.Bymeasuringvalues for theentirerange linear regression isused to findacalibration line that theVoltsignal iscalibrated against tominimize the error.By increasing thenumberof valuesmeasuredduringcalibration intheupperand lowerrangetheuncertainties intheequipmentisreduced.

19

Theequipmentcalibrated in thiscase ispressuregauges,a flowmeterandatorquegauge.

3.5 PressuregaugeThepressuregaugewascalibratedwithanelectronicpressurecalibrator,DruckDPI601. This electronic calibrator uses air as fluid between the device thatshouldbecalibratedand itself.Byusingairtheheightdifferencebetweenthecalibratorandthedevicetobecalibratedcanbe ignoredand isnot importantbecause the surrounding pressure can be seen as constant as atmosphericpressure, so therewillbenowuncertainty in themeasuredvaluebecauseofheight difference. The DRUCK DPI2345 comes with a pre calibrated. ThecalibrationcertificateisfoundinAppendixI.Theelectronic calibratorhasa smallpump to increase the requiredpressureandavalvethatreducespressure.Thepressurecaneasybeadjustedwithfourdigitsinbar.

3.6 TorquegaugeThe torque gauge was calibrated with the dead weight method. The deadweightcalibration iscarriedoutbyaddingweightswithaknownweight.Theweights used are calibrated by the Norwegian Justervesen. The calibrationcertificateof theweights is found inAppendix J.An arm ismountedon theshaft and aweight bed is attached to the arm. They calibratedweights areplacedoneata time in thebedand thevolt signal from the torquegauge isrecorded foreverynewweightadded. It is important to calibrate the torquegaugeforitsintendedmeasuringrangeandwithalargenumberofcalibrationpointstogetaslowuncertaintyinthecalibrationaspossible.

20

Figure33Thedeadweightcalibrationsetup

Whencalibratingthetorquegaugethemeasurementstendedtodeviatefromeachotherevenwhenthesamedeadweightswereused.Thiswasdiscoveredwhen themeasuredvaluekeptalmostconstantwhenweightswereaddedorremoved from theweightbed. Itwasquicklydiscovered that thiswascausedbyfrictionbetweentherunnerbladesandthehousingandfixedbyrunningtheturbine until there was clearance between the blades and the housing. Tosecure that therewere no friction affecting themeasurements, valuesweremeasuredfirstbyaddingweightsintheentirecalibrationrangeandthenvaluesweremeasuredwhenremovingweights.When theweightswere added to theweight bed themeasured volt valuealwayswas lower than the same volt valuemeasured for the sameweightwhenweightswereremovedfromtheweightbed.InFigure34thecalibrationcurveandtheactualvaluesmeasuredcanbeseen.Thisphenomenon iscalledhysteresisand ispresent in ferromagneticmaterials.Ferromagneticmaterialshavememoryduetomagneticproperties inthematerial(4).Hysteresis isacommonphenomenonintorquemeasurements.

21

Figure34CalibrationcurveforthetorquegaugeThe calibration was preformed two times both times resulting in the samevaluesandhysteresis inthemeasurementswasproven.ThecalibrationreportofthetorquegaugeisfoundinAppendixQ

3.7 TripmeterThereisnowknowmethodtocalibratethetripmeter,itisonlydependingontimeandisrecordingapulseeverytimeareflexribbonpassesthesensor.Thetimebetweeneverypulseismeasuredandtherotationalspeediscalculated.

Figure35Tripmeterandreflexribbonreadytouse

Thetripmeter ismountedontheturbineshaftasdisplayed inFigure35Tripmeterandreflexribbonreadytouse.

22

3.8 FlowmeterAKrohneAQUAFLUXF6wasusedtomeasurethevolumeflowintheKaplanrig.Itisanelectromagneticflowmeter.The flow meter was calibrated using the weighing method. The weighingmethod is a primarymethod with a high level of accuracy. The calibrationprocedureisgivenintheISOstandard(5).Thestandardistoleadwaterintoaweighing tankwith known initialweight, the time is taken over the intervalwhenwater is lead into the tank, the volume flow is foundwith theweightdifferencedividedonthetimeintervalwaterisleadintothetank.

2 1 1v m mq t (3.10)

1 1ap

(3.11)

Thelastterminequation(3.10)isthecorrectionfactorforcorrectiondifferentin buoyancy exerted from the atmosphere on themeasuredwater and theweightsusedduringcalibrationoftheweighingtank.a,pandisrespectivelythedensityoftheatmosphere,standardweightsandwater.

Figure36Theflowmeteruseinthetest

ALabViewprogramcreatedbyRemiAndreStoplewasusedtologthevolumeflow.Theprogram logged1000valuesfromtheflowmetereverysecond.Theregression linewas foundusingbuilt in functions inexcelwhileuncertainties

23

linked to the measurements were calculated in Matlab. The flow meter isplacedinalongstraightsectionofthepipeline.

3.9 FrequencyanalysisThe frequency of any fluctuating signal can be analysed and assessed by adiscreteFourierTransform.AndersTrklephasinhisprojectthesisdevelopedaprogram toanalysemeasureddata.RemiA.Stoplehasused thisprogram toevaluate the measured data in this project. The results of this analysis ispresentedinchapter9.6.

3.10 LabViewprogramLabViewwasused to logdataduring testsand calibration.How the LabViewprogramsusedworkaredescribedinAppendixG

3.11 ClearancewatertestAturbinemayhaveleakagesinsealsandothercomponents.Waternotutilisedby the turbine is regarded as loss inefficiency and is therefore important todocument.The clearance water measurements was done by filling a bucket with theclearancewaterfor60secondsandthentheweightdifferencebetweenbeforeand after the fillingwas found giving the volume flow.Measurementsweredoneforconstantpressureheadandrotationsperminute.

3.12 RiskAssessmentInorder toperform testsatNTNUa riskassessmentof the test righas tobecarried out. The risk assessment reveals potential risk to human and otherinstalments in the laboratory related to the test rig. The risk assessment isfoundinAppendixK

24

25

4 UncertaintiesinmeasuringAllmeasurementshaveuncertaintiesattached to them.Uncertainties canberelated to three types of error inmeasurements, error caused by spurious,randomorsystematicerror.

4.1 SpuriouserrorError that causes unreliability can be human errors or default errors ininstruments.These typesoferrorcanmake themeasurementsworthless.Anexample of a spurious error is air trapped in a lead from awater line to amanometer. If the error is of significant value, themeasurement has to berepeatedordiscarded.

