Two-Front Traveling Waves in Filtration Combustion

This paper considers a model of filtration combustion in a porous layer immersed in a bath of gaseous oxidizer at constant pressure p0, which provides for exchange of the oxidizer between the pores, which have initial pressure p0, and the bath. Such models describe the process of combustion synthesi...

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Bibliographic Details
Published in:SIAM journal on applied mathematics 1993-02, Vol.53 (1), p.128-140
Main Authors: Shkadinsky, K. G., Shkadinskaya, G. V., Matkowsky, B. J., Volpert, V. A.
Format: Article
Language:English
Subjects:
400800 - Combustion, Pyrolysis, & High-Temperature Chemistry
ANALYTICAL SOLUTION
Applied mathematics
Applied sciences
CHEMICAL REACTION KINETICS
CHEMICAL REACTIONS
Coefficients
COMBUSTION
COMBUSTION KINETICS
COMBUSTION PROPERTIES
COMBUSTION WAVES
Combustion. Flame
Coordinate systems
Energy
Energy. Thermal use of fuels
Exact sciences and technology
Flame propagation
FLUIDS
Foreign exchange rates
Gas density
Gas flow
Gas temperature
GASES
Heat
HYDRIDES
HYDROGEN COMPOUNDS
INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY
KINETICS
MATERIALS
MATHEMATICAL MODELS
NITRIDES
NITROGEN COMPOUNDS
OXIDATION
Phase velocity
PNICTIDES
POROUS MATERIALS
REACTION KINETICS
Solids
SYNTHESIS
Temperature
Theoretical studies
Theoretical studies. Data and constants. Metering
THERMOCHEMICAL PROCESSES
Traveling waves
TRAVELLING WAVES
WAVE PROPAGATION
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Summary:This paper considers a model of filtration combustion in a porous layer immersed in a bath of gaseous oxidizer at constant pressure p0, which provides for exchange of the oxidizer between the pores, which have initial pressure p0, and the bath. Such models describe the process of combustion synthesis of high-temperature materials. The case is considered when the exchange rate b0between the pores and the bath, and p0are both small, while the filtration coefficient b along the porous layer is large. Thus the model describes the process of combustion synthesis under low-pressure conditions. In this paper, uniformly propagating solutions having two thin reaction zones in which the reaction rate is appreciable, separated by an extended intermediate zone in which the reaction proceeds very slowly, are found. Approximate analytical methods are used to derive explicit analytical expressions for various quantities of interest, including the combustion temperature and the propagation velocity, and to describe the structure of the solution. Also, profiles for the reaction rate, temperature, pressure, density, and depth of conversion are numerically computed, and the two-front structure is shown to be stable for the parameter values considered.
ISSN:0036-1399
1095-712X
DOI:10.1137/0153008