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Modelling dynamic and irreversible powder compaction

Published online by Cambridge University Press:  01 November 2010

RICHARD SAUREL ,
N. FAVRIE ,
F. PETITPAS ,
M.-H. LALLEMAND  and
S. L. GAVRILYUK
RICHARD SAUREL*
Affiliation:
SMASH Project-team, UMR CNRS 6595 IUSTI – INRIA, Polytech Marseille, Aix-Marseille Université, 5 rue E. Fermi, 13 453 Marseille CEDEX 13, France University Institute of France, Polytech Marseille, Aix-Marseille Université, 5 rue E. Fermi, 13 453 Marseille CEDEX 13, France
N. FAVRIE
Affiliation:
SMASH Project-team, UMR CNRS 6595 IUSTI – INRIA, Polytech Marseille, Aix-Marseille Université, 5 rue E. Fermi, 13 453 Marseille CEDEX 13, France
F. PETITPAS
Affiliation:
SMASH Project-team, UMR CNRS 6595 IUSTI – INRIA, Polytech Marseille, Aix-Marseille Université, 5 rue E. Fermi, 13 453 Marseille CEDEX 13, France
M.-H. LALLEMAND
Affiliation:
SMASH Project-team, UMR CNRS 6595 IUSTI – INRIA, Polytech Marseille, Aix-Marseille Université, 5 rue E. Fermi, 13 453 Marseille CEDEX 13, France
S. L. GAVRILYUK
Affiliation:
SMASH Project-team, UMR CNRS 6595 IUSTI – INRIA, Polytech Marseille, Aix-Marseille Université, 5 rue E. Fermi, 13 453 Marseille CEDEX 13, France
*
†Email address for correspondence: richard.saurel@polytech.univ-mrs.fr
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Abstract

A multiphase hyperbolic model for dynamic and irreversible powder compaction is built. Four important points have to be addressed in this case. The first one is related to the irreversible character of powder compaction. When a granular media is subjected to a loading–unloading cycle, the final volume is lower than the initial one. To deal with this hysteresis phenomenon, a multiphase model with relaxation is built. During loading, mechanical equilibrium is assumed corresponding to stiff mechanical relaxation, while during unloading non-equilibrium mechanical transformation is assumed. Consequently, the sound speed of the limit models are very different during loading and unloading. These differences in acoustic properties are responsible for irreversibility in the compaction process. The second point is related to dynamic effects, where pressure and shock waves play an important role. Wave dynamics is guaranteed by the hyperbolic character of the equations. Phase compressibility as well as configuration energy are taken into account. The third point is related to multi-dimensional situations that involve material interfaces. Indeed, most processes with powder compaction entail free surfaces. Consequently, the model should be able to solve interfaces separating pure fluids and granular mixtures. Finally, the fourth point is related to gas permeation that may play an important role in some specific powder compaction situations. This poses the difficult question of multiple-velocity description. These four points are considered in a unique model fitting the frame of multiphase theory of diffuse interfaces (Saurel & Abgrall, J. Comput. Phys., vol. 150, 1999, p. 425; Kapila et al., Phys. Fluids, vol. 13, 2001, p. 3002; Saurel et al., J. Comput. Phys., vol. 228, 2009, p. 1678). The ability of the model to deal with these various effects is validated on basic situations, where each phenomenon is considered separately. Except for the material EOS (hydrodynamic and granular pressures and energies), which are determined on the basis of separate experiments found in the literature, the model is free of adjustable parameter.

JFM classification

Granular media: Granular media Compressible Flows: Shock waves
Type
Papers
Information
Journal of Fluid Mechanics , Volume 664 , 10 December 2010 , pp. 348 - 396
Copyright
Copyright © Cambridge University Press 2010

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