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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: [email protected]
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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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References

REFERENCES

Abgrall, R. 1996 How to prevent pressure oscillations in multicomponent flow calculations: a quasi-conservative approach. J. Comput. Phys. 125, 150–160.CrossRefGoogle Scholar
Alderborn, G. & Nyström, C. (Ed.) 1996 Pharmaceutical Powder Compaction Technology. Marcel Dekker.Google Scholar
Baer, M. & Nunziato, J. 1986 A two-phase mixture theory for the deflagration-to-detonation transition ddt in reactive granular materials. Intl J. Multiphase Flows 12, 861–889.CrossRefGoogle Scholar
Bdzil, J., Menikoff, R., Son, S., Kapila, A. & Stewart, D. 1999 Two-phase modelling of ddt in granular materials: a critical examination of modelling issues. Phys. Fluids 11, 378–402.CrossRefGoogle Scholar
Chinnayya, A., Daniel, E. & Saurel, R. 2004 Computation of detonation waves in heterogeneous energetic materials. J. Comput. Phys. 196, 490–538.CrossRefGoogle Scholar
Duberg, M. & Nyström, C. 1986 Studies on direct compression of tablets XVII. Porosity-pressure curves for the characterization of volume reduction mechanisms in powder compression. Powder Technol. 46, 67–75.CrossRefGoogle Scholar
Elban, W. & Chiarito, M. 1986 Quasi-static compaction study of coarse HMX explosive. Powder Technol. 46 (2–3), 181–193.CrossRefGoogle Scholar
Favrie, N., Gavrilyuk, S. & Saurel, R. 2009 Diffuse solid-fluid interface model in cases of extreme deformations. J. Comput. Phys. 228, 6037–6077.CrossRefGoogle Scholar
Gethin, D., Tran, V., Lewis, R. & Ariffin, A. 1994 An investigation of powder compaction processes. Intl J. Powder Metall. 30 (4), 385–398.Google Scholar
Gonthier, K. 2003 Modelling and analysis of reactive compaction for granular energetic solids. Combust. Sci. Technol. 175 (9), 1679–1709.CrossRefGoogle Scholar
Gonthier, K. 2004 Predictions for weak mechanical ignition of strain hardened granular explosive. J. Appl. Phys. 95 (7), 3482–3494.CrossRefGoogle Scholar
Guillard, H. & Duval, F. 2007 A Darcy law for the drift velocity in a two-phase flow model. J. Comput. Phys. 224, 288–313.CrossRefGoogle Scholar
Jogi, V. 2003 Predictions for multi-scale shock heating of a granular energetic material. Master's Thesis, Louisiana State University. Available at: http://etd.lsu.edu/docs/available/etd-0811103-164117/.Google Scholar
Kapila, A., Menikoff, R., Bdzil, J., Son, S. & Stewart, D. 2001 Two-phase modelling of ddt in granular materials: reduced equations. Phys. Fluids 13 (10), 3002–3024.CrossRefGoogle Scholar
Karni, S. 1994 Multicomponent flow calculations by a consistent primitive algorithm. J. Comput. Phys. 112, 31–43.CrossRefGoogle Scholar
Khasainov, B., Borisov, A., Ermolaev, B. & Korotkov, A. 1981 Two-phase visco-plastic model of shock initiation of detonation in high density pressed explosives. In Seventh International Symposium on Detonation (ed. Office of Naval Research), pp. 435–447. Naval Surface Weapons Center, Annapolis, MD.Google Scholar
Kuo, K., Yang, V. & Moore, B. 1980 Intragranular stress, particle-wall friction and speed of sound in granular propellant beds. J. Comput. Phys. 4 (1), 697–730.Google Scholar
Le Métayer, O., Massoni, J. & Saurel, R. 2004 Élaboration des lois d'état d'un liquide et de sa vapeur pour les modèles d'écoulements diphasiques (in French). Intl J. Therm. Sci. 43, 265–276.CrossRefGoogle Scholar
Lewis, R. & Khoei, A. 2001 A plasticity model for metal powder forming processes. Intl J. Plast. 17, 1659–1692.CrossRefGoogle Scholar
Martin, C., Bouvard, D. & Shima, S. 2003 Study of particle rearrangement during powder compaction by the discrete element method. J. Mech. Phys. Solids 51 (4), 667–693.CrossRefGoogle Scholar
Murrone, A. & Guillard, H. 2005 A five equations reduced model for compressible two-phase flow problems. J. Comput. Phys. 202, 664–698.CrossRefGoogle Scholar
Oliver, J., Oller, S. & Cante, J. 1996 A plasticity model for simulation of industrial powder compaction processes. Intl J. Solids Struct. 33 (20), 3161–3178.CrossRefGoogle Scholar
Passman, S., Nunziato, J. & Walsh, E. 1984 A theory of multiphase mixtures. In Rational Thermodynamics (ed. Trusdell, C.), Appendix 5c, pp. 286–325. Springer.CrossRefGoogle Scholar
Périgaud, G. & Saurel, R. 2005 A compressible flow model with capillary effects. J. Comput. Phys. 209, 139–178.CrossRefGoogle Scholar
Petitpas, F., Massoni, J., Saurel, R., Lapebie, E. & Munier, L. 2009 Diffuse interface models for high speed cavitating underwater systems. Intl J. Multiphase Flow 35, 747–759.CrossRefGoogle Scholar
Rogue, X. 1997 Expériences et simulations d'écoulements diphasiques en tubes à choc (in French). PhD Thesis, Université de Provence, Marseille, France.Google Scholar
Rogue, X., Rodriguez, G., Haas, J. & Saurel, R. 1998 Experimental and numerical investigation of the shock-induced fluidization of a particle bed. Shock Waves 8, 29–45.CrossRefGoogle Scholar
Sandusky, H. & Liddiard, T. 1985 Dynamic compaction of porous bed of porous beds. Tech. Rep. NSWC TR 83-246. Naval Surface Weapons Center.Google Scholar
Saurel, R. & Abgrall, R. 1999 A multiphase Godunov method for compressible multifluid and multiphase flows. J. Comput. Phys. 150, 425–467.CrossRefGoogle Scholar
Saurel, R., Gavrilyuk, S. & Renaud, F. 2003 A multiphase model with internal degree of freedom: application to shock-bubble interaction. J. Fluid Mech. 495, 283–321.CrossRefGoogle Scholar
Saurel, R., Petitpas, F. & Abgrall, R. 2008 Modeling phase transition in metastable liquids. Application to flashing and cavitating flows. J. Fluid Mech. 607, 313–350.CrossRefGoogle Scholar
Saurel, R., Petitpas, F. & Berry, R. 2009 Simple and efficient relaxation methods for interfaces separating compressible fluids, cavitating flows and shocks in multiphase mixtures. J. Comput. Phys. 228, 1678–1712.CrossRefGoogle Scholar
Wood, A. 1930 A Textbook of Sound. G. Bell and Sons Ltd.Google Scholar