Advertisement

Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Motion and filling of cavities in a boundless liquid and close to a plane

Abstract

The motion of bubbles in liquids has been studied in many earlier papers [1–8]. In this paper methods of the projection type are applied to the problem of a cavity in an ideal, incompressible liquid in the absence of vortices. The collapse of a bubble having a finite initial velocity in a boundless liquid is considered; also considered is the collapse of a stationary bubble close to a solid wall. Using the small-parameter method the generation of a jet is examined analytically. A numerical computing method not involving small parameters is developed; it is based on calculating the projection by numerical computation of the corresponding integrals. The method combines economy and simplicity of application with a high accuracy in the region in which the representation of the velocity potential by a series of spherical functions remains effective.

This is a preview of subscription content, log in to check access.

Literature cited

  1. 1.

    L. V. Ovsyannikov, “On the flotation of a bubble,” in: Problems of Mathematics and Mechanics [in Russian], Nauka, Leningrad (1970).

  2. 2.

    Yu. V. Pukhnachev, “Introduction to the dynamics of a bubble inside a liquid,” in: Introduction to the Dynamics of a Solid Containing a Liquid under Conditions of Weightlessness [in Russian], Izd. Vys. Tsent. Akad. Nauk SSSR, Moscow (1968).

  3. 3.

    G. Birkhooff, “Stability of spherical bubbles,” Quart. J. Appl. Math.,13, No. 4 (1956).

  4. 4.

    M. S. Plesset and T. P. Mitchell, “On the stability of the spherical shape of a vapor cavity in a liquid, Quart. J. Appl. Math.,13, No. 4 (1956).

  5. 5.

    C. F. Naude and A. T. Ellis, “On the mechanism of cavitation damage by nonhemispherical cavities collapsing in contact with a solid boundary,” Trans. ASME, Ser. D,83, 648 (1961).

  6. 6.

    A. Shima, “The behavior of a spherical bubble in the vicinity of a solid wall,” Trans. ASME, Ser. D,90, No. 1 (1968).

  7. 7.

    M. S. Plesset and R. B. Chapman, “Collapse of an initially spherical vapor cavity in the neighborhood of a solid boundary,” J. Fluid Mech.,47, Pt. 2 (1971).

  8. 8.

    O. V. Voinov and A. G. Petrov, “Motion of a sphere of variable volume in an ideal liquid near a plane surface,” Izv. Akad. Nauk SSSR, Mekhan. Zhid. i Gaza, No. 5 (1971).

Download references

Author information

Additional information

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 89–95, January–February, 1975.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Voinov, V.V., Voinov, O.V. Motion and filling of cavities in a boundless liquid and close to a plane. J Appl Mech Tech Phys 16, 71–75 (1975). https://doi.org/10.1007/BF00853543

Download citation

Keywords

  • Vortex
  • Mathematical Modeling
  • Mechanical Engineer
  • Numerical Computation
  • Industrial Mathematic