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Shock Tube and Kinetic Modeling Study of Cyclopentane and Methylcyclopentane Zemin Tian, Chenglong Tang,* Yingjia Zhang, Jiaxiang Zhang, and Zuohua Huang* State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Xi’an 710049, People’s Republic of China S Supporting Information *

ABSTRACT: Ignition delay times for 1% cyclopentane/O2 and 0.833% methylcyclopentane/O2 mixtures diluted by argon were measured behind reflected shock waves at pressures of 1.1 and 10 atm, with equivalence ratios of 0.577, 1.0, and 2.0, and in the temperature range from 1150 to 1850 K. Submechanisms for cyclopentane and methylcyclopentane were developed and added to the JetSurF2.0 mechanism for the kinetic interpretation of cyclopentane and methylcyclopentane oxidation chemistry at the high temperature region. Simulations with the model exhibit fairly good agreements with the measured ignition delay times of both cyclopentane and methylcyclopentane under all tested conditions. Cyclopentane shows longer ignition delay time than methylcyclopentane, especially for the fuel-lean mixture. Reaction pathways and sensitivity analyses were conducted to get insights into the oxidation process of cyclopentane and methylcyclopentane. Then, three factors are given for the effect of a cyclic ring and substitution of a methyl group. Substitution of a methyl group weakens the C−C bond to motivate fuel unimolecular decomposition. The shape of the cyclic ring determines the chain alkyl radicals, affecting regeneration and accumulation of H radical. The presence of a methyl group also leads to different alkyl radicals.

1. INTRODUCTION The depletion of fossil fuels and increased public concerns on air pollution require clean and efficient combustion techniques for various fuel-burning setups such as internal combustion engine, gas turbine, and boiler. A fundamental work to achieve precise control of combustion is to understand the oxidation of components of practical fuels. Naphthenes are important components of liquid fuels. There is 40% by weight of this group of hydrocarbons in diesel fuels and more than 20% by volume in jet fuels.1−3 They are also prone to forming aromatic pollutants and polycyclic aromatic soot precursors.4 Hence, it is necessary to investigate the oxidation of naphthenes. The oxidation and pyrolysis of cycloalkanes with a sixmembered ring have been extensively studied in a shock tube, a rapid compression machine (RCM), and a jet-stirred reactor (JSR), etc., over a wide range of pressures, temperatures, and equivalence ratios (ϕ).5−8 Specifically, Lemaire et al.6 measured the ignition delay time and concentration−time profiles of intermediate species during oxidation of cyclohexane (CH) as well as of cyclohexene and cyclohexa-1,3-diene diluted in air at ϕ = 1.0. The experiment was performed in a RCM between 600 and 900 K and between 7 and 14 atm to identify the pathways that lead to benzene formation. Recently, Serinyel et al.8 detected 34 reaction products for CH/O2/He mixtures of 0.667% fuel in a JSR at 1 atm, temperatures ranging from 500 to 1000 K, and equivalence ratios of 0.5, 1.0, and 2.0 with a residence time of 2 s and reported negative temperature coefficient phenomenon. Furthermore, alkylated cyclohexanes have received tremendous attention.9−17 The ignition delay times of methylcyclohexane (MCH) and ethylcyclohexane (ECH) diluted in air, for instance, were measured at 11−59 atm, 881−1319 K, and equivalence ratios of 0.25, 0.5, and 1.0 in a shock tube by Vanderover and Oehlschlaeger to extend the kinetic database.11 Husson et al.12 studied the oxidation of © 2014 American Chemical Society

ECH in a JSR under quasi-atmospheric pressure (800 Torr), at temperatures from 500 to 1100 K, and ϕ = 0.25, 1.0, and 2.0. 47 intermediate products were identified. Besides, autoignition delay chemistry at low and high temperature,14,15 laminar flame,13 and intermediate products during oxidation have been investigated for n-propylcyclohexane (PCH). However, only a few studies have been reported for cycloalkanes with a fivemembered ring which may introduce new kinetic characteristics. Sirjean et al.18 measured the ignition delay time in a shock tube at temperatures between 1230 and 1840 K and pressures from 7.3 to 9.5 atm with equivalence ratios ranging from 0.5 to 2.0 for the cyclopentane (CP)/O2/Ar mixtures containing 0.5% fuel. Subsequently, Daley et al.19 extended the measurements to the ranges of 847−1379 K and 11−61 atm, for CP/air mixtures with equivalence ratios of 1.0, 0.5, and 0.25 in a shock tube. Very little study has been done on alkylated cyclopentanes, even for methylcyclopentane (MCP) which is the simplest substituted cyclopentane. Thus, our first objective is to perform measurements of ignition delay time for CP and MCP in a shock tube to extend the relevant research. Additionally, several mechanisms have been developed to understand the oxidation of cyclohexanes, especially for CH and MCH.20−25 For example, Silke et al.21 developed an oxidation mechanism of 1081 species and 4268 reactions for CH by adding a low temperature reactions scheme to a previous high temperature model. This mechanism well reproduced the ignition delay time and intermediate products profiles in previous literature.6 Wang et al. developed another mechanism for CH which includes 148 species and 557 reactions.25 They measured more than 30 intermediate species Received: November 13, 2014 Revised: December 15, 2014 Published: December 16, 2014 428

DOI: 10.1021/ef502552e Energy Fuels 2015, 29, 428−441

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Energy & Fuels of CH pyrolysis in a plug flow reactor from 950 to 1520 K, at 0.04 atm using synchrotron vacuum ultraviolet (VUV) photoionization mass spectrometry to validate their mechanism. With respect to MCH, Orme et al.11 developed a high temperature kinetic model of 190 species and 904 reactions by analogy with present rate expressions. They also measured the ignition delay times at equivalence ratios of 0.5, 1.0 and 2.0, pressures of 1.0, 2.0, and 4.0 atm, and temperatures between 1200 and 2200 K for MCH/O2/Ar mixture containing 0.5−1% MCH. The numerical predictions agreed well with experimental results. Pitz et al.22 combined a low temperature model for MCH with that by Orme et al. to simulate the ignition delay time they measured at pressures of 10, 15, and 20 atm and temperatures of 650−1000 K for stoichiometric mixture of MCH/O2/diluent (Ar; N2; and Ar:N2 of 1:1). In contrast, there is only one mechanism of 350 species and 2177 reactions for CP developed by Sirjean et al.18 with the help of EXGAS software, a computer package for kinetic model generation. No oxidation mechanism is found available for MCP. Therefore, the second objective of this study is to understand the oxidation kinetics of MCP. In addition, a comparative study on ignition delays times (τ) among CH, MCH, and n-butylcyclohexane (BCH) was made by Hong et al.26 They conducted measurements at pressures of 1.5 and 3 atm, equivalence ratios of 1 and 0.5, and temperatures between 1280 and 1480 K for fuel/O2/Ar mixtures containing 4% O2. The order of τMCH > τBCH ≈ τCH was observed. They suggested that the unique molecular structure of CH significantly facilitates the regeneration of H radical, leading to the shorter ignition delay time of CH than that of MCH. The case in the comparison between CP and MCP is obviously of great interest. Our third objective is to compare the ignition delay time of CP and MCP in the same conditions to deepen the understanding of the effect of cyclic molecular structure and branching substitution on ignition chemistry.

