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P1:JZP0521870526preCUFX045/LawPrinter:cupusbw0521870526July21,20068:49COMBUSTIONPHYSICSCHUNGK.LAWPrincetonUniversityiii

cambridgeuniversitypressCambridge,NewYork,Melbourne,Madrid,CapeTown,Singapore,SãoPauloCambridgeUniversityPressTheEdinburghBuilding,Cambridgecb22ru,UKFirstpublishedinprintformatisbn-13978-0-521-87052-8isbn-13978-0-511-24584-8© Chung K. Law 20062006Information on this title: www.cambridge.org/9780521870528Thispublicationisincopyright.Subjecttostatutoryexceptionandtotheprovisionofrelevantcollectivelicensingagreements,noreproductionofanypartmaytakeplacewithoutthewrittenpermissionofCambridgeUniversityPress.isbn-100-511-24584-Xisbn-100-521-87052-6CambridgeUniversityPresshasnoresponsibilityforthepersistenceoraccuracyofurlsforexternalorthird-partyinternetwebsitesreferredtointhispublication,anddoesnotguaranteethatanycontentonsuchwebsitesis,orwillremain,accurateorappropriate.PublishedintheUnitedStatesofAmericabyCambridgeUniversityPress,NewYorkwww.cambridge.orghardbackeBook(EBL)eBook(EBL)hardback

P1:JZP0521870526preCUFX045/LawPrinter:cupusbw0521870526July21,20068:49TomywifeHelenandtoourchildrenJonathan,Jennifer,andJeffreyv

P1:JZP0521870526preCUFX045/LawPrinter:cupusbw0521870526July21,20068:49ContentsPrefacepagexviiINTRODUCTION......................................10.1.MajorAreasofCombustionApplication10.2.ScientiﬁcDisciplinesComprisingCombustion60.3.ClassiﬁcationsofFundamentalCombustionPhenomena70.4.OrganizationoftheText100.5.LiteratureSources121.CHEMICALTHERMODYNAMICS........................141.1.PracticalReactantsandStoichiometry141.1.1.PracticalReactants141.1.2.Stoichiometry151.2.ChemicalEquilibrium161.2.1.FirstandSecondLaws161.2.2.ThermodynamicFunctions161.2.3.CriterionforChemicalEquilibrium181.2.4.PhaseEquilibrium181.2.5.EquilibriumConstants211.2.6.EquilibriumConstantsinthePresenceofCondensedPhases221.2.7.MultipleReactions241.2.8.ElementConservation241.2.9.RestrictedEquilibrium251.3.EquilibriumCompositionCalculations261.3.1.EquilibriumCompositionofHydrocarbon–AirMixtures261.3.2.TheMajor–MinorSpeciesModel281.3.3.ComputerSolutions301.4.EnergyConservation311.4.1.HeatsofFormation,Reaction,andCombustion311.4.2.EstimationofHeatofReactionfromBondEnergies341.4.3.DeterminationofHeatofReactionfromKp(T)351.4.4.SensibleEnergiesandHeatCapacities35vii

