Page 477 - Practical Design Ships and Floating Structures

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2 THEORY
The right-handed Cartesian coordinate system as shown in Figure 1 is employed. The fluid field in the
presence of a set of tandem fence is assumed steady, viscous and incompressible, which is represented
by
v-u= 0
pu.Vu = -vp +pv2u

where u is the fluid velocity, p the density of water, p the pressure and p the fluid viscosity.
For the given free stream velocity U, the fluid boundaries are the free surface, the rigid two fences, and
the water-bottom surface. On the latter two boundary surfaces, no-slip condition is imposed, and on the
free surface, a vanishing normal velocity condition is imposed i.e. the free surface remains flat.

Lagrangian Particle Tracking
Once the flow velocity field is known, the motion of an oil droplet of diameter 4 can be found by
solving the following equation of motion given by Maxey et al. (1983) and Berlemont et a1.(1990):

where po is the density of oil, Ud the droplet velocity, CA the added mass coefficient normalized by the
droplet volume V, u,.(=ud- u) the relative velocity of the droplet to the fluid velocity, CD the drag
coefficient normalized by p lurfAe, A,(=d;/4) the equivalent cross-section area of the droplet, g = (0,
-g, 0) the gravitational acceleration, and D/Dr the substantial time derivative. The coefficients CA and
CD are obtained by the formulae given by Clift et al(1978).

3 NUMERICAL METHOD

The computations are carried out under the assumption that the fences are very long such that the flow
field is two dimensional. The Navier-Stokes equations are solved by the finite-difference scheme with
body-fitted grids, standard k-E turbulence model of Jones and Launder (1972), and SIMPLE C
algorithm for the velocity-pressure correction to satisfy the continuity Eqn. 1. The computation domain
is x= (-15D, 25D) and y==O, -15D), and the boundary conditions for the steady, viscous flow case are

u=(U,O) at x=-15D (44
ax
&=O at x=25D, and v=O at y=O,-15D (4b)
where D is the fence draft. The exact free-surface condition is that the free surface remains as a
material surface which allows the deformation. However, in the present work, mainly due to the
numerical complexity and uneconomical computation time involved, the v = 0 condition is adopted.

4 EXPERIMENTAL METHOD
4.1 Experimental Facilities and Procedures

The experiment for obtaining flow velocity field by PIV(Partic1e Image Velocimetry) method of Shin
et al.(2000) was carried out at a circulating water channel of which the test section size was