Table 1. Compositions of the Test Mixtures for Cyclopentane (CP) and Methylcyclopentane (MCP) Diluted in Argon and Experimental Pressures fuel

fuel (%)

O2 (%)

Ar (%)

ϕ

CP CP CP MCP MCP MCP

1.0 1.0 1.0 0.833 0.833 0.833

13 7.5 3.75 13 7.5 3.75

86 91.5 95.25 86.167 91.667 95.417

0.577 1.0 2.0 0.577 1.0 2.0

P5 (atm) 1.1 1.1 1.1; 1.1; 1.1; 1.1;

10 10 10 10

Figure 1. Sample pressure and OH* emission profile obtained during a MCP ignition experiment at 1140 K and ϕ = 1.0, with the definition of ignition delay time. the software Gaseq30 with incident wave velocity at the endwall. It is estimated that the uncertainty of measured ignition delay times is about 15%. It is also observed that a pressure rise of 4.2%/ms appears in this experiment. In fact, pressure rise has visible effect on the numerical simulation when the ignition delay time is longer than 1000 μs.31 Thus, the numerical calculations include an average value of 4% to take the effect of pressure rise on the ignition delay into account. Simulations were carried out using SENKIN codes in conjunction with the Chemkin II packages.32 The onset of calculated ignition is defined as the maximum rise in temperature, namely, (dT/dt)max.

2. EXPERIMENTAL SETUP AND PROCEDURE Detailed descriptions of the experimental facility have been provided in previous literature.27,28 It is composed of a 4.0 m long driver section and a 5.3 m long driven section, with a double diaphragm between them. The driven section can be evacuated to pressure below 6 Pa using a Nanguang vacuum system. The driver section is filled with nitrogen (99.999%) and helium (99.999%) as the driver gas. Four pressure transducers (PCB 113B26) are mounted along the last 1.5 m of the driven section to measure the local incident shock wave velocities which are extrapolated to obtain the incident wave velocity at the endwall. Besides, the endwall pressure was recorded by a pressure transducer (PCB 113B26) located at the endwall. A photomultiplier (Hamamstu, CR131) with a filter narrowly centered at 307 ± 10 nm was installed at the endwall to diagnose the OH* emission. Test mixtures were prepared in a 128 L stainless steel tank. At first, CP or MCP with purities of over 98% was injected into the tank. Since their saturation vapor pressures are over 18 kPa at room temperature,29 the fuel condensation is negligible. A highly accurate vacuum gauge was adopted to monitor the partial pressures. Then, oxygen and argon of 99.999% purities were manometrically charged. The mixtures were allowed to mix for 10 h to ensure the homogeneity. Detailed compositions of the test mixtures in this work are listed in Table 1. Figure 1 shows a typical endwall pressure and OH* emission profile gained in an ignition experiment for MCP at 1140 K, ϕ = 1.0, and p = 10 atm. The definition of ignition delay time is presented. It is the interval between the arrival of the incident shock wave at the endwall and the extrapolation of the steepest rise of OH* signal to zero baseline. The pressures of reflected shock wave (P5) were obtained from the endwall pressure profile, as shown in Figure 1. The temperatures (T5) are calculated using the reflected shock model in

3. KINETIC MODELING A kinetic mechanism for CP and MCP including 419 species and 2490 reactions were developed, based on the JetSurF2.0 mechanism of 348 species and 2162 reactions established by Wang et al.33 The determination of the rate constants were specified in detail in following text. Thermodynamic data for MCP and its related radicals were calculated using the THERM program of Ritter and Bozzelli34 based on group additivity estimation developed by Benson et al.35 The obtained values of enthalpies, entropies, and heat capacities are listed in Table 2, together with the enthalpies computed at CBS-QB3 level by Sirjean et al.36 Fairly good agreement between two sets of enthalpies is observed with discrepancy of less than 2 kcal/mol. 3.1. Nomenclature. The naming of species and radicals, similar to that in JetSurF2.0, is given in the Supporting Information for use in this work, along with the mechanism and thermodynamic files. Figure 2a shows several chain hydrocarbon names as examples. Carbons in the main chain are numbered to minimize the label of the double bond. The number of the position of the double bond, if not “1”, and the 429


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Table 2. Thermodynamic Data for MCP and Related Radicals Obtained Using Therm Program and Enthalpies from Sirjean et al.,36 ΔfH° (kcal/mol), S° (cal/mol/K), and Cp (cal/mol/K) ΔfH°36

ΔfH°

S°

species

298 K

298 K

298 K

300 K

400 K

500 K

600 K

800 K

1000 K

1500 K

CH3cC5H9 PXCH2cC5H9 CH3TXcC5H9 CH3S2XcC5H9 CH3S3XcC5H9

−25.70 23.70 16.90 18.80 18.50

−25.91 23.09 18.29 20.09 20.09

81.14 85.93 79.83 78.46 78.46

25.16 24.39 24.84 25.10 25.10

35.13 33.77 33.87 34.61 34.61

44.18 42.27 42.14 43.07 43.07

51.81 49.41 49.18 50.07 50.07

63.55 60.39 60.11 60.70 60.70

71.96 68.22 67.97 68.27 68.27

84.81 80.15 80.00 79.98 79.98

Cp

of the double bond. For radicals, the notation “letter-numberX” is added before the main (no. 2, Figure 2a) or branch (no. 3, Figure 2a) chain formula. The letter includes P (primary), S (secondary), and T (tertiary) for alkyl and V for alkenyl. The number represents the position of a single electron and is omitted if it is “1”. Numbers 2−6 in Figure 2a list examples for applications of all letters (P, S, T, V). There is no difference in the naming for cyclic hydrocarbons except that a lowercase letter “c” is put before the ring formula. In nos. 1−3, Figure 2b, the labels of the carbons on the ring for MCP, methylcyclopentene, and cyclopentene are provided. In nos. 4−6, several examples are given for the naming of cyclic radicals. 3.2. Reactions of Cyclopentane. The submodel of cyclopentane is listed in Table 3, including the unimolecular decomposition, H abstraction, radical decomposition, and isomerization. Initially, CP can directly decompose into 1pentene (R1) or cyclopropane/ethylene (R2) by the unimolecular reactions. The rate constants of 1.25 × 1016 exp(−42850/T) s−1 and 1.77 × 1016 exp(−48000/T) s−1 provided by Tsang37 are applied to reactions R1 and R2, respectively. They are also used in the mechanism of CP oxidation created by Sirjean et al.18 Cyclopentane also undergoes C−H bond cleavage to form H radical plus cyclopentyl (R3). Its rate expression is estimated in reverse direction, analogous to addition of H to isopropyl forming propane, whose rate constant was proposed by Tsang.38 Here the rate constant is taken in the format of Troe parameters for reaction R3.

