Ocean Energy Systems Wave Energy Modelling Task: Modelling, Verification and Validation of Wave Energy Converters
Abstract
:1. Introduction
1.1. The Background of the OES Wave Energy Conversion Modelling Verification and Validation Task
1.2. Paper Contribution
2. Description of the Numerical Tools
2.1. Linear Models
2.2. Weakly Nonlinear Models
2.3. Fully Nonlinear Models
3. Code-to-Code Comparison of a Heaving Semi-Submerged Sphere
3.1. Decay Tests
3.2. Regular Waves
3.3. Irregular Waves
4. Validation Using Existing Experimental Data of a Heaving Float
4.1. Decay Tests
4.2. Radiation Tests
4.3. Diffraction Tests
4.4. Regular Waves
5. Discussion
6. Conclusions
Author Contributions
Funding
Conflicts of Interest
Abbreviations
BEM | boundary element method |
CFD | computational fluid dynamics |
DFS | direct finite element simulation |
FEM | finite element method |
FK | Froude–Krylov |
FNPF | fully nonlinear potential flow |
FVM | finite volume method |
IEA | International Energy Agency |
iLES | implicit large eddy simulation |
IRF | impulse response function |
LCOE | levelized cost of energy |
LS | level set |
OES | Ocean Energy Systems |
PSD | power spectral density |
PTO | power take off |
RAO | response amplitude operator |
RK4 | 4th-order Runge–Kutta |
SS | state space |
SWL | still water level |
URANS | unsteady Reynolds-averaged Navier–Stokes |
VOF | volume of fluid |
WE | wave elevation |
WEC | wave energy converter |
WEMT | Wave Energy Modelling Task |
WS | wave spectrum |
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Participant | Model Name | Frad | Fexc | BEM | Time Integration | Comments |
---|---|---|---|---|---|---|
AAU | - | IRF | WE | WAMIT | RK4-0.01 s (fixed) | IRFs are precalculated, with a 0.01 rad/s frequency resolution, and only values for t < 20 s are used |
DSA | ProteusDS | IRF | WS | NEMOH | RK4-0.01 s (fixed) | - |
DTU | DTUMotion-Simulator | IRF | WS | WAMIT | RK4-0.01 s (fixed) | Radiation IRFs are computed from the Fast Cosine Transform of the damping coefficients, then interpolated to the incident wave time-step size. |
ECN | - | SS | WE | NEMOH | RK4 (adaptive) | - |
EDRMedeso | ANSYS-Aqwa | IRF | WE | ANSYS-Aqwa | Semi-implicit predictor–corrector scheme, dt = 0.01 s | The term ANSYS Aqwa covers both model name and BEM. |
FPP | FPP-Lin | SS | WE | WAMIT | RK4 (adaptive) | Radiation transfer functions are fitted in the frequency domain to the WAMIT data using the Matlab function invfreq. |
Glosten | Python Time-Domain Simulator | IRF | WE | WAMIT | RK4-0.01 s (fixed) | - |
HNEI | WEC-Sim | IRF | WS | WAMIT | RK4-0.01 s (fixed) | - |
INNOSEA | InWave | IRF | WS | Adams–Moulton adaptive time-step solver, dt = 0.01 s | - | |
KRISO | KIMAPS | IRF | AdFLOW | RK4-0.01 s (fixed) | - | |
MARIN | aNySIM | IRF | DIFFRAC | RK4-0.01 s (fixed) | The excitation force was calculated from DIFFRAC wave force RAOs multiplied with wave amplitudes and phase shifted with wave phase for irregular waves. | |
Navatek | Aegir | - | WE | RK4-0.01 s (fixed) | The radiation force was calculated from a purely time-domain approach using a high-order BEM. | |
NREL and Sandia | WEC-Sim | IRF | WS | WAMIT | RK4-0.01 s (fixed) | IRF values for t < 60 s are used |
SAGA | WEC-Sim | IRF | WE | NEMOH | RK4-0.01 s (fixed) | IRF values for t < 19 s are used |
Tecnalia | - | IRF | WS | WAMIT | RK4-0.01 s (fixed) | - |
UCC | SIM-UCC | IRF | WS | WAMIT | RK4-0.01 s (fixed) | Includes nonlinear restoring forces. |
WavEC | WavEC2Wire | SS | WE | WAMIT | RK4 (adaptive) | - |
