Combustion Physics: Flames, Detonations, Explosions, Astrophysical Combustion and Inertial Confinement Fusion

620 Pages·2021·14.124 MB·English

by  Michael A. Liberman

Michael A. Liberman
Combustion
Physics
Flames, Detonations, Explosions,
Astrophysical Combustion and Inertial
Confinement Fusion
Combustion Physics
Michael A. Liberman
Combustion Physics
Flames, Detonations, Explosions,
Astrophysical Combustion and Inertial
Confinement Fusion
MichaelA.Liberman
NORDITA,KTHRoyalInstitute
ofTechnology
StockholmUniversity
Stockholm,Sweden
ISBN978-3-030-85138-5 ISBN978-3-030-85139-2 (eBook)
https://doi.org/10.1007/978-3-030-85139-2
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Preface
In 1825, Michael Faraday initiated popular Christmas lectures in London, which
remain the flagship scientific lectures in the U.K. until today. Eventually, Faraday
presentedaseriesofsixlecturescenteredaroundflame,“TheChemicalHistoryof
a Candle”,1 which proved to be hugely popular—and for a good reason: the quest
forfireilluminatedhumanhistoryformillenniabutonlyatthetimeoftheIndustrial
Revolutioncombustionemergedasadistinctareaofscience,settingouttoanalyze
thechemicalprocessoffueloxidation.Inthepastonehundredandfiftyyears,this
field experienced explosive growth alongside the appearance of the multitude of
uses,fromcombustionenginestogasturbinestojetenginesandspacerockets!At
last,combustionbecameascientificfieldduetothecombinedprogressinchemical
kineticsandfluidmechanics.Itwaspossibletoexplainvariouscombustionmodes,
such as flame, explosions, and detonation, which all make a strong impact on our
lives.
Today,combustionremainsatrulyinterdisciplinarysubject,andassuchitrequires
mergingofvariousfieldsofscience,fromchemicalkineticsandthermodynamicsto
fluidmechanics,nonlinearphenomena,andturbulence.Becauseofthiscomplexity,
thein-depthscientificinvestigationofcombustionisarelativelyrecentphenomenon,
despiteitslong-standingimpactonalltypesofhumanactivities.
Delivering his lectures on The Chemical History of a Candle, Faraday justified
hischoicebyclaimingthatthereisnobetter,thereisnomoreopendoorbywhich
youcanenterintothestudyofsciencethanbyconsideringthephysicalphenomena
ofacandle.Nowadays,combustionremainsafascinatingandfast-developingfield
of physics. Faraday’s words about an open door by which you can enter into the
studyofsciencecanbejustaswellappliedtocombustionphysics.Whileweoften
hearpredictionsabouttheendofnewdiscoveriesinphysics,theactualendofnew
discoveries never seems to come. The elements of combustion, such as a flame,
explosion, and detonation, are known for a long time, but somewhat surprisingly
1TheChemicalHistoryofaCandle:ACourseofLecturesDeliveredBeforeAJuvenileAudience
attheRoyalInstitutionbyMichaelFaraday,D.C.L.,F.R.S.EditedbyWilliamCrookes,F.C.S.
CHATTOANDWINDUS,PUBLISHERS,London.
v
vi Preface
their first principal description was obtained not such a long time ago and for a
limitedrangeofconditions.Amorecoherentpictureemergedinrecenttimes,asa
resultofmanyexperimentalandtheoreticalstudies,sponsoredbyenergyproduction
andindustrialneeds.
Combustionisaprocessofheatreleaseinexothermalreactions,whichisaccom-
panied by mass and heat transfer. The chemical combustion involves a chemical
transformationbetweenfuelsubstancesandoxidizers.Intheseprocesses,nucleiof
theenteringsubstancesarenotalteredbutformednewmoleculesandatoms,which
arecombustionproducts.Heatreleaseintheprocessofbondingismostinteresting
sincethisenergycanbecapturedandusefullyexploited.Combustionmayinvolve
allphasesofmatter—solid,liquid,andgas:solidrocketpropellants,liquiddroplets
burningindiesels,andgaseouscombustioninSIengines.Theprincipaldifficultiesin
understandingcombustionprocessesarethehugedifferencesoftimeandspacescales
involved,chemicalcomplexity,andmultidimensionalnatureoftheflowconfigura-
tion. In turbulent combustion, the strong nonlinear coupling of the turbulence and
thechemistrybringadditionalcomplications.Chemicalreactions’ratesarecoupled
tomoleculardiffusionatthesmallestscalesoftheturbulence.Furthermore,theheat
releaseassociatedwithcombustionaffectstheturbulentflow,bothfromvariationsin
themeandensityfieldandfromtheeffectsoflocaldilatation.Becauseofitsimpor-
tance in many areas of physics and technology, combustion science is developing
rapidlyandthereisanextensivevolumeofliteratureonthesubject.Afastprogress
hasbeenachievedincombustionscienceduringalittlemorethan10yearssincethe
publicationofmybook“IntroductiontoPhysicsandChemistryofCombustion”in
2008. Because of this progress, it was clear that a new book is necessary to bring
readerstothefrontiersofthesubject.
