Construction of a Chemical Kinetic Model of Five-Component Gasoline Surrogates under Lean Conditions
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molecules
Article
Construction of a Chemical Kinetic Model of Five-Component
Gasoline Surrogates under Lean Conditions
Chao Yang and Zhaolei Zheng *
Key Laboratory of Low-Grade Energy Utilization Technologies and Systems, Ministry of Education,
Chongqing University, Chongqing 400044, China; mryangchao@cqu.edu.cn
* Correspondence: zhengzhaolei@cqu.edu.cn; Tel./Fax: +86-023-6510-2473
Abstract: The requirements for improving the efficiency of internal combustion engines and reducing
emissions have promoted the development of new combustion technologies under extreme operating
conditions (e.g., lean combustion), and the ignition and combustion characteristics of fuels are
increasingly becoming important. A chemical kinetic reduced mechanism consisting of 115 species
and 414 elementary reactions is developed for the prediction of ignition and combustion behaviors
of gasoline surrogate fuels composed of five components, namely, isooctane, n-heptane, toluene,
diisobutylene, and cyclohexane (CHX). The CHX sub-mechanism is obtained by simplifying the
JetSurF2.0 mechanism using direct relationship graph error propagating, rate of production analysis,
and temperature sensitivity analysis and CHX is mainly consumed through ring-opening reactions,
continuous dehydrogenation, and oxygenation reactions. In addition, kinetic parameter corrections
were made for key reactions R14 and R391 based on the accuracy of the ignition delay time and
laminar flame velocity predictions. Under a wide range of conditions, the mechanism’s ignition
delay time, laminar flame speed, and the experimental and calculated results of multi-component
gasoline surrogate fuel and real gasoline are compared. The proposed mechanism can accurately
reproduce the combustion and oxidation of each component of the gasoline-surrogate fuel mixture
and real gasoline.
Citation: Yang, C.; Zheng, Z.
Keywords: cyclohexane; simplified chemical kinetic model; ignition delay time; laminar flame speed
Construction of a Chemical Kinetic
Model of Five-Component Gasoline
Surrogates under Lean Conditions.
Molecules 2022, 27, 1080. https://
doi.org/10.3390/molecules27031080 1. Introduction
Academic Editor: Stefano Falcinelli
Strict emission regulations place higher requirements on internal combustion engine
technology (high efficiency and low emissions). Although the popularity of new energy
Received: 28 December 2021 vehicles with batteries as the main power continues to increase, research on hybrid power
Accepted: 28 January 2022 and the design of range extenders is inseparable from research on internal combustion
Published: 6 February 2022 engines. Clean fuels (e.g., alcohol and hydrogen) cannot completely replace traditional
Publisher’s Note: MDPI stays neutral gasoline and diesel in the short-term. Selective catalyst reduction [1,2] to reduce NOx
with regard to jurisdictional claims in emissions and chemical kinetics to control in-cylinder combustion and heat transfer [3] have
published maps and institutional affil- achieved certain results in diesel engines. In addition, new combustion technology research
iations. has also become a feasible method to improve engine efficiency and reduce emissions, such
as homogeneous charge compression ignition [4], premixed charge compression ignition [5],
and reactive control compression ignition (RCCI) [6]. However, these new gasoline engine
technologies are increasingly becoming sensitive to the physical properties (e.g., density and
Copyright: © 2022 by the authors. viscosity) and chemical properties (e.g., flame propagation) of gasoline fuels [7]. Adding
Licensee MDPI, Basel, Switzerland. more real components of gasoline is necessary to ensure that gasoline-surrogate fuels match
This article is an open access article
these physical and chemical properties.
distributed under the terms and
The composition of gasoline-alternative fuels varies from single-component to multi-
conditions of the Creative Commons
component. Single-component and binary alternatives can be used for simple applica-
Attribution (CC BY) license (https://
tions [8,9]. Many alternative fuels with different physical and chemical properties have
creativecommons.org/licenses/by/
been considered. These alternatives include toluene blended fuel (TRF) composed of
4.0/).
Molecules 2022, 27, 1080. https://doi.org/10.3390/molecules27031080 https://www.mdpi.com/journal/molecules
Molecules 2022, 27, 1080 2 of 20
isooctane, n-heptane, and toluene [10–12], four-component fuel alternatives [13–15], and
alcohol-containing alternatives [16,17], which have been verified in extensive experiments
and model studies. Recently, naphthenic hydrocarbons have begun to be emphasized.
Excluding olefins and naphthenic hydrocarbons may lead to inaccuracy in the prediction
of gasoline-alternative fuels [18,19]. Andrae [18] found that adding CHX to a quaternary
mixture including primary reference fuel (PRF), toluene, and diisobutylene (DIB) and partly
replacing the PRF content increases the overall reactivity and improves model predictions
at rapid compression machine (RCM) conditions. According to the study of Chu et al. [20],
the addition of cycloalkane molecules to the laminar diffusion flame of n-heptane and
isooctane promotes the formation of soot particles in the low-temperature region.
Cyclohexane (CHX), which is often used as a representative of cycloalkanes to study
gasoline-surrogate fuels [18,21,22], has the simplest ring structure among cycloalkanes.
Early studies on CHX were conducted in different reactors for CHX oxidation experi-
ments [23,24]. Voisin et al. [23] conducted CHX oxidation studies in a jet stirrer reactor
(JSR), and a chemical kinetic mechanism was proposed to verify its data. Subsequently,
El-Bakali et al. [24] modified the mechanism of Voisin and expanded its validation range.
Buda et al. [25] developed a detailed low-temperature oxidation chemical kinetic mecha-
nism of CHX based on the EXGAS program, and this mechanism was able to satisfactorily
reproduce experimental results obtained in an RCM for temperatures ranging from 650 to
900 K and in a JSR from 750 to 1050 K. Wang et al. [26] developed a JetSurF2.0 mechanism
containing CHX that describes the high-temperature pyrolysis and oxidation of n-alkanes
from n-pentane to n-dodecane and the high-temperature chemical reaction of CHX and
monoalkylated CHX. This mechanism has 348 species and 2163 reactions. Recently, Zou
et al. [27] used SVUV-PIMS and GC+MS to analyze the low-temperature JSR oxidation of
CHX at 1.04 bar and ϕ = 0.25, and they developed a detailed oxidation model for CHX.
However, the previous research on the CHX model mainly focused on describing the
chemical properties of CHX in detail, and it lacked attention to its simplified model.
Some researchers have begun to pay attention to the development of the simpli-
fied mechanism of multi-component gasoline-alternative fuels containing CHX. The five-
component gasoline-alternative fuel chemical kinetic model developed by Li et al. [21] is
composed of n-heptane, isooctane, toluene, DIB, and CHX to predict the ignition delay
time. Although this model has been used many times to discuss the influence of gasoline
components on the combustion and emissions of gasoline direct-injection engines [28,29],
large-scale has caused difficulty in flame-speed verification and three-dimensional numeri-
cal simulation. The six-component diesel/gasoline-alternative fuel chemical kinetic model
proposed by Raza et al. [6] shows a good mechanism scale (168 species and 680 reactions)
and was used to study the combustion characteristics of RCCI. Alternatives with more
components have been developed to match a wider range of fuel characteristics [22]. Con-
sidering the constraints of computing resources and time cost, these models are difficult
for complex three-dimensional engine computational fluid dynamics (CFD) simulations.
Furthermore, to the best of our knowledge, few data on laminar burning velocities have
been reported on any gasoline surrogate with CHX as one of the mixture components.
