Study of Nonclassical Transport by Applying Numerical Methods for Solving the Boltzmann Equation

V. V. Aristov; Аристов В. В.; I. V. Voronich; Воронич И. В.; S. A. Zabelok; Забелок С. А.

doi:10.31857/S0044466923120050

Study of Nonclassical Transport by Applying Numerical Methods for Solving the Boltzmann Equation

Авторлар: Aristov V.¹, Voronich I.¹, Zabelok S.¹
Мекемелер:
1. Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences
Шығарылым: Том 63, № 12 (2023)
Беттер: 2025-2034
Бөлім: МАТЕМАТИЧЕСКАЯ ФИЗИКА
URL: https://journals.rcsi.science/0044-4669/article/view/233028
DOI: https://doi.org/10.31857/S0044466923120050
EDN: https://elibrary.ru/JBEPWO
ID: 233028

Дәйексөз келтіру

Толық мәтін

Ашық рұқсат
Рұқсат жабық

Рұқсат берілді
Рұқсат жабық

Тек жазылушылар үшін

Аннотация
Авторлар туралы
Әдебиет тізімі
Қосымша файлдар
Статистика

Аннотация

This paper overviews the state of the art in the study of nonequilibrium gas flows with nonclassical transport, in which the Stokes and Fourier laws are violated (and, accordingly, the Chapman–Enskog method is inapplicable). For a reliable validation of anomalous transport effects, we use computational methods of different nature: the direct solution of the Boltzmann equation and direct simulation Monte Carlo. Nonclassical anomalous transport is manifested on scales of 5–10 mean free paths, which confirms the fact that a highly nonequilibrium flow is a prerequisite for the detection of the effects. Two-dimensional flow problems are considered, namely, the supersonic flow over a flat plate in the transient regime and the supersonic flow through membranes (lattices), where the flow behind the lattice corresponds to the spatially nonuniform relaxation problem. In this region, nonequilibrium distributions demonstrating anomalous transport are formed. The relationship of the effect with the second law of thermodynamics is discussed, the possibilities of experimental verification are considered, and the prospects of creating new microdevices on this basis are outlined.

Әдебиет тізімі

Akhlaghi H., Roohi E., Stefanov S. A comprehensive review on micro- and nano-scale gas flow effects: slip-jump phenomena, Knudsen paradox, thermally-driven flows, and Knudsen pumps // Phys. Reports. 2023. 997. P. 1–60.
Holway L. Existence of kinetic theory solutions to the shock structure problem // Phys. Fluids. 1964. 7. P. 911–913.
Коган М.Н. Динамика разреженного газа. Кинетическая теория. М.: Наука, 1967.
Бишаев А.М., Рыков В.А. О продольном потоке тепла в течении Куэтта // Изв. АН СССР. МЖГ. 1980. № 3. С. 162–166.
Aristov V.V. A steady state, supersonic flow solution of the Boltzmann equation // Phys. Letters A. 1998. 250. P. 354–359.
Aristov V.V., Frolova A.A., Zabelok S.A. A new effect of the nongradient transport in relaxation zones // Europhys. Letters. 2009. V. 88. 30012.
Aristov V.V., Frolova A.A., Zabelok S.A. Supersonic flows with nontraditional transport described by kinetic methods // Commun. Comput. Phys. 2012. V. 11. P. 1334–1346.
Aristov V.V., Frolova A.A., Zabelok S.A. Nonequilibrium kinetic processes with chemical reactions and complex structures in open systems // Europhys. Letters. 2014. 106. 20002.
Ilyin O.V. Anomalous heat transfer for an open non-equilibrium gaseous system // J. Stat. Mech. Theory Exp. 2017. 053201.
Аристов В.В., Фролова А.А., Забелок С.А. Возможность аномального теплопереноса в течениях с неравновесными граничными условиями // Докл. АН. 2017. V. 473. № 3. С. 286–290.
Myong R.S. A full analytical solution for the force-driven compressible Poiseuille gas flow based on a non-linear coupled constitutive relation // Phys. Fluids. 2011. V. 23. 012002.
Venugopal V., Praturi D.S., Girimaji S.S. Non-equilibrium thermal transport and entropy analyses in rarefied cavity flows // J. Fluid Mech. 2019. V. 864. P. 995–1025.
Todd B.D., Evans D.J. The heat flux vector for highly inhomogeneous nonequilibrium fluids in very narrow pores // J. Chem. Phys. 1995.V. 103. 9804.
Aristov V.V., Voronich I.V., Zabelok S.A. Direct methods for solving the Boltzmann equations: Comparisons with direct simulation Monte Carlo and possibilities // Phys. Fluids. 2019. V. 31. 097106.
Aristov V.V., Voronich I.V., Zabelok S.A. Nonequilibrium nonclassical phenomena in regions with membrane boundaries // Phys. Fluids. 2021. V. 33. 012009.
Kolobov V.I., Arslanbekov R.R., Aristov V.V., Frolova A.A., Zabelok S.A. Unified solver for rarefied and continuum flows with adaptive mesh and algorithm refinement // J. Comp. Phys. 1997. V. 223. P. 589–608.
Voronich I., Vershkov V. Development of VRDSMC method for wide range of weakly disturbed rarefied gas flows // Proc. of 2nd European Conference on Non-equilibrium Gas Flows. 2015. P. 15–44.
Bird G.A. Aerodynamic properties of some simple bodies in the hypersonic transition regime // AIAA J. 1966. V. 4. № 1. P. 55–60.
Черемисин Ф.Г. Решение плоской задачи аэродинамики разреженного газа на основе кинетического уравнения Больцмана // Докл. АН СССР. 1973. Т. 209(4). С. 811–814.
Aoki K., Kanba K., Takata S. Numerical analysis of a supersonic rarefied gas flow past a flat plate // Phys. Fluids. 1997. V. 9. P. 1144.
Abramov A.A., Butkovskii A.V., Buzykin O.G. Rarefied gas flow past a flat plate at zero angle of attack // Phys. Fluids. 2020. V. 32. 087108.
Аристов В.В., Забелок С.А., Фролова А.А. Моделирование неравновесных структур кинетическими методами. М.: Физматкнига, 2017.
Aristov V.V. Direct methods for solving the Boltzmann equation and study of nonequilibrium flows. Dordrecht: Kluwer Academic Publishers, 2001 (2nd ed. Springer, 2012).
Кубо Р. Термодинамика. М.: Мир, 1970.
Nguyen N.N., Graur I., Perrier P., Lorenzani L. Variational derivation of thermal slip coefficients on the basis of the Boltzmann equation for hard-sphere molecules and Cercignani-Lampis boundary conditions: Comparison with experimental results // Phys. Fluids. 2020. V. 32. 102011.
Torrese M. Rapport de stage de M1 Mécanique: Conception d’une tuyère pour des écoulements raréfiés. Dissertation. Marseille: Aix-Marseille Université Château-Gombert, 2022.