Figure 2. Naming scheme for (a) chain hydrocarbons and (b) cyclic hydrocarbons. The carbons in the main chains and rings are labeled.

branch chain formula are added after and before the main chain formula, respectively. The number in the middle of the branch and main chain formulas denotes the position of the branch chain. For example, in the name (CH3-4-C5H9-2) for 4methyl-2-pentene, no.1 in Figure 2a, “CH3” means methyl, “4” indicates the site of the methyl, and “2” represents the position

Table 3. Reaction Rate Constants for CP Submechanism (cm3/mol/s/cal)

a

Estimated by analogy with similar reaction. 430


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Energy & Fuels R4−R11 in Table 3 give H abstraction reactions with small radicals of H, O, OH, CH3, CH2OH, CH3O, and C2H5 as well as O2. Their rate constants are adopted from the mechanism for CP developed by Sirjean et al.18 Cyclopentyl radicals are consumed to produce 1-penten-5-yl (R12) by ring opening or cyclopentene/H radical (R13) by scission. The rate constant for reaction R12 has already been given in JetSurF2.0 by Wang et al.33 Reaction R13 is displayed in reverse direction in Table 3. Its rate constant is estimated by analogy with the addition reaction of H atom to propene (C3H6) yielding isopropyl (iC3H7). Then the rate expression for H + C3H6 = iC3H7 published by Tsang39 is adopted for R13. The A factor is increased by a factor of 2 to account for two carbon sites available for this reaction. This method is used for all added reactions of alkyl radicals forming alkene plus H radical to maintain consistency in this assembled mechanism. Finally, the rate constant of 1-penten-5-yl isomerizing to 1penten-3-yl (R14) through 1,3 p → H shift is given. It is estimated in the same way as that discussed in the section of Isomerization in Reactions of Methylcyclopentane. Moreover, a submodel developed by Gueniche et al.40 for cyclopentene, which is an important product during CP oxidation, is merged into this mechanism. This submodel contains molecular dehydrogenation, isomerization to yield 1,2pentadiene, molecular decomposition by transfer of a H atom, and H abstraction reactions for cyclopentene as well as reactions for derived radicals. Combining with their previous C0 −C 4 mechanism, Gueniche et al. obtained a complete mechanism for cyclopentene of 175 species and 1134 reactions. They qualified various intermediate species in a stabilized flame at 6.7 kPa, 627−2027 K for gas mixtures of 15.3% methane, 26.7% oxygen, and 2.4% cyclopentene diluted in argon to validate the mechanism. Later, this mechanism also well reproduced the ignition delay times for the mixtures of cyclopentene/O2 /Ar containing 0.5−1.0% of fuel at ϕ = 0.5, 1.0, and 1.5, temperatures of 1300−1700 K, and pressures between 7 and 9 atm measured by Yahyaoui et al.41 Because of the reliability, we added 52 reactions associated with cyclopentene oxidation chemistry from Gueniche’s mechanism to our model in order for better understanding of CP oxidation. 3.3. Reactions of Methylcyclopentane. The submechanism developed for modeling the high-temperature oxidation of methylcyclopentane includes unimolecular decomposition, H abstraction, methylcyclopentyl radical decomposition, alkyl radical isomerization, and decomposition, as shown in Tables 4, 5, and 6. Additionally, the brief reaction scheme for methylcyclopentenes is contained in the mechanism as well. The submechanism of cyclopentadiene has been provided in JetSurF2.0. 3.3.1. Unimolecular Decomposition. The methylcyclopentane molecule decomposition can initiate through C−C bond homolysis on the five-membered ring, leading to five C6 alkene isomers: 1-hexene (C6H12), 2-hexene (C6H12-2), 2-methylpentene (CH3-2-C5H9), 3-methylpentene (CH3-3-C5H9), and 4-methylpentene (CH3-4-C5H9). Since the ring strain energies for CP and MCP are the same (7.1 kcal),36 we assume that the activation energies of ring opening reactions for MCP are identical to that for CP without taking into account the influence of the methyl group, implying ring stability similar to that of MCP with CP. Then, in consideration of five different products, the rate expression constant 1.25 × 1016 exp(−42850/T) for cC5H10 = C5H10 (R1,Table 3) is divided by 5

Table 4. Reaction Rate Constants for MCP Submechanism (cm3/mol/s/cal)

a

431

Estimated by analogy with similar reaction. DOI: 10.1021/ef502552e Energy Fuels 2015, 29, 428−441

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Energy & Fuels

Table 5. Rate Expressions Estimated Based on Rules by Matheu et al.48,49 for Isomerization Reactions, i.e., Internal 1,3-H Atom Shift (cm3/mol/s/cal) no.

reaction

62 63 64 65 66

S5XC6H11 = S3XC6H11 P6XC6H11-2 = S4XC6H11-2 CH3-3-P5XC5H8 = CH3-3-T3XC5H8 CH3-2-P5XC5H8 = CH3-2-S3XC5H8 CH3-4-P5XC5H8 = CH3-4-S3XC5H8

A 7.85 7.85 7.85 7.85 7.85

× × × × ×

1011 1011 1011 1011 1011

n

Ea

−0.12 −0.12 −0.12 −0.12 −0.12

29000 28300 27100 28300 28300

type allylic allylic allylic allylic allylic

s−s p−s p−t p−s p−-s

Table 6. Rate Parameters for Alkyl Radical Decomposition Reactions (cm3/mol/s/cal)

a

no.

reaction

67 68 69 70 71 72 73

CH3 + C5H8-14 = CH3-4-P5XC5H8 C2H4 + SXC4H7 = CH3-3-P5XC5H8 C2H4 + iC4H7 = CH3-2-P5XC5H8 CH3 + C5H8-13 = CH3-4-S3XC5H8 CH3 + C5H8-13 = S3XC6H11-2 CH3 + CH3-2-C4H5 = CH3-3-T3XC5H8 CH3 + CH3-2-C4H5 = CH3-2-S3XC5H8

A 3.78 1.32 1.32 1.89 1.76 1.76 1.76

× × × × × × ×

103 104 104 103 104 104 104

n

Ea

type

2.67 2.48 2.48 2.67 2.48 2.48 2.48

6850 6130 6130 6850 6130 6130 6130

int. C3H6+CH3a ext. C2H4+C2H5 ext. C2H4+C2H5 int. C3H6+CH3 ext. C3H6+CH3 ext. C3H6+CH3 ext. C3H6+CH3

A factor is multiplied by 2 accounting for the addition of methyl that occurs to two carbon sites.

