• Structural Engineering and Mechanics
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• v.47 no.5
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• pp.599-622
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• 2013

Seismic response of two dimensional liquid tanks is numerically simulated using fully nonlinear velocity potential theory. Galerkin-weighted-residual based finite element method is used for solving the governing Laplace equation with fully nonlinear free surface boundary conditions and also for velocity recovery. Based on mixed Eulerian-Lagrangian (MEL) method, fourth order explicit Runge-Kutta scheme is used for time integration of free surface boundary conditions. A cubic-spline fitted regridding technique is used at every time step to eliminate possible numerical instabilities on account of Lagrangian node induced mesh distortion. An artificial surface damping term is used which mimics the viscosity induced damping and brings in numerical stability. Four earthquake motions have been suitably selected to study the effect of frequency content on the dynamic response of tank-liquid system. The nonlinear seismic response vis-a-vis linear response of rectangular liquid tank has been studied. The impulsive and convective components of hydrodynamic forces, e.g., base shear, overturning base moment and pressure distribution on tank-wall are quantified. It is observed that the convective response of tank-liquid system is very much sensitive to the frequency content of the ground motion. Such sensitivity is more pronounced in shallow tanks.

• Journal of KSNVE
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• v.4 no.2
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• pp.137-146
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• 1994

An analytical method for linear free vibration of fully liquid-filled circular cylindrical shell with various boundary conditions is developed by the Fourier series expansion based on the Stokes' transformation. A set of modal displacement functions and their derivatives of a circular cylindrical shell is substituted into the Sanders' shell equations in order to explicitily represent the Fourier coefficients as functions of the end point displacements, forces, and moments. For the vibration relevant to the liquid motion, the velocity potential of liquid is assumed as a sum of linear combination of suitable harmonic functions in the axial directions. The unknown parameter of the velocity potential is selected to satisfy the boundary condition along the wetted shell surface. An explicit expression of the natural frequency equation can be obtained for any kind of classical boundary conditions. The natural frequencies of the liquid-filled cylindrical shells with the clamped-free, the clamped-clamped, and the simply supported-simply supported boundary conditions examined in the previous works, are obtained by the analytical method. The results are compared with the previous works, and excellent agreement is found for the natural frequencies of the shells.

• Journal of the Society of Naval Architects of Korea
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• v.47 no.1
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• pp.38-46
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• 2010

This study aims at investigating the effect of the baffle height on the liquid sloshing in the three-dimensional (3D) rectangular tank. In order to simulate the 3D incompressible viscous two-phase flow in the 3D tank with partially filled liquid, the present study has adopted the volume of fluid (VOF) method based on the finite-volume method which has been well verified by comparing with the results of the relevant previous researches. The ratio of the baffle height ($h_B$) to filling level (h) has been changed in the range of $0{\leq}h_B/h{\leq}1.2$ to observe the effect on the impact loads on the side wall and free surface behavior. Generally, as baffle height increases, the impact pressure on the wall decreases and the deformation of free surface becomes weaker. However it seemed that a critical ratio of the baffle height existed to reveal the lowest impact pressure on the wall. Consequently, $h_B/h=0.8$ among $h_B/hs$ considered in the study showed the lowest impact pressure.

• Proceedings of the Earthquake Engineering Society of Korea Conference
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• 2003.09a
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• pp.481-488
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• 2003

A fluid-structure-isolator interaction program was developed in this study. The behavior of liquid regions are simulated by the boundary element method, and then the technique of analyzing the free surface motion in time domain is developed by using the nonlinear free surface boundary condition(NFBC) and the condition of interface between the structure and the fluid. Structure regions are modeled by the finite element method. In order to construct the governing equation of the fluid structure interaction(FSI)problem in time domain, the finite elements for a structure and boundary elements for liquid are coupled using the equilibrium condition, the compatibility condition and NFBC. The isolator is simulated by equation proposedin 3D Basis Me. In order to verify the validity and the applicability of the developed fluid- structure -Isolator interaction program, The horizontal forced vibration analysis was performed. The applicability of the developed method is verified through the artificial seismic analysis of real size liquid storage tank.

• International Journal of Naval Architecture and Ocean Engineering
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• v.11 no.1
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• pp.233-243
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• 2019

In this paper, numerical and experimental studies are performed to investigate the liquid impact on a free falling wedge. In the numerical simulation, the structure is assumed to be rigid and the elastic response is ignored. The fully nonlinear coupling between wedge and water is considered by an auxiliary function method based on the Boundary Element Method (BEM). At the intersection of the wedge surface and liquid surface, two coincident nodes are used to decouple the boundary conditions. The Eulerian free surface conditions in the local coordinate system are adopted to update the deformed free surface. In the experiments, five pressure sensors are fixed on each side of the wedge which is released from an experimental installation. Steel and aluminum wedges that have different structural elasticity are used in the experiments to investigate the influence of structural elasticity on the impact force. Numerical results are compared with experimental data and they agree very well. The influence of fluid gravity, body mass, initial entry speed and deadrise angle on the impact pressure are further investigated.

