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Development of a Unified Numerical Kinetic Approach, Taking into Account Many-Particle Interactions in Liquid-Vapor Systems

Received: 4 September 2021     Accepted: 24 September 2021     Published: 30 September 2021
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Abstract

The study of evaporation and condensation should include consideration of heat and mass transfer processes inside the liquid, in the inter-phase transition domain, in the Knudsen layer, and in the outer area. Possible way to realize it is to use the conjugate approach, in which the description of these regions is carried out employing a single computational method. This method allows us to consider the condensed phase and gas as a single system and use the solution of kinetic equations throughout the region. Currently, processes in the gas phase have been studied quite well. The greatest obstacle to the use of kinetic equations in the condensed phase is the description of collisions involving multiple particles at the same time. In this paper a procedure is proposed to take the multi-particulate interactions within the condensed phase into account. Such approach is applied to the test study of the thermal conductivity problem for argon, neon, xenon, and krypton. Values of thermal conductivity coefficients for different quantities of interacting particles have been obtained. The comparison with corresponding experimental data is presented. Thus, the integral of paired collisions in the Boltzmann kinetic equation can be replaced by the proposed computational procedure. This approach provides a description of both liquid and gas at the level of the distribution function and ensures that the conditions at the interface are set correctly.

Published in American Journal of Physics and Applications (Volume 9, Issue 5)
DOI 10.11648/j.ajpa.20210905.13
Page(s) 116-120
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2021. Published by Science Publishing Group

Keywords

Boltzmann Equation, Interface Phenomena, Joint Solution

References
[1] A. Frezzotti and P. Barbante. Simulation of shock induced vapor condensation flows in the Lennard-Jones fluid by microscopic and continuum models. Phys. Fluids 32, 2020, 122106.
[2] P. Barbante and A. Frezzotti. A comparison of models for the evaporation of the Lennard-Jones fluid. Eur. J. Mech.: B/Fluids 64, 2017, pp. 69–80.
[3] M. Kon, K. Kobayashi, and M. Watanabe. Method of determining kinetic boundary conditions in net evaporation/condensation. Phys. Fluids 26, 2014, 072003.
[4] M. Kon, K. Kobayashi, M. Watanabe, Liquid temperature dependence of kinetic boundary condition at vapor-liquid interface. Int. J. Heat Mass Transfer 99, 2016, pp. 317–326.
[5] S. Busuioc, L. Gibelli, D. A. Lockerby, and J. E. Sprittles. Velocity distribution function on spontaneously evaporating atoms. Phys. Rev. Fluids 5, 2020, 103401.
[6] Shishkova I. N., Kryukov A. P., Levashov V. Yu. Study of evaporation–condensation problems: from liquid through interface surface to vapor. International Journal of Heat and Mass Transfer. V. 112, 2017, pp. 926-932.
[7] V. Ya. Rudyak. Statistical theory of dissipative processes in gases and liquids. Novosibirsk. 1987 (in Russian).
[8] A. A. Tsykalo, M. M. Kontsov. Study of the effect of three-particle non-additive interactions on the thermodynamic properties of dense gases and liquids. Journal of Technical Physics. T. 47, No. 12, 1977, pp. 2601-2607 (in Russian).
[9] Shishkova I. N., Kryukov A. P., Levashov V. Y. Vapour–liquid jointed solution for the evaporation–condensation problem. International Journal of Heat and Mass Transfer. Vol. 141, 2019, pp. 9–19.
[10] I. N. Shishkova, A. P. Kryukov and V. Yu. Levashov. Joint liquid-vapor approach development at solution of different heat and mass transfer problems. Journal of Physics: Conference Series. ICFEPT 2019, 2019, 1370: 012019. doi: 10.1088/1742-6596/1370/1/012019
[11] F. G. Tcheremissine, Discrete approximation and examples of solutions of the Boltzmann equation, in: Computational Dynamics of Rarefied Gas, Computer Center of the Russian Academy of Sciences, 2000, pp. 37–74.
[12] I. N. Shishkova, S. S. Sazhin, J. -F. Xie. A solution of the Boltzmann equation in the presence of inelastic collisions. J. Computational Physics. V. 232, 2013, pp. 87-99.
[13] V. V. Zhakhovsky, A. P. Kryukov, V. Yu. Levashov, I. N. Shishkova, S. I. Anisimov Mass and heat transfer between evaporation and condensation surfaces: Atomic simulation and solution of Boltzmann kinetic equation. Proceedings of the National Academy of Sciences, PNAS April 16, 2018. 201714503; published ahead of print April 16. https://doi.org/10.1073/pnas. 1714503115 or Proc. Nat. Acad. Sci. 116 18209, 2019.
[14] M. N. Kogan, Rarefied Gas Dynamics, Plenum, New York, 1969.
[15] NIST-JANAF Thermochemical Tables. https://janaf.nist.gov/.
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  • APA Style