4.2 RandomerrorSmall numerous independent happenings can influence a series ofmeasurements, this is called random errors. They cause the values in themeasurementscarriedouttodeviatefromeachotherandvaryaroundameanvaluewhenthe input isconstant.Thevaluesnormallydeviatefromthemeanvaluewithintherulesofprobabilityfornormaldistribution,whenthenumberofmeasurements carriedout increases. The areaofuncertaintiesof randomerrors is based on staticallymethods and can be calculated using the samemethodsasforsystematicerrors.

4.3 SystematicerrorYou cannot reduce systematic errors by increasing the number ofmeasurements,unless you change theequipment and the conditions for themeasurements,becausesystematicerrorshavethesamemagnitudeforeverymeasurement at the sameoperationpoint. Systematicerrors areerrors thatstill are present in the equipment and the measuring system after thecalibration is done. Systematic errors should be eliminated before themeasuring starts. This should be done by calibrating the equipment againstanother system,measuringdimensionsandby installingequipmentcorrectly.But even if all this is done extremely precise there will always be errorsremaininginthesystem,theseerrorsarecalledsystematicerrors.

26

Thetotalsystematicerrorcanbefoundbycombiningthesystematicerrorfromeachmeasuringdevicewiththerootsumsquaremethod.Whencalculatingtheuncertaintyconnectedtothemeasurementaconfidenceintervalof95%shouldbeusedaccordingtothestandard.Therootsumsquaremethod isexpressedinequation(4.1).

s Yf f (4.1)Here fs is the combined uncertainty of eachdevice in the systemwhere theuncertaintyineachcomponentisfY.Theuncertaintycaneitherbeknownfromthe manufacturer of each device or it can be calculated. To calculate theuncertaintynnumberofmeasurements istakenataconstantoperationpointandthestandarddeviationisfoundwithequation(4.2)(6)and(7).

2

1

1

n

r rr

Y

Y Ys

n

(4.2)

rY =meanvalueofmeasurementsrY =valueofrthmeasurementn =numberofmeasurementsAfter the standard deviation is calculated the uncertainty in the standarddeviation can be calculated. Since the error have a normal distribution buttherearenotaninfinitenumberofmeasurementsstudenttdistributioncanbeassumed.StudenttvaluescanbefoundintableL2inIEC60193(3).

YY t se n (4.3)

The uncertainty in standard deviation is reduced as the number ofmeasurementsincreases.Finallytheuncertaintywithaconfidencelevelof95%can be calculated. ey is the absolute uncertainty while fy is the relativeuncertainty.

YY ef Y (4.4)

27

4.4 TotaluncertaintyfT is foundbycombining randomandsystematicerror. If theyhave thesameprobabilitydistribution the totaluncertainty is found in the samewayaswecalculate the total systematic error. The total uncertainty then has adistributionwithprobabilitythatthetruevalueofameasurementlieswithinaprobabilityareaof95%.

2 2t r sf f f (4.5)

4.5 UncertaintiesintheCalibrationDuring calibration there are different sources that can lead to uncertainties.TheIEC60193standardhasdefinedthedifferenterrorsinchapter3.9andtheyarerepeatedinTable1inthisthesis.Thetotaluncertaintyisfoundasexplainedin chapter 4.4with combining the different uncertainties and the rootsumsquaremethod(RSSmethod).

Error Description

fa Systematicerroroftheprimarycalibrationmethodfb Randomerroroftheprimarycalibrationmethodfc Systematicerrorofthesecondaryequipmentfd Randomerrorofthesecondaryequipmentfe Physicalphenomenaandexternalinfluencesff Errorinphysicalproperties

Table1Componenterrors

4.5.1 UncertaintiesinthecalibrationoftheflowmeterThe errors that contribute to the uncertainties in the calibrationof the flowmeter are listed in Table 2. The calculation of the uncertainties is found inAppendixA.1

28

Uncertainty Description Value,Q af Systematicerrorintheweighingtanksystem

0.072104% ,Q bf Random error in theweighingtanksystem

0.0565366% ,Q regressionf Systematic andrandom error in the

instrument0.03404%

Table2UncertaintiesinthecalibrationoftheflowmeterBy using the RSSmethod the relative uncertainty for the calibration iscalculatedasfollowsforthehighestefficiencypoint:

2 2 2, , , , 0.097745%Q cal Q a Q b Q regressionf f f f (4.6)The calibration curvewith a confidence interval of 95% for the volume flowmeterisshowninFigure41.TheMatlabprogramsusedarefoundinAppendixC.

29

Figure41Calibrationcurvewitha95%confidenceinterval

4.5.2 UncertaintiesinthecalibrationofthepressuregaugeThe pressure gaugewas calibrated against the electronic pressure calibratorwithknownsystematicuncertaintyaof0.000%giveninthecalibrationreport.Butthecalibrationofthecalibratorwasperformedin1996andanuncertaintyof0.01% is thereforeused in this report.Thisuncertainty is included in theregression uncertainty found in the calibration report. The calibrationcertificatefortheDruckDPI601isfoundinAppendixI.p,c which is the random error in the instrument caused by scatter in themeasuredsignal.Whencalibratingtheinstrumentthesignalisloggedovertimeand the mean value of the signal for a constant pressure is used. Theuncertaintyduetoscatterinthesignalisincludedinthep,regression.Alsothep,cisincludedinthep,regression.

30

The calibration curve for the pressure gauge is shown in Figure 42. ThecalibrationreportcanbefoundinAppendixL.

Figure42Calibrationcurveforthepressuregaugewitha95%confidenceinterval

ewhichistheerrorcausedbyphysicalphenomenaandexternalinfluencescanfor thepressuregaugebe temperature changeswithin the instrument. Sincethepressuregaugehadbeenlocatedinthewaterpowerlaboratorymanydaysbefore the calibrationwas conducted the temperaturewithin the instrumentwasassumed tobe inequilibriumwith the surrounding temperatures. ewasthereforeassumedneglectable.p,f,theerror inphysicalproperties isforthecalibrationofthepressuregaugeassumed tobeneglected. This isbecause thepressure gaugewas calibratedagainst air and the height difference between the pressure gauge and theelectronicallyinstrumentdonotcontributetopressuredifferences.Uncertainty Description Valuep,a Systematic error in the

electronic pressurecalibrator

0.010%

p,regression Systematicandrandomerrorintheinstrument

0.066751%p,f Systematic error in the

positioning of thepressuregauge.

