Combustion waves and fronts in flows : flames, shocks, detonations, ablation fronts and explosion of stars

722 Pages·2016·21.787 MB·English

by  Paul Clavin, Geoff Searby

COMBUSTION WAVES AND FRONTS IN FLOWS
Combustionisafascinatingphenomenoncouplingcomplexchemistrytotransportmecha-
nismsandnonlinearfluiddynamics.Thisbookprovidesanup-to-dateandcomprehensive
presentation of the nonlinear dynamics of combustion waves and other non-equilibrium
energeticsystems.Themajoradvancesinthisfieldhaveresultedfromanalyticalstudiesof
simplifiedmodelsperformedincloserelationwithcarefullycontrolledlaboratoryexperi-
ments.Thekeytounderstandingthecomplexphenomenaisasystematicreductionofthe
complexityofthebasicequations.
Focusingonthisfundamentalapproach,thebookissplitintothreeparts.PartIprovides
physical insights for physics-oriented readers, Part II presents detailed technical analysis
usingperturbationmethodsfortheoreticiansandPartIIIrecallsthenecessarybackground
knowledge in physics, chemistry and fluid dynamics. This structure makes the content
accessible to newcomers to the physics of unstable fronts in flows, whilst also offering
advancedmaterialforscientistswhowishtoimprovetheirknowledge.
paul clavin is Professor Emeritus at Aix-Marseille Universite´ and is an honorary
member of the Institut Universitaire de France (Chair of Me´canique Physique 1993–
2004). In 1995 he founded a renowned research institute, the Institut de Recherche sur
lesPhe´nome`nesHorsE´quilibre(IRPHE),andhasreceivedmajorawardsfromtheSocie´te´
Franc¸aise de Physique (Plumey 1988), French Academy of Sciences (Grand Prix 1995)
andtheCombustionInstitute(ZeldovichGoldMedal,SanFrancisco,August2014).
geoff searby is retired Director of Research at the Institut de Recherche sur les
Phe´nome`nesHorsE´quilibre(IRPHE).Heisarenownedspecialistofthephysicsofthermo-
acousticinstabilitiesincombustionchambersandrocketmotors,andhisexperimentshave
mademajorcontributionstotheunderstandingofthedynamicsofflamefronts.In2004he
obtainedamajorawardfromtheFrenchAcademyofSciences.
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16:59:56
COMBUSTION WAVES AND
FRONTS IN FLOWS
Flames, shocks, detonations, ablation
fronts and explosion of stars
PAUL CLAVIN
AixMarseilleUniversite´,France
GEOFF SEARBY
FormerlyoftheCentreNationaldelaRecherche
Scientifique(CNRS),Marseille,France
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UniversityPrintingHouse,CambridgeCB28BS,UnitedKingdom
CambridgeUniversityPressispartoftheUniversityofCambridge.
ItfurtherstheUniversity’smissionbydisseminatingknowledgeinthepursuitof
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www.cambridge.org
Informationonthistitle:www.cambridge.org/9781107098688
©CambridgeUniversityPress2016
Thispublicationisincopyright.Subjecttostatutoryexception
andtotheprovisionsofrelevantcollectivelicensingagreements,
noreproductionofanypartmaytakeplacewithoutthewritten
permissionofCambridgeUniversityPress.
Firstpublished2016
PrintedintheUnitedKingdombyTJInternationalLtd.PadstowCornwall
AcataloguerecordforthispublicationisavailablefromtheBritishLibrary
LibraryofCongressCataloging-in-Publicationdata
Names:Clavin,Paul,author.|Searby,Geoff,1945–author.
Title:Combustionwavesandfrontsinflows:flames,shocks,detonations,
ablationfrontsandexplosionofstars/PaulClavin(AixMarseille
Universite´,France),GeoffSearby(FormerlyCentreNationaldela
RechercheScientifique(CNRS),Marseille,France).
Description:Cambridge,UnitedKingdom;NewYork,NY:CambridgeUniversity
Press,2016.|©2016|Includesbibliographicalreferencesandindex.
