• Nuclear Engineering and Technology
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• v.52 no.5
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• pp.947-955
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• 2020

Predicting the sloshing motion of a coolant during a seismic assessment of a rectangular spent fuel pool is of critical concern. Linear theory, which provides a simple analytical method, has been used to predict the sloshing motion in rectangular pools and tanks. However, this theory is not suitable for the high-frequency excitation problem. In this study, the authors developed a simple analytical method for predicting the sloshing motion in a rectangular pool for a wide range of excitation frequencies. The correlation among the linear theory parameters, influencing on excitation and convective waves, and the excitation frequency is investigated. Sloshing waves in a rectangular pool with several liquid heights are predicted using the original linear theory, a modified linear theory and computational fluid dynamics analysis. The results demonstrate that the developed method can predict sloshing motion over a wide range of excitation frequencies. However, the developed method has the limitations of linear solutions since it neglects the nonlinear features of sloshing motion. Despite these limitations, the authors believe that the developed method can be useful as a simple analytical method for predicting the sloshing motion in a rectangular pool under various external excitations.

• Ocean Systems Engineering
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• v.1 no.4
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• pp.355-372
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• 2011

Based on the fully nonlinear velocity potential theory, the liquid sloshing in a three dimensional tank under random excitation is studied. The governing Laplace equation with fully nonlinear boundary conditions on the moving free surface is solved using the indirect desingularized boundary integral equation method (DBIEM). The fourth-order predictor-corrector Adams-Bashforth-Moulton scheme (ABM4) and mixed Eulerian-Lagrangian (MEL) method are used for the time-stepping integration of the free surface boundary conditions. A smoothing scheme, B-spline curve, is applied to both the longitudinal and transverse directions of the tank to eliminate the possible saw-tooth instabilities. When the tank is undergoing one dimensional regular motion of small amplitude, the calculated results are found to be in very good agreement with linear analytical solution. In the simulation, the normal standing waves, travelling waves and bores are observed. The extensive calculation has been made for the tank undergoing specified random oscillation. The nonlinear effect of random sloshing wave is studied and the effect of peak frequency used for the generation of random oscillation is investigated. It is found that, even as the peak value of spectrum for oscillation becomes smaller, the maximum wave elevation on the side wall becomes bigger when the peak frequency is closer to the natural frequency.

• Special Issue of the Society of Naval Architects of Korea
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• 2005.06a
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• pp.38-43
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• 2005

The present study is concerned with the numerical analysis of the sloshing impact pressure of the Liquefied Natural Gas (LNG) carriers in rough sea. The reliable predictions of the both random tank motions in irregular waves and violent fluid flow in the LNG tanks are required for practical sloshing analysis procedure of LNG carriers. The three-dimensional numerical model adopting SOLA-VOF scheme is used to predict violent free surface movements of LNG tank in irregular motions. For accurate input motion of tank, a three-dimensional panel method program called SSMP (Samsung Ship Motion Program) is applied for seakeeping analysis. Comparison studies of sloshing analysis are carried out for No.2 tank of 138K and 205K LNG carriers to verify the safety of the LNG containment system of the proposed 205K large LNG carrier.

• Journal of the Korean Society of Visualization
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• v.18 no.3
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• pp.14-22
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• 2020

An experiment, in the cases that satisfies deep water condition, has been performed to observe the strongly nonlinear sloshing flow in a rectangular tank. A variety of parametric study on oscillating frequency and amplitude was conducted and we found that two types of wave motions, sloshing wave and Faraday wave, could be persisting simultaneously even in horizontal sloshing problem. Moreover, it is observed both of symmetric and skewed symmetric Faraday wave exist. A comprehensive explanation is given to the generation mechanism of those waves and how to interact among them.

• Journal of Advanced Marine Engineering and Technology
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• v.37 no.6
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• pp.617-622
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• 2013

The sloshing of liquid inside an ocean floater is caused by disturbances due to waves. For the analysis of sloshing impact within the floater and that of waves on the floater, the coupled analysis method is used. The Stokes $5^{th}$ order non-linear wave theory equations were adapted for wave making. Furthermore, Navier-Stokes equation and Shear-Stress Transport (SST) turbulent model were used to Computational Fluid dynamics, where the ocean floater motions are considered the heave and the pitch motion. The results obtained confirms the mutual relationship between the rigid body motions and that of sloshing, where the sloshing behaviour within the floater is characterized by the wave effects on the floater.

