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

Abstract

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.

Keywords:

• metal-loaded high explosives
• detonation shock dynamics
• wave propagation
• unit cell
• numerical simulation

Acknowledgements

We would like to thank Alberto Hernández and Sunhee Yoo for their guidance in writing this paper, our coworkers for their advice and moral support, and the University of Illinois at Urbana-Champaign for the use of their facilities.

Additional information

Funding

This research was funded by Eglin Air Force Base [grant number FA8651-10-1-0004 (Advanced Modeling and Simulation Technologies for Micro-Munitions)]; the Air Force Office of Scientific Research [grant numbers FA9550-06-1-0044 (Analysis of Multi-Scale Phenomena and Transients in Explosive and Complex Energetic Systems), FA9550-12-1-0422 (Computational and Analytical Modeling of Advanced Energetic Materials)].