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Vienne L, Marié S, Grasso F. Lattice Boltzmann method for miscible gases: A forcing-term approach. Phys Rev E 2019; 100:023309. [PMID: 31574596 DOI: 10.1103/physreve.100.023309] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/04/2019] [Indexed: 11/07/2022]
Abstract
A lattice Boltzmann method for miscible gases is presented. In this model, the standard lattice Boltzmann method is employed for each species composing the mixture. Diffusion interaction among species is taken into account by means of a force derived from kinetic theory of gases. Transport coefficients expressions are recovered from the kinetic theory. Species with dissimilar molar masses are simulated by also introducing a force. Finally, mixing dynamics is recovered as shown in different applications: an equimolar counterdiffusion case, Loschmidt's tube experiment, and an opposed jets flow simulation. Since collision is not altered, the present method can easily be introduced in any other lattice Boltzmann algorithms.
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Affiliation(s)
- Lucien Vienne
- DynFluid Laboratory, Conservatoire National des Arts et Métiers, 151 boulevard de l'hôpital, 75013 Paris, France
| | - Simon Marié
- DynFluid Laboratory, Conservatoire National des Arts et Métiers, 151 boulevard de l'hôpital, 75013 Paris, France
| | - Francesco Grasso
- DynFluid Laboratory, Conservatoire National des Arts et Métiers, 151 boulevard de l'hôpital, 75013 Paris, France
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2
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Zheng L, Zheng S. Phase-field-theory-based lattice Boltzmann equation method for N immiscible incompressible fluids. Phys Rev E 2019; 99:063310. [PMID: 31330677 DOI: 10.1103/physreve.99.063310] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/16/2019] [Indexed: 11/07/2022]
Abstract
From the phase field theory, we develop a lattice Boltzmann equation (LBE) method for N (N≥2) immiscible incompressible fluids, and the Cahn-Hilliard equation, which could capture the interfaces between different phases, is also solved by LBE for an N-phase system. In this model, the interface force of N immiscible incompressible fluids is incorporated by chemical potential form, and the fluid-fluid surface tensions could be directly calculated and independently tuned. Numerical simulations including two stationary droplets, spreading of a liquid lens with and without gravity and two immiscible liquid lenses, and phase separation are conducted to validate the present LBE, and numerical results show that the predictions by LBE agree well with the analytical solutions and other numerical results.
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Affiliation(s)
- Lin Zheng
- MIIT Key Laboratory of Thermal Control of Electronic Equipment, School of Energy and Power Engineering, Nanjing University of Science and Technology, Nanjing 210094, People's Republic of China
| | - Song Zheng
- School of Mathematics and Statistics, Zhejiang University of Finance and Economics, Hangzhou 310018, People's Republic of China
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3
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A Kinetic Perspective on k‒ε Turbulence Model and Corresponding Entropy Production. ENTROPY 2016. [DOI: 10.3390/e18040121] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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Belardinelli D, Sbragaglia M, Biferale L, Gross M, Varnik F. Fluctuating multicomponent lattice Boltzmann model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:023313. [PMID: 25768641 DOI: 10.1103/physreve.91.023313] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/21/2014] [Indexed: 06/04/2023]
Abstract
Current implementations of fluctuating lattice Boltzmann equations (FLBEs) describe single component fluids. In this paper, a model based on the continuum kinetic Boltzmann equation for describing multicomponent fluids is extended to incorporate the effects of thermal fluctuations. The thus obtained fluctuating Boltzmann equation is first linearized to apply the theory of linear fluctuations, and expressions for the noise covariances are determined by invoking the fluctuation-dissipation theorem directly at the kinetic level. Crucial for our analysis is the projection of the Boltzmann equation onto the orthonormal Hermite basis. By integrating in space and time the fluctuating Boltzmann equation with a discrete number of velocities, the FLBE is obtained for both ideal and nonideal multicomponent fluids. Numerical simulations are specialized to the case where mean-field interactions are introduced on the lattice, indicating a proper thermalization of the system.
