A unified multi-phase and multi-material formulation for combustion modeling

Abstract

The motivation of this work is to produce an integrated formulation for material response (e.g., elastoplastic, viscous, viscoplastic) due to detonation wave loading. Here, we focus on elastoplastic structural response. In particular, we want to capture miscible and immiscible behavior within condensed-phase explosives arising from the co-existence of a reactive carrier mixture of miscible materials and several material interfaces due to the presence of immiscible impurities such as particles or cavities. The dynamic and thermodynamic evolution of the explosive is communicated to one or more inert confiners through their shared interfaces, which may undergo severe topological change. We also wish to consider elastic and plastic structural response of the confiners rather than make a hydrodynamic assumption for their behavior. The previous work by these authors has met these requirements by means of the simultaneous solution of appropriate systems of equations for the behavior of the condensed-phase explosive and the elastoplastic behavior of the confiners. To that end, both systems were written in the same mathematical form as a system of inhomogeneous hyperbolic partial differential equations (PDEs), which were solved on the same discrete space using the same algorithms, as opposed to coupling fluid and solid algorithms (co-simulation). In the present work, we employ a single system of PDEs proposed by Peshkov and Romenski [Peshkov and Romenski, “A hyperbolic model for viscous Newtonian flows,” Continuum Mech. Thermodyn. 28, 85 (2016)], which is able to account for different states of matter by means of generalizing the concept of distortion tensors beyond solids. We amalgamate that formulation with a single system of PDEs, which meets the requirement of co-existing miscible and immiscible explosive mixtures. We present the mathematical derivation and construct appropriate algorithms for its solution. The resulting model is validated against exact solutions for several one-dimensional use-cases, including mechanically and thermally induced, inviscid, and viscous detonations. Results indicate that the model can accurately simulate a very broad range of problems involving the nonlinear interaction between reactive and inert materials within a single framework.