riple ames - Stanford University

Center for Turbulence Research

Proceedings of the Summer Program ��

��

The e�ects of complex chemistry on triple �ames

By T� Echekki� and J� H� Chen�

The structure� ignition� and stabilization mechanisms for a methanol �CH�OH��airtriple �ame are studied using Direct Numerical Simulations �DNS�� The methanol�CH�OH��air triple �ame is found to burn with an asymmetric shape due to thedi�erent chemical and transport processes characterizing the mixture� The excessfuel� methanol �CH�OH�� on the rich premixed �ame branch is replaced by morestable fuels CO and H�� which burn at the di�usion �ame� On the lean premixed�ame side� a higher concentration of O� leaks through to the di�usion �ame� Thegeneral structure of the triple point features the contribution of both di�erentialdi�usion of radicals and heat� A mixture fraction�temperature phase plane descrip�tion of the triple �ame structure is proposed to highlight some interesting featuresin partially premixed combustion� The e�ects of di�erential di�usion at the triplepoint add to the contribution of hydrodynamic e�ects in the stabilization of thetriple �ame� Di�erential di�usion e�ects are measured using two methods� a di�rect computation using di�usion velocities and an indirect computation based onthe di�erence between the normalized mixture fractions of C and H� The mixturefraction approach does not clearly identify the e�ects of di�erential di�usion� inparticular at the curved triple point� because of ambiguities in the contribution ofcarbon and hydrogen atoms� carrying species�

�� Introduction

Triple �ames arise in a number of practical congurations where the reactingmixture is partially premixed� The �ame has three branches re�ecting the extent ofpremixedness of the fuel and oxidizer� On the fuel side� a rich premixed �ame forms�while on the oxidizer side� a lean premixed �ame forms� Behind the two branches�a di�usion �ame forms where excess� fuel and oxidizer burn� The premixed �amebranches provide both a source of reactants �excess from the primary premixed�ames� for the di�usion �ame and a mechanism for its stabilization and ignition atthe triple point �the location where the three branches meet��

During the last two decades a number of studies of triple �ames have been car�ried out to understand the mechanisms of stabilization and their structure usingsimplied models of chemistry and transport �Hartley � Dold� � �� Kioni et al�� Lakkaraju� � �� Ruetsch et al�� Domingo � Vervisch� � �� and Wich�man� � �� Recently� computations by Terhoeven � Peters �� have shown

� Sandia National Laboratories

�� T� Echekki � J� H� Chen

the signicance of complex chemistry and realistic transport to the structure andstabilization of triple methane�air �ames�

In the context of complex chemistry and transport e�ects� a number of questionspertaining to the �ame structure� ignition at the triple point and propagation remainunanswered� The structure of the premixed �ame on the rich and lean branches isexpected to be asymmetrical because of the inherent asymmetry in the �ammabilitylimits� reacting mixture composition� and burning rates of the �ame� In the di�usionbranch� the primary fuel may not be the original fuel that burns on the premixedside� In the computations of Terhoeven � Peters �� only a small fractionof the primary fuel� methane� survives near the triple point� Instead� more stablemolecules such as CO and H� provide the needed fuel to burn in the di�usion �ame�

Moreover� the di�usion �ame is anchored to the premixed branches at the triplepoint by both preheating and di�usion of radicals including H� O� and OH� Theseradicals di�use at rates which are signicantly di�erent from di�usion rates of heatand result in di�erential di�usion e�ects at the triple point� The coupling of cur�vature and di�erential di�usion e�ects at the triple point may also display itselfin enhanced burning rates and� thereby� enhanced propagation of the triple point�The same di�erential di�usion e�ects along with chemistry determine the structureand location of the di�usion branch of the triple �ame�

The object of this study is to determine the structure and mechanisms of ignitionand stabilization of triple methanol �CH�OH��air �ames in a laminar free shearlayer conguration using detailed chemistry and a realistic transport model� Thechoice of methanol as a fuel presents some advantages with regard to the complexityof the chemical system and the numerical treatment� The full range of �ammabilitymay be adequately described using C� chemistry� It displays some of the inter�esting features in its structure which are common among hydrocarbons �e�g� thetwo�layer structure corresponding to fuel� and radical consumption� and H� andCO oxidation�� In the following sections� the governing equations and numericalconguration are described� A discussion of the triple �ame structure and the con�tribution of chemistry and transport to its ignition and stabilization is presented�

