FORCED VIBRATIONS OF FUEL TANKS UNDER DIFFERENT OPERATING CONDITIONS
DOI:
https://doi.org/10.32782/KNTU2618-0340/2021.4.1.17Keywords:
forced vibrations, shell of revolution, surface tension, liquid free surface, boundary and finite element methodsAbstract
The study of fluid vibrations in the fuel tanks in launch vehicles is necessary to ensure their stability during flight. Liquid launch vehicles have significant reserves of liquid components on board. In fuel tanks and oxidizer tanks there are oscillations of the free surface of the liquid, the nature of which is also influenced by external factors such as gravity, the level of filling of the tanks, their shape and so on. There is a need to determine the shapes and frequencies of the free surface vibrations of the liquid to ensure a stable state of the aircraft during flight. To solve this problem, mathematical modeling methods are used. A study of the problem of small oscillations in reservoirs partially filled with liquid in the space industry is considered. The works of domestic and foreign authors on solving the problems of fluid oscillations in a nonlinear formulation are also considered. In this article the analysis of forms and frequencies of fluctuations of liquid in the conditions of an overload at various levels of filling is carried out. The study of small oscillations (linear formulation) is performed. It is accepted that the fluid is incompressible and homogeneous, and its motion is vortex-free. There is a potential for velocity that satisfies the Laplace equation. Kinematic and dynamic boundary conditions on a free surface are fulfilled. To take into account the influence of low gravity, the generalization of boundary conditions is performed. In the dynamic state on the free surface, the surface tension is taken into account, which is the governing quantity under microgravity conditions. The relation to be performed on a free surface is obtained. The obtained equation allows us to study the forced oscillations of the rigid shell of revolution which is partially filled with fluid. Numerical results for a cylindrical shell of revolution are obtained. Zero initial conditions are accepted. Calculations were performed at different levels of filling for the cylindrical shell. The lowest vibrations frequencies are obtained. The vibrations of the fluid under the action of the vertical load are also investigated. Phase portraits for different values of vertical excitation frequencies are obtained. The amplitudes of vibrations of the free surface are investigated.
References
Крейн С.Г., Моисеев Н.Н. О колебаниях твердого тела, содержащего жидкость со свободной поверхностью. Прикладная математика и механика. 1957. № 21 (2). С.169–174.
Рабинович Б.И., Докучаев Л.В., Полякова З.М. О расчете коэффициентов уравнений возмущенного движения твердого тела с полостями, частично заполненными жидкостью. Космические исследования. 1965. № 3 (2). С. 179–207.
Моисеев Н.Н., Петров А.А. Численные методы расчета, собственных частот колебаний ограниченного объема жидкости. Москва: ВЦ АН СССР, 1966. 268 с.
Hutton R. E. An investigation of nonlinear, nonplanar oscillations of fluid in cylindrical container: Tech. Rep. 1963. P. 191–194. URL: https://doi.org/10.2514/6.1964-1019 (дата звернення: 05.04.2021).
Abramson H. N., Chu W. H., and Kana D. D. Some studies of nonlinear lateral sloshing in rigid containers. Journal of Applied Mechanics. 1964. Vol. 33. No. 4. P. 777–784.
Abramson H. N. The dynamic behavior of liquids in moving containers with applications to space vehicle technology: Tech. Rep. NASA SP-106. 1966. P. 467.
Dodge F. T. The New “Dynamic Behavior of Liquids in Moving Containers”. San Antonio, Texas: Southwest Research Institute, 2000. 195 p.
Hopfinger E. J., Baumbach V. Liquid sloshing in cylindrical fuel tanks EUCASS Proceedings Series – Advances in AeroSpace Sciences. 2009. Vol. 1. Р. 279-292 URL: https://doi.org/10.1051/eucass/200901279 (дата звернення: 05.04.2021).
Abdollahzadeh Jamalabadi M.Y. Analytical Solution of Sloshing in a Cylindrical Tank with an Elastic Cover. Mathematics. 2019. Vol. 7. Р. 1070.
Raynovskyy I., Timokha A. Steady-State Resonant Sloshing in an Upright Cylindrical Container Performing a Circular Orbital Motion. Mathematical Problems in Engineering.2018. Vol. 2018. Р. 1–8. URL: https://doi.org/10.1155/2018/5487178 (дата звернення: 06.04.2021).
Simonini A., Fontanarosa D., De Giorgi M.G., Vetrano M.R. Liquid dynamics sloshing in cylindrical containers: A 3D free-surface reconstruction dataset. Data in Brief. 2020.Vol. 33. ISSN 2352–3409. URL: http://www.sciencedirect.com/science/article/pii/S2352340920314281 (дата звернення: 06.04.2021).
Simonini A., Fontanarosa D., De Giorgi M.G., Vetrano M.R. Mode characterization and damping measurement of liquid sloshing in cylindrical containers by means of Reference Image Topography. Experimental Thermal and Fluid Science. 2021. Vol. 120. ISSN 0894-1777, URL: http://www.sciencedirect.com/science/article/pii/S0894177720307366(дата звернення: 06.04.2021).
Ardakani H., Bridges T. Shallow-water sloshing in vessels undergoing prescribed rigidbody motion in three dimensions. Journal of Fluid Mechanics. 2011. Vol. 667. Р. 474–519. URL: https://doi.org/10.1017/S0022112010004477 (дата звернення: 07.04.2021).
Strelnikova, E., Kriutchenko. D., Gnitko. V., Degtyarev, K. Boundary element method in nonlinear sloshing analysis for shells of revolution under longitudinal excitations. Engineering Analysis with Boundary Elements. 2020. 111. P. 78–87. URL: https://doi:
1016/j.enganabound.2019.10.008 (дата звернення: 08.04.2021).
Ibrahim R.A. Liquid Sloshing Dynamics / Theory and APlications . Cambridge University Press, 2005. 972 p.
Strelnikova, E., Choudhary, N., Kriutchenko, D., Gnitko, V., Tonkonozhenko, A. Liquid vibrations in circular cylindrical tanks with and without baffles under horizontal and vertical excitations. Engineering Analysis with Boundary Elements. 2020. 120. 13–27.URL: https://doi: 10.1016/j.enganabound.2020.07.024 (дата звернення: 08.04.2021).
Strelnikova E., Gnitko V., Krutchenko D., Naumemko Y. Free and forced vibrations of liquid storage tanks with baffles. J. Modern Technology & Engineering. 2018. Vol.3.No.1. Р.15–52 URL: http://jomardpublishing.com/UploadFiles/Files/journals/JTME/V3No1/StrelnikovaE.pdf(дата звернення: 08.04.2021).
Gnitko V., Degtyariov K., Karaiev A., and Strelnikova E. Multi-domain boundary element method for axisymmetric problems in potential theory and linear isotropic elasticity, WIT Transactions on Engineering Sciences, Boundary Elements and other Mesh Reduction Methods XLII. 2019. Vol. 122. P.13–25. URL: 10.2495/BE410021(дата звернення: 08.04.2021).
