Active wave absorption system
Methods for wave generation with active wave absorption were originally developed for physical wave flume experiments. The basic idea was that the reflected energy must be absorbed by the same wave generator, whose movement is modified to cancel out the reflected waves. This kind of absorption is called Active Wave Absorption System (AWAS). In this work, the water surface elevation η is used and transformed by an appropriate time-domain filter to obtain a control signal that corrects the wave paddle displacement in order to absorb the reflected waves. The reflected wave signal is in general determined as the difference between the measured surface elevation and the generated surface elevation estimated from the wave generator control signal.
A very simple test case has been designed, where a piston wave-maker generates waves in a tank that ends with a vertical wall. The bottom of the tank is fully horizontal and the water depth d is 0.27m. Regular waves (wave height H=0.1m and wave period T=1.3s) were generated by a piston-type wave-maker and reflected on a vertical and fully reflective wall. Differently from the passive absorption (where the wave energy is smoothed at the end of the domain, so no waves are reflected back to the wave-maker), the use of the active absorption system aims to avoid re-reflection from the wave-maker, but not from the structure located on the other side of the domain (a vertical wall in this case). Results for regular waves are shown in the figure where the time series of the piston displacement and water surface elevation at x=2m are depicted, respectively. The wave-maker position is varying during the first 13s of simulation to adapt itself to the different wave conditions. After this time, the wave-maker motion returns to be regular, so that the wave pattern is also stabilised. The final mean position of the wave-maker is drifted from the initial one because of small deviation from 0 of the mean water surface at the front of the wave-maker. However this drift only causes a difference in water level of 0.004m (2% of the water depth and similar to dp) that can be neglected. The water surface elevation, after this transitional phase, becomes regular. The wave amplitude is higher than the target one because a standing wave regime is established inside the domain.
A snapshot at the instant equal to 22.2s of the numerical simulation is shown in the figure. The upper panel of the figure corresponds to the case without active absorption and a chaotic water surface is observed (incident + reflected + re-reflected waves) while the second panel shows the regular pattern with only incident and reflected wave when using AWAS. The behaviour and the applicability of AWAS can be also analysed in terms of the force exerted by the wave train on the vertical wall at the end of the tank. Hence, figure also shows the time series of forces (including the hydrostatic component) exerted by the regular waves with and without AWAS on the wall. It can be observed how there is no difference between the two signals during the first 8 seconds, whereas, after that, only the force measured in the case with AWAS still presents a regular and periodic shape (in agreement with the time series of the water surface elevation). The time series of forces in the case without absorption is totally biased by the wave re-reflection.
More information in:
Altomare C, Domínguez JM, Crespo AJC, González-Cao J, Suzuki T, Gómez-Gesteira M, Troch P. 2017. Long-crested wave generation and absorption for SPH-based DualSPHysics model. Coastal Engineering, 127: 37-54 doi: 10.1016/j.coastaleng.2017.06.004.