Development of Hybrid Airlift-Jet Pump with Its Performance Analysis

18 Pages·2017·5.37 MB·English

applied
sciences
Article
Development of Hybrid Airlift-Jet Pump with Its
Performance Analysis
DanYao1,KwongiLee2,MinhoHa2,CheolungCheong2,* ID andInhiugLee3
1 SchoolofMechanicalEngineering,ShanghaiJiaoTongUniversity,Shanghai200240,China;
[email protected]
2 SchoolofMechanicalEngineering,PusanNationalUniversity,Busan46241,Korea;
[email protected](K.L.);[email protected](M.H.)
3 DongjinMotor,Busan47534,Korea;[email protected]
* Correspondence:[email protected];Tel.:[phone]
(cid:1)(cid:2)(cid:3)(cid:1)(cid:4)(cid:5)(cid:6)(cid:7)(cid:8)(cid:1)
(cid:1)(cid:2)(cid:3)(cid:4)(cid:5)(cid:6)(cid:7)
Received:8July2018;Accepted:17August2018;Published:21August2018
Abstract: Anewpump,calledthehybridairlift-jetpump,isdevelopedbyreinforcingtheadvantages
andminimizingthedemeritsofairliftandjetpumps.First,abasicdesignofthehybridairlift-jetpump
isschematicallypresented. Subsequently,itsperformancecharacteristicsarenumericallyinvestigated
byvaryingtheoperatingconditionsoftheairliftandjetpartsinthehybridpump. Thecompressible
unsteadyReynolds-averagedNavier-Stokesequations,combinedwiththehomogeneousmixture
modelformultiphaseflow,areusedasthegoverningequationsforthetwo-phaseflowinthehybrid
pump. Thepressure-basedmethodscombinedwiththePressure-ImplicitwithSplittingofOperators
(PISO)algorithmareusedasthecomputationalfluiddynamicstechniques.Thevalidityofthepresent
numericalmethodsisconfirmedbycomparingthepredictedmassflowratewiththemeasuredones.
In total, 18 simulation cases that are designed to represent the various operating conditions of
thehybridpumpareinvestigated: eightofthesecasesbelongtotheoperatingconditionsofonly
the jet part with different air and water inlet boundary conditions, and the remaining ten cases
belongtotheoperatingconditionsofboththeairliftandjetpartswithdifferentairandwaterinlet
boundaryconditions. Themassflowrateandtheefficiencyarecomparedforeachcase. Forfurther
investigation into the detailed flow characteristics, the pressure and velocity distributions of the
mixtureinaprimarypipearecompared. Furthermore,aperiodicfluctuationofthewaterflowin
themassflowrateisfoundandanalyzed. Ourresultsshowthattheperformanceofthejetorairlift
pumpcanbeenhancedbycombiningtheoperatingprinciplesoftwopumpsintothehybridairlift-jet
pump,newlyproposedinthepresentstudy.
Keywords: jetpump;airliftpump;hybridpump;two-phaseflow
1. Introduction
Apumpisadevicethatactuatesliquidsbymechanicalactions. Numeroustypesofpumpsexist
accordingtomethodsusedtoactuatethefluid. Boththeairliftandjetpumpscanbeclassifiedinto
indirecttypes,wherethedirectcontactofmechanicalpartsisnotrequiredtodrivethefluid. Airlift
pumpsoperateontheairandareinsertedintoverticalpipes,whichlowersthedensityofthefluid
mixtureandliftsit. Jetpumps(oreducator-jetpumps)useajet,oftenofsteam,tocreatealowpressure.
Thislowerpressuredrawsinthetargetfluidandpropelsitintoahigher-pressureregion. Theprimary
merit of these types of pumps is their simple operating mechanism due to their simple structure,
andtheycanoperateonill-conditionedtargetliquidsandarethusdurable. However,thedemeritof
thesepumpsistheirlowefficiency.Therefore,ouraimistodevelopanewpumpconceptbycombining
Appl.Sci.2018,8,1413;doi:10.3390/app8091413 www.mdpi.com/journal/applsci
Appl.Sci.2018,8,1413 2of18
the operating mechanisms of the airlift and jet pumps, which supplements their weakness of low
efficiency,andreinforcestheiradvantagessimultaneously.
The operating mechanism of a jet pump is based on the principle of kinetic energy exchange
ofaprimaryfluidwithasecondaryfluidinamixturechamber, aswellasdrawingthesecondary
fluid by the static pressure difference. Jet pumps can be characterized according to the types of
primary and secondary fluids as gas-gas, gas-liquid, and liquid-liquid. It has been more than a
century since the basic design of a jet pump was first introduced [1]. Initially, one-dimensional
methodswereusedtopredictthepumpperformance[2–4]. Althoughthesestudiesfacilitatedthe
basicunderstandingofthesimpleoperatingmechanismofajetpump,theycouldnotinvestigatethe
localflowphenomenonthatgenerallystronglydependsonthree-dimensionalflowcharacteristics.
Therefore,studiesusingcomputationalfluiddynamics(CFD)[5–11]andexperimental[12–16]methods
wereperformed. Toobtainmorereliableandaccuratedesignsofjetpumpsindifferentapplications,
CFD techniques are widely used owing to its reasonable cost. Some studies have focused on the
performanceofejectorsforvarioustypesofrefrigerantsusedinheatpumps[5]andejectorrefrigeration
systems [6]. Zhu[7]investigated the influence of the primary nozzle exit position and the mixing
section converging angle on the ejectors’ performance. Li [8] investigated gas–liquid ejectors by
varyingthegeometry,fluidproperty,andoperatingcondition,andcomparedthemwithasingle-phase
ejector. Fan[9]performedaglobaloptimizationtoimprovethejetpumpefficiency. Shahetal.[10,11]
investigatedthecharacteristicsofthesteamjetpumpusingsaturatedsteamandthedirect-contact
condensationmodel.
Additionally, studies using experimental and numerical approaches have been performed.
Narabayashi et al. [12,13] performed visualization experiments and developed a two-phase flow
modelfortheperformancepredictionofthenext-generationnuclearreactors. Bartosiewczetal.[14]
comparedsixdifferentturbulencemodelsandproposedtheShear-StressTransport(SST)k-ωmodel
asthemostappropriateoneforthenumericalmethodtoinvestigatesupersonicejectors. Yanetal.[15]
performed experimental studies to measure the performance of vapor–water ejectors in different
temperature conditions. Chong et al. [16] performed the optimization of the ejector shape using
analyticalandexperimentalapproaches.
Theoperatingprincipleoftheairliftpumpisrelativelysimplecomparedtothatofthejetpump.
It is a type of device that raises liquids or mixtures of liquids and solids through a vertical pipe,
partiallysubmergedintheliquid,usingthecompressedairintroducedintothepipenearthelower
end[17]. Manystudieshavebeenperformedtoinvestigatethefactorsthataffecttheperformanceof
airliftpumps. Thetypicalflowpatterninairliftpumpschangeswiththemassquantity[18],andthe
