Auto-ignition and reaction kinetic characteristics of hydrogen-enriched n-dodecane mixtures under engine-like thermodynamic conditions

Abstract

The hydrogen/diesel dual-fuel engine has attracted extensive attention in recent years. To acquire ignition control methods for a dual-fuel engine, the mutual effects and separate influencing scales of multiple factors on the auto-ignition and reaction kinetic characteristics of a hydrogen/n-dodecane mixture under engine-like thermodynamic conditions were revealed by detailed chemical kinetic mechanism and experimental data based on the colormap and Taguchi methods. The results showed that blending a small amount of n-dodecane induced the initial production of OH and the early oxidation of fuels, which dramatically reduced the IDT of the hydrogen mixture. With a continuous increase in n-dodecane content, the improved reaction rates of the fuels outweighed the reduced reaction rates of active radicals, which resulted in a further reduction in the IDT and an enhancement in NTC behavior. Elevating ϕ and initial pressure apparently reduced the IDT as well. The rates of contribution of temperature, ϕ, pressure, and n-dodecane content on IDT are 62.9%, 27.0%, 5.1%, 5.0%, respectively. The temperature exerted a great influence under all conditions. The ϕ also had a obvious impact in most regions other than a pure hydrogen mixture or under low-temperature/high-ϕ conditions. The effect of pressure was ignorable under low-temperature or pure hydrogen mixture conditions due to the dramatically weakened mixture reactivity. While the influence of n-dodecane fraction was also negligible when it was more than 10% at mid-temperature or 20% at low temperature. Further, the sensitivity analysis showed the sensitivity coefficients of decomposition reactions and H/HO₂ related reactions reduced and increased, respectively, with increasing temperature. The sensitivity coefficients of OH/H₂O₂ related reactions reached their peak values in the NTC region, which represents the region where H₂O₂/OH radicals were the significant intermediate products in the hydrogen/n-dodecane reaction system. This investigation not only revealed the coupled influence law of multiple factors and the internal interaction mechanism between fuels and active radicals in the hydrogen/n-dodecane reaction system, but also provided fundamental insights into precise ignition control methods for a diesel/hydrogen dual-fuel engine.

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1. Introduction

According to the Fourth International Maritime Organization (IMO) Greenhouse Gas (GHG) Study 2020, total shipping generated 1056 million tonnes of CO₂ in 2018, or roughly 2.89% of all anthropogenic CO₂ emissions worldwide. To reduce the atmospheric and marine pollution caused by ships, the IMO set its GHG reduction strategy to reduce these emissions by a minimum of 40% by 2030 and by a minimum of 70% by 2050 compared to 2018. Thus the world's shipbuilding manufacturers are facing severe challenges of lowering GHG emissions. To achieve these goals, the global shipbuilding industry is striving to propel the adoption of zero-carbon fuels like hydrogen and ammonia.

Compared with ammonia, hydrogen has a high flame speed and heat value, which ensure high-efficiency engine combustion performance.¹ The wide ignition limit and low ignition energy of hydrogen increase the ignitable scope of the in-cylinder mixture, which is beneficial to stable combustion over wide operating conditions.² Further, hydrogen has extremely low emission levels because the only combustion pollutant of hydrogen is NO_x.³ Therefore, the excellent combustion and emission characteristics significantly broaden the application prospects of hydrogen in internal combustion engines.

Hydrogen-fueled internal combustion engines (HICEs) had already been proposed early in 1933.⁴ Various investigations suggested that HICEs possess high power performance and reliability with nearly zero carbon emissions.^5–9 The development of HICEs in the automotive industry started at the beginning of the 21st century.^10–18 However, the characteristics of hydrogen, including extremely low ignition energy (0.02 mJ, 0.24 mJ for diesel), high burning rate (200 cm s⁻¹, 45 cm s⁻¹ for diesel) and shorter quenching distance (0.64 mm, 2 mm for gasoline), may induce abnormal combustion and a high combustion temperature in marine HICEs, which threaten engine operational safety and raise NO_x emissions.^19,20 To mitigate these issues, HICEs normally apply a lean combustion mode. Spark ignition is practical for automotive engines due to their high rotation speed and small cylinder bores. However, for marine hydrogen engines, which have much larger cylinder bores and leaner fuel/air mixtures, common spark ignition cannot provide sufficient energy to ignite an ultra-lean mixture and cannot ensure stable flame propagation. It requires cylinders with well-penetrated ignition sources and substantially higher ignition energy. As a result, marine HICEs must inject pilot diesel.

