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Thermodynamics of Non-Equilibrium Gas Flows
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Thermodynamics of Non-Equilibrium Gas Flows

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Thermodynamics".

Deadline for manuscript submissions: closed (31 July 2019) | Viewed by 21369

Special Issue Editor

Dr. Xiaojun Gu

E-Mail
Guest Editor
Daresbury Laboratory, Scientific Computing Department, Science and Technology Facilities Council (STFC), Warrington WA4 4AD, UK
Interests: combustion; turbulence; rarefied gas dynamics; kinetic theory; extended thermodynamics

Special Issue Information

Dear Colleagues,

Non-equilibrium gas flows exist in many industrial applications and scientific research facilities, including mass spectrometry, low-pressure environments, vacuum pumps, micro-electro-mechanical systems (MEMS), high-altitude vehicles, and porous media. A comprehensive understanding of the thermodynamics of non-equilibrium gas flows is essential for the design and operation of application systems, which are beyond the capabilities of conventional thermodynamics. These flows in engineering applications cover a wide range of time and length scales and represent a fundamental modelling and simulation challenge.

The thermodynamics of non-equilibrium gas flows can be described from either microscopic or macroscopic points of view. Both approaches have their advantages and limitations. Significant progress has been made in terms of physical and mathematical models, numerical algorithms, computational implementations and experimental techniques, which improve our ability to explain the non-equilibrium phenomena to enrich the knowledge of non-equilibrium thermodynamics. Multiscale approaches have been developed to solve the real applications accurately and effectively. 

This Special Issue aims at collecting original papers on theoretical, computational and experimental studies of non-equilibrium, low- and high-speed gas flows with the goal of providing readers with an overview of the current research conducted in this field and the possible applications.

Dr. Xiaojun Gu
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • non-equilibrium
  • kinetic scheme
  • moment method
  • extended thermodynamics
  • rarefied gas dynamics
  • direct simulation Monte Carlo (DSMC)
  • Boltzmann equation
  • spacecraft reentry
  • MEMS
  • vacuum

Published Papers (6 papers)

