• Transactions of the Korean Society of Mechanical Engineers
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• v.16 no.7
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• pp.1255-1265
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• 1992

Under uniform heat flow, the thermal stress intensity factors for the interfacial crack on a rigid cusp-type inclusion are determined by Hilbert problem expressed with complex variable. The thermal stress intensity factors are expressed in terms of the periodic function of heat flow angle. When the tip of the interfacial crack meets that of the cusp crack, the thermal stress intensity factors have singularities. The thermal stress intensity factors at the interfacial crack tip located in the distance from the cusp crack tip vary with the location of the interfacial crack tip. From the results of the analysis, the complex potential functions and the thermal stress intensity factors for the cusp-type inclusion without the interfacial crack are derived under the cusp surface boundary conditions insulated or fixed to zero relative temperature.

• Communications of the Korean Mathematical Society
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• v.9 no.4
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• pp.905-915
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• 1994

Let $M_g$ be the moduli space of isomorphism classes of genus g smooth curves. It is a quasi-projective variety of dimension 3g - 3, when $g > 2$. It is known that a complete subvariety of $M_g$ has dimension $< g-1 [D]$. In general it is not known whether this bound is rigid. For example, it is not known whether $M_4$ has a complete surface in it. But one knows that there is a complete curve through any given finite points [H]. Recently, an explicit example of a complete curve in moduli space is given in [G-H]. In [G-H] they constructed a complete curve of $M_3$ as an intersection of five hypersurfaces of the Satake compactification of $M_3$. One way to get a complete curve of $M_3$ is to find a complete one dimensional family $p : X \to B$ of plane quartics which gives a nontrivial morphism from the base space B to the moduli space $M_3$. This is because every non-hyperelliptic smooth curve of genus three can be realized as a nonsingular plane quartic and vice versa. This paper has come out from the effort to find such a complete family of plane quartics. Since nonsingular quartics form an affine space some fibers of p must be singular ones. In this paper, due to the semistable reduction theorem [M], we search singular plane quartics which can occur as singular fibers of the family above. We first list all distinct plane quartics in terms of singularities.

• Journal of Ocean Engineering and Technology
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• v.18 no.5
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• pp.15-21
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• 2004

An edge tone is the discrete tone or narrow-band sound produced by an oscillating free shear layer, impinging on a rigid surface. In this paper, we present a 2-D edge tone to predict the frequency characteristics of the discrete oscillations of a jet-edge feedback cycle, using the finite difference lattice Boltzmann method (FDLBM). We use a modified version of the lattice BGK compressible fluid model, adding an additional term and allowing for longer time increments, compared to a conventional FDLBM, and also use a boundary fitted coordinates system. The jet is chosen long enough in order to guarantee the parabolic velocity profile of the jet at the outlet, and the edge consists of a wedge with an angle of ${\alpha}$ = 23. At a stand-off distance, the edge is inserted along the centerline of the jet, and a sinuous instability wave, with real frequency, is assumed to be created in the vicinity of the nozzle and propagates towards the downstream. We have succeeded in capturing very small pressure fluctuations, resulting from periodical oscillations of a jet around the edge. The pressure fluctuations propagate with the speed of sound. Its interaction with the wedge produces an non-rotational feedback field, which, near the nozzle exit, is a periodic transverse flow, producing the singularities at the nozzle lips.

• Proceedings of the KSME Conference
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• 2004.04a
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• pp.1915-1920
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• 2004

An edge tone is the discrete tone or narrow-band sound produced by an oscillating free shear layer impinging on a rigid surface. In this paper we present a two-dimensional edge tone to predict the frequency characteristics of the discrete oscillations of a jet-edge feedback cycle by the finite difference lattice Boltzmann method. We use a new lattice BGK compressible fluid model that has an additional term and allow larger time increment comparing a conventional FDLB model, and also use a boundary fitted coordinates. The jet is chosen long enough in order to guarantee the parabolic velocity profile of the jet at the outlet, and the edge consists of a wedge with an angle of ${\alpha}=23^{\circ}$ . At a stand-off distance ${\omega}$ , the edge is inserted along the centreline of the jet, and a sinuous instability wave with real frequency f is assumed to be created in the vicinity of the nozzle and to propagate towards the downstream. We have succeeded in capturing very small pressure fluctuations result from periodically oscillation of jet around the edge. That pressure fluctuations propagate with the sound speed. Its interaction with the wedge produces an irrotational feedback field which, near the nozzle exit, is a periodic transverse flow producing the singularities at the nozzle lips.

