Abstract
Validated design tools are one of the key needs for achieving market-competitive levelized cost of energy for wave energy converters (WECs). Sandia National Laboratories recently completed model-scale wave tank tests in the US Navy’s Maneuvering and Sea Keeping (MASK) basin with a point absorber-style WEC. In these tests, the WEC was mounted to the MASK Basin bridge for ease of access and to facilitate thorough investigation of WEC dynamics modelling and control design. In collaboration with Sandia, the University of Texas at Dallas developed coupled models of the dynamics of the Sandia WEC and MASK Basin bridge. Initial modelling efforts focused on developing a simple, but accurate model of the MASK Basin bridge that agrees well with measured modes of vibration and measured static displacement under loading. A coupled dynamics model of the Sandia WEC with the validated bridge model was also developed. This coupled model has been examined to determine the degree of coupling between the dynamic responses of the bridge and WEC. Further, the coupled model is useful in the design of future, safe and well-designed experiments. Additionally, the process of including structural models when considering WEC dynamics and control will become increasingly important for larger scale devices. In this paper, first, the creation and calibration of a simple finite element model of the MASK Basin bridge is described. Next, a spring–mass–damper-inspired WEC model is coupled to the bridge model and the resulting coupled model is mathematically verified and validated against experimental data. Finally, the degree of coupling between the WEC and bridge is quantified, a reduced order model is developed, and linearity of the relationship between the wave input and coupled system output is analyzed.
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Availability of data and materials
The data used to develop and validate the coupled model discussed within this report is from a set of wave tank tests known as MASK2A. This data is not currently publically available. However, data from a later set of tests known as MASK2B is available at https://mhkdr.openei.org/submissions/307. The MASK2B tests supersede the MASK2A tests. The data used to create and validate the bridge model can be found within Appendix C of Coe et al. 2016. The data used to define the spring–mass–damper properties of the Sandia WEC are given within Bacelli et al. 2017.
Code availability
The model discussed within this report was created by the authors using MATLAB and is not available for public use.
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Acknowledgements
Sandia National Laboratories is a multi-mission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-NA0003525. This paper describes objective technical results and analysis. Any subjective views or opinions that might be expressed in the paper do not necessarily represent the views of the U.S. Department of Energy or the United States Government.
Funding
This work was funded by the U.S. Department of Energy’s Water Power Technologies Office.
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LCH primary author, performed majority of modelling and numerical analysis. DTG created bridge finite element model, provided theoretical background and major editing. RGC provided context, funding, data, and minor content editing. GB provided context, funding, and data.
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Appendix
Appendix
1.1 MASK2A trials linearity check
In this section, we perform a brief linearity check on three of the MASK2A datasets. Of the ten total MASK2A trials, trials 002, 003, and 004 all utilized the same waveform (Waveform A). The only difference between these three trials is the gain waveform applied by the heave actuator to excite the WEC (see Table 5). Because the only difference between these trials is their respective gains (i.e., their respective forcing levels) we elected to utilize these three trials to determine whether the system responds linearly to the applied forcing. We began by analysing the heave force to confirm that the heave force is linearly related to the waveform gain. The gain of Trial 002 is 1000. The gain Trial 003 is 1500, 1.5 times the gain of Trial 002. To determine whether the heave force is linearly related to the gain, the heave force from Trial 003 is divided by 1.5. For linearity to hold, the scaled heave force of Trial 003 should be nearly identical to the heave force from Trial 002. Similarly, the gain of Trial 004 is 2000, 2 times that of the gain of Trial 002. If the same procedure is repeated for the heave force of Trial 004, then for linearity to hold, the scaled heave force of Trial 004 should be nearly identical to that of Trial 002. From Fig. 14a, b, it is clear that the heave force is linearly related to the gain of the waveform that is applied.
a Heave force from MASK2A Trials 002, 003, and 004. b Scaled heave forces from MASK2A Trials 002, 003, and 004
This same method of linearity check was applied to both the WEC and bridge accelerations. Figure 15a, b show the results of the linearity check on the filtered WEC acceleration data. While the data of the three trials do align relatively well, indicating that the relationship is near-linear, the motion of the WEC cannot be said to be exactly linearly related to the waveform gain. Figure 16a, b show the results of the linearity check on the moving average of the acceleration data of the bridge. This data is much noisier, so the data is more difficult to analyze. While the peaks of the data appear to be near one another after scaling, it cannot be said that there is a clear linear relationship between the bridge’s acceleration and the gain of the applied waveform. This linearity study is a useful preliminary to help understand the adequacy of linear models of the WEC and bridge structural dynamic behavior.
a WEC acceleration in MASK2A Trials 002, 003, and 004. b Scaled WEC acceleration in MASK2A Trials 002, 003, and 004
a Bridge acceleration in MASK2A Trials 002, 003, and 004. b Scaled bridge acceleration in MASK2A Trials 002, 003, and 004
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Haus, L.C., Griffith, D.T., Coe, R.G. et al. Development and characterization of a coupled structural dynamics model for the Sandia wave energy converter testbed. J. Ocean Eng. Mar. Energy 8, 117–135 (2022). https://doi.org/10.1007/s40722-021-00220-z
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DOI: https://doi.org/10.1007/s40722-021-00220-z