Single droplet ignition

29 Pages·2014·6.04 MB·English

by  Suresh K. Aggarwal

ProgressinEnergyandCombustionScience45(2014)79e107
ContentslistsavailableatScienceDirect
Progress in Energy and Combustion Science
journal homepage: www.elsevier.com/locate/pecs
Review
Single droplet ignition: Theoretical analyses and experimental
findings
*
Suresh K. Aggarwal
DepartmentofMechanical&IndustrialEngineering,UniversityofIllinoisatChicago,842W.TaylorStreet,Room2021,Chicago,IL60607-7022,
UnitedStates
a r t i c l e i n f o a b s t r a c t
Articlehistory: Spray ignition represents a critical process in numerous propulsion and energy conversion devices.
Received3October2013 Comparedtoagaseousmixture,ignitioninasprayissignificantlymorecomplex,asthestateofignitionin
Accepted6May2014 thelattercasecanbedefinedbythreedistinctignitionmodesnamely,dropletignition,dropletcluster
Availableonline2June2014 ignition,andsprayignition.Ignitionforanindividualdropletrepresentstheappearanceofaflamesur-
roundingthedropletorinthewakeregion,withadimensionontheorderofdropletdiameter.Thecluster
Keywords: orgroupignitionreferstotheignitionaroundorinsideadropletcloud,whilethesprayignitionimpliesthe
Dropletignition appearanceofaglobalflamewithacharacteristicdimensionfewordersofmagnitudelargerthanadroplet.
Quasi-steady
Inallthreemodes,ignitionisprecededbytheevaporationoffueldroplets,formationofacombustible
Transientmodel
Two-stageignition gaseousfueleairmixture,andinitiationofchemicalreactionsproducingsufficientradicalspecies.The
Multicomponent identification of the dominantignitionmode for given two-phaseproperties represents aproblemof
significant fundamentaland practicalimportance. Researchdealingwithlaminarand turbulentspray
ignitionhasbeenreviewedbyAggarwal[1]andMastorakos[2],respectively,whileAnnamalaiandRyan
[3] have provided a review of droplet group combustion/ignition. In the present review, we discuss
experimental,theoretical, andcomputational researchdealingwithindividualdropletignition.Topics
includethequasi-steadyandunsteadymodelsfortheignitionofafueldropletinastagnantenvironment,
the droplet ignition in a high-pressure environment, the convective effects on droplet ignition, and
multicomponentfueldropletignition.Studiesdealingwiththetwo-stageandNTCignitionbehaviorfora
dropletarealsodiscussed.Finally,relationshipbetweenthedropletignitionmodetodropletclusterand
sprayignitionmodesisbrieflydescribed.Potentialtopicsforfurtherresearchareoutlined.
©2014ElsevierLtd.Allrightsreserved.
Contents
1. Introduction................................................................ ....................................................... 80
1.1. Quasi-steadyanalysisofdropletignition(QSDImodel) ........................................ ...................................81
1.2. Experimentalstudiesondropletignition ............................................... .........................................86
1.3. Transientdropletignitionanalysis...............................................................................................89
1.3.1. Transientdropletignitionanalysiswithaglobalone-stepchemistrymodel .......................... ........................89
1.3.2. Transientdropletignitionanalysiswithmulti-stepchemistrymodels ........................................................92
1.4. Effectofpressureondropletignition ............................................................................................96
1.5. Fuelpropertiesandmulti-componentsfueleffectsondropletignition ................................. .............................98
1.6. Dropletignitionunderconvectiveconditions.............................................. .......................................99
1.7. Clusterignitionandexternalsprayignition ............................................. ........................................102
2. Concludingremarks ........................................................... ................................................... 104
References................................................................. .......................................................105
* Tel.:þ13129962235.
E-mailaddress:[email protected].
http://dx.doi.org/10.1016/j.pecs.2014.05.002
0360-1285/©2014ElsevierLtd.Allrightsreserved.
80 S.K.Aggarwal/ProgressinEnergyandCombustionScience45(2014)79e107
Nomenclature: X molefraction
Y massfraction
a fuelexponent
F
a oxygenexponent Greekletters
O
B0 preexponentialfactorinArrheniusrateexpression l thermalconductivity
c specificheat n stoichiometriccoefficient
p
d initialdropletdiameter r density
0
E0 activationenergy s stoichiometricoxidizer/fuelratio
Le Lewisnumber
M non-dimensionalburningrate Subscripts
p non-dimensionalpressure f fuel
Q0 heatreleaseperunitmassoffuelconsumed L liquidphase
r non-dimensionalradialcoordinate¼r0=r0 o oxidizer
s
rs instantaneousdropletradius¼r0=rs0o p product
R universalgasconstant s dropletsurface
u
t non-dimensionaltime ∞ ambient(atinfinity)
T non-dimensionaltemperature¼c0T0=Q0
p
T non-dimensionalsurfacetemperature Superscripts
s
T0 activationtemperature((cid:2)K) 0 dimensionalvariable
a
W molecularweight
1. Introduction burning involved, and the rates of mass and heat transport are
significantly altered following its occurrence. A common droplet
Liquid spray combustion is employed in industrial furnaces, ignitionsituation,whichhasreceivedthemostattention,involves
boilers, gas turbines, diesels, spark-ignition, and rocket engines. theignitionorautoignitionofanisolateddropletinahot,oxidizing
Ignition represents a crucial event in the operation of these sys- environment, although some experimental studies have also
tems. It is followed by the appearance of a flame, which then employed an electric spark to ignite an individual droplet. The
propagates at the local flame speed into the spray or two-phase ignition time is defined as the time from the instant a droplet is
mixture or gets stabilized depending upon the mixture condi- introduced into the hot environment to the instant a flame is
tions. Ignition of a fuel spray in a jet engine combustor is an detectedinthevicinityofthedroplet.
