A Numerical Study of CO<sub>2</sub> Decoupled Effects on Extinction Limit and Flame Microstructure in CH<sub>4</sub>/Air Counterflow Diffusion Flame with Various Pressures

Chen, Ying; Wang, Jingfu; Li, Jianrong; Zhang, Jian

doi:https://doi.org/10.1155/2023/4882147

International Journal of Energy Research

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Abstract Introduction Results and Discussion Conclusion Data Availability Conflicts of Interest References Copyright Related Articles

Research Article | Open Access

Volume 2023 | Article ID 4882147 | https://doi.org/10.1155/2023/4882147

A Numerical Study of CO₂ Decoupled Effects on Extinction Limit and Flame Microstructure in CH₄/Air Counterflow Diffusion Flame with Various Pressures

Ying Chen,^1,2Jingfu Wang,^1,2Jianrong Li,³and Jian Zhang^1,2

Academic Editor: Debabrata Barik

Received12 Nov 2022

Revised06 Feb 2023

Accepted13 Feb 2023

Published01 Mar 2023

Abstract

Extinction limits and flame microstructures of CH₄ versus air (N₂/O₂) counterflow diffusion flames with additional CO₂ to oxidizer stream under various pressure conditions were numerically investigated by a proposed decoupled strategy. The chemical and thermal effects of CO₂ addition were isolated from the synergistic effect on extinction limits and flame microstructures. The results show that the extinction limits were decreased due to the CO₂ addition and extended caused by the enhanced pressure, respectively. The changes of flame microstructures from far away from extinction to near extinction mainly are reflected in a narrower combustion zone and thinner flame thickness, while there is no visible displacement of the flame front location. Quantitative analyses manifest the thermal effect of CO₂ addition on extinction limit is greater than chemical effect, and elevated pressure can enhance both thermal and chemical effects. An interesting phenomenon occurred between the thermal and chemical effects resulting from increasing CO₂ mole fraction in an oxidizer on extinction limit; the former monotonically increase along with CO₂ mole fraction, while the latter represents a kind of approximate quadratic-parabola tend along with CO₂ mole fraction. The distributions of the production and consumption rate of hydroxyl (OH) radicals were presented to clarify the contribution of the kinetic term in the asymptotic solution to the extinction limits with increasing CO₂ molar fraction and various pressures.

1. Introduction

Nowadays, countries around the world are striving to build a diversified and resilient low-carbon energy supply system to achieve carbon neutrality. Low CO₂ emission to the environment gains more and more concern in the process of the inevitable energy revolution. Various advanced combustion technologies were proposed to meet the low CO₂ emission, among which the Exhaust Gas Recirculation (EGR) technology [1] can not only lower CO₂ emission, make contribution to CO₂ capture and sequestration (CCS) but also reduce the generation of nitrogen oxide pollution. Higher CO₂ concentration with EGR technology in the combustion zone is clearly distinguished from conventional combustion technology. The participation of CO₂ in oxidizer arises many difficulties and challenges in chemical kinetics process of fuel combustion owning to the differences in chemical and thermal properties between CO₂ and N₂. Numerous studies have been conducted to decouple the effects of above two properties on the flame characteristics, such as flame speed [2–6], intermediate formation [7], NO_X formation [7–10], and flame temperature [11], whereas there are rare reports on the decoupled effects of CO₂ on the extinction limit which is one of fundamental combustion properties to characterize the dynamic laminar flame. The flame cannot be sustained when the rate of chemical heat release is too weak to support the rate of heat loss [12]. From the detailed chemistry analysis viewpoint, the extinction limit is strongly governed by the interaction balance between radical chain-branching and propagating/terminating reactions [12–14]. Thereby, it is a prerequisite to reveal the respective contribution and the effects of the species thermal transport, chemical reaction on the extinction limit, that can provide more fundamental knowledge of the relation between flame extinction limit and decoupling properties effect.

