Machine Building and Engineering Science Aeronautical and Rocket Space Engineering Instrument Engineering, Metrology and Information-Measuring Devices and Systems Informatics, Computer Science_and_Management Mechanics

 General Problems of Engineer Education Engineer in Modern Russia Foreign Education History of Progress
Другие журналы

# SCIENCE & EDUCATION

### Bauman Moscow State Technical University.   El № FS 77 - 48211.   ISSN 1994-0408

Axisymmetric Oscillations of Membrane-Separated Bilayer Fluid in a Closed Vessel

# 12, December 2016
DOI: 10.7463/1216.0852775
Article file: SE-BMSTU...o310.pdf (395.78Kb)
authors: D.A. Goncharov1,*, A.A. Pozhalostin1

 1 Bauman Moscow State Technical University, Moscow, Russia

The paper deals with the problem of small oscillations of bilayer liquid separated by a membrane in a closed vessel. This problem arises when studying the behavior of the liquid component of the fuel in the spacecraft tanks in their interaction with the elements of systems providing the start-up of the propulsion system.
The problem of small oscillations is considered in the linear formulation. We consider symmetrical motion of liquid. The membrane is assumed to be thin, elastic, and non-inertial. The liquid completely fills the cylindrical vessel. We consider motion of an ideal and viscous incompressible liquid. On the vessel walls the flow tangency condition is fulfilled. The liquid container volume satisfies the condition of continuity, which in the area under consideration takes a form of the Laplace equation. The differential equation of membrane motion is written with the right-hand side, which includes the hydrodynamic liquid-induced pressure. Restricted deflection of the membrane center and zero movements of the membrane contour stipulate boundary conditions for the equation of membrane motion.
Integrating the Laplace equation we obtain the expression for the liquid velocity potential in the areas above and below membrane. Writing the equation of the membrane motion for deflection rate, representing the function of membrane deflection rate in accordance with the Fourier method as a product of functions of coordinates and time, we can integrate the expressions for the function of membrane deflection. Fulfilling the boundary conditions for the function of membrane deflection together with the boundary conditions for the Laplace equation, we can obtain an analytical expression for the function of membrane deflection and a frequency equation for the given boundary value problem.
It can be seen that for a range of tensions typical for used materials, which are considered, for example, in V.M. Polyaev’s monograph, the frequency values of natural oscillations of the membrane will be much higher than the frequency of natural oscillations of the liquid that fills the cylinder of a given radius and height determined from the known relationship.

