Critical Initiation Conditions for Gaseous Diverging Spherical Detonations

The diverging spherical detonation wave in gaseous explosives is obtained either with a point source of explosion of energy E or through the transmission of a plane detonation from a cylindrical tube of diameter d into a large volume. The mechanism of detonation initiation in both cases is based on the shock to detonation transition. The experimental critical conditions lead to an initiation criterion for detonation resulting from the competition between the expansion behind the leading shock wave on one hand and the shock-induced chemical heat release on the other. Whatever the type of ignition source, the detonation is obtained when the radius of curvature of the wave overcomes a particular critical value Rc whose size includes a constant and large number of cell width λCJ(Rc≈20λCJ) and then can be considered as intrinsic to the detonative mixture used. λCJ, which is the mean size of the cellular structure of a CJ detonation, is proportional to the global chemical induction length Li, calculated in the ZND scheme, by also a large factor (generally more than 10). Two other criteria define the critical initiation energy Ec and the critical tube diameter dc for obtaining detonation with respect to this intrinsic length Rc