2.1. Investigated Cases
A simplified geometry was chosen to restrict the number of variables in the modelled problem. A rotationally symmetrical design had the big advantage that the wave angle has no significant influence on the model behaviour. Nor did the initial condition of the floating structure when the first wave reaches the model.
Figure 1 presents an overview of the experiment with the two investigated ballast options. A hollow cylinder was chosen with an outer diameter of 0.5 m and a total height of 0.5 m. The transparent plastic structure had a wall thickness of 7 mm for the ground plate and 5 mm for the wall. All edges were sharp, and the mooring is described and investigated in Gabl et al. [
13]. The cylinder incorporates copper tape wave gauges on the wall and floating balls measured by the motion capturing system for additional measurement of the inside free surface [
17].
The investigation was conducted at the FloWave Ocean Energy Research Facility at The University of Edinburgh, which is a unique round wave tank with a diameter of 25 m and water depth 2 m for the upper test volume. The tank has the capability to reproduce complex wave condition from any direction combined with current [
18,
19,
20,
21].
The movement of the body and the free surface markers (six and three degrees of freedom respectively) was captured using a video motion capture system (
Section 2.2), with twin wire resistance wave gauges measuring the incident wave conditions (
Section 2.3). A trigger signal from the wave-making system was used for data synchronisation.
Figure 1b illustrates the solid ballast configuration on the raised tank floor. This was compared with the fluid case, for which the cylinder was filled with water (
Figure 1c) to give an equivalent draft. This was conducted based on the motion capturing system and allows an accuracy of smaller than 1 mm.
Three different solids (two crosses and a cylinder) were used to give a mass distribution in all three axes comparable to the water-filled case. This simplification has only a very small influence on the results as shown by the comparison presented in Gabl et al. [
13].
Table 1 lists ballast weights as well as the four combinations as tested. These ballast configurations give a wide range of drafts
d (distance between the outside bottom of the cylinder and the still water surface), as determined by the inner water height
h. The capital letter identifies the individual test case.
Table 1 also provides a key between the different drafts and the solid (B, C, D, E) and water (F, G, H, J) ballast options. Letter A was used for the preliminary test to test the position of the wave gauges and wave conditions.Those results are not part of the published dataset. Furthermore, this letter was skipped due to possible confusion. The naming was done according the chronological order of the tests, and it was also used for the provided measurement data. The specific files are described in
Section 3.
2.3. Wave Gauges
As presented in
Figure 1, seven wave gauges (WG) were installed on the tank’s instrumentation gantry. They were aligned with the floating cylinder along the x-axis of the tank, which was the primary wave direction.
Table 2 documents the x-coordinate of each gauge, and
Table 3 provides the basic concept how the distances were chosen. The spacing between the WG was initially defined by a reference value
of 1.27 m (available length in the tank for WG installation divided by 17, which would allow the installation of 16 WG with the same distance). The expected maximum movement of the the floating cylinder in the main wave direction, which is relatively large due to the soft moorings [
13], was limiting for the exact location of the WG close to the cylinder. WG 1 was relatively close to the generating wave-makers, therefore the typical working range is in a radius of 7.5 m from the centre of the tank with a diameter of 25 m. With this chosen set-up of wave gauges, the incoming wave including the reflection at the floating cylinder was documented in a cross section. The wave gauges were calibrated at the beginning of each measurement day covering changes of the water surface of ±10 cm. The accuracy of this measurement system is typically in the order of 1 mm [
17,
22,
23].
In the following section, different analyses of the measured wave gauge data are presented. The analysis starts with the fitting of a sine function to the measurement. Those results are compared to the intended waves sent by the wave-makers. To identify a representative wave height, different combinations of the wave gauges in front of the floating cylinder are investigated. This allows to identify for each of the eight cases a representative wave amplitude.Those values are part of the overview file described in
Section 3.
The following analysis only covers the fully developed oscillation and consequently the first 52 s after the wave-makers start are not included, similarly to the motion analysis [
13]. Only the first 5 s are averaged and used to correct the zero value of each individual WG. The remaining 128 s are split in a different number of equal sub-datasets. A sine function is fitted using a least-squares cost approach, implemented in the MATLAB software package. The quality of each individual result is determined from the order of the local extreme values of the measured values as well as a quality parameter (root-mean-square error (RMSE)). Splitting into 8 constant sections delivered a good result across the investigated frequency spectrum. Splitting into 4, 6, 12, 16 and 24 segments showed no significant changes in the results or higher rate of failure for the fitting either at lower or higher frequencies. The successful fitting for the sub-datasets is averaged to deliver one result for each wave gauge and investigated wave frequency.
In a second step, the fitted sine data is compared to the intended waves. The input values for the wave-makers cover a range of the frequencies
between 0.3 and 1.1 Hz (typical range for FloWave) and a constant amplitude
of 50 mm.
Figure 3 presents, as an example, the differences for the test case B (solid ballast option and maximal draft) for each of the seven WG. Very similar results can be found for all other seven cases. The error bar includes the range of the minimum and maximum of the sine fitting and therefore shows the biggest discrepancy before the averaging of the sub-datasets. In the upper row of the
Figure 3, the difference of the amplitude
is shown. Negative values indicate that the measured values are smaller than the intended wave amplitudes, which occurs for nearly the full frequency spectrum. The biggest differences can be found in the wave gauges WG6 and WG7, which are located behind the floating object near the absorbing wave-maker side. The similar analysis for the frequency shows very small differences
between the sent and measured wave frequency. This indicates that no further analysis for the frequency is needed, and the use of the wave frequency
for the presentation of the data is adequate.
Figure 4 presents different mean values of multiple wave gauges to find a representative amplitude. An average of the signal from the wave gauge in front of the cylinder is applied in the blue line (WG1-5). This value includes the very close WG to the wave-maker as well as the closest to the cylinder. Further combinations are investigated. The differences are relatively small and therefore the mean value of the wave gauges WG2-4 are chosen, which excludes the closest WG to the cylinder and the wave-maker. The minimum and maximum for this combination are also shown as dashed lines in
Figure 4. In the higher frequency spectrum, this leads to obvious differences, which are caused by the fact that the receiving wave paddles struggle to absorb the high frequency waves. For the presented investigation, the peak response for heave and pitch is in a smaller frequency spectrum [
13].
In the last step, all eight investigated test cases (solid and water; four different drafts) of the measured amplitude,
a, are combined together in
Figure 5 in relation to the wave frequency,
. Up to 0.6 Hz, the differences between the variations are small. Parallel to the peak of the motion response of the floating cylinder, a slight increase can be observed in connection with a higher spread of the amplitudes. This indicates that the reflections of the tank as well as the floating cylinder are superimposed on the incoming waves. A reduction of the wave amplitude
a from an initial value of 50 mm to 45 mm appears to be a good approach to represent the incoming wave for a validation simulation. This initial assumption can later be replaced by the full time series of the WG.