�� Governing equations and numerical con�guration

The triple �ame in a laminar mixing layer between methanol �CH�OH� fuel andair as oxidizer is computed using DNS with a C� mechanism for chemistry �Warnatzet al�� The numerical scheme is based on the solution of the Navier�Stokes�species� and energy equations for a compressible gas mixture with temperature de�pendent properties� The equations are solved using an eighth�order explicit nitedi�erence scheme �Kennedy � Carpenter� � �� for approximating spatial deriva�tives and a fourth�order low storage Runge�Kutta scheme for time advancement�Kennedy � Carpenter� � �� A modied version of the Navier�Stokes Character�istic Boundary Conditions �NSCBC� procedure originally developed by Poinsot �Lele �� is used to account for variable specic heats �Card et al�� The

Triple �ames ��

Fuel

O2

Leakage of O2

H2/CO at the proximity of

the triple point

triple point/tip: preferential diffusion effects

Fuel(s) diffuse

oxidizer diffuse

diffusion flame

lean premixed flame

rich premixed flame

��

��

Figure �� Numerical conguration�

boundary conditions are non�re�ecting in all directions� The species mass di�usionis modeled with a Lewis number formulation and a prescription of the Lewis num�bers for the di�erent species �Smooke � Giovangigli� � �� The values of the Lewisnumbers for the species is given in Table �� The Prandtl number� Pr � �Cp�� isset to a constant of ��

For the C� methanol �CH�OH� mechanism� conservation equations for fteen re�acting species are considered �see Table �� and the mass fraction of N� is obtained

through the relationshipPN

�� Y� � �� where N � �� The computational con�guration is shown in Fig� �� The initial mixture is preheated to �� K� The eldis initialized with stoichiometric one�dimensional �ame proles which are modiedspatially over a bu�er domain of thickness L to re�ect the desired inlet composition�The inlet conditions are maintained constant during the computations� The inletvelocity is xed at the stoichiometric �ame speed� SL� no attempt to stabilize the�ame is made� The methanol� oxygen� and its corresponding proportion of nitrogen�in air� in the bu�er domain are based on self�similar solution proles of the mixturefraction� �� They are prescribed as follows�

��x� y� t � �� st� �

�� exp

��

�x �L

�

��

�� exp

��

�L

�

�� erf

�y�

�� st� ��

Here� � is the mixture fraction expressed as follows�

� �Z� � Z�

O

Z�

F �Z�

O�


where the subscripts F and O denote the fuel and oxidizer streams� respectively�Z� is expressed in terms of the elemental mixture fraction �three elements make upthe reacting species� C� H� and O�� Zi as follows �Warnatz et al��

Z� �

elem�Xi��

�i Zi� ��

The element mass fraction� Zi� is dened as Zi �PN

�� i�Y�� N �where �i� is the mass proportion of the element i in the species � �e�g� for hydrogenatom in methane� it is �� In terms of the species mass fraction� Z� may be written

as Z� �PN

��

� Y�� where �� Pelem�

i�� i �i��

species Le

H� ��O� ��O ��

OH ��H�O ��

H ��HO� ��H�O� ��CO ��CO� ��

CH�O ��CHO ��

CH�OH ��CH�OH ��CH�O ��

Table �� Lewis Numbers of Reacting Species�

In Eq� �� st denotes the stoichiometric mixture fraction� � is the characteristicthickness of the mixing region in the y direction� � is the bu�er region charac�teristic thickness� In the spatial and temporal variations� the rate of variations ofmixture fraction proles in x are specied as Gaussian functions with characteristicthicknesses� �� For hydrocarbon fuels� Bilger et al� �� propose ��WC � ��WH�and ��WO as coe�cients �i �Eq� �� for the carbon �C�� hydrogen �H�� and oxygen�O� elements� Here� WC � WH and WO are the atomic weights of C� H� and O�The proposed coe�cients have been used in turbulent methanol di�usion �amesby Masri et al� �� The stoichiometric mixture fraction for the methanol�airmixture based on these coe�cients is �st � ��


A single computation is carried out with a mixture fraction characteristic thick�ness of ��F � �� The �ame thermal thickness� �F � corresponds to the stoichio�metric premixed methanol�air �ame and is dened as follows�

�F �Tb � Tu

�dT�dx�max�

where the subscripts u and b refer� respectively� to the unburnt and burnt gases�The bu�er domain size� L��F � and its characteristic thickness� ��F � are �� and�� respectively� The computational domain is �� by �� grid points�

