外文翻译注油式回转双螺杆压缩机工作循环数学模型的建立节选.docx

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外文翻译注油式回转双螺杆压缩机工作循环数学模型的建立节选.docx

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外文翻译注油式回转双螺杆压缩机工作循环数学模型的建立节选.docx

外文翻译注油式回转双螺杆压缩机工作循环数学模型的建立节选

3360汉字，2236单词，11500英文字符

出处：

SeshaiahN,GhoshSK,SahooRK,etal.Mathematicalmodelingoftheworkingcycleofoilinjectedrotarytwinscrewcompressor[J].AppliedThermalEngineering,2007,27

（1）:

145-155.

英文附录

Mathematicalmodelingoftheworkingcycleofoilinjectedrotarytwinscrewcompressor

N.Seshaiah*,SubrataKr.Ghosh,R.K.Sahoo,SunilKr.Sarangi

CryogenicsandGasdynamicsLaboratory,DepartmentofMechanicalEngineering,NationalInstituteofTechnology,Sector-2,NITCampus,Rourkela769008,Orissa,India

Received12July2005;accepted8May2006；Availableonline7July2006

Abstract

Oilinjectedtwin-screwairandgascompressorsarewidelyusedformediumpressureapplicationsinmanyindustries.Lowcostaircompressorscanbeadoptedforcompressionofheliumandspecialgases,leadingtosigniﬁcantcostsaving.Mathematicalanalysisofoilinjectedtwin-screwcompressoriscarriedoutonthebasisofthelawsofperfectgasandstandardthermodynamicrelations.Heattransfercoeﬃcientrequiredforcomputersimulationisexperimentallyobtainedandusedinperformanceprediction,whentheworkingmediumbeingairorhelium.Amathematicalmodelhasbeendevelopedforcalculatingthecompressorperformanceandforvalidatingtheresultswithexperimentaldata.Theﬂowcoeﬃcientsrequiredfornumericalsimulationtocalculateleakageﬂowratesareobtainedfromeﬃciencyversesclearancecurves.Eﬀectofsomeofthecompressoroperatinganddesignparametersonpowerandvolumetriceﬃciencieshavebeenanalyzedandpresented.

Keywords:

Screwcompressor;Oilinjection;Heattransfercoeﬃcient;Leakage;Flowcoeﬃcients

1.Introduction

Thescrewcompressorisapositivedisplacementmachinethatusesapairofintermeshingrotorshousedinasuitablecasingtoproducecompression.Screwcompressorsarecapableofhigh-speedoperationoverawiderangeofoperatingpressures.Inascrewmachines,oilisdeliberatelyinjectedintothecompressionchambertoimproveandtoprovidesealing,lubrication,corrosionresistanceandcoolingeﬀect.Rotarydualscrewcompressorsarewidelyusedinindustryforairandgascompressionandforrefrigerationapplications.Theyareparticularlysuit-

ableforcompressionofairandheliumusedinsmallandintermediatesizecryogenicrefrigeratorsandliqueﬁers.AcomputerizedmethodforgenerationofrotorproﬁlesandanalysisandperformancehasbeensuggestedbySinghetal.[1,2].Duetothehighcostofenergy,particularlyinIndia,itisnecessarythatallmachinesoperateeﬃciently.Thiscanbeachievedonlywhenmachineperformanceiswellunderstoodandispredictable.Unlikeothercompressors,themechanismofgascompressioninanoilinjectedscrewcompressorisextremelycomplex.Itisdiﬃculttoestimatethecompressorperformanceanalytically.Ontheotherhand,experimentalstudiesareprohibitivelyexpensivebecauseanewrotorneedstobefabricatedusingexpensivemachiningtechniquesforeverychangeinrotorgeometry.

2.Modelingofcompressorcycle

Analysisofvolumetricandpowereﬃcienciesisessentialtoestimatethesuitabilityofacompressorforaparticularapplication.Themainobjectiveofthepresentperformanceanalysisistodevelopanumericalmodeltoascertainthesuitabilityofacommerciallyavailableaircompressorfordiﬀerentgascompressionapplications.Eﬃciencyofanycompressordependsontheprocessesinvolvedintheworkingcycle.Majorprocessesofscrewcompressoraresuction,compressionanddischarge.Analysisoftheseindividualprocessesisessentialtomodelthecompressorperformance.

2.1.Suctionprocess

Volumetriceﬃciencyofthecompressorgreatlydependsontheamountofgasmassinductedintothesuctioncavityduringsuctionprocess.This,inturn,dependsonthetemperatureofthecavitywallsatsteadystate.Analysisofthesuctionprocessgivestheaveragetemperatureofthegasinthesuctioncavityattheendofsuctionprocess.ModeloftheworkingchamberduringsuctionprocessisshowninFig.1.Sincethepressureandtemperatureﬂuctuationsduringsuctionprocessaregenerallysmall,thefollowingquantitiesareassumedtobeconstantduringthesuctionprocess:

•Inletvelocitiesofgasandoil.

•Inlettemperatureofgasandoil.

•Pressuredropacrosstheinletport.

•Rateofheatﬂowfromgastooil（orfromoiltogas）.