bestefficiencyislikelytooccurintheslugorslug-churnflowpattern[17,19]. Further,theeffectsof
liquidproperties[20],pipegeometry[17]orgas-injectionmethods[21,22]ontheperformanceofairlift
pumpswereinvestigated.
Indirectpumps,suchasthejetandairliftpumps,havenotbeenusedfrequentlyduetotheirless
efficiencythanthedirecttypeofpumps. However,theefficiencyofthedirecttypesofpumpsstrongly
dependsonthegapdistancebetweenanimpelleranditshousing. Asthegapdistancedecreases,
theefficiencyofdirectpumpsalsoincreases. Moderndirecttypesofpumpskeepthedistancevery
smallduetotheadvancedmodernmanufacturingtechnology,butthesmallerdistanceincreasesthe
possibilitythatsomeparticlesinliquidblockthegapandeventuallycausethefailureofthepump.
Theindirectpumpcanoperateonsuchill-conditionedliquidswithoutsufferingfromsuchproblems.
In this respect, the indirect types of pumps are more durable than the direct pumps. To develop
moreefficientdesignsofindirectpumpsandthustoincreasetheirapplicabilityinwaterpumping
applications,theconceptofhybridairlift/jetpumpisnewlyproposedintheprecedingpatent[23].
Our aim is to develop the baseline design of the hybrid airlift-jet pump and to assess its validity
intermsofitsperformanceandefficiency. Theperformanceandefficiencycharacteristicsofhybrid
airlift-jetpumpsareinvestigatedbynumericallysolvingthecompressibleunsteadyReynolds-averaged
Navier-Stokesequationswithacavitationmodel. Forsimplicity,theoperatingconditionoftheairlift
Appl. Sci. 2018, 8, x FOR PEER REVIEW 3 of 18
Appl.Sci.2018,8,1413 3of18
hybrid pump are investigated: the former eight cases belong to the operating condition of only the
jet pump with different air inlet boundary conditions and the latter ten cases belong to the operating
condiptaiortniss coofn bsiodtehr etdhues ianigrlitfhte ainnldet jbeotu pnadratrsy icno ntdhieti ohnysborfidw apteurm. Apl towgietthh edr,ifefiegrhetenetn asiirm aunladt iownactaesre sinlet
bountdhaartya rceodnedsiitginoends.t oThreep preesrefnotrtmheanvacrei oaunsdo pefefriactiienngccyo cnudritvioens sooff tthhee hhyybbrriiddp puummppa raerien vcoesmtipgaatreedd: for
theformereightcasesbelongtotheoperatingconditionofonlythejetpumpwithdifferentairinlet
each case. For further detailed investigations into the flow characteristics, the pressure and velocity
boundaryconditionsandthelattertencasesbelongtotheoperatingconditionsofboththeairliftandjet
distributions of the mixture in a primary pipe are compared. The periodic fluctuation of the
partsinthehybridpumpwithdifferentairandwaterinletboundaryconditions. Theperformanceand
secondary flow in the mass flow rate is found and analyzed.
efficiencycurvesofthehybridpumparecomparedforeachcase. Forfurtherdetailedinvestigations
In Section 2, the baseline design of a hybrid airlift-jet pump is schematically presented with its
intotheflowcharacteristics,thepressureandvelocitydistributionsofthemixtureinaprimarypipeare
relevant operating principle. In Section 3, the governing equations and the numerical methods are
compared. Theperiodicfluctuationofthesecondaryflowinthemassflowrateisfoundandanalyzed.
described. In Section 4, the detailed geometry of the pump and its computational mesh are presented
InSection2,thebaselinedesignofahybridairlift-jetpumpisschematicallypresentedwithits
with rtehleev adnettoapileerda tibnogupnrdinacriyp lec.oInndSieticotinosn. 3I,nth eSegcotvioenrn i5n,g tehqeu avtiaolnidsiatyn dotfh ethneu mneurmicaelrmicaetlh omdestahroed is
confirdmesecdri bbeyd .tIhneS ceoctmiopna4r,itshoend oetfa tilheed pgeroemdiecttriyonof rtehseuplutsm wpiatnhd thites cmomeapsuutaretidon oanlmese. sShuabresepqrueseennttleyd, the
numewriitchalt hreedseutlatisle danbodu nddiasrcyuscosinodnitsi onasr.eI npSreecsteionnte5d, thteo vaalsidseitsys ofittsh epneurmfoerrmicaalnmcee thaonddi secfofnicfiiremnecdy by
invesbtiygathtiencgo tmhpe adriestoanileodf tfhloewpr cehdiacrtaiocnterreissutilctss. wTihthe cthoencmlueassiounre ids opnreess.enSutebds eiqnu tehnet lfyi,ntahle sneuctmioenri.c al
resultsanddiscussionsarepresentedtoassessitsperformanceandefficiencybyinvestigatingthe
2. Nedwe tCaiolendceflpowt ocfh Haryacbtreirdis tAicisr.lTifhte-Jceotn Pculumsiopn ispresentedinthefinalsection.
I2n. Nthewis Csoencctieopnt,o fthHey bcroidncAeiprlti fto-fJ etthPeu mhpybrid airlift-jet pump is schematically described by
presenting its design with the relevant operating principle.
Inthissection,theconceptofthehybridairlift-jetpumpisschematicallydescribedbypresenting
itsdesignwiththerelevantoperatingprinciple.
2.1. Operating Principle of Jet Pump
2.1. OperatingPrincipleofJetPump
The schematic design of a jet pump is described in Figure 1. The law of quasi-one-dimensional
TheschematicdesignofajetpumpisdescribedinFigure1. Thelawofquasi-one-dimensional
mass conservation leads to:
massconservationleadsto:
(cid:1874)v (cid:1827)A ==(cid:1874)v (cid:1827)A ,, (1)(1)
(cid:2869)1 (cid:2869)1 (cid:2870)2 (cid:2870)2
wherwe hve irse tvhies athxeiaalx filaolwflo vwelvoecliotcyi,t ya,nadn dAA isis tthhee ccrroossss--sseeccttiioonnaalla arerae.a.E Equqautaiotino(n1 )(1a)n danthde tchoen cdoitniodnition
(cid:1827)(cid:2869) (cid:3408)A (cid:1827)1(cid:2870) >reAsu2lrte isnu ltthine tuhneeuqnueaqlu eaqlueqautiaotnio n(cid:1874)(cid:2869)v1 (cid:3407)< (cid:1874)v(cid:2870)2. .FFoorr aann iinnccoommppreresssisbilbel,ei,n ivnisvciisdc,idan, danirdro itrartoiotantailonal
flow, fltohwe ,BtherenBoeurnlloi’usl lei’qsueaqtuioatnio ins issastaistifsiefided inin ththee ffoorrmm::
11 11
(cid:1868)(cid:2869)p1++22(cid:2025)ρ(cid:1874)v(cid:2869)(cid:2870)21==(cid:1868)p(cid:2870)2++22ρ(cid:2025)v(cid:1874)22(cid:2870)(cid:2870) (2)(2)
wherwe hpe irse tphies sthtaetiscta ptircepssreusrseu raenadn dρ ρisi sththe eddeennssiittyy.. EEqquuaattiioonn ((22))a annddt hteheco cnodnitdioitniovn (cid:1874)< (cid:3407)v l(cid:1874)ea dletaod to
1 (cid:2869) 2 (cid:2870)
(cid:1868)(cid:2869) (cid:3408)p (cid:1868)1(cid:2870).> Sup2b.sSeuqbuseenqutleyn, tltyh,eth perpersessusurree (cid:1868)p(cid:2870)2 iissl olwoweretrh athnathne tahtme oastpmhoersipchperreiscs uprereps0s,uwrhe ic(cid:1868)h(cid:2868),i swthheiwcha tiesr the
inletpressure. Thepressuredifferencepumpsthewaterupwards.
water inlet pressure. The pressure difference pumps the water upwards.

