Development of a Detailed Chemical Kinetic Model for 1-Methylnaphthalene

Abstract

1-Methylnaphthalene is a critical component for constructing fuel surrogates of diesel and aviation kerosene. However, the reaction pathways of 1-methylnaphthalene included in existing detailed chemical kinetic models vary from each other, leading to discrepancies in the simulation of ignition and oxidation processes. In the present study, reaction classes and pathways involved in the combustion of 1-methylnaphthalene were analyzed, and effects of rate constants of reactions related to 1-methylnaphthalene and its significant intermediates on ignition delay times and species concentration profiles were discussed, involving hydrogen abstraction and substitution reactions of 1-methylnaphthalene, oxidation, isomerization, and addition reactions of 1-naphthylmethyl, hydrogen abstraction and oxidation reactions of indene, as well as the oxidation of indenyl and naphthalene. On this basis, a new detailed chemical kinetic model for 1-methylnaphthalene was developed, which includes 1389 species and 7185 reactions. The validation of this mechanism shows that it can predict accurately the available experimental ignition delay times, species concentration profiles, and laminar flame speeds of 1-methylnaphthalene. Finally, reaction paths and sensitivity analysis of ignition delay times were performed using the proposed reaction mechanism, and the result shows that the conversion of 1-methylnaphthalene to 1-naphthaldehyde plays an important role in its ignition.

1. Introduction

Diesel fuel remains the primary fuel to power large electrical equipment and the pilot fuel to ignite other fuels with high octane numbers such as natural gas and ammonia. As diesel is a complex mixture comprising thousands of components, existing studies often formulate fuel surrogates to investigate the combustion characteristics of real diesel [1,2,3,4,5]. Diesel typically contains about 15–40% aromatic hydrocarbons, with polycyclic aromatic hydrocarbons (PAHs) playing a crucial role in soot formation during diesel combustion. As a bicyclic aromatic hydrocarbon, 1-methylnaphthalene is frequently selected as a key component in the formulation of diesel surrogate fuels [6,7]. Additionally, due to its high energy density form, it is also commonly used in the development of aerospace fuel models [8].

Establishing a numerically coupled model of chemical kinetics and fluid dynamics facilitates in-depth research on fuel combustion performance in engines and their emission characteristics. An accurate chemical kinetics model is essential for this research. Currently, researchers have conducted numerous experimental studies and detailed mechanism analyses on the combustion characteristics of 1-methylnaphthalene. The experimental studies primarily involve measuring the ignition delay times of 1-methylnaphthalene using shock tubes (ST) and rapid compression machines (RCM). These experiments are conducted under equivalence ratios ranging from 0.5 to 1.5, pressures of 10 to 40 bar, and temperatures between 800 and 1400 K [9,10,11]. Additionally, the jet-stirred reactor (JSR) has been employed to measure species concentration profiles under equivalence ratios ranging from 0.5 to 1.5, pressures of 1 to 10 atm, and temperatures between 800 and 1400 K [12]. Laminar flame speeds of 1-methylnaphthalene at pressure of 1 bar, temperatures of 425, 445, and 484 K, and equivalence ratios between 0.8 and 1.35 were measured through the outwardly propagating spherical flame method [13].

Regarding the mechanisms of 1-methylnaphthalene, detailed kinetic models have been proposed by Wang et al. [11], Mati et al. [12], and Narayanaswamy et al. [14]. Additionally, a diesel surrogate fuel Creck mechanism developed by Ranzi et al. [15] incorporates the reaction pathways of 1-methylnaphthalene. Nobili et al. [13] updated the 1-methylnaphthalene reaction mechanism on the basis of the Creck kinetic model [14] by applying analogy and rate rules from toluene. Jin et al. [16] also proposed a kinetic model for PAHs, which includes 1-methylnaphthalene. Mati et al. [12] developed a detailed kinetic model that includes 146 species and 1041 reactions, validating species concentration profiles with good agreement between the predicted and experimental values. However, this mechanism only accounts for the consumption pathways of 1-methylnaphthalene to 1-naphthylmethyl (A₂ĊH₂) and naphthalene (C₁₀H₈), omitting hydrogen abstraction reactions, substitution reactions involving hydrogen atoms on the ring with radicals, or fuel decomposition reactions. These reactions are important consumption pathways for 1-methylnaphthalene, and along with hydrogen abstraction from the methyl group, they significantly enhance the fuel’s ignition process. Wang et al. [11], building on the kinetic models developed by Bounaceur et al. [17] and Mati et al. [12], incorporated relevant reactions of hydrogen atoms on the 1-methylnaphthalene ring and created a detailed kinetic model comprising 662 species and 3864 reactions. However, this model does not account for some PAHs, such as acenaphthylene, phenanthrene, and pyrene, which could provide additional pathways for the conversion of 1-methylnaphthalene to other PAHs, thereby more accurately reflecting the complexity of real diesel. Moreover, under conditions with an equivalence ratio of 1.5 and a pressure of 10 bar, the simulated ignition delay times exceed the experimental values. Narayanaswamy et al. [14], based on the small-molecule hydrocarbon mechanism by Blanquart et al. [18], developed a detailed kinetic model of 1-methylnaphthalene that includes 158 species and 1804 reactions, incorporating some aromatic species. However, this model also lacks the relevant reactions of hydrogen atoms on the 1-methylnaphthalene ring, and the simulated ignition delay times at high temperatures remain higher than the experimental values. In the diesel surrogate fuel Creck mechanism developed by Ranzi et al. [15], the hydrogen abstraction reactions of hydrogen atoms on the benzene ring of 1-methylnaphthalene are included, but the substitution reactions of radicals with hydrogen atoms are not covered. Based on the Creck mechanism, Nobili et al. [13] introduced reactions related to intermediate products including methylnaphthol radical (${ \dot{\mathrm{O}}\mathrm{C}}_{10}{\mathrm{H}}_6{\mathrm{CH}}_3$), ethyl-naphthalene (C₁₀H₇C₂H₅), and naphthoquinone (C₁₀H₆O₂), and a mechanism for 1-methylnaphthalene was proposed. Through analyzing this mechanism, it can be found it does not take into account the isomers of these intermediate products such as methylnaphthol radical, 1-naphthylmethyl(A₂ĊH₂), and naphthoquinone.

