Cellular combustion at the transition of a spherical flame front to a flat front at the initiated ignition of methane-air, methane-oxygen and n-pentane-air mixtures

Article abstract of DOI:10.1016/j.mencom.2013.11.020

High-speed cinematography was used to study the transition of a spherical flame front to a flat front in n-pentane-air and methane-air mixtures initiated by a spark discharge. Cellular flame structures were observed at the transition. Modeling based on compressible reactive Navier-Stokes equations at a low Mach number showed a qualitative agreement with experimental data.

Full text of DOI:10.1016/j.mencom.2013.11.020

Mendeleev
Communications
Mendeleev Commun., 2013, 23, 358–360
Cellular combustion at the transition of a spherical flame
front to a flat front at the initiated ignition of methane–air,
methane–oxygen and n-pentane–air mixtures
Ideya M. Naboko,a Nikolai M. Rubtsov,*b Boris S. Seplyarskii,b
Kirill Ya. Troshin,c Georgii I. Tsvetkovb and Victor I. Chernyshb
a Joint Institute for High Temperatures, Russian Academy of Sciences, 125412 Moscow,
Russian Federation. E-mail: idnaboko@yandex.ru
b Institute of Structural Makrokinetics and Materials Science, Russian Academy of Sciences,
142432 Chernogolovka, Moscow Region, Russian Federation. Fax: +7 495 962 8025;
e-mail: nmrubtss@mail.ru
c N. N. Semenov Institute of Chemical Physics, Russian Academy of Sciences, 119991 Moscow,
Russian Federation
DOI: 10.1016/j.mencom.2013.11.020
High-speed cinematography was used to study the transition of a spherical flame front to a flat front in n-pentane–air and methane–air
mixtures initiated by a spark discharge. Cellular flame structures were observed at the transition. Modeling based on compressible
reactive Navier–Stokes equations at a low Mach number showed a qualitative agreement with experimental data.
The majority of studies of gas-phase combustion processes are
devoted to a stationary flame front (FF).1–3 Actually, combustion
occurs under conditions of non-stationary flows, density and
pressure fluctuations; a flat flame is hydrodynamically unstable.4
In nonstoichiometric mixtures, thermal diffusive instability is
caused by the selective diffusion of a missing component. Joint
action of thermal diffusive and hydrodynamic instabilities was
studied.5–9 Direct verification of a hypothesis4 was undertaken.10
As the flame instability area is displaced with variation of acoustic
amplitude, a flat flame10 was stabilized by an external acoustic
field. Then, at shutdown of the field the growth rate of cellular
structures on flat flame boundary was directly measured; the inter-
relation10 of the hydrodynamic and acoustic flame instabilities11
was illustrated.
In this work, stoichiometric fuel–oxygen mixtures, in which
thermal diffusion does not play an essential role, were investigated.
The fluctuations of the rate of heat release in time can be a source
of acoustic perturbations;10,11 thus, near combustion limits the
probability of fluctuations of heat release is higher.12 In spherical
FF, perturbations develop more slowly than in a flat flame because
the surface of spherical FF continuously grows.1 However, after
FF gets out of a spherical shape, for example, by transition along
a cylindrical channel, hydrodynamic instability4 can occur. In
the experiment, the external stabilization of FF is not required
because the initial spherical FF before contact with reactor walls
is almost unperturbed.
Using the example of the combustion of stoichiometric
n-pentane–air and lean methane–air mixtures, we studied the
spatial distribution of FF under conditions when FF gets out of a
spherical shape and displays hydrodynamic and acoustic
instabilities of flat FF. For this purpose, the spatial distribution of
FF of stoichiometric n-pentane–air, methane–oxygen mixtures
diluted with an inert gas and lean methane–air mixes at 298 K
and 1 atm in constant-volume reactors were investigated by means
of colour high-speed cinematography.
