Kinetic study of ignition process of ammonia/n‐heptane fuel blends under engine conditions

Pilot‐ignited ammonia‐fueled engines have drawn more and more attention for low carbon emissions compared to traditional diesel engines. The ignition processes of NH3/NC7H16 mixtures under compression ignition engine‐like conditions are numerically investigated. By comparing the ignition delay times (IDTs) calculated by six ammonia mechanisms with experimental data, the Glarborg mechanism is selected. Then, the Glarborg mechanism and the Zhang detailed n‐heptane mechanism are merged into a new mechanism, which is adopted in the present study. Results show that the negative temperature coefficient behavior of the IDTs is only observed as the ammonia mass fraction is 70%. Only temperature has a significant effect on IDTs at all research conditions, and the effect of ammonia mass fraction is significant when the temperature is lower than 1000 K. However, the effects of equivalence ratio and pressure are small, especially at high temperatures, high equivalence ratios, and high pressures. Interestingly, the IDTs are categorized into three regions by temperature and ammonia mass fraction. The sensitivity analysis indicates that the sensitivity coefficients of most reactions associated with ammonia decrease with a decrease in ammonia mass fraction, whereas only R4210 is sensitive to ammonia mass fraction for n‐heptane‐related reactions. Rates of production and consumption (ROP) analyses indicate that the ammonia mass fraction mainly affects the ROPs of NC7H16, NH3, and NNH at low and medium temperatures, whereas the ammonia mass fraction affects the ROP of H2NO before the temperature of 2000 K. The ROPs of NC7H16, NH3, and NNH significantly increase with increasing temperature, whereas the ROP of H2NO slightly increases with increasing temperature. The increase of temperature in the early and middle stages is mainly contributed by the oxidation of n‐heptane, while the increase of temperature in the middle and late stages is mainly contributed by the oxidation of ammonia.


| INTRODUCTION
2][3][4] Furthermore, the reserves of fossil energy are limited and will be exhausted in the near future. 5,6herefore, carbon-neutral or zero-carbon fuels have drawn more and more attention all over the world.][9] Direct use of ammonia in engines results in ignition difficulties, long combustion duration, low thermal efficiency, and high NO x emissions.Due to the excellent antiknock performance of ammonia, ammonia is mainly mixed with other fuels in the application of spark ignition engines in the early research. 10,113][14] Compression ignition engine is not limited by the flame propagation speed of the fuel and has higher thermal efficiency.However, the direct use of ammonia with compression ignition engine also faces enormous challenges due to the extremely high autoignition temperature of ammonia. 8,157][18] The IDT of ammonia has a significant influence on the combustion process of the engine.Too long IDT will lead to a poor combustion process and low thermal efficiency.Thereafter, the current study focuses on the ignition characteristics of ammonia/diesel fuel blends.The results will provide theoretical guidance for the ignition control of ammonia-diesel dual-fuel engines.
Diesel is composed of hundreds of compounds/ species, ranging from alkanes, cycloalkanes, alkenes, cycloolefin, aromatic, and other species. 19Furthermore, the source will lead to great differences in the composition of diesel.Therefore, it is difficult to directly investigate the ignition characteristics on the fundamental experimental facilities.n-Heptane is usually used as a surrogate fuel due to the similar cetane number. 20,21In other words, the IDT of n-heptane is close to that of diesel.The chemical kinetic process of n-heptane has been extensively investigated, and the negative temperature coefficient (NTC) behavior is observed in the ignition process.It is widely believed that the NTC behavior is caused by the pyrolysis reactions of peroxyalkyls in the medium temperature stage.The NTC behavior of NH 3 /NC 7 H 16 has been also found under some conditions, whereas in-depth mechanism investigations on the effect of temperature, pressure, equivalence ratio, and n-heptane content on the NTC behavior need to be further carried out.