In the pilot-diesel/hydrogen dual-fuel engine, the combustion of pilot diesel functions as a huge spark plug with high energy, which ensures continuous reliable ignition and reduces cycle-to-cycle variation.²¹ This combustion mode of the Otto cycle dramatically reduces engine emissions. Therefore, many researchers have investigated the operating performance of diesel/hydrogen dual-fuel engines. Szwaja et al.²² found that a moderate blending ratio of hydrogen could promote the combustion homogeneity of the in-cylinder mixture, which improved the overall combustion performance. Tsujimura et al.²³ showed that the influence of the blended hydrogen on the thermal efficiency of the diesel engine depended on the located engine load. Blending the hydrogen elevated the thermal efficiency at high load; whereas, the variation law showed an opposite trend at low load. Further, with the addition of hydrogen, the CO and soot emissions reduced while the NO_x emissions increased. Naber et al.²⁴ investigated the in-cylinder auto-ignition properties of hydrogen in a diesel engine. The results show that hydrogen's auto-ignition characteristics had strong relevance to in-cylinder temperature and diesel injection timing.

It can be concluded from the above research that the operating performance of the dual-fuel engine depends mainly on the blending ratio of diesel and hydrogen and the located in-cylinder thermodynamic conditions. The actual diesel fuel consists of multiple complex compositions, including cycloalkanes, straight-chain alkanes, and aromatic hydrocarbons.²⁵ For the convenience of the theoretical research in the current study, n-dodecane is treated as a surrogate fuel for diesel because the molecular size and boiling characteristics of n-dodecane are close to those of ordinary diesel.²⁶ Therefore, understanding the auto-ignition mechanism of n-dodecane/hydrogen mixtures with wide blending ratios and thermodynamic conditions are critical to revealing the potential control strategies of combustion progress in a diesel/hydrogen dual-fuel engine.

The auto-ignition characteristics of a mixture of hydrogen and low-carbon fuels have been investigated in many studies. Mohamed²⁷ investigated the influence of the addition of hydrogen on the ignition of C1–C7 natural gas blends. The results demonstrate that hydrogen addition has both an inhibiting and a promoting effect in low- and high-temperature regimes, respectively. He²⁸ revealed the auto-ignition kinetics of hydrogen-enriched ammonia mixtures at intermediate temperatures and high pressures via a rapid compression machine. The experiments demonstrate that a higher hydrogen mole fraction increases the reactivity of hydrogen/ammonia mixtures, while the equivalence ratio has a different influence. Jiang et al.²⁹ constructed a skeletal mechanism for the prediction of ignition delay times and laminar premixed flame velocities of hydrogen–methane mixtures under gas turbine conditions. However, only a few studies have concentrated on the ignition progress of a mixture of hydrogen and high-carbon fuels. Li et al.³⁰ studied the ignition properties of premixed iso-octane/air with hydrogen addition through detailed chemistry numerical simulations. They found the addition of a small amount of hydrogen could reduce the minimum ignition energy of iso-octane/air. Whereas the minimum ignition energy was insensitive to hydrogen addition when the blending ratio of hydrogen is above 60%. Aggarwal et al.³¹ investigated the ignition characteristics of an n-heptane/hydrogen mixture at elevated pressure based on various chemical kinetic mechanisms. The results showed that the addition of n-heptane decreased and increased the IDT of hydrogen mixture at low and high temperature, respectively. Frolov et al.³² found that hydrogen acted as an ignition promoter and an ignition inhibiter, respectively, in the high-temperature (T > 1050 K) and low-temperature (T < 1050 K) reaction system of an n-decane mixture. Furthermore, laminar burning velocity experiments of n-decane/hydrogen mixtures conducted by Xu et al.³³ showed that the laminar burning velocity of an n-decane mixture increased linearly with an increasing blending ratio of hydrogen.

Generally speaking, existing research on the auto-ignition properties of hydrogen-enriched mixtures concentrate on a mixture of hydrogen, low-carbon fuels and some high-carbon fuels (n-decane, iso-octane, n-heptane). However, studies of the ignition characteristics of a hydrogen/n-dodecane mixture under wide thermodynamic conditions and various blending ratios were scarce. In addition, the influence of different ambient gas atmospheres on the chemical reaction kinetic property of the mixture with hydrogen and high-carbon fuels also needed to be explored and compared.

Therefore, in the current study, the auto-ignition properties of hydrogen/n-dodecane mixtures (ϕ: 0.5, 1.0, 2.0) were conducted under high pressures (40–80 bar) and low-to-mid temperatures (750–1050 K) to provide basic research data on the IDT for hydrogen/n-dodecane mixtures, and obtain ignition control methods for a hydrogen/diesel dual-fuel engine. The chemical reaction kinetics properties of hydrogen/n-dodecane mixtures were also investigated by detailed kinetic mechanisms to reveal the differences in auto-ignition properties and reaction kinetics characteristics of n-dodecane/hydrogen mixtures under wide thermodynamic conditions and various blending ratios. Finally, the acquired coupled influence mechanisms of specific thermodynamic conditions and mixture compositions on the auto-ignition progress of hydrogen/n-dodecane mixtures were helpful to reveal the optimization directions for further improving the combustion performance of hydrogen/diesel dual-fuel engines.

