Embed Size (px)
Citation preview
295
AdvancesinProductionEngineering&Management ISSN1854‐6250
Volume15|Number3|September2020|pp295–306 Journalhome:apem‐journal.org
https://doi.org/10.14743/apem2020.3.366 Originalscientificpaper
Computational analysis of cavitation at the tongue of the volute of a centrifugal pump at overload conditions
Hu, Q.a, Yang, Y.a, Cao, W.a,* aResearch Institute of Fluid Engineering Equipment Technology, Jiangsu University, P.R. China
A B S T R A C T A R T I C L E I N F O
Volutepumpisthemostcommonusedcentrifugalpump.Ascavitationhighlycontributes to deteriorating the performance of the pump, anti‐cavitationperformanceisoneofitsdesignspecifications.Toclarifythecavitationevolu‐tionatthetongueofthevoluteofacentrifugalpumpatoverloadconditionsanditsinfluenceontheflowfieldintheimpeller,numericalsimulationwithANSYSCFDandahydraulictestwereconductedonavolutepumpatseveralflowratesaboveoptimalvalue.Thecavitydistributionandthebladeloadingdistributionwereanalyzed.Andthecharacteristicsofthepressurefluctuationofthemonitoringpointslocatedinvolutecasingwereobtainedandcomparedwith each other. Results showed that cavitation may first emerge at thetongueratherthanthe impeller inletatoverloadconditions.Thealternativestressresultingfromperiodicalradialforceincreasesobviouslyastheextentofcavitationatthetongue.Meanwhile,themeancavitylengthgrowsaseachblade comes close to the tongue, and causes a decrease in performancebe‐causeofareductionorclosureofflowpassages.Thepressurepulsationinthevolute is consistent with the blade passing frequency whether cavitationoccursornot,while thepulsation intensity increasesobviouslyaftercavita‐tioninception.Fromthefirstsectiontotheeighthsectionofvolute,thepulsa‐tion intensity of impeller outlet decreases gradually. The results are thencomparedtoprovideareferencefortheoptimumdesignoftheanti‐cavitationperformanceofcentrifugalpump.
©2020CPE,UniversityofMaribor.Allrightsreserved.
Keywords:Centrifugalpump;Numericalsimulation;Computationalfluiddynamics(CFD);Tongue;Cavitation;Bladeloading;Pressurefluctuation
*Correspondingauthor:[email protected](Cao,W.)
Articlehistory:Received18August2020Revised14September2020Accepted16September2020
1. Introduction
Thegenerationofcavitationcancauseseveredamageinhydraulicmachinery.Inliquidflows,thevaporizationof liquid is generallydue to the localpressurebecomes lower than the saturatedvaporpressure [1].Volutepumpsareamong themostused centrifugalpump types,mainly inmining, petrochemical, and paper industries. Cavitation is a major undesirable phenomenon,whichoccursintheoperationofcentrifugalpumps[2].Theoccurrenceofcavitationinpassagesaffectstheenergychangebetweenthewallsurfaceandliquid,whichleadstothebreakdownofperformance, surface erosion, and even the equipment failure [3, 4]. In case of centrifugalpumps,thecavitationinceptiongenerallytakesplaceonthesuctionsurfaceofthebladesneartheirleadingedge,andthecavitypresentsanasymmetricalfeature,whichiscausedbytheinter‐actionbetweenthebladeandtongueofvolute.
Onthisbasis,cavitationincentrifugalpumpshavebeenextensivelystudied[5‐12].Moststud‐ies mainly focused on the cavitation detection in impellers and performance improvementthroughtheapplicationofcavitatingflowsimulation.However,onlyafewstudiesonthecavita‐
Hu, Yang, Cao
296 Advances in Production Engineering & Management 15(3) 2020
tionatthetongueofvolutehavebeenconductedbasedonvisualizationexperimentandsimula‐tion computation. At overload conditions, flow separation, characterized by unsteady vortexshedding from the tongue, causes the low pressure zone near the tongue. The present studydealswithaspecialcase,wherecavitationnearthetongueofthevoluteoccurspriortothecavi‐tationattheleadingedgeofblades.TheheaddropcurvealsohasakneeshapethatheadremainconstantwiththedecreaseofNPSHandrapidlydecreasesatcriticalpoint.Inthiscasethebreak‐down of performance due to cavitation at the tongue rather than cavitation in impeller.Withpressurefluctuationandvisualizationexperiment,andcombiningnumericalsimulation,thecavi‐tationstructureatthetongueanditsinfluencetotheflowfieldinimpellerwasinvestigated.Theresultswerethencomparedtoprovideareferencefortheoptimumdesignofcentrifugalpump.