to obtain the rate constant for reaction R20 (Table 4). We employ the rate expression of MCH decomposition giving methyl and cyclohexyl computed by Wang et al.24 using the CBS-QB3 method. On the other hand, note that this reaction (CH3cC6H11 = CH3 + cC6H11) is also determined by Wang et al.,33 and Orme et al.,11 in their MCH mechanisms, used the reverse combination rate constant of 6.63 × 1014T−0.57 s−1, analogous to addition of methyl to isopropyl proposed by Tsang.45 Reaction R20 was thus estimated in reverse direction in the same way. Then its rate parameters of forward reaction, 1.25 × 1024T−2.15 exp(−45048/T), are obtained using the NUI software.46 Figure 4 shows a comparison of rate constants estimated by these two approaches for reaction R20. Good agreement lends credence to the approach of analogy with the Wang et al.24 approach. Besides, the rate constants of decomposition of MCP by transferring an H atom are estimated by analogy with addition of H atom to n-propyl, isopropyl, and tert-butyl,38,45 depending on the H atom sites on the MCP molecule, shown as R21 −R24 (Table 4).

to use for the formation of C6 alkenes by MCP, shown as R15−R19, Table 4. Another pathway of unimolecular reaction is a methyl group breaking off from the ring (R20). Its rate constant is estimated by analogy with MCH. The molecule structures of MCP and MCH as well as bond dissociation energies (BDEs) of the related C−C bond are shown in Figure 3, with carbon sites labeled for use later in this work. The BDEs of C−H bonds are also given for subsequent H abstraction reactions.

Figure 3. Molecular structures of MCP and MCH. Numbers in red are bond dissociation energies (BDEs) for C−H bonds; numbers in blue are for C−C bonds. Labels in green represent different carbon sites. The unit of BDE is kilocalories per mole.

Various BDEs were estimated in the following way:42,43 If species AB yields A plus B through bond cleavage, namely, AB = A + B, the bond dissociation energy is obtained using the formula BDE = Δf H298(A) + Δf H298(B) − Δf H298(AB)

(1)

where BDE is the bond dissociation energy and ΔfH298(A), ΔfH298(B), and ΔfH298(AB) are enthalpies of formation of species A, B, and AB at 298 K. The standard formation enthalpies of MCH and methylcyclohexyl radicals computed by Chen et al.44 at CBS-QB3, those of MCP and methylcyclopentyl radicals by Sirjean et al.36 using the same method, and those of CH3 and H radical from ref 43 are adopted for estimation of BDEs. All of the formation enthalpies are listed in Table S1 of the Supporting Information. It is observed that the BDE of the C−C bond between methyl and the ring of MCP is 86.4 kcal/mol, similar to that of MCH (87.8 kcal/mol). Thus, an analogy method can be used

Figure 4. Reaction rates for CH3cC5H9 = CH3 + cC5H9 obtained by analogy with that for CH3cC6H11 = CH3 + cC6H11 by Wang et al.24 and from reverse reaction.23,24 432


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Energy & Fuels 3.3.2. H-Abstraction Reactions. H-atom sites (primary, secondary, and tertiary) and C−H BDEs play a significant role on H abstraction. It is shown in Figure 3 that the C−H BDEs of MCP and MCH are in fairly good agreement. Therefore, we adopt the rate constants of H abstraction with hydrogen (H), oxygen (O), hydroxyl (OH), hydroperoxyl (HO2), methyl (CH3) radicals, and oxygen (O2) used for MCH in JetSurF2.0 to those for MCP at the same H atom sites. The corresponding rate constants are shown as R25−R48, Table 4. 3.3.3. Methylcyclopentyl Decomposition. Methylcyclopentyl radicals can break down through ring opening reactions to yield straight and branched alkyl radicals or through C−H scission to form methylcyclopentenes plus H radicals. The rate constants of reactions, radical PXCH2cC5H9 forming n-hexenyl (P6XC 6 H 1 1 ) (R49, Table 4), methylcyclopent-3-yl (CH3S3XcC5H8) forming 1-hexen-5-yl (S5XC6H11) (R50) and forming 4-methylpenten-5-yl (CH3-4-P5XC5H8) (R51), are provided in JetSurF2.0. We compare methylcyclopent-1-yl (CH 3 TXcC 5 H 8 ) forming 2-methylpenten-5-yl (CH 3 -2P5XC 5 H 8 ) (R52) with R51, methylcyclopent-2-yl (CH3S2XcC5H8) forming hex-2-en-6-yl (P6XC6H11-2) (R53) with R50 and forming 3-methylpenten-5-yl (CH3-3-P5XC5H8) (R54) with R51. It is noted that the rate constant of R52 is multiplied with 2 to consider two C−C bond cleavages yielding 2-methylpent-5-yl. In addition, the rate constant of 2methylpentyl (CH3-2-P5XC5H10) forming methyl and npentene, given by McGivern et al.47 was adopted to CH3S2XcC5H8 yielding cyclopentene plus methyl (R55). These analogy approaches are also used in ring opening reaction for MCH in JetSurF2.0. With respect to methylcyclopentyl radicals producing methylcyclopentenes plus H radicals, the rate constants are estimated in reverse direction, analogous to addition of H atom to propene (C3H6) forming isopropyl (iC3H7),39 in the same way of determining rate parameters of reaction R13, Table 3. The results are shown as reactions R56−R60, Table 4. 3.3.4. Isomerization. The JetSurF2.0 has included a cyclic radical isomerization reaction, i.e., methylenecycloptane (PXCH2cC5H9) forming methylcyclopent-3-yl (CH3S3XcC5H8), R61, Table 4. For the alkyl radicals isomerization reactions, the rate constants are estimated according to the general rules derived from the results of high level (B3LYP-ccpVDZ) quantum calculations from Sumathi by Matheu et al.48,49 They also took hindered rotations into account to determine the Arrhenius Afactors and temperature dependent n. However, the activation eneries of 1,3 H shifts forming allylic radicals which is the main type of internal H shift in this work are not directly given. We estimate them through Evans−Polanyi correlation considering the enthalpy of reaction and ring strain energy. Moreover, the 1,4 H shift A-factor and temperature dependence terms are used for 1,3 H shift since an additional rotor loss is involved when an allylic radical is formed outside the transition-state ring.48,49 The reactions, rate parameters, and H shift types are reported in Table 5. Similarly, reaction R14 in Table 3 is estimated based on this rule as well. 3.3.5. Alkyl Radical Decomposition. Alkyl radicals yielded by ring opening and isomerization reactions go through βscission to give alkenes and smaller alkyl radicals. Rate constants of these reactions which are not presented in the JetSurF2.0 originally are estimated in the reverse, exothermic direction based on the rules provided by Curran50 in his study of C1−C4 alkyl and alkoxyl radical decomposition. The

recommended rate expressions are listed in Table 7. Methyl radical addition to a terminal and internal C atom of alkene Table 7. Recommended by Curran50 Rate Constants for Addition of an Alkyl Radical across an Olefinic (CC) Bond (cm3/mol/s/cal) reaction external C3H6 + CH3 = sC4H9 C2H4 + C2H5 = pC4H9 internal C3H6 + CH3 = iC4H9

A

n

Ea

1.76 × 104 1.32 × 104

2.48 2.48

6130 6130

1.89 × 103

2.67

6850

allows for rate constants of 1.76 × 104T2.48 exp(−3086/T) and 1.89 × 103T2.67 exp(−3449/T), respectively. Adding an ethyl (or larger) radical to a terminal carbon leads to 1.32 × 104T2.48 exp(−3086/T). All of the alkyl radical addition to alkene reactions in this study fall into these three categories, and their rate constants are given in Table 7.