Furthermore, certain intermediates in the aforementioned detailed mechanisms remain contentious, particularly the formation and consumption of 1-naphthylmethyl-oxy (${\mathrm{A}}_2{\mathrm{CH}}_2\dot{\mathrm{O}}$), which lacks consensus. In contrast, the analogous benzyl-oxy (${\mathrm{A}}_1{\mathrm{CH}}_2\dot{\mathrm{O}}$) plays an important role in toluene combustion. Similarly, the formation of indene-oxy (${\mathrm{C}}_9{\mathrm{H}}_7\dot{\mathrm{O}}$) and indanone (C₉H₆O) affects the conversion of indenyl to benzene derivatives. Regarding prediction accuracy for detailed mechanisms, Sun et al. [19] compared the ignition delay times of the 1-methylnaphthalene detailed chemical kinetic models constructed by Wang et al. and Narayanaswamy et al. under a broader range of conditions, including equivalence ratios from 0.5 to 1.5, pressures between 10 to 40 bar, and temperatures ranging from 1000 to 1400 K. The results indicated that the simulated values from the Wang model were consistently higher than the experimental values at 40 bar, and similarly elevated at 10 bar for equivalence ratios of 1.0 and 1.5. Meanwhile, the Narayanaswamy model’s simulated values were higher than the experimental values across the temperature range of 1000 to 1400 K.

In summary, the current chemical kinetic models of 1-methylnaphthalene exhibit incomplete reaction pathways, hindering a deeper understanding of soot formation in diesel combustion and its subsequent regulation. Additionally, there mechanisms show deviations in the prediction performance, highlighting the need for a more comprehensive and accurate detailed kinetic model.

Based on the above content, this study first analyzes how the rate constants of key reactions in the 1-methylnaphthalene chemical kinetic models affect ignition delay times. A detailed chemical kinetic model for 1-methylnaphthalene is then developed, and its prediction accuracy is validated by comparing the ignition delay times, species concentration profiles of the species, and laminar flame speeds. On this basis, reaction pathway and sensitivity analyses are employed to thoroughly investigate the consumption pathways and patterns of various species during the ignition process of 1-methylnaphthalene.

2. Results and Discussion

2.1. Validation of Chemical Kinetic Model

This study compared the simulated ignition delay times and the species concentration profiles from the detailed 1-methylnaphthalene mechanism developed in the present study with those from the mechanisms by Wang, Nobili, and Narayanaswamy. Additionally, the present 1-methylnaphthalene mechanism was also validated against the laminar flame speeds and compared with the corresponding modeled results from the study of Nobili et al. [13]. The results indicated that the simulated values from the present 1-methylnaphthalene mechanism closely matched the experimental values.

Figure 1a–c present the predictions of ignition delay times from the present mechanism under conditions from 1000 to 1400 K. Under these conditions, the simulated values of the mechanism developed in this study are consistent with the experimental values, although the simulated values are slightly higher at ϕ = 1.5 and p = 40 bar. In the temperature range of 850–950 K, the overall simulated values align with the experimental values; however, deviations arise near 950 K, as shown in Figure 1d–f, where this phenomenon is consistently observed. To explain this issue, the operating principle of the RCM was investigated. The RCM is an experimental device designed to study the combustion chemistry of fuels under high pressure and low to moderate temperature conditions. Since it is challenging to directly measure the compression temperature during the operation of the RCM, researchers use the adiabatic core hypothesis to estimate the compression temperature based on pressure changes. The relationship between the temperature and pressure at the end of compression stroke is described by Equation (1).

$${\displaystyle {\int }_{T_0}^{T_{\mathrm{C}}}\frac{\gamma }{\gamma -1}}{\displaystyle \frac{\mathrm{d}T}{T}}=\ln \left({\displaystyle \frac{p_{\mathrm{C}}}{p_0}}\right)$$

(1)

where p_C is the measured pressure at the end of compression, T_C the temperature at the end of compression, p₀ and T₀ the initial pressure and temperature, respectively, and γ the temperature-dependent ratio of the mixture.

The higher the compression temperature required for the experiment, the lower the initial pressure must be. Weber et al. [20] noted that the uncertainty of the compression temperature is influenced by the actual value of the initial pressure. In general, lower initial pressure leads to higher compression temperature, which in turn increases the uncertainty in the measured ignition delay times. This observation aligns with the results of their experiments involving methane and cyclohexane [21].

As shown in Figure 2, when comparing the results under non-constant volume conditions that account for heat loss, the simulated ignition delay times from the present mechanism are higher than those under constant volume conditions, which aligns with theoretical expectations. Around 950 K, the experimental values from the RCM tend to deviate from the overall experimental values, and this deviation from the simulated values can be corroborated by the conclusions drawn by Weber et al. [20].

Regarding the differences in ignition delay times from various mechanisms of 1-methylnaphthalene, the performances of the Wang and Narayanaswamy mechanisms in predicting ignition delay times have been analyzed in the study of Sun et al. [19], as mentioned in the Introduction. Additionally, from Figure 1 it can be seen that the simulated ignition delay times of the Nobili mechanism (sourced from reference [13]) are slightly higher than the experimental data from the shock tube at 40 bar above 1000 K and also higher than the RCM data at 15 and 40 bar below 1000 K. Under these conditions, the modeled results of the Nobili mechanism are generally higher, to some extent, than the ones from the present mechanism.

Additionally, Mati et al. [12] measured the concentration profiles of the reactants, products, and various stable intermediates during the oxidation of 1-methylnaphthalene in a jet-stirred reactor (JSR). Figure 3 presents the comparison between the simulated and experimental concentrations profiles of key species during the oxidation of 1-methylnaphthalene under the conditions of ϕ = 1 and p = 10 atm. The detailed mechanisms evaluated include A₂CH₃, O₂, CO, CO₂, H₂, CH₄, C₂H₄, and C₂H₆. The results indicate that the overall simulated concentrations of the components from the present mechanism align well with the experimental values. Specifically, the predictions for A₂CH₃, O₂, and CO₂ are accurate. The predictions for CH₄, C₂H₄, and C₂H₆ are also reliable, though the simulated values slightly underestimate the experimental values after 1100 K. The predictions for CO and H₂ are accurate after 1000 K; however, due to increased ignition activity, A₂CH₃ is consumed earlier in the oxidation process, leading to a corresponding decrease in the temperature at which CO and H₂ are produced. A comparison reveals that the species concentration profiles predicted by the Narayanaswamy and Wang mechanisms exhibit deviations from the experimental values. For the Nobili mechanism, the predicted values are generally close to the experimental values. Only for the small molecule hydrocarbon compounds such as CH₄, C₂H₄, and C₂H₆ do the modeled results seem to be slightly lower.

