• 한국해양공학회지
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• 제37권2호
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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.

• 대한기계학회논문집
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• 제7권4호
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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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• 제16권1호
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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.

• 대한기계학회논문집B
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• 제37권10호
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• pp.895-900
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• 2013

2차원 채널 내의 원형실린더를 지나는 유동에 대한 이론적 연구를 수행하였다. 원형 실린더는 채널의 상하 중앙부에 위치하며, 원형실린더에서 멀리 떨어진 채널 내에는 포아제 유동이 존재한다. 스톡스 근사를 적용하고 유동의 고유함수 전개와 오차의 최소제곱법을 사용하여 유동장을 해석하였다. 해석의 결과로 유동함수와 압력분포 식을 구하였으며, 채널의 벽면과 원형실린더에 작용하는 압력 및 전단응력 분포를 계산하였다. 원형실린더로 인해 부가적으로 발생하는 압력 강하와 원형실린더가 받는 힘을 원형실린더의 반지름 길이의 함수로 계산하였으며, 대표적인 실린더 반지름 길이에 대하여 유선과 압력분포를 도시하였다.

• 대한기계학회논문집B
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• 제35권6호
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• pp.609-615
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• 2011

2차원 채널 내의 수직 평판을 지나는 유동에 대한 이론적 연구를 수행하였다. 수직 평판은 채널의 상하 중앙부에 위치하며, 수직 평판에서 멀리 떨어진 채널 내에는 포아제 유동이 존재한다. 스톡스 근사를 적용하고 고유함수 전개와 점 배열 방법을 사용하여 유동장을 해석하였다. 해석의 결과로 유동 함수와 압력분포식을 구하였으며, 채널의 벽면과 수직 평판에 작용하는 압력 및 전단응력 분포를 계산 하였다. 또한, 수직 평판으로 인해 부가적으로 발생하는 압력 강하와 수직 평판이 받는 힘을 수직 평판 길이의 함수로 계산하였으며, 대표적인 수직 평판의 길이에 대하여 유선과 압력분포도를 도시하였다. 또한, 작은 레이놀즈 수가 유동에 미치는 영향을 알아보기 위하여 레이놀즈 수가 작은 층류유동의 경우에 대하여 수치해석을 수행하였다.

• 대한조선학회논문집
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• 제54권3호
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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.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2001년도 춘계학술대회논문집E
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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.

• 한국철도학회논문집
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• 제12권1호
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• pp.65-71
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• 2009

축대칭 Navier-Stokes 방정식에 기반한 전산유체역학을 이용하여 고속철도차량 객실 내 압력변동을 평가하였다. 차량 내부의 압력변동은 차내 압력변화율과 차 내외부 압력변동의 선형 관계식에 근거한 1차 차분식을 이용하여 계산되었다. 전산해석 결과, 새로운 한국형 고속철도 차량이 경부고속선 터널을 330km/h로 통과할 시 발생하는 객실 실내압 변동은 해당 차량이 기밀도 국내기준을 만족한다고 가정하였을 시 철도차량의 실내압력변동 국내 기준치를 잘 만족하는 것으로 나타났다.

• 한국철도학회논문집
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• 제13권4호
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• pp.371-375
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• 2010

분산형 고속철도차량의 유리창 강도조건을 설정하기 위하여 열차가 터널을 통과하는 동안의 압력변동이 수치적으로 모사되었다. 계산결과를 토대로 객실 내외의 압력차이가 계산되었고, 객실 유리창에 작용하는 하중의 크기가 도출되었다. 열차가 터널을 통과하는 동안의 압력장을 모사하기 위하여 축대칭 Navier-Stokes 방정식에 기반한 전산유체역학이 이용되었다. 차량 내부의 압력변동은 차내 압력변화율과 차 내외부 압력변동의 선형 관계식에 근거한 1차 차분식을 이용하여 계산되었다.

• Journal of Photoscience
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• 제11권1호
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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.