• Journal of Ship and Ocean Technology
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• v.12 no.1
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• pp.1-15
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• 2008

An edgetone is the discrete tone or narrow-band sound produced by an oscillating free shear layer, impinging on a rigid surface. In this paper, 2-dimensional edgetone to predict the frequency characteristics of the discrete oscillations of a jet-edge feedback cycle is presented using lattice Boltmznan model with 21 bits, which is introduced a flexible specific heat ratio y to simulate diatomic gases like air. The blown jet is given a parabolic inflow profile for the velocity, and the edges consist of wedges with angle 20 degree (for symmetric wedge) and 23 degree (for inclined wedge), respectively. At a stand-off distance w, the edge is inserted along the centerline of the jet, and a sinuous instability wave with real frequency is assumed to be created in the vicinity of the nozzle exit and to propagate towards the downward. Present results presented have shown in capturing small pressure fluctuating resulting from periodic oscillation of the jet around the edge. The pressure fluctuations propagate with the speed of sound. Their interaction with the wedge produces an irrotational feedback field which, near the nozzle exit, is a periodic transverse flow producing the singularities at the nozzle lips. It is found that, as the numerical example, satisfactory simulation results on the edgetone can be obtained for the complex flow-edge interaction mechanism, demonstrating the capability of the lattice Boltzmann model with flexible specific heat ratio to predict flow-induced noises in the ventilating systems of ship.

• Journal of the Society of Naval Architects of Korea
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• v.28 no.1
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• pp.38-52
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• 1991

In this paper, a semi-Lagrangian method is used to solve the nonlinear hydrodynamics of a three-dimensional body beneath the free surface in the time domain. The boundary value problem is solved by using the boundary integral method. The geometries of the body and the free surface are represented by the curved panels. The surfaces are discretized into the small surface elements using a bi-cubic B-spline algorithm. The boundary values of $\phi$ and $\frac{\partial{\phi}}{\partial{n}}$ are assumed to be bilinear on the subdivided surface. The singular part proportional to $\frac{1}{R}$ are subtracted off and are integrated analytically in the calculation of the induced potential by singularities. The far field flow away from the body is represented by a dipole at the origin of the coordinate system. The Runge-Kutta 4-th order algorithm is employed in the time stepping scheme. The three-dimensional form of the integral equation and the boundary conditions for the time derivative of the potential Is derived. By using these formulas, the free surface shape and the equations of motion are calculated simultaneously. The free surface shape and fille forces acting on a body oscillating sinusoidally with large amplitude are calculated and compared with published results. Nonlinear effects on a body near the free surface are investigated.

• Journal of the Society of Naval Architects of Korea
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• v.43 no.5 s.149
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• pp.568-577
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• 2006

With the increase of ship size and speed, the loading on the propeller is increasing, which in turn increases the rotational speed in the propeller slipstream. The rudder placed in the propeller slip stream is therefore subject to severe cavitation with the increased angle of attack due to the increased rotational induction speed of the propeller. In the present paper the surface panel method, which has been proved useful in predicting the sheet cavitation on the propeller blade, is applied to solve the cavity boundary value problem on the rudder. The problem is then solved numerically by discretizing the rudder and cavity surface elements of the quadrilateral panels with constant strengths of sources and dipoles. The strengths of the singularities are determined satisfying the boundary conditions on the rudder and cavity surfaces. The extent of the cavity, which is unknown a priori, is determined by iterative procedure. Series of numerical experiments are performed increasing the degree of complexity of the rudder geometry and oncoming flows from the simple hydrofoil case to the real rudder in the circumferentially averaged propeller slipstream. Numerical results are presented with experimental results.

