A Comparative Study between FGM and SLF Approach for Turbulent
Piloted Flame of Methane
MOKHTARI BOUNOUAR, GUESSAB AHMED
Department of Mechanical Engineering,
National Polytechnic School of Oran (Maurice Audin),
Postbox 1523 EL-M’naouer, Es-Senia Oran,
ALGERIA
Abstract: - This study validates the RANS simulation results by comparing them with experimental data.
Numerical simulations were performed for a piloted methane-air jet flame in an axisymmetric burner.
It is noteworthy that RANS simulations have been performed using a Non-premixed model with Steady
Laminar Flamelet (SLF) and a partially premixed model with Flamelet Generated Manifold (FGM) of the
Ansys-Fluent solver are used to express the chemistry-turbulence interaction, to provide an initial solution to
the simulation performed by the Pdf transported, joint two kinetic mechanisms for oxidation of methane,
detailed GRI-Mech 3.0 mechanism (53 species, 325 reactions), and CH4-Skeletal mechanism (16 species,
41-step). The case test consists of a rich premixed flame (Sandia Flame D). A comparison between the results
of the obtained simulations and experimental data shows good agreement, in particular in the context of
RANS/FGM with both mechanisms (GRI 3.0 and CH4-Skel).
Key-Words: - RANS, Flamelet, FGM, CH4-Skeletal, GRI-Mech 3.0, Flame D, Methane.
Received: January 16, 2023. Revised: November 21, 2023. Accepted: December 17, 2023. Published: December 31, 2023.
1 Introduction
Numerical modeling is an extremely important tool
for properly studying reactive turbulent flows.
He probably has some preferences (gain time, less
expensive than the experience, etc.).
Skeletal mechanisms, specific to a particular type of
problem, oxidation, and/or a certain range of
conditions, are often derived from detailed
mechanisms. Among the mechanisms published in
the literature, the basic description of methane
oxidation includes several dozen to a hundred
reactions among 10 to 40 species. To obtain a
skeletal mechanism, eliminate species and reactions
that are not relevant to the problem being
considered. The detailed description of the skeletal
mechanism (CH4-Skel) has been successfully used,
[1], [2], [3], [4], [5], [6]. The CH4 oxidation
mechanism is the basis of the detailed mechanisms
for natural gas and other hydrocarbons. This is the
latest available version of GRI-Mech 3.0, [7].
As for the previous versions, this mechanism was
first developed for natural gas. The mechanism
incorporates the oxidation kinetics of N2.
Note that the FGM [8] and SLF [9], models are
fundamentally different from the steady laminar
flamelet (SLF) model. For example, in the SLF
model, the laminar flamelet is parameterized by
strain, so that as the strain rate decreases toward the
exit of the combustion chamber, the
thermochemistry always strives for chemical
equilibrium. In contrast, the FGM and SLF models
are parameterized by the progression of the reaction,
and the flame can be completely extinguished by
adding dilution air, for example. To properly study
the effect of the two combustion models with
different reaction mechanisms for the oxidation of
methane in the air, we chose the configuration of a
controlled diffusion flame for our test case (Sandia
Flame D). These flames are often used to stabilize
the combustion process under harsh conditions, such
as in gas turbine engines.
Piloted methane-air turbulent jet diffusion
flames, namely, flames D, are numerically studied,
[10], [11], [12], [13]. This flame has been
experimentally recorded, [14]. This configuration
creates a simple parabolic flow and uses a series of
premixed flame heat sources to stabilize the main jet
at the burner exit face. A 41-step skeletal
mechanism of CH4-Skel, and the GRI 3.0
detailed mechanism which involves 53 species are
used in this simulation.
The goal of this work is to provide a compact
skeletal and detailed kinetic mechanism for methane
oxidation, which can be applied to combustion
models: Nom-premixed and partially premixed.
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2 Problem Description and
Numerical Modeling
The geometry of this test is a cylindrical combustion
chamber with coaxial injectors, methane is injected
through the inner tube, and a pilot jet is injected
through the outer tube, as shown in Figure 1.
The composition of the main jet is a mixture of
methane and air, with a molar volume fraction of
25% CH4 and 75% air. For the fuel flow, the
uniform inlet gas velocity is 49.6 m/s at a
temperature of 294 K. The pilot jet is a combustion
product with a temperature of 1880 K and a uniform
inlet gas velocity of 11.4 m/s. The pilot jet operates
at an equivalence ratio of 0.77. Air flows parallel to
the main jet with a speed of 0.9 m /s. Detailed test
conditions for establishing limits and fuel, pilot jet,
and air compositions are shown in Table 1.
