Combustion and Flame 136 (2004) 371–376
www.elsevier.com/locate/jnlabr/cnf
Measurement of propagation speeds in adiabatic flat and
cellular premixed flames of C2H6 + O2 + CO2
A.A. Konnov ∗ and I.V. Dyakov
Department of Mechanical Engineering, Vrije Universiteit Brussel, 1050 Brussels, Belgium
Received 7 July 2003; received in revised form 14 November 2003; accepted 18 November 2003
Abstract
Adiabatic burning velocities of premixed flat flames and propagation speeds of adiabatic cellular flames of
mixtures of ethane + oxygen + carbon dioxide are reported. The oxygen content O2 /(O2 + CO2 ) in the artificial
air was varied from 26 to 35%. Nonstretched flames were stabilized on a perforated plate burner at 1 atm. A heat
flux method was used to determine burning velocities under conditions when the net heat loss of the flame is
zero. Under specific experimental conditions the flames become cellular; this leads to significant modification of
the flame propagation speed. Measurements in cellular flames are presented and compared with those for laminar
flat flames and also with qualitative predictions of a theoretical model. The onset of cellularity was observed
throughout the stoichiometric range of the mixtures studied. Cellularity disappears when the flames become only
slightly subadiabatic.
 2003 The Combustion Institute. Published by Elsevier Inc. All rights reserved.
1. Introduction
Premixed planar flames stabilized on flat burners
have often been used for experimental investigations
of flame structure, since they resemble steady onedimensional adiabatic free flames propagating in the
doubly infinite domain. In the laboratory, however, a
planar flame is stabilized through losing heat to the
surface of the burner, where fresh mixture is introduced. Then the flame becomes adiabatic only in the
limiting case of zero heat loss to the burner when the
flame turns unstable. The method proposed by Botha
and Spalding [1] for the determination of the laminar
burning velocity by linear extrapolation of the burning
velocities to zero heat loss is based on this consideration. A limitation of this method manifested itself by
the onset of cellular instability when the heat losses
approached zero [1,2]. Botha and Spalding [1] described the appearance of these cells and noted that
* Corresponding author.
E-mail address: [email protected] (A.A. Konnov).
the cellular flames propagate much faster than the
corresponding laminar flat flames of the same composition. Using essentially the same technique, the
cellular flame structures have been studied by Vantelon et al. [3] and by Gorman et al. [4–8]. The flames
in all these studies were nonadiabatic. Major attention
has been paid to classification and to quantification of
the cellular patterns.
These scarce experiments [1,3–8] have received
significant attention from the combustion modeling community and have been frequently discussed
[9–12]. It is important to note that cellular instability appears throughout the stoichiometric range
of propane-air flames stabilized on a flat flame
burner [1], contrary to the predictions of diffusivethermal [13–16] models or ones of preferential diffusion [10,17–20]. The onset of cellularity in these
flames has been explained by hydrodynamic influences within the flame holder [12]. The importance
of the coupling of diffusion and hydrodynamics has
been emphasized by Markstein [9], and significant
progress in the analytical investigation of the coupling
problem has been achieved since then [21,22].
0010-2180/$ – see front matter  2003 The Combustion Institute. Published by Elsevier Inc. All rights reserved.
doi:10.1016/j.combustflame.2003.11.005
372
A.A. Konnov, I.V. Dyakov / Combustion and Flame 136 (2004) 371–376
A new method of adiabatic flame stabilization on
a flat burner was introduced by de Goey et al. [23].
This method is based on balancing the heat loss required for flame stabilization with the convective heat
flux from the burner surface to the flame front. It
was demonstrated that the heat flux method is suitable for determining the adiabatic flame temperature
and burning velocity [24–26]. Experimental measurements of the adiabatic burning velocity for laminar
flat flames of methane + oxygen + carbon dioxide
were reported recently [27]. It was noted that under specific experimental conditions these flames became cellular, leading to significant modification of
the flame’s propagation speed [28]. The goal of the
present work therefore was to extend these studies and
to measure adiabatic propagation speeds of premixed
flat and cellular flames of ethane + oxygen + carbon
dioxide, stabilized using the heat flux method. In
the following, an experimental installation is described. Then the experimental measurements in cellular flames are presented and compared with those
for laminar flat flames and also with qualitative predictions of a theoretical model [12].
