CoolFlamesinMicrogravityFormanA.Williams

UniversityofCalifornia,SanDiegoLaJolla,CA

atTheFirstInternationalWorkshoponNear-LimitFlames

BostonUniversity

July29.2017

OutlineofthePresentation

• Reviewofexperimentalresultsfromspace-basedstudiesofdropletburning(spanninga20-yearperiod).

• Maximallysimplifieddescriptionsofnear-limitchemicalkinetics.• Applicationsofchemical-kinetic understandingtothesphericallysymmetricalcombustionofliquid-fueldropletsofnormalalkanes.

• Summaryofthecurrentstatusofourunderstanding,outstandingproblems,neededfutureinvestigations,andplanningahead.

EXTINCTION BOUNDARIES WERE FOUND IN DROPLET-COMBUSTIONEXPERIMENTS PERFORMED IN SPACELAB ON THE SPACE SHUTTLE IN 1997

BUT COOL FLAMES (THAT MAY HAVE OCCURRED) WERE NOT IDENTIFIED

CombustionIntegratedRack(CIR)Because oftheDCEsuccess,theFLEX experiment wasdesigned forSpace Station.

Astronaut MikeFincke ,pictured totheleftof theCIRfacilityinstalled in theDestinymodule oftheISS,2009 (12years later,but8yearsago).

Hislefthand ison thechamber containing theMultiuser DropletCombustion Apparatus(MDCA).

Thechamber isdesignedtoaccommodate othercombustion experimentsaswell(and soon will).

ExperimentalProcedure

• AstronautsplacetheMDCA,gasbottles,andfuelcanistersinCIR,thentheentireexperimentalsequenceisrunremotelyfromCleveland.

• Extendneedles,dispensefueltoformdroplet,retractneedlesslightlytostretchdroplet,thenremoverapidlytoleaveastationaryfreedroplet.

• Energizeextendedhotwires,thenretractthemtoleavethedropletfree.• Recordbacklitdropletphotosforthedropletdiameter,UVandvisiblephotosfortheflameandnarrow-bandandwide-bandradiantemissions.

• 80micronSiC fibersalsomaybeusedtosupportdroplets,forexampletoburnmorethanonedropletatatime.

TheFLEXExperimentsandTeamfortheInternationalSpaceStation

Aphotograph and aschematic diagramoftheMultiuser DropletCombustion Apparatus (MDCA). Thediagram shows thefuel dispensers, deployment needles,igniters, backlight, andcameras.UserswereAvedisian (Cornell), Choi(Connecticut), Dryer(Princeton),Shaw (UCD), andWilliams (UCSD).

UnexpectedObservationsMadeinFLEXTest0035,Friday,November7,2009.

Backlitphotos ofstretcheddropletwith energizedhotwires, forafreeheptanedroplet initially 3.85mm indiameter inairat1atm.

Thevisible imageoftheburning heptane droplet isshown shortly afterignition, withresidual soot receding in thedirection ofigniter retraction(earlier testswerewithmethanol andafewsmall heptanedroplets thatextinguished diffusively). Radiativeextinction occurred soon afterthis.

Thevisible flamedisappears, butthebacklit photos show thedroplet tocontinue tovaporize asiftheflamewerestillthere. Then itapparently stopsvaporizing butforms agrowing vapor cloud thatreflects theredLEDbacklight.

Anomalousn-HeptaneHistoriesFoundinISSNayagam,Dietrich,etal.,C&F159(2012)3583-3588.Took2yearstoknowwhathappened!

Themicrogravityenvironmentinthespacestationaffordslongertesttimesthatpermitlargersphericallysymmetricaldropletstoburntocompletion.

Radiativehot-flameextinctionoccursforlargedroplets(anddiffusiveextinctionforsmallones).Invisiblecool-flamechemistrysupportscontinuedcombustionafterradiativeextinction.Avaporcloudformsatcool-flameextinction.

CharacteristicsoftheCool-FlameStage

Visible hot flames areentirely transient; theyliein theoutertransient zone.Ratioofflame radius todroplet radius, theFlame Standoff Ratio(FRS)⍨ 10.

Thecool flames areinvisible with theinitial instrumentation (in thenewCFIinvestigation, instrumentation is designed todetectthem). ButDietrich hadthespectral filterremoved from theflame-view camerawith itsgainsettingmaximized foradecane droplet held fixedbyaTfiber, obtaining theimage.→Grayscale densitometer analysis (sample alongdashed line shown atbottom)gives FSR=3.2forthecool flame, Nayagam etal.,AIAAJ.54, 1235-1239 (2016).

Cool flames liein theinner quasi-steady (convective-diffusive) zone!

Time-dependent spherical computations showcool flames when low-temperature chemistry(solid curve) isadded tohigh-temperaturechemistry (dotted curve atright)fora3.9mmheptanedroplet. (Noteconst. low-T 2’nd stage)Farouk andDryer, C&F161, 565-581 (2014).

