Numerical Study of the Direct Initiation of Spherical and Cylindrical Detonations by an Energy Source

Abstract

The direct initiation of cylindrical and spherical detonations by an ideal point energy source, is investigated numerically for a one-step irreversible reaction. The study is based on nonlinear curvature effects on the detonation structure. Our results obtained from solving the steady curved detonation front structures, exhibit a critical radius below which generalised ChapmanJouguet (CJ) solutions cannot exist. For sufficiently large activation energy this critical radius is much larger than the thickness of the planar CJ detonation front (typically 500 times larger at ordinary conditions). Numerical simulations of detonation initiation by an energy source, show that a critical energy is associated with the critical solution described above. For initiation energy smaller than the critical value, the detonation initiation fails, the strong detonation which is initially formed decays to a weak shock wave. A successful initiation of a detonation requires a larger source energy. Transient phenomena which are associated with the intrinsic instability of the detonation front, develop on a short time scale and may induce additional failure mechanisms close to the critical condition. In conditions of stable or weakly unstable planar detonations, these unsteady phenomena are important only in the vicinity of the critical conditions and the criterion of initiation based on the nonlinear curvature effects, works with a quite good approximation in cylindrical and spherical geometry.