As mentioned above, it has been identified that the main challenge for new gasoline
engines to achieve high efficiency and low emissions is in-cylinder combustion research.
Constructing a simplified chemical kinetics mechanism can reduce the computational cost
and space complexity of CFD three-dimensional numerical simulation. In this study, the
cyclohexane was chosen as a representative of gasoline naphthenes due to the simple cyclic
structure. The CHX mechanism [26] is simplified under a wide range of conditions, and
added to the DIB mechanism proposed by Zheng [30] and the TRF mechanism developed by
our research group [10]. A five-element simplified mechanism for gasoline suitable for lean
combustion is obtained. The mechanism calculations were performed in a zero-dimensional
single-zone model and a one-dimensional premixed flame model. The proposed mechanism
is evaluated with the ignition delay time, laminar flame velocity, and species distribution
data measured in the literature.
Molecules 2022, 27, 1080 3 of 20
2. Construction of Chemical Kinetic Model
In this study, a chemical kinetic model of a five-component gasoline fuel substitution
mixture containing n-heptane, isooctane, toluene, DIB, and CHX is constructed. The model
mainly includes three parts: (a) the TRF sub-mechanism is derived from our previous study
of the TRF mechanism [10], and the toluene part of the macromolecular reaction is modified
according to the simplified mechanism of Liu et al. [11]; (b) the DIB sub-mechanism is
derived from the model constructed by Zheng et al. [30]; and (c) the CHX sub-mechanism
is simplified from the JetSurF2.0 mechanism [26]. At present, no simplified version of the
CHX mechanism has been found in literature. Therefore, the construction of the CHX
sub-mechanism is focused on in this study.
2.1. CHX Sub-Mechanism
The JetSurF2.0 mechanism developed by Wang et al. [26] considers the oxidation of
various hydrocarbons and is selected as the basic chemical kinetic model of CHX fuel.
It contains 348 species and 2163 elementary reactions. The mechanism of JetSurF2.0 is
complicated, and its direct use in CFD numerical simulation will promote the increase in
computational cost and the decrease in efficiency. Although the available computing power
is growing rapidly, the simplification of the detailed mechanism of CHX is essential for the
construction of a simplified model of the five-component gasoline-alternative fuel.
In this study, direct relationship graph error propagating (DRGEP) is used to simplify
the detailed mechanism into the skeleton mechanism, and then, the rate-of-production
analysis (ROP) and the sensitivity analysis (SA) are used to simplify the skeleton mechanism.
Details on DRGEP, ROP, and SA are presented in Section 4.2.
2.1.1. Simplified DRGEP
The calculation of the DRGEP method uses the closed homogeneous model. The
equivalent ratio is 0.5–1.0, the temperature range is 660–1500 K, and the pressure range is
1–4 MPa. By selecting the absolute error and the relative error of the target parameter in
the simplification process, iterative calculations are performed to achieve the simplification
goal, and finally, the simplification mechanism that meets the error requirements and has
the smallest scale is obtained. The target parameters of the simplified process are selected
as the mole fraction of CHX (cC6 H12 ) and the soot precursor C6 H6 , and the ignition delay
time. Normalized errors are used as the basis for simplified judgment. A normalized error
is defined as
| D − S|
α= , (1)
( R×| D |+ A)
where D represents the calculated value of the target parameter for the detailed mechanism,
S represents the calculated value of the target parameter for the simplified mechanism, R
represents the relative tolerance, and A represents the absolute tolerance. If the normalized
maximum error is less than 1.0, then all tolerance settings of the target parameter are met.
The error of the target parameter setting in this simplified process is shown in Table 1.
Table 1. Error setting of target parameters.
Target Parameters Absolute Tolerance Relative Tolerance
Mole fraction of cC6 H12 1× 10−4 20
Mole fraction of C6 H6 1 × 10−4 20
IDT 1 × 10−6 10
Figure 1 shows the normalized error analysis of the skeleton mechanism species
obtained by simplifying the DRGEP method and the corresponding predicted ignition
delay time. The DRGEP method generates a series of skeletal mechanisms with different
species numbers through the calculation of the original database. For the ignition delay
time, the normalization error gradually increases as the number of species decreases. For
IDT 1 × 10−6 10
Figure 1 shows the normalized error analysis of the skeleton mechanism species ob-
tained by simplifying the DRGEP method and the corresponding predicted ignition delay
Molecules 2022, 27, 1080 4 of 20
time. The DRGEP method generates a series of skeletal mechanisms with different species
numbers through the calculation of the original database. For the ignition delay time, the
normalization error gradually increases as the number of species decreases. For species
species composition
composition between between
122 and 122 and
250, the250, the calculation
calculation error iserror is within
within 50%,the
50%, and and the largest
largest error
error
in theinspecies
the species composition
composition between between
50 and 50100
andcan100becan be close
close to 250%.
to 250%. The normalized
The normalized error
error
of theofmole
the mole fraction
fraction of6H
of cC cC H12 and
126and C6HC 6 Hwithin
6 is 6 is within
50%.50%. Notably,
Notably, the the simplification
simplification cancanbe
be considered successful as long as the normalization error of the calculation
considered successful as long as the normalization error of the calculation is guaranteed is guaranteed
to
to be
be within
within 100%.
100%. However,
However, according
according to to Figure
Figure 1,1, the
the species
species is
is reduced
reduced from
from 122
122 to
to 92,
92,
and
and the normalized error of the ignition delay time has more than doubled. Therefore, the
the normalized error of the ignition delay time has more than doubled. Therefore, the
simplified
simplified mechanism
mechanism of of DRGEP122
DRGEP122 is is selected
selected as as the
the mechanism
mechanism of of subsequent
subsequent reaction
reaction
rate
rate analysis
analysis and
and temperature-sensitivity
temperature-sensitivityanalysis analysis(SA).
(SA).
IDT
250
Mole fraction of cC6H12
Mole fraction of C6H6
200
Normalization error (%)
150 92 species, 67.8%
100 100%
122 species, 31.1%
50
0
100 150 200
Species
Figure 1.1. Skeletal mechanism species obtained by direct
Figure direct relationship
relationship graph
graph error
error propagating
propagating
(DRGEP)and
(DRGEP) andnormalized
normalizederror
errorof
ofthe
thecorresponding
correspondingprediction.
prediction.
The
The DRGEP
DRGEPanalysis method
analysis method is used to simplify
is used the detailed
to simplify mechanism
the detailed of JetSurF2.0,
mechanism of Jet-
and the two
SurF2.0, andskeleton
the twomechanisms DRGEP92 and
skeleton mechanisms DRGEP122
DRGEP92 are obtained.
and DRGEP122 areDRGEP92
obtained.
contains
DRGEP92 92 contains
species and 550 reactions,
92 species and 550 and DRGEP122
reactions, andcontains
DRGEP122 122 species
contains and122725 reactions.
species and
Both are skeletal
725 reactions. mechanisms
Both andmechanisms
are skeletal need to be further
and needsimplified. Figuresimplified.
