3.5.3. Results

Figure 17 shows the time histories of the pitch and heave motions of a light buoy with and without appendages when the frequency of the heading wave was 1.397 rad/s, which is the same as that of the pitch natural frequency of the Base model. The corresponding wave height and length were 0.794 m and 31.583 m, respectively. The effectiveness of the appendages in terms of reducing both motions was confirmed, as shown in the potential-based simulations considering viscous damping. This can also be seen in Figure 18, which shows the snapshots of the free surface and the buoys when the 5th plus peak of the motion was observed. However, unlike the potential-based simulation results, the superiority of the effectiveness of each appendage is difficult to distinguish for the pitch motion, while the plate-type appendages seem to work better for heave motion.

**Figure 17.** Time histories of (**a**) pitch and (**b**) heave motions of the buoys in regular waves, for which the frequency is the same as the pitch natural frequency of the Base model, estimated by CFD simulation.

**Figure 18.** *Cont.*

**Figure 18.** Snapshots of CFD simulations of (**a**) Base, (**b**) Plate, (**c**) Porous Plate, (**d**) Cone and (**e**) Porous Plate models when the 5th plus peak of motion occurs in regular waves, for which the frequency is the same as the pitch natural frequency of the Base model.

Figure 19 shows the time histories of the pitch and heave motion of a light buoy with and without appendages when the frequency of the heading wave was 3.107 rad/s, which is the same as that of the heave natural frequency of the Base model. The corresponding wave height and length were 0.160 m and 6.385 m, respectively. The effectiveness of the appendages in reducing heave motions is clearly seen, while that of the cone-type appendages is trivial for the reduction of pitch motion.

**Figure 19.** Time histories of (**a**) pitch and (**b**) heave motions of the buoys in regular waves, for which the frequency is the same as the heave natural frequency of the Base model, estimated by CFD simulation.

#### *3.6. Comparison of RAOs between the Potential-Based Motion Analysis and CFD Simulations*

The comparison of pitch and heave RAOs, and the maximums of each motion between the potential-based motion analysis and CFD simulations are shown and listed in Figure 20 and Table 6, respectively. The pitch RAOs of both results near the natural frequencies of the buoys are expected to be reduced by adopting the appendages. Although the quantitative superiority of the appendages is different, the qualitative superiority is similar between the results of the potential-based and CFD simulations. In addition, if the frequency of the wave is far from that of the natural frequency of the buoys, there is not a large discrepancy in the RAO by both simulations. In the case of heave RAO, discrepancies exit in the low-frequency region, although the effectiveness of the appendages is confirmed near the heave natural frequencies of each model. There may be some reasons for these differences. First, the viscous damping coefficient was evaluated by subtracting the radiation damping coefficient at the natural frequency of the buoy from the total damping coefficient. Second, the wave heights in the low-frequency region are relatively high because the wave steepness is fixed, which may enhance the non-linearity of the motion. The complex interactions among the incoming wave, flows, and vortex around the buoy, and flows near the buoy, may also be causing these differences.

**Figure 20.** Comparison of (**a**) pitch and (**b**) RAOs between the CFD simulation and potential-based motion analysis.


**Table 6.** Comparison of maximum RAOs estimated from the potential-based simulation with those from the CFD simulation.