The experiments were performed in a stainless steel cylindrical
reactor (reactor 1) 12 cm in diameter and 25 cm long supplied
with an optical quartz window at butt-end [Figure S1(a), Online
Supplementary Materials].13,14 Spark electrodes were placed at the
reactor centre. At ‘side view’ flame visualization a horizontally
located quartz cylindrical reactor (reactor 2) 70 cm in length and
14 cm in diameter [Figure S1(b)] was used.15 The reactor was
fixed in two stainless steel gateways at butt-ends, supplied with
gas inlets.15 Two electrodes of spark ignition (1.5 J) were located
at its centre. In the reactor, a 15.4% CH4 + 30.8% O2 + 46% CO2 +
+ 7.8% Kr mixture was used at an initial pressure of 160 Torr.†
In Figure 1, the video frames of FF propagation in reactor 1
for various gas mixtures are presented. First, an ignition centre13–16
is registered, and then stationary FF propagation until a contact
with reactor surface is observed. Just before the contact, the visible
FF velocity decreases and FF is deformed near the openings of gas
inlets. Further FF propagation occurs in a cylindrical part of
reactor 1 to the butt-end from which filming is carried out. Injection
of gas from the inlets into combustion products [Figure 1(a),(c),(d)]
is accompanied by acoustic fluctuations in the reactor [Figure 1(b)].
As can be seen in Figure 1(c),(d), spherical FF is not actually
perturbed1 [Figure 1(c), shots 54–63]. Then, at propagation along
reactor 1, an unstable flat flame occurs as the theory4 predicts,
which is shown in the development of FF instabilities in the
form of regular structures of combustion cells [Figure 1(c), shots
130–150; Figure 1(d), shots 100–130]. The cells on FF are charac-
teristic of certain extent of inert gas dilution – in fast-burning
(undiluted and poorly diluted) mixtures, the cells do not occur.
With an increase in the extent of dilution, cell structures do
not move [Figure 1(a)]; then, these flame structures containing
hot combustion products move upward due to gravity forces
[Figure 1(c),(d), see also Figure S2 and S316]. Therefore, at dilution
the probability of FF instabilities occurrence near combustion
limits increases in agreement with published data.12 By the time
†
CO2 was added for the reduction of FF velocity to improve the quality
of video filming. Kr was added to reduce an initiation threshold for spark
discharge. Speed filming of ignition dynamics and FF propagation was
carried out from the butt-end [Figure S1(a)] or from the side of the reactor
[Figure S1(b)] by means of a Casio Exilim F1 Pro colour high-speed digital
camera (frames frequency, 60–1200 s–1). The video file was stored in com-
puter memory and its time-lapse processing was performed. The pressure
change in the course of combustion was recorded by means of a piezo-
electric gage synchronized with the discharge. Gases were chemically pure.
© 2013 Mendeleev Communications. All rights reserved.
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Mendeleev Commun., 2013, 23, 358–360
interrelation of hydrodynamic and acoustic instabilities can be
(a)
analyzed on the basis of compressible reactive Navier–Stokes
equations at a low Mach number (that corresponds to subsonic
combustion).‡ As is seen in Figure 1, cells on FF are registered
by flame emission; therefore, an exothermic chemical reaction
accompanied by energy release and temperature change proceeds
in the cells. In Figure S2 (see Online Supplementary Materials),
0.018 s 11
18
88
21
79
90
86
97
89
‡
Compressible dimensionless reactive Navier–Stokes equations in low
Mach number approximation were suggested.17,21–24 The indexes t, x, y
mean differentiation on t, x, y.
100
101 0.17 s
102
rT = P,
(1a)
(1b)
(1c)
(1d)
rt + (rv)y + (pu)x = 0,
(b)
r(ut + vvy + uvx) + Py/gM2 = 1/Fr + Sc(∇2v + 1/3Ky)
r(vt + vuy + uux) + Px/gM2 = 1/Fr + Sc(∇2u + 1/3Kx)
r(Tt + vTy + uTx) – (g – 1)/gPt – (g – 1)M2(Pt + uPx + vPy) =
= ∇2T + b1W,
4
3
2
(1e)
(1f)
(1g)
(1h)
r(Ct + vCy + uCx) = ∇2C + bW,
W = (1 – C)exp(z – z/T),
Ptt – 1/M2∇2P = q(CP – 1)b1Wt,
1
0
where ∇2 = (...)yy + (...)xx is the two-dimensional Laplace operator, K =
= vy + ux is the viscous dissipation, Ptt = d2P/dt2, d(...)/dt is a material
derivative, u, v are the velocity components in the directions x, y, respec-
tively, r is the density and T is the temperature; a chemical reaction is
presented by a single first-order Arrhenius reaction, C is the reagent con-
centration, 1 – C is the extent of transformation, and z is a dimensionless
coefficient. Dimensionless parameters: Schmidt’s criterion Sc = v/D, D is
diffusivity (1 cm2 s–1 at 1 atm25), v is kinematic viscosity (10–5 cm2 s–1),25
g is the relation of constant pressure and constant volume thermal capacities;
b1 characterizes heat release allocation for concentration, b is kinetic coeffi-
cient. The initial values are the following: r0 = 0.001 g cm–3, T0 = 1, P0 = r0T0,
z = 10.5, g = 1.4, b = 0.2, b1 = 0.3, CP = 0.3 kal g–1 K–1 and C0 = 0.25 Lewis’s
number is Le = 1 that assumes the equality of Sc = Pr, where Pr = r0CPv/l,
l is heat conductivity and CP is thermal capacity at constant pressure.
