Cent. Eur. J. Chem. • 12(3) • 2014 • 391-402
DOI: 10.2478/s11532-013-0387-0
Central European Journal of Chemistry
Numerical study of the laminar flame
propagation in ethane-air mixtures
Research Article
Venera Giurcan1, Domnina Razus1*,
Maria Mitu1, Dumitru Oancea2
1
Ilie Murgulescu Institute of Physical Chemistry,
060021 Bucharest, Romania
2
University of Bucharest, Faculty of Chemistry,
Physical Chemistry Department, 030018 Bucharest, Romania
Received 22 February 2013; Accepted 13 November 2013
Abstract: The
structure of premixed free one-dimensional laminar ethane-air flames was investigated by means of numerical simulations performed
with a detailed mechanism (GRI-Mech version 3.0) by means of COSILAB package. The work provides data on ethane-air mixtures with
a wide range of concentrations ([C2H6] = 3.0 – 9.5 vol.%) at initial temperatures between 300 and 550 K and initial pressures between
1 and 10 bar. The simulations deliver the laminar burning velocities and the profiles of temperature, chemical species concentrations
and heat release rate across the flame front. The predicted burning velocities match well the burning velocities measured in various
conditions, reported in literature. The influence of initial concentration, pressure and temperature of ethane-air mixtures on maximum
flame temperature, heat release rate, flame thickness and peak concentrations of main reaction intermediates is examined and discussed.
Keywords: Flame propagation • Ethane-air • Chemical modeling • Laminar burning velocity
© Versita Sp. z o.o.
1. Introduction
The fast depletion of fossil fuel resources necessary for
various fields of human activity and the need for reduction
of polluting automotive emissions support the interest for
alternative fuels, meant to replace common engine fuels.
A widely available, cheap alternative fuel is natural gas,
constituted mainly from methane and ethane. Natural
gas allows engine operation at high compression ratios
since methane, its main component, has a high octane
number; at the same time, natural gas is less polluting
than gasoline or Diesel in terms of CO2 emissions [1,2].
Natural gas has however the drawback of a high ignition
temperature and a slow burning rate, especially due to
methane. The combustion of methane, especially under
engine conditions, was extensively studied and various
strategies have been examined in order to increase its
thermal efficiency and reduce unburned hydrocarbon
emissions at lean operation conditions; among them,
addition of hydrogen in small amounts was found most
promising [1,3-5].
Combustion of ethane-air mixtures has also been
subject of many experimental and numerical studies
[6-35]. The interest for this topic is determined both by the
use of natural gas as an alternative, eco-friendly fuel and
by its presence as an intermediate during the oxidation
of many hydrocarbons like methane, propane and higher
alkanes. The studies have been conducted to examine
the auto-ignition (in jet stirred reactors [10,14], rapid
compression machines [28] or in shock tubes [10,28]) or
the flame propagation in ethane - air mixtures by means
of various methods: conical or flat burners (including
the heat flux technique) [6,7,11,17,20,21,26,30,32,34];
stagnation flow [9,17,19,21,25,31,33]; outwardly
spherical flames [8,11,13,14,18,22,29,32,34]. Extensive
measurements of temperature and chemical species
concentrations during auto-ignition experiments or
within the flame front (the main reaction zone) of flames
stabilized in various burner configurations have been
used to develop and test detailed kinetic models able to
predict the system behavior under extensive variation of
the state parameters. In addition, several detailed kinetic
* E-mail: [email protected]; [email protected]
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Numerical study of the laminar flame
propagation in ethane-air mixtures
models have been validated by comparing experimental
and predicted global parameters such as the ignition
delay and ignition temperature [10,14,28] and/or the
normal burning velocity of premixed flames [11,18,2022,25-27,35].
The combustion of ethane and lower alkanes in
premixed laminar flames was subject of numerous
mechanistic examinations [16,20,23,24,26,27,29-35].
The numerical simulations have been usually focused
on plane, unstretched flames. Warnatz [16] developed
a mechanism describing his own measurements on
CO, H2 and C1-C4 hydrocarbons flames at ambient
initial conditions, improved later by Heghes [23]. This
mechanism successfully predicted the burning velocities
of lean and stoichiometric ethane-air flames, as
measured by Warnatz [16] and Boschaart [21]; for rich
mixtures the computed velocities were overestimated in
comparison with experimental data. Other mechanisms
were developed and tested by Dagaut [10], Taylor [11],
Hassan [18], Davis [19], Konnov [20,26], Naik [24], Ranzi
and Frassoldati [32,35] and Wu [33], in the attempt to
find a kinetic scheme able to predict a large data pool,
which include different reactor types and cover a wide
range of temperatures, pressures, and equivalence
ratios (high-pressure flow reactor studies, shock-tube
studies of ethane oxidation and pyrolysis, and normaland low-pressure flames). Discussions of the predictive
ability of various mechanisms in respect to premixed
laminar ethane-air flames are found in several papers
[9,25-27,29], based on both burning velocities and
concentration profiles of main chemical species.