�� Numerical diagnostics

The DNS yields detailed information about the �ow eld and various scalars char�acterizing the structure of the triple �ame� In this section� diagnostic approachesused to identify the pertinent features of the triple �ame are described�

�� Reaction �ow analysis

The primary objective of reaction �ow analysis �Warnatz et al�� is to iden�tify the primary reactions which contribute to the production or consumption of aparticular species or to the rate of heat release�

�� Quantitative analysis of di�erential di�usion e�ects

Di�erential di�usion represents a non�negligible phenomenon in hydrogen andhydrocarbon �ames in regions of strong curvature� It contributes to the enhance�ment of the burning intensity due to the strong chemical role played by hydrogenatoms and molecules in these �ames and their fast rate of di�usion� To identifythe strength of di�erential di�usion e�ects� in particular at the triple point in the�ame� two approaches are considered� The rst is based on the computation of thedi�usion velocities of the various reactive species in the mixture which representa direct measure of di�erential di�usion e�ects� From the formulation describedearlier� the di�usion velocity of species� �� may be written as follows�

V�j � �D�N

�

Y�

Y�xj

� � � �� N � ��

An alternate and indirect method of identifying strong di�erential di�usion e�ectsis to compute the di�erence between elemental mass fractions �Bilger� � �� Bilger� Dibble� � �� Drake � Blint� � �� Smith et al�� In the present work�the di�erence� zC�H� between elemental mass fractions of C atom and H atoms iscomputed�

zC�H � �C � �H �

where

�C �ZC � ZC�OZC�F � ZC�O

�ZC

�C�CH�OH

� �H �ZH � ZH�O

ZH�F �ZH�O

�ZH

�H�CH�OH �


A di�erent formulation of the di�erential di�usion parameters is to compute corre�lations between �C and �H�

It is important to note that there is a fundamental limitation in the interpretationof the di�erence between �C and �H in terms of di�erential di�usion e�ects alone�The contribution to these quantities comes from carbon�carrying and hydrogen�carrying species in which the particular C and H may not play a signicant role inits transport properties�

�� Flame propagation

The propagation of the �ame may be tracked by evaluating a displacement speedof the front relative to the �ow eld� This quantity may be evaluated exactly fromthe numerical results when a �ame surface is tracked with a particular scalar isocon�tour �such as hydrogen molecule mass fraction�� An expression for the displacementspeed� Sd� based on tracking a constant mass fraction contour may be obtained�Ruetsch et al�� by writing the Hamilton�Jacobi equation and substitution ofthe governing species equation�

Sd � uS�

d ��

jrY�j

xj

�D�

Y�xj

��

� ��

In this expression� S�

d is the density�weighted displacement speed� In this generalform� the displacement speed measures the velocity of a scalar iso�contour �i�e� the�ame�front� relative to the local gas� The value of Sd depends on the location inthe �ame where it is measured� The use of the product Sd or S�

d tends to reducethermal expansion e�ects due to the choice of the location where Sd is measured�Under strictly one�dimensional planar �ame condition� this quantity is constant� Inthe reaction zone� the value of the density�weighted displacement speed� S�

d� re�ectsprimarily the chemical contribution� However� with the exception of perhaps anarrow region in the reaction zone� Sd is subject to additional e�ects resultingfrom the processes in the preheat zone�

A measure of the triple �ame stabilization mechanisms is its speed relative tothe cold gas� It may be evaluated using the same approach adopted by Ruetsch� Broadwell �� This speed contains both the contributions from chemicaland hydrodynamic�di�usive e�ects �Echekki� � � � � �� Poinsot et al�� To evaluate the hydrodynamic�di�usion contribution� the velocity� Vf � of the triplepoint relative to the unburnt gas is evaluated� Vf � at the leading edge of the �ame�may be evaluated using the following relation�

Vf � �Sd � uf � � u��

where uf is the gas velocity at the �ame location where the displacement speed iscomputed� The term �Sd� uf represents the Lagrangian speed of the triple point�The speed u� is the unburnt gas velocity at the inlet of the computational domainprior to the onset of lateral �ow expansion and cross�stream di�usion e�ects� Notethat� although Sd and uf vary along the �ame� the combined speed� �Sd � uf � isconstant in the �ame under steady �ow conditions�


� General structure of the triple ame

In what follows� a description of the general structure of the methanol �CH�OH��air triple �ame is given in terms of reactant� radicals� and heat release rate proles�

