Investigation and Optimization of Existing Laminar Flame Velocity Reaction Mechanisms in NH3 and NH3/H2 Flames

Abstract

With the increasing greenhouse effect and energy crisis, ammonia is one of the most promising alternative fuels. However, the research on the combustion characteristics of ammonia needs to be further improved. In this paper, the combustion characteristics of two kinds of ammonia and ammonia–hydrogen amino fuels (laminar flame velocity) are investigated through experimental data and kinetic mechanism analysis, and the laminar flame predictions are calculated for 20 kinds of ammonia mechanisms with different equivalence ratios, oxygen contents, and hydrogen doping ratios, after which MAPE and sensitivity analysis are used to determine the applicability of the mechanisms. The results indicate that the incorporation of hydrogen and the augmentation of oxygen concentration induce exponential and linear increases in the laminar flame speed of ammonia, respectively. The laminar flame speed of ammonia reaches its maximum at an equivalence ratio of approximately 1.1, with a value ranging from 6 to 7 cm/s. Under a hydrogen addition ratio of 0.4, the laminar flame speed of ammonia even reaches 29–30 cm/s. The Otomo and Zhang mechanisms are recommended for ammonia fuels with different equivalence ratios and oxygen contents. For different equivalence ratios and hydrogen doping ratios of ammonia–hydrogen combustion, the Gotama and Stagni mechanisms are more suitable. For the overall conditions, the Zhang mechanism is recommended in this paper to simulate the laminar flame velocity for ammonia and ammonia–hydrogen mechanisms. Based on the Glarborg mechanism, an optimized mechanism is proposed to simulate the laminar flame velocity for both fuels, which reduces to 9.55% compared to 43% for the average calculation error of the original mechanism.

1. Introduction

In recent years, the threat of a global energy crisis has grown as fossil energy reserves have been gradually depleted. The use of fossil energy is also a key factor in environmental change and pollution. Large amounts of fossil energy consumption cause greenhouse gas emissions, which increase the concentration of greenhouse gases in the atmosphere and strengthen the greenhouse effect, leading to global warming. The global average temperature has increased by 0.4 to 0.8 °C since 1860 [1]. CO₂ is the main component of greenhouse gases, and about 90% or more of anthropogenic CO₂ emissions are caused by fossil energy use [2]. The use of fossil fuels, especially coal, results in large amounts of sulfur dioxide and soot emissions and is also a major source of air pollution. To reduce dependence on fossil energy, many countries have shifted their development direction towards alternative and clean energy and have taken the development of renewable energy as an important measure to alleviate the contradiction in energy supply and respond to climate change.

Ammonia, as a new and very promising clean energy source, has the following advantages: (1) Ammonia does not contain carbon or silicon, and does not produce hazardous gases such as carbon dioxide and methane when burned, but it does emit NO_X [3]. (2) NH₃ has three hydrogen atoms (H) in one molecule, meaning that it is a substance with a high density of hydrogen, and it is a good hydrogen carrier [4] (3) With mature technology for the transportation and storage of large quantities of NH₃, ammonia can be transported by automobiles and railroad tank cars, pipelines, and ammonia carriers. In addition, since the liquefaction conditions for NH₃ are essentially the same as those for liquefied petroleum gas (LPG), LPG infrastructure can be used for NH₃ transportation and storage [5].

Ammonia is therefore an important alternative energy source today. Ammonia is used in a variety of energy devices, such as industrial gas turbines [6,7], fuel cells [8,9], ships [10,11], and automobile engines [12]. However, ammonia also has disadvantages, such as a low calorific value, high auto-ignition temperature, narrow flammability limit, slower combustion rate, and long ignition delay time [13]. As can be seen from Table 1, compared with ammonia alone, hydrogen is very suitable for combustion with ammonia because of its high combustion speed, good diffusivity, and low ignition energy. Research has shown that the addition of hydrogen with better combustion performance to ammonia can effectively improve the combustion, increase the combustion speed, and broaden the flammability limit of ammonia fuel. In additional, the final product of ammonia–hydrogen combustion is water, which has a significant advantage in carbon-free combustion.

Laminar flame velocity is an essential parameter for studying the combustion characteristics of reactive fuels and examining the mechanisms of chemical reactions during the combustion process, as well as an important basis for the theoretical prediction of the combustion process and study of the mechanisms of combustion product generation. Compared with fossil fuels such as oil and natural gas, ammonia’s lower laminar flame speed limits its application in combustion systems. In response to this problem of the low laminar flow flame of ammonia, ammonia combustion under different conditions has been investigated, such as the addition of highly reactive hydrogen and methane, the provision of an oxygen-enriched environment for ammonia combustion, and the wrinkling of the flame by increasing turbulence, which improves the flame’s surface density and, ultimately, increases the flame’s laminar combustion velocity. Chen et al. researched the laminar flow combustion characteristics of H₂/NH₃/air mixtures in a constant-capacity burner. The initial pressures ranged from 0.5 to 1.5 atm, the equivalence ratios ranged from 0.5 to 1.5, and the hydrogen ratios ranged from 0 to 1.0. The laminar combustion velocities increased monotonically with the increase in the hydrogen ratio and showed an inverted U-shaped relationship with the equivalence ratio. The initial pressure had the weakest effect on the laminar combustion velocity of H₂/NH₃/air mixtures compared to the hydrogen ratio and the equivalence ratio. The laminar combustion velocity decreased gradually with the initial pressure [15]. Zhou et al. investigated the laminar combustion rate of NH₃/air, NH₃/H₂/air, NH₃/CO/air, and NH₃/CH₄/air mixtures at different molar fractions and found that NH₃/air had the greatest dependence on temperature, followed by NH₃/H₂/air, NH₃/CH₄/air, and NH₃/CO/air [16]. Lee et al. investigated the laminar flame velocity of ammonia at ambient temperature and pressure with a fuel equivalence ratio of 0.60~1.67 and a molar fraction of hydrogen in the fuel gas of 0.0~0.5. It was found that the ammonia’s laminar flow combustion velocity increased significantly after hydrogenation due to the increase in the number of hydrogen atoms. Moreover, the emission of NO_x and N₂O was lower under the rich fuel hydrogenation condition [17]. Li et al. investigated the laminar flow combustion velocity of NH₃ flames with a hydrogen ratio ranging from 0 to 1.0. It was found that the main reason for the increase in the laminar flow combustion velocity of hydrogenation was the reduction in chemical activation energy due to the high mobility of H₂ and the chemical effect caused by the transport effect [18]. Ji et al. studied the laminar flame velocity of dissociated ammonia and found that dissociated ammonia also promotes an improvement in the laminar flame velocity, and that its laminar combustion velocity monotonously increases with the increase in the degree of dissociation [19]. Mei et al. studied the laminar flame propagation of NH₃/O₂/N₂ mixtures with varying oxygen contents, and the results showed that the laminar combustion velocity increased with the increase in the oxygen content [20].

