螺杆压缩机性能的计算吸入室中占主导地位外文文献翻译中英文翻译外文翻译.docx
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螺杆压缩机性能的计算吸入室中占主导地位外文文献翻译中英文翻译外文翻译.docx
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螺杆压缩机性能的计算吸入室中占主导地位外文文献翻译中英文翻译外文翻译
英文原文
3.1OneDimensionalMathematicalModel51
TheConservationofInternalEnergy
(3.1)
whereθisangleofrotationofthemainrotor,h=h(θ)isspecificenthalpy,m˙=m˙(θ)ismassflowratep=p(θ),fluidpressureintheworkingchambercontrolvolume,˙Q=˙Q(θ),heattransferbetweenthefluidandthecompressorsurrounding,˙V=˙V(θ)localvolumeofthecompressorworkingchamber.
Intheaboveequationthesubscriptsinandoutdenotethefluidinflowandoutflow.
Thefluidtotalenthalpyinflowconsistsofthefollowingcomponents:
(3.2)
wheresubscriptsl,gdenoteleakagegainsuc,suctionconditions,andoildenotesoil.
Thefluidtotaloutflowenthalpyconsistsof:
(3.3)
whereindicesl,ldenoteleakagelossanddisdenotesthedischargeconditionswithm˙disdenotingthedischargemassflowrateofthegascontaminatedwiththeoilorotherliquidinjected.
Therighthandsideoftheenergyequationconsistsofthefollowingtermswhicharemodel
Theheatexchangebetweenthefluidandthecompressorscrewrotorsandcasingandthroughthemtothesurrounding,duetothedifferenceintemperaturesofgasandthecasingandrotorsurfacesisaccountedforbytheheattransfercoefficientevaluatedfromtheexpressionNu=0.023Re0.8.ForthecharacteristiclengthintheReynoldsandNusseltnumberthedifferencebetweentheouterandinnerdiametersofthemainrotorwasadopted.Thismaynotbethemostappropriatedimensionforthispurpose,butthecharacteristiclengthappearsintheexpressionfortheheattransfercoefficientwiththeexponentof0.2andthereforehaslittleinfluenceaslongasitremainswithinthesameorderofmagnitudeasothercharacteristicdimensionsofthemachineandaslongasitcharacterizesthecompressorsize.ThecharacteristicvelocityfortheRenumberiscomputedfromthelocalmassflowandthecross-sectionalarea.Herethesurfaceoverwhichtheheatisexchanged,aswellasthewalltemperature,dependontherotationangleθofthemainrotor.
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.Thechangeofmasshasanegativesign
anditsassumedenthalpyisequaltotheaveragedgasenthalpyinthepressurechamber.
ThethermodynamicworksuppliedtothegasduringthecompressionprocessisrepresentedbythetermpdVdθ.Thistermisevaluatedfromthelocalpressureandlocalvolumechangerate.Thelatterisobtainedfromtherelationshipsdefiningthescrewkinematicswhichyieldtheinstantaneousworkingvolumeanditschangewithrotationangle.InfactthetermdV/dϕcanbeidentifiedwiththeinstantaneousinterlobearea,correctedforthecapturedandoverlappingareas.
Ifoilorotherfluidisinjectedintotheworkingchamberofthecompressor,theoilmassinflowanditsenthalpyshouldbeincludedintheinflowterms.Inspiteofthefactthattheoilmassfractioninthemixtureissignificant,itseffectuponthevolumeflowrateisonlymarginalbecausetheoilvolumefractionisusuallyverysmall.Thetotalfluidmassoutflowalsoincludestheinjectedoil,thegreaterpartofwhichremainsmixedwiththeworkingfluid.Heattransferbetweenthegasandoildropletsisdescribedbyafirstorderdifferentialequation.
TheMassContinuityEquation
(3.4)
Themassinflowrateconsistsof:
(3.5)
3.1OneDimensionalMathematicalModel53
Themassoutflowrateconsistsof:
(3.6)
Eachofthemassflowratesatisfiesthecontinuityequation
(3.7)
wherew[m/s]denotesfluidvelocity,ρ–fluiddensityandA–theflowcrosssection
area.Theinstantaneousdensityρ=ρ(θ)isobtainedfromtheinstantaneousmassmtrappedinthecontrolvolumeandthesizeofthecorrespondinginstantaneousvolumeV,asρ=m/V.
