Laboratory scaling of the free-decay of an oscillating vertical-axis underwater cylinder

In order to extract the energy delivered by ocean waves, efficient energy converters must be engineered. This means that they must operate at resonance with the predominant wave frequency. The behaviour of the converters in the waves is strongly tied to the damping caused by the fluid (ocean) around them. Thus, properly understanding this damping phenomenon is critical in order to tune the converters to the required wave frequency. In common practice, these machines are designed/tested as laboratory models which are later scaled up. In order to properly anticipate full-scale behaviour, the scaling laws (especially when it comes to damping) need to be finely determined. For this reason, free-decay experiments have been conducted in a water tank 1.3 m deep, in which wavelengths were sufficiently short to replicate deep water conditions. Cylindrical floating bodies (modelling a point-absorber wave converter) with a length of 0.35 m and respective diameters of 0.028, 0.034, 0.043, 0.048, 0.062 m were used to mimic the energy extraction devices. These cylinders were made of PVC with an approximate absolute surface roughness coefficient of 0.0015 mm. To resemble the classic “mass-spring” system frequently used in the literature and by some companies operating full-scale wave-power machines, the cylinders were connected to a spring. They were submerged at different depths and displaced vertically. Then, the free-decay of the systems was recorded using an image processing technique from a video camera. The amplitudes of the initial displacements were 0.02, 0.03, 0.04, 0.05 m and the experiments were repeated approximately 30 times for each case. Finally, the decay rates were extracted from the curves. The results show the expected correlation between the variation of the total damping and the respective change in diameter. However, the different damping curves suggest that, for certain regimes and diameter changes, the onset of turbulence has an influence which can prove problematic when scaling up from laboratory models of wave energy machines to real size devices.