• 한국전산유체공학회:학술대회논문집
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• 2010.05a
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• pp.376-379
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• 2010

Bubble rising phenomenon is widely founded in many industrial applications such as a stream generator in power plant. Many experimental and numerical researches have been already performed to predict dynamic behavior of the bubble rising process. Recently numerical approaches are getting popular since it can offer much detailed information which is almost impossible to obtain from the experiments. Rising bubble could penetrate through the top free surface which makes the problem much more complicate in addition to the phase changing effect even with latest numerical techniques. In this paper, the top free surface effect on rising bubble has been investigated. The gas-liquid interface was explicitly tracked using high-order Level Contour Reconstruction Method(LCRM) which is a hybridization of Front-Tracking and Level-Set method. Break-up behavior of rising bubble at free surface showed different characteristics with initial diameter of bubble.

• 한국전산유체공학회:학술대회논문집
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• 1998.05a
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• pp.156-161
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• 1998

This describes a numerical method for predicting the incompressible unsteady laminar three-dimensional flows of fluid behaviour with free-surface. The elliptic differential equations governing the flows have been linearized by means of finite-difference approximations, and the resulting equations have been solved via a fully-implicit iterative method. The free-surface is defined by the motion of a set of marker particles and interface behaviour was investigated by way of a 'Lagrangian' technique. Using the GALA concept of Spalding, the conventional mass continuity equation is modified to form a volumetric or bulk-continuity equation. The use of this bulk-continuity relation allows the hydrodynamic variables to be computed over the entire flow domain including both liquid and gas regions. Thus, the free-surface boundary conditions are imposed implicitly and the problem formulation is greatly simplified. The numerical procedure is validated by comparing the predicted results of a periodic standing waves problems with analytic solutions or experimental results from the literature. The results show that this numerical method produces accurate and physically realistic predictions of three-dimensional free-surface flows.

• Carbon letters
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• v.1 no.1
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• pp.1-5
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• 2000

The effect of surface free energy on the positive temperature coefficient (PTC) of carbon black/thermoplastic resin composites was investigated. The thermoplastic resins such as EVA, LDPE, LLDPE and HDPE were used with the addition of 30 wt.% of the carbon black. The surface free energy of the composites was studied in the context of two-liquid contact angle measurements, i.e., deionized water and diiodomethane. It was observed that the resistivity on PTC composites Was greatly increased near the crystalline melting temperature, due to the thermal expansion of polymeric matrix. From the experimental results, it was proposed that the decrease of surface free energy induced by interactions between carbon black surfaces and polymer chains is an important factor to the fabrication of a PTC composite made of carbon black and polymeric matrix.

• Structural Engineering and Mechanics
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• v.40 no.5
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• pp.665-688
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• 2011

This paper presents a theoretical analysis for the free vibration of rectangular tanks partially filled with an ideal liquid. Wet dynamic displacements of the tanks are approximated by combining the orthogonal polynomials satisfying the boundary conditions, since the rectangular tanks are composed of four rectangular plates. The classical boundary conditions of the tanks at the top and bottom ends are considered, such as clamped, simply supported, and clamped-free boundary conditions. As the facing rectangular plates are assumed to be geometrically and structurally identical, the vibration modes of the facing plates of the tanks can be divided into two categories: symmetric and antisymmetric modes with respect to the planes passing through the center of the tanks and perpendicular to the free liquid surface. The liquid displacement potentials satisfying the Laplace equation and liquid boundary conditions are derived, and the wet dynamic modal functions of a quarter of the tanks can be expanded by the finite Fourier transform for compatibility requirements along the contacting surfaces between the tanks and liquid. An eigenvalue problem is derived using the Rayleigh-Ritz method. Consequently, the wet natural frequencies of the rectangular tanks can be extracted. The proposed analytical method is verified by observing an excellent agreement with three-dimensional finite element analysis results. The effects of the liquid level and boundary condition at the top and bottom edges are investigated.

• Structural Engineering and Mechanics
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• v.35 no.6
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• pp.759-772
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• 2010

Seismic isolation is a well-known method to mitigate the earthquake effects on structures by increasing their fundamental natural periods at the expense of larger displacements in the structural system. In this paper, the seismic response of isolated and fixed base vertical, cylindrical, liquid storage tanks is investigated using a Finite Element Model (FEM), taking into account fluid-structure interaction effects. Three vertical, cylindrical tanks with different ratios of height to radius (H/R = 2.6, 1.0 and 0.3) are numerically analyzed and the results of response-history analysis, including base shear, overturning moment and free surface displacement are reported for isolated and non-isolated tanks. Isolated tanks equipped by lead rubber bearings isolators and the bearing are modeled by using a non-linear spring in FEM model. It is observed that the seismic isolation of liquid storage tanks is quite effective and the response of isolated tanks is significantly influenced by the system parameters such as their fundamental frequencies and the aspect ratio of the tanks. However, the base isolation does not significantly affect the surface wave height and even it can causes adverse effects on the free surface sloshing motion.