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英文原文ScrewCompressorsN.StosicI.SmithA.KovacevicScrewCompressorsMathematicalModellingandPerformanceCalculationWith99FiguresABCProf.NikolaStosicProf.IanK.SmithDr.AhmedKovacevicCityUniversitySchoolofEngineeringandMathematicalSciencesNorthamptonSquareLondonEC1V0HBU.K.e-mail:n.stosiccity.ac.uki.k.smithcity.ac.uka.kovaceviccity.ac.ukLibraryofCongressControlNumber:2004117305ISBN-103-540-24275-9SpringerBerlinHeidelbergNewYorkISBN-13978-3-540-24275-8SpringerBerlinHeidelbergNewYorkThisworkissubjecttocopyright.Allrightsarereserved,whetherthewholeorpartofthematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation,broadcasting,reproductiononmicrofilmorinanyotherway,andstorageindatabanks.DuplicationofthispublicationorpartsthereofispermittedonlyundertheprovisionsoftheGermanCopyrightLawofSeptember9,1965,initscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpringer.ViolationsareliableforprosecutionundertheGermanCopyrightLaw.SpringerisapartofSpringerScience+BusinessM_cSpringer-VerlagBerlinHeidelberg2005PrintedinTheNetherlandsTheuseofgeneraldescriptivenames,registerednames,trademarks,hispublicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevantprotectivelawsandregulationsandthereforefreeforgeneraluse.Typesetting:bytheauthorsandTechBooksusingaSpringerLATEXmacropackageCoverdesign:medio,BerlinPrintedonacid-freepaperSPIN:1130685662/3141/jl543210PrefaceAlthoughtheprinciplesofoperationofhelicalscrewmachines,ascompressorsorexpanders,havebeenwellknownformorethan100years,itisonlyduringthepast30yearsthatthesemachineshavebecomewidelyused.Themainreasonsforthelongperiodbeforetheywereadoptedweretheirrelativelypoorefficiencyandthehighcostofmanufacturingtheirrotors.Twomaindevelopmentsledtoasolutiontothesedifficulties.Thefirstofthesewastheintroductionoftheasymmetricrotorprofilein1973.Thisreducedtheblowholearea,whichwasthemainsourceofinternalleakagebyapproximately90%,andtherebyraisedthethermodynamicefficiencyofthesemachines,toroughlythesamelevelasthatoftraditionalreciprocatingcompressors.Thesecondwastheintroductionofprecisethreadmillingmachinetoolsatapproximatelythesametime.Thismadeitpossibletomanufactureitemsofcomplexshape,suchastherotors,bothaccuratelyandcheaply.Fromthenon,asaresultoftheireverimprovingefficiencies,highreliabilityandcompactform,screwcompressorshavetakenanincreasingshareofthecompressormarket,especiallyinthefieldsofcompressedairproduction,andrefrigerationandairconditioning,andtoday,asubstantialproportionofcompressorsmanufacturedforindustryareofthistype.Despite,thenowwideusageofscrewcompressorsandthepublicationofmanyscientificpapersontheirdevelopment,onlyahandfuloftextbookshavebeenpublishedtodate,whichgivearigorousexpositionoftheprinciplesoftheiroperationandnoneoftheseareinEnglish.ThepublicationofthisvolumecoincideswiththetenthanniversaryoftheestablishmentoftheCentreforPositiveDisplacementCompressorTechnologyatCityUniversity,London,wheremuch,ifnotall,ofthematerialitcontainswasdeveloped.Itsaimistogiveanuptodatesummaryofthestateoftheart.Itsavailabilityinasinglevolumeshouldthenhelpengineersinindustrytoreplacedesignproceduresbasedonthesimpleassumptionsofthecompressionofafixedmassofidealgas,bymoreuptodatemethods.Thesearebasedoncomputermodels,whichsimulaterealcompressionandexpansionprocessesmorereliably,byallowingforleakage,inletandoutletflowandotherlosses,VIPrefaceandtheassumptionofrealfluidpropertiesintheworkingprocess.Also,methodsaregivenfordevelopingrotorprofiles,basedonthemathematicaltheoryofgearing,ratherthanempiricalcurvefitting.Inaddition,somedescriptionisincludedofproceduresforthethreedimensionalmodellingofheatandfluidflowthroughthesemachinesandhowinteractionbetweentherotorsandthecasingproducesperformancechanges,whichhithertocouldnotbecalculated.Itisshownthatonlyarelativelysmallnumberofinputparametersisrequiredtodescribeboththegeometryandperformanceofscrewcompressors.Thismakesiteasytocontrolthedesignprocesssothatmodificationscanbecrossreferencedthroughdesignsoftwareprograms,thussavingbothcomputerresourcesanddesigntime,whencomparedwithtraditionaldesignprocedures.Alltheanalyticalproceduresdescribed,havebeentriedandprovenonmachinescurrentlyinindustrialproductionandhaveledtoimprovementsinperformanceandreductionsinsizeandcost,whichwerehardlyconsideredpossibletenyearsago.Moreover,inallcaseswherethesewereapplied,theimprovedaccuracyoftheanalyticalmodelshasledtocloseagreementbetweenpredictedandmeasuredperformancewhichgreatlyreduceddevelopmenttimeandcost.Additionally,thebetterunderstandingoftheprinciplesofoperationbroughtaboutbysuchstudieshasledtoanextensionoftheareasofapplicationofscrewcompressorsandexpanders.Itishopedthatthisworkwillstimulatefurtherinterestinanarea,where,thoughmuchprogresshasbeenmade,significantadvancesarestillpossible.London,NikolaStosicFebruary2005IanSmithAhmedKovacevicNotationAAreaofpassagecrosssection,oildroplettotalsurfaceaSpeedofsoundCRotorcentredistance,specificheatcapacity,turbulencemodelconstantsdOildropletSautermeandiametereInternalenergyfBodyforcehSpecificenthalpyh=h(),convectiveheattransfercoefficientbetweenoilandgasiUnitvectorIUnittensorkConductivity,kineticenergyofturbulence,timeconstantmMassmInletorexitmassflowratem=m()pRotorlead,pressureintheworkingchamberp=p()PProductionofkineticenergyofturbulenceqSourcetermQHeattransferratebetweenthefluidandthecompressorsurroundingsQ=Q()rRotorradiussDistancebetweenthepoleandrotorcontactpoints,controlvolumesurfacetTimeTTorque,TemperatureuDisplacementofsolidUInternalenergyWWorkoutputvVelocitywFluidvelocityVLocalvolumeofthecompressorworkingchamberV=V()VVolumeflowVIIINotationxRotorcoordinate,drynessfraction,spatialcoordinateyRotorcoordinatezAxialcoordinateGreekLettersTemperaturedilata