Modeling of ammonium dinitramide (ADN) monopropellant combustion with coupled condensed ...

16 Pages·2013·1.46 MB·English

by  Piyush Thakre

CombustionandFlame161(2014)347–362
ContentslistsavailableatScienceDirect
Combustion and Flame
journal homepage: www.elsevier.com/locate/combustflame
Modeling of ammonium dinitramide (ADN) monopropellant combustion
with coupled condensed and gas phase kinetics
⇑
Piyush Thakre , Yi Duan, Vigor Yang
SchoolofAerospaceEngineering,GeorgiaInstituteofTechnology,Atlanta,GA30332-0150,USA
a r t i c l e i n f o a b s t r a c t
Articlehistory: Acomprehensivemulti-phasecombustionmodelhasbeendevelopedtostudythephysiochemicalpro-
Received28May2013 cessesinvolvedinthecombustionofammoniumdinitramide(ADN).Thenumericalmodelisbasedon
Receivedinrevisedform12August2013 theconservationequationsofmass,speciesconcentration,andenergy,andtakesintoaccountfinite-rate
Accepted12August2013
chemicalkineticsinbothcondensedandgasphases.Basedonanextensivereviewoftheliteratureon
Availableonline24September2013
ADNthermaldecomposition,threeglobaldecompositionreactionsinthecondensedphaseofADNare
included.A detailed chemical kineticsscheme involving 34 species and 165reactions is employed in
Keywords:
the gas phase. Detailed combustion-wave structures and burning rate characteristics of ADN are
Ammoniumdinitramide
described.Theoptimizedgas-phasekineticsmechanismwasabletopredictthemulti-stageflamestruc-
ADNpropellantcombustion
ture.Goodagreementsbetweenthepredictedandmeasuredprofilesoftemperatureandspeciesmole
fractionswereobtainedatdifferentpressures.Reasonableagreementsbetweencalculatedandmeasured
valuesofpropellantburningratesandsurfacetemperatureswereobtainedoverabroadrangeofpressure
from0.7to350atm.Theburningrateincreaseswithpressure,exceptinthemidrangeof(cid:2)60–100atm.
Thecoupledcondensed-andgas-phaseanalysisemployedinthecurrentmodelisabletocapturethis
irregular/unstable combustion behavior in the mid range, where the burning rate decreases with the
increaseinpressure.
(cid:2)2013TheCombustionInstitute.PublishedbyElsevierInc.Allrightsreserved.
1.Introduction trophotometry [23,24], molecular beam mass-spectrometry
(MBMS) [12,25], differential scanning calorimetry (DSC) [13,26],
Ammonium dinitramide (ADN) is a novel energetic material thermal gravimetry combined with mass spectrometry (TG-MS)
that can be used as a liquid monopropellant or as an ingredient [13,26],opticalpolarizinglightmicroscopy,laser-Ramanspectros-
in solid-rocket propellants [1]. It is a low-signature environmen- copy,andenergydispersiveX-raydiffractiontechniques[27].The
tallyfriendlypropellant,withchlorine-free combustionproducts. theoreticalmethodsincludeabinitiocalculationbasedonquantum
Becauseitoffershigherperformancethanconventionaloxidizers, chemistry[14–16]andnumericalmodelsbasedondetailedchem-
ADN is a promising alternative to Ammonium Perchlorate (AP) istry[17–21].Bothself-sustained[22–27]andlaser-inducedcom-
andAmmoniumNitrate(AN)[1]. bustion[28,29]havebeenmodeled.Areviewoftheliteratureon
ADN, which is an ionic compound (NHþ½NðNO Þ (cid:3)(cid:4)), was first ADN thermal decomposition and its combustion behavior up to
4 2 2
synthesizedin1971attheZelinskyInstituteofOrganicChemistry 2005isdetailedbyYangetal.[30].
in the former Soviet Union [2–4]. In 1989, it was independently Russelletal.[27]confirmedareversiblephasetransitionofan
synthesizedbytheStanfordResearchInstitute[5,6].Overthepast ADNcrystal,asdescribedbyreaction
fourdecades,significantresearchhasbeenconductedtostudythe
combustion wave structure and burning-rate characteristics of a-ADN2(:0)GPab-ADN ðR1Þ
ADN. Extensive experimental diagnostics [7–13] and theoretical
Theb-ADNhasanewmonoclinicpolymorphicstructure.Themelt-
modeling[14–21]havebeenreportedoverabroadrangeofoper-
ing point of a-ADN is 365–368K [12,25], significantly lower than
ating conditions. The experimental techniques include T-jump/
RDX (478K) [31], HMX (551K) [32], and AP (865K) [33]. The
FTIR spectroscopy [22], micro-thermocouple [9,23,24], UV-spec-
ADNpropellantmodeledinthepresentpaperisassumedtobea-
ADN,withoutanycuringagent.
⇑ Figure1showsschematicallythephysiochemicalprocessesin-
Correspondingauthor.Currentaddress:CD-adapco,Ltd.,Melville,NY11747,
volved in ADN monopropellant combustion. The temperatures
USA.
mentionedinFig.1arerepresentativeofaflameat5atm.Inorder
E-mail addresses: [email protected] (P. Thakre), [email protected] (V.
Yang). tosimplifyanalysis,theentirecombustionwaveissegmentedinto
0010-2180/$-seefrontmatter(cid:2)2013TheCombustionInstitute.PublishedbyElsevierInc.Allrightsreserved.
