• Journal of the Society of Naval Architects of Korea
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• v.33 no.3
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• pp.35-47
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• 1996

A surface panel method treating a boundary-value problem of the Dirichlet type is presented to design a three dimensional body with free surface corresponding to a prescribed pressure distribution. An integral equation is derived from Green's theorem, giving a relation between total potential of known strength and the unknown local flux. Upon discretization, a system of linear simultaneous equations is formed including free surface boundary condition and is solved for an assumed geometry. The pseudo local flux, present due to the incorrect positioning of the assumed geometry, plays a role f the geometry corrector, with which the new geometry is computed for the next iteration. Sample designs for submerged spheroids and Wigley hull and carried out to demonstrate the stable convergence, the effectiveness and the robustness of the method. For the calculation of the wave resistance, normal dipoles and Rankine sources are distributed on the body surface and Rankine sources on the free surface. The free surface boundary condition is linearized with respect to the oncoming flow. Four-points upwind finite difference scheme is used to compute the free surface boundary condition. A hyperboloidal panel is adopted to represent the hull surface, which can compensate the defects of the low-order panel method. The design of a 5500TEU container carrier is performed with respect to reduction of the wave resistance. To reduce the wave resistance, calculated pressure on the hull surface is modified to have the lower fluctuation, and is applied as a Dirichlet type dynamic boundary condition on the hull surface. The designed hull form is verified to have the lower wave resistance than the initial one not only by computation but by experiment.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.35 no.11
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• pp.957-963
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• 2007

this study, helicopter rotor flow is simulated by using a tightly coupled CFD/FreeWake method to describe wake characteristics and to calculate the flow field and rotor aerodynamics. In this tightly coupled CFD/FreeWake method, freewake model provides the boundary condition required in the CFD calculation and CFD provides the pressure distribution on blade surface used in feewake generation. To show the advantage of this method, the pressure distributions on blade surface of a hovering 2-bladed rotor are compared with other numerical methods. This tightly coupled CFD/FreeWake method shows good accuracy in the predicted results and efficient computation time.

• Journal of Ocean Engineering and Technology
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• v.36 no.5
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• pp.303-312
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• 2022

A submarine is optimized to operate below the water surface because it spends most of its time in a submerged condition. However, the performance in free surface conditions is also important because it is unavoidable for port departure and arrival. Generally, potential flow theory is used for seakeeping analysis of a surface ship and is known for excellent numerical accuracy. In the case of a submarine, the accuracy of potential theory is high underwater but is low in free surface conditions because of the nonlinearity near the free surface area. In this study, the seakeeping performance of a Canadian Victoria Class submarine in regular waves was investigated to improve the numerical accuracy in free surface conditions by using computational fluid dynamics (CFD). The results were compared to those of model tests. In addition, the potential theory software Hydrostar developed by Bureau Veritas was also used for seakeeping performance to compare with CFD results. From the calculation results, it was found that the seakeeping analysis by using CFD gives good results compared with those of potential theory. In conclusion, seakeeping analysis based on CFD can be a good solution for estimating the seakeeping performance of submarines in free surface conditions.

• Journal of the Society of Naval Architects of Korea
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• v.41 no.4
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• pp.38-44
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• 2004

The motion response analysis of a submerged elliptic cylinder in waves is presented and the elliptic cylinder is a simplification of the section of submarine in this paper. The method is based on boundary integral method and two-dimensional 3 degree motions are calculated in regular harmonic waves. The fully nonlinear free surface boundary condition is assumed in an numerical domain and this solution is matched along an assumed boundary as a linear solution composed of transient Green function, The large amplitude motions of an elliptic cylinder are directly simulated and effects of wave frequency, wave amplitude and the distance from buoyancy center to gravity center are discussed.

• Journal of the Korean Society of Fisheries and Ocean Technology
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• v.17 no.2
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• pp.109-113
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• 1981

Most existing theories on ship waves and wave resistance are based on the perturbation of the flow field by a small pararr.eter which specifies the slenderness of the ship hull. Since however, ship hulls in practice are neither so slender nor thin enough to secure the validity of the linearized theory, the agreen:ent between the theoretical prediction and the experimental result is not generally satisfactory. The author pointed out that the contribution by the non-linear term in the free surface condition can be represented by sorr.e source distribution over the still water plane. This paper leads to a forrr.ula for the wave resistance of not slender ships at low Froude nurr.bers. and deals with the asynptotic expression. As a nurr.erical example, the wave resistance of Wigley model is calculated, and the result is compared with experimental values. It is concluded that the wave resistance coefficient varies in the rate of Fn6 at low speed limit in general. A comparison with the result derived from the linearized free surface condition shows that the non-linearity of the free surface is irr portant at low speed.