2. Numerical model and calculation settings

2.1 Mechanism selection and validation

The experimental data were obtained from a shock tube and rapid compression machine.^34–36 The zero-dimensional, constant volume and adiabatic reactor in Chemkin-Pro was adopted to reveal the auto-ignition process of n-dodecane/hydrogen mixtures under engine-like conditions. This reactor is a 0-D homogeneous and adiabatic system with equations of mass, energy and species, assuming that fuel molecules are ignited by their own chemical kinetic effects in a homogeneous system, which can be used to calculate the mole fraction and chemical reaction rate of species. The auto-ignition progresses under shock tube conditions are calculated based on the thermodynamic conditions behind reflected shock waves. While the auto-ignition simulations under rapid compression machine conditions rely on the actual variable volume profiles deduced from non-reactive experiments. Although the kinetic mechanisms for the ignition of n-dodecane/hydrogen mixtures are rarely involved, the reaction mechanisms for the ignition of a pure hydrogen mixture or a pure n-dodecane mixture have been studied. LLNL,³⁷ JetsurF 2.0,³⁸ SJTU³⁵ and Li^39–42 mechanisms are the representative n-dodecane mechanisms. Further, the n-dodecane mechanism includes the oxidation mechanism of hydrogen. Therefore, the n-dodecane oxidation mechanism can be used to predict the auto-ignition properties of n-dodecane/hydrogen mixtures.

In order to confirm the accuracy of the n-dodecane oxidation mechanism in predicting the IDT of hydrogen/n-dodecane mixtures, the IDTs of both hydrogen and n-dodecane calculated from LLNL, JetsurF 2.0, SJTU and Li mechanisms are compared to the experimental measurements from Vasu et al.,³⁴ Mao et al.³⁵ and Gersen et al.³⁶Fig. 1 shows the IDT of a pure n-dodecane mixture with ϕ of 0.5, 1.0, and 1.5 and initial pressures of 15 bar and 20 bar. The LLNL mechanism overestimates the IDT in the mid-temperature region and underestimates the IDT in most low-temperature regions. The SJTU mechanism well captures the IDT in most regions and slightly underestimates the IDT in the NTC region. The JetsurF 2.0 and Li mechanisms exhibit greater discrepancies in estimating the IDT compared to the other mechanisms.

Fig. 1 The validation of the IDT of a pure n-dodecane/air mixture.

Fig. 2 shows the IDT of a pure hydrogen mixture with ϕ of 0.5 and 1.0 and initial pressures of 40 bar and 50 bar. Almost all mechanisms overestimate the IDT at mid-temperatures and underestimate the IDT at low temperatures. Relatively speaking, the predictions of the IDT of a hydrogen mixture from LLNL and SJTU mechanisms agree well with the measurements from Gersen et al. The JetsurF 2.0 and Li mechanisms exhibit greater discrepancies in estimating the IDT of a hydrogen mixture compared to the LLNL and SJTU mechanisms.

Fig. 2 The validation of the IDT of a pure hydrogen/air mixture.

Fig. 3 shows the IDT of an n-dodecane/hydrogen mixture with ϕ of 1.0 and initial pressures of 20 bar and 50 bar. The LLNL mechanism overestimates the IDT in mid-temperature and low-temperature regions. Compared with the measurements from the current rapid compression machine setup, the SJTU mechanism well captures the IDT in most regions and slightly underestimates the IDT in the NTC region. The JetsurF 2.0 and Li mechanisms exhibit greater discrepancies in estimating the IDT compared to the other mechanisms.

Fig. 3 The validation of the IDT of an n-dodecane/hydrogen mixture.

In order to select the accurate reaction mechanism to study the chemical kinetics of a hydrogen/n-dodecane mixture, error analysis of experiments and mechanisms was conducted. The calculation methods of errors are derived from He et al.⁴³

The relative error of the ith data point, which reflects the local performance of the mechanisms, is calculated as follows:

where, E_i is the relative error of the ith data point, and τ_modelⁱ and τ_expⁱ are the computed IDT and experimental IDT for the ith data point, respectively.

The mean absolute errors are also calculated to evaluate the overall performance of the mechanisms. The expression is as follows:

where μ is the mean absolute error, and N is the total number of experimental data points.

Fig. 4 shows a comparison of the mean absolute errors among LLNL, JetsurF 2.0, SJTU and Li mechanisms. It can be seen that the mean absolute errors of the SJTU mechanism in predicting the IDT of an n-dodecane mixture and n-dodecane/hydrogen mixture are below about 15%, which are obviously lower than that of other mechanisms. Although the mean absolute errors of the SJTU mechanism in predicting the IDT of the hydrogen mixture is close to 50%, this discrepancy cannot obviously influence the prediction accuracy of the reaction progress of hydrogen/n-dodecane due to the dominant role of n-dodecane in mid- and low-temperature reaction systems of a hydrogen/n-dodecane mixture. Therefore, the SJTU mechanism is selected to explore the chemical reaction kinetics of n-dodecane/hydrogen mixtures under engine-like conditions.