Scales of length and speed are determined as ld2 = Dtd, and Ud = ld/td,
respectively. Reynolds’s number is ldUd/v = 1/Sc. Froude’s number is
Fr = Ud2/gld (g is the acceleration of a free fall) accepted equal to 0.07.
Mach number is M = Ud/c0 and it is accepted equal to 0.025, where c0 is
the speed of sound. It is obvious if M = 0, fluctuations of pressure are
absent. At M ® 0, the reference value of average pressure of P0 becomes
much higher than the average value of r0Ud2 for pressure fluctuations at the
average pressure P0. The velocity field is determined by these fluctuations.
If a standard representation of pressure is used, the usual replacement
of variables P = P0p leads to the occurrence of a factor 1/M2 in the term
gradp in the impulse equation.17,24 It is accepted that pressure values satisfy
a wave equation (1h), which can be obtained from the continuity and impulse
equations taking into account internal power sources and neglecting terms
of order 1/M4.11,26–28 Equation (1h), describing waves in the moving non-
uniform media with a heat source, follows from continuity and impulse
conservation equations [q = ld2/(Ud4r0) – the parameter arising at reduction
to dimensionless form]; therefore, set (1) is overdefined. To provide corre-
spondence of the quantity of the equations with the number of unknowns,
equation (1a) is excluded from set (1) in the further analysis.
0.02 0.03 0.04 0.05 0.06 0.07 0.08
t/s
(c)
0.09 s
54
88
56
63
110
120
0.25 s
130
140
150
(d)
0.0017 s
1
10
45
20
50
35
55
40
70
0.22 s
100
105
130
Figure 1 High-speed filming of FF in reactor 1, 600 frames s–1, the figure
on a frame corresponds to frame number after discharge. (a) 80% (C5H12
+ air)stoich + 20% Ar. (b) Dependence of excess of total pressure over atmo-
spheric on time under conditions of Figure S2. (c) 6.3% CH4 + air, (d) 70%
(C5H12 + air)stoich + 30% Ar.
In a number of calculations, the reaction velocity was presented by an
elementary chain mechanism: C ® 2n(w0) and n + C ® 2n + products.
In this case, the equations (1f), (1g) were replaced with the following
ones (initial condition for concentration changes to C0 = 1).
+
r(Ct + vCy + uCx) = ∇2C – bnW,
r(nt + vny + unx) = ∇2n + 2bnW,
W = Cexp (z – z/T).
of FF contact with the reactor butt-end, a regular cellular FF
structure is observed.
The qualitative consideration of the transition of FF propaga-
tion from a spherical shape to a cylindrical one was performed
by the solution of a two-dimensional problem in ‘side view’
projection to establish further ways of modification of numerical
calculations. Both FF interaction with the reactor butt-end and FF
transition from a circular shape to propagation in a flat channel
at local initiation were considered. As is well known,10,17,18 the
The solution of the problem was carried out by finite element analysis
by means of the package (FlexPDE 6.08, A Flexible Solution System for
Partial Differential equations, 1996-2008 PDE Solutions Inc.29). Initiation
condition was taken T = 10 on the left boundary of the channel (Figure S2),
or an impulse T = 10 in the geometrical centre of the channel (Figure S3).
Boundary conditions were Cx = 0, Cy = 0, n = 0, as well as a convective
heat exchange Tt = T – T0, u = 0, v = 0, rx = 0, ry = 0.
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Mendeleev Commun., 2013, 23, 358–360
the results of qualitative calculations of a temperature field at FF
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Online Supplementary Materials
Supplementary data associated with this article can be found
in the online version at doi:10.1016/j.mencom.2013.11.020.
Received: 4th July 2013; Com. 13/4151
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