2. State of the art
Theinvestigationofflowfiledinthevicinityoforinsidecavitationiscomplexinspiteofremark‐ableprogressontheexperimentaltechniqueandnumericalcalculation.R.F.Kunzetal.[13]pre‐dictedtheoccurrenceandevolutionofsingleairfoilcavitationbyusingatwo‐phaseflowmodelbased on theNavier‐Stokes equation. On this basis, the present study conducted a numericalsimulationanalysisandresearchonacentrifugalpumpandinvestigatedtheanti‐cavitationper‐formance. Luo etal. [14] compared the cavitation prediction for a centrifugal pumpwith andwithoutvolutecasing.Bothmodelspredicted theperformancedeteriorationcausedbycavita‐tion,whiletheasymmetricalfeatureofcavitatingflowexistswhenthecalculationdomainwithvolutecasingisapplied.Andtheperformancedeteriorationcausedbytheasymmetricalcavita‐tionisoverestimatebasedontheexperimentdata.Rudolfetal.[15]providehigh‐speedphoto‐graphicobservationofsuccessivestagesofunsteadycavitationatthetongueofthevoluteofacentrifugalpump.Theexperimentswerecarriedoutata flowrateaboveoptimalvalueandat3%headdropconditions.Thecloudcavitationatthetongueissimilartotheoneonsinglehy‐drofoils.However,onlydirectvisualizationwasconductedtoexplaintheevolutionofcavitationstructuresatthetongueofcentrifugalpumpatoverloadconditions,numericalmethodwasnotemployedtoinvestigatethecavitationphenomenonatthetongue.Toslovethecavitationdam‐ageproblemnearthecasingtongueofanafterburnerfuelpump,Xueetal.[16]investigatedtheseparatedflowcharacteristicsandpressurefluctuationsaroundthetonguebylargeeddysimu‐lations. It is found that at low flow conditions, the fuel backflow fromdiffuser to the annularchambertriggersseriousseparation,whichlowersthelocalstaticpressuretolessthanzero.Thelocationoftheseparatedvortexisinaccordwiththecavitationdamagecoreregion.Mengetal.[17]simulatedandanalyzedthecomplextransientcavitationflowpatternsinsideacentrifugalpump.Thecavitiesinthepassagesexhibitanobviouslifecyclewithafrequencycorrespondingto the impeller rotation frequency under off‐design conditions. The asymmetric cavitation inassociatedwiththeunevenpressuredistributiononvoluteandimpeller‐tongueinteraction.Du‐laretal. [18]employed thePIV‐LIFmethod toobtain thevelocity field insideandoutside thevapourcavityaroundtwohydrofoils.Onthebasisofthecapturedimagesofvaporstructures,itcanbeenseenthatthecavitationbehavesdynamicallyatthefrontwall.Thebackflowcausestheseparationof cavitation cloudand thevortex remainspresent inside the separated cloud.Thedevelopment of unsteady cavitation on impeller blades resembles that on a single hydrofoil.However,inthecaseofacentrifugalpump,theinteractionbetweentheimpellerandthevolutetonguestronglyaffectscavitationevolutionduetotheperiodicallyvariationoftheflowfieldsinpassages.Limbachetal.[19,20]conductedthenumericalcalculationandexperimentalworkonalow‐specific‐speedcentrifugalpump.ItisobservedthattheNetpositivesuctionhead(NPSH)risestowardoverloaddueto incidence, flowseparation,andvaporzonesat thevolute tongue.The numerical simulation has been performed byMicha etal. [21] to study the effect of tip‐vortex cavitation in a centrifugalpumpand its result on the change innuclei size.The sizeofbubblenucleisignificantlyaffecttheincipientofcavitationandunsteadypressuredistributioninpassages and the suction surface of the impeller leads to separation and re‐circulation at off‐designconditionwhichinturninfluencestheonsetofcavitationattheleadingedgeoftheblade.Ahmedetal.[22]analyzedthevibrationsignalinbothtimeandfrequencydomainstodetectand
Computational analysis of cavitation at the tongue of the volute of a centrifugal pump at overload conditions
Advances in Production Engineering & Management 15(3) 2020 297
diagnose the cavitation phenomenonwithin a centrifugal pump.With various flow rates androtationalspeed, thesignalspresentedsimilarstatistical featuresandrevealedthatusing low‐frequencywassensitivetopredictcavitationinthepump.Bymeansofunsteadynumericalcom‐putation,Tangetal.[23]foundthatthebladepassingfrequencyisthedominantfrequencyofthepressurefluctuationsinthecasingexceptthevicinityofthevolutetongueforalloperatingcon‐ditions,andthedominantonenearthevolutetongueisthebladepassingfrequencyatthede‐signpointand0~0.5timesthebladepassingfrequencyatotheroff‐designpoints.Donmezetal.[24]andTaoetal.[25]investigatedtheinfluenceofgeometricparametersofbladeinletoncavi‐tationphenomenonof thecentrifugalpump.Cavitationperformanceofpumpisexcessivelyaf‐fectedbybothblade inletangleandblade leading‐edgeshape. Increasinghubbladeanglehasslightlynegativeeffectoncavitationperformanceofthepump,andtheroundandellipselead‐ing‐edgeimpellershavehigherinceptioncavitationcoefficientthantheoneswithbluntorsharpleading‐edge.Alexetal.[26]compiledanoverviewontheeffectofcavitationintheperformanceofcentrifugalpump.Theytookaccountofparameterssuchasbladenumbers,bladeangle,inletflowangle,flowrates,andinletandoutletpressure.Theseparametersallhaveinfluenceonthecavitationperformance,howeverthecasingtypeorthetongueshapewerenotconsidered
Aboveresearchresultsindicatethattheevolutionofcavitationcausestheperformancedete‐rioration of centrifugal pump and the development of cavitation cloud in passages usuallyemergesatthesuctionsideofbladeleadingedge.Duringtheexperiment,thepumpwasoperat‐ingatoverload flowrateandcavitationcondition leadingto3%headdrop.Detailedobserva‐tionsofcavityevolutionnearthetongueofcasingweremadewhennoobviouscavitationoccurswithin the impeller.On thebasis of numerical simulation andhydraulic testing, this study ex‐ploredcavitationstructureandflowfieldinthevicinityofthetongueofthevolutecasingtopro‐videguidancefortheoptimizationdesignofcentrifugalpumps.