FigFuigruer 1e.1 S.cShchememaatitcicss ooff aa jjeett ppuummpp..
2.2. Operating Principle of Airlift Pump
The schematic design of an airlift pump is described in Figure 2. Based on the dotted line in
Figure 2, the pressure of water, and that of the water/air mixture are the same, which can be written
as:
(cid:2025) (cid:1859)ℎ = (cid:2025) (cid:1859)ℎ (3)
(cid:3050)(cid:3028)(cid:3047)(cid:3032)(cid:3045) (cid:2869) (cid:3040)(cid:3036)(cid:3051) (cid:2870)
Appl.Sci.2018,8,1413 4of18
2.2. OperatingPrincipleofAirliftPump
The schematic design of an airlift pump is described in Figure 2. Based on the dotted line in
Appl. Sci. 2018, 8, x FOR PEER REVIEW 4 of 18
Figure2,thepressureofwater,andthatofthewater/airmixturearethesame,whichcanbewrittenas:
Because the mixture density is lower than the pure water density, Equation (3) results in ℎ (cid:3408)
(cid:2870)
ρ gh = ρ gh (3)
ℎ . This difference causes water to be pumwapteerd u1p. mix 2
(cid:2869)
Appl. Sci. 2018, 8, x FOR PEER REVIEW 4 of 18
Because the mixture density is lower than the pure water density, Equation (3) results in ℎ (cid:3408)
(cid:2870)
ℎ . This difference causes water to be pumped up.
(cid:2869)

