Page 439 - Practical Design Ships and Floating Structures

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To validate our approach, various types of ship geometry, such as the DTMB 5415 model, the KCS
model, the HTC model and the tanker model, are used as the test cases with two turbulence models,
the Baldwin-Lomax model and the Chien's low Reynolds number k-E model. The convergence
performance and the effect of the grid density on the free-surface waves are investigated. The results
obtained are compared well with the experimental data provided by the KRISO, the MSEAN, the
shipyard and the HSVA. For the former two test cases, an improvement for the free-surface waves has
been achieved as compared with our latest work (Li et al., 2000), which has been presented in the
workshop held recently at Gothenburg (Larsson, et al., 2000). Without doubt, the studies from CFD
groups of various countries represent the major advances in this area, although just a few CFD groups
completed these two cases in this workshop.

2 NUMERICAL METHODS

2. I Mathematical Models
On the Cartesian co-ordinate (x, y, z, t) system, where the origin is fixed at the intersection of the bow
with the still free surface, x is positive in the at? direction, y is positive towards the starboard and the z-
direction is positive upwards, the RANS equations can be written in the compact form, namely
- d(F -Fv) + a(G- G,) + d(H - H,)
dU
+
at h ay az =Q
'.
where the variable U=(p, pu, pv, pw, pk, p~) The inviscid fluxes (F, G, H), the viscous fluxes (Fv,
G,, Hv) and the source term Q are e respectively

F= G= H=

Q= the 9-L mod el; Q= (3)
0
OI

rv 1
0

and r=
(4)

p is the density of the fluid, the mean-velocity components in the x-, y- and z-directions are denoted by
u, v and w, and \v is the so-called piezometric pressure. For the k-E model, k and E are the turbulent