3. Materials and methods
3.1 Design of test stand
TheclosedtestbedisshowninFig.1.Thepressurefluctuationandcavitationat tonguedown‐streamexperimentswereconductedonthetestbed,exceptformeasuringtheexternalcharacter‐isticsofthepumpmodelunderdifferentflowrates.InFig.1,impellerandvolutewerepreparedwithPMMA.Thetestbedwasequippedwithapressuretransmitter,aturbineflowmeter,andahigh‐frequencypressure sensor for theeffectivemeasurementof testingparameters: turn fre‐quency (n), spindle torque (T),mass flow (Q), pressure fluctuation, and inlet and outlet pres‐suresofthepumpmodel(pinandpout).DesignparametersofthemodelpumpareshowninTable1.
Table1DesignparametersQd(m3/h) 10H(m) 11n(r/min) 1450P(kW) 3ImpellerdiameterD2(mm) 192ImpellerinletdiameterD1(mm) 54Impellerhubdiameterdh(mm) 20Impellerwidthb2(mm) 5Bladeoutletangleβ2 27.5
Fig.1Three‐dimensionalschematicoftheteststand
Hu, Yang, Cao
298 Advances in Production Engineering & Management 15(3) 2020
3.2 Pressure fluctuation test
The test fieldofpressure fluctuation is shown inFig.2.Theoverall structureof the testbed isshowninFig.2(a).Undertheassistanceofahigh‐frequencydynamicpressuresensor,thepres‐surefluctuationcharacteristicsat thetonguedownstreamweremonitoredwithaHSJ2010hy‐draulic machinery comprehensive tester developed by Huazhong University of Science andTechnology. The distributions of pressure fluctuationmeasurement points are shown in Figs.2(b)and2(c).Thesamplingfrequencyandsamplingtimeoftestdataweresetto8,700Hzand60s,respectively.
(a) (b)(c)
Fig.2Thepressurefluctuationtestingstation
3.3 High‐speed photography experiments
Theexperimentalapparatusforhigh‐speedphotographyisshowninFig.3.ThepositionsinFig.3showthelocationsofthelightsourceandCCDcamerainthetest.Thecapturefrequencywasset to500 images/s,andthepixeldepthof imageswasset to8bitsdue to the lowrevolutionspeedof thetestpump.Thepixelsof theobtained imagewere860×1,280.ThearrowinFig.3showstheshootingdirectionofthecameraandtheincidenceangleof lightsourcetodecreasetheinterferencesofthereflectedlight.
Fig.3High‐speedphotographicexperimentdevice
3.4 Analysis of the test results
TheoverallexternalcharacteristicsofthepumpareshowninFig.4.Theflowheadcurveundernon‐cavitationisshowninFig.4(a),andtheNPSH‐HcurveisshowninFig.4(b)whenQ/Qd=1.52.WiththereductioninNPSH,noevidentcavitationisfoundatthebackoftheimpellerinlet.How‐ever,evidentcloudycavitationisdetectedclosetothetongueneartheflowmeasuringpoints.
(1)
wherepinisthestaticpressureattheimpellerinlet,pvisthesaturatedvaporpressure,takenas3574Pa,vinistheabsolutevelocityattheimpellerinlet.
Computational analysis of cavitation at the tongue of the volute of a centrifugal pump at overload conditions
Advances in Production Engineering & Management 15(3) 2020 299
0.0 0.4 0.8 1.2 1.6 2.0 2.47
8
9
10
11
12
13
H/m
Q/Qd
studiedflowrate
0 1 2 3 4 5 6
9.0
9.5
10.0
10.5
11.0
11.5
H/m
NPSH/m
NPSH3%
(a)(b)
Fig. 4 External characteristic curve of the model pump
Thepressurefluctuationinrotatinghydraulicmachinerycanbedividedintothreetypes,name‐ly, randompressure, blademultifrequency, and axialmultifrequency fluctuations. The randompressurefluctuationisinducedbycavitation,eddies,andunsteadysecondaryflows.Itissimilarwithwhitenoiseonthespectrum.Thebladefrequencyfluctuationhasamultiplerelationwithbladepassing frequencyand is related torotor‐stator interaction.Theshaft frequency fluctua‐tion is related tomechanicalspeed. In thisstudy, therotationalspeedof thecentrifugalpumpwas1,450rpm.ThepatternsoftimeandfrequencydomainsatQ/Qd=1.52andNPSH3%=1.5mareshowninFig.5.Thedomainpressurefluctuationintheflowfieldatthevolutedownstreamismainlybladepassingfrequency.
