Combustion Fundamentals

1 2 CombustionFundamentalsTounderstandthefon nationofpollutantsincombustionsystems,we mustfirstunder-standthenatureofthefuelsb eingburned,thethennodynamicsofthecombust ionpro-cess, ,detonations, spectrumoffuelscurrentlyinwidespreaduse, thesimplestincompositionisnaturalgas,whi chconsistsprimarilyofmethanebutincludesa ,buttheyare,atleast, , ,whichconsistsofmeasurementsoftheelement alcompositionofthefuel,generallypresente dasmassfractionsofcarbon,hydrogen,sulfur ,oxygen,nitrogen,andash, "CH4C2H6C3 HshydrocarbonsCOH2H2SN2CO2(106Jm-3) "p,101kPa;T,25 "Sweetened,"H2S (106 Jkg-I)Kerosene( ) < < ,a measureoftheheatreleaseduringcompletecom bustion, ,physicalpropertiesthatinfluencethehandl inganduseofa ,thespecificgravityorAPIgravity,*viscosi ty(possiblyat severaltemperatures),flashpoint(ameasure ofthetemperatureatwhichthefuelissufficie ntlyvolatiletoignitereadily),anddistilla tionprofiles(fractionvaporizedasa functionoftemperature) ,coalsareclassifiedbyrank,a haveundergonerelativelylittlechange, , ,whichidentifiesthedegreeofcoalifactiono fa solidfuel( ).

2 Coalsamplesthathavebeenairdriedaresubjec tedtoa numberofstandardizedteststodeterminethea mountofmoistureinherenttothecoalstructur e,thequantityofvolatilematterreleasedbyt hecoaluponheatingto1200 Kforseveralminutes,andthemassofashornonc ombustibleinorganic(mineral)impuritiesth atremainsafterlowtemper-ature(700to1050K ) ,volatilematter, , *DegreesAPI=[ (specificgravity16 Cjwaterat16 C) ]. (state)CarbonmatterMoistureAshCHN0S(106 Jkg-I)Meta-anthracite(RI) (PA) (PA) (PA) (PA) (CO) (KY) (IL) (CO) (ND) (Australia) (Douglasfir,asreceived) (C02)fromallofthecarbonandwater(H20)from thehydrogen,thatis,fora hydrocarbonfuelwiththegeneralcomposition CnHm,Evenintheidealizedcaseofcompletecom bustion, , ,manyfuelscontainelementsotherthancarbon , ,combustionis notalwayscomplete, composedofoxygen,nitrogen,andsmallamount sofcarbondioxide,argon, ,forourpurposesit is perfectlyreasonabletoconsiderairasa (molebasis) (molebasis)

3 N2 Thusforeverymoleofoxygenrequiredforcombu stion, ,it doeshavea majorimpactonthethermodynamics,chemicalk inetics, "inert" hydrocarbonfuel,CnHm,becomesThusforevery moleoffuelburned, (n+m14)molofairarerequiredand4. 78(n+m14)+ [ (n+m14)].Gascompositionsaregenerallyrepo rtedintermsofmolefractionssincethemolefr actiondoesnotvarywithtemperatureorpressu reasdoestheconcentration(moles/unitvolum e).Theproductmolefractionsforcompletecom bustionofthishydrocarbonfuelarenYeo2= (n+m14)+ml4ml2YN2= (n+m14)+ml4YH20= (n+m14)+ml43. 78(n+m14) (CSH1S) + (Oz+ )----+-8 COz+9 HzO+ , ,therefore,114=114= (32+ )1723 Thetotalnumberofmolesofcombustionproduct sgeneratedis8+9+ ,theproductgascompositionis,ona molefractionbasis,8 Yeo,=--= ,O=--5= , (802),(Eventhoughtherearecaseswheresulfu rcompoundsinvolvinghigheroxidationstates ofsulfurorreducedsulfurcompoundsareprodu ced,it isa reasonablefirstapproxima-tiontoassumetha tallofthefuelsulfurforms802,)Uponcombust ion,organicallyboundfuel-nitrogenis convertedtobothNzandNO, ,thenoncombustibleinorganic(mineral)