Chemical kinetic modeling of NH₃ and NH₃/H₂ flames has received extensive attention in recent years, and the reaction mechanism of ammonia has been continuously improved. Miller et al. provided the first more detailed and complete description of the reaction mechanism of ammonia’s combustion and oxidation, proposing a reaction mechanism that includes 22 component and 98 primary element reactions, and that the flame structure of NH₃ can be reasonably predicted over a certain range of temperatures and pressures [21]. Konnov et al. developed a mechanism for combining N₂H₃ and N₂H₄ reactions to improve the prediction of flame structure in low-pressure (4.6 kPa) and lean-burning (NH₃/O₂) flames [22]. Tian et al. determined the distributions of intermediates and products in 11 NH₃/CH₄/O₂/Ar flames with different molar ratios and proposed a comprehensive kinetic mechanism incorporating 84 components and 703 radical reactions [23]. Okafor et al. established a detailed reaction mechanism for the combustion of NH₃ and CH₄ mixtures based on GRI Mech 3.0 and the work of Tian et al. The mechanism was validated by experimental results. They concluded that the variation in NH₃/CH₄ flames’ burning rate is mainly realized by influencing the concentrations of H and OH radicals [24]. Otomo et al. proposed an NH₃/air and NH₃/H₂/air combustion mechanism containing 59 components and 356 reactions, based on the mechanism of Song et al. [25] The experimental data on laminar flame velocity and ignition delay time for a wide range of equivalence ratios and pressures were well reproduced [26]. Glarborg et al. developed a detailed mechanism for the nitrogen chemistry associated with combustion processes. While it performs well in simulating the morphology in flames and jet-stirred reactors, especially as a non-optimized mechanism, its prediction of ignition delay times and laminar combustion velocities at high temperatures and pressures is unsatisfactory [27]. Shrestha et al., on the other hand, were the first to develop a mechanistic model specifically for premixed NH₃/H₂ flames. Their reaction mechanism considers the formation and reduction of NO_X. It was validated by laminar flame velocity and ignition delay time [28]. Mei et al. developed a kinetic model for ammonia combustion with 38 components and 265 radicals, based on Shrestha’s model, updating the rate constants of the important reactions. The model was validated by combining the measured laminar flame velocity of ammonia under oxygen-enriched and high-pressure conditions, along with the ignition delay time from other literature [20].

In this paper, available experimental data on ammonia and ammonia–hydrogen laminar flames are used to compare the differences in the simulated values of 20 mechanisms, to analyze the performance of each mechanism, and to perform sensitivity analyses to identify the important kinetic reactions that contribute to laminar flames, as well as to derive the most accurate mechanisms for various combustion conditions. Finally, the mechanisms are also optimized. This study is extremely important to establish the chemical reduction mechanism of ammonia and hydrogen fuels, providing a reference for the selection of ammonia combustion mechanisms, and can enhance the adaptability and accuracy of combustion mechanisms, promoting the practical application of zero-carbon fuels.

2. Computational Details

In this paper, ANSYS Chemkin-Pro2019 software was used to carry out the kinetic analysis of the seed mechanism, the combustion characteristics of the mechanism were analyzed, and the premixed laminar flame velocity calculation model in ANSYS Chemkin-Pro2019 was applied to calculate the laminar flame. All of the simulations of the mechanism were carried out in a one-dimensional computational domain of 20 cm, with a maximum grid size of 500, and the adaptive mesh control based on the solution gradient and curvature was set to 0.01 and 0.05, respectively. Additionally, the mesh dependence was considered, and the accuracy was adjusted for different cases to achieve the most accurate results. The initial conditions for the premixed reactants were as follows: pressure 1 atm, temperature 298 K, fuel/air equivalent ratio range 0.7–1.4, hydrogen mixing ratio 0–0.7, oxygen content 0–0.5. The multicomponent transport method was used in ANSYS Chemkin-Pro2019 to calculate the combustion rate using the Soret effect, based on the Metghalchi and Kech power-law relationship, as per Equation (1):

(1)$s_u=s_{u0}{\left({\displaystyle \frac{T_u}{T_0}}\right)}^{\alpha }{\left({\displaystyle \frac{P}{P_0}}\right)}^{\beta }$

where S_u is the laminar burning velocity (cm/s), T_u and p are the unburned temperature (K) and pressure (atm), respectively, S_u0, $\alpha$, and $\beta$ are constants, and the subscript 0 represents the standard state.

Table 2 illustrates the main inventors, the number of components, and the number of reactions for the proposed 20 mechanisms. The 20 mechanisms used in this paper have been compared and examined.