In the present work, the chemical modeling of
premixed free one-dimensional laminar ethane-air
flames has been made by means of the GRI mechanism
version 3.0 (Gas Research Institute, USA) using the
COSILAB package [36]. The GRI 3.0 mechanism, found
to predict well the laminar burning velocity of methane–
air mixtures within uncertainty limits of experiments for
a wide range of equivalence ratios [29,37] was chosen
for our investigation. In comparison with earlier versions
(2.0 and 2.1), GRI 3.0 was optimized by its authors [38]
by adding propane and C2 oxidation products, and by
including new formaldehyde and NO formation and
reduction steps as well as reactions that are involved
in the combustion of other hydrocarbon constituents
of natural gas (e.g., ethane and propane). Frenklach
and coworkers recommend GRI 3.0 for modeling the
natural gas combustion in a temperature range of 1000–
2500 K, pressures from 10 Torr to 10 atm, and
equivalence ratio from 0.1 to 5 for premixed systems.
The modeling delivered the burning velocities and
the profiles of heat release rate, of concentration for
chemical species in the flame front and of temperature
across the flame of ethane-air mixtures with variable
initial composition (within the flammability limits),
pressure and temperature. The present predictions of
burning velocities are compared with experimental data
reported in literature [7,9,11,13,18,20,26,30,33]. The
flame thicknesses, calculated from the temperature
profiles, are reported and examined in comparison
to other fuel-air mixtures. The influence of initial
concentration, pressure and temperature of ethaneair mixtures on maximum flame temperature, flame
thickness, heat release rate and peak concentrations of
main reaction intermediates is examined and discussed.
2. Computational details
The kinetic modeling of ethane-air flames was made
with the package COSILAB (version 3.0.3) developed
by Rogg and Peters [36], using the GRI (Gas Research
Institute) mechanism version 3.0. This is a chemical
reaction mechanism optimized for combustion of natural
gas in air, where 53 chemical species and 325 elementary
reactions are taken into account. The input data were
taken from thermodynamic and molecular databases
of Sandia National Laboratories, USA, according to the
international standard (format for CHEMKIN).
COSILAB is a package for comprehensive simulation
of chemically reactive flows, including freely propagating
adiabatic premixed flames. It uses preprocessors that
accept molecular and thermodynamic data and reaction
mechanisms fully compatible to the international
standard format put forward by Sandia National
laboratories. As solvers, the package uses a steady
Newton solver (usually 25 iterations, relative tolerance
10-5; absolute tolerance 10-8), an unsteady Newton
solver (usually 15 iterations, relative tolerance 10-4;
absolute tolerance 10-6) and an unsteady Euler solver.
For the adaptive grid parameters, we used GRAD = 0.1,
CURV = 0.2 and maximum ratio of adjacent cell size
between 1.3 and 1.1.
The runs were performed for the isobaric combustion
of ethane-air mixtures at various initial compositions
(φ = 0.52-1.75; [C2H6] = 3.0 – 9.5 vol.%), pressures
(1 – 10 bar) and temperatures (300 – 550 K). The
computations were made for premixed 1D adiabatic
laminar free flames.
3. Results and discussion
The laminar burning velocities of ethane-air mixtures
at ambient initial temperature and pressure computed
with GRI mechanism version 3.0 are plotted against the
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V. Giurcan et al.
Table 1. Reference values of burning velocity for ethane-air at ambient initial conditions, from various literature sources.
Flat flames, heat flux burner
Stagnation flow technique
Spherically expanding flames
Su for the most
reactive mixture (cm s-1)
Ref.
41.0
43.3
[6]
44.5
47.6
[7]
41.0
41.5
[17]
40.7
42.2
[20]
40.7
-
[21]
41.5
42.5
[26]
41.0
42.0
[29]
43.0
44.0
[9]
38.5
41.0
[11]
41.0
41.5
[17]
34.6
-
[8]
38.5
41.0
[11]
40.0
45.3
[13]
36.0
39.0
[15]
42.0
43.0
[18]
38.5
40.0
[22]
37.5
38.5
[34]
equivalence ratio φ1 in Fig. 1, together with literature
data obtained by various experimental techniques.
