Weakly Nonlinear and Numerical Analysis of Auto-Oscillatory Dynamics in a Solid Propellant Combustion Model

In solid combustion, a planar traveling flame wave may lose stability to oscillatory modes in certain parameter regimes. The loss of stability is commonly achieved through a Hopf bifurcation in which linearly unstable modes grow to fixed amplitudes. This situation has been well studied in models of strictly condensed combustion and has been observed experimentally. In this paper, we describe the onset and evolution of oscillatory modes arising in a free-interface model of solid propellant combustion. After a brief introduction, the structure and stability of small perturbations to a planar flame wave are then investigated. Multiple-scale expansions are utilized to describe changes in the amplitude and the phase of a single, weakly unstable mode, and the results are compared to numerical predictions. It is found the over much of the parameter space that the analytical and numerical solutions predict a supercritical Hopf bifurcation similar to those found in models of strictly condensed combustion.