Twenty-First Symposium on Naval Hydrodynamics (1997) / Chapter Skim
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Time-Domain Calculations of First-and Second-Order Forces on a Vessel Sailing in Waves
Time-Domain Calculations of First-and Second-Order Forces on a Vessel Sailing in Waves
Pages 177-188
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From page 177... ...
Results of our computations are compared with measurements and strip theory results. Nomenclature A B AS, AD _ _ F1, F2 En G 9 h k _ _ M1, M2 n At U x,x,y,z added mass damping boundary of interior, exterior first- and second-order forces Froude number Green's function gravitational acceleration depth of the water wave number first- and second-order forces normal time time step uniform velocity of the current coordinate system 177 Or p W ~0 Introduction wave height due to incoming wave linearized relative wave height second coordinate system G density of the fluid total potential unsteady potential steady potential potential due to incoming wave frequency of encounter frequency In recent years many studies have been carried out solving the unsteady ship motion problem.
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From page 178... ...
The computational domain cannot be infinite, so we Have to introduce artificial boundaries and proper boundary conditions. In the literature several methods Have been proposed to absorb free surface waves.
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From page 179... ...
Discretization of the integral equation leads to a matrix equation for the unknown vector ~ with superscripts denoting the time level and f a time- dependent vector. The matrices Di are built up by the Green's function, its derivative and the surface conditions.
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From page 180... ...
The boundary condition absorbs the outgoing waves. The reflections due 180
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From page 181... ...
Also the calculations of the hydrodynamic coefficients and drift forces of a commercial tanker agreed well with measurements. The forward speed of the commercial tanker is very low, the maximum Froude number is 0.018, i.e.
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From page 182... ...
FIGURE 5: The potential, using upwind discretization, Fn = 0.5 FIGURE 6: The free surface around the LNG carrier
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From page 183... ...
drift force calculations for zero and small forward speed were done, using the frequency domain diffraction program, extended to a small forward speed t12~. Calculations for the other velocities were done using strip theory t1, 2~.
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From page 184... ...
In Figure 32 the drift forces or added resistance for higher speed are given. For the higher frequency strip theory doesn't agree very well with the measurements.
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From page 185... ...
i.. art.., .., Id, FIGURE 14: Added damping in pitch
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From page 186... ...
. 3.6 4 4.5 FIGURE 19: Coupled added damping from surge into pitch A13 PA.., 0.04 FIGURE 17: Coupled added repass from heave into surge ._ OWES 0.02 O.O,S 0.0, of - s o ems _n at B13 ·~w \ i.
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From page 187... ...
_o of > ...... C~J~ FIGURE 24: Coupled added damping from heave into Pitch _ Fn-.OO Fn..003 -- Fn..14 - - Fn..17 ~ Fn-.20 O03 0.036 .
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From page 188... ...
Diffrac Fn 003 .. W: 2 2.5 3 3.5 4 4.5 FIGURE 28: Horizontal drift force in head waves for small forward speed.
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