Article
pubs.acs.org/EF
Experimental and Kinetic Modeling Study on trans-3-Hexene Ignition
behind Reflected Shock Waves
Feiyu Yang, Fuquan Deng, Peng Zhang, Zemin Tian, Chenglong Tang,* 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: trans-3-Hexene ignition delay times were measured behind reflected shock waves for fuel-lean (Φ = 0.5),
stoichiometric (Φ = 1.0), and fuel-rich (Φ = 1.5) mixtures between 1080 and 1640 K, at pressures between 1.2 and 10 atm. Two
fuel concentrations (1000 and 5000 ppm trans-3-hexene) diluted in argon were examined, and the ignition delay times were
obtained by following OH* radical chemiluminescence emission. The experimental results satisfied the Arrhenius equation, and
the influences of pressure, equivalence ratio, fuel concentration, and dilution gas on trans-3-hexene ignition behavior were
discussed. The Lawrence Livermore National Laboratory (LLNL) model overestimates the low-temperature reactivity and
underestimates the pressure-dependence at high-temperature. Improvements have been made to the LLNL model, and the
modified mechanism offers better predictions for the ignition delay times of this work as well as the shock tube, rapid
compression machine, and jet stirred reactor experimental data from the literature. Reaction pathway and sensitivity analysis were
performed to gain insight into the trans-3-hexene oxidation chemistry.
channels the simplest among the 3 n-hexene isomers. The
single CC double-bond structure permits its ignition and
oxidation behaviors to be comparable to that of both an olefin
and a linear paraffin.6
Unlike saturated alkanes,7,8 the characteristics of alkene
oxidation have not been sufficiently investigated, especially for
alkenes with a longer chain. Westbrook et al.5 measured the
ignition delay times and species concentration profiles of 2methyl-2-butene (2M2B) in a shock tube and a jet stirred
reactor (JSR), respectively, proposing a kinetic model.
Ribaucour et al.6 measured the ignition delay times of npentane and 1-pentene in a rapid compression machine (RCM)
at 600−900 K and proposed a kinetic model. Touchard et al.9
examined the ignition delay times of 1-pentene in a shock tube
and developed a model with more comprehensive scheme.
Prabhu et al.10 explored the oxidation behaviors of 1-pentene in
a flow reactor. Tanaka et al.11 have reported the pressure
profiles of linear heptene isomer combustion in a RCM. Mehl
et al.12 measured the ignition delay time of two n-pentene
isomers in a shock tube and proposed a kinetic model.
As far as hexenes are concerned, Yahyaoui et al.13,14 studied
the oxidation behaviors of 1-hexene in a JSR at 750−1200 K
and 10 atm and in a shock tube at 1270−1700 K and 0.2−1
MPa. The developed model overestimates the ignition delay
times in the low-temperature region. Using the Exgas15
software, Touchard et al.9 proposed a mechanism for 1pentene and 1-hexene, and modifications have been made to
achieve better predictions. Vanhove et al.16,17 investigated the
autoignition features of 1-, 2-, and 3-hexene after rapid
compression at 630−850 K for stoichiometric mixtures. Mehl
et al.12,18 reported the ignition delay times in shock tube of
1. INTRODUCTION
Since the beginning of the Industrial Revolution in the 18th
century, population growth and industrialization throughout
the world, especially in developing countries, have driven a
steady rise of fossil fuels consumption (in terms of petroleum,
coal, and natural gas consumption). Combustion of petroleum
for transportation accounts for 13% of greenhouse gas
emissions globally,1 while this value in the United States is
28%. Global concerns over increasing carbon emissions and
fossil fuel consumption have motivated the research on
developing environment friendly combustion techniques with
high efficiency.
Chemical kinetics of a specific fuel describe its oxidation
pathways, rate of each path, and the downstream products.
Accurate evaluation of the fuel oxidation kinetics, which is
important for combustion simulation in engines, burners, and
other combustors, holds the potential to increase combustion
efficiency, reduce pollutant emission, and optimize combustor
design. The powerful calculation capabilities of modern
computers can afford high fidelity simulation using detailed
kinetic mechanisms of a specific fuel. However, because
practical fuels consist of hundreds of hydrocarbons with
different functional groups and concentrations, numerical
simulations using practical fuels is so challenging that even
modern computer clusters have difficulty in time cost and
convergence of solution if the compositions are not simplified.
Thus, kinetic studies of gasoline or diesel surrogates2,3 have
received significant research attention.
