a study of flame observables in premixed methane - air flames

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A Study of Flame Observables in Premixed Methane -Air FlamesH. N. NAJM a , O. M. KNIO b , P. H. PAUL a & P.S. WYCKOFF aa Sandia National Laboratories , Livermore, CA, 94551b The Johns Hopkins University , Baltimore, MD, 21218Published online: 05 Apr 2007.

To cite this article: H. N. NAJM , O. M. KNIO , P. H. PAUL & P.S. WYCKOFF (1998) A Study of Flame Observables in PremixedMethane - Air Flames, Combustion Science and Technology, 140:1-6, 369-403, DOI: 10.1080/00102209808915779

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Combust, Sci, andTech., 1998, Vol. 140,pp. 369-403Reprints availabledirectly from the publisherPhotocopyingpermitted by licenseonly

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A Study of Flame Observablesin Premixed Methane - Air Flames

H. N. NAJM·· *,O. M. KNIO b, P.H. PAUL·

and P. S.WYCKOFF·

• Sandia Nationa/ Laboratories, Livermore, CA 94551;b The Johns Hopkins University, Baltimore, MD 21218

(Received 25 June 1998; /n tina/form 30 September 1998)

The use of particular experimental flame observables as flame markers, and as measures offlame burning and heat release rates requires the establishment of robust correlations betweenthe particular observable and the rate in question. In this work, we use a compilation of resultsfrom numerical computations of the interaction of a premixed methane flame with a twodimensional counter-rotating vortex pair using detailed kinetics. The data set involves the useof two different chemical mechanisms, a two-fold variation in flow time scales, and theexamination of both stoichiometric and rich methane flames. Correlations between a numberof flame observables and heat release and burning rates are examined. We study HCO,'\l . v, OH, CH, CO, CH 3, CH 20, CHi, and C2H 2, as well as various concentration products(surrogates for production rates) including [OHJ(CH20), (OHJ(CH4) , and [OHJ(CO). Otherconcentration products expected to relate to chemiluminescent observables such as CH., OH·and CO; are also studied. HCO mole fraction is found to have the best correlation with flameburning and heat release rates for all cases studied. Results suggest that significant scatter due toflow unsteadiness is expected from correlations of peak 'V. v, CO mole fraction gradient, C2H 2mole fraction, and CH· with heat release. Changes in stoichiometry are found to adverselyaffect the correlation expected from peak CO, OH, OH gradient, CH, CH 3, and [OH][CH,O).Little scatter is observed in the [OH][CH20) data, highlighting its utility in the absence ofsignificant variation of reactants composition. We observe evidence of useful correlations ofpeak [OH][CH 4) and [OH][CO). Concentration products of the precursors of OW and COi arealso found to correlate well with peak heal release rate. Peak CH,O data is found to have goodcorrelation with peak burning and heat release rates, with small scatter, and little correlationshift due to changes in reactants composition.

Keywords: Flame; observables; methane; HCO; heat release; premixed

• Address for correspondence: Sandia National Laboratories, P.O. Box 969, MS 9051,Livermore, CA 94551. Tel./Fax:. (925) 294-2054/2595, e-mail: [email protected]

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INTRODUCTION

H. N. NAJM et al.

Proper evaluation of the performance of combustion systems requiresaccurate experimental determination of local flame burning and heat releaserates. However, these rates are not directly measurable. Rather, specificobservable flame parameters are typically measured and used to infer theirvalues. This necessary approach assumes an implicit correlation betweenthe particular flame observable and the rate quantity in question. Detailedcomputations of flame-flow interaction in unsteady multidimensional floware useful for investigating the quality of these correlations, and forhighlighting the utility of specific observables that are found to offer goodcorrelations.