4 Impuritiesinthefuel,undergoesa numberoftransformationsatcombustiontempe ratures,whichwillalsobeneglectedfortheti mebeing, ,theonlychemicalinformationavailableisit selementalcompositionona massbasis, is , , , , , "asreceived"basis, ,thecompositionisthennormalizedwithrespe cttocarbon:wtElement%mol/ ; ; ;-14= ; ;-32= ; ;-16= ; ; ,thus, ,or,aswrittenhere,themasspermoleofcarbon ,includingash,is100ggM=---= ,ash, , +a(Oz+ )--+COz+ + +( + ) +-4-+ (32+ )g/molCThetotalnumberofmolesofgaseouscom bustionproductspermoleofCisNT=1+ + + ,therefore,IYeo,= ,O= ,= ,= (ppm)ona mole(orvolume)basis,a commonformforpresentingdataonminorspecie sinthegas( ).

5 Fewcombustionsystems areoperatedpreciselyatthestoichiometricc onditionbecauseofthedifficultyofachievin gsuchintimatemixingbetweenfuelandairthat perfectconversionis ,combustorsareoperatedwitha ,theyarenota ,cP,isdefinedasthefuel/airrationormalize d withrespecttothestoichiometricfuel/airra tio,mf/macP=( )(mf/ma)sAlternatively,thestoichiometric ratio,A,istheair/fuelrationormalizedwith respecttostoichiometric,thatis,1cP( )Otherratiosthatappearintheliteratureinc ludethepercentexcessair[EA=(A-1)X100%]an dthepercenttheoreticalair(TA=AX100%). (mflma),(malmf)'H, (coke) , ,4>, (excessair,4> <l) ,toa goodapproximation, ,forexample,thecombustionofmethaneat4>= ,(2) +2H20+ 2 O2+ +2H20+ + :1Ye02=-2-= ,thecombustionconditionisnotstatedinterm sofa fuel/airratiobut,rather,intermsoftheamou ntofoxygeninthecombustionproducts( , ).

6 Theproblemofspecifyingtheproductsofcombu stionismorecomplicatedforfuel-richcombus tion,4>>1, ,somecarbonmonoxide,hydrogen,andpossibly , (CO,CO2,H2,H20,N2), veryshorttimewhena fuelisburned, closedsystemoffixedmassandidentityisequa ltotheheattransfertothesystemfromitssurr oundingsminustheworkdonebythesystemonits surroundings;thatis,foraninfinitesimalch angeofstate,dE=oQ-oW( )Thetotalenergyofthesystem,E,includesthe internalenergy,U,thekineticenergy, ,theheattransfer,oQ,andtheworktransfer,o W, totaldifferential, , ,thekineticandpotentialenergytermscanben e-glected,sowemayexpressthesystemenergyi ntermsoftheinternalenergy,thatis,dU=oQ-o W( )Integratingovera finitechangeofstatefromstateI tostate2,thefirstlawfora closedsystembecomes( )

7 Onlyrarelyintheconsiderationofcombustion processescanwelimitourselvestoa fixedmassina ,thefuelandairenterthecombustionzoneacro sscertainboundaries, ,therefore,toderiveanexpressionforthecha ngeinstateofa fixedvolumeinspace,calledacontrolvolume, ratherthana controlvolumethatispre-scribedbya surface, smallincrementofmass,om, ,wefirstdefinea closedsystemthatincludesboththemateriali nitiallyinthecontrolvolume,massm,energyE },andtheincrementofmasstobeadded, ,themassinthecontrolvolumeism+om,andthee nergyinthecontrolvolumeisE2 Thefirstlawforthechangeofstateofthecombi nedclosedsystemmaybewrittenasE2-(E1+eom) =Q12+pvom-Wxl2whereedenotestheenergy/uni tmass(calledthemassspecificenergy)ofom,v =1/pisthemassspecificvolume,pvomisthewor kdoneonthecombinedsystembytheenvironment asthesmallvolumeismovedacrossthecontrolv olumesurface, ,wefindE2-E1=eom+pvom+Q12-Wxl2 Fora smallincrementofchangeofstate,thisbecome sdE=(e+pv)om+oQ-oWx( ) numberofmassincrementsis straightforward.