0.0 0.1 0.2 0.3 0.4
116
118
120
122
124
126
128
p out/Kpa
t/s 0 3 6 9 12 15 18
0
2
4
6
f/fnHz
Fig. 5 Time-domain and frequency-domain of the pressure fluctuation in monitoring point
The high‐speed photography results at the tongue of the pump model at Q/Qd=1.52 areshowninFig.6.Figure6showsthat:a)Alargecavitationstructureisdevelopedattheleadingedgeof the tonguewhentheblade leaves theobservationrange,b)Thecavitationcloudat theleadingedgeofthetonguedevelopsquicklyandshedswhenthenextbladeappearsinthevisualframe,c)Theflowregimedeteriorates,andmanybubblesbegintodevelopattheleadingedgewhenthebladeapproachesthetongue,d)Thecavitationcloudatthetonguetendstoattachonthecavitieswhenthebladeisclosetothetongueposition,e)Thecavitationcloudrapidlyblockstheflowpassagenearthetonguebecausethebladeleavesthetongueandmovestothedown‐streamareas,significantlyinfluencingtheenergytransmissioninthevolute.
abcde
Fig.6Cavitationevolutionatthevolutetongue
Hu, Yang, Cao
300 Advances in Production Engineering & Management 15(3) 2020
4. Result analysis and discussion
4.1 Method of numerical simulation
Time‐averagedN‐Sequationswereutilizedasthebasicgoverningequationsinthesingle‐phasecomputation.TheSSTk‐ω turbulencemodelwasselectedfor3Dturbulencenumericalsimula‐tionbecauseitconsidersthetransmissionofturbulenceshearstressandcanaccuratelypredictthe initial position and results of fluid separationunder turbulent negative‐pressure gradient.Thetransportbehaviorwasobtainedusingtheeddyviscosityequationcontainingthe limitingquantity
(2)
wherevtdenotesdynamicviscosity,α1isaconstanttakenas5/9,kisturbulentkineticenergy,ωisturbulencefrequency,F2ismixingfunctionthatconstrainsthelimitingquantityinthebounda‐rylayer,andSistheinvariantmeasureofshearrate.
Ahomogeneousmodelwasusedinthevapor‐liquidtwo‐phaseflowfield.TheZwartequationbasedontheRayleigh‐Plessetformulawasusedtoanalyzethegenerationandcollapseofcavita‐tionbubblesand themass transfer in the fluid.Theevolutionprocessof cavitationbubbles isgivenas
(3)
whereRBistheradiusofbubble,pvisthepressureinsidethebubble,pisthepressureofthefluidaroundbubble,ρfisthedensityofthefluid,andσisthesurfacetensionoftheinterfacebetweenthefluidandbubble.
ANSYSICEMwasusedtogeneratehigh‐qualityhexahedralmeshesinthecomputationaldo‐mainsofthemodelpump.Fifteenmeshlayerswereaddedtoeachboundarywhileguaranteeingthat thedistributionof blockswas accordancewith the flow regime in the computational do‐mainstoensuretheaccuracyofthenumericalsimulationinthenear‐wallzone.Meshindepend‐encewasappliedunderthedesignconditiontoguaranteecalculationaccuracyandimprovecal‐culationefficiency.When the gridnumberexceeded2.6million, the change in thepumpheadwaswithin1%.Thus,thegridnumberwasdetermined.Fig.7showsa3Dmodelofthecomputa‐tionaldomain,andFig.8showsaschematicofthecomputationmeshes.Theleftsidepresentsthecross‐sectionmeshoftheimpellerandvolute,andtherightsideshowspartialenlargementofthemeshattheinletandoutletofblade.
Steady‐stagecomputationofmultipleworkingconditionswasperformedwithdifferentinletattackanglesbyusingANSYS‐CFX16.0software.GiventhatNPSHiscloselyrelatedtothepres‐sureatthepumpinlet,thetotalpressureintheinletandthemassflowintheoutletwereusedforthecomputationaldomain.Thecalculations fornon‐cavitationsimulationwereusedastheinitialresultsforthecavitationsimulationtoreducethecalculationtime.
Fig.7ComputationaldomainFig8Schematicofthemesh
Computational analysis of cavitation at the tongue of the volute of a centrifugal pump at overload conditions
Advances in Production Engineering & Management 15(3) 2020 301
4.2 Numerical simulation results and analysis
Theone‐sixth cyclenumerical simulation results of cavitationat the tongueatQ/Qd=1.52areshowninFig.9.Theshorttongueadoptedinthisstudydifferssignificantlyfromordinaryairfoilprofilebutitscavitationstructurehasgreatsimilaritiestotheattachmentandsheddingofcavi‐tiesonsingleairfoil.TheinletspeedandStrouhalnumberarethemainfactorsinfluencingperi‐odic cavitation formation and shedding on single airfoil. For the cavitation at the tongue , thedevelopment of cavitation is influenced by the interaction changes in pressure gradients be‐tweenthepressuresurface(PS)andsuctionsurface(SS)ofbladesandtheunsteadychangesinflowfieldneartheleadingedgeofthetonguecausedbyjetwakeattheimpelleroutlet.
AsshowninFig.9(a),thetongueat0Tisinthemiddleofflowpassage.Atthismoment,arel‐atively largecavitationcloudoccursat the leadingedgeof the tongue.At1/4T, thecavitationclouddevelopsquicklyatthetongueandshedswhenthenextbladeapproachesthetongue.At1/2T,thecavitationcloudgraduallymovestowardthetonguedownstreamwhenthebladeap‐proaches the tongue. The cavitation cloud separates in the high‐pressure zone at the tonguedownstream,therebydecreasingtheareaoflow‐pressurezone.At3/4T,thebladeislocatedatthetongue,andanewlyattachedcavitationemergesatthetongue.Thepreviouscavitationcloudbreaksquicklyandthenmovesdownward.Theflowregimeinthevolutedeteriorates,andcavi‐tationwakeoccursatthedownstreamclosetothevoluteoutlet.Thus,thelow‐pressurezoneisexpanded.At1T, theblade leavesthetongue,andthecavitationclouddevelopsat the leadingedgeofthetongue,exertingtheevidentblockingeffectoftheflowpassage.Withthesheddingofcavities,theactualflowareaclosetothetongueincreasessuddenly,therebycausinggreatener‐gylossesinthevolute.
