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1 Archivum Combustionis

1 2001

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One dimensional numerical modeling of gas-solid mixtures ignition using continuum mixture theory with "compressible solid" and "non-compressible solid" sub-models

Benkiewicz K., Hayashi A.

Archivum Combustionis

2001

Vol. 21 nr 1

27-56

In this paper, the two-phase continuum mixture theory and its application to numerical modelling of propagation of shock and detonation waves in dusty gas mixtures are presented. Two sub-models of the multi-phase miwture theory are studied. The first submodel assumes compressibility of the particles while in the second one is this effect is neglected. In both cases gas and solid continua are assumed to be in mechanical and thermal non-equilibrium. The continuous mixture theory and an analysis of entropy inequalitylead to the system of equations that depending on the sub-model is well posed or hyperbolically degenerate. These sets of equations are solved using the time splitting technique. The conservative part is solved using the combination of Harten-Yee flux modified TVD method and MUSCL Hancock TVD method. The non-conservative part and the source terms are solved with the application of the 4-th order Runge-Kutta method. Both sub-models are compared on the simple case of shock wave propagation in the tube with a gas-solid mixture. The computations show that, although the "compressible solid" sub-model is well posed and leads to similar results as "non-compressible" one, it is extremely stiff and might be in practice computationally too expensive. on the contrary, the "nin-compressible solid" sub-model is effective and fast when applied for the ignition problem of oxygen-aluminium mixtures behind a strong shock wave. This study reveals also that more comlex model of aluminium combustion is needed in order to obtain more reliable results.