Shock Waves (2010) 20:217–239 DOI 10.1007/s00193-010-0249-z ORIGINAL ARTICLE Simulation of impulse effects from explosive charges containing metal particles K. Balakrishnan · D. V. Nance · S. Menon Received: 3 December 2009 / Revised: 15 March 2010 / Accepted: 17 March 2010 / Published online: 13 April 2010 © Springer-Verlag 2010 Abstract The propagation of an explosive blast wave con- taining inert metal particles is investigated numerically using a robust two-phase methodology with appropriate models to account for real gas behavior, inter-phase interactions, and inter-particle collisions to study the problem of inter- est. A new two-phase Eulerian–Lagrangian formulation is proposed that can handle the dense nature of the flow-field. The velocity and momentum profiles of the gas and parti- cle phases are analyzed and used to elucidate the inter-phase momentum transfer, and its effect on the impulsive aspects of heterogeneous explosive charges. The particles are found to pick up significant amounts of momentum and kinetic energy from the gas, and by virtue of their inertia, are observed to sustain it for a longer time. The impulse characteristics of heterogeneous explosives are compared with a homogeneous explosive containing the same amount of high explosive, and it is observed that the addition of solid particles augments the impulsive loading significantly in the near-field, and to a smaller extent in the far-field. The total impulsive loading is found to be insensitive to the particle size added to the explo- sive charge above a certain cut-off radius, but the individual impulse components are found to be sensitive, and particles smaller than this cut-off size deliver about 8% higher total impulse than the larger ones. Overall, this study provides crucial insights to understand the impulsive loading charac- teristics of heterogeneous explosives. Communicated by F. Zhang. K. Balakrishnan · S. Menon (B ) School of Aerospace Engineering, Georgia Institute of Technology, 270 Ferst Drive, Atlanta, GA 30332-0150, USA e-mail: suresh.menon@aerospace.gatech.edu D. V. Nance AFRL/RWPC, 101 W. Eglin Blvd. STE 334, Eglin AFB, FL 32542-6810, USA Keywords Detonation · Blast wave · Heterogeneous explosive · Impulsive loading · Multiphase flow 1 Introduction Heterogeneous explosives are formed by the addition of solid metal particles to a charge of a high explosive. The detonation of a heterogeneous explosive results in the interplay of sev- eral fluid-mechanic and thermodynamic parameters, thereby complicating the underlying physics of the problem. When a heterogeneous explosive charge is detonated, it gives rise to an outward moving blast wave that attenuates due to the effects of spreading. At the same time, the solid particles pick up momentum from the gas due to drag (both viscous and pressure drag) and are set into motion, trailing behind the blast wave. This momentum transfer from the gas to the parti- cles can be classified into two phases: the momentum transfer from the gas to the particles during the detonation wave pas- sage; and that due to the flow behind the detonation wave. For small and/or light particles, the former can be more sig- nificant and provide the primary acceleration mechanism at the early time instants. Furthermore, due to the dense nature of the flow-field, the dynamic compaction results in inter- particle interactions in the form of collisions and direct con- tact, which is the other driver of the particles at early times. Subsequently, the particles, owing to their inertia, attain a constant terminal velocity, and sustain it until they catch-up with the attenuating leading blast wave. Some of the leading particles penetrate the leading blast wave into the ambient air, and then slow down due to aerodynamic drag, allowing for the leading blast wave to again re-overtake the particle front. Of preponderant interest is the total deliverable impul- sive loading from such a heterogeneous charge. The total impulse at any location from the charge will be due to both 123