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EN-AVT-162-03 - Kinetic Theory of Reactive Molecular Gases...

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Kinetic Theory of Reactive Molecular Gases Raymond Brun Université d’Aix-Marseille, France [email protected] 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 non-equilibrium 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 Chapman-Enskog 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 Navier-Stokes equations in which transport terms are satisfyingly calculated by the Chapman-Enskog method [1], [2], [3]. Now, when physical and chemical processes take place, the ratio of their characteristic times II ε (inelastic and/or reactive collisions) to the reference flow time can take any value. The problem first is to compare and I II ε ε and to insert the terms of physical and chemical production in the hierarchy imposed by the expansion in a series of I ε and then to compute the modifications brought to the Navier-Stokes system and to the transport terms [4], [5]. It is obvious that a great variety of non-equilibrium situations may exist due to the numerous possible multi-scale 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 Chapman-Enskog expansion (Navier-Stokes level) [6]. The strict application of the Chapman-Enskog method to non-equilibrium 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” non-equilibrium 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 Chapman-Enskog method (GCE), capable of realizing this matching is finally presented and developed [8], [9].
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