Our target fuel in this work is trans-3-hexene because it has a
high octane number (research octane number 94 and motor
octane number 804) and high sensitivity value (RON-MON5)
and it is an important gasoline component or additive. The
CC double bond separates the long paraffin chain from the
midpoint; therefore, the trans-3-hexene molecule possesses a
geometric symmetry which makes its chemical reaction
© 2015 American Chemical Society
Received: November 13, 2015
Revised: December 21, 2015
Published: December 23, 2015
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DOI: 10.1021/acs.energyfuels.5b02682
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Energy & Fuels
three linear hexene isomers and a kinetic mechanism
(Lawrence Livermore National Laboratory (LLNL) model)
was proposed as well. Battin-Leclerc et al.4 observed the
products from the oxidation linear hexene isomers in two JSRs.
To our knowledge, the kinetic study on trans-3-hexene
chemistry has not been adequately conducted, in terms of
experimental data reporting and kinetic modeling. Only the
stoichiometric 3-hexene mixture was measured in previous
works. The first objective of this work is to measure the ignition
delay times of trans-3-hexene at different equivalence ratios
using a shock tube. In addition, a better model was obtained on
the basis of previous investigations, and almost all the
associated experimental databases (including shock tube,
RCM, and JSR) from the literature were used to validate the
trans-3-hexene mechanism; further analysis was performed to
provide clearer insight into trans-3-hexene oxidation chemistry.
Figure 1. Definition of ignition delay time in this work.
2. EXPERIMENTAL SETUP AND PROCEDURE
The shock tube employed in this work has been introduced in
previous contributions.19−22 Only a brief introduction is presented
here. The high-temperature shock tube consists of a 2 m driver section
and a 7.3 m driven section. There is a two PET (polyester
terephthalate) diaphragms section (flange section, 0.06 m long)
between them. The three sections have the same inner diameter of
11.5 cm. Before each test, the shock tube is evacuated to a pressure
below 10−4 Torr. Then, high-purity helium (99.999%) and nitrogen
(99.999%) are charged into the driver and the double diaphragm
section. The driven section is filled with the test mixture, the
preparation of which is described later. The shock wave is triggered by
rupture of the double diaphragm once the flange section is evacuated.
Four pressure transducers (PCB 113B26) are located along the driven
section with an identical interval of 30 cm. The distance between the
last pressure transducer and the end wall is 2.0 cm. The time instant of
the shock wave arrival at each pressure transducer location is sent to
three time counter (Fluke PM6690) with an accuracy of 10 ps, so that
the shock wave velocity profile along the shock tube direction is
determined. A pressure transducer (PCB 113B03) is also mounted at
the end wall flange to measure the end wall pressure. In addition, a
quartz optical window is also mounted at the end wall flange, through
which the OH* emission signal can be detected by a 306 nm narrow
band-pass filter and a photomultiplier (Hamamatsu CR 131). All the
pressure and OH* emission signals are recorded by a digital
oscilloscope (Yokogawa, ScopeCorder DL750). The temperature
behind the reflected shock wave is calculated according to the shock
wave velocity at the end wall (extrapolated by its velocity profile along
the shock tube), the reactant gas property, and the initial temperature
(T1) and pressure (p1) using the normal shock wave module in the
Gaseq software.23
Figure 1 shows the typical pressure and OH* emission signal
profiles captured by the end wall pressure transducer and the narrow
pass filter, respectively. At time t0 = 1269.2 μs, the shock wave arrives
at the end wall. At around t1 = 3737.1 μs, there is a sharp increase in
the pressure profile, which demonstrates the onset of ignition. The
ignition at t1 is also manifested by the steep increase in the OH*
emission signal. Thus, the ignition delay time is defined as (t1 − t0) =
2467.9 μs, which is essentially the time duration between the arrival of
the shock wave at the end wall and the onset of ignition. This
definition is consistent with most of the previous work.20,22
The molecular structure of the trans-3-hexene molecule is depicted
in Figure 2. It is noted that many unsaturated hydrocarbons have cis−
trans isomers, and 3-hexene is no exception. In general, the transisomer exhibits a heat of combustion lower than that of its
corresponding cis-isomer because of its more stabilized structure. In
addition, many trans-isomers can undergo isomerization reaction to
form the corresponding cis-isomers under high-temperature circumstances. Generally, the difference between cis−trans hexenes oxidation
are negligible, that is to say if one mechanism can readily predict the
oxidation behavior of one isomer, usually it is also applicable to both
Figure 2. Real geometry of trans-3-hexene molecule.
cis-, trans-isomers and their blends. In this study, trans-3-hexene are
used.
The trans-3-hexene/oxygen/argon mixtures were prepared in a 128
L stainless steel tank at 298 K (using air conditioner to maintain the
temperarure) before each run. The reactant fractions are determined
by the partial pressure of each component. Because the fuel
concentration in this study is very low, it is important to guarantee
the accuracy of the partial pressure of each component, especially the
fuel. A vacuum meter (Rosemount 3051C) with an accuracy of 1 Pa is
used to measure the partial pressure of the fuel. The tank pressure is
less than 300 kPa so that the condensation of the fuel can be avoided.
