# A Numerical Study of the Performance of Point Absorber Wave Energy Converters
## 3 Results and Discussion
### Effect of WEC Shape
As a result, it appears that the depth of W1 decreases with increased displacement in the \(z\)-direction. However, W3 behaves slightly differently, as seen in Figures 6b and 9b. The effects of submergence d\({}_{s2}\) on the displacement and velocity of all WECs are shown in Figure 10. The irregular displacement of W1 in the \(x\)- and \(z\)-directions increases with depth. However, the horizontal displacements of W2 and W3 are smaller than that of W1. Velocities and forces in the \(x\)- and \(z\)-directions are larger for W3 than for W1 and W2. This is due to the lower kinetic energy that develops in water as the depth increases. The vorticity and pressure contours provide clear information regarding this effect; see Figure 11.  
Figure 8.0 Effect of WEC shape with effective density of 1000 kg/m\({}^{3}\), wave height \(H\) = 0.04 m, submergence depth \(d_{s1}\) = 0.1 m, and \(k_{2}\) = 50 N/m. (**a**,**b**) Horizontal (\(Dx\)) and vertical (\(Dz\)) displacements of WECs as a function of time. (**c**,**d**) Horizontal and vertical velocities of all WECs. (**e**,**f**) Forces on all WECs in \(x\)- and \(z\)-directions. Figure 11a,b show the vorticity contours for W1 and W3. The vorticity is seen to be higher for W3 than for W1. High vorticity shedding is developed at the corners and near the tip of W3; it provides additional lift force to the WEC. Fluctuations usually occur due to both the lift and drag coefficients, but here, the fluctuations are due to a high lift coefficient. The vertical force increases as submergence depth increases, as shown in Figures 9f and 10f. However, the Froude-Krylov force can also be a reason behind this huge fluctuation. The Froude-Krylov force is obtained by integrating the incident-wave pressure over the instantaneous wetted buoy surface, which changes according to the body motions and incident-wave elevations at every time step. This force increases the displacement of the buoy by more than 3 times its actual displacement. Figure 11c,d show that a higher pressure is present for W3. The Reynolds number can be calculated through \(Re=\frac{\rho vd}{\mu}\), where \(\mu\) and \(\rho\) are the viscosity and density of water, respectively, \(d\) = 0.3 m is the characteristic length of the WEC, and \(v\) is the flow velocity. The inlet velocity is calculated through the wavelength (\(\lambda\)) and the time period (T), \(v\ =\frac{\lambda}{T}\). The inlet wave velocity and the maximum velocity of each simulated case are used to establish \(Re\) values, which are found here to be between 15,000 and 48,000 based on the different buoy submergence depths. This shows a laminar flow regime. Although \(Re=10^{5}\) has been suggested [25; 26], there is currently no clear definition in the literature regarding the critical Reynolds number for such applications, with the value being largely dependent on the problem studied [27]. Figure 8.1 Effect of different WEC shapes with effective density of 1000 kg/m\({}^{3}\), wave height \(H\) = 0.04 m, submergence depth \(d_{\text{2}}\) = 0.2 m, and \(k_{\text{2}}\) = 50 N/m. **(a,b)** Horizontal (\(Dx\)) and vertical (\(Dz\)) displacements of WECs as a function of time. **(c,d)** Horizontal and vertical velocities of all WECs. **(e,f)** Forces on all WECs in \(x\)- and \(z\)-directions