This was done recently by Najm et al. [43], where the adequacy of certainflame observables as measures of flame burning and heat release rateswas evaluated using both numerical and experimental data. Numerical resultswere based on a computed interaction between a freely propagating premixedmethane-air flame and a two-dimensional (2D) counter-rotating vortex pair,using a C, chemical mechanism [64] under stoichiometric conditions.Experimental results were based on Planar Laser Induced Fluorescence(PLIF) measurements in a V-flame geometry, where a 2D vortex-pair isgenerated and allowed to impinge into one leg of the V-flame. One flameobservable considered in [43] is the local flow dilatation rate V'. v. Mungalet al. [40] determined V'. v experimentally from 2D PlV velocity fieldmeasurements and used it as a flame marker. Peak V'. v has also been usedas a measure of flame heat release rate [37]. Najm et al., demonstrated thatpeak V'. v is a good measure of peak heat release rate under steady state IDflame conditions. On the other hand, their results indicated that thiscorrelation fails under conditions of high unsteadiness with significantstrain-rate and curvature disturbances to internal flame structure. This is dueto the contribution of the heat diffusion term to V'. v. Another commonly usedflame observable is the mole fraction of OH. Using PLIF, with a judiciouschoice of excitation and detection wavelengths, it is possible to obtain PLIFimages of OH that essentially represent mole fraction [46]. Computed peakOH mole fraction has been found to correlate reasonably with peak heatrelease rate Wr away from regions of high curvature [43]. In highlycurved regions, however, it was practically insensitive to variations in Wr.

Other commonly used measurements include PLIF of CH [46], andchemiluminescence measurements of the electronically excited states CH*,Ci, and OH* [5, 14, 15]. Based on (I) analysis of carbon flux along reactionpathways from CH 4 to CO 2 in one-dimensional (ID) flames using the

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FLAME OBSERVABLES 371

GRImech1.2 [19] mechanism, and (2) the experimental findings of [43,46],sufficient reason has been found to question the utility ofCH, as wel1 as OH',and CH' mole fractions as measures of flame burning and heat release rates[43). On the other hand, numerical results in [43) indicated that the molefraction of HCO exhibits excel1ent correlation with burning and heat releaserates, which suggested its utility as a flame marker and as an experimentalmeasure of these rates. HCO production is directly dependent on theconcentration of CH 20, which is in turn directly dependent on the reactionCH 3 + 0 ~ CH 20 + H, which exhibits the largest fractional influence onchanges in heat release rates. Experimental HCO PLIF measurement was alsodemonstrated in [43], based on the utilization of recent HCO spectroscopydata.

More recently, Paul and Najm [49] found that both peak HCO concentration and the concentration product [OHJ[CH20] are good measures offlame heat release rate IVT at either stoichiometric or rich conditions. Thisconcentration product provides an estimate of the production rate of HCOby the reaction CH 20 + OH ~ HCO + H20. Given the fast removal rate ofHCO, its mole fraction is roughly proportional to its production rate. Theestablished link between HCO mole fraction and heat release rate leads tothe good correlation of [OH][CH20] with IVT. The relatively easier task ofPLIF imaging of OH and CH 20 concentrations, versus that of HCO,highlights the utility of the concentration product approach.

In the present work, we extend the above studies to investigate theseand other flame observables under a wider range of flame, flow, and modelparameters. We investigate correlations of HCO, 'V. v, OH, CH, CO, CH 3,

CH20, CH;, and C2H2 with flame heat release and burning rates. Wealso evaluate correlations of peak concentration products [OH][CH20],

[OH][CO], [OH][CH4J, and others associated with the production of excitedchemiluminescent species OH', CH', and CO; with peak IVT. The parameterrange considered includes a two-fold variation in vortex-pair strength,and the utilization of stoichiometric and rich reactants mixtures. We useboth C, and C\C2 kinetic mechanisms to enable the investigation of theabove ranges of species and stoichiometry, and to cross-compare predictionsfrom the two mechanisms.

