Analytic Combustion : With Thermodynamics, Chemical Kinetics and Mass Transfer

365 Pages·2011·2.71 MB·English

by  Anil W Date

ANALYTIC COMBUSTION
Combustioninvolveschangeinthechemicalstateofasubstancefromafuelstatetoa
productstateviaachemicalreactionaccompaniedbyreleaseofheatenergy.Designor
performanceevaluationofequipmentalsorequiresknowledgeoftherateofchangeof
state.Thisrateisgovernedbythelawsofthermodynamicsandbytheempiricalsciences
ofheatandmasstransfer,chemicalkineticsandfluiddynamics.Theoreticaltreatmentof
combustionrequiresintegratedknowledgeofthesesubjectsandstrongmathematicaland
numericalskills.AnalyticCombustioniswrittenforadvancedundergraduates,graduate
studentsandprofessionalsinmechanical,aeronauticalandchemicalengineering.Topics
werecarefullyselectedandarepresentedtofacilitatelearning,withemphasisoneffective
mathematical formulations and solution strategies. The book features more than 60
solved numerical problems and analytical derivations and nearly 145 end-of-chapter
exercise problems. The presentation is gradual, starting with thermodynamics of pure
and mixture substances and chemical equilibrium and building to a uniquely strong
chapteronapplicationcasestudies.
Professor Anil W. Date received his PhD in Heat Transfer from the Imperial College,
London.HehasbeenamemberoftheThermal&FluidsGroupoftheMechanicalEngin-
eeringDepartmentattheIndianInstituteofTechnologyBombaysince1973.Professor
Datehastaughtbothundergraduateandpost-graduatecoursesinthermodynamics,en-
ergyconversion,heatandmasstransferandcombustion.Heactivelyengagedinresearch
andconsultinginenhancedconvectiveheat/masstransfer,stabilityandphase-changein
nuclearthermo-hydraulicsloops,numericalmethodsappliedtocomputationalfluiddy-
namics,solidificationandmeltingandinterfacialflows.ProfessorDatehaspublishedin
the International Journal of Heat and Mass Transfer, Journal of Enhanced Heat Trans-
fer,JournalofNumericalHeatTransfer,andAmericanSocietyofMechanicalEngineers
JournalofHeatTransferandhascarriedoutimportantsponsoredandconsultancypro-
jectsfornationalagencies.HehasbeenEditorforIndiaoftheJournalofEnhancedHeat
Transfer.ProfessorDatehasheldvisitingprofessorshipsattheUniversityofKarlsruhe,
Germany,andCityUniversityofHongKong,andhasbeenvisitingscientistatCornell
UniversityandUIUC,USA.Hehasdeliveredlectures/seminarsinAustralia,UK,USA,
Germany, Sweden, Switzerland, Hong Kong and China. Professor Date founded the
CenterforTechnologyAlternativesforRuralAreas(CTARA)inIITBombayin1985
and has been its leader again since 2005. He derives great satisfaction from applying
thermo-fluidsandmechanicalsciencetoruraltechnologyproblemsandhasinspiredsev-
eralgenerationsofstudentstoworkonsuchproblems.Hehastaughtcoursesinscience,
technologyandsocietyandappropriatetechnology.ProfessorDatewaselectedFellowof
theIndianNationalAcademyofEngineering(2001),receivedtheExcellenceinTeaching
AwardofIITBombayin2006andwaschosenasthefirstRahulBajajChair-Professor
of Mechanical Engineering by IIT Bombay in 2009. Professor Date is the author of
Introduction to Computational Fluid Dynamics, published by Cambridge University
Press,in2005.
http://ebooks.cambridge.org/ebook.jsf?bid=CBO9780511976759

