On the kinetic modelling of reactive waves in the hydrodynamic limit

Abstract

The present study deals with the extension of the exact and approximate models of the Boltzmann equation to a gas mixture of four constituents undergoing a reversible bimolecular reaction, and its application to wave propagation problems. The paper intends to highlight how Boltzmann type models, on the basis of a shared kinetic framework, can be adopted as the starting point for a consistent derivation of the reactive hydrodynamic equations, at both the Euler and Navier Stokes limit. At this scope, a proper mathematical procedure is applied to obtain an approximate solution to the model equations, which is necessary in order to derive the closed system of the governing equations in the above said hydrodynamic limits. Resorting to this unified kinetic approach which is presented in detail, one can recognize how the dynamics of rather different wave problems well known in literature, as the steady detonation wave and its linear stability, the sound wave propagation and the light scattering phenomena, match a satisfactory description with care for the chemical mechanism at the microscopic scale. The knowledge of the chemical process at this level permits to evaluate the influence of the chemical reaction on the fundamental aspects of the reacting gas system, reinforcing the proposed kinetic approach. Accordingly, some propagation wave problems, recently studied by the authors in this context, are in turn here reviewed at the end of focusing how their formulation and solution depend on the proposed hydrodynamic closure procedure.