0.000%

Table3Uncertaintiesinthecalibrationofthepressuregauge

31

WiththeuseoftheRSSmethodtherelativeuncertaintyofthecalibrationofthepressuregaugewasfoundtobe:

2, , 0.066751%p cal p regressionf f (4.7)

4.5.3 UncertaintiesinthecalibrationofthetorquegaugeErrorscontributing to themaximumrelativeuncertainty for thecalibrationofthetorquegaugeare,arm,,weights,candd.canddiscombinedwiththeRSSmethodtobe,regression.Allcalculationsofuncertaintiesinthecalibrationofthetorque gauge are found in Appendix A. The calibration report is found inAppendixM.Uncertainty Description Value,w Systematic error in

weightsandtheweightbed

0.0114325%

,arm Systematicerror in thelengthofthearm

0.2%,regeression Systematicandrandom

errorintheinstrument1.235138%

Table4Uncertaintiesinthecalibrationofthetorquegauge

BycombiningthegivenerrorswiththeRSSmethodtherelativeuncertaintyforthecalibrationinbestefficiencypointforthetorquegaugewasfoundtobe

2 2 2, , , , 1.25128%cal w arm regressionf f f f (4.8)InFigure43thecalibrationcurveforthetorquegaugeispresented.Asseeninthefigurethecalibrationisaffectedbehysteresis.Hysteresisisaphenomenonwhich isnormalfortorquegauges.Themeasuredvaluehasamemoryfromthepreviousmeasurement.Thismeans that if for instance the torquegaugemeasuresahighervalueforonegivenvalueifthepreviousmeasurementhadahighervaluethanifthepreviousmeasuredvaluewaslower.

32

Figure43Calibrationcurveforthetorquegaugewitha95%confidenceinterval

InFigure43youcanseethehysteresisbecausetherawdataseemstobegiveninpairs.Theactualcase is that the rawdatawith the lowestvoltvalue (herelow value is less negative than a high value) ismeasuredwith addingmoreweights,hencefromalowervalue,andtherawdatawiththehighestvoltvalueismeasuredfromahighervalue.

4.5.4 UncertaintyincalibrationofthethermometerThe thermometer is calibrated by themanufacturer. The uncertainty of thethermometer is0.0010Candwith testtemperaturesaround200Cthisresultsinanuncertaintyof0.005%

4.6 UncertaintiesinthetestsEvenifthecalibrationisdoneaccordingtothestandardserrorswilloccurinthetest measurements which will lead to uncertainty. After the tests wereperformed the total uncertainty was calculated. The total uncertainty is acombinationofuncertaintyinthecalibrationandinthetests.

4.6.1 Generaluncertaintyinthetestsp,h iserrorcausedbydrift in theoutputsignalover time from themeasuringequipment. To check for drift the first test serieswas retested after all theotherseriesweretested.AsseeninFigure44thelasttestserieshasaslightlyhigherefficiencythanthefirstseriesespeciallyforlowpressurehead.IfFigure45isstudiedincorrelationwithFigure44itisbecomesclearthattheincreasein efficiency in the last series is caused by an increase in volume flow. Theincreaseinvolumeflowismostcertaincausedbyinaccuracyinthepositioning

33

of the runner blades when setting the position after it had been tested insettingtwocausingthebladestohaveasteeperangleofattackinthelastruncomparedtothefirstrun.

Figure44Testfordriftinmeasurements300rpm,setting1

By analysing the two graphs it is concluded that the measurements areunaffectedbydriftsothattheuncertaintyrelatedtodriftisneglected.

30

35

40

45

50

55

60

65

70

0 1 2 3 4 5 6 7

Efficiency

Pressurehead

Comparisonoffirstandlastrun,300rpmFirstrunLastrun

34

Figure45Testfordriftinmeasurements300rpm,setting1

Error Descriptioncal Systematicerrorinthecalibrationh Additionalsystematicerrorintheinstrumentj Errorinphysicalpropertiesks Systematic error due to physical phenomena and

externalinfluenceskr Randomerrorduetophysicalphenomenaandexternal

influencesl Randomerrorinrepeatabilityofsecondaryequipment

Table5Errorsinthetestsh ispresentedaboveTable5andcanbepresent inallthemeasuringdevises.But for the tests conducted in this report drift is not present and theuncertaintyisthereforeneglectedinthefollowingcalculations.

4.6.2 UncertaintyinthepressuremeasurementsThe uncertainties is the pressure measurements must be divided into twodifferentuncertaintiesp,1andp,2whicharetheuncertaintieslikedtotheinletandtheoutletpressures.DetailedcalculationsarefoundinAppendixA.cal is the uncertainty from the calibration of the pressure gauge. Theuncertainty is not a constant value but varieswith the operation state. The

0

50

100

150

200

250

0 1 2 3 4 5 6 7

Volumef

low

Pressurehead

Volumeflow,300rpm

FirstrunLastrun

35

pressure transducerwas calibratedagainstairbutduring tests theoperatingfluidiswater.Thiscreatesanuncertaintyinthemeasuredinletpressurevalue.The systematic error due to an offset of 4.65cm in the pressure transducerplacement relative to the centre of the pipe is denoted as fp1,offset. Thesystematicuncertainty is calculated tobewithanoffsetof4.65cmwhile theerror in the rulerusedwas0.2cmwhichgivean fp1,offsetof0.7853% for thepressure measured at the given operation conditions of 500rpm and0.25468meterpressurehead.p1,l is calculatedwith a studentt confidence interval on themeasured datafrom the tests.AMatlab programwas created to do the calculations and isfoundinAppendixC.Therandomuncertaintyfortestseries500rpminsetting2wascalculatedtobe10.6552%.Thisvalue isextremelyhighand iscausedbysevere fluctuations in thepressure readings.Thiswillbediscussed inchapter9.6.The total relative uncertainty in the pressuremeasurementswas calculatedwiththeRRSmethodtobe

2 2 2

1 , 1, 1,

2 2 22 , , 2

10.6843%

2 3.0633%

p p cal p l p z

p p H p flotation v

f f f f

f f f f

(4.9)

It isclearthattherelativeuncertainty intheoutletpressuremeasurements ismuchhigherthantherelativeuncertaintyintheinletpressuremeasurements.Thisisbecauseoftheequipmentusedtocalculatethepressure.Whiletheinletpressure is calculatedwith costlyequipment theoutletpressure ismeasuredwithcheaphomemadeequipmentwithahighlevelofuncertainty.

4.6.3 UncertaintyinthetorquemeasurementsAsforthepressuremeasurementsksandkrareignored,,jisalsoignored.Theerrorsthatinfluencethetorquemeasurementsarelistedintable6.

36

Uncertainty Description Value,cal Systematic error in the

calibration 1.25128%

,l Random error in themeasurements 0.0312%

Table6Uncertaintiesinthetorquemeasurements

BycombiningthetwouncertaintieswiththeRRSmethodatotaluncertaintyinthetorquemeasurementsisfound:

2 2, , 1.2516%cal lf f f (4.10)It isclear that theuncertainty linked to thecalibrationof the torquegauge isdominantinthetestuncertainty.

