Twenty-Third Symposium on Naval Hydrodynamics (2001) / Chapter Skim
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New Green-Function Method to Predict Wave-Induced Ship Motions and Loads
New Green-Function Method to Predict Wave-Induced Ship Motions and Loads
Pages 66-81
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From page 66... ...
It is shown formally in this work by an asymptotic analysis that the source potential is singular and highly-oscillatory for a field point approaching the track of the source at the free surface. To circumvent the above-mentioned difficulties encountered in previous studies, a new numerical method, based on the recent results in both theoretical and numerical aspects of ship-motion Green functions and the higher-order description of shiphull geometry and fluid kinematics, has been developed.
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From page 67... ...
This elaborated approach allows us to evaluate accurately and efficiently the influence coefficients associated with the free-surface part of ship-motion Green functions, in all configurations including the case of two panels at the free surface. Another feature of the new Green-function method is the higher-order description of ship-hull geometry as well as singularity distributions on the hull and along the waterline.
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From page 68... ...
plane coincide with the mean free surface and z-axis be positive upward. Based on the assumptions of perfect fluid, irrotational flow and small wave steepness, the velocity potential A, y, z, t)
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From page 69... ...
Here Gs is the simple singularity part 41r Gs = - 1/~(—~~ + 1/~(—I'd with A' = An, y,—z) the mirror image of ~ with respect to the mean free surface plane z =0.
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From page 70... ...
BI-QUADRATIC PATCH METHOD The hull surface of ship is subdivided into NH curved patches. Among the NH patches, NW patches touch the free surface so that the waterline is constituted by NW curved segments corresponding to the upper
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From page 71... ...
necessary for the purpose of computing influence coefficients.
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From page 72... ...
The integrand includes the jth shape function within kth patch and the ith shape function within Ith patch, and the Green function as well as its normal gradient. Following (15)
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From page 73... ...
Hulme's analytical results at zero forward speed provide naturally the first benchmark for the present numerical method. Figure 2: Mesh used to represent Hulme's hemisphere A mesh composed of a total of 66 bi-quadratic patches representing the hull of a hemisphere of radius Table 1: Added-mass and damping coefficients for Hulme's hemisphere kR all tell a33 b33 0.02 0.5049 0.0000 0.8652 0.0448 0.05 0.5113 0.10 0.5234 0.20 0.5526 0.30 0.5860 0.40 0.6187 0.50 0.6452 0.60 0.6599 0.70 0.6594 0.80 0.6433 0.90 0.6137 1.00 0.5749 1.10 0.5312 1.20 0.4867 1.30 0.4438 1.40 0.4042 1.50 0.3687 1.60 0.3374 1.80 0.2867 2.00 0.2494 2.50 0.1949 3.00 0.1718 3.50 0.1634 4.50 0.1656 6.00 0.1784 8.00 0.1962 10.00 0.2081 R = 1 view (Figure 2~.
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From page 74... ...
Wu used the multipole expansion extended from that developed for zero forward speed in Ursell (1949) to derive directly the velocity potential around a submerged sphere advancing in water waves.
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From page 75... ...
The values of added-mass coefficients and are represented by the solid line obtained from the present numerical method and by the circle symbols 2.0 ~ .0 O— 1 - _ it_ .~-~~~~~-~—-A—-A—-A—~—~—-A—A- - -' 0 0.5 1.0 Figure 7: Added-mass and damping coefficients in heave motion (a33 7 baa) of Wu's sphere 3.0 2.0 ~ 1.0 In' o 0 0.5 1.0 for Wu's semi-analytical solution.
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From page 76... ...
Except at small wavenumber where waterdepth may have noticeable effects, the results of both methods are in very good agreement. In the same way as the added-mass and damping coefficients, the change of flow regime at koR ~ 0.2937 corresponding to the critical value A= 1/4 yields rapid variation in surge forces Fit and heave forces F3.
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From page 77... ...
is used in the computation of added-mass and damping coefficients, wave loadings and waveresistance and lift. Due to the small submergence, differences between the present numerical method involving mj terms derived from the double-body flow and Wu's semi-analytical method involving mj terms derived from the Neumann-Kelvin flow may be expected.
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From page 78... ...
Journee's Wigley-hull The second benchmark study for the general case at { 0 involves confronting the results of experimental measurements on Wigley hulls. Further to the classic experimental data on vertical motions, wave loads and added resistances of two first Wigley hullforms in Gerritsma (1988)
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From page 79... ...
The numerical and experimental results at Fr' = 0.3 are depicted respectively by the solid lines and circles and those at zero forward speed by the dot-dash lines and squares. The important ef
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From page 80... ...
The excellent level of agreement with semianalytical results and experimental measurements is due to several important features of the method. First of all, the new formulation of ship-motion Green function and its gradients expressed by various components makes it possible to deal with different components separately and to develop appropriate algorithms in the accurate and efficient computation of influence coefficients associated with them.
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From page 81... ...
Ohkusu (1992) " The Green function method for ship motions at forward speed", Ship Techn.
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