computed roll R。A。O, particularly near resonance, is greatly over predicted compared to the experimental data of Patel and Brown (1986)。 The inclusion of eddy making roll damping (BV) from developed DVM pro- gram and friction damping (BF) from Kato (Himeno, 1981) reduced the roll R。A。O of resonance area signifi- cantly and showed good agreement with the experimen- tal results。

0。2 0 0 0。1 0。2 0。3 0。4 0。5 0。6 0。7 0。80。9 1 1。1

Roll Frequency

Fig。 6:Comparison of vortex roll damping coefficients(Bv) (Roll amplitude = 0。175 radians, B/D = 2。5)

Fig。 5: Comparison of vortex shedding from a barge (Upper : Experiment Downie et al 1988,

Lower: Present Calculation)

Fig。 6 shows the comparisons of vortex roll damping coefficients ( B*) for the barge with varying frequencies。

The damping was evaluated from calculated moment (Eq。 13) and averaged over two roll cycles。 For the comparison purpose to the experiment data of Ikeda (1977), the damping is non-dimensioned by

Freequency(rad/sec)

Fig。 7:Comparison of roll R。A。O

(Roll amplitude = 3 degrees, B/D = 7。6)

where g is gravitational acceleration and is the vol- ume of the barge。 The calculated vortex roll damping coefficients can be used in the study of the motion of floating body。

Experimentalandthenumericalresultsofthe roll

R。A。O of the barge model of Patel and Brown (1986) are compared in Fig。 7。 Their experiments was carried out on the model barge of length (L) = 2。4m, Beam (B)

= 0。8m and draught (D) = 0。105m with roll amplitude of 3 degrees。 The calculation of R。A。O against roll fre- quency for the experimental barge is carried out using the SSMP (Samsung Ship Motion Program), which is the panel method program developed by SHI (Samsung Heavy Industries)。 The program can be used to predict motion responses, hydrodynamic pressure distribution, the wave loading on the transverse cross section along a mono hull and multiple hull ships and 2nd order drift forces and moments (Kim et al, 1997; Ha et al, 2004)。 Without the inclusion of the viscous roll damping,the4。Ship Hull Calculations and Results

The numerical model was developed to cater for realis- tic ship hulls by refining the transformation procedure and introducing multi vortex capability, as described earlier。 The method is validated for the Series 60 hull form with block coefficient of 0。6, for which detailed experimentaldataforrolldampingcoefficientsand

R。A。O of the hull has been obtained (Ikeda 1977)。 The actual computations were carried out at seven sections (X/L = 0。05, 0。10, 0。30, 0。50, 0。70, 0。90, 0。96) along the hull with 41 nodes girthwise and 25 nodes in radial direction for roll amplitude = 0。175 radian, roll fre- quency = 6。283 rad/sec。 Based on the grid nodes, forty multi vortices at each time were introduced on the hull surface to satisfy a pointwise no-slip condition。

Fig。 8:Comparison of vortex evolution (T/Tp=0。5) Fig。 10:Comparison of velocity vectors (T/Tp=0。5)

Fig。 9:Comparison of vortex evolution (T/Tp=1。0)

Fig。 11:Comparison of velocity vectors (T/Tp=1。0)

Fig。 8 and 9 compares the evolution of the vortex about the three sections (X/L = 0。05, 0。5, 0。95) along one roll cycle (T/Tp = 1。0)。 The results show clear differences of vortex shedding patterns depending on sectional hull shapes。 For the mid ship section (X/L = 0。5), vortices are shed from the curvature bilges and similar to the barge sections。 By the smoothness of the bilge curvature, the strengths of the vortices are weak then barge’s and there is no strong pared vortices。