4. RESULTS AND DISCUSSION 4.1. Ignition Delay Time of CP and MCP. For CP, ignition delay times were measured for the fuel-lean (ϕ = 0.577), stoichiometric (ϕ = 1.0), and fuel-rich (ϕ = 2.0) mixtures of 1% CP/O2/Ar at 1.1 atm and additionally for the fuel-rich mixture at 10 atm, with temperatures ranging from 1220 to 1785 K. The measurements with 15% uncertainty are shown in Figure 5, in comparison with the predictions of the Sirjean et al. mechanism for CP18 and the model of this work, including 4%/ms pressure rise. Also, the data from Orme et al.51 at ϕ = 1.0 and 1.0 atm for 1% CP/O2/Ar are included to compare with present measurements, and good agreement is observed. Both Sirjean et al. and our mechanisms show reasonable consistency with the experimental data. They capture the pressure dependence and the effects of equivalence ratio very well. In Figure 5a, the fuel-lean mixture has a shorter ignition delay time than the stoichiometric mixture because the chain branching reaction H + O2 = OH + O dominates ignition.52 Higher oxygen concentration facilitates this reaction, enhancing overall reactivity and reducing the ignition delay time. It can be noticed that the predictions of this assembled model are higher than those of the Sirjean et al. model, especially at high temperatures, despite the similar overall activation energies. This is ascribed to the different reaction channels related to small intermediate species between two mechanisms. Also, the model of this work overpredicts the ignition delay time at lower temperatures, especially at ϕ = 2.0, p = 1.1 atm when 35% overprediction is present (black line, Figure 5b). It may be due to the imperfect radical decomposition and isomerization reactions. In addition, the measured ignition delay times data at 7.3− 9.5 atm and three equivalence ratios (ϕ = 0.5, 1.0, 2.0) for 0.5% CP/O2/Ar mixtures measured by Sirjean et al.18 are also used to validate both the Sirjean et al. and the present models, as shown in Figure 6. In spite of scatter of the data, both mechanisms fairly reproduce them and the model of this work again gives higher predictions than the Sirjean et al. mechanism. For MCP, measurements of ignition delay time were conducted at pressures of 1.1 and 10 atm, equivalence ratios of 0.577, 1.0, and 2.0, and temperatures of 1150−1850 K for MCP/O2/Ar mixtures constantly containing 0.833% fuel. The experimental and computed results using the present model are 433


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Figure 5. Ignition delay time measurements for CP/O2/Ar mixtures containing 1% CP with comparison to predictions of Sirjean’s mechanism (dashed lines)18 and the present mechanism (solid lines). Data from Orme et al.51 at p = 1.0 atm, ϕ = 1.0, and 1% CP mixtures are also included.

Figure 7. Measured ignition delay times for MCP/O2/Ar mixtures containing 0.833% MCP and simulations by the mechanism of this work at 1.1 and 10 atm: (a) ϕ = 0.577; (b) ϕ = 1.0; (c) ϕ = 2.0.

experimental data illustrates the good performance of this present model on predicting the ignition delay time under tested conditions. 4.2. Comparison between CP and MCP. Figure 8 presents a comparison of the ignition delay time between CP and MCP at 1.1 atm for fuel-lean and -rich mixtures. MCP has shorter ignition delay time than CP for fuel-lean mixtures whereas this discrepancy is moderated at high temperatures (T > 1540 K) and in the fuel-rich mixture. It implies that the oxidation reactivity of MCP which is substituted by a methyl group is higher than CP, an unsubstituted cyclic alkane,

Figure 6. Comparison of ignition delay times obtained by Sirjean et al.18 for CP/O2/Ar mixtures with simulations by the present model (solid lines) and by Sirjean’s model (dashed lines).

displayed in Figure 7. The uncertainty of experimental data is 15%, and 4%/ms in pressure rise is taken into the simulation. The reasonable agreement between numerical simulations and 434


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Figure 8. Direct comparison of CP and MCP ignition delay times at 1.1 atm. Test mixtures are as follows: □, 1% CP/3.75% O2/Ar; ○, 0.833% MCP/3.75% O2/Ar; ■, 1% CP/13% O2/Ar; ●, 0.833% MCP/13% O2/Ar. Simulations are performed using the model of this work.

Figure 9. Flux analysis of CP oxidation at p = 1.1 atm and 20% fuel consumption, including conditions of (red) ϕ = 0.577 and T = 1350 K, (blue) ϕ = 0.577 and T = 1700 K, and (green) ϕ = 2.0 and T = 1700 K. The mixtures contain 1% fuel. The model of this work is used. Numbers are percent contribution to the consumption of the species on the source side of the arrow.

especially at not too high temperatures and in the environment of abundant oxygen. In contrast, some previous studies suggest that methyl substitution on normal and cyclic compounds can reduce fuel reactivity because it tends to increase the production of methyl radicals which can combine to form stable ethane molecules, removing active radicals from the reacting system. For instance, Westbrook et al.53 showed computationally 2,2-dimethylpentane and 2,4-dimethylpentane tended to have the longest ignition delay times among heptane isomers. Davis and Law54 showed that the laminar flame speed of benzene was higher than that of toluene. Additionally, Hong et al.26 observed that the ignition delay time of MCH was longer than that of CH, and they explained it by less regenerated H radicals and more produced methyl radicals during MCH oxidation. However, they pointed out that the yield of methyl radical was not as important as the regeneration of H radicals to ignition. To further interpret the effect of cyclic molecular structure and addition of methyl group on ignition, detailed kinetic analysis was conducted.

