Lewis number effects in laminar diffusion flames near and away from extinction

Transcription

1 Proceedings of the Combustion Institute 3 (27) Proceedings of the Combustion Institute Lewis number effects in laminar diffusion flames near and away from extinction Ruey-Hung Chen a, *, Marcos Chaos b, Anupam Kothawala a a Mechanical, Materials and Aerospace Engineering Department, University of Central Florida, Orlando, FL , USA b Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 8544, USA Abstract An experimental study of the extinction limits of methane air and propane air counterflow diffusion flames is presented. Diffusive-thermal properties (i.e., Lewis numbers) are systematically varied by diluting the fuel stream with helium or argon. For the same level of dilution, the extinction strain rate is considerably lower for -diluted flames than for -diluted flames over the entire range of dilutions tested. The observed experimental results are successfully explained by considering a weighted effective Lewis number of the counterflow flames as they approach the extinction limit. The flames investigated are also modeled using the OPPDIF code from the CHEMKIN package considering multicomponent transport properties. Experimental extinction results are in very good agreement with calculated extinction strain rates based on the detailed chemical kinetic models of the flames studied. It is also found that in counterflow diffusion flames away from extinction limits (i.e., larger Damköhler numbers), calculated flame temperatures follow the trend of the weighted Lewis number due to the finite strain rate ever present in the counterflow configuration. A parallel investigation of lifted laminar CH 4 jet diffusion flames reveals that at the mid-sections of flames, the flame temperature follows the change in the unweighted fuel Lewis number, even for flames near blowout limits. Similar observations are also made in laminar C 3 H 8 jet diffusion flames and the observed differences are discussed. Ó 26 The Combustion Institute. Published by Elsevier Inc. All rights reserved. Keywords: Counterflow flames; Extinction; Lewis number. Introduction * Corresponding author. Fax: address: chenrh@mail.ucf.edu (R.-H. Chen). Counterflow diffusion flames share common one-dimensional features with laminar flamelets [,2] and have been used to gain insight into turbulent non-premixed flame structures. Topics of particular importance in counterflow flames are related to flame extinction and flame stabilization and have been experimentally and theoretically investigated [3 4]. Addition of inert species promotes flame extinction, however, it may also alter the diffusive-thermal properties of fuel and oxidizer flows, such as fuel and oxidizer Lewis numbers (Le F and Le O, respectively), which have a strong influence on the temperature and extinction of diffusion flames [4,8,5]. Under near extinction conditions (i.e., low Damköhler number), reactants may leak through the reaction zone leading to a premixed burning regime in diffusion flames [6]. In this regime, diffusion flames may exhibit cellular and pulsating /$ - see front matter Ó 26 The Combustion Institute. Published by Elsevier Inc. All rights reserved. doi:.6/j.proci.26.7.

2 232 R.-H. Chen et al. / Proceedings of the Combustion Institute 3 (27) modes typical of premixed flames [7,8]. The structure and temperature of near-extinction diffusion flames, thus, cannot be characterized by considering the Lewis numbers of fuel and oxidizer flows separately (i.e., Le F and Le O ). In Refs. [7,8], the behavior of diffusion flames near extinction established in a Wolfhard Parker slot burner was explained by defining an effective Lewis number [6,9] giving larger weight to the Lewis number of the deficient reactant in the premixed burning regime encountered in these near-limit flames. The purpose of this study is to demonstrate the merit of an effective Lewis number [9] in explaining the characteristics of counterflow diffusion flames near and away from extinction limits. To this end, CH 4 air and C 3 H 8 air flames are studied over a wide range of fuel dilution with helium or argon. These gases have the same volumetric heat capacity, therefore, any observed difference in flame behavior cannot be due to the effect of dilution alone and, here, these differences are attributed to thermodiffusive effects. For comparison, results from lifted laminar jet diffusion flames of diluted CH 4 and C 3 H 8 are also reported to demonstrate the fuel Lewis number effect at the midsection of these flames. In addition, experimental results are complemented by simulations performed using available detailed chemical kinetic models of the flames studied. 2. Experiment The details of the counterflow burner apparatus used in this study and the experimental procedure were described in detail previously [9]. Fuel and oxidizer flows were velocity matched rather than momentum matched. Therefore, the flat flames established in the burner were observed to move toward the fuel or oxidizer sides as the degree of fuel dilution changed depending on the density difference between fuel and oxidizer streams. Extinction measurements were performed by gradually increasing the exit velocities of fuel and oxidizer flows, simultaneously, while keeping the degree of fuel dilution fixed. The velocity at which the flame extinguished was recorded and the global strain rate at extinction (a g,ext ) was calculated using the expression derived by Seshadri and Williams [2]: a g;ext ¼ 2V rffiffiffiffiffi ext q þ F ðþ d q O where V ext is the velocity of fuel and oxidizer flows at extinction, d is the burner separation distance, q F is the fuel-diluent mixture density, and q O is the oxidizer (air) density. 