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    Detachment

    Chioc~eofChem.Eng.,7(2)145--153(1999)

    DetachmentSizeMeasurementofTwoInteracting

    BubblePlumesFormedatNeighboringNeedles

    UsinganAcousticMethod

    xi^ngYu(向宇)",SunKexin(~科霞),GuoLiejln($~烈锦)

    andChertXu~un(学俊1

    NationalLaboratoryofMultiphaseFlowinPowerEngineering.?

    'anJia~tongUniversity,Xi'

    710049,China

    AI~traetDetachmentdetermlnatiolitwjthanacousticmethodhasbcarriedoutfortwo interactingbubbleplumesformedatneighboringneedl~inqelescentwater.Twosets0fm~dle

    p,onewith1.5mmand0nuninnetdiametersandtheotherwiththeequal1.5in

    diameters1res~paratelyu?d?thebubb~pairi?

    jecigor~|nthe~xperiments.Coneeqmmtly,

    fourtypicalpatternsofbubblepluminter~tioncouldbeobservedinthetwocases0fneedle pairmatches.Throughmeu

    dgthepre~survpubesradiatedbythebubblepareimmndlat~y a.ft~their'pioching-o~'andbymakinguseofaSophisticated~iotionboecillatione

    c

    0fvolumell~odeandradiusofgasbubble.thedetachmente0fthebubblePinm

    havebeta

    determinedfromtheplhude,

    equencyspectrum0fthesoundpressurepul~s.Thee~perimentaI resultsdemonstratethatthe~coustica3methodvalid|nbothoftheinteractingandnon-ioterac

    ting

    circumstancesinbubblefieldandthebubblesizemeasurementsbytha?

uIticaImethodagreewell

    withthemeasurementsfromphotographicanalysis.FinaUy,acomparisonhasbeenmadeonthe

    sttongandweakpointsoftheavousticaImethodwiththeotherdeterminationmethod~

    Keywordedetackmentsizedetermination,soundprmug-epulses,~coustica3method.bubblein-

    teraetion1bubb~p|吡岫

    1INTR0DUCTIoN

    Bubbleformationatspargersandsinglenozzlesoccu1~inmanydifferentg8B_hd(.8o?

    d)contac-

    tots.Theformationofbubblesyieldslargeinteffaciala

    abetweentwoimmisciblefluidsandthus

    increasestheefficiencyofcontactingoperations.Usually,thesizeofthebubblesformedatthese

    spargersisdi~erentfromtheaveragebubblesizeinthesecontactorsduetobubblecoalescence andbubblebreak.up.However,inaprocesssuchasdistillationanddirectcontactheattransf~. thegas(vapor)phaseisoftendispersedbybubblingthroughperforatedplatesinaHwhose depth.

    relativelyshallow.Theeriectsofcoalescenceandbreakdownarenotsignificantinthese ca8es.Theinitialbubblesizeformedatthespargercadeterminerorstronglyinfluence)the

    interfaclalareaandgasho

    d.up.Therefore.aknowledgeofthesizeofthebubbleatdetachment

    .importantinassessingthegas.1iquidheatandmasstransferrates[1.

    Manytechniquessucha8photography,ultrasonicsandva1"iouskindsofsubmergedprobe havebeenusedtodeterminebubblesizeandthedistribntionofbubblesizes.Howeve~,these techniqueshavedisadvantages,eitherintermsofthe~mitationl,

    thebubblesizer&uge(below

    onemillimeterforultrasonics)orbygivingonlythelocalsizeinformation(probe)ors~erlug fromthelimitationofthemaximumgasconcentrationwhichCallhe~yzed(photography).

Inaddition.theanalysisofphotographs_quitetediousand8l6

    r8inaccuracyfromthefact

    Received1998-02-06.a0oepted1998-10-27.

    'SupportedbYthePoet=DoctorateScienceFoundation.

    ?Towhomcorrespondencehouldbenddre~sed.

1ChineseJ.Ch.E.(vo1.r,No.21

    thatonlytwo-dimenSionalimageisobtainedwhiletheseve?distortionofbubbleinliquidisa

    commonplace.Alsothephotographictechniquecannotbeusedunderopaquesituations.Inthis

    rka?attemptwillbemadetomeasul~ethedetachinentsizeoftwobubbleplRisesfromtwo neighboringneedlesbyusinganacousticmethod.

    Gasbubblescangeneratesoundpressurepulseswhentheydetachfzomasurfaceoranorifice. Experimentalevidenceshowsthatthesoundoriginatesatthemomentwhenthebubblecloses attheendofthetermina]tube.andnotwhenitemergesandburstsatthesurface[51.Such soundpressurepulsescarrytheinformationofthedetachmentsizeofbubbles.Therefore,the detachmentsizeofbubblescanbedeterminedbypickingupthesoundpiIseBandd~odmzthem.

