Modelling detonation of heterogeneous explosives with embedded inert particles using detonation shock dynamics: Normal and divergent propagation in regular and simplified microstructure

This paper discusses the mathematical formulation of Detonation Shock Dynamics (DSD) regarding a detonation shock wave passing over a series of inert spherical particles embedded in a high-explosive material. DSD provides an efficient method for studying detonation front propagation in such materials without the necessity of simulating the combustion equations for the entire system. We derive a series of partial differential equations in a cylindrical coordinate system and a moving shock-attached coordinate system which describes the propagation of detonation about a single particle, where the detonation obeys a linear shock normal velocity-curvature (D_n-κ) DSD relation. We solve these equations numerically and observe the short-term and long-term behaviour of the detonation shock wave as it passes over the particles. We discuss the shape of the perturbed shock wave and demonstrate the periodic and convergent behaviour obtained when detonation passes over a regular, periodic array of inert spherical particles.