Comparative Study on Autoignition Characteristics of

Mar 18, 2015 - Ignition delay times were measured behind reflected shock waves for cyclohexane and methylcyclohexane at pressures of 1.1, 5.0, and 16...
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Comparative Study on Autoignition Characteristics of Methylcyclohexane and Cyclohexane Zemin Tian, Yingjia Zhang,* Feiyu Yang, and Zuohua Huang* State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, People’s Republic of China S Supporting Information *

ABSTRACT: Ignition delay times were measured behind reflected shock waves for cyclohexane and methylcyclohexane at pressures of 1.1, 5.0, and 16.0 atm, temperatures from 1075 to 1750 K, and equivalence ratios of 0.5, 1.0, and 2.0. Correlations of the ignition delay times were performed at the three equivalence ratios in Arrhenius form. Measured ignition delay times showed fairly good agreements with previous data. Several accepted mechanisms (JetSurF 2.0, Wang et al., Sirjean et al., Orme et al., and Silke et al.) were used to simulate the experimental measurements and conduct flux analyses and sensitivity analyses. Comparisons of the simulations and analyses between the mechanisms give insights into the oxidation of methylcyclohexane and cyclohexane. Methylcyclohexane has an evidently longer ignition delay time than cyclohexane at ϕ = 0.5, while its ignition delay time becomes comparative to those of cyclohexane at ϕ = 1.0. Chemical kinetic interpretation is given for this observation.

1. INTRODUCTION Numerous studies on ignition and oxidation of naphthenes have been carried out in various conventional experimental approaches, such as a rapid compression machine (RCM), shock tube, and jet-stirred reactor (JSR). A significant motivation is that naphthenes are important chemical components in practical fuels. Diesel fuel, for instance, contains cyclic alkanes up to 40% by weight.1,2 Particularly, Canadian oilseed-derived fuels have a higher concentration of them.3 Besides, naphthenes are able to raise the formation of the aromatic pollutants and the soot emission. Specially, cyclohexane (CH) and methylcyclohexane (MCH) have received much attention. Numerous experimental investigations were performed. Serinyel et al.4 tested main products for CH at atmospheric pressure with temperatures of 500− 1100 K and ϕ = 0.5, 1.0, and 2.0 in a JSR. A new mechanism was developed to well reproduce the experimental results. Wang et al.5 identified more than 30 intermediate species for the pyrolysis of CH at a temperature from 950 to 1520 K. Daley et al.6 measured the ignition time of the CH/air mixture at equivalence ratios of 1.0, 0.5, and 0.25, pressures of 15.0 and 50.0 atm, and temperatures ranging from 847 to 1379 K. In addition, a recent experimental and modeling study was made by Pitz et al.7 to track the main products of aromatics, cyclic species, and soot precursors in a MCH flame. Mittal et al.8 investigated the autoignition of MCH in a RCM at equivalence ratios of 0.5−2.0 and pressures of 15.1 and 25.5 atm with temperatures from 680 to 905 K. Vasu et al.9 measured the ignition delay times for MCH at ϕ = 1.0 with the pressures of 20 and 45 atm, covering temperatures over 795−1100 K. Vanderover and Oehlschlaeger10 obtained ignition delay times for MCH in a shock tube at temperatures ranging from 881 to 1319 K for equivalence ratios of 0.25, 0.5, and 1.0. Furthermore, many acceptable mechanisms have been developed for CH. Buda et al.11 developed a model of CH oxidation containing 513 species and 2446 reactions in the aid of a © XXXX American Chemical Society

computer program. This model well reproduced the ignition delay times obtained in a RCM at temperatures of 650−950 K and pressures of 7−14 atm and the profiles of products measured in a JSR from 750 to 1050 K at 10 atm from published literature.12 With the help of a computer package, which can automatically generate a kinetic mechanism and quantum chemical calculations, Sirjean et al.13 made a kinetic mechanism of 372 species and 1629 reactions for CH. They measured the ignition delay time for CH/O2/Ar mixtures containing 0.5 or 1% fuel at temperatures from 1230 to 1840 K, pressures of 7.3−9.5 atm, and equivalence ratios of 0.5, 1.0, and 2.0 to validate their model. Besides, Wang et al.14 built a kinetic model to simulate their results of pyrolysis of CH in a plug flow reactor. Over 30 species, including radicals and stable intermediate products, were identified at 0.04 atm with temperatures from 950 to 1520 K. As for MCH, there are mechanisms available as well. Orme et al.15 assembled a chemical mechanism of MCH oxidation based on the previous reaction scheme16 using the rules for reaction rate constants provided by Curran et al.17,18 The simulations by this model for the ignition delay times for MCH/O2/Ar mixtures at 1−4 atm, 1200−2000 K, and ϕ = 0.5, 1.0, and 2.0 and the species profiles at 1 atm and 1058−1092 K agreed well with the experimental results. Pitz et al.7 combined new low-temperature chemistry with Orme’s mechanism to create a new kinetic model for MCH, which was used to predict the ignition delay times for the stoichiometric mixture of MCH/O2 and three diluents (100% Ar, 100% N2, and 100% N2) at 10, 15, and 20 atm with temperatures ranging from 650 to 1000 K. The predictions were in fairly good consistency with the experimental results obtained in a RCM. Additionally, Wang et al.14 built a kinetic model with 249 species and 1570 reactions for MCH. They validated their mechanism with pyrolysis and Received: December 4, 2014 Revised: March 18, 2015