The predictions of this model match well with the most
reported experimental burning velocities, especially on
the lean side of fuel-air mixtures. Thus, the peak burning
velocity Su,max = (42 ± 1) cm s-1 was obtained at the same
composition ([C2H6] = 5.80 – 6.0 vol%; φ = 1.1 – 1.2)
by various measurements [9,18,20] and by the present
chemical modeling. There is, however, a large scatter of
burning velocities at ambient initial conditions, as seen
from data in Table 1.
Higher peak burning velocities were reported
by early measurements of Gibbs and Calcote on
stationary flames anchored on a Bunsen burner [7]
(Su,max = 47.6 cm s-1) and by the measurements on
outwardly propagating spherical flames in a closed
vessel, made by Tseng et al. [13] (Su,max = 45 cm s-1).
Other measurements performed by heat flux method
indicate Su,max = (42 ± 0.5) cm s-1 [20,26,29]. For the
stoichiometric ethane-air mixture, most reported values
range between 37.5 cm s-1, as measured by the spherical
bomb technique [34] and 42.5 cm s-1, as given in [9]. Less
1
The equivalence ratio is defined as
j
[C H ]
 [C2 H 6 ]
  [C2 H 6 ]


3.5  2 6
=
[O2 ]  
[O2 ]  st
[O2 ] 


where the index “st” refers to the stoichiometric mixture, for
which both the fuel (ethane) and oxygen burn completely to CO2
and H2O.
45
40
35
-1
Conical flames
Su for φ = 1.0
(cm s-1)
Su (cm s )
Measuring technique
30
25
20
present data
counter-flow flame technique [9]
spherical bomb technique [18]
heat flux technique [20]
15
10
5
0.6
0.8
1.0
1.2
1.4
1.6
1.8
j
Figure 1.
Computed burning velocities at 1 bar and 298 K and
experimental data, from various literature sources.
experimental data are available for ethane-air mixtures
at initial temperature and/or pressure higher than
ambient, as outlined in a recent review by Frassoldati
[32]. At ambient initial temperature, Hassan found
Su,max = 37 cm s-1 at p0 = 2 bar and Su,max = 31 cm s-1 at
p0 = 4 bar [18]; Jomaas measured Su,max = 34 cm s-1 at
p0 = 2 bar and Su,max = 27 cm s-1 at p0 = 5 bar [22] and
Kochar reported Su,max = 23 cm s-1 at 10 atm [34]. For
preheated mixtures, Veloo found Su,max = (53 ± 1) cm s-1 at
T0 = 343 K and 1 bar [31] and Kochar reported
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Numerical study of the laminar flame
propagation in ethane-air mixtures
80
70
Su (cm s-1)
60
50
40
300 K
333 K
363 K
393 K
423 K
30
20
10
0.6
0.8
1.0
1.2
1.4
1.6
j
Figure 2.
Computed burning velocities of ethane-air mixtures at
1 bar and various initial temperatures.
120
300 K;
400 K;
500 K;
110
100
Su (cm s-1)
90
350 K
450 K
550 K
HCO + M → H + CO + M
C2H5 + M → C2H4 + H +M
80
70
60
50
40
30
20
2
4
6
8
10
p0 (bar)
-1
Su (cm s )
(a)
120
110
100
90
80
70
60
50
40
30
20
1 bar;
3 bar
5 bar;
7.5 bar
10 bar
300
350
400
450
500
550
T0 (K)
Figure 3.
initial temperatures given in Fig. 2 and for flames at
higher initial temperatures and pressures, given in
Figs. 3a and 3b. The lines in Figs. 3a and 3b represent
the best-fit correlations between computed burning
velocities and initial pressure or temperature.
Other numerical experiments reported in literature
deliver close results. Thus, the predictions of Konnov
model (a detailed C/H/N/O reaction mechanism for
the combustion of small hydrocarbons, based on 1200
reactions and 127 species) [20] are within the lower limits
of the data scattering in the diluted C2H6–O2–N2 mixtures.
This may indicate uncertainties in the rate coefficients
of some reactions with third-body participation and/or in
the transport properties used in the flame calculations.
Sensitivity analyses [20] showed that decomposition of
HCO and C2H5 are among the most important reactions
in ethane combustion:
(b)
Computed burning velocities of the stoichiometric
ethane-air mixture. (a) Burning velocities at various
initial pressures; (b) Burning velocities at various initial
temperatures.