Wave Venture | WV Daemon | IRF | WS | WAMIT | 0.01 s | - |
Participant | Wave Theory | Nonlinear Force Calculation |
---|---|---|
COER | Airy + Wheeler | Linear radiation and diffraction + algebraic (mesh-less and computationally efficient) nonlinear FK, computed with respect to the instantaneous wetted surface |
DSA | Airy + Wheeler | Standard |
DTU | Airy + Wheeler | Standard |
ECN | Fenton–Rienecker | BEM with linear triangular elements + fluid structure interaction computed through acceleration potential |
ERMedeso | Airy + Wheeler | Standard |
HNEI | Airy + Wheeler | Standard |
INNOSEA | Standard | |
MARIN | Airy + Wheeler | Standard |
Navatek | Airy + Wheeler | Standard |
NREL and Sandia | Airy + Wheeler | Standard (with 1000 triangular panels) |
WavEC | Airy + Wheeler | Standard |
Wave Venture | Airy + Wheeler | Standard |
Participant | Wave Theory | Model Type | Turbulence Mmodel | Time Step | Numbers of Elements |
---|---|---|---|---|---|
CTH | SHIPFLOW-Motions | FNPF/BEM | inviscid | 0.01 s | 1600 on body, 2000 on free surface |
EDRMedeso | ANSYS Fluent | URANS/FVM/VOF | laminar | dt = 0.02 s (adaptive) | 8.6 × 106 nodes, symmetry condition |
KTH-BCAM | Unicorn-FEniCS-HPC | DFES/FEM/LS | iLES | 0.8 × 106 cells | |
NREL and SNL | StarCCM + | URANS/FVM/VOF | k-ω SST | 0.01–0.015 s | - |
RISE | OpenFOAM-v1712 | URANS/FVM/VOF | k-ω SST | CFL = 0.5 | ~1 × 106 cells |
SSPA | LEMMA-ANANAS | URANS/FVM/LS | Spalart-Allmaras | - | 16 × 106 cells, symmetry condition |
UoP | OpenFOAM-4.1 | URANS/FVM/VOF | laminar | CFL = 0.5 | ~8 × 106 cells, symmetry condition |
T (s) | 3.0 | 4.0 | 5.0 | 6.0 | 7.0 | 8.0 | 9.0 | 10.0 | 11.0 |
---|---|---|---|---|---|---|---|---|---|
H (m) | 0.833 | 1.570 | 1.899 | 2.453 | 3.532 | 4.807 | 7.946 | 9.810 | 11.870 |
S (-) | PTO Damping (Ns/m) | ||
---|---|---|---|
6.2 | 1.0 | 0.0026 | 398,736.034 |
4.4 | 0.5 | 0.0026 | 118,149.758 |
15.4 | 11.0 | 0.0047 | 90,080.857 |
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Wendt, F.; Nielsen, K.; Yu, Y.-H.; Bingham, H.; Eskilsson, C.; Kramer, M.; Babarit, A.; Bunnik, T.; Costello, R.; Crowley, S.; et al. Ocean Energy Systems Wave Energy Modelling Task: Modelling, Verification and Validation of Wave Energy Converters. J. Mar. Sci. Eng. 2019, 7, 379. https://doi.org/10.3390/jmse7110379
Wendt F, Nielsen K, Yu Y-H, Bingham H, Eskilsson C, Kramer M, Babarit A, Bunnik T, Costello R, Crowley S, et al. Ocean Energy Systems Wave Energy Modelling Task: Modelling, Verification and Validation of Wave Energy Converters. Journal of Marine Science and Engineering. 2019; 7(11):379. https://doi.org/10.3390/jmse7110379
Chicago/Turabian StyleWendt, Fabian, Kim Nielsen, Yi-Hsiang Yu, Harry Bingham, Claes Eskilsson, Morten Kramer, Aurélien Babarit, Tim Bunnik, Ronan Costello, Sarah Crowley, and et al. 2019. "Ocean Energy Systems Wave Energy Modelling Task: Modelling, Verification and Validation of Wave Energy Converters" Journal of Marine Science and Engineering 7, no. 11: 379. https://doi.org/10.3390/jmse7110379
APA StyleWendt, F., Nielsen, K., Yu, Y. -H., Bingham, H., Eskilsson, C., Kramer, M., Babarit, A., Bunnik, T., Costello, R., Crowley, S., Gendron, B., Giorgi, G., Giorgi, S., Girardin, S., Greaves, D., Heras, P., Hoffman, J., Islam, H., Jakobsen, K. -R., ... Yasutaka, I. (2019). Ocean Energy Systems Wave Energy Modelling Task: Modelling, Verification and Validation of Wave Energy Converters. Journal of Marine Science and Engineering, 7(11), 379. https://doi.org/10.3390/jmse7110379