Fig. 4 The mean absolute errors of various kinetic mechanisms.

2.2 Calculation setup

In order to reveal the auto-ignition characteristics of hydrogen/diesel mixtures under wide in-cylinder thermodynamic conditions, the calculation conditions are obtained based on the actual operating conditions of a diesel/hydrogen engine. This study concentrates on low-temperature to mid-temperature (750–1050 K) and high-pressure (40–80 bar) in-cylinder operating conditions. The mixture compositions are shown in Table 1.

Table 1 Calculation conditions in the current study

Variable	Range
Mole fraction of hydrogen	100–50%
Mole fraction of n-dodecane	0–50%
ϕ	0.5–2.0
Temperature (K)	750–1050
Pressure (bar)	40–80

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The molar ratio of nitrogen and oxygen is 3.76 : 1 to simulate the actual air composition in an engine.^44,45 In order to comprehensively reveal the auto-ignition properties of hydrogen/n-dodecane under wide blending ratios, mixtures of 100–0, 99–1, 98–2, 95–5, 90–10, 75–25 and 50–50 simulate various molar blending ratios of hydrogen and n-dodecane. For example, the mixture of 90–10 means that the mole fractions of hydrogen and n-dodecane are 90% and 10%, respectively. The ϕ of 0.5, 1.0 and 2.0 represent in-cylinder mixtures with different concentrations. The calculation equation for ϕ is as follows:

where X_C, X_H and X_O are the mole amounts of C, H and O in the mixture.

Therefore, the coupled influence mechanisms of pressure, temperature, blending ratio and ϕ on the auto-ignition progress of hydrogen/n-dodecane mixtures under engine-like conditions are analyzed systematically in later sections.

2.3 Taguchi method

The Taguchi method is used to select the combination of parameters that makes the experimental results stable and less volatile, which evaluates a larger number of factors by fewer combinations of parameters. The design method has three steps. The first step is the selection of variables. The temperature, ϕ, pressure, and n-dodecane content are chosen as the key variables. The second step is the selection of 4 levels for each variable, as shown in Table 2. The third step is the experimental design based on the experimental variables and levels, as illustrated in Table 3. The Taguchi method first identified the factors and levels affecting the performance parameters and designed an orthogonal array. After conducting experiments on the specified orthogonal arrays, the data were analyzed by analysis of variance (ANOVA) and the contribution rates of four factors on the IDT of n-dodecane/hydrogen mixtures were determined. The calculation equations for contribution rates are as follows:

C_i = (S_i/S) × 100% (4)

where C_i is the contribution of the ith variable, S_i is the sum of variances of the ith variable relative to the average result, S is the sum of variances of the all variables relative to the average result, L is the number of level, Y_ij is the average experimental result of the jth level of the ith variable, n is the number of variables, and ȳ is the average result for all levels of all experimental variables.

Table 2 Calculation conditions in the current study

Factor	Designation	Level 1	Level 2	Level 3	Level 4
Temperature (K)	A	750	850	950	1050
ϕ	B	0.5	1.0	1.5	2.0
Pressure (bar)	C	40	50	60	70
n-Dodecane content (%)	D	5	20	35	50

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Table 3 Taguchi's L16 orthogonal arrays

No.	Factor
	A (K)	B	C (bar)	D (%)
1	1 (750)	1 (0.5)	1 (40)	1 (5)
2	1 (750)	2 (1.0)	2 (50)	2 (20)
3	1 (750)	3 (1.5)	3 (60)	3 (35)
4	1 (750)	4 (2.0)	4 (70)	4 (50)
5	2 (850)	1 (0.5)	2 (50)	3 (35)
6	2 (850)	2 (1.0)	1 (40)	4 (50)
7	2 (850)	3 (1.5)	4 (70)	1 (5)
8	2 (850)	4 (2.0)	3 (60)	2 (20)
9	3 (950)	1 (0.5)	3 (60)	4 (50)
10	3 (950)	2 (1.0)	4 (70)	3 (35)
11	3 (950)	3 (1.5)	1 (40)	2 (20)
12	3 (950)	4 (2.0)	2 (50)	1 (5)
13	4 (1050)	1 (0.5)	4 (70)	2 (20)
14	4 (1050)	2 (1.0)	3 (60)	1 (5)
15	4 (1050)	3 (1.5)	2 (50)	4 (50)
16	4 (1050)	4 (2.0)	1 (40)	3 (35)

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3. Results and discussion

3.1 Auto-ignition characteristics of hydrogen/n-dodecane mixtures

3.1.1 Influence of single factors on the auto-ignition characteristics of hydrogen/n-dodecane. The effects of a single factor (ϕ, mixture composition or initial temperature) on the IDT of hydrogen/n-dodecane mixtures under low-to-mid temperature conditions are shown in Fig. 5. The variation tendencies of the IDT with mixture composition under various ϕ (0.5, 1.0, 2.0) conditions are similar. Blending a small amount of n-dodecane (mixture: 99–1) significantly shortens the IDT compared to a pure hydrogen mixture. However, the decrease in amplitude of the IDT gradually reduces with a further increase in n-dodecane content. Increasing ϕ obviously reduces the IDT as well. Further raising the content of n-dodecane apparently enhances the NTC behavior.

