Construction of a Chemical Kinetic Mechanism of Five-Component Surrogate Fuel for RP-3 Kerosene

Abstract

RP-3 is the most widely used aviation kerosene in China. Studying its chemical kinetic model is of great significance for analyzing its combustion characteristics and emissions. This paper proposes a new five-component RP-3 surrogate fuel mixture model. The three low-temperature oxidation reaction pathways of 1,3,5-trimethylbenzene were determined using the Rate of Production (ROP) analysis method, and a simplified mechanism containing 22 species and 69 elementary reactions was constructed. The reaction mechanisms of each component were simplified and coupled with the decoupling method, and the kinetic parameters of the coupled mechanism were corrected with the temperature sensitivity analysis method, obtaining a five-component surrogate fuel mixture mechanism containing 142 species and 502 elementary reactions. The mechanism was well matched with the experimental values in the verification of three parameters, ignition delay time, laminar flame speed, and small-molecule product concentration, within the ranges of 0.1–2 MPa, 500–1300 K, and equivalence ratio of 0.7 to 1.5. Whether under normal pressure or high pressure, the relative error between the simulation data and the experimental data was within ±5%. The mechanism can accurately predict the ignition and oxidation process of RP-3 aviation kerosene.

1. Introduction

Over the past few decades, transportation and travel methods have undergone rapid development, with the aviation industry becoming an important mode. As the main fuel for aircraft engines, aviation kerosene undergoes complex turbulent motion and chemical reactions after entering the combustion chamber. It is difficult to directly obtain the combustion and flow field distribution characteristics inside the engine combustion chamber through experiments. Numerical simulation research centered on fuel chemical kinetic models can achieve the dynamic simulation of complex turbulent combustion processes. However, the combustion process of aviation kerosene also involves hundreds of intermediate species and thousands of elementary reactions. It is very difficult to construct a realistic and detailed fuel chemical kinetic model, and such models are difficult to directly apply in calculations [1,2]. Therefore, a common approach is to use one or more components based on the physical and chemical properties of the actual fuel as a surrogate mixture for the actual fuel, and then construct a chemical reaction kinetic model of the surrogate fuel mixture to simulate the combustion process of the actual fuel [3].

Many scholars have conducted detailed research on the construction of surrogate fuels for Jet A-1, Jet-A, and JP-5 [4,5,6,7]. And the number of components in the surrogate fuel mixtures has gradually increased, and aromatic hydrocarbons, cycloalkanes, and other substances have been gradually added from alkanes. The prediction effect of the mechanism on various parameters of real fuels has become increasingly accurate and comprehensive, but the corresponding chemical kinetic models have also gradually increased [8]. However, compared with Jet-A and JP-5, RP-3, which is widely used as civil aviation fuel in China, has relatively late research on its corresponding chemical kinetic models, but the corresponding research has also begun to increase in recent years [9]. Zheng [10] proposed a four-component fuel mechanism consisting of n-decane, n-dodecane, ethylcyclohexane, and p-xylene, which includes 168 species and 1089 reactions. Experimental results show that this model is basically consistent with the real RP-3 fuel in terms of laminar flame speed, but there is a gap with the experimental values in terms of ignition and combustion characteristics. Xu [11] conducted a detailed analysis of surrogate models containing 1 to 10 species components and constructed a four-component surrogate model that can accurately predict the pseudo-critical temperature under supercritical pressure. Yan [12] developed a two-component surrogate fuel model consisting of n-decane and n-propylbenzene and experimentally verified its accuracy in predicting laminar flame speed and ignition delay. Yi [13], based on the fuel composition of RP-3, proposed a mechanism (toluene, trans-10-hexadecene, n-decane, isohexadecane) containing 231 species and 5591 reactions to match the physical and chemical properties as well as the kinetic characteristics of RP-3 kerosene. Liu [14] constructed a five-component surrogate fuel model (n-decane, n-dodecane, isohexadecane, methylcyclohexane, toluene) based on the physical and chemical properties of RP-3 fuel. The low-temperature oxidation, ignition delay time, and laminar flame speed of the surrogate fuel were in very good agreement with those of RP-3 fuel. Wang [15] improved the predictability of the adiabatic flame temperature of the RP-3 surrogate fuel model at high equivalence ratios by constructing a three-step simplified mechanism involving CO-C₂ and H₂-H₂O equilibria, with only a 9.3% increase in computational time. From the existing research, it can be seen that the current combustion kinetic models of RP-3 surrogate fuels still have problems such as large mechanism size and significant differences between the model’s physicochemical properties and experimental data [15,16].

The main objective of this study is to propose and construct a new surrogate fuel mixture model suitable for RP-3 aviation kerosene and develop the corresponding kinetic reaction mechanism, ensuring that the constructed surrogate fuel mixture mechanism can accurately predict the ignition and combustion characteristics of real RP-3 aviation kerosene. Based on the physical and chemical properties of RP-3 aviation kerosene and the current research status of surrogate fuel mixtures, this paper adds n-tetradecane [17,18,19] and isododecane [20,21,22,23] in the construction of alternative fuels, and proposes a five-component surrogate fuel mixture model of RP-3 aviation kerosene with physical properties more similar to the actual ones, revealing the oxidation behavior of the low-temperature combustion process of RP-3 surrogate fuels and deeply understanding the alternative fuel mechanism.