�� Reactants and products pro�les

Figure � shows the isocontours of the major species �reactants and products�mass fractions in the triple �ame� The gure shows no leakage of the fuel beyondthe primary premixed �ame �Fig� �c�� Beyond the premixed �ame front� methanol�CH�OH� is decomposed into more stable fuels which include CO� H�� and H� Onthe lean side� O� survives through the premixed �ame and di�uses towards thestable reactants from the fuel side� A reduction in the fuel concentration acrossthe premixed �ame has also been observed by Terhoeven � Peters �� in theirmethane�air �ame� albeit to a lesser extent� In addition to its oxidation by radicalspecies in the C� chain� methanol pyrolyzes in the preheat zone �Seshadri et al��

The reaction rates governing the premixed �ame chemistry exhibit additionalasymmetries� as shown in Fig� �� The oxidation of methanol proceeds down theC� path� CH�OH � CH�OH � CH�O � HCO � CO � CO�� The oxidation ofmethanol through HCO occurs in the premixed branches� whereas the remainingoxidation steps are present in all three branches� In addition to CO� the stablemolecule H�� which is produced on the rich premixed �ame side� is also oxidizedin the di�usion �ame� All fuels in the premixed and di�usion �ame are beingoxidized primarily by radical species H� OH� and O� While H and OH play a moreimportant role in the oxidation process on the rich premixed branch� oxidationreactions involving O atom play a more signicant role on the lean side�

The reaction rates governing the premixed �ame chemistry exhibit additionalasymmetries� as shown in Fig� �� For example� the peak production rates of H�

and CO occur on the fuel rich side due to the consumption of H atom and OH byhydrocarbon intermediates� A further asymmetry appears in the inclination of thedi�usion �ame towards the lean premixed �ame� This inclination may be primarilyattributed to the rates of di�usion of H� relative to O� such that the reaction zoneof the di�usion �ame is at the stoichiometric mixture� The consumption rate ofCO� as shown in Fig� �e� also exhibits some inclination towards the lean branch�CO is consumed primarily by OH in the water gas shift reaction� an importantreaction contributing to the overall heat release� the asymmetry is due to the peakproduction of OH occurring on the lean side due to the elementary chain branchingreaction� O� � H � OH � O�

�� Radical pro�les

Figure � shows the radical proles for H� O� OH� and CH�O in the �ame� Thisgure shows that O and H atoms peak at the triple point� OH� on the otherhand� peaks behind the primary reaction zones of the premixed �ames and along


0.0 0.5 1.0 1.5 2.0

-0.5

0.0

0.5

0.0020.004

0.0060.008

0.01

(H2)

a) 0.0 0.5 1.0 1.5 2.0

-0.5

0.0

0.5

0.2

0.16

0.12

0.08

b)

(O2)

0.0 0.5 1.0 1.5 2.0

-0.5

0.0

0.5

0.10.06

0.040.02 0.08

d)

(CO2)

0.0 0.5 1.0 1.5 2.0

-0.5

0.0

0.5

0.04

0.080.12

0.160.2

(CO)

e) 0.0 0.5 1.0 1.5 2.0

-0.5

0.0

0.5

0.0150.045

0.0750.105

0.135

f)

(H2O)

0.0 0.5 1.0 1.5 2.0

-0.5

0.0

0.5

0.07

0.21

0.350.490.630.7

(CH3OH)

c)

Figure �� Major species mass fraction proles �a� H�� b� O�� c� CH�OH� �d�CO�� e� CO� and �f� H�O�

the mean reaction zone of the di�usion �ame branch� The radical OH has a slowrecombination rate compared to O and H atoms and� therefore� accumulates andpeaks in the di�usion �ame�

Figure � shows the the contribution of the di�erent reactions to the productionand consumption of H� O� OH� and CH�O� The radicals H� O� and OH are producedbehind the fuel consumption layer near the burnt gas side of the �ame� and di�useupstream towards the unburnt gas to react in the fuel and radical consumptionlayer� The molecule H�� on the other hand� is produced in the fuel and radicalconsumption layer and is consumed in the region of radical production in the H�

oxidation layer� The convex shape of the triple point �ame towards the burnt gasfocuses H� towards its oxidation layer� The peak production of H� in the triple �ame


0.0 0.5 1.0 1.5 2.0

-0.5

0.0

0.5

a)

(H2)CH3OH+H=CH2O+H2

CH2O+H=HCO+H2

CH2OH+H=CH2O+H2

H2+OH=H2O+H

H2+O=OH+H

0.0 0.5 1.0 1.5 2.0

-0.5

0.0

0.5 (CH3OH)

c)