The purities of trans-3-hexene, oxygen, and argon are 99%, 99.999%,
and 99.999%, respectively. Once the mixtures are prepared, the tank is
stirred and then settled for at least 12 h before experiments. The
measurements were carried out at 1.2, 4.0, and 10 atm for two fuel
concentrations (5000 and 1000 ppm trans-3-hexene) and at
equivalence ratios of 0.5, 1.0, and 1.5. The compositions of the
mixtures are shown in Table 1.
Table 1. Mixture Compositions in This Study
trans-3-hexene (ppm)
O2 (%)
Ar (%)
Φ
P (atm)
5000
5000
5000
1000
9.0
4.5
3.0
1.8
90.5
95.0
96.5
98.1
0.5
1.0
1.5
0.5
1.2/4/10
1.2/4/10
1.2/4/10
1.2/4/10
3. KINETIC MODELING
Parallel to the experimental research, kinetic modeling has been
performed as well. To the best knowledge of the authors, there
are two detailed mechanisms available: the n-hexane mechanism proposed by the National University of Ireland Galway
(NUIG model8) and the gasoline surrogate mechanism
proposed by the Lawrence Livermore National Laboratory
(LLNL model24). Considering the better behavior of the LLNL
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Table 2. Modifications Made to the LLNL Mechanism
no.
R1
R16
R47
R92
R184
R185
R190
R230
R264
R265
R266
R648
R777
R931
R3762
R3763
R3764
R3768
R3769
R3770
R4087
R4207
R4208
R4354
R4428
R4439
R4430
R4431
R4465
reactions
A
H + O2 ⇔ O + OH
H2O2(+M) ⇔ OH + OH(+M)
LOW/ 2.49 × 1024 −2.3 48700 /
TROE/ 4.300 × 10−1 1.000 × 10−30 1.000 × 1030 /
H2O/0.00/CO2/1.60/N2/1.50/O2/1.20/HE/0.65/H2O2/7.70/
CH2O + HO2 ⇔ HCO + H2O2
CH3OH + OH ⇔ CH2OH + H2O
C2H5 + O2 ⇔ C2H4 + HO2
DUP
PLOG/ 0.0400 2.094 × 109 0.490 −391.4 /
PLOG/ 1.0000 1.843 × 107 1.130 −720.6/
PLOG/ 10.0000 7.561 × 1014 −1.010 4749.0/
C2H5 + O2 ⇔ C2H4 + HO2
DUP
C2H5O2 ⇔ C2H4 + HO2
PLOG/ 0.0400 1.782 × 1032 −7.100 32840.0/
PLOG/ 1.0000 2.701 × 1037 −8.470 35840.0 /
PLOG/ 10.0000 1.980 × 1038 −8.460 37900.0 /
CH2CHO + O2 ⇒ CH2O + CO + OH
PLOG / 0.0100 2.680 × 1017 −1.840 6530.0/
PLOG/ 0.1000 1.520 × 1020 −2.580 8980.0/
PLOG/ 1.0000 1.650 × 1019 −2.220 10340.0/
PLOG/ 10.0000 8.953 × 1013 −0.600 10120.0/
C2H3 + O2 ⇔ CH2O + HCO
C2H3 + O2 ⇔ CH2CHO + O
C2H3 + O2 ⇒ H + CO + CH2O
C3H5O ⇔ C2H3CHO + H
C4H71-4 ⇔ C4H6 + H
PLOG/ 1.0000 2.480 × 1043 −12.300 52000.0/
PLOG/ 10.0000 1.850 × 1038 −10.500 51770.0/
NC4KET13 ⇔ CH3CHO + CH2CHO + OH
C5H81-3 + H ⇔ C5H91-3
C5H81-3 + H ⇔ C5H91-4
C5H81-3 + H ⇔ C5H92-4
C5H81-3 + OH ⇔ CH2O + C4H71-3
C5H81-3 + OH ⇔ C2H3CHO + C2H5
C5H81-3 + OH ⇔ CH3CHO + C3H5-S
C6H12-3 + OH ⇒ PC4H9 + CH3CHO
C6H112O2-4 ⇒ C6H102-4 + HO2
C6H112O2−5 ⇒ C6H102-4 + HO2
C6H12-3 + O ⇔ NC3H7 + C2H5CO
C6H101-3 + H ⇔ C6H111-3
C6H101-3 + H ⇔ C6H111-4
C6H101-3 + H ⇔ C6H113-1
C6H101-3 + H ⇔ C6H112-4
C6H11O2-4 ⇔ SC3H5CHO + C2H5
1.04 × 1014
2.00 × 1012
0
0.9
n
Ea (cal/mol)
1.53 × 104
4.87 × 104
35
36
1.88 × 104
3.08 × 104
2.09 × 109
2.7
2.65
0.49
1.15 × 104
−8.07 × 102
−3.91 × 102
37
38
39
6.61 × 100
3.51
1.42 × 104
39
1.78 × 1032
−7.1
3.28 × 104
39
2.68 × 1017
−1.84
6.53 × 103
40
2.38
5.34
3.38
1.00
2.48
×
×
×
×
×
1027
1012
1014
109
1043
−4.86
−0.01
−0.89
0
−12.3
4.91
3.32
2.18
2.91
5.20
1.05
2.50
2.50
2.50
3.00
3.00
3.00
6.00
1.00
5.04
2.00
2.50
2.50
4.25
2.50
1.09
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
1015
1012
1012
1012
1012
1012
1012
1010
1038
1037
1013
1013
1013
1013
1013
1015
0
0.5
0.5
0.5
0
0
0
0
−8.11
−8.11
0
0.5
0.5
0.5
0.5
−1.92
4.16 × 104
2.62 × 103
2.62 × 103
2.62 × 103
0
0
0
−4.00 × 103
4.05 × 104
3.75 × 104
−1.05 × 103
2.62 × 103
2.62 × 103
1.23 × 103
2.62 × 103
1.08 × 104
×
×
×
×
×
103
103
103
104
104
ref.
41
41
41
42
43, 44