2. Development of Chemical Kinetic Mechanisms

Based on the actual fuel properties and the research status of each candidate component, this study selected n-tetradecane, n-dodecane, isododecane, decalin, and 1,3,5-trimethylbenzene as the main components of the RP-3 aviation kerosene simulation surrogate fuel. Among them, n-tetradecane and isododecane, which are more compatible with the actual RP-3 fuel, make the physical and chemical properties of the alternative fuel model closer to those of the actual fuel. After determining the main components of the alternative fuel mixture, the significance of each selection index parameter was comprehensively considered, and combined with the main characteristics of RP-3 aviation kerosene and the research purpose of this paper, the average molecular weight, cetane number, low heat value, hydrogen–carbon ratio, smoke point, and density were finally determined as the selection index parameters for the RP-3 aviation kerosene simulation surrogate fuel mixture to further calculate the proportion of the five components [4,6,24]. The calculation formulas [25], Formulas (1)–(7), for each selection index parameter of the mixed fuel are presented as follows:

Average molecular weight of the surrogate fuel mixture:

$$M{W}_{\mathrm{mix}}={\displaystyle \sum _i{x}_{i}M{W}_{\mathrm{i}}}$$

(1)

Octane number of the surrogate fuel mixture:

$$C{N}_{\mathrm{mix}}={\displaystyle \sum _i{v}_{i}C{N}_{\mathrm{i}}}$$

(2)

Lower heating value of the surrogate fuel mixture:

$$LH{V}_{\mathrm{mix}}={\displaystyle \sum _i{y}_{i}LH{V}_i}$$

(3)

Hydrogen-to-carbon ratio of the surrogate fuel mixture:

$${(H/C)}_{\mathrm{mix}}={\displaystyle \sum _i{x}_i{(H/C)}_i}$$

(4)

Density of the surrogate fuel mixture:

$${\rho }_{\mathrm{mix}}={\displaystyle \sum _i{v}_i{\rho }_i}$$

(5)

Smoke point of the surrogate fuel mixture:

$$TS{I}_{\mathrm{mix}}={\displaystyle \sum _i{x}_{i}TS{I}_i}$$

(6)

Finally, the calculation results are controlled through an objective optimization function to minimize the difference between simulated values and actual values. The objective optimization function used in this study is as follows [26]:

$$E={\left[{\displaystyle \frac{{\displaystyle \sum _i^N{\left(\frac{E_{i,sur}-E_{i,rp3}}{E_{i,rp3}}\right)}^2}}{N}}\right]}^{\frac{1}{2}}$$

(7)

where $x_i$ represents the mole fraction, $v_i$ is the volume fraction, $y_i$ is the mass fraction, ρ is the density of the substance, $E_{i,sur}$ is a certain selection indicator value of the surrogate fuel, $E_{i,rp3}$ is a certain selection indicator value of the real fuel RP-3, and N is the number of selection indicators determined in the previous text.

For the proportion calculation, the Matlab R2022b genetic algorithm toolbox was used for optimization calculation. The optimization evaluation parameter is the optimization function value E, and the target attribute is the six selection indicator values of the selected real RP-3 fuel. In the constraint settings, according to the types of components in actual fuel, the boundary conditions for the species components were set as follows: n-dodecane and n-tetradecane were both 0 to 0.3; isododecane was 0 to 0.4; decalin was 0 to 0.4; 1,3,5-trimethylbenzene was 0 to 0.2; and the sum of the five components was 1. The remaining conditions used default values: population size was 50; the number of elites was 0.05 times the population size; crossover rate was 0.8; and mutation probability was 0.2.

After multiple calculations, the ratios of n-dodecane, n-tetradecane, isododecane, decahydronaphthalene, and 1,3,5-trimethylbenzene were obtained as 0.121, 0.135, 0.318, 0.326, and 0.1, and at this point, the value of the optimized function was approximately 0.022. At this ratio, the molar proportion of alkanes was 57.4% (with straight-chain alkanes accounting for 25.6% and branched alkanes, 31.8%), cycloalkanes accounted for 32.6%, and aromatic hydrocarbons accounted for 10%, which is close to the composition of actual fuel.

Table 1. Selected indicator values of RP-3 aviation kerosene and five-component surrogate fuels.

Item	Octane Number	H/C	Lower Heating Value (MJ/L)	Molecular Weight	Density (20 °C) (g/cm3)	Smoke Point
RP-3 [27]	43.3	1.963	42.8	150	0.778	20
Simulation	43.278	1.9608	43.48	157.02	0.787	20.177

compares the six selection indicator values of the simulated surrogate fuel and real RP-3 fuel at this ratio. The results show that, at the current ratio, the maximum error is the difference between the average molecular weight of the surrogate fuel and the target value, which is less than 5% and within an acceptable range. From the comparison of indicator parameters, the proposed RP-3 aviation kerosene surrogate fuel mixture model in this paper closely matches the data of actual fuel in various property indicators, reflecting the physical and chemical properties of RP-3 kerosene during combustion.

