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英文原文DesignefficiencyoptimizationofonedimensionalmultistageaxialflowcompressorAbstractAmodelfortheoptimaldesignofamultistagecompressor,assumingafixedconfigurationoftheflowpath,ispresented.Theabsoluteinletandexitanglesoftherotor,theabsoluteexitangleofthestator,andtherelativegasdensitiesattheinletandexitstationsofthestator,ofeverystage,aretakenasthedesignvariables.Analyticalrelationsofthecompressorelementalstageandthemultistagecompressorareobtained.Numericalexamplesareprovidedtoillustratetheeffectsofvariousparametersontheoptimalperformanceofthemultistagecompressor.2007ElsevierLtd.Allrightsreserved.KeywordsMultistageaxialflowcompressorEfficiencyAnalyticalrelationOptimization1.IntroductionThedesignoftheaxialflowcompressorispartiallyanart.Thelackofaccuratepredictioninfluencesthedesignprocess.Untiltoday,therearenomethodscurrentlyavailablethatpermitthepredictionofthevaluesofthesequantitiestoasufficientaccuracyforanewdesign.Someprogresseshasbeenachievedviatheapplicationofnumericaloptimizationtechniquestosingleandmultistageaxialflowcompressordesign1–22.EspeciallywiththedevelopmentofcomputationalfluiddynamicsCFD,manymoreaccuratemethodsofcalculatinghavebeenpresentedinmanyreferencesinwhichthetechniquesofCFDhavebeenappliedtotwoandthreedimensionaloptimaldesignsofaxialflowcompressors17–20.However,itisstillofworthwhilesignificancetocalculate,usingonedimensionalflowtheory,theoptimaldesignofcompressors.Boiko23presentedadetailedmathematicalmodelfortheoptimaldesignofsingleandmultistageaxialflowturbinesbyassumingiafixeddistributionofaxialvelocitiesoriiafixedflowpathshape,andobtainedthecorrespondingoptimizedresults.Usingasimilaridea,Chenetal.22presentedamathematicalmodelfortheoptimaldesignofasinglestageaxialflowcompressorbyassumingafixeddistributionofaxialvelocities.Inthispaper,amodelfortheoptimaldesignofamultistageaxialflowcompressor,byassumingafixedflowpathshape,ispresented.Theabsoluteinletandexitanglesoftherotor,theabsoluteexitangleofthestator,andtherelativegasdensitiesattheinletandexitstationsofthestator,ofeachstage,aretakenasthedesignvariables.Analyticalrelationsofthecompressorstageareobtained.Numericalexamplesareprovidedtoillustratetheeffectsofvariousparametersontheoptimalperformanceofthemultistagecompressor2.FundamentalequationsforelementalstagecompressorConsideranstageaxialflowcompressor–seeFig.1.Fig.2showsthespecificenthalpy–specificentropydiagramofthiscompressor.Foranstageaxialflowcompressor,thereare2n1sectionstations.Thestagevelocitytriangleofanintermediatestagei.e.jthstageisshowninFig.3.Thecorrespondingspecificenthalpy–specificentropydiagramisshowninFig.4.Theperformancecalculationofmultistagecompressorisperformedusingonedimensionalflowtheory.Theanalysisbeginswiththeenergyandcontinuityequations,andtheaxialflowvelocitiesoftheworkingfluidandwheelvelocitiesatthedifferentstationsinthecompressorarenotconsideredasconstant,thatis,ijuu,ijccij,whereidenotestheithstationandjdenotesthejthstage.ThemajorassumptionsmadeinthemethodareasfollowsTheworkingfluidflowsstablyrelativetothevanes,statorsandrotors,whichrotateatafixedspeed.Theworkingfluidiscompressible,nonviscousandadiabatic.Themassflowrateoftheworkingfluidisconstant.Thecompressionprocessishomogeneousintheworkingfluid.Theabsoluteoutletangleoftheworkingfluid,injthstage,isequaltotheabsoluteinletangleoftheworkingfluidinj1thstage.Theeffectsofintakeandoutletpipingareneglected.Thespecificenthalpiesateverystationareasfollowsj22ji2ji1/2iihc(1)j22j11i2j1i1/2iihc(2)Thetotalprofilelossesofthejthstagerotorandthestatorarecalculatedasfollows222rjrj2j12j12j12j12j12j12j1rj/2/2//hwGFuGctgF(3)222rjsj2j2j2j2jsj/2/1/2hcGFctg(4)Whereriisthetotalprofilelosscoefficientofjthstagerotorbladeandsjisthatofjthstagestatorblade.Fig.1.FlowpathofanstageaxialflowcompressorFig.2.Enthalpy–entropydiagramofanstagecompressorFig.3.VelocitytriangleofanintermediatestageFig.4.Enthalpy–entropydiagramofanintermediatestage.Thebladeprofilelosscoefficientsriandsjarefunctionsofparametersoftheworkingfluidandbladegeometry.Theycanbecalculatedusingvariousmethodsandareconsideredtobeconstants.Whenriandsjarefunctionsoftheparametersoftheworkingfluidandbladegeometry,thelosscoefficientscanbecalculatedusingthemethodofRef.24,whichwasemployedanddescribedinRef.21.Theoptimizationproblemcanbesolvedusingtheiterativemethod1First,selecttheoriginalvaluesofriandsjandthencalculatetheparametersofthestage.2Secondly,calculatethevaluesofriandsj,andrepeatthefirststepuntilthedifferencesbetweenthecalculatedvaluesandtheoriginalonesaresmallenough.Theworkrequiredbythejthstageisj2ju,2j2j1u,2j12j2j2j12j12j2j2j12j1GGhucucuctguctgFF(5)Theworkrequiredbythejthrotoris22222j12j2j2j1rj22wwuuh(6)Thedegreeofreactionofthejthstagecompressorisdefinedasrjj/hh.Hence,onehasu,2j222a,2j2j2j1ja,2j2j2j11112kctgctgkkctgctg(7)Whereu,ik,a,i12kinarethevelocitycoefficients,andtheyaredefinedasa,ia,ia,111ii//kccFFandu,ii1/kuuTheconstraintconditionscanbeobtainedfromtheenergybalanceequationfortheonedimensionalflowj222j112ji2j2j2ji1/1/20AiihGFctg(8)j22j12j1i2j12j12j1i1/1/20AiihGFctg(9)3.MathematicalmodelforthebehaviourofthemultistagecompressorThecompressionworkrequiredbyeachstageisj1hjn.Thetotalcompressionworkrequiredbythemultistagecompressorisncjj1hh.Thestagnationisentropicenthalpyriseofeverystageiss,jh.Thesumofthestagnationisentropicenthalpyriseofeachstageisns,jj1h,whilethestagnationisentropicenthalpyriseofthemultistagecompressorissch.Onehasns,jzscj11hh,Thestagnationisentropicefficiencyofthemultistageaxialflowcompressoris
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