Untitled - Aerobib - Universidad Politécnica de Madrid

34 CHAPTER 1. THERMOCHEMISTRY
the combination of the rates corresponding to elementary reactions. Denoting species
O, O 2 and O 3 with subscripts 1, 2 and 3 respectively, one obtains for the rate of
consumption of O 3
− w 3
M 3
= k f1 cc 3 − k b1 cc 1 c 3 + k f2 c 1 c 3 − k b2 c 2 2. (1.140)
This expression differs essentially from that obtainable from Eq. (1.136).
The complexity of the system of the elementary reactions that produce within
a mixture of reacting species originates an essential difficulty for the study of these
problems which depend on the reaction rates of the species. One of such problems
is, for example, the calculation of the propagation velocity of a flame throughout a
combustible mixture. 15 A great effort is being made by Chemical Kinetics towards the
enlightenment of the elementary reactions that produce in each case and of their corresponding
rates. Specially in the field of Combustion, the Fifth International Congress
held in 1954 devoted the major part of its work to the study of Combustion Kinetics. 16
In spite of the efforts the actual state of knowledge is still scant making impossible a
full study of the process except for a short number of particular cases. 17
Even when assuming that the system of reactions is known, it is usually too
complicated to be fully included in the study of an Aerothermochemical problem. For
this case the system must be simplified, for example with the steady state assumption,
18 or else by adopting global reaction rates for the mixture such as
w = Aρ n (1 − Y ) n e −E/RT , (1.141)
where Y is the mass fraction of products and n is the molecularity of the overall
reaction. In the following chapters frequent use will be made of similar expressions
for the approximate study of several problems.
References
[1] Corner, J.: Theory of Interior Ballistics of Guns. John Wiley and Sons, Inc.
New York, 1950.
[2] Taylor, J.: Detonation in Condensed Explosives. Oxford, at the Clarendon
Press, 1952.
15 See chapter 6.
16 See the Proceedings of the Congress, soon to be published.
17 See chapter 6.
18 See Ref. [28] where von Kármán and Penner have shown that the introduction of such an assumption
for the oxygen atoms in the ozone flame is justified. Yet, for other cases it appears less justified. For
example, in the Hydrogen–Bromine flame.