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CAVITATION CONTROL BY AERATION AND ITS COMPRESSIBLE CHARACTERISTICS

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CAVITATION CONTROL BY AERATION AND ITS COMPRESSIBLE CHARACTERISTICS

    CAVITATION CONTROL BY AERATION

    AND ITS COMPRESSIBLE

    CHARACTERISTICS

    Availableonlineatwww.sciencedirect.corn

    8CIENCEDIRECT0

    JournalofHydrodynamics

    Set.B,2006,18(4):499504

    499

    sdlj.chinajourna1.net.cn

    CAVITATIoNCoNTRoLBYAERATIoNANDITSCoMPRESSIBLE CHARACTERISTICS

    DONGZhiyong

    SchoolofCivilEngineeringandArchitecture,ZhejiangUniversityofTechnology,Hangzho

    u310032,China,

    Email:dongzy@zjut.edu.cn

    SUPei.1an

    SchoolofForestry,ShanxiAgriculturalUniversity,Taigu030801,China (ReceivedFeb.16,2006)

    ABSTRACT:Thispaperpresentsanexperimental

    investigationandatheoreticalanalysisofcavitationcontrolby aerationanditscompressiblecharacteristicsattheflow velocityV=20m/s50m/s.PressurewavefoIn'iswithandwithout aerationincavitationregionweremeasured.Thevariationof compressionratiowithairconcentrationwasdescribed,andthe relationbetweentheleastairconcentrationtoprevent cavitationerosionandflowvelocityproposedbasedonour

    experimentalstudy.Theexperimentalresultsshowthataeration remarkablyincreasesthepressureincavitationregion.andthe correspondingpressurewaveexhibitsacompression wave/shockwave.Thepressureincreaseincavitationregionof high.velocityflowwithaerationisduetothefactthatthe compressionwaves/shockwaveaftertheflowisaerated.The compressionratioincreaseswithairconcentrationrising.The relationbetweenflowvelocityandleastairconcentrationto preventcavitationerosionfollowsasemi.cubicalparabola. Also,thespeedofsoundandMachnumberofhighvelocity

    aeratedflowwereanalyzed.

    KEYWORDS:cavitationcontrolbyaeration,compression wave/shockwave,leastairconcentration,speedofsound, compressionratio

    1.INTRoDUCTIoN

    Sofaralotofhighdamsthataregreaterthanl00

    minheighthavebeenconstructedinChina.And

    manysuperhighdamsover200minheight.suchas

    thoseattheErtanandLongtanHydropowerStations, werecompletedorareunderconstruction.Someof

    themevenhavetheheightoftheorderof300msuch

    astheonesattheXiaowanandXiluoduHydropower

    StationsIII.Accordingtoincompletestatistics,nearly 30superhighdamsthataregreaterthan200min

    heighthavebeensofarcompletedintheworldlZ1.

    Becauseoftheheadincrease,flowvelocitypassing throughthesehighdamscanreachsevera1.dozen

    meterspersecond,andevenuptoorover50m/s.As

    weknow,thecommonhighvelocityflowproblems

suchasairentrainment,cavitation,fuctuation

    vibration.energydissipationandscourpreventionwill beencounteredinordinaryhighdams.Inspillway dams,spillwaytunnelsandchutespillwaysof highheaddischargestructures,cavitationphenomena willoccurwhileflowvelocityreachesacertainextent andflowpressurelowerstherelevantsaturatedvaDor pressure.Cavitationerosionarisesfromcavitiesflow fromunderpressuretohighpressure.Ascavitation phenomenonisinevitable.inordertopreventthe damsfromtheerosionduetocavitationof

    highvelocityflow,aneconomicandeffective measureistosetaeratorsforforeedaerationin underpressurecavitationregionsor

    

    upperlocations

    liabletocavitationerosion.Peterkajexperimentally

    investigatedcavitationcontrolbyaeration.Theratios ofairtowaterflowratesheaeratedinhisexperiments were0.4%7.4%.Heobservedthatburstingand

    hammerbeatingsoundsduetocavitationerosionin thepipewereattenuatedwiththeincreaseinairflow rate.andthecavitationnoisevanishedwhileabout7% airwasaerated.Manyresearchers'suggestedthat

    ProjectsupposedbytheNationalNaturalScienceFoundationofChina(GrantNo:50279048)

    Biography:DONGZhiyong(1962),Male,Ph.D.,Professor

    cavitationerosioncanbeconsiderablymitigatedwhen airconcentrationnearwallisl%.2%.andthe cavitationerosioncanbeeliminatedwhentheair

concentrationattains5%.7%.