ThevelocitydiagramforthemiddlesectionofthepumpinasinglecycleisshowninFig.9(b).Uniform relative rates are found on themiddle stream surface of the blade, and a local high‐pressure zone is foundat thebladeoutlet close to the tongue.Atoverloadconditions, seriousseparation occurs at the tongue. The negative pressure fluctuation caused by separation andtransitioncantriggertheinitiationofcavitation.Separatedunsteadyeddiesareformednearthetongue,whicharethevibrationandnoisesources.At0T,alow‐ratebackflowzonethatoccupiesapproximately one‐half of the flow passage is formed at the leading edge and tongue down‐stream, significantly blocking the flow passage. The cavitation cloud develops quickly andsqueezestheactual flowarea.At1/4and1/2T, theblockedpassage isreleasedpartiallywiththesheddingofcavities.The low‐ratebackflowzoneshrinks,and theeddiesmovedownward.The flow field near the tongue is divided into backflow andmainstream zones. At 3/4 T, thebladeoutletisclosetothetongue,andtheeddycentermovesdownward.Thepreviouscavita‐tioncloudmovesdownwardtoformacavitationwake.At1T,thebladeleavesthetongue,andanewcavitationcloudemergesattheleadingedgeofthetongue.
0T 1/4 T 1/2 T 3/4 T 1 T
(a)Cavitationevolutionatthetongue
0T 1/4 T 1/2 T 3/4 T 1 T
(b)Velocitydistributiononthecrosssectionofthepump
Fig.9FlowfieldatQ/Qd=1.52
Hu, Yang, Cao
302 Advances in Production Engineering & Management 15(3) 2020
Acentrifugalpumpwithahelicalpumpingchambercangeneratearadialforcethatactsontheimpellerduringoperation.Thus,theaxisbearsalternatingstressesandgeneratesadirected deflection. The pressure in the chamber of the centrifugal pump continuouslychangesduetotheinterferencebytheimpellerandthetongueofthevolute,therebygener‐ating unsteady radial forces. The existence of cavitationmay affect the radial forces. Thevectordiagramofradialforcedistributionontheimpellerinasinglecycleunderdifferentflowrates is shown inFig.10.Cavitationoccurs at the impeller inletwhenQ/Qd=1.3and1.52.However,theradialforcedistributionsatthecriticalcavitationstatearebasicallycon‐sistentunderthreeworkingconditions.Theradialforcedistributionisrelatedtothenum‐berofbladesandisinhexagonalstardistribution.Thisconditioniscausedbytheinterfer‐enceoftheimpellerandthevolute.AtQ/Qd=1.3,thevectordiagramsundercriticalcavita‐tionandnon‐cavitationconditionsareclose.AtQ/Qd=1.52and1.73,theradialforcespro‐ducealternatingstressesundercavitationconditionswhenthebladesweepstheseparationtongue.
-150 -100 -50 0 50 100 150
-150
-100
-50
0
50
100
150
Fy/N
Fx/N
-150 -100 -50 0 50 100 150
-150
-100
-50
0
50
100
150
Fx/N
Fy/N
-150 -100 -50 0 50 100 150
-150
-100
-50
0
50
100
150 cavitation non-cavitation
Fy/N
Fx/N
Q/Qd=1.3Q/Qd=1.5Q/Qd=1.73
Fig.10Distributionofradicalforce
Thesecondaryflowsand“jetwake”phenomenonarecausedbythehigh‐speedrotationoftheimpeller,interferencebetweentheimpellerandthevolute,andtheviscosityoffluidduetothespatialasymmetricstructureofthecentrifugalpump.Theinternalflowfieldpresentscomplicat‐ed unsteady characteristics thatmay cause pressure fluctuation. The circumferential pressurefluctuation of the volute and pressure fluctuation near the tongue are influenced and presentdifferentcharacteristicswhencavitationemergesatthetongue.Themonitoringpointsofpres‐surefluctuationinthevoluteareshowninFig.11.
Fig.11Monitoringpointsofpressurefluctuation
The pressure amplitude of pressure pulsation in the volute is characterized, and the influ‐ences of the static pressure ofmonitoring points on pressure fluctuation are eliminated. ThestrengthofpressurefluctuationisexpressedaspressurecoefficientCp
(4)
wherepistheinstantaneouspressurevalueatthemonitoringpoints,and isthemeanpressureofmonitoringpointsintheinvestigatedcycle.
ThetimedomainofmonitoringpointsP1‐P9whenQ/Qd=1.3,1.52,and1.73isshowninFig.12.Thepressurefluctuationintensityincreasessignificantlywiththeincreaseofflowrate.Alt‐houghthenumberofwavepeaksatdifferentmonitoringpointsinasinglecycleisequaltothenumberofblades,theregularityinasinglecycleweakenswiththeincreaseofflowrate.AtQ/Qd=
Computational analysis of cavitation at the tongue of the volute of a centrifugal pump at overload conditions
Advances in Production Engineering & Management 15(3) 2020 303
1.3, thepressure fluctuation atdifferentmonitoringpoints showsevidentperiodic fluctuationlaws.Thefluctuationamplitudesatdifferentmonitoringpointsareclose,exceptforthemonitor‐ingpointsatthedownstreamofthetongue.Consideringthatallmonitoringpointsareclosetotheflowfieldattheimpelleroutlet,thepressurefluctuationiscausedbythejet‐wakestructureat thepassageoutletof the impeller,and the fluctuationamplitudesaresimilar.AtQ/Qd=1.73,irregular wave peaks are found, indicating the occurrence of serious cavitation close to thetongue.Therefore,theflowfieldbecomesextremelydisordered.
