Eighteenth Symposium on Naval Hydrodynamics (1991) / Chapter Skim
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Numerical Simulation of Ship Waves and Some Discussions on Bow Wave Breaking & Viscous Interactions of Stern Wave
Numerical Simulation of Ship Waves and Some Discussions on Bow Wave Breaking & Viscous Interactions of Stern Wave
Pages 191-206
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From page 191... ...
They are also applied to study precisely on the stern flow of S-103 as to which extensive experimental data are available. A1though it is not yet made clear about the interaction between the separation and the stern wave generation, the effects of the bow wave on the developments of the boundary layer flows are concluded to be significant.
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From page 192... ...
2.1 Basic Equation Numerical simulations of 3-D freesurface flows are carried out by solving the N-S equation basically following to the MAC method. The velocity components u, v and w at (n+1 )
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From page 193... ...
The CPU time and the memory size of the present computation are rather reduced owing to the use of coarse meshes of the second mesh system for the Poisson equation and the diffusion term. 2.3 Body Surface Condition In the numerical solution for viscous flows, the no-slip condition for the solid surface is used by discretiz ing the region fine enough to the imposed condition.
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From page 194... ...
194 In order to check the convergence of the computations, the wave patterns and drag coefficients of Cp, Of and Cw are compared along the marching time step as shown in Figs.2 and 3, where Cp, of and Cw are the pressure, frictional and wave-making resistance coefficients respectively. Schoenherr friction line and the measured wave-making resistance coefficient are shown for comparison.
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From page 195... ...
The laminar flow is subject to separation in the stern region and wider boundary layer thickness, while the turbulent flow is to larger velocity gradient near the hull by which we can guess a larger wallfriction on the body surface. Fig.7 shows the comparison of the wave patterns at Rn= 104 and 106.
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From page 196... ...
Although they can not be compared exactly due to difference of Reynolds number, we can say that the computed patterns are qualitatively reasonable for both the bow and stern waves. Fig.11 shows the velocity vectors on the transverse section near A.P.
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From page 197... ...
~ - `` ~ _ _~` ~ i< i...~N ,~,,`~N ,. `~N ~ ~\ \~\~4 And As XiittitY ~ ~ t~ttti ~ ~ t ~ ' T=3.O Fig.11 Velocity vectors of Wigley model(Rn=106, Fn=0.316 and x/L=1.02)
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From page 198... ...
X (s.s.7) Fig.13 Variation of M/Us and free-surface elevation and lines analyses for bow wave breaking.
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From page 199... ...
The grid size is 74x29x30; computations are carried out on another finer grid scheme to find no significant difference in the resistance. The computing domain is -1.4~x/1~2.0 and 0.0 |
From page 200... ...
This is because the wave profile at Fn=0.27 is a little different from that at other speeds. from the observed wave profiles 4.3 Discussion on Viscous Interaction Fig.19 shows the computed stern wave patterns at the three Froude num 200
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From page 201... ...
The modest elevation of the stern wave at Fn=0.27 may be much related to the development of the boundary layer and separation. Fig.20 shows the velocity profiles in the boundary layer around the stern and close to the free-surface.
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From page 202... ...
The detection of the appearance of sub-breaking waves is made for the stern waves at Fn=0.27 and 0.30. The values of M/US are calculated along FREE SURFACE ~ , _ I, ; ; ; ~_ _ _ _ _ _ _ _ 1 - , ., .
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From page 203... ...
it\ \ \ ~ ~ i~, t`~W \ ~ ~ >\4 ~ ~ We can point out that the bow wave affects much on the separation and eventually the stern wave generation appreciably. The appearance of subbreaking waves makes the flow field completely different and it may be necessary to include them in the computation.
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From page 204... ...
(6) The occurrence of sub-breaking changes the flow fields drastically, especially for the stern waves.
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From page 205... ...
The point of the triple grid method is that the fourth order central difference scheme in the Poisson equation does not so much improve the accuracy even if finer grid is used, while, as you comment, the fine mesh system is necessary for the convective term. This is because the truncation errors which come from the dissipation terms, gradient of pressure and Poisson equation give little influence on the accuracy of the computations.
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