3.1.2SuctionandDischargePorts
Thecross-sectionareaAisobtainedfromthecompressorgeometryanditmaybeconsideredasaperiodicfunctionoftheangleofrotationθ.Thesuctionportareaisdefinedby:
(3.8)
wheresucmeansthestartingvalueofθatthemomentofthesuctionportopening,andAsuc,0denotesthemaximumvalueofthesuctionportcrosssectionarea.Thereferencevalueoftherotationangleθisassumedatthesuctionportclosingsothatsuctionendsatθ=0,ifnotspecifieddifferently.
Thedischargeportareaislikewisedefinedby:
(3.9)
wheresubscriptedenotestheendofdischarge,cdenotestheendofcompressionandAdis,0standsforthemaximumvalueofthedischargeportcrosssectionalarea.
SuctionandDischargePortFluidVelocities
(3.10)
whereμisthesuction/dischargeorificeflowcoefficient,whilesubscripts1and2denotetheconditionsdownstreamandupstreamoftheconsideredport.Theprovisionsuppliedinthecomputercodewillcalculateforareverseflowifh2
543CalculationofScrewCompressorPerformance
3.1.3GasLeakages
Leakagesinascrewmachineamounttoasubstantialpartofthetotalflowrateandthereforeplayanimportantrolebecausetheyinfluencetheprocessbothbyaffectingthecompressormassflowrateorcompressordelivery,i.e.volumetricefficiencyandthethermodynamicefficiencyofthecompressionwork.Forpracticalcomputationoftheeffectsofleakageuponthecompressorprocess,itisconvenienttodistinguishtwotypesofleakages,accordingtotheirdirectionwithregardtotheworkingchamber:
gainandlossleakages.Thegainleakagescomefromthedischargeplenumandfromtheneighbouringworkingchamberwhichhasahigherpressure.Thelossleakagesleavethechambertowardsthesuctionplenumandtotheneighbouringchamberwithalowerpressure.
Computationoftheleakagevelocityfollowsfromconsiderationofthefluidflowthroughtheclearance.TheprocessisessentiallyadiabaticFanno-flow.Inordertosimplifythecomputation,theflowisissometimesassumedtobeatconstanttemperatureratherthanatconstantenthalpy.Thisdeparturefromtheprevailingadiabaticconditionshasonlyamarginalinfluenceiftheanalysisiscarriedoutindifferentialform,i.e.forthesmallchangesoftherotationalangle,asfollowedinthepresentmodel.Thepresentmodeltreatsonlygasleakage.Noattemptismadetoaccountforleakageofagas-liquidmixture,whiletheeffectoftheoilfilmcanbeincorporatedbyanappropriatereductionoftheclearancegaps.
Anidealizedclearancegapisassumedtohavearectangularshapeandthemassflowofleakingfluidisexpressedbythecontinuityequation:
(3.11)
whererandwaredensityandvelocityoftheleakinggas,Ag=lgδgtheclearancegapcross-sectionalarea,lgleakageclearancelength,sealingline,δgleakageclearancewidthorgap,μ=μ(Re,Ma)theleakageflowdischargecoefficient.
Fourdifferentsealinglinesaredistinguishedinascrewcompressor:
theleadingtipsealinglineformedbetweenthemainandgaterotorforwardtipandcasing,thetrailingtipsealinglineformedbetweenthemainandgatereversetipandcasing,thefrontsealinglinebetweenthedischargerotorfrontandthehousingandtheinterlobesealinglinebetweentherotors.
Allsealinglineshaveclearancegapswhichformleakageareas.Additionally,thetipleakageareasareaccompaniedbyblow-holeareas.
Accordingtothetypeandpositionofleakageclearances,fivedifferentleakagescanbeidentified,namely:
lossesthroughthetrailingtipsealingandfrontsealingandgainsthroughtheleadingandfrontsealing.Thefifth,“throughleakage”doesnotdirectlyaffecttheprocessintheworkingchamber,butitpassesthroughitfromthedischargeplenumtowardsthesuctionport.
Theleakinggasvelocityisderivedfromthemomentumequation,whichaccountsforthefluid-wallfriction:
3.1OneDimensionalMathematicalModel55
(3.12)
wheref(Re,Ma)isthefrictioncoefficientwhichisdependentontheReynoldsandMachnumbers,Dgistheeffectivediameteroftheclearancegap,Dg≈2δganddxisthelengthincrement.FromthecontinuityequationandassumingthatT≈consttoeliminategasdensityintermsofpressure,theequationcanbeintegratedintermsofpressurefromthehighpressuresideatposition2tothelowpressuresideatposition1ofthegapto
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