FFiigguurree 22.. SScchheemmaattiiccss ooff aann aaiirrlliifftt ppuummpp..
2.3. OBpeecraautisnegt hPerimnciixptlue roef dHeynbsriitdy Pisumlopw erthanthepurewaterdensity ,Equation(3)resultsinh > h .
2 1
ThisdifferencecauseswatertobFeipguurme 2p. eSdchuemp.atics of an airlift pump.
A schematic diagram of the hybrid airlift-jet pump is shown in Figure 3. As described above,
the driving force of the jet pump is the pressure difference induced by the nozzle (ejector), while that
2.23..3O. OpepreartaitninggP Prrininccipipllee ooff HHyybbrriidd PPuummpp
of the airlift pump is the buoyancy induced by the lower density of the mixture. The basic idea of the
AAs cshchememaatitcicd diiaaggrraamm ooff tthhee hhyybbrriidd aaiirrlliifft-tj-ejet tppuummpp isi sshsohwown nini nFiFguigrue r3e. 3A.sA dsesdcerisbcerdib aebdoavbeo, ve,
hybrid airlift-jet pump, as schematically depicted in Figure 3, is to increase its efficiency by
thtehed rdirviivninggf oforcrceeo offt thhee jjeett ppuummpp iiss tthhee pprreessssuurree ddififfefererenncec einidnudcuecde dbyb tyhteh neonzozlzez (leeje(ectjeocrt)o, wr),hwileh tihleatt hat
arranging these two driving forces to act complementarily. The upper and lower passages guide the
ofotfh tehea iarilrilfitftp puummppi sist thhee bbuuooyyaannccyy iinndduucceedd bbyy tthhee lolowweer rddenensistiyt yofo tfhteh memixtiuxtrue.r eT.hTe hbeasbica siidceiad oefa tohfe the
air flow from an air compressor to drive the jet and airlift parts, respectively. The additional
hyhbyrbirdida iraliirflti-fjte-tjept upmupm,pa,s ascsh secmheamticaatlilcyaldlye pdicetpeidcteind Fiing uFrieg3u,reis 3to, iins ctroe aisnecirtesaesfefi citise necfyficbiyenacryr anbyg ing
advantage of the hybrid pump is its versatile applicability to various operating environments, while
thaersreantwgiongd rtihveisneg tfwoorc desritvoinagc tfocorcmesp tloem acetn ctoamrilpyl.eTmheenutaprpileyr. aTnhde ulopwpeerr panasds alogweserg upaidsseatghees agiurifldoew thfer om
retaining its high efficiency by controlling the flow rate entering each passage. For example, when
air flow from an air compressor to drive the jet and airlift parts, respectively. The additional
anaircompressortodrivethejetandairliftparts,respectively. Theadditionaladvantageofthehybrid
the suction head is high, all the air from the compressor is initially supplied to the airlift part to
advantage of the hybrid pump is its versatile applicability to various operating environments, while
pumpisitsversatileapplicabilitytovariousoperatingenvironments,whileretainingitshighefficiency
overcome such a high head height. As the water column approaches the jet part, some of the air is
retaining its high efficiency by controlling the flow rate entering each passage. For example, when
bycontrollingtheflowrateenteringeachpassage. Forexample,whenthesuctionheadishigh,allthe
diverted to the jet part to drive the water to the exit of the outlet pipe. After this transient state, the
the suction head is high, all the air from the compressor is initially supplied to the airlift part to
airfromthecompressorisinitiallysuppliedtotheairliftparttoovercomesuchahighheadheight.
operating condition of the hybrid pump is set to be in the best efficiency or performance condition. A
overcome such a high head height. As the water column approaches the jet part, some of the air is
Asthewatercolumnapproachesthejetpart,someoftheairisdivertedtothejetparttodrivethe
prdiimvearrtye dg tooa tlh oef j etth pe aprtr etos ednrti vset uthdey wisa tteor tion vtheest eigxaitt eo ft thhee poeurtfleotr mpiapne.c eA fatnerd t heifsf itcriaennsciyen ot fs ttahtee, hthyeb rid
watertotheexitoftheoutletpipe. Afterthistransientstate,theoperatingconditionofthehybrid
puopmepra itnin vga croionudsit ioopne orfa ttihneg h cyobnriddi tpiounmsp. is set to be in the best efficiency or performance condition. A
pumpissettobeinthebestefficiencyorperformancecondition. Aprimarygoalofthepresentstudy
primary goal of the present study is to investigate the performance and efficiency of the hybrid
istoinvestigatetheperformanceandefficiencyofthehybridpumpinvariousoperatingconditions.
pump in various operating conditions.