3. Results and Discussion

3.1. NH₃/Air Flame

• (1). Laminar flame velocity at different equivalent ratios

Figure shows the combustion variations of 20 mechanisms of premixed NH₃/air laminar flame velocity at 1 atm, 298 K, and different equivalence ratios (φ = 0.7~1.4). The experimental flame velocity data were obtained from the works of Li et al. [41], Mei et al. [20], Han et al. [35], and Lhuillier et al. [42]. From Figure 1a, it can be seen that there is a nonlinear relationship between the equivalence ratio and the NH₃/air laminar flame velocity, and the laminar flame velocity exhibits a tendency to increase and then decrease as the equivalence ratio increases. When the equivalence ratio is about 1.1, the laminar flame reaches its maximum value, which is about 6~8 cm/s. Under dilute combustion conditions (φ = 0.7~1), the Konnov, Hadi, Glarborg, Duynslaegher, and Klippenstein mechanisms overpredict the flame velocity, and the predictive ability of the remaining mechanisms is similar and more inconsistent. However, under the rich combustion conditions, the prediction ability of different mechanisms varies greatly, and most of them overpredict the laminar flame speed, leaving only the Otomo, GRI-Mech3.0, and Wang mechanisms with flame speed calculations that are closer to the experimental results. Figure 1b shows the average absolute percentage errors of the calculation results for the 20 mechanisms at equivalence ratios of 0.8 to 1.2. The average absolute percentage error is calculated as shown in Equation (2):

(2)$M={\displaystyle \frac{1}{n}}\sum _{i=1}^n|{\displaystyle \frac{v_e-v_s}{v_e}}|$

where M is the mean absolute percentage error, v_e is the experimental value, v_s is the simulated value, and n is the number of points counted. Based on the error values in Figure 1b, we can conclude that the flame burning rate predicted by the Otomo mechanism is closer to the experimental data, as it has the smallest error compared to the GRI-Mech 3.0, Wang, and Otomo mechanisms, with a mean absolute percentage error of 4%. In addition, the number of components and the number of basic reactions of the Otomo mechanism are less compared to the other two mechanisms. The smaller the number of components and the number of basic reactions, the shorter the simulation calculation time. Finally, based on the differences in the number of components and the number of basic reactions of different mechanisms, the size of the average absolute percentage error, and other factors, this paper recommends the Otomo mechanism to be used for the prediction of NH₃/air laminar flame burning speed.

Figure 2 shows the NH₃/air laminar flame velocity results predicted by eight chemical kinetic reaction mechanisms with low errors, at equivalence ratios ranging from 0.7 to 1.4. The Otomo, Zhang, and Okafor mechanisms are in good agreement with the experimental measurements over the entire φ range. Although the laminar flame velocity is underestimated at φ = 1~1.1, the Otomo mechanism has the smallest discrepancy with the experimental data. The Zhang and Okafor mechanisms perform well under thin combustion conditions, but both overestimate the laminar flame velocity under rich combustion conditions, with laminar flame overestimation values between 8% and 15% for both mechanisms. The Wang mechanism, although it overpredicts the flame over the entire range of φ velocity, performs better under rich combustion conditions.

For investigating the flame speed sensitivity of NH₃/air laminar flame speed, three kinetic reaction mechanisms—Otomo, Zhang, and Wang—were selected to analyze the combustion performance of the mechanisms at equivalence ratios of 0.8, 1, and 1.2. These three mechanisms were chosen because, at equivalence ratios of 0.7~1, the Otomo and Zhang mechanisms have better combustion capabilities, and the Wang mechanism overestimates the laminar flame speed. However, at equivalence ratios of 1 to 1.4, the Zhang mechanism overestimates the laminar flame speed, the Otomo mechanism predicts results that match the experimental results, and the Wang mechanism falls in between, slightly overestimating the laminar flame speed.

The most important reactions for promoting/delaying the laminar flame velocity of pure ammonia for the chosen mechanisms, along with their corresponding sensitivity coefficients, are given in Figure 3. As can be seen from the figure, the results of the sensitivity analyses for all of the selected mechanisms show that H + O₂ <=> O + OH and NH₂ + NO <=> NNH + OH play a major role in increasing the laminar flame velocity. The reaction with a negative sensitivity coefficient, NH₂ + NO <=> N₂ + H₂O, has the greatest effect on suppressing the laminar flame speed. The sensitivity coefficients of most of the important reactions of the selected mechanisms are similar, yet there are still some differences, which are caused by the different parameters selected for the chemical reactions between different mechanisms, and the sensitivity coefficients can be changed by modifying the Arrhenius parameters, the activation energies of the reactions, and the primitives of their mechanisms.

The three mechanisms showed different chemistry when comparing the differences in the sensitivity of the most important reactions between the mechanisms. The Zhang mechanism placed more emphasis on the importance of the NH₂ + NO <=> NNH + OH reaction, while the Wang mechanism showed the importance of the NH₂ + NH <=> N₂H₂ + H reaction. The Otomo mechanism placed more emphasis on the importance of the contribution of the NO + H (+M) <=> HNO (+M) reaction to the flame speed. In addition, compared to Zhang and Wang mechanisms, the Otomo mechanism had a smaller negative sensitivity coefficient for NH₂ + NO <=> N₂ + H₂O reaction at a 1.2 equivalence ratio, promoting the reduction in laminar combustion velocity. This may explain the better predictive ability of the Otomo mechanism under rich combustion conditions. The Wang mechanism also gives kinetic reactions of NH₂ + NH = N₂H₃ and NH₂ + NH₂ = N₂H₃ + H, which cannot be found in the Otomo and Zhang chemical databases, exhibiting the slowing effect of the two reactions on the laminar flame velocity.

• (2). Laminar flame velocities at different oxygen levels

Figure 4 shows the predicted LBV measurements of NH₃/O₂/N₂ mixtures with different oxygen contents for 20 mechanisms at 298 K and 1 atm, along with the mean absolute percentage error of their data results, while Figure 5 shows the predicted NH₃/air laminar flame velocity results for six chemical kinetic reaction mechanisms with lower errors when the oxygen content is 21–50%. The experimental results are from Mei et al. [20] and Shrestha et al. [28]. Among the 20 mechanisms, the Duynslaegher and GRI-Mech3.0 mechanisms have the highest and lowest predicted LBVs, respectively, and the Duynslaegher, Konnov, Hadi, Klippenstein, and Glarborg mechanisms all overpredict their laminar burning velocities. At present, the Otomo, Bertolino, Mei, and Zhang mechanisms can predict the LBVs at different oxygen contents. Although the Zhang and Otomo mechanisms slightly underestimate the laminar flame velocity at more than 35% oxygen content, their simulation results are generally better than those of the other mechanisms, and their average absolute percentage errors are all 4%.