4.6.4 UncertaintyinthevolumeflowmeasurementsThe errors causing uncertainties in the volume flowmeasurements are thesame as for the errors in the torquemeasurements and they are calculatedwith the same equations and the sameMatlab program as in the pressuremeasurements.Uncertainty Description ValueQ,cal Systematic error in the

calibration 0.097745%

Q,l Random error in themeasurements 0.0394%

Table7Uncertaintiesinthevolumeflowmeasurements

WhencombinedtheQ,landQ,calgiveatotaluncertaintyinthevolumeflowof:

2 2, , 0.105387%Q Q cal Q lf f f (4.11)

4.6.5 UncertaintyintherotationalspeedmeasurementsThere isnowmethodavailable tocalibrateanoptical speedcounter.The IECstandard (3)givesa systematicuncertaintyof0.05%used in this thesis.The

37

randomuncertaintyintherpmmeasurementswascalculatedtobe0.0363%.Thisgivesatotaluncertaintyintherotationalmeasurementsof

2 2 , 0.061787%rot IEC rot lf f f (4.12)

4.6.6 UncertaintyinthecalculationofdensityofwaterThedensityofwater iscalculatedasa functionofpressureand temperatureand the uncertainty in the calculation of the density is 0.01% (8). Thisuncertainty is ignored because it is too small to have influence on the totalhydraulicuncertainty.

4.6.7 TotaluncertaintyinthehydraulicefficiencyThe total uncertainty of hydraulic efficiency can be calculatedwith the RSSmethodcombiningallthedifferentuncertaintiesandisgiveninequation(4.13).Theequationisderivedfromequation(3.1).

2 2 2( )hh Q E Ph

ef f f f (4.13)

Tofindthedifferentuncertainties inequation(4.13)theequationsfollowing isusedandexplained. Q is found in chapter4.6.4.Uncertainties in thedensityandthegravitationconstantareassumedtohaveasosmallvaluethattheycanbeneglected.Uncertaintyingis0.01milliGalstatedinthecalibrationreportofmeasuredgravityinthelaboratory.

2 21 21 2

2 222 21 2

2 21 2 1 2

1 2

2 2

( )2

v vp pz z

EE

e ee eg e g e

efp p v vE g z z

(4.14)Theuncertainty inenergy inequation(4.14) isgivenasabsoluteuncertaintieswhileinthisthesisrelativeuncertaintiesareused.Inequation(4.15),(4.16)and(4.17)therelationbetweenabsoluteandrelativeuncertaintyisgiven.

38

p pe p f (4.15)

2 22v

v

ev f (4.16)

2

2 2 rv Qef fr

(4.17)

Nexttheuncertaintyinpressureisfoundbyusingequation(4.18).Whenthisisdonethetotaluncertaintycanbecalculatedusingequation(4.13).

2 2( ) ( )Pf f f (4.18)

rotf f (4.19)Thetotalrelativeuncertaintyinthehydraulicefficiencyiscalculatedwithdatafrom setting 2 at 500rpm. The reason for choosing values from 500rpm andsetting2isbecausethisisthesettingclosesttothebestdesignsettingwhichisaccordingtoAndersAustgrdsetting3and490rpm.ForadetailedcalculationofthetotalrelativeuncertaintyseeAppendixA.Thetotalrelativeuncertaintyinthehydraulicefficiencyiscalculatedtobe

h=2.2145%

39

5 TestrigsetupThewaterpowerlaboratoryprovidestwodifferentalternativeloopstotesttheKaplanturbine. Alternativeone isanopen loopwherewater ispumpedfromthelowerreservoiranduptotheupperreservoir,whichisafreewaterchannelwhere the water is in open air at atmospheric pressure. From the upperreservoir the water runs through the turbine and down into the lowerreservoir.Alternativetwo isalsoanopen loopbutdifferfromalternativeonebecausewater ispumpedfromthe lowerreservoir intoapressuretank.Fromthepressure tankthewater isrunthrough the turbineandbackdowntothelowerreservoir.Alternativeonehasamaximumgrossheadof16meterswhilealternativetwocan deliver a gross head up to 100meters. The head in alternative one isregulated through an energy dissipater while alternative two regulates theheadbychangingtherotationalspeedofthepumpandbyopenandclosingtheairintakeonthepressuretank.RemoteHydrolight representedbyAndersAustgrdhave requested that theturbine istestedwithavolume flowranging from90 litrespersecondto590litrespersecondandapressureheadrangingfrom1to10meters.Inordertomeet the requirement alternative two has to be chosen. This is becausealternative one has a too low gross head to be able to deliver the desiredvolume flow and effective head.Alternative one have 16meters gross headwhiletheeffectiveheadwouldbesignificantlylowerbecauseoflossesinbendsandareachange in thepipeline. Alternative twoalsohave theadvantageofeasiervolumeflowregulationcomparedtoalternativeone.

5.1 DetaileddescriptionoftherigA pipewith diameter of 600mm leads out of the pressure tank, the pipe isquickly reduced down to a pipe diameter of 200mm. The flow meter isconnectedtothe200mmpipe.Aftertheflowmeterthepipecontinuouswithadiameterof200mmbeforethediameter isexpandedto400mm.The400mmpipeisconnectedwiththeturbinewhichalsohasadiameterof400mm.Attheend of the 400mm pipe four taps is mounted which is connected to thepressure gauge. They aremounted tomeasure the pressure in front of theturbineinordertobeabletocalculatetheefficiencyoftheturbine.

40

Therigiscontrolledandrunwithonelaptopwhichcontrolsthepumpandapcthatlogdataandaboxthatcontrolstherotationalspeedofthegenerator.Thiscontrol station is located next to the turbine. The pumps are originallycontrolled from the control room located on the second floor in thewaterpowerlaboratory.TheKaplanturbineandthecontrolstationarelocatedonthefirstfloor.Remotedesktopenablescontrolofthepumpsviathe laptop inthecontrolstation.During calibration of the volume flowmeter the 200mm pipe is connecteddirectlytothe600mmpipethatleadstotheweighttank.Thisimpliesthatthewatercircuitdonotrunthoughtheturbine.

Figure51Testrigsetup

Theunderwater level isdeterminedwith theuseofa floatingcylinderwhichfollows the underwater level. The floater is placed some distance from theoutlettonotbedisturbedbyairinthewatercomingoutofthedrafttube.Thetripmeter ismountedonthetopoftheturbinewhilethereflexribbon isplacedontheshaft.Thetorquegauge isplaced inthemiddleoftheturbineandthegeneratorontheshaft.