to be further 2 further compares
Figure 2
the ignition
further delay time
compares prediction
the ignition values
delay timeofprediction
the two framework
values ofmechanisms
the two frameworkwith species
mecha-92
and 122, respectively. At an equivalent ratio of 0.5, a pressure of 1–4 MPa, and
nisms with species 92 and 122, respectively. At an equivalent ratio of 0.5, a pressure of 1– a temperature
range
4 MPa,ofand660–1500 K, the ignition
a temperature range delay time calculation
of 660–1500 results
K, the ignition of the
delay two
time mechanisms
calculation are
results
in good agreement with the detailed mechanism. The maximum error
of the two mechanisms are in good agreement with the detailed mechanism. The maxi- of the ignition delay
is the maximum
mum error of thevalue of the
ignition error
delay of the
is the ignition value
maximum delay of
time
thecalculated
error of the byignition
the skeleton
delay
mechanism
time calculatedandby thethe
detailed
skeletonmechanism
mechanism atand
threethedifferent
detailedpressures
mechanism in at
thethree
temperature
different
range of 660–1550
pressures K (shown inrange
in the temperature Figureof2b). The maximum
660–1550 K (shown error of DRGEP92
in Figure 2b). The is maximum
obviously
higher than that of DRGEP122. This result is understandable because
error of DRGEP92 is obviously higher than that of DRGEP122. This result is understand- the accuracy of
mechanism prediction will be reduced when the component is decreased.
able because the accuracy of mechanism prediction will be reduced when the component Considering
the accuracy ofConsidering
is decreased. calculation, the
the accuracy
simplifiedofmechanism
calculation,of the
DRGEP122
simplified is selected
mechanism as theof
mechanism of subsequent generation rate analysis and temperature
DRGEP122 is selected as the mechanism of subsequent generation rate analysis and tem- SA.
perature SA.
Molecules
Molecules2022,
2022, 27,
27, x1080
FOR PEER REVIEW 5 5ofof20
20
100 a b DRGEP92
6 DRGEP122
Ignition delay times (ms)
of ignition delay times
10
Maximum error(%)
4
1
0.1
2
Detailed DRGEP92 DRGEP122
0.01 p=1 MPa
p=2 MPa
p=4 MPa 0
0.001 0.6 0.8 1.0 1.2 1.4 1.6
0.6 0.8 1.0 1.2 1.4 1.6
1000/T
1000/T
(a) (b) mechanisms (DRGEP92 and
Figure 2. Detailed mechanism and comparison with two skeletal
DRGEP122) to predict the ignition delay of CHX /air mixture. (a) Ignition delay times and (b) maxi-
Figure 2. Detailed mechanism and comparison with two skeletal mechanisms (DRGEP92 and
mum error of ignition delay times.
DRGEP122) to predict the ignition delay of CHX /air mixture. (a) Ignition delay times and (b) max-
imum
2.1.2. error of ignition
Analysis of thedelay times. Path of CHX
Oxidation
2.1.2. The DRGEP
Analysis analysis
of the method
Oxidation greatly
Path of CHX reduces the simplification pressure of the detailed
mechanism, but it is insufficient. This research aims to construct a simplified mechanism.
The DRGEP
The skeleton analysisofmethod
mechanism greatly reduces
CHX DRGEP122 has been theobtained,
simplification pressure
including of the and
122 species de-
tailed mechanism, but it is insufficient. This research aims
725 elementary reactions. The oxidation path of CHX is analyzed by ROP. The reaction to construct a simplified mech-
anism.
rate ofTheCHX skeleton mechanism
is calculated using of the
CHX DRGEP122mechanism
framework has been obtained,
of DRGEP122 including 122 spe-
under lean
cies and 725 elementary reactions. The oxidation path of CHX
conditions (equivalent ratio is 0.5). The initial conditions are as follows: pressure p = 2 MPa,is analyzed by ROP. The
reaction
temperaturerate is of750
CHX K atis low
calculated using and
temperature the framework
1350 K at high mechanism
temperature, of DRGEP122 under
and the threshold
lean conditions (equivalent
of reaction path analysis is 3%. ratio is 0.5). The initial conditions are as follows: pressure p=
2 MPa, temperature is 750 K at low temperature and 1350
Figure 3 shows the main path of CHX oxidation. The pressure is p = 2 MPa, and theK at high temperature, and the
threshold
temperature of reaction
is 750 K pathfor low analysis is 3%. and 1350 K for high temperature. The blue and
temperature
Figure 3 shows the
red numbers indicate the forward andmain path of CHX
reverse oxidation. The pressure
contributions is p = 2 MPa,
of each reaction. and the
As shown in
temperature
Figure 3, the is 750 K for
oxidation low temperature
process of CHX is mainly and 1350 K forinto
divided highthree
temperature. The blue and
parts: (a) Dehydrogena-
red
tionnumbers
reactions.indicate
At two the forward and
temperatures, CHX reverse contributions and
is dehydrogenated of each reaction.
converted to As shown
cyclohexyl
in
(cCFigure
H
6 11 ).3, the oxidation
Cyclohexyl and process
its of
products CHX is
undergo mainly divided
continuous into three
dehydrogenation parts: (a) Dehydro-
reactions and
genation reactions. At two temperatures, CHX is dehydrogenated
finally generate benzene rings, which is an important way for CHX combustion to generate and converted to cyclo-
hexyl
PAH; (cC H11). Cyclohexyl
(b) 6Oxidation reactions. andWhen
its products
cyclohexyl undergo
radicalscontinuous
are exposed dehydrogenation reac-
to O2 , they produce
tions
cC6 Hand
11 O2finally
(88.6%) generate
and cC6benzene
H10 O2 H-2 rings, which
(9.5%) is an
at 750 K. important
(c) Immediate wayring-opening
for CHX combustion
reactions.
to
Atgenerate PAH; (b) Oxidation
1350 K, cyclohexyl radicals open reactions.
to form When cyclohexyl
1-hexene radicalsradicals
(61%) and are then
exposed to O2a,
undergo
they
seriesproduce
of reactioncC6Hcracks
11O2 (88.6%)
to formand smallcC6molecules
H10O2H-2 (9.5%) such as at1,3-butadiene
750 K. (c) Immediate ring-open-
and ethylene.
ing reactions. At 1350 K,
To avoid deleting thecyclohexyl
reactions that radicals
have aopen to form 1-hexene
low reaction rate and are radicals (61%) and
more sensitive to
temperature
then undergoinathe process
series of generation
of reaction cracksrate analysis,
to form smalltemperature
molecules SA suchis used to obtain the
as 1,3-butadiene
key ethylene.
and reactions at different initial temperatures. Temperature SA can measure the sensitivity
of a certain
To avoid elementary
deleting the reactions
reactions to temperature
that have a low through
reactionthe rate
normalized
and are sensitivity coef-
more sensitive
ficient.
to The negative
temperature value indicates
in the process of generation the promotive
rate analysis,effects of the corresponding
temperature SA is used toreaction
obtain
on ignition,
the key reactionswhileatthe positive
different one denotes
initial the inhibitive
temperatures. Temperatureeffects.SA Figure 4 showsthe
can measure thatsen-
the
elementary
sitivity reactions
of a certain with larger
elementary temperature-sensitivity
reactions to temperature through coefficients are differentsensitiv-
the normalized in differ-
entcoefficient.
ity temperature The regions.
negative In the low-temperature
value zone (750 K),
indicates the promotive the temperature-sensitive
effects of the corresponding
reaction is mainly the macromolecular reaction
reaction on ignition, while the positive one denotes the inhibitive effects.of CHX oxidation. The isomerization
Figure 4 shows of
cC H
that6 the O to cC
11 elementary
2 H O H-2
6 10reactions
2 (R642) and the cleavage of the C–O
with larger temperature-sensitivity coefficients bond of cC H
6 11 O generate
are2different
cyclohexene
in (cC6 H10 ) and
different temperature HO2 radicals
regions. (R643). In the high-temperature
In the low-temperature zone (750 K), thezone (1350 K),
temperature-
most of the
sensitive elementary
reaction is mainly reactions that are more sensitive
the macromolecular reaction of to CHX
temperature
oxidation. areThe
C0 –C 4 small
isomeri-
molecule reactions. O atoms and OH radicals (R1) generated
zation of cC6H11O2 to cC6H10O2H-2 (R642) and the cleavage of the C–O bond of cC6H11O by H atoms colliding with O22
molecules have a large positive sensitivity coefficient.
generate cyclohexene (cC6H10) and HO2 radicals (R643). In the high-temperature zoneMolecules 2022, 27, x FOR PEER REVIEW 6 of 20
(1350 K), most of the elementary reactions that are more sensitive to temperature are C0–
Molecules 2022, 27, 1080 6 of 20
C4 small molecule reactions. O atoms and OH radicals (R1) generated by H atoms collid-
ing with O2 molecules have a large positive sensitivity coefficient.