n-Dodecane and n-tetradecane stand for linear alkanes. The number of carbon atoms in n-dodecane is close to that of aviation kerosene, and its physical properties are rather similar to those of aviation kerosene [28]. Thus, it is frequently selected as a surrogate fuel for simulating aviation kerosene. Likewise, n-tetradecane is a typical constituent in transportation fuels and can effectively represent the properties of heavy alkane substances in aviation kerosene [23]. This research selected the mechanism of n-dodecane and n-tetradecane constructed by Chang [29]. The properties of isododecane are analogous to a 50% isohexadecane and 50% isooctane mixture. Compared to isooctane and isohexadecane, the average carbon number of isododecane is closer to that of the genuine kerosene fuel, thereby presenting an advantage in H/C. The mechanism employed is the simplified one constructed by Liu [21]. Decalin has a six-membered double-ring structure and possesses unique advantages in terms of stability, combustion performance, and energy density. It has been proven to be one of the most thermally stable and heat-absorbing fuels in aviation fuels and is often selected as a surrogate component for cycloalkanes in transportation fuels [30]. The mechanism was chosen from Li’s research [31]. In this research, 1,3,5-trimethylbenzene was chosen to represent the aromatic group as a candidate component for surrogate fuels, and the detailed mechanism constructed by Diévart [32] was selected. The sub-mechanisms of NOx and PAHs were simplified from the detailed mechanism proposed by Slavinskaya [33,34] and refined by Wang [35,36]. The final PAH mechanism comprised 20 species and 139 elementary reactions.

Since the previously selected 1,3,5-trimethylbenzene (C₉H₁₂) mechanism was the detailed one constructed by Diévart [32], which encompasses 450 species and 2569 elementary reactions, it was required to analyze and simplify the detailed mechanism of 1,3,5-trimethylbenzene. Among multiple components, the small-molecule reactions in various components all undergo the same C0–C3 mechanism, and the oxidation path of benzene, the oxidation product of 1,3,5-trimethylbenzene, is consistent with the decalin mechanism constructed by Li [31]. Hence, the approach employed was the ROP analysis method, which analyzes the oxidation of 1,3,5-trimethylbenzene to generate C3 small molecules and products containing benzene rings, and the subsequent reactions were incorporated into the multi-component mechanism. After obtaining the low-temperature oxidation route of 1,3,5-trimethylbenzene, the detailed mechanism was simplified. Considering that the oxidation route from toluene to benzene was not included in the coupling mechanism, the reaction route from toluene to benzene constructed by Zhang [37] was utilized, as presented in

Table 2. Partial elementary reactions of toluene.

NO.	Reactions	Kinetic Parameters
		A	b	Ea (J/mol)
1	C7H8 + O2 = C6H5CH2 + HO2	2.18 × 107	2.5	47,300.0
2	C7H8 + OH = C6H5CH2 + H2O	1.77 × 105	2.4	−602.0
3	C6H5CH2 + O2 = C6H5CHO + OH	3.00 × 1015	−1.6	47.0
4	C6H5CHO +OH = A1− + CO + H2O	2.89 × 108	1.3	−1573.0

¹ A is referred to as the pre-exponential factor; b is the temperature index; E_a represents the activation energy of the reaction.

. This mechanism contains only four elementary reactions and exhibits strong applicability [38]. Eventually, the complete low-temperature reaction route of 1,3,5-trimethylbenzene was determined as depicted in Figure 1. The number of species in the low-temperature reaction is 22, encompassing 69 elementary reactions.

Based on the four single-component mechanisms, the NOx and PAH sub-mechanisms obtained previously, and the simplified mechanism of 1,3,5-trimethylbenzene constructed in this research, the mechanism of the five-component surrogate fuel mixture was developed. To ensure a superior prediction accuracy of the coupled mechanism in single-component parameter predictions, the construction of the coupled mechanism was based on the decoupling approach proposed by Chang [29]. The C0–C1 core mechanism employed was derived from the individual component mechanisms selected in the previous section, with duplicate elementary reactions eliminated. The C2–C3 transition mechanism primarily originates from the simplified mechanism constructed by Patel [39], which encompasses 10 species and 28 elementary reactions and exhibits strong applicability, having been utilized in numerous mechanism construction efforts [21,25,28]. The skeleton mechanism for C4 and above was derived from the large-molecule fuel mechanisms contained in each individual component mechanism. In the process of mechanism coupling, the following principles were adhered to: retain all macromolecular skeleton reactions above C4 for the five components, eliminate the duplicate reactions between C2 and C3, and merge the reactions of C0 to C1 molecules in the mechanisms of each single component. Figure 2 presents the flowchart for the construction of the five-component aviation kerosene fuel surrogate mechanism. The five-component surrogate fuel mixture mechanism encompasses 142 components and 496 elementary reactions. The thermodynamic and transport parameters of the mechanism were derived from the initial mechanisms of each single component, respectively.

3. Modification of Kinetic Parameters for Mechanism of Surrogate Fuel Mixture

3.1. Verification of Multi-Component Mixture Mechanism

Ignition delay time is a significant phenomenon in the autoignition and subsequent combustion of fuel. The laminar flame speed can reflect the characteristics of chemical reactions and transport in premixed flames and is one of the most crucial parameters for the fundamental combustion behavior of fuel. Hence, for the obtained multi-component fuel mechanisms, the zero-dimensional homogeneous module, and the laminar premixed flame module in Chemkin Pro 17.0 were, respectively, employed to predict the two parameters, namely the ignition delay time and the laminar flame speed.