To further validate the mixed NH₃/O₂/N₂ combustion mechanisms with different oxygen contents and their prediction ability, and to analyze the important responses of these mechanisms, the Otomo and Zhang mechanisms, which perform well, and the Glarborg mechanism, which has a large number of prediction deviations, were selected for sensitivity analysis, and the changes in the sensitivity coefficients of the important responses were analyzed for oxygen contents of 21%, 35%, and 50%, as shown in Figure 6.

The sensitivity analysis results show that H + O₂ <=> O + OH remains the most important reaction as the oxygen content increases. Comparing the three mechanisms, Zhang’s mechanism mainly emphasizes the importance of NH + OH <=> HNO + H, Otomo’s mechanism stresses the effects of the reactions N₂O (+M) <=> N₂ + O (+M) and NO + H (+M) <=> HNO (+M), and Glarborg’s mechanism weakens the effect of HNO + OH <=> NO + H₂O. The differences in the simulation values of the Zhang, Otomo, and Glarborg mechanisms mainly resulted from the choice of these reaction parameters. Based on the numerical simulation results, it can be concluded that the Zhang mechanism is the most reliable. The parameters of the relevant reactions in the Zhang mechanism better reflect the importance of the different elemental reactions and are therefore more suitable for predicting the laminar combustion rate of ammonia–hydrogen flames with different oxygen contents.

3.2. NH₃/H₂/Air Flame

• (1). Laminar flame velocity at different hydrogen mixing ratios

Figure 7 shows the ammonia laminar flame velocities modeled by 20 mechanisms at different hydrogen doping ratios (H₂ = 0 to 0.7), 298 K, and 1 atm, as well as the average absolute percentage error of their data results, while Figure 8 shows the ammonia laminar combustion flame velocities predicted by the seven chemical kinetic reaction mechanisms with smaller errors under different hydrogen doping ratios.

The experimental results were obtained from the works of Li et al. [41], Lee et al. [17], Han et al. [35], and Lhuillier et al. [42]. Hydrogen doping in ammonia for mixed combustion can significantly increase the laminar flame velocity of ammonia fuel. The combustion velocity of ammonia–hydrogen mixed flames showed an exponential increase with the increase in the hydrogen doping ratio. The mechanisms of Hadi et al. [32], Konnov et al. [22], Glarborg et al. [27], and Klippenstein et al. [33] overestimated the flame velocity under all conditions. The mechanism of Otomo et al. [26], GRI-Mech3 et al. [29], and Tian et al. [23] underestimated the flame speed under all conditions. The mechanisms of Mei et al. [20], Han et al. [35], Wang et al. [38], and Gotama et al. [39] predicted that the flame speeds were more in line with the measured values when the H₂ content in the fuel mixture was low; however, four mechanisms slightly underestimated the flame speeds when the H₂ content in the mixture was higher than 40%. The mechanism of Song overestimated the flame speeds of ammonia at a hydrogen doping ratio of 0 to 0.4 and slightly underestimated the flame speed for hydrogen doping ratios greater than 0.4. The mechanisms of Stagni et al. [36], Shrestha et al. [28], and Okafor et al. [24] all predicted the laminar flame burning rate for H₂ content well from 0% to 100%. Comparing the three mechanisms for the same computational setups, the Stagni mechanism has the smallest mean absolute percentage error. Moreover, the Stagni mechanism has fewer basic reactions and components than the Shrestha and Okafor mechanisms, and the computational time of the Stagni mechanism is shorter than that of the other two mechanisms. Therefore, the Stagni mechanism is recommended to predict premixed NH₃/H₂/air combustion at different hydrogen doping ratios.

In order to analyze the origin of these differences in the kinetic mechanisms at different hydrogen doping ratios, the Glarborg, Stagni, and Otomo mechanisms were selected for sensitivity analysis. These three mechanisms were chosen because the Glarborg mechanism slightly overestimates the laminar flame velocity, the Otomo mechanism underestimates the laminar flame velocity, and the Stagni kinetic mechanism performs better, presenting consistency with the experimental data. Figure 9 shows the sensitivity coefficients of the above-selected mechanisms for hydrogen doping ratios of 0, 0.3, and 0.5, and demonstrates the most important reactions that promote/delay the laminar flame velocity. As can be seen from the figure, the most important reaction among all of these mechanisms is H + O₂ <=> O + OH, which has a sensitivity value of around 0.6. Compared to the other mechanisms, the Stagni mechanism mainly emphasizes the importance of NH + H <=> N + H₂, NH + NO <=> N₂O + H, with little difference in the sensitivity of the other reactions. Thus, this is the main reason for the problematic predictive ability of the Stagni mechanism versus the remaining two mechanisms. In addition, the Otomo mechanism emphasizes the importance of HNO + H <=> NO + H₂, and the Glarborg mechanism emphasizes the importance of H + O₂ (+M) <=> HO₂ (+M).

• (2). Laminar flame velocity at different equivalent ratios

Figure 10 shows the predicted ammonia laminar flame velocities for 20 mechanisms with different equivalence ratios (φ = 0.7~1.6) and a hydrogen doping ratio of 40%, as well as the average absolute percentage errors of their data results, and Figure 11 shows the predicted ammonia laminar flame velocities for the seven mechanisms with low errors in Figure 10. The experimental results were obtained from the works of Wang et al. [38], Han et al. [35], and Lhuillier et al. [42]. Consistent with the pure ammonia combustion pattern, the ammonia–hydrogen premixed flame also showed a tendency to increase and then decrease after hydrogen doping, and the laminar flame velocity peaked at about 30 cm/s at an equivalence ratio of about 1.1. Among the 20 mechanisms, the Gotama mechanism predicted the most consistent results with the experimental data, but it slightly overestimated the laminar flame velocity results at equivalence ratios greater than 1.2. The Mei mechanism underestimated the laminar combustion velocity under the thin combustion condition and overestimated the laminar combustion velocity at equivalence ratios greater than 1.2. The Glarborg mechanism overestimated the laminar combustion velocity over the entire range of equivalence ratios; however, the Otomo mechanism underestimated the laminar combustion velocity over the entire range of equivalence ratios. The combination of the mean absolute percentage error and the computational gap between the number of components and the number of elementary reactions makes the use of the Gotama mechanism more recommendable for predicting combustion velocities in ammonia–hydrogen laminar premixed flames, as it has the smallest mean absolute percentage error and consumes fewer computational resources than the other mechanisms.