Figure 3. Schematic design of a hybrid pump.
Figure 3. Schematic design of a hybrid pump.
3. Governing Equations and FNiguumree3ri.cSaclh Memeatthicoddess ignofahybridpump.
3. GTohvee rncionmg pErqeussaitbiolen su annsdt eNaduym eRriecyanl Moldetsh-aovdesr aged Navier-Stokes equations are used as the
governTihneg ceoqmuaptrieosnssib lfeo r utnhset efaldoyw Rine ytnhoel dhsy-abvreidra gpeudm pN.a Tviheer -Shtoomkeosg eenqeuoautiso nms ixatrue reu smedo daesl , twheh ich
asgsouvmerensi ntgh aetq euaactiho npsh faosre tthrea vfleorwse si na tt hde ifhfyerbernidt pvuelmocpi.t iTesh eb uhot mwoitghe nae oluocs aml eixqtuuirlei bmrioudme l,o wvehri cshh ort
spaasstiuaml leesn tghtaht secaaclhes p, hisa sues etdra vfoerr stehse a ttw doi-ffpehreanset vfleolwoc.i tTiehse bmuti xwtuitrhe ma olodceall ceoqnusiliisbtrsi uomf t hoev ecro nshtionrut ity,
spatial length scales, is used for the two-phase flow. The mixture model consists of the continuity,
Appl.Sci.2018,8,1413 5of18
3. GoverningEquationsandNumericalMethods
ThecompressibleunsteadyReynolds-averagedNavier-Stokesequationsareusedasthegoverning
equationsfortheflowinthehybridpump. Thehomogeneousmixturemodel,whichassumesthat
eachphasetraversesatdifferentvelocitiesbutwithalocalequilibriumovershortspatiallengthscales,
isusedforthetwo-phaseflow. Themixturemodelconsistsofthecontinuity,momentum,andenergy
equationsforthemixture,andthevolumefractionequationsforthesecondaryphase. Thecontinuity
equationforthemixturecanbedescribedas:
∂ ∂
(ρ )+ (ρ u ) =0 (4)
∂t m ∂x m m,i
i
whereu isthemass-averagedmixturevelocityvectorandρ isthemixturedensity. Themomentum
m m
equationforthemixturecanbeobtainedbyaddingtheindividualmomentumequationsforallphases
andbeexpressedas:
∂(ρ u )+ ∂ (cid:0)ρ u u (cid:1)
∂t m m,i ∂xj m m,i m,j
= −∂(cid:104)∂xpi +(cid:16) ∂∂xj(cid:104)µm(cid:16)∂∂uxm(cid:17)j,i + ∂∂(cid:16)uxmi,j − 32δij∂∂uxm(cid:17)k,k(cid:17)(cid:105)(cid:105)+ρm→g +→F (5)
+ ∂ µ ∂um,i + ∂um,j − 2 ρ k+ ∂um,k δ
∂xj t ∂xj ∂xi 3 m ∂xk ij
→
wherepisthestaticpressure,µ istheviscosityofthemixture,µ istheturbulenceviscosity, g isthe
m t
→
gravity,and F isthebodyforce. Theenergyequationforthemixtureassumesthefollowingform:
∂ ∑n ∑n (cid:16) → (cid:17) (cid:16) (cid:17)
(α ρ E )+∇· α v (ρ E +p) = ∇· k ∇T (6)
∂t k k k k k k k eff
k=1 k=1
wherek istheeffectiveconductivity,andTisthetemperature. Fromthecontinuityequationforthe
eff
secondaryphasep,thevolumefractionequationforthesecondaryphasepcanbeobtained:
∂ (cid:0) (cid:1) ∂ (cid:0) (cid:1)
α ρ + α ρ u =0 (7)
∂t p p ∂x p p m,i
i
Thestandardk-ε modelisusedfortheturbulencemodelandthestandardwallfunctionwas
employed for the near-wall treatment. The effects of turbulence models on two phase numerical
solutions were intensively investigated in the preceding study [24]. The standard k-ε turbulent
modelisbasedonthetransportequationsfortheturbulentkineticenergykanditsdissipationrateε,
respectively. Thetransportequationscanbewrittenas:
(cid:34)(cid:18) (cid:19) (cid:35)
∂ ∂ ∂ µ ∂k
(ρ k)+ (ρ ku ) = µ + t +G +G −ρ ε−Y . (8)
∂t m ∂x m m,i ∂x m σ ∂x k b m m
i j k j
∂ ∂ ∂ (cid:34)(cid:18) µ (cid:19) ∂ε (cid:35) ε ε2
(ρ ε)+ (ρ εu ) = µ + t +C (G +C G )−C ρ (9)
∂t m ∂x m m,i ∂x m σ ∂x 1εk k 3ε b 2ε m k
i j ε j
In these equations, G represents the generation of turbulence kinetic energy due to the
k
mass-averaged mixture velocity gradients. G is the generation of turbulence kinetic energy due
b
tobuoyancy. Y representsthecontributionofthefluctuatingdilatationincompressibleturbulenceto
m
theoveralldissipationrate. C ,C andC areconstants. σ andσ aretheturbulentPrandtlnumbers
1ε 2ε 3ε k ε
forkandε,respectively.
The pressure-based solver in ANSYS Fluent (version 18.2) is used and the pressure–velocity
coupling algorithm is chosen as the PISO to obtain a high computational efficiency. The coupling
between these variables is achieved via velocity and pressure corrections to enforce both global
Appl.Sci.2018,8,1413 6of18
and local mass conservation. The PRessure STaggering Option (PRESTO!) scheme is used for
pressure. First-order upwind schemes are used for density, momentum, energy, volume fraction,
turbulencekineticenergyandturbulentdissipationrate. Thefirst-orderimplicitschemeisusedfor
transientformulation.
Forthetransientcalculation, thetimestepsizewassetas0.001stoobtainanacceptableCFL
number. Theconvergedcriteriaaresetastheresidualof10−3andthemaximumiterationnumberis
setas20. Monitorsofthemassflowrateattheinletsandoutletaresetuptoassesstheperformance
aAnppdl. eSfcfii. c2i0e1n8,c 8y, xo FfOthRe PpEEuRm RpE,VaIEnWd t oobserveanypotentialunsteadycharacteristics. 6 of 18
44.. MMooddeellss ooff TTaarrggeett PPuummpp
44..11.. GGeeoommeettrryy EEjjeeccttoorr
TThhee bbaasseelilnineed edseisgingno fothf ethhey bhryidbraiidr liafitr-jleifttp-juetm ppuimssph oisw snhionwFnig uinre F4i,gwurheic 4h, pwrehsiecnht sptrheesednettsa iltehde
vdieetwailoefdt hveieewje cotfo trhien etjheectjoetr pina rtth.eT jheet poavretr.a Tllhgee oovmeeratrlilc gsehoampeetarnicd sihtaspdee taanilde ditsd dimeteanisleiodn dsiomfethnesiponusm opf
athree dpeutemrmp ianreed dbeytefromllionwedin gbyth feolrleoswulitnpgr tehsee nrteesdulitn pthreespenretvedio uins tshtued pyr.eTvhioeules nsgtuthdyof. Tthheew leantegrthsu ocft itohne
pwipateeirs ssuecttaiosn1 pmip.eT hise sdeitm aesn 1s imon. sTahned dnimamenessioofntsh aengde onmametersi copf atrhaem geetoemrseatrreica plsaoralimsteetderisn aTraeb alels1o.
Nlisotteedt hina tTtahbelea i1r. nNoozztele thinalte tthdei aamir enteorzzisles eintlteot bdeiathmeestaemr ies asestt htoe boeu ttehred siaammee taesr tohfet hoeutaeirr dcoiammperteesrs oorf
uthsee daiirn ctohmepexrepsesroimr uesnetd. in the experiment.

