Untitled - Aerobib - Universidad Politécnica de Madrid

6.13. OZONE DECOMPOSITION FLAME 171
The following is a summary of the von Kármán-Penner study which can be
found fully described in the papers of Refs. [6] and [10].
If we assign subscripts 1, 2 and 3 to species O, O 2 and O 3 respectively, and
making use of the flame equations derived in §11 of this chapter, we obtain the following
system.
Reaction equation
It is sufficient to write two equations corresponding, for example, to species O 2 and
O 3 thus obtaining after Eq. (6.131)
dε 1
dθ = λ λ f
[
Λ 11 θ −3/2 e −θ a1/θ X 3 − Λ 12 θ −5/2 e −θ a2/θ X 1 X 2
− Λ 13 θ −3/2 e −θa3/θ X 1 X 3 + Λ 14 θ −3/2 e −θa4/θ X2
2 ]
(6.143)
+ 2Λ 15 θ −3/2 e −θa5/θ X 2 − 2Λ 16 θ −5/2 e −θa6/θ X1
2
[
] −1,
· θ − 1 + q 1 (ε 1 − ε 1f ) + q 2 (ε 2 − ε 2f ) + q 3 (ε 3 − ε 3f )
dε 3
dθ = λ [
−Λ 31 θ −3/2 e −θa1/θ X 3 + Λ 32 θ −5/2 e −θa2/θ X 1 X 2
λ f
]
− Λ 33 θ −3/3 e −θa3/θ X 1 X 3 + Λ 34 θ −3/2 e −θa4/θ X2
2 (6.144)
[
] −1.
· θ − 1 + q 1 (ε 1 − ε 1f ) + q 2 (ε 2 − ε 2f ) + q 3 (ε 3 − ε 3f )
Diffusion equations
Likewise, the diffusion equations corresponding to O and O 3 are, according to (6.135)
dX 1
dθ = L ( 1
12 2 X ) (
1ε 1 − X 2 ε 1 + 1 L13
3 X )
1ε 1 − X 3 ε 1
θ − 1 + q 1 (ε 1 − ε 1f ) + q 2 (ε 2 − ε 2f ) + q 3 (ε 3 − ε 3f ) , (6.145)
dX 3
dθ = L 31 (3X 1 ε 3 − X 3 ε 1 ) + L 32
( 3
2 X 3ε 2 − X 2 ε 3
)
θ − 1 + q 1 (ε 1 − ε 1f ) + q 2 (ε 2 − ε 2f ) + q 3 (ε 3 − ε 3f ) . (6.146)
The following Table 6.1shows the values of the physico-chemical constants
corresponding to the six reactions of Eq. (6.142).