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Flame Structure at Elevated Pressure Values and Reduced Reaction Mechanisms for the Combustion of CH4/H2 Mixtures

Authors:

Abstract

Understanding and controlling the combustion of clean and efficient fuel blends, like methane + hydrogen, is essential for optimizing energy production processes and minimizing environmental impacts. To extend the available experimental database on CH4 + H2 flame speciation, this paper reports novel measurement data on the chemical structure of laminar premixed burner-stabilized CH4/H2/O2/Ar flames. The experiments cover various equivalence ratios (φ = 0.8 and φ = 1.2), hydrogen content amounts in the CH4/H2 blend (XH2 = 25%, 50% and 75%), and different pressures (1, 3 and 5 atm). The flame-sampling molecular-beam mass spectrometry (MBMS) technique was used to detect reactants, major products, and several combustion intermediates, including major flame radicals. Starting with the detailed model AramcoMech 2.0, two reduced kinetic mechanisms with different levels of detail for the combustion of CH4/H2 blends are reported: RMech1 (30 species and 70 reactions) and RMech2 (21 species and 31 reactions). Validated against the literature data for laminar burning velocity and ignition delays, these mechanisms were demonstrated to reasonably predict the effect of pressure and hydrogen content in the mixture on the peak mole fractions of intermediates and adequately describe the new data for the structure of fuel-lean flames, which are relevant to gas turbine conditions.
Citation: Gerasimov, I.E.; Bolshova,
T.A.; Osipova, K.N.; Dmitriev, A.M.;
Knyazkov, D.A.; Shmakov, A.G.
Flame Structure at Elevated Pressure
Values and Reduced Reaction
Mechanisms for the Combustion of
CH4/H2Mixtures. Energies 2023,16,
7489. https://doi.org/10.3390/
en16227489
Academic Editor: Adonios Karpetis
Received: 30 September 2023
Revised: 3 November 2023
Accepted: 5 November 2023
Published: 8 November 2023
Copyright: © 2023 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
energies
Article
Flame Structure at Elevated Pressure Values and Reduced
Reaction Mechanisms for the Combustion of CH4/H2Mixtures
Ilya E. Gerasimov 1, Tatyana A. Bolshova 1, Ksenia N. Osipova 1,2 , Artëm M. Dmitriev 1,2 ,* ,
Denis A. Knyazkov 1, 2,* and Andrey G. Shmakov 1,2
1Voevodsky Institute of Chemical Kinetics and Combustion SB RAS, Novosibirsk 630090, Russia;
gerasimov@kinetics.nsc.ru (I.E.G.); bolshova@kinetics.nsc.ru (T.A.B.); osipova@kinetics.nsc.ru (K.N.O.);
shmakov@kinetics.nsc.ru (A.G.S.)
2Department of Physics, Novosibirsk State University, Novosibirsk 630090, Russia
*Correspondence: dmitriev@kinetics.nsc.ru (A.M.D.); knyazkov@kinetics.nsc.ru (D.A.K.)
Abstract:
Understanding and controlling the combustion of clean and efficient fuel blends, like
methane + hydrogen, is essential for optimizing energy production processes and minimizing
environmental impacts. To extend the available experimental database on CH
4
+ H
2
flame speciation,
this paper reports novel measurement data on the chemical structure of laminar premixed burner-
stabilized CH
4
/H
2
/O
2
/Ar flames. The experiments cover various equivalence ratios (
ϕ
= 0.8 and
ϕ
= 1.2), hydrogen content amounts in the CH
4
/H
2
blend (X
H2
= 25%, 50% and 75%), and different
pressures (1, 3 and 5 atm). The flame-sampling molecular-beam mass spectrometry (MBMS) technique
was used to detect reactants, major products, and several combustion intermediates, including major
flame radicals. Starting with the detailed model AramcoMech 2.0, two reduced kinetic mechanisms
with different levels of detail for the combustion of CH
4
/H
2
blends are reported: RMech1 (30 species
and 70 reactions) and RMech2 (21 species and 31 reactions). Validated against the literature data for
laminar burning velocity and ignition delays, these mechanisms were demonstrated to reasonably
predict the effect of pressure and hydrogen content in the mixture on the peak mole fractions of
intermediates and adequately describe the new data for the structure of fuel-lean flames, which are
relevant to gas turbine conditions.
Keywords:
methane; hydrogen; hythane; flame structure; flame radicals; flame chemical
speciation; molecular-beam mass spectrometry; kinetic mechanism; reduced mechanism;
mechanism development
1. Introduction
High efficiency and low pollutant emissions are key benchmarks for the development
of modern combustion devices. Unfortunately, these two aspects often appear to be
mutually exclusive [
1
]. The solution seems impossible without transitioning to new types of
fuel. The hydrogen enrichment of methane or natural gas (NG) is considered one of the most
promising and viable alternative strategies to meet these complex goals in gas turbines and
internal combustion (IC) engines [
2
4
]. The combination of methane/NG and hydrogen as
a fuel can synergistically enhance their performance [
5
,
6
]. The addition of hydrogen results
in reduced carbon emissions and an extended stability range. Methane/NG addition to
pure hydrogen, in turn, mitigates the challenges associated with the rapid combustion rate
of hydrogen, low ignition energy and susceptibility to premature ignition [
7
]. Alongside
rapidly emerging technologies for fuel production from biomass, hydrogen admixing
can noticeably reduce our carbon footprint and expedite the transition to carbon-neutral
energy [8].
Decades of engineering have attuned combustion devices to operate only on specific
fuel types. Gas-operated devices often experience increased sensitivity when hydrogen
blending rates are raised, necessitating, therefore, technical adaptation. In this regard,
Energies 2023,16, 7489. https://doi.org/10.3390/en16227489 https://www.mdpi.com/journal/energies
Energies 2023,16, 7489 2 of 30
investigations are needed to optimize and reconfigure combustors for the new fuels, and
numerical simulations are indefeasible in predicting inherent physico-chemical effects in
complex technical devices [
2
,
9
]. Despite the leading role of physical processes in such
systems, combustion chemistry significantly affects the overall performance, and thus
should be thoroughly implemented during simulation [
10
,
11
]. Numerous kinetic studies on
methane–hydrogen combustion have been performed in recent decades, which is reflected
in several overviewing papers [
4
,
12
,
13
], but a comprehensive review is beyond the scope
of this paper. First of all, the main focuses were laminar burning velocities (e.g., [
14
16
]),
ignition delay times (e.g., [
12
,
17
,
18
]), and flammability limits (e.g., [
19
22
]), since these
parameters are crucial for the device engineering. Significant attention has also been
paid to the influence of hydrogen addition on the concentrations of key intermediates
and final products during methane combustion/oxidation [
23
25
]. However, there have
been significantly fewer experimental studies in this direction, which is likely due to
experimental difficulties. Wang et al. [
23
] investigated the low-pressure flames of premixed
methane/hydrogen mixtures with variable hydrogen fractions from 0% to 80% by means
of the molecular-beam mass spectrometry (MBMS) technique with tunable synchrotron
vacuum ultraviolet (VUV) photoionization. The authors measured the mole fraction
profiles of labile intermediates and indicated the effects of additional H radical production
on the peak concentrations of C
1
–C
2
species. The mole fraction profiles of reactants,
formaldehyde (CH
2
O) and ethylene (C
2
H
4
) were obtained during the oxidation of methane
(50%)/hydrogen (50%) mixtures in a jet-stirred reactor (JSR) by Le Cong and Dagaut [
24
].
The authors found that the kinetic mechanism GRIMech 3.0 [
26
] overestimates the reactivity
of the mixtures, particularly, at a high pressure, and provided a new detailed kinetic
scheme. Katoh et al. [
25
] separated the distributions of OH radicals produced during
either methane or hydrogen combustion using the isotope shift effect in planar laser-
induced fluorescence spectroscopy (IS/PLIF). Due to the lack of experimental investigations,
several numerical studies on chemical speciation in hydrogen-doped methane flames were
conducted (e.g., [
27
30
]). These works were focused mostly on the concentration and
pressure effects during combustion. The main effects are associated with the complex
production of the key radicals, since different methane-based and hydrogen-based reactions
are triggered [
31
]. The increased H radical transport from the reaction zone was also
pointed out.
