THE TRANSITION TO NONSTEADY DEFLAGRATION IN GASLESS COMBUSTION

Inherent in premixed combustion theory is the existence of neutral stability boundaries across which the stability of a steadily propagating deflagration is lost to one or more nonsteady, nonplanar modes of burning as a critical parameter is varied. This phenomenon occurs not only in classical premixed flame propagation, but also in the deflagration of solid and liquid propellants, in chemical reactors, and in the combustion of intermetallic solids. Here, the focus is on the theoretical description of both linear and nonlinear stability in the latter, which is often referred to either as 'gasless combustion', or as 'combustion synthesis' due to its application in the synthesis of new refractory materials. The theoretical investigation of stability in these systems is being accomplished through the derivation and analysis of approximate models obtained from activation-energy asymptotics, which in turn have the advantage of admitting an explicit representation of the basic solution that is undergoing a change of stability. The resulting nonsteady, multidimensional models are then able to describe primary and higher-order transitions to various nonuniform and even chaotic modes of combustion. The prediction of these new types of combustion waves not only helps to explain recent experimental observations, but also indicates the existence of totally new phenomena not yet documented by experimental studies. In this review, the analysis of nonsteady instability phenomena and the bifurcation of nonuniformly propagating deflagration waves, which are regarded as intermediate modes of propagation in the transition from steady to chaotic (turbulent) burning, is presented as a distinct discipline that arises not only in gasless combustion, but in virtually all premixed combustion systems.