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Affiliation(s)
- D Belardinelli
- Department of Physics, University of Rome "Tor Vergata," Via della Ricerca Scientifica 1, 00133 Rome, Italy
| | - M Sbragaglia
- Department of Physics, University of Rome "Tor Vergata," Via della Ricerca Scientifica 1, 00133 Rome, Italy
| | - L Biferale
- Department of Physics, University of Rome "Tor Vergata," Via della Ricerca Scientifica 1, 00133 Rome, Italy
| | - M Gross
- Max-Planck-Institut für Intelligente Systeme, Heisenbergstraße 3, 70569 Stuttgart, Germany
- Institut für Theoretische Physik IV, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
| | - F Varnik
- Interdisciplinary Centre for Advanced Materials Simulation (ICAMS), Ruhr-Universität Bochum, Universitätsstrasse 150, 44780 Bochum, Germany
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5
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Kang J, Prasianakis NI, Mantzaras J. Thermal multicomponent lattice Boltzmann model for catalytic reactive flows. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:063310. [PMID: 25019915 DOI: 10.1103/physreve.89.063310] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/10/2014] [Indexed: 06/03/2023]
Abstract
Catalytic reactions are of great interest in many applications related to power generation, fuel reforming and pollutant abatement, as well as in various biochemical processes. A recently proposed lattice Boltzmann model for thermal binary-mixture gas flows [J. Kang, N. I. Prasianakis, and J. Mantzaras, Phys. Rev. E. 87, 053304 (2013)] is revisited and extended for the simulation of multispecies flows with catalytic reactions. The resulting model can handle flows with large temperature and concentration gradients. The developed model is presented in detail and validated against a finite volume Navier-Stokes solver in the case of channel-flow methane catalytic combustion. The surface chemistry is treated with a one-step global reaction for the catalytic total oxidation of methane on platinum. In order to take into account thermal effects, the catalytic boundary condition of S. Arcidiacono, J. Mantzaras, and I. V. Karlin [Phys. Rev. E 78, 046711 (2008)] is adapted to account for temperature variations. Speed of sound simulations further demonstrate the physical integrity and unique features of the model.
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Affiliation(s)
- Jinfen Kang
- Combustion Research Laboratory Paul Scherrer Institute, CH-5232 Villigen PSI, Switzerland
| | - Nikolaos I Prasianakis
- Combustion Research Laboratory Paul Scherrer Institute, CH-5232 Villigen PSI, Switzerland
| | - John Mantzaras
- Combustion Research Laboratory Paul Scherrer Institute, CH-5232 Villigen PSI, Switzerland
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Zudrop J, Roller S, Asinari P. Lattice Boltzmann scheme for electrolytes by an extended Maxwell-Stefan approach. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:053310. [PMID: 25353917 DOI: 10.1103/physreve.89.053310] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/04/2013] [Indexed: 06/04/2023]
Abstract
This paper presents an extended multicomponent lattice Boltzmann model for the simulation of electrolytes. It is derived by means of a finite discrete velocity model and its discretization. The model recovers momentum and mass transport according to the incompressible Navier-Stokes equation and Maxwell-Stefan formulation, respectively. It includes external driving forces (e.g., electric field) on diffusive and viscous scales, concentration-dependent Maxwell-Stefan diffusivities, and thermodynamic factors. The latter take into account nonideal diffusion behavior, which is essential as electrolytes involve charged species and therefore nonideal long and short-range interactions among the molecules of the species. Furthermore, we couple our scheme to a finite element method to include electrostatic interactions on the macroscopic level. Numerical experiments show the validity of the presented model.
