Eighteenth Symposium on Naval Hydrodynamics (1991) / Chapter Skim
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Numerical Solutions for Large-Amplitude Ship Motions in the Time Domain
Numerical Solutions for Large-Amplitude Ship Motions in the Time Domain
Pages 41-66
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From page 41... ...
These results include linear and larg~amplitude motion coefficients and diffraction forces with and without forward speed, calm-water resistance and addedresistance with waves and motions, the largeamplitude motion history of a ship advancing in an irregular seaway, as well as load distributions on the changing submerged hull. Most of the largeamplitude results we obtained are new and illustrate the importance of nonlinear effects associated with the changing wetted hull.
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From page 42... ...
For these linear forward-speed calculations, the quadratic terms are included in the force calculations to account for the forward-speed couplings but the m-terms are otherwise neglected in the body boundary conditions. Linear and large-amplitude computational results are presented for a floating sphere, two Wigley hulls, and the Series 60 (CB = 0.7)
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From page 43... ...
, N the unit normal to P(T) on the free surface, positive out of the fluid domain, and VN the normal velocity of [(T)
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From page 44... ...
in the present earth-fixed coordinate system, the quadratic contributions are included in the pressure integration (Eqs. 16 and 19 ~ to account for forward-speed effects, but the body boundary condition (15)
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From page 45... ...
j=1 which can be solved for the unknown panel source strengths, aM, by standard means. 3.2 Evaluation of the Free Surface Transient Green Function The integrals involving the Rankine part of the Green function G° are evaluated using a method similar to Hess & Smith (1964~.
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From page 46... ...
This is not considered in the present code. 4 RESULTS Numerical computations were performed for linearized radiation and diffraction problems; largeamplitude forced motions and free motions of a floating body with and without forward speed and the presence of ambient waves; as well as wave resistance and added resistance problems.
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From page 47... ...
For radiation problems with forward speed, a forced oscillatory motion is superimposed on a step-function jump of the forward velocity to the prescribed value. The force coefficients are then obtained from Fourier transforms of the SAMP force time histories after steady state is reached.
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From page 50... ...
On the other hand, the Michigan results (which include m-terms) using the same N show unexplained deviations for intermediate values of To Not surprisingly, strip theory performs better for larger To but appears to be affected significantly only for Bss at lower frequencies.
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From page 51... ...
For the SAMP results, N=120 and 30 time steps per incident wave period is used. The comparisons to the time-domain results of Michigan, strip theory and experiments are overall satisfactory.
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From page 52... ...
1 0.0 4.0 8.0 12.0 1 6.0 w2L /9 o o 0 /, 1,, ~,0 ~ ~- a- ~ ~o 1 1 0.0 4.0 8.0 12.0 16.0 w2L /9 Figs. 6: Magnitude and phase of the wave exciting forces on a WSK hull at Fn=0.2.
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From page 53... ...
\ ~ .. , \ "~e' \; x SAMP N=250 O SAMP N_ 180 Michigan N=176 Michigan N=108 -- Strip theory Experiment (Gerritsma, 1960 9"~` ,+~ W ~-o o_ 1 ~ ~ o o 0 o o oco 0 o co o o co / .
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From page 54... ...
O Do 0.25 0~ 50 0 75 Ah/a Fig. 11: Excitation frequency components of the limit-cycle hydrodynamic vertical force on a sphere undergoing large-amplitude heaving motion (w=1.0)
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From page 55... ...
The linearization of the free surface conditions cannot in principle be justified as the motion amplitudes become very large. For many body geometries and motions, however, the nonlinear effects associated with the geometry alone play a predominant role so that the neglect of free-surface nonlinearities may be acceptable.
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From page 56... ...
i 1 0.0 1.0 2.0 3.0 4.0 5.0 t/To Fig. 13: Vertical force time history for a WRT hull moving at Fn=0~3.
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From page 57... ...
, 1/20 2.53 2.84 1.70 l 2.82 1.99 1.48 1.20 1.48 2.50 1/30 2.50 1.37 1.58 l 1.82 1.87 0.94 1.57 1.62 1.60 -1/40 1.68 2.79 1.26 1.22 1.84 1.78 . 1.29 1.64 1.75 Table 3: Wave resistance coefficients Cc x 103 of the WRT hull at Fn=0~4 as a function of grid size and distribution.
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From page 58... ...
0.0 0.1 0.2 0.3 0 4 0 Ah/0 Fig. 18: Excitation frequency components of the limit-cycle forces and moment on a heaving ~ w=1.0, amplitude Ah ~ WRT hull moving with constant forward speed (Fn=0.2~.
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From page 59... ...
As with the sphere with no forward speed, the LAMP damping coefficients here are less sensitive to heave amplitude probably due to the fact that nonlinear radiation mechanisms are absent in the present approximation. 4.6 Motions of a Floating Body and Unsteady Loads With the ability to determine the relevant hydrodynamic forces at any given instant, the complete six degree-of-freedom motion history of the body can be obtained by a direct integration of the dynamical equations.
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From page 60... ...
(20) shows the free sinkage and trim wave resistance of the WRT hull as compared to corresponding experimental measurements as well as the fixed body resistance results of Fig.
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From page 61... ...
at the ship's center of gravity, pitch angle All, and heave displacement (z) of a WRT hull at Fn=0.2 in irregular head seas.
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From page 62... ...
1 o ll 600 90.0 Fig. 23: Incident wave elevation (~)
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From page 63... ...
To validate the approach and evaluate its accuracy, the method was applied extensively to obtain linearized motion coefficients for a number of different geometries with or without forward speed. The results include added-mass and damping coefficients, wave exciting forces and steady wave resistance, sinkage and trim forces and moments.
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From page 64... ...
In the first case, the presence of large-amplitude heaving motions is shown to result in significant increases of the wave resistance and steady sinkage and trim forces. In the latter, the nonlinear "added-mass" is found to decrease markedly with increasing heave amplitude.
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From page 65... ...
(1988) , "Rankine source methods for numerical solutions of the steady wave resistance problem," Proc.
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From page 66... ...
My own results show that at least for a submerged body, the nonlinear phenomena associated to the body boundary condition are very frequency-sensitive. In fact, when dealing with oscillatory motions, even in the time domain, one cannot ignore the importance of frequency and this parameter must be varied before drawing conclusions.
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