41

6 TheAfghaniKaplanturbineThe Kaplan turbine studied in this master thesis is designed by AndersAustegrd.The turbine ismeant toprovide smallvillages inAfghanistanwithelectricity.Itisdesignedwiththethoughtthatitshouldbeeasytomanufacturewithsimplemeansandtools.Thisimpliesthatsomechoicesmadeinthedesignnotareoptimalfortheefficiencyandthe loadrangeoftheturbine.Thereareforexamplenospiralcasingoradjustableguidevanesinthedesign.

6.1 TheTurbinedesignIn frontof the runnerblades curvedplatesarewelded ina fixedposition tocreate spin in thewater flow acting as guide vanes. Thismakes this KaplanturbineasingleregulatedKaplanturbine.

Figure61Completeturbine,(Inventordrawing)

The inlet pipe has a 90 degree bend in front of the guide vanes, this isunfortunate and can cause turbulent and a chaotic flow right in frontof the

Guidevanes

Lower bearing withairandgreaseintake.

Flowcontrollers

Runner

42

turbine. Inordertoreducethisthreebentplatesareplaced in the90degreebendactingasflowcontrollersinacascade.Therunnerconsistsoffourbladesmountedonacube.Fourbladesarechosensimplybecauseaframewith90degreesanglesiseasiertomakethanaframewith fiveorsixsides. If the runner isplacedoffcentre the runnerbladeswillinterferewiththeoutercasinginsectionsoftherevolution,thismaybreaktheturbineorcausesevereefficiencylosses.Itisalsoimportantthattherunnerisplaceddeadcentretoreduceleakagebetweentherunnerbladesandtheoutercasing.Therunnerisproducedwithadiameterafractionwiderthantheinnerdiameter of the outer casing. At first start up the blades should quickly begroundeddowntofittheoutercasingperfectlywhichminimizestheleakage.Underneath the runner the lower bearing is placed. The bearing housing isshapedasa cylinderanda cone.The lowerbearing isheld inplaceby threesupport fins. The pressure after the runner can be lower than the ambientpressure;thismeansthatwatercanbesuckedintothelowerbearing.Toavoidthisair is sucked in througha small tube inoneof the fins fromoutside thedraft tube.Grease is injected into thebearing through the same fin as air issuckedthrough.Ifwaterentersthe lowerbearing itcan leadtocorrosionandthebearingbreakdownbecauseofsandparticlesinthewater.

6.2 SpecificationsAccording toAndersAustegrd the turbine isdesigned for an effectiveheadrangingfrom1.5metersto6metersandavolumeflowfrom0.09to0.41m3/s.Hehasalsogivenanestimatedflowtableandestimatedthecavitationnumbertobe0.7.Head[m] Minimum volume

flow[m3/s]Optimal volumeflow[m3/s]

Maximumvolumeflow[m3/s]

1.5 0.09 0.18 0.212 0.11 0.21 0.243 0.13 0.26 0.294 0.15 0.30 0.346 0.18 0.36 0.418 0.21 0.42 0.4710 0.23 0.47 0.53

Table8Volumeflow

43

Theminimumvolume flow isestimatedvolume flowwhen the runnerbladesare fixed in setting 1,maximum volume flow is in setting 4 while optimalvolumeflowisobtainedinsetting3.

6.3 MaindimensionsThemaindesign characteristicsof the turbine arepresented in Table9. Thevaluespresentedintable9aredesignvalues,notmeasuredvalues.

TurbinecharacteristicsBEPeffectivepressurehead 2mBEPvolumeflow 0.21m3/sBEPrpm 490rpmRunnerdiameter 0.345mBEPsetting 3

Table9Mainturbinecharacteristics

6.4 RunnerbladedesignAnders Austegrd has designed the runner blades used in the turbine. InAppendix N the some of the calculation procedures are presented. TheformulaspresentedareusedinanExcelsheetandresultsfromthecalculationsintheworksheetareexportedintoScilab.ScilabisafreewareprogramsimilartoMatlab.InScilabtheflowaroundthebladeiscalculatedusingpotentialflowtheorypresentedinchapter2.4.Whenthedesiredflowfieldisreachedafteraniteratingprocess coordinatesof thebladeprofile areexported into Inventor.Mechanical drawings can now be made and the runner blades can beproduced.TheformulasusedinexcelarecheckedagainstformulasandequationsgiveninPumperandTurbiner(1)andfoundsatisfying.Designinga runnerblade isextremely time consuminganddemandsa lotofwork.TheScilabprogramAustegrdhavecreatedcouldhavebeenusedcreateanewprofileoraMatlabprogramcouldhavebeencreated.The timedemanded toget familiarwithAustegrdsworkor createaMatlabprogramhavebeenconsideredtobetohighcomparedwiththeactualgain inperformance of the runner. Austegrd has been confronted with this andagreedthattimerathershouldbeusedonoptimizingtheinletbend.

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7 ChangesandlimitationsontherigandturbineBefore and during tests a series of challenges were encounteredmaking itdifficulttocalibrateandruntheefficiencytestontheKaplanturbine.Manyofthe challenges encountered were of such character that they had to beimproved and fixed before the calibration and the test could continuewhileothers could be improved during operation. Some problems were timeconsuming and stopped operation of the rig for several days whileimprovementsweremade.

7.1 PipedimensionsThepressuretankhasthreepipesconnectedtoit.Allpipeshaveadiameterof600mm. The only available volume flow meter was a flow meter with adiameterof200mm.Thismeantthatthepipediameterhadtobereducedfrom600mmto200mm.Thiswasoriginallydonebyweldingapipewithadiameterof200mm toa flatplate; seeFigure71Originalpipe section.Theplatewasconnectedtothepipewithadiameterof600mm.Thesolutioncreatedalargearea reduction over a small distance which created a stagnation point andforcedaheavyaccelerationinthewaterovertheareareduction.

Figure71Originalpipesection

Whenthecalibrationstarteditquicklybecameobviousthatthelargediameterreduction created heavy cavitation. This was problematic because the flow

46

meter is sensitive to air bubbles and noise. Cavitation creates both of theseproblems.Tobeabletocontinuethecalibrationteststheareareductionhadtobedonesmoothertoavoidcavitation.Therewerenoavailablepipeconesavailablewiththerightdiametersinthewaterpowerlaboratory.Anewconethereforhadtobemadereducingthediameterfrom600mmdownto300mm.Aconereducingthediameterfrom300mmto200mmwasavailable.Platesteelwithathicknessof3mmwasusedtocreatethecone.Equation(7.1)withr1,r2,B1andB2wasusedtocalculatethedimensionsofthecone.Bisthearclengththathadtobecuttogivethegivenradius,r.

