The laminar flame speeds of JP-10 were measured under a temperature of 360–453 K and an equivalence ratio of 0.7–1.3. Figure 4 shows the typical Bunsen flame under a preheating temperature of 453 K and atmospheric pressure conditions with constant outlet velocity. With the piloted flame, the main flame of the JP-10/air mixtures can be stabilized over a wide equivalence ratio from φ = 0.7 to φ = 1.3. In the range of equivalence ratios of 0.7–1.0, the intensity of the flame image increases with increasing equivalence ratio, and the height of the flame decreases with increasing equivalence ratio. In the range of equivalence ratios of 1.1–1.2, the opposite trend was observed. As the fuel/air mixture flow was kept constant, according to Eq. 1, the trend of the height variation of the flame is opposite to the laminar flame speed variation, which is indeed observed in the present work.

The flame tip opening phenomenon was observed when the equivalence ratio values were higher than 1.3. Under these conditions, the flame was locally quenched at the flame tip and then reignited above the tip opening region, resulting in another laminar flame with a high soot concentration. Figure 4 shows the phenomenon of flame tip opening and reignition of the flame. It is found that for all the experimental conditions carried out in this work, no matter what temperature and outlet velocity vary, the flame tip opening phenomenon and reignition always occur once the equivalence ratio is higher than 1.3.

Some researchers have studied the flame tip opening phenomenon and attributed it to the curvature effect on nonequi-diffusive preheated mixtures of fuel/air leading to a change in the burning intensity at the flame tip (Ishizuka, 1982; Law et al., 1982; Mizomoto et al., 1985; Mizomoto and Yoshida, 1987; Sakai et al., 1996; Bouvet et al., 2011). The Lewis number, which is defined as the ratio of the mixture thermal diffusivity to the mass diffusivity of the deficient reactant, is generally considered an important parameter relevant to the flame tip opening phenomenon (Mizomoto and Yoshida, 1987). When the Lewis number of the unburned mixtures is less than 1, the flame burning intensity decreases at the tip, causing local quenching of the flame. The reignited flame above the main flame could possibly be due to the fuel unburned at the tip of the flame being reignited by radiation effects. Previous investigations have found that the flame tip opening phenomenon may appear on the very lean fuel side and the very rich fuel side (Mizomoto et al., 1985; Mizomoto and Yoshida, 1987). The Lewis number of the unburned mixtures in the present work with equivalence ratio and temperature variations were calculated referring to the method of literature (Mizomoto and Yoshida, 1987). As illustrated in Table 5, it is observed that the Lewis number decreases with increasing temperature and decreases with increasing equivalence ratio. All the flame tip opening phenomenon observed in this work occur with a Lewis number less than 1.

To investigate the sensitivity to the preheating temperature of the JP-10/air mixture, comparisons of measured and simulated laminar flame speeds for atmospheric pressure and for various preheating temperatures T = 360 K, 423 K, 453 K and φ = 0.7–1.2 are presented in Figure 5.

This shows that the laminar flame speed increases with increasing preheating temperature. The results calculated by using UCSD are generally higher than those calculated by the other two mechanisms and the measurements. The detailed mechanism of Hychem predicts a higher laminar flame speed than the skeletal mechanism. For low-temperature cases (T = 360 K, 423 K), the simulation using Hychem-skeletal and Hychem-detailed mechanisms overestimates the laminar flame speed compared with measurements. For higher preheating temperatures, the simulation produces a fairly close approximation of the measurements. In terms of discrepancy, the measurement results of this study are in good agreement with Hychem detailed mechanism and skeletal mechanism, and there is a large discrepancy compared with the predicted value of UCSD mechanism. Compared with the predicted value of UCSD mechanism, the absolute discrepancy is 10–20 cm/s and the relative discrepancy is 20–30%. In some data points with high equivalence ratio, the relative error is more than 30%. Other literatures also reported the great inconsistency with UCSD mechanism which may result from the overestimation of the sensitivity of cyclopentene oxidation reaction to flame speed (Zhong et al., 2022). Compared with Hychem skeletal mechanism, the absolute discrepancy is within 5 cm/s and the relative discrepancy is within 15%. The discrepancy between the experimental data and the predicted value of the mechanism at 360 K is relatively large. The measurement results reach a good consistency with predicted results at 453 K, the absolute discrepancy is within 2 cm/s and the relative discrepancy is within 5%. Compared with Hychem detailed mechanism, the absolute discrepancy is within 8 cm/s and the relative discrepancy is within 15%. The points with large discrepancy are mainly concentrated in the measurement conditions with equivalence ratio of 0.7 and 1.2. The predicted value of detailed mechanism is in good agreement with the measured value at 453 K. The absolute discrepancy of most of the points is within 3 cm/s and the relative discrepancy is within 5%.

