Extended Thermodynamics of Rarefied Polyatomic Gases: 15-Field Theory Incorporating Relaxation Processes of Molecular Rotation and Vibration

Takashi Arima; Tommaso Ruggeri; Masaru Sugiyama

doi:10.3390/e20040301

Extended Thermodynamics of Rarefied Polyatomic Gases: 15-Field Theory Incorporating Relaxation Processes of Molecular Rotation and Vibration

Entropy (Basel). 2018 Apr 20;20(4):301. doi: 10.3390/e20040301.

Authors

Takashi Arima¹, Tommaso Ruggeri², Masaru Sugiyama³

Affiliations

¹ Department of Mechanical Engineering, Faculty of Engineering, Kanagawa University, Yokohama 221-8686, Japan.
² Alma Mater Research Center on Applied Mathematics (AM2), Department of Mathematics, University of Bologna, Bologna 40123-I, Italy.
³ Graduate School of Engineering, Nagoya Institute of Technology, Nagoya 466-8555, Japan.

Abstract

After summarizing the present status of Rational Extended Thermodynamics (RET) of gases, which is an endeavor to generalize the Navier-Stokes and Fourier (NSF) theory of viscous heat-conducting fluids, we develop the molecular RET theory of rarefied polyatomic gases with 15 independent fields. The theory is justified, at mesoscopic level, by a generalized Boltzmann equation in which the distribution function depends on two internal variables that take into account the energy exchange among the different molecular modes of a gas, that is, translational, rotational, and vibrational modes. By adopting the generalized Bhatnagar, Gross and Krook (BGK)-type collision term, we derive explicitly the closed system of field equations with the use of the Maximum Entropy Principle (MEP). The NSF theory is derived from the RET theory as a limiting case of small relaxation times via the Maxwellian iteration. The relaxation times introduced in the theory are shown to be related to the shear and bulk viscosities and heat conductivity.

Keywords: extended thermodynamics; generalization of Navier–Stokes and Fourier theory; molecular rotation and vibration; rarefied polyatomic gas; relaxation process.