In the past decades, lots of studies have been conducted on the combustion, emission, and performance of diesel-ignited ammonia engines (Table 1).However, these studies have a limited understanding of the ignition characteristics of ammonia/diesel dual fuel.A series of experimental studies have been carried out to investigate the ignition of ammonia/diesel mixtures based on shock tubes, rapid compression machines (RCMs), and single-cylinder engines.Yu et al. 22 measured the IDTs of n-heptane/ammonia mixtures based on an RCM and obtained a n-heptane/ ammonia dual-fuel mechanism by the Zhang detailed nheptane mechanism and the Glarborg ammonia mechanism.It was found that the addition of ammonia has a significant inhibition effect on the ignition of n-heptane and vice versa.This mechanism can accurately predict the inhibition effect of NH 3 on the ignition of NC 7 H 16 , and can qualitatively capture the trend of IDT with equivalence ratio and oxygen concentration.However, the predicted IDTs still have a large deviation from experimental data under some conditions.Feng et al. 24 studied the ignition processes of diesel/ammonia fuel blends based on an RCM.Results showed that an obvious two-stage ignition behavior existed in the ignition processes of diesel/ammonia fuel blends.With the increase of ammonia mole fraction, the ignition of the first and second stages was delayed.NTC behavior existed in the ignition processes.Then, a new diesel/ ammonia dual-fuel mechanism was developed based on the existing diesel and ammonia mechanisms.This mechanism can predict the inhibition effect of ammonia on the ignition of n-heptane, but cannot predict the IDTs of diesel/ammonia mixtures over a wide range of temperatures, especially overpredict the first-stage ignition and the IDTs in the NTC region.Dong et al. 23 investigated the IDTs of ammonia/diesel mixtures in a shock tube.The experimental results showed that the IDTs of ammonia/n-heptane mixtures were prolonged with increasing ammonia mole fraction or decreasing oxygen concentration.A numerical study was performed by them, and the numerical results showed that the interaction between ammonia and n-heptane via H-abstraction reaction from n-heptane by NH 2 is important for the ignition processes of ammonia/nheptane mixtures.Zhang et al. 25 conducted an experimental study on the ignition characteristics of NH 3 / diesel mixtures in an RCM.The results showed that the NTC behavior ignition of NH 3 /diesel mixtures was only observed in the regime where diesel chemistry dominates.The IDTs increased with increasing NH 3 energy fraction (which is defined as the proportion of low calorific value of ammonia to the total calorific value of the mixtures), whereas decreased with rising equivalence ratio.Then, a diesel/ammonia dual-fuel mechanism was developed to further understand the ignition process.However, the mechanism failed to capture the NTC behavior at an ammonia energy fraction of 20%.The failure prediction of IDTs in the NTC range is closely related to the reaction NO + HO 2 = NO 2 + OH.Then, they studied the IDTs of NH 3 /diesel mixtures at pressures above 50 bar.It was found that the IDTs decrease as the pressure increases from 50 to 120 bar.The numerical study found that the reaction RH + NH 2 = R + NH 3 is essential to the prediction of IDT at high pressures.Moreover, the effect of pressure is related to OH production reactions 2OH (+M) = H 2 O 2 (+M) and NO + HO 2 = NO 2 + OH; the reaction rates of these two reactions increase with rising pressure. 26lthough lots of studies have been performed to investigate the ignition characteristics of ammonia or ammonia blended with other fuels, these studies on the influence of temperature, ammonia fuel blend, pressure, and equivalence ratio on the IDTs of ammonia/diesel mixtures are very limited.Therefore, a more accurate and extensive understanding of the ignition processes of ammonia/diesel mixtures is necessary for the ignition control of ammonia-diesel dual-fuel engines.
The objective of the present study is to reveal the effects of temperature, pressure, equivalence ratio, and ammonia content on the ignition process of NH 3 /NC 7 H 16 fuel blend, which intends to provide a theoretical fundament for the ignition control of diesel/ammonia dual-fuel engines.Then, to reveal the effect of the main elementary reactions on the IDT, a sensitivity analysis is conducted.Finally, a chemical kinetic analysis is performed to gain a further understanding of the combustion process of diesel/ammonia dual-fuel engines.The present investigation will provide fundamental guidance for the ignition control of diesel/ ammonia dual-fuel engines.

| NUMERICAL METHOD
The present study is conducted on a zero-dimensional constant volume model with homogeneous and adiabatic boundary conditions based on Chemkin software.The IDT is defined as the duration from the start time to the time when the maximum rise rates of OH radicals occur.The initial conditions, including temperature, pressure, equivalence ratio, and mixture composition, are selected according to the conditions near the top dead center of the compression engine.There are many available mechanisms for both n-heptane and NH 3 in the literature.In the past decade, the n-heptane mechanism has been developed maturely.However, the ammonia mechanism is not quite mature.Therefore, four ammonia mechanisms verified under some conditions were selected and further verified under a wide range of conditions, and the mechanisms include (1) the Glarborg mechanism, 27 (2) the Klippenstein mechanism, 28 (3) the Li mechanism, 29 and (4) the Mei mechanism. 30Moreover, in the study of Peng et al., 31 the performance of Mevel 32 and Mathieu mechanisms 33 was better in predicting the IDTs of ammonia.Therefore, the Mevel mechanism and Mathieu mechanism are also applied to compare with the above four mechanisms.The Glarborg mechanism includes the interaction between nitrogen and hydrocarbon chemistry.Moreover, the NC 7 H 16 /NH 3 dual-fuel mechanisms must include the n-heptane submechanism, NH 3 submechanism, and the submechanism of the interaction between ammonia and hydrocarbon.