Notwithstanding progressing numerical methods and the growth of computing per-
formance, a detailed calculation of chemical-kinetic processes in combustion chambers
remains a difficult task. Taking into account detailed kinetic schemes implies solving stiff
systems of hundreds and thousands of differential equations, which makes calculations not
feasible at present [
32
]. In this regard, implementing reduced chemical kinetics mechanisms
proves to be an optimal and reliable method for achieving a balance between essential
chemical representation and saving computational costs [
10
,
33
]. Conventionally, mech-
anism reduction is usually carried out based on a set of targets, such as ignition delay
times (IDT), laminar burning velocities (LBV), burnt gas temperature, heat release rate
and concentrations of the main products (CO, CO
2
and H
2
O). However, the specifics of
hydrogen-enriched combustion are driven by the complex dynamics of radical chemistry
and transport, and, therefore, a reduced mechanism should be able to effectively mimic
the radical pool development. A certain interest is paid to the OH radical, which, along
with formaldehyde, is commonly used for the LIF visualization of a flame front in complex
combustion devices [
34
36
]. In this regard, a reduced kinetic mechanism suitable for large
eddy simulation (LES) or direct numerical simulation (DNS) and able to quantitatively
reproduce the distributions of H, OH, CH3and CH2O is desirable.
Conventionally, chemical speciation in flames is an important object of study for
the development and validation of detailed kinetic mechanisms. Information on the con-
centrations of individual intermediates enables an in-depth analysis of the formation and
consumption pathways for specific flame components, such as radicals or pollutants. Along
with global combustion parameters (like LBVs and IDTs), the chemical structure of flames
Energies 2023,16, 7489 3 of 30
reflects the system’s response to changes in external parameters, such as ambient pressure.
It is well known that pressure can significantly influence flame chemistry, specifically the
fate of a radical pool. In this context, explicit information about the mole fractions of
individual radicals and intermediates is highly valuable. However, as illustrated above, the
existing literature provides limited data on chemical speciation in the flames of methane
and hydrogen mixtures. Although the impact of elevated pressure on chemical speciation
has been studied in an ideal mixing reactor, there is no literature data on the influence of
pressure on the formation of intermediates during combustion.
Therefore, the first goal of this work is to provide a set of experimental data on
the chemical speciation of hydrogen + methane-fueled flames at various fuel-to-oxidizer
ratios, hydrogen dilutions and elevated pressures. The second goal is to develop reduced
kinetic mechanisms adequately reproducing the literature data available for combustion
macroparameters (LBVs and IDTs) and the new flame structure measurements.
2. Experimental Methods
The chemical structures and temperature profiles of premixed CH
4
/H
2
/O
2
/Ar flames
were measured experimentally using a molecular-beam mass spectrometric setup (MBMS).
Combustible mixtures of three methane/hydrogen ratios (25/75, 50/50 and 75/25 by mol)
were prepared at slightly lean (equivalence ratio of
ϕ
= 0.8) and rich (
ϕ
= 1.2) proportions.
The argon dilution in all mixtures was 75%. Each flame of the corresponding mixture was
investigated at 1, 3 and 5 atm. Therefore, 18 flames in total were scanned. Table 1displays
the composition of the unburnt gas blends.
Table 1. Molar composition of the combustible mixtures in the experiments at 1, 3 and 5 atm.
ϕ
Reactant Mole Fraction Mass Flow Rate
(g/(cm2s)) XH2,%*
CH4H2O2Ar
0.8 0.049 0.049 0.152 0.75 0.04513 50
1.2 0.061 0.061 0.128 0.75 0.04534 50
0.8 0.03 0.09 0.131 0.75 0.04797 75
1.2 0.036 0.108 0.105 0.75 0.05226 75
0.8 0.062 0.021 0.168 0.75 0.04285 25
1.2 0.08 0.027 0.144 0.75 0.04098 25
* H2concentration in the fuel mixture.
A comprehensive description of the experimental setup and data processing is avail-
able in our previous works [
37
], and thus only the crucial details are presented in the
present paper. The flames were stabilized on a flat-flame burner (Botha–Spalding type [
38
])
made of a perforated brass disc (9.7 mm in diameter and 1.5 mm thick) incorporated in a
brass housing. The diameter of the burner holes was 0.2 mm, and the distance between their
centers was 0.28 mm. The burner housing was equipped with a water-cooling jacket; the
burner temperature was maintained constant at 368 K. During the experiments, the burner
moved in the vertical direction with a micro-screw mechanism. The distance between the
burner surface and the probe tip, i.e., the height above the burner (HAB), was controlled
visually by a cathetometer; the accuracy of the HAB measurements was ±0.01 mm.
Gas flows were set using mass flow controllers (Bronkhorst). The linear velocity of the
unburnt gas on the burner surface was chosen to provide a visually flat and stable flame
surface and to ensure the temperature values in the post-flame zone of the flames studied
were as close as possible.
To measure flame structures at 3 and 5 atm, the burner was placed in a high-pressure
chamber pressurized with nitrogen. The chamber construction enabled the maintenance
of the pressure values up to 10 atm. For optical access, the high-pressure chamber was
equipped with a window that was fixed in a side flange. Nitrogen, used for pressurizing the
chamber, was supplied through this flange to prevent water condensation on the window
Energies 2023,16, 7489 4 of 30
and, therefore, ensure its transparency during the experiments. A diaphragm pressure
regulator, placed on the outlet line, was used to control the pressure inside the chamber
with an accuracy of 1%. The chamber was equipped with a safety valve and a pressure
gauge. The upper flange of the chamber was attached to the sampling probe flange of the
MBMS setup.
After sampling, the gas probe formed a molecular beam that passed through the
skimmer, modulator, and collimator before entering the ion source of the quadrupole mass
spectrometer. The ion source performed soft and tunable electron-impact ionization, which
minimized ion fragmentation for the majority of measured peaks. A specially designed
tungsten cathode with a voltage drop compensation system provided an electron beam
with a narrow energy spread (
±
0.25 eV). The energy of the ionizing electrons was selected
individually for each species to ensure an optimal signal-to-noise ratio and to prevent
interference from the fragmentation of other species.
Table 2provides the measured species together with the values of the ionizing electrons
energy as well as the calibration method for each species.
Table 2. Measured species. IE—ionization energy [39]. E—energy of the ionizing electrons.
m/zFormula Species Name IE (eV) E (eV) Calibration Accuracy
1 H atomic hydrogen 13.6 16.2 RICS * vs. H2±50%
2 H2hydrogen 15.43 16.65 Balance O ±20%
15 CH3methyl radical 9.84 12.3 RICS vs. CH4±50%
16 CH4methane 12.71 14.35 Direct ±20%
17 OH hydroxyl radical 13.02 16.2 RICS vs. H2O±50%
18 H2O water 12.62 15.4 Balance O ±20%
26 C2H2acetylene 11.41 12.3 Direct ±50%
28 C2H4ethylene 10.53 12.3 Direct ±50%
28 CO carbon monoxide 14.01 15.4 Balance O ±20%
30 CH2O formaldehyde 10.88 11.5 RICS vs. C2H6±50%
30 C2H6ethane 11.52 12.3 Direct ±50%
32 O2oxygen 12.07 14.35 Direct ±20%
33 HO2peroxide radical 11.35 16.65 RICS vs. O2±50%
34 H2O2hydrogen peroxide 10.58 14.35 Direct ±50%
40 Ar argon 15.76 16.3 Direct ±10%
44 CO2carbon dioxide 13.77 15.4 Balance O ±20%
* Relative ionization cross-section.
To convert the signal intensity (I
i
) of i-th species to its mole fraction (X
i
), an energy-
dependent calibration coefficient (S
i
) is required. Argon dilution can vary between the
experimental and calibration mixtures, and therefore, argon-normalized values were uti-
lized for data processing. In this regard, a simple relation between I
i
and X
i
can be defined:
Ii/IAr = Si/SAr ·Xi/Xar, (1)
where Iiand Sishould be chosen at the same energy of ionizing electrons.
For the reactants (H
2
, CH
4
and O
2
) and some stable intermediates (C
2
H
2
, C
2
H
4
, C
2
H
6
and H
2
O
2
), calibration coefficients were obtained during direct calibration experiments
with gas mixtures of known compositions. During the calibration experiments, the gas
mixtures were preheated to avoid argon clustering. The values of the direct calibration
coefficients were quasi-constant in the pressure range from 1 to 5 atm. The calibration
coefficients for H
2
, H
2
O, CO and CO
2
were obtained from the signals in the post-flame zone
Energies 2023,16, 7489 5 of 30
and O-element balance equations. To calculate the calibration coefficients for the remaining
intermediate species (H, CH
3
, OH, CH
2
O and HO
2
), the method of relative ionization
cross-section (RICS) was applied [
40
]. This method is based on the fact that the calibration
coefficient is proportional to the ionization cross-section σi(E) at a certain electron energy
E. Therefore, there is a proportional relation between the unknown calibration coefficient
of an intermediate species (i) and the known calibration coefficient for the stable species,
having the nearest molecular weight (j):
Si/Sj=σi(Ei)/σj(Ej), (2)
The values of ionization cross-sections at a certain electron energy were taken from
the NIST database [39].
