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2015 | OriginalPaper | Chapter

11. Non-linear ET6 and the Role of the Dynamic Pressure: Phenomenological Approach

Authors : Tommaso Ruggeri, Masaru Sugiyama

Published in: Rational Extended Thermodynamics beyond the Monatomic Gas

Publisher: Springer International Publishing

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Abstract

In this chapter, we present ET of real gases with six independent fields, i.e., the mass density, the velocity, the temperature and the dynamic pressure, without adopting the near-equilibrium approximation. We prove its compatibility with the universal principles (the entropy principle, the Galilean invariance and the stability), and obtain the symmetric hyperbolic system with respect to the main field. The correspondence between the ET 6-field (ET6) theory and the Meixner theory of relaxation processes is discussed. The internal variable and the nonequilibrium temperature in the Meixner theory are expressed in terms of the quantities of the ET6 theory, in particular, the dynamic pressure. As an example, we present the case of rarefied polyatomic gases and study the monatomic-gas limit where the system converges to the Euler system of a perfect fluid.

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previous chapter Molecular ET Theory of Rarefied Polyatomic Gas
next chapter Molecular Non-linear ET6 for Rarefied Polyatomic Gas
Literature
1.
T. Arima, S. Taniguchi, T. Ruggeri, M. Sugiyama, Nonlinear extended thermodynamics of real gases with 6 fields. Int. J. Non-Linear Mech. 72, 6 (2015)CrossRef
2.
T. Arima, S. Taniguchi, T. Ruggeri, M. Sugiyama, Extended thermodynamics of real gases with dynamic pressure: an extension of Meixner’s theory. Phys. Lett. A 376, 2799 (2012)MathSciNetCrossRef
3.
T. Arima, T. Ruggeri, M. Sugiyama, S. Taniguchi, On the six-field model of fluids based on extended thermodynamics. Meccanica 49, 2181 (2014)MathSciNetCrossRef
4.
S. Chapman, T.G. Cowling, The Mathematical Theory of Non-uniform Gases (Cambridge University Press, Cambridge, 1991)MATH
5.
T. Arima, S. Taniguchi, T. Ruggeri, M. Sugiyama, Dispersion relation for sound in rarefied polyatomic gases based on extended thermodynamics. Contin. Mech. Thermodyn. 25, 727 (2013)MathSciNetCrossRef
6.
S. Taniguchi, T. Arima, T. Ruggeri, M. Sugiyama, Thermodynamic theory of the shock wave structure in a rarefied polyatomic gas: beyond the Bethe-Teller theory. Phys. Rev. E 89, 013025 (2014)CrossRef
7.
T. Arima, S. Taniguchi, T. Ruggeri, M. Sugiyama, Monatomic rarefied gas as a singular limit of polyatomic gas in extended thermodynamics. Phys. Lett. A 377, 2136 (2013)MathSciNetCrossRefMATH
8.
S.K. Godunov, An interesting class of quasilinear systems. Sov. Math. 2, 947 (1961)MATH
9.
S.R. de Groot, P. Mazur, Non-equilibrium Thermodynamics (North-Holland, Amsterdam, 1963)
10.
B.D. Coleman, M.E. Gurtin, Thermodynamics with internal state variables. J. Chem. Phys. 47, 597 (1967)CrossRef
11.
G.A. Maugin, W. Muschik, Thermodynamics with internal variables. Part I. General concepts. J. Non-Equilib. Thermodyn. 19, 217 (1994)MATH
12.
G.A. Maugin, W. Muschik, Thermodynamics with internal variables. Part II. Applications. J. Non-Equilib. Thermodyn. 19, 250 (1994)
13.
J. Meixner, Absorption und dispersion des schalles in gasen mit chemisch reagierenden und anregbaren komponenten. I. Teil. Ann. Phys. 43, 470 (1943)MathSciNet
14.