http://dx.doi.org/10.1016/j.combustflame.2013.08.006
348 P.Thakreetal./CombustionandFlame161(2014)347–362
Nomenclature
A cross-sectionalareaofpropellantsample u bulkvelocity
A fractionalcross-sectionalareaconsistingofgasbubbles V diffusionvelocityofspeciesi
g i
intwo-phaseregion D effectivemass-diffusioncoefficientforspeciesi
i
A pre-exponentialfactorofrateconstantofreactionj D thermaldiffusionratio
j Ti
A interfaceareabetweenbubblesandliquidperunitvol- v(cid:2) averagenormalvelocitycomponentofvapormolecule
s n
ume W molecularweightofspeciesi
i
a pre-exponentialfactorofburning-ratelaw w_ massproductionrateofspeciesi
i
B temperatureexponentinrateconstantofreactionj w_ massproductionrateofreactionj
j Rj
C molarconcentrationofspeciesi X molarfractionofspeciesi
i i
C constant-pressurespecificheatofspeciesi Y massfractionofspeciesi
pi i
E activationenergyofreactionj
j
e internalenergy Greeksymbols
Hv enthalpyofvaporization / voidfraction
h enthalpy q density
hi staticenthalpyofspeciesi k thermalconductivity
h(cid:5)fi heatofformationofspeciesiunderstandardcondition x_ molarproductionrate
k rateconstantofreactionj
j
m_00 massflux
Subscripts
N totalnumberofspecies 0+ gas-phasesideofpropellantsurface
n pressureexponent 0(cid:4) foamlayersideofpropellantsurface
N totalnumberofreactions
R c condensedphase
p pressure
c–g fromcondensedphasetogasphase
p pre-exponential factor of vapor pressure in Arrhenius
0 cond condensation
form
eq equilibriumcondition
r propellantburningrate
b evap evaporation
R universalgasconstant
u f mass-averagedquantityinfoamlayer
T temperature
g gasphase
T meltingpointofADN
melt l liquidphase
T initialdecompositiontemperature
d s propellantsurfaceorsolidphase
T temperatureatpropellantsurface
s v vapor
T temperatureinaerosolzone
a
s stickingcoefficient
t time
threeregions:solidphase,foamlayer,andgasphase.ForRDXand reactions within bubbles make the physiochemical processes in
HMX,thechemicalreactionsinthesolidphasecanbeignored,due thesolid-bubblelayerverychallengingtosimulate.
tothehighliquefactiontemperature[34].ForADN,however, the WhenthetemperaturereachesthemeltingpointofADN,ther-
situationismorecomplicated,asitundergoessignificantexother- modynamicphasetransitionoccursasdescribedbyR5.
micreactionsinthesolidphase.Sharpexothermicityoccurredin-
ADN !ADN ðR5Þ
stantlywhenthefirstgasproductwasdetected[33].Brilletal.[22] solid liquid
proposedtwosetsofinitialdecompositionpathways,accordingto The liquid-bubble layer (Fig. 1) starts at about 366K, close to the
observedproductsratiosandtheheat-release.Itissuggestedthat meltingpointofADN.Thethermaldecompositionandevaporation
Reaction (R2), which is mildly endothermic, dominates at lower ofADN,bubbleformation,gas-phasereactionswithinbubbles,and
temperatureswhenthedecompositionrateislow. interfacialtransportofmassandenergybetweenthegasandcon-
densedphasealsotakeplaceintheliquid-bubblelayer.Inthecur-
ADN !NH þHNO þN O ðR2Þ
ðsÞ 3 3 2 rent approach, since the physiochemical processes in the solid-
Reaction(R3),whichisquiteendothermic,islikelytodominateun- bubble and liquid-bubble layers are similar, these two layers are
derrapidthermolysisconditions. treatedtogetherasafoamlayer(alsoreferredtoasthesubsurface
multi-phaseregion).
ADNðsÞ!NH3þHNðNO2Þ2 ðR3Þ Thepropellantundergoesasequenceofrapidevaporationand
decompositioninthenearfieldimmediatelyabovethefoamlayer.
The product HN(NO ) , usually abbreviated as HDN, is not stable
22 Subsequentdegradationandrecombinationreactionsoccuramong
andwilldecomposerapidlythroughreaction
theprimaryproducts.Thesereactionsleadtofinalproductsanda
HNðNO Þ !NO þHNNO ðR4Þ corresponding flame region. Reaction R6, R7, and R8 are some of
2 2 2 2
thepossiblechemicalpathwaysinthegas-phaseregion[30],
Thegaseousdecompositionproductsformbubbleswithinthesolid
ADN.InordertoaccuratelypredictADNcombustioncharacteristics, 4NH3þ4NO2!3N2þ2NOþ6H2O ðR6Þ
thesolidADNhasbeensubdividedintotwosegments,apuresolid 2NH þ2NO !NH NO þN þH O ðR7Þ
3 2 4 3ðsÞ 2 2
ADNlayerandasolid-bubblelayer(Fig.1).Assumingthatthepure 2NH þ2NO !N OþN þ3H O ðR8Þ
3 2 2 2 2
solidADNlayerremainsthermallystable,anythermaldecomposi-
tioncanbeneglected[35]. Onlyheatconductionistakenintoac- AglobalreactionforADNcondensed-phasethermaldecomposition
count in this region. The solid-bubble layer starts around 333K isobtainedfromthesummationofallproposedreactions.Reaction
[30]. ADNthermal decomposition,sublimation, and thegas-phase (R9)isalsoconsistentwiththemeasuredfinalcomposition[17].
P.Thakreetal./CombustionandFlame161(2014)347–362 349
Fig.1. Schematicofcombustion-wavestructureofADNmonopropellant(nottoscale).
101 the combustion process. The heat feedback from the gas phase
can be ignored, on account of a low temperature gradient at the
propellantburningsurface[9,24].Theyalsospeculatethatthecon-
densed-phase species (ADN and AN) are dispersed into the gas
m/s flame due to the high burning rate. The white aerosol zone [24]
c and condensed material dispersion in other condensed-phase
e,
Rat 100 Sinditskii,251K dominating type of combustion [40] seem to support their
g Atwood,298K assumption. AccordingtoSinditskii et al.[23,24], as the pressure
n
ni Strunin,298K increasesmore energy isrequired for ADNdissociation. Thecon-
Bur Zenin,293K densed-phase heatrelease, however, stays nearlyconstant, while
Price
thegas-phaseheatfeedbackisstillinsignificant.Inthismid-pres-
Fogelzang,293K
surerange,thereappearstobeagapbetweentheenergyrequired
Flanagan
toheatupandevaporatethecondensed-phasematerialsandthe
Korobeinichev
10-1 heat released in the condensed phase; this leads to oscillating
100 101 102 103 andunstablecombustionbehaviorandcausestheobservedburn-
Pressure, atm
ing-ratedatascatter.Thecompetitionbetweenthefastbutenergy-
limitedheat-releaseprocessinthecondensedphaseandtheslow
Fig.2. ADNburningratevs.pressurefromvariousmeasurements.
butenergy-richheat-releaseprocessinthegasphaseisconsidered
to be responsible for the burning-rate irregularity in the 40–
12ADN!3NH þ10N Oþ6NO þ15H Oþ2NOþ6N 100atmpressurerange.Athigherpressures,thegas-phaseflame
3 2 2 2 2
ismuchclosertotheburningsurface,resultinginasteeptemper-
þHNO þ2NH NO ðR9Þ
3 4 3ðsÞ
aturegradientandheatfeedbacktothecondensedphase;thegas-
ADNhas ahigherburningratethanAP,RDX,andHMX.At 5atm, phaseheatfeedbackisadequatetosustainADNdeflagration.
theADNburningrateof15mm/s[9]isabout(cid:2)10timeshigherthan InordertoanalyzetheADNcombustionwaveanditsburning
thoseofHMX(1.2mm/s)[36]andRDX(1.5mm/s)[37].ADNexhib- characteristics,manycomputationalstudieshavebeenperformed
itsauniqueburning-rateirregularityinthepressurerangeof40– basedondetailedchemicalreactionsbymanyresearchers[14–21].