A

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Energy & Fuels flame intermediates measured in their experiment and data from the literature. One goal of this work is to further validate these enormous mechanisms for CH and MCH with ignition delay time measured in a shock tube. By analyzing the similarity and difference among the mechanisms, we aim to deepen the understanding of oxidation of CH and MCH and to assess the performances of different mechanisms. In addition, the comparison in ignition delay time between CH and MCH is also useful to understand the oxidation chemistry. Hong et al.19 compared ignition delay time among CH, MCH, and n-butylcyclohexane (BCH). It is found that MCH has a longer ignition delay time than CH. They suggested that the unique molecular structure of CH significantly facilitates the regeneration of the H radical, accounting for the higher activity of CH oxidation. However, the influences of physical characteristics, such as equivalence ratio, pressure, and temperature, were not reported. In this work, the effect of the equivalence ratio on the comparison is investigated. To compare performances of acceptable oxidation mechanisms of CH and MCH and to discuss the influence of equivalence ratios, a wide range of ignition delay times were measured for CH and MCH in a high-temperature shock tube. For CH, measurements were carried out at the equivalence ratios of 0.5, 1.0, and 2.0 and the pressures of 1.1 and 5.0 atm, with fuel mole fractions of 0.5% (for ϕ = 0.5 and 1.0) and 1.0% (for ϕ = 2.0), with temperatures ranging from 1075 to 1750 K. In addition, the tested pressure was extended to 16 atm for the case of ϕ = 1.0. The tested conditions for MCH are identical to those for CH, except that the ignition delay time of another mixture of 1% MCH/10.5% O2/88.5% Ar was measured to compare to published data.

Table 1. List of Detailed Compositions of Fuel Mixtures for Both CH and MCH mix number

ϕ

CH (%)

1 2 3 4 5 6 7

0.5 1.0 2.0 0.5 1.0 1.0 2.0

0.5 0.5 1.0

MCH (%)

O2 (%)

Ar (%)

0.5 0.5 1.0 1.0

9 4.5 4.5 10.5 5.25 10.5 5.25

90.5 95 94.5 89 94.25 88.5 93.75

P (atm) 1.1, 1.1, 1.1, 1.1, 1.1, 1.0 1.1,

5.0 5.0, 16.0 5.0 5.0 5.0, 16.0 5.0

Figure 1. Typical profile of endwall pressure and OH* emission time histories recorded during a CH ignition experiment at ϕ = 1.0, 1250 K, and 16.0 atm. The definition of ignition delay time is presented in this figure.

2. EXPERIMENTAL SECTION The measurements were performed in a shock tube with a 4.0 m driver and 5.3 m driven section, separated by a double polycarbonate diaphragm. A photomultiplier (Hamamatsu, CR131) is installed at the endwall to capture the chemiluminescence emission of OH*. Four pressure transducers (PCB 113B26) are located along the end part of the driven section at a constant distance to measure local incident shock wave velocities. An additional pressure transducer (PCB 113B03) is fixed at the endwall to obtain the shockwave pressure there. The temperature of the reflected shockwave is calculated with the local shockwave velocities, with the help of the reflected shock model in the software Gaseq.20 A detailed description has been made in previous studies.21,22 Helium and nitrogen of 99.999% purity were proportionately mixed as driving gas, which was charged into the driver section of the shock tube. Test mixtures were prepared in a 128 L stainless-steel tank. The fuels (CH and MCH) with purities of 98% were injected, and then oxygen and diluent (argon) are manometrically charged into the tank. At least 12 h of blending allowed the mixture to reach homogeneity. The purities oxygen and argon were 99.995%. The partial pressure of fuels was ensured below a half of the vapor pressure (13 kPa for CH and 5.3 kPa for MCH) to minimize the possibility of condensation. The detailed compositions of the tested mixtures are listed in Table 1. Figure 1 shows a typical profile of endwall pressure and OH* emission obtained in a CH ignition experiment. The definition of ignition delay time in this study is provided. It is the interval between the arrival of the incident shock wave at the endwall and the extrapolation of the steepest rise in the endwall OH* chemiluminescence signal to the zero baseline. The largest uncertainty of ignition delay time is estimated as 15%, and the error bars are added in Figures 4 and 5. The detail of determination is given in the Supporting Information. Numerical simulations of ignition delay time are carried out using Senkin code23 in the Chemkin II package.24 The onset of ignition in the simulation is defined as the maximum rate of temperature rise

(dT/dt)max. There is little difference in the ignition delay times calculated on the basis of these two definitions.

