DOC

Computer Simulation of Turbulent Flow through a Hydraulic Turbine Draft Tube

By George Henry,2014-02-18 00:26
6 views 0
Computer Simulation of Turbulent Flow through a Hydraulic Turbine Draft Tube

    Computer Simulation of Turbulent Flow

    through a Hydraulic Turbine Draft Tube WUJNSWuhanUniversityJournalofNaturalSciences

    ArticleID:1007l202(2006)03064904

    VO1.11No.32006649.652

    ComputerSimulationofTurbulentFlow

    throughaHydraulicTurbineDraftTube

    HUYing',CHENGHeming2,WANGQuanlong3,

    YUZhikun'

    1.SchQolofMechanicalandElectricalEngineering,Kunming UniversityofScienceand"[~echnology,Kunming650093,Yunnan, China;

    2.Sehoo1ofCivilEngineeringandArchitecture,Kunming Universityof~ieneeandI'echnology,Kunming650093,Yunnan, China;

    3.HarbinElectricMachineryCorporationIAmited,Harbin150040, Heilongjiang,China

    Abstract:BasedontheNavier-Stokesequationsandthestandard肛?

    turbulencemode1,thispaperpresentsthederivationofthegoverning equationsfortheturbulentflowfieldinadrafttube.Themathematical modelfortheturbulentflowthroughadrafttubeissetupwhenthe boundaryconditions,includingtheinletboundaryconditions,theoutlet boundaryconditionsandthewallboundaryconditions.havebeenimple mented.ThegoverningequationsareformulatedinadiscretefoITnona staggeredgridsystembythefinitevolumemethod.rhesecondorder centraldifferenceapproximationandhybridschemeareusedfordiscreti zation.Thecomputationandanalysisoninternalflowthroughadraft

    tubehavebeencarriedoutbyusingthesimpleealgorithmandcfx-tasc flowsoftwaresoastoobtainthesimulatedflowfields.Thecalculation resultsatthedesignoperatingconditionforthedrafttubearepresentedin thispaper.Thereby,aneffectivemethodforsimulatingtheinternalflow fieldinadrafttubehasbeenexplored.

    Keywords:bydraulicturbinedrafttube;turbulentflow;numerical sim1ula1ion

    CLCnumber:TK730.2

    Receiveddate:20050923

    Foundationitern:SupportedbytheNationa1Natura1ScienceFoundationofChina (10162002).theKeyProjectofChineseMinistryEducation(204138)andthesc|_ enceFoundationofYunnanEdueationBureau(5Y0020A)

    Biography;HUYing(1963),female,Associateprofessor,researchdirection: computationalfluiddynamicsandfhtktmechanics.Emai1ihuyinhg2003@rip.km1. net

    0IntrOduCtiOn

    4nelbowdrafttubeconsistsessentiallyofashortconicaldiffuserfollowedbya9Odegree elbowofvaryingcrosssection.Itsgeometryisfar

    morecomplexthanastraightconduit.Theflow

    leavingtherunnerisalwaysswirlingoffoptimalop

    cratingconditionssotheinletflowinadrafttakeis

    swirlingtoo.Thus,therearevortexes,secondary

    flowandnonuniformflowinadrafttube.Theflow

    inadrafttubeisatypicalthree-dimensiona1turbu

    lentflow.Sofar,itisimpossibletodescribeitaccu

    rately.

    Traditionally,thedesignofadrafttubeisto

    choosethedimensionsandshapesbasedonexisting

    drafttubes,andtheperformanceassessmenthasre

    liedonlyonlaboratorymodeltesting.Recently,

    alongwiththerapiddevelopmentofcomputational techniquesandcomputationalfluiddynamics,ithas beenanimportantmethodtooptimizethedrafttube designbypredictingtheperformanceofadrafttube bymeansofnumericalsimulation.VuandShyyE~]

    appliedviscousflowanalysistosuccessfullypredict turbulentflowcharacteristicsandenergylossesina hydraulicturbinedrafttube.Itallowsthedesigner toevaluatethedrafttubeperformanceandtoopti

    mizethedrafttubedesign.

    Thecomputationandanalysisoninternalflow throughadrafttubehavebeencarriedoutbyusing cfx-tascflowsoftwaresoastoobtainthesimulated flowfields.

1GoverningEquations

    1.1BasicEquationsforTurbulentflow

    IntheRefs.[35],for3Dsteadyturbulentflow,in aCartesiancoordinatesystem,throughaprocessoftime- averaging,calledReynoldsstressaveraging,thetime- averagingcontinuityequationmaybeexpressedas ()=0(1)

    Reynoldstime-averagingNavier-Stokesequations canbewrittenas

    8(

    ap+

    d

    a鲁一IDu;u/)+s)

    where,(i,J=l,2,3)representrespectively,Y

andcoordinate,u(H)isthevelocitiesu,and,P

    isthestaticpressure,S(iu,,w)andSaresource

    terms,andpu/tuisReynoldsstress.