100atm, as confirmed by many researchers [4,9– Oneofthefirstdetailedgas-phasekineticsmechanismswasdevel-
11,23,24,27,38,39].Theburning-rateinthispressurerangenotonly opedbyErmolinin1990s[19]andimprovedin2004[30].Amech-
has a lot of scatter, but also appears to decrease slightly with anismwith32speciesand152reactionswasproposedbyLinand
increasingpressureasshowninFig.2[4,9–11,23,24,27,38,39]. ParkbasedontheirabinitioMO/cVRRKMcalculations[16].Incor-
TwostablecombustionregionsofADNexistatpressuresbelow porating Park’s scheme and several H/N/O reactions, which have
20atm and above 100atm. According to Sinditskii et al. [23,24], beenwelldevelopedforRDXcombustion[35],amorecomprehen-
the condensed-phase decomposition appears to dominate in the sive ADN gas-phase combustion kinetics mechanism was em-
low-pressure region. Below 20atm, a significant amount of heat ployedbyLiauetal.[17].TheanalysisofADNself-deflagrationat
release from the condensed phase ADN decomposition sustains 6atm obtained a good agreement between predicted and
350 P.Thakreetal./CombustionandFlame161(2014)347–362
measuredresults. Based on a sub-mechanism(22 species and 98 Table2
reaction)fornitraminepropellantcombustionsuggestedbyYetter ThermodynamicandtransportpropertiesofADN.
etal.[41]and74additionalreactionsforADNdecompositionprod- Parameter Units Value Ref.orComments
uctsproposedbyParketal.[16],Korobeinichevetal.[42]devel-
cp,ADN(s) cal/g/K 2.094(cid:6)10(cid:4)1+3.361(cid:6)10(cid:4)4T [44]
oped a 33 species and 172 reaction kinetics mechanism. A cal/g/K 0.59 [45]
kinetics mechanism includingmore than 100 reactions was used J/kg/K 1.26(cid:6)103 [46]
byShmakovetal.tomodelthermaldecompositionofADNvapor cal/g/K 0.49 [24]
inatwo-temperatureflowreactor[43]. cp,ADN(l) cp,ADN(l)=cp,ADN(s)
NoneoftheADNcombustionmodelsmentionedabovelinkthe kp;ADNðsÞ cal/cm/s/K 1.238(cid:6)10(cid:4)3(cid:4)5.78(cid:6)10(cid:4)7T [44]
cal/cm/s/K 0.00193 [45]
condensed- and gas-phase kinetics, due to the lack of reliable J/m/s/K 0.419 [46]
decomposition mechanism and data on the properties of ADN li- kp;ADNðlÞ kp;ADNðlÞ¼kp;ADNðsÞ
quid and its intermediate products. The experimental data avail- qp,ADN(s) g/cm3 1.60–1.84 [46]
able at the surface or in the gas phase were used as initial qp,ADN(l) g/cm3 1.55 [49]
conditionsinthosedetailedgas-phasecombustionmodels.Inor- Hv,ADN kcal/mol 35.1–37.1 [43]
Hmelting,ADN cal/g 32 [9]
dertocircumventthelimitationsofthepreviouscombustionmod- kcal/mol 3.4 [5]
els,animprovedmodelthatcouplesthecondensedandgas-phase
kineticmechanismisneeded.Suchamodelshouldalsobeableto
capturetheirregularityofADNburninginthemid-pressurerange.
to those in the solid phase. Systematic parametric calculations
The first model to couple a global condensed-phase reaction
wereperformedinthecurrentwork,duetoavailabilityofvarious
with detailed gas-phase kinetics was developed by Gross et al.
thermodynamicdataforthecondensedphase.Thevaluesusedin
[21,33] Reasonably good agreement of predicted and measured
themodelappearinboldinTable2.
burning rate in the low pressure (3–10atm) and high pressure
(100–200atm) ranges was obtained. A proposed modification of
2.2.Foamlayerregion
the interpretation of erratic combustionbehavior in the pressure
range of 10–100atm offered by Sinditskii et al. [23,24] was pre-
The foam layer consists of the solid-bubble and liquid-bubble
sented.Table1summarizestheADNcombustionmodelsofseveral
layers(Fig.1).Thephysiochemicalprocessesinthisregionareex-
researchers.
tremely complex, involving thermal decomposition, sublimation,
evaporation,condensation,bubbleformation,gas-phasereactions
2.Theoreticalformulation inbubbles,andinterfacialtransportofmassandenergybetween
thegasandcondensedphases.Atwo-phasefluiddynamicsmodel
Tofacilitateanalysis,thecoordinatesystemisfixedattheADN based on a spatial averaging technique is employed to formulate
propellantburningsurface.Aquasione-dimensionalmodelisfor- these complicated phenomena [35]. The analysis is based on the
mulatedasafirstapproximationoftheproblem.Abriefsummary integral form of the conservation laws for control volumes occu-
ofthetheoreticalformulationof thephysiochemical processesin piedseparatelybythebubblesandcondensedphases.Inestablish-
variousregionsisdescribedinthefollowingsections. ing the gas-phase formulation, the Dupuit-Forchheimer [47]
fractional-volumevoidagedefinitionisemployed,givenby
2.1.Solidphaseregion
A ¼/A ð2Þ
g
ThermaldecompositionofADNandradiationabsorptionisig- With the additional assumption that mass diffusion is negligible,
noredinmodelingthesolid-phaseprocess.Onlyheatconduction theconservationequationsforbothcondensedphaseandgasphase
governedbythefollowingequationisconsidered: canbecombinedandwrittenasfollows.