T A B L E 1 A summary of the studies on ammonia/n-heptane mixture combustion.Figures 1-6 show a comparison of predicted IDT by these four mechanisms for NH 3 and the experimental data in shock tubes. 31,33,34Figures 1 and 2 depict the calculated and measured 34 IDTs of ammonia in air conditions.At equivalence ratios of 1.0 and 2.0, the IDTs of NH 3 /air predicted by Glarborg and Mei mechanisms are in good agreement with the experimental data at an initial pressure of 40 bar.However, at an initial pressure of 20 bar, only the Glarborg mechanism has good predictions in IDTs of ammonia/air mixtures.At an equivalence ratio of 1.0, the predicted IDTs by the Mevel mechanism only match the experimental data well at low temperatures.The predicted IDTs by the Mathieu mechanism are in good agreement with experimental data with experimental data at a pressure of 40 bar.At an equivalence ratio of 2.0, the performance of the Mevel mechanism is only better at medium temperatures.The predicted IDTs of the Mathieu mechanism are close to experimental data at high temperatures with a pressure of 40 bar.Figures 3-5 depict the IDTs versus temperature at high argon dilution ratios. 33At low and medium equivalence ratios, the IDTs predicted by Klippenstein, Glarborg, and Li mechanisms are in good agreement with experiment data at all three pressures.At a high equivalence ratio, when the initial pressure is 1.4 bar, only the Klippenstein mechanism has a good prediction in the IDTs of ammonia, and when the initial pressure is 11 and 30 bar, the Glarborg and Klippenstein mechanisms are able to capture the experimental data with temperature.The IDTs of ammonia predicted by the Mevel mechanism are only close to experimental data when the equivalence ratio and the pressure are 1.4 bar.The IDTs of ammonia predicted by the Mathieu mechanism are slightly higher than experimental data at all the conditions.Figure 6 shows that only the IDTs predicted by the Li mechanism are close to experimental data at a pressure of 11 bar. 31At a pressure of 12 bar and a dilution rate of 73%, only the Mevel mechanism can capture the experimental data.At a pressure of 12 bar and a dilution rate of 61%, the IDTs of ammonia predicted by the Mevel mechanism are slightly higher than experimental data, whereas the IDTs predicted by the other mechanisms are much higher than experimental data.In an engine, fuel is usually injected into the cylinder at compression top dead center, when the mixture in the cylinder is at a high pressure.Therefore, the accuracy of IDT for ammonia predicted by the mechanism is more important.

References
Based on the above comparison, the Glarborg mechanism is selected to predict the ignition process of ammonia.The ignition process of n-heptane is predicted by the Zhang detailed mechanism, which has been validated under a wide range of conditions.In the process of chemical kinetics simulation, only one mechanism can be used.Thereafter, it is necessary to develop an NH 3 /NC 7 H 16 dual-fuel mechanism based on the Glarborg mechanism and Zhang detailed mechanism. 21Since the Zhang detailed mechanism includes more species and elementary reactions, during the merger process, the Zhang detailed mechanism is taken as the main mechanism.The Glarborg mechanism is added to the main mechanism, and the duplicate reactions of C0-C2 are removed.Moreover, the interaction between NH 3 and C1-C2 is included in the Glarborg mechanism, and it does not need to be added to the merge mechanism anymore.Since the reaction n-C 7 H 16 + NH 2 <=> C 7 H 15 + NH 3 has been proven to be important for the ignition processes of ammonia/n-heptane mixtures, 23 the related reactions are added in the new mechanism.
The verification of the new mechanism is shown in Figures 7 and 8.As shown in Figure 7, 33 at a pressure of 1.4 bar, the predicted IDTs of ammonia are in good agreement with experimental data when the temperature F I G U R E 7 Calculated and measured ignition delay times of ammonia with different pressures at an equivalence ratio of 1.0.