Combustionprocessessurroundusinoureverydaylives.Chemicalcombustionis
usedforenergyproductioninpowerplants,gasturbines,andengines.Processesof
thermonuclearcombustionaretheheatsourcefortheSunandstars.Aspecialinterest
tothethermonuclearexplosionsoftypeIasupernovasisduetothepossibilitytouse
theexplodingsupernovasascosmicstandardlightmarkerstoanalyzethefateofthe
universeandtheuniversegeometry.UsingtypeIasupernovasasdistanceindicators
led to the discovery of the accelerated expansion of the universe and changed our
understandingoftheuniversegeometrytoanearlyflatuniversethatisexpandingat
an accelerated rate. It was found that the universe expansion is speeding up rather
thanslowingdown,whereaspreviouslyitwasthoughtthatgravityshouldslowdown
theuniverseexpansion.
Thisbookprovidesacomprehensivepresentationofstateoftheartofthecombus-
tiontheory,focusingonthecombustionfundamentals.Thebookcontainsthemost
recent scientific results in various fields related to combustion. In each chapter of
thebook,andoneachissue,anexhaustivelistofreferencesontheoriginalresearch
isprovided,includingthemostrecentpublications.Thepresentedmaterialisaimed
at illustrating the physics of the phenomena under consideration and its quantita-
tivedescriptionobtainedusinganalyticalmethodsandmultidimensionalcomputer
modeling,aswellascomparisonwithexperimentalresults.Thelevelofthebookis
Preface vii
suitableforgraduateuniversitycoursesincombustionandforanadvancedcombus-
tioncourse.Ingeneral,itwouldrequireasolidbackgroundinthermodynamicsand
fluidmechanics,butItriedtopresentthematerialinawaysuitablefor2nd–3rdyears
andPh.D.studentsofphysical,mathematical,chemical,andengineeringspecialties.
Thelasttwochaptersofthebookdescribeapplicationsoftheoreticalmethodsdevel-
opedincombustiontostudytypeIasupernovaexplosionsandstabilityproblemsin
Inertial Confinement Fusion. Therefore, the book can be useful for astrophysicists
andplasmaphysicists.
I am indebted to many people who helped in the preparation of this book.
ThisespeciallyappliestomycolleaguesatNordicInstituteofTheoreticalPhysics
(NORDITA).Inparticular,IwanttothankAxelBrandenburgforcontinuedcollabora-
tion;GregorySivashinskyforcarefullyreadingmanychaptersofthebookandgiving
usefulcommentsonthebook’slayout;andtoChengengQianforhismeticuloushelp
withpreparingtheillustrations.
Uppsala,Sweden MichaelA.Liberman
June2021
Contents
1 CombustionChemistry ........................................ 1
1.1 ChemicalReactions ...................................... 1
1.2 Non-branchingChainReaction:HydrogenChlorine ........... 10
1.3 FormationMechanismsofNitrogenOxides .................. 13
1.3.1 ThermalNOMechanism ........................... 14
1.3.2 PromptNOMechanism ............................ 18
1.3.3 FuelNO ......................................... 20
1.3.4 FlamesoftheFirst-OrderReaction .................. 21
1.4 Chain-BranchingReactions:Explosions ..................... 22
1.4.1 Hydrogen–OxygenExplosions:ExplosionLimits ..... 23
1.4.2 OxidationandExplosionsofHydrocarbons ........... 28
References .................................................... 30
2 Self-AcceleratingReactions .................................... 33
2.1 AOne-StepChemicalReactionModel ...................... 34
2.2 ElementaryTheoryofThermalExplosion ................... 35
2.3 ThermalSelf-Ignition ..................................... 38
2.4 Frank-KamenetskiiTransformation ......................... 42
2.5 SemenovTheoryofThermalExplosions ..................... 43
2.6 Frank-KamenetskiiTheoryofThermalExplosion ............. 46
2.7 SparkIgnitionandMinimumIgnitionEnergy ................ 49
2.8 InductionTime:One-StepandDetailedChemicalModels ...... 52
2.8.1 Hydrogen–Air: A Single-Step and Detailed
ChemicalModels ................................. 53
2.8.2 Methane–Air: A Single-Step and Detailed
ChemicalModels ................................. 54
References .................................................... 58
3 LaminarFlames .............................................. 61
3.1 ReactionWaves .......................................... 61
3.2 VelocityandThicknessofLaminarFlames ................... 65
3.3 TemperatureandConcentrationDistributions ................. 70
ix
x Contents
3.4 Zel’dovich–Frank-KamentskiiTheory:LaminarFlame
Speed ................................................... 75
3.5 ConsequencesoftheFormulaforNormalFlameVelocity ...... 79
3.6 LaminarNon-premixedFlames ............................. 80
3.6.1 Non-premixedLaminarFlames ..................... 81
3.6.2 CombustionofLiquidFuelDroplets ................. 83
References .................................................... 85
4 HydrodynamicsofPremixedLaminarFlames ................... 87