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
×
0.1
10
10
10
3
3
3
0.6
0.1
0.1
10
10
10
10
10
10
elimination reaction will produce a diene instead of an alkene.
To our knowledge, no investigations on HO2 elimination for
this case are reported. However, in the case of alkenylperoxy
radicals, compared with secondary C−H bond, the weaker allyl
C−H bond can enhance the elimination reaction. For trans-3hexene molecule, the short alkyl chains avoid isomerization
reaction, and as a result, this elimination reaction rules the
reactivity of the system. That is why large quantities of 2,4hexadiene and 1,3-hexadiene are probed during the lowtemperature oxidation. The pre-exponent factor is divided by a
factor of 10 to meet better predictions. The no-barrier reactions
of H addition were emphasized in the pathway analysis of
Battin-Leclerc et al.4 The H radical can add not only to trans-3-
model at low temperature (the JSR and RCM simulations of
the NUIG and LLNL models are attached as Supporting
Information), the LLNL model was adapted in this
investigation. Containing 1389 species and 5935 reactions,
the LLNL model was developed aiming at offering predictions
of gasoline surrogate oxidation. However, when it comes to the
3-hexene submechanism, it has been validated against only a
small number of RCM and shock tube experimental data of 3hexene under only stoichiometric conditions; further validations and necessary modifications are still required.
It is well-known that an alkylperoxy radical (ROO•) can
dissociate directly yielding alkene and hydroperoxy (HO2)
radical.25 In the case of an alkenylperoxy radical, this direct
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hexene but also to dienes, say, hexadienes and pentadienes.
Considering the large concentration of dienes, this H addition
channel exerts significant impact on the oxidation process. To
attach more importance to H addition, the rate constant is
increased by a factor of 10. At low temperature, the trans-3hexene molecule can readily be attacked by OH radical
producing n-butyl (PC4H9) and acetaldehyde (CH3CHO).
This pathway will directly compete the OH radical with the
addition and H-abstraction reactions and can overwhelmingly
determine the species profiles at around 650 K. The produced
PC4H9 radical will proceed the well-known low-temperature
chain-branching channel producing two active OH radicals. In
this study the rate constant is multiplied by 0.6 to correct the
over prediction of low-temperature reactivity. In addition, the
famous chain-branching reaction and the dissociation of H2O2
are updated. The pressure dependence of C2H4 reactions are
introduced. Note that all the modifications are within their
claimed uncertainty, and the modified reactions along with their
references are listed in Table 2.
4. RESULTS AND DISCUSSION
4.1. Ignition Delay Time Data. The measured ignition
delay times of trans-3-hexene are presented in Figure 3 and also
are available in Table S1. Note that the ignition characteristics
of trans-3-hexene obey the Arrhenius rule that the logarithm of
ignition delay times are proportional to the reciprocal of
temperatures.
Westbrook et al.5 suggested eq 1 to obtain the quantitative
relationship between the ignition delay times and the pressures
and equivalence ratios. In eq 1, τign, Ea, R, A, α, and β denote
the ignition delay time (μs), activation energy (kcal/mol), ideal
gas constant (R = 1.968 kcal/(mole·K)), pre-exponential factor,
exponent factor for equivalence ratio, and exponent factor for
pressure, respectively.
