Advertisement

Microgravity Science and Technology

, Volume 31, Issue 3, pp 269–278 | Cite as

Thermal Vibrational Convection of Water near its Density Inversion Point in a Cylindrical Cavity with Constant Heat Flux at the Boundaries in Low Gravity Conditions

  • D. V. Lyubimov
  • V. A. Sharifulin
  • T. P. LyubimovaEmail author
  • A. N. Sharifulin
Original Article
  • 43 Downloads

Abstract

Equations for thermal vibrational convection in a nonuniformly heated liquid with thermal density inversion subjected to high-frequency small-amplitude vibrations are obtained by averaging method. The problem of thermal vibrational convection in a horizontal cylinder filled with a liquid with quadratic temperature dependence of density is studied analytically on the basis of these equations for arbitrary orientations of temperature gradient, gravity and vibration axis. The heating is carried out in such a way that the point of temperature inversion of density is located at the cylinder axis. It is shown that by changing the direction of vibrations and their intensity, it is possible to control the structure and intensity of average flow.

Keywords

Thermal convection High frequency vibrations Density inversion Cylindrical cavity 

Notes

Acknowledgements

The investigation has been supported by Ministry of Education and Science of Russian Federation (project 3.6990.2017/8.9).

References

  1. Dold P., Benz K.W., Croll A., Roux B., Lyubimov D. V., Lyubimova T.P., Scuridin R. Vibration controlled convection — preparation and perspective of the Maxus 4 experiment. Acta. Astronaut., 2001, vol. 48, N 5–12, pp. 639–646Google Scholar
  2. Gaponenko Y., Shevtsova V. Mixing under vibrations in reduced gravity. Micrograv. Sci. Technol., 2008, vol. 20, N 3–4, pp. 307–311Google Scholar
  3. Gershuni, G.Z., Lyubimov, D.V.: Thermal Vibrational Convection. John Wiley&Sons. 358 pр (1998)Google Scholar
  4. Gershuni G. Z., Zhukhovitsky E. M., Sharifulin A. N. Vibrational thermal convection in cylindrical cavity. Num. Methods Contin. Mech., 1983, vol. 14, N 4, pp. 21–31 (in russian)Google Scholar
  5. Goldobin, M.A., Lyubimov, D.V.: The weak vibrational convection in non-uniformly heated cylinder. Bull. Perm Univ. Ser. Phys. 2, 5–11 (2012)Google Scholar
  6. Kozlov V. G., Polezhaev D. A. Stability of rimming flow under vibration. Micrograv. Sci .Technol., 2009, vol. 21, N 1, pp. 79–82Google Scholar
  7. Lappa M. Control of convection patterning and intensity in shallow cavities by harmonic vibrations. Micrograv. Sci. Technol., 2016, vol. 28, N 1, pp.29–39Google Scholar
  8. Lyubimov D.V., Lyubimova T.P., Tcherepanov A.A., Roux B., Billia B.,Nguyen-Thi H. Vibration influence on morphological instability of a solidification front. Micrograv. Sci. Technol., 2005, vol. 16, N 1, pp. 290–294Google Scholar
  9. Lyubimov D. V., Baydin A. Y., Lyubimova T. P. Particle dynamics in a fluid under high frequency vibrations of linear polarization. Micrograv. Sci. Technol., 2013, vol. 25, N 2, pp. 121Google Scholar
  10. Lyubimova T.P., Zubova N.A., Shevtsova V.M. Vibrational convection of ternary mixtures in rectangular cavities in zero gravity conditions. J. Phys. Conf. Ser. IOP Publishing 2016, vol. 681, N 1, 012041Google Scholar
  11. Sharifulin, A. N.: Vibrational convection in cylindrical cavity at nongravity. Convective Flows. Perm: Perm. Pedagogical in-t. , pp.22–29 (in russian) (1981)Google Scholar
  12. Sharifulin A.N. Supercritical vibration-induced thermal convection in a cylindrical cavity. J Paper Fluid Mech. Soviet Res., vol. 15, N 2. 28–23 (1986)Google Scholar
  13. Sharifulin, A.N.: Controllable equilibrium of an Inhomogeneously heated liquid in a vibrational field. J. Exp. Theor. Phys. 110(1), 157–161 (2010)CrossRefGoogle Scholar
  14. Shevtsova, V., Melnikov, D., Legros, J. C., Yan, Y., Saghir, Z., Lyubimova, T., Roux, B. Influence of vibrations on thermodiffusion in binary mixture: a benchmark of numerical solutions. Phys. Fluids, 2007, vol. 19, N 1, 017111Google Scholar
  15. Veronis G. Penetrative convection. Astrophys. J., 1963, vol.137, N 2, pp. 641–663Google Scholar
  16. Zenkovskaya, S.M., Simonenko I.B.: Effect of high frequency vibration on convection initiation, Fluid Dynam. 5, pp. 35–37 (1966)Google Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  • D. V. Lyubimov
    • 1
  • V. A. Sharifulin
    • 2
  • T. P. Lyubimova
    • 1
    • 3
    Email author
  • A. N. Sharifulin
    • 2
  1. 1.Perm State UniversityPermRussia
  2. 2.Perm National Research Polytechnic UniversityPermRussia
  3. 3.Institute of Continuous Media Mechanics of the Ural Branch of Russian Academy of SciencesPermRussia

Personalised recommendations