Article
pubs.acs.org/EF
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
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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
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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.
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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.
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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
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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
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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
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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
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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.
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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.
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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
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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
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DOI: 10.1021/ef502552e
Energy Fuels 2015, 29, 428−441
Article
Energy & Fuels
CP, especially at ϕ = 0.5 and a not too high temperature
(<1500 K). Flux and ignition sensitivity analyses were
conducted to understand the oxidation of CP and MCP.
Then, taking the report that MCH has a longer ignition delay
than CH by Hong et al.26 into account, we ascribe the influence
of substitution of a methyl group and a cyclic ring to three
factors. A methyl group can enhance the unimolecular
decomposition of fuel and serve as a H radical source initially.
The shape of the ring and the presence of a methyl group
determine the subsequent alkyl radicals, leading to a unique
oxidizing environment which is reliable for effective H
generation.
■
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ASSOCIATED CONTENT
S Supporting Information
*
Tables listing species’ formation enthalpies for estimating BDEs
and additional reaction information. This material is available
free of charge via the Internet at http://pubs.acs.org.
■
AUTHOR INFORMATION
Corresponding Authors
*(Tang C.L.) E-mail: [email protected].
*(Huang Z.H.) E-mail: [email protected].
Notes
The authors declare no competing financial interest.
■
ACKNOWLEDGMENTS
This work is supported by the National Natural Science
Foundation of China (Grants 91441203, 51206131, and
51121092) and the National Basic Research Program (Grant
2013CB228406). The support from the State Key Laboratory
of Automotive Safety and Energy (Grant KF14102) is also
acknowledged.
■
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