Performance Investigation of Currently Available Reaction Mechanisms in the Estimation of NO Measurements: A Comparative Study

: Ammonia (NH 3 ) has been receiving the a tt ention of researchers as an alternative promising green fuel to replace fossil sources for energy production. However, the high NOx emissions are one of the drawbacks and restrictions of using NH 3 on a broad scale. The current study investigates NO production/consumption for a 70/30 (vol%) NH 3 /H 2 mixture using kinetic reaction mechanism concepts to shed light on the essential reaction routes that promote/inhibit NO formation. Sixty-seven kinetic reaction mechanisms from the literature have been investigated and compared with recently reported measurements at a wide range of equivalence ratios ( ϕ ) (0.6–1.4), atmospheric pressure and temperature conditions. Both numerical simulations and experimental measurements used the same combustion reactor con ﬁ guration (premixed stabilized stagnation ﬂ ame). To high-light the best kinetic model for the predicting of the NO experimental measurements of NO, a symmetric mean absolute percentage error (SMAPE) has been determined as a preliminary estimation by comparing both numerical and experimental measurements. The results found that the kinetic reaction mechanism of Glarborg showed an accurate prediction with a minor error percentage of 2% at all lean and stoichiometric conditions. Meanwhile, the kinetic model of Wang accurately predicted the experimental data with 0% error at ϕ = 1.2 and underestimated the mole fraction of NO at 1.4 ϕ with an error of 10%. The sensitivity analysis and rate of production/consumption of NO mole fractions analysis have also been implemented to highlight the most important reactions that promote/inhibit NO formation. At lean and stoichiometric conditions, Glarborg kinetic model shows that the kinetic reactions of HNO