3. Modeling approach To supplement the experimental results reported herein, the flames studied were also modeled using the numerical tools provided in the CHEM- KIN package [2] developed by Sandia National Laboratories, namely OPPDIF. This code requires detailed chemical kinetic mechanisms to model the flames. A comprehensive review of such mechanisms for hydrocarbon flames can be found in Ref. [22]. For methane flames the GRI-Mech mechanism [23] was used which consists of 53 species undergoing 325 reactions. Detailed reaction mechanisms for propane combustion have not been as extensively developed as for methane and no widely accepted version comparable to GRI-Mech is available. Several mechanisms were tested [24 27] under the present experimental conditions. The M5 mechanism of Haworth et al. [27] (29 species, 73 reactions) was chosen, since it best matched the experimental data and provided the most stable and fastest computation. The numerical solutions were executed with plug flow boundary conditions (i.e., zero radial velocity gradients at the burner exits) and included the calculation of multicomponent and thermal diffusion velocities. Without using multicomponent properties, the extinction strain rate value may differ by as much as 2% [28]. A direct approach [2] was employed to obtain extinction strain rates for a given fuel dilution level, by slowly increasing the fuel and oxidizer exit velocities (using. cm/s increments), relative to a previous solution, until the solver failed to find a solution or returned a nonburning solution. 4. Results and discussion Extinction curves for diluted methane and propane flames can be found in Figs. and 2, XD (Exp.) (Exp.).2 N 2 (Ref. 9) OPPDIF Model a g,ext (s - ) Fig.. Effect of fuel stream diluent mole fraction on extinction strain rate of CH 4 flames.

3 R.-H. Chen et al. / Proceedings of the Combustion Institute 3 (27) (Exp.) (Exp.).2 N 2 (Ref. 9) OPPDIF Model a g,ext (s - ) Fig. 2. Effect of fuel stream diluent mole fraction on extinction strain rate of C 3 H 8 flames. respectively, as a function of the diluent (i.e., either or ) mole fraction,, in the fuel stream. The global extinction strain rate, a g,ext, for both fuels can be seen to decrease as is increased, as expected. The values of a g,ext for pure CH 4 and C 3 H 8 were measured to be 58 s and 863 s, respectively. These values are in good agreement with data found in the literature [6,9, 3]. It is also worth noting from Figs. and 2 that, in the limit of zero stretch (i.e., zero exit velocities), flames could not be established for fuel molar concentrations below.5 and.8 for CH 4 and C 3 H 8 fuels, respectively. These values are in very good agreement with reported quantities [2,6,8]. The results from the numerical simulation, using OPPDIF, performed in this study can also be found in Figs. and 2 for CH 4 and C 3 H 8 fuels, respectively. Excellent agreement can be seen between the experimental extinction strain rates, within approximately 5% and 4% for CH 4 and C 3 H 8, respectively. The mechanism used to model the propane flames [27], however, is a reduced mechanism and it is expected that the use of more complete mechanisms [24 26] containing a larger number of reactions and species would lower calculated flame temperatures and, thus, extinction strain rates. It is obvious from the experimental and numerical results shown in Figs. and 2, that dilution with or yields drastically different extinction curves. For brevity, it suffices to mention that similar quantitative results were observed by Pitts et al. [2] when or were introduced in the oxidizer stream of their counterflow diffusion flames. Figures and 2 also compare the present experimental data against the results of Chen et al. [9] which used N 2 as the fuel diluent. Molecular nitrogen has a heat capacity that is larger than that of and by approximately 4% (i.e., 29. J/mol K). Both Figs. and 2 show how is more effective in suppressing both CH 4 and C 3 H 8 flames than or N 2 for a given level of dilution. Thus, the observed extinction trends cannot be due to the sheer effect of dilution, as and have the same volumetric heat capacity (i.e., 2.8 J/mol K) but as a result of thermodiffusive effects as explained below. Figures 3 and 4 plot temperature values, near extinction, obtained from OPPDIF for the present methane and propane flames, respectively. Unfortunately, no experimental temperature data is currently available for comparison as the presence of physical probes (i.e., thermocouples) altered the structure and extinction properties of the counterflow flames investigated. As expected, calculated maximum flame temperatures (T max ) for -diluted flames are lower than for -diluted flames. Due to their difference in mass and thermal diffusivities, dilution by or is expected to change the fuel Lewis number, Le F, of the counterflow flames studied. Since air was used as the oxidizer in this study, its Lewis number, Le O, remained fixed and approximately equal to. The change in fuel Lewis number is plotted in T max (K) at Extinction Fig. 3. Maximum flame temperature in near extinction CH 4 flames obtained from OPPDIF T max (K) at Extinction Fig. 4. Maximum flame temperature in near extinction C 3 H 8 flames obtained from OPPDIF.