τign = A ·ϕα ·p β ·exp(Ea /RT )
(1)
Fitted from the entire experimental data at 5000 ppm
concentration, the following correlation (eq 2, R2 = 0.97) can
be derived:
τign (μs) = 3.0 × 10−3· ϕ1.064 ·p−0.421 · exp(33.0 (kcal/mol)/RT )
(2)
This correlation offers a positive equivalence ratio exponent
and a negative pressure exponent, which indicates the inhibition
and promotion effect of equivalence ratio and pressure,
respectively, on trans-3-hexene ignition. It is noted that the
absolute pressure exponent (−0.421) is small compared to that
of real gasoline fuels (−1.0626) and that of n-heptane
(−1.6426), which indicates that pressure exerts only slight
effects on ignition delay times of trans-3-hexene. This feature
makes it a promising fuel or additive to inhibit the knock in
supercharged gasoline engines, in which the in-cylinder
pressure is high compared to that in naturally aspirated
engines. To some extent, this high knock resistance property
can as well be speculated from the high octane number
(research octane number 94) mentioned before.
As reported by Westbrook et al.,5 the pressure exponent of
2M2B (RON = 97.3) is −0.40, which is quite close to that of
trans-3-hexene. Note that both 2M2B and trans-3-hexene have a
CC double bond located at the center of the molecule.
Yahyaoui et al.14,27,28 studied the ignition of 1-hexene in a
shock tube, and although no pressure exponent was given
Figure 3. Experimental data and correlations of trans-3-hexene at
different equivalence ratios.
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4.2. Model Validation. To evaluate the performance of the
modified mechanism, in this section the modified model was
widely validated against not only the ignition delay times of this
work but also the shock tube, RCM, and JSR data from the
literature.
4.2.1. Shock Tube Ignition Delay Times. 4.2.1.1. Shock
Tube Ignition Delay Times of This Work. The measured
ignition delay times of this work were used to validate the
modified model. The simulation has been conducted using the
zero dimensional closed homogeneous model of the SENKIN
code in the CHEMKIN II32 package. The problem type was set
as a constrained volume and solved energy equation. However,
in practice, under the influence of the boundary layer, the
volume shrinks and the pressure rises. The pressure rising rate
(dp/dt) is about 4% per ms, which is an average value obtained
from the pressure time history curves. The dp/dt can obviously
decrease ignition delay time at temperatures below 1300 K.
Figure 4b illustrates the ignition delay time with and without
considering dp/dt. As a result, the dp/dt is considered in all the
simulations of ignition delay time obtained in our shock tube. A
maximum uncertainty of 18%33 is taken into account.
Figure 4 compares the simulations before and after
modification. For 5000 ppm trans-3-hexene mixtures, the
LLNL mechanism underestimates the reactivity at high
pressure and overestimates at low pressure. As for the modified
model, better agreement was achieved for all the measurements.
When the fuel concentration decreases to 1000 ppm, the
simulation of the LLNL model presents a weaker pressure
dependence which is not in agreement with the measurements;
however, the modified model captures this feature readily.
Overall, the predicted ignition delay times of the modified
model are in reasonable agreement with the experimental data.
4.2.1.2. Shock Tube Ignition Delay Times from the
Literature. The shock tube ignition delay times from the
literature were also adopted to validate the modified model.
Mehl et al. 12 explored the ignition characteristics of
stoichiometric 3-hexene/oxygen/nitrogen mixture at 993−
1326 K, 8.9−11.8 atm in a shock tube. In this mixture, 3hexene concentration is maintained at 1.92%, which is
approximately 4 times that in the current research (trans-3hexene % = 0.5%). As depicted in Figure 5, the modified model
provides a better simulation. Note that the ignition delay times
at 10 atm (Φ = 1) in this study are about 4 times longer than
those of Mehl et al.,12 which is likely to result from the
difference in dilution ratio. In addition, the activation energy of
Mehl’s tests is smaller than of this study, which is possibly due
to different diluents. Mathieu et al.34 investigated methane
ignition in NOx environment and reported that nitrous oxide
and nitrogen dioxide can readily decrease the activation energy
of the mixture and facilitate ignition. This theory can be applied
to the exhaust gas recirculation (EGR) system, which has been
widely used in vehicles to reduce NOx emission and raise
combustion efficiency.
4.2.2. RCM Ignition Delay Times. The RCM ignition delay
times reflect the low and intermediate temperature chemistry.
