Mechanics of a non-uniformly heated fluid in two-layer system under longitudinal vibration in weightlessness: the porosity and permeability effects
DOI:
https://doi.org/10.17072/1994-3598-2020-2-38-47Keywords:
uniform porous zone, two-layer system, thermal vibrational convection, microgravity, longitudinal vibra-tion, permeability and porosity effects, Beavers-Joseph conditionAbstract
The effect of the porosity and permeability variations on the onset of average convection in a single-component fluid within an non-uniformly heated horizontal layer partially filled with a porous zone under zero gravity conditions is studied. The system of the fluid and porous layers oscillates as a whole with high frequency and small amplitude in the longitudinal direction. Permeability is uniform within the porous zone and related to porosity by the Carman–Kozeny formula. The method of constructing a fundamental system of solutions as well as the orthogonalization of vectors for partial solutions are applied to simulate a linear stability problem with respect to the fluid quasi-equilibrium state in the layers numerically. The instability threshold relative to the short-wave and long-wave convective rolls is found. An abrupt change in the type of instability from the short-wave to long-wave ones occurs with the growth of the porosity from 0.3 to 0.8. A similar variation also presents in the case of thermal gravitational convection in layered fluid systems with porous zones under Earth conditions. Convection in weightlessness distinguishes from that in the gravitational field by a non-monotonic behavior of the instability threshold with increasing porosity at different fixed frequencies of vibration. The onset of convection delays at low frequencies and, on the contrary, speeds up at high enough frequencies, if the porosity belongs to the interval from 0.3 to 0.8. In addition, one studies the effect of two types of boundary conditions for tangential velocities near the interface between the layers on the instability threshold in the system with a low permeable porous zone.References
Gershuni G. Z., Zhukovitskii E. M. Convective stability of incompressible fluids. Moscow: Nauka, 1972. 392 p.
Gershuni G. Z., Lyubimov D. V. Thermal Vibrational Convection. N.Y.: Wiley, 1998. 358 p.
Zavarykin M. P., Zorin S. V., Putin G. F. An experimental study of the vibrational convection. Doklady Akademii nauk SSSR, 1985, vol. 281, no. 4, pp. 815-816.
Zavarykin M. P., Zorin S. V., Putin G. F. On the thermoconvective instability in a vibrational field. Doklady Akademii nauk SSSR, 1988, vol. 299, no. 2, pp. 309-312.
Demin V. A., Gershuni G. Z., Verkholantsev I. V. Mechanical quasiequilibrium and thermovibrational convective instability in an inclined fluid layer. International Journal of Heat and Mass Transfer, 1996, vol. 39, pp. 1979-1991.
Babushkin I. A., Demin V. A. Vibrational convection in the Hele-Shaw cell. Theory and experiment. Journal of Applied Mechanics and Technical Physics, 2006, vol. 47, no. 2, pp. 183-189.
Babushkin I. A., Demin V. A. On vibration-convective flows in a Hele-Shaw cell. Journal of Engineering Physics and Thermophysics, 2008, vol. 81, no. 4, pp. 739-747.
Zen’kovskaya S. M. The effect of high-frequency vibrations on filtration convection. AMTP, 1992, vol. 33, no. 5, pp. 83-88.
Bardan G., Mojtabi A. On the Horton–Rogers–Lapwood convective instability with vertical vibration. Physics of Fluids, 2000, vol. 12, pp. 2723–2731.
Bardan G., Razi Y. P., Mojtabi A. Comments on the mean flow averaged model. Physics of Fluids, 2004, vol. 16, no. 12, pp. 4535.
Govender S. Linear stability and convection in a gravity modulated porous layer heated from below: Transition from synchronous to subharmonic oscillations. Transport in Porous Media, 2005, vol. 59, pp. 227–238.
Zen’kovskaya S. M., Rogovenko T. N. Filtration convection in high-frequency vibration field. AMTP, 1999, vol. 40, no. 3, pp. 22-29.