Chemical models are used to determine the
source terms of transport equations for chemical
species. Although the CFD code integrates several
combustion models, only non-premixed and
partially premixed models with chemical kinetics
are used in this study (FGM and SLF).
The chemical mechanism used in this comparison
is the detailed kinetic mechanism of GRI-Mech 3.0,
which represents the most comprehensive and
standardized set of mechanisms for methane
combustion. This mechanism includes 53 species
and 325 reactions.
The reaction mechanism of CH4-Skel includes 16
species (H2O, CO2, O2, CH4, CO, H, H2, OH, O,
CH3, HCO, HO2, H2O2, CH2O, CH3O, and N2) and
41 reactions.
Figure 2 shows the computational domain of the
Sandia Flame D RANS simulation. The grid is
composed of 80×88 a node assuming axial
symmetry and the grid is subdivided at the nozzle
exit. The equations to be solved are the equation of
motion for the average velocity component, the
transport equation for the average mixing fraction
and its dispersion, and the transport equation for the
turbulent kinetic energy and its dissipation.
Fig.1: Burner configuration (All sizes are in mm)
Table 1. Condition for SANDIA Flame D [14].
Main jet
Air
Co-flow
Temperature [K]
294
291
Velocity [m/s]
49.6
0.9
Composition
(%)
YCH4
25
0
YO2
15.75
21
YN2
59.25
79
Mixture fraction, f
1
0
Reaction progress
variable, c
0
0
Turbulence intensity
I [%]
10
Hydraulic diameter
72mm
/
Re
22400
/
Fig. 2: (a) The computational mesh, (b) The detailed
mesh
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3 Flamelet Generated Manifold and
Steady Laminar Flamelet
3.1 Flamelet Generated Manifold
Flamelet Generated Manifold (FGM) is a
technology that chemically reduces combustion,
[8], [9]. The method is based on the idea that the
most important aspects of the internal structure of
the flame front should be considered, and is based
on a flamelet approach that reduces the number of
equations to be solved and reduces CPU time.
The FGM model provides the ability to solve
transport equations for the variance of reaction
progress variables or use algebraic expressions. In
front of the flame, the fuel and oxidizer are mixed
but do not burn, and behind the flame, the mixture
burns.
The FGM model assumes that the scalar
expansion of a turbulent flame can be approximated
by the scalar expansion of a laminar flame.
Diffusion FGM is computed using a laminar
diffusion flamelet generator, as described in
Flamelet Generation. A stable diffusion flame is
created over a range of scalar dissipation rates by
starting with a very small stretch (0.01/s by default)
and gradually expanding (5/s by default) until the
flame is extinguished. Diffusion FGM is computed
from laminar flamelets with steady-state diffusion
by converting the flamelet species field into reaction
progress. The partially premixed combustion model
with the FGM chemistry approach solves the
transport equation for the average reaction progress
variable c, the average mixture fraction f, and the
mixture fraction variance,
2"
f
.
In front of the flame (c = 0) the fuel and oxidizer
are mixed but do not burn, and behind the flame
(c = 1) the mixture burns. A density-weighted
average scalar (such as species proportion or
temperature), denoted by
, is computed from the
probability density functions (PDFs) of f and c as
follows:
dcdfcfPcf .,,
1
0
1
0
(1)
In addition to solving the RANS equation, the
FGM model requires solving the following transport
equations for f, f’’2, and c:
j
t
f
j
j
jx
f
DD
x
fu
xt
f
.
.
(2)
c
jt
t
pj
j
jx
c
ScCx
cu
xt
c
.
.
(3)
2
2'
2'
2'
.2
.
.
fD
Sc
x
f
ScCx
fu
xt
f
t
f
t
t
t
jt
t
pj
j
j

(4)
Where
/Cp is the diffusion coefficient for all
species, and
/Sct is the turbulent mass diffusion
coefficient,
c is the reaction progress source term
(s-1). It is retrieved from the framelet library using
the expression (Eq. 1).
