• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 1998년도 춘계 학술대회논문집
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• pp.15-28
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• 1998

As an alternative for solving the incompressible Navier-Stokes equations, we present a vorticity-based integro-differential formulation for vorticity, velocity and pressure variables. One of the most difficult problems encountered in the vorticity-based methods is the introduction of the proper value-value of vorticity or vorticity flux at the solid surface. A practical computational technique toward solving this problem is presented in connection with the coupling between the vorticity and the pressure boundary conditions. Numerical schemes based on an iterative procedure are employed to solve the governing equations with the boundary conditions for the three variables. A finite volume method is implemented to integrate the vorticity transport equation with the dynamic vorticity boundary condition . The velocity field is obtained by using the Biot-Savart integral derived from the mathematical vector identity. Green's scalar identity is used to solve the total pressure in an integral approach similar to the surface panel methods which have been well-established for potential flow analysis. The calculated results with the present mettled for two test problems are compared with data from the literature in order for its validation. The first test problem is one for the two-dimensional square cavity flow driven by shear on the top lid. Two cases are considered here: (i) one driven both by the specified non-uniform shear on the top lid and by the specified body forces acting through the cavity region, for which we find the exact solution, and (ii) one of the classical type (i.e., driven only by uniform shear). Secondly, the present mettled is applied to deal with the early development of the flow around an impulsively started circular cylinder.

• 한국전산유체공학회지
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• 제3권1호
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• pp.11-21
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• 1998

A vorticity-based method for the numerical solution of the two-dimensional incompressible Navier-Stokes equations is presented. The governing equations for vorticity, velocity and pressure variables are expressed in an integro-differential form. The global coupling between the vorticity and the pressure boundary conditions is fully considered in an iterative procedure when numerical schemes are employed. The finite volume method of the second order TVD scheme is implemented to integrate the vorticity transport equation with the dynamic vorticity boundary condition. The velocity field is obtained by using the Biot-Savart integral. The Green's scalar identity is used to solve the total pressure in an integral approach similar to the surface panel methods which have been well established for potential flow analysis. The present formulation is validated by comparison with data from the literature for the two-dimensional cavity flow driven by shear in a square cavity. We take two types of the cavity now: (ⅰ) driven by non-uniform shear on top lid and body forces for which the exact solution exists, and (ⅱ) driven only by uniform shear (of the classical type).

• 한국전산유체공학회지
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• 제11권3호
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• pp.28-36
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• 2006

NSBT(No Slip Boundary Treatment) is a newly developed scheme for the treatment of a no slip condition on the solid wall of obstacle in a flow field. In our research, NSBT was used to perform LBM simulation of a flow over a circular cylinder to determine the flow feature and aerodynamics characteristic of the cylinder. To ascertain the applicability of NSBT on the complex shape of the obstacle, it was first simulated for the case of the flow over a circular and square cylinder in a channel and the results were compared against the solution of Navier-Stokes equation. The simulations were performed in a moderate range of Reynolds number at each cylinder position to identify the flow feature and aerodynamic characteristics of circular cylinder in a channel. The drag coefficients of the cylinder were calculated from the simulation results. We have numerically confirmed that the critical reynolds number for vortex shedding is in the range of 200$\sim$250. For the gap parameter $\gamma$ = 2 cases at Re > 240, the vortex shedding were symmetric and it resembled the Karmann vortex. As the cylinder approached to one wall, the vorticity significantly reduced in length while the vorticity on the other side elongated and the vorticity combined with the wall boundary-layer vorticity. The resultant $C_d$ by LBM concurred with the results of DNS simulation performed by previous researchers.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2003년도 가을 학술발표회 논문집
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• pp.437-443
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• 2003

The object of this paper is the treatment of how to make the vorticity boundary condition instead of pressure in the primitive variable case. An improved algorithm for solving the vorticity-stream function equation is presented. The linear finite element approximation for the solution of Wavier-Stokes and Stokes flows is constructed. Not only regular domain but also complicate domain can be analyze d, using this formulation.

• 대한토목학회논문집
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• 제33권6호
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• pp.2267-2275
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• 2013

기존의 천수흐름 해석 상용모형에서는 내부 경계조건을 단순히 완전활동조건으로 가정하여 유체의 흐름을 해석함으로써 구조물 주위에서의 유속, 와도, 수위, 전단력의 분포, 항력 및 양력의 시간에 따른 변화 등을 올바르게 해석하지 못하였다. 본 연구에서는 구조물 주위에서의 흐름특성을 정확하게 예측할 수 있는 유한요소모형을 개발하고, 구조물에서의 경계조건을 활동길이를 이용한 부분활동조건으로 묘사하여 내부경계조건에 따른 원형 실린더 후면에서의 층류 흐름특성을 분석하였다. 종횡방향 유속 및 와도의 시간에 따른 변화, 후류길이, 활동길이에 따른 와류열의 변화와 질량보존율을 비교한 결과 완전활동조건을 부여한 경우에는 와류열이 전혀 형성되지 않고 완전한 층류흐름이 발생하였다. 부분활동조건을 입력한 경우 실린더 표면에서의 유속분포가 변화되어 전단력의 크기와 와도의 발생에 영향을 미치므로 무활조건을 부여한 경우에 비해 와류열의 발생 주기가 짧아졌다. 최대 질량보존 오차는 무활조건을 적용한 경우 0.73%로 나타났으며, 무활조건에 비해 부분활동조건을 부여한 경우의 오차율이 최대 0.21% 감소하였다.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2004년도 춘계학술대회
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• pp.1601-1606
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• 2004