    Thespeedofsoundisanimportantquantity

    characterizingthefluidcompressibility.Some experimentalresultsLoshowedthatthespeedof

    soundinuniformtwo--phaseair--watermixtureismuch lessthanthatinsingle.phasewaterorair.Inthe standardstatethespeedofsoundinwaterisabout 1450m/sandinairabout340m/s.Thespeedof

    soundinair.watermixture.however.isonlyofthe orderoftensofmeterspersecond.LiLIu]preliminarily analyzedthespeedofsoundinair.watertwo.phase flow,classificationofhighvelocityaeratedflowand basicequationsofair..watertwo..phaseflowaswellas basiccharacteristicsofsupersonicaeratedflow.The firstauthorofthisPaDer_IJ_theoreticallyanalyzed thecompressiblenatureofhigh.velocityaeratedflow, andproposedarelationbetweentheleastair concentrationtopreventcavitationerosionandflow velocityattheflowvelocityV--20m/s.40m/sLJ:~J. Thereisnodoubtthataerationcaneffectivelyprevent orweakenthelevelofcavitationerosion.Though concretestrengthislower,cavitationerosionon concretesurfacecanbeavoidedprovidedthat appropriateairconcentrationwouldbeaerated,even cangreatlyrelaxtherequirementsofirregularityon theconcretesurface.Inversely.iftheflowis non.aerated.cavitationerosionwilloccurthough concretestrengthisratherhigh.

    2.EXPERIMENTALFACILITIESAND

    METHoDoLoGY

Thisexperimentwasperformedina

    non.circulatingwatertunnelintheHydraulics LaboratoryatZhejiangUniversityofTechnology.The experimentalsetupprincipallyconsistedofaeration, contraction.observationanddisionsectionsetc.. whichweremadeofstainlesssteelplateand processedbycomputer.controlledmachinetoolas showninFig.1.Thecross.sectionalareasof observationsectionare0.05×0.05mand

    0.02x0.035m.respectively.Thediffusionsections are0.4mandlmlong.respectively.

    WaterflowratewasmeasuredbyaUFLO2000P ultrasonicDopplerflow.meterandbyanLDBB.150 electro.magneticflow.meter.Airflowratewas determinedbytheLZB.15andLZB.4Orotator flow.meterswithcompressedairsuppliedbyair compressor.Flowvelocitywas20m/s.50m/s. Pressurewithandwithoutaerationwasmeasuredwith anMPXl00Dsilico.resistancepressuretransducer. andtherelateddatawererea1.timeacquiredbya SINOCERA.YE6263dataacquisitionsystem.Contact areabetweenconcretespecimenandwaterflowis 0.04x0.1m.Threemixingproportionsofconcrete specimenwerecast:(1)water.cementratioW/C=O.43. cement.sandratioC/S--1.0.andcompressivestrength atstandardcuringconditionfora4.weekperiodis 15.7MPa,(2)W/C=1.5.C0.21,thecompressive strength2.2MPa,(3)W/C=O.7,C0.25,the

    compressivestrength6.2MPa.

