TY - JOUR
T1 - Two-front traveling waves in filtration combustion
AU - Shkadinsky, K. G.
AU - Shkadinskaya, G. V.
AU - Matkowsky, B. J.
AU - Volpert, V. A.
PY - 1993
Y1 - 1993
N2 - 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 b0 between the pores and the bath, and p0 are 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.
AB - 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 b0 between the pores and the bath, and p0 are 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.
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U2 - 10.1137/0153008
DO - 10.1137/0153008
M3 - Article
AN - SCOPUS:0027539824
VL - 53
SP - 128
EP - 140
JO - SIAM Journal on Applied Mathematics
JF - SIAM Journal on Applied Mathematics
SN - 0036-1399
IS - 1
ER -