• 대한조선학회논문집
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• 제41권1호
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• pp.23-30
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• 2004

In the Lagrangian vortex particle method based on the vorticity-velocity formulation for solving the incompressible Navier-Stokes equations, a numerical scheme for calculating pressure fields is presented. Implementation of the numerical method is directly connected with the well-established surface panel methods, just by dealing with the dynamic coupling among vorticity field. Assuming the vorticity and the velocity fields are to be calculated in time domain analysis, the pressure calculation for a complete set of solution at present time step is performed in a similar way to the one used in the Eulerian description. For a validation of the present method, we illustrate the early development of the viscous flow about an impulsive started circular cylinder for Reynolds number 550. The comparative study with the Eulerian finite Volume method provides an extensive understanding and application of the mesh-free Lagrangian vortex methods for numerical simulation of viscous flows around arbitrary bodies of general shape.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2003년도 추계 학술대회논문집
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• pp.37-42
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• 2003

A vorticity-velocity integro-differential formulation of incompressible Wavier-Stokes equations is described, focusing on a scheme for calculating pressure fields in application of the Lagrangian vortex method in connection with panel methods. It deals with the dynamic coupling among velocity, vorticity and pressure, and the Helmholtz decomposition of the velocity field, through a comparative study with the Eulerian finite volume method, we provide an extensive understanding of the Lagrangian vortex methods for numerical simulations of viscous flows around arbitrary bodies.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2002년도 추계 학술대회논문집
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• pp.47-52
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• 2002

We present an improved Lagrangian vortex method in 2-D incompressible unsteady viscous flows, which is based on a mesh-free integral approach of the velocity-vorticity formulation. Vorticity fields are represented by discrete vortex blobs that are updated by the Lagrangian vorticity transport with the particle strength exchange scheme. Velocity fields are expressed in a form of the Helmholtz decomposition, which are calculated by a fast algorithm of the Biot-Savart integration with a smoothed kernel and by a well-established panel method. No-slip condition is enforced through viscous diffusion of vorticity from a solid body into field. The vorticity flux is determined in such a way that spurious slip velocity vanishes. Through the comparison with the existing finite volume scheme for the transient vortical flows around an impulsively started cylinder at Reynolds number Re=550, we would obtain a more accurate scheme for vortex methods in complicated flows.

• 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 Korean Society for Atmospheric Environment
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• 제9권E호
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• pp.347-357
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• 1993

The Lagrangian grid-free numerical method, the discrete vortex method, was applied to solve the Navier-Stokes euqations. This method avoids the introduction of numerical viscosity swamping the real physical viscosity at high Reynolds number, unlike Eulerian method, e.g. finite difference and element methods. The boundary integral equation method for the potential flow solution was included to make the discrete vortex method more feasible for complex geometries. The fast adaptive multipole expansion method was incorporated to reduce the computational time from $O(N^2)$ to O(N) for the computations of vortex-vortex interactions. The test problems were air flow around one circular cylinder and two circular cylinders in tandem with various gaps. The numerical results were in excellent gareement with the experimental and other computational results. The applicabilty of the method was discussed with the indoor and the outdoor air pollution problems, especially the contaminant transport in the recirculation regions.

• 한국음향학회지
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• 제39권2호
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• pp.77-86
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• 2020

본 연구에서는 날개 끝 와류 공동(Blade-Tip Vortex Cavitation, BTVC)과 이에 기인한 유동 소음을 예측하기 위하여 Eulerian/Lagrangian 연성 해석기법을 제안하였다. 제안한 방법은 크게 연속적인 4단계로 구성되며, 각각 전산유체역학을 이용한 유동장 모사, 와류모델을 이용한 날개 끝 와류의 재구성, 기포 동역학 모델을 이용한 BTVC의 생성, 그리고 음향상사법을 이용한 음향파 예측이다. 일반적으로 전산유체역학 자체가 지니는 고유한 수치감쇠와 과도한 난류 강도로 인해 와류 강도를 심각하게 작게 예측하므로, 유동방향의 날개 끝 와류는 와류모델을 사용하여 재생하였다. 다음으로 Reyleigh-Plesset 방정식에 기반한 기포 동역학 모델을 사용하여 BTVC의 발생과 변화를 모사하였다. 마지막으로 BTVC에 의한 유동소음을 각각의 구형 버블을 그 부피 시간변화율의 변화율에 크기가 비례하는 홀극원으로 모델링하여 예측하였다. 제안한 수치 방법의 유효성을 예측값과 측정값을 비교하여 검토하였다.

• 대한조선학회논문집
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• 제51권6호
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• pp.480-488
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• 2014

Vortex shedding which is the dominant feature of body wakes and of direct relevance to practical engineering problems, has been intensively studied for flows past a circular cylinder. In contrast, vortex shedding from a hydrofoil trailing edge has been studied to much less extent despite numerous practical applications. The physics of the problem is still poorly understood. The present study deals with $K{\acute{a}}rm{\acute{a}}n$ vortex shedding from a truncated trailing-edge hydrofoil in relatively high Reynolds number flows. The objectives of this paper are twofold. First, we aim to simulate unsteady turbulent flows past a two dimensional hydrofoil through a hybrid particle-mesh method and penalization method. The vortex-in-cell (VIC) method offers a highly efficient particle-mesh algorithm that combines Lagrangian and Eulerian schemes, and the penalization method enables to enforce body boundary conditions by adding a penalty term to the momentum equation. The second purpose is to investigate shedding frequencies of vortices behind a NACA 0009 hydrofoil operating at a zero angle of attack.

• 한국자동차공학회논문집
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• 제4권3호
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• pp.130-138
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• 1996

The transient incompressible flow behind the widely-spaced co-axial jet is numerically simulated using the random vortex method(RVM). This numerical approach is based on the Lagrangian approach for the vorticity formulation of the unsteady Navier-Stokes equations, utilizing vortex elements to account for the convection and diffusion processes. The effects of the mass flow rate of an annular air jet and a central fuel jet on the co-axial jet flow dynamics is investigated. To validate the present procedure, the numerical results are compared with the available experimental data the present procedure, the numerical results are compared with the available experimental data in terms of the centerline and off-centerline profiles of the mean axial velocity. Discrepancies between the RVM results and the measurements are discussed in detail.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2011년 춘계학술대회논문집
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• pp.78-85
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• 2011

The Vortex-In-Cell(VIC) method combined with panel method is applied to the analysis of incompressible unsteady viscous flow. The dynamics of resulting flow is governed by the vorticity transport equation in Lagrangian form with vortex particle representation of the flow field. A regular grid which is independent to the shape of a body is used for numerical evaluation based on immersed boundary technique. With an introduction of this approach, the development and validation of the VIC method is presented with some computational results for incompressible viscous flow around two or three dimensional bodies such as wing section, sphere, finite wing and marine propeller.

• 대한기계학회논문집B
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• 제21권3호
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• pp.350-357
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• 1997

The transient incompressible flow behind the axisymmetric bluff body is numerically simulated using the random vortex method(RVM). Based on the vorticity formulation of the unsteady Navier-Stokes equations, the Lagrangian approach with a stochastic simulation of diffusion using random walk technique is employed to account for the transport processes of the vortex elements. The numerical solutions for 2-dimensional recirculating flow behind a backward-facing step in the laminar range of Reynolds number are compared with experimental data. The present simulation focuses on the transitional flow regime where the recirculation zone behind the bluff body becomes highly unsteady and large-scale vortex eddies are shed from the bluff body wake due to intrinsic shear layer instabilities. The unsteady vertical flow structures and the mixing characteristics behind the bluff body are discussed in detail.