RecalltheCool-FlameRegionforNormalAlkanesExample of equimolar(fuel-rich) propane-oxygenmixture (withstoichiometrichydrogen-oxygenshown forcomparison toemphasize thedifferences).Cool-flame rangeoftemperaturesgenerally 500Kto800Kintheexplosion diagram,butthe pressurerangevarieswithfuel and stoichiometry.

PreviouslyDevelopedReduced-FlameChemistryA.Hot-FlameStructure:

Hotalkanepremixed (1987) andnon-premixed (1988) flames canbedescribedbyRate-RatioAsymptotics (RRA), showing afuel-consumption layerandanoxidation layer, explaining oxygen leakage.Damkohler-number Asymptotics(DNA)withmultiple steps,wassummarized in1996 (Seshadri). MultistepDNA=RRA;differs fromActivation-Energy Asymptotics (AEA), Liñán (1974).

B.Hot-FlameAutoignition (>1000K):Alkane autoignition times aredescribedwellby justthree elementary steps, firstCmHn +HO2 →CmHn-1 +H2O2 thenH2O2decomposition, withHO2 steady state.

C.Cool-FlameChemistry (Peters):ACrossover Temperature exists, separating thehot-flame chemistry fromthecool-flame chemistry. RRAdescribes two-stage ignition andtheNTC(negative temperature coefficient) behavior. n-Heptane Autoignition (2002).

MostImportantAspectsoftheChemicalKineticsTheFirstStep: F+OH→R+H2OF=Fuel (Normal Alkane, CnH2n+2)R=Alkyl Radical

Note:BothOHandRareveryreactive andobey accuratechemical-kinetic steady-state approximations.

TheEffectiveOverallHigh-Temperature Path:R+O2 →2OH+P+HeatP=Product Collection (H2O,CO, CO2, etc.).

Notes: Therateofthis step canbe approximated asaunimolecular Rdecomposition with ahigh activation energy E.TheOHhereis asurrogatefor thewhole radicalpool, generatedabove 1000KthroughH2–O2 chain-branching.

Thelow-temperature path:R+O2 →RO2 →QOOH (Call thisI),I+O2 →J, J→K+OH, K→OH+P+Heat.

Notes: Activation energy E=0forthetwoO2 addition steps.BothO2 additions andtheisomerization arereversible.Kis thealkylketohydroperoxide, atlasthaving acarbonyl group(theC=Odouble bond), andunlike theradicalsR,I,and J,itis nominally stable inthatallcovalent bonds aresatisfied, but itdoes decompose unimolecularly.With fourOatoms, Jisveryrestless andmaintains anaccuratepartial equilibrium withI.[J]=KC[I][O2](Forthis reason Jis eliminated inSanDiegoMech, resulting inanegativeactivation energy forKproduction.)InanNTCtemperature range(somewhere between500Kand1000K) theoverall ratedecreases asTincreases.

CharacteristicsofTheLow-TemperaturePath

J.C.Prince and F.A.Williams, “Short Chemical-Kinetic Mechanisms forLow-Temperature Ignition ofPropane andEthane,”Combustion andFlame159, 2336-2344 (2012); theextension ofthismechanism ton-heptane: Fuel 150, 730-731 (2015).

ClarificationsofQuasi-SteadyCoolFlamesResultsfromPetersetal.CTM18(2014)515-531.

Flame structures areshown in amixture-fraction coordinate, Z.With 4πμ themass-loss rateofthedroplet andD thethermal diffusivity, Z isdefined by

with r2⍴D(dZ/dr)=-μ(1-Z) atr=rl (surface)andZ=0atinfinity (in theair).

This results in theinverse transformation:

Numerical integration inZspace employs thecomparatively short (770-step) mechanism of Seiser etal.(2000) for heptane.With radiantheatloss neglected therearehot-flame andcool-flame solutions withthecool flame (atZ =0.3)closer to

thefuel surface (atZ =0.8)than thehotflame. Profiles ofmole fractions show that:→fuel (blue) andoxygen (very lightcurve) bothleakthrough thecool flame, and amainproduct isH2O(lightblue curve), butthereispractically noCO2 (red curve). →

←Otherproducts areCO, CH2O, andC2H4.Species K, fromwings isconsumed in thecenter!

SomeoftheMajorTheoreticalPredictions• Condensationofleakedfuellikelycausesthevaporcloud.• Thequasi-steadycool-flametemperaturedecreaseswith

decreasingdropletdiameterbecausetheresidencetimeinthequasi-steadyreactionzonedecreaseswithdecreasingdiameter,resultinginlessheatrelease;theresidencetimeisproportionaltorl2/D,reciprocalchi.→

• Thequasi-steadycoolflameisstableonlyintheNTCrangesince,forexample,belowthatrangeadecreaseinT decreasestherateofheatrelease,furtherdecreasingT,leadingtoextinction,asmaybereasonedfromtheregionlabeledcoolflameinthediagramoftherateofheatreleaseshownbelow.↓

• TheinstabilityaboveNTCwouldre-ignitethehotflame←(seethediagramattheleft),whichwouldbeexpectedtoextinguishradiatively again,leadingtooscillationsthathavebeenseeninexperimentsandcomputations.

