Modeling and analysis of time-dependent processes in a chemically reactive mixture

Abstract

In this paper we study the propagation of sound waves and the dynamics of local wave disturbances induced by spontaneous internal fluctuations in a reactive mixture. We consider a non-diffusive, non-heat conducting and non-viscous mixture described by an Eulerian set of evolution equations. The model is derived from the kinetic theory in a hydrodynamic regime of a fast chemical reaction. The reactive source terms are explicitly computed from the kinetic theory and are built in the model in a proper way. For both time dependent problems, we first derive the appropriate dispersion relation, which retains the main effects of the chemical process, and then investigate the influence of the chemical reaction on the properties of interest in the problems studied here. We complete our study by developing a rather detailed analysis using the Hydrogen-Chlorine system as reference. Several numerical computations are included illustrating the behaviour of the phase velocity and attenuation coefficient in a low frequency regime and describing the spectrum of the eigenmodes in the small wavenumber limit.

Hydrodynamic Analysis of Sound Wave Propagation in a Reactive Mixture Confined Between Two Parallel Plates

“…This behaviour is in agreement with the results obtained in Refs. [3,15], in the sense that, in Refs. [3,15], it is shown that, for low oscillation frequencies, the attenuation of the sound waves are smaller for the endothermic reaction than for the exothermic one.…”

“…Equations (12)(13)(14) with their constitutive conditions (15)(16)(17)(18) represent the closed set of Navier-Stokes equations for the binary reactive mixture considered here. Such equations have been derived in paper [24] from a kinetic theory dynamics and therefore explicit expressions have been obtained in the quoted paper for the transport coefficients D, η, λ, κ T and reaction rate coefficient .…”

“…On the other hand, some problems associated to sound wave propagation have also been investigated in the context of chemically reactive mixtures [3,6,14,15,16,17,18]. The results indicate that the sound propagation can be considerably influenced by the chemical reaction.…”

“…For instance, in Refs. [3,14,15] the problem is formulated in an unbounded domain, so that no boundary conditions are involved, assuming that the mixture fields are the sum of an equilibrium value plus an harmonic wave of small amplitude. In Refs.…”

“…In Refs. [17,18,14,15], an Eulerian mixture is considered and the transport effects are absent, so that only the effects of chemical reactions on sound propagation are considered. In Ref.…”