Identifiers:LCCN2016011752|ISBN9781107098688(hardback;alk.paper)|
ISBN1107098688(hardback;alk.paper)
Subjects:LCSH:Combustion.|Waves.|Chemicalreactions.|Dynamics.|
Nonlineartheories.|Fluidmechanics.
Classification:LCCQD516.C572016|DDC541/.361–dc23LCrecordavailableat
http://lccn.loc.gov/2016011752
ISBN978-1-107-09868-8Hardback
CambridgeUniversityPresshasnoresponsibilityforthepersistenceoraccuracy
ofURLsforexternalorthird-partyinternetwebsitesreferredtointhispublication,
anddoesnotguaranteethatanycontentonsuchwebsitesis,orwillremain,
accurateorappropriate.
16:59:56
Contents
Preface pageix
Introduction 1
BriefHistoricalIntroduction 1
EnergyandModernSociety 6
CombustionandRelatedPhenomena 8
ScopeoftheBook 8
PartOne PhysicalInsights 11
1 GeneralConsiderations 13
1.1 IntroductoryRemarks 14
1.2 CombustionWavesonEarth 15
1.3 FrontsandThermalWavesinExtremeConditions 30
1.4 Appendix:PhysicalConstantsandConversionofUnits 43
2 LaminarPremixedFlames 45
2.1 MainCharacteristics 48
2.2 HydrodynamicInstability 56
2.3 FlameStretchandMarksteinNumbers 69
2.4 Thermo-DiffusivePhenomena 77
2.5 Thermo-AcousticInstabilities 101
2.6 CurvedFronts 121
2.7 NonlinearDynamicsofUnstableFlameFronts 135
2.8 AdditionalLaboratoryExperiments 146
2.9 Appendix 156
3 TurbulentPremixedFlames 174
3.1 BasicConsiderations 176
3.2 TurbulentWrinkledFlames 188
3.3 TurbulentCombustionNoise 197
3.4 Appendix 203
v
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vi Contents
4 GaseousShocksandDetonations 210
4.1 IntroductoryRemarks 213
4.2 PlanarSupersonicWaves 214
4.3 InitiationofDetonation 231
4.4 DynamicsofShockFronts 261
4.5 InstabilitiesofDetonationFronts 279
4.6 Appendix 300
5 ChemicalKineticsofCombustion 305
5.1 Introduction 306
5.2 BasicsConceptsinChemicalKinetics 307
5.3 CombustionofHydrogen 311
5.4 CombustionofLeanMethaneMixtures 317
6 Laser-DrivenAblationFrontinICF 323
6.1 ApproximationsandConstitutiveEquations 324
6.2 DynamicsoftheAblationFront 329
7 ExplosionofMassiveStars 339
7.1 ConstitutiveEquationsofStars 341
7.2 StellarEquilibrium 346
7.3 InstabilityandGravitationalCollapse 352
7.4 Appendix 370
PartTwo DetailedAnalyticalStudies 375
8 PlanarFlames 377
8.1 GeneralFormulation 379
8.2 ThermalPropagation 381
8.3 Reaction–DiffusionWaves 393
8.4 ChainBranchingandFlamePropagation 403
8.5 FlameQuenching 411
9 FlameKernelsandFlameBalls 429
9.1 FlameKernelsNeartheFlammabilityLimits 431
9.2 StabilityAnalysisofSphericalFlameKernels 440
9.3 FlameExpansionatLewisNumberSmallerThanUnity 447
10 WrinkledFlames 460
10.1 Hydrodynamics 463
10.2 Thermo-DiffusiveInstabilitiesofPlanarFlames 473
10.3 HydrodynamicsandDiffusionCoupling 481
10.4 Appendix 500
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Contents vii
11 AblativeRayleigh–TaylorInstability 504
11.1 LinearAnalysesofSimplifiedModels 506
11.2 AsymptoticAnalysisoftheQuasi-IsobaricModel 511
11.3 NonlinearDynamicsintheLimitofaLargePowerIndex 522
12 ShockWavesandDetonations 527
12.1 LinearDynamicsofWrinkledShocks 529
12.2 DynamicsofDetonationFronts 543
PartThree Complements 565
13 StatisticalPhysics 567
13.1 StatisticalThermodynamics 569
13.2 IdealGases 580
13.3 PhysicalKinetics 591
14 Chemistry 606
14.1 ElementaryCombustionChemistry 607
14.2 ChemicalEquilibrium 620
14.3 ElementsofThermonuclearFusion 633
15 Flows 637
15.1 MacroscopicConservationEquations 640
15.2 Approximations 654
15.3 One-DimensionalCompressibleFlows 663
References 685
Index 704
