DOI: https://doi.org/10.26089/NumMet.v23r419

Evaporation and condensation of pure vapor at the liquid surface in the method of lattice Boltzmann equations

Authors

  • Alexandr L. Kupershtokh
  • Anton V. Alyanov

Keywords:

Lattice Boltzmann equation method
phase transitions
dynamics of multiphase media
evaporation
condensation
mesoscopic methods
computer simulations
parallel computations
graphical processing units (GPU)

Abstract

The regularities of the processes of evaporation and condensation of pure steam in the method of lattice Boltzmann equations were studied. Simulation of these processes was carried out with time-stationary steam flows at the boundary of the computational domain. It is shown that quasi-stationary regimes of evaporation and condensation are realized in this case. A simple numerically efficient method was proposed for setting the steam flow on the flat boundary of the computational domain by calculating the distribution functions on the input characteristics of the lattice Boltzmann method. The calculations show that the mass flow during evaporation of a flat surface is proportional to the difference in the densities of saturated and ambient vapor at a given surface temperature that is in a good agreement with the Hertz–Knudsen law. The results of 3D and 1D modeling by the lattice Boltzmann method coincide with high accuracy. It is shown that the ratio of the density difference to the flow of matter at the phase boundary at a given temperature depends linearly on the relaxation time, both for evaporation and condensation. The effect of temperature on the intensity of evaporation and condensation flows of pure steam has been studied. The dependence of evaporation and condensation processes on the relaxation time, which determines the kinematic viscosity of the fluid, is found.

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Published

2022-10-30

Issue

Vol. 23 (2022): Issue 4.