importantprocessduetothedesirabilityoffastandreliableigni- Theignitionofaliquidfuelspray,ontheotherhand,represents
tionunderawiderangeofconditions,anditsrelationtotheissues theappearanceofaglobalflamethatisassociatedwiththewhole
offlamestabilizationandtransientcombustion.Similarconsider- spray,andhasacharacteristicdimensionfewordersofmagnitude
ationsapplytodirect-injectionsparkignitionengines,inwhicha largerthanadroplet.Sprayignitionmaybeinitiatedbyanexternal
fast,well-controlledignitionisimportanttoengineefficiencyand source,suchasanelectricsparkignitioningasturbinecombustors
emissions.Inadieselengine,theself-ignitionoffuelspraysinjected and spark-ignition engines, or without any localized ignition
into a high-temperature and high-pressure environment repre- source, i.e., spontaneous ignition such as in a diesel engine. The
sentsacriticaleventintheiroperation.Sprayignitionresearchis introduction of an electric spark creates a localized region of
alsomotivatedbythesafetyconsiderationsinvarioussystems,in intensedropletvaporization,highreactivityandheatrelease.This
whichtheignitionmustbeavoided.Examplesincludeexplosions region, which is commonly referred to as an ignition kernel, in-
inminesandindustrialsettings,firesafetyinearthandspaceen- volvesseveralevaporatingdroplets.Duringthesparkduration,the
vironments,andpreventionofautoignitioninthemixturedelivery temperatureintheignitionkernelincreasessharply,butthende-
systemofprevaporized-premixedgasturbinecombustors. creasesduetovaporizationandheatlossestothesurrounding.As
Comparedtoagaseousmixture,theignitionprocessinasprayis the chemical activity intensifies and the heat-releasing reactions
significantlymorecomplex,asthestateofignitioninthelattercase are initiated,the temperaturestartsincreasing again, and the in-
can be defined by three distinct ignition modes, namely, droplet flection point in the temperature time history is often used to
ignition, droplet cluster ignition, and spray ignition. In all three identifytheoccurrenceofignition.Spontaneoussprayignitionin-
modes, ignition is preceded by the evaporation of fuel droplets, volves introduction of a two-phase mixture into a high-pressure,
formationofacombustiblegaseousfueleairmixture,andinitiation high-temperature,oxidizingenvironment.Theconceptofanigni-
of chemical reactions producing sufficient radical species. These tion kernel is generally not employed here though it may be
processesaredeterminedbythelocalandglobalsprayproperties, applicablein several autoignitionsituations. The ignition delayis
whichincludetemperature,pressure,overallandlocalequivalence generally defined as the time interval between the creation of a
ratios,andothergasanddispersedphaseproperties.Theignitionof combustiblemixtureandthe“appearance”ofaflame.Inadiesel
an individual droplet represents the appearance of a flame sur- engine,itisdefinedbythetimeintervalbetweenthestartoffuel
roundingthedropletorinthewakeregion,withadimensionon injectionandtheappearanceofaflameasdetectedbysharprisein
theorderofdropletdiameter.Anignitioneventforadropletdis- temperatureorOHspeciesconcentration.Inthiscase,theignition
tinguishes the state of pure vaporization from that of a diffusion location is also an important property that stronglyaffects flame
flamearoundthedroplet.Thishasimplicationsforspraycombus- stabilization [4,5] and engine combustion and emissions. The
tionwithregardtoflamestabilityandamountofpollutantsformed. ignitionofadropletcloudorcluster[3]representsanintermediate
In spray combustion modeling, the identification of this event is situation,andcanbeutilizedtobridgetheresultsofstudiesdealing
important since it determines the amount of heterogeneous with the other two ignition modes. Here also, a typical physical
S.K.Aggarwal/ProgressinEnergyandCombustionScience45(2014)79e107 81
modelinvolvesagrouporcloudofdropletsinaspecifiedgeometric Thefundamentalproblemconsideredinthisreviewinvolvesthe
configuration, subjected to a hot, oxidizing environment. Then, introductionofanindividualdropletintoahotoxidizingenviron-
dependinguponthetwo-phaseconditions,theignitionmayoccur ment.Duetoheattransferfromtheenvironment,thedropletsur-
outsideorinsidethecloud,andforthelattercase,itmayinvolve face temperature increases, and vaporization commences. The
oneorseveraldroplets. resulting fuel vapor mixes with the oxidizer forming a locally
The above three ignition modes are schematically depicted in combustiblemixture,andthe chemicalactivity involving initially
Fig.1,whichrepresentstheignitionofaliquidfuelsprayflowing premixedcombustionbegins.Asthechemicalactivityintensifies,
overaheatedwall[1].Ofthethreeignitionmodesshown,theone partially premixed and subsequently non-premixed combustion
likely to occur would depend upon the flow conditions, spray becomemoreprevalentastheoxygennearthedropletsurfaceis
properties, liquid fuel loading, and wall temperature etc. Clearly, consumed,andheat-releasingreactionsareinitiated.Consequently,
determination of the dominant ignition mode (and the thegastemperatureinthedropletvicinitystartsrising,andaflame
development of an appropriate criteria for its occurrence) and mayappearinthevicinityofthedroplet.Adropletignitiondelayis
ignition location in a two-phase mixture is of practical and defined bycounting the time from the instant a droplet is intro-
fundamental importance. The ignition mode can significantly in- duced into an hot gas environment to the instant the ignition is
fluencetheensuingsprayflamestructure,aswellasthecombustor detectedaspikeintemperatureorspecies(OH)profile,oranen-
performance, flame stability, and emission characteristics. For velopeflame1isestablished.Theignitiondelayconsistsofaphys-
example, the issue of dominant spraycombustion mode, dealing ical delay, during which the droplet is heated and the fuelvapor
with whether the spray flame occurs around individual droplet, diffusesoutward,andachemicaldelay,whichisthetimerequired
cluster of droplets or globally in the mixture, may be directly for the reactions to reach a runawaycondition. Determination of
relatedtothedeterminationofthedominantignitionmode.Italso critical conditions of the ignition in terms of the physical and
hasimplicationsinregards topollutantformationandflamesta- chemicalprocessesinvolvedisaproblemoffundamentalinterest.
bility. For example, if the combustion process predominantly in- Soisthedeterminationofdropletignitiondelaytimeandparam-
volves individual droplet or group burning, it may significantly etersaffectingthistime.Tothisend,theignitabilityofindividual
influencetheNOx,CO,andsootemissions.Anevidenceofthisis dropletsandtheconditions(intermsofdropletsize,fuelvolatility,
provided by the experimental study of Rah et al. [6,7], who andambientpropertiessuchastemperature,pressureandoxygen
observedthatthesootandNOxemissionscloselycorrelatedwith concentrations) determining this ignitability and ignition delay
the ignition of fuel droplets and the formation of an enveloped timeprovidethefundamentalinformation.
