Twenty-First Symposium on Naval Hydrodynamics (1997) / Chapter Skim
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Nonlinear Ship Motions and Wave-Induced Loads by a Rankine Method
Nonlinear Ship Motions and Wave-Induced Loads by a Rankine Method
Pages 45-63
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From page 45... ...
has been three-dimensional Rankine Panel Method, of under development at MIT. During the early nonlinear ship motions and structural loads in- stages of this research program the fundamental duced by steep ambient waves.
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From page 46... ...
The ship wave disturbance arising from its forward translation, the surge, heave, and pitch oscillatory motions, and the interaction with the ambient wave, are initially treated by linear theory. Heave and pitch motion si~nulations are carried out by combining the non46
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From page 47... ...
Consistent with the stated objectives of this study, the purpose.of these comparisons is to assess the nature and importance of nonlinear effects in the prediction of the heave and pitch motions in head waves. Computations of the vertical bending moment and shear force distributions along the ship length are presented in Section 3.1, along lines similar to the ship motion simulations presented in Section 2.
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From page 48... ...
A further decomposition of the perturbation potential into instantaneous and memory components is used to obtain a stable form for the integration of the equations of motions, as discussed in :64. For an ambient wave steepness and ship motions that are sufficiently small, linear theory allows the decomposition of the incident, radiated and diffracted wave disturbances.
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From page 49... ...
'['hey have been shown In ~74 to con tribute appreciably to the hydrodynamic coeffi cients and therefore must be included in a lin ear formulation. The diffraction body boundary condition merely states that the normal veloc- The evolution equations employ an exity of the sum of the incident and diffraction plicit Euler integration to satisfy the kinematic velocity potentials vanishes over the hull mean free surface condition end animplicit Euler inte position.
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From page 50... ...
The hydrostatic and Fioude-Krylov incident wave-pressures are integrated on the exact, wetted hull surface, to produce the nonlinear forces. At each time step, the intersection of the a priors known ambient wave profile and the ship hull defines this exact wetted surface.
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From page 51... ...
The total wave elevation ~ is decomposed into the incident wave elevation (0 and the disturbance wave elevation (. The weak scatterer hypothesis assllrx~es that the disturbance quantities ~ and ~ are small, so only the first order terms are retained upon linearization about the arnbierIt wave profile.
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From page 52... ...
In the presence of a specified ambient wave profile, the boundary value problem obtained from the weak scatterer hypothesis is An important step in the weak scatterer formulation, involves the evaluation of the Eulerian time derivative of the velocity potential which enters in the free surface condition and the evaluation of the hydrodynamic pressure over the ship huh. The direct approach of extracting the Eulerian time derivative from the Lagrangian derivative of the velocity potential, has been found to introduce n Americas instability and to therefore lead to an excessive restriction of the time-step size.
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From page 53... ...
0.15 0.10 0.05 0.00 -0.05 0.05 0.00 -n or o `- a 2.0 3.0 \ I , , .
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From page 54... ...
,? 2.5 1.0 ,W , \ \\ 1.5 2.0 2.5 ~L Figure 4: Heave and pitch motions for the Snowdrift hull (T=8m)
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From page 55... ...
They include measurements of the ship motions, but also of the global loads which wiB be presented later. 3.1 Global Loads in Regular Waves This section presents results for the computation of global loads on the Snowdrift hull.
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From page 56... ...
On the other hand, if nonlinear hydrodynam~c effects are introduced, the response wiD be, in general, non-Gaussian which may require a simulation of considerable duration. By extending the model for ship motions and global loads beyond linear theory, the physical accuracy of the simulation is reduced for a given deterministic input (i.e.
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From page 57... ...
global loads at Eroude number 0.325.
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From page 58... ...
1—·—NV1418 |- - ~ - SWAN-l l 1 1 I—~—SWAN-2 , ~ , ll 1 | ~ Exp —~—NV1418 · ~~, ~ Figure 6: Linear transfer functions for the Snowdrift (T=11.4m) global loads at EYoude number 0.325.
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From page 59... ...
4000 . 3000 2000 1000 o , -2000 -r Bending moment at U2 (MNm)
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From page 60... ...
1 0000 Bending moment at L/2 (MNm)
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From page 61... ...
found to be in satisfactory agreement with exFor the vertical bending moment of a periments aIt(1 to reveal a clear sensitivity upon container ship, for instance, an estimation of the extreme response with less than five percent statistical uncertainty can be based on simulations of only one percent of what would be needed for a direct time domain simulation. 4 Conclusions A nonlinear seakeeping method has been presented for the simulation of the ship motions and wave induced loads in steep random waves.
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From page 62... ...
"Rapine Panel Methods for Mansient Free Surface Flows", Proceedings of the 6th International Conference on Numericat Ship lIydrodynamics, Iowa City, {owe, 1993. t94 PawToski, J., "A Nonlinear Theory of Ship Motions in Waves", Proceedings of ~ 9th Symposium on Naval Bydrodynam-ics, Seoul, Korea, 1992.
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From page 63... ...
We have compared our relative wave elevation predictions to one set of experiments for the commercial design, TGC's FASTSHIP, and found a favorable comparison. Also, for the purposes of global load predictions presented in this paper, the quantity of relative wave elevation is not directly relevant, since we have not examined slamming.
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