Figure 3 presents the outcomes of simulating the ignition delay time of real fuel using the surrogate fuel mixture mechanism. The experimental data are from the research of Mao [22], with the experimental conditions being P = 1.0 MPa, a temperature range of 600 to 1100 K, and φ = 0.5 and 1.0. As can be observed from the figure, although the simulation values are in accordance with the experimental data in the overall trend, at temperatures ranging from 750 to 900 K, the simulated ignition delay time is larger than the experimental data and fails to reflect the negative temperature coefficient (NTC) behavior of the fuel; in the higher temperature range above 1100 K, the simulation values are smaller compared to the experimental data.

Figure 4 presents the comparison of the predicted and experimental values of the laminar flame speed of real RP-3 fuel using the initial mechanism. The experimental conditions were 400 K to 480 K, with φ from 0.7 to 1.5, and P = 0.1 MPa and 0.3 MPa. The experimental data were from Liu [14]. The results demonstrate that the mechanism overestimated the experimental values to different extents under all working conditions, particularly when φ was greater than 0.8, with considerable errors.

Figure 5 depicts the verification outcomes of the ignition delay times for certain single-component fuels. Taking the ignition delay times of n-dodecane and isododecane as instances, the experimental data were derived from the measurement results of Mao [19] and Vasu [40]. The results indicate that within the temperature range above 750 K, the mechanism underestimates the ignition delay time of n-dodecane; within the temperature range above 900 K, the ignition results predicted with the mechanism are smaller.

Figure 6 presents the predicted outcomes of the laminar premixed flame propagation speed for certain single-component substances. The experimental data were sourced from the research of Zhong [23] and Kumar [41]. As depicted, although the mechanism can reflect the changing trend in the laminar flame speed of different fuels along with φ, in terms of specific numerical values, when compared to the experimental values, particularly around φ = 1.1, the initial mechanism has overestimated the experimental values.

3.2. Modification of Dynamic Parameters

After the mechanism coupling, the prediction accuracy of the mechanism is an issue deserving attention. Due to factors such as cross-reactions between molecules, changes in component reaction pathways and rates, and the fusion of repeated elementary reactions, the ignition delay time and laminar flame speed will change. Whether it is the actual fuel RP-3 or single-component experimental data, there are significant differences in the predicted values of the initial mechanism. Therefore, the initially constructed coupled mechanism must be optimized. The optimization of the mechanism mainly involves the experimental data, by modifying the reaction product pathways and correcting the pre-exponential factors and activation energies that affect the reaction rates, to make the prediction results of the mechanism better match the experimental data.

Sensitivity analysis is an analytical method for assessing the extent to which the uncertainties of different input variables in a model or system affect the output results. It can visually reflect the sensitivity effect of certain disturbance factors in the combustion system, such as reaction conditions, component concentrations, elementary reactions, etc., on the calculated result parameters, thereby determining the importance of each elementary reaction. The orthogonal sensitivity coefficient $\tilde{S}$ between the disturbance factor ${\alpha }_i$ and the calculated result parameter can be expressed by Formula (8):

$$\tilde{S}={\displaystyle \frac{{\alpha }_i}{\phi }}{\displaystyle \frac{\partial \phi }{\partial {\alpha }_i}}={\displaystyle \frac{\partial \ln \phi }{\partial \ln {\alpha }_i}}$$

(8)

In the formula, when the disturbance factor ${\alpha }_i$ changes, it can cause a change in the target parameter $\phi$, thereby obtaining the sensitivity coefficient of various elementary reactions. When the sensitivity coefficient is positive, it promotes the calculated result parameter; otherwise, it inhibits it.

In this research, the optimization process of the mechanism mainly takes the experimental data as the objective. Corresponding modifications are made by comparing the differences between the predicted values of the mechanism and the experimental data, ultimately obtaining a multi-component surrogate fuel mixture mechanism with good prediction performance. The modification method mainly optimizes the mechanism by adjusting the chemical reaction rate constants in this research. Li [31], Bugler [42], Zhang [43], Lin [44], and Wu [45] all adopted this method to fit the experimental values. The principal steps of the modification involve identifying the elementary reactions that exert considerable influence on the system temperature through the temperature sensitivity analysis approach, modifying the kinetic parameters of the related reactions, and then conducting further comparisons and modification until a mechanism that aligns with the experimental data is attained. Temperature sensitivity analysis can gauge the sensitivity of a certain elementary reaction to temperature by means of the normalized sensitivity coefficient. A positive normalized coefficient indicates that the corresponding reaction promotes ignition, whereas a negative value implies an inhibitory effect.

In Figure 7, at P = 1.0 MPa and φ = 1.0, temperature sensitivity analyses were performed for working conditions with initial temperatures of 600 K, 800 K, and 1200 K, respectively. As evident from Figure 7a, at the low temperature of 600 K, the R253 reaction possesses the largest sensitivity coefficient, signifying that this reaction has the greatest influence on temperature. Among the reactions with the highest sensitivity presented in the figure, all elementary reactions are large-molecule reactions. Specifically, R247, R236, R225, and R96 are all dehydrogenation reactions where a large-molecule fuel loses one H to an OH radical, while R235, R224, and R95 are all initial oxidation reactions of the fuel. This demonstrates that in the low-temperature region, the ignition and combustion processes of the fuel are primarily governed by the initial oxidation and dehydrogenation reactions of long-chain large-molecule fuels.

