38 InternatIonal Journal of energy ManageMent

Variable-SpeedPumpEfficiencyCalculationForFluidFlowSystemswithandwithout

Static HeadWei Guo, PhD, PE, CEM; Josage Chathura Perera; Daryl Cox;

Sachin Nimbalkar, PhD; Thomas Wenning, PE, CEM;Kiran Thirumaran; and Eli Levine, JD, CEM

ABSTRACT

Toaccuratelycalculatepumpenergysavingsgained from implementingvariablefrequencydrive(VFD)controls,thevariationof pumpefficiencymustbeconsideredwhenoperatingconditionstransitionfromthedesignoperatingpointtonewoperatingpoints.Manysoftwaretoolsrequireuserstospecifythenewpumpefficiency,or it isassumedtobeunchanged.Unfortunately,manyusershavechallengesof estimatingthepumpefficiencyatnewoperatingpoints. Thisarticlepresentsa simplifiedmethodof estimatingcentrifugalpumpefficiencyatnewoperatingspeedswhenthepumpiscontrolledbyaVFD.Thismethodologyappliestosystemswithandwithoutstaticheadwhenthesystemcurveisnotaffectedbythechange,andalsosystemswherethechangeinoper-ationchangesthesystemcurve. Ahypotheticalfluidflowsystemandcentrifugalpumpwereusedtodemon-stratethecalculationprocess for thesescenarios.Forthishypotheticalsystem,thepump’sefficiencyatnewoperatingpointswasupto5.4%lowerthanthedesignoperatingpoint.

INTRODUCTION

Pumpsystemsareubiquitousinmanufacturingfacilities,waterandwaste-waterplants,andcommercialbuildings.Pumpsystemstransfervarioustypesof fluids toprovideheating,cooling,motive forcesandmaterialsneededforbuildingsandprocesses.Inthemanufacturingsectorof theU.S.,about27%of electricitywasusedbypumps [1].Many technical resources [1,2]andtrainingopportunities [3,4]areavailable for facilitymanagers to improvepumpefficiency.

VoluMe 2, nuMber 3 39

Whenoperatingconditionsrequiremultipleoperatingheadandflowratecombinations, themost frequentlyrecommendedpumpenergyconservationmeasuresinenergyassessmentsaretoinstallavariablefrequencydrive(VFD)andslowdownthepumpspeedinsteadof ridingthepumpcurve[5]. Tocalculate thepumpenergysavings fromimplementingVFDcontrols,inadditiontothemeasuredflowrateandheadatthenewoperatingpoint,thepump’sefficiencyatthenewoperatingpointisalsorequired[6].Thepump’sefficiencyatthenewoperatingpointcanbeverydifferentfromtheefficiencyatthedesignoperatingpoint[1].Unfortunately,somesoftwaretoolssimplyassumethatthepumpefficiencydoesnotvaryunlesstheuserspecifiesadifferentvalue[7],butmanyusershavedifficultiesinestimatingthenewpumpefficiency.Thisarticledescribeshowtoestimatethevariablespeedpumpefficiency for threepossiblesystems:nostaticheadandnochangestosystemcurve;withstaticheadandnochangestosystemcurve;withstaticheadandchangestosystemcurve. Ahypotheticalfluidflowsystemandcentrifugalpumpwereusedtodemon-strate the calculation process for these three scenarios. Thesecalculationsaddresschangesinpumpefficiencyresultingfromspeedcontrolonly.Otherissuessuchasnetpositivesuctionheadavailable(NPSHA)andminimumcontinuousstableflow(MCSF)mustbeevaluatedwhenimple-mentingspeedcontrolof centrifugalpumps.

VARIABLESPEEDPUMPEFFICIENCYCALCULATION

Systems without Static Head Forasystemwithnostatichead(Figure1),typicallyinclosedloopsystems,thepumpoperatesatconstantefficiencyundervariablespeedcontrol[8]. Accordingtotheaffinitylaw,thenewoperatingspeed,S%,canbeobtainedbyusingEquation1.

(1)

whereGPMisthedesignflowrateandGPM′isthenewoperatingflowrate.

