Determination of the lighting radius for detonation shock dynamics and critical ignition transients in condensed explosives

Three-dimensional simulation of detonation shock motion in a condensed explosive, modeled with a reactive flow in a moderately complex geometry can require enormous amounts of computer time, since the reaction zone behind the leading shock is extremely thin compared to the overall dimensions of the computational domain. Therefore algorithms such as program burn, pre-compute the detonation shock arrival time, and then essentially use a delta function model to release the heat of detonation into few computational cells near the shock wave. Previous validation efforts that use a program burn algorithm based on detonation shock dynamics (DSD) highlighted the prescription of the initial detonation shock location needed for the simulation, in a manner that is self-consistent with the theory and physical experiment. In this paper we use a combination of theory, direct multi-material simulation and experiment to determine a critical radius for the starting detonation shock shape. Critical initiation behavior and energies can be calculated.