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英文原文41INTRODUCTIONTHISCHAPTERDEMONSTRATESTHESCOPEOFTHEMETHODDEVELOPEDFORTHETHREEDIMENSIONALANALYSISOFASCREWCOMPRESSORTHECFDPACKAGEUSEDINTHISCASEWASCOMETDEVELOPEDBYICCMGMBHHAMBURG,TODAYAPARTOFCDADAPCOTHEANALYSISOFTHEFLOWANDPERFORMANCECHARACTERISTICSOFANUMBEROFTYPESOFSCREWMACHINESISPERFORMEDTODEMONSTRATEAVARIETYOFPARAMETERSUSEDFORGRIDGENERATIONANDCALCULATIONTHEFIRSTEXAMPLEISCONCERNEDWITHADRYAIRSCREWCOMPRESSORACOMMONCOMPRESSORCASINGISUSEDWITHTWOALTERNATIVEPAIRSOFROTORSTHEROTORSHAVEIDENTICALOVERALLGEOMETRICPROPERTIESBUTDIFFERENTLOBEPROFILESTHEAPPLICATIONOFTHEADAPTATIONTECHNIQUEENABLESCONVENIENTGRIDGENERATIONFORGEOMETRICALLYDIFFERENTROTORSTHERESULTSOBTAINEDBYTHREEDIMENSIONALMODELLINGARECOMPAREDWITHTHOSEDERIVEDFROMAONEDIMENSIONALMODEL,PREVIOUSLYVERIFIEDBYCOMPARISONWITHEXPERIMENTALDATATHERELATIVEADVANTAGESOFEACHROTORPROFILEAREDEMONSTRATEDTHESECONDEXAMPLESHOWSTHEAPPLICATIONOFTHREEDIMENSIONALFLOWANALYSISTOTHESIMULATIONOFANOILINJECTEDAIRCOMPRESSORTHERESULTS,THUSOBTAINED,ARECOMPAREDWITHTESTRESULTSOBTAINEDBYTHEAUTHORSFROMACOMPRESSORANDTESTRIG,DESIGNEDANDBUILTATCITYUNIVERSITYTHEYAREPRESENTEDINTHEFORMOFBOTHINTEGRALPARAMETERSANDAPINDICATORDIAGRAMCALCULATIONSBASEDONTHEASSUMPTIONSOFTHELAMINARFLOWARECOMPAREDTOTHOSEOFTURBULENTFLOWTHEEFFECTOFGRIDSIZEONTHERESULTSISALSOCONSIDEREDANDSHOWNHERETHETHIRDEXAMPLEGIVESTHEANALYSISOFANOILINJECTEDCOMPRESSORINANAMMONIAREFRIGERATIONPLANTTHISUTILISESTHEREALFLUIDPROPERTYSUBROUTINESINTHEPROCESSCALCULATIONSANDDEMONSTRATESTHEBLOWHOLEAREAANDTHELEAKAGEFLOWTHROUGHTHECOMPRESSORCLEARANCESTHEFOURTHEXAMPLEPRESENTSTWOCASES,ONEOFADRYSCREWCOMPRESSORTOSHOWTHEINFLUENCEOFTHERMALEXPANSIONOFTHEROTORONSCREWCOMPRESSORPERFORMANCEANDONEOFAHIGHPRESSUREOILFLOODEDSCREWCOMPRESSORTOSHOWTHEINFLUENCEOFHIGHPRESSURELOADSUPONTHECOMPRESSORPERFORMANCE42FLOWINADRYSCREWCOMPRESSORDRYSCREWCOMPRESSORSARECOMMONLYUSEDTOPRODUCEPRESSURISEDAIR,FREEOFANYOILATYPICALEXAMPLEOFSUCHAMACHINE,SIMILARINCONFIGURATIONTOTHECOMPRESSORMODELLED,ISSHOWNINFIGURE41THISISASINGLESTAGEMACHINEWITH4MALEAND6FEMALEROTORLOBESTHEMALEANDFEMALEROTOROUTERDIAMETERSARE142380MMAND135820MMRESPECTIVELY,WHILETHEIRCENTRELINESARE1084MMAPARTTHEROTORLENGTHTOMAINDIAMETERRATIOL/D177THUS,THEROTORLENGTHIS2520MMTHEMALEROTORWITHWRAPANGLE24840ISDRIVENATASPEEDOF6000RPMBYANELECTRICMOTORTHROUGHAGEARBOXTHEMALEANDFEMALEROTORSARESYNCHRONISEDTHROUGHTIMINGGEARSWITHTHESAMERATIOASTHATOFTHECOMPRESSORROTORLOBESIE15THEFEMALEROTORSPEEDISTHEREFORE4000RPMTHEMALEROTORTIPSPEEDISTHEN447M/S,WHICHISARELATIVELYLOWVALUEFORADRYAIRCOMPRESSORTHEWORKINGCHAMBERISSEALEDFROMITSBEARINGSBYACOMBINATIONOFLIPANDLABYRINTHSEALSEACHROTORISSUPPORTEDBYONERADIALANDONEAXIALBEARING,ONTHEDISCHARGEEND,ANDONERADIALBEARINGONTHESUCTIONENDOFTHECOMPRESSORTHEBEARINGSARELOADEDBYAHIGHFREQUENCYFORCE,WHICHVARIESDUETOTHEPRESSURECHANGEWITHINTHEWORKINGCHAMBERBOTHRADIALANDAXIALFORCES,ASWELLASTHETORQUECHANGEWITHAFREQUENCYOF4TIMESTHEROTATIONALSPEEDTHISCORRESPONDSTO400HZANDCOINCIDESWITHTHENUMBEROFWORKINGCYCLESTHATOCCURWITHINTHECOMPRESSORPERUNITTIMEFIGURE41CROSSSECTIONOFADRYSCREWCOMPRESSORTHECOMPRESSORTAKESINAIRFROMTHEATMOSPHEREANDDISCHARGESITTOARECEIVERATACONSTANTOUTPUTPRESSUREOF3BARALTHOUGHTHEPRESSURERISEISMODERATE,LEAKAGETHROUGHRADIALGAPSOF150MISSUBSTANTIALINMANYSTUDIESANDMODELLING,PROCEDURES,VOLUMETRICLOSSESAREASSUMEDTOBEALINEARFUNCTIONOFTHECROSSSECTIONALAREAANDTHESQUAREROOTOFPRESSUREDIFFERENCE,ASSUMINGTHATTHEINTERLOBECLEARANCEISKEPTMOREORLESSCONSTANTBYTHESYNCHRONISINGGEARSTHELEAKAGETHROUGHTHECLEARANCESISTHENPROPORTIONALTOTHECLEARANCEGAPANDTHELENGTHOFTHELEAKAGELINEHOWEVER,ALARGECLEARANCEGAPISNEEDEDTOPREVENTCONTACTWITHTHEHOUSINGCAUSEDBYROTORDEFORMATIONDUETOTHEPRESSUREANDTEMPERATURECHANGESWITHINTHEWORKINGCHAMBERHENCE,THEONLYWAYTOREDUCELEAKAGEISTOMINIMISETHELENGTHOFTHESEALINGLINETHISCANBEACHIEVEDBYCAREFULDESIGNOFTHESCREWROTORPROFILEALTHOUGHMINIMISING,LEAKAGEISANIMPORTANTMEANSOFIMPROVINGASCREWCOMPRESSOREFFICIENCY,ITISNOTTHEONLYONEANOTHERISTOINCREASETHEFLOWAREABETWEENTHELOBESANDTHEREBYINCREASETHECOMPRESSORFLOWCAPACITY,THEREBYREDUCINGTHERELATIVEEFFECTOFLEAKAGEMODERNPROFILEGENERATIONMETHODSTAKETHESEVARIOUSEFFECTSINTOACCOUNTBYMEANSOFOPTIMISATIONPROCEDURESWHICHLEADTOENLARGEMENTOFTHEMALEROTORINTERLOBESANDREDUCTIONINTHEFEMALEROTORLOBESTHEFEMALEROTORLOBESARETHEREBYSTRENGTHENEDANDTHEIRDEFORMATIONTHUSREDUCEDTODEMONSTRATETHEIMPROVEMENTSPOSSIBLEFROMROTORPROFILEOPTIMISATION,ATHREEDIMENSIONALFLOWANALYSISHASBEENCARRIEDOUTFORTWODIFFERENTROTORPROFILESWITHINTHESAMECOMPRESSORCASING,ASSHOWNINFIGURE42BOTHROTORSAREOFTHE“N”TYPEANDRACKGENERATEDFIGURE42‘N’ROTORS,CASE1UPPER,CASE2LOWERCASE1ISANOLDERDESIGN,SIMILARINSHAPETOSRM“D”ROTORSITSFEATURESIMPLYTHATTHEREISALARGETORQUEONTHEFEMALEROTOR,THESEALINGLINEISRELATIVELYLONGANDTHEFEMALELOBESARERELATIVELYWEAKCASE2,SHOWNONTHEBOTTOMOFFIGURE42,HASROTORSOPTIMISEDFOROPERATINGONDRYAIRTHEFEMALEROTORISSTRONGERANDTHEMALEROTORISWEAKERTHISRESULTSINHIGHERDELIVERY,ARELATIVELYSHORTERSEALINGLINEANDLESSTORQUEONTHEFEMALEROTORALLTHESEFEATURESHELPTOIMPROVESCREWCOMPRESSORPERFORMANCETHERESULTSOFTHESETWOANALYSESAREPRESENTEDINTHEFORMOFVELOCITYDISTRIBUTIONSINTHEPLANESDEFINEDBYCROSSSECTIONSAAANDBB,SHOWNINFIGURE41INTHECASEOFTHISSTUDY,THEEFFECTOFROTORPROFILECHANGESONCOMPRESSORINTEGRALPERFORMANCEPARAMETERSCANBEPREDICTEDFAIRLYACCURATELYWITHONEDIMENSIONALMODELS,EVENIFSOMEOFTHEDETAILEDASSUMPTIONSMADEINSUCHANALYTICALMODELSAREINACCURATEHENCETHEINTEGRALRESULTSOBTAINEDFROMTHETHREEDIMENSIONALANALYSISARECOMPAREDWITHTHOSEFROMAONEDIMENSIONALMODEL421GRIDGENERATIONFORADRYSCREWCOMPRESSORINCASE1,THEROTORSAREMAPPEDWITH52NUMERICALCELLSALONGTHEINTERLOBEONTHEMALEROTORAND36CELLSALONGEACHINTERLOBEONTHEFEMALEROTORINTHECIRCUMFERENTIALDIRECTIONTHISGIVES208AND216NUMERICALCELLSRESPECTIVELYINTHECIRCUMFERENTIALDIRECTIONFORTHEMALEANDFEMALEROTORSATOTALOF6CELLSINTHERADIALDIRECTIONAND97CELLSINTHEAXIALDIRECTIONISSPECIFIEDFORBOTHROTORSTHISARRANGEMENTRESULTSINANUMERICALMESHWITH327090CELLSFORTHEENTIREMACHINETHECROSSSECTIONFORTHECASE1ROTORSISSHOWNINFIGURE43THEFEMALEROTORISRELATIVELYTHINANDHASALARGERADIUSONTHELOBETIPTHEREFORE,ITISMOREEASILYMAPPEDTHANINCASE2WHERETHETIPRADIUSISSMALLER,ASSHOWNINFIGURE44FIGURE43CROSSSECTIONTHROUGHTHENUMERICALMESHFORCASE1ROTORSTHEROTORSINCASE2AREMAPPEDWITH60CELLSALONGTHEMALEROTORLOBEAND40CELLSALONGTHEFEMALELOBE,WHICHGIVES240CELLSALONGBOTHROTORSINTHECIRCUMFERENTIALDIRECTIONINTHERADIALDIRECTION,THEROTORSAREMAPPEDWITH6CELLSWHILE111CELLSARESELECTEDFORMAPPINGALONGTHEROTORAXISTHUS,THEENTIREWORKINGCHAMBERFORTHISCOMPRESSORHAS406570CELLSINTHISCASE,DIFFERENTMESHSIZESAREAPPLIEDANDDIFFERENTCRITERIAARECHOSENFORTHEBOUNDARYADAPTATIONOFTHESEROTORSTHEMAINADAPTATIONCRITERIONSELECTEDFORTHEROTORSISTHELOCALRADIUSCURVATUREWITHAGRIDPOINTRATIOOF03TOOBTAINTHEDESIREDQUALITYOFDISTRIBUTIONALONGTHEROTORBOUNDARIESBYTHISMEANS,THEMORECURVEDROTORSAREMAPPEDWITHONLYASLIGHTINCREASEINTHEGRIDSIZETOOBTAINAREASONABLEVALUEOFTHEGRIDASPECTRATIOTOOBTAINASIMILARGRIDASPECTRATIOWITHOUTADAPTATION,85CELLSWOULDHAVEBEENREQUIREDINSTEADOF60ALONGONEINTERLOBEONTHEFEMALEROTORTHISWOULDGIVE510CELLSINTHECIRCUMFERENTIALDIRECTIONONEACHOFROTORSIFTHENUMBEROFCELLSINTHERADIALDIRECTIONISALSOINCREASEDTOBE8INSTEADOF6BUTTHENUMBEROFCELLSALONGAXISISKEPTCONSTANT,THEENTIREGRIDWOULDCONTAINMORETHENAMILLIONCELLSWHICHWOULD,INTURN,RESULTINASIGNIFICANTLYLONGERCALCULATIONTIMEANDANINCREASEDREQUIREMENTFORCOMPUTERMEMORY