In Figure 4, the present 1-methylnaphthalene mechanism is validated against the experimental laminar flame speeds obtained by Nobili et al. [13] at pressure of 1 bar, initial temperatures from 425 to 484 K, and equivalence ratios between 0.8 and 1.35. The modeled result from the Nobili mechanism is also presented in this figure. The predicted laminar flame speeds of the present mechanism were derived using the PREMIX program [22] in the CHEMKIN-PRO 15131 software. When conducting the simulation, the thermal diffusion was taken into account, and the mixture-averaged method was selected to evaluate the transport properties of species, considering the long calculation time caused by the large scale of the mechanism used. The impact of the grid point on the calculated result of the laminar flame speed was controlled through reducing the values of Gradient and Curvature of the numerical solution. From Figure 4, it is indicated that, on the whole, both of these two mechanisms can predict well the laminar flame speeds of 1-methylnaphthalene, and the Nobili mechanism behaves better than the one developed in the present study. Specifically, the modeled values of the present mechanism are slightly lower than the experimental values at high equivalence ratios, which are also lower than the modeled ones from the Nobili mechanism. While at low equivalence ratios, the modeled values of both mechanisms agree well with the experimental data. The experimental values of laminar flame speeds of 1-methylnaphthalene shown here are the only ones available in the literature, and considering the differences in predicted results of ignition and oxidation between the present and Nobili mechanisms, more experimental data at other conditions may be necessary to validate and improve the 1-methylnaphthalene mechanism.

2.2. Chemical Kinetic Analysis of the Ignition of 1-Methylnaphthalene

Figure 5 illustrates the reaction pathway of 1-methylnaphthalene under the conditions of T = 1200 K, ϕ = 1, p = 10 bar with 20% fuel consumption, highlighting the main reaction pathways with thick arrows. It is evident that hydrogen abstraction reactions play a dominant role in the consumption of 1-methylnaphthalene. Among these reactions, the one that generates 1-naphthylmethyl through hydrogen abstraction is the most significant, accounting for 55.54% of the total consumption. This is followed by hydrogen abstraction reactions on the benzene ring of 1-methylnaphthalene, which account for 10.73% and 8.92% of the total consumption, respectively. This pattern is similar to the primary consumption process of 1-methylnaphthalene in the Wang mechanism.

During the consumption process of 1-naphthylmethyl, the formation of 1-naphthaldehyde and 1-naphthylmethyl radical is significant, accounting for 44.33% and 34.68%, respectively. Additionally, 20.9% of the 1-naphthylmethyl reverts to 1-methylnaphthalene, following a reaction pathway similar to that observed in the consumption process of benzyl. Subsequently, 1-naphthaldehyde decomposes into naphthyl radicals, which are then oxidized into naphthoxy radicals before further decomposing into indenyl radicals. The indenyl radicals undergo ring-opening reactions, yielding phenyl, phenylacetylene, and styrenyl, which participate in subsequent reactions.

Figure 6 presents the sensitivity of the ignition delay time using the developed mechanism at T = 800, 1000, and 1400 K with ϕ = 1 and p = 10 bar. It is evident that the hydrogen abstraction reactions of 1-methylnaphthalene and the oxidation reactions of 1-naphthylmethyl significantly influence the ignition delay time. Specifically, the reactions A₂ĊH₂ + O₂ = A₂CHO + $\dot{\mathrm{O}}\mathrm{H}$ and A₂ĊH₂ + ${\mathrm{H}\dot{\mathrm{O}}}_2$ = ${\mathrm{A}}_2{\mathrm{CH}}_2\dot{\mathrm{O}}$ + $\dot{\mathrm{O}}\mathrm{H}$ consistently enhance fuel reactivity at all temperatures, significantly reducing the ignition delay time. The reactions A₂CH₃ + $\dot{\mathrm{O}}\mathrm{H}$ = A₂ĊH₂ + H₂O and A₂CH₃ + Ḣ = A₂ĊH₂ + H₂ promote ignition at 1000 K; however, as the temperature increases to 1400 K, these reactions start to exhibit a noticeable inhibitory effect on ignition. Conversely, the reaction A₂CH₃ + $\dot{\mathrm{O}}\mathrm{H}$ = ${\mathrm{C}}_6{\mathrm{H}}_4{\dot{\mathrm{A}}}_1{\mathrm{CH}}_3$ + H₂O promotes fuel ignition at high temperatures but begins to inhibit ignition as the temperature decreases below 1000 K. The reaction A₂CH₃ + O₂ = A₂ĊH₂ + ${\mathrm{H}\dot{\mathrm{O}}}_2$ significantly inhibits fuel ignition only at low-temperature conditions (800 K), while at medium to high temperatures (1000–1400 K), it noticeably promotes ignition. Additionally, the chain-propagating reaction of small molecules, O₂ + Ḣ = Ö + $\dot{\mathrm{O}}\mathrm{H}$, enhances fuel ignition across all temperatures, exhibiting a particularly pronounced effect at high temperatures.

3. Materials and Methods

3.1. Chemical Kinetic Model

The detailed mechanisms of large hydrocarbon molecules are typically developed using a hierarchical approach. This includes core mechanisms(C₀–C₅) for small molecules, along with fuel-specific sub-mechanisms tailored for various carbon numbers. In each sub-mechanism, reactions can be categorized into multiple reaction classes [23]. The detailed chemical kinetic model of 1-methylnaphthalene in this study comprises a core mechanism and a fuel sub-mechanism for 1-methylnaphthalene. For the core mechanism, NUIG-mech1.3 [24] was selected, as it has recently been updated with improved reaction pathways for hydrogen and methane. Additionally, the rate constant for the chain termination reaction Ḣ + O₂ (+M) = ${\mathrm{H}\dot{\mathrm{O}}}_2$(+M) has been revised based on experimental data.

