Program burn algorithms based on detonation shock dynamics

摘要

In the design of explosive systems the generic problem that one must consider is the propagation of a well-developed detonation wave sweeping through an explosive charge with a complex shape. At a given instant of time the lead detonation shock is a surface that occupies a region of the explosive and has a dimension that is characteristic of the explosive device, typically on the scale of meters. The detonation shock is powered by a detonation reaction zone, sitting immediately behind the shock, which is on the scale of 1 millimeter or less. Thus, the ratio of the reaction zone thickness to the device dimension is of the order of 1/1000 or less. This scale disparity can lead to great difficulties in computing three-dimensional detonation dynamics. An attack on the dilemma for the computation of detonation systems has led to the invention of sub-scale models for a propagating detonation front that we refer to herein as program burn models. The program burn model seeks not to resolve the fine scale of the reaction zone in the sense of a DNS simulation; instead the goal is to resolve the hydrodynamics in the inert product gases on a grid much coarser than required to resolve a physical reaction zone. We first show that traditional program burn algorithms for detonation hydrocodes used for explosive design are inconsistent and yield incorrect shock dynamic behavior. To overcome these inconsistencies, we discuss a new class of program burn models based on detonation shock dynamic (DSD) theory. This new class yields a more consistent and robust algorithm which better reflects the correct shock dynamic behavior.