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英文原文4.1IntroductionThischapterdemonstratesthescopeofthemethoddevelopedforthethreedimensionalanalysisofascrewcompressor.TheCFDpackageusedinthiscasewasCOMETdevelopedbyICCMGmbHHamburg,todayapartofCDAdapco.Theanalysisoftheflowandperformancecharacteristicsofanumberoftypesofscrewmachinesisperformedtodemonstrateavarietyofparametersusedforgridgenerationandcalculation.Thefirstexampleisconcernedwithadryairscrewcompressor.Acommoncompressorcasingisusedwithtwoalternativepairsofrotors.Therotorshaveidenticaloverallgeometricpropertiesbutdifferentlobeprofiles.Theapplicationoftheadaptationtechniqueenablesconvenientgridgenerationforgeometricallydifferentrotors.Theresultsobtainedbythreedimensionalmodellingarecomparedwiththosederivedfromaonedimensionalmodel,previouslyverifiedbycomparisonwithexperimentaldata..Therelativeadvantagesofeachrotorprofilearedemonstrated.Thesecondexampleshowstheapplicationofthreedimensionalflowanalysistothesimulationofanoilinjectedaircompressor.Theresults,thusobtained,arecomparedwithtestresultsobtainedbytheauthorsfromacompressorandtestrig,designedandbuiltatCityUniversity.Theyarepresentedintheformofbothintegralparametersandapindicatordiagram.Calculationsbasedontheassumptionsofthelaminarflowarecomparedtothoseofturbulentflow.Theeffectofgridsizeontheresultsisalsoconsideredandshownhere.Thethirdexamplegivestheanalysisofanoilinjectedcompressorinanammoniarefrigerationplant.Thisutilisestherealfluidpropertysubroutinesintheprocesscalculationsanddemonstratestheblowholeareaandtheleakageflowthroughthecompressorclearances.Thefourthexamplepresentstwocases,oneofadryscrewcompressortoshowtheinfluenceofthermalexpansionoftherotoronscrewcompressorperformanceandoneofahighpressureoilfloodedscrewcompressortoshowtheinfluenceofhighpressureloadsuponthecompressorperformance.4.2FlowinaDryScrewCompressorDryscrewcompressorsarecommonlyusedtoproducepressurisedair,freeofanyoil.Atypicalexampleofsuchamachine,similarinconfigurationtothecompressormodelled,isshowninFigure41.Thisisasinglestagemachinewith4maleand6femalerotorlobes.Themaleandfemalerotorouterdiametersare142.380mmand135.820mmrespectively,whiletheircentrelinesare108.4mmapart.Therotorlengthtomaindiameterratiol/d1.77.Thus,therotorlengthis252.0mm.Themalerotorwithwrapangle248.40isdrivenataspeedof6000rpmbyanelectricmotorthroughagearbox.Themaleandfemalerotorsaresynchronisedthroughtiminggearswiththesameratioasthatofthecompressorrotorlobesi.e.1.5.Thefemalerotorspeedistherefore4000rpm.Themalerotortipspeedisthen44.7m/s,whichisarelativelylowvalueforadryaircompressor.Theworkingchamberissealedfromitsbearingsbyacombinationoflipandlabyrinthseals.Eachrotorissupportedbyoneradialandoneaxialbearing,onthedischargeend,andoneradialbearingonthesuctionendofthecompressor.Thebearingsareloadedbyahighfrequencyforce,whichvariesduetothepressurechangewithintheworkingchamber.Bothradialandaxialforces,aswellasthetorquechangewithafrequencyof4timestherotationalspeed.Thiscorrespondsto400Hzandcoincideswiththenumberofworkingcyclesthatoccurwithinthecompressorperunittime.Figure41CrosssectionofadryscrewcompressorThecompressortakesinairfromtheatmosphereanddischargesittoareceiverataconstantoutputpressureof3bar.Althoughthepressureriseismoderate,leakagethroughradialgapsof150missubstantial.Inmanystudiesandmodelling,procedures,volumetriclossesareassumedtobealinearfunctionofthecrosssectionalareaandthesquarerootofpressuredifference,assumingthattheinterlobeclearanceiskeptmoreorlessconstantbythesynchronisinggears.Theleakagethroughtheclearancesisthenproportionaltotheclearancegapandthelengthoftheleakageline.However,alargeclearancegapisneededtopreventcontactwiththehousingcausedbyrotordeformationduetothepressureandtemperaturechangeswithintheworkingchamber.Hence,theonlywaytoreduceleakageistominimisethelengthofthesealingline.Thiscanbeachievedbycarefuldesignofthescrewrotorprofile.Althoughminimising,leakageisanimportantmeansofimprovingascrewcompressorefficiency,itisnottheonlyone.Anotheristoincreasetheflowareabetweenthelobesandtherebyincreasethecompressorflowcapacity,therebyreducingtherelativeeffectofleakage.Modernprofilegenerationmethodstakethesevariouseffectsintoaccountbymeansofoptimisationprocedureswhichleadtoenlargementofthemalerotorinterlobesandreductioninthefemalerotorlobes.Thefemalerotorlobesaretherebystrengthenedandtheirdeformationthusreduced.Todemonstratetheimprovementspossiblefromrotorprofileoptimisation,athreedimensionalflowanalysishasbeencarriedoutfortwodifferentrotorprofileswithinthesamecompressorcasing,asshowninFigure42.BothrotorsareoftheNtypeandrackgenerated.Figure42NRotors,Case1upper,Case2lowerCase1isanolderdesign,similarinshapetoSRMDrotors.Itsfeaturesimplythatthereisalargetorqueonthefemalerotor,thesealinglineisrelativelylongandthefemalelobesarerelativelyweak.Case2,shownonthebottomofFigure42,hasrotorsoptimisedforoperatingondryair.Thefemalerotorisstrongerandthemalerotorisweaker.Thisresultsinhigherdelivery,arelativelyshortersealinglineandlesstorqueonthefemalerotor.Allthesefeatureshelptoimprovescrewcompressorperformance.TheresultsofthesetwoanalysesarepresentedintheformofvelocitydistributionsintheplanesdefinedbycrosssectionsAAandBB,showninFigure41.Inthecaseofthisstudy,theeffectofrotorprofilechangesoncompressorintegralperformanceparameterscanbepredictedfairlyaccuratelywithonedimensionalmodels,evenifsomeofthedetailedassumptionsmadeinsuchanalyticalmodelsareinaccurate.Hencetheintegralresultsobtainedfromthethreedimensionalanalysisarecomparedwiththosefromaonedimensionalmodel.4.2.1GridGenerationforaDryScrewCompressorInCase1,therotorsaremappedwith52numericalcellsalongtheinterlobeonthemalerotorand36cellsalongeachinterlobeonthefemalerotorinthecircumferentialdirection.Thisgives208and216numericalcellsrespectivelyinthecircumferentialdirectionforthemaleandfemalerotors.Atotalof6cellsintheradialdirectionand97cellsintheaxialdirectionisspecifiedforbothrotors.Thisarrangementresultsinanumericalmeshwith327090cellsfortheentiremachine.ThecrosssectionfortheCase1rotorsisshowninFigure43.Thefemalerotorisrelativelythinandhasalargeradiusonthelobetip.Therefore,itismoreeasilymappedthaninCase2wherethetipradiusissmaller,asshowninFigure44.Figure43CrosssectionthroughthenumericalmeshforCase1rotorsTherotorsinCase2aremappedwith60cellsalongthemalerotorlobeand40cellsalongthefemalelobe,whichgives240cellsalongbothrotorsinthecircumferentialdirection.Intheradialdirection,therotorsaremappedwith6cellswhile111cellsareselectedformappingalongtherotoraxis.Thus,theentireworkingchamberforthiscompressorhas406570cells.Inthiscase,differentmeshsizesareappliedanddifferentcriteriaarechosenfortheboundaryadaptationoftheserotors.Themainadaptationcriterionselectedfortherotorsisthelocalradiuscurvaturewithagridpointratioof0.3toobtainthedesiredqualityofdistributionalongtherotorboundaries.Bythismeans,themorecurvedrotorsaremappedwithonlyaslightincreaseinthegridsizetoobtainareasonablevalueofthegridaspectratio.Toobtainasimilargridaspectratiowithoutadaptation,85cellswouldhavebeenrequiredinsteadof60alongoneinterlobeonthefemalerotor.Thiswouldgive510cellsinthecircumferentialdirectiononeachofrotors.Ifthenumberofcellsintheradialdirectionisalsoincreasedtobe8insteadof6butthenumberofcellsalongaxisiskeptconstant,theentiregridwouldcontainmorethenamillioncellswhichwould,inturn,resultinasignificantlylongercalculationtimeandanincreasedrequirementforcomputermemory.
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