Mass
@T @T @ (cid:2) @T (cid:3)
qscp;s @tsþqsuscp;s @xc¼@x ks @xs ð1Þ @½ð1(cid:4)/Þqcþ/qg(cid:3)þ @ ½ð1(cid:4)/Þq u þ/q u (cid:3)¼0 ð3Þ
@t @x c c g g
Aclosed-formsolutionofEq.(1)atsteadystateisavailable,subject
Condensedspeciesconcentration
toappropriateboundaryconditionsandthepropellantburningrate.
Thevariouspropertiesemployedinthepresentworkaresum- @½ð1(cid:4)/Þq Y (cid:3) @
c ci þ ½ð1(cid:4)/Þq u Y (cid:3)¼w_ ði¼1;2;...;N Þ ð4Þ
marized in Table 2. The thermal conductivity and specific-heat @t @x c c ci ci c
capacity of solid ADN are available in various Refs.
Gaseousspeciesconcentration
[5,8,9,13,29,34,47,48].ThemeasurementofliquidADNproperties
isdifficultbecausedecompositionusuallytakesplacebeforemelt- @ð/qgYgiÞþ@ð/qgugYgiÞ¼w_ ði¼1;2;...;N Þ ð5Þ
ing,althoughthedensityofliquidhasbeenreportedbyVelardez @t @x gi g
etal.[49].Hence,theliquidpropertiesareassumedtobeidentical
Table1
ComparisonofADNcombustionmodels.
Authors Num.ofspecies Num.ofreactions Characteristics Ref.
Ermolin(1996) 26 256 Gasphasekinetic,experimentaldatawereemployedasboundaryconditions. [19]
Parketal.(1998) 33 152 [16]
Liauetal.(1998) 33 180 [17]
Korobeinichevetal.(2001) 33 172 [42]
Shmakovetal.(2001) >100 [43]
Ermolin(2004) 34 218 [20]
Grossetal.(2006) 33 173 Coupledcondensedandgasphasekinetics [21]
Presentmodel 34 165 Optimizedgasphasekinetics,coupledwithcondensedphasereactions
P.Thakreetal./CombustionandFlame161(2014)347–362 351
Energy data for ADN vapor pressure correlations. The data employed by
Grossetal.[21]isusedinthepresentwork.
qc @Tf (cid:4)@pþquc @Tf ¼ @ (cid:2)k @Tf(cid:3)(cid:4)XNg w_ h Based on the chemical mechanism given by reactions (R10)–
f f @t @t f f f @x @x f @x gi gi (R12), the species production terms in Eqs. (4) and (5) are listed
i¼1
in Table 4. The production terms for reactions in Table 4 are de-
(cid:4)XNg w_ h þXNg h Y w_ finedas
ci ci gi gi c(cid:4)g
i¼1 i¼1 w_ ¼ð1(cid:4)/Þq Y k ð11Þ
R10 c c;1 1
(cid:4)XiN¼c1hciYciw_c(cid:4)g ð6Þ ww__R11¼¼ðA1ð(cid:4)k/Þ(cid:4)qckYc;2kÞ2¼Asv(cid:2) C (cid:2)Pv;eq(cid:4)X (cid:3) ðð1132ÞÞ
R12 s 12f 12b s n ADN p g;3
Thepropertiesaremass-averagedasfollows
(cid:2) Hv(cid:3)
qfcf ¼½ð1(cid:4)/Þqcccþ/qgcg(cid:3) ð7Þ Wheres¼1; pv;eq¼p0exp (cid:4)R T ð14Þ
u
quc ¼½ð1(cid:4)/Þq uc þ/q u c (cid:3) ð8Þ
f f f c c c g g g
kf ¼½ð1(cid:4)/Þqcuckcþ/qgugkg(cid:3)=½ð1(cid:4)/Þqcucþ/qgug(cid:3) ð9Þ 2.3.Gasphaseregion
XNc The species evolved from the burning propellant surface into
c ¼ c Y ð10aÞ
c ci ci thegasphaseincludevaporADNanditsdecompositionproducts.
i¼1 Themodelingofthegasphaseisbasedonthemass,energy,and
XNg speciestransportfor amulti-componentchemicallyreactingsys-
c ¼ c Y ð10bÞ
g gi gi temofNspecies,andaccommodatesfinite-ratechemicalkinetics
i¼1
andvariablethermophysicalproperties.Ifbodyforces,viscousdis-
XNc
k ¼ k Y ð10cÞ sipation, and radiation absorption are ignored, the conservation
c ci ci
i¼1 equationsforanisobaricflowcanbewrittenasfollows.Itshould
XNg benotedthatonlythegasphasewastakenintoaccountinthecur-
kg ¼ kgiYgi ð10dÞ renttreatment.
i¼1 Mass
The mass and energy production terms depend on the specific @ðqAÞ @
þ ðquAÞ¼0 ð15Þ
chemicalreactionmechanisms.Themodelaccommodatesthether- @t @x
maldecompositionofADN,aswellassubsequentreactionsinthe
Speciesconcentration
foamlayer.Theformationofgasbubblesduetosublimation,evap-
oration and thermal degradation is also considered. Two global @ðqAYiÞþ@½qAðuþViÞYi(cid:3)¼w_ ði¼1;2;...;NÞ ð16Þ
decomposition reactions (R10 and R11) are employed for ADN @t @x i
decomposition, as listed in Table 3. Reaction (R10) was proposed
Energy
byBrilletal.,basedonmeasuredcompositionattheburningsur-
!
face[22].Itshouldbenotedthatreaction(R10)isidenticaltoreac- @ðqAeÞ @ðqAuhÞ @ @T XN
þ ¼ kA (cid:4) qAYVh ð17Þ
tion(R9).ReactionR10ishighlyexothermic,andprovidesamajor @t @x @x @x i i i
i¼1
heatsourceinthecondensedphase.InRef.[21],theactivationen-
ergyofADNdecompositionwasartificiallyincreasedattherateof Table4
100cal/mole per 5atm increase in pressure. The adjustment was Descriptionofspeciesformationinfoamlayer.
