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Simple model for calculating shock adiabats of powder mixtures

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Combustion, Explosion, and Shock Waves Aims and scope

Abstract

A model is proposed for calculating the behavior of porous powder mixtures under shock-wave loading in the one-velocity and one-temperature approximations and also under the assumption of identical pressures of all phases. The model takes into account the presence of the gas in pores. The calculated results are compared with available experimental data for solid and porous media (shock adiabats, double compression by shock waves, and adiabatic unloading). The calculated results are in good agreement with the experimental data, including those for two- and three-species (in terms of condensed phases) mixtures.

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References

  1. V. K. Zharkov and V. A. Kalinin, Equations of State of Solids at High Pressures and Temperatures [in Russian], Nauka, Moscow (1968).

    Google Scholar 

  2. Ya. B. Zel’dovich and Yu. P. Raizer, Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena, Academic Press, New York (1967).

    Google Scholar 

  3. A. F. Bushman and V. E. Fortov, “Models of the equation of state of substances,” Usp. Fiz. Nauk, 140, No. 2, 177–232 (1983).

    Article  Google Scholar 

  4. V. K. Kopyshev and A. B. Medvedev, “Review of principal ideas of the models of the equation of state at the Institute of Experimental Physics,” in: High Energy Densities [in Russian], Russian Federal Nuclear Center-Inst. Experimental Physics, Sarov (1997).

    Google Scholar 

  5. V. E. Fortov, L. V. Al’tshuler, R. F. Trunin, and A. I. Funtikov (eds.), Shock Waves and Extreme States of Matter [in Russian], Nauka, Moscow (2000).

    Google Scholar 

  6. A. A. Charakhch’yan, V. V. Milyavskii, and K. V. Khishchenko, “Using models of the mixture to analyze shock wave experiments with an incomplete phase transition,” Teplofiz. Vys. Temp., 47, No. 2, 254–261 (2009).

    Google Scholar 

  7. R. K. Bel’kheeva, “Thermodynamic equation of state used to describe the behavior of a porous mixture under high pressures and temperatures,” J. Appl. Mech. Tech. Phys., 48, No. 5, 664–670 (2007).

    Article  ADS  Google Scholar 

  8. B.A. Lyukshin,A. V. Gerasimov, R. A. Krektuleva, and P. A. Lyukshin, Modeling of Physical and Mechanical Processes in Heterogeneous Structures [in Russian], Izd. Sib. Otd. Ross. Akad. Nauk, Novosibirsk (2001).

    Google Scholar 

  9. S. A. Kinelovskii, K. K. Maevskii, and A. S. Rodikov, “One model for calculating the shock adiabat of a porous heterogeneous medium,” Vestn. Nov. Gos. Univ., Ser. Fiz., 3, No. 1, 3–11 (2008).

    Google Scholar 

  10. S. A. Kinelovskii and K. K. Maevskii, “Calculation of the shock adiabats of powder mixtures with allowance for the dependence of the Grüneisen coefficient on temperature,” Vestn. Novosib. Gos. Univ., Ser. Fiz., 4, No. 4, 71–78 (2009).

    Google Scholar 

  11. V. K. Golubev, “Determination of the range of applicability for the equation of state of metals with a constant Grüneisen coefficient,” Khim. Fiz., 21, No. 10, 30–35 (2002).

    Google Scholar 

  12. P. Caldirola and H. Knoepfel (eds.), Physics of High Energy Density, Academic Press, New York (1971).

    Google Scholar 

  13. K. V. Khishchenko, M. V. Zhernokletov, I. V. Lomonosov, et al., “Study of thermodynamic properties and phase transitions of carbon in shock compression and adiabatic unloading waves,” in: III Khariton’s Topical Scientific Readings, Proc. Int. Conf., Russian Federal Nuclear Center-Inst. Experimental Physics, Sarov (2002), pp. 94–98.

  14. R. G. McQueen, S. P. Marsh, J. W. Taylor, et al., “The equations of state of solids from shock-wave studies,” in: R. Kinslow (ed.), High Velocity Impact Phenomena, Academic Press, New York (1970).

    Google Scholar 

  15. R. Boehler and J. Ramakrishnan, “Experimental results on the pressure dependence of the Grüneisen parameter,” J. Geophys. Res. Ser. B, 85, 6996–7002 (1980).

    Article  ADS  Google Scholar 

  16. S. B. Kormer, A. I. Funtikov, V. D. Urlin, and A. N. Kolesnikova, “Dynamic compression of porous metals and equation of state with variable heat capacity at high temperatures,” Zh. Éksp. Teor. Fiz., 42, No. 3, 686–702 (1962).

    Google Scholar 

  17. A. M. Molodets and M. A. Molodets, “Temperature dependence of the Grüneisen function of chemical elements,” Khim. Fiz., 16, No. 5, 122–126 (1997).

    Google Scholar 

  18. V. M. Fomin, A. I. Gulidov, G. A. Sapozhnikov, et al., High-Velocity Interaction of Bodies [in Russian], Izd. Sib. Otd. Ross. Akad. Nauk, Novosibirsk (1999), pp. 390–391.