(a) 750 K
(b) 1350 K
Figure 3. Main oxidation path of CHX. (a) 750 K and (b) 1350 K.
Figure 3. Main oxidation path of CHX. (a) 750 K and (b) 1350 K.Molecules
Molecules2022,
2022,27,
27,xxFOR
FORPEER
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REVIEW 77 ofof 20
20
Molecules 2022, 27, 1080 7 of 20
R646 cC R637
R646 cC6H 10O2H-2+O2=SOOcC6O2H
6H10O2H-2+O2=SOOcC6O2H
R637 cC
cC6H 11(+M)=cC6H10+H(+M)
6H11(+M)=cC6H10+H(+M)
R645 cC R636
R645 cC6HH10OO2H-2=>OH+CO+C
6 10 H-2=>OH+CO+C5HH10
2 5 10
R636 cC
cC6H11(+M)=PXC
6 H 11 (+M)=PXC6H 11(+M)
6H11(+M)
R643 cC R630 cC H +H=cC H +H
R643 cC6H 11O2=cC6H10+HO2
6H11O2=cC6H10+HO2
R630 cC H +H=cC H +H2
6
6
12
12
6 11
6 11 2
R642 R344
R642 cCcC6H 11O2=cC6H10O2H-2
6H11O2=cC6H10O2H-2
R344 CC4HH6+H=C 2H4+C2H3
4 6+H=C2H4+C2H3
R641 R258 1350
1350KK aC
cC
R641 6 11+O2=cC6H11O2
H
cC6H11+O2=cC6H11O2 R258 aC H +HO2=OH+C
3 H
3
5 +HO =OH+C2HH3+CH
5 2 +CH2OO 2 3 2
R640 R159 CC2HH3+O2=HCO+CH2O
R640 cC
cC6H 11+O2=cC6H10O2H-2
6H11+O2=cC6H10O2H-2
750
750KK R159 2 3+O2=HCO+CH2O
R634 R158 CC2HH3+O2=CH
cC
R634 cC6 6H1212+HO
H +HO2=cC 6H11+H2O2
2=cC6H11+H2O2
R158 2 +O2=CH2CHO+O
3 CHO+O 2
R632 R84
R632 cC6 6H1212+OH=cC6H
cC H +OH=cC 11+H2O
6H11+H2O
R84 CH3+HO
CH 2=CH3O+OH
3+HO2=CH3O+OH
R437 C H +OH=C H +H O R20 HO
R437 C6 H6 +OH=C6 H5 +H2 O
6 6 6 5 2 R20 HO2 +OH=H2O+O
+OH=H
2 O+O2 2 2
R24 HH2OO2+OH=HO 2+H2O
R14 2OH(+M)=H
R24 2 2+OH=HO2+H2O
R14 2OH(+M)=H2O 2(+M)
2O2(+M)
R20 R12 H+O
R20
HO +OH=H O+O
HO +OH=H O+O2
2
2
2
2 2
R12 H+O (+M)=HO2(+M)
2 (+M)=HO
2 (+M) 2
R14 2OH(+M)=H O (+M) R1
R1 H+O
H+O2=O+OH
R14 2OH(+M)=H2 2O2 2(+M) 2=O+OH
−0.8 −0.4 −0.2 0.0 0.2 0.4 0.6 0.8 1.0
−0.8 −0.6
−0.6 −0.4
−0.4 −0.2
−0.2 0.0
0.0 0.2
0.2 0.4
0.4 0.6 0.6 0.8
0.8 1.0
1.0 −0.4 −0.2 0.0 0.2 0.4 0.6 0.8 1.0
Temperature sensitivity coefficient
Temperature sensitivity coefficient Temperature sensitivity coefficient
Temperature sensitivity coefficient
(a)
(a)750
750KK (b)
(b)1350
1350KK
Figure
Figure4.4.Temperature
TemperatureSA
SAof
ofdifferent
differenttemperatures
temperatures(φ(φ===0.5,
0.5,ppp==
=222MPa).
MPa). (a) 750 K and (b) 1350 K.
Figure 4. Temperature SA of different temperatures (ϕ 0.5, MPa). (a)
(a) 750
750 K
K and
and (b)
(b) 1350
1350 K.
K.
The
Thetemperature
temperaturesensitivity
temperature sensitivityof
sensitivity of elementary
ofelementary reactions
elementaryreactions under
reactionsunder
under different
different
different equivalence
equivalence
equivalence ra-
ra-
ratios
tios
tiosis analyzed,
is analyzed,
is analyzed, and
and and some
somesome elementary
elementary
elementary reactions
reactions
reactions with
with with larger
largerlarger sensitivity
sensitivity
sensitivity coefficients
coefficients
coefficients are ob-
are ob-
are obtained,
tained,
tained,
as shownas
asshown
shown
in in
Figure inFigure
Figure
5. Under5.5.Under
Under different
differentdifferent equivalence
ratios,ratios,
equivalence
equivalence large
largemolecule
ratios,molecule
large molecule reactions
reactions
reactions (R634,
(R634,
(R634, R640,
R640, R643, R643,
R640,R645,
R643,andR645,
R645, and
andand
R646) R646)
R646) and small
andmolecule
small molecule
small molecule
reactions reactions
reactions
(R14 and (R14
(R14
R19) and
and R19)
R19)became
became became
equally
equally
equally
sensitivesensitive
sensitive atattemperatures
at temperatures of 1000 of
temperatures of1000
K. 1000K. K.Notably,
Notably, Notably, the
theelementary
the elementary reactionsreactions
elementary R634 andR634
reactions R640and
R634 and
are
R640
R640 are less sensitive
are less at
less sensitive sensitive at
750 andat1350 750 and
750Kand 1350 K
1350 4),
(Figure (Figure
K (Figure 4),
but they4), but
have they
butgreaterhave
they have greater sensitivity
greateratsensitivity
sensitivity 1000 K. The atat
1000
1000
HO2 K.K. The HO
The HO
radical 2 radical in R634 extracts the H atom in CHX, the generated H2O2 is an
2 radical
in R634 in R634
extracts the extracts
H atom the H atom
in CHX, theingenerated
CHX, theHgenerated
2 O2 is an H 2O2 is an
important
important
substancesubstance
important substance for
forthe
for the formation theformation
formation of
ofOH
of OH radicals OHradicals
(R19), and
radicals (R19),
R640
(R19), and
is R640
and an
R640 isisan
animportant
important path for
important path
the
path
for the oxygenation
oxygenation reaction reaction
of CHX.
for the oxygenation reaction of CHX. of CHX.