In order to verify the differences in the significance of the reactions between the relevant mechanisms at different equivalence ratios, the Gotama mechanism, which performs well, and the Glarborg and Otomo mechanisms, which are subject to some errors, were selected for the sensitivity analysis, as shown in Figure 12. H + O₂ <=> O + OH was the most important reaction in the ammonia–hydrogen laminar flow premixed combustion, and the second most important reaction in the Gotama mechanism was NH₂ + NH <=> N₂H₂ + H, but the importance of this reaction decreased in the Glarborg and Otomo mechanisms. The Glarborg mechanism emphasizes the importance of H + O₂ (+M) <=> HO₂ (+M) compared to the other two mechanisms. In addition, the Gotama mechanism gives NH₂ + NH <=> N₂H₃ and 2NH₂ <=> N₂H₃ + H, which are not found in the Glarborg and Otomo mechanisms and manifest the same retarding effect on laminar flame velocity as in the Wang mechanism.

3.3. Mechanisms’ Summary and Recommendations

There are deviations in the calculations between the mechanisms due to the different settings of the reaction rate constants, as well as the differences in the reactions of the included components and primitives. The focus on the reactions also varies between the different mechanisms, with the Otomo mechanism emphasizing the reverse inhibition of the NH₂ + NO <=> N₂ + H₂O reaction and the Zhang mechanism emphasizing the positive promotion of the NH₂ + NO <=> NNH + OH reaction when modeling the laminar burning rate of ammonia laminar flames. In modeling the laminar combustion velocity of ammonia–hydrogen laminar flames, the Gotama mechanism also gives NH₂ + NH <=> N₂H₃ and 2NH₂ <=> N₂H₃ + H, which are not found in the Glarborg and Otomo mechanisms, and emphasizes the reverse inhibition of the two reactions.

In this paper, a table of recommended mechanisms is given based on the prediction result error of the mechanisms and their applicability, as shown in Table 3. For the mean absolute percentage error of 20 mechanisms under different conditions, the results were calculated in this paper, along with the mean error values under the calculated conditions, as shown in Figure 13. The Zhang mechanism is recommended to predict the laminar flame velocity for amino mechanisms.

4. Mechanism Optimizations

The Glarborg mechanism, as a non-optimized mechanism for nitrogen chemistry, has a large deviation in the prediction of NH₃ and premixed NH₃/H₂ combustion, and it grossly overestimates the laminar flame velocity at different equivalence ratios, oxygen ratios, and hydrogen doping ratios. The deviation of the Glarborg mechanism from the experimental data is due to the lack of some primitive reactions in the mechanism for premixed ammonia–hydrogen combustion, along with the fact that the mechanism-related reactions and parameters need to be corrected. The parameters need to be corrected and the mechanism optimized to address these issues.

The optimization mechanism is to optimize the kinetic parameters of the key elementary reactions through sensitivity analysis and adjust the rates of the key elementary reactions. There are four steps in the mechanization process: (1) Remove the carbon-containing species and reactions from the Glarborg mechanism. (2) Compare the Glarborg mechanism with the overall well-performing Zhang, Otomo, and Bertolino mechanisms to determine the lacking and redundant primitive reactions, and then remove the redundant primitive reactions and add the lacking ones to the original mechanism. (3) Compare the differences in reaction parameters between the Glarborg, Zhang, Otomo, and Bertolino motif reactions, identify the motif reactions of Mei and Otomo that have the same reaction parameters, and then update the Glarborg mechanism using these parameters. (4) Perform sensitivity analyses of the Glarborg, Zhang, Otomo, Bertolino, and Mei mechanisms, compare the sensitivity differences between the primitive reactions of the Glarborg mechanism and the other mechanisms, and correct the coefficients of the important reactions with large differences. Improve the accuracy of the mechanism in predicting pure ammonia combustion and ammonia/hydrogen composite combustion. The detailed optimization mechanism process can be found in the Supplementary Materials.

The new mechanisms are therefore based on the Glarborg mechanism as the main framework and are mainly applicable to NH₃/air and NH₃/H₂/air fuels. A total of 29 reactions were improved in the final reaction mechanism, of which 22 reactions were updated, 6 reactions were added, and 1 reaction was deleted. The specific reaction modifications are shown in Table 4.

A comparison of the predictions before and after the optimization of the Glarborg mechanism is shown in Figure 14. Compared to the original mechanism, the optimized version of the mechanism shows a significant improvement in the results, with an average absolute percentage error of around 10%. The predictions of the Glarborg mechanism for both NH₃/air and NH₃/H₂/air fuel mixtures show a certain deviation from the experimental values. The optimized version of the Glarborg mechanism has the same prediction ability (average absolute percentage error of 11.2%) as the Stagni mechanism for the various NH₃/air equivalence ratios, and its prediction results (average absolute percentage error of 11%) are comparable to those of the Stagni mechanism for various oxygen content conditions. The optimized version of the Glarborg mechanism for different NH₃/air equivalence ratios (with an average absolute percentage error of 11.2%) is equivalent to the Stagni mechanism, and for different oxygen contents (with an average absolute percentage error of 8.4%) it is similar to the Okafor mechanism. In contrast, the laminar flame combustion rate prediction for NH₃/H₂/air mixtures is equivalent to the Mei mechanism. The corrected version is called the modified Glarborg model. The computational error of the optimization mechanism is greater than that of the original mechanism when the hydrogen doping ratio is 0.5–0.6, but the prediction results of the modified mechanism are closer to the experimental values than those of the original mechanism under other conditions. In conclusion, the predictive ability of the Glarborg optimization mechanism is better than that of the original mechanism. As shown in Table 5, the average error of the results of the Glarborg correction mechanism for both fuels is also smaller than that of the original mechanism.

