Untitled - Aerobib - Universidad Politécnica de Madrid

172 CHAPTER 6. LAMINAR FLAMES
Reaction
Order
n j
δ j
E j
cal/mol
A j
1 2 1/2 24.14 10.56 × 10 12
2 3 1/2 0.00 0.230 × 10 12
3 2 1/2 6.00 7.15 × 10 12
4 2 1/2 99.21 2.93 × 10 12
5 2 1/2 117.34 8.92 × 10 12
6 3 1/2 0.00 0.482 × 10 12
Table 6.1: Physico-chemical parameters for reactions 6.142.
The boundary conditions for this system are as follows:
a) Hot boundary.
At the hot boundary (θ = 1) the concentration of ozone is zero and the concentration
of atoms of oxygen is very small. Therefore it can be written
θ = 1 : ε 1 ≡ ε 1f ≃ 0, ε 3 ≡ ε 3f = 0, (6.147)
X 1 ≡ X 1f ≃ 0, X 3 ≡ X 3f = 0. (6.148)
b) Cold boundary.
At the cold boundary since no chemical reactions has been yet produced, the
mass flux of ozone is the one corresponding to the initial mixture and the one of
atomic oxygen is zero
θ = θ i : ε 1 ≡ ε 10 = 0, ε 3 = Y 30 (datum). (6.149)
Simplification of the equations
Before proceeding to integrate the system, we will simplify it, following von Kármán
and Penner. For the purpose, we shall begin by analyzing the values of the physicochemical
constants of the reactions which appear summarized in the above Table 6.1,
starting by the activation energies.
We see in this table that for reactions 4 and 5 in (6.142), this is, those producing
atomic oxygen from molecular oxygen, the activation energies are much larger than
for the rest, and consequently the reaction velocities in which they participate will be
very small and may be neglected. Hence, we can eliminate the terms corresponding
to these reactions from equations (6.143) and (6.144).
Let us now consider, coefficients Λ ij which are the ones that may also influence
the order of magnitude of the reaction velocities. In order to simplify this comparison,