According to the power law correlation theory of temperature dependency (Metghalchi and Keck, 1982; Varea et al., 2013) S L = S L 0 ( T T 0 ) α , the laminar flame speed under higher temperatures can be expressed by a laminar flame speed at the reference conditions of temperature and pressure ( S L 0 ) and multiplied by correction factors displaying the temperature dependencies. As shown in Figure 5. (d), the laminar flame speed is plotted as a function of the preheating temperature using log-log scales, while straight lines for all of the equivalence ratios tested are observed which illustrates the temperature dependence on the laminar flame speed. The power exponent α ( φ ) is determined from the slope of the straight lines in Figure 5. (d). By fitting the slope of the Log(S_L)-Log (T/T₀) lines with the third-order polynomial expression Eq. 5, the equivalence ratio dependence coefficients are calculated and listed in Table 6.

With the experimental results obtained in the present work, an empirical temperature dependency correlation was proposed by using the power law equation Eqs. 3–5, where   S L 0 is the flame speed at T = 360 K, p = 0.1 MPa. S L = S L 0 ( T T 0 ) α (3) S L 0 ( φ ) = S L 0 , φ = 1 + S L 0,1 ( φ − 1 ) + S L 0,2 ( φ − 1 ) 2 + S L 0,3 ( φ − 1 ) 3 + S L 0,4 ( φ − 1 ) 4 (4) α ( φ ) = α 0 + α 1 ( φ − 1 ) + α 2 ( φ − 1 ) 2 + α 3 ( φ − 1 ) 3 (5)

Sensitivity analysis is conducted to identify the important reactions related to JP-10/air laminar flame speed, and fourteen reactions with the largest magnitude of sensitivity coefficient are presented in Figure 6. The Hychem detailed mechanism is chosen in the premixed flame simulation for ϕ = 0.8, 1.0, and 1.2 at 1 atm and T = 360 K, 423 K, and 453 K. The normalized sensitivity coefficient ( S i ) of the laminar flame speed is calculated using the following formula: S i = A i S L ∂ S L ∂ A i (6) where   A i is the pre-exponential factor of the i^th reaction. The positive sensitivity indicates that the reactions increase the flame speed, and the negative sensitivity indicates that the reactions slow down the flame speed.

The sensitivity coefficient of most reactions decreases with increasing reaction temperature. Fourteen reactions with the largest magnitude of sensitivity coefficient show that the chain branching reaction H+O₂ = O+OH and chain propagation reaction CO+OH = CO₂+H dominate the chemistry of flame propagation under all conditions studied in the present work. On the other hand, the chain termination reactions H+OH+M = H₂O+M, H+O₂ (+M) = HO₂(+M) and C₅H₅+H (+M) = C₅H₆(+M) play an important role in the slowing the flame speed. The H+O₂ = O+OH reaction is the most sensitive reaction to the flame propagation speed. The formation of the reaction product OH largely affects another reaction with a large sensitivity coefficient, CO+OH = CO₂+H, which in turn affects the rate at which fuel oxidizes to the final product CO₂. At the same time, the competitive reaction of H+O₂ = O+OH, H+O₂ (+M) = HO₂(+M) slows the production of OH, and the competitive reaction of CO+OH = CO₂+H, H+OH+M = H₂O + M hinders the oxidation of CO, so these two reactions with large negative sensitivity coefficients reduce the flame propagation speed. In addition, the reactions C₅H₆+H=C₅H₅+H₂, C₅H₅+H (+M) = C₅H₆(+M) and C₅H₆+H=C₅H₅+H₂ related to the pyrolysis products of JP-10 promote and retard the flame propagation speed, respectively.

Figure 7 gives the simulation results of the 1-D flame structure. The adiabatic flame temperature and the mole fraction of some major species related to flame propagation chemistry show the flame structure of JP-10 at initial temperatures of 360 K, 423 K, and 453 K and a pressure of 1 atm. Under the lean fuel condition of equivalence ratio φ = 0.8, the mole fraction of CO is significantly lower than that under stoichiometric ratio conditions and under rich-fuel conditions, and the mole fraction difference at chemical equilibrium between CO₂ and CO reaches a level close to 0.1, which indicates that CO has been fully oxidized and to a certain extent also illustrates the full combustion of JP-10 fuel.