J. Meixner, Allgemeine theorie der schallabsorption in gasen und flussigkeiten unter berucksichtigung der transporterscheinungen. Acoustica 2, 101 (1952)MathSciNet
15.
P. Ván, D. Berezovski, J. Engelbrecht, Internal variables and dynamic degrees of freedom. J. Non-Equilib. Thermodyn. 33, 235 (2008)CrossRefMATH
16.
W.G. Vincenti, C.H. Kruger Jr., Introduction to Physical Gas Dynamics (Wiley, New York/London/Sydney, 1965)
17.
M.A. Leontovich, Introduction to Thermodynamics. Statistical Physics (Nauka, Moscow, 1983)
18.
D.N. Zubarev, Nonequilibrium Statistical Thermodynamics (Consultants Bureau, New York/London, 1974)
19.
N. Pottier, Nonequilibrium Statistical Physics (Oxford University Press, Oxford, 2010)MATH
20.
H. Grad, On the kinetic theory of rarefied gases. Commun. Pure Appl. Math. 2(4), 331 (1949)
21.
J. Casas-Vázquez, D. Jou, Nonequilibrium temperature versus local-equilibrium temperature. Phys. Rev. E 49, 1040 (1994)CrossRef
22.
J. Casas-Vázquez, D. Jou, Temperature in non-equilibrium states: a review of open problems and current proposals. Rep. Prog. Phys. 66, 1937 (2003)CrossRef
23.
E. Barbera, I. Müller, M. Sugiyama, On the temperature of a rarefied gas in non-equilibrium. Meccanica 34, 103 (1999)CrossRefMATH
24.
R.G. Gordon, W. Klemperer, J.I. Steinfeld, Vibrational and rotational relaxation. Ann. Rev. Phys. Chem. 19, 215 (1968)CrossRef
25.
P. Secchi, Existence theorems for compressible viscous fluid having zero shear viscosity. Rend. Sem. Padova 70, 73 (1983)
26.
V. Shelukhin, Vanishing shear viscosity in a free-boundary problem for the equations of compressible fluids. J. Differ. Equ. 167, 73 (2000)MathSciNetCrossRefMATH
27.
H. Frid, V. Shelukhin, Vanishing shear viscosity in the equations of compressible fluids for the flows with the cylinder symmetry. SIAM J. Math. Anal. 31, 1144 (2000)MathSciNetCrossRefMATH
28.
T. Ruggeri, D. Serre, Stability of constant equilibrium state for dissipative balance laws system with a convex entropy. Quart. Appl. Math. 62, 163 (2004)MathSciNetMATH
29.
T. Ruggeri, Galilean invariance and entropy principle for systems of balance laws. The structure of the extended thermodynamics. Contin. Mech. Thermodyn. 1, 3 (1989)MathSciNetCrossRefMATH
30.
V.A. Cimmelli, D. Jou, T. Ruggeri, P. Ván, Entropy principle and recent results in non-equilibrium theories. Entropy 16, 1756 (2014)MathSciNetCrossRef
31.
T. Ruggeri, M. Sugiyama, Recent developments in extended thermodynamics of dense and rarefied polyatomic gases. Acta Appl. Math. 132, 527 (2014)MathSciNetCrossRefMATH
32.
T. Arima, A. Mentrelli, T. Ruggeri, Molecular extended thermodynamics of rarefied polyatomic gases and wave velocities for increasing number of moments. Ann. Phys. 345, 111 (2014)MathSciNetCrossRef
33.
E. Nagnibeda, E. Kustova, Non-equilibrium Reacting Gas Flow (Springer, Berlin/Heidelberg, 2009)CrossRef
34.
S. Taniguchi, T. Arima, T. Ruggeri, M. Sugiyama, Effect of dynamic pressure on the shock wave structure in a rarefied polyatomic gas. Phys. Fluids 26, 016103 (2014)CrossRef
35.
Y.B. Zel’dovich, Y.P. Raizer, Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena (Dover Publications, New York, 2002)
Metadata
Title
Non-linear ET6 and the Role of the Dynamic Pressure: Phenomenological Approach
Authors
Tommaso Ruggeri
Masaru Sugiyama
Copyright Year
2015
Book
Rational Extended Thermodynamics beyond the Monatomic Gas

Print ISBN: 978-3-319-13340-9

Electronic ISBN: 978-3-319-13341-6

Copyright Year: 2015

DOI
https://doi.org/10.1007/978-3-319-13341-6_11

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