• Tribology and Lubricants
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• v.17 no.5
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• pp.391-398
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• 2001

Two dimensional slow viscous flow around two counter-rotating equal cylinders is investigated based on Stokes'approximation. An exact formal expression of the stream function is obtained by using the bipolar cylinder coordinates and Fourier series expansion. From the stream function obtained, the streamline patterns around the cylinders are shown and the pressure distribution in the flow field is determined. By integrating the stress distributions on the cylinder, the force and the moment exerted on the cylinder are calculated. The flow rate through the gap between the two cylinders is also determined as the distance between two cylinders varies. Special attention is directed to the case of very small distance between two cylinders concerned with the lubrication theory and the minimum pressure is calculated to explain a possible cavitation.

• Proceedings of the Korean Society of Tribologists and Lubrication Engineers Conference
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• 2000.06a
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• pp.142-149
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• 2000

Two dimensional slow viscous flow around two counter-rotating equal cylinders is Investigated based on Stokes' approximation. An exact formal expression of the stream function is obtained by using the bipolar cylinder coordinates and Fourier series expansion. From the stream function obtained, the streamline patterns around the cylinders are shown and the pressure distribution In the flow field is determined. By Integrating the stress distribution on the cylinder, the force and the moment exerted on the cylinder are calculated. The flow rate through the gap between the two cylinders is determined as the distance between two cylinders vary. It Is also revealed that the velocity at the far field has finite non-zero value. Special attention is directed to the case of very small distances between two cylinders by way of the lubrication theory.

• Tribology and Lubricants
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• v.18 no.6
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• pp.411-417
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• 2002

Two dimensional slow viscous flow between a rotating cylinder and a translating plate is investigated using Stokes' approximation. An exact formal expression of the stream function is obtained by using the bipolar cylinder coordinates and Fourier series expansion. From the stream function obtained, the streamline patterns are shown and the pressure distribution in the flow field is determined. By integrating the stress distributions on the cylinder, the farce and the moment exerted on the cylinder are calculated. The flow rate through the gap between the cylinder and the plate is also determined as a function of the distance between the cylinder and the plate. Special attention is directed to the case of very small distance between the cylinder and the plate concerned with the lubrication theory and the minimum pressure is calculated to explain a possible cavitation.

• Journal of Ocean Engineering and Technology
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• v.36 no.2
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• pp.101-107
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• 2022

Dean (1965) proposed the use of the root mean square error (RMSE) in the dynamic free surface boundary condition (DFSBC) and kinematic free-surface boundary condition (KFSBC) as an error evaluation criterion for wave theories. There are well known wave theories with RMSE more than 1%, such as Airy theory, Stokes theory, Dean's stream function theory, Fenton's theory, and trochodial theory for deep-water waves. However, none of them can be applied for deep-water breaking waves. The purpose of this study is to provide a closed-form solution for deep-water waves with RMSE less than 1% even for breaking waves. This study is based on a previous study (Shin, 2016), and all flow fields were simplified for deep-water waves. For a closed-form solution, all Fourier series coefficients and all related parameters are presented with Newton's polynomials, which were determined by curve fitting data (Shin, 2016). For verification, a wave in Miche's limit was calculated, and, the profiles, velocities, and the accelerations were compared with those of 5^th-order Stokes theory. The results give greater velocities and acceleration than 5^th-order Stokes theory, and the wavelength depends on the wave height. The results satisfy the Laplace equation, bottom boundary condition (BBC), and KFSBC, while Stokes theory satisfies only the Laplace equation and BBC. RMSE in DFSBC less than 7.25×10^-2% was obtained. The series order of the proposed method is three, but the series order of 5^th-order Stokes theory is five. Nevertheless, this study provides less RMSE than 5^th-order Stokes theory. As a result, the method is suitable for offshore structural design.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.38 no.9
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• pp.701-709
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• 1989

