• Transactions of the Korean Society of Mechanical Engineers
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• v.11 no.6
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• pp.1026-1035
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• 1987

The injection molding process is used in the fabrication of a large variety of plastic articles. A numerical simulation of the filling stage along the thickness direction is proposed by combining the free surface boundary condition with the relevant governing equations. The mathematical model is based on the equations of continuity, momentum and energy along with inelastic power-law model and relevant boundary conditions. Due to the significant implications for microstructure development in the pro duct, the fountain effect at the advancing free surface is explicitly taken into consideration in the simulation. The model yields data on free surface shape as well as velocity, pressure, temperature and shear stress distributions within the mold cavity. The rearrangement of the velocity and temperature profiles in the vicinity of the melt front is considered in detail.

• Journal of computational fluids engineering
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• v.19 no.2
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• pp.79-85
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• 2014

An air-water free surface flow simulation by using the Lattice Boltzmann Method(LBM) has not been studied a lot compared with the done by the Navier-Stoke equation. This paper shows the LBM is as one of the application tools for the free surface movement over an obstacle. The Mezo scaled application tool has been developed with two dimensional and nine discretized velocity direction using conventional lattice Bhatnagar-Gross-Krook model. Boundary conditions of a halfway-based for solid wall and a kinematic-based for interface are adopted. A validation case with a trapezoidal shape bump to make a comparison between freesurface movements from computational results and experimental ones was described with grid size dependency.

• Journal of Mechanical Science and Technology
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• v.19 no.7
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• pp.1517-1525
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• 2005

Liquid sloshing displays the highly nonlinear free surface fluctuation when either the external excitation is of large amplitude or its frequency approaches natural sloshing frequencies. Naturally, the accurate tracking of time-varying free surface configuration becomes a key task for the reliable prediction of the sloshing time-history response. However, the numerical instability and dissipation may occur in the nonlinear sloshing analysis, particularly in the long-time beating simulation, when two simulation parameters, the relative time-increment parameter a and the fluid mesh pattern, are not elaborately chosen. This paper intends to examine the effects of these two parameters on the potential-based nonlinear finite element method introduced for the large amplitude sloshing flow.

• Journal of Mechanical Science and Technology
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• v.19 no.12
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• pp.2263-2269
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• 2005

The ship wave phenomena in the restricted waterway were investigated by a numerical analysis. The Euler and continuity equations were employed for the present study. The boundary fitted and moving grid system was adopted to enhance the computational efficiency. The convective terms in the governing equations and the kinematic free surface boundary condition were solved by the Constrained Interpolated Profile (CIP) algorithm in order to solve accurately wave heights in far field as well as near field. The advantage of the CIP method was verified by the comparison of the computed results by the CIP and the Maker and Cell (MAC) method. The free surface flow simulation around Wigley hull was performed and compared with the experiment for the sake of the validation of the numerical method. The present numerical scheme was applied to the free surface simulation for various canal sections in order to understand the effect of the sectional shape of waterways on the ship waves. The wave heights on the side wall and the shape of the wave patterns with their characteristics of flow are discussed.

• International Journal of Naval Architecture and Ocean Engineering
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• v.7 no.3
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• pp.610-625
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• 2015

In this paper the wave run-up around a circular column in regular waves is numerically calculated to investigate the applicability of the Modified Marker-Density (MMD) method to prediction of wave run-up around an offshore platform. The MMD method is one of the methods to define the highly nonlinear free surface. The governing equations are the Navier-Stokes equations and the continuity equation which are computed in Cartesian grid system. To validate incident waves generated by numerical simulation, those are compared with the solutions of the Stokes $5^{th}$ order wave theory. The wave run-up simulations are performed varying the steepness and period of incident waves as referred experimental data. The numerical results are compared to the experimental data and the results show good agreements.

