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Kinetic Theory of Reactive Molecular Gases
Raymond Brun
Université d’AixMarseille, France
brunraymond@orange.fr
1.0
INTRODUCTION
In high enthalpy gaseous flows associating high velocities and/or high temperatures, physical and
chemical processes such as vibrational excitation, dissociation, ionisation and various reactions, can take
place. The characteristic times of these processes have often the same order of magnitude as the
“mechanical” or aerodynamic characteristic times, so that these flows constitute typical nonequilibrium
media.
The best way for analysing these reactive flows in continuous or “collisional” regime consists in using a
statistical approach by considering the macroscopic quantities as local averages of various properties of
elementary particles (molecules, atoms, ions,…) and by taking into account their interactions resulting
from their “collisions”. Thus, the Boltzmann equation seems to be an appropriate tool for the description
of these flows.
Among the methods used for solving the Boltzmann equation, the ChapmanEnskog method, consisting in
expanding the distribution function in a series of a “small parameter”
I
ε
equal to the ratio of the
characteristic time between collisions to a reference flow time has known a great success. However, in the
past, it has been generally limited to the case where only one single type of collision is present in the
medium. Thus, at relatively low temperature, when the elastic collisions are “dominant”, the behaviour of
the system is correctly described by NavierStokes equations in which transport terms are satisfyingly
calculated by the ChapmanEnskog method [1], [2], [3].
Now, when physical and chemical processes take place, the ratio of their characteristic times
II
(inelastic
and/or reactive collisions) to the reference flow time can take any value. The problem first is to compare
and
I
II
and to insert the terms of physical and chemical production in the hierarchy imposed by the
expansion in a series of
I
and then to compute the modifications brought to the NavierStokes system
and to the transport terms [4], [5].
It is obvious that a great variety
of nonequilibrium situations may exist due to the numerous possible
multiscale physical and chemical processes. However, it is imperative that the number of collision types
should be restricted to only two (collisions I and II), in order to avoid an expansion beyond the first two
terms in the ChapmanEnskog expansion (NavierStokes level) [6].
The strict application of the ChapmanEnskog method to nonequilibrium situations is first presented: it
leads to two main general approaches called WNE and SNE methods depending on the degree of non
equilibrium considered : WNE for “weak” nonequilibrium situations and SNE for “strong” ones [7]. In
the application of these methods to concrete cases, it is obvious that they do not match in the intermediate
situations. That is why, a generalized ChapmanEnskog method (GCE), capable of realizing this matching
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 Spring '07
 SMITH

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