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Multidimensional Hyperbolic Problems and Computations pp 58–67Cite as

Modeling Two-Phase Flow of Reactive Granular Materials

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Part of the book series: The IMA Volumes in Mathematics and Its Applications ((IMA,volume 29))

Abstract

In this study, we examine a two-phase model proposed by Baer and Nunziato to describe the modes of combustion from deflagration to detonation in reactive granular materials. The model treats all phases in nonequilibrium and fully compressible. A compaction evolutionary equation, describing changes in volume fraction, provides model closure. In contrast to a pressure equilibrium model that has elliptic regions, the system of equations is hyperbolic except at points where the relative flow is locally sonic.

This work supported by the U. S. Department of Energy under Contract Number DE-AC04-76DP00789.

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References

  1. M. R. Baer and J. W. Nunziato, “A Two-Phase Mixture Theory for Deflagration-to-Detonation Transition (DDT) in Reactive Granular Materials,” Intl. J. Multiphase Flow, 12 (1986) pp. 861–889.

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  2. M. R. Baer, R. J. Gross, J. W. Nunziato, and E. A. Igel, “An Experimental and Theoretical Study of Deflagration-to-Detonation Transition (DDT) in the Granular Explosive, CP,” Combustion and Flame 65 (1986) pp. 15–30.

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  3. R. R. Bernecker, “The Deflagration-to-Detonation Transition of High Energy Propellants — A Review,” AIAA Journal 24 (1986) pp. 82–91.

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  4. P. F. Embid and M. R. Baer, “Mathematical Analysis of a Two-Phase Model for Reactive Granular Material,” SAND88–3302, Sandia National Laboratories, 1989, in press.

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  5. J. D. Ramshaw and J. A. Trapp, “Characteristics, Stability and Short-Wavelength Phenomena in Two-Phase Flow Equation Systems,” Nucl. Sci. Eng. 66 (1978) 93–102.

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Author information

Authors and Affiliations

  1. Mathematics Department, University of New Mexico, Albuquerque, New Mexico, 87131, USA

    Pedro F. Embid

  2. Fluid and Thermal Science Department, Sandia National Laboratories, Albuquerque, New Mexico, 87185, USA

    Melvin R. Baer

Authors
  1. Pedro F. Embid
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  2. Melvin R. Baer
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Editor information

Editors and Affiliations

  1. Department of Applied Mathematics and Statistics, SUNY at Stony Brook, Stony Brook, NY, 11794-3600, USA

    James Glimm

  2. Department of Mathematics and Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ, 08544, USA

    Andrew J. Majda

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© 1991 Springer-Verlag New York, Inc.

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Embid, P.F., Baer, M.R. (1991). Modeling Two-Phase Flow of Reactive Granular Materials. In: Glimm, J., Majda, A.J. (eds) Multidimensional Hyperbolic Problems and Computations. The IMA Volumes in Mathematics and Its Applications, vol 29. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-9121-0_5

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  • DOI: https://doi.org/10.1007/978-1-4613-9121-0_5

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4613-9123-4

  • Online ISBN: 978-1-4613-9121-0

  • eBook Packages: Springer Book Archive

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