(A) (B)
F I G U R E 8 Calculated and measured ignition delay times of n-heptane/ammonia mixtures with different n-heptane energy fractions at an equivalence ratio of 1.0.
is lower than 2250 K, and it is slightly higher than experimental data as the temperature is higher than 2250 K.At temperatures of 11 and 30 bar, the predicted IDTs agree well with experimental data over the entire temperature range.Figure 8a shows that the simulated IDTs of NC 7 H 16 agree well with experimental data over the entire temperature range. 22,23At n-heptane energy fractions of 80% and 60%, the predicted IDTs of NC 7 H 16 / NH 3 mixtures are in good agreement with experimental data at medium temperatures, while they are slightly higher than experimental data at low and high temperatures.Figure 8B shows that, at 15 bar, the predicted IDTs of NC 7 H 16 agree well with experimental data. 22The simulated IDTs of NC 7 H 16 /NH 3 mixtures have slightly higher experimental data at low temperatures, whereas they are in good agreement with experimental data at medium temperatures.In summary, the predicted IDTs of ammonia, n-heptane, and n-heptane/ammonia mixtures are in reasonable agreement with experimental data, and they can be used in the present study.The simulation conditions are set up based on diesel pilot ammonia-diesel fuel engines, in which a small amount of diesel is injected into a cylinder near the top dead center and acts as an ignition source for ammonia/ air mixtures.The mass fraction of pilot fuel is usually less than 10% of the total fuel.The amount of pilot fuel is usually less than 30% of the total fuel.Therefore, the mass fraction of n-heptane and ammonia is set from 1% to 30% and 99% to 70%.The pressure, temperature, and equivalence ratio are also set up based on the thermodynamic state of the mixture at TDC of engine compression stroke, which is set from 50 to 200 bar, 800 to 1200 K, and 0.5 to 2.0, respectively.

| Effect of single variable on IDTs
Many experiments and simulation studies have proved the existence of the NTC behavior in the ignition process of n-heptane.However, the NTC behavior is not found in the ignition process of ammonia.Therefore, the mixing of ammonia will have a great impact on the NTC behavior for n-heptane.The IDTs versus temperature at different ammonia mass fractions are shown in Predicted ignition delay times of ammonia/n-heptane mixtures with different (A) ammonia mass fraction, (B) equivalence ratio, and (C) pressure.
Figure 9a.As the ammonia mass fractions are 99%, 90%, and 80%, the NTC behavior is not observed in the ignition process of the fuel blends.As the ammonia mass fraction decreases to 70%, the NTC behavior appears in the ignition processes of the fuel blends, which is also observed in Dong et al., where the NTC behavior is only observed in the regime where diesel chemistry dominates. 23The IDTs as a function of temperature at different equivalence ratios are plotted in Figure 9b.As the equivalence ratio increases from 0.5 to 1.0, the IDTs decrease with the increase of the equivalence ratio throughout the temperature range for the present study.
When the equivalence ratio is greater than 1.0, the change in IDTs is negligible with the increase of the equivalence ratio.At low equivalence ratio conditions, the H-abstractions of the fuel blends are promoted with an increase of equivalence ratio.At medium and high equivalence ratios, although the H-abstractions are promoted, the subsequent reactions are slower owing to insufficient oxygen concentration.Figure 9c plots the IDTs versus temperature at different pressures.At all research pressures, the effect of temperature is mitigated at medium temperatures, whereas the NTC behavior is not observed.As the pressure increases, the effect of temperature is further mitigated at medium temperatures.The influence of pressure on IDTs is pronounced at medium temperature.As the temperature increases or decreases, the effect of pressure decreases.This indicates that the influence of pressure on the decomposition reactions of C 7 H 15 -2, C 7 H 14 OOH2-4, and C 7 KET24 is greater than that on the dehydrogenation reactions of fuel, as shown in Figure 10.At high temperatures, due to the rapid reaction rate, the effect of pressure is weakened (Table 2).

| Effect of multiple variables on IDTs
In this section, the effects of multiple variables on the IDTs of n-heptane/ammonia fuel blends are investigated.Figure 11 plots the effect of NH 3 mass fraction and equivalence ratio on the IDTs at a pressure of 50 bar and different temperatures.At a temperature of 800 K, the effect of equivalence ratio on IDT is quite small when the equivalence ratio is less than 1.5 and the ammonia mass fraction is less than 85%.In this regime, the effect of ammonia mass fraction is slightly mitigated.As the equivalence ratio is greater than 1.5 and the ammonia mass fraction is greater than 85%, the effect of equivalence ratio is negligible and the effect of equivalence ratio.As temperature increases, the region with slight effect of equivalence ratio expands, and in this regime, the effect of equivalence ratio is slightly enhanced.
The effect of ammonia mass fraction and pressure on the IDTs of ammonia/n-heptane fuel blends of an equivalence ratio and different temperatures is plotted in Figure 12.At all three temperatures, the ammonia mass fraction has a significant impact on the IDTs of ammonia/n-heptane mixtures.At a temperature of 800 K, the effect of pressure on IDTs is not significant.As the temperature increases, the effect of pressure is slightly enhanced.Figure 13 shows the temperature history at different temperatures and pressures.At a temperature of 800 K, the initial increase in temperature is quite small with the increase of pressure, and even at 100 bar, the initial increase in temperature is lower than that at 75 bar.As the temperature increases, the initial increase in temperature is enhanced with the increase of pressure.Therefore, the effect of pressure on IDTs is enhanced with an increase in temperature.
