• Proceedings of the KSME Conference
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• 2001.06e
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• pp.456-462
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• 2001

Comprehensive numerical computations are made of a homogenous spin-up in a cylindrical cavity with a time-dependent rotation rate. Numerical solutions are acquired to the governing axisymmetric cylindrical Navier-Stokes equation. A rotation rate formula is ${\Omega}_f={\Omega}_i+{\Delta}{\Omega}(1-{\exp}(-t/t_c))$. If $t_c$ is large, it implies that a rotation change rate is small. The Ekman number, E, is set to $10^{-4}$ and the aspect ratio, R/H, fixed to I. For a linear spin-up(${\epsilon}<<$), the major contributor to spin-up in the interior is not viscous-diffusion term but inviscid term, especially Coriolis term, though $t_c$ is very large. The viscous-diffusion term only works near sidewall. But for spin-up from rest, when $t_c$ is very large, viscous-diffusion term affects interior area as well as sidewall, initially. So azimuthal velocity of interior for large $t_c$ appears faster than that of interior for relatively small $t_c$. However, the viscous-diffusion term of interior decreases as time increases. Instead, inviscid term appears in the interior.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.28 no.7
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• pp.771-779
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• 2004

Unsteady behavior of the early wake in the viscous flow field past an impulsively started semicircular cylinder is studied numerically. In this paper, we propose the hybrid diffusion scheme to simulate dynamic characteristics of wake such as a fishtail-like flapping and an alternate vortex-shedding more accurately. This diffusion scheme based on particle strength exchange is mixed with the stochastic nature of random walk method. Also, the viscous splitting algorithm which calculates convective and diffusion terms successively is applied in order to handle random walk method effectively. Consequently, the early behavior of wake due to the breakdown of symmetrical vortici balance is more practically simulated with the vortex particle method.

• Proceedings of the KSME Conference
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• 2001.06e
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• pp.518-523
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• 2001

Vortex methods were originally conceived as a tool to model the evolution of unsteady, incompressible, high Reynolds number flows of engineering interest. Recently various methods have been proposed for simulating the diffusion in vortex methods for two-dimensional incompressible flows. We test the diffusion schemes of vortex methods. In this paper we directly compare the particle strength exchange scheme with the vorticity redistribution scheme in tenus of their accuracy and computational efficiency. Comparisons between both viscous models described are presented for short-time runs of impulsively started flows past a circular cylinder for Reynolds number of 60. The particle strength exchange scheme has been shown more accurate and efficient than the vorticity redistribution scheme.

• 한국전산유체공학회:학술대회논문집
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• 2004.03a
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• pp.161-165
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• 2004

In the vortex particle method based on the vorticity-velocity formulation for solving the Wavier-Stokes equations, the unsteady, incompressible, viscous laminar flow over a NACA 0012 foil is simulated. By applying an operator-splitting method, the 'convection' and 'diffusion' equations are solved sequentially at each time step. The convection equation is solved using the vortex particle method, and the diffusion equation using the particle strength exchange(PSE) scheme which is modified to avoid a spurious vorticity flux. The scheme is improved for variety body shape using one image layer scheme. For a validation of the present method, we illustrate the early development of the viscous flow about an impulsively started NACA 0012 foil for Reynolds number 550.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.26 no.2
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• pp.194-200
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• 2002

A method for simulating flow of extremely low Reynolds number in a vortex-in-cell (VIC) was studied. The viscous diffusion was represented by the random walk method. The validity of this method was proven by applying it to the flows passing over a fence placed vertically at an extremely low Reynolds number. The effects of parameters of the VIC method on the random walk method, such as the number of point vortices, the mesh density and the time increment, were investigated by numerical analysis using a one-dimensional diffusion equation. Changes in the relative error of vorticity depending on those parameters were clarified.

• Bulletin of the Korean Mathematical Society
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• v.53 no.3
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• pp.843-852
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• 2016

A vortex sheet is susceptible to the Kelvin-Helmhotz instability, which leads to a singularity at finite time. The vortex blob model provided a regularization for the motion of vortex sheets in an inviscid fluid. In this paper, we consider the blob model for viscous vortex sheets and present a linear stability analysis for regularized sheets. We show that the diffusing viscous vortex sheet is unstable to small perturbations, regardless of the regularization, but the viscous sheet in the sharp limit becomes stable, when the regularization is applied. Both the regularization parameter and viscosity damp the growth rate of the sharp viscous vortex sheet for large wavenumbers, but the regularization parameter gives more significant effects than viscosity.

• Proceedings of the KSME Conference
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• 2004.04a
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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.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.28 no.7
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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.

• 한국전산유체공학회:학술대회논문집
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• 2011.05a
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• pp.407-413
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• 2011

VIC (Vortex-In-Cell) method for viscous incompressible flow is presented to simulate the wake behind a modified NACA16 foil. With uniform rectangular grid, the velocity in field is calculated using streamfunction from vorticity field by solving the Poisson equation in which FFT(Fast Fourier Transform) is combined with 2nd order finite difference scheme. Here, LES(Large Eddy Simulation) with Smagorinsky model is applied for turbulence calculation. Effective viscosity is formulated using magnitude of strain tensor(or vorticity). Then the turbulent diffusion as well as viscous diffusion becomes particle strength exchange(PSE) with averaged eddy viscosity. The well-established panel method is combined to obtain the irrotational velocity and to apply the no-penetration boundary condition on the body panel. And wall diffusion is used for no-slip condition numerical results of turbulent stresses are compared with experimental results (Bourgoyne, 2003). Before comparing process, LES(Large Eddy Simulation) SGS(Subgrid scale) stress is transformed Reynolds averaged stress (Winckelmans, 2001).

• Journal of Advanced Marine Engineering and Technology
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• v.29 no.7
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• pp.769-778
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• 2005

The velocity and pressure fields of a ship's Weis-Fogh type propulsion mechanism are studied in this paper using an advanced vortex method. The wing (NACA0010 airfoil) and channel are approximated by source and vortex panels. and free vortices are introduced away from the body surfaces. The viscous diffusion of fluid is represented using the core-spreading model to the discrete vortices. The velocity is calculated on the basis of the generalized Biot-Savart law and the pressure field is calculated from an integral, based on the instantaneous velocity and vorticity distributions in the flow field. Two-dimensional unsteady viscous flow calculations of this propulsion mechanism are shown. and the calculated results agree qualitatively with the measured thrust and drag due to un-modeled large fluctuations in the measured data.