Parameters defining the absence of dissipative losses in the rotating liquid ring

Authors

  • Евгений Александрович Гербер (Evgeniy Gerber) Tyumen higher military engineering command school named after A. I. Proshlyakov
  • Александр Давидович Гербер (Alexander Gerber) Tyumen higher military engineering command school named after A. I. Proshlyakov

DOI:

https://doi.org/10.17072/1994-3598-2017-1-5-10

Abstract

The article covers the problem of studying thermal processes in rotating by inertia in the absence of gravity capillary viscous fluid ring with free boundaries that are acted by pressure of gas medium. Thus there is no heat exchange with the environment at the boundaries of the ring. System under consideration depending on the initial angular velocity, initial radial perturbation and geometry is able to be in different move modes such as infinite expansion, collapse, periodic oscillations. In a series of numerical experiments where only one parameter that determine the character of motion changed and the rest remaining unchanged the effect of minimization dissipative losses was detected at certain critical values of the parameters (viscosity, size, pressure in the cavity). That is, a new mode of ring motion was detected; mode in which regardless of the initial radial perturbations it has minimum dissipative losses. That means that the distribution of the tangential component of the velocity vector is close to a linear function of ring radius. Such kind of dependence inherent to a rigid body motion. That distribution causes liquid layers do not move relative to each other and therefore there are no friction effects, no heat losses of the ring and no loses of initial rotational energy. Analysis of the mathematical model of the motion of liquid ring yielded analytical formulas for calculating the critical values of dynamic viscosity, surface tension, the difference of the gas pressures in the cavities of the ring, the ring sizes. Critical parameters, calculated according to the formulas and found in the course of the numerical experiment coincide with good accuracy.Received 11.12.2016; accepted 02.02.2017

References

Bytev V. O. Unsteady motion of rotating ring of viscous incompressible liquid with free boundary. Journal of Applied Mechanics and Technical Physics, 1970, vol. 11, no. 3, pp. 432–438.

Pukhnachev V. V. Neklassicheskie zadachi teorii pogranichnogo sloia (Non-classical problems of the boundary-layer theory). Novosibirsk: Novosibirs State University, 1980, 74 p. (In Russian).

Lavrent'eva O. M. Neustanovivsheesia dvizhenie vrashchaiushchegosia kol'tsa viazkoi kapilliarnoi zhidkosti. Dinamika sploshnoi sredy (Continuum Mechanics): Bulletin of the Hydrodynamics Institute of Siberian Branch of Academy of Sciences of the USSR. Novosibirsk, 1978, vol. 31, pp. 52–60 (In Russian).

Lavrent'eva O. M. Predel'nye rezhimy dvizheniia vrashchaiushchegosia viazkogo kol'tsa Dinamika sploshnoi sredy (Continuum Mechanics): Bulletin of theHydrodynamics Institute of Siberian Branch of Academy of Sciences of the USSR. Novosibirsk, 1980. vol. 44, pp. 15–34 (In Russian).

Vallander S. V. Lectures in Hydroaeromechanics. Leningrad: Leningrad State University, 1978, 295 p. (In Russian).

Gerber E. A., Kutrunov V. N. On the mechanism and on the laws of periodic motions of ring of capillary liquid. Bulletin of Tyumen State University, 2011, no. 7, pp. 136–142 (In Russian).

Gerber E. A., Kutrunov V. N., Dvizhenie kol'tsa viazkoi kapilliarnoi zhidkosti (Motion of viscous capillary liquid ring). Abstr. Of All-Russian Conf. “Nonlinear waves: theory and ne applications”. Novosibirsk: Lavrentyev Institute of Hydrodynamics, Siberian Branch of the RAS, 2011, pp. 23–24 (In Russian).

Gerber E. A., Kutrunov V. N. Ring v1.2. Certificate of state registration of the computer program N. 2011613120. 2011

Gerber A. D., Gerber E. A. About dissipative losses into rotating capillary liquid ring. Bulletin of Perm University. Physics, 2016, no. 2 (33), pp. 21–26.

Published

2017-06-30

How to Cite

Гербер (Evgeniy Gerber) Е. А., & Гербер (Alexander Gerber) А. Д. (2017). Parameters defining the absence of dissipative losses in the rotating liquid ring. Bulletin of Perm University. Physics, (1(35). https://doi.org/10.17072/1994-3598-2017-1-5-10

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