In this paper, the unsteady behavior of the viscous flow field past an impulsively started elliptic cylinder is studied numerically. In order to analyze flow field, we introduce vortex particle method. The vorticity transport equation is solved by fractional step algorithm which splits into convection term and diffusion term. The convection term is calculated with Biot-Savart law, the no-through boundary condition is employed on solid boundaries. The diffusion term is modified based on the scheme of particle strength exchange. The particle redistributed scheme for general geometry is adapted. The flows around an elliptic cylinder are investigated for various attack angles at Reynolds number 200. The comparison between numerical results of present study and experimental data shows good agreements.

• 대한기계학회논문집B
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• 제28권7호
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• pp.809-817
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• 2004

In this paper, the unsteady behavior of the viscous flow field past an impulsively started elliptic cylinder is studied numerically. In order to analyze flow field, we introduce vortex particle method. The vorticity transport equation is solved by fractional step algorithm which splits into convection term and diffusion term. The convection term is calculated with Biot-Savart law, the no-through boundary condition is employed on solid boundaries. The diffusion term is modified based on the scheme of particle strength exchange. The particle redistributed scheme for general geometry is adapted. The flows around an elliptic cylinder are investigated for various attack angles at Reynolds number 200. The comparison between numerical results of present study and experimental data shows good agreements.

• 항공우주시스템공학회지
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• 제16권4호
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• pp.35-44
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• 2022

이·착륙하는 항공기에서 발생하는 후류의 거동에 대한 연구는 근접 후행 항공기의 비행안정성과 공항의 경제성 등과 관련하여 매우 중요하다. 특히 이착륙 비행단계에서 발생한 와들의 거동 연구는 지면효과가 반드시 고려해야 한다. 본 연구에서는 기존의 2차원 스펙트럴법에 와도경계조건 및 이미지법을 적용하여, 지면효과가 고려될 수 있는 수치해법을 도출하였다. 개선된 수치기법을 사용하여 얻은 결과를 참고문헌의 수치해석 결과 및 실험결과와 비교하여 타당성을 검증하였다. 특히, 본 연구의 수치해석방법으로 지면근처에서 발생하는 이차와(secondary vortex)의 생성과 박리, 그리고 거동을 예측할 수 있음을 보였다. 향후 본 연구방법을 확장하여 Stratification, Wind Shear 등 다양한 기상조건이 와의 거동에 미치는 영향을 연구할 계획이다.

• 대한기계학회논문집B
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• 제24권5호
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• pp.733-743
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• 2000

We solve the integral representation of the Navier-Stokes equations in a lagrangian view by tracking the particles, which have vortex strengths. We simulate the unsteady viscous flow around an impulsively started cylinder using the vortex particle method. Particles are advanced via the Biot-Savart law for a lagrangian evolution of particles. The particle strength is modified based on the scheme of particle strength exchange. The solid boundary satisfies the no-slip boundary condition by the vorticity generation algorithm. We newly modify the diffusion scheme and the boundary condition for simulating an unsteady flow efficiently. To save the computation time, we propose the mixed scheme of particle strength exchange and core expansion. We also use a lot of panels to ignore the curvature of the cylinder, and not to solve the evaluation of the surface density. Results are compared to those from other theoretical and experimental works.

• Journal of Mechanical Science and Technology
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• 제18권2호
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• pp.313-324
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• 2004

A rich phenomenon in the dynamics of azimuthal vortices in a circular cylinder caused by the inertial oscillation is investigated numerically at high Reynolds numbers and moderate Rossby numbers. In the actual spin-up flow where both the Ekman circulation and the bottom friction effects are included, the first appearance of a seed vortex is generated by the Ekman boundary-layer on the bottom wall and the subsequent roll-up near the corner bounded by the side wall. The existence of the small vortex then rapidly propagates toward the inviscid region and induces a complicated pattern in the distribution of azimuthal vorticity, i.e. inertial oscillation. The inertial oscillation however does not deteriorate the classical Ekman-pumping model in the time scale larger than that of the oscillatory motion. Motions of single vortex and a pair of vortices are further investigated under a slip boundary-condition on the solid walls. For the case of single vortex, repeated change of the vorticity sign is observed together with typical propagation of inertial waves. For the case of a pair of vortices with a two-step profile in the initial azimuthal velocity, the vortices' movement toward the outer region is resisted by the crescent-shape vortices surrounding the pair. After touching the border between the core and outer regions, the pair vortices weaken very fast.