From the transport coefficients of a relaxation kinetic model to harmonic wave solutions

Abstract

For a gas system of four constituents which experiences the bimolecular chemical reaction A1+A2=A3+A4, and in a regime close to the chemical equilibrium, the BGK-type model proposed by the authors in a previous paper is here considered with the aim of studying plane harmonic wave solutions to the system of the reactive field equations. The Chapman-Enskog method has been used to determine a first-order approximate solution to the BGK equations, which includes the transport features of shear viscosity, diffusion and thermal conductivity. Such approach leads to the constitutive equations and permits to close the reactive field equations at the Navier-Stokes, Fourier and Fick level. The propagation of plane harmonic waves in a reactive mixture where the transport effects are relevant can then be studied by a normal mode analysis. Numerical results are provided for two different mixtures of the Hydrogen-Chlorine system where the elementary reaction H2+Cl = HCl+H takes place. The behavior of diffusion, shear viscosity and thermal conductivity coefficients, as well as the one of phase velocity and attenuation coefficient, is described focusing the influence of the chemical reaction on the transport properties and harmonic wave solutions.