Introduction
Energy plays a crucial role in human life, while the combustion of conventional fuels, such as coal, significantly contributes to most of the total energy production throughout Citation: Alnasif, A.; Mashruk, S.; Hayashi, M.; Jójka, J.; Shi, H.; human history.The vast increase in worldwide population and the increase in relevant industrial processes has contributed to the deterioration of the ecosystem causing environmental issues such as climate change.Carbon dioxide (CO2) is the most prominent GHG responsible for raising global temperatures, since 30% of the global warming impact is caused due to the production of CO2 [1].Due to the role of combustion as an important contributor to GHG emissions, finding fuel sources to attain zero carbon emissions is critical [2].Both ammonia (NH3) and hydrogen (H2) can be used as carbon-free fuels.However, it is preferred to use NH3 over H2-in some circumstances-as NH3 is an efficient H2 carrier with high gravimetric hydrogen density, which makes it a potential medium for hydrogen storage; further, the handling, transportation, and distribution of NH3 are comparatively more accessible and safer compared to H2 [3].
Furthermore, the vast existing infrastructure and the ease of NH3 liquefication compared to pure H2 significantly impact transport processes and final costs [4].Despite the significant advantages provided by NH3, there are some concerns about the drawbacks represented by the low burning velocity and high nitrogen oxides (NOx) formation when using this molecule [4].High-fuel NOx formation coincides with increasing environmental challenges [3].The ideal combustion of NH3 produces only nitrogen (N2) and water (H2O) without having NOx traces [5].However, in practical combustion systems, NOx production is substantial, especially under fuel-lean conditions [5].
Similarly, the low burning velocity is a practical challenge.To overcome this drawback of NH3 and improve its combustion characteristics, it is recommended to blend NH3 with another fuel such as H2 [6].Moreover, as there will be no CO2 production in the byproducts, H2 can be considered the cleanest additive when mixed with NH3.In addition, the capability of producing H2 as a product from the cracking process of NH3 can have further benefits.The effects of adding H2 to the NH3 flames have been investigated experimentally by Choi et al. [7] using counterflow non-premixed NH3/H2/air flames.Their study found that the radical pools of H, OH, and O increase when the H2 fractions increase in the mixture, resulting in an increase in the maximum flame temperatures and the blowoff resistance.
Several experimental studies [8][9][10][11][12][13][14] have been carried out on ammonia-based combustion.Tohoku University's studies have focused on developing turbine burners with low-NOx formation [8,9].The research group used both pure NH3 as fuel and blended fuel of NH3/H2.Their outcomes showed that the NO mole fraction rapidly decreased in rich conditions, whereas the concentration of unburned NH3 increased under the same conditions [9].Additionally, the total NH3 emission resulting from swirling flows is affected by the unburnt NH3 flowing nearby the liner wall [9].Several experimental studies have been performed at Cardiff University, United Kingdom, on H2/NH3 blends by using a generic tangential swirl burner to burn a variety of mixtures at different power outputs NH3 [10][11][12][13].Their studies have investigated various equivalence ratios and blending ratios, such as spectrometric profiles and emissions (NO, N2O, NO2, and NH3).Their finding showed that the maximum concentration of NO hits the peak in lean conditions (ϕ ≈ 0.9) for pure NH3 and NH3/H2 blends.
In contrast, NOx concentration decreases when moving the equivalence ratio to the leaner or richer conditions, typically more towards the rich side.Studies have shown that the concentration of NH2 increases at rich conditions, and both NH2 and NNH have high sensitivity to NO formation/decomposition [13].Along with this effect, NH3 oxidation processes and NOx production were experimentally investigated by Abián et al. [14] using a laboratory quartz tubular flow reactor.The experimental outcomes showed that increasing O2 levels would decrease the temperature requirements to attain the complete oxidation of NH3, and high levels of O2 promote NO formation.
Since NH3 lacks carbon, NO is the major harmful pollutant from NH3 combustion.In most cases, the fuel-bound nitrogen is the main contributor to NOx formation in NH3 flames rather than the thermal NOx produced by atmospheric nitrogen [15].Consequently, a deep understanding of NH3 combustion chemistry is required.Furthermore, a detailed analysis of NOx production pathways is necessary to precisely estimate emissions due to fuel-bound nitrogen.Nowadays, the development and optimization processes on NH3 as fuel for practical applications such as gas turbines and internal combustion engines are carried out using high-accuracy computer modeling of fluid and gas dynamics of the conversion process inside the combustion chamber.In addition, NH3, as a promising fuel, needs reliable kinetic mechanisms.The chemical kinetic reaction mechanisms should be based on a comprehensive understanding of the chemical conversion of the fuel and intermediate formations due to fuel oxidation.Several attempts have been made to establish reliable, comprehensive models for NH3 oxidation [16][17][18].The previously established mechanisms [16,[18][19][20][21][22] have been used as baseline mechanisms for development and optimization purposes in the oxidation of NH3 mixtures.
Improving the kinetic mechanisms for NH3 involves investigating the rate constants parameters of the reactions that have nitrogen-containing species, which in turn contribute considerably to the oxidation process of NH3.Updating the rate constant parameters and thermochemical data for nitrogen-containing species and highlighting the key gasphase reactions of NH3 combustion affect the optimization process of NH3 oxidation and move it closer to the practical level.Many studies have been carried out in previous years that aimed to improve NH3 kinetics based on the experimental tests of combustion of NH3 using several combustion systems, such as burner-stabilized premixed flames, shocktube, jet-stirred reactors, and plug-flow reactors [23][24][25][26][27][28].Nozari and Karabeyoglu [29] developed a kinetic reaction mechanism for predicting the NOx formation for the combustion of NH3/H2 blends, containing detailed nitrogen-related sub-mechanisms, which consisted of 30 species and 240 reactions.Their findings indicate excellent consistency with the experimental measurements and data from the developed model reactions.Another study was carried out by Zhang et al. [30] by implementing a jet-stirred reactor (JSR) to oxidize NH3/H2 blends at atmospheric conditions and using the experimental results to develop a kinetic model able to estimate the NOx measurements reliably.Based on the analysis of their developed model, they found that H2 effectively impacts the nitrogenrelated radicals (NH2, NH, and N), where the concentration of these radicals decreases when the H2 blending ratio increases, which, in turn, reduces NO formation.Conversely, the promotion of the oxygenated radicals (O, OH, and HO2) has improved with an increasing H2 level resulting in the enhancement of NO formation.
Recently, a comprehensive study was carried out by András et al. [31] by investigating the performance of 18 recently published kinetic reaction mechanisms using a wide range of experimental measurements reported by previous studies of different fuel combinations of pure NH3, NH3/H2, and NH3/syngas blends.The experimental measurements included a data set of ignition delay times measured in a shock tube, concentration measurements in jet-stirred (JSR) and flow reactors (FR), and laminar burning velocity measurements.Their methodology has included a quantitative method that compared the outcomes of the tested mechanisms to the collected experimental measurements using a unique framework code, Optima ++.A sensitivity analysis of the best-performing kinetic models determined the most influential model parameters based on the simulation outcomes.Their findings showed that although essential reactions are not the same for different types of combustion experiments, most of these reactions contain NH3, NH2, and NNH species.Furthermore, the radical species of H, O, OH, HO2, NH3, NH2, O2, and H2 have the most sensitive effect on thermodynamic properties.
Although numerous attempts have been made to improve the accuracy of model predictions, the optimization for the developed models has been restricted to specific conditions.Additionally, the enhancement process must be comprehensive and rely on massive data sets of experimental measurements with broad boundary conditions for the combustion of NH3 and its blends.Therefore, the current study aims to investigate combustion chemistry's performance in kinetic modeling of a 70/30 (vol%) NH3/H2 mixture.The investigation process includes the following steps: (1) utilization of recently reported NO measurements by Hayakawa et al. [32], which is based on using stagnation flame configurations for accurate measurements employing better-collected samples, especially at very lean conditions where maximum NO formation takes place, as well as to avoid stabilization issues which take place at lean conditions of NH3-based fuels [9,[32][33][34]; (2) modeling of 67 kinetic reaction mechanisms from the literature by studying their performance in the estimation of NO mole fractions at atmospheric conditions of pressure and temperature and various equivalence ratio (0.6-1.4); and (3) applying symmetric mean absolute percentage error (SMAPE) analyses for a preliminary estimation to highlight the best-performing kinetic model for the estimation of NO mole fractions at lean, stoichiometric, and rich conditions.

Numerical Setup and Kinetic Modeling
Sixty-seven chemical kinetic mechanisms have been analyzed numerically by ANSYS Chemkin-PRO 2022 R2 software.A burner-stabilized stagnation flame model was adopted in this study.All numerical simulations have been implemented in a one-dimensional computational model 2 cm in length that mimics the same distance applied from experiments (the distance from the nozzle burner to the top plate).For all tested cases, the grid properties, such as the maximum number of grid points allowed and the adaptive grid control based on solution gradient and curvature, were set to 5000, 0.01, and 0.01.This study has also considered mesh dependency to achieve precise results.Table 1 shows each tested mechanism in terms of the number of species and reactions.
To avoid stabilization issues and obtain accurate measurements, a stagnation flame configuration has been used to determine the mole fraction of NO from the combustion of 70/30 (vol%) NH3/H2 blended fuel.Experimental work has been carried out at Tohoku University using a stagnation flame configuration.The detail of the experimental setup can be found elsewhere [32].Ammonia and hydrogen were used as fuel, and the air was used as an oxidizer.All the experimental tests have been conducted under atmospheric conditions (T = 295 K, P = 1 atm).The experimental measurements of NO concentration have been employed for various equivalence ratios, ϕ.A top stagnation plate was mounted 2 cm above the burner outlet to generate a stagnation flow.The values of the top plate surface temperature (Tw) and the mixture inlet velocity (Vin) were varied due to the variation in equivalence ratios, which caused the laminar burning velocity to change.Experimental measurements from [32] were selected regarding the same condition of interest, such as the mole fraction of hydrogen in the fuel, the range of the equivalence ratio, and the standard conditions of the unburned gas.
A symmetric mean absolute percentage error (SMAPE) formula was utilized [35] to determine the optimal kinetic reaction mechanism with superior performance compared to experimental measurements [32].This formula involved computing the discrepancy between the experimental measurements and the numerical simulation, thereby generating more accurate estimations of the selected mechanism's performance across various equivalence ratios, as specified in Equation (1).
It is worth noting that the SMAPE method is preferred for error estimation when the actual value reported by experiments is close to zero [36].This preference arises from the sensitivity of error estimates to small values reported by experiments, which may lead to a reduction in estimation accuracy.This phenomenon can be observed in the absolute percentage error (APE) when utilized as a means of error estimation.
where Ft is the forecasting value standing for numerical calculations, and At is the actual value from experiments.