Formostcentrifugalpumps,whenthenewoperatingspeedisgreaterthan66.7%of fullspeed,itistypicallyacceptabletoassumethatthepumpefficiencyatthenewoperatingpointisthesameastheefficiencyatthedesignoperatingpoint[9],asshowninEquation2.

η′=η (2)

40 InternatIonal Journal of energy ManageMent

whereηisthepumpefficiencyatthedesign,andη′istheefficiencyatthenewoperatingpoint.

Whenthenewoperatingspeedislessthan66.7%of fullspeed,thepumpefficiencydegradationcausedbyspeedvariationcanbeexpressedasEquation3[9].Itshouldbenotedthatoperationbelowtheminimumcontinuousstableflow(MCSF)isnotrecommended.

(3)

CombiningEquations1and3resultsinEquation4.

(4)

Whenthenewoperatingspeedislessthan66.7%,thepumpefficiencycanbeobtainedbyusingEquation4.

Systems with Static Head Forsystemswithstatichead (Figure2), thepumpdoesnotmaintaincon-stantefficiencywhenoperatedwithspeedcontrol[8].

Figure 1. Fluid Flow System without Static Head

VoluMe 2, nuMber 3 41

For this case, the calculation procedure is described in the three steps pre-sentedbelow.Step1 is todetermine therequiredpumpoperatingspeed forthenewoperatingpoint,Step2istocalculatethenominalflowratewiththesamepumpefficiencyasatthenewoperatingpoint,andStep3istotheusethenominalflowrateandnominalpumpefficiencycurvetodeterminethepumpefficiencyatthenewoperatingpoint. Thisalgorithmrequiresquadraticcurvefitsforpumpheadandefficiency.Thecurvefitscanbedirectlyprovidedbytheuser,ortheycanbederivedfrommultiple performance data points.

Step 1: Determine the required pump speed for the new operating point Assumethatthepumpheadandflowrelationshipatthenominalor100%speedcanbepresentedinaquadraticequation,asinEquation5[10].

(5)

Atthenewoperatingspeed,S%,theheadandflowratearedesignatedasH′andGPM′.Accordingtotheaffinitylaw,therelationshipsbetweenH′andGPM′andHandGPMareshowninEquations6and7.

Figure 2. Fluid Flow System with Static Head

42 InternatIonal Journal of energy ManageMent

(6)

(7)

ApplyfunctiontransformationbypluggingEquations6and7intoEquation5.

(8)

RearrangeEquation8,andEquation9willbeobtained:

(9)

Withthemeasuredflowrateandpumpheadat thenewoperatingpoint,Equation10canbeobtainedbysolvingEquation9,andtheresultcanbeusedtoobtainS%[11].

(10)

Step 2: Determine the flow rate at the nominal or 100% speed with the same pump efficiency as at the new operating point Basedontheaffinitylaw,theiso-efficiencylinesforvariablespeedsfollowEquation11.Inotherwords,theηandη′forGPMandGPM′arethesame.

(11)

Step 3: Determine the pump efficiency at the new operating point Assumethepumpefficiencycurveat thenominalor100%speedcanbepresentedinaquadraticequation,asinEquation12.

(12)

Equation13canbeobtainedbycombiningEquations11and12.

(13)

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Whenthenewoperatingspeedisgreaterthan66.7%,thepumpefficiencycanbeobtainedbyusingEquation13.Whenthenewoperatingspeed is lessthan66.7%,thepumpefficiencycanbeobtainedbyusingEquation14,withtheconsiderationof thepumpefficiencydegradationcausedbyspeedvariation,asinEquation3above[9].

(14)

Systems with Static Head and Changed System Curve Changestotheresistancetoflowinasystemwillchangetherelationshipbetweenflowrateandheadandwillmanifestaschangestothesystemcurve.Thischangecanresult fromchanges invalveposition,flowpath,equipmenton-line(e.g.,numberof chillers,heatexchanges,orcoolingtowersbeingserved)(Figure3).

Figure 3. Fluid Flow System with Static Head and Changed System Curve

Thethree-stepcalculationdescribedaboveisagnostictothechangeof thesystemcurve(i.e.,systemflowrateandheadrelationship).Therefore,Equations13 and 14 can be also used for this scenario.