Numerous research efforts have been devoted to expound the influence of different parameters on flame extinction limit. Experiments and numerical simulations were conducted by Yang et al. [15] to reassess the 2-D velocity boundary effect on the determination of extinction stretch rate in the counterflow flame, and the results showed that the burner exit stretch rate, the burner separation distance, and the impinged flow temperature can strongly affect the extinction stretch rate. H₂O addition and elevated pressure can also extremely extend the extinction limit due to the reduced amount of dissociation and the enhanced radiation reabsorption of H₂O for the counterflow methane/air flames [16]. Maruta et al. [17] and Li et al. [18] also experimentally and computationally studied the influence of enhanced pressure and high temperature on the extinction limit for the CH₄/CO₂ versus O₂/CO₂ flames, respectively. Both of their study reported that the appearance of CO₂ can generate significant influence on the flame extinction limits. Li et al. [19] also carried out series theoretical calculation and numerical simulation to reveal the stretch extinction characteristics of CH₄/CO₂ versus O₂/H₂O/CO₂ and O₂/H₂O counterflow nonpremixed flames at different oxidizer temperatures. The decoupling chemical and radiation effect of CO₂ dilution in O₂/N₂-CH₄, O₂/CO₂-CH₄, and O₂/N₂/CO₂-CH₄ counterflow diffusion flame on extinction limit were investigated by Kim et al. [20], the chemical effect and radiation effect on extinction limit display different behaviors at low strain rate and high strain rate, especially for the latter. Moreover, Shih [21] computed extinction limits of syngas counterflow diffusion flames with CO₂ dilution and categorized the CO₂ dilution effect on extinction limits as dilute effect, chemical effect, and radiation effect.

Nerveless so far, most scholars emphasize synergistic effect of CO₂ on the flame extinction limit. Rare researchers touch on this topic that the decoupled effects of CO₂ on the flame extinction limit. Additionally, a lack of critical data for the flame extinction limit with high CO₂ under the diverse conditions in practical facility, such as elevated pressure, could be a barrier for the designer and operator of the combustor.

Inspired by the above previous reference and discussion, taking CH₄/air counterflow diffusion flame with additional CO₂ to oxidizer stream as target, the coherent objectives of the present study were highlighted as follows: (1) the changes of flame microstructure from far away from extinction to near extinction with high CO₂ addition at different pressure were exhibited; (2) the decoupled effects (thermal and chemical effects) of CO₂ addition on extinction limits and flame microstructures under various pressures were conducted, and quantitative comparisons on above both decoupled effects were achieved to demonstrate the dominant role of CO₂ addition decoupled effects on extinction limit under various pressures; and (3) the critical parameters governing the extinction limits were discussed by chemical kinetics analysis to reveal the contribution of the kinetic term in the asymptotic solution with increasing CO₂ molar fraction and various pressures on the extinction limits. Those explorations could be in favor of better comprehension in flame extinction phenomenon of the EGR combustor and make contribution to the carbon capture.

2. Numerical Modelling

2.1. The Combustion Model

The adopted counterflow diffusion flame in the present study is schematically shown in Figure 1 which consisted of two concentric, circular nozzles directed towards each other. This configuration produces an axisymmetric flow field with a stagnation plane between the nozzles. And the momentum balance of the two streams decides the location of the stagnation plane. By mathematically simplifying the radial velocity which varies linearly in the radial direction , the fluid properties are functions of the axial distance only (one-dimensional) [22]. The detailed mathematical description (including mass, momentum, energy, and composition equations, as well as boundary conditions) can be found in Refs [16, 18]. In the present paper, the global strain rate is defined as the following formula: where the subscripts O and F represent the oxidizer and fuel flow streams, respectively, and denote the density and the velocity of the flow streams, and is the distance between the fuel and oxidizer nozzles and is specified as 4 cm.

The numerical simulation was successfully achieved by applying the OPPDIF module [23] of the CHEMKIN package [24–26] which predicted the flame extinction limits with a special technique called arc-length continuation through an iterative series of opposed-flow flame simulations. The two-point continuation method [27] was chosen to avoid this case that it may be difficult or even impossible to go through the extinction point with one-point control [27]. The CHEMKIN addresses both the mixture-averaged approach and the full multicomponent approach to the transport properties. Ji et al. [28] and Li et al. [29] reported that the obvious difference between the above approaches appears on the prediction of extinction limit for the diffusion flame. Therefore, it is strongly necessary to comprehensively evaluate the influence of them on the flame characteristic parameters and extinction limit. Figures 2 and 3 show the flame temperature distribution and the flame extinction limit, respectively, with the mixture-averaged approach and the full multicomponent approach under different pressure and CO₂ addition. What can be seen in Figure 2 is that the relative error of flame temperature distribution between the mixture-averaged approach and the full multicomponent approach is less than 0.83% and can be ignored. Nevertheless, in Figure 3, the gaps existed in the prediction of the flame extinction limit between the above two approaches, furthermore, which enlarge with the elevated pressure and CO₂ dilution ratio. The accuracy of calculations is of paramount importance at the reasonable expense of more CPU storage (CPU speed of 2.4 GHz each) and computational time. Thus, the full multicomponent approach is adopted to calculate the diffusion velocity for the mixture in the current study.