Fig. 5 The variation trends of the IDT with mixture compositions and initial temperatures.

Fig. 6a clearly illuminates the variation law of the IDT with ϕ under low-to-mid-temperature conditions. The ϕ plays a key role in the IDT under all operating conditions. Fig. 6b shows that increasing pressure can apparently accelerate the progress of the auto-ignition reaction due to the increase in reactant concentration per volume and effective collision frequency among molecules. The turning point of the NTC region moves to higher temperature conditions with increasing pressure.

Fig. 6 The variation trends of the IDT with ϕ and initial pressure.

3.1.2 Coupled influences of multiple factors on the auto-ignition characteristics of hydrogen/n-dodecane. The coupled influences of various factors on IDT and NTC behavior is discussed below. The X and Y axes represent two variables. The colormap represents the IDT. Fig. 7 shows the effect of initial temperature and n-dodecane concentration on the IDT. The IDT is influenced by both temperature and n-dodecane concentration under low-temperature (750–850 K) and low n-dodecane concentration (0–10%) conditions. Further, n-dodecane concentration has a significant effect on ignition even with a very low mass fraction of n-dodecane. Whereas n-dodecane concentration has little influence on ignition progress when the mole fraction of n-dodecane is greater than 10%, which is consistent with the previous analysis.

Fig. 7 The influences of temperature and n-dodecane fraction.

As shown in Fig. 8, NTC behavior is clearly illuminated after blending n-dodecane. With 50% n-dodecane fraction, the IDT is influenced by both pressure and temperature in the temperature range of 850–1050 K. Whereas, it is mainly influenced by temperature when the temperature is below 850 K because the IDT changes apparently with temperature but slightly with pressure. The result with 5% n-dodecane is similar to that with 50% n-dodecane. As for a pure hydrogen mixture, the NTC behavior disappears. The temperature plays a decisive role in the IDT.

Fig. 8 The influences of temperature and pressure.

Fig. 9 shows that the IDT is influenced by both ϕ and temperature under low-temperature (750–850 K) and low-ϕ (0.5–1.0) conditions when the n-dodecane fraction is 5% or 50%. Whereas temperature plays a decisive role in the IDT under low-temperature (750–850 K) and high-ϕ (1.0–2.0) conditions. The ϕ is not the significant factor. With an increase in temperature, the IDT is influenced by both temperature and ϕ under higher-temperature (850–1050 K) conditions. As for a pure hydrogen mixture, the temperature remains a more critical factor than ϕ.

Fig. 9 The influences of temperature and ϕ.

The coupled influences of ϕ and n-dodecane content are exhibited in Fig. 10. Under mid-temperature conditions (1050 K), the IDT is influenced by both ϕ and n-dodecane content at low n-dodecane content (0–10%). With an increase in n-dodecane content, the IDT is almost solely affected by ϕ. Under low-temperature conditions (750 K), the IDT is influenced by both ϕ and n-dodecane content at low n-dodecane content (0–20%). With an increase in n-dodecane content, the IDT is less influenced by ϕ and n-dodecane content because of the significantly weakened mixture reactivity.

Fig. 10 The influences of n-dodecane fraction and ϕ.

The coupled influences of ϕ and pressure are illustrated in Fig. 11. The IDT is apparently influenced by both ϕ and pressure under various mixture composition conditions. The influence of ϕ on IDT outweighs that of n-dodecane content. With a gradual increase in n-dodecane content, the influence of pressure increases.

Fig. 11 The influences of pressure and ϕ.

3.1.3 Results of the Taguchi method. The calculation results of the Taguchi method are illustrated in Fig. 12 and Table 4. The contribution rates of temperature, ϕ, pressure, and n-dodecane content on the IDT are 62.9%, 27.0%, 5.1%, 5.0%, respectively. In other words, temperature and ϕ are the main factors influencing the IDT of n-dodecane/hydrogen mixtures. While the pressure and n-dodecane content are not crucial factors compared with temperature or ϕ. Therefore, the quantitative analyses are consistent with previous results.

Fig. 12 The influence law of the Taguchi method.

Table 4 Contribution rates calculated by the Taguchi method

Factor	Contribution rate (%)
	Temperature	ϕ	Pressure	n-Dodecane content
IDT	62.9	27.0	5.1	5.0

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3.2 Chemical kinetic properties at mid-temperature and low temperature

3.2.1 ROP and mole fraction of fuels at mid-temperature and low temperature. The mole fraction and rate of production (ROP) analysis of fuels and active radicals, and sensitivity analysis were conducted to reveal the chemical kinetic properties of hydrogen/n-dodecane mixtures. The variations in mole fraction of the fuels are shown in Fig. 13. The ROP analysis of n-dodecane and hydrogen are shown in Fig. 14 and 15, respectively. The key reactions of the fuels are shown in Table 5.