necessary to obtain a smooth transition between the low- and i Species w_ciorw_gi
high-pressure regions. In the current model, this adjustment was
notnecessary.SomeofthesolidANparticlesproducedbyreaction 1 ADN(s) (cid:4)ðw_R10þw_R12Þ
(R10) disperse into aerosol zone, while the remaining particles 2 AN(s) 16WW21w_R10(cid:4)w_R11
3 ADN(g) w_R12
dtieocno,maspocosemtpharroeudghtorereaacctitoionn(R(R1110),)w. hichisalessexothermicreac- 4 NH3 W4(cid:4)14w_WR110þ112w_WR121(cid:5)
Thermodynamicphasetransition(R12)consistingofbothevap- 5 N2O W5(cid:4)ð56w_WR110þ254w_WR121(cid:5)
oration (sublimation) and condensation of ADN, is considered to 6 H2O(g) W6(cid:4)ð54w_WR110þ2112w_WR121(cid:5)
pemxrooasvcttidreeexstaeeancrotcmhoefprAlseDtseNeedemevsatcporoiaprgtairtoeionenothifsattnhoseotmmknaeoseswvtnarpawonrsitafhetirocneprrdtoaocieensstsyt.,aTbkhueest 78 NNO2 WW78(cid:4)(cid:4)ðð1612ww__WWRR111100þþ2121434ww__WWRR112211(cid:5)(cid:5)
place. To achieve the right balance of the condensed- and gas- 9 HNO3(g) W9(cid:4)ð112w_WR110þ14w_WR121(cid:5)
penhdasoethheeramtiflcuAxDaNttehveapsourrafaticoen,.itTahpepreeaarrsenseecveesrsaalrsyettosoalfloawvaisloamblee 10 NO2 W10(cid:4)ð12w_WR110þ18w_WR121(cid:5)
Table3
Subsurfacechemicalreactionsandrateparameters.
No. Reactions A E(kcal/mol) Ref.
R10 ADNðsÞ!0:25NH3þð5=6ÞN2Oþ0:5NO2þ1:25H2Oþð1=6ÞNOþ0:5N2þð1=12ÞHNO3þð1=6ÞANðsÞ 3.5e15s(cid:4)1 32 [25]
R11 ANðsÞ!ð1=12ÞNH3þð5=24ÞN2Oþð1=8ÞNO2þð21=12ÞH2Oþð1=24ÞNOþð13=24ÞN2þ0:25HNO3 2.5e14s(cid:4)1 47.2 [50]
R12 ADNðsÞ()ADNðgÞ 5.0e17Pa 40 [21]
5.1e21Pa 37 [25]
2.8e20Pa 40 [43]
2.5e23Pa 40 [17]
352 P.Thakreetal./CombustionandFlame161(2014)347–362
Thespecificenthalpyofamixtureisthemass-weightedsumofthe @q¼@u¼@Yi¼@T¼0 atx!1 ð26Þ
speciesenthalpyh, @x @x @x @x
i
h¼Xi¼N1hiYi andhi¼ZTrTefcpidTþh(cid:5)fi ð18Þ maGTtchaheseppdhhaaytssetichaaenldpprrfooopacemesllsaleansyteinbruitnhrtneeirngfagascsepuhrfaasceea,ntodpforoamvidleaytehrembuoustnbde-
Consequently,thespecificinternalenergybecomes ary conditions for each region. This procedure requires balances
ofmassandenergy,andeventuallydeterminestheburningsurface
p
e¼h(cid:4) ð19Þ conditionsandburningrate.Withtheapplicationofconservation
q
lawstotheburningsurface,thematchingconditionsareexpressed
The mass diffusion velocity V consists of contributions from both asfollows:
i
concentrationandtemperaturegradients, Mass
V ¼(cid:4)D 1 @XiþD DTi 1@T ð20Þ ½ð1(cid:4)/Þqcucþ/qgug(cid:3)0(cid:4) ¼ðquÞ0þ ð27Þ
i iX @x i X T @x
i i Speciesconcentration
Finally,theequationofstateforamulti-componentsystemisde- ½ð1(cid:4)/Þq u Y þ/q u Y (cid:3) ¼½qðuþVÞY(cid:3) ð28Þ
rivedtoclosetheformulation. c c ci g g gi 0(cid:4) i i0þ
Energy
p¼qRuTXi¼N1WYii ð21Þ (cid:6)kfddTxf þð1(cid:4)/ÞqcucYADNðcÞhADNc—g(cid:7) ¼(cid:2)kgddTxg(cid:3) ð29Þ
0(cid:4) 0þ
ForasetofN elementaryreactionsinvolvingNspecies,thereac-
R
Thetemperatureisidenticalonbothsidesoftheinterface,butspe-
tionequationscanbewritteninthefollowinggeneralform
cies mass fractions could be different. A distinct phase transition
XN m0M (k)fj XN m00M; j¼1;2;...;N ð22Þ from liquid to vapor ADN is assumed to prevail at the interface
i¼1 ij i kbj i¼1 ij i R [35],giving
(cid:6) (cid:2)p (cid:3)(cid:7)
awphpeeraerimn0igj aansdamre0i0jaactraentthientshtoeicjthhiofmorewtraircdcaonedffibcaiecnktwsafrodrrsepaecctiioenssi, ½ð1(cid:4)/ÞqcucYADNðcÞ(cid:3)0(cid:4) ¼ sv(cid:2)nCADNðgÞ vp;eq(cid:4)XADNðgÞ 0þ ð30Þ
respectively,andMiisthechemicalsymbolforspeciesi.Thereac- Eqs. (27)–(30), coupled with the assumption that qu =q u and
l l g g
tion rate constant k (either k or k ) is given empirically by the
j fj bj T=T [48], are sufficient to solve the set of unknowns (u,T,/,Y)
l g c s i
Arrheniusexpression
atthepropellantsurface.
kj¼AjTBjexpð(cid:4)Ej=RuTÞ ð23Þ Foamlayerandsolidphaseinterface
The boundary conditions at the interface between solid phase
Therateofchangeofmolarconcentrationofspeciesibyreactionjis andfoamlayer(meltingfront)are:
!