The computations focus on the interaction of a freely propagating premixed methane-air flame with a 2D counter-rotating vortex pair. This flowhas been investigated both experimentally [24,29,38,39,46,49, 53,55,58]and numerically [1,23, 33,41 - 45,52, 57]. The available experimental dataincludes flow-visualization of the interaction process between the vortexpair and the flame, quantitative PlY measurements of velocity, vorticity,

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372 H. N. NAJM et al.

and dilatation, as well as PLIF measurements of OR, CR, CR 20 , andRCO. Available numerical results include flame response based on bothsingle-step and detailed kinetics, along with computed flow and vorticitydynamics, and the generation of baroc1inic vorticity. In the present workwe shall not re-examine the flow and flame dynamics observed in this flow,rather we focus on the investigation of flame observables. We proceed nextto give a brief description of the model before discussing the results.

MODEL FORMULATION

The governing equations are presented in their non-dimensional form in 2D.The assumptions of zero bulk viscosity [62], negligible body forces, and lowMach number [32] give the conservative continuity and momentumequations:

ap- + V'. (pv) = 0al (I)

(2)

(3)

where p is the density, v = (u, v) is the velocity vector, P is the pressure, Re isthe Reynolds number, and <I>x, <I>y are the viscous stress terms.

We assume a detailed 'chemical reaction mechanism involving N speciesand M elementary reactions. The energy equation is developed allowing forvariable transport properties, and a constant stagnation pressure Po, i.e., anopen domain. We neglect Soret and Dufour effects [68], since they are notexpected to play a significant role in hydrocarbon flames (versus sayHydrogen flames). We also neglect radiant heat transfer and soot formation.Minimal soot production is expected under the present Nrdiluted flameconditions. This, and the small size of the flow domain suggest a minor rolefor radiation. We also assume a perfect gas mixture, with individual speciesmolecular weights, specific heats, and enthalpies offormation, using Fickian

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binary mass diffusion. The resulting low-Mach-number energy equation is:

8T = -v."\7T + I "\7. (>'"\7T) +_I_Z. "\7T+ Da WT (4)8t RePr pCp ReSc cp pCp

'where T is the temperature, >. is the thermal conductivity, WT = - 'L:, h.w,is the chemical heat release rate source term, hi is enthalpy and Wi is theproduction rate of species i, cp is the mixture specific heat at constant pressure, Pr, Sc, and Da are the Prandtl, Schmidt, and Damkohler numbersrespectively, and Z = 'L:I Cp,iDiN"\7Yi. The N-th species, here N z, isassumed dominant such that the diffusion velocity of any other species iin the mixture is approximated by Vi = -DiN "\7 Yi/Yi, where DiN is thebinary mass diffusion coefficient of species i into the N-th species, and Yi isthe mass fraction of species i. VN is found from the identity 'L:, YiV i = O.For computational efficiency, mixture transport properties (J.L, >') are set tothose of the dominant species at the local temperature. Using GRlmechl.2[19], we find that this simplified transport model, and the present numericaldiscretization, lead to less than 9% deviation in peak radical mole fractionsin the ID freely-propagating stoichiometric 20% Nj-diluted methane-airflame, as compared to the solution using Chemkin [27,26].

The i-th species conservation equation, for i = 1, ... , N - I, is written as

8(pYi) I~ = -"\7. (pvY;) + ReSc"\7· (pDiN"\7Yi) + Da Wi, (5)

and the mass fraction YN is found from the identity 'L:, Y; = I.The perfect gas state equation is:Po = pT/ W, where W = 1/'L:, (Yi/ Wi),

is the local effective molar mass of the mixture. The production rate for eachspecies is given by the sum of contributions ofelementary reactions [68], withArrhenius rates r« = AkTb'e-E,/RT, k = I, ... , M, including forward andbackward rates, and third-body efficiencies [27].

Finally, for the purpose of the numerical implementation describedbelow, the time rate of change of density is found by differentiating the stateequation,

8p = p( _.!.. 8T _ wt-I 8Yi)8t T 8t ;=1 Wi 8t

(6)

with 8T/8t from Eq. (4), and 8Yi/8t = [8(pYi)/8t + Yi"\7 '(pv)]/p fromEq. (5).