H radical. Despite the addition of the cyclopentene submechanism, the major of cyclopentene (98.9%) ends up with cyclopentadiene by direct dehydrogenation (cC5H8 = H2 + cC5H6) and partially by transfer of H atom from cyclopentenyl radicals. In contrast, as temperature increases (1700 K, ϕ = 0.577), unimolecular reaction of CP resulting in 1-pentene takes significant effect on decomposition (34.9%) and correspondingly the H abstraction become less important. Also, there is 2.2% CP decomposing into ethylene/cyclopropane (not shown in Figure 9). Then 96.5% 1-pentene cracks to ethyl plus allyl, and a small amount of 1-pentene dissociates to ethylene and propene (not shown in Figure 9). Ethyl is of great importance, known as a significant H radical precursor. It should be noted that the percentage of ring opening reaction occurring to cyclopentyl producing 1-penten-5-yl evidently goes up from 38.5% to 68.9% when temperature rises from 1350 to 1700 K and that of producing 1-penten-3-yl also arises from 37% to 50.9%. Together with the increased percentage of unimolecular reaction (cC5H10 = C5H10), it may be explained by the high enthalpy and entropy activation energy in the transition state which increases reaction activation energy and the A-factor as well as temperature dependence, respectively, according to transition-state theory. Enormous energy can be provided to overcome the high energy barrier at high temperature, and then a large amount of energy is released. Especially, the isomerization of 1-penten-5-yl to 1-penten-3-yl falls into this category since its transition state has a fourmembered ring. Comparing ϕ = 0.577 and 2.0 at 1700 K, we find the equivalence ratio has much less influence on reaction pathways than temperature, also evidenced by comparison between ϕ = 0.577 and 2.0 at 1350 K (not shown in Figure 9). The fuel molecule (CP) is destructed through H abstraction by the attack of H and OH radicals and through unimolecular decomposition. The former is an oxidation inhibiting process because of consumption of major chain carriersH/OH radicals. The latter is a chain initiation reaction but is of less significance to CP dissociation than H abstraction. Hong et al.26 claimed that nearly 100% of H radical is recovered after H

5. FLUX AND SENSITIVITY ANALYSIS 5.1. Flux Analysis. 5.1.1. Analysis for CP. A reaction flux analysis for 1% CP/O2/Ar mixtures is performed using the present model at 1.1 atm and 20% fuel consumption in order to understand the CP oxidation, as shown in Figure 9. Three conditions (ϕ = 0.577, T = 1350 K; ϕ = 0.577, T = 1700 K; ϕ = 2.0, T = 1700 K) are selected to discuss the effect of temperature and equivalence ratio on reaction pathways. It is suggested that the majority of CP is consumed through H abstraction mainly with H and OH radicals to form cyclopentyl at 1350 K and ϕ = 0.577. Strong selectivity that 75.3% CP is abstracted by H radical while 13.8% is by OH radical is observed, implying the significance of H radical on the depletion of CP. Cyclopentyl breaks down through scission into 1-penten-5-yl radical (38.5%) and cyclopentene/H radical (61.3%). Obviously, the formation of H radical can promote ignition. A 42.3% amount of 1-penten-5-yl radical produces allyl radical plus ethylene through β-scission, 37% yields 1,3butadiene/methyl radical by first isomerization to 1-penten-3yl and then β-scission, and 20.6% forms 1,3-pentadiene casting 435


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Energy & Fuels abstraction. The seldom methyl radical produced are responsible to turn the chain termination reactions, i.e., H abstraction, to chain propagation reactions, enhancing the reactivity during CH oxidation. In the case of CP at 1350 K, 1 mol of CP consumes 0.75 mol of H radicals, and 0.55 mol of H radicals are returned shortly after about 0.90 mol of cyclopentyl radicals formed. Additionally, 0.35 mol of 1-penten-5-yl radicals given by cyclopentyl can also shed 0.07 mol of H radicals. Besides, decomposition of 1-pentene contributes to 0.08 mol of H radicals as well. Hence, 0.7 mol of H radicals are regenerated. This means 93% H radical is recovered after H abstraction. Then OH can be produced through essential chain branching reaction H + O2 = OH + O. Also, a little methyl radical (0.13 mol) is generated. At 1700 K, 1 mol of CP produces 0.33 mol of ethyl which can easily give H radical to form stable ethylene, leading to efficient H radical recovery. 5.1.2. Analysis for MCP. A similar flux analysis is conducted for MCP/O2/Ar mixtures containing 0.833% MCP using the model of this work. The conditions are ϕ = 0.577, T = 1350 K; ϕ = 0.577, T = 1700 K; and ϕ = 2.0, T = 1700 K at 1.1 atm and 20% fuel conversion, identical to the conditions in the analysis of CP oxidation. The results are separately displayed in Figures 10−13.

Figure 11. Reaction pathways following MCP-R0 and MCP-R1 radicals at p = 1.1 atm and 20% fuel consumption, including conditions of (red) ϕ = 0.577 and T = 1350 K, (blue) ϕ = 0.577 and T = 1700 K, and (green) ϕ = 2.0 and T = 1700 K. The mixtures contain 0.833% fuel. Numbers are percent contribution to the consumption of the species on the source side of the arrow.

With respect to the conditions of ϕ = 0.577 and T = 1350 K, 18.1% MCP is consumed through unimolecular decomposition among which 12.3% of MCP undergoes methyl breakoff and 5.8% ring opening reactions giving C5 alkenes (not shown in Figure 10). The rest of MCP goes through H abstraction to produce methylcyclopentyl radicals. MCP-R3 (31.5%) is the most isomer followed by MCP-R2 (27.5%). It is due to the molecular symmetry of MCP rendering four H atoms available for abstraction to yield each of them. The possibilities of forming MCP-R0 (12.1%) and MCP-R1 (11.8%) are almost equal since the number of primary H atoms for the generation of MCP-R0 is three times of that of tertiary H atom for MCPR1 although the tertiary C−H bond is much weaker than the primary C−H bond. The selectivity of abstracting radicals is less strong compared to that in the case of CP. For instance, the percentage (11.2%) of OH radical attacking MCP to form MCP-R2 approximates that of H radical (12.3%). As temperature goes up to 1700 K, a much larger portion of MCP decomposes by unimolecular reactions: 19.5% MCP through ring opening and 21.4% through methyl breakoff. In spite of the assumption of similar ring stability with CP, methyl substitution causes a larger amount of MCP consumed through unimolecular dissociation than CP. It is noticed that the percentage of H abstraction with OH radical decreases substantially, whereas that with H radical declines a little. Additionally, a fuel-rich mixture tends to favor unimolecular and H abstraction with H radical reactions. Figure 11 depicts reaction pathways of MCP-R0 and MCPR1 radicals. MCP-R0 and MCP-R1 radicals give a single product, i.e., 1-hexen-6-yl and 2-methylpenten-5-yl, respectively, through ring opening reactions because of their symmetric molecular structure. 1-Hexen-6-yl radicals are consumed through four pathways. At 1350 K, the dominant one (57.9%) is cracking to ethylene plus 1-buten-4-yl through β-scission. By the second one (36.1%), 1-hexen-6-yl isomerizes to 1-hexen-3-yl radicals and then dissociates to 1,3-butadiene/ ethyl. These two pathways lead to important ethyl and 1-buten4-yl radicals which can release H radicals readily when they

Figure 10. Flux analysis of MCP oxidation at p = 1.1 atm and 20% fuel consumption, including conditions of (red) ϕ = 0.577 and T = 1350 K, (blue) ϕ = 0.577 and T = 1700 K, and (green) ϕ = 2.0 and T = 1700 K. The mixtures contain 0.833% fuel. Numbers are the percent contribution to the consumption of the species on the source side of the arrow.

