The Proceedings Fifth International Conference on Numerical Ship Hydrodynamics (1990) / Chapter Skim
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Side-Wall Effects on Hydrodynamic Forces Acting on a Ship with Forward and Oscillatory Motions
Side-Wall Effects on Hydrodynamic Forces Acting on a Ship with Forward and Oscillatory Motions
Pages 499-512
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From page 499... ...
Ohkusu Kyushu University Fukuoka, Japan Abstract A rational slender-ship theory is presented for predicting the side-wall effects on the added-mass and damping coefficients of a ship, moving with forward velocity and performing heave and pitch motions in a waterway with vertical and parallel side walls. Satisfaction of the side-wall boundary condition in the far-field solution is acheived by the method of mirror images, with a closed-form expression obtained of the resultant infinite series.
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From page 500... ...
Starting from the ring wave at ~=0, the wave pattern changes to the complicated one dominated by the diverging-wave component, as the parameter ~ increases across the critical value 1/4. Corresponding to this complicated variation of the wave pattern, the added-mass and damping coefficients including the sidewall effects show complex variations.
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From page 501... ...
In this theory, the flow field to be analyzed will be divided into the inner and outer regions, and in each region the governing equation and boundary conditions may be simplified, making it possible to obtain the inner and outer solutions respectively with relative ease. However, both of these solutions include indeterminate coefficients, since nothing has been prescribed about the respective asymptotic behavior far away in the inner problem and close to the ship in the outer problem.
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From page 502... ...
to be compatible with the outer expansion of an appropriate inner solution. For this matching procedure, the inner expansion of the Green function must be sought.
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From page 503... ...
Thus the flow in the inner region may be described by the 2-D Laplace equation subject to the free surface condition which is independent of forward velocity and applicable to the 2-D problem in the y-z plane; this can be mathematically justified by the coordinate stretching argument with the assumption of x=O(1)
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From page 504... ...
3. Added-mass and damping coefficients Since the inner solution has been determined, we proceed to the calculation of hydrodynamic pressure force and moment acting on a ship with forced heave and pitch motions.
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From page 505... ...
Therefore the mterms should be evaluated from the 3-D precise calculation for the steady perturbation potential. Fortunately, according to his numerical study, a better agreement with experiments is provided by simply omitting the m-terms in the unified theory.
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From page 506... ...
, , , , I 5 0.3 0.2[ Fig.4 Pitch added moment of inertia of a prolate spheroid (~/B=8) at F~=O.1 in waterway of B~/B=16 506 F Ba3/~V/~7[ Fig.3 Heave damping coefficient of a prolate spheroid (~/B=8)
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From page 507... ...
Comparing the predictions of the strip theory with those of the unified slender ship theory, we can understand that the effects of three dimensionality are prominent only in the low frequencies. Since the forward velocity is present, with the incensing wavenumber KL, the parameter =Um/g-FniKL increases and takes the critical value ~=l/4 at KL=6.
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From page 508... ...
For ~=0.224, all computed coefficients appear to converge as the number of division increases, although the coefficients associated with the pitch mode dictate a finer discretization relative to that necessary for the heave-mode calculations. (Here we note that the relative error in Bss might be noticeable but its absolute error is not so large, because the value itself is small at KL=5.0 as seen in Fig.5.)
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From page 509... ...
in Open Sea | - Strip Theory ~ ~ Slender Ship Theory 0.10 j + 3-D Panel Method \ with Side-Wall Effect (BT/B=16)
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From page 510... ...
Computations were performed for the heave and pitch added-mass and damping coefficients of a prolate spheroid of length-beam ratio 8.0, moving at the Froude number 0.1 in the waterway of width twice the spheroid's length. The computed hydrodynamic forces show complex variations as the frequency increases.
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From page 511... ...
If the calculations of wave-exciting force and moment are completed, the ship motion in waves can be readily computed from them, using the added-mass and damping coefficients predicted by the present theory. Therefore, I think that the computed results of ship motions in waves can be shown in the foreseeable near future.
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