Vanhove et al.17 measured the ignition delay times of
stoichiometric trans-3-hexene/air mixture at 6.8−8.5 bar,
630−850 K with RCM. As shown in Figure 6, the LLNL
model exhibits longer ignition delay times and a slight negative
temperature coefficient (NTC) phenomenon occurs. As
reported by Vanhove et al.,17 no cool flame and NTC occur
for trans-3-hexene ignition under this condition. This
directly from their experimental data, a pressure exponent of
−0.30 was derived by Westbrook et al.5 Mehl et al.18 compared
the octane numbers of 1-, 2-, and 3-alkene and those of their
corresponding alkanes. They found the octane numbers of
alkenes are larger than that of their corresponding alkanes,
especially when CC double bond locates at the center of the
molecule. More recently, the conjecture that the weak pressure
dependence of some unsaturated hydrocarbons result from
their high octane number are proposed to be supported by
some experiments. However, this point of view is challenged
when the pressure exponent of 1-hexene and 3-hexene are
concerned. This discrepancy may perhaps result from the
different octane sensitivity,5 and further studies are required.
Compared with methane (Ea = 47.2 kcal/mol29) and
ethylene (Ea = 47.4 kcal/mol30), trans-3-hexene presents a
rather smaller activation energy of 33.0 kcal/mol, being equal to
that of ethane (Ea = 33.0 kcal/mol31), which indicates that the
paraffin chain at each end of the CC double bond facilitates
the reactivity.
To obtain the effect of equivalence ratio and fuel
concentration on trans-3-hexene ignition, multiple linear
regression was conducted for each set of operating conditions.
The ignition data are correlated as
τign (μs) = 5.7 × 10−4 ·p−0.436 · exp(35.4 (kcal/mol)/RT ),
ϕ = 0.5, 5000 ppm
(3)
τign (μs) = 1.8 × 10−3·p−0.452 · exp(34.2 (kcal/mol)/RT ),
ϕ = 1.0, 5000 ppm
(4)
τign (μs) = 1.1 × 10−2 ·p−0.459 · exp(30.9 (kcal/mol)/RT ),
ϕ = 1.5, 5000 ppm
(5)
τign (μs) = 3.3 × 10−4 ·p−0.434 · exp(39.3 (kcal/mol)/RT ),
ϕ = 0.5, 1000 ppm
(6)
With the increase in equivalence ratio, the concentration of
oxygen decreases and, consequently, the dominating Habstraction reactions of O and OH radicals (C6H12-3 + O ⇔
C6H112-4 + OH and C6H12-3 + OH ⇔ C6H112-4 + H2O) are
replaced by the addition and H-abstraction reactions of H
radical (C6H13-3 ⇔ C6H12-3 + H, C6H12-3 + H ⇔ C6H112-4 +
H2 and C6H12-3 + H ⇔ C6H113-1 + H2). It is obvious that the
C6H112-4 radical with a resonance-stabilized allylic structure is
relatively more stable than the C6H111-3 and C6H13-3 radical.
What is more, the preferred H addition reaction exhibits
significant pressure dependence. As a consequence, when it
comes to a fuel-rich mixture, the absolute pressure exponent
increases (0.436 < 0.452 < 0.459) and activation energy
declines (35.4 > 34.2 > 30.9).
When eqs 3 and 6 are compared, the increase in dilution
ratio gives rise to a smaller absolute pressure exponent (0.436 >
0.434) and a larger activation energy (35.4 < 39.3). Under
highly diluted conditions, more argon atoms are contained;
however, argon has almost the smallest enhanced three-body
coefficient (about 0.7024), which may lead to weaker pressure
dependence. In addition, high argon concentration reduces the
probability of collision between reactive molecules, which
inhibits the reaction processes.
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Figure 5. Validation against the shock tube data of Mehl et al.12 and
this work at 10 atm.
Figure 6. Validation against the RCM ignition delay times of Vanhove
et al.17
discrepancy can be readily attributed to the overestimate of
low-temperature activity in the LLNL mechanism.
4.2.3. JSR Data. To further clarify the reaction pathway and
intermediate speciation, validation against JSR data is required.
Battin-Leclerc et al.4 reported the concentration profile during
the oxidation of stoichiometric 3-hexene/oxygen/argon mixture
at 500−1100 K, 800 Torr with a residence time of 2 s. The
comparison between the predictions and experimental data are
depicted in Figures 7 and 8. From 600 to 775 K, the trans-3hexene consumes slowly and many products, say 1-3-hexanene,
formaldehyde, and methanol, reach the first peak. At this
temperature range, the hydroxyl addition and H-abstraction
reactions dominate and reaction R4087 C6H12-3 + OH ⇒
PC4H9 + CH3CHO is of significant importance as well. The
produced PC4H9 radical proceeds through the following chainbranching channel: PC4H9 ⇒ PC4H9O2 ⇒ PC4H8OOH1-3 ⇒
PC4H8OOH13O2 ⇒ NC4KET13 + OH ⇒ CH3CHO +
CH2CHO + OH + OH. This degeneration pathway can
overwhelmingly improve the OH radical and CH3CHO
concentration and therefore facilitates the reactivity. This
pathway accounts for 14% in the LLNL mechanism, which
leads to the overestimate of many products at about 650 K.