As depicted in Figure 7b, at the medium temperature of 800 K, there are notable differences between the reactions with larger sensitivity coefficients and those in the low-temperature region. Under this temperature condition, small-molecule reactions such as R212, R158, R14, and R12 begin to emerge among the reactions that influence the temperature. Among them, R14 has the greatest sensitivity coefficient, followed by R158. Since reaction R14 is the reaction of two OH radicals to generate H₂O₂ radicals under the action of a third body, this reaction promotes the temperature rise in the fuel system. In terms of reactant types, there are still six large-molecule reactions in the fuel, accounting for more than half, which still exert considerable influence on the ignition delay time.

The sensitivity reaction results under the high-temperature working condition of 1200 K are presented in Figure 7c. At the high-temperature stage, although there are still large-molecule reactions such as R104, R106, R235, and R274 in the temperature sensitivity reaction, their sensitivity coefficients are relatively small. More reactions involve small molecules, and in terms of sensitivity coefficients, R1 has the largest sensitivity coefficient, while R14, R158, and R212 all have relatively large ones. This indicates that at the high-temperature stage, the reactions involving small molecules control the temperature rise in the fuel system [31].

From the foregoing analysis, it can be observed that in the low-temperature region, the system reactions are mainly influenced by the reactions of large-molecule fuels; in the high-temperature region, they are affected by the reactions of small molecules; and in the medium-temperature region, they are jointly influenced by the reactions of both types of fuel molecules. Based on the comparison results between the predictions of the ignition delay time with the mechanism in the preceding text and the experimental values, the predicted values of the mechanism in the NTC temperature region are larger, while in the high-temperature region, they are smaller. Therefore, the kinetic parameters of some elementary reactions in the coupling mechanism have been modified.

Table 3. Modification of kinetic parameters for some sensitive primitive reactions.

Reactions	Modification	Kinetic Parameters			Ref.
		A	b	E (J/mol)
R1.:H + O2 = O + OH	Before	2.644 × 1016	−0.671	1.7041 × 104
	After	1.04 × 1014	0.0	1.5286 × 104	[31]
R12: H + O2(+M) = HO2(+M)	Before	5.116 × 1012	0.440	0.0
	After	1.475 × 1012	0.6	0.0	[46]
R14: 2OH(+M) = H2O2(+M) H2O2(+M) = 2OH(+M)	Before	1.110 × 1014	−0.370	0.0
	After	2.0 × 1012	0.9	4.875 × 104	[31]
R212: CH3 + HO2 <=> CH4 + O2	Before	3.1600 × 1012	0.00	0.00
	After	1.160 × 105	2.230	−3022.0	[29]
R28: CO + OH = CO2 + H	Before	8.0 × 1011	0.1	7352.0
R29: CO + OH = CO2 + H	Before	8.78 × 1010	0.0	−16.0
	After	1.04 × 1014	0.0	1.5286 × 104	[47]
R36: HCO + M = CO + H + M	Before	1.87 × 1017	−1.0	1.70 × 104
	After	5.7 × 1011	0.66	1.487 × 104	[31]
R37: HCO + H2O = CO + H + H2O	Before	2.2440 × 1018	−1.0	1.70 × 104
	After	1.5 × 1018	−1.0	1.70 × 104	[48]

below presents the modification of the kinetic parameters of the relevant elementary reactions in the mechanism.

In terms of laminar flame speed, the temperature sensitivity analysis method was likewise employed. Figure 8 depicts the temperature sensitivity reactions of the laminar premixed flame under different φ. The simulation conditions were three working conditions with φ = 0.8, 1.1, and 1.4, at a temperature of 420 K and P = 0.1 MPa.

At φ = 0.8, as depicted in Figure 8a, for the one-dimensional laminar premixed flame, the reaction with the largest temperature sensitivity reaction coefficient is R28: CO + OH = CO₂ + H. This reaction releases a considerable amount of heat and facilitates the generation of H radicals, which is conducive to the augmentation of the laminar flame speed. Among them, R28 and R29 are the identical reactions corresponding to distinct kinetic parameters, jointly governing the oxidation of CO [47]. As depicted in Figure 8b, at φ = 1.1, the reaction with the maximal sensitivity coefficient is R1. Reaction R28 still possesses a relatively large positive sensitivity coefficient, while the sensitivity coefficients of reactions R36, R37, and R175 decline. When φ continues to increase to 1.4, as shown in Figure 8c, the reaction with the greatest sensitivity coefficient is R1. Moreover, the sensitivity coefficients of the other several reactions decrease significantly, contributing less to the temperature increase. Among the reactions with larger negative sensitivity coefficients, the contributions of R36 and R37 are more prominent. Since both reactions are endothermic processes where HCO radicals generate small-molecule radicals, although they promote the generation of H radicals, they consume a relatively large amount of heat from the system, exerting a certain inhibitory effect on the laminar flame speed [31,48]. Under three distinct operating conditions, the temperature sensitivity analyses all demonstrated that reactions such as R1 and R36, which involve small molecules like H radicals and OH radicals, have a more significant influence on the laminar flame speed. This indicates that the laminar flame speed is closely associated with the concentrations of H and OH radicals.