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Affiliation(s)
- Jens Zudrop
- Applied Supercomputing in Engineering, German Research School for Simulation Sciences, RWTH Aachen, Schinkelstrasse 2a, Aachen, Germany and Simulation Techniques and Scientific Computing, University Siegen, Hölderlinstrasse 3, Siegen, Germany
| | - Sabine Roller
- Applied Supercomputing in Engineering, German Research School for Simulation Sciences, RWTH Aachen, Schinkelstrasse 2a, Aachen, Germany and Simulation Techniques and Scientific Computing, University Siegen, Hölderlinstrasse 3, Siegen, Germany
| | - Pietro Asinari
- Department of Energy, Politecnico di Torino, Corso Duca degli Abruzzi 24, Torino, Italy
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Kang J, Prasianakis NI, Mantzaras J. Lattice Boltzmann model for thermal binary-mixture gas flows. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 87:053304. [PMID: 23767654 DOI: 10.1103/physreve.87.053304] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/20/2012] [Indexed: 06/02/2023]
Abstract
A lattice Boltzmann model for thermal gas mixtures is derived. The kinetic model is designed in a way that combines properties of two previous literature models, namely, (a) a single-component thermal model and (b) a multicomponent isothermal model. A comprehensive platform for the study of various practical systems involving multicomponent mixture flows with large temperature differences is constructed. The governing thermohydrodynamic equations include the mass, momentum, energy conservation equations, and the multicomponent diffusion equation. The present model is able to simulate mixtures with adjustable Prandtl and Schmidt numbers. Validation in several flow configurations with temperature and species concentration ratios up to nine is presented.
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Affiliation(s)
- Jinfen Kang
- Combustion Research Laboratory, Paul Scherrer Institute, CH-5232 Villigen PSI, Switzerland.
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Shan X. Multicomponent lattice Boltzmann model from continuum kinetic theory. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 81:045701. [PMID: 20481779 DOI: 10.1103/physreve.81.045701] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/17/2009] [Revised: 11/30/2009] [Indexed: 05/29/2023]
Abstract
We derive from the continuum kinetic theory a multicomponent lattice Boltzmann model with intermolecular interaction. The resulting model is found to be consistent with the model previously derived from a lattice-gas cellular automaton [X. Shan and H. Chen, Phys. Rev. E 47, 1815 (1993)] but applies in a much broader domain. A number of important insights are gained from the kinetic theory perspective. First, it is shown that even in the isothermal case, the energy equipartition principle dictates the form of the equilibrium distribution function. Second, thermal diffusion is shown to exist and the corresponding diffusivities are given in terms of macroscopic parameters. Third, the ordinary diffusion is shown to satisfy the Maxwell-Stefan equation at the ideal-gas limit.
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Affiliation(s)
- Xiaowen Shan
- Exa Corporation, 55 Network Drive, Burlington, Massachusetts 01803, USA.
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Zheng L, Guo Z, Shi B, Zheng C. Finite-difference-based multiple-relaxation-times lattice Boltzmann model for binary mixtures. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 81:016706. [PMID: 20365501 DOI: 10.1103/physreve.81.016706] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/08/2009] [Revised: 10/06/2009] [Indexed: 05/29/2023]
Abstract
In this paper, we propose a finite-difference-based lattice Boltzmann equation (LBE) model with multiple-relaxation times (MRT), in which the distribution functions of individual species evolve on a same regular lattice without any interpolations. Furthermore, the use of the MRT enables the model more flexible so that it can be applied to mixtures of species with different viscosities and adjustable Schmidt number. Some numerical tests are conducted to validate the model, the numerical results are found to agree well with analytical solutions/or other numerical results, and good numerical stability of the proposed LBE model is also observed.
