Untitled - Aerobib - Universidad Politécnica de Madrid

144 CHAPTER 6. LAMINAR FLAMES
a) Reaction zone.
After substituting (6.34) into (6.26), we have
dθ
dξ = θ i − θ 0
1 − θ 0
(1 − θ), (6.46)
where the following dimensionless distance was introduced
being
ξ = x l , (6.47)
l =
λ
mc p
(6.48)
a characteristic length of the wave. The integration of (6.46), once it is assumed that
reaction starts at point x = 0, gives
Likewise, one obtains for ε and Y
1 − θ = (1 − θ i ) e −θ i − θ 0
1 − θ i
ξ
. (6.49)
1 − ε = e −θ i − θ 0
1 − θ i
ξ
, (6.50)
1 − Y =
(
1 + 1 ) −1
θ i − θ 0
e −θ i − θ 0
ξ
1 − θ i . (6.51)
L 1 − θ i
1.0
0.8
Y(L=0.5)
0.6
ε, Y
0.4
Y(L=1)
ε
0.2
Y(L=2)
0.2 θ 0.6 0.8 1.0
i
=0.4
θ =0.125 0 θ
Figure 6.3: Distributions of Y and ε as a function of θ when the activation energy is zero.