44 InternatIonal Journal of energy ManageMent

SAMPLECALCULATIONS

Table1 shows thedatapoints for theflowrate,pumphead,andpumpefficiencyat100%speedforahypotheticalcentrifugalpump.ThepumpheadcurvefitwasgeneratedasEquation15,andthepumpefficiencycurvefitwasgeneratedasEquation16:

(15)

(16)

At thedesignoperatingpointA, theflowrate is1,800GPM,theheadis31.3ftw.g.,andthepumpefficiencyis83.6%.Threecasesarepresentedbelow:onesystemwithoutstatichead,onewithstatichead,andonewithstaticheadandchangedsystemcurve.

Table 1. Pump Flow Rate, Head, and Efficiency Data Points at 100% Pump Speed

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Case Study 1: System without Static Head Theflowrateof thenewoperatingpointBis900GPM,andtheheadis7.8ftw.g.Thesystemcurve,thedesignoperatingpointA,andthenewoperatingpointBarepresentedinFigure4.Thepumpheadandefficiencycurvesatnewoperatingspeedswerecreatedusing theaffinity lawandarealso included inFigure4tovalidatethemathematicallycalculatednewpumpefficiency.

Figure 4. System without Static Head

Becausethissystemhasnostatichead,Equation1wasusedtocalculatethenewoperatingpumpspeed:

Becausethenewoperatingpumpspeedislessthan66.7%,Equation4wasusedtocalculatethepumpefficiencyatoperatingpointB.

ThepumpefficiencyatoperatingpointBis1.2%lowerthanatdesignoper-atingpointA.

46 InternatIonal Journal of energy ManageMent

Case Study 2: System with Static Head Theflowrateof thenewoperatingpointCis900GPMandtheheadis15.3ftw.g.Figure5presentsthesystemflowratevs.theheadcurve,thedesignoperatingpointA,andthenewoperatingpointC.Figure5also includes thepumpheadandefficiencycurvesatthenewoperatingspeed,whichwerecre-atedusingtheaffinitylawtovalidatethemathematicallycalculatednewpumpefficiency.

Figure 5. System with Static Head

UsingEquation10tocalculatethenewoperatingpumpspeed,

Becausethenewpumpspeedislowerthan66.7%,Equation14wasusedtocalculatethepumpefficiencyatthenewoperatingpoint.

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ThepumpefficiencyatoperatingpointCis4.6%lowerthanatthedesignoperatingpointA.

Case Study 3: System with Static Head and Changed System Curve Theflowrateof thenewoperatingpointDis900GPM,andtheheadis17.8ftw.g.Thesystemcurvesbeforeandafterthechangedflowrate,thedesignoperatingpointA,andthenewoperatingpointDarepresentedinFigure6.Tovalidatethemathematicallycalculatednewpumpefficiency,thepumpheadandefficiencycurvesatthenewoperatingspeedwerecreatedusingtheaffinitylawandareincludedinFigure6.

Figure 6. System with Static Head and Changed System Curve

UsingEquation10tocalculatethenewoperatingpumpspeed,

Becausethenewpumpspeedishigherthan66.7%,Equation13wasusedtocalculatethepumpefficiencyatthenewoperatingpoint:

48 InternatIonal Journal of energy ManageMent

ThepumpefficiencyatoperatingpointDis5.4%lowerthanatthedesignoperatingpointA.

CONCLUSIONS

WhenusingVFDcontrolstoreducepumpenergyconsumption,thepumpefficiencyat thenewoperatingpoint is required toaccuratelycalculate thepumpenergysavings.Thisarticleprovidesaprocedureonhowtoestimatethenewpumpefficiencyfor threepossiblescenarios:systemswithoutstatichead,systemswith statichead,and systemswith staticheadandchanged systemcurve.Thecalculationprocedureisveryeasyforusersto implement inExcelspreadsheet calculators and in modern, stand-alone software, or it can be used toenhancecurrentlyexistingsoftwaretoolstoobtainmoreaccuratepumpener-gysavingsresults.Forthehypotheticalfluidflowsysteminthecasestudies,thepumpefficiencyatnewoperatingpointswasupto5.4%lowerthanatthedesignoperatingpoint.

