Macroscopic and kinetic modelling of rarefied polyatomic gases
Date
2016
Authors
Rahimi, Behnam
Struchtrup, Henning
Journal Title
Journal ISSN
Volume Title
Publisher
Journal of Fluid Mechanics
Abstract
A kinetic model and corresponding high-order macroscopic model for the accurate
description of rarefied polyatomic gas flows are introduced. The different energy
exchange processes are accounted for with a two term collision model. The proposed
kinetic model, which is an extension of the S-model, predicts correct relaxation of
higher moments and delivers the accurate Prandtl (Pr) number. Also, the model has
a proven linear H-theorem. The order of magnitude method is applied to the primary
moment equations to acquire the optimized moment definitions and the final scaled set
of Grad’s 36 moment equations for polyatomic gases. At the first order, a modification
of the Navier–Stokes–Fourier (NSF) equations is obtained. At third order of accuracy,
a set of 19 regularized partial differential equations (R19) is obtained. Furthermore,
the terms associated with the internal degrees of freedom yield various intermediate
orders of accuracy, a total of 13 different orders. Thereafter, boundary conditions for
the proposed macroscopic model are introduced. The unsteady heat conduction of a
gas at rest is studied numerically and analytically as an example of a boundary value
problem. The results for different gases are given and effects of Knudsen numbers,
degrees of freedom, accommodation coefficients and temperature-dependent properties
are investigated. For some cases, the higher-order effects are very dominant and the
widely used first-order set of the NSF equations fails to accurately capture the gas
behaviour and should be replaced by the proposed higher-order set of equations.
Description
Keywords
Citation
Rahimi, B., & Struchtrup, H. (2016). Macroscopic and kinetic modelling of rarefied polyatomic gases. J. Fluid Mechanics, Vol. 806, pp. 437-505.