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NUMERICAL SCHEME

H. N. NAJM et al.

The above equations are solved using a second-order predictor-correctorfinite difference projection scheme. The projection method was firstintroduced by Chorin [10], and is discussed more recently by Kim andMoin [28]. McMurtry et al. [36] presented a formulation for reacting flow,using the continuity equation to update the density field. The presentmethod follows more closely that of [31,57], in using the energy equation.

Depending on the chemical mechanism considered, and the associatedstiffness of the resulting governing equations, a stiff or non-stiff version ofthis scheme is used. The non-stiff version, which employs a second-orderRunge Kutta (RK2) formulation in the corrector step, is presented in detailin [44], and has been used to study premixed methane-air flames, with C I

kinetics, under stoichiometric conditions [43,44]. The stiff version, whichemploys an additive (non-split) semi-implicit formulation of the scalarconservation equations in the corrector step, is discussed in [45]. A briefoutline of both implementations is provided below.

, An open 2D rectangular domain is considered, and is overlaid by auniform mesh. Velocity components are evaluated at cell edges, while otherfields are evaluated at cell centers. Spatial derivatives are discretized usingsecond-order central differences, and a second-order Adams-Bashforth(AB2) scheme is used for explicit time integration in the predictor. Thenumerical solution for each time step, from I" to In + I, involves the followingsteps [45]:

Predictor

• Evaluate predicted pn+1 and Y7+ ', using AB2 integration of Eqs. (5)and (6).

• Evaluate predicted T,,+I from the state equation.• Evaluate predicted vn + 1 using a variable-density projection scheme [44].

2 Corrector

• Evaluate scalar time gradients, the right-hand-sides of Eqs. (5) and (6),from the predicted fields at 1,,+ I.

• Non-stiff: Evaluate corrected p"+I, and Y7+ ' using an RK2 formulationof Eqs. (5) and (6), based on their right-hand-side values at In and thosepredicted at In + I.

• Stiff: Evaluate corrected p,,+I, and Y7+1 using the stiff ODE integratorDVODE [6], operating on a semi-implicit discretization of Eqs. (5) and(6). This uses an RK2 formulation for the convection and diffusion

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terms based on their values at In and their predicted values at 1.+"

added to an implicit formulation for the chemical source terms. Thus,for the scalar vector ¢ = {p,pYi } , the following ODE system is integrated in each computational cell from In to In+"

(7)

where C, D, R, are the convection, diffusion, and reaction right-handside terms of the scalar conservation equations. Note that, except forR(¢), every term on the right-hand-side of Eq. (7) is a known constantfor the purpose of ODE integration.

• Evaluate corrected rr:' from the state equation .• Evaluate corrected v"+ I using a variable-density projection scheme [44].

COMPUTED FLOW

We study the interaction of a premixed methane-air flame, 20% N2"diluted,with a counter-rotating vortex pair in 2D, under atmospheric pressureconditions. The premixed reactants are at ambient temperature 298 K. Fourflow-flame cases are considered, as follows:

C I-1.0-F Using a C) mechanism [64], at stoichiometric conditions(equivalence ratio <P = 1.0), with a "Fast" vortex-pair (strongcirculation).

C)-1.0-S Using a C) mechanism [64], at <P= 1.0, with a "Slow" vortexpair with 1/2 the circulation in C)-1.0-F.

C1CZ-1.0 Using a C)C Z mechanism [19], at <P = 1.0, with the fast vortexpair of C)-1.0-F.

C jC2"1.2 Using a C1CZ mechanism [19], at <P = 1.2, with the fast vortexpair of C)-1.0-F.

The C) mechanism used involves 16 species and 46 reaction steps [64].The dominant path of carbon in this mechanism under the present conditions, and the associated active species, are given by:

The C)CZ mechanism used is GRlmechl.2 [19] (32 species and 177reactions), with the carbon flow diagram illustrated in Figure I. One-dimensional premixed flame comparisons between the two mechanisms may