5. Conclusions

This article investigated laminar flame velocities under atmospheric pressure and temperature conditions relating to different equivalence ratios, hydrogen doping ratios, and oxygen contents. The ability of 20 chemical kinetic mechanisms to predict laminar flame velocities was evaluated based on experimental results previously reported in the literature. The main conclusions are as follows:

• (1). In ammonia combustion, the addition of hydrogen and the increase in oxygen content resulted in exponential and linear increases in laminar flame velocity, respectively. At an equivalence ratio of about 1.1, the combustion intensity of NH₃ fuel reached a maximum, and the laminar flame velocity of ammonia reached a peak of about 6–7 cm/s. The laminar flame velocity of ammonia at an oxygen content of 45% was equivalent to the numerical quantity at a hydrogen doping ratio of 0.5.

• (2). Twenty mechanisms were tested for their ability to predict laminar flames for NH₃/air and NH₃/H₂/air fuel combustion to obtain the optimal mechanism for each case. For NH₃/air combustion, the Otomo and Zhang mechanisms are recommended for different equivalence ratios and oxygen contents. For NH₃/H₂/air combustion, the Gotama mechanism is recommended for laminar flame velocity prediction at different equivalence ratios. For different hydrogen doping ratios, the Stagni mechanism is recommended.

• (3). The Glarborg mechanism was used as the main framework, which is mainly applicable to the optimization mechanism of NH₃/air and NH₃/H₂/air fuels. Compared with the original mechanism, the optimized mechanism improves a total of 29 elemental reactions, of which 22 are updated, 6 are added, and 1 is deleted. The mechanism shows a large improvement in its laminar flame prediction capability compared with the original mechanism, with an error of 10% from the experimental data.

Author Contributions

Software, L.X.; Formal analysis, Z.L.; Investigation, H.C.; Resources, Y.C.; Writing—original draft, S.X.; Writing—review & editing, Y.C. All authors have read and agreed to the published version of the manuscript.

Data Availability Statement

The original contributions presented in this study are included in the article/Supplementary Material. Further inquiries can be directed to the corresponding authors.

Acknowledgments

The author expresses gratitude to the Jiangxi Provincial Department of Education of China for the financial support provided to this research through its Science and Technology Research Project, under Grant No. GJJ210806.

Conflicts of Interest

The authors declare no conflict of interest.

Footnotes

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Figures and Tables

Figure 1. (a) Laminar flame velocities predicted by 20 mechanisms at φ = 0.7 to 1.4. (b) Mean absolute percentage error (MAPE) in the prediction of laminar flame velocities with 20 kinetic response mechanisms at φ = 0.7 to 1.4. (Mei [20], Konnov [22], Tian [23], Okafor [24], Otomo [26], Glarborg [27], Shrestha [28], GRI-Mech3.0 [29], Dagaut [30], Duynslaegher [31], Hadi [32], Song [25], Klippenstein [33], Nakamura [34], Han [35], Stagni [36], Zhang [37], Wang [38], Gotama [39], Bertolino [40], Li [41], Lhuillier [42]).

Figure 2. Laminar flame speeds predicted by eight kinetic reaction mechanisms with low-level differences at φ = 0.7 to 1.4. Lines are numerical data; symbols are measurements reported in the literature. (Mei [20], Okafor [24], Otomo [26], Glarborg [27], Shrestha [28], GRI-Mech3.0 [29], Zhang [37], Wang [38], Li [41], Lhuillier [42]).

Figure 3. Sensitivity analysis of NH3/air laminar combustion velocity at different equivalence ratios (φ = 0.8~1.2) (Wang [38], Zhang [37], Otomo [26]).

Figure 4. (a) Laminar flame speeds predicted by 20 kinetic response mechanisms at an equivalence ratio of 1 and different oxygen contents (O2 = 21–50 percent). (b) Mean absolute percentage error (MAPE) of laminar flame speeds predicted by the 20 kinetic response mechanisms. (Mei [20], Konnov [22], Tian [23], Okafor [24], Otomo [26], Glarborg [27], Shrestha [28], GRI-Mech3.0 [29], Dagaut [30], Duynslaegher [31], Hadi [32], Song [25], Klippenstein [33], Nakamura [34], Han [35], Stagni [36], Zhang [37], Wang [38], Gotama [39], Bertolino [40]).

Figure 5. Laminar flame velocities predicted by six kinetic reaction mechanisms with low-level differences at various oxygen contents (O2 = 21–50%) (Mei [20], Otomo [26], Glarborg [27], Nakamura [34], Han [35], Stagni [36], Zhang [37]).

Figure 6. Sensitivity analysis of NH3/air laminar combustion velocity at different oxygen contents (21–50%) (Glarborg [27], Zhang [37], Otomo [26]).

Figure 7. (a) Ammonia laminar flame velocities modeled by 20 mechanisms at different hydrogen doping ratios (XH2 = 0–0.7). (b) Mean absolute percentage error (MAPE) of laminar flame velocities predicted by 20 kinetic reaction mechanisms. (Lee [17], Mei [20], Konnov [22], Tian [23], Okafor [24], Otomo [26], Glarborg [27], Shrestha [28], GRI-Mech3.0 [29], Dagaut [30], Duynslaegher [31], Hadi [32], Song [25], Klippenstein [33], Nakamura [34], Han [35], Stagni [36], Zhang [37], Wang [38], Gotama [39], Bertolino [40], Li [41], Lhuillier [42]).

Figure 8. Laminar flame velocities predicted by seven kinetic reaction mechanisms with low-level differences at different hydrogen doping ratios (XH2 = 0–0.7). Lines are numerical data; symbols are measurements reported in the literature. (Lee [17], Otomo [26], Glarborg [27], Shrestha [28], Dagaut [30], Stagni [36], Zhang [37], Bertolino [40], Li [41], Lhuillier [42]).