P1:JZP0521870526preCUFX045/LawPrinter:cupusbw0521870526July21,20068:49viiiContents1.4.5.EnergyConservationinAdiabaticChemicalSystems371.4.6.AdiabaticFlameTemperatureandEquilibriumComposition37PROBLEMS492.CHEMICALKINETICS................................512.1.PhenomenologicalLawofReactionRates522.1.1.TheLawofMassAction522.1.2.ReversibleReactions532.1.3.MultistepReactions542.1.4.Steady-StateApproximation542.1.5.PartialEquilibriumApproximation552.1.6.ApproximationsbyGlobalandSemiglobalReactions562.1.7.ReactionOrderandMolecularity572.2.TheoriesofReactionRates:BasicConcepts582.2.1.TheArrheniusLaw582.2.2.TheActivationEnergy592.2.3.CollisionTheoryofReactionRates622.2.4.TransitionStateTheoryofReactionRates642.3.TheoriesofReactionRates:UnimolecularReactions672.3.1.LindemannTheory682.3.2.Rice–Ramsperger–Kassel(RRK)Theory702.3.3.RepresentationofUnimolecularReactionRateConstants712.3.4.ChemicallyActivatedReactions722.4.ChainReactionMechanisms742.4.1.Straight-ChainReactions:TheHydrogen–HalogenSystem742.4.2.Branched-ChainReactions762.4.3.FlameInhibitors792.5.ExperimentalandComputationalTechniques80PROBLEMS813.OXIDATIONMECHANISMSOFFUELS.....................843.1.PracticalFuels853.2.OxidationofHydrogenandCarbonMonoxide893.2.1.ExplosionLimitsofHydrogen–OxygenMixtures893.2.2.CarbonMonoxideOxidation943.2.3.InitiationReactionsinFlames943.3.OxidationofMethane953.3.1.GeneralConsiderationsofHydrocarbonOxidation953.3.2.MethaneAutoignition963.3.3.MethaneFlames993.4.OxidationofC2Hydrocarbons1003.5.OxidationofAlcohols1023.6.High-TemperatureOxidationofHigherAliphaticFuels1033.6.1.Theβ-ScissionRule1043.6.2.OxidationMechanisms1063.7.OxidationofAromatics109

P1:JZP0521870526preCUFX045/LawPrinter:cupusbw0521870526July21,20068:49Contentsix3.8.HydrocarbonOxidationatLowtoIntermediateTemperatures1123.9.ChemistryofPollutantFormation1153.9.1.OxidesofNitrogen1163.9.2.SootFormation1193.10.MechanismDevelopmentandReduction1223.10.1.PostulatedSemiglobalMechanisms1223.10.2.NeedforComprehensivenessandReduction1243.11.SystematicReduction:TheHydrogen–OxygenSystem1243.11.1.ReductiontoSkeletalMechanisms1253.11.2.LinearlyIndependentRepresentation1283.11.3.ReductionthroughQSSAssumption1293.12.TheoriesofMechanismReduction1323.12.1.SensitivityAnalysis1323.12.2.TheoryofDirectedRelationGraph1333.12.3.TheoryofComputationalSingularPerturbation1353.12.4.MechanismValidation137PROBLEMS1394.TRANSPORTPHENOMENA............................1414.1.PhenomenologicalDerivationofDiffusionCoefﬁcients1434.1.1.Derivation1434.1.2.DiscussiononDiffusionCoefﬁcients1454.1.3.CharacteristicDiffusionRatesandNondimensionalNumbers1454.1.4.Second-OrderDiffusion1464.2.SomeUsefulResultsfromKineticTheoryofGases1464.2.1.GeneralConcepts1464.2.2.CollisionPotentialsandIntegrals1484.2.3.TransportCoefﬁcients151PROBLEMS1555.CONSERVATIONEQUATIONS..........................1575.1.ControlVolumeDerivation1575.1.1.ConservationofTotalMass1585.1.2.ConservationofIndividualSpecies1585.1.3.ConservationofMomentum1605.1.4.ConservationofEnergy1605.1.5.ConservationRelationsacrossanInterface1625.2.GoverningEquations1635.2.1.ConservationEquations1635.2.2.ConstitutiveRelations1635.2.3.AuxiliaryRelations1665.2.4.SomeUsefulApproximations1675.3.ASimpliﬁedDiffusion-ControlledSystem1705.3.1.Assumptions1705.3.2.Derivation170