R646
R646 cC
cC6H10O2H-2+O2=SOOcC6O2H
6H10O2H-2+O2=SOOcC6O2H
R645
R645 cC
cC6H 10O2H-2=>OH+CO+C5H10
6H10O2H-2=>OH+CO+C5H10
R643
R643 cC
cC6HH11OO2=cC
=cC6HH10+HO
+HO2
6 11 2 6 10 2
R642
R642 cC
cC6H 11O2=cC6H10O2H-2
6H11O2=cC6H10O2H-2
R640
R640 cC
cC6HH11+O
+O2=cC
=cC6HH10OO2H-2
H-2
6 11 2 6 10 2
R637
R637 cC6H
cC 11(+M)=cC6H10+H(+M)
6H11(+M)=cC6H10+H(+M)
R636 cC6 H11(+M)=PXC
cC H (+M)=PXC6HH11(+M)
(+M)
R636 6 11 6 11
R634 cC
cC6H 12+HO2=cC6H11+H2O2
R634 6H12+HO2=cC6H11+H2O2
R633
R633 cC
cC6 H12+O
H +O2=cC
=cC6HH11+HO
+HO2
6 12 2 6 11 2
R211 CC2HH5+HO φ
φ=1.0
R211 2=CH3+CH2O+OH =1.0
2 5+HO2=CH3+CH2O+OH φ
R209 CC2HH5+O φ=0.75
=0.75
R209 +O2 =C2HH4+HO
=C +HO2 φ
2 5 2 2 4 2 φ=0.5
=0.5
R19
R19 2HO
2HO2=O2+H2O2
2=O2+H2O2
R14 2OH(+M)=H2OO2(+M)
2OH(+M)=H (+M)
R14 2 2
−1.0
−1.0 −0.5
−0.5 0.0
0.0 0.5
0.5 1.0
1.0
Temperature sensitivity coefficient
Temperature sensitivity coefficient
Figure 5. Temperature SA of different equivalence ratios (T = 1000 K, p = 2 MPa).
Figure
Figure5.5.Temperature
TemperatureSA
SAof
ofdifferent
differentequivalence
equivalenceratios
ratios(T
(T==1000
1000K,
K,pp==22MPa).
MPa).
In this part of the work, the generation rate analysis retains the elementary reactions
withIna this
In thispart
larger part of
ofthe
thework,
reaction work,
rate inthe
thegeneration
the frameworkrate
generation rate analysis
analysisretains
mechanism. It alsothe
retains theelementary
elementary
removes reactions
reactions
the elementary
with
with aalarger
reactionslarger reaction
withreaction rate
a smallerrate in
inthe
theframework
reaction rate. So far,mechanism.
framework a simplifiedItItmechanism
mechanism. also
alsoremoves
removesforthe
theelementary
CHXelementary
has been
reactions
reactions with
obtained, with a smaller
a smaller
including reaction
reaction
81 species rate.
andrate.So far, a simplified
280Soelementary
far, a simplified mechanism
reactionsmechanism for CHX has
hasbeen
for CHXMaterials
(Supplementary been
obtained,
Text including 81 species and 280 elementary reactions (Supplementary
S1). including 81 species and 280 elementary reactions (Supplementary Materials
obtained, Materials
Text
TextS1).
S1).Molecules 2022, 27, x FOR PEER REVIEW 8 of 20
Molecules 2022, 27, 1080 8 of 20
2.2. Mechanism Merger and Modification
2.2. Mechanism Merger and Modification
The TRF, DIB, and CHX sub-mechanisms are coupled. The principle of mechanism
The is
coupling TRF, DIB, and
to retain all CHX sub-mechanisms
the macromolecular are coupled.
reactions aboveThe C5 inprinciple
the fiveofcomponents,
mechanism
coupling
delete the is to retainelementary
repeated all the macromolecular
reactions between reactions
C1 and above
C4, andC5 in the five
retain the Ccomponents,
0 molecular
delete thein
reactions repeated
the TRF elementary reactionsFinally,
sub-mechanism. between aC 1 and C4 , and
simplified retainkinetic
chemical the C0 molecular
model of
reactions in the TRF sub-mechanism. Finally, a simplified chemical
CDTRF with 115 species and 414 elementary reactions is constructed (Supplementary kinetic model of CDTRF Ma-
with 115
terials Textspecies
S2). and 414 elementary reactions is constructed (Supplementary Materials
Text After
S2). the mechanism is coupled, the prediction accuracy of the mechanism is an issue
worthyAfter the mechanism
of attention. is coupled,between
Cross-reactions the prediction
molecules,accuracy of theinmechanism
changes componentisreaction
an issue
worthy
paths andof rates,
attention.and theCross-reactions between
fusion of repeated molecules,
elementary changeswill
reactions in component reaction
all lead to changes
paths and rates, and the fusion of repeated elementary reactions
in ignition delay time and laminar flame velocity. SA can be based on the sensitivity of a will all lead to changes
in ignition delay time and laminar flame velocity. SA can be based on the sensitivity
component or elementary element reaction to measure the degree of influence of the com-
of a component or elementary element reaction to measure the degree of influence of
ponent or elementary element reaction on the calculation results of the target parameters
the component or elementary element reaction on the calculation results of the target
(ignition delay time and laminar flame speed).
parameters (ignition delay time and laminar flame speed).
The newly constructed simplified mechanism is used to conduct preliminary predic-
The newly constructed simplified mechanism is used to conduct preliminary pre-
tions on the ignition delay time of the four-component gasoline-fuel substitute DTRF (Fig-
dictions on the ignition delay time of the four-component gasoline-fuel substitute DTRF
ure 6). In Figure 6a, Fikri et al. [15] measured the ignition delay time of the four-compo-
(Figure 6). In Figure 6a, Fikri et al. [15] measured the ignition delay time of the four-
nent alternative fuel value DTRF (25% of isooctane, 20% of n-heptane, 45% of toluene, 10%
component alternative fuel value DTRF (25% of isooctane, 20% of n-heptane, 45% of
of DIB, by volume fraction) in the high-pressure shock tube. The experimental conditions
toluene, 10% of DIB, by volume fraction) in the high-pressure shock tube. The experimental
were as follows: the pressures are 1, 3, and 5 MPa, and the equivalent ratio was 1. The
conditions were as follows: the pressures are 1, 3, and 5 MPa, and the equivalent ratio was
ignition delay time was predicted using the mechanism constructed in this study. The
1. The ignition delay time was predicted using the mechanism constructed in this study.
ignition delaydelay
The ignition time time
is defined as the
is defined asinterval fromfrom
the interval the initial statestate
the initial to thetotemperature
the temperature 400
K higher than the initial temperature. The newly constructed
400 K higher than the initial temperature. The newly constructed mechanism reproduces mechanism reproduces the
ignition of the
the ignition fuelfuel
of the at 1atMPa.
1 MPa.However,
However, it underestimates
it underestimatesthe theignition
ignitiondelay
delaytime
timein in the
the
low-temperature region (T < 1000 K) at 3 and 5 MPa and makes
low-temperature region (T < 1000 K) at 3 and 5 MPa and makes the negative temperature the negative temperature
region
region tend
tend to to the
the high
high temperature
temperature part.
part. Figure
Figure6b 6bfurther
furtherinvestigates
investigatesthe thetemperature-
temperature-
sensitive
sensitive response at the temperature (T = 850 K) at which the maximum error
response at the temperature (T = 850 K) at which the maximum error ofof ignition
ignition
delay
delay occurs, the pressure is 3 MPa, and the equivalence ratio is 1. The figure shows that
occurs, the pressure is 3 MPa, and the equivalence ratio is 1. The figure shows that
the
the macromolecular
macromolecular reactions reactions (R7,
(R7, R12,
R12, R13,
R13, R14)
R14) of of n-heptane
n-heptane in in the
the system
system have
haveaagreater
greater
effect
effect on
on the
the ignition
ignition delay
delay time.
time.The
Theelementary
elementaryreaction
reactionR14 R14shows
showsthe thelargest
largestsensitivity
sensitivity
coefficient, and C H OOH is generated from C H
coefficient, and C7 H14 OOH is generated from C7 H15 OO isomerization.