2. Experimental details
The experimental setup for stabilizing an adiabatic flame using the heat flux method has been
described elsewhere [26,29]; however, the most relevant details are repeated below. The scheme of
the burner is shown in Fig. 1. It consisted of the
burner head mounted on a plenum chamber. The
2-mm-thick burner plate perforated with small holes
was attached to the burner outlet. The burner mouth
had a diameter of 30 mm and a heating jacked
supplied with thermostated water to keep the temperature of the burner plate constant. Recent measurements of the burning velocity in mixtures of
ethane + oxygen + nitrogen [30] were performed
with the heating jacket at 353 K. However, at this temperature flames of ethane + oxygen + carbon dioxide
were unstable with a clear cellular instability. Increasing the temperature of the burner plate suppressed this
instability; lowering the temperature of the burner
plate extended the range of equivalence ratios over
which the cellularity was observed. In the present experiments this temperature was fixed at 368, 353, or
338 K, as described below. The plenum chamber had
a separate cooling system supplied with water at a
temperature of 298 K to control the initial temperature of a mixture. The heating jacket kept the edges
of the burner plate at a certain temperature higher
than the initial gas temperature, thus warming up the
unburned gases flowing through. If the flame was stabilized under subadiabatic conditions, the gas velocity
Fig. 1. The perforated plate burner.
was lower than the adiabatic flame burning velocity and the sum of the heat loss and heat gain was
higher than zero. Then the center of the burner plate
was hotter than the heating jacket. If the unburned gas
velocity was higher than the adiabatic burning velocity (superadiabatic conditions), the net heat flux was
lower than zero, and the center of the burner plate
was cooler than the heating jacket. By changing the
flow rate of the gas mixture, an appropriate value of
the gas velocity could be found to nullify the net heat
flux. In this case the radial temperature distribution in
the burner plate was uniform and equal to the temperature of the heating jacket. Experimentally the series
of thermocouples attached to the burner plate allowed
the temperature distribution in it to be measured. The
flow rate at which the net heat flux was zero was
shown to be an adiabatic flame burning velocity [24].
A schematic illustration of the principle of flame
stabilization using the heat flux method is shown
in Fig. 2. It displays an adiabatic flame temperature profile and position of the flame front, which
in the present work was flat or wrinkled. The reference plane in this case is the burner surface, which
was heated to some fixed temperature, as noted above.
The physical properties of the flat flame were identical to those of the flat freely propagating adiabatic
flame [23]. Variation of the burner plate’s temperature
led to a tiny change in the position of the flame front.
An increase of this temperature from 338 to 368 K
shifted the flame by only 0.05 mm along the calculated adiabatic flame temperature profile (see Fig. 2).
This physical principle of flame stabilization resembles the computational principle of the adiabatic flame
stabilization in the infinite domain employed in the
Premix code [31]. By fixing the temperature at one
point in the flame-fixed coordinate system (keyword
A.A. Konnov, I.V. Dyakov / Combustion and Flame 136 (2004) 371–376
Fig. 2. Schematic illustration of the principle of the flame
stabilization using the heat flux method. Solid line, adiabatic
temperature profile; vertical dashed line, arbitrary position
of the burner plate; hatched area, flame front.
TFIX), the program calculated the flame’s burning velocity as an eigenvalue.
