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.
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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. 639–646
Gaponenko Y., Shevtsova V. Mixing under vibrations in reduced gravity. Micrograv. Sci. Technol., 2008, vol. 20, N 3–4, pp. 307–311
Gershuni, G.Z., Lyubimov, D.V.: Thermal Vibrational Convection. John Wiley&Sons. 358 pр (1998)
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)
Goldobin, M.A., Lyubimov, D.V.: The weak vibrational convection in non-uniformly heated cylinder. Bull. Perm Univ. Ser. Phys. 2, 5–11 (2012)
Kozlov V. G., Polezhaev D. A. Stability of rimming flow under vibration. Micrograv. Sci .Technol., 2009, vol. 21, N 1, pp. 79–82
Lappa M. Control of convection patterning and intensity in shallow cavities by harmonic vibrations. Micrograv. Sci. Technol., 2016, vol. 28, N 1, pp.29–39
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. 290–294
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. 121
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, 012041
Sharifulin, A. N.: Vibrational convection in cylindrical cavity at nongravity. Convective Flows. Perm: Perm. Pedagogical in-t. , pp.22–29 (in russian) (1981)
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)
Sharifulin, A.N.: Controllable equilibrium of an Inhomogeneously heated liquid in a vibrational field. J. Exp. Theor. Phys. 110(1), 157–161 (2010)
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, 017111
Veronis G. Penetrative convection. Astrophys. J., 1963, vol.137, N 2, pp. 641–663
Zenkovskaya, S.M., Simonenko I.B.: Effect of high frequency vibration on convection initiation, Fluid Dynam. 5, pp. 35–37 (1966)
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The investigation has been supported by Ministry of Education and Science of Russian Federation (project 3.6990.2017/8.9).
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Lyubimov, D.V., Sharifulin, V.A., Lyubimova, T.P. et al. 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. Microgravity Sci. Technol. 31, 269–278 (2019). https://doi.org/10.1007/s12217-019-9686-1
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DOI: https://doi.org/10.1007/s12217-019-9686-1