Etude de la combustion de gaz de synthèse issus d'un processus de ...

Chapter 4
4.1 Laminar burning velocity
4.1.1 Constant pressure method
Laminar burning velocity and Markstein length can be deduced from schlieren
photographs of the flame (Bradley et al., 1998). For an outwardly spherical propagating
flame, the stretched flame speed, S n , is derived from the flame radius versus time data
as follows:
S
n
dr
f
= (4.1)
dt
tel-00623090, version 1 - 13 Sep 2011
where r f represents the flame radius in the schlieren photographs and t the time. The
total stretch rate acting on a spherical expanding flame, κ, is defined as Bradley et al.,
(1996):
1 dA 2 drf
2
κ = = = Sn
(4.2)
Adt r dt r
f
where A is the flame surface area. A linear relationship between the flame speed and
the total stretch exists (Clavin, 1985), and this is quantified by a burned Markstein
length, L b , as follows:
where
0
n n b
f
S − S = L κ
(4.3)
0
Sn
is the unstretched flame speed, and L b the Markstein length of burned gases.
The unstretched flame speed is obtained as the intercept value at κ = 0, in the plot of
S n against κ, and the burned gas Markstein length is the negative slope of S n –κ curve.
Markstein length can reflect the stability of flame (Liao et al., 2004). Positive values of
L b indicate that the flame speed decreases with the increase of flame stretch rate. In
this case, if any kind of perturbation or small structure appears on the flame front
(stretch increasing), this structure tends to be suppressed during flame propagation,
and this makes the flame stability. In contrast to this, a negative value of L b means that
the flame speed increases with the increase of flame stretch rate. In this case, if any
kinds of perturbation appear on the flame front, the flame speed in the flame front will
be increased, and this increases the instability of the flame. When the observation is
limited to the initial part of the flame expansion where the pressure does not vary yet,
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