The fuel sub-mechanism was developed by reviewing existing chemical kinetic models for 1-methylnaphthalene, similar aromatic hydrocarbon fuels, and their derivatives. Considering the ignition process, the fuel sub-mechanism constructed in this study encompasses hydrogen abstraction reactions, substitution reactions, and high-temperature decomposition of the fuel. It also includes oxidation reactions of 1-naphthylmethyl, reverse reactions to 1-methylnaphthalene, addition reactions with radicals, and isomerization reactions. Additionally, the model addresses the oxidation and decomposition of 1-naphthylmethyl-oxy (${\mathrm{A}}_2{\mathrm{CH}}_2\dot{\mathrm{O}}$) and naphthaldehyde (A₂CHO), as well as conversions among naphthalene, naphthoxy, and naphthol, including their decomposition. Lastly, it considers reactions between indene and indenyl species, along with conversions to monocyclic compounds. The specific reaction classes and key reactions are shown in

Table 1. Reaction classes and key reactions discussed in this study for 1-methylnaphthalene.

Species	Reaction Class	Key Reactions
1-Methylnaphthalene	Hydrogen abstraction	${\mathrm{A}}_2{\mathrm{CH}}_3 +\dot{\mathrm{R}}\to {\mathrm{A}}_2\dot{\mathrm{C}}{\mathrm{H}}_2+\mathrm{RH};{\mathrm{A}}_2{\mathrm{CH}}_3 +\dot{\mathrm{R}}\to$A2−CH3 + RH
	Substitution	${\mathrm{A}}_2{\mathrm{CH}}_3+Ö/\dot{\mathrm{O}}\mathrm{H}$$\to { \dot{\mathrm{O}}\mathrm{A}}_2{\mathrm{CH}}_3$A2CH3/HOA2CH3 + Ḣ
	Decomposition	A2CH3→A2ĊH2 + Ḣ; A2CH3→A2− + ĊH3
1-Naphthylmethyl	Oxidation	${\mathrm{A}}_2Ċ{\mathrm{H}}_2+{\mathrm{O}}_2\to {\mathrm{A}}_2{\mathrm{CH}}_2\dot{\mathrm{O}}$$/{\mathrm{A}}_2\mathrm{CHO}+Ö/\dot{\mathrm{O}}\mathrm{H}$
	reverse reactions	${\mathrm{A}}_2\dot{\mathrm{C}}{\mathrm{H}}_2+\mathrm{RH}\to {\mathrm{A}}_2{\mathrm{CH}}_3 +\dot{\mathrm{R}}$
	Addition	${\mathrm{A}}_2\dot{\mathrm{C}}{\mathrm{H}}_2+\dot{\mathrm{R}}$→A2CH2R
	Isomerization	A2ĊH2 = cĊ11H9 = Ċ9H6C2H3
Indenyl	conversion of indene to indenyl	C9H8 + $\dot{\mathrm{R}}$→Ċ9H7 + RH
Naphthalene	Oxidation	A2 + Ö = A2OH

. Then, this study discusses the rate constant of each reaction class and adjusts the rate constants of certain reactions. The main adjusted reactions and their recommended rate constants are shown in

Table 2. Key reactions and recommended rate constants in the 1-methylnaphthalene mechanism. Rate constant in Arrhenius form (k = ATⁿexp(-E/RT)); units are cm³, K, mol, s, and kJ, A₀ is from reference.

Reaction Classes	Key Reactions	A	A0×	n	E	Source
Hydrogen abstraction of 1-methylnaphthalene	${\mathrm{A}}_2{\mathrm{CH}}_3+{\mathrm{O}}_2={\mathrm{A}}_2Ċ{\mathrm{H}}_2+{\mathrm{H}\dot{\mathrm{O}}}_2$	2.40 × 1014	1.2	0	43,000	Creck [15]
	${\mathrm{A}}_2{\mathrm{CH}}_3+Ö={\mathrm{A}}_2Ċ{\mathrm{H}}_2+ \dot{\mathrm{O}}\mathrm{H}$	1.48	1.2	4.09	2545	Narayanaswamy [14]
	${\mathrm{A}}_2{\mathrm{CH}}_3+ \dot{\mathrm{O}}\mathrm{H}$ = C6H4A1CH3 + H2O	9.60 × 107	1.2	1.42	1450	Wang [11]
	${\mathrm{A}}_2{\mathrm{CH}}_3+{ \dot{\mathrm{O}}\mathrm{C}}_6{\mathrm{H}}_4{\mathrm{A}}_1{\mathrm{CH}}_3$ = A2ĊH2 + HOC6H4A1CH3	1.92 × 1011	1.2	0	15,100	Wang [11]
Decomposition of 1-methylnaphthalene	A2CH3 = A2ĊH2 + Ḣ	6.25 × 1017	0.5	−0.6	94,787	Narayanaswamy [14]
Substitution reactions of 1-methylnaphthalene and post-substitution decomposition	${\mathrm{A}}_2{\mathrm{CH}}_3+Ö={ \dot{\mathrm{O}}\mathrm{C}}_6{\mathrm{H}}_4{\mathrm{A}}_1{\mathrm{CH}}_3$ + Ḣ	1.73 × 1013	2.0	0	3600	Wang [11]
Substitution reactions of 1-methylnaphthalene and post-substitution decomposition Oxidation of 1-naphthylmethyl	${\mathrm{A}}_2{\mathrm{CH}}_3+Ö={\mathrm{C}}_{11}{\mathrm{H}}_9\dot{\mathrm{O}}$ + Ḣ	4.33 × 1012	0.5	0	3600	Wang [11]
	${\mathrm{C}}_{11}{\mathrm{H}}_9\dot{\mathrm{O}}$ = Ċ10H9 + CO	6.00 × 1011	2.0	0	43,800	Wang [11]
	${\mathrm{A}}_2Ċ{\mathrm{H}}_2+{\mathrm{H}\dot{\mathrm{O}}}_2$$={\mathrm{A}}_2{\mathrm{CH}}_2\dot{\mathrm{O}}$$+ \dot{\mathrm{O}}\mathrm{H}$	2.38 × 109	2.0	1.03	−2249	Narayanaswamy [14]
Oxidation of 1-naphthylmethyl Addition reactions of 1-naphthylmethyl with radicals and oxidation of the products	${\mathrm{A}}_2Ċ{\mathrm{H}}_2+ \dot{\mathrm{O}}\mathrm{H}$$={\mathrm{A}}_2{\mathrm{CH}}_2\dot{\mathrm{O}}$ + Ḣ	1.00 × 1013	0.5	0	0	Narayanaswamy [14]
	${\mathrm{A}}_2Ċ{\mathrm{H}}_2+Ö={\mathrm{A}}_2{\mathrm{CH}}_2\dot{\mathrm{O}}$	1.14 × 1014	0.5	0	0	Narayanaswamy [14]
	${\mathrm{A}}_2Ċ{\mathrm{H}}_2+{\mathrm{O}}_2={\mathrm{A}}_2\mathrm{CHO}+ \dot{\mathrm{O}}\mathrm{H}$	2.00 × 1013	2.0	0	40,000	Creck [15]
	${\mathrm{A}}_2Ċ{\mathrm{H}}_2+ \dot{\mathrm{O}}\mathrm{H}$ = A2CH2OH	1.00 × 1013	0.5	0	0	Wang [11]
Addition reactions of 1-naphthylmethyl with radicals and oxidation of the products Decomposition of 1-naphthylmethyl-oxy	A2ĊH2 + ĊH3 = A2C2H5	5.95 × 1012	0.5	0	221	Wang [11]
	${\mathrm{A}}_2{\mathrm{CH}}_2\mathrm{OH}+{\mathrm{O}}_2=> {\mathrm{A}}_2\mathrm{CHO}+{\mathrm{H}\dot{\mathrm{O}}}_2$ + Ḣ	6.00 × 1014	2.0	0	41,348	Wang [11]
	${\mathrm{A}}_2{\mathrm{CH}}_2\mathrm{OH}+{\mathrm{O}}_2={\mathrm{A}}_2{\mathrm{CH}}_2\dot{\mathrm{O}}$$+{\mathrm{H}\dot{\mathrm{O}}}_2$	1.00 × 1014	0.5	0	41,400	Wang [11]
	${\mathrm{A}}_2{\mathrm{CH}}_2\dot{\mathrm{O}}$ = A2CHO + Ḣ	2.63 × 1028	2.0	−5.08	22,249	Narayanaswamy [14]
Oxidation of naphthalene	A2 + Ö = A2OH	3.66 × 1013	2.0	0	4529	Narayanaswamy [14]
Decomposition of indene	Ċ9H7 + Ḣ = C9H8	6.32 × 1013	0.5	0.281	179	NUIG-mech [24]
Oxidation of indenyl	${Ċ}_9{\mathrm{H}}_7+{\mathrm{H}\dot{\mathrm{O}}}_2$$={\mathrm{C}}_9{\mathrm{H}}_7\dot{\mathrm{O}}$$+ \dot{\mathrm{O}}\mathrm{H}$	7.50 × 1012	0.5	0	0	Wang [11]

