Моделирование динамики всплытия одиночного пузыря методом решёточных уравнений Больцмана

Моделирование динамики всплытия одиночного пузыря методом решёточных уравнений Больцмана

Федосеев А. В., Сальников М. В., Остапченко А. Е.
Сибирский журнал индустриальной математики, 26, 1(93), 191-200 (2023)
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УДК 536.248.2 
DOI: 10.33048/SIBJIM.2023.26.117

Аннотация:

Для исследования процесса кипения на поверхности твёрдого нагревателя представлена гибридная модель на основе метода решёточных уравнений Больцмана и уравнения теплопроводности. Исследовался процесс формирования и всплытия одиночного пузыря при кипении над одиночной лиофобной зоной, размещённой на гладкой лиофильной поверхности. Получены зависимости частоты отрыва и отрывного диаметра пузыря от ширины лиофобной зоны и теплового перегрева стенки. Показано, что отрывной диаметр пузыря растёт с размером ширины лиофобной зоны, а частота отрыва пузыря растёт с температурным перегревом. На основании полученных данных определён оптимальный размер лиофобной зоны на лиофильной поверхности с точки зрения интенсификации теплообмена.

Литература:
  1. Liang G., Mudawar I. Review of pool boiling enhancement by surface modification // Internat. J. Heat Mass Transfer. 2019. V. 128. P. 892–933.
     
  2. Nam Y., Wu J., Warrier G., Sungtaek Y. Experimental and numerical study of single bubble dynamics on a hydrophobic surface // J. Heat Transfer. 2009. V. 131, N 12. Article 121004.
     
  3. Phan H. T., Caney N., Marty P., Colasson S., Gavillet J. Surface wettability controlled by nanocoating: the effects on pool boiling heat transfer and nucleation mechanism // Internat. J. Heat Mass Transfer. 2009. V. 52. P. 5459–5471.
     
  4. Li Y., Zhanga K., Lu M. C., Duan C. Single bubble dynamics on superheated superhydropho-bic surfaces // Internat. J. Heat Mass Transfer. 2016. V. 99. P. 521–531.
     
  5. Teodori E., Valente T., Malavasi I., Moita A. S., Marengo M., Moreira A. L. N. Effect of extreme wetting scenarios on pool boiling conditions // Appl. Thermal Engrg. 2017. V. 115. P. 1424–1437.
     
  6. Bourdon B., Rioboo R., Marengo M., Gosselin E., De Coninck J. Influence of the wettability on the boiling onset // Langmuir. 2012. V. 28, N 2. P. 1618–1624.
     
  7. Betz A. R., Jenkins J., Kim C. J., Attinger D. Boiling heat transfer on superhydrophilic, superhydrophobic, and superbiphilic surfaces // Internat. J. Heat Mass Transfer. 2013. V. 57, N 2. P. 733–741.
     
  8. Kim S. H., Lee G. C., Kang J. Y., Moriyama K., Park H. S., Kim M. H. The role of surface energy in heterogeneous bubble growth on ideal surface // Internat. J. Heat Mass Transfer. 2017. V. 108. P. 1901– 1909.
     
  9. Kupershtokh A. L., Medvedev D. A., Karpov D. I. On equations of state in a lattice Boltzmann method // Comput. Math. Appl. 2009. V. 58, N 5. P. 965–974.
     
  10. Gong S., Cheng P. Numerical investigation of droplet motion and coalescence by an improved lattice Boltzmann model for phase transitions and multiphase flows // Comput. Fluids. 2012. V. 53. P. 93–104.
     
  11. Li Q., Kang Q. J., Francois M. M., He Y. L., and Luo K. H. Lattice Boltzmann modeling of boiling heat transfer: The boiling curve and the effects of wettability // Internat. J. Heat Mass Transfer. 2015. V. 85. P. 787–796.
     
  12.  Gong S., Cheng P. Lattice Boltzmann simulation of periodic bubble nucleation, growth and departure from a heated surface in pool boiling // Internat. J. Heat Mass Transfer. 2013. V. 64. P. 122–132.
     