• International Journal of Naval Architecture and Ocean Engineering
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• v.7 no.3
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• pp.580-594
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• 2015

Liquid sloshing in two-dimensional (2-D) and three-dimensional (3-D) rectangular tanks is simulated by using a level set method based on the finite volume method. In order to examine the effect of natural frequency modes on liquid sloshing, we considered a wide range of frequency ratios ($0.5{\leq}fr{\leq}3.2$). The frequency ratio is defined by the ratio of the excitation frequency to the natural frequency of the fluid, and covers natural frequency modes from 1 to 5. When fr = 1, which corresponds to the first mode of the natural frequency, strong liquid sloshing reveals roof impact, and significant forces are generated by the liquid in the tank. The liquid flows are mainly unidirectional. Thus, the strong bulk motion of the fluid contributes to a higher elevation of the free surface. However, at fr = 2, the sloshing is considerably suppressed, resulting in a calm wave with relatively lower elevation of the free surface, since the waves undergo destructive interference. At fr = 2, the lower peak of the free surface elevation occurs. At higher modes of $fr_3$, $fr_4$, and $fr_5$, the free surface reveals irregular deformation with nonlinear waves in every case. However, the deformation of the free surface becomes weaker at higher natural frequency modes. Finally, 3-D simulations confirm our 2-D results.

• Computational Structural Engineering
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• v.9 no.1
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• pp.55-64
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• 1996

Sloshing frequencies of the fluid in rectangular tanks with a bottom-mounted rectangular block are determined by linear water wave theory. Velocity potential is decomposed into those for the wall-induced waves, and the reflected, transmitted, and scattered waves by the block. The reflection and transmission coefficients are determined using the continuity conditions of mass flux and energy flux on the common vertical boundaries of the fluid regions, and the boundary conditions on the both sides of the block. The analysis results indicate that the sloshing frequencies reduce, as the block becomes tall and vade and as the block moves toward the center. The variations of the sloshing frequencies due to the block are found to be more sensitive in broad thanks than is tall tanks.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.13 no.10
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• pp.751-759
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• 2003

The theoretical method is developed to investigate the vibration characteristics of the sloshing and bulging mode for the circular cylindrical storage tank with an annular plate on free surface. The cylindrical tank is filled with an inviscid and incompressible liquid. The liquid domain is limited by a rigid cylindrical surface and a rigid flat bottom. As the effect of free surface waves Is taken into account in the analysis, the bulging and sloshing modes are studied. The solution for the velocity potential of liquid movement is assumed as a suitable harmonic function that satisfies Laplace equation and the relevant boundary conditions. The Rayleigh-Ritz method is used to derive the frequency equation of the cylindrical tank. The effect of Inner-to-outer radius ratio and thickness of annular plate and liquid volume on vibration characteristics of storage tank is studied. The finite element analysis is performed to demonstrate the validity of present theoretical method.

• Journal of Ocean Engineering and Technology
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• v.33 no.2
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• pp.106-115
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• 2019

The interaction between a sloshing liquid damper (SLD) tank and a rectangular pontoon was investigated under the assumption of the linear potential theory. The eigenfunction expansion method was used not only for the sloshing problem in the SLD tank but also for analyzing the motion responses of a rectangular pontoon in waves. If the frictional damping due to the viscosity of the SLD tank was ignored, the effect of the SLD appeared to be an added mass in the coupled equation of motion. The installation of the SLD tank had a greater effect on the roll motion response than the sway and heave motion of the pontoon. One resonance peak for rolling motion showed up in the case of a frozen liquid in the SLD tank. However, if liquid motion in the SLD tank was allowed, two peaks appeared around the first natural frequency of the fluid in the SLD tank. In particular, the peak value located in the low-frequency region had a relatively large value, and the peak frequency located in the high-frequency region moved into the high-frequency region as the depth of the liquid in the tank increased.

• Proceedings of the Korea Committee for Ocean Resources and Engineering Conference
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• 2000.10a
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• pp.189-195
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• 2000

New concept of LNG-FPSO ship with moonpool and bilge step in bottom is considered and investigated in the point of motion reduction and sloshing phenomena of the cargo and operation tanks. The cargo capacity of the ship of which principle dimensions is L x B x D x t(design) =270.0 x 51.0 x 32.32 x 13.7(m) 16K at 98% loading condition. The two moonpools and rectangular step at bilge part are setted up specially for getting the effect of motion decrease. For the motion analysis, linearized three dimensional diffraction theory with the simplified boundary conditions is used. The six-degree of freedom coupled motion responses are calculated for the LNG-FPSO ship. Viscous effects on the roll motion responses of a vessel are taken into account in this calculation program using an empirical formula suggested by Ikeda, Himeno and Tanaka is used. The case study for the moonpool size had been carried out by theoretical estimation and experimental method. For the optimization of the moonpool size and effect of the step, 9 cases of its size and with and without step are considered. From the results of calculation and experiment, it can be concluded that this designed LNG-FPSO ship have possibility to carry out her missions in the rough sea as for the owner's demand waves condition. The motion responses, especially roll motion, for the designed LNG-FPSO ship are much lower than those of another drillship and shuttle tanker and limit criterions are satisfied. For the check of the cargo tank and operation tank sizes we have performed sloshing analysis in the irregular waves which focuses on the pressure distribution on the tank wall and the time history of pressure and free surface for No.2 and No5. tanks of LNG-FPSO with chamfers. Finally we got the tank size which has no resonance and no impact pressure in all filling in the bow quartering and beam sea.