Abstract
In this article, we present a new formulation and an associated algorithm for the simultaneous numerical simulation of multiple condensed phase explosives in direct contact with each other, which may also be confined by (or interacting with one or more) compliant inert materials. Examples include composite rate-stick (i.e., involving two explosives in contact) problems, interaction of shock waves with chemically active particles in condensed-phase explosives, and devices such as detonators and boosters. There are several formulations that address the compliant or structural response of confiners and particles due to detonations, but the direct interaction of explosives remains a challenge for most formulations and algorithms. The proposed formulation addresses this problem by extending the conservation laws and mixture rules of an existing hybrid formulation (suitable for solving problems involving the coexistence of reactants and products in an explosive mixture and its immiscible interaction with inert materials) to model the interaction of multiple explosive mixtures. An algorithm for the solution of the resulting system of partial differential equations is presented, which includes a new robust method for the retrieval of the densities of the constituents of each explosive mixture. This is achieved by means of a multi-dimensional root-finding algorithm, which employs physical as well as mathematical considerations in order to converge to the correct solution. The algorithm is implemented in a hierarchical adaptive mesh refinement framework and validated against results from problems with known solutions. Additional case studies demonstrate that the method can simulate the interaction of detonation waves produced by military grade and commercial explosives in direct contact, each with its own distinct equation of state and reaction rate law.
Highlights
This paper is concerned with the numerical simulation of ignition and transition to detonation of condensed-phase commercial- and military-grade explosives
The proposed formulation addresses this problem by extending the conservation laws and mixture rules of an existing hybrid formulation to model the interaction of multiple explosive mixtures
We present a selection of numerical results to illustrate the full capability of our extended model and demonstrate its applicability to scenarios involving two reactive materials in direct contact with each other
Summary
This paper is concerned with the numerical simulation of ignition and transition to detonation of condensed-phase commercial- and military-grade explosives. Diffuse interface approaches have been extensively used for the numerical simulation of explosives and their interaction with confiners These may be broadly be divided into (i) models that are based on an augmented version of the Euler equations and (ii) models that are based on a multi-phase approach. Versions of the Baer–Nunziato system that are based on systematic asymptotic reductions in the limit of zero relaxation times have been considered, including the five-equation (single-pressure and single-velocity) models of Kapila et al.,[21] Allaire et al.,[22] and Murrone and Guillard.[23] Each of those approaches has advantages and disadvantages, often as a trade-off between accuracy, robustness, and complexity. It is shown that the new model is able to robustly simulate the direct interaction of reacting military-grade and commercial explosives, while retaining the properties of the original formulation
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