C_ ¼ðm0 (cid:4)m00Þ k YN Cm0ij(cid:4)k YN Cm0i0j ð24Þ Tc¼Tf ¼Td; and/¼0atx¼xd ð31Þ
ij ij ij fj i bj i
i¼1 i¼1 Unreactedpropellantboundary(coldboundary)
Theboundaryconditionattheunburnedsideofthepropellant
ThetotalrateofchangeofspeciesiinEq.(16)isobtainedbysum-
(x?(cid:4)1)is
mingupthechangesduetoallreactions:
T ¼T atx!(cid:4)1 ð32Þ
w_i¼WiXNR C_ij ð25Þ wshereinTiiniistheinitialtemperatureofthepropellant.
j¼1
Thedetailedgas-phasekineticmechanismemployedinthepresent 3.Numericalmethod
model was developed by optimizing the mechanism used by Liau
et al. [17]. The NO mole fraction in Liau’s model was underesti- Theoverallcalculationproceedsaccordingtoadouble-iteration
mated,andN Omolefractionwasoverestimated.The13reactions procedure, with propellant surface temperature (T) and burning
2 s
related to NO consumption and N O production were removed. rate (r ) as the eigenvalues. The inner loop is used to correct T
2 b s
Manyparametricvariationswereperformedtogetthebestagree- andtheouterlooptocorrectr .ForagiveninitialguessofT and
b s
ment between predicted and measured temperature and species r , the conservation equation for the subsurface region is solved
b
concentrationsprofilesat3,6,and40atm.Basedonthis,pre-expo- first. The resulting species concentrations at the surface are used
nentialfactorsoftworeactionsðHNNO þM¼OHþN OþMand to determine the boundary conditions for the gas phase through
2 2
HNNO þNO )HN O Þwerechangedslightly.Finally,anoptimal theinterfacialmatchingconditions.Thenextstepinvolvesintegra-
2 2 3 4
34-speciesand165-reactiongas-phasekineticsmechanismwasob- tionofthegas-phaseconservationequationstoprovidethetem-
tainedandemployed.Thechemicalkineticswaskeptconstantfor perature and species-concentration profiles. The non-equilibrium
alloperatingpressures. evaporationrepresentedbyEq.(30)isemployedtocheckthecon-
vergence of T. If not successful, another inner iteration is per-
s
2.4.Boundaryconditions formed using an updated value of T. The outer iteration follows
s
the same procedure as the inner one, except that r is used as
b
TherearefourboundariesorinterfacesintheADNcombustion the eigenvalue to check the interfacial energy balance given by
wave:thefar-fieldboundaryofthegas-phaseflame,theinterface Eq. (29). Since only the burning rate and surface temperature,
between gas phase and foam layer, the interface between foam butnotinterfacialspeciesconcentrations,areinvolvedintheiter-
layerandsolidphase,andtheunreactedpropellantboundary. ativeprocedure,thecurrentalgorithmperformsquitewellandsig-
Far-fieldgasphaseboundary nificantlyreducesthecomputationalburden.
Thefar-fieldconditionsforthegasphaserequirethatthegradi- Eqs.(3)–(6)forthefoamlayerregionaresolvedinanuncoupled
entsofflowpropertiesbezero. manner. The method first estimates the new temperature profile
P.Thakreetal./CombustionandFlame161(2014)347–362 353
bysolvinganinertenergyequation.Conservationequationsofspe- 850
ciesconcentrationandvoidfractionarethenintegratedusingthe
fourth-order Runge–Kutta method with the temperature profile.
The energy equation is subsequently solved with the newly ob-
800
tained void fraction and species concentration profiles. Since the
K
conservationequationsaresolvedinanuncoupledfashion,several e,
iterations are required to get a converged solution to satisfy all ur
conservationequations. erat 750
p
Eqs. (15)–(17) for the gas-phase region are also fully coupled. m
e
TheyaresolvedusingtheChemkin-Premix[51]packagewithsome T
modifications.Therearetwotypesofcomputationaldifficultiesin 700 Predicted
the present theoretical formulation. One is the stiffness due to a Measured
wide variety of time and length scales associated with chemical
reactionsandtransportprocesses,whiletheotheristhecomplex-
650
ityarisingfromtheintertwinedmatchingconditionsatthepropel- 0.0 0.1 0.2 0.3 0.4 0.5 0.6
lantsurface.Thestiffnessproblemofthegas-phaseprocessescan Distance above burning surface, cm
beeffectivelycircumventedbyusingacombinedNewton-iteration
Fig.3. Predictedandmeasuredprofilesoftemperatureat3atm.
and time-integration scheme originally developed by Kee et al.
[51]. The Newton method functions efficiently for steady-state
solutions,butneedsareasonableinitialguessforsmoothconver-
0.4
gence.Thetime-integrationtechniqueismorerobust,butlesseffi-
cient.Tooptimizethebenefitsofthesetwoalgorithms,calculation
usuallystartswiththeNewtonmethodand thenswitchestothe HO
0.3 2
integrationschemewhentheiterationfailstoconverge.Afteran-
othertrialsolutionisobtainedwithseveraltime-marchingsteps, n NO
theNewtonmethodisresumedtogainefficiency.Anadaptive-grid ctio 2
a
systemisemployedtofurtherimprovetheconvergencerate,while Fr 0.2
simultaneouslyacquiringthespatialresolutionoftherapidlyvary- ole NO
M
ingflowpropertiesintheflamezone.
0.1
NH
4.Resultsanddiscussion 3
The results of the current work are divided into two sections. 0.0
0.00 0.05 0.10 0.15 0.20
First,theADNgas-phasekineticsmechanismandflamestructure
Distance above burning surface, cm
are discussed in detail. Then, results from coupled condensed-
andgas-phaseanalysesarepresentedtogiveacompletedescrip- Fig.4. Predictedandmeasuredprofilesofspeciesmolefractionsat3atm.
tionoftheADNcombustionmodel.
0.10
4.1.Gas-phasecombustionanalysis
N
2
Inordertovalidatethecurrentgas-phasekineticsmechanism, 0.08
experimental data of Korobeinichev et al. [12,42,52] were em-
HNO
ployed. The conservation equations in the gas phase are solved n 3
o 0.06
andADNgas-phaseflamestructuresat3,6,and40atmarecom- cti
puted and analyzed. The boundary conditions for gas species are Fra HONO+NO
summarizedinTable5. ole 0.04 2
Figures 3–5 show a comparison of predicted (lines) and mea- M
sured(symbols)profilesoftemperatureandspeciesmolefractions
0.02
of ADN gas-phase flame at 3atm. The agreement between pre-
dictedandmeasuredtemperatureprofileinFig.3isquitesatisfac- HDN ADN(g)
tory.ThemainproductsofADNcombustionat3atmareH O,N , 0.00
2 2
NO,N2O,andNH3.Figures4and5showthatthecalculatedcon- 0.00 0.05 0.10 0.15 0.20
centrations of NH3, N2O, NO and HNO3 match closely with the Distance above burning surface, cm
available data [42]. The N species concentration, however, is
2
slightly over-predicted. It should be noted that NO and HONO Fig.5. Predictedandmeasuredprofilesofspeciesmolefractionsat3atm.
