Modeling and numerical simulation of deflagration-to-detonation transition in porous energetic materials

An understanding of the deflagration-to-detonation transition (DDT) in porous energetic materials is important for various engineering applications. Safety issues for damaged explosives is one example. In this work, two topics related to multi-dimensional simulation of DDT in energetic materials are presented.; The objective of the first part is to develop a simple and predictive model for multidimensional simulations. Models constructed by two-phase mixture theory usually have complicated mathematical formulation, and admit complex dispersive wave structures. Three simplified single-velocity models, named BKS, SVG and GISPA, are considered in this work. The BKS model was derived--using asymptotic theory--from the two-phase theory by assuming a large interphase drag. The SVG model is newly developed, based on solid-void-gas three-phase formulation. The GISPA model is a new single-phase model which utilizes two independent rate processes for compaction and reaction. In addition to model simplification, a new reaction rate law is developed which describes the slow and the fast energy-release processes during DDT. A comparative study is carried out and the study shows that the SVG and GISPA models are able to predict all the events measured in 1-D DDT-tube experiments.; The second part of the study describes the development of a high-quality numerical method for two-dimensional DDT simulations. The new fourth-order method integrates total variation diminishing and essentially non-oscillatory schemes with an extension to a general equation of state. In order to handle complex geometry, an internal boundary algorithm is developed on a structured grid, which allows a two-dimensional, non-deformable body of an arbitrary shape to be inserted in a flow field. A DDT simulation is carried out for cases of both blunt-body and sharp-body impact on porous energetic materials. The radius effect (in the case of blunt-body impact) and the angle effect (in the case of sharp-body impact) on detonation properties are studied.