flame around the droplet array. Substantial amount of soot was While the problem of droplet vaporization and combustion
producedwhenanenvelopeflameisformedaroundtheburning [9,10] has been examined quite extensively, there are relatively
droplets. In addition to the three ignition modes, other ignition fewer studies on droplet ignition. Theoretical/computational
scenariosareofinterest.OnesuchscenarioexaminedbyRussoand researchdealingwithdropletignitioncanbebroadlyclassifiedinto
Gomez[8]involvesdropletsthatsurviveanenvelopesprayflame twogroups,namelyquasi-steadyanalysisandtransientanalysis.A
andareignited.AcriticalvaporizationDamko€hlernumber,repre- majorobjectiveofthequasi-steadyanalysisistodevelopadroplet
sentingtheratioofvaporizationtimetoresidencetime,wasusedto ignitioncriterion,basedonacriticalDamko€hlernumber,thatcan
define the ignition of these droplets. Their study indicates the beusedtoidentifythestateofignitionforadropletofgiveninitial
possibilityofallthreeignitionmodesoccurringinaspray. sizeinanenvironmentofknowntemperatureandotherproperties.
Theliteraturereviewrevealsthatallthreeignitionmodeshave PreviousinvestigationsonthisaspectarediscussedinSection1.1.
beenextensivelystudied.Thispaperfocusesonthedropletignition ExperimentalresultsondropletignitionaresummarizedinSection
mode,sincereviewsofstudiesonsprayignitionhavebeenreported 1.2. The transient droplet ignition analysis involves a numerical
byAggarwal[1]andMastorakos[2],whiletheresearchondroplet solution of relevant partial differential equations governing the
cluster ignition has been reviewed by Annamalai and Ryan [3]. processes of fluid mechanics, and heat and mass transfer in the
Ignition of an isolated droplet represents a very fundamental liquid phase (droplet interior) and gas phase surrounding the
problem involving fluid mechanics, thermodynamics, heat and droplet.ThistopicisreviewedinSection1.3.Studiesdealingwith
mass transport, and chemical kinetics. A fundamental study of the effect of pressure and fuel properties on droplet ignition are
dropletignitionisalsorelevanttothecombustionofhigh-density discussedinSections1.4and1.5,respectively.Therehasalsobeen
fuels, liquid-propellant combustion, material synthesis, and fire somelimitedexperimentalandcomputationalworkontheeffects
safety. ofnaturalandforcedconvectionondropletignition,whichisdis-
cussedinSection1.6.Abriefsummaryofworkdealingwithdroplet
groupignitionandsprayignitionisgiveninSection1.7.Concluding
remarksareprovidedinSection2.
1.1. Quasi-steadyanalysisofdropletignition(QSDImodel)
Thequasi-steadyanalysisisbasedontheconsiderationthatat
moderate pressures, the gas density is two to three orders of
magnitudesmallerthantheliquidfueldensity.Consequently,the
time scale associated with the gas-phase transport is small
compared to that for the liquid-phase processes (droplet surface
regression), and, therefore, the gas-phase processes can be
assumedquasisteady.Clearly,thisapproachisnotapplicableifthe
systempressureisclosetoorabovethecriticalpressureofthefuel
Fig.1. Aschematicofatwo-phasemixtureignitedinthethermalboundarylayerofa
heatedsurface.Threedifferentignitionmodes,namely,thedropletignition,droplet
clusterignition,andsprayignitionareillustrated. 1 Notethatthe“envelopeflame”isusedhereinagenericsenseandincludes
FromRef.[1]. bothanenvelopeflamesurroundingadropletorinitswake.
82 S.K.Aggarwal/ProgressinEnergyandCombustionScience45(2014)79e107
[11].Thequasi-steadyanalysisisalsonotvalidifthegasflowfieldis
ibnuhsetiroenntilnysutanbsitleitayd,ys,infocer ethxeamapnlael,ysdiuseretqouflirueisdthdaytnathmeicboourncdoamry- w_ ¼(cid:3)DMY2oaToaYofaþfaf expð(cid:3)Ta=TÞ (4)
conditions at infinity be constant. Furthermore, the quasi-steady
assumption breaks down in regions far from the droplet, since withtheDamko€hlernumberDas
thecharacteristictransporttimebecomescomparable tothesur-
(cid:6) (cid:7)
faceThreegrbeasssiiconastsimume.ptions involved in the quasi-steady droplet D¼nfB0s.ao W(cid:8)f0 ð1(cid:9)(cid:3)afÞ(cid:3)p0c0p(cid:4)aoþaf(cid:8)M0r0(cid:9)2 (5)
iignntihtieond(eQriSvDatI)iomnoodfelthaerecelasssseinctailaldly2-tlhawesaremlaetiaosnth[9o]sefoermdprloopyleedt l0∞ c0p∞ Wo0 ao R0Q0 s
vaporization/combustion. The assumptions include spherical TheboundaryconditionsforEq.(2)are
symmetry,anisolatedsingle-componentfueldroplet,constantgas-
phase and liquid-phase thermo-transport properties, unity gas-
phase Lewis number, constant droplet surface temperature, and at r¼∞ Yo¼Yo∞=s¼a
Y ¼0 (6)
saturationvaporpressureatthedropletsurface.Onenotabledif- f
ferenceistheinclusionoffinite-ratechemistrybasedonaglobal T ¼T∞
one-step mechanism in the quasi-steady ignition analysis, in
cgoansitfircaasttiotonmthoedflela.mSoemseheeeatrlaieprpsrtouxdimiesateiomnpluosyeeddiandthhoeccalpapssriocxa-l at r¼10 ddYro¼MYos
imations to the Arrhenius term. For example, Tarifa et al. [12] (cid:6) (cid:7)
dY
representedthetemperaturedistributionintheflamezonebyan f ¼(cid:3)M 1(cid:3)Y
algebraic expression, while Peskin et al. [13e15] used a delta dr fs (7)
functiontorepresenttheheat-releaseterm.Theignitioncondition dT
¼MH
was identified by a sudden jump in mass burning rate. Another dr
approach,consideredbyFendell[16]andKassoyandWilliams[17], T ¼Ts
employedaperturbationtechniqueusingtheDamko€hlernumberD
as a small or a large parameter. This approach can study pertur- where H (non-dimensional) is the effective latent heat of vapor-
bationsinthedropletgasificationrateandotherproperties,butis ization which includes the latent heat of vaporization L, and the
incapableofprovidingignitionandextinctionconditions. amount of heat conducted to the droplet interior to heat up the
Linan[18]employedthemethodoflargeasymptoticanalysisin dropletperunitmassoffuelvaporized.