3.2 Steady Laminar Flamelete Approach
The steady laminar flamelet approach models, [9],
the turbulent flame brush as a collection of
individual steady laminar flames called diffusion
flamelets. Individual diffusion flames are assumed
to have the same structure as laminar flames in
simple configurations and are determined by
experiment or calculation. Laminar flamelet
modeling of turbulent combustion is a two-step
process. First, a laminar flame library is calculated
by solving the governing equations for laminar
flames. In the second step, the framelet profile is
used as an input dataset for his CFD code. The
advantage of the diffusion flame approach using
detailed chemical mechanisms is that realistic
chemical kinetic effects can be integrated into
turbulent flames. Chemical reactions can then be
preprocessed and tabulated, resulting in significant
computational savings. However, the steady-state
diffusion flamelet model is limited to modeling
combustion due to relatively fast chemical reactions.
The CFD code solves the transport equations for the
average mixture fraction f and the mixture fraction
variance
2"
f
(Eqs.2 and 3). The average scalar
loss rate can be modeled as:
2"
2
~f
k
(5)
where k and
are the turbulent average kinetic
energy and energy dissipation rate, respectively.
Finally, the distribution of scalars within the
diffusion flame is defined as:
ddffPf .,,
0
1
0
(6)
The assumption of statistical independence
leads to
PfPfP ,
where
fP
is
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constructed from transport equations 2 and 3.In
this study uses the
-function PDF shape is given by
the following function:
dfff
ff
fp 1
1
1
1
1.
1
(7)
where:
1
1
2'
f
ff
f
(8)
and
1
1
12'
f
ff
f
(9)
The PDF format p(f) is a function only of the
first two moments: the mean mixed fraction, f, and ,
f’2, the variance of the mixed fraction. Species and
temperature are obtained from the flamelet library
(Equation 10 and Equation 11).
n
ii
i
h
f
T
t
T
1
2
2
.
2
(10)
i
ii
f
Y
t
Y
2
2
2
(11)
4 Numerical Procedures
The steady-state, Reynolds Averaged Navier-Stokes
equations for mass, momentum, energy, scalar
transport, mean mixture fraction and mean mixture
fraction variance, premixed combustion and
progress variable variance are used to describe the
flow physics and combustion process. The reaction
rate is computed by finite rate for FGM approach
and steady diffusion flamelet for the Steady
Laminar Flamelet approach. The realizable k-
turbulence model is adopted. The realizable model
is used to obtain the correct spreading of a round jet.
The governing equations and the associated
boundary conditions are solved by a CFD code
using a finite volume method. The pressure
distribution is estimated by the SIMPLE technique.
Calculations are performed with a uniform grid
distribution. The under-relaxation factors are
different for different variables varying
from 0.3 to 0.7. The numerical calculations are
performed on a DELL computer with CPU time of
around 45 min.
5 Results and Discussions
Table 2 presents the comparison of the two models
used in this study, FGM and SLF. A flamelet was
produced by a counterflow flame with a strain rate
of 100s-1. A
-function was utilized to generate the
corresponding PDF using flamelet.
The boundary conditions for the temperature
and species of the problem are replaced by the
boundary conditions for the mean mixture fraction,
f, in this approach. In this case, the value of the
mixture fraction specified in the literature, [14], f =
0.2755, was used as a boundary condition. At this
value, the species distribution and temperature of
the pilot gas are approximated accurately enough.
Figure 3 and Figure 4 shows the flamelet used
in this study.
Table 2. PDF table creation in CFD code.
FGM
SLF
Number of grid points in
mixture fraction space
64
/
Number of grid points in
reaction progress space
32
/
Initial scale dissipation (1/s)
0.01
0.01
Scale dissipation step (1/s)
1
1
Number of grid points in
flamelet
/
64
Maximum number of
flamelets
/
32
Fig. 3: Flamelet used in the simulation
(RANS/FGM)
0,00 0,25 0,50 0,75 1,00
0
500
1000
1500
2000
2500
GRI-Mech 3,0
CH4-Skel
Flamelet Generate Manifold
Mean Mixture Fraction, f
Temperature [k]
0,00
0,05
0,10
0,15
0,20
Mass Fraction of CH4
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Fig. 4: Flamelet used in the simulation RANS/SLF
5.1 Flow Field and Mixing
Figure 5 and Figure 6 show a comparison between
computed and experimental profiles for the mean
mixture fraction in the axial direction. Along the
axial direction, the computed and experimental
mean mixture fraction profiles show a good
agreement. The deviation of the predicted profile is
slightly increasing with the axial coordinate.