    However,.ftwoneighboringneedlessimultaneouslyandperiodicallyinjectbubblesintoaliquid,

    twobubbleplumeswillbeformed.Becauseeverybubbleineachoneoftheplumeswillradiate oscillatorysoundpressureofattenuationimmediatelyafterits'pinching-off',thebubblerising

    sidebysidewithitintheotherplumeortheupperbubbleaboveitinthesalneplumemust besensibleofthesoundfield.Thusthereisanacousticalinteractionbetweensuchtwobubbles presentedinasoundfieldduetothecrossscattering[.Actually,theacousticalinteraction

    betweenthebubblesriin-linesequentiallyineachbubbleplumeislessthanthatbetween thetwobubblesdetachingsidebysidefromthetwoneighboringneedlesbecausetheattenuation

ofeachbubble'sosciUation_

    quitelarge.Itisobviousthatthedecodingofthesoundpressure

    Pulunderthebubbleinteractionwillbemorecomplicatedthanthatwithnointeractionand thevnlidityofthisacousticalmethodshouldbeappraised.Re~usedthesanleprincipleto

    estimatethebubblesizedistributioninafastmovinggas.1iquidjetflowbuttheinfluenceofthe acousticalinteractionbetweenbubblesonthemeasurementswRsnottakenintoconsiderationin

    it.

    2FUNDAMENTAL

    Itiswellknownthatthesoundpressurewavesgeneratedbybubblesatthe|rdetachmentsare associatedwiththevolumepulsationsofbubbles.Thevolumepuisationofbubblegivespressure

    pulseduetotheoscillatorymotionassociatedwiththebubblewal1.Asamatteroffact,the frequencyofbubblepu~arionatitsvolumemodecanbegivenas[s]

    =

    鬻一(1)

    wherep..isthe~aricpressurefarfromthebubble,istheradiusofthebubbleinmechanical

    equilibriumatp?,thedensityofthefiquldsurroundingthebubble,istheratioofthe specificheatcapacitiesofgaswithinthebubbleandcristhegas-liquidsurfacetension.Itcan bereadilyshownthat,fortheair-waterorthenitrogen-watersystem,thecontributionofthe secondtermontheright-handsideofEq,(1)isnegligible;therefore,Eq.(1)canbeapproximated

    withoutalossofaccuracyto

    ()/

    (2)whichmeansauniquerelationshiptingbetweentheeqofvolumepulsatioitsandthe radiusofbubbleataparticularstaticpressttre.Bysubstitutingtheambientparsu~eters,suchas theatmospherep?,l_013x10Pa,thedeusityofwaterP,1000kg-m.,theratioofthespecific

    heatcapacitiesfornitrogengas,1.41intoEq.(2),asimplerelationexistsbetweenthevolume frequency,0andtheradiusofbubbleas

,0)3.(3)

    Ju_M.1999

Detacl~aentSizeMeasurementofTwoInteractingBubblePlumes147

    Here,0issubstitutedinkHzand_RI)isinmillimeters.FromEq.(3),itmbeseenthatthe radiusofbubbleisinverselyproportionaltoitsvolmnemodefI~quency,0Thebubblesize c&nbeestimated80longasthevolumemodefrequencyofbubbleisexperimentallydetermined

    fromitssoundwaveradiation.

    3TWOPLUMES0FNITR0GENGASBUBBLESRISINGINWrER:EXPERI.

    MNTANDRESUrS

    3.1Experimentalsetupandtechniques

    AschematicdescriptionoftheexperimentalsetupispresentedinFig.1.Itconsistsofan experimentalcellandfo111"measuringapparatuses:aresistance-eleetricpressuretransducer,a

    data-acquisltionandsignaldisp~ysystem.aB&K2034dyna~cspectrumanalyzerandacama.

    The~-pethneuta1cellisanopentoppedtransparentbox.appsoximatdy10crux10crux16cmin

    size,filledwithcommerciallyavailabledistilledwaterafterdegassed.Atthecenterofthecell'8

    bottom,twuneedles,connectedtoanitrogengassupply,aremonntedverticallywithcertain separation.Therearetwopairsofneedleswithdifferentmatchesofinnerdiameters,ouewith 1.5milland0.8mmiimerdiametersandtheotherwiththeequal1.5ran1innerdiameters,respect-

    ively.The~esiztance-electxicpre8getransducer(OlOkP

    )waspoisonedwithequaldistance

    of1cmawayfromthetyroneedlesanditsBenngelementwaslevelledwiththetipsoftheneedles.

