Numerical and Experimental Modelling of a Wave Energy Converter Pitching in Close Proximity to a Fixed Structure
Abstract
:1. Introduction
2. Research Question
3. Numerical Model Description
3.1. Geometry Definition
3.2. Equation of Motion
3.3. Model Versions
3.3.1. Water Surface Elevation:
3.3.2. Radiation Moment:
3.3.3. Hydrostatic Moment:
Linear Hydrostatic Moment
Gravity Moment, :
Buoyancy Moment, :
3.3.4. Excitation Moment:
Froude-Krylov, :
Scattering Moment:, :
Implementation of Measured Water Surface Elevation
3.3.5. Quadratic Drag Moment:
- (a)
- Exact formulation of quadratic drag forcesThe quadratic force opposes the velocity of the WEC. To select which submerged panels contribute to the quadratic drag force the condition that has to be met is that the angle defined by the panel normal vector and the panel velocity vector is less than 90 degrees. A quadratic drag force in the translational modes can be implemented as follows,At , the angles of inclination of the WEC are known at and at the previous time step . These angles are used to calculate the instantaneous location of the centroids of the panels (see Section 3.1) at and . The cartesian coordinates defining these positions are used to calculate the translational panel velocities using the following equation.For heading waves the fluid velocity in the y direction is , and the horizontal and vertical velocity components are given by:The corresponding moments in roll, pitch and yaw are
- (b)
- Approximated formulation of quadratic drag forcesIn order to simplify and improve the computational efficiency, three simplifications to Equation (22) are applied. The first simplification is that the instantaneous submerged body surface area is approximated by single flat panel (Figure 4). The second simplification is that the fluid velocity is neglected. The third simplification is that the drag forces are only computed when the WEC is pitching clockwise (when the WEC rotates in the opposite direction the projected area is small hence the quadratic drag forces can be neglected).Applying these three simplifications, Equation (22) reduces to,
3.3.6. Friction in the Bearings,
3.3.7. Numerical Model Solver
4. Wave Basin Experiments
4.1. Laboratory Setup
4.2. Wave Basin Experimental Data
4.2.1. Undisturbed Waves
- Waves are generated and measured in the basin without the WEC in place (undisturbed waves) using the software “Awasys” from Aalborg University, including active absorption.
- A non-linear wave analysis is performed to separate incident and reflected waves using the software “WaveLab” from Aalborg University [28]. WaveLab takes into account the propagation speed of the waves in a non-linear manner.
- The same waves are then repeated with the device in position.
4.2.2. Slow-Motion Experiments
4.2.3. Decay Tests
4.2.4. Fixed WEC Experiments
4.2.5. Regular Waves
4.2.6. Free Motion in Regular Waves
4.2.7. Quadratic Drag Moment
5. Results
5.1. Wave Reflections and Repeatability
5.2. Modelling of Hydrostatics and Friction
5.3. Decay Tests Simulations
5.4. Wave Excitation
5.5. Free motion in Regular Waves
6. Discussion
7. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Semisubmersible | WEC | WEC Scale Model | |||||
---|---|---|---|---|---|---|---|
Length main body | 86.5 m | Length main body | 10.8 m | Length main body | 343.5 mm | ||
Length hinged arms | 99.3 m | Width | 18.3 m | Width | 1105.0 mm | ||
Width | 36.0 m | Height | 11.0 m | Height | 423.0 mm | ||
Height | 25.0 m | Length hinged arms | 6.2 m | Length hinged arms | 228.5 mm | ||
Water depth | >45.0 m | Water depth | 650.0 mm |
Wave condition | R01 | R02 | R03 | R04 | R05 | R06 | R07 | R08 |
(s) | 2.500 | 2.000 | 1.667 | 1.429 | 1.250 | 1.176 | 1.111 | 1.053 |
(m) | 0.019 | 0.020 | 0.019 | 0.019 | 0.019 | 0.019 | 0.020 | 0.021 |
Wave condition | R09 | R10 | R11 | R12 | R13 | R14 | R15 | R16 |
(s) | 1.000 | 0.952 | 0.909 | 0.870 | 0.833 | 0.769 | 0.714 | 0.667 |
(m) | 0.021 | 0.023 | 0.021 | 0.022 | 0.021 | 0.021 | 0.023 | 0.023 |
Wave condition | R09 | R17 | R18 | R19 | R20 |
(s) | 1.00 | 0.95 | 0.98 | 0.99 | 0.98 |
(m) | 0.042 | 0.020 | 0.059 | 0.076 | 0.092 |
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Heras, P.; Thomas, S.; Kramer, M.; Kofoed, J.P. Numerical and Experimental Modelling of a Wave Energy Converter Pitching in Close Proximity to a Fixed Structure. J. Mar. Sci. Eng. 2019, 7, 218. https://doi.org/10.3390/jmse7070218
Heras P, Thomas S, Kramer M, Kofoed JP. Numerical and Experimental Modelling of a Wave Energy Converter Pitching in Close Proximity to a Fixed Structure. Journal of Marine Science and Engineering. 2019; 7(7):218. https://doi.org/10.3390/jmse7070218
Chicago/Turabian StyleHeras, Pilar, Sarah Thomas, Morten Kramer, and Jens Peter Kofoed. 2019. "Numerical and Experimental Modelling of a Wave Energy Converter Pitching in Close Proximity to a Fixed Structure" Journal of Marine Science and Engineering 7, no. 7: 218. https://doi.org/10.3390/jmse7070218