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Research

19 pages, 4249 KiB  
Article
Modelling Thermally Induced Non-Equilibrium Gas Flows by Coupling Kinetic and Extended Thermodynamic Methods
by Weiqi Yang, Xiao-Jun Gu, David R. Emerson, Yonghao Zhang and Shuo Tang
Entropy 2019, 21(8), 816; https://doi.org/10.3390/e21080816 - 20 Aug 2019
Cited by 6 | Viewed by 2860
Abstract
Thermally induced non-equilibrium gas flows have been simulated in the present study by coupling kinetic and extended thermodynamic methods. Three different types of thermally induced gas flows, including temperature-discontinuity- and temperature-gradient-induced flows and radiometric flow, have been explored in the transition regime. The [...] Read more.
Thermally induced non-equilibrium gas flows have been simulated in the present study by coupling kinetic and extended thermodynamic methods. Three different types of thermally induced gas flows, including temperature-discontinuity- and temperature-gradient-induced flows and radiometric flow, have been explored in the transition regime. The temperature-discontinuity-induced flow case has shown that as the Knudsen number increases, the regularised 26 (R26) moment equation system will gradually loss its accuracy and validation. A coupling macro- and microscopic approach is employed to overcome these problems. The R26 moment equations are used at the macroscopic level for the bulk flow region, while the kinetic equation associated with the discrete velocity method (DVM) is applied to describe the gas close to the wall at the microscopic level, which yields a hybrid DVM/R26 approach. The numerical results have shown that the hybrid DVM/R26 method can be faithfully used for the thermally induced non-equilibrium flows. The proposed scheme not only improves the accuracy of the results in comparison with the R26 equations, but also extends their capability with a wider range of Knudsen numbers. In addition, the hybrid scheme is able to reduce the computational memory and time cost compared to the DVM. Full article
(This article belongs to the Special Issue Thermodynamics of Non-Equilibrium Gas Flows)
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17 pages, 734 KiB  
Article
Mesoscopic Simulation of the Two-Component System of Coupled Sine-Gordon Equations with Lattice Boltzmann Method
by Demei Li, Huilin Lai and Chuandong Lin
Entropy 2019, 21(6), 542; https://doi.org/10.3390/e21060542 - 28 May 2019
Cited by 8 | Viewed by 2626
Abstract
In this paper, a new lattice Boltzmann model for the two-component system of coupled sine-Gordon equations is presented by using the coupled mesoscopic Boltzmann equations. Via the Chapman-Enskog multiscale expansion, the macroscopical governing evolution system can be recovered correctly by selecting suitable discrete [...] Read more.
In this paper, a new lattice Boltzmann model for the two-component system of coupled sine-Gordon equations is presented by using the coupled mesoscopic Boltzmann equations. Via the Chapman-Enskog multiscale expansion, the macroscopical governing evolution system can be recovered correctly by selecting suitable discrete equilibrium distribution functions and the amending functions. The mesoscopic model has been validated by several related issues where analytic solutions are available. The experimental results show that the numerical results are consistent with the analytic solutions. From the mesoscopic point of view, the present approach provides a new way for studying the complex nonlinear partial differential equations arising in natural nonlinear phenomena of engineering and science. Full article
(This article belongs to the Special Issue Thermodynamics of Non-Equilibrium Gas Flows)
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20 pages, 2401 KiB  
Article
Mesoscopic Simulation of the (2 + 1)-Dimensional Wave Equation with Nonlinear Damping and Source Terms Using the Lattice Boltzmann BGK Model
by Demei Li, Huilin Lai and Baochang Shi
Entropy 2019, 21(4), 390; https://doi.org/10.3390/e21040390 - 11 Apr 2019
Cited by 8 | Viewed by 3404
Abstract
In this work, we develop a mesoscopic lattice Boltzmann Bhatnagar-Gross-Krook (BGK) model to solve (2 + 1)-dimensional wave equation with the nonlinear damping and source terms. Through the Chapman-Enskog multiscale expansion, the macroscopic governing evolution equation can be obtained accurately by choosing appropriate [...] Read more.
In this work, we develop a mesoscopic lattice Boltzmann Bhatnagar-Gross-Krook (BGK) model to solve (2 + 1)-dimensional wave equation with the nonlinear damping and source terms. Through the Chapman-Enskog multiscale expansion, the macroscopic governing evolution equation can be obtained accurately by choosing appropriate local equilibrium distribution functions. We validate the present mesoscopic model by some related issues where the exact solution is known. It turned out that the numerical solution is in very good agreement with exact one, which shows that the present mesoscopic model is pretty valid, and can be used to solve more similar nonlinear wave equations with nonlinear damping and source terms, and predict and enrich the internal mechanism of nonlinearity and complexity in nonlinear dynamic phenomenon. Full article
(This article belongs to the Special Issue Thermodynamics of Non-Equilibrium Gas Flows)
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19 pages, 3709 KiB  
Article
Lattice Boltzmann Model for Gas Flow through Tight Porous Media with Multiple Mechanisms
by Junjie Ren, Qiao Zheng, Ping Guo and Chunlan Zhao
Entropy 2019, 21(2), 133; https://doi.org/10.3390/e21020133 - 01 Feb 2019
Cited by 4 | Viewed by 3084
Abstract
In the development of tight gas reservoirs, gas flow through porous media usually takes place deep underground with multiple mechanisms, including gas slippage and stress sensitivity of permeability and porosity. However, little work has been done to simultaneously incorporate these mechanisms in the [...] Read more.