Results and Discussion
Figure 1 refers to the data estimated numerically by Chemkin-Pro 2022 R2 software for 67 chemical kinetic reaction mechanisms from the literature and formed according to the SMAPE formula for preliminary estimations.Figure 2 presents the experimental measurements and the numerical data of three of the most accurate kinetic reaction mechanisms based on the SMAPE calculations that predicted the NO mole fractions closer to the experimental measurements at various equivalence ratios (0.6-1.4); see Figure 1.The mole fraction of NO was taken at the end of the computational domain (at X = 2 cm), where the NO concentrations are defined under steady-state conditions while corresponding to the experimental emission sampling point of interest.Due to the estimation of the selected mechanisms, which present different trends when the equivalence ratio has changed from lean to rich conditions, analyses of the results will be divided into two categories, namely, lean to stoichiometric flames (ϕ = 0.6-1) and rich flames (ϕ = 1.2-1.4).In this way, the rationale behind obtaining different levels of NO formation/decomposition prediction by the mechanisms will be appropriately highlighted.

Lean Condition Flames
As shown in Figure 1, at ϕ = 0.6, most of the kinetic reaction mechanisms would not be able to estimate the mole fraction of NO properly and gave 100% as a percentage error.This number decreased severely when the equivalence ratio increased to 0.8 and 1, and then the estimation accuracy improved.The inefficient prediction of most kinetic reaction mechanisms at the very lean condition (ϕ = 0.6) is due to the instabilities of ammonia flames, causing difficulties in interpreting its chemical kinetics.Along with the lean conditions, many of the selected mechanisms gave a sharp variation with a high level of discrepancy compared to experimental measurements.In addition, when the equivalence ratio moves along the lean condition, most of the selected mechanisms' estimation fluctuates from low to high error values.Interestingly, along the lean range (0.6-1 of ϕ), both Glarborg [90] and Nakamura [69] mechanisms recorded low discrepancy values with errors ranging between 2-4%, respectively.Therefore, both mechanisms have been selected to study the characteristics of 70/30 vol% NH3/H2 flames at atmospheric conditions and along the lean stoichiometric range of ϕ, hence, comparing the outcomes of each mechanism to shed light on the reasons behind the discrepancies.
As shown in Figure 2, when ϕ is 0.6 to 1, the variation of estimated data obtained by Glarborg and Nakamura has the same trend as the measured data from experiments.Meanwhile, Wang's mechanism [46] has predicted those trends randomly.However, Wang's mechanism predicts NO mole fractions satisfactorily with a minor level of discrepancies at rich conditions, which will be explained later in the following section.
According to Figure 2, both the Glarborg and Nakamura kinetic models produced similar results when estimating the amount of H2.The figure shows that the mole fraction of H2 is at its lowest levels between 0.6 and 0.8 of ϕ.After this point, it gradually increases until reaching a high value at 1.4 of ϕ.This can be explained by the fact that a significant amount of H2 is consumed in the post-flame zone for lean conditions of ϕ (0.6 and 0.8), but the mole fraction remains constant after passing through the flame zone at higher values of ϕ (1-1.4),indicating that it is not completely consumed in the post-flame zone (as shown in Figure 3).Figure 4 shows that the kinetic reaction NH2 + H ⇌ NH + H2 (R1) significantly affects the formation of H2, and its production rate increases sharply with increasing equivalence ratios.Additionally, both kinetic reactions NH3 + H ⇌ NH2 + H2 (R2) and NH + H ⇌ N + H2 (R3) positively promote H2 production, demonstrating a considerable increase in the production rate at lean conditions.In addition, the kinetic reaction HNO + H ⇌ NO + H2 (R4) shows opposite trends to what has been observed from the previous two reactions with a rate of production of H2 governed by this kinetic reaction which decreases gradually with increasing equivalence ratio from 0.6 to 1.It is likely that due to the decrease in the level of HNO concentration, NO is also reduced.Sensitivity analyses have been performed at ϕ = 0.8 to highlight the reasons behind the discrepancies among the selected kinetic mechanisms, where NO concentration was the highest.Glarborg and Nakamura's mechanisms are selected for this analysis due to their better performance when compared to experimental results, as in Figure 2, giving minimum SMAPE among other tested mechanisms at lean conditions, as in Figure 1.  Figure 6 presents the reactions with negative sensitivity towards NO production.The negative sensitivity coefficients are normalized to their sum separately and shown as a percentage.As shown in Figure 6, Glarborg's mechanism shows high negative sensitivity coefficients for the kinetic reactions 'NH2 + NO ⇌ N2 + H2O (R18)' and NH2 + NO ⇌ NNH + OH (R19).In contrast, for Nakamura's mechanism, the same kinetic reactions demonstrate 4% and 1% negative sensitivities, respectively.Both reactions consume the important key radical (NH2), destroying NO to form N2 and NNH.Additionally, the sensitivity coefficient of the reaction NH + NO ⇌ N2O + H (R20) has a higher effect in Nakamura's model (12%) than in Glarborg's, where it is estimated at 5%.In both mechanisms, the latter reaction impedes the system reactivity by producing less reactive H radicals.In addition, Nakamura's kinetic model shows how 8 of the kinetic reactions hinder the reactivity of the NO mole fraction.Those kinetic reactions do not influence the system reactivity in Glarborg's mechanism; see Figure 6.The present study has also considered the ROP analysis of NO to shed light on the most important kinetic reactions contributing to NO formation/consumption.Figures 7-9 outline the variation of the key reactions of NO production/decomposition along the axial axis of the computational domain in terms of equivalence ratio.The figures have been established based on Nakamura kinetic model's estimation.The spatial distribution of the key reactions with the maximum mole fraction of NO formation/decomposition has been selected for each equivalence ratio using the mechanism chosen to highlight the variation of the reactions.As can be seen from Figure 7, the total mole fraction of NO decreased at first and then increased downstream along the lean range of equivalence ratios.The declining pattern in NO formation is due to the high reactivity of R18, R19, and R20 in the reduction of NO mole fraction.Besides all the mentioned reactions having the most significant consuming effect of