3. RESULTS AND DISCUSSION 3.1. Correlation and Comparison to Previous Data. Table 2 shows all of the measured data in this study. They can be correlated for the three equivalence ratios using an Arrhenius formula:25 τ = Ap−n exp(Ea/RT), where τ is the ignition delay time in microseconds, p is the reflected shock pressure in atmospheres, T is the temperature in kelvins, R is the universal gas constant of 1.986 × 10−3 kcal mol−1 K−1, and Ea is the activation energy in kilocalories. The results are shown as follows. For CH ϕ = 0.5:

τ = 7.67 × 10−4p−0.58 exp(34.2/RT )

(1)

ϕ = 1.0:

τ = 3.11 × 10−3p−0.59 exp(32.8/RT )

(2)

ϕ = 2.0:

τ = 4.87 × 10−2p−0.58 exp(26.7/RT )

(3)

ϕ = 0.5:

τ = 7.86 × 10−4p−0.51 exp(35.0/RT )

(4)

ϕ = 1.0:

τ = 1.91 × 10−3p−0.59 exp(34.7/RT )

(5)

ϕ = 2.0:

τ = 1.19 × 10−2p−0.61 exp(31.0/RT )

(6)

For MCH

It can be seen that only an ignorable change of pressure-scaling parameters is observed as the equivalence ratio changes for CH, B

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Table 2. Measured Ignition Delay Times of (a) CH and (b) MCH Mixtures (Table 1) in Units of atm, K, and μs for p, T, and τ (a) CH mixture 1

mixture 2

mixture 2

mixture 3

p

T

τ

p

T

τ

p

T

τ

p

T

τ

1.06 1.06 1.08 1.08 1.04 1.08 1.08 0.97 1.06 5.01 5.10 5.07 5.06 5.00 4.98 4.96 5.09

1321 1387 1477 1537 1236 1191 1137 1456 1290 1352 1447 1281 1199 1112 1072 1279 1157

283 207 78 56 876 1570 2569 116 437 82 37 270 544 1604 2247 244 1049

1.09 1.09 1.06 1.05 1.09 1.03 1.08 1.08 1.00 1.07 1.07 4.99 5.07 4.96 5.17 4.97 5.14

1262 1331 1379 1447 1568 1165 1231 1274 1533 1618 1476 1377 1299 1201 1159 1470 1568

1575 702 460 255 112 3457 2017 1417 128 78 278 184 455 1168 2095 76 39

5.11 5.13 5.07 16.2 14.0 15.1 15.7 16.4 16.8 16.3 15.9 15.7 15.7

1267 1333 1451 1355 1184 1268 1403 1247 1280 1144 1239 1295 1521

618 351 98 112 572 249 83 368 278 877 369 222 32

1.10 1.07 1.02 1.13 1.09 0.99 1.00 1.09 1.05 4.95 5.17 5.05 5.09 5.01 5.01 5.12 5.14 5.11

1379 1481 1551 1773 1646 1240 1210 1341 1302 1310 1432 1506 1586 1247 1175 1137 1385 1225

885 449 329 72 159 2059 2335 1242 1714 610 228 127 84 904 1782 2507 317 1160

τ

p

T

τ

1404 1493 1243 1254 1179 1137 1326 1285 1188

97 47 532 451 962 1346 179 398 816

mixture 6 1254.1 1307.5 1358.3 1439.7 1502.5 1545 1404.9 1407.1 1386.2 1448.1

1508 1014 619 263 137 106 270 308 409 226

1.04 1.05 1.13 1.10 1.12 1.04 1.09 1.07 1.04 1.09 1.06 1.00 5.33 5.12 5.08 5.14 4.89 5.30 5.10 5.16 5.11

1381 1503 1691 1724 1663 1440 1338 1291 1530 1620 1258 1243 1282 1190 1129 1242 1287 1441 1500 1586 1357

944 435 106 117 111 617 1531 1921 328 173 2543 3189 1047 2175 3635 1536 859 229 135 65 464

(b) MCH mixture 4

mixture 5

mixture 5

p

T

τ

p

T

τ

p

1.08 1.10 1.05 1.08 1.05 1.09 1.05 1.09 1.07 1.10 1.09 1.05 4.75 5.09 5.10 4.94 5.08 4.97 5.12

1334 1418 1453 1546 1481 1536 1236 1150 1175 1309 1525 1343 1306 1227 1148 1075 1435 1377 1122

483 189 130 50 125 61 1270 3124 2403 705 73 380 286 745 1739 2905 70 124 2256

1.10 1.10 1.06 1.12 1.13 1.08 1.06 1.08 1.04 1.10 1.08 1.04 5.09 4.89 5.04 5.05 5.31 5.11 4.95 4.96 5.12 5.08 15.2 14.8 14.0

1264 1327 1366 1479 1546 1196 1270 1416 1510 1615 1242 1577 1307 1348 1225 1439 1552 1149 1370 1251 1481 1184 1358 1212 1203

1734 1156 713 242 125 3208 1941 449 207 78 2191 96 554 267 1554 140 54 2943 262 981 87 2216 170 563 461

