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Modeling for Control of HCCI Engines - Stanford University

Singlecylinderresearchengineusingvariabl evalve actuation(VVA)atStanfordUniver-sity. ,whichutilizeda temperaturethresholdtomodeltheonsetofthe combustionreaction, , , IntroductionExperimentalstudiesatStanfor dUniversity([1], [4])andelsewhere[6]demonstratethatvariab levalve actuation(VVA)canbeusedtoinitiatehomogen eouschargecom-pressionignition(HCCI).Thi sisachievedbyreinductingcombustionproduc tsfromthepreviouscycle, thermalsinkduringcombustion,thisprocessl owersthepeakcombustiontemperature, is importanttonotethatothermethodsexisttoin itiateHCCI,suchasheatingorprecompressing thein-take air([10],[7]) orvaryingthecompressionratio[2].Duetothe natureofHCCI,a sparkignition(SI)ordieselengines,whereth ecombustionis initiatedviasparkandfuelinjec-tion,respe ctively, ,ensuringthatcombustionoccurswithaccepta bletimingis ,whichdependsonin-cylinderspeciesconcent rations, synthesizea controllertostabilizeHCCI usingtheVVAsystem,a modelofthesystemwithspecialattentionpaid tocombustionphasingisthereforenecessary.

out of the cylinder through the exhaust valve, m˙2, po is the cylinder pressure, p, and pT is the exhaust manifold pres- sure, assumed to be atmospheric. For the reinducted ex-haust from the previous cycle through the exhaust valve, m˙3, po is the exhaust manifold pressure, and pT is the cylinder pressure,p.

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Transcription of Modeling for Control of HCCI Engines - Stanford University

1 Singlecylinderresearchengineusingvariabl evalve actuation(VVA)atStanfordUniver-sity. ,whichutilizeda temperaturethresholdtomodeltheonsetofthe combustionreaction, , , IntroductionExperimentalstudiesatStanfor dUniversity([1], [4])andelsewhere[6]demonstratethatvariab levalve actuation(VVA)canbeusedtoinitiatehomogen eouschargecom-pressionignition(HCCI).Thi sisachievedbyreinductingcombustionproduc tsfromthepreviouscycle, thermalsinkduringcombustion,thisprocessl owersthepeakcombustiontemperature, is importanttonotethatothermethodsexisttoin itiateHCCI,suchasheatingorprecompressing thein-take air([10],[7]) orvaryingthecompressionratio[2].Duetothe natureofHCCI,a sparkignition(SI)ordieselengines,whereth ecombustionis initiatedviasparkandfuelinjec-tion,respe ctively, ,ensuringthatcombustionoccurswithaccepta bletimingis ,whichdependsonin-cylinderspeciesconcent rations, synthesizea controllertostabilizeHCCI usingtheVVAsystem,a modelofthesystemwithspecialattentionpaid tocombustionphasingisthereforenecessary.

2 Thismodelshouldbeassimpleaspossible,asit isoftendifficulttosynthesizecontrollersf rommorecomplex single-cylinderresearchengineout-fittedw itha , andtheproductsofcombustionfromthepreviou scy-clethroughtheexhaustvalve, compression, flowduringtheinductionandexhaustportions ofthecyclearemodeledwithcompressible,ste adystate,one-dimensional, Inthefirstmodel,thesimplestofthethree,a , ,a twostepmechanismimplementinga found,withslightdiscrepancy inpres-sureat modelsthroughtheuseofanintegratedArrheni usrateasa ,butshowsslightdiscrepancy ([8],[3])andmulti-dimensionalCFDmodels[5 ].Whiletheseapproachescanbeexpectedtomor eaccuratelypredicttheperformanceandemiss ionsinHCCI combustion,thegoalofthisworkis is ModelingApproachForeachofthethreeapproac hesinvestigated,themodel-ingwasbasedonan opensystemfirstlawanalysis,withsteadysta tecompressibleflowrelationsusedtomodelth emassflow throughtheintake :thetemperature,T; theconcentrationsofpropane,[C3H8], oxygen,[O2], Nitrogen,[N2], carbondioxide,[C2O],water, [H2O],andcarbonmonoxide,[CO];thecrankang le.

