On the Propagation of Spherical Detonation Waves

A novel theory for the propagation of a spherical detonation wave is presented. The model is that of a point spherical blast in a detonating medium. The reaction rates are assumed to be finite but the coupling between the shock motion and the chemical reactions is modelled by a global function which leads to an effective chemical energy release at the detonation front which depends on the local shock strength and the shock radius. The important result obtained is the demonstration of the existence of finite steady-state velocities which are below the theoretical planar Chapman-Jouguet value. The magnitude of these final steady-state velocities depends on the value of the ignition energy used to initiate the detonation wave itself.