14.8 15.9 17.6 16.7 16.0 16.7 15.8 15.8 15.5

1.13 1.09 1.08 1.21 1.02 1.18 1.03 1.17 1.17 1.02

T

mixture 7

longer ignition delay times (ϕ = 2.0) than fuel presented at ϕ = 1.0, which inclines to approach the ignition delay time at ϕ = 1.0 when the temperature drops, as shown in Figure 2. Just as stated by Curran et al.,18 reaction H + O2 ⇄ OH + H dominants the ignition at a high temperature, while reactions related to the HO2 radical become prominent at a low temperature and high pressure. Therefore, the reactivity of oxidation is favored by a high concentration of fuel as the temperature falls. Extensive measurements of the ignition delay time of CH and MCH have been conducted in shock tubes. Hong et al.19

but the pressure-scaling factor increases with the increase in the equivalence ratio for MCH. This is different from the observation by Daley et al.6 for CH/air ignition and by Vanderover and Oehlschlaeger10 for MCH/air. They reported that the dependence of pressure declined from 0.99 at ϕ = 1.0 to 0.66 at ϕ = 0.25. This reason is that a high fuel concentration can promote the global reactivity and enhance the pressure dependence of ignition delay time. Additionally, the activation energy at ϕ = 2.0 is obviously lower than that at ϕ = 1.0 and 0.5, especially for CH. Generally, the fuel-rich mixture exhibits C

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Figure 2. Experimental measurements and correlations of CH at ϕ = 1.0 and 2.0 and p = 1.1 and 5.0 atm. Solid lines, correlation; symbols, measurements.

provided the data of ignition delay times of CH, MCH, and BCH at 1.5 and 3.0 atm and equivalence ratios near 1.0 and 0.5 with a fixed O2 concentration of 4%, in a temperature range of 1280−1480 K. Although there is a slight difference in test conditions, the current experiments of CH and MCH at 1.1 atm and ϕ = 1.0 were compared to those of Hong et al. at 1.5 atm and ϕ = 1.0, as shown in Figure 3a. It can be seen that both of them are concordant quite well, although a slightly higher ignition delay time at high temperatures in this work is observed. Orme et al.15 developed and validated a new hightemperature mechanism of MCH using the ignition delay times of 1.0% MCH/O2/Ar at 1.0−4.0 atm and ϕ = 0.5−2.0. Figure 3b depicts the comparison of ignition delay time data between the current study and Orme et al.15 near 1.0 atm for MCH/O2/Ar mixtures. As expected, the fairly good agreements are seen again. In addition, Sirjean et al.13 also measured ignition delay time for 0.5% CH/O2/Ar mixtures at 7.3−9.5 atm and ϕ = 0.5−2.0 to validate their CH oxidation mechanism. Unlike the direct comparison to the data of Hong et al. and Orme et al., we use expressions 1 and 2 to scale the data of this study at an average pressure of 8.4 atm to compare to those of Sirjean et al., as shown in Figure 3c. Although two sets of data show similar dependence of ignition on the temperature and global activation energy, there is a large discrepancy in ignition delay times between them. This may be caused by some different experimental conditions. 3.2. Comparison to Mechanism Predictions. Various kinetic models have been developed for CH and MCH, and they can perform fairly good predictions on the ignition and oxidation of CH and MCH. However, these kinetic mechanisms provide different interpretation on the details of dissociation of CH and MCH, causing different predictions of ignition delay time. In this study, the simulations are conducted for CH and MCH using several mechanisms, and further chemical analyses are then performed to deeply understand the oxidation process of CH and MCH. The following five mechanisms are considered: (1) JetSurF 2.0,26 developed by Wang et al. at University of Southern California, consists of 346 species and 2163 reactions. It is available for not only CH and MCH but also ethylcyclohexane (ECH), n-propylcyclohexane (PCH), and BCH because of comprehensive submechanisms of alkanes included in it. This mechanism is used to simulate ignition delay times of both CH and MCH. (2) Wang et al.

Figure 3. Comparison between the measured and previous data: (a) data for CH and MCH to those from Hong et al. at about 1.5 atm and ϕ = 1.0, (b) data for MCH to those from Orme et al. at 1 atm and ϕ = 1.0 and 2.0, and (c) correlation using current data to data from Sirjean et al. at about 8.4 atm and ϕ = 0.5 and 1.0.

mechanism,14 constructed using a high level of quantum calculation, has 1570 reactions and 249 species. It is used for prediction of ignition delay times of MCH and CH. (3) Sirjean et al. mechanism,13 which is created with the help of EXGAS software, is adopted for CH simulation. (4) Orme et al. mechanism,15 including 190 species and 904 reactions, is made with an analogy method for high-temperature oxidation of MCH. Here, it is employed to simulate MCH ignition. (5) Finally, D

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Figure 5. Ignition delay times for MCH/O2/Ar mixtures and predictions using JetSurF2.0,26 Silke et al.,27 Wang et al.,14 and Orme et al.13 mechanisms: (a) ϕ = 1.0, XMCH = 0.5%, and p = 1.1, 5.0, and 16 atm; (b) p = 1.1 atm: ϕ = 0.5, XMCH = 0.5%; ϕ = 2.0, XMCH = 1%; and (c) p = 5.0 atm: ϕ = 0.5, XMCH = 0.5%; ϕ = 2.0, XMCH = 1%.