The time-averaged behavior of the three-phase Inductor-Converter Bridge (ICB) circuit has been analyzed by using the state-space averaging method. Especially, a second order approximation in the matrix expansion makes the analysis possible. The results are in a closed form which is quite different from the conventional solution obtained by using the Fourier Series. Therefore, the computational difficulties in evaluating the infinite Fourier series can be avoided and the results derived in this paper are available expecially in real time control. By comparing with the Fourier result, it has been verified that the analysis by means of the state-space averaging method is more accurate and simple. The digital simulation and the equivalent experiments have also been carried out to confirm the theoretical results.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.4 no.4
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• pp.219-224
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• 1992

A numerical method using the truncated Fourier series is presented to predict the wave potential and water surface profile for two dimensional nonlinear standing waves. The unknown coefficients of the series are to be determined through the Newton solution of nonlinear simultaneous equations given by the governing equation and boundary conditions of the problem. In order to prove the effectiveness of the present method. an existing Stokes-like perturbation method is considered together, and a hydraulic experiment for measuring water surface profile and wave pressure is performed as well. The results are such that the present method can generally give exact solutions even for relatively big wave stiffness regardless of the water depth condition. It also demonstrates its validity by showing double humps in the crest of temporal wave pressure profile which normally appear in strongly nonlinear standing waves.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.19 no.9
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• pp.968-977
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• 2008

In this paper, an analysis of TE-wave scattering from transversal-shifted tandem slits using fourier transform analysis and Wiener-Hopf technique are derived and the electrical performances have been compared with a commercially availabel software. In Fourier transform analysis, it is shown that a fast-convergent series solution can be obtained when the distance between the slits is very narrow, while in Wiener-Hopf technique, it is found that the highly-accurate approximation can be obtained when the gap between the slits becomes wider. In addition, this paper has dealt with a good agreement between two analytical solutions.

• Proceedings of the KIEE Conference
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• 2001.05a
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• pp.34-37
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• 2001

This paper presents some results after comparing the characteristics of 3 algorithms, which are discrete Fourier transform based algorithm, least square method, and modified differential approximation algorithm, used at most distance relays all over the world. In case of the DFT based distance relaying algorithm, the length of the algorithm data window and the cut-off frequency of an anti-aliasing low-pass filter adopted are fixed. On the other hand, the data window lengths are changed according to the corresponding low-pass filters in the rest two algorithms. In series of tests, the apparent impedance estimated by the modified differential approximation algorithm shows faster and more stable characteristics of convergence than the two others.

• Computational Structural Engineering
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• v.8 no.1
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• pp.147-160
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• 1995

Based on the weighted residual concept[4], a three-dimensional plate theory is derived using a Fourier series expansion of a dependent variable and a weighted residual approximation of the basic elasticity equations. The weighted residual equilibrium equations of the plate are expressed in terms of weighted displaced quantities, and the results are then interpreted by means of a potential energy functional. The potential energy expression is used to develop a finite element implementation. For illustrative purposes, the application of the theory to a strip plate is considered and two numerical examples of a cantilever and a simply-supported strip plate are studied.

• Journal of Ocean Engineering and Technology
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• v.37 no.6
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• pp.256-265
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• 2023

Many numerical methods have been developed since 1961, but unresolved issues remain. This study developed a numerical method to address these issues and determine the coefficients and properties of rotational waves with a shear current in a finite water depth. The number of unknown constants was reduced significantly by introducing a wavelength-independent coordinate system. The reference depth was calculated independently using the shooting method. Therefore, there was no need for partial derivatives with respect to the wavelength and the reference depth, which simplified the numerical formulation. This method had less than half of the unknown constants of the other method because Newton's method only determines the coefficients. The breaking limit was calculated for verification, and the result agreed with the Miche formula. The water particle velocities were calculated, and the results were consistent with the experimental data. Dispersion relations were calculated, and the results are consistent with other numerical findings. The convergence of this method was examined. Although the required series order was reduced significantly, the total error was smaller, with a faster convergence speed.