• International Journal of Naval Architecture and Ocean Engineering
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• v.13 no.1
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• pp.35-49
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• 2021

This paper presents a direct numerical simulation of turbulent flows over a bump in an open channel to examine the turbulence characteristics near divergent waves emanating from the bump and to investigate the interaction of the turbulences with the divergent waves. To verify the reliability of the simulations, the mean velocity profile and root-mean-square of velocity fluctuations are compared with previous data. The anisotropic invariant maps show that the ratio of the streamwise to spanwise velocity fluctuations plays an important role in characterizing the anisotropic nature of the separated shear layer behind the bump in the vicinity of the free surface. The vortex identification discloses a large-scale streamwise vortical structure from the mean velocity field and a cluster of small coherent structures from the instantaneous velocity field, which are responsible for the anisotropic characteristics of the turbulence beneath the free surface.

• Korean Journal of Optics and Photonics
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• v.25 no.5
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• pp.273-278
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• 2014

We present an algorithm for surface reconstruction from the second-derivative data for free-form aspherics, which uses a subaperture scanning system that measures the local surface profile and determines the three second-derivative values at those local sampling points across the free-form surface. The three second-derivative data were integrated to get a map of x- and y-slopes, which went through a second Southwell integration step to reconstruct the surface profile. A synthetic free-form surface 200 mm in diameter was simulated. The simulation results show that the reconstruction error is 19 nm RMS residual difference. Finally, the sensitivity to noise is diagnosed for second-derivative Gaussian random noise with a signal to noise ratio (SNR) of 16, the simulation results proving that the suggested method is robust to noise.

• Journal of the Society of Naval Architects of Korea
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• v.31 no.2
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• pp.45-56
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• 1994

A computationally efficient numerical method based on potential flow is developed for time-domain simulation of the nonlinear free-surface flows around a 2-dimensional hydrofoil. This numerical method, namely, spectral/boundary-element method, is a mixed one of the high-order spectral method and the boundary-element method in time-domain. The high-order spectral method is used to calculate the nonlinear evolution of free-surface, and the boundary-element method is used to calculate the effects of the hydrofoil and the shed vortex. As application examples, nonlinear free-surface flows around a 2-dimensional hydrofoil which starts from the rest and translates near the free-surface with or without harmonic oscillations are calculated. Nonlinear/unsteady results of free-surface waves and hydrodynamic farces are shown and discussed. Particularly, the results of steady-state which are obtained as a special case of the present unsteady solution are compared with others' calculated and experimental results, and good agreements are observed.

• Nuclear Engineering and Technology
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• v.48 no.2
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• pp.360-367
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• 2016

A windowless spallation target can provide a neutron source and maintain neutron chain reaction for a subcritical reactor, and is a key component of China's nuclear waste transmutation of coupling accelerator and subcritical reactor. The main issue of the windowless target design is to form a stable and controllable free surface that can ensure that energy spectrum distribution is acquired for the neutron physical design when the high energy proton beam beats the lead-bismuth eutectic in the spallation target area. In this study, morphology and flow characteristics of the free surface of the windowless target were analyzed through the volume of fluid model using computational fluid dynamics simulation, and the results show that the outlet cross section size of the target is the key to form a stable and controllable free surface, as well as the outlet with an arc transition. The optimization parameter of the target design, in which the radius of outlet cross section is $60{\pm}1mm$, is verified to form a stable and controllable free surface and to reduce the formation of air bubbles. This work can function as a reference for carrying out engineering design of windowless target and for verification experiments.

• Journal of the Society of Naval Architects of Korea
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• v.30 no.1
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• pp.104-114
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• 1993

In this paper, effects of free surface on viscous flow is investigated. Continuity equation coupled with Navier-Stokes equations are solved numerically by using an artificial compressibility method[1, 2]. The body-fitted generalized curvilinear coordinate system is employed to deal with arbitrary body shape. The IAF scheme with finite difference method is used to solve the equations, and a diagonal algorithm is applied to time-varying Jacobian matrices for the computational economics. Free surface shape is obtained by applying zero pressure condition to still water surface at each time step. A numerical test is made for larminar flow around a circular cylinder vertically piercing the free surface. Computed flow patterns are largely affected by the existance of free surface in low Reynolds number flows treated in this paper. Free surface causes viscous pressure drag to vary much in depth direction in accordance with the variations of flow pattern.