Experimental errors for each species are also provided in Table 2. For such species as
H
2
, CH
4
, H
2
O, CO, O
2
and CO
2
, the uncertainty values were estimated as
±
20% of their
maximum mole fraction. For other species, the uncertainty values did not exceed
±
50%.
There are two main factors contributing to the uncertainty value: the measurement error
of the mass peak intensity and the accuracy of calibration coefficient determination. The
uncertainty of the mass peak measurements is mainly statistical and depends on factors
such as background signal, the mole fraction of a certain species and setup sensitivity to a
certain species. For the calibration coefficients obtained in the direct calibration experiments,
the uncertainty values are lower due to similar sampling and detecting conditions. The
calibration coefficients evaluated by the RICS method are less precise since the accuracy of
ionization cross section determination is lower at energies close to the ionization potential
of a certain compound.
Self-constructed S-type thermocouples (Pt/Pt + 10%Rh) were utilized for the tem-
perature measurements [
41
,
42
]. The thermocouples were made from wires of 30
µ
m in
diameter. The thermocouple surface was coated with a thin layer of SiO
2
in order to prevent
catalytic reactions. The junction of the thermocouple was fixed 0.2 mm upstream of the
sampling probe, obtaining the “disturbed” flame temperature profiles. To account for
radiation heat loss, corrections of the thermocouple readings were performed according
to the procedure from Shaddix et al. [
43
]. The absolute experimental error did not exceed
±
40 K. All the temperature profiles obtained were used as input data during the chemical
kinetics simulations.
3. Modeling Details
3.1. Chemical Kinetics Simulations
To simulate the combustion parameters, the Ansys Chemkin-Pro v.17.0 [
44
] software
was utilized. The ignition delay times were calculated using 0-D closed homogeneous
reactor model, which considers the time-resolved chemical process proceeding in a closed
reactor with a uniform distribution of all concentrations under a constant volume or
pressure conditions. Laminar flame speed and flame structure calculations were performed
with 1-D premixed laminar flame models, which solve the set of governing differential
equations that describe the flame dynamics in the model with a uniform inlet flow, using
different mathematical methods and provide a steady-state solution. In the case of a burner-
stabilized flame, two boundary conditions were set: a fixed gas flow through the surface
of the burner and its surface temperature. A burner-stabilized flame requires additional
information on heat losses, and for this purpose, each flame was simulated using the
experimentally measured temperature profile obtained for each experimental condition. In
the case of a freely-propagating flame, the model considers a front-moving flame with a
constant velocity toward the unburned mixture of a fixed composition and temperature. In
this case, there are no heat losses (by definition), and thus the temperature profiles should
be computed from the energy equation. The transport properties as well as thermodynamic
parameters were obtained from the AramcoMech 2.0 mechanism [
45
]. All the computed
solutions were mesh-independent.
Energies 2023,16, 7489 6 of 30
3.2. Reduction in Kinetics Mechanism
For the development of a reduced mechanism suitable for various CH
4
/H
2
fuel com-
positions, the modern and well-tested mechanism AramcoMech 2.0 with the corresponding
conditions was selected [
46
]. The mechanism reduction was performed using the Mecha-
nism Workbench v.1.0 software from Kintech Lab. [
47
], which utilizes an optimized iterative
combination of several methods: directed relation graph (DRG), rate of production (ROP),
and computational singular perturbation (CSP). The reduction procedure was performed
using an adiabatic constant-pressure reactor, with various initial conditions: pressure—1, 3,
5 and 20 atm; temperature—varied between 1000 and 2000 K, with a step of 200 K; equiva-
lence ratio of
ϕ
= 0.8, 1.0, 1.2; and hydrogen molar fraction in the fuel mixture—25%, 50%
and 75%. To ensure the efficiency of the reduced mechanism after automated processing,
careful attention should be paid to assigning reduction targets: these targets should be a set
of reference parameters whose deviation range is limited by a relative or absolute value
(tolerance). Firstly, to keep the general reactivity at the same level, two macro-parameters
were added to the reduction targets: the ignition delay time (with a relative tolerance of
10%) and the maximum reactor temperature (with an absolute tolerance of 50 K). Secondly,
since the interaction of the fuels in a two-component mixture occurs mainly through a
radical pool, it is important to keep concentrations of these species at the same levels.
Thus, for our purpose, we controlled the maximum values of following intermediates: H
(5%), OH (10%), HO
2
(10%), CH
3
(20%), HCCO (20%), CO (10%) and CH
2
O (20%). After
the application of the reduction procedure, a reduced kinetic mechanism named RMech1
was obtained. It comprises 30 components and 70 reactions, striking an optimal balance
between size and the quality of the simulation results.
However, most computational fluid dynamic (CFD) simulations require even smaller
kinetic mechanisms to minimize the demand on computational resources. To fulfill this goal,
a comprehensive analysis of reaction rates and sensitivity coefficients for the mechanism
RMech1 was performed, and the following measures were taken:
(1)
A set of species and reactions that are only important during low-temperature oxida-
tion, namely, CH3O2H and CH3O2, were removed;
(2)
According to our previous studies [
48
], there are two most important reaction path-
ways of methane transformation in flames: CH
4
CH
3
CH
3
O
CH
2
O
HCO
CO
CO
2
, and CH
4
CH
3
C
2
H
6
C
2
H
5
C
2
H
4
C
2
H
3
C
2
H
2
HCCO
CO
CO
2
. The second pathway becomes important only in fuel-rich
flames and was therefore removed. This included C
2
hydrocarbons, singlet CH
2
(s)
and all reactions involving them;
(3) Since several paths of CH
3
consumption in the previous modification were deleted, the
concentration of CH
3
concentration increased considerably. This resulted in higher
flame speed values, particularly at elevated pressures. To compensate this effect,
the pre-exponential factors of 3 reactions, identified via a sensitivity analysis, were
modified. The rate constant of reaction CH
3
+ HO
2
CH
4
+ O
2
(R14) was increased
2 times, while the rate constant of CH
3
+ HO
2
CH
3
O + OH (R19) were reduced by
a factor of 2. Also, for the reaction CH
3
+ OH
CH
2
OH + H (R17), the rate constants
were reduced by a factor of 2, but only for pressures above 1 atm;
(4)
The reaction rate constant of HO
2
+ HO
2
H
2
O
2
+ O
2
(R7) was initially expressed
by two sets of reaction rate parameters, responsible for low and high temperature
ranges. Both sets were merged and then approximated as a single set of reaction rate
constants. Figure 1shows the comparison between the sum of original reaction rates
and the new approximated reaction rate.
Energies 2023,16, 7489 7 of 30
Energies2023,16,xFORPEERREVIEW7of31
Figure1.ReactionrateparametersofthereactionR7.Theblackcurvecorrespondstotheresulting
approximation.
Table3.ThereducedmechanismRMech2forthecombustionofCH4/H2fuelmixturesin
nearstoichiometricconditionsat1–18atmpressures.Rateconstantsareexpressedintheformk=
ATbexp(E/RT).
NReactionA,molecmsecKbE,cal/mole
R1H2+OH+OH5.08×1042.676292.0
R2H2+OHH+H2O4.38×10130.06990.0
R3O2+HO+OH1.04×10140.015,286.0
R4
H2O2(+M)2OH(+M)
Lowpressurelimit:
TROEcentering:0.43,1.0×1030,1.0×1030
Enhancedthirdbodyefficiencies:O2=1.2,H2=3.7,H2O=
7.65,CO=2.8,CO2=1.6,H2O2=7.7
2.00×1012
2.49×1024
0.9
2.3
48,749.0
48,749.0
R5HO2+H2OH7.079×10130.0295.0
R6
H+O2(+M)HO2(+M)
Lowpressurelimit:
TROEcentering:0.67,1.0×1030,1.0×1030,1.0×1030
Enhancedthirdbodyefficiencies:H2=1.3,H2O=10,CO=
1.9,CO2=3.8,CH4=2,AR=0.5
4.65×1012
1.737×1019
0.44
1.23
0.0
0.0
R7HO2+HO2H2O2+O21.40×1014.0−4000.0
Figure 1.
Reaction rate parameters of the reaction R7. The black curve corresponds to the resulting
approximation.
As a result, the final version of the reduced combustion mechanism RMech2 consisted
of 21 species and 31 reactions, presented in Table 3. Both reduced combustion mechanisms,
RMech1 and RMech2, are available in CHEMKIN format in the Supplementary Materials.