2
could not be separated in mass-spectra experiments due to their
Table5
Boundaryconditionsforgasphaseflamecalculation.
P(atm) xa(mm) m_00(g/cm2/s) NH3 H2O N2 NO N2O ADN(v) HNO3 O2 Ref.
3 0.2 2.15 0.08 0.30 0.08 0.19 0.24 0.03 0.08 – [25]
6 4.19 3.4 0.0675 0.35 0.07 0.25 0.2225 – 0.04 – [17]
40 1.5 3.85 – 0.42 0.18 0.21 0.14 – – 0.05 [52]
a xisthedistanceabovethepropellantburningsurface.
354 P.Thakreetal./CombustionandFlame161(2014)347–362
close molecular weights (46g/mol for NO2, 47g/mol for HONO). 1500 0.5
ThepredictionofcombinedNO andHONOconcentrationsisquite
2
closetothemeasurements. T
1400
Figure5showsthatsmallconcentrationofHN(NO ) (i.e.,HDN) 0.4
22
ispredictedclosetotheburningsurface.ThepresenceofHDNin
theADNgasflamewasconfirmedbyKorobeinichev[25],although K 1300 n
taghnioenimm,pporoloermtfarpnatctitnsiopgnetchpieersopfiathlretaitwaldaoesxcniodomattpriooesnpeoosrft(eNRd4H.)3Iti(nRwt6ah)s.eIcnnoentahsrei-dsseuarrmefdaectzeoornbeee- mperature, 1200 N2O 00..23 ole Fractio
(0–0.1cm),thereisatemperatureriseofabout150K. Te 1100 M
Figure 6 shows the entire ADN gas-phase flame structure at N
2
3atm.Thefour-zoneflamestructureshowingthetemperaturerise 0.1
1000
to820K(0.1–4cm),1350K(4–9cm),1680K(10–25cm),and fi-
NH
nallyto2100K(55–100cm)isclearlyseen.Thelatterthreeflames 3
occuratfardownstreamlocationsandthereforecanbepractically 900 0.0
0.5 1.0 1.5 2.0
observed only at high pressures. The major exothermicity in the
Distance above burning surface, cm
second flame zone ((cid:2)1350K) is due to NH oxidation reactions
3
by NO2 R6, R7, and R8. The corresponding heat-releasing mecha- Fig.7. Predictedandmeasuredprofilesoftemperatureandspeciesmolefractions
nisms in the 3rd and 4th flames are the conversion of N O and at6atm.
2
NOtoN ,respectively.Theexistenceofaregionclosetothepro-
2
pellant surface, where the temperature gradient is close to zero
was obtained both in predicted and measured [24] temperature 0.5
profiles (0–0.3mm). A non-luminous region, also known as dark
zone,isseenat(cid:2)0.1–2cm,markedbyaplateauinthetemperature
0.4
profile.Inthepressurerangeof5–40atm,dark-zonetemperature
HO
plateaus were observed experimentally from 843 to 1273K [39]. 2
The existence of such dark zones in nitrate esters and nitramine on 0.3
propellantshasbeenaddressedindetailbyYangetal.[53].Figures cti
a
7and8showacomparisonofpredictedandmeasuredprofilesof Fr
temperatureandspeciesmolefractionsofADNgasflameat6atm. ole 0.2 NO
M
Theagreementsareverygood.
The present calculation results were compared with those of
Liauetal.[17]andKorobeinichevetal.[25].Theboundarycondi- 0.1
tionsusedareidentical,andtheonlydifferenceisinthegas-phase
HNO
kineticsmechanisms.Figures9–12showthatthematchobtained 3
0.0
withexperimentaldatausingthecurrentgas-phasekineticsmech- 0.0 0.5 1.0 1.5 2.0
anismismuchbetterthanthepreviousresultsfromLiauetal.[17] Distance above burning surface, cm
andKorobeinichevetal.[25].Subscripts‘‘(0),(1),and(2)’’indicate
resultsfromthepresentwork,Liauetal.[17],andKorobeinichev Fig.8. Predictedandmeasuredprofilesofspeciesmolefractionsat6atm.
et al. [25], respectively. The improvement in predictions derived
byemployingtheoptimal34speciesand165reactionsgas-phase
0.5
kineticsmechanismat6atmisevident.
T
Three distinct flames, which increase the gas-phase tempera- 1500 (1)
ture to 1400K (1–4cm), 1840K (5–15cm), and 2100K (25–
T 0.4
100cm)respectively,areshowninFig.13.Thenear-surfacezone 1400 (0)
isnotshownintheflamestructureat6atm,sincethemodelcal-
2000 0.4 emperature, K 11230000 N2O(0) N2O(1) 00..23 Mole Fraction
T
1100 N N
HO T 2(1) 2(0)
K 2 0.3 0.1
T), 1600 N on 1000 NH
emperature (1200 NH3 NN2OO NO2 2 O2 0.2 Mole Fracti 900 0.5Distance abo1v.0e burni3n(0g) surN1fa.H5ce3(,1 )cm 2.00.0
T 0.1
ADN HDN Fig.9. ComparisonofresultsofLiauetal.[17]andpresentstudyat6atm.
HNO
800 3 0.0
culations began at 0.419cm from the propellant surface, where
10-2 10-1 100 101 102 the experimental boundary conditions for species were available
Distance above burning surface, cm assummarizedinTable5.Comparingthetemperatureandspecies
profiles in Figs 6 and 13, it can be concluded that similar
Fig.6. Predictedtemperatureandspeciesmolefractionsat3atm.
P.Thakreetal./CombustionandFlame161(2014)347–362 355
0.5 2200 0.5
HO
1500 T 2
T (0) 2000
(2) 0.4
0.4
1400
K 1800 T
mperature, K 11230000 N2O(2) N2O(0) 00..23 ole Fraction emperature (T), 11460000 4 NNOO2 N2O N2 O2 00..23Mole Fraction
Te 1100 N2(2) M T 1200 NHH3NO 0.1
N 3
2(0)
0.1 1000 0.0
1000 NH
3(0) NH 100 101 102
3(2)
900 0.0 Distance above burning surface, cm
0.5 1.0 1.5 2.0
Distance above burning surface, cm Fig.13. Predictedtemperatureandspeciesmolefractionsat6atm.