    Eq.(1)andEq.(2)arenotclosed.Newturbulence modelsshouldbegiventoclosetheequations. 1.2TurbulentFlowModels

    SomehypothesesaboutReynoldsstressshouldbe madetocloseEqs.(1)and(2).Thatistosettheex

    pressionofReynoldsstressorturbulentflowmodels.by whichtheinstantaneousvaluesinEqs.(1),(2)areex

    pressedintermsofmeanandfluctuatingcomponents.As nospecia1physical1awisusedtosetturbulencemodels. theyarebasedonlyonagreatdealoftestresultsatpres

    ent.Inthispaper,aneddyviscositymodelissetupand turbulentviscosity(i.e.eddyviscosity)isused.The Reynoldsstressandturbulentfluxtermsarerelatedto themeanflowvariablesusingBoussinesqassumption~.

    /

    \

    au,Ou,

    /~pu;u一号(ID3)\a,.a/(ID走十)

    where,istheturbulentviscosity,kistheturbulentki

    neticenergy,,isKroneckerdehaconstant(&).1when i=j,,=Owhen?).

    SubstituteEq.(3)intoEq.(2)andexpandthesum, Eq.(2)canbewrittenas:

    +aG+:R(4)8xay'az

    where,F,G,H,RareshownintheRef.r7].

eff一—f

    TheReynoldsstressisrelatedtothemeanvelocity gradientsusingthetwoequationstandard肛?turbulence

    model,i.e.theturbulentviscosityfisrelatedtothe turbulentkineticenergykandthedissipationrate]. 650

    k

    ===IDLLbJ

    a(pku~)=:=

    +okl+o,(6)

    a(pEu~)=

    8+at4+一譬

    (7)

    where,isthedynamicviscosityofthefluid,rcalled "theequivalentviscosity".LaunderandSpalding[]gave theconstantsas:

    C1:1.44,C2=1.92,Cu=0.09,=1.0,1.3

    )2++]+).

    ++)}

    TheEqs.(4)(7)asc1.suref.rc.mprisetheg.v

    erningequationswhichcandescribe3-Dturbulentflowin ar1rftt11hp

    2NumericalAlgorithm

    Thegoverningequationsareformulatedinadiscrete formforastaggeredgridsystembythefinitevolume method.Thecentra1differencingschemeandhybrid schemeareusedfordiscretization.Thediscretizedgover ningequationsaresolvedbythesimplecalgorithmof pressurecorrectionmethodE.

    Forspecifiedpressure

    field,thevelocitiescanbeobtainedfromthesolutionof thediscretizedmomentumequations.Thesevelocities, whensubstitutedintothecontinuityequation.wil1not necessarilysatisfythatequation.Hence,usingtheconti

    nuityequation,constructapressurecorrectionwhichwill bringthevelocityfieldmoreintoagreementwiththecon

    tinuityequation.Repeattheprocessuntilavelocityfield isfoundthatdoessatisfythecontinuityequation.When thisisachieved,thecorrectflowfieldisathand. 3BoundaryConditions

    3.1lnletBoundaryConditions

    Attheinletoftheflowdomain(i.e.theinletofa drafttube),thevelocityprofilesareimposedbytherun

    nerexitflow.

    3.2OutletBoundaryConditions

    Attheoutletoftheflowdomain(i.e.theoutletofa drafttube),theflowisapproximatelyfullydeveloped

anddoesnotvaryalongflowdirections.Asurfaceper

    pendiculartotheflowdirectioniSchosenasanoutletsur

    face,onwhichoutletboundaryconditionscanbeimple

    mented.Thegradientsofallvariables(exceptforthe staticpressure)arezeroattheoutlet.Themathematical descriptionofoutletboundaryconditionsaredefinedby =0,=",,,k,?

    where"islocallynormaltotheoutletboundaryface. 3.3WallBoundaryConditions

    Thestandard肛?modelisvalidonlyforfullyturbu

    lentflowsandavailabletohighReynoldsnumberturbu

lentflow.Closetosolidwalls,thereareinevitablyre

    gionswherethelocalReynoldsnumberOfturbulenceis sOsmallthatviscouseffectspredominateoverturbulent ones.Theadoptedturbulentmodelneedsaspecial treatmentnearthesolidwalltotakeintoaccountthevis

    COUSturbulentinteraction.Noslipconditionsareapplied toal1nodesatsolidwalls.Atthenodalpositionnextto thesolidwal1.theSOcalledwal1functionapproachis

    used.ItsmeritiSthatitdoesnotrequirethedirectionOf thevelocityatthefirstnodenearthewal1.Thisnotonly impliesaneasyimplementationfor3Dcodesbutalsoa reductiononthecomputingtimeandstorageaswel1. 4TheResultsandAnalysis

