The experiment was carried out in a wind-wave flume of length 5 m, width 0.4 m, and height 0.85 m and a wind tunnel cross section of 400 mm × 400 mm (Figure 1). A piston type wave generator was located at one end of the tunnel with a five-phase stepping motor (PK596AWM) connected to it. A wave absorber was installed at the other end of the tunnel. A blow-down type wind tunnel has a maximum speed of 35 m/s and not used in this measurement, but the combination of wind and wave will be one of the interesting studies for further works.

Two wave gauges (KENEK Wave Height Meter CH-606) were used in the experiment, and the distance between them is denoted by ∆l where 0.1L < ∆l < 0.5L (L is the wavelength), so that the incident waves and the reflected waves are distinguished clearly. The two wave gauges were installed depending on the experimental conditions, but their positions were suitably chosen in the direction of wave propagation, which is considered as a different wave zone to measure the maximum and minimum wave heights while evaluating the incident and reflected waves. Waves were generated by a combination of the piston cylinder assembly and a stepping motor controlled by an AVR 128 electric circuit and a visual basic program. The output probes of the wave gauges were connected to a data logging unit (NI USB-9151), which stores the analog signal and transfers the data to a computer hard disk. The schematic diagram of the setup is shown in Figure 2.

Figure 1: 
Snapshot of a wind and wave tunnel used in the experiment

Figure 2: 
Schematic diagram of the wave flume experimental design

It is assumed that a wave paddle helps the waves propagate forward in a wave flume, and the waves are reflected back at the other end. Then, the reflected waves move back toward the wave paddle and are reflected again. The re-reflected waves propagate forward again and this process is repeated until the multi-reflected waves are fully attenuated. The wave train in the positive direction is called the incident waves and that in the negative direction is called the reflected waves. The amplitude of the incident waves is denoted by a_R and the amplitude of the reflected waves by a_R[2]. Wave modeling in this condition is summarized from equation 1 to equation 13 to obtain the incident and reflected waves followed by appropriate curve fitting. Two different waves can be formulated as follows:

where η_I and η_R are incident and reflected waves, respectively, L is the wavelength and k is the number of 2π/L.

The observed profiles of composite waves will be:

In the equation above, all the constant can be calculated and X₁, Y₁, X₂, Y₂ can be calculated by Fourier analysis.

Therefore, the reflectance (K_r) can be calculated by using equation (3).

Figure 3 (a) shows the variation in the calculated reflectance against different locations of the wave absorber plate (the angle of the absorber plate remains constant α=β=γ). Figure 3 (b) shows that the wave absorber with a larger volume exhibits lower values of reflectance because of the high absorption of wave propagation in the flume. The reflectance increases with increasing wave period. As a result, the change in the location of the frame from 0.95 m to 1.15 m had no significant effect on the reflectance. However, when the frame was moved to 1.35 m (further upstream), the reflectance was substantially reduced to less than 0.1 and remained stable. In this study, the wave absorber exhibited the lowest reflectance and remained stable when the absorber frame was at 1.35 m. The lowest reflectance was 0.035 at a non-dimensional frequency of 0.9.

Figure 4 (a) shows the variation of the angles of the absorber plate (37°, 45°, and 60°) with the volume enclosing the water inside the mesh fixed at 0.13 m². As shown in Figure 4 (b), the best absorption was observed at an angle of 37°, whereas, the other two cases had a relatively high values of reflectance. The reflectance attained a minimum value when the non-dimensional frequency was 1. The reflectance increased when σ²h/g was between 1 and 1.32 and decreased thereafter. When the angle reduced to 37°, the reflectance substantially reduced less than 0.1 and remained stable. An additional experiment was carried out to show that when the plate angle is less than 37°, the reflectance obtained would be less than 0.1. Therefore, at a fixed volume, reducing the angle of the wave absorber plate can increase the wave absorption and produce a stable reflectance. In Figure 3 (b), to find out the possible effect of the volume of the wave absorber, the angle of the wave absorber frames was set to be approximately 37°. Further studies will be carried out to confirm whether these two parameters have an isolated effect or a coupled effect on the reflectance coefficient.

Figure 5 (a) shows the configurations of the installed wave absorber plates. In this case, the number of wave absorber plates in the wave flume was varied, i.e., single, double,and triple absorber plates, at a constant filler volume.As shown in Figure 5 (b), the wave reflectancevalues are scattered. As the number of absorber platesincreases, the overall reflectance decreases. In addition, as the non-dimensional frequency decreases, the reflectance increases. In comparison, the results are in good agreement even with different combinations of the absorber plates. While using a single absorber plate, the highest reflectancewas approximately 0.25 at σ²h/g = 0.8. On the other hand,while using triple absorber plates, the lowest reflectance was0.045 at σ²h/g = 1.55. A similar reflection distribution ineach case indicates that the absorption of the wave absorber is mainly dependent upon the fillers, whereas the number of absorber plates did not substantially influence the variation in wave reflectance.

Figure 3: 
Reflectance coefficient against non-dimensional frequency with a fixed angle of 37 at different locations of wave absorber plate

Figure 4: 
Reflectance distribution against non-dimensional frequency with a certain volume (0.13m²) for different angles of plate.

Figure 5: 
Reflectance distribution of multiple wave absorbers against non-dimensional frequency with a fixed distance from the end wall at different angle

In order to evaluate our experimental results, a comparison has been made between the current work and a numerical result of Mallayachari [8] on the reflectance (K_R) as shown in Figure 6. In his work, the porosity and wall slope of the wave absorber were set to 0.5 and 45°, respectively. For a feasible comparison, kD is used in the abscissa instead of the non-dimensional frequency (σ²h/g) where D is the width of the wave absorber. Both the results indicate that the wave reflectance decreases and attains a minimum value of approximately 0.46 at kD = 3 (numerical) and 0.03 at kD = 3.8 (experiment). As shown in Figure 6, the results are in good agreement within a certain range. In addition, most of the reflectance data are less than 0.1. Therefore, a sloping-type wave absorber in a short-distance wave flume can be used for further studies.

Figure 6: 
The comparison between theoretical solution and current experimental results

Figures 7 and 8 show a typical example of the sinusoidal wave generated by the wave maker in the transverse direction of the wave flow. The two wave gauges were placed at a certain distance((Δl)), and the recorded data is shown in Figure 7. It can be observed that the differences in wave amplitude at the two measurement stations are within 1 mm, which is negligible, and the phase difference seems to be due to the separation distance. It can also be observed that only one regular wave is propagating through the flume. In other words, the optimized wave absorber suppresses most of the reflected waves. As shown in Figure 8, the wave generator operation cuts in and cuts off at around 0 s and 28 s. While using the absorber, the maximum wave height substantially reduces to approximately 11 mm in a regular pattern. When the motor stops instantly, the wave height becomes stationary. On the other hand, without the absorber, the reflective waves were generated at the other end even though the wave generator ceased for a certain period. Therefore, the designed absorber significantly reduces the reflected waves in the laboratory-scale wave flume.

Figure 7: 
Typical wave signal from two wave gauges with optimized absorber

Figure 8: 
Wave height variation with and without wave absorber