7 14 7 15 OO isomerization.
R14 C7H15OO=>C7H14OOH
10 DTRF,φ=1.0 R7 C7H16+OH=>C7H15-2+H2O
R409 H2O2+M=OH+OH+M
Ignition delay time (ms)
R347 CH3+HO2=CH3O+OH
R12 C7H15-2+O2=>C7H15OO
R6 C7H16+OH=>C7H15-1+H2O
1 R34 AC8H16OOH+O2=AOOC8H16OOH 850 K
R358 CH2O+OH=HCO+H2O
R21 C7H15-2=>PC4H9+C3H6
EXP. This work R13 C7H15OO=>C7H15-2+O2
1 MPa
R38 AC8H17+O2=JC8H16+HO2
3 MPa
0.1 5 MPa R406 OH+HO2=H2O+O2
0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 −0.8 −0.6 −0.4 −0.2 0.0 0.2 0.4 0.6 0.8 1.0
1000/T (1/K) Sensitivity coefficient
(a) (b)
Figure 6. Prediction of ignition delay time and temperature-sensitivity coefficient of DTRF fuel. (a)
Figure 6. Prediction of ignition delay time and temperature-sensitivity coefficient of DTRF fuel.
Prediction of ignition delay time and (b) temperature-sensitivity coefficient.
(a) Prediction of ignition delay time and (b) temperature-sensitivity coefficient.
The laminar flame speed of the three-component gasoline-fuel substitute TRF is pre-
The laminar flame speed of the three-component gasoline-fuel substitute TRF is pre-
liminarily verified in Figure 7. The experimental data for laminar flame speed comes from
liminarily verified in Figure 7. The experimental data for laminar flame speed comes from
Sileghem et al. [31]. The laminar flame speed is overestimated in the area of 1.0–1.3
Sileghem et al. [31]. The laminar flame speed is overestimated in the area of 1.0–1.3 equiv-Molecules 2022, 27, 1080 9 of 20
Molecules 2022, 27, x FOR PEER REVIEW 9 of 20
alence ratio (Figure 7a). In Figure 7b, at a temperature of 358 K, a pressure of 0.1 MPa,
equivalence ratio (Figure 7a). In Figure 7b, at a temperature of 358 K, a pressure of 0.1
and an equivalence ratio of 1.1, the sensitivity of OH radicals is analyzed. The elementary
MPa, and an equivalence ratio of 1.1, the sensitivity of OH radicals is analyzed. The ele-
reaction R391 is found to have a greater sensitivity, which is the main way of generating
mentary reaction R391 is found to have a greater sensitivity, which is the main way of
OH radicals.
generating OH radicals.
60
Gasoline surrogate/Air, p=0.1 MPa R391 O+OH=O2+H
55 1/3 isooctane, 1/3 n-heptane and 1/3 toluene R347 CH3+HO2=CH3O+OH
Laminar flame speed (cm/sec)
R389 CO+OH=CO2+H
50
R61 C6H5O=C5H5+CO
45
R98 IC4H7+O2=aC3H4+CH2O+OH
40 R14 358 K C7H15OO=>C7H14OOH
35 R16 OOC7H14OOH=>HO2C7H13O2H
R62 C6H5O+H=C6H5OH
30
R385 HCO+H=CO+H2
EXP. This work
25
298 K
R7 C7H16+OH=>C7H15-2+H2O
20 328 K R345 CH3+CH3(+M)=C2H6(+M)
358 K R36 IC8H18+OH=>AC8H17+H2O
15
0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 −0.6 −0.4 −0.2 0.0 0.2 0.4 0.6 0.8 1.0
Equivalence ratio Sensitivity coefficient
(a) (b)
Figure 7. Prediction of laminar flame speed and temperature-sensitivity coefficient of TRF fuel. (a)
Figure 7. Prediction of laminar flame speed and temperature-sensitivity coefficient of TRF fuel.
Prediction of laminar flame speed and (b) temperature-sensitivity coefficient.
(a) Prediction of laminar flame speed and (b) temperature-sensitivity coefficient.
According to
According to the
the predicted
predicted results,
results,temperature
temperatureSA SAisisused
usedtotofind
findthe key
the reaction
key of
reaction
the newly constructed mechanism under different combustion conditions.
of the newly constructed mechanism under different combustion conditions. Elementary Elementary re-
actions with
reactions withhigher
highersensitivity
sensitivity(R14.
(R14.C7CH15HOO=>C 7H14OOH and R391. O + OH = O2 + H)
7 15 OO=>C7 H14 OOH and R391. O + OH = O2
+are
H)selected, and the
are selected, andchemical kinetic
the chemical parameters
kinetic of the of
parameters reaction are modified.
the reaction The kinetic
are modified. The
parameters of R14 refer to the research results of Li et al. [21], while R391 is derived
kinetic parameters of R14 refer to the research results of Li et al. [21], while R391 is derived from
the mechanism
from of JetSurF2.0
the mechanism [26], [26],
of JetSurF2.0 as shown in Table
as shown 2. 2.
in Table
Table2.2.Modified
Table Modifiedkey
keyreactions
reactionsand
andkinetic
kineticparameters.
parameters.
Kinetic Parameters
Kinetic Parameters
Reactions Modification Ref.
b Reactions
E (J/mol) Modification
A Ref.
A b E (J/mol)
R14. C7H15OO=>C7H14OOH Before 2 × 1011 0.0 11 17,010.0 [10]
R14. C7 H15 OO=>C7 H14 OOH Before 2 × 10 0.0 17,010.0 [10]
After 1.51 × 1011 0.0 19,000.0 [21]
After 1.51 × 1011 0.0 19,000.0 [21]
R391. O + OH = O2 + H Before 2 × 1014 −0.4 14 0.0 [10]
R391. O + OH = O2 + H Before 2 × 10 −0.4 0.0 [10]
H + O2 = O + OH After 2.64 × 1016 −0.67 16 17,041.0 [26]
H + O2 = O + OH After 2.64 × 10 −0.67 17,041.0 [26]
After the mechanism is revised, the accuracy of prediction is greatly improved. The
After
revised the mechanism
simplified is revised,
mechanism thedelay
ignition accuracy
timesofand
prediction
laminarisflame
greatly improved.
speeds The
prediction
revised simplified mechanism ignition
will be discussed in the next section. delay times and laminar flame speeds prediction
will be discussed in the next section.
3. Results and Discussion
3. Results and Discussion
Whether the constructed chemical kinetic model can be used for the numerical sim-
Whether the constructed chemical kinetic model can be used for the numerical simula-
ulation of the combustion process depends on the model’s prediction of the fuel combus-
tion of the combustion process depends on the model’s prediction of the fuel combustion
tion characteristics. The proposed mechanism has verified the combustion characteristics
characteristics. The proposed mechanism has verified the combustion characteristics of pure
of pure component fuels under lean conditions based on extensive experimental data
component fuels under lean conditions based on extensive experimental data [16,26,30–42]
[16,26,30–42] (Supplementary Materials Figures S1–S10). This study will verify the com-
(Supplementary Materials Figures S1–S10). This study will verify the combustion char-
bustion characteristics of multi-component alternative fuels from three perspectives—ig-
acteristics of multi-component alternative fuels from three perspectives—ignition delay
nition delay time, laminar combustion speed, and concentration distribution of important
time, laminar combustion speed, and concentration distribution of important combustion
combustion substances. Table 3 shows the composition ratio of gasoline-alternative fuel
substances. Table 3 shows the composition ratio of gasoline-alternative fuel componentsMolecules 2022, 27, x FOR PEER REVIEW 10 of 20
Molecules 2022, 27, 1080 10 of 20
components used in this section. The research octane number (RON) of the six alternative
used in this section. The research octane number (RON) of the six alternative fuels ranges
fuels ranges from 74 to 95, which can represent most commercial gasoline in the market.
from 74 to 95, which can represent most commercial gasoline in the market.
