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Entropy Conditions Involved in the Nonlinear Coupled Constitutive Method for Solving Continuum and Rarefied Gas Flows

by Ke Tang 1 and Hong Xiao 1,2,3,*
1
School of Power and Energy, Northwestern Polytechnical University, Xi’an 710072, China
2
Department of Engineering, University of Cambridge, Cambridge CB2 1PZ, UK
3
Department of Aerospace and Software Engineering, Gyeongsang National University, Jinju, Gyeongnam 52828, Korea
*
Author to whom correspondence should be addressed.
Entropy 2017, 19(12), 683; https://doi.org/10.3390/e19120683
Received: 5 September 2017 / Revised: 19 November 2017 / Accepted: 8 December 2017 / Published: 12 December 2017
The numerical study of continuum-rarefied gas flows is of considerable interest because it can provide fundamental knowledge regarding flow physics. Recently, the nonlinear coupled constitutive method (NCCM) has been derived from the Boltzmann equation and implemented to investigate continuum-rarefied gas flows. In this study, we first report the important and detailed issues in the use of the H theorem and positive entropy generation in the NCCM. Importantly, the unified nonlinear dissipation model and its relationships to the Rayleigh–Onsager function were demonstrated in the treatment of the collision term of the Boltzmann equation. In addition, we compare the Grad moment method, the Burnett equation, and the NCCM. Next, differences between the NCCM equations and the Navier–Stokes equations are explained in detail. For validation, numerical studies of rarefied and continuum gas flows were conducted. These studies include rarefied and/or continuum gas flows around a two-dimensional (2D) cavity, a 2D airfoil, a 2D cylinder, and a three-dimensional space shuttle. It was observed that the present results of the NCCM are in good agreement with those of the Direct Simulation Monte Carlo (DSMC) method in rarefied cases and are in good agreement with those of the Navier–Stokes equations in continuum cases. Finally, this study can be regarded as a theoretical basis of the NCCM for the development of a unified framework for solving continuum-rarefied gas flows. View Full-Text
Keywords: nonlinear coupled constitutive method; continuum-rarefied gas flows; positive entropy generation; Boltzmann equation nonlinear coupled constitutive method; continuum-rarefied gas flows; positive entropy generation; Boltzmann equation
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Tang, K.; Xiao, H. Entropy Conditions Involved in the Nonlinear Coupled Constitutive Method for Solving Continuum and Rarefied Gas Flows. Entropy 2017, 19, 683.

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