• Journal of the Society of Naval Architects of Korea
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• v.28 no.2
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• pp.159-173
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• 1991

This paper describes a potential-based panel method formulated for the analysis of a super-cavitating two-dimensional hydrofoil. The method employs normal dipoles and sources distributed on the foil and cavity surfaces to represent the potential flow around the cavitating hydrofoil. The kinematic boundary condition on the wetted portion of the foil surface is satisfied by requiring that the total potential vanish in the fictitious inner flow region of the foil, and the dynamic boundary condition on the cavity surface is satisfied by requiring thats the potential vary linearly, i.e., the tangential velocity be constant. Green's theorem then results in a potential-based integral equation rather than the usual velocity-based formulation of Hess & Smith type. With the singularities distributed on the exact hydrofoil surface, the pressure distributions are predicted with improved accuracy compared to those of the linearized lilting surface theory, especially near the leading edge. The theory then predicts the cavity shape and cavitation number for an assumed cavity length. To improve the accuracy, the sources and dipoles on the cavity surface are moved to the newly computed cavity surface, where the boundary conditions are satisfied again. This iteration process is repeated until the results are converged. Characteristics of iteration and discretization of the present numerical method are much faster and more stable than the existing nonlinear theories. The theory shows good correlations with the existing theories and experimental results for the super-cavitating flow. In the region of small angles of attack, the present prediction shows and excellent comparison with the Geurst's linear theory. For the long cavity, the method recovers the trends of the Wu's nonlinear theory. In the intermediate regions of the short super-cavitation, the method compares very well with the experimental results of Parkin and also those of Silberman.

• Journal of the Korean Society of Fisheries and Ocean Technology
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• v.21 no.2
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• pp.131-136
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• 1985

The calculation of the resulting fluid motion is an important problem of ship hydrodynamics. For a partially immersed body the condition of constant pressure at the free surface can be linearized. The resulting linear boundary-value problem for the velocity potential is the Neumann-Kelvin problem. The two-dimensional Neumann-Kelvin problem is studied for the half-immersed circular cylinder by Ursell. Maruo introduced a slender body approach to simplify the Neumann-Kelvin problem in such a way that the integral equation which determines the singularity distribution over the hull surface can be solved by a marching procedure of step by step integration starting at bow. In the present pater for the two-dimensional Neumann-Kelvin problem, it has been suggested that any solution of the problem must have singularities in the corners between the body surface and free surface. There can be infinitely many solutions depending on the singularities in the coroners.

• Structural Engineering and Mechanics
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• v.19 no.4
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• pp.425-440
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• 2005

In this paper, the behavior of a crack between two half-planes of functionally graded materials subjected to arbitrary tractions is resolved using a somewhat different approach, named the Schmidt method. To make the analysis tractable, it is assumed that the Poisson's ratios of the mediums are constants and the shear modulus vary exponentially with coordinate parallel to the crack. By use of the Fourier transform, the problem can be solved with the help of two pairs of dual integral equations in which the unknown variables are the jumps of the displacements across the crack surfaces. To solve the dual integral equations, the jumps of the displacements across the crack surfaces are expanded in a series of Jacobi polynomials. This process is quite different from those adopted in previous works. Numerical examples are provided to show the effect of the crack length and the parameters describing the functionally graded materials upon the stress intensity factor of the crack. It can be shown that the results of the present paper are the same as ones of the same problem that was solved by the singular integral equation method. As a special case, when the material properties are not continuous through the crack line, an approximate solution of the interface crack problem is also given under the assumption that the effect of the crack surface interference very near the crack tips is negligible. It is found that the stress singularities of the present interface crack solution are the same as ones of the ordinary crack in homogenous materials.