3 Andthecylindervolume, aregivenbythefollowingwell-knownslider-c rankformulas:V=Vc+ B24(l a acos pl2 a2sin2 )(1) V= 4B2a sin (1+acos p(L2 a2sin2 ))(2)with: = (3)where is therotationalspeedofthecrankshaft,ais halfofthestroke length,Lis theconnectingrodlength,Bis Flow EquationsThemassflowthroughthevalvescons istsofflowfromintake manifoldtocylinder, m1, fromcylindertoexhaustmanifold, m2, andfromexhaustmanifoldtocylinder, m3, VALVEEXHAUST VALVE-Figure 1:Valve MassFlows:left- inductionwithintake andexhaustvalvesopen,right- exhaustratesaredevelopedusinga compressible,steadystate,one-dimensional ,isentropicflowanalysisfora restriction,whererealgasfloweffectsarein cludedbymeansofa dis-chargecoefficient,CD.

4 Therelationsforthemassflowsare: m=CDARpopRTo pTpo 1= "2 1"1 pTpo ( 1)= ##(4)forunchokedflow (pT=po>[2=( +1)] =( 1)), and: m=CDARpopRTop 2 +1 ( +1)=2( 1)(5)forchokedflow (pT=po [2=( +1)] =( 1)), whereARis theeffective openareaforthevalve,pois theupstreamstagna-tionpressure,Tois thedownstreamstagnationtemperatureandpTi s showsthegeneralshapeofa valve valve opening(IVO)andexhaustvalve clos-ing(EVC) 10 4 Effective Open Area [m]Crankshaft Intake ValveExhaust ValveIVO EVC Figure 2:GeneralValve Profilecylinderthroughtheintake valve, m1,pois theintake man-ifoldpressure,assumedtobeatmospheric ,andpTisthecylinderpressure,p. Forthemassflowofburntproductsoutofthecyl inderthroughtheexhaustvalve, m2,pois thecylinderpressure,p, andpTis theexhaustmanifoldpres-sure, , m3,pois theexhaustmanifoldpressure,andpTis thecylinderpressure,p.

5 [9],andcouldbeimplementedhereina is assumedthatthereis noflowfromcylinderto intake a reasonableassumptionfortheexperimentalsy stemstudiedinthispaper. However,allowingflowfromcylindertointake manifoldis straight-forwardif , [ Xi] isrelatedtonumberofmolesofspeciesiinthec ylinder,Ni,by: [Xi] =ddt NiV = NiV V NiV2=wi V NiV2(6)wherewi, therateofchangeofmolesofspeciesiperunitv olumehasbeendefinedas:wi= NiV(7)Ithastwo contributions:therateofchangeofmolesofsp eciesiperunitvolumeduetothecombustionrea ctions,wrxn;i, andduetoflow throughthevalvesunderthecontroloftheVVA system,wvalves;i, suchthat:wi=wrxn;i+wvalves;i(8)Thecombus tionreactionrate,wrxn;i, is determinedthroughtheuseofa ,themechanismusedisthedifferencebetweent hethreemodelspresentedinthispaper.

6 Rates( m1, m2and m3) ,therateofchangeofmolesofspeciesiperunit volumeduetoflow throughthevalves,wvalves;i, canbefoundusingthespeciesmassfractions:w valves;i=w1;i+w2;i+w3;i(9)where:w1;i=Y1; i m1V MWi(10)w2;i=Y2;i m2V MWi(11)w3;i=Y3;i m3V MWi(12)HereY1;i,Y2;iandY3;iarethemassfra ctionsofspeciesiintheinletmanifold,exhau stmanifoldandcylinder, respec-tively. It is assumedthata stoichiometricmixtureis presentintheintake , it is assumedthatonlythemajorcombustionproduct sofCO2, ;iandY2; andexhaustmanifoldcompositionscanbeconsi dered,butinany , themassfractionofspeciesiinthecylin-der, Y3;i, isconstantlychanging,andcanberelatedtoth econcentrationstatesas:Y3;i=[Xi]MWi [Xi]MWi(13) RateEquationsInordertoderive a differentialequationforthetemperatureoft hegasinsidethecylinder, thefirstlaw ofthermodynam-icsforanopensystemandtheid ealgaslawarecombinedasoutlinedbelow.