4 234 R.-H. Chen et al. / Proceedings of the Combustion Institute 3 (27) Le F CH 4 C 3 H Fig. 5. Fuel stream Lewis number as a function of diluent mole fraction for CH 4 and C 3 H 8. Fig. 5 as a function of the diluent mole fraction in the fuel stream for CH 4 and C 3 H 8 fuels. It can be seen that there is a cross-over of Le F values at =.6 and.7 for CH 4 -inert and C 3 H 8 -inert mixtures, respectively. Since a lower Lewis number strengthens the flame against extinction by increasing its temperature due to an increase in reactant mass diffusion [4], the results shown in Fig. 5 suggest that, for low dilution levels, a g,ext for mixtures would be higher than for mixtures. This trend is not seen in Figs. 4. As discussed above, when diffusion flames approach near extinction conditions (i.e., low Damköhler number), incomplete reactant consumption takes place and one or both reactants partially leak through the reaction zone. Thus, intermixing of fuel and oxidizer occurs resulting in premixed burning [6]. In this regime, the Lewis number of the deficient reactant has substantial effects on the near-extinction diffusion flames [8,6 9]. Following the numerical study of Kim and Lee [9] based on activation-energy asymptotics [6], an effective Lewis number, Le e, applicable to the near-extinction premixed burning regime found in diffusion flames, may be defined as: Le e ¼ L F þ A F L O ð2þ þ A F where L F and L O are fuel and oxidizer Lewis numbers. These values are defined considering the combined (non-stoichiometric) mixture of fuel, oxidizer, and diluent flows as the ratio of the mixture thermal diffusivity to the mass diffusivities of fuel and oxidizer, respectively [8], evaluated at room temperature and pressure. For example, for a CH 4 air flame with a 5% fuel dilution with helium ( =.5), the mixture ([.5 CH ] + [.2 O N 2 ]) thermal diffusivity is.37 cm 2 /s whereas the mixture mass diffusivities of CH 4 and O 2 are.3 and.25 cm 2 /s, respectively, leading to L F =.2 and L O =.5. The parameter A F can be considered a measure of the equivalence ratio or mixture strength [9] of the premixed burning regime and is defined as A F = my F /Y O, where m is the stoichiometric oxidizer-to-fuel mass ratio (i.e., 3.63 and 3.99 for C 3 H 8 O 2 and CH 4 O 2 flames, respectively) and Y F and Y O are the fuel and oxidizer mass fractions in their respective streams. Equation (2), thus, places a larger weight on the Lewis number of the deficient reactant based on the value of A F. Such an effective Lewis number definition helped explain the onset of cellular and pulsating instabilities in diffusion flames in the experiments of Chen et al. [7] and Chaos and Chen [8]. Figure 6 shows the variation of Le e as a function of the diluent mole fraction in the fuel stream for the counterflow diffusion flames investigated. In contrast to Fig. 5, the trends are substantially different. However, the data shown in Fig. 6 is in good qualitative agreement with the extinction curves of Figs. and 2. For the entire range of values, the effective Lewis number, Le e, for -diluted flames is always larger than that for -diluted flames. This implies a lower flame temperature for -diluted flames, near extinction, which would explain the lower extinction strain rate of these flames. Furthermore, as the dilution level is increased, the difference between the effective Lewis number of and mixtures increases. This qualitative trend correlates well with the results shown in Figs. and 2 as the extinction strain rate difference between and diluted flames increases for increasing for both methane and propane flames. These trends can be explained by the effective Lewis number, Le e, near extinction (Fig. 6) as flames with lower values of Le e lead to higher flame temperatures (Figs. 3 and 4) and, thus, would require larger strain rates to extinguish the flames (Figs. and 2). It is also of interest to note the trend of T max at strain rates lower than the extinction values in Le e CH 4 C 3 H Fig. 6. Effective Lewis number in the near-extinction premixed burning regime as a function of diluent mole fraction for CH 4 and C 3 H 8.

