Comparative Study on the Performances of a Hinged Flap-Type Wave Energy Converter Considering Both Fixed and Floating Bases
Abstract
:1. Introduction
2. Mathematical Modeling
2.1. Frequency Domain Hydrodynamics
2.2. Hinged Motion of Floating Multi-Body Geometries
2.3. WEC Power Generation Evaluation
3. Hydrodynamic Modeling and Analysis
3.1. WEC and Multi-Body Geometries
3.2. Multi-Body Hydrodynamic Analysis
4. Power Optimization Based on the Frequency Domain Model
4.1. Verification of the Multi-Body Formulation
4.2. Natural Period Optimization
4.3. Optimal Damping Optimization
4.4. Comparative Optimization of Power Generation
4.5. Wave Absorbed Power Optimization
5. Conclusions
- (1)
- The effects of hydrodynamic interaction in the hybrid configuration can be neglected for the floating platform. It has a great influence on the flap-type WEC; the resonant behavior is small in the mode of heave but much more significant in the modes of surge and pitch, especially at high frequencies. Even if the gap between the two floating bodies considered is not a regular rectangle, the resonant modes in Equation (5) and the observed resonance frequencies are still consistent at the high frequency.
- (2)
- With an increase in density, the natural period of the flap-type WEC increases for both single-flap and FWFP configurations. The natural frequencies also increase with Kpto. The observed trends are rather smooth for the single-flap WEC, mainly due to the smooth behavior of the hydrodynamic coefficients of the WEC. The natural frequencies of the flap-type WEC in the FWFP configuration present a similar trend; the natural period of the flap-type WEC when in the FWFP configuration normally relates in a nonlinear way with an increase in the Kpto parameter. However, due to the hydrodynamic interaction between the different floating bodies, WECs’ added mass and damping oscillate at the wave periods around 2~4 s and that is reflected in the natural period of the WEC when modifying the PTO parameters around the same wave periods.
- (3)
- The flap-type WEC considered in this paper has a high capture width in the range of a 4~6 s wave period. However, after it is combined with the floating platform, there is a main wave frequency where the WEC is capturing a significant amount of wave energy, which is due to the multi-body coupling and shifts the peak of absorbed power to a higher frequency. Due to the influences of the floating platform, the WEC presents a small peak at around a 7~10 s wave period. In addition, under the same Bpto parameters, the higher the WEC density, the higher the capture width at low frequencies.
- (4)
- The parameter optimization results obtained are mostly applicable to the different working conditions considered, for both the natural period optimization and optimal damping method. Although the single-flap WEC and the flap-type WEC in the FWFP present quite different responses in the frequency domain regarding wave power generation, the expected amount of wave absorbed power is actually similar when employed at the same operation site in the South China Sea.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Nomenclature
Total velocity potential [-] | Capture width [-] | ||
Incident potential [-] | The width of the flap-type WEC [m] | ||
Diffraction potential [-] | Incident wave energy in a unit-width sectional area [W] | ||
Radiation potential [-] | The acceleration of gravity [m/s2] | ||
Complex wave excitation force [N] | Wave amplitude [m] | ||
Added mass coefficient matrix [-] | Wave number [-] | ||
Radiation damping coefficient matrix [-] | Water depth [m] | ||
Water density | Incident wave speed [m/s] | ||
The wet surface of the floating body [m2] | Wave spectral density function [-] | ||
The gap between two floating bodies [m] | Significant wave height [m] | ||
The wavelength associated with the resonant mode [-] | Peak enhancement factor [-] | ||
Frequency domain response amplitude operator matrix [-] | Wave peak period [s] | ||
Rigid-body mass-inertia matrix [-] | Wave frequency [rad/s] | ||
Hydrodynamic restoring matrix [-] | Peak shape parameter [-] | ||
Local coordinate system [-] | Expected power [W] | ||
Global coordinate system [-] | The occurrence probability of each frequency [-] | ||
Transpose matrix [-] | The average wave height of each frequency [m] | ||
,, | The unit vectors of the local articulation axes with respect to the global axes [-] | Abbreviations | |