Figure 4. Ignition delay times for CH/O2/Ar mixtures and predictions using JetSurF 2.0,26 Wang et al.,14 and Sirjean et al.13 mechanisms: (a) ϕ = 1.0, XCH = 0.5%, and p = 1.1, 5.0, and 16 atm; (b) p = 1.1 atm: ϕ = 0.5, XCH = 0.5%; ϕ = 2.0, XCH = 1%; and (c) p = 5.0 atm: ϕ = 0.5, XCH = 0.5%; ϕ = 2.0, XCH = 1%.

Silke et al.27 extend the MCH oxidation mechanism to low temperature and achieved a model of 1081 species and 4267 reactions. They also used the experimental data from the study of Lemaire et al.12 to test their model. This mechanism is used for MCH simulation here. In consideration of the non-ideal facility effect on ignition delay time, an average of 4.0% pressure rise rate is taken into account in all of the simulations using SENKIN/VTIM approach.28

Figure 4 shows the measured ignition delay times for CH/ O2/Ar mixtures at pressures of 1.1−16.0 atm and equivalence ratios of 0.5−2.0. The simulations were performed using three mechanisms: JetSurF 2.0,26 Wang et al. mechanism,14 and Sirjean et al. mechanism.13 It is seen that JetSurF 2.0 and Wang et al. mechanisms perform approximately good predictions under the tested conditions. However, the prediction of the Sirjean et al. E

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Figure 6. Comparison of ignition delay times between CH and MCH mixtures at p = 5 atm and ϕ = 0.5 and 2.0.

mechanism exhibits an evident deviation with those of other mechanisms as the temperatures decrease, especially for the fuel-lean mixture and high pressure. For instance, at 1180 K, the Sirjean et al. mechanism overpredicts the ignition delay time by 40% at 1.1 atm and 108% at 16 atm for the fuelstoichiometric mixture and by 40% at 1.1 atm and 102% at 5.0 atm for the fuel-lean mixture. It means that a high pressure and high oxygen concentration tend to worsen the prediction of the Sirjean et al. mechanism. The difference in some important fuel-related reactions should be responsible for the deviation and will be discussed below. Figure 5 compares the measured ignition delay times to the model simulation for MCH mixtures under similar test conditions to those used for CH mixtures. Four mechanisms are employed here. They are JetSurF 2.0,26 Silke et al.,27 Wang et al.,14 and Orme et al.15 mechanisms. It is found that all of them present good performance on modeling the experimental data under current test conditions. Because the MCH submechanism in the Silke et al. mechanism at a high temperature is identical to that of Orme et al., these two mechanisms represent quite similar simulations, especially at p = 5.0 atm, as shown in panels b and c of Figure 5. However, owing to the difference in reactions of small radicals, a higher prediction of the Silke et al. mechanism than that of the Orme et al. mechanism is observed at p = 1.1 atm. As for JetSurF2.0, while it can reproduce the experimental data at 1.1 and 5.0 atm for fuel-rich and -stoichiometric mixtures, underprediction is seen at 16.0 atm and fuel-lean mixtures. To clarify the quantitative difference of autoignition behavior between CH and MCH, we compare the ignition delay time of CH and MCH mixtures at equivalence ratios of 0.5 and 2.0 and pressure of 5.0 atm, as shown in Figure 6. The result indicates that MCH shows a distinctly longer ignition delay time than CH for fuel-lean conditions, whereas the ignition delay time of MCH becomes much closer to those of CH for fuel-rich conditions, even at the same temperature. 3.3. Flux Analysis. Flux analyses of CH and MCH oxidation were conducted at p = 5.0 atm, T = 1250 and 1450 K, and ϕ = 0.5 after 20% fuel consumption, as shown in Figures 7 and 8. The percentages of contribution to the consumption of the species on the source side of the arrow are determined by the ratio of the reaction rate of a certain pathway to the total consumption rate of this species at the moment of 20% fuel consumption. For CH, three mechanisms, JetSurF2.0,26 Wang et al.,14

Figure 7. Flux analyses for CH using Wang et al.,14 Sirjean et al.,13 and JetSurF2.026 mechanisms: ϕ = 0.5, p = 5.0 atm, and T = 1250 and 1450 K. Numbers are percent contribution to the consumption of the species on the source side of the arrow.

and Sirjean et al.13 mechanisms, were used to detail the reaction pathway, as shown in Figure 7. Initially, the CH molecule decomposes via unimolecular dissociation of the ring-opening reaction to form 1-hexene or biradical hex-1,6-yl or via H-abstraction to form cyclohexyl radicals. The cyclohexyl radical is then broken down to form a chain alkyl radical (1-hexen-6-yl) via the ring-opening reaction or produce a cyclohexene and a H radical via C−H cleavage. Subsequently, the 1-hexen-6-yl radicals are rapidly consumed according to two reaction pathways as follows: One is the formation reaction of the ethyl (C2H5) radical and 1,3-butadiene (C4H6) via β-scission. Another one is the formation reaction of the n-butenyl (C4H7) radical and ethylene (C2H4) via first isomerization and then β-scission. It is well-known that the C2H5 radical and C4H7 radical are important precursors of the H radical, and thus, their production can promote ignition. In general, JetSurF2.0 and Wang et al. mechanisms perform good agreement. For these two mechanisms, the majority of CH molecules are consumed by H-abstraction and each pathway contributes to essentially the same percentage for the consumption of species. In contrast, the Sirjean et al. mechanism presents a clear difference. The unimolecular decomposition of CH leads to f biradical according to the Sirjean et al. mechanism, while 1-hexene is generated according to the other two mechanisms. It should be noted that 14% of CH molecules consumed by unimolecular decomposition using the Sirjean et al. mechanism is considerably larger than that using other mechanisms at 1450 K, such as more than 15% of the consumption pathway of cyclohexyl radicals via C−H cleavage in the Sirjean et al. mechanism compared to the other two mechanisms. Nevertheless, the differences are not the main reasons causing the obviously different predictions of ignition delay time using the Sirjean et al. mechanism (Figure 4c). F