    Irina Shishkova, Alexei Kryukov. (2021). Development of a Unified Numerical Kinetic Approach, Taking into Account Many-Particle Interactions in Liquid-Vapor Systems. American Journal of Physics and Applications, 9(5), 116-120. https://doi.org/10.11648/j.ajpa.20210905.13

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    ACS Style

    Irina Shishkova; Alexei Kryukov. Development of a Unified Numerical Kinetic Approach, Taking into Account Many-Particle Interactions in Liquid-Vapor Systems. Am. J. Phys. Appl. 2021, 9(5), 116-120. doi: 10.11648/j.ajpa.20210905.13

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    AMA Style

    Irina Shishkova, Alexei Kryukov. Development of a Unified Numerical Kinetic Approach, Taking into Account Many-Particle Interactions in Liquid-Vapor Systems. Am J Phys Appl. 2021;9(5):116-120. doi: 10.11648/j.ajpa.20210905.13

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  • @article{10.11648/j.ajpa.20210905.13,
      author = {Irina Shishkova and Alexei Kryukov},
      title = {Development of a Unified Numerical Kinetic Approach, Taking into Account Many-Particle Interactions in Liquid-Vapor Systems},
      journal = {American Journal of Physics and Applications},
      volume = {9},
      number = {5},
      pages = {116-120},
      doi = {10.11648/j.ajpa.20210905.13},
      url = {https://doi.org/10.11648/j.ajpa.20210905.13},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajpa.20210905.13},
      abstract = {The study of evaporation and condensation should include consideration of heat and mass transfer processes inside the liquid, in the inter-phase transition domain, in the Knudsen layer, and in the outer area. Possible way to realize it is to use the conjugate approach, in which the description of these regions is carried out employing a single computational method. This method allows us to consider the condensed phase and gas as a single system and use the solution of kinetic equations throughout the region. Currently, processes in the gas phase have been studied quite well. The greatest obstacle to the use of kinetic equations in the condensed phase is the description of collisions involving multiple particles at the same time. In this paper a procedure is proposed to take the multi-particulate interactions within the condensed phase into account. Such approach is applied to the test study of the thermal conductivity problem for argon, neon, xenon, and krypton. Values of thermal conductivity coefficients for different quantities of interacting particles have been obtained. The comparison with corresponding experimental data is presented. Thus, the integral of paired collisions in the Boltzmann kinetic equation can be replaced by the proposed computational procedure. This approach provides a description of both liquid and gas at the level of the distribution function and ensures that the conditions at the interface are set correctly.},
     year = {2021}
    }
    

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    T1  - Development of a Unified Numerical Kinetic Approach, Taking into Account Many-Particle Interactions in Liquid-Vapor Systems
    AU  - Irina Shishkova
    AU  - Alexei Kryukov
    Y1  - 2021/09/30
    PY  - 2021
    N1  - https://doi.org/10.11648/j.ajpa.20210905.13
    DO  - 10.11648/j.ajpa.20210905.13
    T2  - American Journal of Physics and Applications
    JF  - American Journal of Physics and Applications
    JO  - American Journal of Physics and Applications
    SP  - 116
    EP  - 120
    PB  - Science Publishing Group
    SN  - 2330-4308
    UR  - https://doi.org/10.11648/j.ajpa.20210905.13
    AB  - The study of evaporation and condensation should include consideration of heat and mass transfer processes inside the liquid, in the inter-phase transition domain, in the Knudsen layer, and in the outer area. Possible way to realize it is to use the conjugate approach, in which the description of these regions is carried out employing a single computational method. This method allows us to consider the condensed phase and gas as a single system and use the solution of kinetic equations throughout the region. Currently, processes in the gas phase have been studied quite well. The greatest obstacle to the use of kinetic equations in the condensed phase is the description of collisions involving multiple particles at the same time. In this paper a procedure is proposed to take the multi-particulate interactions within the condensed phase into account. Such approach is applied to the test study of the thermal conductivity problem for argon, neon, xenon, and krypton. Values of thermal conductivity coefficients for different quantities of interacting particles have been obtained. The comparison with corresponding experimental data is presented. Thus, the integral of paired collisions in the Boltzmann kinetic equation can be replaced by the proposed computational procedure. This approach provides a description of both liquid and gas at the level of the distribution function and ensures that the conditions at the interface are set correctly.
    VL  - 9
    IS  - 5
    ER  - 

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Author Information
  • Low Temperature Department, National Research University Moscow Power Engineering Institute, Moscow, Russia

  • Low Temperature Department, National Research University Moscow Power Engineering Institute, Moscow, Russia

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