Analytic Combustion
WITH THERMODYNAMICS, CHEMICAL KINETICS,
AND MASS TRANSFER
Anil W. Date
IndianInstituteofTechnology,Bombay
cambridgeuniversitypress
Cambridge,NewYork,Melbourne,Madrid,CapeTown,
Singapore,Sa˜oPaulo,Delhi,Tokyo,MexicoCity
CambridgeUniversityPress
32AvenueoftheAmericas,NewYork,NY10013-2473,USA
www.cambridge.org
Informationonthistitle:www.cambridge.org/9781107002869
(cid:2)C AnilW.Date2011
Thispublicationisincopyright.Subjecttostatutoryexception
andtotheprovisionsofrelevantcollectivelicensingagreements,
noreproductionofanypartmaytakeplacewithoutthewritten
permissionofCambridgeUniversityPress.
Firstpublished2011
PrintedintheUnitedStatesofAmerica
AcatalogrecordforthispublicationisavailablefromtheBritishLibrary.
LibraryofCongressCataloginginPublicationdata
Date,AnilW.(AnilWaman)
AnalyticCombustion:WithThermodynamics,ChemicalKinetics,andMassTransfer/
A.W.Date.
p. cm
Includesbibliographicalreferencesandindex.
ISBN978-1-107-00286-9(hardback)
1.Combustion–Mathematicalmodels. 2.Thermodynamics–
Mathematicalmodels. I.Title.
QD516D26 2011
541(cid:3).361015118–dc22 2010049634
ISBN978-1-107-00286-9Hardback
CambridgeUniversityPresshasnoresponsibilityforthepersistenceoraccuracyofURLs
forexternalorthird-partyInternetWebsitesreferredtointhispublicationanddoesnot
guaranteethatanycontentonsuchWebsitesis,orwillremain,accurateorappropriate.
TotheMTechandPhDstudentsofthe
ThermalandFluidsEngineeringSpecialization
intheMechanicalEngineeringDepartment,IITBombay
fortheirappreciativeevaluationsofmyteaching
and
TomywifeSuranga,sonKartikeya,anddaughterPankaja
fortheirpatienceandsupport,andfor
caringtocallmehomefrommyoffice,
howling,“Itiswellpastdinnertime!”