Chen F., Chen C. F. Experimental investigation of convective stability in a superposed fluid and porous layer when heated from below. Jour-nal of Fluid Mechanics, 1989, vol. 207, pp. 311–321. DOI: 10.1017/S0022112089002594
Hirata S. C., Goyeau B., Gobin D. Stability of thermosolutal natural convection in superposed fluid and porous layers. Transport in Porous Media, 2009, vol. 78, pp. 525-536. DOI: 10.1007/s11242-008-9322-9
Kolchanova E., Lyubimov D., Lyubimova T. The onset and nonlinear regimes of convection in a two-layer system of fluid and porous medium saturated by the fluid. Transport in Porous Media, 2013, vol. 97, no. 1, pp. 25–42. DOI: 10.1007/s11242-012-0108-8
Lyubimov D. V., Lyubimova T. P., Muratov I. D., Shishkina E. A. Vibration effect on convection onset in a system consisting of a horizontal pure liquid layer and a layer of liquid saturated porous medium. Fluid Dynamics, 2008, vol. 43, no. 5, pp. 789-798.
Lyubimov D., Kolchanova E., Lyubimova T. Vibration effect on the nonlinear regimes of thermal convection in a two-layer system of fluid and saturated porous medium. Transport in Porous Media, 2015, vol. 106, pp. 237–257.
Kolchanova E. A., Kolchanov N. V. Vibration effect on the onset of thermal convection in an inhomogeneous porous layer underlying a fluid layer. International Journal of Heat and Mass Trans-fer, 2017, vol. 106, pp. 47-60.
Kolchanova E. A., Kolchanov N. V. Nonlinear convection regimes in superposed fluid and porous layers under vertical vibrations: Positive porosity gradients. International Journal of Heat and Mass Transfer, 2018, vol. 121, pp. 37-45.
Kolchanova E. A., Kolchanov N. V. Nonlinear convection regimes in superposed fluid and porous layers under vertical vibrations: Negative porosity gradients. International Journal of Heat and Mass Transfer, 2018, vol. 127, pp. 438-449.
Nield D., Bejan A. Convection in Porous Media. USA: Springer, 2013. 778 p.
Carman P. C. Fluid flow through granular beds. Transactions of the Institution of Chemical Engineers, 1937, vol. 15, pp. S32–S48.
Liubimov D. V., Muratov I. D. O konvectivnoi neustoichivosti v sloistoi sisteme (On convective instability in a layered system). Gidrodinamica (Hydrodynamics), 1977, vol. 10, pp. 38–46. (In Russian)
Beavers G. S., Joseph D. D. Boundary conditions at a naturally permeable wall. Journal of Fluid Mechanics, 1967, vol. 30, pp. 197–207.
Lobov N. I., Liubimov D. V., Liubimova T. P. Chislennie metodi resheniya zadach teorii gidrodinamicheskoi ustoichivosti. Study guide, Perm: PSU, 2004. 101 p.
Downloads
Published
How to Cite
Issue
Section
License
Автор предоставляет Издателю журнала (Пермский государственный национальный исследовательский университет) право на использование его статьи в составе журнала, а также на включение текста аннотации, полного текста статьи и информации об авторах в систему «Российский индекс научного цитирования» (РИНЦ).
Автор даёт своё согласие на обработку персональных данных.
Право использования журнала в целом в соответствии с п. 7 ст. 1260 ГК РФ принадлежит Издателю журнала и действует бессрочно на территории Российской Федерации и за её пределами.
Авторское вознаграждение за предоставление автором Издателю указанных выше прав не выплачивается.
Автор включённой в журнал статьи сохраняет исключительное право на неё независимо от права Издателя на использование журнала в целом.
Направление автором статьи в журнал означает его согласие на использование статьи Издателем на указанных выше условиях, на включение статьи в систему РИНЦ, и свидетельствует, что он осведомлён об условиях её использования. В качестве такого согласия рассматривается также направляемая в редакцию справка об авторе, в том числе по электронной почте.
Редакция размещает полный текст статьи на сайте Пермского государственного национального исследовательского университета: http://www.psu.ru и в системе OJS на сайте http://press.psu.ru
Плата за публикацию рукописей не взимается. Гонорар за публикации не выплачивается. Авторский экземпляр высылается автору по указанному им адресу.
