CAVITATION CONTROL BY AERATION
AND ITS COMPRESSIBLE
CHARACTERISTICS
Availableonlineatwww.sciencedirect.corn
8CIENCEDIRECT0
JournalofHydrodynamics
Set.B,2006,18(4):499—504
499
sdlj.chinajourna1.net.cn
CAVITATIoNCoNTRoLBYAERATIoNANDITSCoMPRESSIBLE CHARACTERISTICS
DONGZhi—yong
SchoolofCivilEngineeringandArchitecture,ZhejiangUniversityofTechnology,Hangzho
u310032,China,
E—mail:dongzy@zjut.edu.cn
SUPei.1an
SchoolofForestry,ShanxiAgriculturalUniversity,Taigu030801,China (ReceivedFeb.16,2006)
ABSTRACT:Thispaperpresentsanexperimental
investigationandatheoreticalanalysisofcavitationcontrolby aerationanditscompressiblecharacteristicsattheflow velocityV=20m/s一50m/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,thespeedofsoundandMachnumberofhigh—velocity
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,thecommonhigh—velocityflowproblems
suchasairentrainment,cavitation,fuctuation—
vibration.energydissipationandscourpreventionwill beencounteredinordinaryhighdams.Inspillway dams,spillwaytunnelsandchutespillwaysof high—headdischargestructures,cavitationphenomena willoccurwhileflowvelocityreachesacertainextent andflowpressurelowerstherelevantsaturatedvaDor pressure.Cavitationerosionarisesfromcavitiesflow fromunderpressuretohighpressure.Ascavitation phenomenonisinevitable.inordertopreventthe damsfromtheerosionduetocavitationof
high—velocityflow,aneconomicandeffective measureistosetaeratorsforforeedaerationin under—pressurecavitationregionsor
…
upperlocations
liabletocavitationerosion.Peterka【jexperimentally
investigatedcavitationcontrolbyaeration.Theratios ofairtowaterflowratesheaeratedinhisexperiments were0.4%一7.4%.Heobservedthatburstingand
hammer—beatingsoundsduetocavitationerosionin thepipewereattenuatedwiththeincreaseinairflow rate.andthecavitationnoisevanishedwhileabout7% airwasaerated.Manyresearchers【'suggestedthat
ProjectsupposedbytheNationalNaturalScienceFoundationofChina(GrantNo:50279048)
Biography:DONGZhi—yong(1962一),Male,Ph.D.,Professor
cavitationerosioncanbeconsiderablymitigatedwhen airconcentrationnearwallisl%.2%.andthe cavitationerosioncanbeeliminatedwhentheair
concentrationattains5%.7%.
Thespeedofsoundisanimportantquantity
characterizingthefluidcompressibility.Some experimentalresultsLo一showedthatthespeedof
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
手OfCv1
1+OfpR
(pdfl+)
ThevolumeratioofairtowaterofthemixtureisDifferentiatingEq.(8)gives
h
Ow
Themeandensityoftheaeratedflowis +
Therefore,
=一
1+
—
l+—fl}
Itfollowsfromthefirstlawofthermodynamics de=g
de=
,
f1,Ij
mHC手mC
+?
dT=C+OfC
1+
d(10)
whereCwdenotesthespecificheatforwaterphase,
Cvthespecificheatofconstantvolumeforairphase?
Undertheadiabaticcondition,wehave 6q=0
Assumingairphaseisperfectgas,weobtain 71:旦:
RPRap
DifferentiatingEq.(12),wehave dT=
OfpR
(pdfl+)(13)
+)P
p'
5Ol
ConsideringR=Cp—C,withCPbeingthe
specificheatofconstantpressure,fromEqs.(14)and
(15),weobtain
')=const
Equation(16)issimilartotheisentropicrelations
ofperfectgas.inwhich1+istheratioofspecific
heat,thatis,
1+(=
C,+
C手aC
As..,1+=CP/c=
Thespeedofsoundaforfluidcanbewritten aS
2
=
(]==@dfl
SubstitutingEqs.(15),(16)intoEq.(18),wehave
1+cP(1+)az一
l+of—P
w
—
b
orapproximately
a
1B
8
p
Noticethat8=C/(1一
concentrationCiSdefinedas
SubstitutingEqs.(10).(13)intoEq.(9)yieldsC= +Q
(20)
C),inwhichtheair
一
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 reasonab】e.
Airconcentration
4
Fig.2Comparisonofspeedofsoundbetweentheoretical andmeasuredvaluesforaeratedflow
4.TYPICALWAVEFoRMSoFPRESSUREIN
CAVITATIoNREGIoN
4.1Typicalpressurewaveforms
ThetypicalwavefoI'[i1sofpressureincavitation regionwithandwithoutaerationareshowninFig.3. TheairconcentrationinthefigureisC:10.9%. andthecorrespondingvelocityis21.3ln/s. ItfollowsfromtheFig.3thatthepressureof high—velocityflowafteraeratedisappreciably enhanced,thepressureamplitudeincreases,andthe pressureincrementwiththeincreaseintheair concentration.Thetime—averagedpressurewithout
aerationisl=一23.45kPa,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%
4.2尸ressurewavqformsSClf-aeratedflow
ThepressurewaveforlTISofhigh—velocityaerated
flowareshowninFigs.4fa)and4fb).Tofacilitatethe test,aerationwasfirstlyarrangedandthenthe non—aerationone.Sothelefthalf-partinthestepped waveformreferstothecaseofaeration,andthe