ACKNOWLEDGMENTS

ThisworkwassupportedbytheAdvancedManufacturingOffice(AMO)of theU.S.Departmentof Energy(DOE).

References [1] U.S.DOEAdvancedManufacturingOffice(AMO),Improving Pumping System Performance: A

Sourcebook for Industry, 2nd ed., 2006. [2] U.S.DOEAMO,PumpSystemsTipSheets,2007.Availableatwww.energy.gov/eere/amo/

tip-sheets-system. [3] W.Guo,T.Wenning,S.Nimbalkar,J.Travis,andE.Levine.U.S.DOEIn-PlantTrainings

toDevelopExpertiseandReplicateSuccess,ACEEESummerStudyonEnergyEfficiencyinIndustry,2019.

[4] W.Guo,T.Wenning,S.Nimbalkar,D.Cox,andK.Thirumaran.IndustrialEnergyTrain-ingandCertification,Plant Engineering, 70 (2017) (11) 31-38.

[5] D.Kaya,E.A.Yagmur,K.S.Yigit,F.C.Kilic,A.S.Eren,andC.Celik.Energy Efficiency in Pumps, Energy Conversion and Management,49(2008)1662-1673.https://doi.org/10.1016/j.enconman.2007.11.010.

[6] M.A.BarnierandB.Bourret.PumpingEnergyandVariableFrequencyDrives,ASHRAE Journal, 41 (1999) (12) 37-40.

[7] A.-M.Georgescu,C.-I.Cosoiu,S.Perju,S.C.Georgescu,L.Hasegan,andA.Anton.Estimationof theEfficiencyforVariableSpeedPumpsinEPANETComparedwithExper-imental Data, Procedia Engineering,89(2014)1404-1411.https://doi.org/10.1016/j.pro-eng.2014.11.466.

[8] HydraulicInstitute.VariableSpeedPumping:AGuidetoSuccessfulApplications.U.S.DOEAMO.Availableatwww.eere.energy.gov/manufacturing/tech_assistance/pdfs/vari-

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able_speed_pumping.pdf. [9] I.SárbuandI.Borza.EnergeticOptimizationof WaterPumpinginDistributionSystems,

Periodica Polytechnica Mechanical Engineering, 42 (1998) (2) 141-152.[10] S.LeonowandM.Mönnigmann.SoftSensorBasedDynamicFlowRateEstimationinLow

SpeedRadialPumps,2013EuropeanControlConference(ECC),IEEE,778-783.[11] L.Nygren.SavingsCalculatorforCentrifugalPumps,Bachelor’sthesis,LappeenrantaUni-

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≥

AUTHORBIOGRAPHIES Wei Guo, PhD, PE, CEM,works in theEnergyEfficiencyResearchandAnalysisGroupatOakRidgeNationalLaboratory (ORNL).Hisresearcharea ismainlyfocusedonimprovingenergyandmaterialefficiencyforgeneralandspecialmanufacturingequipmentandprocesses.Hehasbeenworkingonsmartmanufac-turinganddataanalytics,combinedheatandpower,industrialwatermanagement,andrecyclingandwastemanagementprojectsfortherecentyears.Dr.WeiGuoisaSeniormemberof Associationof EnergyEngineers.HeisanAEECertifiedEnergyManager (CEM)andregisteredProfessionalEngineer (PE).Dr.WeiGuomaybecontactedatguow@ornl.gov.

Josage Chathura PereraisaninternatOakRidgeNationalLaboratorywiththeEnergyEfficiencyResearchandAnalysisgroup.Hisbackground is in smartmanufacturingandindustrialenergyefficiency.Hereceivedhisbachelor’sdegreeinindustrialengineeringfromPennStateandiscurrentlypursuingamaster’sdegreeinindustrialengineeringatWestVirginiaUniversity,whereheisaresearchassistantfor the DOE Industrial Assessment Center.