When the flame was wrinkled, the concave and
convex regions of it were stabilized at different distances from the burner plate; also the heat fluxes from
these regions were different and the local temperature
profiles were generally different, because preferential
diffusion changed the local composition. In this case
the radial temperature distribution in the burner plate
was locally nonuniform, but was approximated by a
parabolic fit [32], and by changing the flow rate of the
gas mixture, an appropriate value of the gas velocity
was found to make the average radial temperature distribution in the burner plate uniform and to nullify the
net heat flux. The cellular flame was, therefore, adiabatic since the net heat loss from the flame to the
burner is zero. The corresponding flow rate of the gas
mixture in the following is referred to as the propagation speed of an adiabatic cellular flame. One should
note that the propagation speed of an adiabatic cellular flame is not a characteristic of the mixture, unlike
the adiabatic burning velocity of a flat flame. It has
been realized and discussed long ago (e.g., [9,13,14,
18]) that due to changes of the local temperature and
mixture composition, the concave and convex regions
of the wrinkled flame have different local burning
velocities. In the present experiments the number of
cells varied from 15 to 65; thus, the propagation speed
of a cellular flame was an averaged value over the ensemble of cells.
The stabilized flames employing the heat flux
method resembled steady one-dimensional adiabaticfree flames inasmuch as the heat flux from the flame
to the burner was zero. However, due to the finite size
373
of a flame, the influence of ambient conditions was
not negligible. The development and testing of the installation used in the present study, together with an
analysis of errors in apparent burning velocities, have
been described earlier [26]. The overall accuracy of
a measured burning velocity was estimated to be better than ±0.8 cm/s (double standard deviation with
95% confidence level) over the whole range of velocities from about 10 to 40 cm/s. The relative accuracy of the equivalence ratio was ±0.54%. To achieve
this accuracy, the installation was calibrated before
each experimental run [26]. The uncertainties on a
long-term basis were found to be somewhat higher
(±1% for equivalence ratio and ±1 cm/s for burning velocities in rich and lean mixtures) [32]. The
experimental measurements of the adiabatic burning velocity for methane + oxygen + nitrogen and for
ethane + oxygen + nitrogen were found to be in very
good agreement with the literature [26,30]. The pure
gases were used as delivered by the supplier. The
stated purity of ethane, oxygen, and carbon dioxide
was 99.995% or better.
3. Modeling details
A detailed C/H/N/O reaction mechanism for the
combustion of small hydrocarbons was used for the
adiabatic flame modeling [33]. The current version
of the mechanism (Release 0.5) consisted of 1200
reactions of 127 species. This mechanism has been
validated with experimental measurements for the oxidation, ignition, and flame structure of hydrogen,
carbon monoxide, formaldehyde, methanol, methane,
ethane, propane, and some of their mixtures. The
CHEMKIN-II collection of codes [31,34,35], including transport properties [36] from Sandia National
Laboratories, was used. Multicomponent diffusion
and thermal diffusion options were taken into account. Adaptive mesh parameters were GRAD = 0.1
and CURV = 0.5.
4. Results and discussion
As noted above, the burner plate’s temperature
defined the appearance of a flame. In mixtures of
CH4 + O2 + CO2 [28] it was observed that when
the temperature was fixed at 368 K, the flame stabilized closer to the surface, making the flame perfectly flat for any dilution ratio D = O2 /(O2 + CO2 ).
In the present work measurements were performed
in mixtures of C2 H6 + O2 + CO2 with the dilution
ratio D equal to 0.26, 0.29, 0.3155, and 0.35. At
higher dilution ratios (0.3155 and 0.35) the flames
were corrugated, even with the burner plate at its
374
A.A. Konnov, I.V. Dyakov / Combustion and Flame 136 (2004) 371–376
Fig. 3. Adiabatic burning velocities in C2 H6 + O2 + CO2
flames with different dilution ratios (D) at standard temperature (298 K) and pressure. Symbols, experiment; lines,
modeling. Solid line, D = 35%; dashed line, D = 31.55%;
dash-dot line and crosses, D = 29%; dash-dot-dot line and
squares, D = 26%.
