• Journal of Ocean Engineering and Technology
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• v.37 no.2
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• pp.49-57
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• 2023

Since Chappelear developed a Fourier approximation method, considerable research efforts have been made. On the other hand, Fourier approximations are unsuitable for deep water waves. The purpose of this study is to provide a Fourier approximation suitable even for deep water waves and a numerical method to determine the Fourier coefficients and the wave properties. In addition, the convergence of the solution was tested in terms of its order. This paper presents a velocity potential satisfying the Laplace equation and the bottom boundary condition (BBC) with a truncated Fourier series. Two wave profiles were derived by applying the potential to the kinematic free surface boundary condition (KFSBC) and the dynamic free surface boundary condition (DFSBC). A set of nonlinear equations was represented to determine the Fourier coefficients, which were derived so that the two profiles are identical at specified phases. The set of equations was solved using Newton's method. This study proved that there is a limit to the series order, i.e., the maximum series order is N=12, and that there is a height limitation of this method which is slightly lower than the Michell theory. The reason why the other Fourier approximations are not suitable for deep water waves is discussed.

• Transactions of the Korean Society of Mechanical Engineers
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• v.7 no.4
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• pp.386-391
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• 1983

Two-dimensional slow viscous flow due to a stokeslet near a slit is investigated on the basis of Stokes approximation. Velocity fields and stream function are obtained in closed forms by finding two sectionally holomorphic functions which are determined by reducing the problem to Riemann-Hilbert problems. The force exerted on a small cylinder is calculated for the arbitrary position of the cylinder translating in an arbitrary direction. The features of fluid flow are also investigated.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.16 no.1
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• pp.65-84
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• 2012

We present an application of the variational multiscale methodology to the computation of concentric annular pipe flow. Isogeometric analysis is utilized for higher order approximation of the solution using Non-Uniform Rational B-Splines (NURBS) functions. The ability of NURBS to exactly represent curved geometries makes NURBS-based isogeometric analysis attractive for the application to the flow through the curved channel.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.37 no.10
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• pp.895-900
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• 2013

A two-dimensional Stokes flow past a circular cylinder in a channel is analyzed. The circular cylinder is located at the center of the channel, and a plane Poiseuille flow exists upstream and downstream far from the circular cylinder. The Stokes approximation is used, and the flow is investigated analytically by using the eigenfunction expansion and the least square methods. From the analysis, the stream function and pressure distribution are obtained, and the pressure and shear stress distributions on the circular cylinder and channel wall are calculated. The additional pressure drop induced by the circular cylinder and the force exerted on it are calculated as functions of the length of the radius of the circular cylinder. For a typical length of the radius of the circular cylinder, the streamline pattern and pressure distribution are shown.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.35 no.6
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• pp.609-615
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• 2011

A two-dimensional Stokes flow past a vertical plate in a channel is analyzed. The vertical plate is located at the center of the channel, and plane Poiseuille flow exists far upstream and downstream of the vertical plate. The Stokes approximation is used, and the flow is investigated analytically using the method of eigenfunction expansion and the point collocation method. From the analysis, the stream function and pressure distribution are obtained, and the pressure and shear stress distributions on the plate and channel wall are calculated. The additional pressure drop induced by the vertical plate and the force exerted on it are calculated as functions of the length of the vertical plate. For a typical length of the vertical plate, the streamline pattern and pressure distribution are shown. In addition, numerical analysis of laminar flow with a small Reynolds number is carried out to analyze the effect of a small Reynolds number on the flow pattern.

• Journal of the Society of Naval Architects of Korea
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• v.54 no.3
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• pp.250-257
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• 2017

It is desirable to have a way to predict the pressure drag due to various appendages attached to stern. As a mathematical model for these, a sphere and a singularity behind it, both in the uniform flow can be considered. We may use the Butler's sphere theorem to find the Stokes' stream function when the resulting flow is axisymmetric, and then the extended Lagally's theorem to get the force upon the sphere due to the singularity. Assuming the separation distance between the sphere and the singularity is small, the leading order approximation for the force is obtained and it is found out that if the separation distance and the square root of the strength of the dipole are of the same order, the effect of the image of the dipole with respect to the sphere is the most important.

• Proceedings of the KSME Conference
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• 2001.06e
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• pp.410-415
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• 2001

An analytical and numerical examination of second-order fractional-step methods and boundary condition for the incompressible Navier-Stokes equations is presented. In this study, the compatibility condition for pressure Poisson equation and its boundary conditions, stability, and numerical accuracy of canonical fractional-step methods has been investigated. It has been found that satisfaction of compatibility condition depends on tentative velocity and pressure boundary condition, and that the compatible boundary conditions for type D method and approximately compatible boundary conditions for type P method are proper for divergence-free velocity for type D and approximately divergence-free for type P method. Instability of canonical fractional-step methods is induced by approximation of implicit viscous term with explicit terms, and the stability criteria have been founded with simple model problems and numerical experiments of cavity flow and Taylor vortex flow. The numerical accuracy of canonical fractional-step methods with its consistent boundary conditions shows second-order accuracy except $D_{MM}$ condition, which make approximately first-order accuracy due to weak coupling of boundary conditions.

• Journal of the Korean Society for Railway
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• v.12 no.1
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• pp.65-71
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• 2009

The pressure transient inside the passenger cabin of high-speed train has been assessed using computational fluid dynamics (CFD) based on the axi-symmetric Navier-Stokes equation. The pressure change inside a train have been calculated using first order difference approximation based on a linear equation between the pressure change ratio inside a train and the pressure difference of inside and outside of the train. The numerical results show that the pressure change inside the new Korean high-seed train passing through a tunnel of Seoul-Busan high-speed line at the speed of 330km/h satisfied well the Korean regulation for pressure change inside a passenger cabin if the train is satisfying the train specification for airtightness required by the regulation.

• Journal of the Korean Society for Railway
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• v.13 no.4
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• pp.371-375
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• 2010

In order to decide the strength requirement of the window glass for the high-speed train, the pressure change during the passage of the EMU type high-speed train has been numerically simulated. Based on the calculation results, the pressure difference between the inner and outer pressure of the cabin has been calculated to yield the amount of load acting on the window glass of the cabin. To simulate the pressure field generated by the high-speed train passing through the tunnel, computational fluid dynamics based on the axi-symmetric Navier-Stokes equation has been employed. The pressure change inside a train has been calculated using first order difference approximation based on a linear equation between the pressure change ratio inside a train and the pressure difference of inside and outside of the train.

• Journal of Photoscience
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• v.11 no.1
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• pp.11-17
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• 2004

Fluorescence quenching of l,4-bis [2-(2-methylphenyl) ethenyl]-benzene (Bis-MSB) by carbon tetrachloride in five different solvents namely hexane, cyclohexane, toluene, benzene and dioxane has been carried out at room temperature with a view to understand the quenching mechanisms. The Stern-Volmer plot has been found to be non-linear with a positive deviation for all the solvents studied. In order to interpret these results we have invoked the Ground state complex and Sphere of action static quenching models. Using these models various rate parameters have been determined. The magnitudes of these parameters imply that sphere of action static quenching model agrees well with the experimental results. Hence the positive deviation in the Stem-Volmer plots is attributed to the static and dynamic quenching. Further, with the use of Finite Sink approximation model, it was possible to check whether these bimolecular reactions as diffusion limited and to estimate independently distance parameter R' and mutual diffusion coefficient D. Finally an effort has been made to correlate the values of R'and D with the values of the encounter distance R and the mutual diffusion coefficient D determined using the Edwardis empirical relation and Stokes-Einstein relation.