Figure 9. Sensitivity analysis of NH3/H2/air laminar combustion velocity at a hydrogen doping ratio of 0.0 to 0.5 (Glarborg [27], Stagni [36], Otomo [26]).

Figure 10. (a) The average absolute percentage error (MAPE) of ammonia laminar flame velocity predicted by 20 mechanisms under different equivalence ratios (0.7–1.6), with a hydrogen doping ratio of 0.4. (b) Mean absolute percentage error (MAPE) of 20 kinetic reaction mechanisms for predicting laminar flame velocity. (Mei [20], Konnov [22], Tian [23], Okafor [24], Otomo [26], Glarborg [27], Shrestha [28], GRI-Mech3.0 [29], Dagaut [30], Duynslaegher [31], Hadi [32], Song [25], Klippenstein [33], Nakamura [34], Han [35], Stagni [36], Zhang [37], Wang [38], Gotama [39], Bertolino [40], Lhuillier [42]).

Figure 11. The predicted laminar flame velocities of seven kinetic reaction mechanisms with low-level differences under different equivalence ratios (0.7–1.6), with a hydrogen doping ratio of 0.4. Lines are numerical data, and the symbols are measured values reported in the literature. (Mei [20], Otomo [26], Glarborg [27], Han [35], Zhang [37], Wang [38], Gotama [39], Bertolino [40], Lhuillier [42]).

Figure 12. Sensitivity analysis of NH3/H2/air laminar combustion velocity when the equivalence ratio is 0.8–1.2 (Glarborg [27], Gotama [39], Otomo [26]).

Figure 13. Overall mean absolute percentage error (MAPE) of 20 kinetic reaction mechanisms for predicting laminar flame velocity. (Mei [20], Konnov [22], Tian [23], Okafor [24], Otomo [26], Glarborg [27], Shrestha [28], GRI-Mech3.0 [29], Dagaut [30], Duynslaegher [31], Hadi [32], Song [25], Klippenstein [33], Nakamura [34], Han [35], Stagni [36], Zhang [37], Wang [38], Gotama [39], Bertolino [40]).

Figure 14. (a) Optimized laminar combustion velocity of NH3 fuel with different equivalence ratios. (b) Optimized laminar combustion velocity of NH3/H2 fuel with different hydrogen doping ratios. (c) Optimized laminar combustion velocity of NH3/H2 fuel with different equivalence ratios. (d) Optimized laminar combustion velocity of NH3 fuel with different oxygen contents. (Lee [17], Mei [20], Glarborg [27], Shrestha [28], Han [35], Li [41], Lhuillier [42]).

Table 1

Ammonia’s combustion characteristics and comparisons with other fuels [13,14].

Characteristic Parameter	NH3	H2	CH4
Density/(g/L)	0.771	0.089	0.716
Low calorific value/(MJ/kg)	18.6	120	50
Critical boiling temperature/(°C)	−33.4	−253	−161
Adiabatic flame temperature/(°C)	1800	2100	1950
Flammable limit (vol. %)	15–28	4.7–75	5–15
Laminar burning velocity/(cm/s)	7	291	37
Minimum auto-ignition temperature/(°C)	650	520	630
NOx emission/(ppm)	200–5000	0	0
Volumetric energy density (GJ/m3) at 300 K and 0.1 MPa	11.3	4.7	9.35

Table 2

Chemical kinetic mechanisms applied in this work.

No.	Mechanism	Year	Components	ElementaryReactions	Ref.
1	GRI-Mech3.0	2000	53	325	[29]
2	Dagaut	2008	41	250	[30]
3	Tian	2009	84	703	[23]
4	Konnov	2009	127	1207	[22]
5	Duynslaegher	2012	19	80	[31]
6	Hadi	2015	22	93	[32]
7	Song	2016	32	204	[25]
8	Klippenstein	2018	33	211	[33]
9	Nakamura	2017	33	232	[34]
10	Otomo	2018	32	213	[26]
11	Shrestha	2018	124	1081	[28]
12	Glarborg	2018	39	231	[27]
13	Okafor	2019	59	356	[24]
14	Mei	2019	38	265	[20]
15	Han	2021	36	298	[35]
16	Stagni	2020	31	203	[36]
17	Zhang	2021	38	263	[37]
18	Wang	2021	91	444	[38]
19	Gotama	2022	26	119	[39]
20	Bertolino	2021	38	264	[40]

Table 3

Description of the recommended mechanisms and their applicability.

Fuel Type	Independent Variable	Recommended Mechanism	Description of Mechanism Applicability
NH3	Equivalence ratio	Otomo [26]	The predicted results are in general agreement with the experimental data.
	Oxygen content	Zhang [37]	Slight deviation in the range of 40–50% oxygen content; the rest of the range is in general agreement with the experimental data.
NH3/H2	Equivalence ratio	Gotama [39]	Some variation in predictions under enriched combustion conditions, but other ranges in general agreement with experimental results.
	Hydrogen doping ratio	Stagni [36]	Generally consistent with experimental data.
Overall scope		Zhang [37]	Minimum mean error under four conditions.

Table 4

List of reactions that have been modified or added to the reaction mechanism.