hottest (368 K). Only at lower dilution ratios (0.26
and 0.29) could the adiabatic burning velocity in
a laminar flat flame be determined. The measurements and calculated adiabatic burning velocities in
flames of C2 H6 + O2 + CO2 with different dilution
ratios are shown in Fig. 3. The overall agreement between the experiment and the modeling is very good
over the whole range of equivalence ratios for D
equal to 0.26 and 0.29. The deviations of the calculations from the experiments exceeded the evaluated uncertainty of the heat flux method (±0.8 cm/s)
only in the richest, highly diluted mixtures. Taking
into account the good performance of the detailed
reaction mechanism shown in diluted mixtures and
also in C2 H6 + O2 + N2 (Ar) flames [30], one can
assume that the calculated adiabatic burning velocities in flames of C2 H6 + O2 + CO2 with D = 0.3155
and 0.35 (solid and dashed lines in Fig. 3) are accurate. These calculated burning velocities are compared with the propagation speeds of adiabatic cellular flames in the following.
All the experimental measurements in flames having dilution ratios of 0.35 and 0.3155 are summarized
in Figs. 4 and 5, respectively. First, the calculated laminar adiabatic burning velocities shown in Fig. 3 are
repeated as lines for comparison. Also shown are the
propagation speeds of the adiabatic cellular flames
with the burner plate at 338 or 353 K. These burning velocities are systematically higher than in laminar flat flames; the difference is more pronounced
at lower temperatures of stabilization. To observe a
transition between the cellular and flat flames, similar
Fig. 4. Burning velocities in C2 H6 + O2 + CO2 flames with
dilution ratio D = 35% at standard temperature (298 K)
and pressure. Line, laminar adiabatic burning velocity (cf.
Fig. 3); solid diamonds and solid squares, propagation
speeds of the adiabatic cellular flames at the burner plate
temperature of 338 and 353 K, respectively; open diamonds
and open squares, propagation speeds of the subadiabatic flat
flames at the burner plate temperature of 338 and 353 K, respectively.
Fig. 5. Burning velocities in C2 H6 + O2 + CO2 flames
with dilution ratio D = 31.55% at standard temperature
(298 K) and pressure. Line, laminar adiabatic burning velocity (cf. Fig. 3); solid diamonds and solid squares, propagation speeds of the adiabatic cellular flames at the burner plate
temperature of 338 and 353 K, respectively; open diamonds
and open squares, propagation speeds of the subadiabatic flat
flames at the burner plate temperature of 338 and 353 K, respectively.
A.A. Konnov, I.V. Dyakov / Combustion and Flame 136 (2004) 371–376
to that found by Botha and Spalding [1], the velocity
of the fresh gas mixture was gradually reduced until
the moment when the flame was flattened out. These
velocities are denoted in Figs. 4 and 5 as the propagation speeds of the subadiabatic flat flames, also at the
burner plate temperature of 338 and 353 K.
In agreement with earlier experiments [1] and with
theoretical predictions [12], the onset of cellularity
was observed throughout the stoichiometric range. In
addition, the cellularity disappeared when a flame became only slightly subadiabatic. The perforated plate
flame holder therefore served to stabilize a flat flame
when the flame approached it due to a reduction in
the velocity of the fresh mixture or due to an increase
of the burner plate’s temperature. In the last case the
flame was still adiabatic, since the net heat loss of the
flame was zero. The theoretical model [12] showed
that for hypodermic-type flame holders, where transverse velocities are not allowed, the instability is removed for subadiabatic conditions. The perforated
plate burner used in the present study can be considered as an intermediate case between the porousplug and the hypodermic-type flame holders. Therefore any comparison of theory with an experiment
can only be qualitative. Similar to observations in
mixtures of CH4 + O2 + CO2 [28], the propagation
speeds of adiabatic cellular flames shown in Figs. 4
and 5 depend on the burner plate’s temperature. One
can expect that in the limit of the burner plate’s temperature approaching the temperature of the initial
mixture (298 K), the structure and the propagation
speeds would approach those of the “free” or quasistabilized flames, extensively studied in vertical wide
tubes [9]. Unfortunately, due to the limitations of the
heat flux method, these flames cannot be stabilized
on a flat flame burner, and direct comparison with the
numerous studies of the quasi-stabilized flames is impossible.