1 1 0

2 2 0

180

180

B r

B r

(7.1)

The finished conemounted in the rig setup is shown inFigure72.After theinstallation of the new cone the pressure head to be able to reach desiredvolumeflowwasdrasticallyreducedandcavitationwaseliminatedinthispipesection.

Figure72Configuredpipesection

Eventhoughthecavitationwaseliminated fromthe firstpipesectionwithanareachangecavitationstilloccurredduring tests inanotherpipesection.The

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inleton the turbinehasapipediameterof400mm.Since thepipediameterfrom the firstarea reduction is200mm itdemandsanewareachange tobeable to connect the two diameters together. This area expansion is doneimmediatelyaftera90degreebenda fewmeters infrontoftheturbine.Thecavitationbecamesosevereinsettingtwothattheinletpressurecouldnotbeincreased asdesired.The cavitationbubbles created in the expansion got sosevere that they entered the turbine,making the tests invalid. Some of themeasuring series preformed in setting two is therefor stopped before apressureheadof6metersisreached.

7.2 RunnerbladefrictionTherunnerbladesand the turbinehousingshouldbeproducedsuch that therunnerbladesouterdiameter isafractionsmallerthanthehousingdiameter.Thisisdonetoreduceleakagehencereducelossinhydraulicefficiency.Beforethe tests and the calibration the turbine therefor had to be run to tear theblades down so that there were no friction between the blades and thehousing.In setting one this caused little problem, after a couple of hours the bladeswere torndownandhadno frictionwith thehousing.Theproblemoccurredwhenbladesshouldbeadjustedtosettingtwo.Thehousingisnotproducedtofollow the curvature of the runner blades in setting 3 or higher causing thebladestojaminthehousingmakingitalmostimpossibletorotatetheturbine.To not destroy the torque gauge and the generator the calibration armwasmountedontheshaftandtheturbinewasmanuallytorndown.Thiswasdonebypushing thearmarounduntil therewasalmostno friction left.When thefrictionwasassumedtobe lowenoughsothatthemomentumonthetorquegaugewouldnotbesohighthatitwouldbedestroyed,waterwasletthroughtheturbinemakingtheturbinetearthebladesdownwhilerotating.

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Figure73Runnerbladewithbrokenbladesection,seenfrombelow

Asseen inFigure73therearandoftherunnerblade istouchingthehousingmarkedwithareadcircle.Bylookingcloselyitispossibletoseethatapieceofthebladeisbrokenoffinsidetheredcircle.Whiletherearendisjammedintothehousingthefrontparthasa largegapbetweenthebladeandthehousingmarkedwithagreen circle. In theareaof theyellow circleerosion from thebladeonthehousingcanbeseen.An attempt to adjust the blades to setting three was made but was notmanaged.Apieceofoneofthebladesbrokeoff in theattempt toadjusttheblades into setting three. Thismade it impossible topreform test in settingthreeandfour.

7.3 UpperbearingWhilerunningthetestsitwasdiscoveredbyanincidentthattheupperbearingbecamewarm. The bearing is a spherical roller bearing that takes all forcesacting in the axial direction in the shaft. The bearing also takes small forces

49

acting in the radialdirection.C0of thebearing is supposed tohavevalueof200kNaccordingtoAndersAustegrd.C0isaconstantthatgivethelifetimeabearing depending on force, revolutions per second and the viscosity of thegreaseused in thebearing.AhighC0 indicates thatabearing canwithstandhighforcesandhighnumbersofrevelationsperminutefora longerperiodoftimethanabearingwithalowerC0.HarryOpdalattheSKFgroupwascontactedandgaveanintroductioninhowtocalculatelifetimeonbearingsusingacalculationtoolontheSKFhomepageoninternet.Withanaxialforceof10kN,1000rpmandaviscosityof25mm2/sthelife timeofabearingwith thesamespecificationsas thebearingused in theturbine is calculated to be 497300 hours or 56 years. Thismeans that thebearing should be able towithstand the forces acting in the axial directionwithout any problems. A screenshot of the calculation page is found inAppendixE.Anextremeaxial forceof20kNwasalso calculatedandgaveanexpected lifetimeof5.6years.This isaforcewayoutsidethedesignrangeoftheturbine.When the life timesareevaluated thequalityof thebearinghas tobe takenintoconsideration.ThecalculationsaremedwithanSKFbearingwhichisahighqualityproduct.ThebearingintheturbineismostlikelyproducedinChinaanddonothavethesamequalityandwearresistanceastheSKFbearing.Theshaftusedintheturbineisnotcompletelystraightandhaveamaximalcastof0.25mm.Radialmovements in theshaft results incyclicalhigh radial forceactingonthebearing.Sincethebearing isdesignedtowithstandforces intheaxialdirectionthismaycausetheincreaseintemperature.

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Figure74Temperatureplottedvs.rpmat2.5meterpressurehead.Setting2

Figure75Temperatureplottedvs.pressurehead.Setting1,800rpm

Figure76Temperatureplottedvs.pressurehead.Setting2,650rpm

Asseen in the three figuresabove the temperature increasewith revolutionsand pressure head. In the figureswhere temperature is plotted vs. pressurehead the revolutions per second is kept constant andwhen temperature isplottedvs. rpm thepressurehead iskept constant.Theoperating conditions

253035404550

300 400 500 600 700 800

Tempe

rature

rpm

3742475257

0 2 4 6 8

Tempe

rature

Pressurehead[m]

37

42

47

52

0 1 2 3 4 5

Tempe

rature

Pressurehead[m]

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werekeptconstant ineachmeasuringpointuntilthetemperaturewasalmostconstant.Thesemeasurementswere done to find if therewas an upper limit for thetemperature increase andwhere itmay be. It is clear that the temperaturewouldincreaseifthepressureornumberofrevolutionswereincreased.Sincethetemperaturealsoincreasewithpressureheadthebearingmostlikelyheatsupduetofrictioninthebearingitself.The situationwasdiscussedwithprofessorOleGunnarDalhaug,what shouldbe done regarding the temperature to be able to continue the tests. Todismount theentire turbine,change thebearingandstraighten theshaftwasconsideredbywasfoundtobewaytotimeconsuming.Theconclusionwastoconstantly measure the temperature on the bearing house and stopmeasurements if the temperatureapproached temperatures thatcouldcausethebearing tomalfunctionor jam.The criticalvalueof the temperaturewasassumedtobearound600CbasedonpreviousexperiencesoftechnicianTrygveOplandandengineerBrdBrandst.Thesetemperaturesettclearboundariesforthetestsconducted.

