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

Bibliographic revision
δVG
= − aδx + Sgaδt (2.50)
In which S g , is the mean unburned gas velocity averaged over the tube cross-sectional
area a. Equations (2.47) and (2.50) give
S =− a S −S
A
( )
u n g
(2.51)
This equation was given by Coward and Payman, (1937) and applied by Gerstein et
al., (1951), who measured the gas velocity from the growth of a soap bubble formed
over the orifice. As the flame propagates along the tube, the viscous drag of the burned
gas at the wall increasingly retards this gas flow and the pressure in both the burned
gas near the flame front and the unburned gas increases.
tel-00623090, version 1 - 13 Sep 2011
2.5.2.3 Constant volume method
In this method, a containing envelope surrounds the explosive mixture. It is assumed
that central ignition occurs and that laminar flame that is smooth and spherical
propagates outwards without any significant movement due to natural convection. The
pressure is equalized throughout the vessel and the unburned gas is isotropic.
Starting from the above assumptions, a differential equation for the pressure can be
derived. Mass conservation gives:
m = m + m
(2.52)
dm u
dm dx
dt dt dt
u
b
b
=− = ρiV
(2.53)
In which m is the mass of gas and subscripts u, b indicate de unburned and burned gas
states at time t, and the initial reference state at time t equal to zero, V is the vessel
volume. The burned mass fraction x is uniquely related to the pressure, so
dx
dt
dx dp
= (2.54)
dp dt
It follows from the definition of burning velocity, S u , that:
dm
dt
u
=− 4πr
ρ S
(2.55)
2
b u u
52