Eighteenth Symposium on Naval Hydrodynamics (1991) / Chapter Skim
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A Numerical Research of Nonlinear Body-Wave Interactions
A Numerical Research of Nonlinear Body-Wave Interactions
Pages 103-118
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From page 103... ...
number of elements on Sb+Sc+Sd+Sf ~I~,Nc number of elements on So, Sc Nd,Nf number of elements on Sd,Sf SO wetted body surface Sc outer boundary or SO bottom surface Sf free surface Zig vertical position wave elevation p fluid density ~ total wave potential Zhenquan thou and flaoxiang Gu, China Ship Scientific Research Center, P.O. Box 115, Audi 214082, Jiangsu, China to gravity axes velocity potential of incident waves (s scattered wave potential I .
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From page 104... ...
In the present method' the body wave interaction is treated as a transient problem. The development of the flow is obtained by a time stepping procedure, the velocity potential is obtained by utilizing a panel method, in which simple source are distributed over all boundary surfaces, including the free surface, the immersed surface of the body and the bottom surface.
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From page 105... ...
2+z2 ] 2 The normal induced velocity is then N where ni j-1 ii i i=1,2, ,~1 (-2n j= i ~Jsjr3 ilk In conducting the time stepping procedure the boundary conditions at each time interval t+6t are established in explicit forms containning quantities at times At and t- At which are known from previous iterations e.g: (3n~t+At F ($t ~t-At~3n~t' On~t-At)
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From page 106... ...
where CR is the phase velocity for potential function. Let R denote the intersection point of the free surface and the outer boundary, and point R-1 a neighbouring point AR distant from point R along the radial direction, the phase velocity CR is then obtained from ~ of the free-surface as: t -¢tR l+¢tR 1 RC = 4~_1 26t(Vr)
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From page 107... ...
induces a ingoing reflection of the scattered slaves. It is the interference of the scattered waves that causes the chage in the period of the wave forces.
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From page 108... ...
Four cases of large amplitude forced heaving motions are investigated in which R=8.0, w-ln, d=4.0, T=16.0, t=Q.1 and in case (a) H =0.05, da=H'=lQZ, h is the mean draft.
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From page 109... ...
NONLINEAR WAVE DIFFRACTION AROUND LARGE STRUCTURES l6S 4. 1 Formu l at i on In approach to the diffraction problem, the wave diffraction is treated as a transient probl em wi th known i n i ti al cond i ti ons correspondi ng to sti l l water i n the immedi ate vi ci ni ty of the structure, and `'i th a prescribed incident wave form approaching froin x=~ and propagati ng past the structure, Fi g.
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From page 110... ...
e. an a¢O an On ~ = to (30' however, when T > Tc, where Tc is the tine when the scattered waves travel l i no at i ts group vel oci ty Yogi n to meet the outer boundary, the Qrlansl i's condition is adopted: at ~ C,p(KrarS + K~r¢9)
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From page 111... ...
5. IFITER;ACTIONS OF 51Q~ILIi'5~AR SURFACE '`lAVE WITH A FREELY FLOATI FIG BODY 5.1 Formulation In order to consider the effects of three dimensional nonlinear interactions between slave and body, the boundary conditions on the immersed body surface are expressed in terms of velocity Uk (k=1,2,...6)
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From page 112... ...
Here, a circular cyl i ndri cal surface i s ado,oted as the outer boundary, the radi us of whi ch i s P`/a=9.
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From page 113... ...
For illustration, the results of simulati ng the di ffracti on ~x,oeriment of a 1 arge floating dock , ixed on the free surface and subjected to an approaching nonlinear wave with a wave front generated by a cyl i ndri cal wave maker numeri cal l y are presented. The computi onal model i s as Fi g.
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From page 114... ...
Fig. 12 Nonl inear radial free surface profi les, case b, ampl itlJde H=O.
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From page 115... ...
Fig. 13 Nonlinear radial free surface profiles~case c, amplitude H=0.15, 6=30% (1<~<8, t=0.1, 0.3,...)
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From page 116... ...
Fig. 26 Heave motion of a floating dock in the incident waves.
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From page 117... ...
tan k of novel idea o, ~ heaving cylinder is attempted, and validated by cor~iputa' ion t'nat such waves `~i th a wave front ;.~aiy be brought upon an offshore structure wi th proper i ni ti ail conditions and nu~.r,erical ly treated to Field non1 i near wave forces of the ri ght order.
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From page 118... ...
In our paper, we adopt a pragmatic treatment to local singularity. We have tested many methods for treating the intersection points in 3-D problem, the direct interpolation method may be the best one in these methods from our numerical test; it keeps the computation robust and efficient.
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