Two-phase modeling of deflagration-to-detonation transition in granular materials: A critical examination of modeling issues

Abstract

The two-phase mixture model developed by Baer and Nunziato ͑BN͒ to study the deflagration-to-detonation transition ͑DDT͒ in granular explosives is critically reviewed. The continuum-mixture theory foundation of the model is examined, with particular attention paid to the manner in which its constitutive functions are formulated. Connections between the mechanical and energetic phenomena occurring at the scales of the grains, and their manifestations on the continuum averaged scale, are explored. The nature and extent of approximations inherent in formulating the constitutive terms, and their domain of applicability, are clarified. Deficiencies and inconsistencies in the derivation are cited, and improvements suggested. It is emphasized that the entropy inequality constrains but does not uniquely determine the phase interaction terms. The resulting flexibility is exploited to suggest improved forms for the phase interactions. These improved forms better treat the energy associated with the dynamic compaction of the bed and the single-phase limits of the model. Companion papers of this study ͓Kapila et al., Phys. Fluids 9, 3885 ͑1997͒; Kapila et al., in preparation; Son et al., in preparation͔ examine simpler, reduced models, in which the fine scales of velocity and pressure disequilibrium between the phases allow the corresponding relaxation zones to be treated as discontinuities that need not be resolved in a numerical computation.

Phase diagram of crushed powders

“…The system volume is measured, and the granular bed solid volume fraction is deduced, as a function of the applied constraint. This type of experiment is described for example in Kuo et al (1980), Elban and Chiarito (1986), Bdzil et al (1999) and in the present work. Such measurements consequently summarize all three dimensional contacts and efforts and record their collective effects.…”

“…This granular pressure represents collective intergranular contact resistance effects to compression. Details are given in Bdzil et al (1999) where this pressure is linked to a surface energy and in Saurel et al (2010) where a convenient and accurate EOS formulation is given. When compression continues, some critical granular pressure level is reached and the second stage begins.…”

Application of a generalized multiphase Riemann solver to a finite-volume method with nozzling sources

“…However, unlike A(x), the solid volume fraction φ s (x,t) is not known initially, and its evolution is governed by the compaction equation given by the final entry in Eqn. (1). Consequently, this system of equations cannot be expressed in conservative form.…”

“…These models are commonly used to simulate deflagration-to-detonation transition in granular explosives [1] and predict the dispersal of solid particles induced by the post-detonation blast wave [2]. The well-established Baer-Nunziato (BN) model [3] is the primary formulation used in these predictions:…”

Mechanistic Reactive Burn Modeling of Solid Explosives

“…The complexity of the mixture theory is known to generate its own problems. Interested readers are referred to an excellent review article (Bdzil et al 1999) for the discussions of the strength and weakness of models based on continuum mixture theory.…”