Transverse waves in detonations

Abstract

The observation of spontaneous transverse waves in detonations has led us to construct a simple acoustic theory which presents a criterion for their development. As a first step, the theory shows that any high frequency sound source located in the reaction zone of the detonation will yield an acoustic ray which asymptotically approaches a plane parallel to the shock and then travels parallel to the shock for long distances. Furthermore, after becoming asymptotic, this ray bundle is shown to spread at a characteristic rate dependent on the local heat release rate and the local flow properties. Since this ray is travelling in a region of constant properties, an acoustic treatment, including the rate of spreading of the ray and taking into account the effect of reaction kinetics for the irreversible exothermic reaction, yields a criterion for the linear amplification of transverse waves. The analysis shows that any reasonable reaction kinetics will supply a mechanism for amplifying infinitesimal high frequency transverse waves in the exothermic reaction zone of a Chapman-Jouguet detonation. The generality of this result is discussed.