Table 3. Composition of different gasoline-surrogate fuels (by volume fraction).
Table 3. Composition of different gasoline-surrogate fuels (by volume fraction).
Fuels Isooctane(%) N-Heptane(%) Toluene(%) DIB(%) CHX(%) RON Ref.
Fuels
PRF Isooctane
77 (%) N-Heptane
23 (%) Toluene
0 (%) DIB
0 (%) CHX0(%) RON
77 Ref.
[9]
TRF1
PRF 63
77 17 23 20 0 0 0 00 77 88 [14]
[9]
TRF1
TRF2 63
69 17 17 14 20 0 0 00 88 87 [14]
[32]
TRF2 69 17 14 0 0 87 [32]
TRF3 33.33 33.33 33.33 0 0 74 [31]
TRF3 33.33 33.33 33.33 0 0 74 [31]
DTRF
DTRF 25
25 20 20 45 45 10 10 00 94.6
94.6 [15]
[15]
CDTRF
CDTRF 30.812
30.812 11 11 38.2 38.2 10.342
10.342 9.646
9.646 95 95 [21]
[21]
3.1.
3.1. Ignition
Ignition Delay
Delay Times
Times
This work chooses
This work chooses the the equal-volume
equal-volume closed
closed homogeneous
homogeneous zero-dimensional
zero-dimensional model model
to simulate ignition delay. Figure 8 shows the comparison of the ignition
to simulate ignition delay. Figure 8 shows the comparison of the ignition delay time delay time cal-
culated by the experiment and the model at different pressures of TRF1
calculated by the experiment and the model at different pressures of TRF1 and TRF2. The and TRF2. The
experimental
experimental data
data was
was obtained
obtained by by Gauthier
Gauthier et et al.
al. [43]
[43] inin aa low-temperature
low-temperature and and high-
high-
pressure shock tube.
pressure shock tube. The
The two
two experimental
experimental pressures
pressures were were 1.5–2.5
1.5–2.5 MPa
MPa and and 4.5–6
4.5–6 MPa.
MPa.
TRF1 data scaled to 2 and 5.5 MPa are denoted
TRF1 data scaled to 2 and 5.5 MPa are denoted as p as −p −0.83 and TRF2 as p
0.83 and TRF2 as p − −0.96
0.96 . The proposed
. The proposed
simplified
simplified mechanism
mechanism is is used
used to calculate the
to calculate the ignition
ignition delay
delay time.
time. The
The simulation
simulation results
results
using
using this
this mechanism
mechanism are are consistent
consistent with
with the
the experimental
experimental data. data.
EXP. This work EXP. This work
10 2 MPa 10 2 MPa
5.5 MPa 5.5 MPa
Ignition delay time (ms)
Ignition delay time (ms)
TRF2 , φ=1
TRF1 , φ=1
1 1
0.1 0.1
0.85 0.90 0.95 1.00 1.05 1.10 1.15 0.85 0.90 0.95 1.00 1.05 1.10 1.15
1000/T (1/K) 1000/T (1/K)
(a) TRF1 (b) TRF2
Figure 8. Verification of the ignition delay time of TRF1 and TRF2. (a) TRF1 and (b) TRF2.
Figure 8. Verification of the ignition delay time of TRF1 and TRF2. (a) TRF1 and (b) TRF2.
For
For four-component
four-component fuel, fuel, Figure
Figure 99 shows
shows thethe comparison
comparison between
between the
the simulated
simulated
value
value of the fuel mixture DTRF described in Table 3 and the experimental value of
of the fuel mixture DTRF described in Table 3 and the experimental value of the
the
high-pressure shock tube by Fikri et al. [15]. The model prediction results in
high-pressure shock tube by Fikri et al. [15]. The model prediction results in this studythis study are
consistent with the experimental results. However, the calculated ignition delay
are consistent with the experimental results. However, the calculated ignition delay time time un-
derestimates
underestimates thethe
experimental
experimentalvalue in the
value range
in the of 740–910
range of 740–910K. The possible
K. The reasons
possible for
reasons
the
for pre-ignition in the
the pre-ignition inlow
the temperature
low temperatureregion are that
region arethe coupling
that of different
the coupling sub-mech-
of different sub-
anisms changes
mechanisms the reaction
changes path and
the reaction pathreaction rate of
and reaction theofmacromolecular
rate the macromolecularfuel and
fuel that
and
there is cross-reaction between the fuel macromolecules.
that there is cross-reaction between the fuel macromolecules.Molecules 2022,
Molecules 2022, 27,
27, 1080
x FOR PEER REVIEW 11
11 of 20
of 20
Molecules 2022, 27, x FOR PEER REVIEW 19 of 21
DTRF,φ=1.0
10
1
EXP. This work
1 MPa
3 MPa
.1 5 MPa
0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5
Figure 9. Verification of the ignition delay time of DTRF.
References Figure 9. Verification of the ignition delay time of DTRF.
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in a shocktube,
in a shock tube,asasshown in in
Figure 10. 10.
A negative correlation between pressure and equiv-
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of CDTRF fuel.fuel.
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model
modelreproduces thethe
reproduces ignition
ignitionofofthe
the five-component
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five-component fuel
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CDTRF over the entire temperature range. range.
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https://doi.org/10.1016/j.applthermaleng.2016.07.024.
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et al. A comprehensive iso-octane combustion model with improved thermochemistry and chemical kinetics. Combust. Flame
1 2017, 178, 111–134. https://doi.org/10.1016/j.combustflame.2016.12.029. 1
9. AlAbbad, M.; Badra, J.; Djebbi, K.; Farooq, A. Ignition delay measurements of a low-octane gasoline blend, designed for gasoline
compression ignition (GCI) engines. Proc. Combust. Inst. 2019, 37, 171–178. https://doi.org/10.1016/j.proci.2018.05.097.
10. Zheng, Z.L.; Liang, Z.L. R educed Chemical Kinetic Model of a Gasoline Surrogate Fuel for HCCI Combustion. Acta Phys.-
Chim. Sin. 2015, 31, 1265–1274. https://doi.org/10.3866/PKU.WHXB201505131. (In Chinese)
11. Liu, Y.D.; Jia, M.; Xie, M.Z.; Pang, B. Development of a New Skeletal Chemical Kinetic Model of Toluene Reference Fuel with
Application to Gasoline Surrogate Fuels for Computational Fluid Dynamics Engine Simulation. Energy Fuels 2013, 27, 4899–
4909. https://doi.org/10.1021/ef4009955.
CDTRF, p=2 MPa
CDTRF, φ=1.0
0.1 0.1
0.75 0.80 0.85 0.90 0.95 1.00 1.05 0.75 0.80 0.85 0.90 0.95 1.00 1.05
1000/T (1/K) 1000/T (1/K)
(a) φ = 1.0 (b) p = 2 MPa
Figure 10.