. Reaction rate constant adjustments are implemented by modifying the pre-exponential factor A. In this study, all rate constant adjustments range between 0.5 and 2 times the reaction rate constants derived from calculations, experiments, or analogies in the reference. The process for determining the data in Table 2 can be found in detail in Section 3.2, Section 3.3, Section 3.4 and Section 3.5 below. The detailed 1-methylnaphthalene mechanism developed in this study contains 1389 species and 7185 reactions. The thermodynamic data were primarily obtained from the Burcat database [25], while the thermodynamic data for certain aromatic hydrocarbon derivatives were derived from calculations by Bounaceur [17] and Blanquart [18]. The mechanism as well as the thermodynamic and transport data can be found in the Supplementary Material.

In addition, the modeled values of ignition delay times and species concentration profiles involved were derived using the CHMEKIN-PRO 15131 software. Specifically, the ignition delay times are modeled with the zero-dimensional, homogeneous, adiabatic assumption. The perfectly stirred reactor (PSR) in the CHMEKIN-PRO 15131 software was utilized to predict the concentration profiles of concerned species.

3.2. Rate Constants of Reactions of 1-Methylnaphthalene

3.2.1. Hydrogen Abstraction of 1-Methylnaphthalene

The hydrogen abstraction reactions of A₂CH₃ serve as the primary pathways for fuel consumption and play a crucial role in both fuel ignition and oxidation. The existing hydrogen abstraction reaction rate constants for the methyl group on A₂CH₃ are illustrated in Figure 7. In the Wang mechanism, the reaction rate constants are sourced from Mati’s work, which is based on the hydrogen abstraction rate constants of toluene. These rate constants were obtained by Emdee et al. [26] through the QRRK calculation method [27]. The reaction rate constants in the Narayanaswamy mechanism were similarly derived by analogy to the hydrogen abstraction of toluene, with rate constants calculated by Seta [28] using transition state theory (TST) and the B3LYP/6-31G(d) method. Additionally, the rate constants analyzed in the Creck and Nobili mechanisms are included. The rate constants selected for this study are indicated by the black lines in Figure 7.

By comparing the hydrogen abstraction reactions of A₂CH₃ in the various 1-methylnaphthalene mechanisms, it was found that in the Mati and Narayanaswamy mechanisms, the radicals initiating the reactions are primarily small molecular radicals. In contrast, the Wang and Creck mechanisms consider a greater variety of large molecular radicals in the hydrogen abstraction reactions of A₂CH₃, derived by analogy to the hydrogen abstraction reactions of toluene. The Creck mechanism also involves additional small molecular radicals. In this study, by drawing an analogy to the corresponding reactions of toluene, small molecular radicals involved in the hydrogen abstraction reactions of 1-methylnaphthalene are considered up to C₄. Meanwhile, the large molecular radicals include important intermediate radicals generated during the reaction processes of 1-methylnaphthalene, such as ${ \dot{\mathrm{O}}\mathrm{C}}_6{\mathrm{H}}_4{\mathrm{A}}_1{\mathrm{CH}}_3$ (), ${\mathrm{A}}_2{\mathrm{CH}}_2\dot{\mathrm{O}}$, A₂−, Ċ₉H₇, A₁CHĊH, ${\mathrm{A}}_1{\mathrm{CH}}_2\dot{\mathrm{O}}$, and A₁−.