Visual observations of the flames were performed
to compare their cellular structure with that in mixtures of CH4 + O2 + CO2 [28]. It was noted that
the appearance of the cells varies with equivalence
ratio, dilution by CO2 , and the temperature of the
burner plate. In rich mixtures with an equivalence
ratio 1.7–1.8, the flame broke down to form a number of individual cells. These cells had the shape of
a hemisphere convex toward the fresh mixture and
were separated by nonluminous relatively wide zones.
Similar cells have been observed in lean flames of
methane [28]. When the mixture composition was
changed toward the stoichiometric one or when the
temperature of the burner plate was increased, the
cells joined to form a continuous corrugated flame
front. The cells in lean mixtures were usually asymmetric and possessed different sizes. In many cases,
especially in very lean or very rich mixtures, the cells
375
in the center of the flame and on the edges differed
in size dramatically. The variation of the appearance
of ethane flames with equivalence ratio inversely mirrored that of methane flames. This is not surprising,
since the diffusion coefficients of methane and ethane
are respectively higher and lower than that of oxygen. One can assume therefore that the cells observed
in rich mixtures of ethane and in lean mixtures of
methane were formed mostly due to the diffusivethermal instability. In the opposite case of lean ethane
and rich methane flames, the mechanism of instability was probably mostly hydrodynamic in nature. The
cellular structure of the flames was obviously sensitive to any nonuniformity in the flow and to the local
mixture composition. Entrainment of the ambient air
caused dilution of the burnt gases in very lean mixtures, while in very rich mixtures it caused oxidation
of the combustion products [29]. These nonidealities
led to disparities in the cell size in the center and on
the edges of the burner. Sometimes jumping changes
of the cellularity picture were observed.
5. Conclusions
This work extends that performed with mixtures
of CH4 + O2 + CO2 [28]. For the first time adiabatic burning velocities of premixed flat flames are reported, together with propagation speeds of adiabatic
cellular flames of ethane + oxygen + carbon dioxide.
The propagation speeds of cellular flames with the
burner plate at 338 and 353 K were systematically
higher than those in laminar flat flames. The difference is more pronounced at lower temperatures of stabilization. In agreement with earlier experiments [1]
and with theoretical predictions [12], the onset of cellularity was observed throughout the stoichiometric
range. In addition, the cellularity disappeared when
a flame became only slightly subadiabatic. The perforated plate flame holder therefore served as a flat
flame stabilizer when the flame approached it, due to
a reduction of the velocity of the fresh mixture or due
to an increase of the burner plate’s temperature. The
experimental results presented in this paper are useful
for developing theoretical models of the coupling of
hydrodynamic and diffusive-thermal mechanisms of
instability.
Acknowledgments
This work has been financially supported by the
European Government within the “Safekinex” Project
EVG1-CT-2002-00072 and by the NATO Research
Fellowship to I.V. Dyakov.
376
A.A. Konnov, I.V. Dyakov / Combustion and Flame 136 (2004) 371–376
References
[1] J.P. Botha, D.B. Spalding, Proc. R. Soc. London A 225
(1954) 71–96.
[2] J.A. Eng, D.L. Zhu, C.K. Law, Combust. Flame 100
(1995) 645–652.
[3] J.P. Vantelon, P.J. Pagni, C.M. Dunsky, Prog. Astron.
Aeron. 105, 131–151.
[4] M. Gorman, C.F. Hamill, M. el-Hamdi, K.A. Robbins,
Combust. Sci. Technol. 98 (1994) 25–35.
[5] M. Gorman, M. el-Hamdi, K.A. Robbins, Combust.
Sci. Technol. 98 (1994) 37–45.
[6] M. Gorman, M. el-Hamdi, K.A. Robbins, Combust.
