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

Chapter 2
velocity is obtained from the equation of mass conservation for the unburned gas. It
follows from the definition of burning velocity that:
∂ρ
V
u
∂t
u
=−ρ
AS
u
u
(2.46)
This assumes that S u is a constant value over the entire cross section of the tube. If ρ u
is also constant, then:
∂V
u
∂t
=−AS
u
(2.47)
If the flame speed S n is uniform over the tube cross section, then
tel-00623090, version 1 - 13 Sep 2011
∂
V u
∂x
= −a
(2.48)
Where a is the cross-sectional area of the tube and x the abscissa along the tube axis.
As Sn
= dx dt , it follows from equations (2.46) and (2.48) that
S
u
a
=− S
A
n
(2.49)
This is the expression founded experimentally by Coward and Hartwell, (1932).
Unfortunately, the flame aerodynamics change as the flame propagates along the tube
and invalidates the assumption of constant flame speed over the cross section. The
flame area is also variable. For these reasons, there are significant errors (±20%) in the
use of this method for burning velocity measurements.
2.5.2.2 Soap bubble method
Guénoche et al., (1948) have demonstrated theoretically and experimentally that an
orifice placed at the ignition end of the tube reduces the pressure waves which disturb
the flame. This give arise to the soap bubble method, where a homogeneous
combustible mixture is used to blow a soap bubble around a pair of spark electrodes.
At time zero, the gas mixture contained in the spherical soap bubble is ignited by the
spark. Eq. (2.46) and (2.47) are still applicable, Eq. (2.49) is not. Consideration of the
volume of unburned gas now gives:
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