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FIGURE I A reaction pathway diagram for a freely propagating premixed methane-airflame, based on the integrated reaction rates from computed ID flame profiles with a stoichiometric 20% N,-diluted reactants mixture at room temperature, using Chemkin [26,27) andthe GRImechl.2 C,C, [19] mechanism. Where convenient, several reaction paths have beenlumped with relevant participating srcies listed. Again for convenience, reaction paths withintegrated rates below 10- 6 moles/em -shave been excluded from the schematic. Some reactionpaths that fall below this threshold are included for completeness, and are delineated withdashed lines. Excited species CH', OH', and CO; are not included in the mechanism, but arelisted here based on their commonly accepted formation/consumption paths.

be found in [43]. Selected species peak mole fractions and profile widths foran atmospheric 10 freely propagating stoichiometric premixed methane-airflame computed using Chemkin [26,27] and GRImechJ.2 [19], with no N2

dilution and under adiabatic conditions, are listed in Table I. This data isuseful for assessing expected signal levels and spatial resolution requirements in experimental measurements of specific flame observables.

The 20 computational domain is a 0.4 x 2.0cm2 region for the slow C,case, and 0.4 x 1.6cm2 for the other cases. The spatial discretization is basedon a uniform cell-size of 15.6 urn in each direction. The flow evolution forcase C,C2-1.2 is illustrated in Figure 2. We impose symmetry boundaryconditions in the horizontal x-direction, and outflow boundary conditionsin the y-direction. The initial vorticity and temperature field contours areshown in the I = 0 frame in the figure. The vertical right edge of the domainis the centerline of the vortex pair under consideration, which is one memberof an infinite periodic row of vortex pairs along the horizontal x-direction.This periodic construction is computationally convenient. It is of courseexpected to affect the vorticity dynamics of the flow. Allowing for theseeffects, the present work investigates the resulting flame response under theensuing local strain-rate and curvature conditions.

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TABLE I Computed peak mole fractions and profile thicknesses of various species in astoichiometric ID freely propagating premixed adiabatic methane-air flame, using Chernkin[26,27] and GRlmech1.2 [19] at atmospheric pressure, with no N, dilution. Profile thickness isFull Width at Half Maximum (FWHM) except where indicated

Species

OHoH0,H,H,OHO,H,O,CH.CH 3CH,OCH,OHCH 30CH30HHCOCOCO,CHiCH,CHC,H6C,H,C,H.C,H3C,H,C,H

Peak mole fraction

7.7 X 10- 3

3.1 X 10- 3

6.5 X 10-3

0.1918 x 10- 3

0.180.15 x 10-3

18 X 10- 6

0.0952.1 x 10-3

1.3 X 10- 3

5.5 X 10-6

19 X 10-6

0.14 X 10-3

62 X 10- 6

0.0480.085

5.4 x 10-6

58 X 10- 6

7.1 X 10- 6

1.2 X 10-3

47 X 10- 6

0.69 X 10-3

16 X 10-6

0.14 X 10-3

0.081 X 10- 6

Profile thickness (mm)

0.21'0.18'0.22'0.37'0.50'0.39'0.300.270.3"0.150.240.130.130.230.150.26'0.52'0.130.130.110.180.130.190.110.170.11

• Profile thickness based on maximum gradient, 6= (XrnaK - Xmin)/ldXjdn!mu'

The initial condition for each flow-flame case is a superposition of thevelocity (u, v) field due to the x-row of vortex pairs, and the (T, p, Y j ) fieldsin the y-direction from a ID premixed flame solution based on the selectedkinetic mechanism using Chemkin [26,27]. The Chernkin solution is relaxedon a ID uniform grid prior to its use in the 20 model. The vorticity fieldcorresponding to each initial vortex is a second-order Gaussian. The initialflame thickness (defined, along with burning speed, in the Appendix) is inthe range 6; = [0.067 - 0.084Jem depending on the particular flow case. Theinitial flame burning speed is in the range SL = [13.2 - 17.7Jcm/s. Themaximum rotational velocity in the domain is around IOm/s for the slowcase and 20 m/s for the fast cases, giving a maximum Mach number in therange 0.03- 0.06, a small value as required by the present formulation. TheDarnkohler number (Da), defined as the ratio of the vortex-pair time scaleto the flame time scale, is in the range 0.02-0.05. With Oa« I, the flow isfaster than the flame, and significant flame contortion is expected.