Section

Methods and algorithms of computational mathematics and their applications

Author Biographies

Alexandr L. Kupershtokh

Lavrent'ev Institute of Hydrodynamics of SB RAS
• Head of Laboratory

Anton V. Alyanov

Lavrent'ev Institute of Hydrodynamics of SB RAS
• Junior Researcher

References

  1. M. Potash and P. C. Wayner, “Evaporation from a Two-Dimensional Extended Meniscus,” Int. J. Heat Mass Transf. 15 (10), 1851-1863 (1972).
    doi 10.1016/0017-9310(72)90058-0.
  2. D. L. Albernaz, M. Do-Quang, and G. Amberg, “Lattice Boltzmann Method for the Evaporation of a Suspended Droplet,” Interfacial Phenom. Heat Transf. 1 (3), 245-258 (2013).
    doi 10.1615/InterfacPhenomHeatTransfer.2013010175.
  3. A. L. Karchevsky, I. V. Marchuk, and O. A. Kabov, “Calculation of the Heat Flux near the Liquid-Gas-Solid Contact Line,” Appl. Math. Model. 40 (2), 1029-1037 (2016).
    doi 10.1016/j.apm.2015.06.018.
  4. V. S. Ajaev and O. A. Kabov, “Heat and Mass Transfer near Contact Lines on Heated Surfaces,” Int. J. Heat Mass Transf. 108, Part A, 918-932 (2017).
    doi 10.1016/j.ijheatmasstransfer.2016.11.079.
  5. R. Zhang and H. Chen, “Lattice Boltzmann Method for Simulations of Liquid-Vapor Thermal Flows,” Phys. Rev. E 67 (6) (2003).
    doi 10.1103/PhysRevE.67.066711.
  6. M. I. Moiseev, A. Fedoseev, M. V. Shugaev, and A. S. Surtaev, “Hybrid Thermal Lattice Boltzmann Model for Boiling Heat Transfer on Surfaces with Different Wettability,” Interfacial Phenom. Heat Transf. 8 (1), 81-91 (2020).
    doi 10.1615/InterfacPhenomHeatTransfer.2020033929.
  7. B. A. Satenova, D. B. Zhakebayev, and O. L. Karuna, “Simulation of Nucleate Boiling Bubble by the Phase-Field and Lattice Boltzmann Method,” J. Math. Mech. Comput. Sci. 111 (3), 107-121 (2021).
    doi 10.26577/JMMCS.2021.v111.i3.09.
  8. A. A. Fedorets, I. V. Marchuk, and O. A. Kabov, “Role of Vapor Flow in the Mechanism of Levitation of a Droplet-Cluster Dissipative Structure,” Pis’ma Zh. Tekh. Fiz. 37 (3), 45-50 (2011) [Tech. Phys. Lett. 37 (2), 116-118 (2011)].
    doi 10.1134/S1063785011020064.
  9. A. A. Fedorets, I. V. Marchuk, and O. A. Kabov, “Coalescence of a Droplet Cluster Suspended over a Locally Heated Liquid Layer,” Interfacial Phenom. Heat Transf. 1 (1), 51-62 (2013).
    doi 10.1615/InterfacPhenomHeatTransfer.2013007434.
  10. O. A. Kabov, D. V. Zaitsev, D. P. Kirichenko, and V. S. Ajaev, “Investigation of Moist Air Flow near Contact Line Using Microdroplets as Tracers,” Interfacial Phenom. Heat Transf. 4 (2-3), 207-216 (2016).
    doi 10.1615/InterfacPhenomHeatTransfer.2017020203.
  11. D. V. Zaitsev, D. P. Kirichenko, A. I. Shatekova, et al., “Experimental and Theoretical Studies of Ordered Arrays of Microdroplets Levitating over Liquid and Solid Surfaces,” Interfacial Phenom. Heat Transf. 6 (3), 219-230 (2018).
    doi 10.1615/InterfacPhenomHeatTransfer.2019029816.
  12. J. G. Leidenfrost, De Aquae Communis Nonnullis Qualitatibus Tractatus (Ovenius, Duisburg, 1756).
  13. V. V. Zhakhovskii and S. I. Anisimov, “Molecular-Dynamics Simulation of Evaporation of a Liquid,” Zh. Eksp. Teor. Fiz. 111 (4), 1328-1346 (1997) [J. Exp. Theor. Phys. 84 (4), 734-745 (1997)].
    doi 10.1134/1.558192.
  14. R. Meland, A. Frezzotti, T. Ytrehus, and B. Hafskjold, “Nonequilibrium Molecular-Dynamics Simulation of Net Evaporation and Net Condensation, and Evaluation of the Gas-Kinetic Boundary Condition at the Interphase,” Phys. Fluids. 16 (2), 223-243 (2004).
    doi 10.1063/1.1630797.
  15. I. A. Graur, E. Ya. Gatapova, M. Wolf, and M. A. Batueva, “Non-Equilibrium Evaporation: 1D Benchmark Problem for Single Gas,” Int. J. Heat Mass Transf. 181 (2021).
    doi 10.1016/j.ijheatmasstransfer.2021.121997.
  16. I. A. Graur, M. A. Batueva, M. Wolf, and E. Ya. Gatapova, “Non-Equilibrium Condensation,” Int. J. Heat Mass Transf. 198 (2022).
    doi 10.1016/j.ijheatmasstransfer.2022.123391.
  17. J. P. Hirth and G. M. Pound, Condensation and Evaporation (Pergamon Press, Oxford, 1963).
  18. D. A. Labuntsov and A. P. Kryukov, “Analysis of Intensive Evaporation and Condensation,” Int. J. Heat Mass Transf. 22 (7), 989-1002 (1979).
    doi 10.1016/0017-9310(79)90172-8.
  19. I. W. Eames, N. J. Marr, and H. Sabir, “The Evaporation Coefficient of Water: A Review,” Int. J. Heat Mass Transf. 40 (12), 2963-2973 (1997).