    Thecellrestedonaspongecushionforvibrationisolation.Thus,twobubbleplumesofdifferen

t

    sizesorsimilarsizescanbefomedinthecellsimultaneously.

    Figure1Aschematicdescriptionoftheexplrtlsetup

    gaugepre~surecontainingsoundpulsesmeasuredbythep|嘲札retransducerwasfedto

    thedataacquisitionsystemwaitingforthelateanalysisofaconsticalinteractionbetweenbubble

    plumesononehandandtotheB&K2034dynamicspectrumanalyzerontheotherhand.Through

    thespectrumanalyzer,thesepulseswereresolvedintoamplitudeflrequencyspectrabYperforminE

    afastFouriertrandom(FFT)forthepurposeofunderstandingthefrequencycomponentsinthe

    soundwaves.SincenoartificialvibrationsaI1rceasin~oducedintotheexperimentsystem.the

    ampHtude/frequencyspectrum?

    dominatedbythesoundenergyduetothevolumepulsations

    ofthebubblesaftertheydepartedomthetipsoftheneedles.peakscorrespondingto thevolumemodefrequencyofthebubblewe

    quiteaccessibletobeidentitlediuthespectrum.

    Thus.bysubstitutingtheexperimentallydeterminedsoundfrequenc/esofthepeaksintoEq.(3),

    thebubbledetachmentsizecouldbecalcu]ated.

    Tocalibratetheacousticmeasurementofbubb~detachmentsizeandtorecordtherisetrajec- toriesofthetwububbleplumesunderinteraction,stillphotographsweretakenwithstrohe illumination.Arulergraduatedinmillimeterswasflushedwiththeneedlesforthephotographic

148ClaineBeJ.ch.1g.(Vot.r,No.2)

    scale.Thefrequencyofstrobet~Jatwa8adjustedcarefullytobecoincidentwiththegeneration'

    frequencyofbubblesinoneoftheplumes.hencealineofbubbleswithvariousshapes8eenlBto bestablysuspendedinthewaterwhenwatchingwiththenakedeye8andtheblurringofthe profilesofbubblescouldbepreventedeffectivelyfromthephotogr~plas.Additionally,byreason

    ofthebubbledistortionbeing8evel~eduringitsrise.thepicture~wereselectedtobetakenatthe

    speeialinstantswhenstilltmtternswhichshowedabubblewaB8ittinzatthetipofoneneedle withMmostsphericalslopeappeared.Thusthebubbledetachme~ltsizeCallbeestimated. 3.2/~eoustlealmeasurementanditscalibration,rudern0bubbleinteraction Whenonlyoneofthelaneedlebeingsuppliedwithnitrogengasatverylowrate,onebubble p]tmaewithrelativelylarge8epmt|0nwaBformedinthequiescentwater.Fig.2(a)showsthe soundpressurew8emittedbyalargebubbledllr.

    itsgrowthandtheconsequentdeparture

    fromthelargeneedle.Itol~ervedthat.whenebubble?inembryo8tthetipofthe

    needle.aweakcompressivewavecouldbegeneratedbythequickexpansionofthevolumeof bubble.Alo

    withthevolumeexpansionr&teaeereasinginthematurityofthebubble,the presmtreiathewaterz~coveredveryquicklyandlevelledofftotheanabientpre~ttre.Whenthe

    dynamicequilibriumofthematurebubble_

    brokendownduetotheincre~ingofthebuoy~uacy,

    thebubblebegantodetsf2afromthetipoftheneedleandradiatedanattenuatesinasoidalsound waveattheflametime.Theamplitude/frequencysDectl~ulllofthesoundpressureseriesin8ucha

    caseisshowninFig.2(b].Itisobvioustlaatauniquepeakofcentralfrequency944Itzprotrudes relntivelyhighinthespectrum.Therefore.thedetachmentdiameterofthebubblewiththe volumefrequency944ttzapproximatesto6.95millaccordingtoEq.(3).AlsoaphotographWaB

    takeninsuchacase.Throughmeaauringthebubblesizewiththeruler0?thephotograph,the

    detachmentcli~mao.terofthislargebubblecanbeevaltmteda8aabout7mm.Itcanbeseentla~

t

    themes/~ltementfromtheacousticalmethodisveryelosetotla~tfromthephotographicanalysis

    inthisearle.