NO, the former reactions' consumption rate (R18) decreases when the equivalence ratio increases from 0.6 to 1.At the same time, the reaction (R20) demonstrates a climbing trend with an increasing equivalence ratio; see Figure 8. Furthermore, the kinetic reaction N2 + O ⇌ N + NO (R21) substantially impacts the NO decomposition rate at lean conditions when the temperature of the reaction increase as a function of the equivalence ratio.This is because the kinetic reaction R21 is one of the thermal NO reactions governed by high temperature; hence, it is listed under the Zeldovich mechanism [65], as in Figures 7 and 8.In addition, NH + NO ⇌ N2 + OH (R22) also demonstrates an increasing trend with an equivalence ratio, and its reactivity peaks at stoichiometry due to the increase in NH radicals availability; see Figures 8 and 10.The NO mole fraction increases significantly downstream due to the high reactivity of the reactions R13 and R4, which demonstrate a dominant effect in the formation of NO, as well as the contribution from the reactions NO2 + H ⇌ NO + OH (R23), N + O2 ⇌ NO + O (R24), and R11.The thermal reactions R24 and R11 hardly take part in the formation of NO, especially at ϕ = 0.6, due to the temperature dependency of these reactions.As a result, they show a rapid response to NO formation when the equivalence ratio increases to the stoichiometric condition where the temperature is the highest; see Figures 7 and 9.The NO production rate from the reaction R13 reaches the maximum at ϕ = 0.6 and then decreases as ϕ increases, even though the OH radical availability increases; see Figure 10.R4 shows the opposite trend, where the NO production rate is directly proportional to ϕ; see Figure 9.
To justify the opposite behavior of the latter kinetic reactions (R4 and R13) in promoting NO formation, Table 2 lists the key reactions of NO production and shows that the kinetic reaction 'R13' has a more remarkable pre-exponential factor (A) than that of R4.Both reactions are sensitive to the temperature, but the kinetic reaction 'R4' is more sensitive, and its reactivity increases more rapidly with temperature than reaction R13.Additionally, the abundance of H radicals improves the R4 reactivity to become more dominant at stoichiometry, compared to the reaction R13; see Figures 9 and 10.The kinetic formation process of NO is mainly governed by HNO, NH, N, and NO2 mole fractions, and then it is consumed early by the DeNOx process through the action of NH2, NH, and N radicals at the reaction zone; see Figure 11.Glarborg's mechanism shows the same NO formation/consumption trend as Nakamura's kinetic model.The NO formation rate through the reactions of HNO radicals is considerably higher than the NO consumption rate via NH2 and NH radicals.Therefore, the total rate of NO is increased downstream due to the high promotion of NO mole fraction; see Figure 12.Additionally, the kinetic reactions of R4, NH + O ⇌ NO + H (R25), and R9, as well as the thermal NO reactions (R24 and R11), contribute towards the increasing NO formation rate; see Figures 13 and 14.On the other hand, the chain-termination reaction 'R18', chain-branching reaction 'R19', R20, and the temperature-dependent reaction 'N + NO ⇌ N2 + O (R26)' in Nakamura's kinetic model are the dominant kinetic reactions in the consumption of NO; Figures 12 and 13    Figure 15 shows the kinetic schemes predicted by the best-performing models.It illustrates the chemical reaction pathways of NO formation/decomposition and the net reaction rate of the kinetic reactions that influence NO mole fractions.It also demonstrates the tendency of the radical's percentage (%) reactivity toward either formation or decomposition of NO.Reaction pathway analyses were conducted at equivalence ratios that yield the highest NO formation (ϕ = 0.8) and at a temperature of 1770 K, which corresponds to the point of maximum occurrence of the total NO component; see Figure 12.As shown in Figure 15, the kinetic mechanisms of Glarborg and Nakamura show that HNO, NH, and N radicals form the main pathways for NO formation.At the same time, N, NH, and NH2 are responsible for consuming the majority of NO.The kinetic scheme of Glarborg demonstrates the substantial contribution of the HNO → NO pathway (65%) towards NO formation through the reaction R4.On the other side, N, NH, and NH2 radicals tend to consume NO at different concentrations and produce N2 through the kinetic reactions R26, R20, R22, R18, and R19, where activities of N, NH2, and NH radicals are 53%, 25%, and 22%, respectively, while 96% of NH2 is consumed via the reaction R19 to convert NO to NNH.Even though the kinetic models display similar NO production/destruction patterns, the concentration of the reactions varies from one kinetic model to another.Figures 16 and 17 demonstrate the most important reactions that take part in promoting/consuming NO, respectively.As shown in Figure 16, the kinetic reaction R13 plays a significant role in NO formation in Nakamura's mechanism, especially at ϕ = 0.6, but contributes only 1% in NO formation in Glarborg's kinetic model.The reason can be justified by the effect of the Arrhenius parameters that govern the reaction, especially the activation energy.As seen in Table 2, the activation energy of reaction R13 is set to 0 in Nakamura's model.The reaction here is independent of temperature compared to its effect on Glarborg's mechanism, identified as a temperature-dependent reaction.An absence in the contribution of the latter reaction in the formation of NO when ϕ equals 0.8 and 1 in Glarborg's mechanism has also bee noticed.Further, the NO production rate for the kinetic reactions R4, R9, R25, and HNO + O2 ⇌ HO2 + NO (R27) is higher in Glarborg's kinetic model compared to Nakamura's at lean conditions.The figures for the consumption rate are illustrated in Figure 17, where predictions by both kinetic models show nearly the same level of estimation.Despite some kinetic reactions demonstrating a slight increase in the estimation by Glarborg's mechanism, the variations between the kinetic reactions by both mechanisms are still narrow and not substantial compared to those of Figure 16.The overprediction in the formation of NO by Glarborg's mechanism is also due to the high heat release rate (HRR).Figures 11 and 18 illustrate the variation of mole fractions of key species responsible for the formation/consumption of NO.It has been noticed that the heat release rate calculated by Glarborg's mechanism is higher than that estimated by Nakamura's model.Since increasing the heat release rate will improve the system reactivity and boost the speed of the reaction, according to Chen et al. [1], both NH2 and OH radicals can be considered as criteria/markers for the growth of HRR.