Table 3.
The reduced mechanism RMech2 for the combustion of CH
4
/H
2
fuel mixtures in
near-stoichiometric conditions at 1–18 atm pressures. Rate constants are expressed in the form
k=A·Tb·exp(E/RT).
N Reaction A, mole-cm-sec-K b E, cal/mole
R1 H2+ O H + OH 5.08 ×1042.67 6292.0
R2 H2+ OH H+H2O4.38 ×1013 0.0 6990.0
R3 O2+ H O + OH 1.04 ×1014 0.0 15,286.0
R4
H2O2(+M) 2OH (+M)
Low-pressure limit:
TROE centering: 0.43, 1.0 ×1030 , 1.0 ×1030
Enhanced third-body efficiencies: O
2
= 1.2, H
2
= 3.7, H
2
O = 7.65,
CO = 2.8, CO2= 1.6, H2O2= 7.7
2.00 ×1012
2.49 ×1024
0.9
2.3
48,749.0
48,749.0
R5 HO2+ H 2OH 7.079 ×1013 0.0 295.0
R6
H+O2(+M) HO2(+M)
Low-pressure limit:
TROE centering: 0.67, 1.0 ×1030 , 1.0 ×1030, 1.0 ×1030
Enhanced third-body efficiencies: H2= 1.3, H2O = 10, CO = 1.9,
CO2= 3.8, CH4= 2, AR = 0.5
4.65 ×1012
1.737 ×1019
0.44
1.23
0.0
0.0
Energies 2023,16, 7489 8 of 30
Table 3. Cont.
N Reaction A, mole-cm-sec-K b E, cal/mole
R7 HO2+ HO2H2O2+ O21.40 ×1014.0 4000.0
R8 CH3+ O CH2O+H 1.00 ×1013 0.1 136.0
R9 CO + OH CO2+ H 7.015 ×1042.053 355.7
R10
CH3+ H (+M) CH4(+M)
Low-pressure limit:
TROE centering: 0.783, 74.0, 2941.0, 6964.0
Enhanced third-body efficiencies: H2= 2, H2O = 6, CO = 1.5,
CO2= 2, CH4= 2, AR = 0.7, N2= 1.5
1.27 ×1016
2.477 ×1033
0.63
4.76
383.0
2440.0
R11 CH4+ H CH3+ H26.14 ×1052.5 9587.0
R12 CH4+ O CH3+ OH 1.02 ×1091.5 8600.0
R13 CH4+ OH CH3+ H2O5.83 ×1042.6 2190.0
R14 CH3+ HO2CH4+ O22.32 ×1052.23 3022.0
R15 CH2+ O2HCO + OH 1.06 ×1013 0.0 1500.0
R16 CH3+ O2CH2O + OH 2.641 3.283 8105.0
R17
CH3+ OH CH2OH + H
P = 1 atm: 4.686 ×1010 0.833 3566.0
P = 10 atm: 7.00 ×1012 0.134 5641.0
P = 100 atm: 1.259 ×1014 0.186 8601.0
R18 CH3+ OH CH2+ H2O4.293 ×1042.56 3997.8
R19 CH3+ HO2CH3O + OH 5.00 ×1011 0.269 687.5
R20 CH2OH + O2CH2O + HO22.41 ×1014 0.0 5017.0
R21 CH3O+O2CH2O + HO24.38 ×1019 9.5 5501.0
R22 CH2O+HHCO + H25.74 ×1071.9 2740.0
R23 CH2O + OH HCO + H2O7.82 ×1071.63 1055.0
R24 CH2O + CH3HCO + CH43.83 ×10 3.36 4312.0
R25
HCO (+M) H + CO (+M)
Enhanced third-body efficiencies: H2= 2, H2O = 6, CO = 1.5,
CO2= 2, CH4= 2
5.70 ×1011 0.66 14,870.0
R26 HCO + O2CO + HO27.58 ×1012 0.0 410.0
R27 HCO + H CO + H27.34 ×1013 0.0 0.0
R28 HCO + OH CO + H2O3.011 ×1013 0.0 0.0
R29 HCO + CH3CH4+ CO 2.65 ×1013 0.0 0.0
R30
CH2O + H (+M) CH2OH (+M)
Low-pressure limit:
TROE centering: 0.7187, 103.0, 1291.0, 4160.0
Enhanced third-body efficiencies: H2= 2, H2O = 6, CO = 1.5,
CO2= 2, CH4= 2
5.40 ×1011
1.27 ×1032
0.454
4.82
3600.0
6530.0
R31
CH3O (+M) CH2O + H (+M)
Low-pressure limit:
TROE centering: 0.9, 2500.0, 1300.0, 1.0 ×1099
Enhanced third-body efficiencies: H2= 2, H2O = 6, CO = 1.5,
CO2= 2, CH4= 2
6.80 ×1013
1.867 ×1025
0.0
3.0
26,170.0
24,307.0
3.3. Validation of the Reduced Models against LBV and IDT
For the comprehensive validation of the reduced models, the flame structure mea-
surements presented in this paper were supplemented with a range of literature-known
Energies 2023,16, 7489 9 of 30
experimental data, which were obtained at similar experimental conditions. This included
the laminar burning velocity (LBV) measurements published by Moccia et al. [
49
] and
Dirrenberger et al. [
50
] as well as the ignition delay time (IDT) measurements in a shock
tube published by Zhang et al. [
17
] and by Cheng et al. [
51
]. For validation purposes, only
the measurements corresponding to fuel mixtures with equivalence ratios ranging from 0.8
to 1.2 and hydrogen content in the fuel mixture between 25% and 75% were chosen from
these publications.
Figure 2compares the LBV predictions of the reduced mechanisms RMech1 and
RMech2 with those of the full-set mechanism AramcoMech 2.0 and corresponding exper-
imental data from [
49
]. These data were obtained for the stoichiometric air-fuel mixture
with 30% of hydrogen. The initial temperature was T
0
= 293 K. As it can be seen, both
reduced models effectively capture the trend of LBV variation with the increase in pressure.
Only a slight overestimation was observed for the case of 3 bars.
Energies 2023, 16, x FOR PEER REVIEW 9 of 31
ranging from 0.8 to 1.2 and hydrogen content in the fuel mixture between 25% and 75%
were chosen from these publications.
Figure 2 compares the LBV predictions of the reduced mechanisms RMech1 and
RMech2 with those of the full-set mechanism AramcoMech 2.0 and corresponding ex-
perimental data from [49]. These data were obtained for the stoichiometric air-fuel mix-
ture with 30% of hydrogen. The initial temperature was T
0
= 293 K. As it can be seen, both
reduced models effectively capture the trend of LBV variation with the increase in pres-
sure. Only a slight overestimation was observed for the case of 3 bars.
Figure 2. Comparison between LBVs predicted by the reduced models RMech1 and RMech2,
full-set model AramcoMech 2.0 and the experimental data from [49]: X
H2
= 30%, T
0
= 293 K, stoi-
chiometric air-fuel mixtures.
The effect of the hydrogen concentration was examined on the dataset from [50],
obtained at atmospheric pressure. Three hydrogen concentrations from 30% to 67% at
three stoichiometric conditions in the range of 0.8–1.2 were targeted. The comparison of
the experimental values with the LBV predictions by AramcoMech 2.0, RMech1 and
RMech2 is listed in the Table 4.
Table 4. Comparison between LBVs predicted by the reduced models RMech1 and RMech2,
full-set model AramcoMech 2.0 and experimental data from [50].
φ X
H2
, % Laminar Burning Velocity, cm/s
Experiment [50] AramcoMech 2.0 RMech1 RMech2
0.8 67 58.8 54.9 55.2 55.3
1.0 67 89.0 75.3 76.9 76.7
1.2 67 95.6 80.3 82.0 78.2
0.8 50 42.8 40.0 39.9 40.8
1.0 50 62.0 56.1 57.3 58.5
1.2 50 66.2 56.2 57.8 56.6
0.8 30 31.9 32.2 31.9 33.4
1.0 30 47.5 44.3 45.1 46.9
1.2 30 49.1 42.8 44.2 44.0
Both reduced schemes demonstrated a good performance against the full mecha-
nism AramcoMech 2.0. All the values predicted by RMech1 and RMech2 did not deviate
more than 5% from the AramcoMech predictions. However, the predictive capability of
AramcoMech itself has been called into question for several data points, namely, for rich
conditions and high hydrogen concentrations. This fact indicates the necessity of addi-
tional kinetic studies on hydrogen-enriched combustion.
Figure 2.
