Calculation of hydrodynamic interaction in superfluid liquid by methods of computational theory of potential

Authors

  • Юлия Владимировна Бразалук Oles Gonchar Dnepropetrovsk National University Gagarina Av, 72, Dnepropetrovsk, Ukraine, 49010, Ukraine

DOI:

https://doi.org/10.15587/1729-4061.2013.18102

Keywords:

superfluid liquid, cryogenic liquid, hydrodynamic interaction, boundary element method

Abstract

The problems of superfluid liquid hydrodynamics are quite relevant today. Previously uninvestigated problem of multiphase flow of superfluid liquid is considered in the paper. The tasks of streamline of groups of objects of different shapes by a flat stationary flow of superfluid liquid is formulated in terms of velocity potential in the form of differential equations in specific derived and boundary integral equations of potential theory. It was shown that for such a flow, the main force, affecting objects, is the strength of hydrodynamic interaction. Calculations were made using a standard algorithm for the boundary element method. The dependences of hydrodynamic interaction forces on the distance between the streamlined objects were obtained for circular and elliptical shaped objects. The cases of a large number of regularly situated circular objects were considered. It was shown that such a system is stable relating to perturbations along the flow velocity vector, and is unstable with respect to perturbations perpendicular to the vector. The considered problems illustrate the features of multiphase flow of superfluid liquid and can serve as model problems for studying such flows.

Author Biography

Юлия Владимировна Бразалук, Oles Gonchar Dnepropetrovsk National University Gagarina Av, 72, Dnepropetrovsk, Ukraine, 49010

Main researcher

Aerohydromechanics and Energy and Mass Transfer Chair

References

  1. Ландау, Л. Д. Гидродинамика [Текст] / Л. Д. Ландау, Е. М. Лифшиц // Гидродинамика. – 3-е изд. – М.: Наука, 1986. – 736 с.
  2. Паттерман, С. Гидродинамика сверхтекучей жидкости [Текст] / С. Паттерман. – М.: Мир, 1978. – 520 с.
  3. Халатников, И. М. Введение в теорию сверхтекучести [Текст] / И. М. Халатников. – М.: Наука, 1965.
  4. Костюков, А. А. Взаимодействие тел, движущихся в жидкости [Текст] / А. А. Костюков. – Л.: Судостроение, 1972. – 312 с.
  5. Бразалук, Ю. В. Совместное применение метода малого параметра и метода граничных элементов для численного решения эллиптических задач с малыми возмущениями [Текст] / Ю. В. Бразалук, Д. В. Евдокимов, Н. В. Поляков // Вестник Харк. нац. ун-та. – Серия «Математическое моделирование. Информационные технологии. Автоматизированные системы управления». – 2005. – № 703. – Вып. 5. – С. 50-66.
  6. Бразалук, Ю. В. Применение комбинированного метода граничных элементов и дискретных вихрей для решения некоторых задач гидродинамического взаимодействия в плоских потоках [Текст] / Ю. В. Бразалук, Д. В. Евдокимов, Н. В. Поляков // Вестник Харьковского национального университета. – Серия «Математическое моделирование. Информационные технологии. Автоматизированные системы управления». – 2003. – № 590. – Вып. 1. – С. 55-60.
  7. Бразалук, Ю. В. Численное определение присоединенных масс методами теории потенциала [Текст] / Ю. В. Бразалук, Д. В. Евдокимов, Н. В. Поляков // Вісник ХНУ. – № 661. – Харків, 2005. – С. 24-36.
  8. Бразалук, Ю. В. Применение метода граничных элементов для расчета присоединенных масс [Текст] / Ю. В. Бразалук, Д. В. Евдокимов, Н. В. Поляков // Труды междунар. симпозиума "Методы дискретних особенностей в задачах математической физики". – Харьков - Херсон, 2005. – C. 42-46.
  9. Кочин, Н. Е. Теоретическая гидромеханика [Текст]: монографія / Н. Е. Кочин, И. А. Кибель, Н. В. Розе. – М.: Физматгиз, 1965. – Т. 1. – 758 с.
  10. Кочин, Н. Е. Теоретическая гидромеханика [Текст]: монографія / Н. Е. Кочин, И. А. Кибель, Н. В. Розе. – М.: Физматгиз, 1965. – Т. 2. – 772 с.
  11. Бенерджи, П. Метод граничных элементов в прикладных науках [Текст] / П. Бенерджи, Р. Баттерфилд. – М.: Мир, 1984. – 494 с.
  12. Бреббия, К. Методы граничных элементов [Текст] / К. Бреббия, Ж. Теллес, Л. Вроубел. – М.: Мир, 1987. – 524 с.
  13. Landau, L. D., Lifshits, E. M. (1986). Gidrodinamika. Gidrodinamika. Ed. 3. M.: Nauka, 736.
  14. Patterman, S. (1978). Gidrodinamika sverkhtekuchey zhidkosti. M.: Mir, 520.
  15. Khalatnikov, I. M. (1965). Vvedenie v teoriyu sverkhtekuchesti. M.: Nauka,
  16. Kostyukov, A. A. (1972). Vzaimodeystvie tel, dvizhushchikhsya v zhidkosti. L.: Sudostroenie, 312.
  17. Brazaluk, Yu. V., Evdokimov, D. V., Polyakov, N. V. (2005). Sovmestnoe primenenie metoda malogo parametra i metoda granichnykh elementov dlya chislennogo resheniya ellipticheskikh zadach s malymi vozmushcheniyami. Vestnik Khar'kovskogo natsional'nogo universiteta. Seriya «Matematicheskoe modelirovanie. Informatsionnye tekhnologii. Avtomatizirovannye sistemy upravleniya», № 703, Vyp. 5, 50-66.
  18. Brazaluk, Yu. V., Evdokimov, D. V., Polyakov, N. V. (2003). Primenenie kombinirovannogo metoda granichnykh elementov i diskretnykh vikhrey dlya resheniya nekotorykh zadach gidrodinamicheskogo vzaimodeystviya v ploskikh potokakh. Vestnik Khar'kovskogo natsional'nogo universiteta. Seriya «Matematicheskoe modelirovanie. Informatsionnye tekhnologii. Avtomatizirovannye sistemy upravleniya», № 590, Vyp. 1, 55-60.
  19. Brazaluk, Yu. V., Evdokimov, D. V., Polyakov, N. V. (2005). Chislennoe opredelenie prisoedinennykh mass metodami teorii potentsiala. Vіsnik KhNU, № 661. Kharkіv, 24-36.
  20. Brazaluk, Yu. V., Evdokimov, D. V., Polyakov, N. V. (2005). Primenenie metoda granichnykh elementov dlya rascheta prisoedinennykh mass. Trudy mezhdunar. simpoziuma "Metody diskretnikh osobennostey v zadachakh matematicheskoy fiziki". Khar'kov - Kherson, 42-46.
  21. Kochin, N. E., Kibel', I. A., Roze, N. V. (1965). Teoreticheskaya gidromekhanika: monografіya. M.: Fizmatgiz. T. 1, 758.
  22. Kochin, N. E., Kibel', I. A., Roze, N. V. (1965). Teoreticheskaya gidromekhanika: monografіya. M.: Fizmatgiz. T. 2, 772.
  23. Benerdzhi, P., Batterfild, R. (1984). Metod granichnykh elementov v prikladnykh naukakh. M.: Mir, 494.
  24. Brebbiya, K., Telles, Zh., Vroubel, L. (1987). Metody granichnykh elementov. M.: Mir, 524.