Rich Condition Flames
Most tested kinetic models gave a high estimation error based on SMAPE at ϕ = 1.2; see Figure 1.Both Nakamura and Glarborg kinetic models recorded 100% SMAPE, indicating a very high level of discrepancies compared to the experimental results.The kinetic reaction mechanism of Wang [46] has displayed excellent estimation of NO mole fraction among other investigated mechanisms; see Figures 1 and 2. The prediction of Wang's mechanism obtained 0% SMAPE at ϕ = 1.2 and 10% at ϕ = 1.4.Therefore, the kinetic mechanism of Wang has been selected to analyze the chemical kinetic behavior of the reactions under rich conditions.Further, due to the deterioration in the performance of Nakamura's mechanism at rich conditions, especially when ϕ = 1.2, the Nakamura mechanism will also be compared to Wang's outcomes to investigate the reasons behind the discrepancy in NO mole fractions at rich conditions.
Figures 19 and 20 show the reactions with the largest positive and the negative sensitivity coefficients for NO mole fractions in the Nakamura and Wang's kinetic models at ϕ = 1.2.The positive and negative sensitivity coefficients are normalized to their sum separately and shown as a percentage.Figure 19 highlights the kinetic reactions with the most significant sensitivity coefficients in percentage (%) and indicates a positive influence towards the promotion of NO mole fraction.It should be noted that most kinetic reactions promote the reactivity of the system by producing either more reactive OH, H, O, or HO2 radicals, such as the chain branching reactions R5, H2 + O ⇌ H + OH (R28), R12, and H2 + M ⇌ 2H + M (R29).To show the differences in the prediction among the selected mechanisms, Figure 19 indicates that Wang's kinetic model shows a slight increase in reactivity for the kinetic reactions R28, R12, O + H + M ⇌ OH + M (R30), and H + OH + M ⇌ H2O + M (R31).Along with that, Wang's mechanism also demonstrates a higher value of estimation for the reaction R5 and a lower value for R29 compared to Nakamura's model, which, in turn, shows the opposite trend for Wang's model in the estimation of sensitivity coefficients of the reactions mentioned above.The reason behind the variation of the sensitivity values of the kinetic reactions R5 and R29 among the mentioned mechanisms can be attributed to the difference in Arrhenius parameters that governed the rate of reaction for each kinetic reaction, and their values differ among the selected mechanisms; see Table 3.   Figure 20 shows sensitivity analyses of kinetic reactions with negative coefficients in percentage (%) and illustrates the tendency of the reactions towards impeding NO production.Both models demonstrate different kinetic reactions controlling the retardation of NO production.The results only share three kinetic reactions with different values, namely, N2H2 + NH2 ⇌ NH3 + NNH (R32), R4, and R24.Even though the kinetic reaction R32 has the same Arrhenius parameters listed in both selected models, Table 3, the negative value of the activation energy tends to decrease the reactivity of the kinetic reaction when the system's temperature increases.As Nakamura's mechanism has higher temperature estimation than Wang's model, this can be attributed to the high estimation value of the latter reaction by Wang's mechanism rather than Nakamura's model; see Figure 21.Further, the reaction rate of the other kinetic reactions, R4 and R24, increases with temperature.The former reaction (R4) also has the same values of Arrhenius parameters in both tested models, but its reaction rate estimated by the Nakamura's kinetic model is higher than that of Wang's mechanism due to the high-temperature estimation by Nakamura's mechanism.Figure 26 illustrates the kinetic schemes for the best-performing kinetic models, which present the chemical kinetic pathways of the kinetic reactions taking part in the formation/consumption of NO at the reaction zone when the system's temperature is equal to 1513 K at ϕ = 1.2.The target temperature of 1513 K was selected based on the optimal point of total NO component occurrence, as observed in Figure 23.The temperature was chosen as it corresponded to the maximum yield of the NO component, thereby enabling a more comprehensive analysis of the reaction pathways.As shown in Figure 26, both Wang and Nakamura's kinetic models demonstrate the HNO → NO pathway, which still plays a substantial role at rich conditions in the consumption of HNO and produces NO.The kinetic scheme pathways of Wang mechanisms demonstrate the tendency of high reactive H radical (68%) with HNO through the reaction R4, followed by NH2 with 17% via R33.Most importantly, the net reaction rate of the former reaction (R4) decreased to nearly half of its value compared to the same reaction at lean conditions.For reducing NO, NH2 radicals show a high intensity of reactivity of 96% in consuming NO to produce NNH radicals.The net reaction rate of the latter reaction increased by 0.084 kmol/m 3 s compared to the value of the same reaction in lean conditions.In addition, the NO → N2 pathway has a substantial role in NO consumption, with 0.107 kmol/m 3 s compared to other consuming pathways.An amount of 88% of NH2 radicals tend to consume NO and produce N2 through the chain-terminating reaction R18.Further, the kinetic mechanism of Nakamura shows another NO formation pathway (NH3 → NH2 → N2H2 → NO) at rich conditions which is not present in Wang's mechanism.The NO mole fraction increases by the reaction of N2H2 with high reactive O radicals through the kinetic reaction N2H2 + O ⇌ NO + NH2.Additionally, the kinetic schemes of both kinetic models show different concentrations of reactive radicals that tend to react with HNO, NH, and N to form NO.  [46] and Nakamura et al., [69] kinetic models.Arrow lines refer to chemical transformations, percentages (%) show the contribution of a reactant to the transformation, numbers stand for the net reaction rate in kmol/m 3 s, which is also visualized by line thickness.Some of the kinetic reactions of Nakamura's model show higher levels of reactivity than those of Wang's model; see Figure 27.For example, the thermal NO reactions of the Zeldovich mechanisms R24 and R11 in NO formation [65].Even though the activation energy of the former reaction (R24) is the same in both models, the system's temperature varies among the model's predictions.It positively affects the reactivity of the mentioned reactions.Similar observations can be drawn for the thermal NO reaction (R11) by including another affecting factor: activation energy.The latter reaction (R11) in Nakamura's model works as an independent temperature reaction (has zero activation energy).The case is not the same with the same kinetic reaction of Wang's model reaction with an activation energy equal to 49，500 cal/mol, making it a highly temperature-dependent reaction; see Table 3.   3, the Arrhenius parameters' values differ among the tested kinetic models, where the former reaction (R26) has positive activation energy, accelerating the system's reactivity as temperature increases.However, this is not the case for Wang's model, which shows negative activation energy values with opposite effects on temperature.The other Zeldovich reaction, 'R22', has different values listed among the selected mechanisms and shows independent temperature reaction in Nakamura's model and has a negative effect on reactivity when the system's temperature increases; see Table 3.

