ISSN 2658–5782
DOI 10.21662
Electronic Scientific Journal


© Институт механики
им. Р.Р. Мавлютова
УФИЦ РАН

Яндекс.Метрика web site traffic statistics

Toporkov D.Yu. Сollapse of weakly-nonspherical cavitation bubble in acetone and tetradecane. Multiphase Systems. 13 (2018) 3. 23–28.
2018. Vol. 13. Issue 3, Pp. 23–28
URL: http://mfs.uimech.org/mfs2018.3.003
DOI: 10.21662/mfs2018.3.003
Сollapse of weakly-nonspherical cavitation bubble in acetone and tetradecane
Toporkov D.Yu.
Institute of Mechanics and Engineering, Kazan Scientific Center of the RAS, Kazan

Abstract

Collapse of a weakly-spherical cavitation bubble in acetone and tetradecane is studied. The bubble radius is 500 μm, the temperature and pressure of the liquid are 293 K and 15 bar in the case of acetone and 663 K and 50 bar in the case of tetradecane. A hydrodynamic model is used in which the compressibility of the liquid, the nonstationary thermal conduction of the vapor and the liquid, and nonequilibrium heat and mass transfer on the bubble surface, as well as imperfection of the vapor, are considered. Realistic wide-range equations of state are used. It has been found that converging shock waves appear in the bubbles during its collapses in acetone and tetradecane. The maximum values of the thermodynamic parameters are comparable. A comparison of the evolution of the bubble sphericity perturbation and motion of the shock wave in the bubble allows suggesting that tetradecane is a more favorable medium for the realization of a near-spherical cumulation in a bubble than acetone.

Keywords

bubble collapse,
shock waves,
nonsphericity,
perturbation of spherical shape

Article outline

Problem: Numerical study of the evolution of the sphericity perturbation of cavitation bubbles during their collapse in acetone and tetradecane.

Methods: The system of gas dynamics equations is solved numerically by the method of S.K. Godunov with a moving grid that is nonuniform in the vapor and in the liquid (the cells size increases exponentially in the direction from the surface of the bubble). The evolution of deviations from the spherical shape of the bubble is described using a second-order ordinary differential equation, which is solved numerically using a Runge–Kutta method of high-order accuracy with a variable time step.

In a study was determined:

1. Converging shock waves appear inside the bubbles during its collapse (in acetone and tetradecane). The maximum values of the thermodynamic parameters reach comparable values by focusing of the waves in the case of their spherical shape. The radius of the bubble in tetradecane at the moment of maximum vapor compression is 6.5 times greater than that of the bubble in acetone. The radius of the shock wave arising in the bubble in the case of tetradecane changes from the moment of its formation to focusing much larger (by a factor of 6) then in acetone.

2. The growth of the small perturbations of the bubble sphericity during its collapse in acetone is much larger. The difference exceeds 12 times for the investigated interval of spherical harmonics numbers 2–10.

3. Taking into account that the growth of the perturbation of the bubble sphericity during the decrease of the radius of the bubble is more intense than the increase of the nonsphericity of the shock wave during its radius decreasing, it can be expected that the cumulation in the central area of the bubble during its collapse in tetradecane will be closer to spherical than in the case of acetone. For a more detailed answer to the question of the level of nonsphericity of the shock wave near the moment of its focusing, an additional study of the evolution of a nonspherical shock wave is necessary.