Examination of these two figures shows that the
average mixture fraction f maintains a unit value at
the outlet of the injector for the two combustion
models (Partially premixed and Non-premixed) up
to a distance close to x/Djet =10. This reveals a delay
in the mixing of the fuel (CH4) with the oxidant
(Air) at the central axis due to the round nature of
the jet leaving the burner. Downstream of this
station (x/Djet > 10), the decrease begins to be felt by
mixing first with the products of the pilot flame,
then with the air co-current. The limit reached by
the average mixture fraction corresponds to a value
lower (f = 0.1) than its value at the injection of the
pilot flame, (f = 0.2755). This value confirms that
the air from the Co-current manages to reach (by
entrainment) the central axis from the axial station
(x/Djet >60). The stoichiometric value (fst = 0.35) of
the mixing fraction as given by experimental
measurements [14] is reached at the level of the
axial station x/Djet=50. In this position, part of the
average flame front is supposed to be positioned
(f =fst). Figure 7 and Figure 8 show the contours of
temperature distribution from the Flamelet
Generated Manifold (FGM) and Steady Laminar
Flamelet (SLF) combustion model descriptions with
CH4-Skel and GRI-3.0, kinetic reactions
mechanisms, respectively. The visible flame extends
over 35 diameters along the axial direction for the
SLF combustion model and 40 diameters for the
FGM combustion model, and this is in agreement
with experimental data which report a visible flame
length equal to about 45 diameters. In this study, the
loss in accuracy, as well as the gain in run-time of
the reduced description, is reported by comparing it
against the full description with ISAT. The steady
laminar flamelet model can simulate local chemical
non-equilibrium due to the aerodynamic straining of
the flame by the turbulent flow field. Species that
respond quickly to this turbulence such as the OH
radical can be modeled accurately (Figure 9). The
OH species is representative of the important
intermediate species. The impact of the reduced
description on the convergence of the simulations is
also reported. As shown in Figure 10, for each
model, the reduced description with 16 represented
species agrees well with the full description.
We can see the distribution of OH radical for the
CH4-skel mechanism reaction with the use of the
Steady Laminar Flamelet method and, different from
this, uses the GRI v 3.0 mechanism. By count, for
the second approach ie, using the FGM method there
is not a difference in the presentation of the
distribution of OH. Figure 10 and Figure 11 showed
different static temperature profiles on the central
axis of the jet. These profiles come from calculations
using two different combustion models
(Partially premixed and Non-premixed) with two
reaction mechanisms for the oxidation of methane in
the air (GRI-Mech 3.0 and CH4-Skel). We see the
effects of two combustion models and even the two
reaction mechanisms on the temperature peak and
the position of this peak. In Figure 11, for the two
models of combustion with the CH4-Skel, the
section relating to the temperature rise appears
upstream of the experimental rate. On the other
hand, in Figure 12, the section relating to the rise in
temperature appears downstream of the experimental
rate. Also, the decrease in temperature noted
downstream of the station x/Djet =50 for the two tin
configurations. Table 3, illustrates this difference.
Table 3. The maximum temperature predicted by the
different chemistry schemes (deviation =
(prediction-measurement)/measurement)*100%).
Tmax.[K]
x/Djet
Dev.[%]
Exp.
/
1960.18
45.15
/
CH4-Skel
SLF
1841.53
37.8
-6.05
FGM
1963.86
41.15
0.187
GRI v 3.0
SLF
1870.02
37.76
-4.6
FGM
1905.02
38.0
-2.81
0,00 0,25 0,50 0,75 1,00
0
500
1000
1500
2000
GRI-Mech 3,0
CH4-Skel
Steady Laminar Flamelet
Mean mixture Fraction, f
Temperature [K]
0,00
0,04
0,08
0,12
0,16
0,20
Mass Fraction of CH4
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Fig. 5: Axial distribution of mean mixture fraction
with CH4-Skel Mechanism
Fig. 6: Axial distribution of mean mixture fraction
with GRI v 3.0 Mechanism
Fig. 7: Temperature distribution with CH4-Skel
mechanism: (a) RANS/SLF; (b) RANS/FGM
Fig. 8: Temperature distribution with GRI 3.0
mechanism: (a) RANS/SLF; (b) RANS/FGM
020 40 60 80 100
0,0
0,2
0,4
0,6
0,8
1,0
1,2
Mean Mixture Fraction
x/Djet
Numerical RANS/FGM
Numerical RANS/SLF
Experiment
CH4_Skel Mechanism
020 40 60 80 100
0,0
0,2
0,4
0,6
0,8
1,0
1,2
Mean mixture fraction
x/Djet
Numerical RANS/FGM
Numerical RANS/SLF
Experiment
GRI-Mech 3,0
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Ch4-Skel GRI 3.0
Steady Laminar Flamelet
Method
CH4-Skel GRI 3.0
Flamelet Generated
Manifold
Fig. 9: Contours of mean OH mass fraction from the
CH4-Skel mechanism and GRI v 3.0 Mechanism
descriptions with SLF and FGM, Methods
Fig. 10: Axial distribution of mean temperature:
(CH4-Skel mechanism)
Fig. 11: Axial distribution of mean temperature:
(GRI v 3.0 mechanism)
The results of the model consist of properties of
the flow and the chemistry. To determine the
properties of the flow, the magnitude of the velocity
vector U and the turbulent kinetic energy k can be
compared to the experimental data, [14].