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Using data from ID normal flame cuts at various time instances duringeach set of results, we study peak-to-peak correlations between relevantfields. Point-to-point correlations are also used where appropriate. Itshould be noted that this latter approach must be used with caution, as asimple shift of any field normal to the flame would result in a very poorpoint-to-point self-correlation, even when the peak values at each flame cutare perfectly correlated. When the object is comparison of spatially distinctcomponents of flame structure between different spatial locations or overtime intervals, the peak-to-peak approach is more relevant. On the otherhand, when two fields are not spatially shifted within the flame structure,then point-to-point correlations provide a more powerful and generalstatement.

Peak-to-peak correlation data is generated by examining normal cutsthrough the flame along the whole flame length for the four flow-flame casesconsidered. Data is included at 0.2 ms time intervals from the fast flow cases(I ms total flow time), and at 0.4 ms from the slow case (4 ms flow time). Inorder to generate a correlation plot between two specific flame fields, e.g.,OH mole fraction and heat release rate, the peak values of both quantities inthe flame are extracted from each normal cut, and used to determine onepoint on the plot. The two peak values are not necessarily at the same physical location, but are within the flame structure. The number of normalflame cut samples is determined by the overall length of the flame within thecomputational domain, i.e., the length of the above 10% CH 4 mass fractioncontour line. One cut is selected in each computational cell that intersectsthis contour, in the direction of the local flame normal R. The cut locationis selected at the contour-point closest to the cell center. These peak-topeak correlations exclude regions of high flame curvature (defined in theAppendix), where, 111;18; > I, because of the ambiguity in defining the local"flame front" and associated peaks in regions of high curvature.

RESULTS

We now proceed to examine correlations between various experimentalflame observables and burning and heat release rates. Note that the peakburning rate (burning rate is defined here as the rate of consumption ofmethane, lVCH,) and peak heat release rate lVr are very well correlatedtogether for all the cases considered, as seen in Figure 3. Thus, goodcorrelation with peak heat release rate can also be inferred to indicate asimilar correlation with peak CH4 consumption rate. In the following,

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high (C,C2-I.O) and low (C 1C2-1.2) WT regions, values of 'V . v spanning thefull range of the plot are evident. Moreover, the effect of flow unsteadiness isevident by comparing the degree of vertical scatter in the 'V . v data betweenthe fast and slow C 1 cases. The faster flow leads to a higher degree of unsteadiness at the flame, resulting in the increased scatter of the data inFigure 6 for case C,-1.0-F versus that of C I-1.0-S.

OH

The mole fraction of OH is commonly measured in flames using PUFtechniques [39,46). With a judicious choice of excitation and detectionwavelengths, measured PUF signals are essentially representative of molefraction with little dependence on temperature and composition of thecollisional bath [46). A reasonable model for OH UF signal, using A-Xexcitation and nonresonant fluorescence detection, can be developedowing to the availability of collisional quenching and vibrational relaxationcross sections for a number of collision partners over a wide range oftemperatures [47,48).

It is noteworthy that OH is relatively stable at high temperature, andexists in significant concentrations in the hot products. Accordingly, Nguyenand Paul [46) suggest that the use of OH as a flame marker must rely onabsolute signal levels or gradients. The utility of peak OH as a flame markerwas studied in [43]. Experimental evidence [46) suggests that as the vortexpair propagates into the rich flame (1) = 1.2), a four-fold increase in OHmole fraction is observed on the vortex-pair centerline, coincident in timewith the disappearance of CH. No such rise is observed at stoichiometricconditions. As indicated in [42) this behaviour is not observed numericallywith GRlmech1.2 [19). Rather, and as found in the present results (notshown), peak OH decays monotonically on the vortex-pair centerline for allcases considered. Moreover, no penetration of OH into the cold reactants(reported in [46)) is observed using the present flow, chemical, and transportmodels.