Based on the above analysis results, the kinetic parameters of some elementary reactions in the mechanism were modified. Except for R1, the main modified reactions are shown in Table 3.

Figure 9 presents the comparison between the prediction outcomes before and after the modification of the mechanism kinetic parameters and the experimental data of RP-3 fuel. Regarding the ignition delay time, the optimized mechanism conspicuously reduces the predicted values in the medium- and low-temperature regions and elevates the predicted values in the high-temperature region, significantly enhancing the matching with the experimental values. With respect to the laminar flame speed, the optimization measures likewise lower the predicted values of the mechanism within φ values of 0.7 to 1.5, achieving better alignment with the experimental values. The optimized coupled mechanism encompasses 142 species and 504 elementary reactions (Supplementary Materials Tables S1 and S2) and still maintains a relatively small size.

4. Result and Discussion

The accuracy of the chemical kinetic model for surrogate fuels is of paramount importance for the reliability of the numerical simulation research results. Hence, the acquired coupled mechanism requires verification to ascertain whether the model can fulfill the requirements of subsequent studies. The mechanisms of multi-component surrogate fuels ought to precisely predict the oxidation and combustion processes of individual components, their mixtures, and actual fuels [2]. In this research, the validity of three key parameters, namely the ignition delay time, laminar flame speed, and product concentration of the surrogate fuel mixture mechanism, was analyzed.

4.1. Verification of RP-3 Combustion Parameters

Figure 10 presents the comparison between the predicted ignition delay times of the surrogate fuel mechanism and the experimental data obtained by Mao [22] in shock tubes and rapid compressors. The experimental conditions were P from 1.0 to 1.5 MPa, T from 600 to 1100 K, and φ = 0.5, 1.0, and 1.5. Another set of data was derived from the experimental findings of Zhang [49] in a shock tube, with P = 1.0 MPa, T from 651 to 1220 K, and φ = 1.0. The outcomes reveal that at φ = 0.5, the coupled mechanism fails to precisely simulate the variations in the NTC region. However, at equivalence ratios of 1.0 and 1.5, the NTC phenomenon of the simulation values is more pronounced. In the high-temperature region where the temperature exceeds 1000 K, the mechanism can effectively predict the approximate linear relationship between the logarithm of the fuel ignition delay time and the reciprocal of the temperature. Based on the pre-exponential analysis, the ignition delay time of the fuel in the low and medium-temperature regions is influenced by the low-temperature oxidation reactions of large molecules. The subsequent analysis results indicate that the mechanism demonstrates a certain degree of reliability for the ignition delay time of single-component fuels. Hence, it is hypothesized that the reactions associated with the PAH sub-mechanism result in the formation of large-molecule polycyclic aromatic hydrocarbon products with lower reactivity from the small-molecule products of the fuel, causing a longer ignition delay time.

Figure 11 depicts the comparison between the predicted outcomes of the mechanism under oxygen-dilution conditions and the experimental data. The experimental data originated from Mao [22], where the selected experimental conditions for the dilution scenarios were N₂/(N₂ + O₂) = 0.895 and N₂/(N₂ + O₂) = 0.93, with P = 1.0 MPa and 2.0 MPa, and φ = 1.0 and 1.5, respectively. It can be observed from the figure that under oxygen dilution conditions, there are certain shortcomings in the mechanism’s prediction of the experimental data. The predicted values in the high-temperature region are relatively low, and the prediction of the fuel’s NTC behavior is inadequate. This is attributed to the fact that the mechanism has not conducted the calculation and optimization of the corresponding kinetic parameters for the oxygen dilution conditions, leading to a narrow application scope and weak predictive capability. Nevertheless, on the whole, the mechanism can reflect the variation pattern of the fuel’s ignition delay time with temperature.

Figure 12 presents the verification outcomes of the mechanism with respect to the laminar flame speed experimental data of RP-3. The experimental results are the measurement data of Liu [14] in a rapid compression machine, with P from 0.1 MPa to 0.3 MPa, T from 420 to 480 K, and φ from 0.7 to 1.4. The results demonstrate that the coupled mechanism can precisely predict the variation pattern of the laminar flame speed with φ. Furthermore, as the temperature varies, both at atmospheric pressure and high pressure, the simulation data are in good accordance with the experimental data, and the relative errors are all within ±5%. This indicates that the surrogate fuel mechanism constructed in this research can fulfill the prediction requirements for the laminar flame speed of the actual RP-3 fuel.

4.2. Verification of Single-Component Combustion Parameters

4.2.1. n-Dodecane

Figure 13 presents the comparison between the predicted values of the mechanism and the ignition experimental data of n-dodecane. The experimental data stem from the research of Vasu [40] and Mao [50]. The experimental conditions of Mao were P = 1.5 MPa, φ = 0.5, and T from 633 to 1266 K. In the experiment, Mao also took into account the condition where oxygen was diluted (N₂/(N₂ + O₂) = 0.895), as depicted in Figure 13d. Vasu’s experimental conditions were P = 2.2 MPa, φ = 0.5 and 1.0, and T within the range of 720 to 1200 K. The results suggest that under several distinct conditions, the matching of the predicted results of the mechanism with the experimental data is favorable, successfully reproducing the NTC trend of the n-dodecane component and the ignition behavior at both high and low temperatures. The performance is also satisfactory under the condition where oxygen is diluted.

