Untitled - Aerobib - Universidad Politécnica de Madrid

6.13. OZONE DECOMPOSITION FLAME 173
in the following table we give their values, referred to the value of Λ 31 which we are
adopting as a reference according to the reasons stated in the foregoing.
Λ 11
Λ 31
= 0.333
Λ 14
Λ 31
= 0.925
Λ 32
= 3.486 × 10 −3 T −1
f
Λ 31
Λ 12
= 1.162 × 10 −3 T −1
f
Λ 31
Λ 15
Λ 31
= 0.282
Λ 33
Λ 31
= 0.677
Λ 13
Λ 31
= 0.226
Λ 16
= 2.435 × 10 −3 T −1
f
Λ 31
Λ 34
Λ 31
= 0.277
Table 6.2: Values of the ratios Λ ij/Λ 31 appearing in Eqs. (6.145) and (6.146).
It appears here that Λ 12 , Λ 16 and Λ 32 , which correspond to reactions 2 and 6
in (6.142), are much smaller than the others, due to the following two reasons. First,
because the corresponding coefficients A j are smaller, as shown by Table (6.1), and
second because they are reactions requiring triple collision, as shown by Eq. (6.142),
which explains the presence of term T −1
f
in these coefficients.
Hence, it results that we can also eliminate the corresponding terms in reaction
equations (6.143) and (6.144).
Finally, with reference to the denominator of these equations, it can also be
simplified, keeping in mind that:
1) In accordance with boundary conditions (6.147) it is ε 1f = ε 3f = 0.
2) Moreover, ε 1 is very small compared to unity throughout the flame, and therefore,
the corresponding term may be neglected.
3) Finally, in accordance with Eq. (6.124) and considering that h 0 2 is zero, it is
q 2 = 0.
following
Taking into account these considerations, the said denominator reduces to the
θ − 1 + q 1 (ε 1 − ε 1f ) + q 2 (ε 2 − ε 2f ) + q 3 (ε 3 − ε 3f )1 ≃ θ − 1 + q 3 ε 3 . (6.150)
Consequently if we introduce the above simplifications into the system of reaction
equations (6.143) and (6.144), this system reduces to
dε 1
dθ = Λ λ θ ( )
−3/2 e −θa1/θ X 3 − e −θa3/θ X 1 X 3
, (6.151)
λ f θ − 1 + q 3 ε 3
dε 3
dθ = −Λ λ λ f
θ −3/2 ( e −θ a1/θ X 2 + e −θ a3/θ X 1 X 3
)
θ − 1 + q 3 ε 3
. (6.152)