×

Extended thermodynamics of dense gases in the presence of dynamic pressure. (English) Zbl 1327.76116

Summary: Extended thermodynamics (ET) developed up to now fails when a gas is very dense and is composed of molecules with small internal degrees of freedom because the condition of convexity (stability) is violated. The aim of this paper is to explore a possible approach to construct an ET theory that is valid for any dense gas with the condition that it reduces to the usual ET theory when a gas is sufficiently rarefied. We restrict our study, for simplicity, within the simplest case in which the dissipation is only due to the dynamic pressure. Therefore the basic system of equations is the simplest variant of the Euler system, that is, the system composed of the equations for the conservation laws and an equation for the dynamic pressure (6-field theory).

MSC:

76N15 Gas dynamics (general theory)
82C35 Irreversible thermodynamics, including Onsager-Machlup theory
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Müller, I., Ruggeri, T.: Rational Extended Thermodynamics, 2nd edn. Springer, New York (1998) · Zbl 0895.00005 · doi:10.1007/978-1-4612-2210-1
[2] Ruggeri, T., Sugiyama, M.: Rational Extended Thermodynamics Beyond the Monatomic Gas. Springer, New York (2015) · Zbl 1330.76003 · doi:10.1007/978-3-319-13341-6
[3] Liu, I.-S., Müller, I.: Extended thermodynamics of classical and degenerate ideal gases. Arch. Rational Mech. Anal. 83(4), 285 (1983) · Zbl 0554.76014 · doi:10.1007/BF00963838
[4] Liu, I.-S., Müller, I., Ruggeri, T.: Relativistic thermodynamics of gases. Ann. Phys. 169, 191 (1986)
[5] Engholm Jr, H., Kremer, G.M.: Thermodynamics of a diatomic gas with rotational and vibrational degrees of freedom. Int. J. Eng. Sci. 32(8), 1241 (1984) · Zbl 0899.76059 · doi:10.1016/0020-7225(94)90035-3
[6] Kremer, G.M.: Extended thermodynamics and statistical mechanics of a polyatomic ideal gas. J. Non-Equilib. Thermodyn. 14, 363 (1989) · Zbl 0677.76076
[7] Kremer, G.M.: Extended thermodynamics of molecular ideal gases. Contin. Mech. Thermodyn. 1, 21 (1989) · doi:10.1007/BF01125884
[8] Liu, I.-S.: Extended thermodynamics of fluids and virial equations of state. Arch. Rational Mech. Anal. 88, 1 (1985) · Zbl 0584.76002
[9] Kremer, G.M.: Extended thermodynamics of non-ideal gases. Physica 144A, 156 (1987) · doi:10.1016/0378-4371(87)90150-6
[10] Liu, I.-S., Kremer, G.M.: Hyperbolic system of field equations for viscous fluids. Math. Appl. Comput. 9(2), 123 (1990) · Zbl 0713.76038
[11] Liu, I.-S., Salvador, J.A.: Hyperbolic system for viscous fluids and simulation of shock tube flows. Contin. Mech. Thermodyn. 2, 179 (1990) · Zbl 0825.76130 · doi:10.1007/BF01129596
[12] Kremer, GM; Sieniutycz, S. (ed.); Salamon, P. (ed.), On extended thermodynamics of ideal and real gases, 140 (1992), New York
[13] Carrisi, M.C., Pennisi, S.: Some open problems in non-linear extended thermodynamics and their possible solutions. Ric. Mat. 60, 45 (2012) · Zbl 1311.80004 · doi:10.1007/s11587-010-0095-4
[14] Arima, T., Taniguchi, S., Ruggeri, T., Sugiyama, M.: Extended thermodynamics of dense gases. Contin. Mech. Thermodyn. 24, 271 (2012) · Zbl 1318.80001 · doi:10.1007/s00161-011-0213-x
[15] Arima, T., Sugiyama, M.: Characteristic features of extended thermodynamics of dense gases. Atti Accad. Pelorit. Pericol. 91(Suppl. No. 1), A1 (2013) · Zbl 1419.82046
[16] Ruggeri, T., Sugiyama, M.: Recent developments in extended thermodynamics of dense and rarefied polyatomic gases. Acta Appl. Math. 132, 527 (2014) · Zbl 1304.80001 · doi:10.1007/s10440-014-9923-y
[17] Arima, T., Taniguchi, S., Ruggeri, T., Sugiyama, M.: Monatomic rarefied gas as a singular limit of polyatomic gas in extended thermodynamics. Phys. Lett. A 377, 2136 (2013) · Zbl 1297.76143 · doi:10.1016/j.physleta.2013.06.035
[18] Pavić, M., Ruggeri, T., Simić, S.: Maximum entropy principle for polyatomic gases. Physica A 392, 1302 (2013) · doi:10.1016/j.physa.2012.12.006
[19] Arima, T., Mentrelli, A., Ruggeri, T.: Molecular extended thermodynamics of rarefied polyatomic gases and wave velocities for increasing number of moments. Ann. Phys. 345, 111 (2014) · Zbl 1343.76063 · doi:10.1016/j.aop.2014.03.011