Themultiplicationofrotatingfrequencyisdefinedas
(5)
whereFisthepracticalfrequencyafterFouriertransform,nistherotatingspeedoftheimpeller,andFnistherotatingfrequencyunderthecorrespondingrotatingspeed.
AsshowninFig.13,theexcitationfrequencyatdifferentmonitoringpointsisthebladepass‐ingfrequencyunderdifferentflowrates.Theshaftfrequencyandotherlow‐frequencyandhigh‐frequencybandshavesmallamplitudes.Thisfindingrevealsthatthepressurefluctuationcausedbythe“jetwake”flowstructureunderhighflowrateisthemainexcitationfrequency.Withtheincrease in flow rate, the pressure fluctuation strength increases significantly. In particular, amagnitudeof jumpsofpulsationstrength is foundafterthecavitationoccursat the tongue.AtQ/Qd=1.3, thepressure fluctuation isweak.Themain excitation frequency firstdecreasesandthenincreasesfromthefirsttotheeighthsections.Thepressurefluctuationstrengthdeclinesasthemonitoringpointmovesawayfromthetongue.AtQ/Qd=1.52and1.73,thecavitationinthevolute becomes evident, and the pressure fluctuation in the volute shows different laws. Thepressurefluctuationatthedownstreamofthetongueis lowerthanthatattheimpelleroutlet.The fluctuationstrengthat the impelleroutletdecreasesgradually fromthe first to theeighthsections.
0 60 120 180 240 300 360‐10
0
10
20
30 Q/Q
d=1.3
Q/Qd=1.52
Q/Qd=1.73C p
0 60 120 180 240 300 360
‐10
0
10
20
30
C p
0 60 120 180 240 300 360
‐10
0
10
20
30
C p
P1 P2 P3
0 60 120 180 240 300 360‐10
0
10
20
30
C p
Q/Qd=1.3
Q/Qd=1.52
Q/Qd=1.73
0 60 120 180 240 300 360‐10
0
10
20
30
C p
0 60 120 180 240 300 360
‐10
0
10
20
30
C p
P4 P5 P6
0 60 120 180 240 300 360‐10
0
10
20
30
C p
Q/Qd=1.3
Q/Qd=1.52
Q/Qd=1.73
0 60 120 180 240 300 360‐10
0
10
20
30
C p
0 60 120 180 240 300 360
‐10
0
10
20
30
C p
P7 P8 P9
Fig.12Pressurefluctuationofmonitoringpointsaroundtheimpelleroutlet
Hu, Yang, Cao
304 Advances in Production Engineering & Management 15(3) 2020
0 6 12 18 24
0.00
0.02
0.04
0.06
0.08
0.10
P1P2P3P4P5P6P7P8P9
NF
C p
0 6 12 18 24
0
1
2
3
4
P1P2P3P4P5P6P7P8P9
NF
C p
0 6 12 18 24
0123456789
P1P2P3P4P5P6P7P8P9
NF
C p
Q/Qd=1.3Q/Qd=1.52Q/Qd=1.73
Fig.13Frequencydomainofpressurefluctuation
ThetimedomainsofpressurefluctuationatP10‐P15areshowninFig.14.Thepressurefluc‐tuationhassixwavepeaksunderdifferentworkingconditions,andthepressurefluctuationatdifferentmonitoringpointsiscausedbytheinterferenceofthetongue.Thepressurefluctuationstrength increaseswith the increase of flow rate. The fluctuation strengthweakenswhen thedistancebetweenthemonitoringpointandthetongueincreases.Theinfluenceofthetongueonpressurefluctuationandtheinfluenceofjet‐wakestructureattheimpelleroutletdeclinewhenthemonitoring point approaches thewall surface facing the tongue. The pressure fluctuationstrengthwithoutcavitationclosetothetongueatQ/Qd=1.3issignificantlylowerthanthatwithcavitationat the tongueatQ/Qd=1.52and1.73.This findingreflectsthat theunsteady flowatthetongueiscomplicated,andthechangesinpressuredistributionareintenseaftertheoccur‐renceof cavitation.At actual operation, these conditionsmay trigger serious vibrationnoises,therebyinfluencingthestableoperationofthepump.
The frequencydomains of pressure fluctuations at differentmonitoring points close to thetongueunderdifferentworkingconditionsareshowninFig.15.Thedominantfrequencyunderworking conditions is the blade passing frequency. The rapid increase in dominant frequencyamplitudecausedbycavitationreflectstheinfluencesofcavitationdevelopmentonthepressurefluctuationstrengthclosetothetongue.ThepressurefluctuationatthedownstreammonitoringpointP1is0.41ofthedominantfrequencyamplitudeundernon‐cavitationcondition.However,it increases to2.12 and3.84whenQ/Qd=1.52 andQ/Qd=1.73, respectively.A strongpressurefluctuationmaybefoundatthedownstreampositionofthetongueduetothedevelopmentandbreakage of cavities. In accordancewith the changes in dominant frequency amplitude underdifferent working conditions, the pressure fluctuation intensity declines gradually when themonitoringpointapproachesthewallsurfacefacingtheseparationtongue.
