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
V. K. Zharkov and V. A. Kalinin, Equations of State of Solids at High Pressures and Temperatures [in Russian], Nauka, Moscow (1968).
Ya. B. Zel’dovich and Yu. P. Raizer, Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena, Academic Press, New York (1967).
A. F. Bushman and V. E. Fortov, “Models of the equation of state of substances,” Usp. Fiz. Nauk, 140, No. 2, 177–232 (1983).
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).
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).
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).
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).
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).
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).
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).
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).
P. Caldirola and H. Knoepfel (eds.), Physics of High Energy Density, Academic Press, New York (1971).
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.
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).
R. Boehler and J. Ramakrishnan, “Experimental results on the pressure dependence of the Grüneisen parameter,” J. Geophys. Res. Ser. B, 85, 6996–7002 (1980).
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).
A. M. Molodets and M. A. Molodets, “Temperature dependence of the Grüneisen function of chemical elements,” Khim. Fiz., 16, No. 5, 122–126 (1997).
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.
A. P. Babichev, N. A. Babushkina, A. M. Bratkovskii, et al., Physical Quantities, Reference Book [in Russian], Énergoatomizdat, Moscow (1991).
S. I. Novikova, Thermal Expansion of Solids [in Russian], Nauka, Moscow (1974).
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).
V. F. Kuropatenko, “Equation of state in mathematical models of mechanics and physics,” Mat. Model., 4, No. 12, 112–136 (1992).
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).
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).
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).
M. V. Zhernokletov (ed.), Methods of Studying Material Properties under Intense Dynamic Loads [in Russian], Russian Federal Nuclear Center-Inst. Experimental Physics, Sarov (2005).
R. F. Trunin and G. V. Simakov, “Studying shock compressibility and isentropic expansion of zinc,” Mat. Model., 5, No. 8, 108–117 (1993).
R. G. McQueen and S. P. Marsh, “Equation of state for nineteen metallic elements,” J. Appl. Phys., 31, 1253–1269 (1960).
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).
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).
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).
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).
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).
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).
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).
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).
M. van Thiel (ed.), “Compendium of Shock Wave Data,” Report No. UCRL-50108, Lawrence Livermore Laboratory, Livermore (1977).
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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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DOI: https://doi.org/10.1134/S001050821106013X