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外文翻译--有限时间热力学优化活塞行动改进的发动机性能.doc

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外文翻译--有限时间热力学优化活塞行动改进的发动机性能.doc

Proc.Natl.Acad.Sci.USAVol.78,No.4,pp.19861988,April1981AppliedPhysicalSciencesFinitetimethermodynamicsEngineperformanceimprovedbyoptimizedpistonmotionOttocycle/optimizedheatengines/optimalcontrolMICHAELMOZURKEWICHANDR.S.BERRYDepartmentofChemistryandtheJamesFranckInstitute,TheUniversityofChicago,Chicago,Illinois60637ContributedbyR.StephenBerry,December29,1980ABSTRACTThemethodsoffinitetimethermodynamicsareusedtofindtheoptimaltimepathofanOttocyclewithfrictionandheatleakage.Optimalityisdefinedbymaximizationoftheworkpercyclethesystemisconstrainedtooperateatafixedfrequency,sothemaximumpowerisobtained.Theresultisanimprovementofabout10intheeffectivenesssecondlawefficiencyofaconventionalnearsinusoidalengine.Finitetimethermodynamicsisanextensionofconventionalthermodynamicsrelevantinprincipleacrosstheentirespanofthesubject,fromthemostabstractleveltothemostapplied.Theapproachisbasedontheconstructionofgeneralizedthermodynamicpotentials1forprocessescontainingtimeorrateconditionsamongtheconstraintsonthesystem2andonthedeterminationofoptimalpathsthatyieldtheextremacorrespondingtothosegeneralizedpotentials.Heretofore,workonfinitetimethermodynamicshasconcentratedonratheridealizedmodels27andonexistencetheorems2,allontheabstractsideofthesubject.Thisworkisintendedasastepconnectingtheabstractthermodynamicconceptsthathaveemergedinfinitetimethermodynamicswiththepractical,engineeringsideofthesubject,thedesignprinciplesofarealmachine.Inthisreport,wetreatamodeloftheinternalcombustionenginecloselyrelatedtotheidealOttocyclebutwithrateconstraintsintheformofthetwomajorlossesfoundinrealengines.Weoptimizetheenginebycontrollingthetimedependenceofthevolumethatis,thepistonmotion.Asaresult,withoutundertakingadetailedengineeringstudy,weareabletounderstandhowthelossesareaffectedbythetimepathofthepistonandtoestimatetheimprovementinefficiencyobtainablebyoptimizingthepistonmotion.THEMODELOurmodelisbasedonthestandardfourstrokeOttocycle.Thisconsistsofanintakestroke,acompressionstroke,apowerstroke,andanexhauststroke.Herewebrieflydescribethebasicfeaturesofthismodelandthemethodusedtofindtheoptimalpistonmotion.Adetailedpresentationwillbegivenelsewhere.Weassumethatthecompressionratio,fueltoairratio,fuelconsumption,andperiodofthecycleallarefixed.Theseconstraintsservetwopurposes.First,theyreducetheoptimizationproblemtofindingthepistonmotion.Also,theyguaranteethattheperformancecriterianotconsideredinthisanalysisarecomparabletothoseforarealengine.Relaxinganyoftheseconstraintscanonlyimprovetheperformancefurther.Wetakethelossestobeheatleakageandfriction.Bothoftheseareratedependentandthusaffectthetimeresponseofthesystem.Theheatleakisassumedtobeproportionaltotheinstantaneoussurfaceofthecylinderandtothetemperaturedifferencebetweentheworkingfluidandthewallsi.e.,Newtonianheatloss.Becausethistemperaturedifferenceislargeonlyonthepowerstroke,heatlossisincludedonlyonthisstroke.Thefrictionforceistakentobeproportionaltothepistonvelocity,correspondingtowelllubricatedmetalonmetalslidingthus,thefrictionallossesaredirectlyrelated,tothesquareofthevelocity.Theselossesarenotthesameforallstrokes.Thehighpressuresinthepowerstrokemakeitsfrictioncoefficienthigherthanintheotherstrokes.Theintakestrokehasacontributionduetoviscousflowthroughthevalve.Thefunctionwehaveoptimizedisthemaximumworkpercycle.Becausebothfuelconsumptionandcycletimearefixed,thisalsoisequivalenttomaximizingbothefficiencyandtheaveragepower.Infindingtheoptimalpistonmotion,wefirstseparatedthepowerandnonpowerstrokes.Anunspecifiedbutfixedtimetwasallottedtothepowerstrokewiththeremainderofthecycletimegiventothenonpowerstrokes.Bothportionsofthecyclewereoptimizedwiththistimeconstraintandwerethencombinedtofindthetotalworkpercycle.Thedurationtofthepowerstrokewasthenvariedandtheprocesswasrepeateduntilthenetworkwasamaximum.Theoptimalpistonmotionforthenonpowerstrokestakesasimpleform.Becauseofthequadraticvelocitydependenceofthefrictionlosses,theoptimummotionholdsthevelocityconstantduringmostofeachstroke.Attheendsofthestroke,thepistonacceleratesanddeceleratesatthemaximumallowedrate.Becausethefrictionlossesarehigherontheintakestroke,theoptimalsolutionallotsmoretimetothisstrokethantotheothertwo.ThepistonvelocityasafunctionoftimeisshowninFig.1.Thepowerstrokewasmoredifficulttooptimizebecauseofthepresenceoftheheatleak.Theproblemwassolvedbyusingthevariationaltechniqueofoptimalcontroltheory8.Theformalismyieldstheequationofmotionofthepistonasafourthordersetofnonlineardifferentialequations.Theseweresolvednumerically.TheresultingmotionisshowninFig.1fortheentirecycle.Theasymmetricshapeofthepistonmotiononthepowerstrokearisesfromthetradeoffbetweenfrictionandheatleaklosses.Atthebeginningofthestrokethegasesarehot,capableofyieldinghighefficiency,andtherateofheatlossishigh.Itisthereforeadvantageoustomakethevelocityhighonthispartofthestroke.Asworkisextracted,thegasescoolandtherateofheatleakagediminishesrelativetofrictionallosses.Consequentlytheoptimalpathmovestolowervelocitiesasthepowerstrokeproceeds.Thesolutionswereobtainedfirstwithunlimitedaccelerationandthenwithlimitsonaccelerationanddeceleration.Thelattersituationyieldsaresultfamiliarinothercontextsunderthenameofturnpikesolution9.Thesystemtriestooperateaslongaspossibleatitsoptimalforwardandbackwardvelocities,byacceleratinganddeceleratingbetweenthesevelocitiesatthemaximumrates.Inthisway,thesystemspendsasmuchtimeaspossiblemovingalongitsbestorturnpikepath.RESULTSParametersforthecomputationsweretakenfromref.10or,inthecaseofthefrictioncoefficient,adjustedtogivefrictionallossesofthemagnitudecitedinref.10.ThoseparametersaregiveninTable1.TheresultsofthecalculationsofsometypicalcasesaregiveninTable2,wheretheyarecomparedwiththeconventionalOttocycleenginehavingthesamecompressionratiobutastandardnearsinusoidalmotion.Theeffectivenessεtheratiooftheworkdonetothereversiblework,alsocalledthesecondlawefficiencyisslightlyhigherfortheoptimizedenginewhosepistonaccelerationislimitedto5x103m/sec2,themaximumoftheconventionalengineofthefirstrow.Ifthepistonisallowedtohave4timesthe

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