Thequantityofgasmassinductedintothesuctioncavitiesdependsonthetemperaturesofinletgasandthecavitywalls.Duringthesuctionprocessthecavitywalltemperatureishigherthantheinductedgastemperaturebecauseoftheheatﬂowfromthecompressedgasduringthecompressionprocess.Thecavitywalliscoveredwithaﬁlmoflubricatingoilwhichleaksfromtheadjoiningcompressionspacewhentheoilisinjected.Theamountofheattransferredfromthehotsuctioncavitywall（lubricatingoilﬁlm）totheinductedgasduringsuctionprocesscanbeestimatedbytheexpression

Ifthetemperatureriseoftheinductedgasissmallcomparedtothetemperaturediﬀerencebetweenthelubricatingoilﬁlmandtheinductedgas,theheattransferbetweentheleakedoilandinductedgasmaybewrittenasbelow:

Underidealconditions,theheatlostbytheoilﬁlmmustbeequaltoheatgainedbythefreshgasmass.FromEqs.

（1）and

（2）,themeantemperatureofinductedgasattheendofsuctionprocesscanbeobtainedas

Theamountofgasmassinductedintothegeometricalvolumeatsuctioncondition（Ps,Ts）is

thegeometricalvolumeofapairofmaleandfemalerotorcavitiesisdeﬁned[3]asbelow:

and

beingthecrosssectionalareasofthemaleandfemalecavitiesrespectivelyandLtherotorlength.

Thegasmassinthesuctioncavityatcondition（Ps,T1）canbeestimatedbytheexpression

Thisgasmassisthesumoffreshchargeinducted（M1）andthemassleakedthroughinterlobeclearance（

）

Eliminatingthetotalmass

betweenEqs.（5）and（6）,thefreshgasmassinductedduringsuctionprocessisobtainedasbelow:

Substitutingthisvalueof

valueinEq.（3）,thefollowingquadraticequationisobtainedintermsofthegastemperature

2.2.Compressionanddischargeprocess

Boththecompressionandthedischargeprocessesareunsteadyprocesses.Thermodynamicpropertiesofthegasandoilvarycontinuouslyduringcompressionprocess.Thegasintheworkingchamberiscompressedtoahighpressurebytherotationalmovementoftherotors.Tosimplifytheanalysis,itisassumedthattheoilandgasareseparateﬂuids,andonlyheatisexchangedbetweenthem.Thedischargeportissolocatedthatthecavitiesconnecttothedischargeportwhenthepressureintheworkingchamberreachesthedesigneddischargepressureanddischargecontinuestillthemalerotorlobecompletelydisengagefromfemalerotorgroove.

Thefollowingfactorsaretakenintoaccountinthemodel:

1.volumechangeduetorotorrotation,

2.massandenthalpyﬂowsofgas，enteringorleavingtheworkingspacethroughdischargeportandleakagepaths,

3.massandenthalpyﬂowsofoil,enteringorleavingtheworkingspacethroughdischargeportandleakage　paths,

4.heatexchangebetweengasandoil.

Tosimplifythecalculations,thefollowingassumptionsaremade:

•Gasandoiltemperaturesarehomogeneousatanyinstantintheworkingspace.

•Gasandoilneverchangephase.

•Pressureisuniformthroughouttheworkingspaceatanystage.

•Theworkinggasisanidealgas.

•Oilisanincompressibleﬂuid.

•Heatexchangebetweengasandoilisinproportiontothetemperaturediﬀerencebetweenthem.

•Apressureﬂuctuationacrossthedischargeportisnegligible.

FujiwaraandOsada[4]derivedthefundamentalequationsbasedonstandardthermodynamiclawsandthelawsofperfectgas.Thefollowingequationsarederivedwithsomemodiﬁcationsandotherdetailsareintroducedasneeded.

Theﬁrstlawofthermodynamicsforunsteadyﬂowofgasthroughtheworkingchambercanbeexpressedas

isthesumofinternal,potentialandkineticenergies.Assumingthepotentialandkineticenergiesofgastobenegligible,fromtheaboveequationthechangeininternalenergyintimedtcanbecomputedas

Changeininternalenergycanalsobeexpressedasafunctionofmassandtemperaturechangeanddeﬁnedasbelow:

Thechangeofenthalpyduetoleakagecanbeexpressedas

Thegasworkmaybeexpressedintermsofgeometricalvolumechange,andoilvolumechangeduetoleakage.Sincetheoilisanincompressibleﬂuid,thegasworkisexpressedas

Heatexchangebetweenthegasandtheoilintime

isassumedtofollowtheNewton’slawofcoolingandisexpressedas

Substituting（11）–（14）in（10）,andrearranging,therateofchangeofworkinggastemperatureisobtained

Theﬁrsttermontheright-handsideoftheaboveequationrelatestothechangeinvolumeincludingtheleakagerateofoil.Thesecondandthirdtermsrepresenttheeﬀectofgasleakageintoandoutofthecompressorcavityrespectively.Thelasttermisderivedfromtheheattransferfromgastotheoil.

Therateofchangeofnetgasvolumeoftheworkingchamber[4]canbewrittenasbelow:

Therateofchangeofgasmassduetointernalleakageisgivenbytheexpression

Theequationofstateofperfectgasmaybewrittenasfollows:

Thediﬀerentialformoftheaboveequationcanbewrittenasfollows:

SubstitutingEqs.（15）–（17）inEq.（18）,therateofchangeofpressureisobtainedasfollows:

Therateofchangeofoiltemperatureisobtainedfromenergybalanceintermsofleakageoiltemperatureandheattransferredfromthegas.Theincreaseofoiltemperatureintheworkingchambersisduetoheatgainedfromtheleakageoil（whichisathighertemperature）andth

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