P1:JZP0521870526preCUFX045/LawPrinter:cupusbw0521870526July21,20068:49xContents5.4.ConservedScalarFormulations1725.4.1.CouplingFunctionFormulation1735.4.2.LocalCouplingFunctionFormulation1765.4.3.Near-EquidiffusionFormulation1775.4.4.ElementConservationFormulation1785.4.5.MixtureFractionFormulation1795.4.6.ProgressVariableFormulation1825.5.Reaction-SheetFormulation1825.5.1.JumpRelationsforCouplingFunctions1825.5.2.AdiabaticFlameTemperature1855.6.FurtherDevelopmentoftheSimpliﬁedDiffusion-ControlledSystem1875.6.1.ConservationEquations1875.6.2.NondimensionalNumbers188NOMENCLATURE190PROBLEMS1926.LAMINARNONPREMIXEDFLAMES.....................1946.1.TheOne-DimensionalChamberedFlame1966.1.1.CouplingFunctionFormulation1966.1.2.Reaction-SheetFormulation1996.1.3.MixtureFractionFormulation2006.1.4.ElementConservationFormulation2016.2.TheBurke–SchumannFlame2026.3.CondensedFuelVaporizationandtheStefanFlow2086.4.DropletVaporizationandCombustion2136.4.1.Phenomenology2136.4.2.d2-LawofDropletVaporization2146.4.3.d2-LawofDropletCombustion2176.4.4.ExperimentalResultsonSingle-ComponentDropletCombustion2226.5.TheCounterﬂowFlame224PROBLEMS2307.LAMINARPREMIXEDFLAMES.........................2347.1.CombustionWavesinPremixtures2357.1.1.Rankine–HugoniotRelations2357.1.2.DetonationandDeﬂagrationWaves2387.1.3.Chapman–JouguetWaves2397.1.4.PreliminaryDiscussionofDetonationWaves2407.2.PhenomenologicalDescriptionoftheStandardFlame2417.2.1.FlameStructure2417.2.2.LaminarBurningFluxandFlameThickness2447.3.MathematicalFormulation2467.3.1.GoverningEquations2467.3.2.TheColdBoundaryDifﬁculty249

P1:JZP0521870526preCUFX045/LawPrinter:cupusbw0521870526July21,20068:49Contentsxi7.4.ApproximateAnalyses2507.4.1.IntegralAnalysis2507.4.2.Frank-KamenetskiiSolution2537.5.AsymptoticAnalysis2557.5.1.DistinguishedLimit2557.5.2.AsymptoticSolution2567.5.3.DependenceofBurningFluxonFlameTemperature2637.6.DeterminationofLaminarFlameSpeeds2637.6.1.BunsenFlameMethod2657.6.2.FlatandOne-DimensionalFlameMethods2667.6.3.OutwardlyPropagatingSphericalFlameMethod2687.6.4.StagnationFlameMethod2717.6.5.NumericalComputation2737.6.6.Proﬁle-BasedDetermination2747.7.DependenceofLaminarBurningVelocities2757.7.1.DependenceonTadandLe2757.7.2.DependenceonMolecularStructure2777.7.3.DependenceonPressure2787.7.4.DependenceonFreestreamTemperature2827.7.5.DependenceonTransportProperties2837.8.ChemicalStructureofFlames2847.8.1.ExperimentalMethods2857.8.2.DetailedStructure2867.8.3.AsymptoticStructurewithReducedMechanisms294PROBLEMS3018.LIMITPHENOMENA................................3038.1.PhenomenologicalConsiderationsofIgnitionandExtinction3058.1.1.QuenchingDistancesandMinimumIgnitionEnergies3058.1.2.AdiabaticThermalExplosion3078.1.3.NonadiabaticExplosionandtheSemenovCriterion3098.1.4.TheWell-StirredReactorAnalogy3118.1.5.TheS-CurveConcept3138.2.IgnitionbyaHotSurface3178.2.1.AsymptoticAnalysisoftheReactionZone3188.2.2.IgnitionofaConﬁnedMixturebyaFlatPlate3228.2.3.IgnitionofanUnconﬁnedMixturebyaFlatPlate3248.2.4.NusseltNumberCorrelation3268.2.5.Convection-FreeFormulation3268.3.IgnitionofHydrogenbyHeatedAir3278.3.1.GlobalResponsetoStrainRateVariations3288.3.2.SecondIgnitionLimit3308.3.3.FirstandThirdIgnitionLimits3338.3.4.DecoupledEnvironmentandKineticversusThermalFeedback3358.3.5.MultipleCriticalityandStagedIgnition338

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