Numerical study of the influence of axial vibrations of finite amplitude and frequency on flows and meniscus deformations in a liquid zone under zero gravity conditions
DOI:
https://doi.org/10.7242/1999-6691/2019.12.4.39Keywords:
liquid zone, axial vibrations, average flow, waves at the interface, direct numerical simulationAbstract
Vibrational effect on heterogeneous systems is one of the mechanisms for controlling the processes occurred in these systems. For hydrodynamical systems, vibrations can greatly affect the type of flows and the shape of the interfaces, leading to the behavior that is significantly different from that in static fields. In this paper, the flows and interface deformations are studied numerically for a cylindrical liquid zone surrounded by a coaxial layer of gas. In vertical direction the system is bounded by the parallel rigid plates subjected to the axial vibrations of finite frequency and amplitude. The aim of the work is to study and explain the nature of new vibrational phenomena observed experimentally. The study is performed in the framework of a full non-average approach using the fluid volume method. The data are obtained on the instantaneous and average velocity fields and the instantaneous and average shape of the interface at various frequencies and amplitudes of vibrations. It is shown that the axial vibrations of the rigid plates induce the waves at the interface which propagate from the plates to the zone center. These waves generate an average flow with the direction near interface from the oscillating plates to the zone center. Additionally, vibrations generate an average flow near rigid plates in the form of toroidal vortices with the direction near rigid plates from interface to the zone axis.
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References
Strutt J.W. (Baron Rayleigh). The theory of sound. Macmillan, 1877. Vol. 1. 984 p.
Schlichting H., Gersten K. Boundary-layer theory. Springer, 2000. 817 p. https://doi.org/10.1007/978-3-642-85829-1">https://doi.org/10.1007/978-3-642-85829-1
Longuet-Higgins M.S. Mass transport in water waves. Phil. Trans. Roy. Soc. Lond. Math. Phys. Sci., 1953, vol. 245, pp. 535‑581. https://doi.org/10.1098/rsta.1953.0006">https://doi.org/10.1098/rsta.1953.0006
Gershuni G.Z., Lyubimov D.V. Thermal vibrational convection. Wiley, 1998. 372 p.
Wolf G.H. The dynamic stabilization of the Rayleigh–Taylor instability and the corresponding dynamic equilibrium. Z. Physik, 1969, vol. 227, pp. 291-300. https://doi.org/10.1007/BF01397662">https://doi.org/10.1007/BF01397662
Lyubimov, D.V., Cherepanov, A.A. Development of a steady relief at the interface of fluids in a vibrational field. Fluid Dyn., 1986, vol. 21, pp. 849-854. https://doi.org/10.1007/BF02628017">https://doi.org/10.1007/BF02628017
Lyubimov D.V., Lyubimova T.P. Ob odnom metode skvoznogo scheta dlya resheniya zadach s deformiruyemoy poverkhnost’yu razdela [About one end-to-end calculation method for solving problems with a deformable]. Modelirovaniye v mekhanike, 1990, vol. 4(21), no. 1, pp. 136-140.
Lyubimov D.V., Cherepanov A.A., Lyubimova T.P., Roux B. Orienting effect of vibrations on interfaces. C.R.Acad. Sci. Paris, 1997, vol. 325, serie IIb, pp. 391-396.
Lyubimov D.V., Khenner M.V., Shots M.M. Stability of a fluid interface under tangential vibrations. Fluid Dyn., 1998, vol. 33, pp. 318-323. https://doi.org/10.1007/BF02698179">https://doi.org/10.1007/BF02698179
Khenner M.V., Lyubimov D.V., Belozerova T.S., Roux B. Stability of plane-parallel vibrational flow in a two-layer system. Eur. J. Mech. B Fluids, 1999, vol. 18, pp. 1085-1101. https://doi.org/10.1016/S0997-7546(99)00143-0">https://doi.org/10.1016/S0997-7546(99)00143-0
Lyubimov D., Lyubimova T., Roux B. Mechanisms of vibrational control of heat transfer in a liquid bridge. Int. J. Heat Mass Tran., 1997, vol. 40, pp. 4031-4042. https://doi.org/10.1016/S0017-9310(97)00053-7">https://doi.org/10.1016/S0017-9310(97)00053-7
Lyubimov D.V., Lyubimova T.P., Skuridin R.V., Chen G., Roux B. Numerical investigation of meniscus deformation and flow in an isothermal liquid bridge subject to high-frequency vibrations under zero gravity conditions. Comput. Fluid., 2002, vol. 31, pp. 663-682. https://doi.org/10.1016/S0045-7930(01)00078-0">https://doi.org/10.1016/S0045-7930(01)00078-0
Lyubimova T.P., Scuridin R.V., Cröll A., Dold P. Influence of high frequency vibrations on fluid flow and heat transfer in a floating zone. Cryst. Res. Technol., 2003, vol. 38, pp. 635-653. https://doi.org/10.1002/crat.200310078">https://doi.org/10.1002/crat.200310078