The code also allows for thermal diffusion, variable thermochemical properties, and variable transport properties [30]. Refs [31, 32]. can support more detail about the OPPDIF code. The GRI-Mech 3.0 mechanism involving 53 species and 325 reactions was employed as reaction mechanism, the applicability of which was also well verified in simulating the flame with CO₂ addition [4, 16, 18, 33] under elevated pressure [17] and high temperature [18].

It is commonly known that the extinction limit is categorized as radiation extinction limit [34, 35] and stretch extinction limit [34, 35]. The former was primarily caused by excessive radiative heat loss for the low-stretched flame, whereas the latter is caused by stretch-induced incomplete reaction for high-stretched flame and was the emphasis in the present study. The prediction of stretch extinction limits with the models taking accounting for reabsorption of gas component (such as SNB model) is between the results gained by adiabatic and optically thin models [17]. Both Ju et al. [34] and Kim et al. [20] also pointed out that the distinction lied on the calculation of the extinction limit between the optical thin model and SNB model was inconspicuous, even for the low stretched flame. Therefore, based on the previous studies, the optical thin model was employed to calculate the radiation emission and the Planck mean coefficients. More details about optical thin model can be seen in Ref. [34].

2.2. The Decoupled Strategy

The aims of the study are to isolate the decoupled effects of CO₂ addition (chemical, thermal) on the flame stretched extinction limit. Two groups of artificial species were introduced, named as FCO₂ and TCO₂, which own certain different properties from ordinary CO₂ according to their roles in the decoupled strategy. Our team also have conducted a series of comprehensive calculations on the CO₂ decoupled effects on flame characteristics of the diffusion flames, and the similar strategy originating and inspired from Liu et al. [36] was utilized in the present study. Thus, the strategy will be briefly described; see Ref. [31] for more details.

For the sake of separating the decoupled effects, FCO₂ is an inert specie without any participation in reaction process, while with the identical thermodynamic and transport properties of ordinary CO₂. Any differences in the results between FCO₂ and CO₂ are entirely contributed by the chemical effect of CO₂. Distinguishing TCO₂ and FCO₂ only lies in the thermodynamic property, the former is consistent with N₂, and any differences in the results between FCO₂ and TCO₂ are totally caused by the thermal effect of CO₂.

As illustrated and demonstrated in the study of Xie et al. [2], it is feasible to isolate the various decoupled effects of CO₂ by calculating the gap values of target parameter with CO₂ and any kind of fictitious species under different initial conditions. For an instance, taking (stretched extinction limit) as the target parameter, the detailed calculation methods can be carried out as the following formulas: where and are the quantitative chemical and thermal effects of CO₂ on the stretched extinction limits, respectively. And , , and represent the stretched extinction limits diluted with CO₂, FCO₂, and TCO₂, respectively.

Taking the objective of this paper as the guidance, the dilution ratio of the CO₂ in the counterflow diffusion flames (CH₄ versus CO₂/air) is 0 to 0.6 which is defined as the mole fraction of CO₂ in the CO₂/air oxidizer stream. The fuel and oxidizer stream temperature were fixed to 298 K. The various pressure conditions took place from 1 atm to 5 atm.

3. Results and Discussion

3.1. The Flame Stretched Extinction Limits

3.1.1. The CO₂ Dilution Ratio

Figure 4 exhibits the predicted maximum flame temperature along with the strain rate for the CH₄-CO₂/air diffusion flame of -0.6 at atmospheric pressure, . A linearly decreased tendency in maximum flame temperature with increasing strain rate is found in the figure except for the near extinction and low strain rate showing sharply decline. For the low-stretched flame, the complicated interactions among species reactions, flame stretch, and radiation heat loss caused the sharp decline in flame temperature maximum, whereas the heat release from combustion is inadequate for counteracting the convection heat loss and thus resulting in the high-stretched flame extinction. Also, it is observed that the extinction limits are suppressed with increasing CO₂ dilution ratio, indicating that more CO₂-diluted flames can be more easily extinguished with increasing strain rate.