Figure 14 shows the effects of ammonia mass fraction and temperature on the IDTs at a pressure of 50 bar and different equivalence ratios.Figure 14a shows that both the effects of temperature and ammonia mass fraction on IDTs are significant as the temperature is below 1000 K and the ammonia mass fraction is greater than 85%.As the temperature is lower than 940 K and the ammonia mass fraction is less than 85%, the effect of temperature is mitigated, whereas the effect of ammonia mass fraction is still significant.As the temperature is higher than 1000 K, the effect of temperature is significant, while the effect of ammonia mass fraction is slightly mitigated.| 1097 F I G U R E 11 Predicted ignition delay times of ammonia/n-heptane mixtures versus ammonia mass fraction and equivalence ratio at P = 50 bar and T = 800, 1000, and 1200 K.

F I G U R E 12
Predicted ignition delay times of ammonia/n-heptane mixtures versus ammonia mass fraction and pressure at Φ = 1.0 and T = 800, 1000, and 1200 K.
As shown in Figures 14B and 14C, the effect of temperature and ammonia mass fraction remains almost unchanged with the increase of equivalence ratio.Figure 15 plots the predicted IDTs versus equivalence ratio and pressure.At all research conditions, the effects of equivalence ratio and pressure on the IDTs of NH 3 / NC 7 H 16 mixtures are mitigated.Figure 15a shows that, at an ammonia mass fraction of 90%, the figure can be divided into two regions: the positive effect region of equivalence ratio and the negative effect region of equivalence ratio.The boundary of the two regions is an equivalence ratio.The left side of the equivalence ratio of 1.45 is the positive effect region of equivalence ratio.On the right side, the equivalence ratio has a negative effect on the IDTs.As the equivalence ratio increases, the consumption rate of active groups increases, and the IDTs are delayed.Figures 15A and  15C show shat, as the ammonia mass fraction decreases, the positive effect region of equivalence ratio increases, whereas the negative effect region of equivalence ratio becomes the negligible effect region of equivalence ratio.At lower ammonia mass fractions, the active groups generated by the oxidation of n-heptane increase; therefore, the negative effect of the equivalence ratio is mitigated.
Figure 16 plots the simulated IDTs of NH 3 /NC 7 H 16 mixtures as a function of temperature and pressure at an equivalence ratio of 1.0 and different ammonia mass fractions.At an ammonia mass fraction of 90%, the effect of temperature on IDTs of NH 3 /NC 7 H 16 mixtures is pronounced, whereas the effect of pressure on IDTs is mitigated.As the ammonia mass fraction decreases to 80%, the effect of temperature is pronounced, and the effect of pressure is still weak at temperatures above 950 K.When the temperature is below 950 K, the effect of temperature is Temperature history of ignition process of ammonia/n-heptane mixture with different temperatures and pressure at Φ = 1 an ammonia mass of 80%.

(A) (B)
F G U E 14 Predicted ignition delay times of ammonia/n-heptane mixtures versus ammonia mass fraction and temperature at P = 50 bar and Φ = 0.5, 1.0, and 2.0.
Predicted ignition delay times of ammonia/n-heptane mixtures versus equivalence ratio and pressure at T = 1000 K and three ammonia mass fractions of 90%, 80%, and 70%.
F I G U R 16 Simulated ignition delay times of ammonia/n-heptane mixtures versus pressure and temperature at Φ = 1.0 and three ammonia mass fractions of 90%, 80%, and 70%.
F I G U R E 17 Simulated ignition delay times of ammonia/n-heptane mixtures versus equivalence ratio and temperature at P = 50 bar and three ammonia mass fractions of 90%, 80%, and 70%.mitigated and the effect of pressure is strengthened owing to the NTC behavior.As the ammonia mass fraction decreases to 70%, the NTC behavior is more significant.The effect of temperature is more mitigated and the effect of pressure is more enhanced at temperatures below 950 K.
Figure 17 shows the IDTs of NH 3 /NC 7 H 16 mixtures as a function of equivalence ratio and temperature at a pressure of 50 bar and different ammonia mass fractions.At an ammonia mass fraction of 90%, the effect of temperature on IDTs is significant, and the effect of equivalence ratio is negligible.As the ammonia mass fraction decreases to 80%, the effect of temperature on IDT is slightly mitigated at temperatures below 900 K, and the effect of equivalence ratio is slightly enhanced at temperatures below 850 K and equivalence ratios less than 1.0.As the ammonia mass fraction decreases to 70%, the region where the effect of temperature on IDT is slightly mitigated extends to 950 K.In addition, the region where the effect of equivalence ratio is enhanced extends to a temperature of 920 K and an equivalence ratio of 1.0.
