A macroscopic approach to model rarefied polyatomic gas behavior

Description

A high-order macroscopic model for the accurate description of rarefied polyatomic gas flows is introduced based on a simplified kinetic equation. The different energy exchange processes are accounted for with a two term collision model. 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. 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 H-theorem. At the first order, a modification of the Navier-Stokes-Fourier (NSF) equations is obtained, which shows considerable extended range of validity in comparison to the classical NSF equations in modeling sound waves. At third order of accuracy, a set of 19 regularized PDEs (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. Attenuation and speed of linear waves are studied as the first application of the many sets of equations. For frequencies were the internal degrees of freedom are effectively frozen, the equations reproduce the behavior of monatomic gases. Thereafter, boundary conditions for the proposed macroscopic model are introduced. The unsteady heat conduction of a gas at rest and steady Couette flow are studied numerically and analytically as examples of boundary value problems. 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 Navier Stokes Fourier equations fails to accurately capture the gas behavior and should be replaced by a higher order set of equations. / Graduate / 0346, 0791, 0548, 0759 / [e-mail]

Links & Downloads

1. http://hdl.handle.net/1828/7258
2. B. Rahimi and H. Struchtrup, “Kinetic model and moment method for polyatomic gases,” AIP Conference Proceedings, vol. 1628, no. 1, 2014.
3. B. Rahimi and H. Struchtrup, “Capturing non-equilibrium phenomena in rarefied polyatomic gases: A high-order macroscopic model,” Physics of Fluids, vol. 26, no. 5, 2014.
4. B. Rahimi and H. Struchtrup, “Refined navier-stokes-fourier equations for rarefied polyatomic gases,” in ASME 2014 12th International Conference on Nanochannels, Microchannels, and Minichannels collocated with the ASME 2014 4th Joint US-European Fluids Engineering Division Summer Meeting, pp. V001T01A001–V001T01A001, American Society of Mechanical Engineers, 2014
5. H. Niazmand and B. Rahimi, “Mixed convective rarefied flows with symmetric and asymmetric heated walls,” Computational Thermal Sciences, vol. 5, no. 4, pp. 261–272, 2013.
6. B. Rahimi and H. Niazmand, “Effects of high order slip/jump, thermal creep and variable thermo-physical properties on natural convection in microchannels with constant wall heat fluxes,” Heat Transfer Engineering, vol. 35, no. 18, pp. 1528– 1538, 2014.
7. H. Niazmand and B. Rahimi, “Mixed convective slip flows in a vertical parallel plate microchannel with symmetric and asymmetric wall heat fluxes,” Transactions of the Canadian Society for Mechanical Engineering, vol. 36, no. 3, pp. 207– 218, 2012.

Tags

Rarefied gases

Kinetic theory

Polyatomic gases

Mathematical modeling

Fluid dynamics

CFD

Additional Fields

Identifer	oai:union.ndltd.org:uvic.ca/oai:dspace.library.uvic.ca:1828/7258
Date	02 May 2016
Creators	Rahimi, Behnam
Contributors	Struchtrup, Henning
Source Sets	University of Victoria
Language	English, English
Detected Language	English
Type	Thesis
Rights	Available to the World Wide Web, http://creativecommons.org/licenses/by/2.5/ca/