Su,max = 28 cm s-1 at T0 = 325 K and 5.06 bar [34]. These
burning velocities confirm well the predictions of the GRI
mechanism, obtained for flames at 1 bar and various
Therefore, small systematic deviations of the
calculations from the experimental results may
indicate some uncertainties in the rate constant of the
C2H5 decomposition. In a later paper, Dyakov, Ruyck
and Konnov [26] brought some modifications to this
mechanism: an update of the thermodynamic data
for OH radicals and many other species and some
changes of the reaction rate constants in the H2–O2
combustion sub-mechanism. The validity check was
made by comparing experimental and predicted Su
and concentration profiles of the molecular species,
especially NO. The authors compared the predictions
of the GRI-mech. 3.0 with those of their mechanism and
concluded that both agree well with the measurements
in lean mixtures as well as near the equivalence ratio
of 1.0, where the thermal-NO mechanism is dominant.
However, in rich mixtures the behavior of these models
is clearly different. The same remark was made by
Taylor [11], who used his own mechanism and Heghes
[23], who used an improved Warnatz mechanism.
Comparisons between predictions made with GRI 3.0
mechanism and with other mechanisms have been
made by Bergthorson [25] (who used a C3 model
developed by Davis et al. to describe the combustion
of C1–C3 hydrocarbons, based on use of 71 species
and 469 reactions and two versions of the San Diego
mechanism) and Kishore [29]. Bergthorson found that
both GRI-Mech 3.0 and the DLW99 models accurately
predict experiment for methane– and ethane–air flames
(data on counterflow flames), but the revision of the San
Diego mechanism made in 2005 gives the best overall
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0.2
d (mm)
0.4
0.6
0.8
1.0
1.2
-0.2
2200
1800
1600
1400
1200
1000
800
dQ/dt
600
400
200
-0.2
0.20
0.2
0.4
0.6
d (mm)
0.8
1.0
-0.2
d (mm)
0.4
0.6
0.8
1.0
1.2
2000
T
0.12
1800
1600
0.10
1400
H2
0.08
0.06
NO
0.04
0.00
0.0
0.2
0.4
0.6
d (mm)
1000
600
400
C2H2
-0.2
1200
800
CO
0.02
-0.02
2200
200
0.8
1.0
1.2
0.8
1.0
1.2
(a)
0.0
0.2
d (mm)
0.4
0.6
0.8
1.0
O2
1.2
-0.2
2200
T
1800
1000
H2 O
C2H6
800
600
400
0.00
200
0.0
0.2
0.4
0.6
d (mm)
0.8
1.0
d (mm)
0.4
0.6
1.2
2200
2000
T
1800
1600
xOH
1400
0.003
1200
0.002
1000
xO
0.001
T (K)
0.10
1200
0.2
0.004
T (K)
CO2
1400
0.0
0.005
2000
1600
-0.2
0.2
Temperature and volumetric rate of heat release profiles in the stoichiometric C2H6-air flame
0.15
0.05
1.2
2*xH; xOH; xO
0.25
0.0
0.0
0.14
2000
T
Figure 4.
xC2H6; xO2; xCO2; xH2O
0.0
xCO; 100*xC2H2; 100*xH2; 500*xNO
-0.2
T (K)
6.5
6.0
5.5
5.0
4.5
4.0
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0
T (K)
-dQ/dt*10-9(J s-1 m-3)
V. Giurcan et al.
800
600
xH
400
0.000
200
-0.2
0.0
0.2
0.4
0.6
d (mm)
0.8
1.0
1.2
(b)
Figure 5.
Mass fractions profiles of reactants and major products in the stoichiometric C2H6-air flame.
agreement with experiment for methane, ethane, and
ethylene flames. Kishore et al. [29] found quite a good
agreement between their own experimental burning
velocities (heat flux method) and those predicted by
the GRI 3.0 mechanism. In other recent publications,
different mechanisms such as GDF-Kin [27], a reduced
high-T mechanism [30] derived from the Lawrence
Livermore comprehensive mechanism, USC Mech II
[31], a semi-detailed reaction mechanism [32] or a C4
mechanism [34] have been used to model ethane-air
flames. All these mechanisms were able to capture the
temperature and pressure dependence of the laminar
flame speed across the full range of pressures and
temperatures examined, but some predicted burning
velocities overestimated experimental data, especially
at conditions different from ambient.
The GRI 3.0 mechanism was also used by
Browne, Liang and Shepherd [39] to simulate the hightemperature, shock-induced combustion for several fuelair mixtures by assuming the process can be modeled
as constant volume combustion. They validated the
Figure 6.