As the equivalence ratio increases, the mole fraction difference at chemical equilibrium between CO₂ and CO continues to shrink. Under the condition of equivalence ratio φ = 1.2, the peak concentration of CO is even higher than the peak concentration of CO₂, which indicates that CO has not been fully oxidized. The change of CH₂O mole fraction with temperature is not significant, but the change trend with equivalence ratio is the same as that of flame speed, which first increases and then decreases. From the previous laminar flame speed sensitivity analysis, it can be seen that H+O₂ = O+OH and CO+OH = CO₂+H are the two most sensitive reactions regarding the laminar flame speed. Therefore, under rich fuel conditions, the relative shortage of O₂ and the relative excess of CO may lead to a decrease in reactivity, which may be one of the reasons for the decrease in laminar flame speed. The flame combustion temperature increases with increasing equivalence ratio, but in the process of increasing the equivalence ratio from 1 to 1.2, the change in the adiabatic flame temperature is not obvious, which also reflects the temperature dependence of the laminar flame speed. Within the range of equivalence ratios φ = 0.7–1.2, the increase in laminar flame speed is more obvious than that in the range of 1–1.2.

The measured ignition delay times of JP-10/O₂/Ar mixtures are shown in Figure 8, and the available values from the literature (Davidson et al., 2000; Wang et al., 2007) are also adopted for comparison. The ignition delay time of JP-10 decreases markedly with increasing temperature, and the τ peak decreases from 2016 μs at 1221 K to 185 μs at 1422 K. Our measurements have a similar temperature dependence but give lower values in comparison to those of Davidson et al. (Davidson et al., 2000). At temperatures of 1249–1381 K, our measured ignition delay times agree well with the results of Wang et al. (Wang et al., 2007). In the investigated temperature range, however, the reported ignition delay times of JP-10 do not match well with each other. Due to the varying industrial standards, production processes, and preservation conditions, the constituents of JP-10 are usually slightly different. To confirm the reliability of the ignition delay times, some points are repeatedly measured at least two times, and the results indicate that our measurements are credible.

In this work, the detailed mechanism of the hychem is selected to simulate the ignition process of JP-10. The reaction model is a closed homogeneous batch reactor. In the simulation calculation, the time corresponding to the intersection of the tangent at the maximum slope of the temperature curve and baseline is defined as the ignition time.

Figure 9 shows the measurement results of the ignition delay time of JP-10 and the numerical calculation results using the detailed mechanism of Hychem. Figure 9 shows that the ignition delay time decreases with increasing premixed gas temperature, and the premixed gas needs a longer time to absorb heat at lower temperatures to reach the ignition conditions. As mentioned above, the experimental data obtained in this paper show an overall smaller trend compared with the experimental data under similar working conditions in the literature, and it is also lower compared with the numerical calculation results, which may be related to the differences in the definitions of ignition delay time and experimental samples.

To further explore the key reactions leading to the ignition process, sensitivity analysis was carried out on the basis of the Hychem mechanism. The sensitivity coefficient is defined as S = τ ( 2.0 k i ) − τ ( 0.5 k i ) 1.5 τ ( k i ) (7) where τ is the ignition delay time and k_i is the pre-exponential factor of the ith reaction. In this paper, the positive sensitivity coefficient indicates that it can inhibit the ignition process, and the negative sensitivity coefficient indicates that it can promote the ignition process. Figure 10 shows the key sensitive reactions of JP-10/O₂/Ar mixture ignition at T = 1478 K, p = 3.6 atm and φ = 1.0.

As shown in Figure 10, the chain branching reaction H+O₂ = O+OH dominates the ignition chemical process of JP-10. One of the fourteen most important reactions is related to JP-10 fuel. R4 involves the cracking of fuel into C₂, C₃, and C₅ low-carbon molecules, while other key reactions are related to these low-carbon molecules. The reaction of C₃H₃ and C₂H₂ to produce C₅H₅ has a significant impact on the ignition process, and the second largest negative sensitivity coefficient is given. Small radical reactions such as OH have a significant impact on the ignition delay time and participate in most of the fourteen key radical reactions. In addition, the bonding reaction of C₃H₅ and C₅H₅ absorbing H radicals can inhibit the ignition process.