NO.	Reaction	A	n	Ea	Source
	Update
1	NH2 + H = NH + H2	1.0 × 106	2.32	799	Otomo [26]
2	O + NH2 = H + HNO	1.4602 × 1015	−0.529	563.26	Bertolino [40]
	DUPLICATE	9.1358 × 1013	−0.215	1785.61	Bertolino [40]
3	NH2 + NO = N2 + H2O	1.3 × 1016	−1.25	0	Otomo [26]
	DUPLICATE	−3.1 × 1013	−0.48	1180	Otomo [26]
4	NH2 + NO = NNH + OH	4.29 × 1010	0.29	−870	Otomo [26]
5	NH2 + NH = N2H2 + H	1.5 × 1015	−0.5	0	Otomo [26]
6	NH2 + HO2 = H2NO + OH	5.0 × 1013	0.0	0	Otomo [26], Mei [20]
7	NH2 + HO2 = NH3 + O2	9.2 × 105	1.940	−1152	Mei [20]
8	N2O + H = N2 + OH	3.31 × 1010	0.0	5090	Otomo [26]
	DUPLICATE	7.83 × 1014	0.0	19,390	Otomo [26]
9	HNO + H = NO + H2	9.68 × 1011	0.620	356	Otomo [26]
10	N2H3 = N2H2 + H	3.6 × 1047	−10.380	69,009	Otomo [26]
	0.1 atm	2.3 × 1043	−9.55	64,468
	1 atm	3.6 × 1047	−10.38	69,009
	10 atm	1.8 × 1045	−9.39	70,141
11	H + OH + M = H2O + M	3.5 × 1022	−2.00	0.00	Bertolino [40]
	Third body efficiency	H2/0.73/H2O/3.65/AR/0.38/
12	OH + NH = H + HNO	2.0000 × 1013	0.00	0.00	Bertolino [40]
13	NO + NH = H + N2O	5.3280 × 1012	0.026	−2893.90	Bertolino [40]
14	H + NH = H2 + N	3.01 × 1013	0.00	0.00	Bertolino [40]
15	H + O2 (+M) = HO2 (+M)	4.65 × 1012	0.440	0.00	Bertolino [40]
	Low pressure limit:	1.74 × 1019	−1.230	0.0
	TROE/0.67   1 × 10−30   1.0 × 1030   1 × 1030/
	Third body efficiency	H2/1.30/HE/0.64/H2O/10.00/AR/0.50/
16	NH3 + OH = NH2 + H2O	1.56 × 105	2.372	118.9	Bertolino [40]
17	O2 + NH3 = HO2 + NH2	1.1457 × 1010	1.310	55,096.09	Bertolino [40]
18	H + NH3 = H2 + NH2	2.9635 × 104	2.921	8478.86	Bertolino [40]
19	N2H2 = H + NNH	1.8 × 1040	−8.410	73,353.00	Bertolino [40]
	0.1 atm	8.772620 × 1036	−7.756021	69,899.3
	1 atm	2.819771 × 1040	−8.416021	73,037.30
	10 atm	4.856272 × 1041	−8.426021	75,688.50
20	H + OH + M <=> H2O + M	1.4818 × 1024	−2.53792	120.79	Gotama [39]
21	H2NO + NO2 = HONO + HNO	6.0 × 1011	0.0	2000	Zhang [37]
22	N2O + O = N2+O2	3.7 × 1012	0.0	15,930	Zhang [37]
	Addition
23	N2 + M = N + N + M	1.89 × 1018	−0.85	224,950	Otomo [26], Mei [20]
24	N + O + M = NO + M	7.60 × 1014	−0.1	−1770	Otomo [26], Mei [20]
25	N + NO2 = N2O + O	1.8 × 1012	0.0	0	Otomo [26], Mei [20]
26	HNO + N = NO + NH	1.0 × 1013	0.0	1990	Otomo [26], Mei [20]
27	N2O + N = N2 + NO	1.0 × 1013	0.0	19,870	Otomo [26], Mei [20]
28	N2H2 + H = N2 + H2 + H	4.820 × 108	1.76	739.2	Han [35]
	Omission
29	H2NN = N2 + H2	2.5 × 1014	0.000	52,785

Table 5

Optimized mean absolute percentage error.

			NH3 ($\mathit{\phi }/$%)		NH3/H2 ($\mathit{\phi }/$%)		NH3/H2 (XH2/%)		NH3 (O2/%)
$\mathit{\phi }$	XH2	O2	Before	After	Before	After	Before	After	Before	After
0.7	0	0.21	-	-	30.4	6.1	62.6	6.1	63.1	6.1
0.8	0.1	0.25	73.0	15.7	26.6	0.2	28.3	17.3	77.2	19.3
0.9	0.2	0.30	61.7	6.7	25.2	4.4	45.3	5.3	53.7	9.6
1.0	0.3	0.35	55.4	1.4	25.9	5.9	33.5	8.8	40.9	5.8
1.1	0.4	0.40	56.8	13.0	28.8	2.2	24.3	7.2	35.4	5.7
1.2	0.5	0.45	56.3	19.1	35.1	3.2	2.2	18.8	28.9	3.6
1.3	0.6	0.50	-	-	40.2	9.6	0.6	8.4	-	-
1.4	-	-	-	-	40.7	13.2	-	-	-	-
1.5	-	-	-	-	41.2	16.7	-	-	-	-
1.6	-	-	-	-	40.5	20.8	-	-	-	-
Average			60.6	11.2	33.5	8.2	28.1	10.3	49.9	8.4

Supplementary Materials

The following supporting information can be downloaded at: https://www.mdpi.com/article/10.3390/pr13020466/s1, Table S1: Parameters for modifying reactions and their sources; Figure S1: (a) NH₃/air flame combustion at different equivalence ratios (b) Optimized simulation results of NH₃/H₂/air flame combustion at different hydrogen doping ratios N₂ + M = N + N + M and H₂NN = N₂ + H₂; Table S2: Parameters for modifying reactions and their sources; Figure S2: (a) NH₃/air flame combustion at different equivalence ratios (b) Optimized simulation results of NH₃/H₂/air flame combustion at different hydrogen doping ratios NH₂ + HO₂ = H₂NO + OH and HNO + OH = NO + H₂O; Figure S3: (a) Laminar burning velocity sensitivity analysis of NH₃/ air flames, T = 298 K, P = 1 atm, φ = 1. (b) Laminar burning velocity sensitivity analysis of NH₃/H₂/air flames T = 298 K, P = 1 atm, H₂ = 30%, φ = 1.0; Table S3: Parameters for modifying reactions and their sources; Figure S4: (a) NH₃/air flame combustion at different equivalence ratios (b) Optimized simulation results of NH₃/H₂/air flame combustion at different hydrogen doping ratios NH₂ + NH = N₂H₂ + H, H + OH + M = H₂O + M, OH + NH = H + HNO and NO + NH = H + N₂O.

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