• Bulletin of the Society of Naval Architects of Korea
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• v.26 no.3
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• pp.41-50
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• 1989

A basic formulation of the panel method, which is based on the potential field formulation, is reviewed for the case of two-dimensional hydrofoil problems. Numerical procedures to improve the computational efficiency of the panel method are suggested. By investigating local behavior of the flow around the trailing edge, a wedge type Kutta condition is formulated. By subdividing the trailing edge panels, where dipole strengths of the subdivided panels follow the local behavior of the potential values of the flow outside a wedge, the circulation around a hydrofoil is calculated accurately with a relatively small number of panels. The subdividing technique to improve the accuracy of the numerical Kutta condition is proved to be efficient. A local behavior of the flow around the leading edge is also investigated. By matching the flow around the leading edge with that around a parabola, a very accurate velocity distribution is obtained with relatively small number of panels. An accurate prediction of the stagnation point and the pressure distribution near the leading edge may contribute to improve the accuracy of cavity predictions and boundary layer calculations around hydrofoils.

• Bulletin of the Society of Naval Architects of Korea
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• v.26 no.4
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• pp.27-34
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• 1989

A potential-based panel method is formulated for the analysis of a partially cavitating 2-dimensional hydrofoil. The method employs dipoles and sources distributed on the foil surface to represent the lifting and cavity problems, respectively. The kinematic boundry condition on the wetted portion of the foil surface is satisfied by requiring that the total potential vanish in the inner flow region of the foil. The dynamic boundary condition on the cavity surface is satisfied by requiring that the potential vary linearly, i.e., the velocity be constant. Green's theorem then results in a potential-based boundary value problem rather than a usual velocity-based formulation. With the singularities distributed on the exact hydrofoil surface, the pressure distributions are predicted with more improved accuracy than the zero-thickness hydrofoil 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. It was found that five iterations are necessary to obtain converged values, while only two iterations are sufficient for engineering purpose.

• Journal of Advanced Marine Engineering and Technology
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• v.34 no.5
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• pp.718-724
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• 2010

This paper studies the differences due to the wall effect in propeller open water(POW) characteristics tested in a towing tank and in a medium size cavitation tunnel(CT). When the advanced velocity of the propeller is defined as the flow velocity measured in the plane of propeller, POW characteristics resulting from CT has a better relationship with them of towing tank. To obtain the wall effect in the propeller plane, numerical computation using the lifting panel theory is performed with and without the wall around a propeller. Then, POW results in CT are corrected based on the wall effect from numerical results. The POW results obtained from this procedure show a better agreement with the experimental results in the towing tank.

• 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.

• Bulletin of the Society of Naval Architects of Korea
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• v.27 no.4
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• pp.15-26
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• 1990

This paper describes a potential-baoed panel method formulated for the analysis cf a supercavitating two-dimensional symmetri strut. 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 that 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 lifting 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.

• Journal of the Society of Naval Architects of Korea
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• v.30 no.2
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• pp.112-122
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• 1993

A potential-based panel method is presented for the analysis of a partially or supercavitating two-dimensional hydrofoil at a finite submergence beneath a free surface, treating without approximation the effects of the finite Froude number and the hydrostatic pressure. Free surface sources and normal dipoles are distributed on the foil and cavity surfaces, their strength being determined by satisfying the kinematic and dynamic boundary conditions on the foil-cavity boundary. The cavity surface is determined iteratively as a part of the solution. Numerical results show that the wave profile is altered significantly due to the presence of the cavity. The buoyancy effect due to the hydrostatic pressure, which has usually been neglected in most of the cavitating flow analysis, is found playing an important role, especially for the supercavitating hydrofoil; the gravity field increases the cavity size in shallow submergence, but decreases it when deeply submerged, while the lift reduces at all submergence depth.

• Bulletin of the Society of Naval Architects of Korea
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• v.27 no.2
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• pp.1-12
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• 1990

Interactions between a propeller and vortex system contained in a ship stern flow is treated theoretically. A new formulation to determine the effective velocity distributions is developed, which may be immediately applicable to the design and analysis of compound propulsors under the influence of severe vortical cross-flows around ship stern. An axisymmetric shear flow is represented by a system of ring vortices and the axial variation of the stream lines due to the action of propeller is represented by a cubic function. The strengths of ring vortices, which are varying along the stream lines, are determined by the conservation of angular momentum. Two simplified effective velocity models are proposed to confirm the theory. Sample calculations using the simplified models are made to compare with the results by other investigators.

• Journal of the Society of Naval Architects of Korea
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• v.28 no.2
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• pp.69-76
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• 1991

A design method based on the surface vorticity distribution is developed to generate a two-dimensional blade section for prescribed velocity distribution in potential flow. The boundary condition used to determine the strength of vorticity distribution requires that the surface of blade section should be a streamline of the resulting flow. In order to obtain the required final geometry of a two-dimensional blade section, an iterative procedure is used. A computer program is developed and several numerical results are presented.

• Journal of the Society of Naval Architects of Korea
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• v.31 no.3
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• pp.100-111
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• 1994

This study was carried out for understanding the characteristics of the spray around high speed vessels. Prismatic planing hull made of an acrylate board was used to the tests. The distribution of local spray velocity were estimated from the analysis of the spray visualization. A new test system for measuring the spray thickness is proposed, and was used to estimate the local spray thickness in the model. The pressure distributions on the bottom of the hull are measured and integrated to estimate the pressure drag of the model in the towing tests. Finally. the spray drag/lift component is separated from the total drag/lift on the prismatic hull. These test results show that the spray drag component on high speed vessels is relatively large and important in total drag.

• Journal of the Society of Naval Architects of Korea
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• v.30 no.2
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• pp.66-75
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• 1993

Flow control devices, such as flow liners, are frequently introduced hi a cavitation tunnel in order to reduce the tunnel blockage effect, when a three-dimensional wake distribution is simulated using a complete ship model or a dummy model. In order to estimate the tunnel wall effect and to evaluate the effect of flow liners on the simulated wake distribution, a surface panel method is adopted for the calculation of the flow around a ship model and flow liners installed in a rectangular test section of a cavitation tunnel. Calculation results on the Sydney Express ship model show that the tunnel wall effect on the hull surface pressure distribution is negligible for less than 5% blockage and can be appreciable for more than 20% blockage. The flow liners accelerate the flow near the after body of the ship model, so that the pressure gradient there becomes more favorable and accordingly the boundary layer thickness would be reduced. Since the resulting wake distribution is assumed to resemble the full scale wake, flow liners can also be used to simulate an estimated full scale wake without modifying the ship model. Boundary layer calculation should be incorporated in order to correlate the calculated wake distribution with tole measured one.