Peak OH mole fraction XO H and peak OH gradient normal to the flamedXOH/dn are shown plotted against peak WT in Figures 7 and 8 respectively.The scatter in both figures is an indication of the effect of unsteady strainrate and curvature as well as flame stoichiometry on these correlations. Thestoichiometric C, and C 1C2 data are not coincident, but are generally close.On the other hand, the effect of stoichiometry is clearly evident. While eachof the stoichiometric and rich flame data may be used to construct a roughlocal correlation, no general correlation is feasible. Therefore, the use of

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C;

Chemiluminescence from Cz d3ng(C;) has been a widely applieddiagnostic for the study of premixed flames. It is generally accepted thatC; is produced by reaction of CH with C atom or CH. Bleekrode andNieuwpoort [3] studied CH' and C; production and spectral signatures ina low pressure flame. Based on measured concentrations, they concludedagainst production of C; via a reaction of CH with CH because the rateconstant would need to be unrealistically high (since C atom is present ineven lower concentration the reaction C + CH ~ C; + H would require aneven higher rate coefficient). This conclusion was further supported by thesubsequent studies of Bulewicz et al. [7]. Vanpee and Quang [67] restatedsupport for 2CH ~ C; + Hz, but this relied on the presumption that theirmeasured CH' signal reflected ground state CH concentration whichcannot be substantiated given the recently reported mechanism for CH'production [14, 15]. At present there is no C; production mechanism whichappears to explain the reported signal levels and spectral signatures.However if either of the above mechanisms is correct then the C; signalwould be linear or quadratic in CH concentration and would be thusexpected to suffer the same difficulties and even accentuate the undesirablecharacteristics of CH as a measure of heat release. Finally C; exhibits amaximum in signal at even richer conditions (lower heat release) than CH'signal, suggesting a complicated relation with heat release as a functionof local stoichiometry.

CONCLUSIONS

We have presented a numerical study of methane-air flame observables inan unsteady 2D flow environment. We focused on a flame-flow interactioninvolving a freely propagating premixed methane-air flame and a counterrotating vortex pair. Four flow-flame cases were considered using twodifferent chemical mechanisms. Flow conditions spanned a two-fold variation of vortex-pair strength, while flame conditions included stoichiometricand rich (g> = 1.2) conditions. Results were analyzed and used to examinecorrelations between various flame observables and heat release rate.Correlations were studied using both point-to-point plots involving allpoints in the computational domain independent of flame structure, andpeak-to-peak plots based on the observed peak values of relevant fieldsobserved in normal cuts of flame structure. The latter technique was limited

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to flame regions where the radius of curvature is smaller than the initialflame thickness.

We demonstrated excellent peak-to-peak correlation between CH 4 consumption rate and peak Wr. Thus, all statements regarding the quality ofcorrelations with peak Wr may be extended to peak CH 4 consumption rate.

For all the cases studied, HCO mole fraction was found to have an excellent correlation with heat release rate Wr, based both on point-to-pointand peak-to-peak studies. HCO is a good flame marker and a quantitativemeasure of heat release and burning rates.

Peak flow dilatation rate '\l. v was found to have generally poor correlation with peak Wr under unsteady flow conditions, in agreement withearlier findings [43].

Peak OH, CO, and CH were found to have some positive correlation withpeak Wr for a given reactants mixture composition. Here again, large scatterdoes exist, however, due to flow disturbances. On the other hand, allowing forvariations in mixture composition leads to essentially uncorrelated data.Thus, in a turbulent reacting flow, where local mixture stoichiometry may notbe known, it is generally not possible to use peak OH, CO, or CH as localmeasures of flame burning or heat release rate. On the other hand, the presentdata suggests that one exception may be the use ofCH at low burning rate, asthe flame approaches extinction, where meaningful overlap of the rich andstoichiometric flame data is evident. We recall however earlier experimentaldata [43,46] that suggests continued flame burning after CH has completelydisappeared, both at rich and stoichiometric conditions. This is clearly notevident here. Further studies are necessary with other chemical mechanisms,broader ranges of parameters, and slower vortices, to allow more extensivecomparison with the experimental data and examine this discrepancy.