4.1 FlameHydrodynamics:CombustionRegimes ................ 87
4.2 CompleteSystemofEquationsforPropagatingFlame ......... 95
4.3 IsobaricApproximation ................................... 96
4.4 TheoryofPlanarFlames .................................. 98
References .................................................... 103
5 FlameInstabilities ............................................. 107
5.1 Darrieus-LandauInstabilityofZeroThicknessFlame .......... 107
5.2 HydrodynamicInstability;FlamesofFiniteThickness ......... 113
5.3 FlameinaGravitationalField;Rayleigh–TaylorInstability ..... 123
5.3.1 ComparisonwithNumericalSimulations ............. 125
5.4 Thermal-DiffusiveInstability .............................. 130
5.4.1 ThermalDiffusiveInstability(Le(cid:2)=1) ............... 131
5.4.2 ThermalDiffusiveInstabilityofSolidPropellant ...... 137
5.5 FlameDynamics;EvolutionEquation ....................... 141
5.5.1 EvolutionEquation;InfinitelyThinFlameFront ....... 141
5.5.2 EvolutionEquation;InfluenceofFiniteFlame
Thickness ....................................... 144
5.5.3 EvolutionEquation;ArbitraryEquationofState ....... 148
5.5.4 InfluenceofCompressibility ........................ 153
References .................................................... 167
6 Flame–AcousticInteraction:ThermoacousticandParametric
Instabilities ................................................... 171
6.1 Early Experimental Research on the Flame–Acoustic
Interaction .............................................. 171
6.2 FlameStabilizationbyAcousticWaves ...................... 173
6.3 ParametricFlameInstabilityandSoundWaves ............... 177
6.4 ExperimentalStudyoftheDarrieus–LandauInstability ........ 182
6.5 Flame–AcousticInteraction:ThermoacousticInstabilities ...... 185
6.6 ApplicabilityofAnalyticalModels ......................... 187
References .................................................... 190
7 InteractionofFlameswithWeakShocks ........................ 193
7.1 LinearTheoryofFlame–ShockInteraction ................... 193
7.2 NonlinearEffectsofFlame–ShockInteractions ............... 201
7.3 Hydrodynamic Instability of Planar Flame in Closed
Chambers ............................................... 211
Contents xi
References .................................................... 216
8 DynamicsofCurvedFlamesPropagatinginTubes ............... 219
8.1 NonlinearStageofInstability;CellularFlame’sStructure ...... 219
8.2 NonlinearEquationforCurvedStationaryFlames ............. 224
8.3 Velocityof2DCurvedFlame .............................. 229
8.4 VelocityandShapeof2DFlame ............................ 232
References .................................................... 238
9 DynamicsofFlamesUnderConfinement ........................ 241
9.1 Hydrodynamic Instability of Planar Flame in Closed
Chambers ............................................... 241
9.2 NumericalSimulationsoftheDLInstabilityinClosed
Tubes ................................................... 246
9.2.1 FlamesoftheFirst-OrderReaction .................. 248
9.2.2 FlamesoftheThird-OrderReaction ................. 251
9.3 FlammabilityLimitsandFlameQuenching .................. 254
9.3.1 FlammabilityLimits .............................. 254
9.3.2 HeatLossesandFlameQuenching .................. 256
9.4 TulipFlames.EffectoftheBoundaryLayer .................. 259
9.4.1 Experimental,Theoretical,andNumericalStudies ..... 259
9.4.2 MechanismsoftheTulipFlameFormation ........... 263
9.4.3 NumericalSimulationsandMechanismofTulip
FlameFormation ................................. 266
References .................................................... 274
10 FlameinaGravitationalField .................................. 279
10.1 TheRayleigh–TaylorInstability ............................ 279
10.2 VelocitiesofRisingBubbles ............................... 281
10.3 CurvedFlamesinVerticalTubes ........................... 282
10.4 FlameinHorizontalTubes ................................. 286
References .................................................... 289
11 StabilityLimits;SphericallyExpandingFlames .................. 293
11.1 FlameInstabilitiesinWideTubes ........................... 293
11.2 MorphologyofUnconfinedSphericallyExpandingFlames ..... 299
11.3 FractalStructureandSelf-similarRegime .................... 302
11.3.1 Fractal Dimension of 2D and 3D Expanding
Flames .......................................... 302
11.3.2 StabilityofSelf-similarSphericallyExpanding
Flames .......................................... 304
11.4 Self-acceleration and Fractal Structure of Expanding
Flames .................................................. 310
References .................................................... 314