Figure 4. Schematics of a hybrid airlift-jet pump (units: mm; red-colored numbers and symbols
Figure4.Schematicsofahybridairlift-jetpump(units:mm;red-colorednumbersandsymbolspresent
present dimensions of a nozzle).
dimensionsofanozzle).
Table 1. Geometry dimensions of a hybrid airlift-jet pump (units: mm).
Table1.Geometrydimensionsofahybridairlift-jetpump(units:mm).
Air nozzle inlet diameter 6.5
AirAnior znzoleziznllee tddiaiammeetteerr 6.524
Airnozzlediameter 24
Air nozzle exit diameter 8
Airnozzleexitdiameter 8
Water nozzle diameter 50
Waternozzlediameter 50
DiDstisatnancece bbeettwweeeenn aann aaiirrn noozzzlzelee xeixtiatn adnadm ai xminigxisnegct sioenction 25 25
MMiixxiinnggs seecctitoinond idaimameteerter 24 24
DDiiffffuusseerro ouutlteltedt idaimaemteerter 34 34
Mixingsectionanddiffuserlength 200
Mixing section and diffuser length 200
4.2. MeshandBoundaryConditions
4.2. Mesh and Boundary Conditions
Toevaluatetheindependenceofnumericalsolutionstothemeshused,agridrefinementstudyis
To evaluate the independence of numerical solutions to the mesh used, a grid refinement study
carriedout. TheboundaryconditionsofCaseNo. 7inTable2areapplied. Figure5showstheresult
is carried out. The boundary conditions of Case No. 7 in Table 2 are applied. Figure 5 shows the
intermsofthewatermassflowrateattheoutletandthenumberofgridsused. Basedonthisresult,
result in terms of the water mass flow rate at the outlet and the number of grids used. Based on this
ameshof1.5milliontetrahedronelements,asshowninFigure6a,isusedinthecomputationdomainin
result, a mesh of 1.5 million tetrahedron elements, as shown in Figure 6a, is used in the computation
alloffollowingcomputations. Themeshgeometriesattheairinletandtheairnozzleexitaredensified
domain in all of following computations. The mesh geometries at the air inlet and the air nozzle exit
toobtainamoreprecisesimulationofthelocaldetailedflowcharacteristics,asshowninFigure6b,c.
are densified to obtain a more precise simulation of the local detailed flow characteristics, as shown
in Figure 6b,c. The mesh size is set to be around 0.25 mm for the air inlet and the air nozzle, and 2.5
mm for the other parts. The maximum y-plus (y+) values are around 500 in the nozzle and 800 in the
diffuser.
Appl.Sci.2018,8,1413 7of18
Themeshsizeissettobearound0.25mmfortheairinletandtheairnozzle,and2.5mmfortheother
parts. Themaximumy-plus(y+)valuesarearound500inthenozzleand800inthediffuser.
Table2.Casesandtheirboundaryconditions.
TotalPressureatAirInlet TotalPressureatWaterInlet VolumeFractionofWaterat
CaseNo.
(kPa)-AirCompressor (kPa)-WaterHeight WaterInlet-AirliftPump
1 100
2 200
1 1
3 300
4 400
5 100
6 200
6 1
7 300
8 400
9 100
10 200
1 0.5
11 300
12 400
13 300 6 0.5
14 0.05
15 0.1
16 300 1 0.2
17 0.7
18 0.9
Thetotalpressureboundaryconditionswereappliedattheinletsectionoftheairnozzleandthe
verticalpipe. Therangeoftotalpressureattheairinletisdeterminedaccordingtothecapacityofair
compressorusedinthevalidationexperimentshowninFigure7. Thetotalpressureatthewaterinlet
isdeterminedbyincludingtheeffectsofsuctionpipelengthsubmergedinwater;thetotalpressuresof
1kPaand6kPacorrespondtothesubmergedsuctionpipeheighth (showninFigure7g)of0.1mand
s
0.6m,respectively. However,thevolumefractionofwateratthewaterinlet,whichdependsonthe
capacityofaircompressor,thegeneratedcavitationtypesandthewaterflowvelocity(watermassflow
rate)arerelativelydifficulttodetermine. Therefore,therangeofwatervolumefractionatthewater
inletissettoinvestigatetheeffectsofairliftpumpontheoverallperformanceofhybridpumpinits
wideoperationrange. Altogether,eighteencasesareinvestigatedincludingtheoperatingconditionsof
onlythejetpart,andboththeairliftandjetparts. Forthejet-pump-onlyoperation,thetotalpressure
attheairinletisvariedalongwithspecifyingthevolumefractionofairasone. Atthewaterinlet,
thevolumefractionofairisspecifiedaszero. Inthehybridmode,forsimplicity,thevolumefraction
ofair,aswellasthetotalpressureatthewaterinlet,isvariedtosimulatetheeffectsoftheairliftpump
andthesubmergedsuctionpipeheight. Thetotalpressureequationcanbewrittenas:
(cid:18) γ−1 (cid:19)γ/(γ−1)
p = p 1+ M2 (10)
T s
2
wherep isthetotalpressure,p isthestaticpressure,MistheMachnumberandγistheratioof
T S
specificheats.
TheboundaryconditionsofeachcasearelistedinTable2. Thetotalpressureboundaryconditions
aresetattheairandwaterinlets. Attheoutlet,thestaticpressureconditionisappliedandsetaszero
gaugepressure. Thetotalpressurerangeattheairinletisvariedfrom100kPato400kPa. Thecases
denotedbyNo. 1–8aresettosimulatetheinfluenceoftheairinletpressurefordifferentwaterinlet
pressures,whicharedeterminedtorepresentdifferentsuctionlengths(interpretedasthewatersuction
pipe being buried into water or reducing the length of the suction pipe). Cases No. 9–12 are set
Appl. Sci. 2018, 8, x FOR PEER REVIEW 7 of 18
Appl.Sci.2018,8,1413 8of18

to investigate the performance of the hybrid airlift-jet pump in different air inlet pressures; Cases
Figure 5. The grid refinement study.
No. 14–18aresettodifferentvolumefractionsofwateratthewaterinlet. CaseNo. 13isoneexample
where both the abovementioned conditions are applied simultaneously. The hybrid initialization
Table 2. Cases and their boundary conditions.
methodthatsolvestheLaplaceequationisused.
Appl. Sci. 2018, 8, x FOR PEER REVIEW 7 of 18
Case Total Pressure at Air Inlet Total Pressure at Water Inlet Volume Fraction of Water at Water
No. (kPa)-Air Compressor (kPa)-Water Height Inlet-Airlift Pump
1 100
2 200
1 1
3 300
4 400
5 100
6 200
6 1
7 300
8 400
9 100
10 200
1 0.5
11 300
12 400
13 300 6 0.5
14 0.05
15 0.1
16 300 1 0.2

17 0.7
18 Figure 5. The grid refinement study. 0.9
Figure5.Thegridrefinementstudy.

Table 2. Cases and their boundary conditions.
Case Total Pressure at Air Inlet Total Pressure at Water Inlet Volume Fraction of Water at Water
No. (kPa)-Air Compressor (kPa)-Water Height Inlet-Airlift Pump
1 100
2 200
1 1
3 300
4 400
5 100
6 200
6 1
7 300
8 400
9 100
10 200
Appl. Sci. 2018, 8, x FOR PEER REVIEW 1 0.5 8 of 18
11 300
12 400 (a)
13 300 6 0.5
14 0.05
15 0.1
16 300 1 0.2
17 0.7
18 0.9

(b) (c)
Figure6.Meshgeometriesofapumpmodel:(a)volumemeshesoftotaldomain;(b)volumemeshes
Figure 6. Mesh geometries of a pump model: (a) volume meshes of total domain; (b) volume meshes
withthezoomednozzlepart;(c)volumemesheswiththeinletpart.
with the zoomed nozzle part; (c) volume meshes with the inlet part.