Temperature and mass fractions of intermediates in
the stoichiometric C2H6-air flame at p0 = 1 bar and
T0 = 298 K. (a) Profiles of temperature and mass fractions
of molecular intermediates; (b) Profiles of temperature
and mass fractions of several radical intermediates
mechanism against the induction times and the temporal
evolution of the species. For mixtures with methane
and ethane as fuels, simulations of near-stoichiometric
mixtures with air showed no evidence of any sort of
dramatic mechanism shift or cross-over effect for a wide
range of temperature-pressure conditions.
Relevant data on the structure of a 1D stoichiometric
ethane-air flame at ambient initial conditions are given
in Figs. 4-6. In each plot, the temperature profile was
drawn as to reveal the position of the peak values for
the heat release rate and for concentrations of main
molecular and radical species present in the flame front
and a vertical line has marked the boundary between the
pre-heat and the reaction zone of the flame, set at the
inflection point of T(d) diagram. The features of these
two zones are the same for flames of all hydrocarbonair mixtures [10]: the preheat zone of ethane-air flame
is quite large; here are generated the major radicals,
but their concentrations are still low so that the heating
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propagation in ethane-air mixtures
0.65
2100
5.5 %
1800
5.0 %
4.5 %
1200
300 K
363 K
423 K
0.55
0.50
3.5 %
δ / mm
1500
T (K)
0.60
4.0 %
900
0.45
0.40
0.35
600
0.30
300
-0.20
0.00
0.20
0.40
0.60
0.80
1.00
0.25
1.20
0.6
0.7
0.8
0.9
d (mm)
Figure 7.
1.0
1.1
1.2
Temperature profiles of lean C2H6-air flames p0 = 1 bar and T0 = 298 K.
j = 1.00
j = 0.88
j = 0.70
0.45
0.35
0.40
0.30
δ (mm)
δ (mm)
1.5
various initial temperatures.
j = 1.00
j = 0.88
j = 0.70
0.40
1.4
Figure 8. The flame thickness of C2H6-air flames at p0 = 1 bar and 0.50
0.45
1.3
j
0.25
0.20
0.15
0.35
0.30
0.10
0.05
2
4
6
8
300
10
p0 (bar)
340
360
380
400
420
T0 (K)
(a)
Figure 9.
320
(b)
Flame thickness of lean and stoichiometric C2H6-air mixtures. (a) C2H6-air mixtures at T0 = 300 K and various initial pressures;
(b) Preheated C2H6-air mixtures at p0 = 1 bar.
occurs mostly by thermal conduction. In the reaction
zone, the regions of radical production and radical
recombination are found; here, the heat release rate
and the concentrations of CO and radicals reach their
peak values. Similar diagrams have been computed
for ethane-air flames with various initial concentrations,
pressures and temperatures.
Significant results referring to ethane-air flames
with variable ethane concentration at p0 = 1 bar and
T0 = 298 K are given in Figs. 7-10. In Fig. 7, the progressive
increase of maximum flame temperature when
ethane concentration approaches the stoichiometric
concentration (φ = 1.0; [C2H6] = 5.65 vol.%) and the
corresponding diminution of flame width are observed;
a similar trend of variation was found for rich ethane-air
mixtures, when ethane concentration goes increasingly
far from stoichiometry.
The flame thickness δ, plotted in Figs. 8 and 9, was
calculated from the temperature profile as the ratio of
the maximum temperature difference and the maximum
slope of the temperature profile [40,41]:
δ =
Tb − Tu
(dT / dx )max
(1)
The flame thickness δ reaches the lowest value
in the rich domain of ethane concentration, at the
equivalence ratio φ = 1.05 - 1.10. For this most reactive
ethane-air mixture, the calculated flame thickness at
ambient initial conditions is δ = 0.29 mm and it lies
close to similar values reported for CH4-air [42-46] and
C3H8-air mixtures [41]. The flame thickness decreases
as pressure and/or temperature increase, as seen from
data in Figs. 9a and 9b.
The flame thickness of a laminar flame may be
further used for calculation of the quenching distance
of deflagrations, defined as the minimum diameter
of a channel below which a laminar flame cannot
propagate, since a constant ratio was found between
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12
6
6.5 %
7.0 %
-1
-3
-dQ/dt*10 (J s m )
7.5 %
3
8
1.2 bar
6
1.0 bar
-9
-9
-1
-3
-dQ/dt*10 (J s m )
5
4
1.5 bar
10
2
8.0 %
1
0
0.8 bar
0.6 bar
2
0
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0.0
d (mm)
(a)
Figure 10.
0.4
0.6
0.8
1.0
1.2
(b)
The volumetric rate of heat release in the flame front of C2H6-air mixtures. (a) Rich C2H6-air mixtures, at T0 = 298 K and p0 = 1 bar; (b) Stoichiometric C2H6-air flames, at T0 = 298 K and various initial pressures.