  13. Fedoseev A. V., Surtaev A. S., Moiseev M. I., Ostapchenko A. E. Lattice Boltzmann simulation of bubble evolution at boiling on surfaces with different wettability // J. Phys. Conf. Series. 2020. V. 1677. Article 012085. 
     
  14. Li Q., Yu Y., Zhou P., Yan H. J. Enhancement of boiling heat transfer using hydrophilic-hydrophobic mixed surfaces: A lattice Boltzmann study // Appl. Thermal Engrg. 2018. V. 132. P. 490–499.
     
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Работа выполнена при финансовой поддержке Российского научного фонда (проект 22-29-01251).

А. В. Федосеевa
  1. Институт теплофизики им. С. С. Кутателадзе СО РАН, 
    просп. Акад. Лаврентьева, 1, г. Новосибирск 630090, Россия

E-mail: fedoseev@itp.nsc.ru

М. В. Сальников
  1. Институт теплофизики им. С. С. Кутателадзе СО РАН, 
    просп. Акад. Лаврентьева, 1, г. Новосибирск 630090, Россия

E-mail: salnikovitsbras@gmail.com

А. Е. Остапченко
  1. Институт теплофизики им. С. С. Кутателадзе СО РАН, 
    просп. Акад. Лаврентьева, 1, г. Новосибирск 630090, Россия

E-mail: a.ostapchenko@g.nsu.ru

Статья поступила 12.08.2022 г.
После доработки — 12.08.2022 г.
Принята к публикации 29.09.2022 г.

Abstract:

To study the process of boiling on a solid heater surface, a hybrid model based on lattice Boltzmann method (LBM) and heat transfer equation is presented. The process of formation and rise of a single bubble during boiling over a single lyophobic zone located on a smooth lyophilic surface was studied. Dependences of the bubble detachment frequency and bubble detachment diameter on the width of the lyophobic zone and the wall superheat were obtained. It is shown that the bubble detachment diameter increases with the width of the lyophobic zone, and the frequency of bubble detachment increases with the wall superheat. Based on the obtained data, the optimal size of the lyophobic zone on the lyophilic surface was determined from the point of view of heat transfer enhancement.

References:
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  2. Nam Y., Wu J., Warrier G., Sungtaek Y. Experimental and numerical study of single bubble dynamics on a hydrophobic surface. J. Heat Transfer, 2009, Vol. 131, No. 12, article 121004.
     
  3. Phan H. T., Caney N., Marty P., Colasson S., Gavillet J. Surface wettability controlled by nanocoating: the effects on pool boiling heat transfer and nucleation mechanism. Internat. J. Heat Mass Transfer, 2009, Vol. 52, pp. 5459–5471.
     
  4. Li Y., Zhanga K., Lu M. C., Duan C. Single bubble dynamics on superheated superhydropho-bic surfaces. Internat. J. Heat Mass Transfer, 2016, Vol. 99, pp. 521–531.
     
  5. Teodori E., Valente T., Malavasi I., Moita A. S., Marengo M., Moreira A. L. N. Effect of extreme wetting scenarios on pool boiling conditions. Appl. Thermal Engrg., 2017, Vol. 115, pp. 1424–1437.
     
  6. Bourdon B., Rioboo R., Marengo M., Gosselin E., De Coninck J. Influence of the wettability on the boiling onset. Langmuir, 2012, Vol. 28, No. 2, pp. 1618–1624.
     
  7. Betz A. R., Jenkins J., Kim C. J., Attinger D. Boiling heat transfer on superhydrophilic, superhydrophobic, and superbiphilic surfaces. Internat. J. Heat Mass Transfer, 2013, Vol. 57, No. 2, pp. 733–741.
     
  8. Kim S. H., Lee G. C., Kang J. Y., Moriyama K., Park H. S., Kim M. H. The role of surface energy in heterogeneous bubble growth on ideal surface. Internat. J. Heat Mass Transfer, 2017, Vol. 108, pp. 1901– 1909.
     