References
1. Ibrahim R.A. Liquid sloshing dynamics: theory and applications. Camb., N.Y., Cambridge Univ. Press, 2005. 948 p.
2. Poliaev V.M., Bagrov V.V., Kurpatenkov A.V. Kapilliarnye sistemy otbora zhidkosti iz bakov kosmicheskikh letatel’nykh apparatov[Capillary system of selection of the liquid from the tank to the spacecraft]. Moscow, Energomash Publ., 1997. 327 p. (in Russian).
3. Sapozhnikov V.B., Menshikov V.A., Partola I.S., Korolkov A.V. Development of ideas of professor V.V. Polyaev on application of porous-meshed materials for internal tank devices providing repeated many times start-up of liquid propellant engines. Vestnik MGTU im. N.E. Baumana. Ser. Mashinostroenie [Herald of the Bauman MSTU. Ser. Mechanical Engineering], 2006, no. 2, pp. 78–88 (in Russian).
4. Ivanov V.P., Partola I.S. The combined fuel draining control system for liquid oxygen and liquid hydrogen upper stage. Vestnik Samarskogo Universiteta. Aerokosmicheskaia tekhnika, tekhnologii i mashinostroenie [Vestnik of Samara Univ. Aerospace and Mechanical Engineering], 2011, no. 3-1(27), spec. iss., pp. 28–34 (in Russian).
5. Sapozhnikov V.B., Krylov V.I., Novikov Yu.M., Yagodnikov D.A. Ground tests of capillary phase separators based on combined porous mesh material for fuel tanks of liquid propellant engine in propulsion installations of space crafts, top steps of carrier rockets and upper-stage rockets. Inzhenernyj zhurnal: nauka i innovatsii [Engineering J.: Science and Innovation], 2013, no. 4(16). DOI: 10.18698/2308-6033-2013-4-707 (in Russian).
6. Sances D.J., Gangadharan S.N., Sudermann J.E., Marsell B. CFD fuel slosh modeling of fluid-structure interaction in spacecraft propellant tanks with diaphragms. 51st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference(Orlando, Florida, USA, 12-15 April, 2010): Collection of technical papers. Wash., AIAA, 2010.
7. Schlee K., Gangadharan S.N., Ristow J., Sudermann J., Walker C., Hubert C. Modeling and parameter estimation of spacecraft fuel slosh. 29th Annual AAS Rocky Mountain Section Guidance and Control Conference(Breckenridge, Colorado, USA, Febr. 4-8, 2006): Proc. San Diego, AAS, 2006.
8. Kononov Yu.N., Tatarenko E.A. Free vibrations of two-layer fluid with an elastic membrane on the free and internal surfaces. Akustichnij visnik [Acoustic Bulletin], 2003, vol. 3, no. 6, pp. 44-52. Available at: http://dspace.nbuv.gov.ua/handle/123456789/982, accessed 01.12.2016.
9. Aliev I.N., Yurchenko S.O., Nazarova E.V. On the problem of instability of the boundary of two media of finite thickness. J. of Engineering Physics and Thermophysics, 2007, vol. 80, no. 6, pp. 1199-1205. DOI: 10.1007/s10891-007-0154-1
10. Sretenskij L.N. Teoriia volnovykh dvizhenij zhidkosti [The theory of wave motions of fluid]. Modcow, Nauka Publ., 1977. 815 p. (in Russian).
11. Bukreev V.I., Sturova I.V., Chebotnikov A.V. Seiche oscillations in a reservoir filled with a double-layer fluid. Izvestiia RAN. Mekhanika zhidkosti i gaza [Fluid Dynamics], 2014, vol. 49, no. 3, pp. 395 - 402. DOI: 10.1134/S0015462814030119
12. Sturova I.V. Internal seiches in a basin filled with a continuously stratified fluid. Izvestiia RAN. Mekhanika zhidkosti i gaza [Fluid Dynamics], 2014, vol. 49, no. 6, pp. 761-769. DOI: 10.1134/S0015462814060076
13. Kalinichenko V.A., Korovina L.I., Nesterov S.V., Aung Naing Soe. The features of fluid oscillations in a rectangular vessel with local bottom irregularities. Inzhenernyj zhurnal: nauka i innovatsii [Engineering J.: Science and Innovation], 2014, no. 12(36). DOI: 10.18698/2308-6033-2014-12-1345 (in Russian).
14. Kalinichenko V.A., Aung Naing Soe. An experimental study of coupled vibrations of the tank with liquid. Vestnik MGTU im. N.E. Baumana. Ser. Estestvennye nauki  [Herald of the Bauman MSTU. Ser.: Natural sciences], 2015, no. 1(58). DOI: 10.18698/1812-3368-2015-1-14-25 (in Russian).
15. D’yachenko M.I., Orlov V.V., Temnov A.N. A problem of propellant oscillations in cylindrical and conical tanks. Nauka i obrazovanie MGTU im. N.E. Baumana [Science and Education of the Bauman MSTU], 2013, no. 11, pp. 175 - 192. DOI: 10.7463/1113.0623923 (in Russian).
16. Pozhalostin A.A., Goncharov D.A. Free axisymmetric oscillations of two-layered liquid with the elastic separator between layers in the presence of surface tension forces. Inzhenernyj zhurnal: nauka i innovatsii [Engineering J.: Science and Innovation], 2013, no.12(24). DOI: 10.18698/2308-6033-2013-12-1147 (in Russian).
17. Kochin N.E., Kibel’ I.A., Roze N.V. Teoreticheskaia gidromekhanika[Theoretical hydromechanics]. Moscow, Fizmatgiz Publ., 1963. Pt. 1. 584 p. (in Russian).
18. Mikhlin S.G. Linejnye uravneniia v chastnykh proizvodnykh [Linear partial differential equations]. Moscow, Vysshaia shkola Publ., 1977. 431 p. (in Russian).

Thematic rubrics:
Поделиться:

Photos

Events

News

 Authors Press-releases Library Conferences About Project
Phone: +7 (915) 336-07-65 (строго: среда; пятница c 11-00 до 17-00)
 RSS
© 2003-2019 «Наука и образование»
Перепечатка материалов журнала без согласования с редакцией запрещена
Phone: +7 (915) 336-07-65 (строго: среда; пятница c 11-00 до 17-00)