Численное исследование динамики каверны при ударе капли воды о слой масла

Численное исследование динамики каверны при ударе капли воды о слой масла

Лукьянов А. А., Вожаков И. С., Мулляджанов Р. И.
Сибирский журнал индустриальной математики, 29, 2(106), 56-64 (2026)
Скачать статью

УДК 532.5 
DOI: 10.33048/SIBJIM.2026.29.204

Аннотация:

Влияние скорости столкновения на динамику каверны при ударе капли воды о слой масла исследовалось с помощью трёхмерного численного моделирования в программном пакете Basilisk. Используя метод объёма жидкости с адаптивным измельчением сетки и учётом сил поверхностного натяжения, были изучены режимы при числах Вебера We = 23–360. Установлено, что с увеличением We происходит переход от капиллярного режима схлопывания каверны, описываемого классической инерционно-капиллярной временной шкалой, к режиму, где доминирующую роль играют гидростатическое давление и силы вязкой диссипации.

Литература:
  1. Rein M. Phenomena of liquid drop impact on solid and liquid surfaces // Fluid Dynamics Research. 1993. V. 12, N 2. P. 61–93; DOI: 10.1016/0169-5983(93)90106-K
     
  2. Prosperetti A., Oguz H. N. The impact of drops on liquid surfaces and the underwater noise of rain // Annual Review of Fluid Mechanics. 1993. V. 25, N 1. P. 577–602; DOI: 10.1146/annurev.fl.25.010193.003045
     
  3. Vozhakov I. S., Misyura S. Y., Morozov V. S., Piskunov M. V., Piskunova A. E., Orlova E. G., Mullyadzhanov R. I. High-speed droplet impact on solid surfaces: review on the prospects of modeling fluid flow // Experiments in Fluids. 2025. V. 66, N 3. Article number C-65; DOI: 10.1007/s00348-025-03982-w
     
  4. Worthington A. M. A Study of Splashes. London: Longmans, Green, and Company, 1908.
     
  5. Cherdantsev A., Vozhakov I. Fast droplets impacting liquid layer under a small angle: a numerical analysis of experimental observations // Internat. J. Multiphase Flow. 2024. V. 175. Article number 104826; DOI: 10.1016/j.ijmultiphaseflow.2024.104826
     
  6. Ray B., Biswas G., Sharma A. Generation of secondary droplets in coalescence of a drop with a liquid surface // J. Fluid Mechanics. 2015. V. 768. P. 492–523; DOI: 10.1017/jfm.2015.93
     
  7. Yarin A. L. Drop impact dynamics: splashing, spreading, receding, bouncing. . . // Annual Review of Fluid Mechanics. 2006. V. 38, N 1. P. 159–192; DOI: 10.1146/annurev.fluid.38.050304.092144
     
  8. Popinet S. An accurate adaptive solver for surface-tension-driven interfacial flows // J. Comput. Physics. 2009. V. 228, N 16. P. 5838–5866; DOI: 10.1016/j.jcp.2009.04.042
     
  9. Scardovelli R., Zaleski S. Direct numerical simulation of free-surface and interfacial flow // Annual Review of Fluid Mechanics. 1999. V. 31, N 1. P. 567–603; DOI: 10.1146/annurev.fluid.31.1.567
     
  10. Brackbill J. U., Kothe D. B., Zemach C. A continuum method for modeling surface tension // J. Comput. Physics. 1992. V. 100, N 2. P. 335–354; DOI: 10.1016/0021-9991(92)90240-Y
     
  11. Vozhakov I., Hrebtov M., Yavorsky N., Mullyadzhanov R. Two-component swirling jet atomization with static vortex generators // Physics of Fluids. 2025. V. 37, N 7; DOI: 10.1063/5.0251986
     
  12. Apostol Y. S., Vozhakov I. S., Hrebtov M. Y., Mullyadzhanov R. I. Direct numerical simulation of two-component swirling jet atomization // Eurasian J. Math. Comput. Appl. 2024. V. 12, N 4. P. 4–11; DOI: 10.32523/2306-6172-2024-12-4-4-11
     