Conclusions
The present study investigated the formation/consumption of NO mole fraction for a 70/30 (vol%) NH3/H2 mixture at atmospheric conditions and a wide range of equivalence ratios (0.6-1.4).Different chemical kinetic reaction mechanisms (67) designed for ammonia combustion have been examined to assess their performance in NO prediction compared to experimental data from the literature.The main conclusion points are listed as follows: 1. Within the lean and stoichiometric range of equivalence ratios (0.6-1.0), Glarborg  Since Nakamura's model predicts a higher system temperature than Wang's, these reactions become more reactive, resulting in discrepancies in the predicted NO mole fractions; 6.The variation in NO mole fraction predictions between the studied kinetic models can be attributed to the distinct ways in which NO chemistry is represented among the chosen models.

Figure 1 .
Figure 1.NO mole fractions for 67 reaction mechanisms calculated by symmetric mean absolute percentage error (SMAPE) formula at various equivalence ratios (ϕ).

Figure 2 .
Figure 2. Variation of NO, NH3, H2 mole fractions as a function of equivalence ratio.

Figure 2
Figure 2 also presents the variation of NO mole fraction as a function of equivalence ratio.The mole fraction of NO peaked at ϕ = 0.8.It has been noticed that the mole fraction of NO decreased gradually at either leaner or richer conditions than ϕ = 0.8.NO mole fractions estimated by Glarborg and Nakamura's kinetic models produced better performance compared to the other models considered here in the lean and close to stoichiometric zones.At ϕ = 0.6, the estimated NO value by Glarborg is identical to the experimental data.At the same time, Nakamura's prediction slightly underpredicts the NO mole fractions; see Figure 2. Concurrently, Wang's kinetic model predicted zero NO at very lean conditions.The Nakamura kinetic model demonstrates the same underestimation at 0.8 of ϕ, while the Glarborg mechanism showed overestimation by 4% compared to experimental measurements.The error estimation of Wang's model has improved from 100% at ϕ = 0.6 to 13% at ϕ = 0.8; see Figure 1.At the stoichiometric condition, Glarborg and Wang's model reaction gives nearly the same figures of NO mole fraction values, while the Nakamura model diverts slightly from the experimental result to give an underestimation trend of 7% SMAPE.Sensitivity analyses have been performed at ϕ = 0.8 to highlight the reasons behind the discrepancies among the selected kinetic mechanisms, where NO concentration was the highest.Glarborg and Nakamura's mechanisms are selected for this analysis due to their better performance when compared to experimental results, as in Figure2, giving minimum SMAPE among other tested mechanisms at lean conditions, as in Figure1.Figure5refers to the positive sensitivity coefficients of the kinetic reactions while demonstrating the most important kinetic reactions that promote the system reactivity and increase the mole fraction of NO.The positive sensitivity coefficients are normalized to their sum separately and shown as a percentage.Both kinetic models of Glarborg and Nakamura have displayed high positive sensitivity toward the chain branching reaction H + O2 ⇌ O + OH (R5).This reaction promotes the system's reactivity by producing more reactive OH radicals.Even though the Nakamura mechanism has a higher sensitivity coefficient of the kinetic reaction R5 than Glarborg, both kinetic models gave nearly the same sensitivity coefficient of the reaction NH + OH ⇌ HNO + H (R6), which in turn increases HNO pools to promote NO formation.In Nakamura's mechanism, the kinetic reactions N2O + O ⇌ 2NO (R7), NO + HO2 ⇌ NO2 + OH (R8), HNO + O ⇌ NO + OH (R9), NH + O2 ⇌ HNO + O (R10), N + OH ⇌ NO + H (R11), H2 + OH ⇌ H + H2O (R12), and HNO + OH ⇌