A sensitivity analysis is conducted to identify the dominant reactions associated with the ignition processes of NH 3 /NC 7 H 16 fuel blends under the conditions of 70%, 80%, and 90% ammonia mass fraction, Φ = 1, P = 50 bar, and three different temperatures of 800, 1000, and 1200 K.The sensitivity coefficient is defined as where the τ is IDT and ki is the specific rate coefficient.A positive value indicates a negative effect on the IDT and vice versa.Based on previous sensitivity analysis, the top 14 greatest sensitive reactions to the ignition process of NH 3 /NC 7 H 16 fuel blends have been chosen, as listed in Table 3.These reactions can be divided into three parts, including the reactions important for the ignition process of both ammonia and n-heptane (R21-30), reactions only important for the ignition process of n-heptane (R4210-4405), and reactions only important for the ignition process of ammonia (R5738-5807).Figures 18 and 19 depict the sensitivity analysis on the IDTs of NH 3 /NC 7 H 16 fuel blends in various conditions.It can be seen in Figure 18 that the sensitivity coefficient of is highest, which indicates that R5738 has the greatest inhibition effect on the ignition process of NH 3 /NC 7 H 16 mixtures.R5756 and R5760 also have an inhibition effect on the ignition process of NH 3 / NC 7 H 16 mixtures.At a temperature of 800 K, the sensitivity coefficient of R5738 is maximum at an ammonia mass fraction of 80%.At temperatures of 1000 and 1200 K, the sensitivity coefficient of R5738 F I G U R 18 Sensitivity of ignition delay times for ammonia/n-heptane mixtures with different temperatures under Φ = 1.0 and P = 50 bar.
increases with a decrease in ammonia mass fraction.At a temperature of 800 K, the reaction activities of NH 3 / NC 7 H 16 mixtures are low, and the concentration of OH generated is low.Thereafter, when the ammonia mass fraction decreases from 90% to 80%, the increase of nheptane concentration results in an increase in generated OH concentration.As the ammonia mass fraction decreases from 80% to 70%, the concentration of OH generated by the n-heptane reaction further increases.However, due to the low reaction activities of NH 3 / NC 7 H 16 mixtures, the increases in concentration of OH are limited, while the concentration of ammonia is lower, resulting in a slight decrease in the sensitivity coefficient of R5738.At temperatures of 1000 and 1200 K, the reaction activities of NH 3 /NC 7 H 16 mixtures are high; therefore, the sensitivity coefficient of R5738 increases with the decrease in ammonia mass fraction.The inhibition effects of R5756 and R5760 are mitigated with a decrease in ammonia mass fraction.R30, R4214, R4302, and R5745 have negligible effects on the ignition process of NH 3 /NC 7 H 16 mixtures at all the research conditions.At a temperature of 800 K, R4210 has the greatest promotion effect on the ignition process of NH 3 / NC 7 H 16 mixtures.The sensitivity coefficient of R4210 decreases with decreasing ammonia mass fraction, as R4210 is associated with the ignition of n-heptane.R5757, R5759, and R5807 also have a significant effect on the ignition of NH 3 /NC 7 H 16 mixtures.Owing to these reactions associated with the ignition of ammonia, the sensitivity coefficients decrease with decreasing ammonia mass fraction.At temperatures of 1000 and 1200 K, R5757 becomes the reaction with maximum promotion effect on the ignition of NH 3 /NC 7 H 16 mixtures.R21, R4218, and R4405 have a small effect on the ignition processes of NH 3 /NC 7 H 16 mixtures at a temperature of 800 K.At a temperature of 1000 K, the effects of R21 and R4218 are enhanced, whereas the effect of R4405 is weakened.At a temperature of 1200 K, only the effect of R4218 is enhanced, and the effects of R21 and R4405 become negligible.
Figure 19 shows that R5738 and R4210 are highly sensitive to temperature, the sensitivity coefficients of R5738 and R4210 sharply decrease with increasing temperature.At an ammonia mass fraction of 90%, the effects of R5756, R5760, R5757, R5759, and R5807 on the ignition of NH 3 /NC 7 H 16 mixtures are also significant at a temperature of 800 K.The effects of R5756, R5759, and R5760 are sensitive to temperature, whereas the sensitivity coefficients of R5757 and R5807 first increase and then decrease with increasing temperature.At all three temperatures, the sensitivity coefficients of R21, R4218, and R4405 are relatively low, and the effects of R30, R4214, R4302, and R5745 are negligible.