Comparison between LBVs predicted by the reduced models RMech1 and RMech2, full-set
model AramcoMech 2.0 and the experimental data from [
49
]: X
H2
= 30%, T
0
= 293 K, stoichiometric
air-fuel mixtures.
The effect of the hydrogen concentration was examined on the dataset from [
50
],
obtained at atmospheric pressure. Three hydrogen concentrations from 30% to 67% at three
stoichiometric conditions in the range of 0.8–1.2 were targeted. The comparison of the
experimental values with the LBV predictions by AramcoMech 2.0, RMech1 and RMech2 is
listed in the Table 4.
Both reduced schemes demonstrated a good performance against the full mecha-
nism AramcoMech 2.0. All the values predicted by RMech1 and RMech2 did not deviate
more than 5% from the AramcoMech predictions. However, the predictive capability of
AramcoMech itself has been called into question for several data points, namely, for rich
conditions and high hydrogen concentrations. This fact indicates the necessity of additional
kinetic studies on hydrogen-enriched combustion.
Energies 2023,16, 7489 10 of 30
Table 4.
Comparison between LBVs predicted by the reduced models RMech1 and RMech2, full-set
model AramcoMech 2.0 and experimental data from [50].
ϕXH2, % Laminar Burning Velocity, cm/s
Experiment [50] AramcoMech 2.0 RMech1 RMech2
0.8 67 58.8 54.9 55.2 55.3
1.0 67 89.0 75.3 76.9 76.7
1.2 67 95.6 80.3 82.0 78.2
0.8 50 42.8 40.0 39.9 40.8
1.0 50 62.0 56.1 57.3 58.5
1.2 50 66.2 56.2 57.8 56.6
0.8 30 31.9 32.2 31.9 33.4
1.0 30 47.5 44.3 45.1 46.9
1.2 30 49.1 42.8 44.2 44.0
Figure 3demonstrates the comparison between the IDT predictions of RMech1 and
RMech2 and those of the AramcoMech 2.0, as well as the experimental data from [
17
,
51
].
The experimental data from Cheng et al. [
51
], corresponding to 50% of hydrogen and a
pressure of 2 atm, were reproduced accurately by both the full mechanism AramcoMech 2.0
and the reduced model RMech1. The IDTs simulated by RMech2 turned out to be slightly
underpredicted at temperatures below 1750 K. This outcome is evidently associated with
the substantial contraction of the low-temperature reaction set.
Energies 2023, 16, x FOR PEER REVIEW 10 of 31
Figure 3 demonstrates the comparison between the IDT predictions of RMech1 and
RMech2 and those of the AramcoMech 2.0, as well as the experimental data from [17,51].
The experimental data from Cheng et al. [51], corresponding to 50% of hydrogen and a
pressure of 2 atm, were reproduced accurately by both the full mechanism AramcoMech
2.0 and the reduced model RMech1. The IDTs simulated by RMech2 turned out to be
slightly underpredicted at temperatures below 1750 K. This outcome is evidently associ-
ated with the substantial contraction of the low-temperature reaction set.
Figure 3. Comparison between IDTs predicted by the reduced models RMech1 and RMech2,
full-set model AramcoMech 2.0 and experimental data from [17,51].
IDTs from the work of Zhang et al. [17] were derived at the engine-relevant pressure
of 18 atm. All simulations appeared to be moderately overestimated against the experi-
mental measurements in the whole temperature diapason. For the mixture with 40% of
hydrogen, the IDT predictions of AramcoMech 2.0 and RMech1 were consistent over the
entire temperature range. The RMech2 predictions somewhat differed from the more
complete models for temperatures over 1300 K. At lower temperature regimes, RMech2
diverged from the other models more markedly. Similar comparison figures for different
concentrations of hydrogen in the mixture are provided in the Supplementary Materials.
4. Results and Discussion
The primary objective of this work was to systematically obtain new experimental
data on the flame structure of CH
4
/H
2
blends across a wide range of different parameters.
Such data are very useful for the development and validation of kinetic models. In this
section, the new experimental data for the structures of CH
4
/H
2
/O
2
/Ar flames at different
equivalence ratios, hydrogen content and pressures are presented. The performances and
deficiencies of the reaction mechanisms considered in this work in their ability to capture
the experimental observations and tendencies are discussed. The species mole fraction
and temperature profiles measured in all 18 flames are provided in the Supplementary
Materials (Table S1).
4.1. Flame Temperature and Mole Fraction Profiles of Major Flame Species
The temperature profiles measured in all CH
4
/H
2
/O
2
/Ar flames are presented in
Figure 4. They are divided into six groups. Three temperature profiles in each group
correspond to the flames with three different hydrogen contents (X
H2
) with all other
conditions constant (pressure, total flow rate and equivalence ratio). The point with HAB
Figure 3.
Comparison between IDTs predicted by the reduced models RMech1 and RMech2, full-set
model AramcoMech 2.0 and experimental data from [17,51].
IDTs from the work of Zhang et al. [
17
] were derived at the engine-relevant pressure of
18 atm. All simulations appeared to be moderately overestimated against the experimental
measurements in the whole temperature diapason. For the mixture with 40% of hydrogen,
the IDT predictions of AramcoMech 2.0 and RMech1 were consistent over the entire temper-
ature range. The RMech2 predictions somewhat differed from the more complete models
for temperatures over 1300 K. At lower temperature regimes, RMech2 diverged from the
other models more markedly. Similar comparison figures for different concentrations of
hydrogen in the mixture are provided in the Supplementary Materials.
Energies 2023,16, 7489 11 of 30
4. Results and Discussion
The primary objective of this work was to systematically obtain new experimental
data on the flame structure of CH
4
/H
2
blends across a wide range of different parameters.
Such data are very useful for the development and validation of kinetic models. In this
section, the new experimental data for the structures of CH
4
/H
2
/O
2
/Ar flames at different
equivalence ratios, hydrogen content and pressures are presented. The performances and
deficiencies of the reaction mechanisms considered in this work in their ability to capture
the experimental observations and tendencies are discussed. The species mole fraction
and temperature profiles measured in all 18 flames are provided in the Supplementary
Materials (Table S1).
4.1. Flame Temperature and Mole Fraction Profiles of Major Flame Species
The temperature profiles measured in all CH
4
/H
2
/O
2
/Ar flames are presented in
Figure 4. They are divided into six groups. Three temperature profiles in each group
correspond to the flames with three different hydrogen contents (X
H2
) with all other
conditions constant (pressure, total flow rate and equivalence ratio). The point with
HAB = 0 mm
was assigned a temperature equal to 368 K, corresponding to the temperature
of the burner surface.
Energies 2023, 16, x FOR PEER REVIEW 11 of 31
= 0 mm was assigned a temperature equal to 368 K, corresponding to the temperature of
the burner surface.
Figure 4. Temperature profiles measured in all CH4/H2/O2/Ar flames. Numeric values show the
maximum temperature reached in each flame.
It can be seen that the maximum temperature reached in the flame varies in the
range of about 1820–2120 K, i.e., in some cases, it exceeds the maximum temperature that
the S-type thermocouple can withstand (~2020 K for short-term exposure). However, it
should be noted that the thermocouple junction experiences a lower temperature than the
surrounding gas due to heat loss to radiation. The latter is taken into account as discussed
in Section 2. The temperature correction for radiative losses in the flame reaches ~200 K
due to the power dependence (~T4).
The following tendencies can be seen from the temperature profile measurements.
First, contrary to what one might expect, a higher is hydrogen content in the fuel mixture
shows a lower maximum flame temperature (with other constant conditions). This is,
however, not surprising since the more hydrogen in the mixture, the higher the flame
speed, and, therefore, the flame comes closer to the burner, which is also seen in Figure 4.
This, in turn, results in the flame losing more heat into the burner, and as a consequence,
the flame temperature decreases.
Second, the higher the pressure, the closer the flame is to the burner (in other words,
the flame reaction zone narrows), i.e., the position where the maximum flame tempera-
ture is attained shifts toward the burner. This is especially notable when the pressure
rises from 1 atm to 3 atm. For example, the reaction zone width of the lean flame with XH2
= 25% reduces from 0.7 to 0.5 mm when switching between these pressures. This is be-
cause the linear velocity of the unburnt gas decreases with a decrease in pressure (~1/p),
since the mass flowrate of the unburnt mixtures is kept constant at different pressures
(with other parameters fixed), thus causing the flame to be pressed against the burner
surface.