thelimitoflargeactivationtemperaturetoanalyzethestructureof Asnotedearlier,theaboveequationsdifferfromthoseofLaw
counterflow diffusion flames. The entire range of Damko€hler [19]intheexponentsofYoandYfinEqs.(4)e(5)whichaccountsfor
numberwasrepresentedbyplottingtheclassicalS-shapedcurvein the nonlinear dependence of the reaction rate on the fuel and
terms of the maximum temperature versus D. As the maximum oxidizer concentrations. Using the Shvab-Zeldovich formulation
temperature in the flow varied from the ambient value to the [19], the species mass fractions can be expressed in terms of T,
adiabatic flame temperature, four regimes were defined on this whichreducestheproblemtothesolutionoftheenergyequation.
curve,namelyanearlyfrozenregime,apartialburningregime,a The resulting energy equation can be solved numerically to
premixedflameregime,andadiffusionflameregime.Law[19,20] examine the structure of the reaction region and thus determine
developed the basic quasi-steady droplet ignition (QSDI) model the ignition/extinction states. The solution can be represented in
byextendingLinan'sapproachtoanalyzethestructureofdiffusion terms of a plot of the burning rate (M) versus D, which typically
flames around an evaporating droplet. The finite-rate chemistry yields the classical S curve for large activation energies. A repre-
wasrepresentedbyaone-stepirreversiblereaction: sentativeplotfromRef.[19]isshowninFig.2.ForD~0,theflowis
chemically frozen, and the solution corresponds to the pure
vaporization. As D is increased along the lower branch of the S
nfFþnoO/k npP (1) curve,thechemicalactivityisinitiated.Withcontinuousincreaseof
D, the system approaches the ignition state at D ¼ DI. As D is
and the four combustion regimes were identified, as the flame increasedbeyondDI,thesystemabruptlymovesfromthelowerto
temperaturevariedfromtheambientvaluetotheadiabaticflame theupperbranch,whichrepresentsdropletcombustionstates,and
temperature.Thefirstregime,whichisthenearlyfrozenorignition D / ∞ corresponds to the flame sheet approximation. Conse-
regimewasfurtheranalyzedtoderiveanexplicitignitioncriterion quently, increasing D above represents the ignition or thermal
in termsof a critical Damko€hler number for ignition. Mawid and runawaycondition,andtheDamko€hlernumberDIcanbedefined
Aggarwal [21] extended Law's analysis to include the effects of asthecriticalignitionDamko€hlernumber.Inasimilarmanner,as
arbitrary reaction orders with respect to the fuel and oxidizer. wedecreaseDalongtheupperbranch,thesystemapproachesthe
SimilartoLaw'sanalysis,thestartingpointisthegoverningequa- extinctionstateandthen DErepresentsanextinctionDamko€hler
tionsforgastemperatureandspeciesmassfractions,whichunder number.
thequasi-steady,sphericallysymmetricassumptionscanbewrit- Inordertoderiveanexplicitignitioncriterion[19,21],theen-
teninthenon-dimensionalformas ergyequationhasbeensolvedbyusingthelargeactivationenergy
asymptotic analysis. Then, considering ε ¼ T∞/Ta as a small
UfYo=sg¼UfYFg¼(cid:3)UfTg¼w_ (2) parameter, the flow field can be separated into a frozen region,
wherediffusionbalancesconvection,andanarrowreactionregion
wheretheoperatorU{}andthereactionratearegivenas where diffusion balances chemical reaction. A representative so-
lutionfromRef.[21]isshowninFig.3,wheretheperturbedtem-
(cid:1) (cid:3) (cid:4)(cid:5) peratureisplottedinthereactionzoneforb¼0.5andfordifferent
U M d (cid:3) 1 d r2d fg (3) values of the modified Damko€hler number D. Here D, X (the
r2 dr r2 dr dr stretchedspatialcoordinate)andbare,respectively,givenby
S.K.Aggarwal/ProgressinEnergyandCombustionScience45(2014)79e107 83
Fig.4. Maximumperturbedtemperature(correspondingtoX/∞inFig.3)versusD
Fig. 2. Characteristic S-curve showing all possible modes of droplet gasification, fordifferentvaluesofb.
includingpurevaporization(D~0),ignition(D¼DI),purecombustion(D¼∞)and FromRef.[21].
extinction(D¼DE).
FromRef.[19].