Figure 10 presents the primary pathways of MCP decomposition including unimolecular dissociation and H abstraction reactions mainly with H, O, OH, and CH3 radicals. Two types of unimolecular reactions of a methyl group breaking off the ring and ring opening reactions are involved in unimolecular decomposition. Methylcyclopentyl radicals produced by H abstraction have four isomers because of the presence of a methyl group. 436


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Figure 12. Reaction pathways following MCP-R2 radical at p = 1.1 atm and 20% fuel consumption, including conditions of (red) ϕ = 0.577 and T = 1350 K, (blue) ϕ = 0.577 and T = 1700 K, and (green) ϕ = 2.0 and T = 1700 K. The mixtures contain 0.833% fuel. Numbers are the percent contribution to the consumption of the species on the source side of the arrow.

Figure 13. Reaction pathways following MCP-R3 radical at p = 1.1 atm and 20% fuel consumption, including conditions of (red) ϕ = 0.577 and T = 1350 K, (blue) ϕ = 0.577 and T = 1700 K, and (green) ϕ = 2.0 and T = 1700 K. The mixtures contain 0.833% fuel. Numbers are the percent contribution to the consumption of the species on the source side of the arrow.

convert to stable species. Besides, 1,5-hexadiene/H-radical and cyclohexyl radical are also introduced by small portion of 1hexen-6-yl radicals. However, 2-methylpenten-5-yl radical by MCP-R1 exclusively goes down to ethylene and isobutenyl radicals with little isomerization since the ring strain energy in the transition state is very high for 2-methylpenten-5-yl isomerizing to 2-methylpenten-3-yl by 1,3 H shift. In addition, there is 43.0% MCP-R1 converting to 1-methylcylopentene releasing H radicals. Figure 12 shows three decomposition pathways of MCP-R2 radical through C−C cleavage to yield cyclopentene/methyl radicals, hex-2-en-6-yl radical, and 3methylpenten-5-yl radical. The latter two radicals are reduced by β-scission or first isomerization and then β-scission. Note that considerable methyl radicals (51%) can be generated during this process. Moreover, 14% and 20.1% MCP-R2 form 1-methylcylopentene and 3-methylcylopentene, respectively, shedding H radicals. Figure 13 profiles MCP-R3 decomposition. It breaks down through pathways similar to those of MCP-R2 except cyclic isomerization to form MCP-R0. Finally, it can be observed in Figures 11−13 that an increase in temperature increases the percentage of ring open and isomerization reactions as well.

Although the unimolecular reactions have larger influence on the oxidation of MCP than CP, H abstraction reactions and regeneration of H radical are crucial to MCP oxidation. The recovery of H radical is calculated using a method similar to that used for CP. However, four methylcyclopentyl isomers lead to a mixture of various intermediate radicals, complicating the calculation. MCP-R0 radicals can return H radical at the rate of close to 100% because all four decomposition pathways can regenerate H radical effectively. MCP-R1 and MCP-R2 radicals generate H radical mainly through formation of methylcyclopentenes. In addition to the identical pathway of giving H to MCP-R1/MCP-R2, MCP-R3 can partially isomerize to MCP-R0 and then cast H radicals. To sum up, if 1 mol of MCP is consumed at 1350 K, 0.39 mol of H radical is used for abstraction and subsequently 0.52 mol of H and 0.29 mol of CH3 radicals are generated. This is to say that the chain carrier, H radical, is multiplied during the initial fuel decomposition. 5.2. Sensitivity Analysis. Sensitivity analysis of ignition delay time provides an approach to detect the significant reactions that dominate ignition chemistry. We use the model of this work to perform sensitivity analysis of ignition for CP and MCP mixtures. 437


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(cC5H10 + H = cC5H9 + H2), is a significant chain termination. Increase in a unimolecular decomposition channel means a decrease in the H abstraction channel. On the other hand, the product, 1-pentene, cracks to form ethyl which easily returns H radical. Therefore, both competition with other parallel pathways and its products contribute to the behavior of a reaction during oxidation. This can also explain the effect of 1penten-5-yl (R85, R88, and R89) and cyclopentyl dissociation (R12 and R13) on ignition. In the same way, a sensitivity analysis is performed for 0.833% MCP/Ar/O2 mixtures in conditions identical to those for CP, as shown in Figure 15. For intermediate radicals, similar

The sensitivity coefficient is defined as S=

τ(2ki) − τ(0.5ki) 1.5τ

(2)

where ki is the preexponential factor of the ith reaction, τ is the ignition delay time, and S is the normalized sensitivity coefficient. Negative values of S suggest that the ignition delay time decreases with an increase in the rate constant, implying an ignition-promoting reaction, and vice versa. Figure 14 shows the most sensitive 22 reactions for CP obtained under three different conditions (ϕ = 0.577, 1350 K;

Figure 14. Sensitivity analysis of ignition delay at ϕ = 0.577, 1350/ 1700 K and ϕ = 2.0, 1700 K for CP/O2/Ar mixtures containing 1% CP at 1.1 atm using the model of this work. For reaction R74, the sensitivity coefficient is divided by 4.

Figure 15. Sensitivity analysis of ignition delay at ϕ = 0.577, 1350/ 1700 K and ϕ = 2.0, 1700 K for MCP/O2/Ar mixtures containing 0.833% MCP at 1.1 atm. For reaction R74, the sensitivity coefficient is divided by 4.

ϕ = 0.577, 1700 K; ϕ = 2.0, 1700 K) at the pressure of 1.1 atm for 1% CP/O2/Ar mixtures. Expectedly, the H + O2 reacting system (R74) has extremely high sensitivity coefficients, implying its dominance over ignition and the fundamental importance of the accuracy of its rate constant. Although methyl radical can inhibit ignition through CH3 + CH3 = C2H6 (R78) and CH3 + O = CH2O + H (R75), there are also chain propagating reactions such as R76 (CH3 + OH = CH2* + H2O) and R77 (CH3 + HO2 = CH3O + OH). Thus, it is inferred that methyl radical has far more limited effect than H radical during CP oxidation. Allyl radical (aC3H5) can be produced by dissociation of 1-pentene and 1-penten-5-yl (Figure 9). As a resonantly stabilized radical, allyl radical can combine with H radical to form propene (R80), being a chain terminating channel. However, it also reacts with hydroperoxyl radical (HO2) to give formaldehyde (CH2O), hydroxyl (OH), and vinyl (C2H3) radicals, which notably promote ignition. As a result, the inhibiting effect of allyl can be limited. It is also observed that 1,3-butadiene produced by 1-penten-3-yl (Figure 9) serves as an ignition promoting species through C4H6 + H = C2H4 + C2H3 (R84) since further reaction of vinyl and O2 is a chain branching step (R86) and ethylene can also yield vinyl to promote oxidation (R90). Some species closely related to fuel CP are also clearly influential. Unimolecular decomposition (R1: cC5H10 = C5H10) has a considerably negative sensitivity coefficient for two reasons. On one hand, its competitor, R5

