Symmetric model of compressible granular mixtures with permeable interfaces

Abstract : Compressible granular materials are involved in many applications, some of them being related to energetic porous media. Gas permeation effects are important during their compaction stage, as well as their eventual chemical decomposition. Also, many situations involve porous media separated from pure fluids through two-phase interfaces. It is thus important to develop theoretical and numerical formulations to deal with granular materials in the presence of both two-phase interfaces and gas permeation effects. Similar topic was addressed for fluid mixtures and interfaces with the Discrete Equations Method (DEM) [R. Abgrall and R. Saurel, ``Discrete equations for physical and numerical compressible multiphase mixtures,''J. Comput. Phys. 186 (2), 361-396 (2003)] but it seemed impossible to extend this approach to granular media as intergranular stress [K. K. Kuo, V. Yang, and B. B. Moore, ``Intragranular stress, particle-wall friction and speed of sound in granular propellant beds,'' J. Ballist. 4 (1), 697-730 (1980)] and associated configuration energy [J. B. Bdzil, R. Menikoff, S. F. Son, A. K. Kapila, and D. S. Stewart, `` Two-phase modeling of deflagration-to-detonation transition in granular materials: A critical examination of modeling issues,'' Phys. Fluids 11, 378 (1999)] were present with significant effects. An approach to deal with fluid-porous media interfaces was derived in Saurel et al. [''Modelling dynamic and irreversible powder compaction,'' J. Fluid Mech. 664, 348-396 (2010)] but its validity was restricted to weak velocity disequilibrium only. Thanks to a deeper analysis, the DEM is successfully extended to granular media modelling in the present paper. It results in an enhanced version of the Baer and Nunziato [''A two-phase mixture theory for the deflagration-to-detonation transition (DDT) in reactive granular materials,'' Int. J. Multiphase Flow 12 (6), 861-889 (1986)] model as symmetry of the formulation is now preserved. Several computational examples are shown to validate and illustrate method's capabilities. (C) 2014 AIP Publishing LLC.
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Richard Saurel, Sebastien Le Martelot, Robert Tosello, Emmanuel Lapebie. Symmetric model of compressible granular mixtures with permeable interfaces. Physics of Fluids, American Institute of Physics, 2014, 26 (12), ⟨10.1063/1.4903259⟩. ⟨hal-01459320⟩

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