    Fig.1Workingsection

3.SPEEDoFSoUNDINAERATEDFLOW

    FhespeedofsoundandtheMachnumberarethe importantquantitiesforcompressibilityanalysisof fluidflow.Themassandvolumeoftheaeratedflow inaunitvolumecanberespectivelyexpressedas Formass

    w

    +a

    Forvolume

    V=+

    (1)

    (2)

    inwhichthesubscriptsw,adenotewaterandair, respectively.Themassratioofairtowaterofthe mixturecanbeexpressedas

    m

    =const

    w

    Thedensitiesofwaterandairphasescanbe respectivelywrittenas,

    Forwaterphase

    :const

    Forairphase

    (4)

m,,

    pap——

    P

OfCv1

    1+OfpR

    (pdfl+)

    ThevolumeratioofairtowaterofthemixtureisDifferentiatingEq.(8)gives

    h

    Ow

    Themeandensityoftheaeratedflowis +

    Therefore,

    =

    1+

    

    l+fl}

    Itfollowsfromthefirstlawofthermodynamics de=g

    de=

    ,

    f1,Ij

    mHCmC

    +?

    dT=C+OfC

    1+

    d(10)

    whereCwdenotesthespecificheatforwaterphase,

    Cvthespecificheatofconstantvolumeforairphase?

    Undertheadiabaticcondition,wehave 6q=0

    Assumingairphaseisperfectgas,weobtain 71::

    RPRap

    DifferentiatingEq.(12),wehave dT=

    OfpR

    (pdfl+)(13)

    +)P

    p'

    5Ol

    ConsideringR=CpC,withCPbeingthe

    specificheatofconstantpressure,fromEqs.(14)and

    (15),weobtain

    ')=const

    Equation(16)issimilartotheisentropicrelations

    ofperfectgas.inwhich1+istheratioofspecific

    heat,thatis,

    1+(=

    C,+

    CaC

    As..,1+=CP/c=

    Thespeedofsoundaforfluidcanbewritten aS

    2

    =

    (]==@dfl

    SubstitutingEqs.(15),(16)intoEq.(18),wehave

    1+cP(1+)az

    l+ofP

    w

    

    b

    orapproximately

a

    1B

    8

    p

    Noticethat8=C/(1

    concentrationCiSdefinedas

    SubstitutingEqs.(10).(13)intoEq.(9)yieldsC= +Q

    (20)

    C),inwhichtheair

    

502

    whereQa,Qwaretheairflowrateandwaterflow rate,respectively.

    SoEq.(201canbefurtherexpressedas

    (22)

    TheMachnumberMstandsforaratioofflow velocityVtoitsspeedofsounda,thatis, M=Via(23)

    ItfollowsfromEq.(22)thatifPiskept

    constant,thespeedofsoundfortheaeratedflowa isonlyafunctionofairconcentrationC.Obviously thevariationinthespeedofsoundinthecaseofl atmosphericpressureismainlydependentuponair concentration.AcomparisonofEq.(221wifh experimentalresultisshowninFig.2.Thoughasmall differenceoftheresultsexists.theagreementis reasonabe.

    Airconcentration

4

    Fig.2Comparisonofspeedofsoundbetweentheoretical andmeasuredvaluesforaeratedflow

    4.TYPICALWAVEFoRMSoFPRESSUREIN

    CAVITATIoNREGIoN

    4.1Typicalpressurewaveforms

    ThetypicalwavefoI'[i1sofpressureincavitation regionwithandwithoutaerationareshowninFig.3. TheairconcentrationinthefigureisC:10.9%. andthecorrespondingvelocityis21.3ln/s. ItfollowsfromtheFig.3thatthepressureof highvelocityflowafteraeratedisappreciably enhanced,thepressureamplitudeincreases,andthe pressureincrementwiththeincreaseintheair concentration.Thetimeaveragedpressurewithout

    aerationisl=23.45kPa,whilethatwith

    aerationbecomes=29.527kPa,soaeration makespressureincreaseby52.986kPa.Wecan deducefromEqs.(22)and(23)thatthespeedof soundfortheaeratedflowisa=32.1m/s,andthe correspondingMachnumber,=0.64.

    t/s

    Fig.3Waveformsofcompressionwaveat//--21.3m/s andC=10.9%

    4.2ressurewavqformsSClf-aeratedflow

    ThepressurewaveforlTISofhighvelocityaerated

    flowareshowninFigs.4fa)and4fb).Tofacilitatethe test,aerationwasfirstlyarrangedandthenthe nonaerationone.Sothelefthalf-partinthestepped waveformreferstothecaseofaeration,andthe

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