In the development of tight gas reservoirs, gas flow through porous media usually takes place deep underground with multiple mechanisms, including gas slippage and stress sensitivity of permeability and porosity. However, little work has been done to simultaneously incorporate these mechanisms in the lattice Boltzmann model for simulating gas flow through porous media. This paper presents a lattice Boltzmann model for gas flow through porous media with a consideration of these effects. The apparent permeability and porosity are calculated based on the intrinsic permeability, intrinsic porosity, permeability modulus, porosity sensitivity exponent, and pressure. Gas flow in a two-dimensional channel filled with a homogeneous porous medium is simulated to validate the present model. Simulation results reveal that gas slippage can enhance the flow rate in tight porous media, while stress sensitivity of permeability and porosity reduces the flow rate. The simulation results of gas flow in a porous medium with different mineral components show that the gas slippage and stress sensitivity of permeability and porosity not only affect the global velocity magnitude, but also have an effect on the flow field. In addition, gas flow in a porous medium with fractures is also investigated. It is found that the fractures along the pressure-gradient direction significantly enhance the total flow rate, while the fractures perpendicular to the pressure-gradient direction have little effect on the global permeability of the porous medium. For the porous medium without fractures, the gas-slippage effect is a major influence factor on the global permeability, especially under low pressure; for the porous medium with fractures, the stress-sensitivity effect plays a more important role in gas flow. Full article
(This article belongs to the Special Issue Thermodynamics of Non-Equilibrium Gas Flows)
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29 pages, 5409 KiB  
Article
Evaporation Boundary Conditions for the Linear R13 Equations Based on the Onsager Theory
by Alexander Felix Beckmann, Anirudh Singh Rana, Manuel Torrilhon and Henning Struchtrup
Entropy 2018, 20(9), 680; https://doi.org/10.3390/e20090680 - 06 Sep 2018
Cited by 12 | Viewed by 4752
Abstract
Due to the failure of the continuum hypothesis for higher Knudsen numbers, rarefied gases and microflows of gases are particularly difficult to model. Macroscopic transport equations compete with particle methods, such as the Direct Simulation Monte Carlo method (DSMC), to find accurate solutions [...] Read more.
Due to the failure of the continuum hypothesis for higher Knudsen numbers, rarefied gases and microflows of gases are particularly difficult to model. Macroscopic transport equations compete with particle methods, such as the Direct Simulation Monte Carlo method (DSMC), to find accurate solutions in the rarefied gas regime. Due to growing interest in micro flow applications, such as micro fuel cells, it is important to model and understand evaporation in this flow regime. Here, evaporation boundary conditions for the R13 equations, which are macroscopic transport equations with applicability in the rarefied gas regime, are derived. The new equations utilize Onsager relations, linear relations between thermodynamic fluxes and forces, with constant coefficients, that need to be determined. For this, the boundary conditions are fitted to DSMC data and compared to other R13 boundary conditions from kinetic theory and Navier–Stokes–Fourier (NSF) solutions for two one-dimensional steady-state problems. Overall, the suggested fittings of the new phenomenological boundary conditions show better agreement with DSMC than the alternative kinetic theory evaporation boundary conditions for R13. Furthermore, the new evaporation boundary conditions for R13 are implemented in a code for the numerical solution of complex, two-dimensional geometries and compared to NSF solutions. Different flow patterns between R13 and NSF for higher Knudsen numbers are observed. Full article
(This article belongs to the Special Issue Thermodynamics of Non-Equilibrium Gas Flows)
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30 pages, 670 KiB  
Article
Stability Analysis on Magnetohydrodynamic Flow of Casson Fluid over a Shrinking Sheet with Homogeneous-Heterogeneous Reactions
by Rusya Iryanti Yahaya, Norihan Md Arifin and Siti Suzilliana Putri Mohamed Isa
Entropy 2018, 20(9), 652; https://doi.org/10.3390/e20090652 - 30 Aug 2018
Cited by 29 | Viewed by 4136
Abstract
Two-dimensional magnetohydrodynamic (MHD) stagnation point flow of incompressible Casson fluid over a shrinking sheet is studied. In the present study, homogeneous-heterogeneous reactions, suction and slip effects are considered. Similarity variables are introduced to transform the governing partial differential equations into non-linear ordinary differential [...] Read more.
Two-dimensional magnetohydrodynamic (MHD) stagnation point flow of incompressible Casson fluid over a shrinking sheet is studied. In the present study, homogeneous-heterogeneous reactions, suction and slip effects are considered. Similarity variables are introduced to transform the governing partial differential equations into non-linear ordinary differential equations. The transformed equations and boundary conditions are then solved using the bvp4c solver in MATLAB. The local skin friction coefficient is tabulated for different values of suction and shrinking parameters. The profiles for fluid velocity and concentration for various parameters are illustrated. It was found that two solutions were obtained at certain ranges of parameters. Then, the bvp4c solver was used to perform stability analysis on the dual solutions. Based on the results, the first solution was more stable and physically meaningful than the other solution. The skin friction coefficient increased when suction increased, but decreased when the magnitude of shrinking parameter increased. Meanwhile, the velocity and concentration profile increased in the presence of a magnetic field. It is also noted that the higher the strength of the homogeneous-heterogeneous reactions, the lower the concentration of reactants. Full article
(This article belongs to the Special Issue Thermodynamics of Non-Equilibrium Gas Flows)
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