Untitled - Aerobib - Universidad Politécnica de Madrid

170 CHAPTER 6. LAMINAR FLAMES
Thus, the problem reduces to the integration of only one reaction equation
(that corresponding to O 2 or to O 3 ), which may be performed by means of one of the
methods enumerated in the aforesaid.
Lewis and von Elbe carried out a more arduous calculation, through the numerical
integration of the resulting equation. A detailed information on their calculations
may be found in the above reference or in [9]. Even when the values of the flame velocity
obtained from this calculation are several times larger than those experimentally
observed, considering the state of knowledge at the time, their work was published,
the fact that predicted and experimental values were of the same order of magnitude
was considered an important success.
Recently, von Kármán and Penner [10] have recomputed the flame velocity for
a set of mixtures of O 2 and O 3 , using the kinetic scheme proposed by Lewis and von
Elbe, but applying the semi-analytical methods developed in §9. The results agree
with those obtained by Lewis and von Elbe and they shown that the influence of the
composition of the mixture on velocity of the flame obtained through this procedure,
differ essentially from those observed by experimentation. This discrepancy is basically
due to the fact that the set of chemical reactions proposed by Lewis and von Elbe
and, in particular, the distribution of oxygen atoms within the flame, are different from
the actual ones.
Hirschfelder and his associates [25] have recently calculated the same flame,
applying the following complete kinetic scheme
O 3 + G → O + O 2 + G 1)
O + O 2 + G → O 3 + G 2)
O + O 3 → 2 O 2 3)
2 O 2 + G → O + O 3 4)
O 2 + G → 2 O + G 5)
(6.142)
2 O + G → O 2 + G 6)
This computation was carried out by means of an arduous numerical integration
for which electronic computers were used.
Later on, von Kármán and Penner [6] performed a simplified analysis of the
problem, utilizing the same kinetic scheme and physico-chemical constants as Hirschfelder
but applying Kármán’s analytical method of integration, and postulating a distribution
of oxygen atoms within the flame determined through the extension of the
steady state assumption which is widely used in classical Chemical Kinetics.