The axial velocity plots in Figure 17 and Figure
18 show overall a very good agreement between
simulation and experiment. In Figure 12, a plot of
Uaxe/Ujet on the x-axis is presented for partially
premixed combustion with the FGM chemistry
approach. At the upstream part of the domain (x/Djet
< 20), the velocity profile predicted by the models is
very close to the measurements. Downstream (20 <
x/Djet < 60), the models give far too low values.
Furthermore, it can be seen that the models give
approximately the same values for the velocity
magnitude in the entire domain.
But in Figure 13, a plot of Uaxe/Ujet on the x-axis
is presented for non-premixed combustion with a
steady laminar flamelet chemistry approach.
At the upstream part of the domain (x/Djet > 30), the
velocity profile predicted by the models is very
close to the measurements.
Downstream (30 > x/Djet), the models give far too
low values. The deviation between the models and
the experiments in the prediction of axial velocity in
the upstream part of the domain is caused by
neglecting the velocity profile of pilot gas flowing
out of the main jet inlet.
The shape of turbulent kinetic energy (Figure 14
and Figure 15) is reproduced by two models (FGM
and SLF), except in the region of the fuel inlet. The
high values of the turbulent kinetic energy near the
fuel inlet are a consequence of the boundary
conditions. The specified turbulence intensity of the
fuel stream of 10% is too high. The maximum in
the curve of k predicted by the simulations is too
high. In addition, the experimental curve is broader
than the simulations indicate. Again, it can be
observed that the difference in the curves of both
models is very small except for the height of the
maximum.
020 40 60 80 100
0
200
400
600
800
1000
1200
1400
1600
1800
2000
Temperature [K]
x/Djet
Experiment
Numerical RANS/SLFM
Numerical RANS/FGM
CH4-Skel Mech,
020 40 60 80 100
0
500
1000
1500
2000
Temperature [K]
x/Djet
Experiment
Numerical RANS/FGM
Numerical RANS/FLS
GRI 3,0 Mechanism
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Fig. 12: Mean axial velocity (RANS/FGM)
Fig. 13: Mean axial velocity (RANS/SLF)
Fig. 14: Turbulent kinetic energy (RANS/FGM)
Fig. 15: Turbulent kinetic energy (RANS/SLF))
5.2 Species Prediction
Axial different species profiles (CH4, CO2, H2O
and O2) along the centerline for the partially
premixed combustion and non-premixed
combustion as well as the FGM and SLF models are
shown in Figure 16, Figure 17, Figure 18 and Figure
19, and the experiment results, [14], are also shown.
These figures show that the calculated results
using FGM and SLF using the two reaction
mechanisms for GRI-Mech 3.0 and CH4-Skel agree
with experimental data. The accuracy of numerical
predictions is good up to the height of x/Djet = 40.
We can see in Figure 9, that the temperature profile
for the SLF method coincides well with the results
of the experimental one in the region close to the
exit of the jet (0 < x/Djet < 40) and misrepresented in
the region of 40 < x/Djet < 70.
These remarks and contrary to the notice for the
second method, that is to say, the profile of the
temperature with the FGM method and low in the
region located between (0 < x/Djet <40), and indeed
converges with the data from the experimental one
in the region far from the exit of the jet
(40 < x/Djet < 80).
We also see the two figures which represent the
evolutions of the mass fractions of the chemical
species (CH4, H2O, CO2 , and O2) as for the methane
fraction and well presented by the two models (SLF
and FGM). It is identical when it comes to the mass
fraction of oxygen. It is well represented by the two
methods in the zone located between the outlet of
the jet, between (x/Djet = 0) and x/Djet = 40), beyond
this measuring station there is a difference between
the numerical calculation and the experimental one.