1820
1800
1750
1780
1700
1760
Ti (K)
1650
1600
298 K
363 K
423 K
1550
1500
1740
1720
1700
1680
1450
1400
0.2
d (mm)
1800
Ti (K)
4
1660
0.6
0.8
1.0
1.2
1.4
1.6
1.8
1640
Figure 11.
The ignition temperature in ethane-air flames of variable
initial composition and temperature, at ambient initial
pressure.
the flame thickness and the quenching distance of
deflagrations for various fuel-air mixtures [47]. Both
the quenching distance and the minimum ignition
energy, calculated from the quenching distance by
a recent model [48,49] are important flammability
parameters of fuel-air deflagrations [50], used for safety
recommendations.
Another important parameter obtained by chemical
modeling of laminar flames, playing a dominant role in
flame propagation, is the volumetric rate of heat release.
The rate of heat release has a peak value in the reaction
zone; this value goes through a maximum in the most
reactive ethane-air mixtures (usually, mixtures with
an equivalence ratio φ = 1.10 – 1.20). In Fig. 10a the
rates of heat release for several rich ethane-air mixtures
have been plotted; a similar variation was observed for
lean ethane-air mixtures, when ethane concentration
approached the lower flammability limit.
For hydrocarbon-air flames, Dixon-Lewis [51] defined
a characteristic temperature within the flame front, where
the production rate of abundant radicals (H, O, OH, CH3,
2
4
6
8
10
p0 (bar)
j
Figure 12.
The ignition temperatures in the stoichiometric ethaneair flames at various initial pressures and T0 = 300 K.
C2H5, HO2 and CHO) becomes positive. Dixon-Lewis
considered it defines the limit of the chain-branching
region in the flame and named it “ignition temperature”.
From Fig. 6b it is however seen that the generation
rates of various radical intermediates become positive
at different positions in the flame front and it would be
difficult to find the ignition temperature of ethane-air
flames after examining H or OH or other radicals. It is
easier to observe the position of the maximum rate of
heat release, which appears at temperatures close to
the “ignition temperature” according to Taylor [11]. In
fact, Taylor considered that this “ignition temperature”
corresponds to the temperature of maximum rate of fuel
consumption, where the radical pool production rate
becomes positive. Accordingly, a more adequate name
for this temperature would be “cutoff temperature” in
respect to the rate of formation of radicals. In the present
case, the influence of initial concentration and pressure
on Ti, the ignition temperature defined according to the
peak value rate of heat release rate, is shown by plots
from Figs. 11 and 12.
397
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Numerical study of the laminar flame
propagation in ethane-air mixtures
Table 2. Baric coefficients ν
of burning velocity and overall reaction orders n for ethane-air .
φ
T0 = 300 K
T0 = 425 K
-ν
n
-ν
n
0.592
0.401 ± 0.039
1.20
0.441 ± 0.025
1.12
0.703
0.336 ± 0.037
1.33
0.329 ± 0.035
1.34
0.842
0.318 ± 0.012
1.36
0.290 ± 0.013
1.42
1.012
0.287 ± 0.011
1.43
0.235 ± 0.011
1.53
1.129
0.243 ± 0.011
1.51
0.216 ± 0.012
1.57
1.250
0.255 ± 0.019
1.49
0.217 ± 0.015
1.57
1.370
0.285 ± 0.038
1.43
0.218 ± 0.038
1.56
2 2
2
4
p0 (bar)
6
8
10
8
2300
7
10
2250
6
8
2200
C2H2;
OH;
6
NO
H;
2150
O
2050
2
0
2000
0
Figure 13.
2
4
6
8
10
1950
-1
-3
2100
4
-9
T
-dQ/dt*10 (J s m )
2350
12
Tb (K)
xC H .104; xNO.105; xOH.103; xH.104; xO.103
0
3.1. Pressure influence on flame structure and burning velocity
393 K
5
333 K
4
300 K
3
2
1
0
0.0
p0 (bar)
Pressure influence on end flame temperature and
mass fractions of several intermediates in the
flame front of a stoichiometric C2H6-air mixture, at
T0 = 300 K.
423 K
0.2
0.4
0.6
0.8
1.0
d (mm)
Figure 14.
The volumetric rate of heat release for the
stoichiometric C2H6-air mixture, at p0 = 1 bar and
various initial temperatures.
together with the overall reaction orders obtained with
the equation [52]:
As shown in Fig. 9a, the flame thickness of all flames
n 2 (ν + 1) (3)
decreases as pressure increases; in accord to this, the =
quenching distance will follow the same dependence.