In addition to hydrogen abstraction from the methyl group, Wang et al. studied the hydrogen abstraction reactions occurring on the aromatic ring of A₂CH₃. They confirmed the significance of this reaction class through reaction pathway analysis, demonstrating that it accounts for 18% of all consumption pathways for A₂CH₃. Similarly, this study incorporates these reactions, with reaction rate constants derived from Wang’s mechanism, which analogized Bounaceur’s work on the hydrogen abstraction reaction rate constants of the toluene ring. Furthermore, this study includes hydrogen abstraction reactions on the aromatic ring of A₂CH₃ with O₂ that are absent in the Wang mechanism, such as A₂CH₃ + O₂ = ${\mathrm{C}}_6{\mathrm{H}}_4{\dot{\mathrm{A}}}_1{\mathrm{CH}}_3$ + ${\mathrm{H}\dot{\mathrm{O}}}_2$ and A₂CH₃ + O₂ = Ċ₆H₃A₁CH₃ + ${\mathrm{H}\dot{\mathrm{O}}}_2$. The rate constant of the hydrogen abstraction reaction A₂CH₃ + $\dot{\mathrm{O}}\mathrm{H}$ = ${\mathrm{C}}_6{\mathrm{H}}_4{\dot{\mathrm{A}}}_1{\mathrm{CH}}_3$ + H₂O has also been adjusted.

The predicted ignition delay times for 1-methylnaphthalene under conditions of ϕ = 1 and p = 10 bar are displayed in Figure 8. In the hydrogen abstraction reactions of A₂CH₃, the reaction between A₂CH₃ and $\dot{\mathrm{O}}\mathrm{H}$ serves as the primary consumption pathway. According to the trend of reaction rate constants in Figure 7b, the rate constants in the Creck mechanism are higher than those in the Wang mechanism. In addition, the rate constants in the Narayanaswamy mechanism surpass those of the Creck mechanism at temperatures above 1200 K, while remaining slightly lower than Wang rate constants below 950 K. Consequently, the influence of A₂CH₃ hydrogen abstraction rate constants on ignition delay times is expected to show a similar trend in speed. However, in this reaction class, apart from the hydrogen abstraction reactions with Ḣ atoms, the rate constants for the reactions in the Wang mechanism are lower than those in the Narayanaswamy mechanism, leading to slower ignition at lower temperatures under the Wang rate constants. Figure 8 shows the simulated results for ignition delay times under different 1-methylnaphthalene hydrogen abstraction rate constants, and it can be seen that the ignition delay times predicted with Wang rate constants are longer under 800–1400 K. The adjusted mechanism shows that the hydrogen abstraction reaction rate constants of 1-methylnaphthalene with $\dot{\mathrm{O}}\mathrm{H}$, Ö and Ḣ radicals are similar to those of Narayanaswamy mechanism, and these radicals are more reactive. Therefore, the predicted ignition delay times from the mechanism with adjusted hydrogen abstraction reaction rate constants of 1-methylnaphthalene in this study are closer to those predicted based on the Narayanaswamy rate constants.

3.2.2. Other Reaction Classes of 1-Methylnaphthalene

In addition to the hydrogen abstraction reactions of 1-methylnaphthalene, its consumption pathways also include substitution reactions and decomposition reactions. Substitution reactions significantly influence ignition delay times at high pressures, whereas decomposition reactions play a crucial role in high-temperature ignition.

Among the existing mechanisms, only the Wang mechanism has studied the substitution reactions of 1-methylnaphthalene, using reaction rate constants obtained by analogy to those of toluene. These rate constants for toluene were determined through experimental studies conducted by Bounaceur et al. [16]. The substitution reactions of A₂CH₃ with Ö and $\dot{\mathrm{O}}\mathrm{H}$ radicals occur at the ring positions, resulting in the formation of ${ \dot{\mathrm{O}}\mathrm{C}}_6{\mathrm{H}}_4{\mathrm{A}}_1{\mathrm{CH}}_3$ and ${\mathrm{C}}_{11}{\mathrm{H}}_9 \dot{\mathrm{O}}$ (). Additionally, the substitution of a Ḣ atom with an $\dot{\mathrm{O}}\mathrm{H}$ radical at the same positions produces HOC₆H₄A₁CH₃ and C₁₁H₉OH. The formation and consumption of ${ \dot{\mathrm{O}}\mathrm{C}}_6{\mathrm{H}}_4{\mathrm{A}}_1{\mathrm{CH}}_3$ and ${\mathrm{C}}_{11}{\mathrm{H}}_9 \dot{\mathrm{O}}$ significantly influence the simulations under conditions of ϕ = 0.5 and p = 40 bar with low temperatures. In this study, the rate constants of the following reactions from the Wang mechanism were adjusted: A₂CH₃ + Ö = ${\mathrm{C}}_{11}{\mathrm{H}}_9 \dot{\mathrm{O}}$ + Ḣ, A₂CH₃ + Ö = ${ \dot{\mathrm{O}} \mathrm{C}}_6{\mathrm{H}}_4{\mathrm{A}}_1{\mathrm{CH}}_3$ + Ḣ, and ${\mathrm{C}}_{11}{\mathrm{H}}_9 \dot{\mathrm{O}}$ = Ċ₁₀H₉ () + CO, as shown in Table 2. From Figure 9, it can be observed that after the adjustments, the simulated ignition delay times for 1-methylnaphthalene under ϕ = 0.5 and p = 40 bar significantly decrease, bringing them closer to the experimental values. Additionally, the methyl group of A₂CH₃ can undergo substitution reactions with $\dot{\mathrm{O}} \mathrm{H}$ and Ḣ to form A₂OH and A₂, respectively. However, these two reaction classes contribute only a small fraction to the overall consumption of 1-methylnaphthalene.