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Figure 8. Flux analyses for MCH using Wang et al.,14 Sirjean et al.,13 and JetSurF 2.026 mechanisms: ϕ = 0.5, p = 5.0 atm, and T = 1250 and 1450 K. Numbers are percent contribution to the consumption of the species on the source side of the arrow.

Hence, further analysis is necessary to investigate and discuss the difference using sensitivity analysis. For MCH, JetSurF2.0, Wang. et al., and Silke et al. mechanisms were used to describe the main reaction pathways, as shown in Figure 8. The MCH molecule is primarily dissociated by unimolecular decomposition, including breakoff of the methyl group, C−H cleavage, and ring-opening reaction. According to the Silke et al. mechanism, MCH can decompose to form the biradicals (not shown here in Figure 8), while the Wang et al. mechanism14 shows that MCH decomposes directly to C7 alkenes. However, this reaction pathway consumes only a few MCH and has limited influence on the MCH oxidation in Wang et al. and Silke et al. mechanisms. In contrast, JetSurF2.0 exhibits a significantly large portion (50% at 1250 K and 75% at 1450 K) of MCH via the ring-opening reaction to produce 1-heptene and 2-heptene. This is the main reason causing the underprediction of ignition delay times using JetSurF2.0 at an elevated pressure (Figure 5) Figure 9 shows the comparison of ring-opening reaction rate constants for MCH and CH (CH3cC6H11 = C7H14-2 and cC6H12 = C6H12) in JetSurF2.026 and Wang et al.14 mechanisms. It can be seen that JetSurF2.0 recommends a remarkably larger reaction rate constant for the reaction of CH3cC6H11 = C7H14-2 than Wang et al.; the latter calculated the rate parameters at the CBS-QB3 level. Moreover, it should be unreasonable that the rate constant of reaction CH3cC6H11 = C7H14-2 is so much greater than that of reaction cC6H12 = C6H12. The reason is that CH and MCH have similar strain energies29 and similar ring structure, and the rate constants of ring-opening reactions for CH and MCH should be comparable. Hence, the reaction rate for MCH ring-opening reactions recommended by JetSurF 2.0 might be too fast. To further understand the consumption pathways of MCH, flux analysis on H-abstraction reactions was performed at ϕ = 0.5, 5.0 atm, and 1450 K, as shown in Figure 10. It can be found that MCH-R2 and MCH-R3 are the major products (>25% for each pathway), while the percentage of pathways leading to MCH-R0, MCH-R1, and MCH-R4 is less than half of that leading to MCH-R2 and MCH-R3. The results agree

Figure 9. Comparison of rate constants between ring-opening reactions of MCH and CH in the Wang et al.14 and JetSurF 2.026 mechanisms.

well with those reported by Hong et al.19 Four methylcyclohexyl isomers make the mixture of the intermediate species complex. All five isomers can be consumed through β-scission. Because of molecular symmetry, MCH-R0, MCH-R1, and MCH-R4 produce only one type of chain alkyl radicals, i.e., 1-hepten-7-yl, 2-methylhexen-6-yl, and 5-methylhex-6-yl radicals, respectively, via ring-opening reactions. However, MCHR2 and MCH-R3 can form both straight and branched chain alkyl radicals, respectively. In addition, about 10% of MCH-R0 undergoes cyclic isomerization to form MCH-R4. A total of 13.3% of MCH-R1 and 30.5% of MCH-R4 generate the methylcyclohexenes via dehydrogenation. The chain alkyl radicals are then dissociated directly to form smaller radicals, such as C3H5, C2H5, C2H4, C2H3, and CH3 radicals. It is noted that the isomerization reactions play an important role in the consumption of chain alkyl radicals. The reason is manly that transition state species, which consist of a five-membered ring formed via a 1,4 internal H-shift, have only a small strain G

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Figure 10. Flux analysis on H-abstraction reactions for MCH using the Wang et al. mechanism:14 ϕ = 0.5, p = 5.0 atm, and T = 1450 K.