Figure 14 presents the validation outcomes of the surrogate fuel reaction mechanism regarding the laminar flame speed of n-dodecane. The experimental data were derived from the measurements of Zhong [23], Kumar [41], and Hui [51]. The results suggest that at a temperature of 470 K, the predicted value of the mechanism is slightly lower; under the remaining several conditions, the coupled mechanism can effectively predict the premixed laminar flame speed of n-dodecane, and the prediction results are overall in good alignment with the experimental data. It can effectively predict the variations in the laminar flame speed of n-dodecane under diverse operating conditions.

Figure 15 presents the comparison between the predictions of the oxidation product concentrations of n-dodecane with the mechanism and the experiments of Mao [50]. The experimental conditions were P = 0.1 MPa and T of 600 to 1100 K, and the diluent gas was argon. As can be observed from the figure, when the temperature is within the range of 600 to 700 K, the consumption curve of O₂ suddenly decreases and then rapidly increases, forming a consumption peak. This could be attributed to the relatively high rate of oxygen addition reactions of n-dodecane, resulting in an increased consumption of oxygen and the emergence of the consumption peak. Nevertheless, as the oxidation reaction progresses further, the occurrence of reactions that generate oxygen in small-molecule reactions or the reverse reactions of oxygen-consuming reactions, such as the oxidation reaction of CH₃ radicals with HO₂ radicals (CH₃ + HO₂ <=> CH₄ + O₂) and the reaction of HO₂ radicals with O radicals (HO₂ + O <=> O₂ + H), may all lead to the recovery of oxygen concentration. On the whole, the surrogate fuel mixture mechanism can essentially reflect the variation pattern of the concentrations of n-dodecane oxidation products with temperature.

4.2.2. n-Tetradecane

Figure 16 presents the verification of the ignition delay time for n-tetradecane fuel. The experimental data are from Shen [52], with φ = 0.5 and 1.0, P = 1.2 MPa and 4.0 MPa, and T from 900 to 1300 K. The results suggest that under the relatively low-pressure condition of 1.2 MPa, regardless of φ, the mechanism constructed in this research can effectively predict the ignition behavior of n-tetradecane. When the pressure is elevated to 4.0 MPa, the predicted curves of the reaction mechanism exhibit considerable discrepancies from the experimental data within the temperature range below 1000 K. It is speculated that this is because of the significant pressure sensitivity of the low-temperature reaction part of n-tetradecane in the mechanism, resulting in an increased reaction rate under high-pressure conditions and a weakened prediction performance. Nevertheless, from the overall prediction situation, the coupled mechanism can essentially satisfactorily meet the prediction requirements for the ignition delay time of the n-tetradecane component.

Figure 17 validates the laminar flame speed of n-tetradecane. The experimental data were derived from the measurements of Zhong [23] and Li [53], respectively. It can be observed from the figure that regardless of the pressure value, the simulation results effectively reflect the variation trend of the laminar flame speed of n-tetradecane with the equivalence ratio and are in good accordance with the experimental values.

4.2.3. Iso-Dodecane

Figure 18 presents a comparison between the predicted values of the ignition delay time of isododecane with the reaction mechanism and the experimental results of Mao [19]. The experimental conditions were introduced earlier. Under all working conditions, the coupled mechanism constructed can effectively predict the ignition behavior of isododecane in the temperature range above 900 K. In the medium- and low-temperature region below 900 K and φ = 0.5, the prediction of the NTC phenomenon with the mechanism is relatively low. However, at φ = 1.0 and 1.5, the mechanism can basically well meet the prediction targets. This is attributed to the scarcity of experimental data for the isododecane component and the limited research on the related reaction mechanism. The kinetic parameters of the macromolecular oxidation reaction in the mechanism refer to the related reactions of the n-dodecane component. Moreover, the reactivity of isododecane is lower than that of n-dodecane, and the mechanism fails to consider the property differences between the two components, resulting in a shorter ignition delay time. Nevertheless, on the whole, the coupled mechanism demonstrates certain reliability in predicting the ignition delay time of the isododecane component.

4.2.4. Decalin

Figure 19 shows the comparison outcomes of the ignition data of decalin with the reaction mechanism of surrogate fuels. The experimental data were measured by Zhu [54], with T from 769 to 1202 K, P from 1.17 to 5.12 Mpa, and φ = 0.5 and 1.0, respectively. As depicted in Figure 19a, although the predicted values of the mechanism are smaller than the experimental values under high-temperature conditions above 1000 K, it can, on the whole, effectively reproduce the variation trend of the ignition delay time of decalin with temperature. As shown in Figure 19b, at φ = 1.0, the predicted results of the mechanism are in good accordance with the experimental values, and it also well predicts the NTC behavior of the decalin component in the medium-temperature region.

The laminar flame speed of decalin was compared with the experimental data of Zhong [23] and Comandini [55], as depicted in Figure 20. As indicated in Figure 20a, within φ values of 0.7 to 1.5, the predicted results of the mechanism are all larger than those of the experimental data, whereas the good match with the experimental data in Figure 20b reflects the variation trend of the laminar flame speed of decalin with φ and enables reasonable predictions to be made regarding the ignition behavior of the fuel.

