• 한국전산유체공학회지
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• 제4권1호
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• pp.19-26
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• 1999

This paper describes a numerical method for predicting the incompressible unsteady laminar three-dimensional flows with free-surface. The Navier-Stokes equations governing the flows have been discretized by means of finite-difference approximations, and the resulting equations have been solved via the SIMPLE-C algorithm. The free-surface is defined by the motion of a set of marker particles and the interface behaviour was investigated by means 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. The results show that this numerical method produces accurate and physically realistic predictions of three-dimensional free-surface flows.

• International Journal of Naval Architecture and Ocean Engineering
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• 제13권1호
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• pp.1-11
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• 2021

Performance of a NACA 63₄-021 hydrofoil in motion under and in close proximity of a free surface for a large range of angles of attack is studied. Lift and drag coefficients of the hydrofoil at different submergence depths are investigated both numerically and experimentally, for 0° ≤ AoA ≤ 30° at a Reynolds number of 10⁵. The results of the numerical study are in good agreement with the experimental results. The agreement confirms the new finding that for a submerged hydrofoil operating at high angles of attack close to a free surface, the interaction between the hydrofoil-motion induced waves on the free surface and the hydrofoil results in mitigation of the flow separation characteristics on the suction side of the foil and delay in stall, and improvement in hydrofoil performance. In comparing with a baseline case, results suggest a 55% increase in maximum lift coefficient and 90% average improvement in performance for, based on the lift-to-drag ratio, but it is also observed significant decrease of lift-to-drag ratio at lower angles of attack. Flow details obtained from combined finite volume and volume of fluid numerical methods provide insight into the underlying enhancement mechanism, involving interaction between the hydrofoil and the free surface.

• 대한조선학회논문집
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• 제40권4호
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• pp.8-15
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• 2003

This paper presents the method for developing an optimum hull form with minimum wave resistance using SQP(sequential quadratic programming) as an optimization technique. The wave resistance is evaluated by a Rankine source panel method with non-linear free surface conditions and the ITTC 1957 friction line is used to predict the frictional resistance coefficient. The geometry of the hull surface is represented and modified using B-spline surface patches. The optimization method is applied to Series 60 hull and KCS(KRISO 3600 TEU Container Ship). The obtained results prove that the method is appropriate for preliminary hull form design.

• 대한기계학회논문집B
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• 제21권9호
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• pp.1230-1243
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• 1997

A numerical technique for simulating incompressible viscous flow with free surface is presented. The flow field is obtained by penalty finite element formulation. In this work, a modified volume of fluid (VOF) method which is compatible with 4-node element is proposed to track the moving free surface. This scheme can be applied to irregular mesh system, and can be easily extended to three dimensional geometries. Numerical analyses were done for two benchmark examples, namely the broken dam problem and the solitary wave propagation problem. The numerical results were in close agreement with the existing data. Illustrative examples were studied to show the effectiveness of the proposed numerical scheme.

• 대한조선학회논문집
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• 제35권1호
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• pp.15-23
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• 1998

뭉툭한 스트럿에 의하여 생성되는 자유 표면의 난류 현상에 대한 기본 특성을 수치해석적 방법으로 연구하였다. 지배 방정식으로는 3차원 Navier-Stokes 방정식과 연속 방정식을 사용하였으며, 이들 지배 방정식은 유한 차분법으로 이산화 하였다. 물체앞 자유 표면에서의 난류 유동을 모사하기 위하여 임의의 작은 외부 교란을 도입하여 Large Eddy Simulation을 수행하였다. 물체앞 자유 표면은 어떠한 속도 이상에서 격렬하게 진동하는데 그 기본 특성은 물체 주위의 난류 흐름과 유사함을 수치 계산으로 보였다.

• 대한조선학회지
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• 제17권4호
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• pp.13-20
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• 1980

The integral equation method to solve the boundary-value problem of a 2-dimensional body oscillating in the presence of a free surface generally breaks down at and near irregular frequencies due to the hypothetical flow inside the body. In this paper singularity distributions were extended to an inner free surface to remove the irregular frequency as Ohmatsu's work in 1978, and the solution for the above problem was found by using stream function. For various bodies including Lewis form cylinders, the hydrodynamic forces were calculated numerically at various wave numbers. From the results we concluded that the irregular frequencies can be removed even for the Lewis form cylinder as Ohmatsu done for circular cylinders, and calculated hydrodynamic forces by the present method are little higher than those of Ohmatsu's when the singularities are put on the inner free surface of the body. We specially point out that the solution for heaving motion converges in an oscillatory manner but not for swaying and rolling motions.