thereforesuggestedtoobtainDІ directlyfromFig.5.However,as
discussed by Law [20], the range of b relevant for the ignition
D¼Daaoε(cid:3)3εaf expð(cid:3)Ta=T∞Þ (8) phenomenon is 0 (cid:4) b (cid:4) 1.0. Moreover, for most practical com-
ðT∞Þaoþaf bustion systems involving hydrocarbon fuels, b is typically 0.1 or
less.Then,anexplicitcriterionfordropletignitioncanbewrittenas
X¼ð1=εÞð1(cid:3)expð(cid:3)M=rÞÞ (9)
D(cid:4)DðbÞ (12)
I
b¼T∞(cid:3)TsþH (10) where the modified system Damko€hler number can be written,
Thelowerbend of theScurveisthengeneratedbyplottingq aftercombiningEqs.(5)and(8),as
(X/∞)asafunctionoftheDamko€hlernumber.Theseplotsfor
sptdhhaifeorfsaewemrsecentuthterevrveabcslrufiyoteiirsceablodlofDtthbhaemuanrckerio€tiythgilicaevanreldnnignuinnomintbFi-oieugnrn.piD4tly.aomTt(tahekFedo€¼hvale0ser.ra2ti5ncf)uualnemxctbatpienoorgnnsee.nonFftitsgst.hto5oef D¼8><>:l8B0∞0(cid:6).Wc0pf0∞(cid:7)(cid:8)ðW1(cid:3)o0a(cid:9)faÞo(cid:3)Rp0u0cQ0p0(cid:4)aoþaf9>=>; 9
DfcurIiet¼licca0ol:n9Dc8ae6mn5tkreo€axhtiploeðnr6.n:4Fur6mo3mbbeþtrhc0ias:n3p5blÞoet,ofabontraienbxep(cid:4)dlic[02i:t13]0exapsression for(1th1e) (cid:5)>>>>><>>>>>:ðYo∞ Þac0poTe∞0x!pa(cid:8)oþ(cid:3)afT a0c(cid:10)0pTT∞0∞20!(cid:9)3(cid:8)(cid:3)Ma0frs0(cid:9)2>>>>>=>>>>>; (13)
Forlargervaluesofb,itwasfoundimpracticaltoapproximatea Q0 Ta0Q0
relation between DІ and b due to very large values of DІ. It was
Withao¼aF¼1.0,theaboveequationyieldsthesystemDam-
ko€hler number of Law [20]. In spite of its limitations, the QSDI
model can be extremely useful in distinguishing between evapo-
ratingandcombustingdropletsinasprayenvironment.Infact,the
criterionhasbeenemployedinseveralinvestigationsdealingwith
sprayflames;forexample,seeBuchholtzandTapper[22],andSeth
etal.[23].Furthermore,ithasbeenusedandsubsequentlymodi-
fiedbyseveralresearcherstopredicttheignitiondelaytimefora
dropletthatissuddenlyintroducedintoahot,oxidizingenviron-
ment.Thebasicprocedurefollowedbytheseresearcherstopredict
theignitiondelaytimeisasfollows.Adropletisintroducedintoa
hotoxidizingenvironmentattimet¼0.Asitreceivesheatfromthe
gas phase, its surface temperature starts increasing, and vapor-
ization is initiated. The droplet surface temperature (Ts) is calcu-
latedbyusinganappropriateliquid-phasemodel,suchasinfinite-
conductivityorconduction-limitmodels[24],whiletheinstanta-
neousdropletradiusr0 isobtainedfrom
s
Fstirge.t3c.heVdarviaatriioanbleofftohrebp¼ert0u.5rbaenddtedmiffpeerreanttuDreaimnktoh€helreeranctuimonbzeorsn.easafunctionofthe drs02¼(cid:3)2r0∞D0∞M (14)
FromRef.[21]. dt0 r0L
84 S.K.Aggarwal/ProgressinEnergyandCombustionScience45(2014)79e107
Fig.6. Computedandmeasuredignitiondelaysplottedasafunctionoftheinitialdrop
sizeforn-hexadecanedroplets.
FromRef.[21].
time. For droplet sizes smaller than this optimum, the ignition
delay increases as the drop size is decreased, approaching the
ignitablelimit.Thisisprobablyduetothedecreaseinthesystem
Damko€hlernumberneartheignitionlimit,sincetheignitioncri-
terion indicates that ignition is favored for larger droplets. How-
ever,fordropletsizeslargerthantheoptimum,theignitiondelay
increasesasthedropletsizeisincreased.Thisiscausedbythein-
creaseindropletheat-uptime,anevidenceofwhichisprovidedby
Fig.5. VariationofignitionDamko€hlernumberwithb.
FromRef.[21].
Thetemporalhistoryofrelevantdropletpropertiessuchasr0,T0
s s
etc. is then followed, and the system and ignition Damko€hler
numbersarecalculatedateachinstanttochecktheignitioncrite-
rion given by Eq. (12). The instant when the ignition criterion is
satisfied is defined as the droplet ignition delay time. Some
representativeresultsfromRef.[21],obtainedbyusingtheabove
equationsfortheignitionofn-hexadecanedroplets,areshownin
Figs.6and7.Thechemicalkineticparameters,E0 ¼45.0kcal/mol
andB0¼1.9(cid:5)109cm3/mol-s,wereextractedfromtheignitiondata
ofFaethandOlson[25]forYo∞ ¼0:23,ao¼1.5andaF¼0.25.The
parametersTsandHwerecalculatedbyusingtheconduction-limit
model[24].
Fig. 6 compares the predicted ignition delay time with the
experimentaldataofFaethandOlson[25]andSaitohetal.[26]asa
functionofinitialdropsize.Asexpected,thepredictionsagreequite
wellwiththemeasurementsofFaethandOlson,sincethekinetics
constantswereobtainedfromtheirexperimentaldata.Thereisalso
satisfactoryagreementbetweenthepredictedignitionlagsandthe
measured data of Saitoh et al., although minordifferences in the
initialconditions,T∞0 andTs0o,ofthepresentcalculationsandtheir
experiments exist. In addition, the predicted ignition delay plot
Fig.7. Computedandmeasuredignitiondelaysplottedversusambienttemperature
indicatesthatneartheignitablelimit(do¼0.7mm),thereexistsan forn-hexadecanedroplets.
optimumdropletsizecorrespondingtoaminimumignitiondelay FromRef.[21].
S.K.Aggarwal/ProgressinEnergyandCombustionScience45(2014)79e107 85
severalexperimentalandtheoreticalstudiesasdiscussedlater.Itis
also important to note that the existence of an optimum droplet
sizecorrespondingtoaminimumignitiondelay,andthebehavior
near the ignition limit indicated in Fig. 6, have been observed in
experimental studies as well as in numerical studies based on
transient models. These are discussed in later sections in this
review.
Fig.7showsthecomputedandmeasuredignitiondelaytimes
plottedversustheambienttemperaturefortwodifferentdroplet
sizes.Again,itisindicatedthatsmallerdropletsareignitedearlier
than the larger ones in the droplet-heating-controlled regime,
whereasinthekinetically-controlled(lowerambienttemperature)
regime, they may fail to ignite as the ambient temperature is
decreased.Theminimumambienttemperatureforignitionisseen
tobeafunctionofthedropletsize.Itdecreasesasthedropletsizeis
increased.FortheresultsshowninFig.7,theminimumtempera-
ture values are 1005 K and 900 K for r0 ¼0:0208 and 0.078 cm
so
respectively.ItshouldalsobenotedthataFaffectsboththesystem
(D)andtheignitionDamko€hlernumbers(DІ),whileaohasonlya
weakinfluenceonDІ.Thiscanbeexpectedsinceignitionoccursin
theoxidizer-richregionandtheoxidizerconcentrationintheinner
reaction region is typically much greater than the stoichiometric
value.Thisalsoimpliesthatfordropletignitioninanoxidizer-lean
environment,theeffectofaoonDІ wouldbestronger. Fig.8. Computedandmeasuredignitionlimitsforn-hexadecanedroplets.CurveA:
Severalstudieshaveemployedthequasi-steadydropletignition Cpl¼0.69cal/gm/K,p¼1atm,B:Cpl¼0.52cal/gm/K,p¼1atm,C:SameascurveA
(QSDI) model to examine the effects of various parameters on butactivationenergyreducedby12percent,D:Cpl¼0.69cal/gm/K,p¼10atm.