  9. Kupershtokh A. L., Medvedev D. A., Karpov D. I. On equations of state in a lattice Boltzmann method. Comput. Math. Appl., 2009, Vol. 58, No. 5, pp. 965–974.
     
  10. Gong S., Cheng P. Numerical investigation of droplet motion and coalescence by an improved lattice Boltzmann model for phase transitions and multiphase flows. Comput. Fluids, 2012, Vol. 53, pp. 93–104.
     
  11. Li Q., Kang Q. J., Francois M. M., He Y. L., and Luo K. H. Lattice Boltzmann modeling of boiling heat transfer: The boiling curve and the effects of wettability. Internat. J. Heat Mass Transfer, 2015, Vol. 85, pp. 787–796.
     
  12. Gong S., Cheng P. Lattice Boltzmann simulation of periodic bubble nucleation, growth and departure from a heated surface in pool boiling. Internat. J. Heat Mass Transfer, 2013, Vol. 64, pp. 122–132.
     
  13. Fedoseev A. V., Surtaev A. S., Moiseev M. I., Ostapchenko A. E. Lattice Boltzmann simulation of bubble evolution at boiling on surfaces with different wettability. J. Phys. Conf. Series, 2020, Vol. 1677, article 012085. 
     
  14. Li Q., Yu Y., Zhou P., Yan H. J. Enhancement of boiling heat transfer using hydrophilic-hydrophobic mixed surfaces: A lattice Boltzmann study. Appl. Thermal Engrg., 2018, Vol. 132, pp. 490–499.
     
  15. Wolf-Gladrow D. A. Lattice-Gas Cellular Automata and Lattice Boltzmann Models. N. Y.: Springer-Verl., 2005. 
     
  16. He X., Luo L. S. Theory of the lattice Boltzmann method: From the Boltzmann equation to the lattice Boltzmann equation. Phys. Rev. E, 1997, Vol. 56, No. 6, article 6811.
     
  17. Shan X., Yuan X. F., Chen H. Kinetic theory representation of hydrodynamics: a way beyond the Navier— Stokes equation. J. Fluid Mech., 2006, Vol. 550, article 413.
     
  18. Qian Y. H., d’Humieres D., Lallemand P. Lattice BGK Models for Navier—Stokes Equation. Europhys. Lett., 1992, Vol. 17, No. 6, article 479.
     
  19. Succi S. The Lattice Boltzmann Equation for Fluid Dynamics and Beyond. Oxford: Univ. Press, 2001.
     
  20. Bhatnagar P. L., Gross E. P., Krook M. A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems. Phys. Rev., 1954, Vol. 94, pp. 511–525.
     
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  25. Kupershtokh A. L., Karpov D. I., Medvedev D. A., Stamatelatos C. P., Charalambakos V. P., Pyrgioti E. C., and Agoris D. P. Stochastic models of partial discharge activity in solid and liquid dielectrics. IET Sci. Meas. Technol., 2007, Vol. 1, No. 6, pp. 303–311.
     
  26. Kupershtokh A. L., Karpov D. I., Medvedev D. A., Stamatelatos C. P., Charalambakos V. P., Pyrgioti E. C., Agoris D. P. Stochastic models of partial discharge activity in solid and liquid dielectrics. IET Sci. Meas. Technol., 2007, Vol. 1, No. 6, pp. 303–311.
     
  27. Yuan P., Schaefer L. Equations of state in a lattice Boltzmann model. Phys. Fluids, 2006, Vol. 18, article 042101. 
     
  28. Peng D. Y., Robinson, D. B. A New two-constant equation of state. Indust. Engrg. Chemistry. Fundamentals, 1976, Vol. 15, pp. 59–64.
     
  29. Blundell S., Blundell K. M. Concepts in Thermal Physics. Oxford: Univ. Press, 2006.