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DOI 10.21662
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Aganin A.A., Davletshin A.I., Khalitova T.F. Numerical simulation of bubble dynamics in central region of streamer. Multiphase Systems. 13 (2018) 3. 11–22.
2018. Vol. 13. Issue 3, Pp. 11–22
URL: http://mfs.uimech.org/mfs2018.3.002,en
DOI: 10.21662/mfs2018.3.002
Numerical simulation of bubble dynamics in central region of streamer
Aganin A.A., Davletshin A.I., Khalitova T.F.
Institute of Mechanics and Engineering, Kazan Scientific Center of the RAS, Kazan

Abstract

A mathematical model and a numerical technique for studying strong expansion and collapse of cavitation bubbles located in the central region of a streamer where the bubbles are almost motionless are developed. They are essentially efficient combinations of the models and techniques previously created by the authors for calculating the dynamics of interacting weakly-non-spherical bubbles in a streamer and the dynamics of a single axisymmetric bubble. The first model and technique are applied at the low-speed stage of expansion and compression of bubbles where their hydrodynamic interaction is significant. The second ones are used at the final high-speed stage of their collapse where the interaction is inessential. The simplest case of the streamer comprising three bubbles is considered as an example to illustrate the features of the developed model and numerical technique. It is shown that under the strong expansion and collapse of an initially spherical cavitation bubble, the presence of neighboring bubbles can substantially deflect the bubble cavity vapor dynamics from what is realized inside a similar but single bubble.

Keywords

cavitation bubble,
hydrodynamic interaction of bubbles,
shock waves,
deformation of bubbles

Article outline

Purpose. Numerical simulation of dynamics of bubbles in the central region of a streamer under their strong expansion and collapse with taking into account their interaction and strong non-uniformity of the bubble contents in the final stage of the bubble collapse.

Methodology. The model and the numerical technique are essentially an effective combination of the models and the methods previously created by the authors for calculating the dynamics of interacting weakly-non-spherical bubbles in a streamer and the dynamics of a single axisymmetric bubble.

At the low-speed stage of expansion and collapse the hydrodynamic interaction between the bubbles significantly influences the evolution of their shape, whereas the bubbles remain nearly homobaric and their deformations keep small. At this stage, a model of the dynamics of weakly-non-spherical bubbles is used. In the final high-speed stage of the bubble collapse, the interaction between the bubbles is inessential. However, it is necessary to take into account the liquid compressibility, the non-uniformity of the vapor in the bubbles, the formation of radially convergent non-spherical shock waves inside the bubbles. Taking this into account, the model of the dynamics of a single axisymmetric bubble is applied in this stage.

Findings. A mathematical model and an effective numerical technique for study of strong expansion and collapse of cavitation bubbles located in the central region of a streamer where the bubbles are almost motionless are developed. The features of the model and the technique are illustrated by an example of calculating the dynamics of the central bubble in a streamer comprising three bubbles. It is shown that under the strong expansion and collapse of an initially spherical cavitation bubble the presence of the neighboring bubbles can substantially deflect the dynamics of the vapor in its cavity from what is realized inside a similar single bubble.

Originality/value. The proposed mathematical model and numerical technique can be used for studying the properties of the bubble dynamics in the central region of streamers.

References

  1. Flannigan D. J., Suslick K. S. Inertially confined plasma in an imploding bubble // Nature Physics. 2010. V. 6. P. 598–601.
    (DOI: 10.1038/nphys1701)
  2. Taleyarkhan R.P. et al. Evidence for nuclear emissions during acoustic cavitation // Science. 2002. V. 295, no. 5561. P. 1868–1873.
    (DOI: 10.1126/science.1067589)
  3. Taleyarkhan R.P. et al. Nuclear emissions during self-nucleated acoustic cavitation // Phys. Rev. Let. 2006. V. 96. P. 034301.
    (DOI: 10.1103/PhysRevLett.96.034301)
  4. Suslick K.S. Sonochemistry // Science. 1990. V. 247. P. 1439–1445.
    (DOI: 10.1126/science.247.4949.1439)
  5. Нигматулин Р.И., Аганин А.А., Топорков Д.Ю., Ильгамов М.А. Образование сходящихся ударных волн в пузырьке при его сжатии // ДАН. 2014. Т. 458, № 3. C. 282–286.
    (DOI: 10.7868/S0869565214270115)
  6. Nigmatulin R.I., Akhatov I.Sh., Topolnikov A.S. et. al. The theory of supercompression of vapor bubbles and nano-scale thermonuclear fusion // Phys. Fluids. 2005. V. 17, no. 10. P. 1–31.
    (DOI: 10.1063/1.2104556)
  7. Hilgenfeldt S., Grossmann S., Lohse D. Sonoluminescence light emission // Phys. Fluids. 1999. V. 11, no. 6. P. 1318–1330.
    (DOI: 10.1063/1.869997)
  8. Аганин А.А., Ильгамов М.А., Нигматулин Р.И., Топорков Д.Ю. Эволюция искажений сферичности кавитационного пузырька при акустическом сверхсжатии // Известия РАН. МЖГ. 2010. № 1. С. 57–69.
    (https://elibrary.ru/item.asp?id=13001975)
  9. Аганин А.А., Халитова Т.Ф., Хисматуллина Н.А. Численное моделирование радиально сходящихся ударных волн в полости пузырька // Математическое моделирование. 2014. Т. 26, № 4. С. 3–20.
    (DOI: 10.1134/S2070048214060027)
  10. Аганин А.А., Халитова Т.Ф. Деформация ударной волны при сильном сжатии несферических пузырьков // Теплофизика высоких температур. 2015. Т. 53, № 6. С. 923–927.
    (DOI: 10.1134/S0018151X15050016)
  11. Xu Y., Butt A. Confirmatory experiments for nuclear emissions during acoustic cavitation // Nuclear Engin. and Design. 2005. V. 235, No 11–12. P. 1317–1324.
    (DOI: 10.1016/j.nucengdes.2005.02.021)
  12. Аганин А.А., Давлетшин А.И., Топорков Д.Ю. Динамика расположенных в линию кавитационных пузырьков в интенсивной акустической волне // Вычислительные технологии. 2014. Т. 19, № 1. С. 3–19.
    (http://www.ict.nsc.ru/jct/annotation/1587)
  13. Аганин А.А., Давлетшин А.И. Моделирование взаимодействия газовых пузырьков в жидкости с учетом их малой несферичности // Математическое моделирование. 2009. Т. 21, № 6. С. 89–102.
    (http://mi.mathnet.ru/mm2847)
  14. Gavrilyuk S.L., Teshukov V.M. Drag force acting on a bubble in a cloud of compressible spherical bubbles at large Reynolds number // European Journal of Mechanics B/Fluids. 2005. V. 24, No 4. P. 468–477.
    (DOI: 10.1016/j.euromechflu.2004.12.001)
  15. Doinikov A.A. Equations of coupled radial and translational motions of a bubble in a weakly compressible liquid // Phys. Fluids. 2005. V. 17, No 12. 128101.
    (DOI: 10.1063/1.2145430)
  16. Хайрер Э., Нерсетт С., Ваннер Г. Решение обыкновенных дифференциальных уравнений. Нежесткие задачи. М.: Мир, 1990. 512 с.