Analysis of Accelerating Detonation Using Large Activation Energy Asymptotics

Abstract
Galloping one-dimensional detonations exhibit a pulsating nonlinear instability characterized by rapid bursts of the detonation velocity followed by a slow-down and a longer re-acceleration. This has been observed experimentally as well as in numerical simulations, but to date there is no satisfactory theoretical description of this phenomenon that includes large amplitude deviations of the lead shock velocity. The present paper summarizes an extension of a recent analysis of the author based on large activation energy asymptotics. This earlier work exhibited a nonlinear slow-time instability for near-CJ detonations which leads to either an irreversible decomposition of the shock-reaction-zone complex or to a nonlinear continous acceleration, driving the wave speed away from the CJ-regime at an ever exceeding rate. Even though this analysis is based on an assumption of a slow characteristic evolution time scale, the insight gained seems to be worth a closer examination of the large amplitude regime that follows the above-mentioned acceleration stage. The present analysis, as well as the earlier study for the near-CJ regime, are in many respects close to the work by Buckmaster (1988), but they are not identical and seem to yield some new insight.