Fig. 13 Mole fractions of n-dodecane and hydrogen.

Fig. 14 ROP for n-dodecane.

Fig. 15 ROP for hydrogen.

Table 5 Key reactions of fuels

Hydrogen	n-Dodecane
R2: H2 + O ⇔ H + OH	R2727: NC12H26(+M) ⇔ C5H11-1 + C7H15-1(+M)
	R2728: NC12H26(+M) ⇔ 2C6H13-1(+M)
R3: H2 + OH ⇔ H + H2O	R2741: NC12H26 + OH ⇔ C12H25-1 + H2O
	R2742: NC12H26 + OH ⇔ C12H25-2 + H2O
R28: HO2 + H ⇔ H2 + O2	R2743: NC12H26 + OH ⇔ C12H25-3 + H2O
	R2746: NC12H26 + OH ⇔ C12H25-6 + H2O

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The increases in n-dodecane content and ϕ advance the rapid consumption of n-dodecane. At low temperatures (T = 750 K), the increase in n-dodecane content has a more apparent ignition promotion effect than that of ϕ. Whereas the mid-temperature condition exhibits the opposite trend. Further, the variation trend of the mole fraction of hydrogen is similar to that of n-dodecane. It is worth noting that when the n-dodecane is blended, both hydrogen and n-dodecane experience a slow oxidation process before the ignition time point.

The ROP analysis of n-dodecane shows that the consumption of n-dodecane is dominated by the OH induced H-abstraction reactions (R2741, R2742, R2743, R2746). The formation of n-dodecane is controlled by recombination reactions (R2727, R2728). At low temperature, an increase in n-dodecane content (50–50, ϕ: 1.0) can greatly raise the relevant reaction rates, which is consistent with previous analysis. With an increase in initial temperature, the reaction temperature region of n-dodecane also apparently increases. Further, the reaction duration under mid-temperature conditions is obviously longer than that under low-temperature conditions. Thus the absolute reaction rate under mid-temperature condition is obviously lower than that under low-temperature conditions.

The ROP analysis of hydrogen shows that the consumption of hydrogen is dominated by the O and OH induced H-abstraction reactions (R2, R3). The formation of hydrogen is controlled by the recombination reaction of active radicals (R28). At low temperature, the increase in n-dodecane content (50–50, ϕ: 1.0) can greatly reduce the relevant reaction rates of hydrogen due to the decrease in hydrogen content. With an increase in initial temperature, the reaction region temperature and the reaction rate of hydrogen slightly increase. Further, after blending the n-dodecane, the OH related H-abstraction reaction (R3) is responsible for the initial consumption of hydrogen, which is helpful for shortening the IDT.

3.2.2 Reaction pathway and sensitivity analysis. The reaction pathway of the initial oxidation stage after blending the n-dodecane is shown in Fig. 16. It can be seen that the OH radical is formed after the H-abstraction, decomposition and isomerization reactions of n-dodecane. Then the produced OH radical further promotes the advanced slow oxidation of hydrogen (via R3, as illustrated in Fig. 15) and the H-abstraction of n-dodecane (via R2741, R2742, R2743, R2746, as illustrated in Fig. 14), which is responsible for the improvement in whole-system reactivity and the advance of the ignition time point.

Fig. 16 Reaction pathway of the OH radical in the initial reaction stage.

Sensitivity analysis on the IDT of an n-heptane/methane mixture was conducted to study the significant reactions in the ignition process. The normalized sensitivity index is defined as follows:⁴⁴

where S_i is the IDT sensitivity, τ is the IDT, and k_i is the rate of the ith reaction in the kinetic mechanism. A negative sensitivity index means that an increase in the rate constant of a specific reaction will enhance the overall reactivity and reduce the IDT. A positive sensitivity index means that increasing the rate constant of a specific reaction can prolong the IDT.

Fig. 17 shows that under low-temperature conditions, key ignition-promoting reactions include the H-abstraction reactions of n-dodecane induced by OH and HO₂ radicals (R2741–R2746), the decomposition reaction of H₂O₂ (R21) and C₁₂KET (R3203, R3208, R3214, R3229) which forms the active OH radical. The main ignition inhibition reaction is R3, which converts the OH radical to an H radical. Increases in n-dodecane content and ϕ reduce the sensitivity coefficients of almost all critical reactions.

Fig. 17 Sensitivity analysis under low-temperature conditions.

