Shock structure for the seven-equation, two-phase continuum-mixture model

Bdzil, J. B.; Kapila, A. K.; Hennessey, Michael Patrick

doi:10.1080/13647830.2021.1889683

Cited by 3 publications

(1 citation statement)

References 20 publications

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“…where e is the internal energy that includes the enthalpy of formation, h 0 f . The BN equations have a long history of success in modeling reactive burn [32][33][34], shock-to-detonation transition (SDT), deflagration-to-detonation transition [35], etc. The BN equations, however, can be difficult to solve and are computationally intensive due to the non-conservative spatial gradient terms [33,36].…”

Section: Governing Equationsmentioning

confidence: 99%

A simplified burn model for simulating explosive effects and afterburning

Houim

2021

Shock Waves

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A simplified burn model (SBM) was developed for use in simulating the effects of explosive detonations. The goal of SBM is to provide a subgrid model for detonation propagation on grids that are many times coarser than the physical width of the reaction zone. Similar to traditional programmed burn (PB), SBM provides accurate enough initial conditions for simulating largescale blasts and afterburning processes resulting from the detonation. The governing equations are based on the five-equation compressible multiphase flow model that describes reaction and post-detonation processes similar to reactive burn models. The model uses highly simplified reactant equations of state and reaction rate laws. The reaction model is based on burning rates from traditional PB approaches and is designed to spread the reaction zone over a small number of grid points regardless of the mesh resolution. The detonation velocity and state are independent of the input parameters for the reactant equation of state and reaction model, provided the inputs are physically realistic. The single input parameter for the equation of state must be selected such that the reactant and product Hugoniot curves do not cross, otherwise unphysical weak detonations result. Numerical experiments show that the velocity, state, and bulk structure of Chapman-Jouguet detonations can be reproduced by the model. The resulting blast profiles, pressure-time traces, and detonation velocity for multidimensional simulations are relatively independent on the input parameters, again, provided the inputs are physically reasonable. The simplified burn model shows great potential for simulating afterburning processes with detailed reaction models or explosive particle dispersal. The SBM is relatively straightforward to implement in compressible multiphase flow codes.

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Section: Governing Equationsmentioning

confidence: 99%

A simplified burn model for simulating explosive effects and afterburning

Houim

2021

Shock Waves

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Efficient Finite Difference WENO Scheme for Hyperbolic Systems with Non-conservative Products

Balsara

Bhoriya

Shu

et al. 2023

Commun. Appl. Math. Comput.

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

2021

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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.

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Shock structure for the seven-equation, two-phase continuum-mixture model

Cited by 3 publications

References 20 publications

A simplified burn model for simulating explosive effects and afterburning

A simplified burn model for simulating explosive effects and afterburning

Efficient Finite Difference WENO Scheme for Hyperbolic Systems with Non-conservative Products

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

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