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Preface
Combustionisafascinatingphenomenoncouplingcomplexchemistrytotransportmech-
anisms and nonlinear fluid dynamics. The combustion of reactive mixtures, frozen far
fromchemicalequilibrium,isanirreversibleprocessinwhichtheapproachtoequilibrium
proceedsthroughthepropagationofnonlinearwavesintheformofsharpfrontsexhibiting
complexgeometricalforms.Thesewaveswerediscoveredinthenineteenthcentury,butthe
understandingoftheirstructureanddynamicsisquiterecent.Ingaseousmixtures,therate
ofchemicalheatreleaseissmallcomparedwiththerateofelasticcollisions,sothatcom-
bustion is described by the macroscopic equations for the conservation of mass, species,
momentumandenergy,assuminglocalequilibrium(exceptfortheinnerstructureofshock
waves). The full system of equations is complicated and is not useful to describe each of
theelementaryphenomena,separatefromtheothers.Eventhecouplingoftwophenomena,
as for example a quasi-isobaric flame and acoustic waves, is represented by simplified
equations.Themajoradvanceshaveresultedfromanalyticalstudiesofsimplifiedmodels
performed in close relation to carefully controlled laboratory experiments. A systematic
reduction of the complexity of the basic equations, validated by the confrontation with
experiments, is the key to understanding. It is also the most difficult step. The analytical
andnumericalsolutionsofsimplifiedequationsofrelevantmodelscanbecompletedina
secondstepbydirectnumericalsimulationsofamoredetailedsystemofequations.
The book is written along this line and attention is focused on fundamental aspects.
It is meant to be a survey of the nonlinear dynamics of combustion waves, which now
constituteamaturescientificfield.Asimilarapproachisusedtoimprovetheunderstanding
ofothertypesofwavessuchasablationfontsininertialconfinementfusion.Theapproach
isalsotentativelyextendedtotheexplosionofstarsattheendoftheirlifetime,thefamous
supernovae.Alargevarietyofphenomenaispresented.Thepurposeistoprovideawide
view of the physical problems involved in different domains that can benefit from cross-
fertilisation.Themostimportantscientificresultsarereported,rangingfromthepioneering
worksofthelastcenturytotheadvancedresearchofthelastdecade.
The book is aimed at both newcomers to the physics of unstable fronts in flows and
scientistswhowishtoimprovetheirknowledge. Itisself-containedandcanalsobeused
as a textbook by students. The background in physics, chemistry and fluid mechanics is
given in the last part as complements. Physical insights into the phenomena occupy half
ix
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.001
x Preface
ofthebookandarepresentedfirst.Detailedanalyticalstudiesaredevelopedinthesecond
partandnoprerequisitesinappliedmathematicsarerequiredconcerningtheperturbation
methodsthatareused(multiple-scaleandasymptoticanalyses).
This book would never have been written without 40 years of activity in our research
group, interacting closely with our friends and colleagues, Louis Boyer, Bruno Denet,
AlainPocheau,JoelQuinardandEmmanuelVillermaux.Wearealsogratefultoourclose
friends and outstanding theoretical physicists for fruitful collaboration and enlightening
discussions of great help to improve our understanding of nonlinear problems related to
combustion, particularly Guy Joulin, Amable Lin˜an, Yves Pomeau, Grisha Sivashinsky
andFormanA.Williams.
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.001