  13. Rayleigh L. On the capillary phenomena of jets // Proceedings of the Royal Society of London. 1879. V. 29. P. 71–97; DOI: 10.1098/rspl.1879.0015
     
  14. Bisighini A., Cossali G. E., Caserta C. M., Guido S. Crater evolution after the impact of a drop onto a semi-infinite liquid target // Physical Review E. 2010. V. 82, N 3. Article number 036319; DOI: 10.1103/PhysRevE.82.036319
     
  15. Fedorchenko A. I., Wang A. B. On some common features of drop impact on liquid surfaces // Physics of Fluids. 2004. V. 16, N 5. P. 1349–1365; DOI: 10.1063/1.1652061
     
  16. Mohasan M., Lv P., Duan H. Cavity dynamics of water drop impact onto immiscible oil pool with different viscosity // Acta Mechanica Sinica. 2021. V. 37, N 3. P. 447–455; DOI: 10.1007/s10409-021-01070-4
     
  17. Liu S., Wang G., Liu L., Wang S. Energy conversion and cavity depth model in droplet impact on an immiscible deep pool: A generalized analysis approach // Physical Review Fluids. 2026. V. 11, N 1. Article number 014004; DOI: 10.1103/PhysRevFluids.11.014004
     
  18. Tang X., Saha A., Law C. K., Sun C. Nonmonotonic response of drop impacting on liquid film: mechanism and scaling // Soft Matter. 2016. V. 12, N 20. P. 4521–4529; DOI: 10.1039/C6SM00251J

Исследование выполнено при финансовой поддержке Российского научного фонда (проект № 22-79-10246-П). Других источников финансирования проведения или руководства данным конкретным исследованием не было.

А. А. Лукьянов
  1. Институт теплофизики им. С. С. Кутателадзе СО РАН, 
    просп. Академика Лаврентьева, 1, Новосибирск 630090, Россия

E-mail: a.lukyanov1@g.nsu.ru 

И. С. Вожаков
  1. Институт теплофизики им. С. С. Кутателадзе СО РАН, 
    просп. Академика Лаврентьева, 1, Новосибирск 630090, Россия

E-mail: vozhakov@gmail.com 

Р. И. Мулляджанов
  1. Институт теплофизики им. С. С. Кутателадзе СО РАН, 
    просп. Академика Лаврентьева, 1, Новосибирск 630090, Россия

E-mail: r.mullyadzhanov@g.nsu.ru 

Статья поступила 09.09.2025 г.
После доработки — 21.11.2025 г.
Принята к публикации 13.05.2026 г.

Abstract:

The effect of collision velocity on cavity dynamics during the impact of a water droplet on an oil layer was investigated using three-dimensional numerical simulations in the Basilisk software package. Using the volume-of-fluid method with adaptive mesh refinement and taking surface tension forces into account, regimes were studied for Weber numbers We = 23–360. It was found that with increasing We, a transition occurs from the capillary collapse regime of the cavity, described by the classical inertial-capillary time scale, to a regime where hydrostatic pressure and viscous dissipation forces play a dominant role.

References:
  1. Rein M. Phenomena of liquid drop impact on solid and liquid surfaces. Fluid Dynamics Research, 1993, Vol. 12, No. 2, pp. 61–93; DOI: 10.1016/0169-5983(93)90106-K
     
  2. Prosperetti A., Oguz H. N. The impact of drops on liquid surfaces and the underwater noise of rain. Annual Review of Fluid Mechanics, 1993, Vol. 25, No. 1, pp. 577–602; DOI: 10.1146/annurev.fl.25.010193.003045
     
  3. Vozhakov I. S., Misyura S. Y., Morozov V. S., Piskunov M. V., Piskunova A. E., Orlova E. G., Mullyadzhanov R. I. High-speed droplet impact on solid surfaces: review on the prospects of modeling fluid flow. Experiments in Fluids, 2025, Vol. 66, No. 3, Article number C-65; DOI: 10.1007/s00348-025-03982-w
     