FromRef.[27].
droplet ignition. In some investigations, the model was further
modified to extend its applicability and examine the effects of
various assumptions employed in the original analysis. In some realistic sprays, wherein the gas phase (droplet ambiance) is ex-
cases,expressionsforthemodifiedsystemDamko€hlernumber(D) pectedtocontainfuelvapor.ImportantmodificationstotheQSDI
andignitionDamko€hlernumber(DІ)weremodifiedbasedonthe modelincludedchangingtheambientboundaryconditionforthe
relaxation of some assumptions. Aggarwal [27] employed the fuelvapormassfraction,andmovingthelocationoftheambient
ignition criterion of Law [20] to examine the role of transient boundary frominfinitytofinite distance, see Eq. (6). A represen-
dropletheatingintheignitionprocess.Theeffectofthreedifferent tativeresultshowingtheplotofDІversusbforvariousvaluesofthe
liquid-phase heating models, namely, infinite-conductivity, con- parameterg(¼Yf∞/ε)ispresentedinFig.9.Asexpected,thepres-
duction-limit,andvortexmodels,onthedropletignitiondelaywas ence of fuel vapor reduces the ignition Damko€hler number,
examined.Resultsindicatedthatforlessvolatilefuels,thedroplet implyingenhanceddropletignitability.Thepresenceoffuelvapor
heating time is comparable to the ignition delay time. Conse- also reduces the vaporization rate and thus affect ignitability.
quently,forsuchfuels,thetransientdropletheatinghasnoticeable However, the chemical effect of fuel vapor is more dominant in
influence on ignition delay, especially in the vaporization- mostsituations.
controlled (higher ambient temperature) regime. Since the AnotherkeyassumptionintheQSDImodelisthatofconstant
conduction-limit model predicts a higher surface temperature thermo-transport properties and unity Lewis number. Li and
duringthedropletheatingperiod,ityieldsashorterignitiondelay Renksizbulut[31]extendedtheQSDImodeltoincludetheeffectsof
comparedtothatpredictedbytheinfinite-conductivitymodel.This variable properties and arbitrary Lewis numbers. The thermo-
effecthasalsobeenexaminedbySazhinetal.[28]forn-dodecane transport properties were considered to be temperature- and
droplets.Theyobservedthatusingtheeffectiveconductivitymodel concentration-dependent, and the system (reduced) and ignition
yielded lower ignition delays compared to those predicted using Damko€hlernumberswererederivedusingthematchedasymptotic
the infinite conductivity model. Note that a higher surface tem- technique.Itwasobservedthattheeffectsofvariablepropertieson
perature reduces the ignition Damko€hler number. Using the ignition appear through the vaporization rate M0 which modifies
conduction-limit model, the ignition limits in terms of the mini- the reduced Damko€hler number (D), and through b which in-
mum ambient temperature and the minimum droplet size were fluencestheignitionDamko€hlernumber(DІ).Itwasrecommended
also computed and compared with the experimental results of thatthemixtureLewisnumbershouldbedefinedas
Faeth and Olson [25], and Wood and Rosser [29]. As indicated in
X
Fig. 8, the computed ignition limits are in good agreement with
measurements.Anotherimportantobservationfromthisfigureis Le¼S Lef;iXi (15)
i
thattheminimumdropletsizeforignitionincreasesastheambient
temperature is reduced, which is consistent with the results dis- Here Lef,i is the Lewis number of fuel vapor with respect to
cussedearlier.Thecomputedresultsalsoindicatethattheeffectof species i in the environment, and Xi is the mole fraction of that
pressure is to extend the ignitability limits. Both the minimum species.AnincreaseinthisLewisnumberwouldenhancedroplet
ambient temperature and the minimum droplet size for ignition ignitability (reduce the ignition delay time) because of the
decrease as pressure is increased. This result is confirmed by enhancedrateofheattransporttothedroplet.Itwasalsoobserved
experimentalstudiesdiscussedinthenextsection. thattheappropriatespecificheat(cp)shouldbethatoffuelvapor
Law and Chung [30] extended the QSDI model to include the rather than thatof inert species in the environment. Further, the
presence of fuel vapor in the ambient gas. The objective was to variable specific heat (cp) would increase b and thus increase DІ
improvetheapplicabilityoftheclassicalignitioncriteriontomore becauseofitsexponentialdependenceonb.Thisimpliesthatthe
86 S.K.Aggarwal/ProgressinEnergyandCombustionScience45(2014)79e107
importantparametersonthedropletignitiondelaytime.Inaddi-
tion, the model has been used to determine a critical droplet
diameter(asafunctionofotherparameters)belowwhichdroplets
fail to ignite and undergo complete vaporization without com-
bustion. Important limitations of the QSDI model should also be
noted. Its applicability is limited to the ignition of an isolated
droplet2 under moderate-pressure, mildly convective conditions.
Also,itcannotprovidedetailsoftheignitionprocess,whichcanbe
obtainedbyusingatransientanalysis.Forexample,thetransient
model can analyze the detailed transition from premixed com-
bustion to diffusion combustion, as well as the ignition location
withrespecttothedroplet,althoughitrequiresanumericalsolu-
tionofcoupled,nonlinearpartialdifferentialequations.Inaddition,
asdiscussedinlatersections,thetransientmodelcanalsobeused
toexaminetheeffectsofdetailedchemicalkinetics,multicompo-
nentspeciesdiffusion,andhighpressure(criticalandsupercritical)
on the droplet ignition phenomena. It can also be employed to
examine the validity and applicability of the QSDI model. This
aspectisdiscussedinSection1.3.
1.2. Experimentalstudiesondropletignition
Severalresearchershavereportedexperimentaldataondroplet
ignition under various conditions. In addition to ignition delays,
they have provided data on ignition limits in terms of minimum
dropletsizeandambienttemperature,differentignitionregimesin
terms of ambient temperature and pressure, and the effects of
variousparametersincludinggravity,pressure,andfuelvolatility.