References

  1. Taleyarkhan R.P., West C.D., Cho J.S., Lahey R.T. (Jr), Nigmatulin R.I., Block R.C. Evidence for nuclear emissions during acoustic cavitation // Science. 2002. V. 295. P. 1868–1873.
    (DOI: 10.1126/science.1067589)
  2. Нигматулин Р.И., Лэхи Р.Т.(мл.), Талейархан Р.П., Вест К.Д., Блок Р.С. О термоядерных процессах в кавитирующих пузырьках // УФН. 2014. Т. 184, № 9. С. 947–960.
    (DOI: 10.3367/UFNr.0184.201409b.0947)
  3. Taleyarkhan R.P., West C.D., Cho J.S., Lahey R.T. (Jr), Nigmatulin R.I., Block R.C. Additional evidence of nuclear emissions during acoustic cavitation // Phys. Rev. E. 2004. V. 69. 036109.
    (DOI: 10.1103/PhysRevE.69.036109)
  4. Taleyarkhan R.P., West C.D., Cho J.S., Lahey R.T. (Jr), Nigmatulin R.I., Block R.C. Nuclear emissions during selfnucleated acoustic cavitation // Phys. Rev. Lett. 2006. V. 96. 034301.
    (DOI: 10.1103/PhysRevLett.96.034301)
  5. Xu Y., Butt A. Confirmatory Experiments for Nuclear Emissions During Acoustic Cavitation // Nucl. Eng. Des. 2005. V. 235. P. 1317–1324.
    (DOI: 10.1016/j.nucengdes.2005.02.021)
  6. Nigmatulin R.I, Akhatov I.Sh., Topolnikov A.S., Bolotnova R.Kh., Vakhitova N.K., Lahey R.T. (Jr), Taleyarkhan R.P. The Theory of Supercompression of Vapor Bubbles and Nano-Scale Thermonuclear Fusion // Phys. Fluids. 2005. V. 17. 107106.
    (DOI: 10.1063/1.2104556)
  7. Нигматулин Р.И., Аганин А.А., Топорков Д.Ю., Ильгамов М.А. Образование сходящихся ударных волн в пузырьке при его сжатии // Доклады РАН. 2014. Т. 458, № 3. С. 282–286.
    (DOI: 10.7868/S0869565214270115)
  8. Аганин А.А., Топорков Д.Ю. Оценка возникновения ударных волн в кавитационном пузырьке при его коллапсе // Учен. зап. Казан. ун-та. Сер. Физ.-матем. науки. 2017. Т. 159, кн. 3. С. 271–281.
    (https://kpfu.ru/portal/docs/F_1783512310/159_3_phys_mat_1.pdf)
  9. Нигматулин Р.И., Аганин А.А., Топорков Д.Ю., Ильгамов М.А. Эволюция возмущений сферичности пузырька при его сильном сжатии // Доклады РАН. 2016. Т. 467, № 2. С. 168–172.
    (DOI: 10.7868/S0869565216080119)
  10. Нигматулин Р.И., Болотнова Р.Х. Широкодиапазонное уравнение состояния органических жидкостей на примере ацетона // Доклады РАН. 2007. Т. 415, № 5. С. 617–621.
    (https://elibrary.ru/item.asp?id=9533722)
  11. Нигматулин Р.И., Болотнова Р.Х. Широкодиапазонные уравнения состояния бензола и тетрадекана в упрощенной форме // ТВТ. 2017. Т. 55, № 2. С. 206–215.
    (DOI: 10.7868/S004036441701015X)
  12. Lin H., Storey B.D., Szeri A.J. Inertially driven inhomogeneities in violently collapsing bubbles: the validity of the Rayleigh–Plesset equation // J. Fluid Mech. 2002. V. 452. P. 145–162.
    (DOI: 10.1017/S0022112001006693)
  13. Plesset M.S., Mitchell T.P. On the stability of the spherical shape of a vapor cavity in a liquid // Quart. Appl. Math. 1956. V. 13, N 4. P. 419–430.
    (DOI: 10.1090/qam/79931)
  14. Нигматулин Р.И., Аганин А.А., Ильгамов М.А., Топорков Д.Ю. Эволюция возмущений сферической формы кавитационного пузырька при его взрывном коллапсе // Учен. зап. Казан. ун-та. Сер. Физ.-матем. науки. 2014. Т. 1556, кн. 1. С. 79–108.
    (http://mi.mathnet.ru/rus/uzku/v156/i1/p79)
  15. Somogyi Z., Roberts P.H. Stability of an Imploding Spherical Shock Wave in a van der Waals Gas II // Quart. J. Mech. Appl. Math. 2007. V. 60. P. 289–309.
    (DOI: 10.1093/qjmam/hbm006)