5 R.-H. Chen et al. / Proceedings of the Combustion Institute 3 (27) comparison with fuel and effective Lewis numbers. Figures 7 and 8 show, respectively, maximum flame temperatures for CH 4 and C 3 H 8 flames at 4% dilution for a wide range of strain rates up to their respective extinction values. For this level of dilution, the -/-diluted flames extinguish at a global strain rate (a g,ext ) approximately equal to 275 s /575 s and 425 s /82 s for CH 4 and C 3 H 8 flames, respectively. It can be seen from Fig. 7 that even for low strain rate values (i.e., a g = 95 s ), the -diluted CH 4 flames have larger T max values than the -diluted flames. For example, at a g =5s, the values for the - and -diluted CH 4 flames are approximately 9 and 2 K, respectively. At 4% dilution, the - and -diluted CH 4 flames have effective Lewis numbers, Le e, approximately equal to.4 and.5, respectively (Fig. 6). This observation corresponds to the trends shown in Fig. 3 for flames close to a g,ext, where the flame with smaller value of Le e yields a higher value of T max. Similar observations can be made for C 3 H 8 flames, as Strain Rate (s - ) Temperature(K) Fig. 7. Maximum flame temperatures of CH 4 counterflow diffusion flames as a function of strain rate for a 4% fuel dilution level, denotes extinction conditions. Strain Rate(s - ) Temperature(K) Fig. 8. Maximum flame temperatures of C 3 H 8 counterflow diffusion flames as a function of strain rate for a 4% fuel dilution level, denotes extinction conditions. shown in Fig. 8. It can be said that even at reasonably low strain rates, the flame temperature qualitatively follows the above mentioned Le e trends. Questions arise as to under what low strain rates (i.e., large Damköhler number) the flame temperature might follow Le F, if such a strain rate exists at all. To answer these questions, laminar CH 4 and C 3 H 8 jet diffusion flames, in quiescent air, with similar dilutions levels were investigated [29,3]. The mid-section of these flames is expected to have large Damköhler numbers and be relatively unstrained since fuel and oxidizer flows are nearly parallel. Conditions for the jet flames studied are given in Tables and 2 for CH 4 and C 3 H 8 flames, respectively, where maximum flame temperatures (T max ) were measured by radially traversing a fine-wire C-type thermocouple (nominal bead diameter = 76 lm) at several axial positions and appropriately correcting for radiation heat losses. The uncertainty in the T max measurements is 25 K; experimental details can be found in Ref. [29]. It can be seen from Table that for the same level of dilution, the diluent giving a lower value of Le F yields a higher value of T max,mid (maximum Table Experimental conditions and flame temperatures of diluted CH 4 laminar jet flames in quiescent air near blow-off velocities (U BO ) (jet exit diameter =.8 cm) Diluent species/dilution level 2% 4% 6% 2% 4% 6% Le F Le e T max,mid (K) a U (m/s) U BO (m/s) a The mid-section of the flame was determined as the mid-point between the flame base and tip. Table 2 Experimental conditions and flame temperatures of diluted C 3 H 8 laminar jet flames in quiescent air near blow-off velocities (U BO ) (jet exit diameter =.8 cm) Diluent species/dilution level 4% 6% 8% 4% 6% 8% Le F Le e T max,mid (K) a U (m/s) U BO (m/s) a The mid-section of the flame was determined as the mid-point between the flame base and tip.