CH3OH+H=CH2OH+H2

CH3OH+OH=CH2OH+H2OCH3OH+O=CH2OH+OH

0.0 0.5 1.0 1.5 2.0

-0.5

0.0

0.5 (O2)

O2+H=OH+O

b)

0.0 0.5 1.0 1.5 2.0

-0.5

0.0

0.5 (CO2)

d)

CO+OH=CO2+H

0.0 0.5 1.0 1.5 2.0

-0.5

0.0

0.5(CO)HCO+M=CO+H+M

HCO+H=CO+H2HCO+OH=CO+H2OHCO+O2=CO+HO2

CO+OH=CO2+H

e) 0.0 0.5 1.0 1.5 2.0

-0.5

0.0

0.5CH2O+OH=HCO+H2O

CH3OH+OH=CH2OH+H2O

H2+OH=H2O+H

f)

(H2O)

Figure �� Major species reaction rate proles �a� H�� b� O�� c� CH�OH� �d�CO�� e� CO� and �f� H�O� Production rates� � consumption rates� �

occurs at the triple point region on the rich side of the premixed �ame� It resultsprimarily from the break up of the fuel and its reactions with radicals� especiallyH� The primary mechanism for H� consumption results from radical production �inthe H� oxidation layer� through the following reactions�

H� �OH� H�O�H�

andH� �O� OH�H�

The latter reaction is a signicant chain branching reaction which plays a majorrole in the rate of �ame propagation and radical production� By the focusingof H� towards its oxidation �consumption� zone� the rate of radical production isenhanced and the propagation speed is increased� An additional chain branchingreaction which is responsible for the bulk of production of O and OH is the followingreaction�

O� �H� O�OH�


0.0 0.5 1.0 1.5 2.0

-0.5

0.0

0.5

0.000450.00030.00020.0001

a)

(H)

0.0 0.5 1.0 1.5 2.0

-0.5

0.0

0.5

0.004

0.002

b)

(O)

0.0 0.5 1.0 1.5 2.0

-0.5

0.0

0.5

0.0090.008

0.003

c)

(OH)

0.0 0.5 1.0 1.5 2.0

-0.5

0.0

0.50.045

0.030.015

d)

(CH2O)

Figure �� Minor species mass fraction proles �a� H� �b� O� �c� OH� and �d�CH�O�

0.0 0.5 1.0 1.5 2.0

-0.5

0.0

0.5

a)

(H)CH2O+H=HCO+H2

H2+OH=H2O+H

H2+O=OH+HCO+OH=CO2+H

HCO+M=CO+H+M

O2+H=OH+OHO2+H=OH+OH

0.0 0.5 1.0 1.5 2.0

-0.5

0.0

0.5

b)

(O)CH3OH+O=CH2OH+OH

CH2O+O=HCO+OHH2+O+OH+H

HO2+O=OH+O2

O2+H=OH+O

H2+O=OH+H

0.0 0.5 1.0 1.5 2.0

-0.5

0.0

0.5

d)

(CH2O)CH2OH+O2=CH2O+HO2

CH2OH+M=CH2O+HM

CH2OH+H=CH2O+H2

CH2O+OH=HCO+H2O

CH2O+O=HCO+OH

CH2O+H=HCO+H2

0.0 0.5 1.0 1.5 2.0

-0.5

0.0

0.5

c)

(OH)CH3OH+OH=CH2OH+H2O

CH2O+OH=HCO+H2OH2+OH=H2O+HHO2+OH=H2O+O2

O2+H=OH+O

H2O+O=OH+OH

H2+O=H+OH

Figure �� Minor species reaction rate proles �a� H� �b� O� �c� OH� and �d�CH�O� Symbols as in Fig� ��


While the H atom in this reaction is defocused at the triple point by the samemechanism that focuses H�� the net e�ect is the enhanced concentration of radicalspecies at the triple point� The enhanced activity in this region also contributes tothe ignition and anchoring of the trailing di�usion �ame�

�� Parameterization of triple �ame structure

The two�dimensional structure of the triple �ame and the variation of the de�gree of premixedness in the reacting mixture suggest that at least two phase�spaceparameters may be required to fully describe the triple �ame structure� Figure �shows overlays of the mixture fraction �Bilger et al�� proles with H� reac�tion rate and temperature� The consumption rate of H� is used to illustrate thealignment of reaction rates in the di�usion �ame with isocontours of the mixturefraction� The mixture fraction changes monotonically across the di�usion �ame�This suggests that the mixture fraction may be a useful progress variable in thisbranch� Temperature plays a similar role in the premixed branches� In this section�we choose temperature and mixture fraction to parameterize the �ame structure�The two parameters� � and T � e�ectively span the entire range of reaction andmixedness� The mixture fraction is a measure of the degree of mixedness� while thetemperature is a measure of the extent of reaction�

Figures � and � show the mass fractions and reactions rates for the major speciesin phase space� while the corresponding gures for the minor species are shown inFigs� and �� Overlayed on these gures is the maximum consumption rate of O�

in the premixed �thick solid lines� and the di�usion �thick dashed lines� branches�The maximum consumption rate of O�� the only reactant which is consumed inthe premixed and di�usion �ames� is used to demarcate the three branches of the�ame� These gures highlight the di�erent topologies of the �ame which may not beapparent in physical coordinates� particularly if the �ame is distorted signicantlyby the �ow eld� Shifts in concentration or reaction peaks on the lean and richsides and the delineation between di�usion and premixed branches are made morepronounced using this parameterization� Similarly the delineation of reactions andspecies that are present in the premixed branches versus the di�usion �ame is mademore clear� For example�

�� the peak production rates for formaldehyde �CH�O�� H� and CO occur on therich side of the �ame in the premixed branch� while the peak consumption ofH� and CO persists to very lean conditions�

�� the peak consumption of H occurs on the rich side� whereas the peak consump�tion of O atoms occurs on the lean side of the �ame�

�� the peak concentrations of CH�O� H�� and CO exist well into the rich side�

�� the peak radical concentrations for O and H exist near the triple point and onthe lean sides respectively� whereas OH peaks in the di�usion �ame�


0.0 0.5 1.0 1.5 2.0

-0.5

0.0

0.5

0.0 0.5 1.0 1.5 2.0

-0.5

0.0

0.5

0.05

0.150.250.350.50.60.7

0.0 0.5 1.0 1.5 2.0

-0.5

0.0

0.5

0.0 0.5 1.0 1.5 2.0

-0.5

0.0

0.5 9001100

1300160

0

1800

2000

2200

0.0 0.5 1.0 1.5 2.0

-0.5

0.0

0.5

0.05

0.150.250.350.50.60.7

0.0 0.5 1.0 1.5 2.0

-0.5

0.0

0.5

Figure �� Overlay of mixture fraction proles with H� reaction rate �left� andtemperature �right�� The wide solid line denotes the stoichiometric mixture fractionisocontour� The mixture fraction isocontours are shown in dashed lines�

0.1 0.2 0.3 0.4 0.5 0.6 0.7800

1000

1200

1400

1600

1800

2000

2200

0.001

0.003

0.0050.007

0.01

T (K)

ξa)

(H2)

0.1 0.2 0.3 0.4 0.5 0.6 0.7800

1000

1200

1400

1600

1800

2000

2200

0.07

0.14

0.21

0.28

0.35

0.42

0.49

0.56 0.63

0.7

T (K)

ξc)

(CH3OH)

0.1 0.2 0.3 0.4 0.5 0.6 0.7800

1000

1200

1400

1600

1800

2000

2200

0.01

0.03

0.05

0.07

T (K)

ξ

(CO2)

d)

0.1 0.2 0.3 0.4 0.5 0.6 0.7800

1000

1200

1400

1600

1800

2000

2200

0.02

0.06

0.10.16

T (K)

ξe)

(CO)

0.1 0.2 0.3 0.4 0.5 0.6 0.7800

1000

1200

1400

1600

1800

2000

2200

0.014

0.042

0.07

0.098

0.126

T (K)

ξ

(H2O)

f)

0.1 0.2 0.3 0.4 0.5 0.6 0.7800

1000

1200

1400

1600

1800

2000

2200

0.2

0.16

0.12

0.08

0.04

T (K)

ξ

(O2)

b)

Figure �� Major species mass fraction for H�� O�� CH�OH� CO�� CO and H�Oin ��T phase space� The bold solid line demarcates the premixed branches� Thebold dashed line demarcates the di�usion branch�


�� while O� exists behind the premixed �ame� there is no leakage of methanol orformaldehyde behind the premixed branches�

