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Combustion in hydraulically resisted flows.

Gregory I. Sivashinsky (2007)


The effects of hydraulic resistance on premixed gas combustion in tubes and inert porous beds are discussed on the basis of recent research. It is found that the hydraulic resistance causes a gradual precompression and preheating of the unburned gas adjacent to the advancing deflagration which may lead (after an extended induction period) to a localized thermal explosion triggering an abrupt transition from deglagrative to detonative combustion. The hydraulic resistance has a profound effect also...

Coupling of chemical reaction with flow and molecular transport

Ulrich Maas (1995)

Applications of Mathematics

During the last years the interest in the numerical simulation of reacting flows has grown considerably. Numerical methods are available, which allow to couple chemical kinetics with flow and molecular transport. However, the use of detailed physical and chemical models, involving more than 100 chemical species, and thus more than 100 species conservation equations, is restricted to very simple flow configurations like one-dimensional systems or two-dimensional systems with very simple geometries,...

Diffusion with dissolution and precipitation in a porous medium: Mathematical analysis and numerical approximation of a simplified model

Nicolas Bouillard, Robert Eymard, Raphaele Herbin, Philippe Montarnal (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

Modeling the kinetics of a precipitation dissolution reaction occurring in a porous medium where diffusion also takes place leads to a system of two parabolic equations and one ordinary differential equation coupled with a stiff reaction term. This system is discretized by a finite volume scheme which is suitable for the approximation of the discontinuous reaction term of unknown sign. Discrete solutions are shown to exist and converge towards a weak solution of the continuous problem. Uniqueness...

Discrete coagulation-fragmentation system with transport and diffusion

Stéphane Brull (2008)

Annales de la faculté des sciences de Toulouse Mathématiques

We prove the existence of solutions to two infinite systems of equations obtained by adding a transport term to the classical discrete coagulation-fragmentation system and in a second case by adding transport and spacial diffusion. In both case, the particles have the same velocity as the fluid and in the second case the diffusion coefficients are equal. First a truncated system in size is solved and after we pass to the limit by using compactness properties.

Dynamics of a Reactive Thin Film

P.M.J. Trevelyan, A. Pereira, S. Kalliadasis (2012)

Mathematical Modelling of Natural Phenomena

Consider the dynamics of a thin film flowing down an inclined plane under the action of gravity and in the presence of a first-order exothermic chemical reaction. The heat released by the reaction induces a thermocapillary Marangoni instability on the film surface while the film evolution affects the reaction by influencing heat/mass transport through convection. The main parameter characterizing the reaction-diffusion process is the Damköhler number. We investigate the complete range of Damköhler...

Fluid-dynamic equations for reacting gas mixtures

Marzia Bisi, Maria Groppi, Giampiero Spiga (2005)

Applications of Mathematics

Starting from the Grad 13-moment equations for a bimolecular chemical reaction, Navier-Stokes-type equations are derived by asymptotic procedure in the limit of small mean paths. Two physical situations of slow and fast reactions, with their different hydrodynamic variables and conservation equations, are considered separately, yielding different limiting results.

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