Two commonly employed configurations are the suspended
droplet technique and the freely falling or moving droplet tech-
nique. In the first configuration, a fiber-suspended droplet is
exposedtoahot,stagnantenvironmentinapreheatedfurnace,and
the ignition delay time is measured, based on an appropriate
ignitioncriterion,byusinganopticaltechnique.Thisapproachhas
Fig.9. IgnitionDamko€hlernumberasfunctionofheattransferparameter(b)andfuel beenusedbyNishiwaki[35],El-WakilandAbdou[36],Faethand
concentrationparameter(g). Olson[25],Kadotaetal.[37],Saitohetal.[26],BergeronandHallett
FromRef.[30]. [38,39], Tanabe et al. [40,41], Marchese et al. [42,43], and many
others.Thesecondconfigurationinvolvesafreelyfallingdropletin
a furnace or a droplet injected into a heated stream. It has been
variablecpwouldincreasetheignitiondelaytime.Li[32]further employedbyRahetal.[6],WoodandRosser[29],Sangiovanniand
extendedtheaboveanalysistostudydropletignitioninfuel-lean,
Kesten[34],Satcunanathan[44]andothers.GoodgerandEissa[45]
oxidizer-lean,andfuel/oxidizer-leanenvironments.Foreachcase,
reportedareviewofexperimentalstudiesreportedpriorto1987.
theignitionDamko€hlernumberwasobtainedasafunctionofthe
El-WakilandAbdou[36]measuredignitiondelaytimesforpure
parameterb.Inaddition,Makino[33]obtainedmoregeneralcor- alkanedropletssuspendedonafilamentinafurnace.Saitohetal.
relations between the ignition Damko€hler number (DІ) and the [26]alsousedthistechniquefortheignitionofn-heptaneandn-
parameter b, DІ (b). This further extends the applicability of the hexadecanedroplets.Theirobjectivewasalsotovalidatetheresults
QSDImodel.
of their numerical simulations [49]. The droplet diameter was
Insummary,theQSDImodelwasfirstdevelopedbyLaw[19,20],
measuredphotographically,andtheinstantofignitionwasdetec-
based on the analysis of Linan [18]. Subsequently several in-
tedbyachangeintheintensityofinfraredrays.Ignitiondelaytimes
vestigators modified it to extend its applicability. The extensions werereportedford0¼ 0.7e2.2mm,Ta¼650e800(cid:2)C,andinitial
includethegeneral(non-unity)reactionorderswithrespecttofuel droplet temperature ¼ 5e35 (cid:2)C. Representative results from this
and oxidizer [21], transientdroplet heating [27], presence of fuel
study for n-heptane and n-hexadecane droplets are shown in
vaporinthegasphase[30],andvariablethermo-transportprop-
Figs. 10 and 11, respectively. The ignition delay for n-heptane
erties and non-unity Lewis numbers [31,32]. The QSDI model is
droplets appears to be nearly independent of initial droplet size,
quiteuseful in spraycomputations fordistinguishing the state of
exceptneartheignitionlimit,wheretheignitiondelayincreasesas
purevaporizationfromthatofcombustion.Intwo-phasecompu-
d0isdecreased,andeventuallyreachesanon-ignitablecondition.
tationsemployingeithertheEulerianorLagrangianapproachfor
Inaddition,theminimumdropletsizeforignitionincreasesasTais
theliquidphase,thequasi-steadydropletignitioncriterioncanbe
increased. For n-hexadecane droplets, the ignition delay exhibits
appliedinacontinuousmanner,andtheratesofinterphaseheat
andmasstransfermodifiedaccordingly.TheQSDImodelhasalso strongersensitivitytotheinitialsize;itincreasesasd0isincreased,
whichcanbeattributedtotheincreaseindropletheatingtimefor
beenemployedtopredicttheignitiondelaytimeofanindividual
droplet,whichissuddenlyintroducedintoahot,oxidizingdroplet.
Bycouplingthequasi-steadygas-phaseanalysiswiththeunsteady
2 Agroupofdropletsmaybedeemedasonelargedropletandthentheabove
liquid-phaseanalysis,Law[20],AggarwalandMawid[21],Aggar-
criterionmaybeusedtopredicttheignitiondelaytime.Thissituationisakinto
wal[27],andSangiovanniandKestin[34]examinedtheeffectsof externalgroupcombustion.
S.K.Aggarwal/ProgressinEnergyandCombustionScience45(2014)79e107 87
one-stepchemistrywithnon-unityreactionorderswithrespectto
fuelandoxygenconcentrations.Thegas-phasemodelwasfurther
simplified by including the reaction terms only in the energy
equation,andthedroplettemperaturewascalculatedbyusingthe
infinite-conductivitymodel.Notethatstudiesemployingtransient
models of various complexities are reviewed in Section 1.3. The
experimentalinvestigationemployedafiber-suspendeddropletin
aheatedfurnace.Thefiberwas0.2mmindiameterwitha0.6mm
beadatthetip.Thedropletdiameterwasmeasuredphotographi-
cally,andtheignitioneventwasdetectedbyphotodiodes.Ignition
delaysweremeasuredford0¼1.2e1.6mmandTa¼900e1100K.
SomerepresentativeresultsareprovidedinFigs.12and13.Results
aregenerallysimilartothosereportedbySaitohetal.[26]inthat
theignitiondelayincreaseswiththeincreaseind0,andwiththe
decreaseinTaorfuelvolatility.Simulationsshowgoodagreement
with measured data, as the kinetic constants were obtained by
matching predictions with experiments. Further, the numerical
resultsindicateaminimumdropletdiameterbelowwhichdroplets
vaporizewithoutignition.Inaddition,theminimumdiameterde-
creasesasTaisincreased,whichisconsistentwithseveralresults
Fig.10. Measuredignitiondelaytimeversusdropletdiameterforn-heptanedroplets discussedearlier.Theexistenceofaminimumdiameterforignition
fordifferentambientgastemperatures. and its dependence on the ambient temperature have been
FromRef.[26].
observed in previous theoretical studies based on quasi-steady
modelsofFaethandOlson[25],Law[20],andMawidandAggar-
larger droplets. For both fuels, the data indicate a decrease in wal[21],aswellasintheexperimentalstudiesofSaitohetal.[26]
ignitiondelaysasTaisincreased.Animportantimplicationfromthe andWoodandRosser[29].
