Initiation criteria for diverging gaseous detonations

Abstract

Further experiments on the direct initiation of spherical detonation waves in oxy-acetylene mixtures in the pressure range 20–120 torr have been carried out with detailed monitoring of the time history of the energy deposition. The magnitude of the spark energy required for direct initiation is found to depend on the discharge time, increasing in magnitude as the discharge time increases. For a fixed discharge time, the dependence of the magnitude of the source energy is found to be inversely proportional to the mixture composition. On the basis of an average power density correlation [i.e., (total spark energy/(total discharge time) × (source volume)], the discrepancies in the magnitude of the critical initiation energy can be resolved. The order of magnitude of the critical power density required for direct initiation is found to be of comparable order of magnitude as the power density of a self-sustained detonation wave. The dependence of the critical power density on initial pressure is similar to that obtained previously based on source energy (i.e., increases with decreasing pressure or increasing induction delay). Since the power density itself cannot be a meaningful parameter as the source energy can be made vanishingly small with an appropriate reduction in the discharge time or source volume or both, it is proposed that the critical energy in the limit of infinite power density should be used as the universal parameter to correlate with the properties of the explosive mixture. In view of the good agreement between the ideal-point-blast theory and experiments on laser-generated blast waves, even at very early times after the termination of the laser pulse, we concluded that the experimental value of the critical energy using a laser spark should represent the limiting value at infinite power density. A phenomenological model is proposed to gain physical insight into the coupling mechanisms between chemical kinetics and hydrodynamics in a transient flow structure such as that of the spherical wave. The coupling mechanisms are modelled by a global function which leads to an effective energy release at the front which is independent of either the local shock strength or the shock radius. The model recovers the essential features of the three propagation regimes of the reacting blast corresponding to different magnitudes of the source energy. Particularly interesting is the theoretical prediction that unless the source energy is very large, the reacting blast first decays to sub-Chapman-Jouguet velocity and then approaches its final C-J conditions extremely slowly. This prediction finds experimental confirmation in the experimental work of Struck and Brossard. Using an experimentally determined induction-zone thickness of the order of magnitude of the recently defined hydrodynamic thickness, quantitative results on the critical energy as well as transverse wave spacings from the present model were found to agree unexpectedly well with experiments.