Downloads

Published

2013-10-24

How to Cite

Бразалук, Ю. В. (2013). Calculation of hydrodynamic interaction in superfluid liquid by methods of computational theory of potential. Eastern-European Journal of Enterprise Technologies, 5(5(65), 6–10. https://doi.org/10.15587/1729-4061.2013.18102

Issue

Vol. 5 No. 5(65) (2013): Applied physics

Section

Applied physics

License

Copyright (c) 2014 Юлия Владимировна Бразалук

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

The consolidation and conditions for the transfer of copyright (identification of authorship) is carried out in the License Agreement. In particular, the authors reserve the right to the authorship of their manuscript and transfer the first publication of this work to the journal under the terms of the Creative Commons CC BY license. At the same time, they have the right to conclude on their own additional agreements concerning the non-exclusive distribution of the work in the form in which it was published by this journal, but provided that the link to the first publication of the article in this journal is preserved.

A license agreement is a document in which the author warrants that he/she owns all copyright for the work (manuscript, article, etc.).
The authors, signing the License Agreement with TECHNOLOGY CENTER PC, have all rights to the further use of their work, provided that they link to our edition in which the work was published.
According to the terms of the License Agreement, the Publisher TECHNOLOGY CENTER PC does not take away your copyrights and receives permission from the authors to use and dissemination of the publication through the world's scientific resources (own electronic resources, scientometric databases, repositories, libraries, etc.).
In the absence of a signed License Agreement or in the absence of this agreement of identifiers allowing to identify the identity of the author, the editors have no right to work with the manuscript.
It is important to remember that there is another type of agreement between authors and publishers – when copyright is transferred from the authors to the publisher. In this case, the authors lose ownership of their work and may not use it in any way.