Peak gradient of OH mole fraction in the flame was also found to beaffected significantly by mixture composition, thus rendering it a questionable measure of peak Wr in a general turbulent flow. Worse performancewas evident from the peak CO mole fraction gradient, where both extensivescatter due to flow disturbances, and mixture composition lead to essentiallyuncorrelated data.

Both CH 3 and CH 20 data exhibited strong dependence on the chemicalmechanism used in the study, for the same flow-flame conditions.Significantly higher CH 3 and CH 20 mole fractions were predicted by theC\ versus the C\C2 mechanism. We observe no useable general correlationfor peak CH 3 with peak Wr, allowing for variations in mixture composition.On the other hand, composition had no significant influence on the observedcorrelation of CH 20 with peak heat release rate, as predicted by the present

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C, Cz kinetics. A good, albeit non-linear, correlation is evident, suggestingthe adequacy of peak CHzO as a measure of flame burning and heat releaserates.

Peak CHi mole fraction was also found to exhibit reasonable correlationwith peak WT. albeit with significant scatter. This suggests that measurementof CHi ('CHz) mole fraction may be a good measure of peak burning andheat release rates in this flame.

Poor correlation was found between peak CzH z mole fraction and heatrelease rate, primarily due to data scatter. What correlation does exist revealsan inverse relationship with peak WT, consistent with earlier ID flame studiesfor the present equivalence ratio range. On the other hand, both lower CzH zand WT would be expected from leaner mixtures with cJ> < I.

Concentration products were also studied to examine their utility asmeasures of flame burning and heat release rates. The peak [OH][CH4] and[OH][CO] data was found to give useful correlations with peak WT, with littlesystematic effect due to stoichiometry or flow disturbances, but sizeablescatter. On the other hand, despite the remarkably low scatter in the peak[OH][CHzO] data, this particular correlation reveals a systematic shift dueto mixture composition.

Finally, as possible respective measures of the production rates of CH',OH', and COi (which are not included in the present kinetics), we studiedthe concentration products [CzH][O]. [CHI[Oz], and [CO][O]. Large scatterwas observed in the [CzH][O] data, while very low scatter and a compactlinear correlation was observed between peak [CH][Oz] and peak WT. Usefulcorrelation was also observed for peak [CO][O], with no systematic effect offlow disturbances or stoichiometry, although with significant scatter. Wealso discussed Ci chemiluminescence and the relationship between Ci andCH. Further studies on the chemiluminescence and kinetics of CH', OH',Ci, and COi are necessary to establish their relationships with flameburning and heat release rates.

In closing, it is important to note that these findings are necessarilyspecific to the range of parameters investigated. Additional work is necessary to evaluate their extension to wider ranges of operating conditions, or toother fuels and mixture compositions.

Acknowledgments

This work was supported by the US Department of Energy (DOE), theDOE Office of Basic Energy Sciences, Chemical Sciences Division, and theDOE Defense Programs Accelerated Strategic Computing Initiative (ASCI).

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APPENDIX

Following the notation in the Flame Diagnostics section, the tangentialstrain rate at the flame, 7" is evaluated from the strain-rate tensor ~ [68]:7{ = t-e-t. Flame curvature [8], K., is defined positive when the flame isconvex to the reactants, in 20: K. = I/R = V' . n, where R is the radiusof curvature.

The flame displacement speed [8,51,66] is defined as the speed ofdisplacement of a given contour-level of a scalar field variable relative to thelocal flow velocity. Thus, at the 10% methane contour level, the displacement speed is defined, positive for propagation into the reactants, as:

The laminar burning speed relative to the unburnt fluid is a density-weighteddisplacement speed defined as SL = PSd/Pu, where P is the gas density at thesame location as Sd, and Pu is the unburnt reactants density.

We also define the flame thermal thickness as:

where Ti; Tu are the burnt and unburnt gas temperatures respectively, andaT/an is the temperature gradient along the flame normal direction.

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a study of flame observables in premixed methane - air flames

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