Study on Equivalent Sloshing Mass Locations for Liquid-Filled Cylindrical Tanks

To protect flat-bottom cylindrical tanks against severe damage from uplift motion, accurate evaluation of accompanying fluid pressures is indispensable. This paper presents a mathematical solution for evaluating the fluid pressure on a rigid flat-bottom cylindrical tank in the same manner as the procedure outlined and discussed previously by the authors (Taniguchi, T., and Ando, Y., 2010, “Fluid Pressures on Unanchored Rigid Rectangular Tanks Under Action of Uplifting Acceleration,” ASME J. Pressure Vessel Technol., 132(1), p. 011801). With perfect fluid and velocity potential assumed, the Laplace equation in cylindrical coordinates gives a continuity equation, while fluid velocity imparted by the displacement (and its time derivatives) of the shell and bottom plate of the tank defines boundary conditions. The velocity potential is solved with the Fourier–Bessel expansion, and its derivative, with respect to time, gives the fluid pressure at an arbitrary point inside the tank. In practice, designers have to calculate the fluid pressure on the tank whose perimeter of the bottom plate lifts off the ground like a crescent in plan view. However, the asymmetric boundary condition given by the fluid velocity imparted by the deformation of the crescent-like uplift region at the bottom cannot be expressed properly in cylindrical coordinates. This paper examines applicability of a slice model, which is a rigid rectangular tank with a unit depth vertically sliced out of a rigid flat-bottom cylindrical tank with a certain deviation from (in parallel to) the center line of the tank. A mathematical solution for evaluating the fluid pressure on a rigid flat-bottom cylindrical tank accompanying the angular acceleration acting on the pivoting bottom edge of the tank is given by an explicit function of a dimensional variable of the tank, but with Fourier series. It well converges with a few first terms of the Fourier series and accurately calculates the values of the fluid pressure on the tank. In addition, the slice model approximates well the values of the fluid pressure on the shell of a rigid flat-bottom cylindrical tank for any points deviated from the center line. For the designers’ convenience, diagrams that depict the fluid pressures normalized by the maximum tangential acceleration given by the product of the angular acceleration and diagonals of the tank are also presented. The proposed mathematical and graphical methods are cost effective and aid in the design of the flat-bottom cylindrical tanks that allow the uplifting of the bottom plate.

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FREE VIBRATION ANALYSIS OF CYLINDRICAL TANKS PARTIALLY FILLED WITH LIQUID

Journal of Sound and Vibration ◽

10.1006/jsvi.1996.0436 ◽

1996 ◽

Vol 195 (3) ◽

pp. 429-444 ◽

Cited By ~ 22

Author(s):

P.B. Gonçalves ◽

N.R.S.S. Ramos

Keyword(s):

Free Vibration ◽

Vibration Analysis ◽

Free Vibration Analysis ◽

Cylindrical Tanks

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Sloshing in Rectangular and Cylindrical Tanks

Journal of Ship Research ◽

10.5957/jsr.2002.46.3.186 ◽

2002 ◽

Vol 46 (03) ◽

pp. 186-200 ◽

Cited By ~ 2

Author(s):

Pierre C. Sames ◽

Delphine Marcouly ◽

Thomas E. Schellin

Keyword(s):

Free Surface ◽

Finite Volume ◽

Temporal Evolution ◽

Numerical Study ◽

Computational Method ◽

Test Cases ◽

Grid Refinement ◽

Cylindrical Tank ◽

Excitation Period ◽

Cylindrical Tanks

To validate an existing finite volume computational method, featuring a novel scheme to capture the temporal evolution of the free surface, fluid motions in partially filled tanks were simulated. The purpose was to compare computational and experimental results for test cases where measurements were available. Investigations comprised sloshing in a rectangular tank with a baffle at 60% filling level and in a cylindrical tank at 50% filling level. The numerical study started with examining effects of systematic grid refinement and concluded with examining effects of three-dimensionality and effects of variation of excitation period and amplitude. Predicted time traces of pressures and forces compared favorably with measurements.

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