3.3. Rate Constants of Reactions of 1-Naphthylmethyl

3.3.1. Oxidation of 1-Naphthylmethyl

The oxidation of A₂ĊH₂ is a crucial pathway in the consumption of A₂CH₃, as most A₂ĊH₂ progresses through this reaction to form other intermediate products of 1-methylnaphthalene. This is one of the key reaction classes that significantly influences the performance of the kinetic model, playing a crucial role in the ignition and oxidation of 1-methylnaphthalene. A key difference in the oxidation of A₂ĊH₂ among existing 1-methylnaphthalene mechanisms is found in the formation and consumption of ${\mathrm{A}}_2{\mathrm{CH}}_2 \dot{\mathrm{O}}$. In the Creck mechanism, the formation and consumption of this species are absent, with A₂ĊH₂ primarily converting to A₂CHO. Similarly, in the Wang mechanism, A₂ĊH₂ mainly forms A₂CHO. Although ${\mathrm{A}}_2{\mathrm{CH}}_2 \dot{\mathrm{O}}$ is included, it is generated through the hydrogen abstraction reaction of A₂CH₂OH with O₂, and both this reaction and A₂CH₂OH itself contribute very little. The reaction rate constants for this part were also derived from Bounaceur et al. [16]. However, in the Narayanaswamy mechanism, ${\mathrm{A}}_2{\mathrm{CH}}_2 \mathrm{O}\dot{}$ is equally important asA₂CHO as an oxidation product of A₂ĊH₂, and ${\mathrm{A}}_2{\mathrm{CH}}_2 \mathrm{O} \dot{}$ subsequently reacts to form A₂CHO. To understand this difference, a comparison was made to the oxidation of benzyl (A₁ĊH₂), revealing that the Narayanaswamy mechanism reflects a similar relationship between the oxidation of A₁ĊH₂ to ${\mathrm{A}}_1{\mathrm{CH}}_2 \dot{\mathrm{O}}$ and A₁CHO. Therefore, in this study, the oxidation of A₂ĊH₂ to ${\mathrm{A}}_2{\mathrm{CH}}_2 \dot{\mathrm{O}}$ was considered, with rate constants taken from the Wang and Narayanaswamy mechanisms for comparison. Additionally, the shared reaction rate constant of A₂ĊH₂ + O₂ = A₂CHO + $\dot{\mathrm{O}}\mathrm{H}$, shown in Figure 10, was selected from the Creck mechanism. The rate constants of several key reactions, including this one, were adjusted, as detailed in Table 2.

In the decomposition of ${\mathrm{A}}_2{\mathrm{CH}}_2\dot{\mathrm{O}}$, two different reaction pathways exist: ${\mathrm{A}}_2{\mathrm{CH}}_2\dot{\mathrm{O}}$ = A₂− + CH₂O and ${\mathrm{A}}_2{\mathrm{CH}}_2\dot{\mathrm{O}}$ = A₂ + HĊO. In the Narayanaswamy mechanism, the decomposition predominantly favors the former pathway. The decomposition of ${\mathrm{A}}_1{\mathrm{CH}}_2\dot{\mathrm{O}}$ produce both benzene + formyl (HĊO) and phenyl + formaldehyde (CH₂O). Therefore, this study incorporated the reaction pathway for ${\mathrm{A}}_2{\mathrm{CH}}_2\dot{\mathrm{O}}$ to produce naphthalene and formyl, as shown in Figure 11, and compared it to the reaction rate constants for ${\mathrm{A}}_1{\mathrm{CH}}_2\dot{\mathrm{O}}$ to produce benzene and formyl in the Narayanaswamy mechanism. Additionally, the reaction rate constant for ${\mathrm{A}}_2{\mathrm{CH}}_2\dot{\mathrm{O}}$ = A₂CHO + Ḣ was also adjusted in this study.

The selection of rate constants for the oxidation of A₂ĊH₂ and the consumption of its oxidation product, ${\mathrm{A}}_2{\mathrm{CH}}_2\dot{\mathrm{O}}$, significantly enhanced the fuel’s reactivity. Figure 12 compares the predicted ignition delay times, after adjusting the rate constants for these key reactions, with those from different mechanisms. It can be observed that the ignition delay times predicted by this study’s mechanism are significantly reduced across the entire temperature range. The Wang rate constants exhibit similar behavior in predicting ignition delay times based on the rate constants of A₂CH₃ hydrogen abstraction reaction, where lower reaction rate constants result in higher ignition delay times. The Narayanaswamy rate constants predict much shorter ignition delay times at lower temperatures, while above 1250 K, the predictions do not show significant difference compared to those of the Creck rate constants.

3.3.2. Other Reaction Classes of 1-Naphthylmethyl

The conversion of 1-naphthylmethyl to 1-methylnaphthalene represents a significant proportion of its consumption, particularly under high-temperature conditions. The Wang mechanism proposes reaction rate constants for this process, which are derived from the same sources as the hydrogen abstraction reactions of 1-methylnaphthalene. Although the isomerization of 1-naphthylmethyl and its addition reactions with radicals account for a relatively small portion of the overall combustion process of 1-methylnaphthalene, they are important pathways for the formation of PAHs during combustion. This process slows down the combustion, and both Jin et al. and Mati et al. have studied the rate constants associated with this class of reactions. The isomerization rate constants were derived by analogy to those calculated by Jasper et al. [29] using Ab initio, TST, and ME methods for the isomerization between fulvene and benzene. The rate constants for the addition reactions with radicals were based on the benzyl-related reaction rate constants calculated by Brand et al. [30] using the Statistical Adiabatic Channel Model (SACM).

A₂ĊH₂ can be reconverted to A₂CH₃ by reacting with Ḣ atoms from other intermediate products of 1-methylnaphthalene, as seen in the reactions A₂ĊH₂ + A₂CHO = A₂CH₃ + A₂ĊO and A₂ĊH₂ + A₂OH = A₂CH₃ + ${\mathrm{A}}_2\dot{\mathrm{O}}$. Under high-temperature conditions (above 1000 K), A₂ĊH₂ can also directly react with a Ḣ atom to form A₂CH₃ through the reaction A₂ĊH₂ + Ḣ = A₂CH₃. As the temperature increases, this reaction increasingly contributes to the consumption of A₂ĊH₂. Additionally, A₂ĊH₂ can be consumed through other pathways, including reactions with radicals to form new compounds, isomerizing into different substances, or direct decomposition into low-carbon molecules. Although these reactions contribute only a small portion to the overall flux in the 1-methylnaphthalene reaction process, the combination of A₂ĊH₂ with radicals represents an important pathway for converting 1-methylnaphthalene into other polycyclic aromatic hydrocarbons. Among these, the reactions A₂ĊH₂ + ĊH₃ = A₂C₂H₅ and A₂ĊH₂ + $\dot{\mathrm{O}}\mathrm{H}$ = A₂CH₂OH were proposed by Mati et al. [10]. A₂C₂H₅ influences the formation and consumption of ethyl-naphthalene, vinyl-naphthalene, A₂ĊHCH₃, and A₂CH₂ĊH₂ radicals, while A₂CH₂OH further reacts to produce ${\mathrm{A}}_2{\mathrm{CH}}_2\dot{\mathrm{O}}$ and A₂CHO, both of which are key intermediates in the main consumption pathways of A₂ĊH₂. Additionally, the isomerization of the 1-naphthylmethyl radical has been investigated by Jin et al. [16]. By drawing parallels to the experimentally verified isomerization between benzyl and C₇ ring-like species (cĊ₇H₇, vĊ₇H₇), they proposed a similar isomerization process of 1-naphthylmethyl, as illustrated in Figure 13. The detailed kinetic model in this study incorporates these reactions.