The total pressure boundary conditions were applied at the inlet section of the air nozzle and
(a)
the vertical pipe. The range of total pressure at the air inlet is determined according to the capacity of
air compressor used in the validation experiment shown in Figure 7. The total pressure at the water
inlet is determined by including the effects of suction pipe length submerged in water; the total
pressures of 1 kPa and 6 kPa correspond to the submerged suction pipe height ℎ (shown in Figure
(cid:3046)
7g) of 0.1 m and 0.6 m, respectively. However, the volume fraction of water at the water inlet, which
depends on the capacity of air compressor, the generated cavitation types and the water flow
velocity (water mass flow rate) are relatively difficult to determine. Therefore, the range of water
volume fraction at the water inlet is set to investigate the effects of airlift pump on the overall
performance of hybrid pump in its wide operation range. Altogether, eighteen cases are investigated
including the operating conditions of only the jet part, and both the airlift and jet parts. For the
jet-pump-only operation, the total pressure at the air inlet is varied along with specifying the volume
fraction of air as one. At the water inlet, the volume fraction of air is specified as zero. In the hybrid
mode, for simplicity, the volume fraction of air, as well as the total pressure at the water inlet, is
varied to simulate the effects of the airlift pump and the submerged suction pipe height. The total
pressure equation can be written as:
(cid:2011)−1 (cid:3082)⁄(cid:4666)(cid:3082)(cid:2879)(cid:2869)(cid:4667)
(cid:1868) =(cid:1868) (cid:3436)1+ (cid:1839)(cid:2870)(cid:3440) (10)
(cid:3021) (cid:3046) 2
where pT is the total pressure, pS is the static pressure, M is the Mach number and γ is the ratio of
specific heats.

(a) (b)
Appl. Sci. 2018, 8, x FOR PEER REVIEW 8 of 18

(b) (c)
Figure 6. Mesh geometries of a pump model: (a) volume meshes of total domain; (b) volume meshes
with the zoomed nozzle part; (c) volume meshes with the inlet part.
The total pressure boundary conditions were applied at the inlet section of the air nozzle and
the vertical pipe. The range of total pressure at the air inlet is determined according to the capacity of
air compressor used in the validation experiment shown in Figure 7. The total pressure at the water
inlet is determined by including the effects of suction pipe length submerged in water; the total
pressures of 1 kPa and 6 kPa correspond to the submerged suction pipe height ℎ (shown in Figure
(cid:3046)
7g) of 0.1 m and 0.6 m, respectively. However, the volume fraction of water at the water inlet, which
depends on the capacity of air compressor, the generated cavitation types and the water flow
velocity (water mass flow rate) are relatively difficult to determine. Therefore, the range of water
volume fraction at the water inlet is set to investigate the effects of airlift pump on the overall
performance of hybrid pump in its wide operation range. Altogether, eighteen cases are investigated
including the operating conditions of only the jet part, and both the airlift and jet parts. For the
jet-pump-only operation, the total pressure at the air inlet is varied along with specifying the volume
fraction of air as one. At the water inlet, the volume fraction of air is specified as zero. In the hybrid
mode, for simplicity, the volume fraction of air, as well as the total pressure at the water inlet, is
varied to simulate the effects of the airlift pump and the submerged suction pipe height. The total
pressure equation can be written as:
(cid:2011)−1 (cid:3082)⁄(cid:4666)(cid:3082)(cid:2879)(cid:2869)(cid:4667)
(cid:1868) =(cid:1868) (cid:3436)1+ (cid:1839)(cid:2870)(cid:3440) (10)
(cid:3021) (cid:3046) 2
Appl.wSchi.e2r0e1 8p,T8 i,s1 4th13e total pressure, pS is the static pressure, M is the Mach number and γ is the ratio of9 of18
specific heats.
Appl. Sci. 2018, 8, x FOR PEER REVIEW 9 of 18

(a) (b)

(c) (d)

(e) (f)

