The Proceedings Fifth International Conference on Numerical Ship Hydrodynamics (1990) / Chapter Skim
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Ship Wave-Resistance Computations
Ship Wave-Resistance Computations
Pages 593-606
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From page 593... ...
G(p, ~ potential at point q due to unit source at p 593 n p p q r R Ru S So s,t T T A U vn H water depth k point on tangential sphere lPp ship length between perpendiculars M source strength unit normal pointing into body point projection of a point on the body surface onto the tangential sphere pressure point ratio between the area of the projection and that of the original surface element radius of tangential sphere wave resistance wetted or panelized body surface wetted surface at rest vectors tangential to the body surface moment due to pressure on body additional moment on body free stream velocity velocity component normal to body surface vs. v' components of velocity tangential to body sur face point on free surface x,y,z right-handed coordinate system; the x and y axes are on the undisturbed free surface, x points upstream, z vertically downward point of action of towing force center of gravity of ship's mass towing force xz XG z do p submergence of dipole moment of dipole trim angle (bow down trim is positive)
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From page 594... ...
To circumvent this difficulty, most known methods use, apart from the physical simplifications stated above, additional mathematical simplifications: Almost exclusively a linearized free-surface boundary condition is implied at the location of the undisturbed free surface, and in most cases the solution is described by a superposition of complicated singularities that meet this linearized free-surface condition identically. All linear methods show good agreement with measurements only for special hull forms or high Froude numbers En = U2/~, where U is ship speed, g acceleration of gravity, and Lpp the ship length between perpendiculars.
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From page 595... ...
Therefore the equilibrium conditions are The velocity potential is subject to the following F + G + Z + F O (~10) boundary conditions: No flow across the body surface with normal direction and n: TV = 0 on the wetted body surface.
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From page 596... ...
To validate this simple scheme to enforce the radiation condition and the open boundary condition, the flow around a submerged dipole with Kelvin condition at the free surface was computed and compared to analytical solutions given by Nakatake A
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Fig.2. Contour lines of surface elevation due to a submerged dipole for F = 3.0 The upper half shows the analytical solution due to Nakatake t6]
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points where the boundary condition is fulfilled, and as integration points for the numerical integration over the body surface, which is performed simply by adding the products of integrand times panel area. This gives a system of linear equations for the unknown source strengths.
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The body boundary condition will always be violated near such a corner. The panel method may still be applicable for practical purposes if the overall solution is not disturbed.
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From page 600... ...
· Further, all these sources are mirrored both at the symmetry plane of the ship and - in case of shallow water - at the bottom to satisfy the respective boundary conditions. The source strengths are determined from the following conditions: · On the ship surface up to the plane somewhat above the water surface, the condition of vanishing flow velocity normal to the surface is satisfied.
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From page 601... ...
In Fig. 4 our computed wave resistance coefficients are compared to Ogiwara's measurement evaluations.
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From page 602... ...
~ ~ / ~~/~-: / Ad/ V ////~d' Fig. 7 shows the computed elevation of the free surface for the solution obtained with the linearized free-surface condition (Kelvin condition)
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From page 603... ...
Forward trim usually encountered on shallow water can reduce yaw stability so severely that ships may loose their ability to keep course. Figure 8 shows results for the draught at the forward perpendicular divided by the stagnation height U2/2g depending on depth Froude number F72h and length Froude number An.
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From page 604... ...
11. Computed total resistance coefficients for SWATH ship and values measured by HSVA Only in a few cases a nonlinear solution succeeded.
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From page 605... ...
[34 NI, S.-Y.: "Higher Order Panel Methods for Potential Flows with Linear or Nonlinear Free Surface Boundary Conditions", Chalmers University of Technology, Goteborg, 1987.
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From page 606... ...
The novel treatment of the radiation condition deserves f urther study to see how it behaves with high resolution surface grids. Author's Reply We did not try the non-linear calculation with fixed trim and sinkage for the Series 60.
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