3.4.2. Results

Table 3 lists the estimated coefficients of the added and total mass moment of inertia, the viscous and radiation damping, and the ratio of viscous damping to total damping for the pitch motion at the natural frequencies of each model from the potential-based motion analysis. As seen in the table, the added mass moment of inertia and viscous damping, which is much larger than the radiation damping, becomes larger with the adopted appendages, which may result in the reduction of motion.

**Table 3.** Added mass moment of inertia, total mass moment of inertia, coefficients of viscous and radiation damping, and ratio of viscous damping to total damping for a pitch motion at natural frequencies of the models from the potential-based motion analysis.


Figure 13 shows the pitch response amplitude operators (RAOs) of the buoys. Near the natural frequencies of the buoys, the RAOs of all models become very small when the viscous damping is considered. The maximum pitch motions are expected to be reduced by approximately 20%–40% with the adoption of the appendages. Because the radiation damping is small, and the viscous damping was estimated and applied from the CFD simulations of free decay tests, plate-type appendages are more effective than the conical-type ones.

**Figure 13.** Pitch pitch response amplitude operators (RAOs) estimated from the potential-based motion analysis of the light buoys (**a**) without and (**b**) with the consideration of viscous damping.

Table 4 shows the estimated added mass, total mass, coefficients of viscous and radiation damping, and ratio of viscous damping to total damping for heave motion at the natural frequencies of each model from the potential-based motion analysis. Unlike for pitch motion, radiation damping is greater than viscous damping except for that of the Cone model. The reason for this can be easily deduced, as the vertical translation motion of a cylinder generates more waves than the rotation motion.


**Table 4.** Added mass, total mass, coefficients of viscous and radiation damping, and ratio of viscous damping to total damping of a lightweight light buoy from the potential-based motion analysis.

The heave RAOs of the light buoys without and with considering the viscous damping coefficients are shown in Figure 14. Near the natural frequencies of the buoys, the RAOs of the models with appendages become small when viscous damping is considered, while there is not much difference with the Base model. In the comparison of the maximum heave motions of each model, porous appendages are expected to be more effective than non-porous ones for all frequencies in reducing the heave motion even if the differences are not large.

**Figure 14.** Heave RAOs estimated from the potential-based motion analysis of the light buoys (**a**) without and (**b**) with the consideration of viscous damping.

#### *3.5. Motion Simulation in Regular Waves Using CFD*

#### 3.5.1. Computational Domain and Grid System

Figure 15 shows the computational domain and boundary conditions for the motion simulation in regular waves using CFD. To enhance the accuracy of CFD simulations including waves, it is important to minimize the artificial diffusion of generated waves and wave reflections at boundaries. One of the methods to reduce wave reflection and computational cost while maintaining accuracy is the wave forcing method. As an inflow boundary condition, second-order Stokes wave theory was applied as the "velocity inlet" to express waves with the Euler-overlay method (EOM), which is a built-in forcing method of STAR-CCM+ [25,26]. In the overlay zone located from the inlet boundary to 2.4 m ahead of the buoy in the x-direction, analytic solutions and CFD solutions are gradually blended by applying source terms to VOF and momentum equations. No-slip conditions were imposed on the buoy surface and bottom boundary. For outflow boundary, the "pressure outlet" boundary condition was used while adopting grid damping technique [27] to minimize the wave reflection at the boundary. For the side boundaries, the "symmetry plane" boundary condition was used [25,26].

**Figure 15.** Computational domain and boundary conditions for motion simulations of lightweight light buoys in regular waves using CFD.

Figure 16 shows the grid system for the CFD simulations. The numbers of cells per wavelength and height were 140 and 30, respectively. The minimum and maximum numbers of the total generated cells were approximately 3.0 and 3.74 million for the Base and Porous Cone models, respectively.

**Figure 16.** Grid system for motion simulations of lightweight light buoys in regular waves using CFD.

#### 3.5.2. Regular Wave Conditions for Motion Analysis Using CFD

Table 5 shows the wave conditions (i.e., simulation cases) for the CFD motion analysis. Eight waves of different wave frequencies, including the pitch and heave natural frequencies of the Base model, were selected. The amplitude of each wave was determined under the assumption that the wave steepness was 1/40.