7.3.1 BearingloadcalculationThevaluesabove isasmentionedcalculatedusingtheSKF lifetimecalculatorwithguidance fromHarryOpdal foundon theSKFhomepage.Thegoverningequations in theprogramareherepresented.Valuesofvariablesand factorscanbefoundinPDFfile(9).When loadsareacting inradialandaxialdirectiononthebearingatthesametimethehypothetical loadacting inthecentreofthebearingwhichgivesthelifetimeofthebearingwhenonlyaxial forcesareacting iscalled thedynamicequivalentload.Thedynamicequivalentaxialloadofasphericalthrustrollerbearingisgiveninequation(7.2).

1,2a rP F F (7.2)

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Staticequivalentaxialloadisahypotheticalloadwhichwouldcausepermanentdeformationonthebearingatthepointonthebearingundermoststresswhenbothaxialand radial force isapplied.Fora spherical rollerbearing the staticequivalentaxialloadiscalculatedwithequation(7.3)providedthatFr/Fa0.55.

0 2.7 [ ]a a rP F F N (7.3)P0a isthestaticequivalentaxial load,FaandFrareactualaxial loadandactualradialloadrespectively.The operating life time of a spherical roller thrust bearing can be calculatedusingequation(7.4).

10/3

1nm skfCL a aP

(7.4)

7.4 PlexiglasscoverThe turbinehadoriginally two stealcovers thatcanbeopened toaccess therunnersothattherunnerbladescanbeadjustedwithouthavingtodismountthecompleteturbine.Onecoverisplacedabovetherunnerandoneundertherunner.Thecoverunder the runnerwas replacedwithaPlexiglascover.Thiswasdone inorder tobeable touseahighspeedcamera to recordand takepictures in the draft tube to check for cavitation on the runner blades.MechanicaldrawingsofthePlexiglascoverarefoundinAppendixO.

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Figure77FlowaftertheturbineoutsideBEP

Figure77showshowtheflow looks likeoutsidebestpoint.Asseentheflowalmostappearsasamistflowingthroughtheturbine.Airbubblesfromtheairintakeinthe lowerbearingandcavitationcontributetocreatethemist.Themistmadeitimpossibletodocumentcavitationontherunnerbladesbecauseitwas impossible to see theblades.When thewaterhadno spin the flowwasclearerhence lessbubblesbut itwas still impossible todocument cavitationwithahighspeedcamera.

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8 OptimisationsofinletbendusingCFD.CFD is short for Computational FluidDynamics and is a simulating tool thatsolves fluid flow or heat exchange characteristics. CFD iswidely used in theindustry because of its capability to give accurate solutions at a low costcomparedwithmodeltests in laboratories(10).EventhoughresultswithCFDmaybeobtainedquickly and costeffectiveCFDwillnotalways give the realsolution. It is therefore recommended to preform tests to validate the CFDresults.CFD simulationsofwater flowing thoughpipesarebasically solvedusing twogoverningequations. The twoequationsare theNavierStokesequationandtheconservationofmassequation.When performing CFD test there is a wide range of settings, factors andparameters touseandmonitor togetgood results.Adetaileddescriptionoftheseparameters,factorsandsettingsisfoundinAppendixF.

8.1 CFDanalysisofinletbendSharpcornersarenever ideal inpipe flow.Sharpcornerscancausebackflow,cavitationandseparationrightafterthecornerformingalowpressureregion.Flowinpipebendswilltendtohavehighvelocityandlowpressureattheinnercornerofthebendwhiletheoutercornerthenwillhavehighpressureandlowvelocity.Ifaturbineisplacedrightaftersuchabendthiscouldbeunfortunatefor the efficiency of the turbine since the velocity and pressure distributionacrossthepipeareawillbeunevenlydistributed.

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Figure81Velocityandpressuredistributioninpipebend.

In Figure 81 the velocity and pressure distribution is shown right after thebend.Thedifferenceinvelocityandpressuredistributionwillincreasewiththevelocityintheflow.Theturbinetestedinthisthesisisplacedafterasharpcornerbendasdescribedabove.ACFDanalysiswasthereforeconductedtocheck ifthebendcouldbeoptimized.Awide range of different bend solutionswere tested in the CFDanalysis and compared against the geometry of the actual inlet bend of theAfghaniturbine.The geometryof the actual inletbend is complex andpartsof thebend aredifficulttomeasure.Measuresandthegeometryusedtocreate themodel inFLUENTare thereforebasedonmeasurements takenon thephysical turbineandmeasures found in the Inventor drawings created byAndersAustegrd.ThereasonfornotbaseallmeasuresontheInventordrawingsisthattherearesignificantdifferencesinthedrawingsandtheactuallyproducedturbine.TheintendedvolumeflowrangefortheKaplanturbineis0.09m3/sto0.53m3/swhichgivesaninletvelocityinaverageof0.71619m/sand4.2176m/s.Optimaldesign inletvelocity is1.6711m/s.CFDsimulationsofthedifferentgeometrieswasdoneatinletvelocitiesrangingfrom1.0814m/sto2.387m/s.Four different geometries are tested, the original geometry plus three newgeometries.Thefourgeometriesarepresentedinthefiguresbelow.

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Figure82Originalgeometry

Figure83Geometry1

Figure84Geometry2

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Figure85Geometry3

InGeometry1thebendisroundedoneflowcontrollerisplaced inthemiddleofthebendspendingfromtheinlettotheoutletofthebend,thesectionafterthebendisextendedwith50cmcomparedtotheoriginalgeometry.Geometry2hasthesamedimensionsasgeometry1andtheonlydifferenceisthatgeometry2hastwoflowcontrollersinthebend.Geometry3has thesamebendasgeometry2buthas thesame lengthafterthebendastheoriginalgeometry.

8.2 VelocitymeasurementsininletbendVelocity testwhere performed to be able to check if the CFD resultswhererealistic. The velocity testwas donewith a Pitot tube and different volumeflowswheremeasured.

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Figure86Pitottubemountedontheturbine

The velocity from the measurements is calculated with equation(8.1). TheequationisderivedfromHydrauliskMleteknikk(2).

2 [ / ]h gc m s (8.1)

h is here the height difference between the hydraulic pressure and thestagnationpressurewhile isthePitotcoefficientgivenbyKjlle(2)torangefrom0.98to1.00.Themeasurementsareonlyvalid iftheReynoldsnumber isabove100.

