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

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

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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