Reasonable agreements are obtained when the rate constant of
R4087 decreases by 40% and the corresponding pathway
Figure 4. Validation against the LLNL and modified mechanism with
current data at different equivalence ratios. Dashed line, LLNL model;
solid line, modified model; dash−dotted line, LLNL model without
dp/dt; symbols, measurements.
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Figure 7. Validation of the LLNL and the modified mechanism against the concentration profile data of 3-hexene, oxygen, carbon monoxide, carbon
dioxide, methane, ethylene, propene, 1-butene, and 1,3-butadiene from JSR. Symbols, experimental data; blue line, LLNL model; black line, modified
model.
Figure 8. Validation of the LLNL model and the modified mechanism against the concentration profile data of 1,3-pentadiene, 2,4-hexadiene, 1,3hexadiene, acrolein, 2-butenal, formaldehyde, acetaldehyde, propanal, and n-butanal from JSR. Symbols, experimental data; blue line, LLNL model;
black line, modified model.
decreases to 6%. From 775 to 1100 K, almost all products peak
and the reactants are consumed sharply because of the higher
concentration of radical pool. At intermediate temperature, the
alkene are chiefly consumed through O atom collision (R4354
C6H12-3 + O ⇔ NC3H7 + C2H5CO) and H atom addition
(R4066 C6H13-3 ⇔ C6H12-3 + H) channel, and the hexadienes
are produced through OH H-abstraction channel. The LLNL
mechanism attaches less importance to the O atom collision
and H atom addition channels, and these two channels will
directly compete with the OH H-abstraction channel. As a
consequence, the LLNL model predicts more dienes and less
alkenes.
4.3. Kinetic Analysis. 4.3.1. Pathway Analysis. Because
initiation reactions involve only the reactant species, there are
only four possible reactions in the present trans-3-hexene/
oxygen/argon system, namely, the dissociation of C6H12-3, the
dissociation of O2, and the reaction between C6H12-3 and O2,
as in
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C6H12‐3 ⇔ CH3 + C5H 91‐3
O2 + M ⇔ O + O + M
(R4073, Ea = 72 kcal/mol)
(R6, Ea = 119 kcal/mol)
C6H12‐3 + O2 ⇔ C6H112‐4 + HO2
(R4175, Ea = 37 kcal/mol)
C6H12‐3 + O2 ⇔ C6H111‐3 + HO2
(R4176, Ea = 53 kcal/mol)
The activation energies of those four reactions are 72, 37, 53,
and 119 kcal/mol, respectively. Note that R4175 and R4176 are
the most important initiation reactions under almost all
conditions. R4037 may also contribute to initiation only at
high temperature, and R6 is usually not preferred because of
the large dissociation energy of oxygen. When an oxygen
molecule abstracts a secondary H atom from a carbon atom in
α position, the obtained 3-hexen-2-yl radical (C6H113-2)
isomerizes to a resonance-stabilized 2-hexen-4-yl radical
(C6H112-4). However, when H-abstraction reaction takes
place at β-carbon atom, the produced 3-hexen-1-yl (C6H1131) radical is not a resonance-stabilized allylic radical, so the
R4175 channel with a smaller activation energy is more
preferred than R4176.
As shown in Figure 9, the dominant reactions shift at
different temperature regions. At low temperature, OH radical
Figure 9. Dominant reactions at different temperature regions.
addition reaction dominates; the product C6H12OH-3 will
easily add to O2, forming O2C6H12OH-3. Then two propanal
molecules are generated through O2C6H12OH-3 ⇔ C2H5CHO
+ C2H5CHO + OH, which results in the first peak of propanal
at 650 K in Figure 8h. The OH radical H-abstraction reactions
are of secondary importance. For long chain alkanes or alkenes
with long saturate carbon chain, the H-abstraction products can
easily transform to ketohydroperoxides and OH radical at low
temperature. The ketohydroperoxides decompose to generate
OH radical. The rapid production of OH radical significantly
facilitates the reactivity and results in the NTC phenomenon.
This is the well-known degeneration channel of ketohydroperoxides. Nevertheless, a transition state with 5-member-cycle or
6-member-cycle is required for alkanylperoxide to isomerize
forming alkanylhydroperoxide radical. This is due to the lower
ring strain of the 5-member cycle or 6-menber cycle. In the
trans-3-hexene molecule, the four atoms connected to the
double bond locate in one plane. The location of the double
bond and the short saturated carbon chain fail to form a
transition state with 5-member-cycle or 6-member-cycle. As a
consequence, instead of forming ketohydroperoxides, the Habstraction products of trans-3-hexene react with hydroperoxygen radical and decompose, forming small aldehydes
and alkenes (Figure 10a).