6 236 R.-H. Chen et al. / Proceedings of the Combustion Institute 3 (27) temperature at the mid-section of the flame). First, consider the 4% dilution. The -diluted flame has a lower Le F value than the -diluted flame (.489 vs..85) and yields a higher T max,mid value (97 K vs. 895 K). Similar results are also seen for the 6% dilution, where the -diluted flame also has a lower Le F value (.7 vs..4) and a higher T max,mid value (794 K vs. 7 K). On the contrary, with 8% dilution, both - and -diluted flames have similar Le F values (.28 vs..4) and, consequently, T max,mid values (63 K vs. 639 K). The values of Le e for each of the three levels of dilution are higher for -diluted flames than -diluted flames (Fig. 6). C 3 H 8 flames (Table 2) show similar results. The 4% -diluted flame has a lower Le F value than the -diluted flame (.379 vs..775) and yields a higher T max,mid (29 K vs. 966 K). For the 6% dilution level, the -diluted flame also has a lower Le F value (.696 vs..949) and a higher temperature at the flame midsection (822 K vs. 787 K). On the other hand, with 8% dilution, the -diluted flame has a higher Le F value (.46 vs..27) and a lower T max,mid value (525 K vs. 68 K). Similar to the CH 4 flames, the value of Le e for each of the three levels of dilution is higher for -diluted flames than -diluted flames. The above jet flame results suggest that in unstrained flame regions the flame temperature follows the qualitative Le F trends, rather than Le e. If the flame temperatures were to follow the Le e trends, for each and every dilution level the -diluted flames should always have a lower temperature, which is clearly not the case as shown in Tables and 2. However, in counterflow diffusion flames, the flame temperature of the strained flames follows the trend of Le e. The moderate strain rates, although quite low compared to the extinction values (Figs. 7 and 8), in the counterflow configuration appear to cause finite rate chemistry and some partial premixing, which suggests the need to consider the effects of Le e rather than Le F. 5. Conclusion The extinction limits of methane and propane counterflow diffusion flames diluted by helium and argon was experimentally and numerically investigated in order to improve the understanding of the effect of fuel dilution (i.e., Lewis number) on diffusion flame extinction and flame temperature. Experimental results from laminar jet diffusion flames were also used to better clarify the trends observed at low strain rates. In the numerical counterflow flame simulations, realistic molecular as well as thermal transport properties were included. The calculated extinction strain rates were found to be in very good qualitative and quantitative agreement with the experimental data. In the counterflow configuration, helium addition to the fuel stream resulted in extinction strain rates that were always considerably lower than those of -diluted flames with the same dilution level. This is consistent with the fact that the associated lower effective Lewis numbers (Le e, which considers partial premixing of fuel and oxidizer flows due to reactant leakage present in counterflow flames near extinction) in -diluted flames also resulted in higher flame temperatures. The variation in Lewis number of the diluted fuel stream, Le F, alone cannot explain the extinction trends measured and calculated. This is because -diluted fuels have lower fuel Lewis numbers than -diluted fuels over a wide range of dilution levels, which should have strengthened the flames yielding larger extinction strain rates. Under moderate strain rates in the counterflow configuration, the flame temperature again can only be qualitatively explained by considering the effect of Le e, rather than Le F. However, it has been shown that at the mid-section of laminar jet diffusion flames where relatively low strain rates exist, the flame temperature trends can be successfully explained by considering the Lewis number of the fuel in the fuel stream, Le F, rather than Le e. These results suggest that finite Damköhler numbers (and, thus, partial premixing) exist even under moderate strain rates in counterflow diffusion flames. References [] N. Peters, Combust. Sci. Technol. 3 (983) 7. [2] H. Tsuji, Prog. Energy Combust. Sci. 8 (982) [3] R.-H. Chen, J.F. Driscoll, J. Kelly, M. Namazian, R.W. Schefer, Combust. Sci. Technol. 7 (99) [4] C.K. Law, S.H. Chung, Combust. Sci. Technol. 29 (982) [5] G. Dixon-Lewis, T. David, P.H. Gaskell, J.A. Miller, R.J. Kee, M.D. Smooke, N. Peters, E. Effelsberg, J. Warrantz, F. Behrendt, Proc. Combust. Inst. 2 (985) [6] I.K. Puri, K. Seshadri, Combust. Flame 4 (986) [7] H.K. Chelliah, C.K. Law, T. Ueda, M.D. Smooke, F.A. Williams, Proc. Combust. 