Stability of Non-Adiabatic Solid-Solid Combustion

Abstract

In this study, the synthesis of inorganic materials by combustion of solid cylindrical preforms is addressed. The reaction between two solid reactants is analyzed when the reaction proceeds in the combustion regime. This process is characterized by a thin propagating reaction front. The elevated temperature levels reached at the combustion front usually prevent this process from being carried out under ideal adiabatic conditions. The planar model of propagation manifests then as a curved moving front. Previous studies on this subject have followed the approach of lumping the temperature in the radial direction to make the problem more tractable. In this work, such an approach is discarded and a two-dimensional stability analysis is performed. It is shown that planar propagation can become unstable, developing into (i) auto-oscillations, (ii) spinning combustion with a single or multiple heads located near the outer surface, and (iii) multiple-head spinning waves with one or multiple heads near the surface and the rest inside the preform. It is observed that the burning rates of the heads decrease with an increase in the radial position. This phenomenon can give rise to “fingering” effects and lead to inhomogeneous degrees of conversion of the solid fuel. Also the increase in number of potential modes of unstable combustion with increasing diameter of the preform suggests a mechanism for the development of chemical turbulence.

Key words:

• Solid-solid combustion
• stability analysis
• non-adiabatic combustion
• self-propagating high-temperature synthesis.

Additional information

Notes on contributors

HENDRIK J. VILJOEN

Author to whom all correspondence should be addressed.

NICOLAAS F. J. VAN RENSBURG

Departments of Malhematics, University of Pretoria, Pretoria 0001, Republic of South Africa.