Untitled - Aerobib - Universidad Politécnica de Madrid

Chapter 3
General equations
3.1 Introduction
In the present chapter we shall establish the general equations of Aerothermochemistry,
that is, the general equations of transformation of a mixture of gases that react
one to another and are in motion. It is assumed herein that the gas can assimilate to
a continuous medium as previously done in the preceding chapter when analyzing the
transport coefficients. This assumption is well justified except in the following cases:
a) When a characteristic length of the macroscopic scale of the process, for example
the size of an obstacle submerged in the gas, is of the order of magnitude of the
molecular mean free path.
b) In the case where the phenomenological variables suffer considerable variations
within a distance of the order of magnitude of the said mean free path.
The first case occurs when dealing with a very rarefied gas (Knudsen gas). The
second case occurs, for example, in the analysis of the structure of a shock wave. In
fact, the thickness of a sock wave is only a few times larger than the molecular free
path, except when the wave is very weak. In such cases, to speak of the macroscopic
functions of a point has no sense, and it is necessary to take into consideration the
molecular structure of the gas. Such cases are excluded from the present study.
The equations that govern the transformations of a mixture of reacting gases are
similar to the general Gas Dynamics equations. Their difference is due to the fact that
while Gas Dynamics deal with gases of homogeneous chemical composition invariable
with time, in Aerothermochemistry the composition of the mixture varies. Such
variation is due to chemical reactions taking place between the various species that
form the mixture and to their mutual diffusion, and has the following consequences:
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