Figure 21 presents the concentration changes in the major species during the oxidation process of decalin. The experimental data were the measurement results obtained by Zeng [56] using a McKenna burner in an O₂/Ar atmosphere, with T = 300 K, P = 0.1 MPa, and φ = 0.75 and 1.8. The lines represent the simulation values, and the symbols represent the experimental values. The outcomes demonstrate that the mechanism constructed in this research can effectively predict the main products and their concentration distributions of decalin during the combustion process.

4.2.5. 1,3,5-trimethylbenzene

Under the experimental conditions of Diévart [32], the ignition delay time of 1,3,5-trimethylbenzene was validated using the coupled mechanism, as depicted in Figure 22 below. The results suggest that, under all conditions, the logarithm of the ignition delay time of 1,3,5-trimethylbenzene exhibits a linear relationship with the reciprocal of the temperature and can effectively predict the variation pattern of the ignition delay time of 1,3,5-trimethylbenzene fuel.

Figure 23 presents the verification outcomes of the laminar flame speed of 1,3,5-trimethylbenzene using the coupled mechanism and the experimental measurements of Diévart [32], Hui [57], and Wen [58]. Within the range where φ is less than 1.2, the mechanism can precisely predict the laminar flame speed of the fuel. Nevertheless, when φ exceeds 1.1, the predicted results exhibit an overestimation. Previous studies in this research have indicated that an increase in φ promotes the generation of more polycyclic aromatic hydrocarbon products. Both in the formation and oxidation decomposition reactions of polycyclic aromatic hydrocarbons, a considerable amount of H and OH radicals are produced, thereby resulting in an increase in the laminar flame speed of this component.

Figure 24 depicts the comparison between the predicted outcomes of the mechanism regarding the concentrations of small-molecule products of 1,3,5-trimethylbenzene and the experimental data. The experimental data were obtained by Wang [59] using a spherical jet stirrer (JSR) with a diameter of 50 mm in an O₂/Ar atmosphere, at T from 500 to 1100 K, with φ = 2.0 and at atmospheric pressure. The lines represent the simulation values, and the symbols represent the experimental values. The results demonstrate that the alternative fuel mixture mechanism effectively replicates the concentration variations in products such as C₉H₁₂, H₂, CO, and CO₂ during oxidation and also exhibits reliability in the prediction of A1 and toluene (C₇H₈) products.

5. Conclusions

Based on the physicochemical properties of RP-3 fuel, this study constructed a surrogate fuel composed of five components: n-dodecane, n-tetradecane, isododecane, decalin, and 1,3,5-trimethylbenzene. The accuracy of the mechanism in predicting the combustion process of the RP-3 series of fuels was verified by comparing the ignition delay time, laminar flame speed, and partial component product data with the experimental results:

(1)

The reaction pathways of 1,3,5-trimethylbenzene were analyzed using the generation rate analysis method, and three main low-temperature reaction pathways of 1,3,5-trimethylbenzene were determined. A simplified mechanism consisting of 22 species and 69 elementary reactions was obtained.

(2)

Based on six selection criteria, including MW, H/C, CN, LHV, TSI and density, five-component surrogate fuels consisting of n-dodecane, n-tetradecane, isododecane, decalin, and 1,3,5-trimethylbenzene (12.1%, 13.5%, 31.8%, 32.6%, and 10% by mole) were constructed. The single-component mechanisms of each fuel and the simplified mechanism of 1,3,5-trimethylbenzene were coupled with the transitional C2–C3 mechanism and the detailed C0-C1 mechanism using the decoupling method, resulting in a five-component surrogate fuel mechanism containing 142 species and 502 elementary reactions.

(3)

The mechanism of the surrogate fuel mixture was analyzed using the temperature sensitivity analysis method. Based on the comparison between the predicted values and the experimental values of the mechanism, the kinetic parameters of the key reactions involving small molecules such as R1, R36, and R37 containing H radicals and OH radicals, as well as the reactions generating small-molecule radicals through the endothermic reaction of HCO radicals, were corrected. The reliability of the corrected mechanism was verified by comparing the ignition delay time, laminar flame speed, and combustion products of some components with the experimental data. The comparison between the simulation results and the experimental data shows that in the high-temperature region at 1 MPa and above 1000 K, the mechanism can well predict the ignition delay time of the fuel, especially at 1.0 and 1.5, where the NTC phenomenon of the simulation values is more obvious.

The mechanism constructed in this research is of a relatively small size and can represent the ignition, oxidation, and flame propagation characteristics of RP-3 aviation kerosene. It offers a reference for the investigation of surrogate fuel mixture mechanisms, facilitating an in-depth understanding of the combustion characteristics of RP-3 aviation kerosene and being applicable to the high-precision numerical simulation of the combustion reaction flow.

However, the PAH sub-mechanism employed in this research fails to consider the pathways for the formation of polycyclic aromatic hydrocarbons through the interaction among large-molecule fuels. Meanwhile, the incorporation of the sub-mechanism, to some extent, weakened the predictive performance of the surrogate fuel mixture. In subsequent studies, corresponding research should be carried out to address these issues.