0 60 120 180 240 300 360‐4
‐2
0
2
4
6
C p
Q/Qd=1.3
Q/Qd=1.52
Q/Qd=1.73
0 60 120 180 240 300 360‐4
‐2
0
2
4
6
C p
0 60 120 180 240 300 360
‐4
‐2
0
2
4
6
C p
P10 P11 P12
0 60 120 180 240 300 360‐4
‐2
0
2
4
6
C p
Q/Qd=1.3
Q/Qd=1.52
Q/Qd=1.73
0 60 120 180 240 300 360‐4
‐2
0
2
4
6
C p
0 60 120 180 240 300 360
‐4
‐2
0
2
4
6
C p
P13 P14 P15
Fig.14Pressurefluctuationnearthetongue
Computational analysis of cavitation at the tongue of the volute of a centrifugal pump at overload conditions
0 6 12 18 24
0.00.10.20.30.40.50.6
P10P11P12P13P14P15
NF
C p
0 6 12 18 24
0.00.51.01.52.02.53.0
P10P11P12P13P14P15
NF
C p
0 6 12 18 24
0123456
P10P11P12P13P14P15
NF
C p
Q/Qd = 1.3 Q/Qd = 1.52 Q/Qd = 1.73
Fig. 15 Frequency domain of pressure fluctuation of monitoring points near the tongue
5. Conclusion In this study, an attempt is made to investigate the cavitation at the tongue of centrifugal pump at overload conditions. By means of numerical computation and visualization measurement, un-steady flow structures in cavitation zone were studied to associate with blade loading and pres-sure fluctuation. From the present research following conclusions can be drawn:
• As the increase of flow rate, the shedding of the separated vortex lowers the static pres-sure near the tongue. And the flow separation at the tongue brings dramatic pressure fluc-tuation and strong shearing vortex which induce cavitation.
• At overload conditions, higher radical velocity and deviation of relative flow angle contrib-ute to periodical variation of flow field near the tongue, which results in periodical cavita-tion evolution. Thus, the frequency of the cavitation cloud shedding is equal to the blade passing frequency.
• Cavitation at the tongue not only enhances the pressure fluctuation in volute, but also affects the blade loading distribution: The pressure pulsation in the volute is consistent with the blade passing frequency whether cavitation occurs or not, while the pulsation intensity increases obviously after cavitation inception. From the first section to the eighth section of volute, the pulsation intensity of impeller outlet decreases gradually.
The study showed that it is possible that the head drop at overload conditions is caused by the appearance of cavitation at the tongue of volute, which may provide guidance for the optimi-zation of the anti-cavitation performance of centrifugal pump. In future, more accurate visualiza-tion measurement and vibration experiment can be conducted to investigate the cavitation phe-nomenon at the tongue of casing.
Acknowledgement This research was funded by the National Key R&D Program of China (2018YFC0810506) and the Key R&D Program of Zhenjiang (SH2017049).
References [1] Brennen, C.E. (2011). Hydrodynamics of Pumps, Cambridge University Press, Cambridge, United Kingdom, doi:
10.1017/CBO9780511976728. [2] Franc, J.-P., Michel, J.-M. (2005). Fundamentals of cavitation, Springer, New York, USA, doi: 10.1007/1-4020-2233-6. [3] SŠ irok, B., Dular, M., Hocevar, M., Novak, M., Stoffel, B., Ludwig, G., Bachert, B. (2002). The influence of cavitation
structures on the erosion of a symmetrical hydrofoil in a cavitation tunnel, Strojniški Vestnik – Journal of Mechan-ical Engineering, Vol. 48, No. 7, 368-378.
[4] Wang, S.-L., Tan, L., Wang, Y.-C. (2013). Characteristics of transient cavitation flow and pressure fluctuation for a centrifugal pump, Journal of Vibration and Shock, Vol. 32, No. 22, 168-173, doi: 10.13465/j.cnki.jvs.2013.22.024.
[5] Bilus, I., Predin, A. (2009). Numerical and experimental approach to cavitation surge obstruction in water pump, International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 19, No. 7, 818-834, doi: 10.1108/096155 30910984091.
[6] Lu, J., Yuan, S., Ren, X., Liu, Y., Si, Q. (2015). Investigation of instabilities of cavitation at low flow rate of centrifugal pump, Transactions of the Chinese Society for Agricultural Machinery, Vol. 46, No. 8, 54-58, doi: 10.6041/j.issn. 1000-1298.2015.08.009.
Advances in Production Engineering & Management 15(3) 2020 305
Hu, Yang, Cao
[7] CŠudina, M., Prezelj, J., CŠernetic, J. (2012). Use of noise and vibration spectra to detection cavitation in kinetic pumps, In: Proceedings of the 8th International Symposium on Cavitation, Singapore, 978-971, doi: 10.3850/978-981-07-2826-7_172.
[8] Lu, Z., He, X., Wang, C. (2018). Influencing factors of self-priming time of multistage self-priming centrifugal pump, DYNA – Ingeniería e Industria, Vol. 93, No. 6, 630-635, doi: 10.6036/8930.
[9] Ključanin, D., Manđuka, A. (2019). The cantilever beams analysis by the means of the first-order shear defor-mation and the Euler-Bernoulli theory, Tehnički Glasnik, Vol. 13, No. 1, 63-67, doi: 10.31803/tg-2018080221 0608.