Figure 5
Figure 2 also presents the variation of NO mole fraction as a function of equivalence ratio.The mole fraction of NO peaked at ϕ = 0.8.It has been noticed that the mole fraction of NO decreased gradually at either leaner or richer conditions than ϕ = 0.8.NO mole fractions estimated by Glarborg and Nakamura's kinetic models produced better performance compared to the other models considered here in the lean and close to stoichiometric zones.At ϕ = 0.6, the estimated NO value by Glarborg is identical to the experimental data.At the same time, Nakamura's prediction slightly underpredicts the NO mole fractions; see Figure 2. Concurrently, Wang's kinetic model predicted zero NO at very lean conditions.The Nakamura kinetic model demonstrates the same underestimation at 0.8 of ϕ, while the Glarborg mechanism showed overestimation by 4% compared to experimental measurements.The error estimation of Wang's model has improved from 100% at ϕ = 0.6 to 13% at ϕ = 0.8; see Figure 1.At the stoichiometric condition, Glarborg and Wang's model reaction gives nearly the same figures of NO mole fraction values, while the Nakamura model diverts slightly from the experimental result to give an underestimation trend of 7% SMAPE.Sensitivity analyses have been performed at ϕ = 0.8 to highlight the reasons behind the discrepancies among the selected kinetic mechanisms, where NO concentration was the highest.Glarborg and Nakamura's mechanisms are selected for this analysis due to their better performance when compared to experimental results, as in Figure2, giving minimum SMAPE among other tested mechanisms at lean conditions, as in Figure1.Figure5refers to the positive sensitivity coefficients of the kinetic reactions while demonstrating the most important kinetic reactions that promote the system reactivity and increase the mole fraction of NO.The positive sensitivity coefficients are normalized to their sum separately and shown as a percentage.Both kinetic models of Glarborg and Nakamura have displayed high positive sensitivity toward the chain branching reaction H + O2 ⇌ O + OH (R5).This reaction promotes the system's reactivity by producing more reactive OH radicals.Even though the Nakamura mechanism has a higher sensitivity coefficient of the kinetic reaction R5 than Glarborg, both kinetic models gave nearly the same sensitivity coefficient of the reaction NH + OH ⇌ HNO + H (R6), which in turn increases HNO pools to promote NO formation.In Nakamura's mechanism, the kinetic reactions N2O + O ⇌ 2NO (R7), NO + HO2 ⇌ NO2 + OH (R8), HNO + O ⇌ NO + OH (R9), NH + O2 ⇌ HNO + O (R10), N + OH ⇌ NO + H (R11), H2 + OH ⇌ H + H2O (R12), and HNO + OH ⇌

Figure 7 .
Figure 7.The rate of production/consumption of NO in 70/30 (vol%) NH3/H2 mixture at lean conditions estimated by the Nakamura et al., [69] kinetic model.

Figure 8 .
Figure 8. Rate of consumption (in %) as a function of equivalence ratio estimated by the Nakamura et al., [69] kinetic model.

Figure 9 .
Figure 9. Rate of production (in %) as a function of equivalence ratio estimated by the Nakamura et al., [69] kinetic model.

Figure 10 .
Figure 10.Varieties of mole fractions of OH, H, O, NH2, NH, HNO as a function of equivalence ratio estimated by two selected kinetic models.

Figure 11 .
Figure 11.Variation of mole fractions of N, NH, NH2, NO, OH, H, and HNO and heat release rate (HRR) in flame structure estimated by the Nakamura et al., [69] mechanism at ϕ = 0.8. .

Figure 13 .
Figure 13.Rate of consumption (in %) as a function of equivalence ratio estimated by the Glarborg, [90] kinetic model.

Figure 14 .
Figure 14.Rate of production (in %) as a function of equivalence ratio estimated by the Glarborg, [90] kinetic model.

Figure 15 .
Figure 15.Chemical reaction pathways of NO formation/consumption at flame zone (T = 1770 K) and at ϕ = 0.8 predicted by the Glarborg, [90] and Nakamura et al., [69] kinetic models.Arrow lines refer to chemical transformations, percentages (%) show the contribution of a reactant to the transformation, numbers stand for the net reaction rate in kmol/m 3 s, which is also visualized by line thickness.

Figure 16 .
Figure 16.Rate of production (in %) of NO mole fractions at lean conditions estimated by the Nakamura et al., [69] and Glarborg, [90] kinetic models.

Figure 17 .
Figure 17.Rate of consumption (in %) of NO mole fractions at lean conditions estimated by the Nakamura et al., [69] and Glarborg, [90] kinetic models.

Figures 22 and 23
Figures 22 and 23 present the variation of the rate of production/consumption of NO estimated by Wang and Nakamura's kinetic mechanisms, respectively, at rich conditions and indicate the spatial distribution of the most important kinetic reactions in the formation/consumption of NO.The total component of NO starts to decrease to a negative value at the earlier stage of the reaction zone due to the action of R18, R19, and R20, which are responsible for NO consumption due to the high reactivity of the NH2 and NH radicals.The total NO formation then increases due to the positive effects of the kinetic reactions R4, R25, R13, R11, and NH2 + HNO ⇌ NH3 + NO (R33), where the kinetic reaction 'R4' has the highest reactivity among the other kinetic reactions.The total component of NO decreased afterward due to the thermal NO reactions of Zeldovich mechanism R26 and R22', as well as the reaction NH + NO ⇌ NNH + O (R34) in lowering the mole fraction of NO downstream by consuming it via the high reactivity of N, and NH radicals.Most importantly, the amplitude of the total NO formation decreases when the equivalence ratio increases from 1.2 to 1.4.This effect leads to a rate of consumption that is more than the NO production rate, which, in turn, lowers the mole fraction of NO; see Figures 24 and 25.
Figures 22 and 23 present the variation of the rate of production/consumption of NO estimated by Wang and Nakamura's kinetic mechanisms, respectively, at rich conditions and indicate the spatial distribution of the most important kinetic reactions in the formation/consumption of NO.The total component of NO starts to decrease to a negative value at the earlier stage of the reaction zone due to the action of R18, R19, and R20, which are responsible for NO consumption due to the high reactivity of the NH2 and NH radicals.The total NO formation then increases due to the positive effects of the kinetic reactions R4, R25, R13, R11, and NH2 + HNO ⇌ NH3 + NO (R33), where the kinetic reaction 'R4' has the highest reactivity among the other kinetic reactions.The total component of NO decreased afterward due to the thermal NO reactions of Zeldovich mechanism R26 and R22', as well as the reaction NH + NO ⇌ NNH + O (R34) in lowering the mole fraction of NO downstream by consuming it via the high reactivity of N, and NH radicals.Most importantly, the amplitude of the total NO formation decreases when the equivalence ratio increases from 1.2 to 1.4.This effect leads to a rate of consumption that is more than the NO production rate, which, in turn, lowers the mole fraction of NO; see Figures 24 and 25.

