外文翻译--一维数学模型.doc

英文原文3.1OneDimensionalMathematicalModel51TheConservationofInternalEnergy.ddvpQhmhmdQduoutoutinin+=（3.1）whereisangleofrotationofthemainrotor,h=h()isspecificenthalpy,m=m()ismassflowratep=p(),fluidpressureintheworkingchambercontrolvolume,Q=Q(),heattransferbetweenthefluidandthecompressorsurrounding,V=V()localvolumeofthecompressorworkingchamber.Intheaboveequationthesubscriptsinandoutdenotethefluidinflowandoutflow.Thefluidtotalenthalpyinflowconsistsofthefollowingcomponents:oiloilglglsucsuvininhmhmhmh.,.m+=(3.2)wheresubscriptsl,gdenoteleakagegainsuc,suctionconditions,andoildenotesoil.Thefluidtotaloutflowenthalpyconsistsof:lllldisdisououthmhmhm,.+=(3.3)whereindicesl,ldenoteleakagelossanddisdenotesthedischargeconditionswithmdisdenotingthedischargemassflowrateofthegascontaminatedwiththeoilorotherliquidinjected.TherighthandsideoftheenergyequationconsistsofthefollowingtermswhicharemodelTheheatexchangebetweenthefluidandthecompressorscrewrotorsandcasingandthroughthemtothesurrounding,duetothedifferenceintemperaturesofgasandthecasingandrotorsurfacesisaccountedforbytheheattransfercoefficientevaluatedfromtheexpressionNu=0.023Re0.8.ForthecharacteristiclengthintheReynoldsandNusseltnumberthedifferencebetweentheouterandinnerdiametersofthemainrotorwasadopted.Thismaynotbethemostappropriatedimensionforthispurpose,butthecharacteristiclengthappearsintheexpressionfortheheattransfercoefficientwiththeexponentof0.2andthereforehaslittleinfluenceaslongasitremainswithinthesameorderofmagnitudeasothercharacteristicdimensionsofthemachineandaslongasitcharacterizesthecompressorsize.ThecharacteristicvelocityfortheRenumberiscomputedfromthelocalmassflowandthecross-sectionalarea.Herethesurfaceoverwhichtheheatisexchanged,aswellasthewalltemperature,dependontherotationangleofthemainrotor.Theenergygainduetothegasinflowintotheworkingvolumeisrepresentedbytheproductofthemassintakeanditsaveragedenthalpy.Assuch,theenergyinflowvarieswiththerotationalangle.Duringthesuctionperiod,gasenterstheworkingvolumebringingtheaveragedgasenthalpy,523CalculationofScrewCompressorPerformancewhichdominatesinthesuctionchamber.However,duringthetimewhenthesuctionportisclosed,acertainamountofthecompressedgasleaksintothecompressorworkingchamberthroughtheclearances.Themassofthisgas,aswellasitsenthalpyaredeterminedonthebasisofthegasleakageequations.Theworkingvolumeisfilledwithgasduetoleakageonlywhenthegaspressureinthespacearoundtheworkingvolumeishigher,otherwisethereisnoleakage,oritisintheoppositedirection,i.e.fromtheworkingchambertowardsotherplenums.Thetotalinflowenthalpyisfurthercorrectedbytheamountofenthalpybroughtintotheworkingchamberbytheinjectedoil.Theenergylossduetothegasoutflowfromtheworkingvolumeisdefinedbytheproductofthemassoutflowanditsaveragedgasenthalpy.Duringdelivery,thisisthecompressedgasenteringthedischargeplenum,while,inthecaseofexpansionduetoinappropriatedischargepressure,thisisthegaswhichleaksthroughtheclearancesfromtheworkingvolumeintotheneighbouringspaceatalowerpressure.Ifthepressureintheworkingchamberislowerthanthatinthedischargechamberandifthedischargeportisopen,theflowwillbeinthereversedirection,i.e.fromthedischargeplenumintotheworkingchamber.Thechangeofmasshasanegativesignanditsassumedenthalpyisequaltotheaveragedgasenthalpyinthepressurechamber.ThethermodynamicworksuppliedtothegasduringthecompressionprocessisrepresentedbythetermpdVd.Thistermisevaluatedfromthelocalpressureandlocalvolumechangerate.Thelatterisobtainedfromtherelationshipsdefiningthescrewkinematicswhichyieldtheinstantaneousworkingvolumeanditschangewithrotationangle.InfactthetermdV/dcanbeidentifiedwiththeinstantaneousinterlobearea,correctedforthecapturedandoverlappingareas.Ifoilorotherfluidisinjectedintotheworkingchamberofthecompressor,theoilmassinflowanditsenthalpyshouldbeincludedintheinflowterms.Inspiteofthefactthattheoilmassfractioninthemixtureissignificant,itseffectuponthevolumeflowrateisonlymarginalbecausetheoilvolumefractionisusuallyverysmall.Thetotalfluidmassoutflowalsoincludestheinjectedoil,thegreaterpartofwhichremainsmixedwiththeworkingfluid.Heattransferbetweenthegasandoildropletsisdescribedbyafirstorderdifferentialequation.TheMassContinuityEquationoutoutininhmhmdmd.