�� Propagation of the triple ame and its stabilization

In this section� the values of the propagation speeds are reported using the massfraction of H� to track the �ame surface� Other scalars yield similar results� Theratio of density�weighted displacement speed� S�

d � to the laminar stoichiometric�ame value� SL� at the leading edge of the triple �ame is �� Since S�

d is measuredin the reaction zone� its enhancement relative to the laminar value is primarilyattributed to an enhancement in the burning intensity of the �ame �Sec� �� dueto the coupling of di�erential di�usion with curvature�

Another quantity of relevance to the stabilization mechanism of the triple �ameis the �ame speed relative to the unburnt gas� Vf �Sec� �� The ratio� Vf�SL��based on H� mass fraction is �� The approximately �� enhancement in Vf maybe attributed primarily to hydrodynamic�di�usive e�ects associated with lateral�ow expansion and cross�stream di�usion� Ruetsch et al� �� show that theratio� Vf�SL�� may be approximated by the square�root of the inverse density

ratio across the �ame�pu�b� or by the temperature ratio�

pTb�Tu� In the current

computation� the quantitypTb�Tu �

p�� compares well with the

computational values for Vf�SL�� after subtraction of the chemical contribution�

�� Di erential di usion e ects

In the previous sections� we have identied some contributions to the triple �amestructure which result from di�erential di�usion e�ects� �a� the inclination of thedi�usion branch towards the lean premixed branch� �b� the enhancement of thedisplacement speed� and �c� the ignition at the triple point� There are a number ofapproaches in the literature which attempt to quantify these e�ects� In this section�two approaches to investigate di�erential di�usion e�ects are compared� Figure ��shows correlations of the elemental mixture fractions based on C and H in thetriple �ame� Elemental mixture fractions may only be modied by transport sincereaction does not modify the atomic composition of a mixture� The gure showsthat on the unburnt gas side� the values of �C and �H are the same� and that bothre�ect the local unburnt gas composition of the methanol �the correlation is shownby the diagonal line of �C vs� �H�� In the reaction zone of the premixed branches��C is smaller than �H � although this di�erence is not signicant and it re�ects theproduction of relatively fast di�usive species such as H�� The di�erence between thetwo quantities is reversed behind the rich branch� There� the greatest contributionto �C comes from CO� while the main contribution to �H is from H�O and H�� Inthis region� the decit in H may be a result of the di�usion of H� and H towardsthe di�usion �ame� On the oxidizer side of the di�usion �ame� �C is lower than�H � In this region� the main contribution to �H is from H�O� and for �C is CO��There is no distinct behavior at the triple point from �C and �H contours� The


0.1 0.2 0.3 0.4 0.5 0.6 0.7800

1000

1200

1400

1600

1800

2000

2200

ξ

T (K)

a)

(H2)

0.1 0.2 0.3 0.4 0.5 0.6 0.7800

1000

1200

1400

1600

1800

2000

2200

(O2)

ξ

T (K)

b)

0.1 0.2 0.3 0.4 0.5 0.6 0.7800

1000

1200

1400

1600

1800

2000

2200

T (K)

ξ

(H2O)

f)

0.1 0.2 0.3 0.4 0.5 0.6 0.7800

1000

1200

1400

1600

1800

2000

2200

T (K)

d) ξ

(CO2)

0.1 0.2 0.3 0.4 0.5 0.6 0.7800

1000

1200

1400

1600

1800

2000

2200

T (K)

(CO)

e) ξ

0.1 0.2 0.3 0.4 0.5 0.6 0.7800

1000

1200

1400

1600

1800

2000

2200

T (K)

(CH3OH)

c) ξ

0.1 0.2 0.3 0.4 0.5 0.6 0.7800

1000

1200

1400

1600

1800

2000

2200

T (K)

(CO)

e) ξ

Figure �� Major species reaction rate for H�� O�� CH�OH� CO�� CO and H�Oin ��T phase space� Symbols as in Fig� ��

0.1 0.2 0.3 0.4 0.5 0.6 0.7800

1000

1200

1400

1600

1800

2000

2200

0.00010.0002

T (K)

ξ

(H)

a) 0.1 0.2 0.3 0.4 0.5 0.6 0.7800

1000

1200

1400

1600

1800

2000

2200

0.00

1

0.00

2

T (K)

ξb)

(O)

0.1 0.2 0.3 0.4 0.5 0.6 0.7800

1000

1200

1400

1600

1800

2000

2200

0.002

0.00

5

T (K)