| Chemical kinetic analysis
To further understand the ignition process of NH 3 / NC 7 H 16 mixtures, the fuel consumption history is conducted, as shown in Figure 20.The temperature is set from 800 to 1200 K, the pressure is set to 50 bar, the equivalence ratio is set to 1.0, and the ammonia mass fraction is set from 70% to 90%.Note that the concentrations of both ammonia and n-heptane remain unchanged for a long period, but they are rapidly consumed near the ignition timing for all the conditions.n-Heptane is consumed rapidly within a short period for all the cases.As ammonia mass fraction deceases, the rapid consumption period of n-heptane shortens.In the lowtemperature reaction stage, the consumption of nheptane is relatively slow.By comparing the consumption history of n-heptane at temperatures of 800, 1000, and 1200 K, it can be seen that the period of lowtemperature reaction stage of n-heptane increases with increasing temperature.As the temperature increases or the ammonia mass fraction decreases, the rapid consumption stage of ammonia advances, whereas the time interval of the rapid consumption stage of ammonia remains unchanged.
The rates of production and consumption (ROP) analysis is an important way to understand the mechanism of fuel ignition.Four important species (NC 7 H 16 , NH 3 , NNH, and H 2 NO) are selected to perform the ROP analysis.The ROP of NC 7 H 16 is shown in Figure 21.At an initial temperature of 800 K, the ROPs of NC 7 H 16 are relatively low at an ammonia mass fraction of 90%.The decrease of ROPs at high temperatures is on the one hand due to the consumption at low and medium temperatures, and on the other hand due to the decrease of ammonia mass fraction.However, the reaction rate of R5752 (2NH 2 = NH 3 + NH) is not impacted by ammonia mass fraction at low and medium temperatures and decreases with a decrease in ammonia mass fraction.The ROPs of NH 3 significantly increase with an increase in temperature.
Figure 23 shows the ROPs of NNH (R5757 (NH 2 + NO = NNH + OH), R5777 (NNH = N 2 + H), R5783 (NNH + O 2 = N 2 + H 2 O), and R5898 (N 2 H 2 + M = NNH + H + M) at different temperatures.The results demonstrate that the ROPs of NNH increase with the decrease of ammonia mass fraction at low and medium temperatures and decrease at high temperatures.The ROPs of NH 3 increase with increasing initial temperature.
Figure 24 depicts the ROPs of H 2 NO at different temperatures.The reaction rate of R5806 (H 2 NO + HO 2 = HNO + H 2 O 2 ) increases at low temperatures and decreases at medium and high temperatures with a decrease in ammonia mass fraction.As the ammonia mass fraction decreases, the reaction rates of R5746 (NH 2 + HO 2 = H 2 NO + OH), R5801 (H 2 NO + M = HNOH + M), and R5805 (H 2 NO + OH = HNO + H 2 O) increase before the temperature of 2000 K, and decrease after the temperature of 2000 K.As the temperature increases, the ROPs of H 2 NO slightly increase.Note that the ROPs of NC 7 H 16 tend to zero before 1800 K, whereas the ROPs of species associated with NH 3 rapidly increase after the temperature of 1500 K and tend to zero at a temperature of 2800 K.These results indicate that the increase of temperature in the early and middle stages is mainly contributed by the oxidation of n-heptane, whereas the increase of temperature in middle and late stages is mainly contributed by the oxidation of ammonia.

