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A two-phase mixture theory for the deflagration-to-detonation transition (DDT) in reactive granular materials. (English) Zbl 0609.76114
Summary: In this paper, a two-phase mixture theory is presented which describes the deflagration-to-detonation transition (DDT) in reactive granular materials. The theory is based on the continuum theory of mixtures formulated to include the compressibility of all phases and the compaction behavior of the granular material. By requiring the model to satisfy an entropy inequality, specific expressions for the exchange of mass, momentum and energy are proposed which are consistent with known empirical models. The model is applied to describe the combustion processes associated with DDT in a pressed column of HMX. Numerical results, using the method-of-lines, are obtained for a representative column of length 10 cm packed to a 70% density with an average grain size of \(100\, \mu\)m. The results are found to predict the transition to detonation in run distances commensurate with experimental observations. Additional calculations have been carried out to demonstrate the effect of particle size and porosity and to study bed compaction by varying the compaction viscosity of the granular explosive.

76T99 Multiphase and multicomponent flows
76L05 Shock waves and blast waves in fluid mechanics
80A25 Combustion
76M99 Basic methods in fluid mechanics
80A30 Chemical kinetics in thermodynamics and heat transfer
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