STABILITY ANALYSIS OF ONE-DIMENSIONAL GASEOUS DETONATIONS

A theoretical study is conducted on the propagation of planar detonations to elucidate the basic mechanism responsible for the longitudinal instability and to show the rich dynamical properties of the detonation front. Based on the small heat release, small difference of the specific heats and large activation energy assumption, a minimum model describing the instability is deduced. The basic mechanisms involved in this model are: i) the disturbance of the heat release rate is controlled by the shock perturbations with a retarded effect related to the propagation of entropy waves from the shock to the reaction sheet, ii) the response to the shock perturbation depends on the total heat release disturbance along the forward acoustic path with a delay related to the propagation of the forward acoustic waves from the reaction sheet to the shock, iii) detonations become unstable when the response is larger than the initial shock perturbation. It is revealed that, contrary to the existing explanation in the literature, the instability does not result from the thermal acoustic instability. The results obtained from the model are in good agreement with numerical solutions for both linear and non-linear instability.