Very similar tendencies with pressure and hydrogen content in the fuel mixture are
also observed in the measurements and predictions of the spatial distributions of mole
fractions of reactants (methane, hydrogen and oxygen) and major flame products (water,
CO and CO2). A comparison of the experimental and simulated mole fraction profiles of
these species in the flames with XH2 = 50% (p = 1, 3 and 5 atm; φ = 0.8 and 1.2) is shown in
Figure 5 as a representative case. For the flames with XH2 = 25% and XH2= 75%, similar
data are provided in Appendix A (Figure A1). The profiles predicted by all three kinetic
mechanisms are presented in the abovementioned figures.
Figure 4.
Temperature profiles measured in all CH
4
/H
2
/O
2
/Ar flames. Numeric values show the
maximum temperature reached in each flame.
It can be seen that the maximum temperature reached in the flame varies in the
range of about 1820–2120 K, i.e., in some cases, it exceeds the maximum temperature that
the S-type thermocouple can withstand (~2020 K for short-term exposure). However, it
should be noted that the thermocouple junction experiences a lower temperature than the
surrounding gas due to heat loss to radiation. The latter is taken into account as discussed
in Section 2. The temperature correction for radiative losses in the flame reaches ~200 K
due to the power dependence (~T4).
The following tendencies can be seen from the temperature profile measurements.
First, contrary to what one might expect, a higher is hydrogen content in the fuel mixture
shows a lower maximum flame temperature (with other constant conditions). This is,
however, not surprising since the more hydrogen in the mixture, the higher the flame speed,
and, therefore, the flame comes closer to the burner, which is also seen in Figure 4. This, in
turn, results in the flame losing more heat into the burner, and as a consequence, the flame
temperature decreases.
Second, the higher the pressure, the closer the flame is to the burner (in other words,
the flame reaction zone narrows), i.e., the position where the maximum flame temperature
is attained shifts toward the burner. This is especially notable when the pressure rises from
1 atm to 3 atm. For example, the reaction zone width of the lean flame with X
H2
= 25%
reduces from 0.7 to 0.5 mm when switching between these pressures. This is because the
Energies 2023,16, 7489 12 of 30
linear velocity of the unburnt gas decreases with a decrease in pressure (~1/p), since the
mass flowrate of the unburnt mixtures is kept constant at different pressures (with other
parameters fixed), thus causing the flame to be pressed against the burner surface.
Very similar tendencies with pressure and hydrogen content in the fuel mixture are
also observed in the measurements and predictions of the spatial distributions of mole
fractions of reactants (methane, hydrogen and oxygen) and major flame products (water,
CO and CO
2
). A comparison of the experimental and simulated mole fraction profiles of
these species in the flames with X
H2
= 50% (p = 1, 3 and 5 atm;
ϕ
= 0.8 and 1.2) is shown in
Figure 5as a representative case. For the flames with X
H2
= 25% and X
H2
= 75%, similar
data are provided in Appendix A(Figure A1). The profiles predicted by all three kinetic
mechanisms are presented in the abovementioned figures.
Energies 2023, 16, x FOR PEER REVIEW 12 of 31
Figure 5. Spatial mole fraction profiles of the major species in the flames with X
H2
= 50% at the
pressures of 1, 3 and 5 atm and φ = 0.8 and 1.2 (6 flames in total). Symbols: measurements; lines:
simulation. Dashed (blue) line: AramcoMech 2.0; solid (green) line: RMech1; dotted (red) line:
RMech2.
Figure 5 (as well as Figure A1) clearly show that all three models are quite adequate
in predicting the measured mole fraction profiles of the major flame species. Neverthe-
less, it is worth noting that the predictions of AramcoMech 2.0 and the RMech1 model are
identical for all conditions and throughout the flame zone, whereas the profiles predicted
by the RMech2 mechanism within the flame zone are somewhat different in the flames
with φ = 1.2. Furthermore, the discrepancy becomes greater with the pressure rise. This is
obviously due to the reaction of CH
3
recombination (CH
3
+ CH
3
(+M) C
2
H
6
(+M), in-
cluded in both AramcoMech 2.0 and RMech1) increasingly contributing to the overall
process of methane oxidation with the increase in the equivalence ratio and pressure (its
rate constant is pressure-dependent). Since this reaction is missing from the RMech2
model, as it is the major pathway initiating the formation of C
2
hydrocarbons, its predic-
tive ability for the slightly rich flame is not quite adequate. However, it should be noted
that, at atmospheric pressure, RMech2 provides a good fit to the experimental data and
predictions of the models with a higher degree of detail. Therefore, the mechanism
RMech2 can be expected to be quite reliable in predicting the distribution of major spe-
cies under the fuel lean conditions that are typically experienced in gas turbines (φ 0.8).
4.2. Measurements and Predictions of the Mole Fractions of Intermediates
Since a large number of mole fraction profiles for the intermediates were obtained
experimentally in this work (six intermediates in nine fuel-lean flames and nine inter-
mediates in nine fuel-rich flames; therefore, 134 spatial profiles in total), their comparison
with the predictions by three kinetic models is presented in Figures A2A7 in Appendix
A. From these data, we derived the measured and simulated values of the peak mole
fraction of the intermediates, as they are key parameters for the validation of the kinetic
Figure 5.
Spatial mole fraction profiles of the major species in the flames with X
H2
= 50% at the
pressures of 1, 3 and 5 atm and
ϕ
= 0.8 and 1.2 (6 flames in total). Symbols: measurements; lines:
simulation. Dashed (blue) line: AramcoMech 2.0; solid (green) line: RMech1; dotted (red) line:
RMech2.
Figure 5(as well as Figure A1) clearly show that all three models are quite adequate in
predicting the measured mole fraction profiles of the major flame species. Nevertheless,
it is worth noting that the predictions of AramcoMech 2.0 and the RMech1 model are
identical for all conditions and throughout the flame zone, whereas the profiles predicted
by the RMech2 mechanism within the flame zone are somewhat different in the flames
with
ϕ
= 1.2. Furthermore, the discrepancy becomes greater with the pressure rise. This
is obviously due to the reaction of CH
3
recombination (CH
3
+ CH
3
(+M)
C
2
H
6
(+M),
included in both AramcoMech 2.0 and RMech1) increasingly contributing to the overall
process of methane oxidation with the increase in the equivalence ratio and pressure (its
rate constant is pressure-dependent). Since this reaction is missing from the RMech2 model,
as it is the major pathway initiating the formation of C
2
hydrocarbons, its predictive ability
for the slightly rich flame is not quite adequate. However, it should be noted that, at
Energies 2023,16, 7489 13 of 30
atmospheric pressure, RMech2 provides a good fit to the experimental data and predictions
of the models with a higher degree of detail. Therefore, the mechanism RMech2 can be
expected to be quite reliable in predicting the distribution of major species under the fuel
lean conditions that are typically experienced in gas turbines (ϕ0.8).
4.2. Measurements and Predictions of the Mole Fractions of Intermediates
Since a large number of mole fraction profiles for the intermediates were obtained
experimentally in this work (six intermediates in nine fuel-lean flames and nine interme-
diates in nine fuel-rich flames; therefore, 134 spatial profiles in total), their comparison
with the predictions by three kinetic models is presented in Figures A2A7 in Appendix A.
From these data, we derived the measured and simulated values of the peak mole fraction
of the intermediates, as they are key parameters for the validation of the kinetic models.
In this section, we first discuss how AramcoMech 2.0, the base detailed kinetic model
considered in this work, captures the relevant experimental values. Then, we present an
analysis of how the reduced model predictions deviate from the predictions of the detailed
kinetic mechanism.
To assess the predictive ability of AramcoMech 2.0, for each measured intermediate
species in the flames, we calculated a percentage deviation Dof the predicted value
of the peak mole fraction (X
sim
) from the relevant experimental value (X
exp
) using the
following relation:
D=
Xsim Xex p
Xsim
×100%. (3)
The resultant D-values are listed in Tables 5and 6for the fuel-lean and fuel-rich
flames, respectively. It should be noted that, in lean conditions the concentration of C
2
-
hydrocarbons is much lower compared to fuel-rich conditions. Therefore, Table 5contains
no data for C
2
H
2
, C
2
H
4
and C
2
H
6
. These tables also include the data for CO, which also
peaks in the reaction zone in all flames studied, as seen in Figures 5and A1. Positive and
negative D-values indicate that the model overpredicts and underpredicts the measurement
data, respectively.
Tables 5and 6clearly show that the predictions of the H, OH, HO
2
and H
2
O
2
peak
mole fractions agree with the experimental data, in general, within the measurement uncer-
tainty. While CO post-flame mole fractions in the flames are in reasonable agreement with
the experimental data (see Figures 5and A1), its peak mole fraction is underpredicted, es-
pecially in fuel-rich conditions. We assumed that this is related to the fact that experimental
values were overestimated due to the contribution of C
2
H
4
to the mass peak m/z = 28 at
15.4 eV. Although this contribution was subtracted, the associated additional uncertainty in
the pure CO signal in the reaction zone was inevitable.