The baric coefficients of burning velocities for ethaneThe pressure increase determines an important increase
of the heat release rate, as seen from Fig. 10b for data air are within the range found for mixtures of other lower
computed for the stoichiometric C2H6-air mixture at hydrocarbons with air (-0.30 for stoichiometric methaneair [53]; between -0.26 and -0.12 for propane-air
ambient initial temperature.
The presure influence on burning velocity could be [8,54-56]; -0.11 for stoichiometric butane-air [57]). For
examined in Fig. 3a. The data were analyzed according ethane-air, baric coefficients between -0.27 and -0.12
have been reported, referring to experimental burning
to a power-law equation:
velocities at ambient initial temperature [8,9,18,34]. In
ν
 p 
the present case, the baric coefficients range within
(2)
Su = Su,ref 

 pref 
-0.40 and -0.24 (at T0 = 300 K) and within -0.44 and
where Su,ref is the normal burning velocity at reference -0.22 (at T0 = 425 K) with minimum values at the most
pressure pref and ν is the baric coefficient. Choosing reactive composition (corresponding to φ = 1.13). The
pref = 1 bar, the baric coefficients of normal burning corresponding overall reaction orders range between
velocities for ethane-air mixtures were calculated by a 1.10 and 1.60.
Another diagram, plotting the end flame temperature
non-linear regression analysis of Su = f(p0) data. Some
values for the examined mixtures are given in Table 2 Tb and the peak mass fractions of several important
398
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V. Giurcan et al.
xC H .104; xNO.105; xOH.103; xH.104; xO.103
300
350
C2H2;
OH;
10
400
NO
H;
T0 (K)
450
500
550
2080
O
9
2060
8
7
Tb (K)
T
2040
Ethane-air, 1 bar
6
5
2020
4
2 2
3
2
2000
300
350
400
450
500
550
T0 (K)
Figure 15.
Initial temperature influence on end flame temperature
and mass fractions of several intermediates in the
flame front of the stoichiometric C2H6-air mixture, at
p0 = 1 bar.
1760
1750
1740
Ti (K)
1730
1720
Linear Regression for Data1_E:
Y =A +B *X
Parameter
Value Error
---------------------------------A
1592.3
15.62999
B
0.294
0.03431
---------------------------------R
SD
N
P
---------------- ----------------0.980 5.4252 5 0.00334
1710
1700
1690
350
400
450
500
550
T0 (K)
Figure 16.
The ignition temperatures in the stoichiometric ethaneair flame at various initial temperatures and p0 = 1 bar.
Table 3. Thermal coefficients μ of burning velocity.
φ
p0 = 1.0 bar
p0 = 2.0 bar
0.592
2.310 ± 0.103
2.351 ± 0.007
0.703
1.883 ± 0.022
1.917 ± 0.024
0.842
1.682 ± 0.011
1.718 ± 0.019
1.012
1.579 ± 0.015
1.616 ± 0.025
1.129
1.562 ± 0.015
1.593 ± 0.018
1.250
1.605 ± 0.011
1.660 ± 0.026
1.370
1.736 ± 0.018
1.823 ± 0.020
intermediate species against initial pressure is given
in Fig. 13. The initial pressure increase, determining
the decrease of dissociation extent within the reaction
zone, is accompanied by the increase of end flame
temperature. At the same time, as observed by Hassan et
al. [18], the increased rates of three-body recombination
reactions at elevated pressures determine significant
concentration reductions of important radical species,
in spite of increased reaction zone temperatures. The
reduced radical concentrations in the reaction zone are
responsible in a large extent for the reduction of laminar
burning velocities with increasing pressure shown in
Fig. 3a.
3.2. Temperature influence on flame structure and burning velocity
The initial temperature increase has a lesser influence
on the rate of heat release, as shown in Fig. 14. Other
diagrams, plotting the end flame temperature Tb and the
peak mass fractions of several important intermediate
species against initial temperature, are given in Fig. 15.
The initial temperature increase is accompanied
by a slight increase of concentration for all examined
intermediate species (C2H2, NO, H, OH, O) [18]. This
is explained by the well known proportionality between
radical concentrations in the reaction zone and the
laminar burning velocities [58]. In a similar way, one can
understand the increase of laminar burning velocities
with increasing initial temperature. The preheating
determines also the increase of “ignition temperature”,
as shown in Fig. 16 for results referring to flames
propagating at 1 bar.