Fig. 18 shows that under mid-temperature conditions, the key ignition-promoting reaction is R21, which converts H₂O₂ to OH. R5 and R23, which convert H to OH or HO₂, also have a considerable ignition-promotion effect. The H-abstraction reactions of n-dodecane, R2754 and R2755, which consume HO₂ and form H₂O₂, can also induce a reduction in the IDT due to the subsequent formation of OH. R49 converts the active H₂O and CH₃ to stable CH₄, which has a positive sensitivity coefficient. The adverse reactions of R32 and R33 convert H₂O₂ to HO₂, also prolonging the IDT. The increases in n-dodecane content and ϕ also reduce the sensitivity coefficients of almost all critical reactions, similar to the low-temperature conditions.

Fig. 18 Sensitivity analysis under mid-temperature conditions.

The effect of initial temperature (low temperature: 750 K, NTC region: 850 K and 900 K, mid-temperature: 1050 K) on the sensitivity coefficients is shown in Fig. 19. With an increase in initial temperature, the sensitivity coefficient of the decomposition reactions reduces, which shows the decomposition reactions are weakened. The sensitivity coefficient of those reactions relevant to H and HO₂ increases with rising temperature. Whereas the sensitivity coefficient of those reactions relevant to OH and H₂O₂ reaches its peak value during the NTC region, which means the H₂O₂ and OH radicals are the significant intermediate products in the NTC region.

Fig. 19 Sensitivity analysis at various initial temperatures.

3.2.3 ROP and mole fraction of active radicals at mid-temperature and low temperature. Generally speaking, H, OH, HO₂ and H₂O₂ play critical roles in the auto-ignition progress of hydrogen/n-dodecane mixtures. Therefore, variations in mole fractions of H, OH, HO₂ and H₂O₂ radicals are illustrated in Fig. 20. Increases in n-dodecane content and ϕ advance the rapid formation of active radicals. At low temperatures (T = 750 K), an increase in n-dodecane content has a more apparent promotion effect on radical formation than that of ϕ. Whereas the mid-temperature condition exhibits the opposite trend. Further, the variation trends of the mole fractions of active radicals (H, OH, HO₂, H₂O₂) are similar to that of n-dodecane. When the n-dodecane is blended, these active radicals experience an advanced oxidation process before the ignition time point.

Fig. 20 Mole fractions of active radicals.

In order to systematically reveal the influence of the addition of n-dodecane on the reaction pathway of active radicals, ROP analyses of H and OH radicals are shown in Fig. 21 and 22, respectively. The key reactions of active radicals are shown in Table 6. The results show that the initial consumption of H radicals is induced by R34 (H + O₂(+M) ⇔ HO₂(+M)) after blending the n-dodecane. An increase in n-dodecane content further enhances this reaction process. Near the ignition time point, the oxidation reactions (R5: O₂ + H ⇔ O + OH and R34: H + O₂(+M) ⇔ HO₂(+M)) are the dominant consumption reactions of H. For a pure hydrogen mixture, R2: H₂ + O ⇔ H + OH and R3: H₂ + OH ⇔ H + H₂O are the main reactions forming H radicals. After blending the n-dodecane, R36: CO + OH ⇔ CO₂ + H and R163: HCO + M ⇔ H + CO + M also become key reactions forming H radicals. However, with an increase in n-dodecane content, the reaction rates of the H radical reduce apparently due to the decrease in hydrogen content. Further, an increase in initial temperature slightly elevates the reaction temperature of the H radical.

Fig. 21 ROP analysis of the H radicals.

Fig. 22 ROP analysis of the OH radical.

Table 6 Key reactions of H and OH radicals

H & OH
R1: H2 + M ⇔ 2H + M	R2: H2 + O ⇔ H + OH
R3: H2 + OH ⇔ H + H2O	R5: O2 + H ⇔ O + OH
R6: H + OH + M ⇔ H2O + M	R7: O + H2O ⇔ 2OH
R8: O + H + M ⇔ OH + M	R21: H2O2(+M) ⇔ 2OH(+M)
R23: H2O2 + H = H2 + HO2	R27: HO2 + H ⇔ 2OH
R28: HO2 + H ⇔ H2 + O2	R30: OH + HO2 ⇔ H2O + O2
R31: OH + HO2 ⇔ H2O + O2	R34: H + O2(+M) ⇔ HO2(+M)
R36: CO + OH ⇔ CO2 + H	R43: CH3 + H(+M) ⇔ CH4(+M)
R44: CH4 + H ⇔ CH3 + H2	R46: CH4 + OH ⇔ CH3 + H2O
R111: CH3OH(+M) ⇔ CH3 + OH(+M)	R155: CH2O + H ⇔ HCO + H2
R156: CH2O + OH ⇔ HCO + H2O	R163: HCO + M ⇔ H + CO + M
R248: C2H4 + OH ⇔ C2H3 + H2O	R266: C2H2 + H(+M) ⇔ C2H3(+M)
R310: C2H2 + O ⇔ HCCO + H	R387: HCCO + OH ⇔ H2 + 2CO