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Affiliation(s)
- Lin Zheng
- National Laboratory of Coal Combustion, Huazhong University of Science and Technology, Wuhan, People's Republic of China
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Ubertini S, Asinari P, Succi S. Three ways to lattice Boltzmann: a unified time-marching picture. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 81:016311. [PMID: 20365464 DOI: 10.1103/physreve.81.016311] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/25/2009] [Revised: 08/31/2009] [Indexed: 05/29/2023]
Abstract
It is shown that the lattice Boltzmann equation (LBE) corresponds to an explicit Verlet time-marching scheme for a continuum generalized Boltzmann equation with a memory delay equal to a half time step. This proves second-order accuracy of LBE with respect to this generalized equation, with no need of resorting to any implicit time-marching procedure (Crank-Nicholson) and associated nonlinear variable transformations. It is also shown, and numerically demonstrated, that this equivalence is not only formal, but it also translates into a complete equivalence of the corresponding computational schemes with respect to the hydrodynamic equations. Second-order accuracy with respect to the continuum kinetic equation is also numerically demonstrated for the case of the Taylor-Green vortex. It is pointed out that the equivalence is however broken for the case in which mass and/or momentum are not conserved, such as for chemically reactive flows and mixtures. For such flows, the time-centered implicit formulation may indeed offer a better numerical accuracy.
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Affiliation(s)
- S Ubertini
- Dipartimento per le Tecnologie (DiT), Centro Direzionale, Università di Napoli Parthenope, Napoli, Italy
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Asinari P. Lattice Boltzmann scheme for mixture modeling: analysis of the continuum diffusion regimes recovering Maxwell-Stefan model and incompressible Navier-Stokes equations. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 80:056701. [PMID: 20365090 DOI: 10.1103/physreve.80.056701] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/19/2007] [Revised: 09/28/2009] [Indexed: 05/29/2023]
Abstract
A finite difference lattice Boltzmann scheme for homogeneous mixture modeling, which recovers Maxwell-Stefan diffusion model in the continuum limit, without the restriction of the mixture-averaged diffusion approximation, was recently proposed [P. Asinari, Phys. Rev. E 77, 056706 (2008)]. The theoretical basis is the Bhatnagar-Gross-Krook-type kinetic model for gas mixtures [P. Andries, K. Aoki, and B. Perthame, J. Stat. Phys. 106, 993 (2002)]. In the present paper, the recovered macroscopic equations in the continuum limit are systematically investigated by varying the ratio between the characteristic diffusion speed and the characteristic barycentric speed. It comes out that the diffusion speed must be at least one order of magnitude (in terms of Knudsen number) smaller than the barycentric speed, in order to recover the Navier-Stokes equations for mixtures in the incompressible limit. Some further numerical tests are also reported. In particular, (1) the solvent and dilute test cases are considered, because they are limiting cases in which the Maxwell-Stefan model reduces automatically to Fickian cases. Moreover, (2) some tests based on the Stefan diffusion tube are reported for proving the complete capabilities of the proposed scheme in solving Maxwell-Stefan diffusion problems. The proposed scheme agrees well with the expected theoretical results.
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Affiliation(s)
- Pietro Asinari
- Department of Energetics, Politecnico di Torino, Corso Duca degli Abruzzi 24, Torino, Italy
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Guo Z, Asinari P, Zheng C. Lattice Boltzmann equation for microscale gas flows of binary mixtures. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 79:026702. [PMID: 19391869 DOI: 10.1103/physreve.79.026702] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/17/2008] [Indexed: 05/27/2023]
Abstract
Modeling and simulating gas flows in and around microdevices are a challenging task in both science and engineering. In practical applications, a gas is usually a mixture made of different components. In this paper we propose a lattice Boltzmann equation (LBE) model for microscale flows of a binary mixture based on a recently developed LBE model for continuum mixtures [P. Asinari and L.-S. Luo, J. Comput. Phys. 227, 3878 (2008)]. A consistent boundary condition for gas-solid interactions is proposed and analyzed. The LBE is validated and compared with theoretical results or other reported data. The results show that the model can serve as a potential method for flows of binary mixture in the microscale.
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Affiliation(s)
- Zhaoli Guo
- National Laboratory of Coal Combustion, Huazhong University of Science and Technology, Wuhan 430074, People's Republic of China.
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