• 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.

• Journal of Hydrospace Technology
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• v.1 no.1
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• pp.1-13
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• 1995

Vortex shedding from a circular cylinder is simulated by means of the discrete vortex method. The shear layer emanating from the separation point is approximated as a sheet vortex which is in turn represented by a sequence of discrete vortices. The strength of these vortices is calculated from the vorticity shedding rate and introduced at a small distance off the side ($\Theta=\pm\pi/2$) of the cylinder surface in regular time step. Sheet vortex cutting, rediscretization and replacement of vortex by vortex segment are put to use to enhance stability of the sheet vortex evolution. The simulated vortex distribution pattern very well reproduces structure like the Karman vortex street. However, as for the force coefficients, the qualitative properties are correctly predicted but some more improvements are needed for the quantitative accuracy.

• Journal of the Society of Naval Architects of Korea
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• v.30 no.1
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• pp.94-103
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• 1993

This study deals with an investigation on the tip vortex generated by an elliptic wing with section shapes of NACA 0020. The flow structure on the wing surface is investigated by using tufts test as well as observing the cavitation pattern. The surface pressure on a foil surface is measured to complement the visualized flow field. Results show that a strong spanwise pressure gradient is a definite contributor on the formation of tip vorex, and the fluids from both sides contribute to the evolutionary process of tip vortex. On the other hand, a series of experiments are conducted to investigate the detailed structure of tip-vortex at various angles of attack. The tip-vortex formation and development are observed by producing a cavitation, and then by a laser sheet technique in conduction with a dye injection method. The shape of tip-vortex and the distance between a vortex core and the trailing vortex sheet are found to vary with the angle of attack. Overall features of tip flow are evaluated to complement the vortex model based on inviscid theory.

• Proceedings of the KSME Conference
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• 2002.08a
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• pp.307-310
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• 2002

A two-dimensional numerical method for inviscid two-fluid flows with evolution of density interface is developed, and an initially stationary two-dimensional fluid sheet surrounded by another fluid is studied. The Interface between two fluids is modeled as a vertex sheet, and the flow field u÷th the evolution of interface is solved by using vortex-in-cell/front-tracking method. The edge of the sheet Is pulled back into the sheet due to surface tension and a blob is formed at the edge. This blob and fluid sheet are connected by a thin neck. In the inviscid limit, such process of the blob and neck formation is examined in detail and their kinematic characteristics are summarized with dimensionless parameters. The edge recedes at $V=1.06({\sigma}/{\rho}h)^{0.5}$ and the capillary wave Propagating into the fluid sheet must be considered for bettor understanding of the edge receding.

• Journal of the Korean Society for Marine Environment & Energy
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• v.2 no.2
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• pp.70-77
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• 1999

The disturbance of oil-water interface confined between tandem fences caused by a sequence of traveling vortices below the interface is investigated. The traveling vortices are assumed to be those detached from the tip of the fore fence. The potential flow is assumed and the density interface is replaced as a sheet of vortex. The shape of the interface is predicted by tracing a finite number of marker particles placed at the interface. The velocity of the marker particles is determined by the Biot-Savart integral along the vortex sheet plus the contribution from the traveling point vortices. The rate of change of vortex-sheet strength is predicted by using an evolution equation for vorticity. The calculated results obtained for various conditions demonstrate that the large amplitude of interfacial wave following the moving vortek can be generated by the vortices.

• Journal of the Korean Society for Marine Environment & Energy
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• v.10 no.2
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• pp.107-111
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• 2007

A two-dimensional numerical method for inviscid two-fluid flows with evolution of density interface is developed, and an initially stationary two-dimensional fluid sheet surrounded by another fluid is studied. The interface between two fluids is modeled as a vortex sheet, and the flow field with the evolution of interface is solved by using vortex-in-cell/front-tracking method. The edge of the sheet is pulled back into the sheet due to surface tension and a blob is formed at the edge. This blob and fluid sheet are connected by a thin neck. In the inviscid limit, such process of the blob and neck formation is examined in detail and their kinematic characteristics are summarized with dimensionless parameters. The edge recedes at and the capillary wave propagating into the fluid sheet must be considered for better understanding of the edge receding.

• Journal of the Korea Institute of Military Science and Technology
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• v.5 no.3
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• pp.77-86
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• 2002

An experimental study of the vortex interaction characteristics of a delta wing/LEX configuration was conducted in a wind tunnel using the micro water droplet and laser beam sheet visualization technique. The main focus of this study was to analyze the effect of the angle of attack and sideslip angle on the vortex interaction and vortex breakdown. These tests were accomplished at angles of attack between $16^{\circ}$ and $28^{\circ}$ and sideslip angle between $0^{\circ}$ and $-15^{\circ}$ at free-stream velocity of 6.2 m/s. Flow visualization data provide a description of the vortex interaction between LEX and wing vortices, and of the vortex breakdown. The introduction of LEX vortex stabilized the vortical flow, and delayed the vortex breakdown up to higher angle of attack. The vortex interaction and breakdown was promoted on the windward side, whereas they are suppressed on the leeward side.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.23 no.11
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• pp.1444-1452
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• 1999

The turbulence structure of e. tip vortex generated by e. fixed wing was investigated with the use of two-dimensional laser Doppler velocimetry. The velocity field, composed of circumferential end axial components, was measured on the vertical section to the vortex trail, located at 2C downstream from the wing tip in the incoming flow condition of $Re=2.24{\times}10^5$. A quasi 3-dimensional measurement technique by use of 2-dimensional LDV system was suggested for Reynolds stresses and the higher moments. The validity of this technique was confirmed with the uncertainty analysis. The budget of the turbulence kinetic energy was analyzed by those results in the radial direction of the vortex core. It is resulted that the production is to be very likely balanced with the dissipation in most range of the vortex core.

• Water for future
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• v.27 no.3
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• pp.95-105
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• 1994

The boundary layer flow under a sluice gate is numerically solved by the random vortex sheet method combined with the vortex-in-cell method in a boundary-fitted coordinate system. The numerical solution shows that the boundary layer developed along the vertical sluice gate wall is the primary cause for the discrepancy in the contraction ratio between the laboratory experiments and inviscid theory; the bottom boundary layer plays much a smaller role in the discrepancy. By dimensional analysis it is concluded that the discrepancy is inversely proportional to the 3/4th power of the gate opening, as analyzed by Benjamin(1956). The results of the numerical simulation and dimensional analysis show a good agreement with experimental results obtained by Benjamin(1956).

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.27 no.4
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• pp.232-244
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• 2023

The unsteady dynamics of the starting flow of a flat plate is studied by using a vortex shedding model. The model describes the body and separated vortex from the trailing edge of the plate by vortex sheets, retaining a singularity at the leading edge. The model is applied to simulate the flow of an accelerated plate for small angles of attack. For numerical computations, we take two representative cases of the translational velocity of a plate: impulsive translation and uniform acceleration. The model successfully demonstrates the formation of wakes shed from the plate. The wake behind the plate is stronger for a larger angle of attack. Predictions for the lifting force from the model are in agreement with results of Navier-Stokes simulations.