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Applied Mathematics Colloquium

Friday, March 14, 11:30 am
Cullimore Lecture Hall II
New Jersey Institute of Technology

Detonation Failure in the Ignition-and-Growth Model

Ashwani Kapila

Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY

and

Division of Mathematical Sciences, National Science Foundation

Abstract

Heterogeneous high-energy explosives are morphologically, mechanically and chemically complex. As such, their ab-initio modeling, in which well-characterized phenomena at the scale of the microstructure lead to a rationally homogenized description at the much larger scale of observation, is a subject of active research but not yet a reality. An alternative approach is to construct phenomenological models, in which forms of constitutive behavior are postulated with an eye on the perceived picture of the micro-scale phenomena, and which are strongly linked to experimental calibration. Most prominent among these is the ignition-and-growth (I&G) model conceived by Lee and Tarver.

This presentation will describe an analytical/computational study of the I&G model, with emphasis on the extent to which the model captures experimentally observed detonation failure. Attention is focused on two configurations: detonation turning a corner, where experiments show dead zones, and detonation propagating down a conical charge, where experiments show detonation failure near the cone tip. While the computational results are in reasonable agreement with the cone test, sustained dead zones in the corner-turning test elude the model. In both cases, mechanisms underlying the behavior of the computed solutions are identified. It is concluded that disagreement between computation and experiment in the corner-turning case lies in the absence, in the model, of a mechanism that allows the explosive to undergo desensitization when subjected to a weak shock. A desensitization submodel is proposed, and is found to be capable of producing dead zones.

The computational framework consists of a Godunov-type fractional-step scheme with adaptive mesh refinement on overlapping grids, extended to multi-material reactive flow.