and R180 (C2H3 + O2 = CH2CHO + O) and enhance the reactivity of the reacting system. However, the H radical and HO2/OH radicals are consumed through reactions R946 (cC6H12 + H = cC6H11 + H2) and R20 (HO2 + OH = H2O + O2) and inhibit the oxidation. On the other hand, reactions producing radical precursors can expedite the CH ignition, such as reaction R883 (PXC6H11 = C4H7 + C2H4), because the important H-radical precursor C4H7 is generated via reaction R883. Furthermore, its competitor reaction R885 (PXC6H11 = SAXC6H11) inhibits the CH ignition. Through comparing the sensitivity coefficients at 1250 and 1450 K, it can be found that the change of the temperature only causes an insignificant effect. Figure 11b displays the result obtained using the Sirjean et al. mechanism. Although the importance of relevant reactions to small radicals is still highlighted, this mechanism reports that the reverse of reaction G56 (cC6H11 = cC6H10 + H) plays an important positive role in promoting ignition because of the generation of a high active H radical. Its competitive pathway, cyclohexyl forming 1-hexenyl (G55), has a large positive sensitive coefficient, suggesting a strong inhibiting effect on ignition. This is obviously different from that presented in the Wang et al. mechanism.14 In Figure 11a, the reactions of cyclohexyl producing 1-hexenyl and cyclohexene/H radical are not displayed and the decomposition reactions of 1-hexenyl (R883 and R885) have large sensitivity coefficients. It implies the importance of production of 1-hexentyl instead of cyclohexene/H radical by cyclohexyl. This is different from what was

energy. Moreover, a comparison of the percentage of pathways between T = 1250 and 1450 K shows that the effect of temperatures is limited in this range. 3.4. Sensitivity Analysis. To interpret the difference between Sirjean et al. and Wang et al. mechanisms for predicting CH ignition and determine the important chemical reactions for oxidation of CH, sensitivity analysis of ignition delay times was performed for the CH/O2/Ar mixture at ϕ = 0.5, p = 5.0 atm, and T = 1250 and 1450 K using Sirjean et al. and Wang et al. mechanisms. The sensitivity coefficient is defined as S=

τ(2.0ki) − τ(0.5ki) 1.5τ(ki)

where τ is the ignition delay time, ki is the rate constant for the ith reaction, and S is the sensitivity coefficient. A positive value of S indicates a global inhibiting effect on reactivity, while a negative value of S means a promoting effect. Figure 11 shows the most sensitive reactions for CH ignition. It can be seen that reaction H + O2 = OH + O is always dominant because it is the most important chain-branching channel at a high temperature. According to the Wang et al. mechanism14 (Figure 11a), the reactions producing small active radicals generally promote the oxidation of CH molecules, while reactions consuming active radicals inhibit the ignition. For instance, the oxygen atom and hydroxyl radical can be formed through the reactions R99 (CH3 + HO2 = CH3O + OH) H

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of predictions between the Sirjean et al. mechanism and the modified mechanism. It can be clearly seen that the numerical ignition delay time decreases significantly and better predictions are presented when using the modified mechanism. It is thus inferred that the inadequate CH submechanism in the Sirjean et al. mechanism is mainly responsible for the failed prediction. In addition, sensitivity analysis of ignition delay times was also carried out using the Wang et al. mechanism for MCH at 5.0 atm and 1250 and 1450 K, as shown in Figure 13. The

Figure 13. Sensitivity analysis of MCH at ϕ = 0.5, p = 5 atm, and T = 1250 and 1450 K using the Wang et al. mechanism.14 The normalized sensitivity coefficient of reaction H + O2 = O + OH is divided by 3.

result indicates that the reactions relevant to small radicals still dominate the ignition and oxidation of MCH. However, the reactions associated with the resonant ally radical (R349, aC3H5 + H (+M) = C3H6 (+M); R354, C3H6 + H = aC3H5 + H2) have large positive sensitivity coefficients and inhibit the overall reaction. It is due to the fact that the presence of a methyl group facilitates the production of propene and allyl radicals relative to CH. However, the temperature has generally little influence on essential reactions. Figure 14 shows the most sensitive reactions in oxidations of CH and MCH using the Wang et al. mechanism14 at ϕ = 2.0,

Figure 11. Sensitivity analysis of CH at ϕ = 0.5, p = 5.0 atm, and T = 1250 and 1450 K using the (a) Wang et al. mechanism14 and (b) Sirjean et al. mechanism.13 The normalized sensitivity coefficient of reaction H + O2 = O + OH is divided by 3.

Figure 12. Comparison between measured and simulated results. Symbols, experimental data; dot-dash line, Sirjean et al. model; and solid line, modified model.

reported by the Sirjean et al. mechanism. It is implied that the submodel of CH oxidation in the Wang et al. mechanism is different from that in the Sirjean et al. mechanism. We modified the Sirjean et al. mechanism by replacing its CH submodel with that of the Wang et al. mechanism. The reactions used for substitution are listed in Table 3. Figure 12 shows the comparison

Figure 14. Sensitivity analysis of CH and MCH at ϕ = 2.0, p = 5.0 atm, and T = 1450 K using the Wang et al. mechanism.14 The normalized sensitivity coefficient of reaction H + O2 = O + OH is divided by 3. I