Daryl Coxhasbeenamemberof theresearchstaffattheOakRidgeNationalLaboratory(ORNL)since1990.Hehasbeenheavilyinvolvedintheanalysisof fail-urecharacteristicsforfluidsystemcomponentsusedincommercialnuclearpowerplants.HiscurrentfocusisenergyoptimizationeffortsinindustrialpumpingsystemsandmanaginginteractionswithindustrialprogrampartnersintheBetterBuildingsBetterPlantsProgramfor theDepartmentof EnergyAdvancedManufacturingOffice.DarylisaqualifiedspecialistandseniorinstructorforthePumpingSystemAssessmentTool (PSAT)software toolandhasconductedtrainingonthetool foroveradecade.Darylisaformermemberof theASMEOperations&MaintenanceWorkingGrouponair-operatedvalvesandcurrentlyco-chairsthecodesandstan-dardsworkinggroup for thedevelopmentof standards forenergyassessmentof pumpingsystems.HeholdsaBSinmechanicalengineeringfromtheUniversityof Cincinnati.Mr.CoxisaCertifiedPractitionerinEnergyManagementSystems,andanSEP-PerformanceVerifier.

Sachin Nimbalkar, PhD,isagroupleaderattheOakRidgeNationalLabo-ratory.Dr.NimbalkarprovidestechnicalsupporttoDOE’sBetterBuildings,Better

50 InternatIonal Journal of energy ManageMent

PlantsProgramPartners (mainly industrialandwastewater treatmentpartners)throughenergyroadmapdevelopment,baselininganalysis, in-plant training,andfieldvisitstoinvestigatefeasiblemeasuretoreduceprocessenergyrequirements.Dr.NimbalkarhasconductedseveraltraininganddemonstrationworkshopsthroughouttheU.S.,India,China,Ukraine,CostaRica,andTurkeycoveringenergyefficiencyinprocessheat systems, systemspecificandcross-cuttingenergyaudits,andISO50001 implementation steps and tools. Dr. Nimbalkar has contributed to the devel-opmentof severalDOEsoftwaretools,includingtheprocessheatingtools(PHASTandPHMT)andtheEnPItool.Dr.NimbalkarhasachievedtheQualifiedSpecialistrecognitioninusingthreekeyDOEenergyefficiencysoftwaretools(PHAST,SSAT,andPSAT).

Thomas Wenning, PE, CEM, isaprogrammanager for industrialenergyefficiencyat theU.S.Departmentof Energy’sOakRidgeNationalLaboratory(ORNL)andaJoint-FacultyAssistantProfessor in theDepartmentof IndustrialandSystemsEngineeringattheUniversityof Tennessee.Mr.Wenninghasledthecreationanddeliveryof severalof theDepartmentof Energy’stechnicalassistanceanddeploymentefforts.Chief among them,hehas led the implementationanddeliveryof theDOE’sBetterBuildings,BetterPlantsProgramPartnerswhichworkswithover200majorcompanies tohelp themimprove theirenergymanagementprogramsandreducetheircompany-wideenergyintensity.Inaddition,heisleadingtheDOE’sefforttomodernizetheirenergysystemsoftwaretoolsuiteandassociatedtrainingresources.Mr.WenninghasalsoledandrepresentedtheDOEinnumerousinternationalindustrialenergyefficiencyworkshops,trainings,andassessments.Mr.WenningisaregisteredProfessionalEngineer,anAEECertifiedEnergyManager,aCertifiedPractitionerinEnergyManagementSystems,anSEP-PerformanceVer-ifier,andaDOEQualifiedSpecialist intheareasof steam,pumps,andfans.Mr.ThomasWenningmaybecontactedatwenningtj@ornl.gov.

Kiran ThirumaranisanR&DAssistantStaffmemberintheEnergyEfficien-cyResearchandAnalysisGroupatOakRidgeNationalLaboratory(ORNL).Hesupportsseveralresearchactivities intheareasof energyanalytics,electrification,waterefficiencyandoptimizationof industrialenergysystems.Hehasledthedevel-opmentof numeroustoolsandresourcesonenergyandwaterefficiencyforindus-trieswhichhavebeenextensivelyusedbyDOE’sBetterPlantsProgram.Kiranholdsamaster’sdegreeinmechanicalengineeringfromNorthCarolinaStateUniversitywherehewasheavilyinvolvedwiththeDOE’sIndustrialAssessmentCenter.

Eli Levine, JD, CEM,isaprogrammanagerfortheBetterPlantsprogramintheAdvancedManufacturingOfficeattheU.S.Departmentof Energy.