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外文翻译--模拟气体运动的快速压缩机 英文版.pdf

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外文翻译--模拟气体运动的快速压缩机 英文版.pdf

JOURNALOFENGINEERINGMATHEMATICS4457–82,20022002KLUWERACADEMICPUBLISHERSPRINTEDINTHENETHERLANDSMODELLINGGASMOTIONINARAPIDCOMPRESSIONMACHINEMGMEERE1,BGLEESON1ANDJMSIMMIE2DEPARTMENTOFMATHEMATICALPHYSICS,NUI,GALWAY,IRELAND2DEPARTMENTOFCHEMISTRY,NUI,GALWAY,IRELANDRECEIVED25JULY2001;ACCEPTEDINREVISEDFORM8MAY2002ABSTRACTINTHISPAPER,AMODELWHICHDESCRIBESTHEBEHAVIOUROFTHEPRESSURE,DENSITYANDTEMPERATUREOFAGASMIXTUREINARAPIDCOMPRESSIONMACHINEISDEVELOPEDANDANALYZEDTHEMODELCONSISTSOFACOUPLEDSYSTEMOFNONLINEARPARTIALDIFFERENTIALEQUATIONS,ANDBOTHFORMALASYMPTOTICANDNUMERICALSOLUTIONSAREPRESENTEDUSINGASYMPTOTICTECHNIQUES,ASIMPLEDISCRETEALGORITHMWHICHTRACKSTHETIMEEVOLUTIONOFTHEPRESSURE,TEMPERATUREANDDENSITYOFTHEGASINTHECHAMBERCOREISDERIVEDTHERESULTSWHICHTHISALGORITHMPREDICTAREINGOODAGREEMENTWITHEXPERIMENTALDATAKEYWORDSGASDYNAMICS,RAPIDCOMPRESSIONMACHINES,SHOCKWAVES,SINGULARPERTURBATIONTHEORY1INTRODUCTION11RAPIDCOMPRESSIONMACHINESARAPIDCOMPRESSIONMACHINEISADEVICEUSEDTOSTUDYTHEAUTOIGNITIONOFGASMIXTURESATHIGHPRESSURESANDTEMPERATURES,WITHPARTICULARREFERENCETOAUTOIGNITIONININTERNALCOMBUSTIONENGINES;SEE1–3ATYPICALCOMBUSTIONENGINEISAVERYDIRTYANDCOMPLEXENVIRONMENT,ANDTHISHASPROMPTEDTHEDEVELOPMENTOFRAPIDCOMPRESSIONMACHINESWHICHENABLETHESCIENTIFICSTUDYOFCOMPRESSIONANDIGNITIONINENGINESINACLEANERANDSIMPLERSETTINGINFIGURE1WESCHEMATICALLYILLUSTRATEATWOPISTONRAPIDCOMPRESSIONMACHINE,SUCHASTHEONEINTHEDEPARTMENTOFCHEMISTRYATNUI,GALWAYHOWEVER,SINGLEPISTONMACHINES,WITHAPISTONATONEENDANDASTATIONARYSOLIDWALLATTHEOTHER,AREMORETYPICALTHEANALYSISDEVELOPEDINTHISPAPERISAPPROPRIATETOBOTHSINGLEANDTWOPISTONMACHINESTHEOPERATIONOFARAPIDCOMPRESSIONMACHINEISVERYSIMPLETHEPISTONSARESIMULTANEOUSLYDRIVENINPNEUMATICALLY,COMPRESSINGTHEENCLOSEDGASMIXTURE,THEREBYCAUSINGTHEGASPRESSURE,TEMPERATUREANDDENSITYTORISEQUICKLYINFIGURES1A,1BAND1CWESCHEMATICALLYREPRESENTARAPIDCOMPRESSIONMACHINEPRIORTO,DURING,ANDAFTERCOMPRESSION,RESPECTIVELYTHERATIOOFTHEFINALVOLUMETOTHEINITIALVOLUMEOFTHECOMPRESSIONCHAMBERFORTHEMACHINEATNUI,GALWAYISABOUT112,THISVALUEBEINGTYPICALOFOTHERMACHINESATTHEENDOFTHECOMPRESSION,THEGASMIXTUREWILLTYPICALLYHAVEBEENPUSHEDINTOAPRESSUREANDTEMPERATUREREGIMEWHEREAUTOIGNITIONCANOCCURINFIGURE2,WEDISPLAYANEXPERIMENTALPRESSUREPROFILEFORAH2/O2/N2/ARMIXTUREWHICHHASBEENTAKENFROMBRETTETAL4,WITHTHEKINDPERMISSIONOFTHEAUTHORSINTHISGRAPH,THETIMET0CORRESPONDSTOTHEENDOFTHECOMPRESSIONTIMEWENOTETHAT,FORTHEGREATERPARTOFTHECOMPRESSION,THEPRESSUREINTHECHAMBERISRISINGQUITEGENTLY,BUTTHATTOWARDSTHEENDOFTHECOMPRESSIONTHATIS,JUSTBEFORET0,THEREISASTEEPRISEINTHEPRESSUREAFTERCOMPRESSION,THEPRESSUREPROFILELEVELSOFFASEXPECTED;THEEXTREMELYSTEEPRISEATTHEENDOF58MGMEEREETALFIGURE1SCHEMATICILLUSTRATINGTHEOPERATIONOFARAPIDCOMPRESSIONMACHINE;WEHAVESHOWNTHECONFIGURATIONAPRIORTOCOMPRESSION,BDURINGCOMPRESSIONANDCAFTERCOMPRESSIONFIGURE2ANEXPERIMENTALPRESSUREPROFILEFORAGASMIXTUREH2/O2/N2/AR2/1/2/3,ASMEASUREDINTHERAPIDCOMPRESSIONMACHINEATNUI,GALWAYITISTAKENFROM4,ANDHASANINITIALPRESSUREOF005MPAANDANINITIALTEMPERATUREOF344KMODELLINGGASMOTIONINARAPIDCOMPRESSIONMACHINE59THEPROFILECORRESPONDSTOTHEIGNITIONOFTHEMIXTUREWENOTETHATTHECOMPRESSIONTIMEANDTHETIMEDELAYTOIGNITIONAFTERCOMPRESSIONAREBOTHO10MSTHEPRESSUREHISTORYISTHEONLYQUANTITYWHICHISMEASUREDINEXPERIMENTSHOWEVER,THETEMPERATUREINTHECOREAFTERCOMPRESSIONISTHEQUANTITYWHICHISOFPRIMARYINTERESTTOCHEMISTSSINCEREACTIONRATESDEPENDMAINLYONTEMPERATUREFORALMOSTALLSYSTEMS,ALTHOUGHTHEREMAYALSOBESOMEWEAKERPRESSUREDEPENDENCEMEASURINGTEMPERATUREACCURATELYINTHECORECANBEPROBLEMATICBECAUSEOFTHEPRESENCEOFATHERMALBOUNDARYLAYER;SEETHECOMMENTSBELOWONROLLUPVORTICESHOWEVER,WITHTHEEXPERIMENTALPRESSUREDATAINHAND,THECORRESPONDINGTEMPERATURESCANBEESTIMATEDUSINGTHEISENTROPICRELATIONLNP/PIINTEGRALDISPLAYTTIΓSSΓS−1DS,1WHERETI,PIARETHEINITIALVALUESFORTHECORETEMPERATUREANDPRESSURE,T,PARETHESEQUANTITIESATSOMELATERTIME,ANDΓSISTHESPECIFICHEATRATIOATTEMPERATURESINEXPERIMENTS,THEINITIALCORETEMPERATUREISTYPICALLYO300K,WHILETHECORETEMPERATUREAFTERCOMPRESSIONISUSUALLYO1000KINTHISPAPER,WESHALLCONSIDERONLYTHEBEHAVIOUROFTHEGASMIXTUREDURINGCOMPRESSION;THEPOSTCOMPRESSIONBEHAVIOURISNOTCONSIDEREDHERE,BUTTHISWILLFORMTHESUBJECTFORFUTUREWORKNEVERTHELESS,THEMODELPRESENTEDHEREDOESPROVIDEAREASONABLEDESCRIPTIONOFTHEPOSTCOMPRESSIONBEHAVIOUROFASINGLESPECIESPUREGAS,ORANINERTGASMIXTURE;SEESECTION3512THEMODELWESUPPOSETHATTHECOMPRESSIONCHAMBERISLOCATEDALONG0X2LATT0,WITHX0GIVINGTHEINITIALLOCATIONOFTHELEFTPISTONANDX2LBEINGTHEINITIALLOCATIONOFTHERIGHTPISTONITISASSUMEDTHROUGHOUTTHISPAPERTHATTHEGASMOTIONISONEDIMENSIONALSOTHATTHEFLOWVARIABLESDEPENDONLYONTHEPOSITIONXALONGTHECHAMBERANDTIMET0THISASSUMPTIONISACTUALLYQUITEASTRONGONEINTHISCONTEXTSINCEHIGHERDIMENSIONALEFFECTSAREFREQUENTLYOBSERVEDINEXPERIMENTS,ROLLUPVORTICESNEARTHECORNERREGIONSDEFINEDBYTHEPISTONHEADSANDTHECHAMBERWALLBEINGPARTICULARLYNOTEWORTHY;SEE,FOREXAMPLE,5THESEVORTICESARISEDUETOTHESCRAPINGBYTHEPISTONSOFTHETHERMALBOUNDARYLAYERATTHECHAMBERWALL,ANDTHEYCAN,ANDFREQUENTLYDO,DISTURBTHEGASMOTIONINTHECOREOFTHECOMPRESSIONCHAMBERHOWEVER,THEJUSTIFICATIONFORTHEONEDIMENSIONALMODELSTUDIEDHEREISTWOFOLDITHECORNERVORTICESCANBESUCCESSFULLYSUPPRESSEDBYINTRODUCINGCREVICESATTHEPISTONHEADSWHICHSWALLOWTHETHERMALBOUNDARYLAYERASTHEPISTONSMOVEINSEELEE6,RENDERINGTHEGASMOTIONAWAYFROMTHECHAMBERWALLSONEDIMENSIONALTOAGOODAPPROXIMATION,AND,IITHESTUDYOFTHEONEDIMENSIONALMODELPROVIDESAUSEFULPRELIMINARYTOTHESTUDYOFHIGHERDIMENSIONALMODELSWENOWGIVETHEGOVERNINGEQUATIONSFOROURONEDIMENSIONALMODELAREASONABLYCOMPLETEDERIVATIONOFTHEGOVERNINGEQUATIONSFORAMULTICOMPONENTREACTINGGASCANBEFOUNDINTHEAPPENDICESOF7;THESESTANDARDDERIVATIONSARENOTREPRODUCEDHERETHEMODELWHICHWESHALLSTUDYINCLUDESANUMBEROFSIMPLIFYINGASSUMPTIONSANDTHESEWILLBECLEARLYSTATEDASTHEYARISETHEEQUATIONEXPRESSINGCONSERVATIONOFMASSISGIVENBY∂Ρ∂T∂∂XΡV0,60MGMEEREETALWHEREΡΡX,TANDVVX,TARETHEDENSITYANDTHEVELOCITYOFTHEGAS,RESPECTIVELY,ATLOCATIONXANDTIMETITSHOULDBEEMPHASIZEDTHATTHESEQUANTITIESREFERTOAGASMIXTURE,SOTHATIFTHEREARENDIFFERENTSPECIESINTHEMIXTURETHENΡNSUMMATIONDISPLAYI1ΡI,WHEREΡIΡIX,TISTHEDENSITYOFSPECIESIALSO,THEVELOCITYVABOVEREFERSTOTHEMASSAVERAGEDVELOCITYOFTHEMIXTURE,THATIS,VNSUMMATIONDISPLAYI1YIVI,WHEREYIΡI/ΡANDVIVIX,TARETHEMASSFRACTIONANDVELOCITY,RESPECTIVELY,OFSPECIESI;SEE7NEGLECTINGBODYFORCESANDVISCOUSEFFECTS,THEEQUATIONEXPRESSINGCONSERVATIONOFMOMENTUMISGIVENBY∂V∂TV∂V∂X−1Ρ∂P∂X,WHEREPPX,TISTHEPRESSUREWEASSUMETHATTHEGASMIXTUREISIDEAL,SOTHATTHEEQUATIONOFSTATEISGIVENBYPRMΡT,2WHERETTX,TISTHETEMPERATURE,RISTHEUNIVERSALGASCONSTANT8314JK−1MOL−1,ANDMISTHEAVERAGEMOLECULARMASSOFTHEMIXTURETHISLASTQUANTITYISGIVENBYMNSUMMATIONDISPLAYI1NIWIMA,WHERENIANDWIGIVETHENUMBERFRACTIONANDMOLECULARWEIGHT,RESPECTIVELY,OFSPECIESI,MISTHEATOMICMASSUNIT166110−27KGANDAISAVOGADRO’SNUMBER60221023MOLECULESMOL−1THEEQUATIONEXPRESSINGCONSERVATIONOFENERGYISGIVENBYSEE7OR8ΡPARENLEFTBIGG∂U∂TV∂U∂XPARENRIGHTBIGG−MPARENLEFTBIGG∂Q∂XP∂V∂XPARENRIGHTBIGG,3WHEREUUX,TISTHEINTERNALENERGYOFTHEGASMIXTUREANDQQX,TISTHEHEATFLUXWEALSOHAVETHETHERMODYNAMICIDENTITYUNSUMMATIONDISPLAYI1HIYI−MP/Ρ,4WHERETHEENTHALPIESHIHITAREGIVENBYHITHIT0INTEGRALDISPLAYTT0CP,ISDS,I1,2,,N,5

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