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.
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December 2014
Research Article|
December 15 2014
Symmetric model of compressible granular mixtures with permeable interfaces
Richard Saurel;
Richard Saurel
1
University Institute of France and Aix-Marseille University
, CNRS IUSTI, 5 rue E. Fermi, 13453 Marseille Cedex 13, France
2
RS2N
, Chemin de Gaumin, 83640 Saint-Zacharie, France
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Sébastien Le Martelot;
Sébastien Le Martelot
2
RS2N
, Chemin de Gaumin, 83640 Saint-Zacharie, France
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Robert Tosello;
Robert Tosello
3
DGA-TN
, 83050 Toulon, France
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Emmanuel Lapébie
Emmanuel Lapébie
4
CEA, DAM GRAMAT
, F-46500 Gramat, France
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Physics of Fluids 26, 123304 (2014)
Article history
Received:
March 20 2014
Accepted:
November 15 2014
Citation
Richard Saurel, Sébastien Le Martelot, Robert Tosello, Emmanuel Lapébie; Symmetric model of compressible granular mixtures with permeable interfaces. Physics of Fluids 1 December 2014; 26 (12): 123304. https://doi.org/10.1063/1.4903259
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