Contents
Preface pagexiii
SymbolsandAcronyms xvii
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 ImportanceofThermodynamics 1
1.2 LawsofThermodynamics 5
1.3 ImportanceofCombustion 7
2 ThermodynamicsofaPureSubstance. . . . . . . . . . . . . . . . . . . . . . .12
2.1 Introduction 12
2.2 ImportantDefinitions 12
2.2.1 System,SurroundingsandBoundary 12
2.2.2 WorkandHeatInteractions 13
2.2.3 Closed(Constant-Mass)System 13
2.2.4 Open(Constant-Volume)System 14
2.2.5 In-BetweenSystems 14
2.2.6 ThermodynamicEquilibrium 15
2.2.7 PropertiesofaSystem 16
2.2.8 StateofaSystem 17
2.3 BehaviorofaPureSubstance 18
2.3.1 PureSubstance 18
2.3.2 TypicalBehavior 18
2.4 LawofCorrespondingStates 21
2.5 ProcessandItsPath 23
2.5.1 RealandQuasistaticProcesses 24
2.5.2 ReversibleandIrreversibleProcesses 25
2.5.3 CyclicProcess 27
2.6 FirstLawofThermodynamics 27
2.6.1 FirstLawforaFiniteProcess–ClosedSystem 28
2.6.2 Joule’sExperiment 30
2.6.3 SpecificHeatsandEnthalpy 31
vii
viii Contents
2.6.4 IdealGasRelations 32
2.6.5 FirstLawforanOpenSystem 32
2.7 SecondLawofThermodynamics 35
2.7.1 ConsequenceforaFiniteProcess–ClosedSystem 36
2.7.2 IsolatedSystemandUniverse 38
2.7.3 FirstLawinTermsofEntropyandGibbsFunction 40
2.7.4 ThermalEquilibrium 40
2.7.5 EquilibriumofaGeneralClosedSystem 42
2.7.6 Phase-ChangeProcesses 43
2.7.7 SecondLawforanOpenSystem 44
3 ThermodynamicsofGaseousMixtures . . . . . . . . . . . . . . . . . . . . . . 48
3.1 Introduction 48
3.2 MixtureComposition 49
3.2.1 MassFraction 49
3.2.2 MoleFractionandPartialPressure 50
3.2.3 MolarConcentration 51
3.2.4 SpecifyingComposition 51
3.3 EnergyandEntropyPropertiesofMixtures 51
3.4 PropertiesofReactingMixtures 54
3.4.1 StoichiometricReaction 54
3.4.2 Fuel–AirRatio 56
3.4.3 EquivalenceRatio(cid:2) 57
3.4.4 Effectof(cid:2)onProductComposition 57
3.4.5 HeatofCombustionorHeatofReaction 60
3.4.6 EnthalpyofFormation 62
3.4.7 EntropyofFormation 63
3.4.8 AdiabaticFlameTemperature 63
3.4.9 Constant-VolumeHeatofReaction 64
3.5 UseofPropertyTables 64
4 ChemicalEquilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
4.1 ProgressofaChemicalReaction 70
4.2 DissociationReaction 71
4.3 ConditionsforChemicalEquilibrium 72
4.3.1 ConditionforaFiniteChange 72
4.3.2 ConsequencesforanInfinitesimalChange 72
4.4 EquilibriumConstantK 74
p
4.4.1 DegreeofReaction 74
4.4.2 DerivationofK 75
p
4.5 ProblemsinChemicalEquilibrium 78
4.5.1 SingleReactions 78
4.5.2 Two-StepReactions 80
4.5.3 MultistepReactions 82
4.5.4 Constant-VolumeCombustion 86
Contents ix
5 ChemicalKinetics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .90
5.1 ImportanceofChemicalKinetics 90
5.2 ReformedViewofaReaction 91
5.3 ReactionRateFormula 92
5.3.1 TypesofElementaryReactions 92
5.3.2 RateFormulaforA+B→C+D 94
5.3.3 Tri-andUnimolecularReactions 98
5.3.4 RelationbetweenRateCoefficientandK 98
p
5.4 ConstructionofGlobalReactionRate 101
5.4.1 UsefulApproximations 101
5.4.2 ZeldovichMechanismofNOFormation 104
5.4.3 Quasi-GlobalMechanism 108
5.5 GlobalRatesforHydrocarbonFuels 109
6 DerivationofTransportEquations . . . . . . . . . . . . . . . . . . . . . . . . 112
6.1 Introduction 112
6.2 Navier-StokesEquations 113
6.2.1 MassConservationEquation 113
6.2.2 MomentumEquationsu (i=1,2,3) 113
i
6.3 EquationsofMassTransfer 115
6.3.1 SpeciesConservation 115
6.3.2 ElementConservation 116
6.4 EnergyEquation 117
6.4.1 RateofChange 117
6.4.2 ConvectionandConduction 117
6.4.3 VolumetricGeneration 118
6.4.4 FinalFormofEnergyEquation 120
6.4.5 EnthalpyandTemperatureForms 120
6.5 Two-DimensionalBoundaryLayerFlowModel 121
6.5.1 GoverningEquations 122
6.5.2 BoundaryandInitialConditions 123
6.6 One-DimensionalStefanFlowModel 125
6.7 ReynoldsFlowModel 126
6.8 TurbulenceModels 128
6.8.1 BasisofModeling 128
6.8.2 Modeling|u(cid:3)|andl 128
7 ThermochemicalReactors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
7.1 Introduction 134
7.2 Plug-FlowReactor 135
7.2.1 GoverningEquations 135
7.2.2 NonadiabaticPFTCR 144
7.3 Well-StirredReactor 146
7.3.1 GoverningEquations 146
7.3.2 Steady-StateWSTCR 148
7.3.3 LoadingParameters 152
x Contents
7.4 Constant-MassReactor 155
7.4.1 Constant-VolumeCMTCR 156
7.4.2 Variable-VolumeCMTCR 159
8 PremixedFlames . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
8.1 Introduction 164
8.2 LaminarPremixedFlames 165
8.2.1 LaminarFlameSpeed 165
8.2.2 ApproximatePredictionofS andδ 166
l
8.2.3 RefinedPredictionofS andδ 169
l
8.2.4 CorrelationsforS andδ 173
l
8.3 TurbulentPremixedFlames 176
8.4 FlameStabilization 178
8.5 ExternallyAidedIgnition 182
8.5.1 SphericalPropagation 182
8.5.2 PlanePropagation 184
8.6 Self-orAuto-Ignition 188
8.6.1 IgnitionDelayandFuelRating 188
8.6.2 EstimationofIgnitionDelay 189
8.7 FlammabilityLimits 192
8.8 FlameQuenching 194
9 DiffusionFlames. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .198
9.1 Introduction 198
9.2 LaminarDiffusionFlames 200
9.2.1 VelocityPrediction 200
9.2.2 FlameLengthandShapePrediction 203
9.2.3 Correlations 207
9.2.4 SolvedProblems 208
9.3 TurbulentDiffusionFlames 210
9.3.1 VelocityPrediction 210
9.3.2 FlameLengthandShapePrediction 212
9.3.3 CorrelationsforL 216
f
9.3.4 CorrelationsforLiftoffandBlowout 217
9.4 SolvedProblems 218
9.5 BurnerDesign 220
10 CombustionofParticlesandDroplets . . . . . . . . . . . . . . . . . . . . . . 223
10.1 Introduction 223
10.2 GoverningEquations 226
10.3 DropletEvaporation 228
10.3.1 InertMassTransferwithoutHeatTransfer 228
10.3.2 InertMassTransferwithHeatTransfer 234
10.4 DropletCombustion 239
10.4.1 DropletBurnRate 240
10.4.2 InterpretationofB 240
10.4.3 FlameFrontRadiusandTemperature 242