[10] Luo, X., Zhang, Y., Peng, J., Xu, H. (2008). Effect of impeller inlet geometry on centrifugal pump cavitation perfor-mance, Journal of Tsinghua University (Science and Technology), Vol. 48, No. 5, 836-839, doi: 10.3321/j.issn:1000-0054.2008.05.019.
[11] Castorani, V., Landi, D., Mandolini, M., Germani, M. (2019). CFD simulations of filter houses for power plant gas turbine: Evaluation of differences between 2D and 3D models, DYNA – Ingeniería e Industria, Vol. 94, 145-149, doi: 10.6036/8901.
[12] Blecich, P., Senčić, T., Wolf, I., Bonefačić, I. (2018). Numerical investigation of heat and mass transfer inside a wet cooling tower, Tehnički Glasnik, Vol. 12, No. 3, 131-138, doi: 10.31803/tg-20171017145907.
[13] Kunz, R.F., Boger, D.A., Stinebring, D.R., Chyczewski, T.S., Lindau, J.W., Gibeling, H.J., Venkateswaran, S., Govindan, T.R. (2000). A preconditioned Navier–Stokes method for two-phase flows with application to cavitation predic-tion, Computers & Fluids, Vol. 29, No. 8, 849-875, doi: 10.1016/s0045-7930(99)00039-0.
[14] Luo, X., Wei, W., Ji, B., Pan, Z., Zhou, W., Xu, H. (2013). Comparison of cavitation prediction for a centrifugal pump with or without volute casing, Journal of Mechanical Science and Technology, Vol. 27, No. 6, 1643-1648, doi: 10.1007/s12206-013-0411-5.
[15] Bachert, R., Stoffel, B., Dular, M. (2010). Unsteady cavitation at the tongue of the volute of a centrifugal pump, Journal of Fluids Engineering, Vol. 132, No. 6, Article No. 061301, doi: 10.1115/1.4001570.
[16] Xue, M., Park, Y. (2012). Large eddy simulations of separated flow at the casing tongue of an afterburner fuel pump, Journal of Tsinghua University (Science and Technology), Vol. 52, No. 11, 1638-1642, doi: 10.16511/j.cnki. qhdxxb.2012.11.023.
[17] Meng, L., He, M., Zhou, L., Yang, J., Wang, Z., Karney, B. (2016). Influence of impeller-tongue interaction on the unsteady cavitation behavior in a centrifugal pump, Engineering Computations, Vol. 33, No. 1, 171-183, doi: 10.1108/EC-09-2014-0179.
[18] Dular, M., SŠ irok, B., Bachert, R., Stoffel, B. (2005). Transient simulation, visualization and PIV-LIF measurements of the cavitation on different hydrofoil configurations, Strojniški Vestnik – Journal of Mechanical Engineering, Vol. 51, No. 1, 13-27.
[19] Limbach, P., Kimoto, M., Deimel, C., Skoda, R. (2014). Numerical 3D simulation of the cavitating flow in a centrifu-gal pump with low specific speed and evaluation of the suction head, In: Proceedings of the ASME Turbo Expo 2014: Turbine Technical Conference and Exposition. Volume 2D: Turbomachinery, Dusseldorf, Germany, 16-20, doi: 10.1115/GT2014-26089.
[20] Limbach, P., Skoda, R. (2017). Numerical and experimental analysis of cavitating flow in a low specific speed centrifugal pump with different surface roughness, Journal of Fluids Engineering, Vol. 139, No. 10, Article No. 101201, doi: 10.1115/1.4036673.
[21] Micha Premkumar, T., Sathish Babu, R., Vinoth Kumar, M., Hariram, V., Seralathan, S. (2019). Numerical simula-tion of hydrodynamic cavitation in centrifugal pump, International Journal of Innovative Technology and Explor-ing Engineering, Vol. 8, No. 11, 2689-2693, doi: 10.35940/ijitee.k2140.0981119.
[22] Al-Obaidi, A.R. (2019). Investigation of effect of pump rotational speed on performance and detection of cavita-tion within a centrifugal pump using vibration analysis, Heliyon, Vol. 5, No. 6, Article No. E01910, doi: 10.1016/ j.heliyon.2019.e01910.
[23] Tang, X., Zou, M., Wang, F., Li, X., Shi, X. (2017). Comprehensive numerical investigations of unsteady internal flows and cavitation characteristics in double-suction centrifugal pump, Mathematical Problems in Engineering, Vol. 2017, Article ID 5013826, doi: 10.1155/2017/5013826.
[24] Donmez, A.H., Yumurtacı, Z., Kavurmacıoglu, L. (2018). The effect of inlet blade angle variation on cavitation performance of a centrifugal pump: A parametric study, Journal of Fluids Engineering, Vol. 141, No. 2, Article No. 021101, doi: 10.1115/1.4040557.
[25] Tao, R., Xiao, R., Wang, Z. (2018). Influence of blade leading-edge shape on cavitation in a centrifugal pump im-peller, Energies, Vol. 11, No. 10, Article No. 2588, doi: 10.3390/en11102588.
[26] George, A., Muthu, P. (2015). Review on effects of cavitation in the performance of centrifugal pump, Internation-al Journal of Advance Engineering and Research Development, Vol. 2, No. 11, 298-303, doi: 10.21090/ijaerd. 021148.
306 Advances in Production Engineering & Management 15(3) 2020
