Influence of reaction heat on time dependent processes in a chemically reacting binary mixture

Marques, Wilson; Kremer, Gilberto M.; Soares, Ana Jacinta

doi:10.1063/1.4769490

Cited by 4 publications

(15 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The reaction rate results then to be of second order, namely it is proportional to the square of the product concentrations, see Ref. [16]. In particular, the rate law incorporates both the effects of the reactive binary encounters and the effects due to the specific reaction heat and forward activation energy.…”

Section: Introductionmentioning

confidence: 99%

Equilibrium and stability properties of detonation waves in the hydrodynamic limit of a kinetic model

Marques¹,

Soares²,

Bianchi³

et al. 2015

J. Phys. A: Math. Theor.

Self Cite

View full text Add to dashboard Cite

A shock wave structure problem, as the one which can be formulated for the planar detonation wave, is analyzed here for a binary mixture of ideal gases undergoing the symmetric reaction A 1 + A 1 A 2 + A 2 . The problem is studied at the hydrodynamic Euler limit of a kinetic model of the reactive Boltzmann equation. The chemical rate law is deduced in this frame with a second-order reaction rate, in a chemical regime such that the gas flow is not far away from the chemical equilibrium. The caloric and the thermal equations of state for the specific internal energy and temperature are employed to close the system of the balance laws. With respect to other approaches known in the kinetic literature for detonation problems with a reversible reaction, this paper is addressed to improve some aspects of the wave solution. Within the mathematical analysis of the detonation model, the equation of the equilibrium Hugoniot curve of the final states is explicitly derived for the first time and used to define the correct location of the equilibrium Chapman-Jouguet point in the Hugoniot diagram. The parametric space is widened to investigate the response of the detonation solution to the activation energy of the chemical reaction. At last, the mathematical formulation of the linear stability problem is given for the wave detonation structure via a normal-mode approach, when bidimensional disturbances perturb the steady solution. The stability equations with their boundary conditions and the radiation condition of the considered modeling are explicitly derived for small transversal deviations of the shock wave location. The paper shows how a second-order chemical kinetics description, derived at the microscopic level, and an analytic deduction of the equilibrium Hugoniot curve, lead to an accurate picture of the steady detonation with reversible reaction, as well as to a proper bidimensional linear stability analysis.

show abstract

Section: Introductionmentioning

confidence: 99%

Equilibrium and stability properties of detonation waves in the hydrodynamic limit of a kinetic model

Marques¹,

Soares²,

Bianchi³

et al. 2015

J. Phys. A: Math. Theor.

Self Cite

View full text Add to dashboard Cite

show abstract

“…For the analysis developed in this paper, it is convenient to write the reactive Euler Eqs. (8)(9)(10) in matrix form, and we obtain…”

Section: Basic Quantities and Hydrodynamic Modelmentioning

confidence: 99%

“…Among others, we quote here Refs. [1,4,5,6,7,8]. However, in our opinion, other contributions at the level of theoretical and modelling approaches should be of interest in order to deeply investigate the effects of the chemical kinetics on sound propagation within reactive systems.…”

Section: Introductionmentioning

confidence: 99%

“…The starting point for the present investigation is the study initiated in paper [8], where the focus was on the effects of the reaction heat on time dependent problems within a binary reactive mixture. The modelling proposed in Ref.…”

Section: Introductionmentioning

confidence: 99%

“…The modelling proposed in Ref. [8] is here extended to a quaternary mixture with bimolecular reaction, and then applied taking as reference the Hydrogen-Chlorine system when the reaction is specialized in H 2 +Cl HCl+H. The complexity of a quaternary reactive mixture enriches the description but, at the same time, brings many additional complications at the modelling level.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

Ramos

Ribeiro

Soares

2017

Continuum Mech. Thermodyn.

View full text Add to dashboard Cite

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.

show abstract

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

Kalempa

Silva

Soares

2018

Springer Proceedings in Mathematics &Amp; Statistics

Self Cite

View full text Add to dashboard Cite

The aim of this work is to study the problem of sound wave propagation through a binary mixture undergoing a reversible chemical reaction of type A + A B + B, when the mixture is confined between two flat, infinite and parallel plates. One plate is stationary, whereas the other oscillates harmonically in time and constitutes an emanating source of sound waves that propagate in the mixture. The boundary conditions imposed in our problem correspond to assume that the plates are impenetrable and that the mixture chemically react at the surface plates, reaching the chemical equilibrium instantaneously. The reactive mixture is described by the Navier-Stokes equations derived from the Boltzmann equation in a chemical regime for which the chemical reaction is in its final stage. Explicit expressions for transport coefficients and chemically production rates are supplemented by the kinetic theory. Starting from this setting, we study the dynamics of the sound waves in the reactive mixture in the low frequency regime and investigate the influence of the chemical reaction on the properties of interest in the considered problem. We then compute the amplitude and phase profiles of the relevant macroscopic quantities, showing how they vary in the reactive flow between the plates in dependence on several factors, as the chemical activation energy, concentration of products and reactants, as well as oscillation speed parameter.

show abstract

Influence of reaction heat on time dependent processes in a chemically reacting binary mixture

Cited by 4 publications

References 10 publications

Equilibrium and stability properties of detonation waves in the hydrodynamic limit of a kinetic model

Equilibrium and stability properties of detonation waves in the hydrodynamic limit of a kinetic model

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

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

Contact Info

Product

Resources

About