conclusions are reached. H + O2 = OH + O dominates oxidation. Methyl and allyl radicals have both promoting and inhibiting pathways. 1,3-Butadiene can evidently promote ignition despite a stable species. The unimolecular reaction of a methyl group breaking off the ring (R20) displays a high negative sensitivity coefficient, and H abstraction reaction with H radical (R26, R27, R28) has positive values, which is consistent with the case of CP. MCP-R0 radical forms 1-hexen6-yl (R49) to enhance reactivity because four decomposition pathways of 1-hexen-6-yl can easily release H radical (Figure 11). This favors the isomerization of MCP-R3 to MCP-R0 (R61) promotes ignition. Competing with R61, reactions R50 (MCP-R3 = S5XC6H11) and R51 (MCP-R3 = CH3-4P5XC5H8) inhibit oxidation. The subsequent production of propene (Figure 13) also contributes to their inhibiting effect because propene consumes H radical to yield allyl (R94), as a net radical sink. Similarly, MCP-R2 radical forms 3-methylpenten-5-yl radical (R54) shortening ignition delay whereas it forms hex-2-en-6-yl radical slowing ignition. 5.3. Insights for Comparison. Three main factors are introduced to interpret the effect of methyl group and cyclic ring. First, the presence of a methyl group stimulates the fuel decomposition since the unimolecular decomposition is accelerated due to the weak C−C bond between methyl and ring, and consequently it causes the fuel molecule to 438


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Energy & Fuels decompose easily to form cyclic alkyl and methyl radicals. Also, cyclic radical can decompose to give H radical to enhance reactivity. Second, the cyclic ring determines subsequent alkyl radicals, affecting the ability to regenerate and accumulate H radical. Finally, the substitution of a methyl group can change those alkyl radicals as well. For some fuels, the molecular structures of their chain alkyl radicals significantly facilitate the production of H radical along with intermediate species which can propagate the reaction chain. As a result, H radical is easy to accumulate at an initial stage of oxidation, resulting in quick consumption of fuel. Oppositely, the alkyl radicals either return H radical difficultly or yield H consuming byproducts. Consequently, it is hard to build up H radicals to expedite fuel consumption. What should be mentioned is that the recombination reaction of methyl radicals to form ethane is not as inhibiting as expected, according to the sensitivity analysis. In consideration of the fact CH has shorter ignition delay time than MCH26 and CP has one longer than MCP in this work, we take CH, MCH, CP, and MCP to illustrate the factors by analyzing the consuming rates of the unimolecular decomposition and the contribution of methyl breaking off the ring as well as H radical mole fraction. We use the model developed based on quantum chemical calculation by Wang et al.24 to do computation for MCH and CH and the model of this work for MCP and CP. The results are shown in Figure 16. The computation is made for fuel/O2/Ar mixtures containing 13% O2 at 1.1 atm, 1350 K, and ϕ = 0.577. In panel a, MCH exhibits a longer ignition delay time. However, its initial unimolecular reaction rate (pink dotted line) which is contributed to largely by reaction MCP = cC6H11 + CH3 (orange dashed−double dotted line) is larger than that for CH (pink dashed line). Consequently, the total consumption rate of MCH (blue solid line) is larger than that of CH (blue dashed−dotted line). The presence of a methyl group renders a weaker C−C bond, causing a larger unimolecular reaction rate and then multiplies H radical through the dissociation of cyclohexyl radical (cC6H11), evidenced by comparison of H radical mole fractions between MCH and CH. Nevertheless, during the subsequent oxidation, H abstraction reactions take control. CH has six carbons in the ring and yields cyclohexyl radical through H abstraction. As analyzed by Hong et al.,26 cyclohexyl radical can easily release H radical through reactions cC6H11 = cC6H10 + H and cC6H11 = PXC6H11 and then isomerization and β-scission of 1-hexen-6yl radical (PXC6H11). This facilitates the H radical formation in the oxidizing system. It can be observed in the red dashed line in panel a, Figure 16. In contrast, a methyl group disturbs the mixture of intermediate radicals produced by H abstraction MCH. Some of them cannot release H radicals effectively, detracting from the level of H production in the system. Consequently, MCH loses its lead in the production of H radical, causing slower depletion of fuel. In panel b for CP and MCP, the presence of a methyl group again stimulates production of H radical and unimolecular decomposition of fuel. Although the regeneration of H radical for CP is considerable, other species hard to decompose are introduced. For example, cyclopentene is produced with the production of the majority of H radical and forms cyclopentadiene to inhibit ignition. Allyl radical consumes H radical to form stable propene. It can indirectly lower the consumption rate of fuel by removing H radical although other radicals are produced by allyl through alternative pathways. In comparison,

Figure 16. Rate of production of fuel and unimolecular reaction as well as H radical mole fraction for (a) MCH and CH O2/Ar mixtures containing 13% O2 calculated using the Wang et al.24 mechanism; (b) MCP and CP calculated using model of this work at ϕ = 0.577, p = 1.1 atm, and 1350 K.

little such hazards are yielded during CH oxidation, creating effective H generation. As for MCP, its oxidizing environment is complicated and the ability to regenerate H is somewhat higher than that of CP but not prominent. Hence, generally speaking, H regeneration has a little influence on the discrepancy of ignition between MCP and CP.

6. CONCLUSION Ignition delay time was measured for the cyclopentane/O2/Ar mixtures containing 1% CP and methylcyclopentane/O2/Ar mixtures containing 0.833% MCP with equivalence ratios of 0.5, 1.0, and 2.0. Reflecting shock wave conditions were 1.1 and 10 atm as well as temperatures of 1150−1850 K. Submodels for cyclopentane and methylcyclopentane were added to the JetSurF2.0 mechanism developed by Wang et al.33 to develope a model for CP and MCP including 419 species and 2490 reactions. The predictions by this model agreed well with the experimental data. Though most of the reactions of CP oxidation are obtained from the CP mechanism by Sirjean et al.,18 prediction with this model is higher than that with the Sirjean et al. model at high temperature. In addition, good agreement in ignition delay time between the MCP mechanism and experimental data is achieved. In comparison of the ignition delay time between CP and MCP, it is found that MCP has a shorter ignition delay than 439


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Energy & Fuels CP, especially at ϕ = 0.5 and a not too high temperature (

Shock Tube and Kinetic Modeling Study of ... - ACS Publications

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