These remarks are visibly noted for the other mass
fractions for CO2 and H2O. Local chemical non-
equilibrium caused by aerodynamic straining of the
flame in the turbulent flow field can be simulated by
020 40 60 80 100
0,0
0,2
0,4
0,6
0,8
1,0
1,2
Uaxe/Ujet
x/Djet
Experiment
FGM- CH4-Skel
FGM-GRI 3,0
020 40 60 80 100
0,0
0,2
0,4
0,6
0,8
1,0
1,2
Uaxe/Ujet
x/Djet
Experiment
SLF_CH4_Skel
SLF-GRI 3,0
020 40 60 80 100
0
10
20
30
40
50
60
Turbulent Kinetic Energu [m2 s-2]
x/Djet
CH4-Skel
GRI-Mech 3,0
Experiment
020 40 60 80 100
0
10
20
30
40
50
60
70
80
Turbulent Kinetic Energy [m2 s-2]
x/Djet
CH4-Skel
GRI-Mech 3,0
Experiment
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the steady laminar flamelet model. Species that
respond quickly to this turbulent straining (such as
the OH radical) can be modeled accurately.
In methane combustion, a high concentration of
CO2 will affect the flame through a direct chemical
reaction of CO2 with the fuel oxidation process.
Also, as indicated from the above equilibrium
calculation results, gas phase combustion
mechanisms are found to play a much more
important role in methane combustion modeling
than in CH4-air modeling.
Fig. 16: Axial profiles of species mass fractions:
(symbols) experiment, (lines) simulation with FGM
Fig. 17: Axial profiles of species mass fractions:
(symbols) experiment, (lines) simulation with FGM
Fig. 18: Axial profiles of species mass fractions:
(symbols) experiment, (lines) simulation with SLF
Fig. 19: Axial profiles of species mass fractions:
(symbols) experiment, (lines) simulation with SLF
6 Conclusion
The goal of this work is to create and use a
numerical method to simulate a diffusion flame.
The transport probability density (Pdf) model has
been compared to four reacting flow test cases,
including the Sandia D Flame test, in which
methane and air are burned.
A steady laminar flamelet and GRI-Mech 3.0
are used for non-premixed combustion;
Non-premixed combustion with a Steady
Laminar Flamelet and CH4-Skel mechanism
Partially premixed combustion with FGM and
GRI-Mesh 3.0
Partially premixed combustion with FGM and
CH4-Skel mechanism
In the context of RANS/FGM and RANS/SLF, a
good agreement can be observed when comparing
simulation results with experimental data
020 40 60 80 100
0,00
0,02
0,04
0,06
0,08
0,10
0,12
0,14
0,16
0,18
0,20
Mass Fraction
x/Djet
CH4
O2
H2O
CO2
CH4-Skel Mech
020 40 60 80 100
0,00
0,05
0,10
0,15
0,20
Mass fraction
x/Djet
GRI-Mech 3,0
CH4
O2
CO2
H2O
020 40 60 80 100
0,00
0,02
0,04
0,06
0,08
0,10
0,12
0,14
0,16
0,18
0,20
Mass Fraction
x/Djet
CH4-Skel Mech.
CH4
O2
H2O
CO2
020 40 60 80 100
0,00
0,05
0,10
0,15
0,20
Mass Fraction
x/Djet
GRI-Mech 3,0
CH4
O2
H2O
CO2
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concerning temperature, velocity, chemical species,
etc.
We can conclude that the use of a global kinetic
mechanism such as the CH4-Skeletal mechanism
introduces an advanced variable more representative
of the evolution of chemical species in the flame.
Some perspectives that could be interesting to
explore for our future research can be mentioned,
including:
Start the calculations again with another
reaction mechanism to create the turbulent
flamelet library.
Separate transport equations are used to
determine the NOx that can be added, but their
chemistry is slow and cannot be analyzed in the
flamelet library.
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Mokhtari Bounouar, Guessab Ahmed
E-ISSN: 2224-347X
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Contribution of Individual Authors to the
Creation of a Scientific Article (Ghostwriting
Policy)
At every stage of the present research, the authors
contributed equally, from the formulation of the
problem to the final findings and solutions.
Sources of Funding for Research Presented in a
Scientific Article or Scientific Article Itself
No funding was received for conducting this study.
Conflict of Interest
The authors have no conflicts of interest to declare.
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BY 4.0)
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WSEAS TRANSACTIONS on FLUID MECHANICS
DOI: 10.37394/232013.2023.18.26
Mokhtari Bounouar, Guessab Ahmed
E-ISSN: 2224-347X
282
Volume 18, 2023