8 Simplysumoverallmassflowsenteringandleav ingfromthecontrolvolume, controlvolumewitha numberofenteringandexitingmassflowsmayth enbewrittendE"-"-- +.,u(ej+pvj)fj-~(ei+pvi)fi=Q-WxdtJ,outI, m( )wherehand];arethemassflowrates(masspert ime)leavingorenteringthecontrolvolume,Qi s therateofheattransfertothesystem(energyp ertime),andWxis therateatwhichworkis ,inthecombustionapplica-tionsofinteresth erewecangenerallyneglectthekineticandpot entialenergycontri-butionstothetotalener gy,givingdU"--,,---=,ufihi-,Ufjhj+Q-Wxdt i,inj,outwherethemassspecificenthalpy,Ii ,isdefinedash=Ii+pvTheenergyequationmaya lsobewrittenona molarbasis,thatis,du=~fihi-~fjhj+Q-Wxdti ,inj,out( )( )( )whereh=u+pvdenotesthemolarspecificentha lpy,andfiis +bB----cC+ ( )tothissystemgivescfhc(T1)+dfhD(T1)-afhA (T1)-bfhB(T1)

9 =Qwherenoworkisdonebythecombustiongasese xceptthatduetoflowsacrosstheboundary,soW x=O.(Theexpansionworkisalreadyaccountedf orintheenthalpy.)ThemolarflowofAintothec ontrolvolumeisaf,thatofCiscf,andsoon,and thetemperatureisT1 DividingthroughbyfyieldsTheheattransferp ermolethatis requiredtomaintaintheprocessata constanttemper-ature,T=TI>is calledtheenthalpyofreaction,andis giventhesymboll>.hr(T1), ~T1CI----~ , ( ) speciesrequiresa ,thereferencetemperatureandpressureareta kentobeTo=298 KandPo=1 atm=101kPa, ,however, usuallybasedonthepureelementsintheirpred ominantformsatToandPo,thatis, Cassolidgraphite HasHzgas NasNzgas asOzgas compoundrelativetothereferencestatesofit sconstituentelementsistheenthalpyofthere actionoftheseelementalspeciesthatform1 thesametemperature,T, ,theenthalpiesofformationoftheelementalr eferencecompoundsarezero,72thatis, ;'c,= ;'H2= ;'N2=.

10 '02=0 Theenthalpyofa compoundatanytemperaturemaybewrittenasth esumoftheenthalpyofformationatthereferen cetemperatureanda ( )( )Thesensibleenthalpytermmaybeevaluatedas anintegralovertemperatureofthespecifiche atatconstantpressure,cp=(ah/aT)p,thatis, h;(T)-h;(To)=[Tcp,;(T')dT' ,asiscommonlythecaseincombustionapplicat ions,onemustaccountforthedependenceofcp, ; ,it issufficienttoapproxi-matethespecifichea tasa linearfunctionoftemperature,( )Thisapproximateformallowscalculationoft hesensibleenthalpyovertherangeoftemperat urescommonlyencounteredincombustioncalcu lations( ,300to3000K)withinabout10%. ,enthalpiesofformation, ,tabulationsofthermodynamicdatasuchasthe JANAFT hermochemicalTables(StullandProphet,1971 )shouldbeused,ingeneral, chemically reactingopensystemmaynowbewrittenasddU+. ]