    doi 10.1016/S0017-9310(96)00339-0.
  20. A. L. Kupershtokh, “An Evaporation Flux of Pure Vapor in the Method of Lattice Boltzmann Equations,” J. Phys.: Conf. Ser. 2057 (2021).
    doi 10.1088/1742-6596/2057/1/012070.
  21. G. R. McNamara and G. Zanetti, “Use of the Boltzmann Equation to Simulate Lattice-Gas Automata,” Phys. Rev. Lett. 61 (20), 2332-2335 (1988).
    doi 10.1103/PhysRevLett.61.2332.
  22. F. J. Higuera and J. Jiménez, “Boltzmann Approach to Lattice Gas Simulations,” Europhys. Lett. 9 (7), 663-668 (1989).
    doi 10.1209/0295-5075/9/7/009.
  23. S. Chen and G. D. Doolen, “Lattice Boltzmann Method for Fluid Flows,” Annu. Rev. Fluid Mech. 30 (1), 329-364 (1998).
    doi 10.1146/annurev.fluid.30.1.329.
  24. C. K. Aidun and J. R. Clausen, “Lattice-Boltzmann Method for Complex Flows,” Annu. Rev. Fluid Mech. 42 (1), 439-472 (2010).
    doi 10.1146/annurev-fluid-121108-145519.
  25. T. Krüger, H. Kusumaatmaja, A. Kuzmin, et al., The Lattice Boltzmann Method: Principles and Practice (Springer, Cham, 2017).
  26. P. L. Bhatnagar, E. P. Gross, and M. Krook, “A Model for Collision Processes in Gases. I. Small Amplitude Process in Charged and Neutral One-Component Systems,” Phys. Rev. 94 (3), 511-525 (1954).
    doi 10.1103/PhysRev.94.511.
  27. J. M. V. A. Koelman, “A Simple Lattice Boltzmann Scheme for Navier-Stokes Fluid Flow,” Europhys. Lett. 15 (6), 603-607 (1991).
    doi 10.1209/0295-5075/15/6/007.
  28. A. L. Kupershtokh, “Criterion of Numerical Instability of Liquid State in LBE Simulations,” Comput. Math. Appl. 59 (7), 2236-2245 (2010).
    doi 10.1016/j.camwa.2009.08.058.
  29. Y.-H. Qian, D. d’Humières, and P. Lallemand, “Lattice BGK Models for Navier-Stokes Equation,” Europhys. Lett. 17 (6), 479-484 (1992).
    doi 10.1209/0295-5075/17/6/001.
  30. A. L. Kupershtokh, “New Method of Incorporating a Body Force Term into the Lattice Boltzmann Equation,” in Proc. 5th Int. EHD Workshop, Poitiers, France, August 30-31, 2004 (Univ. of Poitiers, Poitiers, 2004), pp. 241-246.
    http://ancient.hydro.nsc.ru/sk/EHD-2004/FR2004-LBE.pdf . Cited October 20, 2022.
  31. A. L. Kupershtokh, “Incorporating a Body Force Term into the Lattice Boltzmann Equation,” Vestn. Novosib. Gos. Univ., Ser.: Mat., Mekh., Inform. 4 (2) 75-96 (2004).
    http://ancient.hydro.nsc.ru/sk/VESTNIK/Vestn-NGU-2004.pdf . Cited October 20, 2022.
  32. A. L. Kupershtokh, “Three-Dimensional Simulations of Two-Phase Liquid-Vapor Systems on GPU Using the Lattice Boltzmann Method,” Numer. Methods Program. 13 (1), 130-138 (2012).
    https://num-meth.ru/index.php/journal/article/view/505 . Cited October 20, 2022.
  33. J. Hardy, O. de Pazzis, and Y. Pomeau, “Molecular Dynamics of a Classical Lattice Gas: Transport Properties and Time Correlation Functions,” Phys. Rev. A 13 (5), 1949-1961 (1976).
    doi 10.1103/PhysRevA.13.1949.
  34. Y.-H. Qian and S. Chen, “Finite Size Effect in Lattice-BGK Models,” Int. J. Mod. Phys. C 8 (4), 763-771 (1997).
    doi 10.1142/S0129183197000655.
  35. A. L. Kupershtokh, “Simulation of Flows with Liquid–Vapor Interfaces by the Lattice Boltzmann Method,” Vestn. Novosib. Gos. Univ., Ser.: Mat., Mekh., Inform. 5 (3), 29-42 (2005).
    https://lib.nsu.ru/xmlui/handle/nsu/5214 . Cited October 20, 2022.
  36. A. L. Kupershtokh, D. A. Medvedev, and D. I. Karpov, “On Equations of State in a Lattice Boltzmann Method,” Comput. Math. Appl. 58 (5), 965-974 (2009).
    doi 10.1016/j.camwa.2009.02.024.
  37. A. L. Kupershtokh, E. V. Ermanyuk, and N. V. Gavrilov, “The Rupture of Thin Liquid Films Placed on Solid and Liquid Substrates in Gravity Body Forces,” Commun. Comput. Phys. 17 (5), 1301-1319 (2015).
    doi 10.4208/cicp.2014.m340.
  38. A. L. Kupershtokh and D. A. Medvedev, “Lattice Boltzmann Method in Hydrodynamics and Thermophysics,” J. Phys.: Conf. Ser. 1105 (2018).
    doi 10.1088/1742-6596/1105/1/012058.
  39. A. L. Kupershtokh, D. A. Medvedev, and I. I. Gribanov, “Modeling of Thermal Flows in a Medium with Phase Transitions Using the Lattice Boltzmann Method,” Numer. Methods Program. 15 (2), 317-328 (2014).
    https://num-meth.ru/index.php/journal/article/view/770 . Cited October 20, 2022.

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