The Proceedings Fifth International Conference on Numerical Ship Hydrodynamics (1990) / Chapter Skim
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Slamming of Flat-Bottomed Bodies Calculated with Exact Free Surface Boundary Conditions
Slamming of Flat-Bottomed Bodies Calculated with Exact Free Surface Boundary Conditions
Pages 251-268
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From page 251... ...
Falch Norwegian Marine Technology Research Institute Trondheim, Norway ABSTRACT OF The impact of a flat-bottomed two-dimensional body which y falls vertically towards initially calm water is studied theoretically and numerically. The flow in the ~ compressible air layer between the body and the water ° surface is calculated by assuming that the air is i nv i sc i d and t he f 1 ow i s one-d i dens i one 1 .
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From page 252... ...
The pressure distribution is calcu1 ated unt i 1 the edge of the body makes contact wi th the elevated water surface, and Koehler and Kettleborough assumes that the maximum impact pressure is reached at this time-instant. Verhagen also calculates the pressure in the trapped air bubble after this time by a simplified method assuming that the pressure in the bubble and the downward velocity of the water surface within the bubble is only a f unc t i on of t i me .
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From page 253... ...
Or in other words, before the body makes contact the flow in the water and particular the free surface elevation depends on the pressure in the air above the water surface. On the other hand the calculation of the pressure in the air
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From page 254... ...
and [71. The initial height, Ho' of the falling body is assumed to be sufficiently above the free surface so that the air is not behaving compressible and the pressure distribution within the air layer is essential ly atmospheric so that no initial effect wi l l be felt by the water.
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From page 255... ...
ect_n 4.2 A boundarv-inteural-equation technique Let the water be infinite in extent and be of infinite depth. Since we have assumed irrotational flow in an incompressible fluid, there wi l l exist a velocity potential ~ which satisfies the Laplace equation in the fluid: 2 2 0 Ox ay 'he pressure p in the air over the water surface may differ from the atmospheric pressure pO, and since the surface tension is neglected, the dynamic free surface condition can be written as: at + 2[(ax)
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From page 256... ...
, the wetted body surface and that part of the free surface lying between x = -bF and x = bF are divided into straight-line elements (see Fig.
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From page 257... ...
~ is known on the body by the use of the body boundary condition, and ~ is known on the water free surface in the same way as in section 4.2. Vinje and Brevig chooses ~ to be the known function at the intersection point between the body and the free surface.
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From page 258... ...
The method described in this section is used in a computer program. This has been run for the case of a cylinder oscillating vertically in the free surface.
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From page 259... ...
4.8. The free surface elevation which is the result of the pressure-element, is calculated by a method which is based on potential theory and with 1 i near f ree surf ace cond i t i on.
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From page 260... ...
, lla/r ~ 0.6, .','r/q - 1.0 ,,~ ~ == ~ on SURFACE ELEVATION DUE rc PRESSURE El£MLNT I I b ~ x Up o o to in o to _ 10.
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From page 261... ...
5.11-12. The inf luence on the pressure and the surface elevation at the centerl ine is seal l, but the shape of the free surface and the pressure close to the edge of the body is very different.
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From page 262... ...
may also be partly explained by assuming that the maximum pressure will not be reached until a short time-period after the calculated contact. The argument for this was stated above.
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From page 263... ...
5.6 Case A, '=l.O SURFACE ELEVAT I ON AND POS I T I ON OF BODY N 0: 8 o O— ~ I 1 1 1 ' 1 ' 1 - 1 ' 1 ' 1 t0 0 0.2 0.4 0.6 o.e 1.0 1.2 1.4r 1.6 1.8 2.0 THETA - 0.500 deg b - 1.500 ~ M - 40 ~ S.OOO kg/ HO ~ 0.500 ~ VO ~ -~.880 - /.
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From page 264... ...
5.11 Case A, .=1.4 PRESSURE O I STR I BUT I ON SURFACE ELEVAT I ON AND POS I T I ON OF BODY I 8 o ; THETA ~ O .000 deo b - O .200 m n - 20 .000 kg/m HO = 0 .020 m VO = -O .626 m/c NA - 20 NF - 80 (VO/b ~ O .0150 0.0840 0.0882 ~_ o _ · ~ · I · I · I · I 0.0 0.2 O.' 0.6 0.8 t.0 l 1.2 l.4 1.6 1.8 2.0 x/b Fig.
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From page 265... ...
kind along the entire boundary. The comparison with Doctors which was made in section 4.4 also indicates that the surface elevation due to a pressure distribution acting on the water surface is calculated quite correct l y.
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From page 266... ...
x(P ) = Xb Append i x A This appendix describes how new elements on the free surface are generated and how the velocity potential ~ at the midpoints of the new elements is calculated in the programme SLM which is based on section 4.2.
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From page 267... ...
First of all, since I only carry on the calculation until the moment when the body makes contact with the water-surface, I do not find the maximum pressure. Secondly, I did not make any comparison with slamming loads calculated without the effect of air cushion, so I don't know the limit value of the deadrise angle.
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