The boundary condition of the constraint matrix [-] | FOWT | Floating offshore wind turbine | |
Complex wave excitation force matrix [-] | STC | Spar–torus combination | |
Frequency domain RAO matrix in constrained multi-body configurations [-] | WEC | Wave energy converter | |
Constraint reaction force/moment matrix acting on the structure at the articulation axes | OWC | Oscillating water column | |
Total stiffness matrixes [-] | PTO | Power take-off | |
Equivalent stiffness matrix of the PTO [-] | FWFP | Floating wind-flap platform | |
Equivalent damping matrix of the PTO [-] | RAO | Response amplitude operator | |
Frequency domain average power generation [W] | DOF | Degrees of freedom | |
Natural period [s] | PSD | Power spectrum density | |
Natural frequency [rad/s] |
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Designation, Parameter (Unit) | Value |
---|---|
Width, W (m) | 12 |
Height, h (m) | 6 |
Thickness, t (m) | 1.8 |
Density, ρ (t/m3) | 0.3/0.4/0.5/0.6 |
Designation (Unit) | Value |
---|---|
Total draft (m) | 20 |
Elevation of main column above SWL (m) | 10 |
Elevation of offset column above SWL (m) | 12 |
Spacing between offset columns (m) | 50 |
Height of upper columns (m) | 26 |
Height of base columns (m) | 6 |
Depth to top of base columns below SWL (m) | 14 |
Diameter of main column (m) | 6.5 |
Diameter of offset columns (m) | 12 |
Diameter of base columns (m) | 24 |
Displacement of platform (t) | 1.34 × 104 |
CoG location below SWL (m) | 13.46 |
Case | Density (t/m3) | Kpto (N·m/rad) | Natural Period of Single-Flap WEC (s) | Natural Period of WEC in FWFP (s) |
---|---|---|---|---|
1 | 0.3 | 2 × 107 | 4.62 | 4.64 |
2 | 0.4 | 4 × 107 | 4.56 | 4.64 |
3 | 0.5 | 5 × 107 | 4.62 | 4.54 |
4 | 0.6 | 6 × 107 | 4.74 | 4.35 |
Case | Density (t/m3) | Kpto (Nm/rad) | Bpto of Single-Flap WEC (Nm/(rad/s)) | Bpto of WEC in FWFP (Nm/(rad/s)) |
---|---|---|---|---|
LC1 | 0.3 | 3 × 107 | 2.5 × 108 | 3.9 × 107 |
LC2 | 0.3 | 2 × 107 | 3.7 × 108 | 3.4 × 107 |
LC3 | 0.3 | 1 × 107 | 3.6 × 108 | 3.8 × 107 |
LC4 | 0.4 | 5 × 107 | 2.4 × 108 | 5.1 × 107 |
LC5 | 0.4 | 4 × 107 | 3.5 × 108 | 4.9 × 107 |
LC6 | 0.4 | 3 × 107 | 4.0 × 108 | 4.7 × 107 |
LC7 | 0.5 | 6 × 107 | 2.8 × 108 | 7.1 × 107 |
LC8 | 0.5 | 5 × 107 | 4.0 × 108 | 6.8 × 107 |
LC9 | 0.5 | 4 × 107 | 3.9 × 108 | 6.1 × 107 |
LC10 | 0.6 | 7 × 107 | 3.8 × 108 | 9.2 × 107 |
LC11 | 0.6 | 6 × 107 | 4.0 × 108 | 8.5 × 107 |
LC12 | 0.6 | 5 × 107 | 3.4 × 108 | 4.4 × 107 |
Wave Average Period (Tav, s) | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
Significant Wave Height (Hs, m) | 1.5 | 3.5 | 4.5 | 5.5 | 6.5 | 7.5 | 8.5 | 9.5 | 10.5 | 11.5 | 12.5 | |
7.5 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
6.5 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 0.002% | 9 0.014% | 2 0.003% | 0 | |
5.5 | 0 | 0 | 0 | 0 | 0 | 0 | 28 0.044% | 54 0.084% | 24 0.037% | 1 0.002% | 0 | |
4.5 | 0 | 0 | 0 | 0 | 0 | 50 0.078% | 373 0.581% | 240 0.374% | 37 0.058% | 7 0.011% | 0 | |
3.5 | 0 | 0 | 0 | 0 | 163 0.254% | 1317 2.051% | 950 1.480% | 436 0.679% | 84 0.134% | 0 | 0 | |
2.5 | 0 | 0 | 0 | 874 1.361% | 4743 7.387% | 2891 4.502% | 1459 2.272% | 546 0.850% | 56 0.084% | 0 | 0 | |
1.5 | 0 | 19 0.030% | 3720 5.793% | 9300 14.484% | 5011 7.804% | 2925 4.555% | 1131 1.761% | 149 0.232% | 7 0.011% | 1 0.002% | 0 | |
0.5 | 531 0.827% | 4859 17.597% | 11,299 17.597% | 6525 10.162% | 3159 4.920% | 997 1.553% | 189 0.294% | 38 0.059% | 3 0.005% | 2 0.003% | 0 |
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Chen, M.; Yun, Q.; Hallak, T.S.; Zhou, H.; Zhang, K.; Yang, Y.; Tao, T.; Liu, S.; Jiang, W.; Li, C. Comparative Study on the Performances of a Hinged Flap-Type Wave Energy Converter Considering Both Fixed and Floating Bases. J. Mar. Sci. Eng. 2024, 12, 1416. https://doi.org/10.3390/jmse12081416
Chen M, Yun Q, Hallak TS, Zhou H, Zhang K, Yang Y, Tao T, Liu S, Jiang W, Li C. Comparative Study on the Performances of a Hinged Flap-Type Wave Energy Converter Considering Both Fixed and Floating Bases. Journal of Marine Science and Engineering. 2024; 12(8):1416. https://doi.org/10.3390/jmse12081416
Chicago/Turabian StyleChen, Mingsheng, Qihao Yun, Thiago S. Hallak, Hao Zhou, Kai Zhang, Yi Yang, Tao Tao, Shi Liu, Wei Jiang, and Changjie Li. 2024. "Comparative Study on the Performances of a Hinged Flap-Type Wave Energy Converter Considering Both Fixed and Floating Bases" Journal of Marine Science and Engineering 12, no. 8: 1416. https://doi.org/10.3390/jmse12081416