| CONCLUSION
In the present study, the effects of temperature, pressure, equivalence ratio, and mass fraction on IDTs of NH 3 / NC 7 H 16 mixtures were numerically investigated.Moreover, the sensitivity analysis of temperature and ammonia mass fraction on the IDTs was performed to provide the theoretical basis for the ignition process of ammonia/ diesel dual-fuel engine.Furthermore, the consumption history of fuel and ROP analysis of species was conducted to further understand the ignition processes of NH 3 / NC 7 H 16 mixtures.The main conclusions are summarized as follows: 1.The NTC behavior is only observed in the ignition processes of NH 3 /NC 7 H 16 mixtures when the ammonia mass fraction is less than 70%.At a low equivalence ratio, the effect of equivalence ratio is relatively small.However, the effect of equivalence ratio becomes negligible as the equivalence ratio is greater than 1.0. 33he effect of pressure on the IDT is more pronounced at medium temperature, and it decreases with the decrease or increase of temperature.2. Only temperature has a significant impact on the IDTs over a wide range of present conditions.The effect of ammonia mass fraction on the IDTs is pronounced as the temperature is lower than 1000 K.The effects of ammonia mass fraction and equivalence ratio are mitigated with the increase of temperature. 23The effect of equivalence ratio is relatively small, especially when the equivalence ratio is greater than 1.0. 33The effects of pressure and equivalence ratio are small, and they become negligible at high equivalence ratio and high pressure.The IDTs of NH 3 /NC 7 H 16 mixtures can be categorized into three regions.The region with a significant effect of ammonia mass fraction becomes smaller with the increase of equivalence ratio.3. R5738, R5756, and R5760 have significant negative effects on the ignition of NH 3 /NC 7 H 16 mixtures, whereas R4210, R5757, R5759, and R5807 have positive significant effect on the ignition of NH 3 /NC 7 H 16 mixtures.The sensitivity coefficients of reactions associated with ammonia decrease with the decrease of ammonia mass fraction, except for R5738, which has a higher sensitivity coefficient at low and medium ammonia mass fractions.R5738 and R4210 are very sensitive to temperature at three ammonia mass fractions of 70%, 80%, and 90%, whereas R5756, R5759, and R5760 are only sensitive to temperature at an ammonia mass fraction of 90%. 4. The rapids consumption of both ammonia and n-heptane are near the ignition timing.The low-temperature reaction stage is improved with the decrease of ammonia mass fraction or the increase of temperature.The rate of production and consumption demonstrates that ammonia mass fraction mainly affects the ROPs of NC 7 H 16 , NH 3 , and NNH at low-and medium-temperature stages.The ROPs of NC 7 H 16 , NH 3 , and NNH significantly increase with the increase of temperature.However, the ROP of H 2 NO is impacted by the ammonia mass fraction before the temperature of 2000 K.The increase of temperature in the early and middle stages is mainly contributed by the oxidation of n-heptane, whereas the increase of temperature in the middle and late stages is mainly contributed by the oxidation of ammonia.The present study can provide a theoretical guidance for the ignition control of diesel/ammonia dual-fuel engines.

F I G U R E 1
Calculated and measured ignition delay times of ammonia with different pressures at an equivalence ratio of 1.0.F I G U R E 2 Calculated and measured ignition delay times of ammonia with different pressures at an equivalence ratio of 2.0.F I G U R E 3 Calculated and measured ignition delay times of ammonia with different pressures at an equivalence ratio of 0.5.F I G U R E 4 Calculated and measured ignition delay times of ammonia with different pressures at an equivalence ratio of 1.0.F I G U R E 5 Calculated and measured ignition delay times of ammonia with different pressures at an equivalence ratio of 2.0.F I G U R E 6 Calculated and measured ignition delay times of ammonia with different dilution rates at an equivalence ratio of 1.0.

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I G U R 19 Sensitivity of ignition delay times for ammonia/n-heptane mixtures with different ammonia mass fractions under Φ = 1.0 and P = 50 bar.F I G U R E 20 Time evolution of ammonia and n-heptane different temperatures and ammonia mass fractions at Φ = 1.0 and P = 50 bar.F I G U R E 21 Rates of production and consumption of NC 7 H 16 with different temperatures and different ammonia mass fractions under Φ = 1.0 and P = 50 bar.

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I G U R E 22 Rates of production and consumption of NH 3 with different temperatures and different ammonia mass fractions under Φ = 1.0 = 50 F I G U R E 23 Rates of production and consumption of NNH with different temperatures and different ammonia mass fractions under Φ = 1.0 and P = 50 bar.F I G U R E 24 Rates production and consumption of H 2 NO with different temperatures and different ammonia mass fractions under Φ = 1.0 and P = 50 bar.
Figure 22A-C plots the ROPs of NH 3 at different temperatures.Due to the low reaction activity of NH 3 , the consumption reactions of NH 3 rarely occur at the initial temperature.As the initial temperature increases, the ROPs of NH 3 start earlier.It can be seen in Figure 17A-C that, as the ammonia mass fraction decreases, the ROPs of R5736 (NH 3 + H = NH 2 + H 2 ), R5737 ((NH 3 + O = NH 2 + OH), and R5738 ((NH 3 + OH = NH 2 + H 2 O) slightly increase at low and medium temperatures, but they decrease at high temperatures.
However, the main reactions of NC 7 H 16 begin at the initial temperature, owing to the temperature increase during the low-temperature reaction stage mainly provided by the oxidation of n-heptane.As the ammonia mass fraction decreases, the reaction rate of R4196 (NC 7 H 16 = PC 4 H 9 + NC 3 H 7 ) increases significantly at