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7 R.-H. Chen et al. / Proceedings of the Combustion Institute 3 (27) [2] W.M. Pitts, J.C. Yang, M.L. Huber, L.G. Blevins, Report NISTIR 644, 999. [3] E.J.P. Zegers, B.A. Williams, E.M. Fisher, J.W. Fleming, R.S. Sheinson, Combust. Flame 2 (2) [4] A.R. Masri, R.W. Dibble, R.S. Barlow, Prog. Energy Combust. Sci. 22 (996) [5] S.-H. Chung, L.P. Chew, Combust. Sci. Technol. 37 (984) [6] A. Liñán, Acta Astronaut. (974) [7] R.-H. Chen, G.B. Mitchell, P.D. Rooney, Proc. Combust. Inst. 24 (992) [8] M. Chaos, R.-H. Chen, Combust. Sci. Technol. 76 (24) [9] J.S. Kim, S.R. Lee, Combust. Theory Model. 3 (999) [2] K. Seshadri, F.A. Williams, Int. J. at Mass Transfer 2 (978) [2] R.J. Kee, F.M. Rupley, J.A. Miller, M.E. Coltrin, J.F. Grcar, E. Meeks, H.K. Moffat, A.E. Lutz, G. Dixon-Lewis, M.D. Smooke, J. Warnatz, G.H. Evans, R.S. Larson, R.E. Mitchell, L.R. Petzold, W.C. Reynolds, M. Caracotsios, W.E. Stewart, P. Glarborg, C. Wang, and O. Adigun, CHEMKIN Collection, Release 3.6, Reaction Design, Inc., San Diego, CA. [22] J.M. Simmie, Prog. Energy Combust. Sci. 29 (23) [23] C.T. Bowman, R.K. Hanson, D.F. Davidson, et al., available at < [24] F.A. Williams, available at < [25] S.G. Davis, C.K. Law, H. Wang, Combust. Flame 9 (999) [26] Z. Quin, V.V. Lissianski, H. Yang, W.C. Gardiner, S.G. Davis, Proc. Combust. Inst. 28 (2) [27] D.C. Haworth, R.J. Blint, B. Cuenot, T.J. Poinsot, Combust. Flame 2 (2) [28] B.A. Williams, Combust. Flame 24 (2) [29] A. Kothawala, The effects of transport properties on blow-off velocities, lift-off characteristicsnand maximum temperatures of laminar diffusion flames, MSME thesis, University of Central Florida, Orlando, FL, 23. [3] R. H. Chen, A. Kothawala, M. Chaos, L.P. Chew, Combust. Flame 4 (25) Comments L.P.H. de Goey, TU Eindhoven, Netherlands. How do your results compare with the results of de Goey et al. [] at the previous symposium? Reference [] L.P.H. de Goey, T. Plessing, R.T.E. rmanns, N. Peters, Proc. Combust. Inst. 3 (25) Reply. The work of de Goey et al. [ in the above comment] was concerned with the flame thickness of instantaneous flamelets observed in a swirl burner and how flame stretch, preferential diffusion, and density variations might affect this flame thickness. In the present study no attempt was made to experimentally measure the temperature gradient or thickness of the flames studied and no direct comparisons with the results of de Goey et al. can be made; this is a good subject for further work. However, as discussed by de Goey et al. flame thickness seems to be affected by the Lewis number of the deficient reactant and, as such, there could exist a relationship between the flame thickness of stretched flamelets and the effective Lewis number described in our study. d Paul Papas, Colorado School of Mines, USA. In explaining your results, why do you refer to an effective Lewis number which applies to premixed flames? For non-premixed flames recent work [] has show that both Lewis numbers (the fuel and oxygen Lewis numbers) are important in addition to parameters such as the initial mixture strength, in explaining the extinction limits of gaseous non-premixed flames. What are your results in light of this theory? Reference [] S. Cheatham, M. Matalon, J. Fluid Mech. 44 (2) Reply. For diffusion flames near extinction, such as the ones considered in this study, leakage of one or both reactants develops due to the low Damköhler number established leading to a premixed burning regime. This premixed burning regime was first identified by Liñán ([6] in paper) when he described the structure of counterflow diffusion flames based on the assumption of a large activation energy parameter. In fact, the analysis of Cheatam and Matalon ([] in above comment) parallels that of Liñán ([6] in paper). The effective Lewis number described in our work is taken from the linear stability analyses of Kim and Lee ([9] in paper) which were applied to near-extinction counterflow diffusion flames. It takes into account both oxidizer and fuel Lewis numbers and uses the mixture strength as a weighing parameter, consistent with the conclusions drawn by Cheatam and Matalon which showed that the unstable behavior of near-extinction diffusion flames is largely influenced by the Lewis number of the reactant that is more completely consumed. Indeed, we have recently confirmed this latter observation for unstable flames established in a slot burner ([8] in paper) by considering the effective Lewis number described in this study.