Sci. Technol. 98 (1994) 47–56.
[7] M. Gorman, M. el-Hamdi, K.A. Robbins, Combust.
Sci. Technol. 98 (1994) 71–78.
[8] M. Gorman, M. el-Hamdi, K.A. Robbins, Combust.
Sci. Technol. 98 (1994) 79–93.
[9] G.H. Markstein, Non-steady Flame Propagation, Pergamon, Oxford, 1964, p. 75.
[10] M. Hertzberg, Prog. Energy Combust. Sci. 15 (1989)
203–239.
[11] B.H. Chao, Combust. Flame 126 (2001) 1476–1488.
[12] A.C. McIntosh, J. Fluid Mech. 161 (1985) 43–75.
[13] Ya.B. Zeldovich, The Theory of Combustion and Detonation of Gases, USSR Academy of Sciences, Moscow,
1944.
[14] G.I. Barenblatt, Ya.B. Zeldovich, A.G. Istratov, Zh.
Prikl. Mekh. Tekh. Fiz. 4 (1962) 21–26.
[15] G.I. Sivashinsky, Combust. Sci. Technol. 15 (1977)
137–146.
[16] G. Joulin, P. Clavin, Combust. Flame 35 (1979) 139–
153.
[17] T. Mitani, F.A. Williams, Combust. Flame 39 (1980)
169–190.
[18] J. Manton, G. von Elbe, B. Lewis, J. Chem. Phys. 20
(1952) 153–157.
[19] G. Joulin, T. Mitani, Combust. Flame 40 (1981) 235–
246.
[20] S.B. Margolis, Proc. Combust. Inst. 18 (1981) 679.
[21] P. Clavin, Prog. Energy Combust. Sci. 11 (1985) 1–59.
[22] P. Clavin, Proc. Combust. Inst. 28 (2000) 569.
[23] L.P.H. de Goey, A. van Maaren, R.M. Quax, Combust.
Sci. Technol. 92 (1993) 201.
[24] A. van Maaren, L.P.H. de Goey, Combust. Sci. Technol. 102 (1994) 309–314.
[25] A. van Maaren, D.S. Thung, L.P.H. de Goey, Combust.
Sci. Technol. 96 (1994) 327–344.
[26] I.V. Dyakov, A.A. Konnov, J. De Ruyck, K.J. Bosschaart, E.C.M. Brock, L.P.H. de Goey, Combust. Sci.
Technol. 172 (2001) 81–96.
[27] A.A. Konnov, I.V. Dyakov, J. De Ruyck, Arch. Combust. 22 (2002) 13–24.
[28] A.A. Konnov, I.V. Dyakov, in: Proceedings of the Third
Mediterranean Combustion Symposium, Marrakech,
2003, pp. 1–10.
[29] A.A. Konnov, I.V. Dyakov, J. De Ruyck, Combust. Sci.
Technol. 169 (2002) 127–154.
[30] A.A. Konnov, I.V. Dyakov, J. De Ruyck, Exp. Thermal
Fluid Sci. 27 (2003) 379–384.
[31] R.J. Kee, J.F. Grcar, M.D. Smooke, J.A. Miller, Sandia
National Laboratories Report, SAND85-8240,1990.
[32] K.J. Bosschaart, L.P.H. de Goey, Combust. Flame 132
(2003) 170–180.
[33] A.A. Konnov, Detailed reaction mechanism for small
hydrocarbons combustion, Release 0.5, 2000, available
at http://homepages.vub.ac.be/~akonnov/.
[34] R.J. Kee, F.M. Rupley, J.A. Miller, Sandia National
Laboratories Report, SAND89-8009, 1990.
[35] A.E. Lutz, R.J. Kee, J.A. Miller, Sandia National Laboratories Report, SAND87-8248, 1990.
[36] R.J. Kee, G. Dixon-Lewis, J. Warnatz, M.E. Coltrin,
J.A. Miller, Sandia National Laboratories Report,
SAND86-8246, 1990.