At intermediate temperature region, H-abstraction of OH
radical and addition of H radical dominate in turn. The
conversion of reactants accelerates, and many intermediates
reach the maximum at about 850 K because of the booming of
the radical pool. Only a few derivatives of oxirane are produced.
At temperatures above 1275 K, initiation reaction dominates
and the radicals decompose rapidly through beta-scission
channel.
4.3.2. Sensitivity Analysis. To have a further look into the
mechanism and find the most sensitive reactions at different
Figure 10. Pathways analysis of trans-3-hexene oxidation at low (a, 650
K), intermediate (b, 850 K), and high (c, 1350 K) temperature.
temperature regions, sensitivity analysis was conducted for
stoichiometric mixture at 4 atm for 650, 850, and 1350 K. The
sensitivity coefficient is defined as
S=
τ(2ki) − τ(0.5ki)
1.5τ(ki)
(7)
where ki is the rate constant of the ith reaction and τ is the
ignition delay time. A negative sensitivity coefficient indicates
the promotion effect of the reaction, and a positive value
indicates the inhibition effect. The results are illustrated in
Figure 11.
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consume the active OH radical and yield relatively inactive
products; therefore, R4142 and R4142 are the chief inhibition
reactions. When considering 850 K, the major channel is Habstraction and H addition. Reaction R4147 C6H12-3 + HO2 ⇔
C6H112-4 + H2O2 converts the slow reacting radical HO2 to the
H2O2 molecule, which can sequentially produce two OH
radicals and promote ignition. Reactions R110 CH3 + HO2 ⇔
CH4 + O2 and R4183 CH3 + C5H81-3 ⇔ C6H112-4 are typical
chain termination reactions and can overwhelmingly reduce the
system activity. In addition, for the high-temperature region, say
1350 K, the main promoting reactions are those involving small
radicals and small molecules. The well-known chain-branching
reaction R1 H + O2 ⇔ O + OH offers the most prominent
promoting effect. Chain termination reactions such as R110
CH3 + HO2 ⇔ CH4 + O2, R4141 C6H12-3 + H ⇔ C6H112-4 +
H2, and R239 HCCO + OH ⇒ H2 + 2CO are the chief
inhibitive reactions.
5. CONCLUSIONS
In the present work, the ignition delay times of trans-3-hexene/
oxygen/argon mixtures have been measured at 1.2, 4, and 10
atm for equivalence ratios ranging from 0.5 to 1.5. To the best
knowledge of the authors, these are the first experimental data
reported for 3-hexene under nonstoichiometric conditions. The
LLNL model overestimates the low-temperature reactivity and
fails to capture the pressure dependence at high temperature.
Improvements have been made to the LLNL model, and the
modified model can successfully predict the experimental data
of the shock tube, RCM, and JSR. The reaction pathway
analysis shows that at low-, intermediate-, and high-temperature
regions the trans-3-hexene system is dominated by OH
addition, OH H-abstraction, and initiation reactions, respectively. The short alkyl chain inhibits the formation of cyclic
compounds, and no cool flame or NTC phenomena occur.
■
ASSOCIATED CONTENT
S Supporting Information
*
The Supporting Information is available free of charge on the
ACS Publications website at DOI: 10.1021/acs.energyfuels.5b02682.
Measured ignition delay times for trans-3-hexene in
shock tube and JSR and RCM simulations of the NUIG
and LLNL models (PDF)
■
AUTHOR INFORMATION
Corresponding Author
*E-mail: [email protected].
Notes
The authors declare no competing financial interest.
■
Figure 11. Ignition delay time sensitivity of trans-3-hexene at low (a,
650 K), intermediate (b, 850 K), and high (c, 1350 K) temperature.
ACKNOWLEDGMENTS
This work is supported by the National Natural Science
Foundation of China (91541107, 51206131, and 91441203)
and the National Basic Research Program (2013CB228406).
The support of the State Key Laboratory of Engines, Tianjin
University (K2015-01) is also acknowledged.
As mentioned above, at 650 K the major consumption
channel of trans-3-hexene is OH addition (R4459) and its
subsequent low-temperature O2 addition pathway. The
produced PC4H9 from reaction R4087 C6H12-3 + OH ⇒
PC4H9 + CH3CHO undergoes the well-known low-temperature degeneration pathway producing OH radical and
promoting ignition. As a result, R4087 offers the strongest
promoting effect. Reaction R4142 C6H12-3 + OH ⇔ C6H113-1
+ H2O and R341 C2H5CHO + OH ⇔ C2H5CO + H2O
■
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