    WecanseeFig.1Fig.5.Theanalysisandcomputa

    tiononflowthroughthedrafttubeOfthehydraulictur

    binemodelappliedforahydropowerstationareper formedbvthecfx-tascflowsoftwareforfluidflow.The resultsOfnumerica1simulationOfturbulentflowsare presentedinthispaper.Thecalculationoperatingcondi

    tioniStheoptimaloperatingcondition,atwhichtheunit Fig.11_1hreedimensionalview

    "Lk~iversityJournalo亭壮聃望,霸棚砷.翻?"...-j

    flowQllis0.56m./sandtheunitspeedn11is74.19 r/min.ThemodeldiameterDlis374.4mm.Figure1 showsathreedimensionalviewOfit.

    

    Fig.2Velocityfieldonthemid-planeofleft-right ?}i)

    4lI4I

    4iH4l.

3_Il'jI

    7l3

    523I

    jj0;

    3083E

    28h2l.

    [102l

    141l

    !:{)I

    I_H?.

    If1?

    15{II

    IIl'II

    Fig.3Velocityvectorsatdifferentcrosssections Fig.4Staticpressurecontoursonthemid-planeofleft-right

    ,

    ,

    ,

    

    Fig.5Three-dimensionalflowvisualization 651

    ????????????????…

    DL卜卜卜川?…

    44333j;2rIrj?,

    nnB".-Bn

    ...._lll,??0

    Figure2representsthevelocityfieldonthemid- planeofleftright.Theseshowthatflowvelocitiesare

    reasonablethroughtheentiredrafttube.0bservation fromvelocitiesindicatesthatnoflowrecirculationisoc

    curring.Atthebeginningofthebend,themaximumof thevelocityappearsneartheinnerwal1.Astheflowpro

    gressesintotheduct.andasaconsequenceoftheinertia forces,thismaximumrapidlymovestowardstheouter wal1.Thispredictedflowbehaviouragreeswiththere

    suitsofreferenceAgouzoulandReggiolI(1J.

    Thedisplayofvelocityvectorsatdifferentcrosssec

    tionsofthedrafttube,asshowninFig.3,illustrates uniformdistribution.Figure4displaysthestaticpressure contoursonthemid-planeof1eft-right.Theseshowthat.. pressuresattheinletandexitofthedrafttubearewell distributed.Thereisapressuredifferenceneartheinner andouterwal1oftheelbow.Thepressureneartheouter wallishigherthanneartheinnerwal1.Accordingto this.theplacewhereaventissetmaybechosenreason

    ably.Thus,thecavitationresistanceforahydraulictur

    binewillincrease.Three~dimensionalflowvisualization, asshowninFig.5,displaysvisuallyflowstates.This showsthatstreamlinesarewelldistributedandthestate

    offlowisgood.

    Theresultsofcfdanalysisshowthattheperform

    anceofthisdrafttubeishigh.Thisisalsoconfirmedby theenergyrecoveryfactor0.713.Forhydraulicturbines withthehighspecificspeed,theenergyrecoveryfactorof adrafttubeaffectstheefficiencyofhydraulicturbineim portantly.Thebiggertheenergyrecoveryfactoris,the 1owerhydraulic1ossesandthekineticenergyattheoutlet

inadrafttube,andthehigherthehydraulicturbineeffi

    ciencyistoo.Theenergyrecoveryfactorofanelbow drafttubeis0.6-0.75generally.

    5Conclusion

    BasedonNSequations,thestandard肛?turbulence

    modelandtheboundaryconditions,afterthecomputa- tionandanalysisoninternalflowthroughadrafttubeare 652

    performedbyapplyingtascflowsoftware,thesimulating flowfieldsatthesectionsofadrafttubehavebeenob

    tained.Withthehelpofflowanalysisforthedrafttube, drafttubeprofileswithhighperformancecanbedesigned bythemodificationandimprovementofanexistingdraft tube.Theresultspresentedinthispapershowthatnu

    merica1flowsimulationscanbeintegratedsuccessfullyin

    toadesignprocedureforadrafttubebycfdmethod. whichcanensureperformanceofit,dramaticallyshorten thetimeneededforanewone,reducenumbersoftest anddesigncost.ThemethodhasbeenvalidatedandaD

    pliedtothesimulationoftheflownanndustrialhy

    draulicturbinedrafttube.Theproposedflowsimulation canbeusedasacomplementfortheunderstandingand designofasatisfactorydrafttube.

    References

    [1]

    [22

    [3]

    [42

    VuI'c,ShyyW.Navier-StokesFlowAnalysisforHydraulic TurbineDraftTubesEJ].JournaloJ'FluidsEngineering.

Report this document

For any questions or suggestions please email
cust-service@docsford.com