Twenty-First Symposium on Naval Hydrodynamics (1997) / Chapter Skim
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Nonlinear Shallow-Water Flow on Deck Coupled with Ship Motion
Nonlinear Shallow-Water Flow on Deck Coupled with Ship Motion
Pages 220-234
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From page 220... ...
The finite difference scheme is a second-order Total Variation Diminishing scheme which is able to tackle Continuities in the Dow and gives satisfactory respite. The nonlinear ship motions with considering water Bow on deck are solved in the time domain.
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From page 221... ...
The time domain added ma - , hydrodynamic damping and hydrodynamic restoring force coefficients are calculated using the impulse potential (King, et al., 1988~. The equations of ship motion also include the nonlinear Froude-Krylov forces, nonlinear restoring forces and nonlinear viscous roll damping.
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From page 222... ...
where FRY are the restoring forces; Fk ~ are nonlinear Proud - Krylov forces; Fk the diffracted wave forces; Fk the radiated wave forces; Fk the viscous damping forces; Fk k the nonlinear forces due to water flow on deck; and the force compm nent F° may include the hydrodynamic maneuvering forces, the rudder force, propeller thrust, viscous resistance and crossbow drag. The ship translational displacements (~1., (2, BOOT in the steady moving System and the Eulerian angles (e:, e2, es)
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From page 223... ...
If the water depth is shallow compared with the horizontal dimension of the deck space, it can be assumed that w is a small quantity compared with u and v; and the dependence of u and v on z may beignored,i.e.u=u(x,y,t) andv=v(x,y,t)
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From page 224... ...
,'+} +/o + 90 (15) ~ the numerical computation, the governing equation can be split into two equations using the Fractional Step meth.od as given by Yanenko (1971)
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From page 225... ...
Nonlinear Eroude~Krylov Forces . At each time intact, the ship motions (~42~3, e~,e2,e3)
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From page 226... ...
. viscous Rot Damping Moment Various forms of formulation of the roll damping moment have been applied to the nonlinear roll motion, such as the linear plus quadratic model, the linear plus cubic model, etc (Haddara and Bass, 1990~.
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From page 227... ...
Rudder Forces and Autopilot It is defined that the rudder angle ~ is positive when the rudder is turned to the port side. From where ~ is the aspect ratio of the rudder, As the rudder area of single side, Vie the relative velocity of the water particle to the rudder, and °c the elective rudder angle: tic = ~ + tangs U2 ~ ire6 + lxe.4 Up, Suppose that the normal force acts on the prep sure point Coup on the rudder, the rudder force components can be obtained as follows: FRUIT =—FIN ~ sin ~ FRUd=F,~cos~ F4 =1'FNCO86 and (47)
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From page 228... ...
2 ~ 24 WE ~111 I Sty All Fig. 6 Pitch Motion ~ Head Seas The nondimensional double amplitude of roll in b earn seas with a nominal forward speed of 5 kts is given in Fig.
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From page 229... ...
0 0.5 1 1 S 2 Wow l~~hiSffp L~h Fig. 7 Nondimensional Roll Motion In Beam Seas 25 20 1S 1n ·1C .15 -2C 68 ~~ To · 72 74 76 tom)
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From page 230... ...
i Fig. 12 Wave Profile, a4 = 7.5 deg; w = 4.712 rad/sec, t=3 see The wave motion and the velocity distribution under the excitation of multi-degrees of freedom of ship motions are more complicated than those under the roll excitation only.
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From page 231... ...
Ship motions irt six-degree~of-freedom have been computed, all motions are couled on another. The heave, roll and pitch motions with and without 15%Vo water on deck are 80 in Fig.
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From page 232... ...
U = 5 kts 1 In this particular case, the resonant frequency of water sloshing inside the dew rs much lower than the roll natural frequency, the water flow on deck may increase the roll motion amplitude and can alter the frequency of roll motion.
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From page 233... ...
E., "The Impulse Response Function and Ship Motions,n 5~iffstechnik, Vol.
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From page 234... ...
C.,"Application of the Flux Difference Splitting Method to Compute Nonlinear Shallow Water Flow on Deck", Proceedings of the Fifth International Workshop on Water Waves and Floating Bodies, KuJu, Oita, Japan, April 1994. Huang, Z
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