Untitled - Aerobib - Universidad Politécnica de Madrid

152 CHAPTER 6. LAMINAR FLAMES
the first is satisfied by adopting the following value for C
C = − 1
1 − θ 0
. (6.82)
This value when taken into Eq. (6.41) gives for Y the expression (6.76) which is, in
fact, the desired solution valid throughout the interval of temperatures as the boundary
conditions are met at both extremes.
θ = θ 0 : Y = 0, θ = 1 : Y = 1. (6.83)
0.40
θ a
=4
0.35
θ 0
=0.125
Λ −1/2
0.30
0.25
0.20
0.5 1.0 1.5 2.0
L
Figure 6.8: Dimensionless flame velocity as a function of the Lewis number for θ a = 4 and
θ 0 = 0.125.
Lewis-Semenov number different from unity
Actually the Lewis-Semenov number is only identical to unity when dealing with pure
mono-atomic gases (in which case D is the coefficient of autodiffusion). Generally
in more complex cases L differs from unity and it varies with the composition and
temperature of the mixture. However, it is frequently very close to unity and the
preceding approximation is satisfactory. Moreover, the influence of the value of the
Lewis-Semenov number on the flame velocity is, generally speaking, quite small. This
is verified in Fig. 6.8 taken from Ref. [22] which shows, as an example, that when
L doubles its value, the flame velocity increases less than 20 per cent, in this case
corresponding to a first-order reaction with an activation temperature θ a = 4, which