  4. Worthington A. M. A Study of Splashes. London: Longmans, Green, and Company, 1908.
     
  5. Cherdantsev A., Vozhakov I. Fast droplets impacting liquid layer under a small angle: a numerical analysis of experimental observations. Internat. J. Multiphase Flow, 2024, Vol. 175, Article number 104826; DOI: 10.1016/j.ijmultiphaseflow.2024.104826
     
  6. Ray B., Biswas G., Sharma A. Generation of secondary droplets in coalescence of a drop with a liquid surface. J. Fluid Mechanics, 2015, Vol. 768, pp. 492–523; DOI: 10.1017/jfm.2015.93
     
  7. Yarin A. L. Drop impact dynamics: splashing, spreading, receding, bouncing. . . . Annual Review of Fluid Mechanics, 2006, Vol. 38, No. 1, pp. 159–192; DOI: 10.1146/annurev.fluid.38.050304.092144
     
  8. Popinet S. An accurate adaptive solver for surface-tension-driven interfacial flows. J. Comput. Physics, 2009, Vol. 228, No. 16, pp. 5838–5866; DOI: 10.1016/j.jcp.2009.04.042
     
  9. Scardovelli R., Zaleski S. Direct numerical simulation of free-surface and interfacial flow. Annual Review of Fluid Mechanics, 1999, Vol. 31, No. 1, pp. 567–603; DOI: 10.1146/annurev.fluid.31.1.567
     
  10. Brackbill J. U., Kothe D. B., Zemach C. A continuum method for modeling surface tension. J. Comput. Physics, 1992, Vol. 100, No. 2, pp. 335–354; DOI: 10.1016/0021-9991(92)90240-Y
     
  11. Vozhakov I., Hrebtov M., Yavorsky N., Mullyadzhanov R. Two-component swirling jet atomization with static vortex generators. Physics of Fluids, 2025, Vol. 37, No. 7; DOI: 10.1063/5.0251986
     
  12. Apostol Y. S., Vozhakov I. S., Hrebtov M. Y., Mullyadzhanov R. I. Direct numerical simulation of twocomponent swirling jet atomization. Eurasian J. Math. Comput. Appl., 2024, Vol. 12, No. 4, pp. 4–11; DOI: 10.32523/2306-6172-2024-12-4-4-11
     
  13. Rayleigh L. On the capillary phenomena of jets. Proceedings of the Royal Society of London, 1879, Vol. 29,pp. 71–97; DOI: 10.1098/rspl.1879.0015
     
  14. Bisighini A., Cossali G. E., Caserta C. M., Guido S. Crater evolution after the impact of a drop onto a semi-infinite liquid target. Physical Review E, 2010, Vol. 82, No. 3, Article number 036319; DOI: 10.1103/PhysRevE.82.036319
     
  15. Fedorchenko A. I., Wang A. B. On some common features of drop impact on liquid surfaces. Physics of Fluids, 2004, Vol. 16, No. 5, pp. 1349–1365; DOI: 10.1063/1.1652061
     
  16. Mohasan M., Lv P., Duan H. Cavity dynamics of water drop impact onto immiscible oil pool with different viscosity. Acta Mechanica Sinica, 2021, Vol. 37, No. 3, pp. 447–455; DOI: 10.1007/s10409-021-01070-4
     
  17. Liu S., Wang G., Liu L., Wang S. Energy conversion and cavity depth model in droplet impact on an immiscible deep pool: A generalized analysis approach. Physical Review Fluids 2026, Vol. 11, No. 1, Article number 014004; DOI: 10.1103/PhysRevFluids.11.014004
     
  18. Tang X., Saha A., Law C. K., Sun C. Nonmonotonic response of drop impacting on liquid film: mechanism and scaling. Soft Matter, 2016, Vol. 12, No. 20, pp. 4521–4529; DOI: 10.1039/C6SM00251J