(g)
Figure 7. Experiment using the prototype hybrid pump: (a) prototype of hybrid pump; (b) jet pump
Figure7.Experimentusingtheprototypehybridpump:(a)prototypeofhybridpump;(b)jetpump
part; (c) airlift pump part; (d) water tank; (e) air compressor; (f) prototype hybrid pump connected
part;(c)airliftpumppart;(d)watertank;(e)aircompressor;(f)prototypehybridpumpconnected
with an air compressor in water tank; and (g) schematics of an experimental setup.
withanaircompressorinwatertank;and(g)schematicsofanexperimentalsetup.
The boundary conditions of each case are listed in Table 2. The total pressure boundary
conditions are set at the air and water inlets. At the outlet, the static pressure condition is applied
and set as zero gauge pressure. The total pressure range at the air inlet is varied from 100 kPa to 400
kPa. The cases denoted by No. 1–8 are set to simulate the influence of the air inlet pressure for
different water inlet pressures, which are determined to represent different suction lengths
(interpreted as the water suction pipe being buried into water or reducing the length of the suction
pipe). Cases No. 9–12 are set to investigate the performance of the hybrid airlift-jet pump in different
air inlet pressures; Cases No. 14–18 are set to different volume fractions of water at the water inlet.
Appl.SAcip.p2l.0 S1c8i,. 280,1184,1 83, x FOR PEER REVIEW 10 of 1180 of18
Case No. 13 is one example where both the abovementioned conditions are applied simultaneously.
5. ResTuhlet shyabnrdidD iniistciauliszsaitoionn method that solves the Laplace equation is used.
5. Results and Discussion
5.1. ValidationofNumericalMethods
T5o.1v. Valaildidaatteiotnh oef cNuurmreenritcanl uMmetehroidcsa lmethods,experimentsusingtheprototypehybridpumpshown
inFigure7areperformed. TheaircompressorofSP5-150-5[25]isusedandcancompressesairup
To validate the current numerical methods, experiments using the prototype hybrid pump
to9.0sbhoawr.nT ihne Fpigruorteo t7y apree hpeyrbforirdmepdu. mThpe iasirc oconmnepcrteesdsotro oft hSeP5a-i1r5c0o-5m [2p5r]e isss uosretdo apnrdo cvaind ecotmhepraeisrsseos urce
totheaijer tuapn tdo a9i.0r lbifatrp. Tarhtes .pAromtootynpge thhyebcriads epsulmispt eids cionnTnaebctleed2 t,oC tahsee asiro fcoNmop.r5es–s8orth toa tprreopvridesee tnhte tahier sole
operastoiounrcoe ftoth teheje jtetp aanrtdf aoirrltihfte psaurtbsm. Aemrgoendgh tehieg chatsoesf 0li.s6temd ianr eTasbellee c2t,e Cdafsoers coof mNpo.a 5ri–s8o tnh.aFt irgeuprrees7ensth ows
thewtahtee rsotlaen okp,ethraetiaoinr ocof mthpe rjeets spoarrta nfodr tthhee psurbomtoetrygpeed hhyebigrhidt opfu 0m.6 pmc oanren eseclteecdtetdo ftohre caoimrpcaormisopnre. ssor,
togethFeigruwrei t7h sthhoewssc htheem waattiecrs toafntkh, etheex apier rciommepnrteaslssoer taunpd. tThhe epsrotatotitcypper ehsysburried aptutmhep icnolnenteocftethd etoje tthpe ump
air compressor, together with the schematics of the experimental setup. The static pressure at the
ismeasuredbyusingthemanometerofP110[26],whichcanbemeasuredupto1MPa,andthewater
inlet of the jet pump is measured by using the manometer of P110 [26], which can be measured up to
massflowrateismeasuredbyweighingthewaterexpelledfromthepumpduring10s.
1 MPa, and the water mass flow rate is measured by weighing the water expelled from the pump
Figure 8 compares the variation in static pressure at the inlet of the airflow versus the water
during 10 s.
flowratebetweentheexperimentalandcomputationresults. Althoughthedifferencebetweenthe
Figure 8 compares the variation in static pressure at the inlet of the airflow versus the water
tworfelosuwl trsatien cbreetwaseeesn athset heexpsetraitmicenptrael sasnudr ecoimncpruetaasteiosn, aregsuolotsd. Aagltrheoeumghe nthteb detifwfeereenncteh beettwweoenr etshue ltsis
foundtwino treersumltss oinfctrheeasiensc ares athsien sgtattriecn pdreossfuwrea tinercrmeaasesss, flao gwoorda taegraetetmheenot ubteltewt,eaens tthhee atwiroi nrelseutlptsr eiss sure
increafosuesn.d Tinh eterlamrsg eorf tdhief fienrcerenacseinagt ttrheendh oigf hwearteari rmianslse ftlopwre rsastuer aet stheee moustlteot, baes tdhue eaitro intlheet pfarecststuhrea tthe
numeirniccraelasseims. uTlhaet iloanrgaers sduifmfeeresntchee acto tnhset hanigthteort aailrp inrelests uprreesasutrteh esewematse troi nbele dt,uwe htoi ltehteh feactto tthaaltp trhees sure
inthenuexmpeerirciaml esinmtudlaetciroena assessuwmeitsh thaer ceodnustcatniot ntoitnal tphreesssuubrem aet rthgee dwastuecrt iinolnet,p wipheileh ethige htottwal hperensswuaret erin
in the experiment decreases with a reduction in the submerged suction pipe height when water in
the tank is pumped out. The more realistic boundary condition may be needed to reproduce the
the tank is pumped out. The more realistic boundary condition may be needed to reproduce the
experimentalconditionmoreclosely. However,sincetheaimofpresentstudyistoassesstherelative
experimental condition more closely. However, since the aim of present study is to assess the
performanceandefficiencyofthehybridpumpinvariousoperationconditions,thevalidationofthe
relative performance and efficiency of the hybrid pump in various operation conditions, the
presentnumericalmethodissufficientinthisrespect.
validation of the present numerical method is sufficient in this respect.

Figure 8. Comparison of predicted water flow rate with measured data according to air inlet pressure.
Figure8.Comparisonofpredictedwaterflowratewithmeasureddataaccordingtoairinletpressure.
5.2. Performance and Efficiency of Hybrid Pump
5.2. PerformanceandEfficiencyofHybridPump
Figure 9a,b shows the average mass flow rate of the water versus the average mass flow rate of
Fthigeu arier 9foar,b asllh oofw tsheth ceaasevse raangde tmhea sasveflroawge rmataesos fftlohwe wraattee rofv ethrseu wsathteer avveersruags ethme awssatfleor wvorlautmeeo fthe
airforfraalcltioofnt ahte thcae swesataenr dintlhete faovr ethrae gheybmriads scaflsoesw, rreastpeecotfivtheley.w Aast esrhovwerns uins Cthaesew Naote. r1,v tohleu mmaessf rfalocwtio nat
rate of water is zero, implying that the airflow is not sufficiently strong to pump the water to 0.9 m
thewaterinletforthehybridcases,respectively. AsshowninCaseNo. 1,themassflowrateofwater
high. For the other cases, the water mass flow rate increases with the air mass flow rate. In Cases No.
iszero,implyingthattheairflowisnotsufficientlystrongtopumpthewaterto0.9mhigh. Forthe
5–8, which are set to simulate a shorter suction height of 0.4 m, the air mass flow rate does not
othercases,thewatermassflowrateincreaseswiththeairmassflowrate. InCasesNo. 5–8,whichare
settosimulateashortersuctionheightof0.4m,theairmassflowratedoesnotchangeenormously
inthesameairinletboundarycondition,whilethewatermassflowrateisincreasedsignificantlyin
comparisonwithCasesNo. 1–4. Thisrelativelylargermassflowrateisduetothelessworkrequired
toobtaingravitationalpotentialenergywithalmostthesameenergyfromtheairflow. Inthehybrid