This study adjusted the rate constants for the following reactions: A₂ĊH₂ + ĊH₃ = A₂C₂H₅, A₂ĊH₂ + $\dot{\mathrm{O}}\mathrm{H}$ = A₂CH₂OH, A₂CH₂OH + O₂ = ${\mathrm{A}}_2{\mathrm{CH}}_2\dot{\mathrm{O}}$ + ${\mathrm{H}\dot{\mathrm{O}}}_2$, and A₂CH₂OH + O₂ => A₂CHO + ${\mathrm{H}\dot{\mathrm{O}}}_2$ + Ḣ, as detailed in Table 2. Figure 14 shows that these adjustments to the reaction rate constants resulted in a reduction of the ignition delay times of 1-methylnaphthalene for 40 bar.

3.4. Rate Constants of Reactions of Indene and Indenyl

In the main consumption pathways of 1-methylnaphthalene, indene (C₉H₈) and indenyl (Ċ₉H₇) serve as representative species in the process of converting bicyclic structures into monocyclic structures. This class of reactions is crucial for the formation of small molecules during combustion. Currently, reaction rate constants for this process have been calculated in the Wang, Narayanaswamy, Creck, and NUIG-mech1.3 mechanisms.

The bicyclic structure of 1-methylnaphthalene primarily breaks down into indenyl, indene-oxy (${\mathrm{C}}_9{\mathrm{H}}_7\dot{\mathrm{O}}$), and indanone (C₉H₆O), resulting in the formation of benzene derivatives such as styrenyl, phenyl, and phenylacetylene. These compounds subsequently undergo reactions to form small molecules, highlighting the importance of this class of reactions. The reaction rate constants for the hydrogen abstraction of indene to form indenyl are shown in Figure 15. This study utilizes the rate constants from the Narayanaswamy mechanism. The reactions of indene and indenyl are modeled by analogy to the C₅ chemical kinetics model. The mechanism presented in this study incorporates the formation and consumption of indene-oxy, as proposed in the Wang mechanism, as well as the formation and consumption of indanone from the Narayanaswamy mechanism, both of which have been validated in the study by Jin et al. [16].

This study adjusted some of the reaction rate constants for the interconversion of indene, indenyl, and indene-oxy. This includes the reactions between indene and indenyl (Ċ₉H₇ + Ḣ = C₉H₈) and the reactions leading to the formation of indene-oxy (Ċ₉H₇ + ${\mathrm{H}\dot{\mathrm{O}}}_2$ = ${\mathrm{C}}_9{\mathrm{H}}_7\dot{\mathrm{O}}$ + $\dot{\mathrm{O}}\mathrm{H}$), as detailed in Table 2. This, along with the oxygenation of naphthalene, elevated the concentrations of small molecules above 1050 K during the oxidation of 1-methylnaphthalene, as illustrated in Figure 16.

3.5. Rate Constants of Reactions of Naphthalene

In addition to the reaction classes discussed above, the formation and consumption of naphthalene (A₂) also occur during the combustion of 1-methylnaphthalene, though the flux of these reactions is generally minimal. This study focused solely on adjusting the reaction rate constant for the oxygen addition to naphthalene (A₂ + Ö = A₂OH). This adjustment, along with the modifications to the reaction rate constants for indene and indenyl discussed in Section 3.4, collectively enhances the concentration profiles of small molecular species during the oxidation of 1-methylnaphthalene at temperatures above 1050 K.

4. Conclusions

In this study, reaction pathways and reaction classes of 1-methylnaphthalene were investigated, and the effects of reaction rate constants from existing detailed mechanisms on ignition delay times were compared. Based on the above research, a detailed kinetic model of 1-methylnaphthalene was constructed. Then, reaction paths and sensitivity analysis were conducted for the ignition of 1-methylnaphthalene. The main conclusions are as follows:

(1)

Reactions on the ring of 1-methylnaphthalene, isomerization of 1-naphthylmethyl, formation and consumption of polycyclic aromatic hydrocarbons such as acenaphthene, phenanthrene, and pyrene, as well as formation and consumption of 1-naphthylmethyl-oxy, indenyl-oxy, and indanone were all taken into account in the reaction pathway of 1-methylnaphthalene.

(2)

The rate constants of reactions involving 1-methylnaphthalene and its intermediate species were discussed, including hydrogen abstraction, decomposition, and substitution reactions of 1-methylnaphthalene, followed by post-substitution decomposition. Additionally, the oxidation, decomposition, and addition reactions of 1-naphthylmethyl were examined, along with the oxidation of the resulting products. Further reactions discussed include the oxidation of naphthalene, hydrogen abstraction, oxidation, and decomposition of indene, and the oxidation of the indenyl radical. Specific recommended reaction rate constant values were provided for these reactions.

(3)

The newly developed chemical kinetic model of 1-methylnaphthalene was comprised of 1389 species and 7185 reactions. This kinetic model was validated against the ignition delay times of 1-methylnaphthalene under equivalence ratios of 0.5, 1.0, and 1.5, pressures ranging from 10 to 40 bar, and temperatures between 800 and 1400 K and the concentration profiles at an equivalence ratio of 1.0, pressure of 10 atm, and temperatures between 800 and 1200 K. Additionally, the present mechanism was also validated against the laminar flame speeds at pressure of 1 bar, initial temperature from 425 to 484 K, and equivalence ratio between 0.8 and 1.35, and the result shows a good agreement was achieved.

(4)

The reaction pathway and sensitivity analyses of the ignition process of 1-methylnaphthalene at an equivalence ratio of 1 and a pressure of 10 bar revealed that the conversion of 1-methylnaphthalene to 1-naphthaldehyde through processes such as hydrogen abstraction and oxidation plays an important role in the ignition of 1-methylnaphthalene.