Eighteenth Symposium on Naval Hydrodynamics (1991) / Chapter Skim
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Adequacy of Free Surface Conditions for the Wave Resistance Problem
Adequacy of Free Surface Conditions for the Wave Resistance Problem
Pages 375-396
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From page 375... ...
All are implemented in a Rankine-source method of the type proposed by Dawson. The comparisons concern the predicted wave resistance and wave patterns, the magnitude of the nonlinear terms neglected in the FSC, and the remaining errors in the dynamic and kinematic conditions at the predicted free surface.
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From page 376... ...
WAVE RESISTANCE PREDICTIONS 2.1. Background The mathematical model pertinent to calculation of the wave pattern and wave resistance of a ship is that of a potential flow subject to kinematic and dynamic free surface conditions (FSC's)
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From page 377... ...
( ~ WAVE RESISTANCE (MODEL FIXED AT ZERO TRIM AND SINKAGE, CALISAL, 1980) Calculated (Dawson FSC)
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From page 378... ...
This is in marked contrast with the general conviction' Since in commercial projects the present use of the predicted wave resistance values is generally qualitative or comparative rather than quantitative, we can safely state that the Kelvin FSC performs just as well as the slow-ship FSC. unto Fig.
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From page 379... ...
THE PARADOX OF NEGATIVE WAVE RESISTANCE 3.1. General The fact that a negative value of the wave resistance is sometimes predicted by Dawson's method is known to more people that Dawson Kelvin 1 11 l,\: 1,\.
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From page 380... ...
Therefore, contrary to the general belief discretization errors can probably be rejected as cause for the negative resistance, at least in some of the case investigated. A negative value of the wave resistance in the presence of a physically realistic wave pattern radiated by the ship as shown in Fig.
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From page 381... ...
Therefore, the origin of the paradox, being a contradiction of the calculation and our physical insight, must be sought in the difference between both expressions. Substitution of the potential of a free harmonic wave in Rwf shows that the wave resistance so obtained is positive definite, in agreement with our physical observation of the radiated wave pattern.
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From page 382... ...
In the extreme case the pressure integration over the hull can give a negative resistance: the ship rides on waves generated by the free surface condition, in this case governed by the double-body flow nonuniformity. In order to obtain a more realistic wave resistance prediction for such extreme cases, two approaches now suggest themselves.
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From page 383... ...
3.4. Energy Flux Through The Free Surface Another, more fundamental remedy for the occurrence of a negative wave resistance could be to modify the FSC so as to eliminate the excess energy flux through the free surface.
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From page 384... ...
Summary Summarizing some of the findings of this section, the paradoxical occurrence of negative wave resistance in the presence of a plausible radiated wave pattern can be explained by the possibility of an energy flux through the undisturbed free surface differing from the amount needed to represent the potential energy variations. This energy flux can be expressed in the remaining normal velocity and pressure at the calculated free surface.
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From page 385... ...
The best estimate of the wave elevation is that which includes the nonlinear terms and the transfer terms; it is noted n below. For the Kelvin condition, the perturbation param eter is the wave steepness ~ = ~ .
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From page 386... ...
Including this term reduces the wave resistance by 20% in this case.
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From page 387... ...
\~J 0.1 - Eggers ~ Jilt -G.l ~ (Vl/ Fig. It Nonlinear terms in free surface conditions; Series 60, Fn = .35 -- - Term 1 _ Terms 3 + 4 + 5 + 6 1160 1' 1\ ~0 ~1 ~0 The transfer term 8 is now quite large at the bow, about 70% of the vertical velocity (Fig.
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From page 388... ...
1J Fig. 12 Nonlinear terms in free surface conditions; Series 60, Fn = .22 Term 1 - - Terms 3 + 4 + 5 + 6 o in.
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From page 389... ...
There are significant differences between the velocities on the undisturbed free surface and those on the actual free surface, particularly for the vertical velocity. Including the transfer terms from Taylor expansions makes the tangential velocities fairly accurate except at the stern wave; but the difference in vertical velocity is not well represented by the consistent term 8 (Fig.
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From page 390... ...
For Dawson's condition it is 0.152 times the ship speed. This agrees with the bad wave resistance prediction obtained with the Neumann-Kelvin method.
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From page 391... ...
But the vanishing coefficient is an artefact of the Taylor expansion used for transferring the boundary condition; and as shown here, this expansion tends to diverge if the coefficient vanishes. Therefore I believe that no physical interpretation may be given to the change of sign, and that it simply imposes a bound on the hull fullness for which this free surface condition is applicable (and perhaps even theoretically preferable)
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From page 392... ...
Even the occurrence of negative wave resistances could not be cured within the framework of linearized methods. From the practical point of view, therefore, this study contributes nothing at all.
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From page 393... ...
These comparisons concerned the wave resistance and wave profile predictions, the magnitude of the terms neglected in the FSC, and the remaining errors in the dynamic and kinematic FSC at the predicted free surface. The main conclusions are summarized below.
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From page 394... ...
Wave energy can locally be supplied through the free surface which has no counterpart in a wave resistance acting on the hull. If the linearized free surface condition is consistently formulated, the possible negative contribution from the free surface energy flux is reduced to a higher order in the perturbation parameter than the wave resistance itself.
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From page 395... ...
DISCUSSION J Nicholas Newman Massachusetts Institute of Technology, USA One thought is prompted by the case shown in Figure 4 where, for the lowest Froude number, the Kelvin free-surface condition overestimates the wave resistance whereas the Dawson condition yields a negative value.
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