Comparison of Wave Energy Park Layouts by Experimental and Numerical Methods
Abstract
:1. Introduction
2. Theory and Numerical Model
Mathematical Model
3. Physical Experiments
3.1. Wave Tank
3.2. Experimental Set-Up
3.3. Tests
3.4. Array Layouts
4. Simulations
5. Results and Discussion
5.1. Power Output
5.2. q-Factor
6. Conclusions
6.1. Performances of Different Array Layouts under Several Wave Conditions
6.2. Comparison of Simulation Optimization Predictions with Experimental Data
- The experimental data show that in regular waves and for the PTO damping used, the power obtained from the float and the PTO motion is the same, so the assumption of a stiff line is valid. In the irregular waves, however, the WEC shows clear two-body dynamics with different displacement of the float and the PTO due to slack and elasticity in the connection line. As a result, the power obtained from the float and the PTO can differ significantly, and the assumption no longer holds. The virtual power obtained from the float’s motion is in this case higher than the actual power obtained from the PTO; in other words, if a stiff connection between the float and the PTO were to be assumed, the predicted power would be higher than the one that will be obtained in reality. This is confirmed by comparing the power computed in the simulations (which assume a stiff line) with the experimental data: the simulations generally overestimate the absorbed power by the PTO. This conclusion holds both for the total power of the park (Figure 7) and for the power absorbed by the individual buoys (Figure 8).
- The results from the simple one-DoF simulation model are able to reproduce the qualitative behavior of the absorbed power at least to an approximate degree (Figure 7 and Figure 10), as long as non-linear dynamics such as Mathieu instabilities are not present. In the experiments, Mathieu instabilities mostly occurred in some of the regular wave cases; hence, in realistic, irregular waves, the simulations can give an estimation of the power output of the UU WEC. In summary, in the wave conditions wherein we neither observe extensive sway nor non-linear behavior, the results of the optimization are reliable. However, when non-linear dynamics or motions in multiple degrees of freedom are present, then the optimization routine does not provide accurate results. In other words, the discrepancy between the experimental and numerical results is mostly due to either slack line condition (mostly in irregular waves) or Mathieu-type instability (mostly in regular waves). In addition, losses, friction and reflections in the wave tank, and other sources of uncertainty in the experimental set-up, also play roles in the outcome of the present study.
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Nomenclature
Numerical model: | |
buoy position in surge | |
buoy position in sway | |
buoy position in heave | |
PTO position | |
PTO damping | |
WEC power output (ith WEC) | |
park power output | |
Experimental data: | |
buoy position in surge measured by the optical system | |
buoy position in sway measured by the optical system | |
buoy position in heave measured by the optical system | |
buoy position along the connection line calculated from the optical measurements | |
PTO damping | |
WEC experimental PTO power output | |
park experimental PTO power output | |
WEC experimental virtual power output computed from the buoy motion along the connection line | |
park experimental virtual power output computed from the buoy motion along the connection line |
Abbreviations
DoF | Degrees of freedom |
IW | Irregular wave |
LG | Linear generator |
PTO | Power take-off |
RW | Regular wave |
UU | Uppsala University |
WEC | Wave energy converter |
Appendix A
Appendix A.1. WEC’s Power Output
Appendix A.2. WEC’s q-Factor
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Regular Waves | ||||||
---|---|---|---|---|---|---|
Scale 1:10 | Full scale | |||||
T | Run time | T | Run time | |||
Wave ID | [m] | [s] | [min] | [m] | [s] | [min] |
RW1 | 0.124 | 1.11 | 1.8 | 1.24 | 3.5 | 5.8 |
RW2 | 0.124 | 1.42 | 2.4 | 1.24 | 4.5 | 7.5 |
RW3 | 0.124 | 1.74 | 2.9 | 1.24 | 5.5 | 9.2 |
RW4 | 0.124 | 2.06 | 3.4 | 1.24 | 6.5 | 10.8 |
RW5 | 0.124 | 2.37 | 4.0 | 1.24 | 7.5 | 12.5 |
Irregular Waves | ||||||
Scale 1:10 | Full scale | |||||
Run time | Run time | |||||
Wave ID | [m] | [s] | [min] | [m] | [s] | [min] |
IW1 | 0.175 | 1.11 | 6 | 1.75 | 3.5 | 20 |
IW2 | 0.175 | 1.42 | 6 | 1.75 | 4.5 | 20 |
IW3 | 0.175 | 1.74 | 6 | 1.75 | 5.5 | 20 |
IW4 | 0.175 | 2.06 | 6 | 1.75 | 6.5 | 20 |
IW5 | 0.175 | 2.37 | 6 | 1.75 | 7.5 | 20 |
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Giassi, M.; Engström, J.; Isberg, J.; Göteman, M. Comparison of Wave Energy Park Layouts by Experimental and Numerical Methods. J. Mar. Sci. Eng. 2020, 8, 750. https://doi.org/10.3390/jmse8100750
Giassi M, Engström J, Isberg J, Göteman M. Comparison of Wave Energy Park Layouts by Experimental and Numerical Methods. Journal of Marine Science and Engineering. 2020; 8(10):750. https://doi.org/10.3390/jmse8100750
Chicago/Turabian StyleGiassi, Marianna, Jens Engström, Jan Isberg, and Malin Göteman. 2020. "Comparison of Wave Energy Park Layouts by Experimental and Numerical Methods" Journal of Marine Science and Engineering 8, no. 10: 750. https://doi.org/10.3390/jmse8100750
APA StyleGiassi, M., Engström, J., Isberg, J., & Göteman, M. (2020). Comparison of Wave Energy Park Layouts by Experimental and Numerical Methods. Journal of Marine Science and Engineering, 8(10), 750. https://doi.org/10.3390/jmse8100750