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

The two-phase mixture model developed by Baer and Nunziato (BN) to study th e deflagration-to-detonation transition (DDT) in granular explosives is cri tically reviewed. The continuum-mixture theory foundation of the model is e xamined, with particular attention paid to the manner in which its constitu tive functions are formulated. Connections between the mechanical and energ etic phenomena occurring at the scales of the grains, and their manifestati ons on the continuum averaged scale, are explored. The nature and extent of approximations inherent in formulating the constitutive terms, and their d omain 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 phas e interaction terms. The resulting flexibility is exploited to suggest impr oved forms for the phase interactions. These improved forms better treat th e energy associated with the dynamic compaction of the bed and the single-p hase limits of the model. Companion papers of this study [Kapila et al., Ph ys. Fluids 9, 3885 (1997); Kapila et al., in preparation; Son et al., in pr eparation] examine simpler, reduced models, in which the fine scales of vel ocity and pressure disequilibrium between the phases allow the correspondin g relaxation zones to be treated as discontinuities that need not be resolv ed in a numerical computation. [S1070-6631(99)02002-4].