# Hydrodynamic Investigation on a Land-Fixed OWC Wave Energy Device under Irregular Waves
## 4 Results and Discussions
### Characteristic of the Wave Height and Pneumatic Pressure  
Figure 6 presents the results of a typical numerical case to exhibit the time histories of the performance characteristics. The input wave spectrum parameters are selected to be \(H_{s}=0.06\) m, \(T_{p}=1.545\) s. Figure 6a shows the time series of the incident wave elevation, and Figure 6b shows the corresponding free surface elevation at the chamber center. The statistical characteristic values of the wave parameters for the incident wave and surface elevation at the chamber center are listed in Table 1. From this table, it can be seen that \(H_{1/3}=0.060\) m and the statistical peak period is \(T_{p0}=1.560\) s. This statistical result, together with the wave spectrum verification as shown in Figure 2, confirms the accuracy of the irregular wave generation in the numerical model. The maximum free surface displacement observed at the chamber center is \(H_{\text{max}}=0.094\) m, which is slightly lower than the statistical value of incident wave \(H_{\text{max}}=0.111\) m, and the statistically significant height at the chamber center is \(H_{1/3}=0.054\) m, compared with the statistically significant height of the incident wave \(H_{1/3}=0.060\) m. As shown in Figure 6c, the maximum and significant values of pneumatic pressure in the chamber calculated by the same statistical method are 0.554 kPa and 0.306 kPa, respectively. Figure 5: Profile of wave elevation along the numerical wave flume for \(T_{p}=1.366\) s with \(t=20\ T_{p}\), and \(t=220\ T_{p}\). (**a**) Profile along the flume, (**b**) local view at the OWC chamber. The instantaneous pneumatic power of the OWC device is presented in Figure 6d. The peak power is 32.95 W, which exceeds 14 times the average power, computed as 2.29 W.  
To investigate the detailed hydrodynamic behavior of the device under the irregular wave conditions, the free surface elevation and the chamber pneumatic pressure in the period range 86 < \(t\)/\(T_{p}\) < 94 in Figure 6b,c are analyzed. This region of data exhibits an obvious Gaussian distribution envelop form. The time series of the non-dimensional surface elevation at the mid-point of the chamber and the pneumatic pressure in the chamber for various \(k_{p}h\) values are shown Figure 7. From Figure 7a, it is shown that the \(H_{\text{max}}\) of the free surface elevation at the mid-point of the chamber increases with decreasing \(k_{p}h\). Figure 7b indicates that the pneumatic pressure in the chamber is greater in the low wave-frequency range. In addition, Figure 7b also indicates a quarter wave cycle phase difference between the surface displacement and the pneumatic pressure, which is significant for the average power computed according to Equation (4). This phenomenon is comparable \begin{table}
\begin{tabular}{c c c c c c} \hline  & \(T_{p0}\) **(s)** & \(T_{H\text{V3}}\) **(s)** & \(H_{\text{V1/3}}\) **(m)** & \(H_{\text{V1/0}}\) **(m)** & \(H_{\text{max}}\) **(m)** \\ \hline Incident wave & 1.560 & 1.625 & 0.060 & 0.080 & 0.111 \\ Chamber center & & 1.812 & 0.054 & 0.076 & 0.094 \\ \hline \end{tabular}
\end{table} 
Table 1: Statistical characteristic value of wave parameters at \(H_{\text{s}}\) = 0.06 m, \(T_{p}\) = 1.545 s.  
Figure 6: Time histories of key hydrodynamic performance parameters at \(T_{p}\) = 1.545 s. (**a**) incident wave elevation, (**b**) Surface elevation at chamber center, (**c**) Pneumatic pressure, (**d**) Pneumatic power. to the observed numerical results in the regular wave condition by [PERSON] et al. [6] and irregular-wave physical experiments performed by [PERSON] et al. [19]. Figure 8a shows the characteristic values of wave heights at different input peak periods. All three of the characteristic wave heights \(H_{1/3}\), \(H_{1/10}\) and \(H_{\text{max}}\) decrease with the increase of \(k_{p}h\). This can be explained by the transmission ability of the incident waves into the chamber. A smaller \(k_{p}h\) value (i.e., with longer incident wavelength) has a stronger transmission ability.