3.1.2. The Elevated Pressure

Figure 5 demonstrates the effects of elevated pressure on extinction strain rate which is called extinction limit with different CO₂ dilution ratios. The tendency of the reduced extinction limits with increasing CO₂ dilution ratio is apparently consistent with Figure 4. The extinction limits are extended with elevated pressure for certain CO₂ dilution ratio, which indicate that more CO₂ can be added to the oxidizer at elevated pressure. To be honest, the extended extinction limits are foreseeable [21], since burning near extinction was intensified due to the reduced amount of dissociation [16] at elevated pressure. Particularly, it is worthy to note that the effect of the pressure on extinction limit is more obvious in a low CO₂ dilution ratio than in a high CO₂ dilution ratio, which resulted from both the effects of CO₂ dilution and elevated pressure. As discussed in the former section, more CO₂ diluted flames can be more easily extinguished, while no significant changes were observed when the elevated pressure effect on such flames (). What can be reasonably concluded based on above discussion is the CO₂ dilution effect on the extinction limits are more dominant rather than the pressure on that.

3.2. The Flame Microstructure

3.2.1. The CO₂ Dilution Ratio

Figure 6 manifests the flame microstructure near extinction and far from extinction under different CO₂ dilution ratio in the ambient pressure. The solid lines and the dash lines represent the flame parameters near extinction and far from extinction, respectively. The vertical lines exhibit the stagnation surface of the flames. A tendency is found that the stagnation surface moves towards oxidizer side with the flame extinction. The flame front can be characterized as the location of the peak value of the flame temperature [37], whereas no significant deviation value of the flame front was captured from far away extinction to near extinction due to the ratio of oxidizer to fuel in the stream [16, 30]. By comparing the distribution of the main combustion species (including the intermediate radicals), the relatively remarkable decreases of those were observed when the flames are gradually extinct, accompanying the narrower reaction zone and thinner flame as well. The distribution of O, H, and OH radicals takes important roles in hydrocarbon fuel combustion process, especially for OH radical which can reveal the burning intensity [19]. Hereafter, the chemical kinetic analysis of flame extinction limit mainly focuses on the distribution of OH radical concentration in the subsequent sections.

Figure 7 illustrates the effects of CO₂ dilution ratio on microstructure of the extinction flame, which displays the distribution of the flame temperature, main species, and active radicals such as O, OH, and H for CH₄-CO₂/air diffusion flame at extinction, partial enlarge supplementary diagram of Figure 7 is seen in Figure 8. The extinction limits with dilution ratio , 0.3, and 0.6 for the flame are 664.97 s^-1, 275.68 s^-1, and 72.06 s^-1, respectively. The obvious finding in the figure is the stagnation surface moving towards the fuel side along with increased CO₂ dilution ratio, since the oxidizer owned greater momentum with enhanced CO₂ dilution ratio than the fuel stream injected at the same velocity. Moreover, more CO₂ addition, the maximum flame temperature, and the flame thickness are lower and thicker, respectively, with a broader reaction zone. Meanwhile, the flame front is also closer to the stagnation surface due to the stoichiometry [38] for the reactions between CH₄ and CO₂/air. It is still of interest to observe in Figure 7 that the mole fractions of the active radicals such as O, OH, and H were reduced with improving CO₂ dilution ratio, indicating, and supporting the behaviors of the extinction limits in Figure 4.

3.2.2. The Elevated Pressure

Flame microstructures at extinction under various pressure ( atm, 3 atm, and 5 atm) with a certain CO₂ dilution ratio are compared and shown in Figure 9. The flame remarkably displays a narrower reaction zone and thinner flame thickness with elevated pressure. Also, the flame becomes closer to the stagnation surface. Surprisingly, the flame maximum temperature shows insignificant change with improving pressure. However, the mole fraction of the active radicals such as O, OH, and H has been declined with elevated pressure, which indicated the burning near extinction was intensified due to the reduced amount of dissociation with substantially elevated pressure. The behavior of extinction with elevated pressure is also a hint that the near extinction flame can be maintained by improving pressure until beyond the new larger extinction limit.