    Google Scholar 

  19. A. P. Babichev, N. A. Babushkina, A. M. Bratkovskii, et al., Physical Quantities, Reference Book [in Russian], Énergoatomizdat, Moscow (1991).

    Google Scholar 

  20. S. I. Novikova, Thermal Expansion of Solids [in Russian], Nauka, Moscow (1974).

    Google Scholar 

  21. L. V. Al’tshuler, S. B. Kormer, A. A. Bakanova, and R. F. Trunin, “Equations of state for aluminum, copper, and lead in the range of high pressures,” Zh. Éksp. Teor. Fiz., 38, No. 3, 790–798 (1960).

    Google Scholar 

  22. V. F. Kuropatenko, “Equation of state in mathematical models of mechanics and physics,” Mat. Model., 4, No. 12, 112–136 (1992).

    Google Scholar 

  23. J. M. Walsh, M. H. Rice, R. G. Mcqueen, and F. L. Yarger, “Shock-wave compressions of twenty-seven metals equations of state of metals,” Phys. Rev., 108, 196–216 (1957).

    Article  ADS  Google Scholar 

  24. W. H. Isbell, F. H. Shipman, and A. H. Jones, “Hugoniot equation of state measurements for eleven materials to five megabars,” Mat. Sci. Lab. Report No. MSL-68-13, General Motors Corp. (1968).

  25. R. F. Trunin, L. F. Gudarenko, M. V. Zhernokletov, and G. V. Simakov, Experimental Data on Shock-Wave Compression and Adiabatic Expansion of Condensed Substances [in Russian], Russian Federal Nuclear Center-Inst. Experimental Physics, Sarov (2001).

    Google Scholar 

  26. M. V. Zhernokletov (ed.), Methods of Studying Material Properties under Intense Dynamic Loads [in Russian], Russian Federal Nuclear Center-Inst. Experimental Physics, Sarov (2005).

    Google Scholar 

  27. R. F. Trunin and G. V. Simakov, “Studying shock compressibility and isentropic expansion of zinc,” Mat. Model., 5, No. 8, 108–117 (1993).

    Google Scholar 

  28. R. G. McQueen and S. P. Marsh, “Equation of state for nineteen metallic elements,” J. Appl. Phys., 31, 1253–1269 (1960).

    Article  ADS  Google Scholar 

  29. A. B. Medvedev, “Model of the equation of state with allowance for evaporation, ionization, and melting,” Vopr. Atom. Nauki Tekh. Teor. Prikl. Fiz., No. 1, 12–19 (1992).

  30. E. N. Avrorin, B. K. Vodolaga, V. A. Simonenko, and V. E. Fortov, “Strong shock waves and extreme states of matter,” Usp. Fiz. Nauk, 163, No. 5, 1–34 (1993).

    Article  Google Scholar 

  31. W. J. Nellis, A. C. Mitchell, and D. A. Young, “Equation-of-state measurements for aluminum, copper, and tantalum in the pressure range 80–440 GPa (0.8–4.4 Mbar),” J. Appl. Phys., 93, No. 1, 304–310 (2003).

    Article  ADS  Google Scholar 

  32. M. V. Zhernokletov, V. N. Zubarev, and Yu. N. Sutulov, “Porous-specimen adiabats and solid-copper expansion isentropes,” J. Appl. Mech. Tech. Phys., 25, No. 1, 107–110 (1984).

    Article  ADS  Google Scholar 

  33. R. F. Trunin, G. V. Simakov, Yu. I. Sutulov, et al., “Compressibility of porous metals in shock waves,” Zh. Éksp. Teor. Fiz., 96, No. 3(9), 1024–1038 (1989).

    Google Scholar 

  34. L. F. Gudarenko, O. N. Gushchina, M. V. Zhernokletov, et al., “Shock compression and isentropic expansion of porous samples of tungsten, nickel, and tin,” Teplofiz. Vys. Temp., 38, No. 3, 437–444 (2000).

    Google Scholar 

  35. I. V. Lomonosov, V. E. Fortov, A. A. Frolova, et al., “Numerical study of shock compression of graphite and its transformation to diamond in conical targets,” Zh. Tekh. Fiz., 73, No. 6, 66–75 (2003).

    Google Scholar 

  36. R. F. Trunin, Study of Extreme States of Condensed Substances by the Method of Shock Waves. Hugoniot Equations [in Russian], Russian Federal Nuclear Center-Inst. Experimental Physics, Sarov (2006).

    Google Scholar 

  37. M. van Thiel (ed.), “Compendium of Shock Wave Data,” Report No. UCRL-50108, Lawrence Livermore Laboratory, Livermore (1977).

    Google Scholar 

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Correspondence to S. A. Kinelovskii.

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Translated from Fizika Goreniya i Vzryva, Vol. 47, No. 6, pp. 101–109, November–December, 2011.

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Kinelovskii, S.A., Maevskii, K.K. Simple model for calculating shock adiabats of powder mixtures. Combust Explos Shock Waves 47, 706–714 (2011). https://doi.org/10.1134/S001050821106013X

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