Weak detonations, their paths and transition to strong detonation

Previously, a quasi-steady form of the classical Rankine-Hugoniot weak detonation has been shown to play an integral part in describing certain forms of detonation initiation, arising during an intermediate stage between the thermal ignition of the material and the first appearance of a strong detonation with Zeldovich-von Neumann-Döring (ZND) structure. In this paper, we use a parametric variable integration to calculate numerically the path of the weak detonation in two important initiation scenarios, shock-induced and initial disturbance-induced transition to detonation, via a large activation energy induction domain model. The influence that the nature of the path may have on the weak detonation structure is also discussed. In each case these calculations enable us to predict how, where and when the transition to a strong detonation with ZND structure will occur. Explanations for several phenomena observed in both experiments and numerical studies on transition to detonation are also uncovered by these calculations.