ξ

(OH)

c) 0.1 0.2 0.3 0.4 0.5 0.6 0.7800

1000

1200

1400

1600

1800

2000

2200

0.005

0.01

0.015

0.020.025

T (K)

ξ

(CH2O)

d)

Figure � Minor species mass fraction for H� O� OH and CH�O in ��T phasespace� Symbols as in Fig� ��


0.1 0.2 0.3 0.4 0.5 0.6 0.7800

1000

1200

1400

1600

1800

2000

2200

T (K)

ξ

(H)

a) 0.1 0.2 0.3 0.4 0.5 0.6 0.7800

1000

1200

1400

1600

1800

2000

2200

T (K)

ξ

(O)

b)

0.1 0.2 0.3 0.4 0.5 0.6 0.7800

1000

1200

1400

1600

1800

2000

2200

T (K)

ξ

(OH)

c) 0.1 0.2 0.3 0.4 0.5 0.6 0.7800

1000

1200

1400

1600

1800

2000

2200

T (K)

d) ξ

(CH2O)

Figure �� Minor species reaction rate for H� O� OH� and CH�O in ��T phasespace� Symbols as in Fig� ��

0.0 0.5 1.0 1.5 2.0

-0.5

0.0

0.5

1.0

0.010.03

0.05

0.1-0.03-0.03

-0.02

-0.04

0.06 0.070.08

0.09

-3.72E-9

-0.01

-0.02

-0.0

1

0.0 0.2 0.4 0.6 0.80.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

ξH

ξC

Figure �� Correlation of C and H elemental mixture fractions� Left� �C � �H�right� �C vs� �H�

principal limitation of the mixture fraction approach as a measure of di�erentialdi�usion e�ects is now more apparent� the value of the elemental mixture fractiondoes not tell us whether the higher or lower element composition in a given regionis a result of its transport by a species which is fast or slow di�using� Hydrogen� forexample� may be present in both H�O or H�� but the two species have very di�erentdi�usivities� At the triple point� minor species such as H atom may not contribute


0.0 0.2 0.4 0.6 0.8 1.0

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.15

0.2

0.25

0.3

0.0 0.2 0.4 0.6 0.8 1.0

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.01

0.0110.011

0.0120.013

Figure �� Di�usion velocities of H and CO normalized by the stoichiometricone�dimensional �ame speed� Left� VH�SL� right� VCO�SL�

signicantly to the elemental mixture fraction despite their important role in thechemistry of the �ame�

Another indication of the role played by di�usional transport and its couplingwith curvature may be demonstrated by the magnitudes of the di�usion velocity ofH and CO shown in Fig� �� This gure shows that the maximum di�usion velocityis found near the triple point of the �ame� This velocity corresponds to more thana two�fold increase for H relative to the remaining premixed branches� The increasein the di�usion velocity of CO is only �� The peak value of the di�usive velocityfor H is approximately thirty times higher than that of CO� The use of di�usionvelocities to quantify di�erential di�usion e�ects shows signicantly di�erent trendsthan the elemental mixture fraction approach�

�� Concluding remarks

The structure� propagation and stabilization mechanisms of a methanol�air triple�ame is investigated using DNS� The computations show that the primary fuel�methanol� is consumed entirely through the premixed branches of the �ame and isconverted to more stable fuels� H� and CO� for the di�usion �ame behind the triplepoint�

In the triple point region� the coupling of curvature and di�erential di�usion ofhydrogen molecules results in enhanced radical production and� in turn� an enhance�ment in the �ame propagation speed� However� hydrodynamic e�ects �associatedwith heat release in the �ame� are more important in the current computations�These e�ects are predicted adequately by the model by Ruetsch et al� ��

A mixture fraction�temperature parameterization of the triple �ame structureis proposed� The approach attempts to separate mixedness and reactivity� andhighlights some of the interesting features of partially�premixed combustion�


A comparison between two approaches to identify the e�ects of di�erential dif�fusion is carried out� The rst approach is based on a direct computation of themagnitude of the di�usion velocity of the various species� The second is basedon the comparison of elemental mixture fractions based on carbon and hydrogenatoms� The comparison between the two approaches shows that the second ap�proach is strongly dependent on the species carrying the atoms and may not be agood indicator of di�erential di�usion e�ects�

Acknowledgments

This research was supported by the United States Department of Energy� O�ceof Basic Energy Sciences� Chemical Sciences Division� We would like to thank Profs�Amable Li�n�an and Forman Williams� and Drs� Greg Reutsch and Arnaud Trouv�efor many fruitful discussions�

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