Twenty-Fourth Symposium on Naval Hydrodynamics (2003) / Chapter Skim
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A Flow Model for a Displacement-Type Fast Ship with Shallow Draft in Regular Waves
A Flow Model for a Displacement-Type Fast Ship with Shallow Draft in Regular Waves
Pages 491-501
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From page 491... ...
With this equation used as an integral equation for the pressure distribution associated with the disturbance of a ship, we can satisfy the Kutta condition requiring a smooth flow at the stern in addition to the kinematic condition of water surface being equal to the vertical position of a ship. An accurate numerical solution method is also presented, using-Chebyshev polynomials for the unknown pressure and employing a Galerkin scheme.
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From page 492... ...
Excellent numerical accuracy is confirmed through the check of theoretical relations derived from Hanaoka's reciprocity theorem (Hanaoka, 1959) and from the energy conservation principle associated with the damping coefficients in heave and pitch modes.
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From page 493... ...
, a homogeneous solution exists, as well known in the airfoil theory, which makes it possible to satisfy the Kutta condition requiring a smooth flow at the stern. In this case, however, the resulting surface elevation at X ~ 1 may not be equal to the vertical position of ship's bottom, which must also be satisfied in the problem of a flat ship.
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From page 494... ...
The basic solutions necessary in this problem may be obtained by considering the following body boundary conditions: a) Heave mode (j = 3)
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From page 495... ...
Let the pressure distribution be expressed in terms of the first-kind Chebyshev function Tn(X) ' or equivalently the Fourier series similar to that used in the airfoil theory: N T ( )
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From page 496... ...
With these results, it is straightforward to compute hydrodynamic forces, the Kochin function and wave-induced motions. RECIPROCITY THEOREM Applying Hanaoka's reciprocity theorem (Hanaoka, 1959)
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From page 497... ...
/L = 2.0 (with Kutta condition) Table 1: Accuracy of numerical results, errors in Hanaoka's reciprocity theorems and the energy conservation principle (Frz = 0.5, A/L = 2.0 in head wave; w = 3.343, ~ = 1.672)
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From page 498... ...
The accuracy for other parameters of En and A/L was confirmed to be of the same order as Table 1, implying that the present boundary-value problem is without Kuffa coed. En 50 without Kuffa coed.
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From page 499... ...
, the flow model in the present paper gives necessarily a gap in the wave amplitude at the bow, corresponding mathematically to the amplitude of a homogeneous component of the wave elevation, Ace. The nondimensional value of this amplitude is shown in Fig.
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From page 500... ...
On the other hand, the results for the case of satisfying the Kutta condition seem to be reasonable in magnitude and variation tendency, which supports the validity of the proposed flow model. CONCLUDING REMARKS In the hydrodynamic problem of a displacement type ship with shallow draft, a solution must satisfy the kinematic condition of water surface being equal to ship's vertical position and the Kutta condition of
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From page 501... ...
Numerical results were confirmed to be very accurate through checking several relations derived from Hanaoka's reciprocity theorem and the energyconservation principle. It was also confirmed that computed results satisfying the Kutta condition were reasonable judging from the magnitude and variation tendency of the pressure, wave profile, hydrodynamic forces, and wave-induced motions.
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