Re c d (8.2)

WhenmeasuringthevelocityaPitottubewiththreepressureholeswasused.The centreholemeasures the stagnationpressure and the twoholeson theside of the tube, in this case the side of the knifemeasures the hydraulicpressure. The height of the two water columns leading from the hydraulicpressure measurements have to be levelled in order to have a validmeasurement. In Figure87 the two columnsmeasuringdynamicpressure islevelled and themeasurement is valid. The velocity in the flow can then becalculatedusing equation(8.1). In realmeasurements it isdifficult to get thetwohydruliccolumnstobeexactlylevelledduetofluctuationsintheflowand

60

timelaginthemeasurements,meaningthatwhenthePitotistwistedinordertolevelthewatercolumnsittakestimefromwhenthetubeistwistedtowhenthewaterlevelisstable.In the testsperformed in this thesisanallowedheightdifference in the twodynamic measurements is set to 5mm. A 5mm height difference is foundacceptable since the goalwith themeasurements is to confirm CFD resultswhichhaveahigh levelofuncertainty.Thevelocitymeasurementsalsohaveuncertainties linked to them, theyarenot considered in this thesis since theuncertaintiesinthemeasurementsaresmallcomparedtotheCFDanalysis.

Figure87HeightdifferenceinaknifePitotmeasurement

Thevelocitydistribution intheoutletmayvarywithdifferentpressureheads.TobeabletocomparethemeasuredvelocityprofilewiththeCFDresultswherethe inlet and the outlet pressure is governed by the volume flow the actualvelocitymeasurementshavetobescaledagainstadimensionlessfactor.

*2

' [ / ]2gH

c c m sgH

(8.3)

Inequation(8.3)H*andHistheheightdifferencethemeasuredstaticpressureintheinletandoutlet.H*isthereferencevaluekeptconstantandhastobesetatanappropriatevalue.Thevaluecanbesetwhen for instance foradesired

h

Ph PhP0

61

volume flow. If the pressure is kept constant during the test this is notnecessary.

8.3 OutletTheoutletoftheturbineconsistsofadrafttube,threefinsandahubundertheturbine. The draft tube and the hub help improve the performance of theturbine. The fins on the other hand do not necessary give a positivecontributiontotheperformanceoftheturbine.FrequencyanalysisconductedbyRemiAndreStoplealsoshowthatfluctuationsinthemeasurementscanbecausedbythebladespassingthethreesupportfins.The water coming out of the runner have inmost cases swirl because theturbineisnotoperatingatbestefficiencypoint.Thefinswilldisturbthewaterswirlandmaycausepressurefluctuationswhentherunnerbladespassthefins.Toavoiddisturbanceoftheswirlaftertheturbinethebearingplacedundertheturbine can bemoved into the already existing guide vane housing directlyabovetherunner.

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Figure88Bearingwhenplacedinsidetheguidevanecentrepiece

AcylindricalrollerbearingischosenwithanNUdesign.NUdesignlettherebeminormovementsintheaxialdirection.Thistypeofbearingdoesnottakeanyloadintheaxialdirection.InFigure88thebearingisindicatedwithindex3.Thebearingshouldbeplacedasclosetotherunneraspossibletopreventcastintheshaftandrunner.Toprevent leakage from thewaterway into thebearing a viper seal canbechosen, index 4. AHPseals (11) offers a wide range of seals for rotatingequipment. The Rotaflon series is a high performance series of seals forrotatingshafts.TheRBseriesischosenforthisparticularcase.TheRBseriesischosen because it can tolerate the pressure, temperature and rpm of theturbineshaftproducesandoperatingconditions.Thelifetimeofthesealisnotgivenbecause it ishighlydependenton theworking conditions.An identicalsealisnecessaryunderthebearing.Thissealisnotincludedinthedrawing.Index5 is thegrease intake fromoutside the turbine.Asmall tubehas tobeinsertedintotheguidevanesconnectingtheoutsidewiththebearing.ThemechanicaldrawingofthebearingisfoundinAppendixP.

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9 Results9.1 EfficiencytestsTo create the hill diagram curve fittingwas performed inMatlab to createsmooth lines.Fourdifferentcurve fitting functionswere tried inorder to findthe function that created the best curve for theHill diagram. The functionsusedwerea2nd,3rdand4thdegreepolynomialcurvefittingfunctionsaswellasasmoothingsplinefunction.Anuncertaintyof2% ineachpointwasselectedto evaluate if the fitted curve is within an acceptable range of the actualmeasurements.

Figure912ndorderpolyfit

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Figure923rdorderpolyfit

Figure934thorderpolyfit

65

Figure94Smoothingspline

Above the four curve fitting functions are presented used on a measuredsetting2serieswitharotationalspeedof687rpmandvaryingeffectivehead.Thebluedotsarethemeasureddatawhiletheredlineisthefittedcurve.Theverticallinesareerrorbarswithavalueof2%relativetothemeasureddata.ThecurvefittingforallthemeasuredseriesarefoundinAppendixH.Smoothingofcurves isdone inordertoobtainaHilldiagramwhich iseasytoread and to find values between themeasured values. The fitting functioncreatesafunctionwhichallowstheuseroftheMatlabprogramdevelopedtofindtheefficiencyatanygivenoperationalpoint.The smoothing spline function is the function which results in the lowestdeviationbetween the fitteddatacurveand themeasureddatawhile the2ndorderpoly fit functiongives thehighestdeviation.Even though the2ndorderpoly fit function results in thehighestdeviationonlyonepointon the fittedcurve lies outside the 2% uncertainty value. The 2nd order function is thefunctionwhichgivesthemostrealisticcurvewhenevaluatingallthelinesforallthe functions. The 3rd and 4th order functions creates unrealistic gains inefficiencyatlowheads.Thisiscausedbyhighuncertaintyinthemeasurementswhilethesmoothingsplinecreatesunevencurves.

66

Theefficiencytestwerestronglyaffectedandlimitedbythetestrigsetupandthe turbine. For a detailed description of the limitations and challengesencounteredwhiletestingseechapter7.1,7.2and7.3.

9.1.1 Setting1TheHilldiagramspresentedinFigure95andFigure97arepresentedasHevs.rotationalspeeddiagram.Thereason fornotpresenting theHilldiagramasaQEDvs.nEDdiagramisthattheturbineisnotamodeloraprototypesothattheflow,headandrotationalspeeddoesnothavetobescaledwhentheturbineistaken into production to find the efficiency and power output. The turbinesperformance isgovernedbytheheadandtherotationalspeed.Therotationalspeedgovernsthevolumeflow.A2ndorderpolyfitfunction isusedtocreatethecurvesusedtocreatetheHilldiagrams.

Figure95Hilldiagram,efficiencyplottedagainsteffectiveheadandrotationalspeed

TheHilldiagraminFigure95indicatesthatthereisabestefficiencypointwithefficiencyof76.4%ataround575rp