Table 5.
Percent deviation (D) of the peak mole fractions simulated with AramcoMech 2.0 from
the measured values in the fuel-lean flames (
ϕ
= 0.8). The D-values were rounded to the nearest
whole number.
P, atm XH2, % H CH3OH HO2H2O2CO CH2O
1 25 14 36 6 24 50 30 320
3 25 38 65 13 62 20 11 168
5 25 2 85 41 57 25 10 81
1 50 18 23 24 31 72 26 260
3 50 32 56 63 50 37 12 206
5 50 10 69 30 64 55 24 61
1 75 9 51 15 21 641 209
3 75 51 44 25 59 47 6 100
5 75 33 48 35 55 52 5100
Energies 2023,16, 7489 14 of 30
Table 6.
Percent deviation (D) of the peak mole fractions simulated with AramcoMech 2.0 from
the measured values in the fuel-rich flames (
ϕ
= 1.2). The D-values were rounded to the nearest
whole number.
P, atm XH2, % H CH3OH HO2H2O2CO CH2O C2H2C2H4C2H6
1 25 29 59 40 35 148 14 313 63 58 19
3 25 36 68 51 46 139 35 164 67 73 41
5 25 21 79 55 40 3 13 133 80 79 32
1 50 23 61 53 33 130 35 223 63 54 120
3 50 27 73 15 40 533 237 73 72 43
5 50 22 73 35 51 12 11 76 80 80 19
1 75 11 64 37 47 106 37 61 68 6244
3 75 16 56 40 32 22 224 43 73 16
5 75 11 67 13 54 41 6 104 80 76 18
It is noteworthy that, in all the 18 flames, AramcoMech 2.0 systematically overpredicts
CH
3
and underpredicts the formaldehyde peak mole fraction, with discrepancies for the
latter significantly exceeding the experimental error (in some cases, greater than 200%). It
is clear that the abundances of these species mutually influence each other in the flames of
methane, since there are two major pathways of CH
3
consumption: reaction with atomic
oxygen to form formaldehyde, which plays a key role in fuel-lean conditions, and CH
3
self-recombination to form ethane, predominating in fuel-rich flames.
To reveal the reactions whose rates determine the formation and consumption of
formaldehyde, we carried out a sensitivity analysis for HAB, where its maximum abun-
dance was attained in the flame
ϕ
= 0.8/1 atm/X
H2
= 50%. Figure 6shows the resultant
CH
2
O sensitivity coefficients calculated using AramcoMech 2.0. As it can be seen, there
are two key reactions, one of which (responsible for its consumption) is H-abstraction
from CH
2
O by the hydrogen atom to form a formyl radical, and the other one is the chain-
branching reaction that plays a dominant role in the general combustion process. The
abovementioned reaction of CH
2
O formation via the interaction of CH
3
and O radicals,
as observed, exhibits a lower sensitivity. Therefore, to improve the prediction of CH
2
O
concentration in the flames, the rate constant of the reaction CH
2
O + H
HCO + H
2
needs
to be revised.
Energies 2023, 16, x FOR PEER REVIEW 14 of 31
peak m/z = 28 at 15.4 eV. Although this contribution was subtracted, the associated addi-
tional uncertainty in the pure CO signal in the reaction zone was inevitable.
It is noteworthy that, in all the 18 flames, AramcoMech 2.0 systematically overpre-
dicts CH3 and underpredicts the formaldehyde peak mole fraction, with discrepancies for
the latter significantly exceeding the experimental error (in some cases, greater than
200%). It is clear that the abundances of these species mutually influence each other in the
flames of methane, since there are two major pathways of CH3 consumption: reaction
with atomic oxygen to form formaldehyde, which plays a key role in fuel-lean conditions,
and CH3 self-recombination to form ethane, predominating in fuel-rich flames.
To reveal the reactions whose rates determine the formation and consumption of
formaldehyde, we carried out a sensitivity analysis for HAB, where its maximum abun-
dance was attained in the flame φ = 0.8/1 atm/XH2 = 50%. Figure 6 shows the resultant
CH2O sensitivity coefficients calculated using AramcoMech 2.0. As it can be seen, there
are two key reactions, one of which (responsible for its consumption) is H-abstraction
from CH2O by the hydrogen atom to form a formyl radical, and the other one is the
chain-branching reaction that plays a dominant role in the general combustion process.
The abovementioned reaction of CH2O formation via the interaction of CH3 and O radi-
cals, as observed, exhibits a lower sensitivity. Therefore, to improve the prediction of
CH2O concentration in the flames, the rate constant of the reaction CH2O + H HCO +
H2 needs to be revised.
Figure 6. Sensitivity coefficients of the CH2O mole fraction calculated using AramcoMech 2.0 in the
flame φ = 0.8/1 atm/XH2 = 50% at HAB, where its peak mole fraction is reached (at 1400 K).
As for C2-intermediate hydrocarbons, they were measured with an appropriate
signal-to-noise ratio in the fuel-rich flames only, since their abundance is higher in these
conditions. One can see from Table 6 that acetylene and ethylene peak mole fractions are,
at most, systematically overpredicted by AramcoMech 2.0. it is noteworthy that this de-
ficiency of AramcoMech 2.0, as well as of other detailed kinetic models, was also pointed
out earlier for the premixed flames fueled by methane [48], propene [52], propane and
propane/methane/hydrogen blends [53].
Therefore, we can conclude that the AramcoMech 2.0 mechanism provides a rea-
sonable prediction of our measurements for H, OH, HO2, H2O2 and CO peak mole frac-
tions in both fuel-lean and fuel-rich conditions; however, it fails to capture the mole
fractions of CH3 and C2 hydrocarbons in fuel-rich conditions. This indicates that the
mechanism is expected to be good in describing the chemistry in the fuel-lean flames
occurring in gas-turbine conditions.
To trace the changes in the predictive ability of the flame structure by the reduced
mechanisms from that provided by AramcoMech 2.0, we analyzed the corresponding
percentage deviations Dreduced for different flames determined using the following relation:
-1 -0.5 0 0.5 1
O2 + H=O + OH
CH3 + O= CH2O + H
CH4 + H=CH3 + H2
CH4 + OH=CH3 + H2O
CH3 + OH= CH2OH + H
CH3 + H(+M)= CH4(+M)
H2 + O=H + OH
2CH3(+M)=C2H6(+M)
CH2O + OH = HCO + H2O
CH2O + H = HCO + H2
CH2O Normalized Sensitivity
Figure 6.
Sensitivity coefficients of the CH
2
O mole fraction calculated using AramcoMech 2.0 in the
flame ϕ= 0.8/1 atm/XH2 = 50% at HAB, where its peak mole fraction is reached (at 1400 K).
As for C
2
-intermediate hydrocarbons, they were measured with an appropriate signal-
to-noise ratio in the fuel-rich flames only, since their abundance is higher in these condi-
tions. One can see from Table 6that acetylene and ethylene peak mole fractions are, at
most, systematically overpredicted by AramcoMech 2.0. it is noteworthy that this defi-
ciency of AramcoMech 2.0, as well as of other detailed kinetic models, was also pointed
Energies 2023,16, 7489 15 of 30
out earlier for the premixed flames fueled by methane [
48
], propene [
52
], propane and
propane/methane/hydrogen blends [53].
Therefore, we can conclude that the AramcoMech 2.0 mechanism provides a reasonable
prediction of our measurements for H, OH, HO
2
, H
2
O
2
and CO peak mole fractions in
both fuel-lean and fuel-rich conditions; however, it fails to capture the mole fractions
of CH
3
and C
2
hydrocarbons in fuel-rich conditions. This indicates that the mechanism
is expected to be good in describing the chemistry in the fuel-lean flames occurring in
gas-turbine conditions.
To trace the changes in the predictive ability of the flame structure by the reduced
mechanisms from that provided by AramcoMech 2.0, we analyzed the corresponding
percentage deviations D
reduced
for different flames determined using the following relation:
Dreduced =
Xreduced XAramco
XAramco
×100% (4)
where X
reduced
and X
Aramco
are the values of the peak mole fraction predicted by the reduced
model and AramcoMech 2.0, respectively.