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Energy & Fuels Table 3. Reactions for CH Oxidation from the Wang et al. Mechanism,14 Which Replace Those in the Sirjean et al. Mechanism13 number

reaction

1 2 3 4 5 6

cC6H12 + H = cC6H11 + H2 cC6H12 + CH3 = cC6H11 + CH4 cC6H12 + OH = cC6H11 + H2O cC6H12 + O = cC6H11 + OH cC6H12 + O2 = cC6H11 + HO2 cC6H11 = PXC6H11 PLOG/1.0 PLOG/10.0 PLOG/100.0 cC6H11 = cC6H10 + H PLOG/1.0 PLOG/10.0 PLOG/100.0 PXC6H11 (+M) = C4H7 + C2H4 (+M) low

7

8

9

PXC6H11 (+M) = SAXC6H11 (+M) low

10

SAXC6H11 (+M) = C4H6 + C2H5 (+M) low

A 2.70 × 1010 9.06 × 100 5.85 × 105 2.58 × 106 2.40 × 1014 1.26 × 1022 2.59 × 1032 2.07 × 1041 5.79 × 1044 8.38 × 1020 5.73 × 1032 1.37 × 1043 7.21 × 1047 3.98 × 1012 3.30 × 10−43 Troe, −13.59, 214, 28, 50000.0 1.55 × 102 1.50 × 10−30 Troe, −13.59, 214, 28, 50000.0 3.39 × 1011 4.00 × 10−42 Troe, −18.50, 246, 28, 50000.0

1450 K, and 5.0 atm. In comparison to the case at ϕ = 0.5, no significant difference is observed. Hence, there is little change in the major reactions with the change in the equivalence ratio. In Figure 6, it can be seen that CH has evidently a shorter ignition delay time than MCH for a fuel-lean mixture, while CH and MCH have comparative ignition delay times for a fuel-rich mixture. It is due to the fact that sufficient oxygen in the fuellean mixture can largely motivate the reaction: H + O2 = OH + O, leading to abundant small radicals of OH and O. They are in favor of consumption of intermediate hydrocarbon species. As a result, ignition is promoted. CH is able, as analyzed before, to release more H radical during its decomposition than MCH. Hence, more active radicals can be produced in a fuel-lean mixture for CH. Thus, a much shorter ignition delay time of CH is shown at ϕ = 0.5. However, at ϕ = 2.0, there are excessive intermediate species, requiring more small radicals, and HO2 becomes very important, which weakens the effect of the production of the H radical. As a result, the advantage of producing more H radical during CH decomposition is suppressed, resulting in comparative ignition delay times of CH and MCH.

n

Ea

1.39 3.46 2.45 2.60 0.00 −3.85 −6.32 −8.51 −9.15 −3.63 −6.47 −9.02 −9.98 0.12 18.35

8229 5480 −1164 2565 47590.0 22627 32020 40814 46530 23771 34206 44242 51272 27571.6 −602.5

2.83 14.56

15566.2 −602.4

0.66 18.05

32262.9 −602.6

fuel-lean mixture when using the Sirjean et al. mechanism. Flux analysis and sensitivity analysis of the ignition delay time are carried out using these three mechanisms to understand the oxidation of CH and MCH. Both CH and MCH decompose mainly through H-abstraction reactions, and these reactions show a large positive sensitivity coefficient because they consume active radicals, such as H and OH radicals. JetSurF2.0 reports differently that a large part of MCH undergoes unimolecular decomposition to form alkenes. It is due to the corresponding reaction rates being too high. The ignition delay time of MCH is longer than CH for a fuellean mixture. However, a low oxygen concentration tends to cut down the tendency, leading to similar ignition delay times of CH and MCH. It is attributed to the fact that CH can generate more H radical than MCH. In the fuel-lean mixture, sufficient oxygen motivates H + O2 = OH + O. This can quickly consume the intermediate species. In a fuel-rich mixture, excessive fuels consume the active radicals and HO2 becomes dominant. As a result, the predominance of CH is suppressed.

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ASSOCIATED CONTENT

S Supporting Information *

4. CONCLUSION In this study, ignition delay times for MCH and CH are measured at pressures of 1.0−16.0 atm, equivalence ratios of 0.5−2.0, and temperatures of 1100−1650 K in a shock tube. A comparison to the previous data in similar conditions shows fairly agreement to experimental data. Correlations are also made for CH and MCH at three equivalence ratios. The dependence upon pressure is around 0.58, and the perceivable decrease in activity energy for a fuel-rich mixture is ascribed to stimulation of the HO2 radical at a low temperature. Several current mechanisms are adopted to reproduce the experimental results. The CH submechanism in the Sirjean et al. mechanism13 is different from the Wang et al.14 and JetSurF2.026 mechanisms, leading to overprediction of the ignition delay time for a

Determination of uncertainty of ignition delay time. This material is available free of charge via the Internet at http:// pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Authors

*Telephone: 86-29-82665075. Fax: 86-29-82668789. E-mail: [email protected]. *Telephone: 86-29-82665075. Fax: 86-29-82668789. E-mail: [email protected]. Notes

The authors declare no competing financial interest. J

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ACKNOWLEDGMENTS This work is supported by the National Natural Science Foundation of China (51206132 and 91441203) and the National Basic Research Program (2013CB228406). Authors also appreciate the funding support from the Fundamental Research Funds for the Central Universities and State Key Laboratory of Engines (SKLE201305).

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