[20] Arima, T., Mentrelli, A., Ruggeri, T.: Extended thermodynamics of rarefied polyatomic gases and characteristic velocities. Rend. Lincei Mat. Appl. 25, 275 (2014) · Zbl 1304.82059 · doi:10.1007/s12210-014-0319-8
[21] Arima, T., Taniguchi, S., Ruggeri, T., Sugiyama, M.: Extended thermodynamics of real gases with dynamic pressure: an extension of Meixner’s theory. Phys. Lett. A 376, 2799 (2012) · Zbl 1396.80001 · doi:10.1016/j.physleta.2012.08.030
[22] Arima, T., Taniguchi, S., Ruggeri, T., Sugiyama, M.: Dispersion relation for sound in rarefied polyatomic gases based on extended thermodynamics. Contin. Mech. Thermodyn. 25, 727 (2013) · Zbl 1341.80004 · doi:10.1007/s00161-012-0271-8
[23] Arima, T., Taniguchi, S., Sugiyama, M.: Light scattering in rarefied polyatomic gases based on extended thermodynamics. In: Proceedings of the 34th Symposium on Ultrasonic Electronics, vol. 15 (2013) · Zbl 0584.76002
[24] Taniguchi, S., Arima, T., Ruggeri, T., Sugiyama, M.: Thermodynamic theory of the shock wave structure in a rarefied polyatomic gas: beyond the Bethe-Teller theory. Phys. Rev. E. 89, 013025 (2014) · doi:10.1103/PhysRevE.89.013025
[25] Taniguchi, S., Arima, T., Ruggeri, T., Sugiyama, M.: Effect of the dynamic pressure on the shock wave structure in a rarefied polyatomic gas. Phys. Fluids 26, 016103 (2014) · doi:10.1063/1.4861368
[26] Arima, T., Barbera, E., Brini, F., Sugiyama, M.: The role of the dynamic pressure in stationary heat conduction of a rarefied polyatomic gas. Phys. Lett. A 378, 2695 (2014) · Zbl 1298.76149 · doi:10.1016/j.physleta.2014.07.031
[27] Carrisi, M.C., Pennisi, S.: An 18 moments model for dense gases, entropy and Galilean relativity principles without expansions. Entropy 17, 214-230 (2015) · doi:10.3390/e17010214
[28] Arima, T., Ruggeri, T., Sugiyama, M., Taniguchi, S.: On the six-field model of fluids based on extended thermodynamics. Meccanica 49, 2181 (2014) · Zbl 1299.76007 · doi:10.1007/s11012-014-9886-0
[29] Arima, T., Ruggeri, T., Sugiyama, M., Taniguchi, S.: Non-linear extended thermodynamics of real gases with 6 fields. Int. J. Non-Linear Mech. 72, 6 (2015) · Zbl 1318.80001 · doi:10.1016/j.ijnonlinmec.2015.02.005
[30] Ruggeri, T.: Galilean invariance and entropy principle for systems of balance laws. The structure of the extended thermodynamics. Contin. Mech. Thermodyn. 1, 3 (1989) · Zbl 0759.35039 · doi:10.1007/BF01125883
[31] Ikenberry, E., Truesdell, C.: On the pressure and the flux of energy in a gas according to Maxwell’s kinetic theory. J. Rational Mech. Anal. 5, 1 (1956) · Zbl 0070.23504
[32] Münster, A.: Statistical Thermodynamics, vol. 2. Springer, Berlin (1974) · Zbl 0177.57302
[33] Barker, J.A., Henderson, D.: What is “liquid”? Understanding the states of matter. Rev. Mod. Phys. 48, 587-671 (1976) · doi:10.1103/RevModPhys.48.587
[34] Hansen, J.P., McDonald, J.R.: Theory of Simple Liquids. Academic Press, London (1986) · Zbl 0756.00004
[35] Taniguchi, S., Mentrelli, A., Zhao, N., Ruggeri, T., Sugiyama, M.: Shock-induced phase transition in systems of hard spheres with internal degrees of freedom. Phys. Rev. E 81, 066307 (2010) · doi:10.1103/PhysRevE.81.066307
[36] Carnahan, N.F., Starling, K.E.: Equation of state for nonattracting rigid spheres. J. Chem. Phys. 51, 635 (1969) · doi:10.1063/1.1672048
[37] Ruggeri, T.: Galilean invariance and entropy principle for systems of balance laws. Contin. Mech. Thermodyn. 1, 3 (1989) · Zbl 0759.35039 · doi:10.1007/BF01125883
[38] Liu, I.-S.: Method of Lagrange multipliers for exploitation of the entropy principle. Arch. Rational Mech. Anal. 46, 131 (1972) · Zbl 0252.76003
[39] Pennisi, S., Ruggeri, T.: A new method to exploit the entropy prnciple and Galilean invariance in the macroscopic approach of extended thermodynamics. Richerche Mat. 55, 159-179 (2006) · Zbl 1378.74006 · doi:10.1007/s11587-006-0019-5
[40] Meixner, J.: Absorption und Dispersion des Schalles in Gasen mit chemisch Reagierenden und Anregbaren komponenten. I. Teil. Ann. Phys. 43, 470 (1943) · doi:10.1002/andp.19434350608
[41] Meixner, J.: Allgemeine Theorie der Schallabsorption in Gasen und Flussigkeiten unter Berucksichtigung der Transporterscheinungen. Acoustica 2, 101 (1952)
[42] de Groot, S.R., Mazur, P.: Non-Equilibrium Thermodynamics. Dover, New York (1984) · Zbl 1375.82004
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.