Phenomenological model of shock initiation in heterogeneous explosives

TLDR

An ignition‑and‑growth model in a one‑dimensional Lagrangian hydrodynamic code assumes a leading shock ignites localized hot spots that grow at a pressure‑dependent rate similar to high‑pressure laminar burning experiments. The model’s predictions of shock‑to‑detonation buildup, run distances, and reaction zone lengths agree quantitatively with experimental data for PBX‑9404, TATB, cast TNT, and PETN.

Abstract

An ignition and growth concept is used, within the framework of a one-dimensional Lagrangian hydrodynamic code, to model the shock initiation of heterogeneous solid explosives. The leading shock wave of an initiating pulse is assumed to ignite a small fraction of the explosive at localized heated regions. These ignited regions then grow as material is consumed at their boundaries. The growth rate for a particular material is assumed to have the characteristic pressure dependence of high-pressure laminar burning experiments. Results of the model calculations are in good quantitative agreement with recent manganin pressure gage and particle velocity gage measurements of the buildup of the initiating shock front to detonation for both sustained and short duration pulses in four solid explosives: PBX−9404, TATB, cast TNT, and PETN. The predicted run distances to detonation as functions of shock pressure at various initial densities and the predicted reaction zone lengths of the fully developed detonation waves also correlate well with experimental data for these four solid explosives.