# Hydrodynamic Investigation on a Land-Fixed OWC Wave Energy Device under Irregular Waves
## 3 Validation
### Model Validation  
The numerical flume length is set to 5.5 times the peak wavelength (5.5\(\lambda_{p}\)), in which 1.5\(\lambda_{p}\) is used as the damping layer. Therefore, the length of the wave transportation is 4.0\(\lambda_{p}\) (from inner wave generation source to the OWC front wall), which is twice the maximum wavelength (2.0\(\lambda_{\text{max}}\)) of the 200 input wave components.  
Figure 2: Comparison between input spectrum and incident wave elevation spectrum at different position in the NWT for two peak wave periods. (**a**) \(T_{p}\) = 1.5 s, (**b**) \(T_{p}\) = 3.0 s.  
The geometrical parameters of the OWC device are identical to the experiments carried out by [PERSON] et al. [25]: the static water depth \(h\) = 0.8 m, chamber breadth \(B\) = 0.55 m, front wall draught \(d\) = 0.14 m, front-wall thickness \(c\) = 0.04 m, air duct width \(e\) = 0.0036 m and air chamber height \(h_{c}\) = 0.20m. The values of the viscous coefficient \(\mu_{2}\) and the linear pneumatic damping coefficient \(C_{dm}\) are also maintained identical as the study under regular wave, i.e., \(\mu_{2}\) = 0.2 and \(C_{dm}\) = 9.5.  
Convergence analyses on the spatial and temporal discretization were performed. The mesh elements size in the \(x\) and \(z\) direction is set as \(\Delta x\), \(\Delta z=\lambda_{p}/10\), \(\lambda_{p}/20\) and \(\lambda_{p}/30\), respectively with the peak wave period \(T_{p}\) = 3.0 s and \(H_{s}\) set to 0.06 m (corresponding to regular wave \(A_{\text{inc}}\) = 0.03 m). The free surface elevations at the chamber center-point are shown on Figure 3a, and the pneumatic pressures in the chamber are shown on Figure 3b. It can be seen from Figure 3 that the free surface displacement and pneumatic pressure results have both converged at the intermediate mesh size \(\Delta x=\Delta z=\lambda_{p}/20\).  
The time step is set as 0.5\(\Delta t\), 1.0\(\Delta t\), 2.5\(\Delta t\) for the temporal discretization convergence analysis. The duration of the spectral analysis is the complete repeat interval (100 \(T_{p}\)) and 16,384 continuous data points are selected for the FFT, therefore the time step is designed as \(\Delta t\) = 50 \(T_{p}/8192\). The time step convergence results are showed in Figure 4 for \(T_{p}\) = 3.0 s. It is found that the time step duration set to \(\Delta t\) = 50 \(T_{p}/8192\) is sufficient for temporal convergence.  
Subsequent to the spatial and temporal convergence analyses, the spacing of the numerical grid in the \(x\) and \(z\) is set as \(\Delta x=\Delta z=\lambda_{p}/20\) respectively. For different peak wave periods, the number of mesh elements for the OWC device is set to a constant value by  
Figure 4: Time histories of the (**a**) free surface elevations at chamber center and (**b**) pneumatic pressures in the chamber for different temporal step intervals.  
Figure 3: Time histories of the (**a**) surface elevations at chamber center and (**b**) pneumatic pressures in the chamber for different mesh sizes.  
adjusting the mesh encryption number. For each simulation case, a simulation duration of \(100\ T_{p}\) is performed with time step \(\Delta t=50\ T_{p}/8192\).  
Figure 5 presents the profile of the non-dimensional wave elevation (\(A_{m}=H_{s}/2\)) along the wave flume for \(T_{p}=1.366\) s with \(t=20\ T_{p}\), and \(t=220\ T_{p}\), respectively. It can be seen that the two wave profiles match each other very well, irrespective of whether the location is inside or outside the chamber. Notably, the surface elevation progressively approaches zero in the damping layer, which confirms the wave damping capacity of the damping layer.