Figure 22 .
Figure 22.The rate of production/consumption of NO in 70/30 (vol%) NH3/H2 mixture at rich conditions estimated by the Z. Wang et al., [46] model reaction.

Figure 23 .
Figure 23.The rate of production/consumption of NO in 70/30 (vol%) NH3/H2 mixture at rich conditions estimated by the Nakamura et al., [69] model reaction.

Figure 24 .
Figure 24.Rate of production figures in (%) as a function of equivalence ratio estimated by the Z. Wang et al., [46] kinetic model.

Figure 25 .
Figure 25.Rate of consumption figures in (%) as a function of equivalence ratio estimated by the Z. Wang et al., [46] kinetic model.

Figure 26 .
Figure 26.Chemical reaction pathways of NO formation/consumption at flame zone (T = 1513 K) and at ϕ = 1.2 predicted by the Z. Wang et al.,[46] and Nakamura et al.,[69] kinetic models.Arrow lines refer to chemical transformations, percentages (%) show the contribution of a reactant to the transformation, numbers stand for the net reaction rate in kmol/m 3 s, which is also visualized by line thickness.

Figure 27 .
Figure 27.Rate of production of NO in (%) at rich conditions estimated by the Nakamura et al.,[69] and Z. Wang et al.,[46] kinetic models.

Figure 28
Figure 28 presents the values of the consumption rate of the most important kinetic reactions in NO consumption in terms of equivalence ratio.Most kinetic reactions in Wang's model demonstrate higher values than those in Nakamura's model.The kinetic reactions of the Zeldovich mechanism R26 and R22 depict higher values of NO consumption rate in Nakamura's model than in Wang's.The reason can be justified based on the Arrhenius parameters that governed these two reactions.As seen from Table3, the Arrhenius parameters' values differ among the tested kinetic models, where the former reaction (R26) has positive activation energy, accelerating the system's reactivity as temperature increases.However, this is not the case for Wang's model, which shows negative activation energy values with opposite effects on temperature.The other Zeldovich reaction, 'R22', has different values listed among the selected mechanisms and shows independent temperature reaction in Nakamura's model and has a negative effect on reactivity when the system's temperature increases; see Table3.

Figure 28 .
Figure 28.Rate of consumption of NO in (%) at rich conditions estimated by the Nakamura et al., [69] and Z. Wang et al., [46] kinetic models.
and Nakamura's mechanisms demonstrated strong predictive capabilities and closely approximated experimental measurements, exhibiting minimal discrepancies.Similarly, Wang's kinetic model yielded accurate estimations of the experimental data, although minor errors and deviations were observed at ϕ = 1.4; 2. Under lean conditions in 70/30 (vol%) NH3/H2 mixture, the kinetic reactions HNO + OH ⇌ NO + H2O, HNO + H ⇌ NO + H2, N + O2 ⇌ NO + O, and N + OH ⇌ NO + H were identified as the primary drivers of NO formation.Conversely, the reactions NH2 + NO ⇌ N2 + H2O, NH + NO ⇌ N2O + H, NH2 + NO ⇌ NNH + OH, NH + NO ⇌ N2 + OH, and N + NO ⇌ N2 + O were found to be the predominant NO-consuming reactions, leading to a reduction in the NO mole fraction; 3. Examination of lean flames demonstrated that the kinetic reactions HNO + H ⇌ NO + H2, HNO + O ⇌ NO + OH, and NH + O ⇌ NO + H are the primary contributors to NO formation.These reactions exhibit higher production rates in Glarborg's mechanism compared to Nakamura's kinetic model, thus contributing to the overestimation of NO by the former; 4.Under rich conditions, the kinetic reactions HNO + H ⇌ NO + H2, N + O2 ⇌ NO + O, NH2 + HNO ⇌ NH3 + NO, and N + OH ⇌ NO + H were identified as the primary drivers of NO production.Conversely, the reactions NH + NO ⇌ N2O + H, NH2 + NO ⇌ NNH + OH, NH2 + NO ⇌ N2 + H2O, and N + NO ⇌ N2 + O were found to be the main NO consumption reactions, leading to a decrease in NO mole fractions; 5. Upon analyzing the performance of the chosen kinetic mechanisms under rich conditions, it was found that the reactions N + O2 ⇌ NO + O, N + OH ⇌ NO + OH, and N2 + H2O ⇌ NH2 + NO may account for the overestimation of NO production observed in Nakamura's kinetic model when compared to Wang's model.Specifically, the first two reactions are part of the NO thermal mechanism in the Zeldovich model and exhibit strong temperature dependence.

Table 1 .
Kinetic reaction mechanisms adopted in the present study.

Table 2 .
Key reactions of NO formation generated from Nakamura's kinetic model.Units are mol, cm, s, cal.

Table 3 .
Key reactions influencing NO formation/consumption of NH3-H2 flames at rich conditions and for two kinetic mechanisms.Units are mol, cm, s, cal.