About Journal of the Korean Society for Marine Environment & Energy

A schematic of the OWC air chamber is shown in Fig. 1, where L_f denotes the chamber width, D_s is the draft of the chamber skirt, W is the width of chamber, and D_u is the still water depth. The width length ratio of the chamber is 1.6. The dimensions of the chamber are summarized in Table 1, at both the model and full scales. The incident wave conditions employed in the experiment are summarized in Table 2. H_m denotes the incident wave height of model and full scale, H_p is for full scale. T_m, T_p is the incident wave period at model and full scale respectively.

Fig. 1. 
Schematics of OWC chamber.

The experiment was conducted in the 3-D wave basin of the Ocean University of China. The water depth during the experiment was 0.6 m. A piston type wave maker system was installed at one end of the wave basin and a wave absorber was installed at the opposite end.

The OWC chamber model shown in Fig. 2 was fixed at a 40 m distance from the wave maker which is the position of 2/3 according to length of wave basin. The model is made of poly methyl methacrylate (PMMA) acrylic. The scale ratio of the OWC model for the basin test to the prototype was 1/16 and the water depth for the prototype was 9.6 m. The wave height inside the chamber denoted by H₀, was measured at the center of the chamber using a wire-type capacitance wave gauge. The sampling time step was 0.002s, and the number of wave crests was 10-12.

Fig. 2. 
Experimental set up.

Airflow motion and wave energy absorption are related to the oscillation of water column in a chamber. Therefore, it is important to investigate the response of free-surface to demonstrate the effects of the corresponding wave directions on power conversion. To investigate the effects of wave directions on the performance of the OWC chamber, a very simple model was employed where the top of the chamber was open along the entire length. Considering the capacity of wave basin, three incident waves with periods varying from 4 to 8 seconds were chosen when the wave height was 2.0 m in full scale. Five wave directions varying from 0^o to 90^o were selected to demonstrate the effects of wave direction.

Fig. 3 shows results for the effects of wave direction at an incident wave height of 2.0 m in full scale. The dimensionless relative wave heights were compared in each wave period, where H_P is the incident wave height, H₀ is the oscillating height of the water column in the chamber, and the wave direction was varied from 0o to 90o. It is noted that, at 90^o of wave angle, the incident wave approaches normal to the OWC chamber.

Fig. 3. 
Experimental results on the wave amplification in a chamber for five different wave directions.

In the case without cover, the results show that the wave height in a chamber varies as a function of the incident wave periods. The effect of wave direction was not so prominent at the wave angles higher than 67.5^o. As the wave angle became smaller, the relative wave height decreased at every incident wave conditions. The numerical result at the wave angle of 90^o was also shown in Fig. 3 to figure out the general feature of the performance of simple OWC chamber. It can be seen that the peak wave height inside chamber occurred around the period of 8~9 seconds. Unfortunately, the experiment at the incident wave period longer than 8 seconds could not be performed due to the load limitation of experimental set-up. It is however worth noting for the present OWC chamber model that the present experiments well demonstrate the effects of incident wave angle in general sense. More detailed analysis can be seen in the next section.

For the converting stage, in which wave energy is converted into bi-directional air flow energy, the NWT-based tow-phase VOF model (Fluent) established by Liu et al. [2007] was used for incident wave generation and propagation. The OWC system was placed at the end opposite to the wave maker. The VOF model has been demonstrated to simulate the complex free surface interaction, predicting not only the wave motion but also the pressure distribution and air flow motion. It has been successfully employed in the investigation of both the OWC and overtopping wave energy converting facilities by Liu et al. [2007, 2008].

The effects of wave direction were investigated using the NWT based on the two-phase VOF model. The boundary conditions and the grid structures are given in Fig. 4. Four direction angles of 90^o, 67.5^o, 45^o, and 22.5^o, in addition to 0^o were employed in the numerical study. Four incident wave periods varying from 4 to 10s were applied, and the incident wave height was 2.0 m.

Comparisons of wave amplification in a chamber between numerical and experimental results are shown in Fig. 5. Obviously the small θ produces the less wave amplification. The numerical calculation shows qualitatively fair agreement with the corresponding experimental data, while experiment gives a little higher amplification factors in quantity. It is likely that the nonlinear wave amplification phenomenon is more prominent in experiment at W/L_f = 1.6.

Fig. 4. 
Schematics of grid structure.

Fig. 5. 
Comparison with experimental results at 5 different wave directions.

Fig. 6 shows the instantaneous pressure contours near the free surface at difference wave directions around the chamber. The incident waves arrive from the left. The pressure contours shown in Fig. 6(a) shows the case of 90^o of wave angle, where the pressure field inside the chamber was rather uniform. As the angle of the incident waves decreased, an inequitable pressure contour was found, especially at 0^o. This may be evident that highly complex motions such as sloshing phenomenon and various wave interactions each other occurred inside a chamber because of the presence of the side walls, dominant reason of high 3-D effects in the range of studies in this paper.

Fig. 6. 
Calculated pressure contours near free surface (H_p=2.0 m, T_p=6.0 s).

The instantaneous velocity vectors near the free surface at various wave angles are shown in Fig. 7. High velocity gradients are observed at the corners of a chamber. Based on the velocity vectors, it can be seen that complex flows appeared outside the chamber may also influenced the pressure field inside a chamber.

Fig. 7. 
Calculated velocity vectors near free surface (H_p=2.0 m, T_p=6.0 s).

In this study, It is now interested to investigate the effect of the width-length ratio. Fig. 8 shows the wave amplification inside a chamber with varying chamber widths at the wave direction of 45o. Here the width-length ratio of W/L_f = 1.6 is the chosen case in this study, while W/L_f = 10 is the case of very large chamber width, almost comparable to the wave length. It is shown that the chosen case, W/L_f = 1.6, gives the best performance among the cases investigated. This kind of tendency becomes more prominent with the larger width-length ratio. It even shows the 80% reduction of wave at W/L_f = 10 compared to W/L_f = 1.6 in case of longer wave period. It could be anticipated that the wave interactions inside a chamber are the major reason of the reduction of wave height at the larger chamber width.

Fig. 8. 
Effect of chamber width on the wave amplification inside a chamber.

It is well demonstrated in Fig. 9 showing the time series wave profiles at typical locations in a chamber. The three locations along the chamber width are chosen; y/W=0.2, 0.5(center), 0.8, where y is the direction in chamber width. The wave amplification is clearly seen at W/L_f = 1.6 without any interaction along the chamber width. The case is quite different in Fig. 9(b) that the wave interactions each other create the cancellation of the overall wave elevation, that is the reduction of total airflow in air chamber. It is concluded that the selection of chamber width plays the critical role in designing OWC, especially at oblique wave conditions.

Fig. 9. 
Time series wave profiles at typical locations in a chamber.