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The ROP analysis of the OH radical shows that the initial consumption of OH radicals is induced by R3: H₂ + OH ⇔ H + H₂O after blending n-dodecane. An increase in n-dodecane content further enhances this reaction process. In other words, the addition of n-dodecane enhances the whole-system reactivity, which is beneficial to the progress of OH-relevant reactions. For a pure hydrogen mixture, near the ignition time point, the oxidation reactions (R3: H₂ + OH ⇔ H + H₂O and R6: H + OH + M ⇔ H₂O + M) are the dominant consumption reactions of the OH radical. R2: H₂ + O ⇔ H + OH, R5: O₂ + H ⇔ O + OH and R27: HO₂ + H ⇔ 2OH are the main reactions forming the OH radical. After blending n-dodecane, R31: OH + HO₂ ⇔ H₂O + O₂ and R36: CO + OH ⇔ CO₂ + H also become key consumption reactions of the OH radical. R7: O + H₂O ⇔ 2OH becomes the key reaction forming an OH radical. However, with an increase in n-dodecane content, the reaction rates of the OH radical reduce apparently due to the decrease in hydrogen content. The increase in initial temperature slightly elevates the reaction temperature and the reaction rate of the OH radical.

4. Conclusions

In the current study, the coupled influence mechanisms of specific thermodynamic conditions and mixture compositions on the auto-ignition characteristics of n-dodecane/hydrogen mixtures were revealed by detailed chemical reaction kinetic mechanisms. Chemical reaction kinetic properties, including mole fractions of fuels and active radicals, ROP, sensitivity and reaction pathway analyses, were carried out to acquire the internal interaction mechanisms among hydrogen and n-dodecane and multiple active radicals during the auto-ignition progress of hydrogen/n-dodecane mixtures. The conclusions can be summarized as follows:

(1) Under engine-like conditions, blending a small amount of n-dodecane dramatically reduced the IDT of a hydrogen mixture. However, the decrease in amplitude of the IDT gradually reduced with a continuous increase in n-dodecane content. Increasing ϕ and initial pressure also obviously reduced the IDT. Further, raising the content of n-dodecane apparently highlighted the NTC behavior. The progress of the auto-ignition of hydrogen/n-dodecane mixtures relied on the coupled effects of fuel composition and located thermodynamic conditions. The initial temperature exerted a great influence on the IDT under all conditions. The ϕ also had a obvious impact on the IDT in most regions other than a pure hydrogen mixture or under low-temperature/high-ϕ conditions. The effect of pressure and n-dodecane content on the IDT depended on the located conditions. The effect of pressure was ignorable under low-temperature or pure hydrogen mixture conditions due to the dramatically weakened mixture reactivity. The influence of n-dodecane fraction was negligible when the n-dodecane fraction was greater than 10% at mid-temperature or 20% at low temperature. The contribution rates of temperature, ϕ, pressure, and n-dodecane content on the IDT are 62.9%, 27.0%, 5.1%, 5.0%, respectively.

(2) The addition of n-dodecane induced the initial production of OH radical, which was responsible for the advanced slow oxidation of n-dodecane and hydrogen. With an increase in n-dodecane content, the relevant reaction rates of the fuels was further improved, which outweighed the reduced reaction rates of active radicals. Thus the IDT was reduced. The variation laws of mole fractions of active radicals (H, OH, HO₂, H₂O₂) were similar to those of n-dodecane and hydrogen. Further, with an increase in initial temperature, the temperatures of the reaction region of n-dodecane obviously increased. Whereas the temperatures of the reaction regions of hydrogen and H and OH radicals were slightly elevated.

(3) The main ignition-promoting reactions were the reactions related to OH and HO₂ and H₂O₂ (H-abstraction reactions of n-dodecane induced by OH and HO₂ radicals (R2741–R2746), decomposition reaction of H₂O₂ (R21) and C₁₂KET (R3203, R3208, R3214, R3229) which formed the active OH radical) under low-temperature conditions. Under mid-temperature conditions, the key ignition-promoting reactions were still those reactions related to OH and HO₂ and H₂O₂ (R5 and R23 which covert H to OH or HO₂, H-abstraction reactions of n-dodecane (R2754 and R2755) which consume HO₂ and form H₂O₂, and R21). With an increase in initial temperature, the sensitivity coefficients of decomposition reactions and those reactions relevant to H and HO₂ reduced and increased, respectively. Further, the sensitivity coefficients of those reactions relevant to OH and H₂O₂ reached their peak values in the NTC region, which meant the H₂O₂ and OH radicals were the significant intermediate products.

Abbreviations

IDT	Ignition delay time
NOx	Nitrogen oxide
NTC	Negative temperature coefficient
ROP	Rate of production
ϕ	Overall equivalence ratio of mixture
p	Initial pressure
T	Initial temperature
ANOVA	Analysis of variance

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

The work in this study received financial support from the Science Fund of State Key Laboratory of Engine and Powertrain System (No. SKLEPS-202104), the Fundamental Research Funds for the Central Universities (Grant No. JZ2023HGQA0139).

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