An analysis of the Burnett equations based on the second law of thermodynamics

Comeaux, Keith; Chapman, Dean R.; Ma, Kaixue; Cormack, Robert A.

doi:10.2514/6.1995-415

Cited by 53 publications

(45 citation statements)

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“…It is widely known that, when conducting a Chapman-Enskog type of expansion in K n on the Boltzmann kinetic equation without any spatial diffusion modification, the second order hydrodynamic model beyond that of Navier-Stokes-Fourier, namely the Burnett equations, violates many conventional mechanical and thermodynamical properties [14][15][16][17]. We note that the volume-mass diffusion contributions in our hydrodynamic set of equations (for example, in the momentum equation 34b) are also of Burnett order.…”

Section: Discussionmentioning

confidence: 99%

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Analysis of the thermomechanical inconsistency of some extended hydrodynamic models at high Knudsen number

Dadzie

Reese

2012

Phys. Rev. E

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This version is available at https://strathprints.strath.ac.uk/39217/ Strathprints is designed to allow users to access the research output of the University of Strathclyde. Unless otherwise explicitly stated on the manuscript, Copyright © and Moral Rights for the papers on this site are retained by the individual authors and/or other copyright owners. Please check the manuscript for details of any other licences that may have been applied. You may not engage in further distribution of the material for any profitmaking activities or any commercial gain. You may freely distribute both the url (https://strathprints.strath.ac.uk/) and the content of this paper for research or private study, educational, or not-for-profit purposes without prior permission or charge.Any correspondence concerning this service should be sent to the The collision integral dominates in the small local Knudsen number regime, which is associated with the exact traditional continuum limit. We find a sub-domain of the continuum range which the conventional Knudsen number classification does not account for appropriately. In this sub-domain, it is possible to obtain a fully mechanically-consistent volume (or mass) diffusion model that satisfies the second law of thermodynamics on the grounds of extended non-local-equilibrium thermodynamics.

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Section: Discussionmentioning

confidence: 99%

“…Typical examples include the class of high order hydrodynamics models obtained as terms beyond Navier-Stokes-Fourier order when approximating the original Boltzmann kinetic equation. [14][15][16][17];…”

Section: Introductionmentioning

confidence: 99%

Analysis of the thermomechanical inconsistency of some extended hydrodynamic models at high Knudsen number

Dadzie

Reese

2012

Phys. Rev. E

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“…As Navier-Stokes-Fourier's model becomes invalid, Burnett and super-Burnett models are thought to improve flow predictions. Instead, however, these models become subject to mechanical, thermodynamic, and instability problems (Woods 1983;Comeaux et al 1995;Karlin & Gorban 2002;Bobylev 2006).…”

Section: Introductionmentioning

confidence: 99%

A thermo-mechanically consistent Burnett regime continuum flow equation without Chapman–Enskog expansion

Dadzie

2013

J. Fluid Mech.

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Chapman-Enskog expansion is the orthodox approach to derive continuum flow models from Boltzmann's kinetic equation for dilute gases. Beyond the Navier-Stokes-Fourier order, these models known as Burnett hydrodynamic-regime equations violate a number of fundamental mechanical and thermodynamic principles in their original forms. This has generated a widely investigated problem in the kinetic theory of gases. In this short article, we derive a Burnett hydrodynamic-regime continuum model that is systematically consistent with all known mechanical and thermodynamic principles without using any series' expansion. Close comparison with the conventional Burnett hydrodynamic set of equations is considered and their linear stabilities around an equilibrium point under small perturbations are presented.

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“…To fulfill the abovementioned rules and essential construction of the thermodynamic theory of irreversible processes, the definition of the distribution function is expressed via Eu Methods [17] as follows:…”

Section: Treatment Of the Distribution Function In The Boltzmann Equamentioning

confidence: 99%

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

Tang

Hong

2017

Entropy

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Abstract: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.

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An analysis of the Burnett equations based on the second law of thermodynamics

Cited by 53 publications

References 4 publications

Analysis of the thermomechanical inconsistency of some extended hydrodynamic models at high Knudsen number

Analysis of the thermomechanical inconsistency of some extended hydrodynamic models at high Knudsen number

A thermo-mechanically consistent Burnett regime continuum flow equation without Chapman–Enskog expansion

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

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