    Figure2(SoundprempulJeemittedby

    -bubblodlg?itsgrm?tbtillib

    dotael~montl0maneedle

    _

    _

    :

    

    ^Ih

    Figure2(b)PowerJpeet~mdtyof

    soundpurpIllBeaashowninFIJ2(-)

    3.3ACOuIstiealm脚圃1rement8underbubbleinteraction

    3.3.1Igeedlep&mm?tinnerdiameters

    whent0needle~ofdifferentsizes(1.5?皿and0.8inlninnerdinters)were8idtae0u8ly

    suppliedwithgasandthegenerationfrecIuofbubbl~frombothofflaeneedleswustIto

    JuI?ltm

Detachmm~tSiamMegsttreme~tofTwoIntora~ingBubbleP|ttmes149

    beequal,averyinterestinginteractionpatternappearedasshowninFig. 3(a).Here,forthesake

    ofclearness,thetypicalinteractionpatternbetweenbubblesinpairfromthestillphotographs takenintheexperimentsaresketched.Fig.3(a)depictsonepatternofattractiveinteractionthat eachnallbubbleisattractedtoalargeoneimmediatelyaftertheydetachsidehvidefromthe

    tipsoftheseparateneedles.Thecorrespondingpressllrepulsesradiatedbythe1;~rgeandsmall

    bubblesinpairinthesetwoplumesareshowninFig.3(b),fromwhichitcouldbefoundthatthe detachmentoflargebubbleisallttlebitearlierthanthatofsmalloneineverybubblepairand

    thesound6eldradiatedfromthesmallbubble(B)overlapsthatfromthelargebubble(A)in timehistory.Consequently,akindofattractiveinteractionmayexistbetweenthepairedbubbles

    duetothecrossscatteringLg1.Fig.3(c)sho'wsthepowerspectrumdeamityofthesoundpressure

    seriesinFig.3(b).ItisobviousthatthesoundenergyconcentratesOiltwodifferentfrequency bandspeakingat922Hzand1428Hz,respectively.AccordingtoEq.(3),theformercorresponds

    tothelargebubble(A)of7.1illlndetachmentdiameterandthelattertothesmallbubblefB)0f 4.6illln.

    

    FigureS(i)Attractiveinteractionpattern

    betweeneachpairofbubble6ofdhTerenti'ize8

    Figure3(b)SoundpresSUrefromthe

    bubblepalra?showninF_.3(a

    2?

    2?

    1.

    -e

    1.

    O

    142SHJ

    ,.Hg

    F[SurQ3'c)powerspectrumd|j.yof

    soundwavesMshowninFig.S(b,

    IfthegenerationfrequencyofthenaUbubbles_adjustedtobetwicethatofthehrge

    bubbles,anothertypeofinteractionpatternasshowninFig.4(B)]appearsthat,foreverytwo smallbubbles(BandC)thatdetachfromthesmallneedlesequentially,therewillbeonebubble (B)bdagattractedtothelargebubble(A)whiletheotherone(c)stillverticallyalongits normaltrajectory.FromFig.4(b)whichshowsthetitlehistoryofthepressurepulsesoriginate

d

    ChlnmmJ.Ch.E.7(2)14is~(1'

Clatn~BJ.Ch.B.(Vo1.7,No.2)

    fromthelargeandsmallbubblesinsuchacase,itcanbeseenthatthereoretwotimesof 'pindaing-off'ofsm~llbubblesatregulaxintervalsbetweentwolnrgebubblesdetaclamentsand

    thedetachmentofalargebubbleisstillalittleearlierthaaathatofthesmallone.Also.sucha smallbubbleisbeingexposedtothesoundfieldfromthelargebubblewhenitradiatesthesound pressurewaveofits0w

    ?.Sothesetwobubblesofdifferentsizeswilloonsistofabubblepairwith

    aeoust|ca1interaction.TheothersmallbubblefC),however,iustradiatesitsaw?soundwav

    a8

    nolargebubbledetardasidebsidefromtheneighboringbneedleduringitssoundatelu

    i0n

    timeperiod.Consequently,thissmallbubbleriltesjnitsnormaltrectorywithi11theareaclose t0theneedlea8ifthereenootherbubblesexi~i.garoundit.ThepowersDecla'umdeJasity inFig.4(c)show8thattwosoundenergygroupspeakat991ttzand1555andthegeneration freque.eyofthelargebubblesis14ttz.AlsobyEq.(3),thedeta~nentdiameterlsofthebubbles inthiscageareestimatedabout6.6IllDaand4.2n1n1.

    Figure41(AttractiveJltltet-actionpattern

    betweencertai?bubbleoelrmof(1|t~erent,Bil

    FIg~et(b)Bodpfuref}omthe

    bubblep山翻_ho?nInIi41:a)

    |h

    PIuret(c)P?,"ectrldoml~of

    ??dwl?}?.boFjg.40')

    3.3.2Nee0/epBireIlajinnerd~蜘e

    UnderthiBcondition,plumof8imUarlargebubblesize8canbeformedintheliquid.In

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