=（3.4）Themassinflowrateconsistsof:oilglsucininmmmhm.,.（3.5）3.1OneDimensionalMathematicalModel53Themassoutflowrateconsistsof:.,.lldisoutmmm(3.6)EachofthemassflowratesatisfiesthecontinuityequationAm.(3.7)wherewm/sdenotesfluidvelocity,fluiddensityandAtheflowcrosssectionarea.Theinstantaneousdensity=()isobtainedfromtheinstantaneousmassmtrappedinthecontrolvolumeandthesizeofthecorrespondinginstantaneousvolumeV,as=m/V.3.1.2SuctionandDischargePortsThecross-sectionareaAisobtainedfromthecompressorgeometryanditmaybeconsideredasaperiodicfunctionoftheangleofrotation.Thesuctionportareaisdefinedby:sucosucAAsin,suc(3.8)wheresucmeansthestartingvalueofatthemomentofthesuctionportopening,andAsuc,0denotesthemaximumvalueofthesuctionportcrosssectionarea.Thereferencevalueoftherotationangleisassumedatthesuctionportclosingsothatsuctionendsat=0,ifnotspecifieddifferently.Thedischargeportareaislikewisedefinedby:secodisAAsin,dis(3.9)wheresubscriptedenotestheendofdischarge,cdenotestheendofcompressionandAdis,0standsforthemaximumvalueofthedischargeportcrosssectionalarea.SuctionandDischargePortFluidVelocities)(212hh(3.10)whereisthesuction/dischargeorificeflowcoefficient,whilesubscripts1and2denotetheconditionsdownstreamandupstreamoftheconsideredport.Theprovisionsuppliedinthecomputercodewillcalculateforareverseflowifh2h1.543CalculationofScrewCompressorPerformance3.1.3GasLeakagesLeakagesinascrewmachineamounttoasubstantialpartofthetotalflowrateandthereforeplayanimportantrolebecausetheyinfluencetheprocessbothbyaffectingthecompressormassflowrateorcompressordelivery,i.e.volumetricefficiencyandthethermodynamicefficiencyofthecompressionwork.Forpracticalcomputationoftheeffectsofleakageuponthecompressorprocess,itisconvenienttodistinguishtwotypesofleakages,accordingtotheirdirectionwithregardtotheworkingchamber:gainandlossleakages.Thegainleakagescomefromthedischargeplenumandfromtheneighbouringworkingchamberwhichhasahigherpressure.Thelossleakagesleavethechambertowardsthesuctionplenumandtotheneighbouringchamberwithalowerpressure.Computationoftheleakagevelocityfollowsfromconsiderationofthefluidflowthroughtheclearance.TheprocessisessentiallyadiabaticFanno-flow.Inordertosimplifythecomputation,theflowisissometimesassumedtobeatconstanttemperatureratherthanatconstantenthalpy.Thisdeparturefromtheprevailingadiabaticconditionshasonlyamarginalinfluenceiftheanalysisiscarriedoutindifferentialform,i.e.forthesmallchangesoftherotationalangle,asfollowedinthepresentmodel.Thepresentmodeltreatsonlygasleakage.Noattemptismadetoaccountforleakageofagas-liquidmixture,whiletheeffectoftheoilfilmcanbeincorporatedbyanappropriatereductionoftheclearancegaps.Anidealizedclearancegapisassumedtohavearectangularshapeandthemassflowofleakingfluidisexpressedbythecontinuityequation:glllAm.(3.11)whererandwaredensityandvelocityoftheleakinggas,Ag=lggtheclearancegapcross-sectionalarea,lgleakageclearancelength,sealingline,gleakageclearancewidthorgap,=(Re,Ma)theleakageflowdischargecoefficient.Fourdifferentsealinglinesaredistinguishedinascrewcompressor:theleadingtipsealinglineformedbetweenthemainandgaterotorforwardtipandcasing,thetrailingtipsealinglineformedbetweenthemainandgatereversetipandcasing,thefrontsealinglinebetweenthedischargerotorfrontandthehousingandtheinterlobesealinglinebetweentherotors.Allsealinglineshaveclearancegapswhichformleakageareas.Addition