Construction of basic functions for problems of fluid oscillations in a tank
Abstract
Considerable number of studies and publications is devoted to issues of dynamic behavior of liquids, the impact on the surface tension of a liquid in partially filled tanks in particular. The study of liquid vibrations in partially fluid-filled cylindrical containers with the presence of a free surface is an important technical task. The influence of the free surface curvature of the tank filler on the oscillation frequency is taken into account. It is assumed that the liquid is incompressible and inviscid, and its motion is irrotational. The method to solve a boundary value problem for determining fluid oscillations in a reservoir has been developed, and an integral presentation of an unknown velocity potential is proposed. The geometrical characteristics of the free liquid surface have been determined. It is taken into account that the free liquid surface deviates from the equilibrium position and assumes a spherical shape. A system of singular integral equations has been obtained for unknown values of the potential and flow. The method of boundary elements with constant approximation of an unknown density on the elements has been used to solve the system numerically. The oscillation frequencies for the zero harmonic are determined in accordance with the level of the free-surface elevation. It has been determined that the deviation of the free surface shape from the flat and even a slight rise in the free surface level leads to noticeable changes in the vibration frequencies. The vibrational modes obtained in the study mostly coincide with the modes for a flat free surface and can serve as the basic system of functions in the studies of free and forced fluid vibrations in tanks, as well as, in the study of the intrinsic and forced sloshing in the reservoirs provided surface tension is taken into account.
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Hung R.J., Lee C.C., and Leslie F.W. Response of gravity level fluctuations on the Gravity Probe-B spacecraft propellant system. Journal of Propulsion and Power. no.7. 1991. pp. 556–564.
Hung R.J., Pan H.L. Sloshing dynamics modulated fluid angular momentum and moment fluctuations driven by orbital gravity gradient and jitter accelerations in microgravity. Applied Scientific Research. Volume 54, Issue 1. January 1995. pp. 51–68.
Hung R.J., Long Y.T., Pan H.L., Actuation of sloshing modulated force and moment on liquid container driven by jitter accelerations associated with siew motion in microgravity. Applied Mathematics and Mechanics. Volume 16. Issue 9. September 1995. pp. 859–876.
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Hung R. J., Tsao Y. D., Hong B. B., and Leslie F. W. «Dynamical behavior of surface tension on rotating fluids in low and microgravity environments». International Journal for Microgravity Research and Applications. no. 11. 1989. pp. 81–95.
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Dillon Sances, Joshua Gibson, Shayna Neumann, Brenton Thompson, Sathya Gangadharan, Thomas Smith and Keith Schlee, Modeling of Free-Surface Fuel Slosh in Microgravity for Off-Axis Spacecraft Propellant Tanks. AIAA Modeling and Simulation Technologies Conference. August 2009. DOI: https://doi.org/10.2514/6.2009-6039
Nathan Silvernail, Dillon Sances, Sathya Gangadharan and James Sudermann. Model of Spacecraft Fuel Slosh with Diaphragms in Microgravity. AIAA Modeling and Simulation Technologies Conference. August 2009. DOI: https://doi.org/10.2514/6.2009-6040
Brandon Marsell, David Griffin, Dr. Paul Schallhorn, Jacob Roth. High Accuracy Liquid Propellant Slosh Predictions Using an Integrated CFD and Controls Analysis Interface. Conference Paper. Thermal and Fluids Analysis Workshop 2012. 13 Aug. 2012. Pasadena. CA; United States. January 01. 2012. Document ID: 20120010782 https://ntrs.nasa.gov/search.jsp?R=20120010782 2019-10-08T13:08:49+00:00Z
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Gnitko, V., Naumemko, Y., Strelnikova E. Low frequency sloshing analysis of cylindrical containers with flat and conical baffles. International Journal of Applied Mechanics and Engineering. no. 22 (4). 2017. pp.867–881.