Figure 10. Verification
Verificationof
ofthe
theignition
ignitiondelay
delaytime
timeof
ofCDTRF.
CDTRF.(a)
(a)ϕφ==1.0;
1.0;(b)
(b)pp== 22 MPa.
MPa.
3.2.
3.2. Laminar
Laminar Flame
Flame Speeds
Speeds
Few experimental
Few experimental studies studieshave
havebeenbeenconducted
conducted onon thethe laminar
laminar flameflame velocity
velocity of
of gas-
gasoline-fuel substitutes with four components. Thus, this study only
oline-fuel substitutes with four components. Thus, this study only predicts the laminar predicts the laminar
flame
flame speed
speed ofof three-component
three-component mixtures.
mixtures.
Sileghem
Sileghemetetal. al.[31]
[31]found
foundthat a mixture
that a mixture of 1/3 isooctane,
of 1/3 isooctane,1/3 1/3
n-heptane,
n-heptane,and and
1/3 toluene
1/3 tol-
(TRF3) can have a similar laminar flame to the anaerobic gasoline
uene (TRF3) can have a similar laminar flame to the anaerobic gasoline mixture (Exxonmixture (Exxon 708629-60)
speed. Therefore,
708629-60) speed. on the basisonofthe
Therefore, thisbasis
ratio,
ofthe
thislaminar
ratio, the flame speed
laminar of toluene
flame speed ofreference
toluene
fuel is measured using the heat flux method on a flat flame adiabatic
reference fuel is measured using the heat flux method on a flat flame adiabatic burner. burner. In this study,
In
three
this study, three different ratios of toluene reference fuels are used for simulation, and are
different ratios of toluene reference fuels are used for simulation, and the results the
shown
results inareFigure
shown 11.inThe prediction
Figure 11. Theresults of TRF1-3
prediction results areofconsistent
TRF1-3 arewith the experimental
consistent with the
data of Sileghem. The mechanism constructed in this study can
experimental data of Sileghem. The mechanism constructed in this study can accurately accurately reproduce the
flame velocity characteristics of TRF fuel.
reproduce the flame velocity characteristics of TRF fuel.Molecules 2022, 27, 1080
x FOR PEER REVIEW 12 of
12 of 20
50 TRF1-3/Air
Laminar flame speed (cm/sec)
358 K
40 P=0.1 MPa 328 K
298 K
30
Sileghem et al.
TRF3，This work
20 TRF1，This work
TRF2，This work
0.6 0.8 1.0 1.2 1.4
Equivalence ratio
Figure 11.
Figure 11. Verification of the
Verification of the laminar
laminar flame
flame speed
speed of
of TRF.
TRF.
3.3. Vital Species Distributions in Premixed Flames
In addition to the ignition delay time and laminar flame speed, the transport process
of fuel
fuel molecules
moleculesshould shouldalsoalsobebe described
described by by verifying
verifying the the distribution
distribution of important
of important sub-
substances
stances in the in the premixed
premixed flame.
flame. In Inthethe previousconstruction
previous constructionprocess
processof ofthis
this mechanism,
mechanism,
the distribution of important species in the premixed premixed fuel/air flame was
fuel/air flame was not
not verified.
verified.
Therefore, in this study, the important species of premixed flames of
Therefore, in this study, the important species of premixed flames of isooctane, n-heptane, isooctane, n-heptane,
toluene,
toluene, andand CHX
CHX are are verified
verified in
in Figure
Figure 12.12.
El-Bakali
El-Bakali et al. [44] used gas chromatography
et al. [44] used gas chromatography and and GC–MS
GC–MS analysis
analysis to to measure
measure the the
distribution
distribution of of the
the main
mainsubstances
substancesmole molefraction
fractionofofthe
thetwo
twofuels
fuelsininthe
then-heptane/O
n-heptane/O 2 /N
2/N22
and
and isooctane/O
isooctane/O22/N /N laminarpremixed
laminar
2 2
premixedflames.flames.TheTheprocess
processisissimulated
simulatedusing using the
the mech-
mech-
anism constructed in this study. The initial temperature is 450 K, the
anism constructed in this study. The initial temperature is 450 K, the initial pressure is 0.1 initial pressure is
0.1 MPa, the equivalent ratio is 1.9, and N is used for dilution. The
MPa, the equivalent ratio is 1.9, and N2 is used for dilution. The premixed gas inlet velocity
2 premixed gas inlet
velocity
is 4.12 cm/sis 4.12 cm/s (isooctane),
(isooctane), 4.98 cm/s (n-heptane).
4.98 cm/s (n-heptane). As shown inAs shown
Figure in Figure
12a,b, 12a,b,
the model the
accu-
model accurately predicts the mole fraction curve of each
rately predicts the mole fraction curve of each substance (IC8H18, C7H168, CO, substance (IC H , C
18 and H ,
7 16CO2).CO,
and CO2 ). it
However, However,
predicts ita predicts
lower Oa2 value.
lower O 2 value.
We We performed
performed a temperature-sensitivity
a temperature-sensitivity analysis
analysis of this system and found that the rapid consumption of
of this system and found that the rapid consumption of the oxidant was mainly attributedthe oxidant was mainly
attributed to the elementary
to the elementary reaction R391.Hreaction
+ O2R391.H
= O + OH, +O 2 = O + aOH,
showing highshowing
positive asensitivity.
high positive The
sensitivity. The dehydrogenation reaction of isooctane and n-heptane at low temperatures
dehydrogenation reaction of isooctane and n-heptane at low temperatures and low pres-
and low pressure produces a large number of H radicals, and the collision of H radicals
sure produces a large number of H radicals, and the collision of H radicals with O2 mole-
with O2 molecules consumes the oxidant.
cules consumes the oxidant.
The concentration of important substances in the premixed flame of toluene was
The concentration of important substances in the premixed flame of toluene was
measured by Li et al. [45] using synchrotron vacuum ultraviolet photoionization mass
measured by Li et al. [45] using synchrotron vacuum ultraviolet photoionization mass
spectrometry. The initial temperature was 410 K, the initial pressure was 4 kPa, the
spectrometry. The initial temperature was 410 K, the initial pressure was 4 kPa, the equiv-
equivalence ratio was 0.75, Ar was used for dilution, and the premixed gas inlet velocity
alence ratio was 0.75, Ar was used for dilution, and the premixed gas inlet velocity was
was 35 cm/s. Figure 12c shows the comparison between the experimental and model
35 cm/s. Figure 12c shows the comparison between the experimental and model calcula-
calculations of the molar fraction distribution of the main substances in the flame. As
tions of the molar fraction distribution of the main substances in the flame. As observed,
observed, the mole fractions of toluene and O2 are continuously decreasing, and toluene
the mole fractions of toluene and O2 are continuously decreasing, and toluene is com-
is completely consumed under lean fuel conditions, while O2 is incompletely consumed.
pletely
The mole consumed
fraction underof CO lean fuel conditions,
calculated by the modelwhiledoes
O2 isnotincompletely
show an obvious consumed.
trendThe of
mole fraction of CO calculated by the model does not show
first increasing and then decreasing, while CO2 maintains a consistent trend with an obvious trend of first the
in-
creasing and data.
experimental then decreasing, while CO2 maintains a consistent trend with the experi-
mental data.
Figure 12d shows the comparison between the experiment of Ciajolo et al. [46] and
the calculation curve of the species in the CHX premixed flame calculated by the model
in this study. The decrease rate of CHX is faster than the experimental value. In general,
our model reproduces the distribution of mole fractions of these main substances in a sat-
isfactory manner.You can also read