3.3. The Decoupled Effects

The reasons for the previously discussed behavior of the extinction limits due to CO₂ addition can be principally classified into chemical and thermal effects. To isolate the pure chemical and thermal effects from synergistic effect, the artificial species FCO₂ and TCO₂ were introduced, and calculations were conducted several times. Figure 10 exhibits the isolate chemical and thermal effects of CO₂ on flame extinction strain rate which is called extinction limit at various pressures. Note that in Figure 10 both of chemical and thermal properties of CO₂ addition result in a decrease of extinction limit, and the discrepancy between these two isolated effects becomes larger with increasing CO₂ dilution ratio. The tendencies of pure chemical and thermal effects on the extinction limit with CO₂ addition are displayed in Figures 11 and 12, respectively. As shown in Figure 11, here, the chemical effect of CO₂ addition on extinction limit decrease represents a kind of approximate quadratic-parabola tend along with the CO₂ dilution ratio, which surprisingly have a vertex corresponding to the CO₂ dilution ratio . Emergence of vertices implies that there is a critical CO₂ dilution ratio which can make the largest chemical effect on extinction limit if only considering the chemical effect on extinction limit. Dissimilarly, the thermal effect of CO₂ dilution on the decrease of extinction limits shows monotone growing trend, like near-linearly in Figure 12, indicating more CO₂ dilution and more decrease of extinction limit due to the thermal effect. For a certain CO₂ dilution ratio, both chemical and thermal effects on extinction limit enhanced with elevated pressure, while the degree of the enhancement is declined, i.e., higher pressure and less positive influence of pressure on the above isolated effects.

3.4. The Scaling Analysis for Extinction Limit

The stretched extinction flame of diffusion flame has been comprehensively and theoretically derived by an asymptotic method with large activation energy according to Arrhenius one-step reactions of Liñán [39]. Liu et al. [40] carried out a further study on the asymptotic solution taking radiative heat loss into consideration. The key parameters governing the extinction of counterflow diffusion flame can be classified into two terms based on employing several approximations [12, 18] by eliminating the radiative heat loss in asymptotic solution [12, 40], as flowing expression:

Here, the notations are consistent with those in Ref. [20]. and are the fuel and oxidizer Lewis numbers, is the pressure, and are mass fractions of fuel and oxidizer at the fuel and oxidizer streams, is heat of combustion of unit mass of fuel, is the configuration factor (1 for planar geometry and 2 for axisymmetric one), and are the specific heat at constant pressure and the universal gas constant, and and are the adiabatic temperature and the activation temperature, respectively. By employing the same consideration for those governing parameters [12], Equation (3) can be further rewritten with the governing parameters of the present study:

The right first term of Equation (4) was referred to the total fuel enthalpy flux, and the second term was named the kinetic term. However, for the current study, the fuel stream is constant methane without any dilution, representing that the total fuel enthalpy fluxes are the same and the influence of the fuel stream on the extinction limits can be reasonably neglected. The magnitude of radical OH formation was proposed as a representative marker of the kinetic term [18, 19]. Moreover, Kim et al. [20] employed a quasi-steady-state approximation for OH and conducted calculation to provide the theoretical basis of reasonability of OH formation determining the kinetic contribution to the diffusion flame extinction. Therefore, the flowing analysis of OH formation rate is quantitatively examined to evaluate the chemical kinetic effect on extinction limits.

Figure 13 shows the local OH generation and consumption rate of the flame at extinction of CH₄-air diffusion flame with CO₂ dilution ratio , 0.,3 and 0.6 and atm. It can be seen from Figure 13(a) that reaction absolutely dominates the OH generation rate, which is also the most important chain initiating reaction as the first step of CH₄ combustion process and generate abundant high-activation energy radicals. show great contribution as chain branching reactions to the OH generation as well. Additionally, the OH generation rates of (chain-branching reaction) and (chain-propagating reaction) were distinctly affected by CO₂ dilution and therefore displayed in the figure. The OH generation rates of those reactions significantly decrease with the enhanced CO₂ dilution ratio for the extinction flame, especially for . Meanwhile, the overall distribution of OH generation rate of above each reaction shifts towards the fuel side, due to the lower extinction rate with greater CO₂ dilution ratio, and the reaction zone closer to the stagnation plane. With regard to the OH consumption rate in Figure 13(b), (chain-branching reaction) and (chain-propagating reaction) are predominantly accounted for OH consumption. Moreover, play important roles in the process of OH consumption as well; noticeable change of those reactions caused by CO₂ dilution in extinction flame cannot be neglected. It is appreciable in Figure 13(b) that the OH consumption rates of those above reactions are suppressed due to the CO₂ addition for extinction flame. The exhibited curves in Figure 13 indicate that both of OH generation and consumption are appreciably inhibited for the extinction flame with CO₂ dilution, more CO₂ dilution ratio, and more extremely inhibition. To comprehensively analyze such inhibition, the numerical integration for entire reaction zone of OH reaction rate is shown in Figure 14: positive value for generation and negative value for consumption.