resultsinFigs.10and11isthatdropletheatingismoreimportant Sangiovanni and Kesten [34] employed the moving droplet
for larger droplets and for less volatile fuels, since heat-up time configurationtodeterminetheinfluenceofambienttemperature,
occupiesasignificantpartoftotalignitiontime. oxygencontent,dropletrelativevelocity,dropletsize,andfueltype
BergeronandHallett[38]conductedanumericaleexperimental
investigation on droplet ignition for four n-alkanes. Simulations
werebasedonatransientspherical-symmetricmodelusingglobal
Fig. 11. Measured ignition delay time versus droplet diameter for n-hexadecane Fig.12. Predictedandmeasuredignitiondelaytimesforn-hexadecanedropletsasa
dropletsfortwodifferentambienttemperatures. functionofdropletdiameter.
FromRef.[26]. FromRef.[38].
88 S.K.Aggarwal/ProgressinEnergyandCombustionScience45(2014)79e107
performed in the 5- and 110-m drop towers and the parabolic
flights.Theinvestigationfocusedontwoimportantaspects,namely
thetwo-stageignitionprocessandtheeffectofgravity.Morede-
tails including the chemical kinetic aspects of two-stage ignition
are discussed in the next section. In general, the phenomenon is
characterized by the low-temperature (cool flame) oxidation at
temperatures of about 500e800 K, followed by the high-
temperature oxidation. The two stages are distinguished by
differentchainbranchingsteps.Whilethisphenomenonhasbeen
extensivelyexaminedforhomogeneousmixtures,itwasobserved
perhapsforthefirsttimeinthecontextofdropletignition.Fig.14
from Ref. [47] illustrates the two-stage ignition process by plot-
tingthepeaktemperaturehistoryinthedropletvicinity.Thefirst
temperaturejumpmarkstheonsetoffirst-stageignition,whilethe
second jump represents the occurrence of second-stage ignition.
The first-stage ignition or induction period involves the droplet
heat-up,slowvaporization,andlow-temperatureoxidation,while
the second period involves faster vaporization and high-
temperature ignition chemistry. Increasing the ambient pressure
or temperature decreases the transition period from the first to
secondstage,orthesecondinductionperiodt2.Thisisillustratedin
Fig.15 from Ref. [40], which shows the different droplet ignition
regions at 1 g. In the cool flame region, characterized by low
Fig.13. Predictedandmeasuredignitiondelaytimesplottedasafunctionofdroplet
diameterfordifferentfuels. ambienttemperaturesandpressures(1e2atm),onlythefirst-stage
FromRef.[38]. ignitionoccurs;thesecond-stageignitiondoesnotfollow,implying
thatthedropletundergoesextinctionorvaporizescompletelyprior
totheoccurrenceofsecond-stageignition.Athigherpressures,the
ontheignitionofsinglefueldroplets.Amonosizedstreamofliquid two-stage ignition is observed, and the transition from the first
fuel droplets was injected in a hot environment provided by the
stagetosecondbecomesincreasinglyshortaspressureisincreased
post-combustion zone of lean, premixed, laminar methaneeair
further. The effect of gravity is shown in Fig.16, which plots the
flameonaflatflameburner.High-speedphotographywasusedto
totalignitiondelayasafunctionofambientgastemperaturefor1g
recordthetimehistoryofdropletsastheyenterthehotregion.The andmg conditions.The presence ofgravity increasesboththe in-
ignition delay time was obtained from the ignition delay height,
ductionperiods,andthusthetotalignitiondelaytimebyafactorof
measuredfromthephotographs,andtheaveragedropletvelocity. upto3.Thebuoyancy-inducedflowenhancestheratesofheatand
Theyalsoemployedanumericalmodelbasedonthequasi-steady,
mass transport, which reduce the droplet heat-up time and in-
gas-phaseequationsfortheheatandmasstransportinthegasfilm
crease the vaporization rate, but decreases the temperature rise
surrounding a droplet. The effect of droplet relative velocity was
due to chemical reaction as it removes heat and chemical in-
includedbyusingthestandardRanzandMarshallcorrelation[46].
termediatesfromtheignitionzone.Thelattereffectisfoundtobe
Asexpected,theresultsindicatedapronouncedeffectofambient
moredominant,especiallywhentheambienttemperatureislow
temperature, with the ignition delay time decreasing with
(kinetically-controlledregime).Thiseffectivelyreducesthesystem
increasingtemperatureinthekinetically-controlled(lowambient Damko€hlernumber,andincreasestheignitiondelayat1g.Asalso
temperatures)regime,butarelativelyweakeffectinthediffusion-
controlledregime.However,contrarytoexpectations,theeffectsof
dropletsizeandfueltypewerefoundtobemoresignificantinthe
kinetically-controlledregime.Thepresenceofdropletrelativeve-
locitydecreasedtheignitiondelaytimeslightly,whiletheoxygen
concentration(aboveacertain)hadnegligibleeffect.Thetheoret-
ical results, however, indicated a decrease in ignition delay with
decreasingoxygenconcentration,whichappearstobeacounter-
intuitiveresult.
Another notable studyusingthe suspendeddroplettechnique
wasreportedbyTanabeetal.[40].Adistinguishingfeatureofthis
study was the investigation of two-stage ignition3 process for a
droplet bysimultaneously using a fine thermocouple to measure
the temperature as a function of time, and an interferometer to
detect the cool (invisible) and hot flame ignition. A n-dodecane
dropletof0.7mmdiameterwassuspendedinahotenvironment,
where Ta was varied from 500 to 800 K, and pressure from 1 to
10atm.ThedropletdiameterwasmeasuredusingaCCDcamera.
Experiments were carried out under normal-gravity (1 g) and
microgravity conditions. Microgravity (mg) experiments were
Fig.14. Two-stageignitionprocessforan-heptanedropletillustratedbythetemporal
variationofthepeakgastemperature.Thedropletdiameter¼0.7mm,Ta¼650K,and
3 Thechemicalkineticaspectsofthetwo-stageignitionphenomenonaredis- p¼5atm.Thefirst(t1),second(t2),andtotalignitiontimesareindicated.
cussedinalatersection. FromRef.[47].