Other consequences of initial temperature increase
are the decrease of flame thickness (Fig. 9b) and the
increase of burning velocity (Fig. 3b). The burning
velocity variation against temperature, at constant initial
pressure, was fitted by the power-law equation:
µ
 T 
(4)
Su = Su,ref 
  Tref 
where Su,ref is the normal burning velocity at reference
temperature Tref and μ is the thermal coefficient. Using
the ambient temperature as a reference, the thermal
coefficients μ of normal burning velocities for ethaneair mixtures were calculated by non-linear regression
analysis of Su = f(T0) data. Several results characteristic
for ethane-air at 2 initial pressures, for the temperature
range within 300 and 450 K, are given in Table 3.
The thermal coefficients at p0 = 1 bar range from
1.55 to 2.30, values within the domain characteristic
to hydrocarbon-air mixtures. Measurements made
in a constant volume spherical vessel yielded close
values: 1.55 (ethane-air with j = 1.0) [8], 2.13 [54]
(propane-air mixture with j = 1.0); 1.81 [59] (propaneair mixture with j = 1.1). At all pressures, the mixtures
characterized by the lowest burning velocity (mixtures
far from stoichiometric) are affected in a higher
degree by preheating and have the largest thermal
coefficients.
399
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propagation in ethane-air mixtures
In an earlier study, Burke et al. [60] defined the
average flame front temperature in correlation to
the initial temperature T0 and the maximum flame
temperature Tb:
Tf =T0 + 0.74 ⋅ (Tb − T0 ) (5)
Using the characteristic ignition temperature Ti
instead of average flame front temperature Tf , it is
possible to calculate the overall activation energies from
examination of normal burning velocities computed for
preheated fuel-air mixtures by means of the following
equation [33]:

  −n +1
E
 Su ≈  λ
⋅ exp  a

  C0
⋅
⋅
ρ
c
R
T
p
i





(6)
where the burning velocity Su is expressed as a
function of thermal diffusivity D = λ ρ ⋅ C (with λ – thermal
p
conductivity; ρ – density; cp – heat capacity), initial
fuel concentration C0, the ignition temperature Ti and
overall kinetic parameters of the oxidation (n – overall
reaction order; Ea – overall activation energy). Assuming
that the thermal diffusivity D, the overall reaction order
n and the initial fuel concentration C0 from Eq. 6 are
constant within the examined initial temperature range
for the stoichiometric mixture at constant initial pressure
p0 = 1 bar, we calculated Ea = 358 kJ mol-1 by
examining the burning velocities in correlation to Ti and
Ea = 374 kJ mol-1 by examining the burning velocities
in correlation to Tf . For comparison, Ea = 210 kJ mol-1
was reported by Taylor [11] from experimental values
of normal burning velocities and adiabatic flame
temperatures of ethane-air flames.
4. Conclusions
The propagation of ethane-air free laminar premixed
flames has been numerically investigated for initial
temperatures between 300 and 550 K, initial pressures
between 1 and 10 bar and fuel equivalence ratios between
0.52 and 1.75 ([C2H6] = 3.0 – 9.5 vol.%). The modeling
delivered the laminar burning velocities together with
the temperature, chemical species concentrations
and heat release rate profiles across the flame front.
Examination of results, in comparison with experimental
data extracted from various literature sources and with
the results of other numerical experiments, afford the
following concluding remarks:
1. The present predictions of burning velocities,
made with the GRI 3.0 mechanism, lie within the scatter
of experimental data and match well predictions made
with other mechanisms, based on reaction schemes with
increased number of chemical species and reactions.
2. The validation of the GRI 3.0 mechanism against
data obtained at high temperature and/or pressure
experiments in shock tubes constitutes a support for
using this mechanism in simulation studies of laminar
premixed flames propagating in fuel-air mixtures, at
elevated pressures.
3. The initial pressure and temperature influence
on burning velocities of ethane-air mixtures has been
expressed in the form of power law equations, where
thermal and baric coefficients (μ and ν) of burning
velocities range within the usual range of variation for
C1-C3 hydrocarbons.
4. The correlation of burning velocities of preheated
ethane-air mixtures with the average flame temperature
afforded calculation of an overall activation energy; the
correlation of burning velocities with initial pressure
(mixtures at constant initial temperature) afforded
calculation of overall reaction orders. The overall
activation parameters are useful input parameters for
CFD (Computational Fluid Dynamics) simulations of
flame propagation in various conditions.
At the same time, the observed effects of initial
temperature and initial pressure on maximum flame
temperature, heat release rate, flame thickness and
peak concentrations of main reaction intermediates
support a better understanding of the influence of these
parameters on the laminar burning velocities.
Acknowledgements
This work was supported by a grant of the Romanian
National Authority for Scientific Research, CNCS –
UEFISCDI, project PN-II-RU-PD-2011-3-0053.
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