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Comparison of methods for calculating the shock hugoniot of mixtures

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Abstract

Various methods used to determine the shock Hugoniot of condensed phase multi-component mixtures are reviewed and compared to available experimental data. The assumptions inherent in the different models are presented in this overview and their implications are discussed. The comparisons of the various models demonstrate that the predicted shock Hugoniots are in good agreement with published data despite the simplifying assumptions that are associated with the models. Averaging models are shown to be among the simplest methods to implement and result in the closest agreement with experimental data.

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References

  1. Baer M.R., Nunziato J.W.: A two-phase mixture theory for the deflagration to detonation transition (DDT) in reactive granular materials. Int. J. Multiph. Flow 12, 861–889 (1986)

    Article  MATH  Google Scholar 

  2. Bdzil J.B., Menikoff R., Son S.F., Kapila A.K., Stewart D.S.: Two-phase modeling of deflagration-to-detonation transition in granular materials: a critical examination of modeling issues. Phys. Fluids 11(2), 378–402 (1999)

    Article  MATH  Google Scholar 

  3. Powers J.M.: Two-phase viscous modeling of compaction of granular materials. Phys. Fluids 16(8), 2975–2990 (2004)

    Article  Google Scholar 

  4. Saurel R., Lemetayer O.: A multiphase model for compressible flows with interfaces, shocks, detonation waves and cavitation. J. Fluid Mech. 431, 239–271 (2001)

    Article  MATH  Google Scholar 

  5. Truesdell, C., Toupin, R.: The classical field theories. In: Encyclopedia of Physics, vol. III/I. Springer, Berlin (1960)

  6. Nikolaevskii V.N.: Hydrodynamic analysis of shock adiabats of heterogeneous mixtures of substances. J. Appl. Mech. Tech. Phys. 10(3), 406–411 (1969)

    Article  Google Scholar 

  7. Kenyon D.E.: Thermostatics of solid–fluid mixtures. Arch. Ration. Mech. Anal. 62, 117–129 (1976)

    MATH  MathSciNet  Google Scholar 

  8. Kapila A.K., Menikoff R., Bdzil J.B., Son S.F., Stewart D.S.: Two-phase modeling of deflagration-to-detonation transition in granular materials: reduced equations. Phys. Fluids 13(10), 3002–3024 (2001)

    Article  Google Scholar 

  9. Dremin A.N., Karpukhin I.A.: Method of determination of shock adiabat of the dispersed substances (in russian). Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki 1(3), 184–188 (1960)

    Google Scholar 

  10. Alekseev Yu.F., Al’tshuler L.V., Krupnikova V.P.: Shock compression of two-component paraffin–tungsten mixtures. J. Appl. Mech. Tech. Phys. 12(4), 624–627 (1971)

    Article  Google Scholar 

  11. Krueger B.R., Vreeland T.: A Hugoniot theory for solid and powder mixtures. J. Appl. Phys. 69(2), 710–716 (1991)

    Article  Google Scholar 

  12. Saurel R., Le Metayer O., Massoni J., Gavrilyuk S.: Shock jump relations for multiphase mixtures with stiff mechanical relaxation. Shock Waves 16(3), 209–232 (2007)

    Article  Google Scholar 

  13. Gavrilyuk S.L., Saurel R.: Rankine–Hugoniot relations for shocks in heterogeneous mixtures. J. Fluid Mech. 575(1), 495–507 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  14. Batsanov S.S.: Effects of explosions on materials: modification and synthesis under high-pressure shock compression. Springer, Berlin (1994)

    Google Scholar 

  15. McQueen R.G., Marsh S.P., Fritz J.N.: Hugoniot equation of state of twelve rocks. J. Geophys. Res. 72, 4999–5036 (1967)

    Article  Google Scholar 

  16. Duvall G.E., Taylor S.M.: Shock parameters in a two component mixture. J. Compos. Mater. 5(2), 130–139 (1971)

    Article  Google Scholar 

  17. Murnaghan F.D.: The compressibility of media under extreme pressures. Proc. Natl. Acad. Sci. 30, 244–247 (1944)

    Article  MATH  MathSciNet  Google Scholar 

  18. Marsh S.P.: LASL Shock Hugoniot Data. University of California Press, California (1980)

    Google Scholar 

  19. Trunin R.F.: Shock Compression of Condensed Materials. Cambridge University Press, Cambridge (1998)

    Book  Google Scholar 

  20. Adadurov G.A., Dremin A.N., Ryabinin Yu.N.: About behaviour of some substances at shock compression. Zhurnal Prikladnoi Mekhaniki Tekhnicheskoi Fiziki 4, 115–119 (1964)

    Google Scholar 

  21. Kalashnikov N.G., Pavlovskii M.N., Simakov G.V., Trunin R.F.: Dynamic compressibility of the minerals of calcite group. Izvestiya Akademii Nauk SSSR, Fizika Zemli 2, 23–29 (1973)

    Google Scholar 

  22. van Thiel, M.: Compendium of shock wave data. Technical report, Lawrence Livermore Laboratory Report UCRL-50108 (1977)

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Authors and Affiliations

  1. Department of Mechanical Engineering, McGill University, 817 Sherbrooke W., Montreal, QC, H3A 2K6, Canada

    Oren E. Petel & Francois X. Jetté

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  1. Oren E. Petel
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  2. Francois X. Jetté
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Correspondence to Oren E. Petel.

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Communicated by F. Zhang.

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Petel, O.E., Jetté, F.X. Comparison of methods for calculating the shock hugoniot of mixtures. Shock Waves 20, 73–83 (2010). https://doi.org/10.1007/s00193-009-0230-x

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