Fig.10. ComparisonofresultsofKorobeinichevetal.[25]andpresentstudyat
6atm. theflamestand-offdistance,due totheincreasein thepressure-
dependentreactionrates.
Figures14and15showacomparisonofpredicted(lines)and
0.5 measured(symbols)profilesoftemperatureandspeciesmolefrac-
tions of ADN gas-phase flame at 40atm. The agreement again is
quite good at high pressure. These calculations were started at
0.4 H2O(0) HO 0.15cm,duetotheavailabilityofspeciesboundaryconditionsat
2 (1) thatlocation,as described in Table5. Figure 16shows the entire
n
e Fractio 0.3 NO oflarxaeimdsaeetesiontrnuhrceetrauecr.teiToohnfesAihDseNnaoti-tnrsehtlheoaewsgenacbsoepnchatrauisbseeu.ttOihonenlmyotofwdneoelaidnri-gsstduinorcfmatcafleianNmeHexs3-
ol 0.2 (0) tendedfrom0.15to10cm.TheconversionofN OandNOtoN is
M NO 2 2
(1) stillthemainsourceinsecondandthirdflames,respectively.The
finalflameoccursat(cid:2)10cm,muchcloserthanthecorresponding
0.1
onesobservedatlowerpressures.
Further analysis was performed to accurately estimate the af-
0.0 fectofpressureontheflamestructureandontheconcentrations
0.5 1.0 1.5 2.0
of some key species. Figures 17 and 18, respectively, show the
Distance above burning surface, cm
near-surfaceviewandtheoverallflamestructurecomparisonsat
Fig.11. ComparisonofresultsofLiauetal.[17]andpresentstudyat6atm. 3,6and40atm.Theflamestand-offdistanceisshortenedsharply
byincreasingthepressure,duetoenhancedreactionratesatele-
vatedpressure.Theagreementbetweenmeasuredandcalculated
temperature profiles at all the studied pressures is quite reason-
0.5 able.Theexistenceofdark-zonetemperatureplateausatdifferent
0.4
1800 0.5
HO HO
on 0.3 2 (2) 2 (0) 40atm
cti 1600
Fra T 0.4
ole 0.2 NO(0) 1400
M
00..01 HNO3(2)HNO3(0) NO(2) emperature, K 11020000 NO 00..23 Mole Fraction
T
0.5 1.0 1.5 2.0
Distance above burning surface, cm 800
0.1
Fig.12. ComparisonofresultsofKorobeinichevetal.[25]andpresentstudyat 600
6atm. NO
2
400 0.0
0.0 0.2 0.4 0.6 0.8 1.0
heat-release mechanisms are at play. There is a difference, how-
Distance above burning surface, cm
ever,inthelocationoftheflamesatthetwopressures.Theflames
at 6atm are closer to the propellant burning surface than their
Fig. 14. Predicted and measured profiles of temperature and mole fractions at
counterpartsat3atm.Increaseinpressureleadstoadecreasein 40atm.
356 P.Thakreetal./CombustionandFlame161(2014)347–362
0.5
40atm 2000
HO
2
0.4
40atm
ole Fraction 00..23 N2 mperature, K1500 6atm
M e
T
O 1000 3atm
0.1 2
0.0
0.0 0.2 0.4 0.6 0.8 1.0
10-1 100 101
Distance above burning surface, cm
Distance above burning surface, cm
Fig.15. Predictedandmeasuredprofilesofspeciesmolefractionsat40atm.
Fig.18. Temperatureprofilesatvariouspressures(0.1–10cm).
0.5 ucts H O, N , O , and NO and their mole fractions (0.396, 0.395,
2 2 2
40atm T 0.194, and 0.008, respectively), at various pressures (shown in
2000
HO Figs.6,13and16)arequiteclose.Pressurehaslittleinfluenceon
2 0.4 ADN final combustion products. It should also be noted that the
mole fraction of NOx in final products is less than 1%, making
mperature (T), K 11680000 N2 NO 00..23Mole Fraction ArdpeirDcaeNtTcstshtiuaeohnrnemesesAo.nATDdvDheiNrNleoinpncggormaomsrefie-bnpsleuuhtsaslatltoslsiyefosflnfkhraioinflmeweanetmdtitchleeysamtpmsptrtrehoeucperchaetcatluuulnarrrienressetma.nnatctd3alns4opwsaepdceeiaecqnsiuedmastmoaenlleeyddfpir1uar6emc5--
Te tions at pressures exceeding 40atm have not yet been obtained/
O2 compared, due to the lack of experimental data for appropriate
1400
0.1 boundaryconditions.ThereliabilityofcurrenttheADNgas-phase
kinetics mechanism in predicting temperature and species mole
NO fractions at pressures higher than 40atm should be further
2
1200 0.0 evaluated.
10-1 100 101
Distance above burning surface, cm
4.2.Coupledgasandcondensedphaseanalysis
Fig.16. Predictedprofilesoftemperatureandspeciesmolefractionsat40atm.
Theresultscalculatedbythecoupledcondensed-andgas-phase
combustionmodelareshownanddiscussedinthissubsection.Fig-
1800
ure 21a and b, respectively, show the comparison between pre-
dicted (line) and measured [25] (symbols) temperature profiles
1600 40atm inADNgasphaseflameat6atmand40atm.Thetemperaturepro-
fileisshownstartingfromthepropellantburningsurface.At6atm,
K 1400 the agreement between predictions and data is excellent up to
e, 6atm 1.4cm above the propellant surface. The difference in values
ur
at 1200
er
p
m 0.5
e
T 1000 6 3
40
0.4
800
3atm
n
6000.0 0.5 1.0 1.5 2.0 actio 0.3 3
Distance above burning surface, cm e Fr 40atm 6
ol 0.2
M
Fig. 17. Calculated and measured temperature profiles at various pressures (0–
2cm).
0.1 HO
2
NO
pressuresclose totheburningsurface isalsopredictedwell. Fig-
ures 19 and 20 show the influence of pressure on major species 0.0
10-1 100 101
(H O,N ,O ,andNO).Thecontoursofspeciesmolefractionpro-
2 2 2 Distance above burning surface, cm
files look similar in shape, except that the pressure increase has
displacedthecurvesclosertotheburningsurface.Thefinalprod- Fig.19. Speciesmolefractionprofilesatvariouspressures(0.1–10cm).