Untitled - Aerobib - Universidad Politécnica de Madrid

6.13. OZONE DECOMPOSITION FLAME 169
Be Λ ij the parameter chosen to express the rest of them as functions of it. Once
its value is known, the value for velocity u 0 of the flame, by virtue of Eqs. (6.22) and
(6.132), is
√
u 0 =
M iλ f B j T δj−nj
f
ρ 2 0 c p
Λ −1/2
ij . (6.139)
6.13 Ozone decomposition flame
The ozone decomposition flame in a mixture of this gas with oxygen is the first example
we have chosen among the few cases of flame propagation which have been
calculated. Its first theoretical study was due to Lewis and von Elbe [8] who thus became
the first to analyze flame propagation considering, in addition to the effects of
heat transfer, those of the diffusion of reactants and products, as well as the influence
of the radicals (oxygen atoms) in the process. For this purpose they applied the law of
chemical reaction which includes the influence of temperature and the concentrations
of the various species on the reaction rate. The three chemical species in the process
are ozone, molecular oxygen and atomic oxygen. Lewis and von Elbe simplified the
problem by adopting the following assumptions:
1) The Lewis-Semenov number for the mixture O 2 - O 3 is equal to unity. This
assumption enables the expression of the concentrations of ozone and molecular
oxygen as functions of temperature.
2) The chemical processes take place in accordance with the following kinetic
scheme
O 3 ⇆ O 2 + O, (6.140)
O + O 3 → 2 O 2 . (6.141)
The first of these two reaction equations expresses that the concentration of
atoms of oxygen at each point of the flame is the one that would correspond
to a mixture of O, O 2 and O 3 in chemical equilibrium at the temperature and
composition of the point.
Having stated the problem, and if, furthermore, we take into account that the
molar fraction of atomic oxygen is much smaller than unity, its solution is straightforward.
In fact, the first of the above assumptions allows the expression of the molar
fractions of O 2 and O 3 as functions of temperature, as shown in §9 of this chapter,
and equation (6.140) allows the same for the molar fraction of O.