(a) OH generation

(b) OH consumption

For the extinction flame with CO₂ dilution, the global reaction rates of those reactions involving OH generating and consuming dramatically reduced along with the enhanced CO₂ dilution in Figure 14. As previous analysis, high CO₂ dilution ratio in air results in a low extinction rate, which means the flame with more CO₂ dilution and being easier to extinction. For instance, the flame extinction limit is as low as 72.06 s^-1 with CO₂ dilution ratio . The fuel stream and oxidizer stream in such extinction flames are injected from the nozzles with slow velocity into the combustor. Nonetheless, the results shown in Figure 14 give a hint of the reason for the flame extinction with high CO₂ dilution ratio, which was caused by combustion intensity decrease reflecting in the suppression of OH generation, rather than the scarcity of residence time, and insufficiency of the fuel combustion.

Figure 15 demonstrates the pressure effect on the OH generation and consumption rate of the CH₄/air diffusion flame with CO₂ dilution ratio at extinction limit, only considering the reactions with relatively remarkable contribution to OH generation and consumption. It is observed that the elevated pressure accelerates the reaction rates of not only OH generation but also OH consumption. And the enhanced pressure shows significant positive effect on reactions , indicating that more OH radicals were produced under higher pressure for extinction flame. Meanwhile, the reactions consuming OH radicals are promoted by the elevated pressure such as the first step of CH₄ exothermic reaction and the chain termination reactions . Reaction as chain termination reaction which is remarkable for the OH consumption under pressure 5 atm is not significant for the OH consumption under pressure 1 atm and 3 atm. The agglomeration zone of the reactions rate displays obvious deviation towards the fuel side along with the elevated pressure, corresponding to the behavior of the flame front in Figure 9. The global generation rates of OH radicals for the extinction flame with CO₂ dilution ratio under different pressure as a function of the distance from the fuel nozzle are plotted in Figure 16, positive value for generation and negative value for consumption. It is obviously shown that the elevated pressure results in acceleration on the overall generation rates of OH radicals in the extinction flame. The reason for that acceleration is the elevated pressure which led to thicker reactant species concentration and more violent reaction.

(a) OH generation

(b) OH consumption

4. Conclusion

Extinction limits and flame microstructure of CH₄ versus air (N₂/O₂) counterflow diffusion flame with CO₂ addition to oxidizer stream under various pressure conditions were numerically investigated by a proposed decoupled strategy, which can extract the relatively pure chemical and thermal effects of CO₂ addition from the synergistic effect on extinction limits and flame microstructure.

The quantitative analysis showed that the synergistic effect of CO₂ addition results in the reduction of the extinction limit. More specifically for that negative effect of CO₂ addition on the extinction limit, the thermal effect of CO₂ addition by employing decoupled strategy is more significant than the chemical effect. An interesting comparison reveals that the thermal effect of CO₂ addition on the extinction limit monotonically increases along with CO₂ mole fraction, while a kind of approximate quadratic-parabola tends for the chemical effect on which. With elevated pressure, the extinction limits are generally extended due to the enhanced concentration of combustion species, indicating that flame can be sustained under higher strain rate with the assistance of elevated pressure. What more, the elevated pressure plays positive role in both thermal effect and the chemical effect of CO₂ addition on the extinction limit. Flame microstructure analysis exhibits that the flame extinction process is accompanied by narrower combustion zone and thinner flame thickness, while there is no visible displacement of the flame front location. The distribution of active radical such as OH, H, and O indicates that depressed burning intensity and inadequate heat release result in flame extinction. The OH production rate successfully elucidates the contribution of the kinetic term in the asymptotic solution with increasing CO₂ molar fraction and various pressures to the extinction limits, which can reasonably be important tools to predict the extinction limit of CH₄-air (O₂/N₂) flame.

Nomenclature

:	Specific heat at constant pressure
:	Heat of combustion of unit mass of fuel
:	Configuration factor
:	Distance
Le:	Lewis number
:	Pressure
:	Universal gas constant
:	Temperature
:	Velocity
:	Mass fraction
:	Global strain rate
:	Extinction strain rate
:	Dilution ratio
:	OH formation rate.

Subscripts

F:	Fuel
O:	Oxidizer
CO₂:	Dilution with CO₂
FCO₂:	Dilution with FCO₂
TCO₂:	Dilution with TCO₂
chem:	Effect of chemical property
therm:	Effect of thermal property.

Data Availability

The data are available upon request.

Conflicts of Interest

There is no conflict of interest to report.

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