7 Thefirstlawofthermodynamicsforanopensyst emis:d(mu)dt=Q W+ m1h1+ m2h2+ m3h3(14)wheremis themassofspeciesinthecylinder,uis thein-ternalenergy,Qis theheattransferrate,Wis thework,h1is theenthalpy ofspeciesintheintake manifold,h2is theenthalpy ofspeciesintheexhaustmanifold,andh3isthe enthalpy ofthespeciesinthecylinder. Forthecaseofthepistoncylindertheworkis:W =p V(15)where , giventhattheenthalpy is relatedto theinternalenergyas:h=u+p (16)Equations14,15and16canbecombinedtoyi eld:d(mh)dt= mpV=m+ pV+ m1h1+ m2h2+ m3h3(17)Expansionoftheenthalpy toshowthecontributionsofthespeciesinthec ylindercanberepresentedas:mh=H= Ni hi(18)whereNiis thenumberofmolesofspeciesiinthecylin-der , andHis thetotalenthalpy ofspeciesinJoulesinthecylinder, and hiis theenthalpy ofspeciesiona perunitmoleofspeciesicanberepresentedas hi=cp;i(T) T, wherecp;i(T)is thespecificheatofspeciesipermoleattemper atureT,Equations18and6 canbecombinedtogive:d(mh)dt=V [Xi] hi+ T [Xi]cp.

8 I(T) + V [Xi] hi(19)In-cylinderpressureanditsderivativ e canberelatedtotheconcentrationsandtemper aturethroughtheidealgaslawas:p= [Xi]RT(20) p=p [Xi] [Xi]+p TT(21)Meanwhile,theincylindermassanditsd erivative mayberelatedto thespeciesconcentrations,molecularweight sandvolumeas:m=V [Xi]MWi(22) m= V [Xi]MWi+V [Xi]MWi(23)EquatingtherightsidesofEquati ons17and19,substitutingEquations21,22,an d23,andrearrangingyieldsa differen-tialequationfortemperature: T= ( [Xi] hi) V( [Xi] hi)V+p [Xi] [Xi]+ mihiV( [Xi] cp;i(T)) p=T(24)Equations2,3,6 ,thecombustionreactionrate,wrxn;i, inEquation6 CombustionChemistryModelingThecombustion chemistrymechanismutilizedis ,thestoichiometricreactionofpropaneandai ris assumedsincethisis ,suchthattheglobalreactionforcombustionc anbewrittenas:C3H8+5O2+18:8N2!

9 3CO2+4H2O+18:8N2(25) ThresholdApproachAsa firstpassa simpletemperaturethresholdmethodwasdevel opedinwhichthecombustionreactionsareassu medtostartoncethein-cylindertemperaturer eachesa ,therateofreactionofthepropaneisapproxim atedasbeinggaussianinnature,suchthat:wC3 H8=8> <>:[C3H8]iVi ex ph (( init) )2 2iV p2 T Tth0T<Tth9>=>;(26)where init,Viand[C3H8]iarethecrankangle,volume andpropaneconcentration,respectively, at thepointwherecom-bustionbegins( ). Further, and arethestandarddeviationandmeanassociated withthegaussianreactionrateexpression, ,suchasa directly:wO2=3:5wC3H8(27)wN2=0(28)wCO2= 3wC3H8(29)wH2O= 4wC3H8(30)Figures3 and4 showthata duetothefacttheinitiationofthecom-bustio nreactiondependsnotonlyonthetemperature, butalsotheconcentrationofspeciespresenti n-cylinder.

10 Thisdependenceonbothtemperatureandconcen trationsises-peciallyimportantinthecaseo fHCCI, , phenomenaleadstoa self-stabilizingeffect,whichcorrespondst oexperimentalobservationsofHCCI usingVVA. 50050010203040506070 Crankshaft ATCP ressure (bar)experimenttemp. thresholdFigure StepMechanismInordertocapturetheeffectso fbothconcentrationandtemperatureoncombus tiontiming,a moredetailed,yetstillsimple, :C3H8+3:5O2+18:8N2!3CO+4H2O+18:8N2(31)CO +:5O2$CO2(32) 50050010203040506070 Crankshaft ATCP ressure (bar)experimenttemp. thresholdFigure @185 ThereactionratesforC3H8oxidationandCOoxi dationaregivenin[11] as:wC3H8=4:83e9ex p 15098T [C3H8]:1[O2]1:65(33)wCO;ox=2:24e12ex p 20130T [CO][H2O]:5[O2]:25 5e8ex p 20130T [CO2](34)TheseArrhenius-typerelationsare commonlyusedtomodelreactionratesin ,theotherreactionratesfollow as:wO2=3:5wC3H8+:5wCO;ox(35)wN2=0(36)wCO 2= wCO;ox(37)wH2O= 4wC3H8(38)wCO= 3wC3H8+wCO.


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