• BecausethereisinstabilitybelowtheNTCrange,thedropletdiameterat(diffusive)cool-flameextinctionisachemical-kinetic/heat transferinstabilityphenomenon,notsimplyabalancebetweenratesofheatreleaseanddiffusiveheat loss;theextinctiondiametercorrespondstothemaximumintheheat-release-ratecurve!

AsymptoticAnalysisforthePartial-BurningRegimeKdecomposes unimolecularly, leading tobranching forthelow-temperature path,with aprefactor AK =4☓1013 s-1 and anactivation energy ofroughly EK =180kJ/mole (TK=20,000 K)high enough forAEAtoapply tothedip inthe Kconcentration seen atthehighest temperature.Seshadri etal.,CTM20 (2016) 1118-1130.

Theheptyl radicalRdecomposes mainly by thehigh-temperature pathabove thecrossover temperature T* withaneffective unimolecular ratehaving aprefactor AH =4☓1013 s-1 andactivation energy ER =120 kJ/mole (TR=14,000 K),butitmainly experiences theaddition stepR+O2 →RO2belowT*,with aconstant bimolecular rateconstant givenbyAL =2☓1012 cm3/mol sand arateproportional totheconcentration [O2].Nearcrossover, thefractionofRconsumed bythelow-temperature pathisα=½ - (T– T*)TR/ (4T*2),where clearly T*=TR/ln{AH /(AL [O2])}, andthemolar rateofproduction of Kisproportional to(2α - 1)[K]AK exp(-TK/T).Thus, thelow-T pathdominates forα>½and thehigh-T pathforα<½.

Conservation equations forenergy andforKhavebeen expanded about T*byAEAtodetermine thevalues oftheflame temperature anddroplet radiusatthemaximum of theheat-release rate(theabovepaper inCTM), withrepresentative results for droplet diametersde atextinction shown here.→

Theagreement issurprisingly good, since extinction mayoccur beyondtherangeofvalidity oftheexpansion, forexample, andanalysis oversimplifies chemistry, neglects Soret, andhas Le=1.

NeedsforFutureInvestigationsAlthough thecool flame isin thequasi-steady region, it’s history isaffectedbyprocesses occurring intheouter transient zone.This isshown by theincrease of themeasured extinction diameterwithincreasing initial droplet diameter, aswellasby thefailureof time-dependent computations toshow anydecrease in flametemperaturewith timeduring thesecond stage.Theincrease intheeffectiveambient temperature andproduct concentration with timeduringcombustion isinneed ofanalysis tofind their influence onthequasi-steady cool-flame combustion. Besides theinitial dependence ondiameter shown here, thereis anincrease inextinction diameterwithincreasing ignition energy.

Formation of vapor clouds by condensing fuel also has notbeenpredicted and isinneedof analysis.

Further study ofthechemical kinetics isneeded. While reasoning has notyetindicated thatdecomposition of ItoHO2and theconjugate alkene (shown in aprevious figure) hasanyqualitative effect, itmaybeofquantitative importanceinthatpredictions ofa62-stepmechanism omitting itgiveextinction diameters tentimes thereasonable 770-step values.

Experimental extinction diameters inthecool-flame stagedecrease muchmore rapidlywith increasing pressure thanpredicted. Despite some suggestions, these results areunexplained andareinneedof furtherwork, and soot needs study.

CurrentStatusandFuturePlansBecause ofthediscovery, FLEXhasbeen extended into CFI(Cool FlameInvestigation) which twoweeks agocompleted testFLEX 1314.Besidesdatafor heptane, octane, anddecane in various atmospheres (e.g.→dataarenowavailable fornormal andiso-dodecane; asexpecxted,mixtures ofthe n- andiso- fuels exhibit less cool-flame tendenciesthanpure n-.Farouk andDryerarecontinuing computational work.

Alargeamount ofdataremains tobeanalyzed!CFIand FLEX arescheduled toendnextmonth, and theMDCA istoberemoved from theCIR,whichwill terminate 8years ofdropletcombustion experiments inISS, likely never toresume (badnews),butconsiderably longer thanoriginally planned; stillmore tolearn.(Besides FLEX, there havebeen ItalianandJapanese experiments.)

Theschedule calls fornextreplacing theMDCAbyACME, illustrated→These aregaseous-fuel investigations involving Law,Quintiere, andothers.Thegoodnews is thatlastweek (July 19,2017) PeterSutherland wasinformed byNSF thathis CASIS project forACMEwillbe funded, investigating cool flames ofpropane, butane,…!