• Journal of computational fluids engineering
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• v.21 no.1
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• pp.110-116
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• 2016

The present study numerically investigated the deformation of the interface of two-phase fluids flow in a blast furnace. To simulate three-dimensional(3D) incompressible viscous two-phase flow in the furnace filled with the air and molten iron, the volume of fluid(VOF) method based on the finite volume method has been utilized. In addition, the porous medium with the porosity has been considered as the bed of the particles such as cokes and char etc. For the comparison, the single phase flow and the two-phase flow without the porosity have been simulated. The two-phase flow without porosity condition revealed the smooth parabolic profile of the free surface near the outlet. However, the free surface under the porosity condition formed the viscous finger when the free surface was close to the outlet. This viscous finger accelerated the velocity of the free surface falling and the outflow velocity of the fluids near the outlet.

• Bulletin of the Society of Naval Architects of Korea
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• v.17 no.1
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• pp.31-37
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• 1980

Herein the flow past a submerged circular cylinder with a free surface is mapped onto a reference plane, in which the free surface is transformed to a straight line and the cylinder to a certain shape. A global mapping function between two planes is sought in a manner that linear free-surface elevation is generated in the physical plane. Hereby the Froude mumber $F_h$, based on the submergence depth h', is assumed to be of order 0(1) and the ratio a'/h'(a'=cylinder radius) of order o(1). Wave thus obtained are slightly different in magnitude and phase from usual linear solution. The resulting free wave starts advanced ahead compared to the classical result and its amount depends on Froude number. Based on the present concept wave forces are calculated. In this type of approach the body boundary condition gives more influence on wave resistance than that by the free surface in the speed range $F_h>1$.

• Journal of computational fluids engineering
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• v.18 no.1
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• pp.13-21
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• 2013

Cavitating flow is usually formed on the surface of a high speed underwater object. When a object moves near a free surface at very high speed, the cavity signature becomes one of the major factors to be overcome by sensors of military satellite. The present work was to study the free surface effect on the ventilated cavitation. The governing equations were Navier-Stokes equations based on a homogeneous mixture model. The multiphase flow solver used an implicit preconditioning method in the curvilinear coordinate system. The cavitation model used here was the one first presented by Merkle et al.(2006) and redeveloped by Park & Ha(2009). Computations considered the free surface effects were carried out with a NACA0012 hydrofoil and the corresponding results were compared with the experimental data to have a good agreement. Calculations were then performed considering the ventilated cavitation, including the effect of non-condensable gas under the free surface effects.

• Journal of the Society of Naval Architects of Korea
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• v.30 no.1
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• pp.104-114
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• 1993

In this paper, effects of free surface on viscous flow is investigated. Continuity equation coupled with Navier-Stokes equations are solved numerically by using an artificial compressibility method[1, 2]. The body-fitted generalized curvilinear coordinate system is employed to deal with arbitrary body shape. The IAF scheme with finite difference method is used to solve the equations, and a diagonal algorithm is applied to time-varying Jacobian matrices for the computational economics. Free surface shape is obtained by applying zero pressure condition to still water surface at each time step. A numerical test is made for larminar flow around a circular cylinder vertically piercing the free surface. Computed flow patterns are largely affected by the existance of free surface in low Reynolds number flows treated in this paper. Free surface causes viscous pressure drag to vary much in depth direction in accordance with the variations of flow pattern.

• Geophysics and Geophysical Exploration
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• v.6 no.2
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• pp.77-86
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• 2003

We designed a new time-domain, finite-difference, elastic wave modeling technique, based on a displacement formulation. which yields nearly correct solutions to Lamb's problem. Unlike the conventional, displacement-based, finite-difference method using a node-based grid set (where both displacements and material properties such as density and Lame constants are assigned to nodal points), in our new finite-difference method, we use a cell-based grid set (where displacements are still defined at nodal points but material properties within cells). In the case of using the cell-based grid set, stress-free conditions at the free surface are naturally described by the changes in the material properties without any additional free-surface boundary condition. Through numerical tests, we confirmed that the new second-order finite differences formulated in the cell-based grid let generate numerical solutions compatible with analytic solutions unlike the old second-order finite-differences formulated in the node-based grid set.