• 대한조선학회지
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• 제19권2호
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• pp.33-39
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• 1982

It is one of the basic problems of naval architecture and ocean engineering how to describe the wave kinematics normally under the assumption of an ideal fluid. At present, there are many wave theories available for design purposes. These can be classified into two groups: One is the analytic theory and the other is the numerical theory. This paper briefly introduces the stream function method of R.G. Dean which belongs to the latter group and shows its numerical evaluations exemplified for two cases: One is applied to observed waves and the other is for design waves. In the former case, the wave profiles are calculated by the stream function method and compared with those of the observed waves and also with the results of R.G. Dean. They show good agreement. In the latter case, the wave kinematics and wave loads on a column of diameter 1m are calculated by the stream function method and these are compared with those resulted from the 5th-order gravity wave theory. As a result of comparison the values by the stream function method are slightly larger than those by the 5th-order gravity wave theory but the difference are negligible. From this it is concluded that the stream function method is very useful. And as characteristics of the numerical theories, the stream function method of R.G. Dean can be easily extended to the higher order terms and can include easily the current velocity and the pressure distribution on the free surface. In addition, when the data of observed wave profile are given, this method can reproduced the observed wave profile as closely as possible so that this method seems to describe the ocean wave more realistically. And from standpoint of a mathematical principle the stream function method exactly satisfies the kinematic free-surface boundary condition.

• 한국해안해양공학회지
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• 제14권2호
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• pp.171-181
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• 2002

최근, 구조물에 의한 쇄파를 수반한 다양한 파랑변형 해석법중에 자유수면의 추적기법인 VOF법을 이용한 수치해석기법이 각광을 받고 있다. 본 연구는 수중투과성구조물(잠제)에 의한 파랑변형 및 유속장의 해석을 위해 조파를 위한 line-source와 파의 재반사를 방지하기 위한 부가감쇠영역이 설치된 2차원수치파동수조에 잠제를 설치하고 구조물에 의한 파랑변형의 자유수면 추적을 위해 VOF법을 적용하였다. 2차원수치파동수조를 이용한 본 연구의 수치해석수법의 타당성 검증을 위해 수리실험을 실시하였으며 그 결과 본 수치해석결과와 잘 일치하였다. 일열잠제와 이열잠제에 대한 수치해석을 통해 잠제 주변 유속장 해석으로부터 일열잠제의 경우 배후에서 와가 발생하고 이열잠제의 경우 잠제사이와 잠제배후에서 와가 발생함을 확인하였으며 잠제의 천단상에서는 강한 비선형성분파가 발생하고 투과층내의 유속방향은 자유수면의 형상에 의해 좌우됨을 확인하였다

• 대한기계학회논문집B
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• 제24권12호
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• pp.1555-1569
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• 2000

Numerical simulation of fluid flow with moving free surface has been carried out. For the free surface flow, a VOF(Volume of Fluid)-based algorithm utilizing a fixed grid system has been investigated. In order to reduce numerical smearing at the free surface represented on a fixed grid system, a new free surface tracking algorithm based on the donor-acceptor scheme has been presented. Novel features of the proposed algorithm are characterized as two numerical tools; the orientation vector to represent the free surface orientation in each cell and the baby-cell to determine the fluid volume flux at each cell boundary. The proposed algorithm can be easily implemented in any irregular non-uniform grid systems that are usual in finite element method (FEM). Moreover, the proposed algorithm can be extended and applied to the 3-D free surface flow problem without additional efforts. For computation of unsteady incompressible flow, a finite element approximation based on the explicit fractional step method has been adopted. In addition, the SUPG(streamline upwind/Petrov-Galerkin) method has been implemented to deal with convection dominated flows. Combination of the proposed free surface tracking scheme and explicit fractional step formulation resulted in an efficient solution algorithm. Validity of the present solution algorithm was demonstrated from its application to the broken dam and the solitary wave propagation problems.

• 대한조선학회지
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• 제27권4호
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• pp.32-42
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• 1990

선체표면 및 자유표면에 Rankine Source를 분포하는 방법에 의하여 선체 주위의 유동의 수치계산을 수행하였다. 선체표면 및 자유표면은 사각형 Panel들로 표시되며 자유표면 조건은 이중모형 흐름에 의해 선형화 되어 C.W. Dawson의 유한차분법에 따라 교란없는 자유표면에 적용되었다. Wigley 선형 및 Series 60, $C_B=0.6$ 선형에 대한 Fixed Condition에서의 조파저항, 선측파고, 압력분포 및 Trim & Sinkage 등을 계산하였으며 계산된 결과는 국내외 수조에서의 계측치와 비교하였다. 또한, 선체표면과 자유표면의 Panel 분할조건 및 자유표면의 설정영역의 변화에 따른 계산치의 영향도 아울러 조사하였다.