Table 7shows the resultant D
reduced
values for the mechanism RMech1. One can clearly
see that this reduced model is as good as AramcoMech 2.0 in predicting H, OH and CH
3
concentrations in the flames. More specifically, for these species, the D
reduced
values do not
exceed
±
10% for most flames, except for the fuel-rich flames with X
H2
= 75% at p = 3 and
p = 5 atm. It is noteworthy that the CO and CH
2
O peak mole fractions are predicted by
RMech1 in the same way as by AramcoMech 2.0 for the fuel-rich flames, and only slightly
overpredicted in fuel-lean conditions. For CO, this indicates that the RMech1 mechanism is
better in capturing its mole fraction in the flames with
ϕ
= 0.8 than AramcoMech 2.0, since
the latter one underpredicts the experimental values, as was mentioned above.
Table 7.
Percent deviation (D
reduced
) of the peak mole fractions simulated with the reduced mechanism
RMech1 (30 species and 70 reactions) from those predicted by AramcoMech 2.0.
ϕP, atm XH2, % H CH3OH HO2H2O2CO CH2O C2H2C2H4C2H6
0.8 1 25 7 0 2 26 81 8 11 54 93 24
0.8 3 25 7 1 0 16 34 14 13 52 117 10
0.8 5 25 6 0 7 4 14 17 14 64 122 7
0.8 1 50 6 0 2 15 69 8 11 59 77 22
0.8 3 50 5 3 2 45 65 14 13 51 123 16
0.8 5 50 5 3 8 10 20 18 17 60 135 12
0.8 1 75 5 2 2 1 9 8 13 63 46 24
0.8 3 75 0 22 29 83 16 12 60 126 30
0.8 5 75 2 6 10 19 32 20 21 55 164 20
1.2 1 25 2 6 4 62 77 1 1 7 68 16
1.2 3 25 2 7 3230 1 3 9 82 9
1.2 5 25 8 9 8633 0 6 17 90 10
1.2 1 50 2 8 1 50 89 2 2 8 66 18
1.2 3 50 544 13 49 0 1 7 87 8
1.2 5 50 10 9 10 6 29 1 1 23 95 11
1.2 1 75 3 9 2 5 44 3 2 25 40 8
1.2 3 75 7 13 7 19 52 4 2 25 98 14
1.2 5 75 25 10 30 11 25 4 8 48 128 18
RMech1, however, is not as accurate as AramcoMech 2.0 in the reproduction of the
mole fractions of peroxy species (HO
2
and H
2
O
2
) and C
2
hydrocarbons (C
2
H
2
, C
2
H
4
and C
2
H
6
). More specifically, as it can be seen in Table 7, the greatest deviations from
AramcoMech 2.0 predictions are for ethylene in the flames with both equivalence ratios.
Energies 2023,16, 7489 16 of 30
This can be explained by the fact that the low-temperature chemistry and hydrocarbon
chemistry are subjected to reduction when building RMech1.
The performance of RMech2 can also be analyzed in terms of D
reduced
values, which are
listed in Table 8. As it can be seen, this mechanism retains a good predictive ability for CO
in all flames. For H and OH radicals, the predictions are close to those by the detailed model
only for fuel-lean conditions (for all X
H2
and pressures) and for atmospheric-pressure fuel-
rich flames. The deviations (underestimation) from the AramcoMech 2.0 predictions for
the radicals increase with pressure. Table 8clearly shows that RMech2 provides values for
the CH
2
O peak mole fraction close to those provided by the detailed model in the flames
with a high hydrogen content (X
H2
= 75%); however, in other flames, their inessential
overestimation takes place. The discrepancies with the predictions by AramcoMech 2.0
for HO
2
, and specifically for H
2
O
2
, are fairly high due to the same reason as in the case
of RMech1. The methyl radical peak mole fraction is markedly overestimated by RMech2
because it lacks the CH
3
self-recombination reaction (to form ethane) and further C
2
chemistry subset in this model. As a consequence, the overestimation is more notable in
the fuel-rich flames.
Table 8.
Percent deviation (D
reduced
) of the peak mole fractions simulated with the reduced mechanism
RMech2 (21 species and 31 reactions) from those predicted by AramcoMech 2.0.
ϕP, atm XH2, % H CH3OH HO2H2O2CO CH2O
0.8 1 25 9 113 5 74 101 3 7
0.8 3 25 12 158 12 44 54 5 20
0.8 5 25 16 160 14 42 72 5 18
0.8 1 50 8 129 5 38 219 3 2
0.8 3 50 8 153 11 12 4 4 12
0.8 5 50 11 161 14 27 39 5 17
0.8 1 75 3 172 5 71 984 4 1
0.8 3 75 5 121 18 4 118 18
0.8 5 75 2 163 15 15 80 3 12
1.2 1 25 6 126 5 36 44 0 11
1.2 3 25 13 218 915 87 1 23
1.2 5 25 58 237 50 44 78 0 31
1.2 1 50 3 134 2 7 1 0 4
1.2 3 50 25 189 19 33 84 0 16
1.2 5 50 67 248 58 44 67 1 22
1.2 1 75 1 165 1 44 267 0 7
1.2 3 75 48 236 43 34 29 4 1
1.2 5 75 72 258 63 24 20 3 9
4.3. Effect of the Pressure on the Flame Intermediates
In this section, the effect of the pressure on the peak mole fractions of the key inter-
mediates is discussed. To explain the observed tendencies, we performed the analysis
of the rates of production of relevant intermediates in the flames using the three kinetic
mechanisms, which showed very similar results. However, for the sake of brevity, the plots
of the rate-of-production profiles for the species of interest in the flames are not presented,
and only the significant points are discussed below.
Figure 7depicts a comparison of the measurements and simulations of the maximum
mole fractions of the major flame radicals (H and OH) at different pressures. It should be
first noted that all the kinetic mechanisms provide a good fit to the experimental data. The
plots provided clearly demonstrate that the pressure rise results in decreasing H and OH
peak mole fractions, as was observed in the flames of pure hydrogen [
54
] and methane [
48
].
This occurs primarily due to the rate constant of the reaction H + O
2
(+M)
HO
2
(+M),
the main responsible for chain termination, being pressure-dependent. HO
2
radicals, in
Energies 2023,16, 7489 17 of 30
turn, take part in the OH consumption reaction HO
2
+ OH
H
2
O+O
2
. Elevated pressure
conditions facilitate more frequent collisions, which accelerate the transformation of H and
OH into HO
2
and H
2
O, respectively. The partial substitution of methane with hydrogen
results in the higher production of H radicals and, as a consequence, in a higher rate of the
major chain-branching reaction H + O2O + OH.
Energies 2023, 16, x FOR PEER REVIEW 17 of 31
Figure 7. Pressure dependence of the peak mole fractions of H and OH radicals. Symbols: experi-
ment; lines: simulation. Dashed (blue) line: AramcoMech 2.0; solid (green) line: RMech1; dotted
(red) line: RMech2.
Figure 8 compares the simulated peak mole fractions of formaldehyde with the
corresponding experimental points in the flames. Although all mechanisms are not quite
accurate in predicting the measured values, as already was discussed in Section 4.2, they
provide reasonable trends with pressure. In particular, in all flames at a higher pressure,
the CH
2
O peak mole fraction becomes lower.
This behavior of formaldehyde abundance with pressure is explained by a decrease
in the methyl peak mole fraction with pressure (see Figures A2A7), which is the main
CH
2
O precursor in the flames via the reaction with O radicals: CH
3
+ O CH
2
O + H.
The consumption of methyl radicals, in turn, enhances with the pressure since the rate
constant of their recombination to form ethane (CH
3
+ CH
3
(+M) C
2
H
6
(+M)) increases
with the pressure.
Figure 8. Pressure dependence of the peak mole fractions of formaldehyde. Symbols: experiment;
lines: simulation. Dashed (blue) line: AramcoMech 2.0; solid (green) line: RMech1; dotted (red) line:
RMech2.
The measured and calculated peak mole fraction of acetylene (key C
2
intermediate)
in the fuel-rich flames as a function of pressure is shown in Figure 9. As it can be seen, the
kinetic mechanisms AramcoMech 2.0 and RMech1 predict an increase in its mole fraction
in the whole range of pressures. Additionally, according to both mechanisms, the higher
hydrogen content in the reactant mixture, the stronger the pressure dependence. How-
Figure 7.
Pressure dependence of the peak mole fractions of H and OH radicals. Symbols: experiment;
lines: simulation. Dashed (blue) line: AramcoMech 2.0; solid (green) line: RMech1; dotted (red)
line: RMech2.
Figure 8compares the simulated peak mole fractions of formaldehyde with the cor-
responding experimental points in the flames. Although all mechanisms are not quite
accurate in predicting the measured values, as already was discussed in Section 4.2, they
provide reasonable trends with pressure. In particular, in all flames at a higher pressure,
the CH2O peak mole fraction becomes lower.