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日本航空宇宙学会関西支部分科会「流体力学における現代的アプローチ」のご案内

日時 2013年03月08日
15時30分 から 17時30分 まで
場所 桂キャンパスCクラスタ総合研究棟III(C3棟)1階 講義室5
連絡先
機械理工学専攻 高田准教授
URL http://www.mfd.me.kyoto-u.ac.jp/jsass23-25.htm

会場案内: 京都大学 桂キャンパスCクラスタ総合研究棟III(C3棟)1階 講義室5

Extended Thermodynamics of Dense Gases

Part I: Macroscopic Approach

Prof. Masaru Sugiyama
(Department of Mechanical Engineering, Nagoya Institute of Technology, Japan)

Part II: Maximum Entropy Principle for Rarefied Polyatomic Gases

Prof. Tommaso Ruggeri
(Faculty of Engineering, University of Bologna, Italy)

 

要旨

The kinetic theory and Extended Thermodynamics (ET) are important theories for rarefied non-equilibrium gases. Nevertheless the weak point is that the range is limited mainly to monatomic gases. In this talk we want to present recent new approach to deduce hyperbolic system for dense gases not necessarily monatomic.  In the first part of the talk we study extended thermodynamics of dense gases by adopting the system of field equations with a different hierarchy structure to that adopted in the previous works. It is the theory of 14 fields of mass density, velocity, temperature, viscous stress, dynamic pressure and heat flux. As a result, all the constitutive equations can be determined explicitly by the caloric and thermal equations of state as in the case of monatomic gases. It is shown that the rarefied-gas limit of the theory is consistent with the kinetic theory of gases.  In the second part, we limit the result to the physically interesting case of rarefied polyatomic gases and we show a perfect coincidence between ET and the procedure of Maximum Entropy Principle. The main difference with respect to usual procedure is the existence of two hierarchies of macroscopic equations for moments of suitable distribution function, in which the internal energy of a molecule is taken into account.

References:
1) I. Mueller and T. Ruggeri: Rational Extended Thermodynamics, 2nded., Springer Tracts in Natural Philosophy 37, (1998) Springer-Verlag (New York).
2) G. Boillat and T. Ruggeri: Moment equations in the kinetic theory of gases and wave velocities, Continuum Mech. Thermodyn. 9 (1997) 205-212.
3) T. Arima, S. Taniguchi, T. Ruggeri and M. Sugiyama: Extended thermodynamics of dense gases, Continuum Mech. Thermodyn. 24 (2012) 271-292.
4) T. Arima, S. Taniguchi, T. Ruggeri and M. Sugiyama: Extended thermodynamics of real gases with dynamic pressure: An extension of Meixner theory, Phys. Lett. A376 (2012) 2799-2803.
5) T. Arima, S. Taniguchi, T. Ruggeri and M. Sugiyama: Dispersion relation for sound in rarefied polyatomic gases based on extended thermodynamics, Continuum Mech. Thermodyn. (2012) DOI 10.1007/s00161-012-0271-8.
6) M. Pavic, T. Ruggeri and S. Simic: Maximum entropy principle for rarefied polyatomic gases, Physica A (2012) (to be published).