# Experimental Investigation of the Flow Field in the Vicinity of an Oscillating Wave Surge Converter

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## Abstract

**:**

## 1. Introduction

## 2. Experimental Setup and Procedures

#### 2.1. Wave Flume

#### 2.2. OWSC Model

#### 2.3. Full Experimental Setup and Instrumentation

#### 2.4. Data Collection

#### 2.5. Repeatability of Experimental Tests

#### 2.6. Data Analysis

## 3. Laboratory Evidence and Linear Wave Theory

#### 3.1. Dynamic Equilibrium

#### 3.2. Hydrodynamic Torque: Experimental and Analytical Results

#### 3.3. Dynamics of OWSC: Comparison between Experimental and Analytical Results

## 4. Mean and Turbulent Flow Field in Front of the OWSC

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

OWSC | oscillating wave surge converter |

PTO | power take-off |

UVP | ultrasonic velocity profiler |

WP | wave probe |

UP | ultrasonic velocity profiler probe |

RO | rated output |

PPR | pulses per revolution |

## Appendix A. Analytical Hydrodynamic Parameters

## Appendix B. Friction Force Model

## References

- Folley, M.; Whittaker, T.; Osterried, M. The Oscillating Wave Surge Converter. In Proceedings of the Fourteenth International Offshore and Polar Engineering Conference, Toulon, France, 23–28 May 2004. [Google Scholar]
- Whittaker, T.; Folley, M. Nearshore oscillating wave surge converters and the development of Oyster. Philos. Trans. R. Soc. Math. Phys. Eng. Sci.
**2012**, 370, 345–364. [Google Scholar] [CrossRef] [Green Version] - Lucas, J.; Livingstone, M.; Vuorinen, N.; Cruz, J. Development of a wave energy converter (WEC) design tool—Application to the WaveRoller WEC including validation of numerical estimates. In Proceedings of the Fourth International Conference on Ocean Energy, Dublin, Ireland, 17 October 2012. [Google Scholar]
- Schmitt, P.; Asmuth, H.; Elsäßer, B. Optimising power take-off of an oscillating wave surge converter using high fidelity numerical simulations. Int. J. Mar. Energy
**2016**, 16, 196–208. [Google Scholar] [CrossRef] [Green Version] - Renzi, E.; Doherty, K.; Henry, A.; Dias, F. How does Oyster work? The simple interpretation of Oyster mathematics. Eur. J. Mech.-B/Fluids
**2014**, 47, 124–131. [Google Scholar] [CrossRef] [Green Version] - Whittaker, T.; Collier, D.; Folley, M.; Osterried, M.; Henry, A.; Crowley, M. The development of Oyster—A shallow water surging wave energy converter. In Proceedings of the 7th Annual European Wave & Tidal Energy Conference, Porto, Portugal, 11–13 September 2007. [Google Scholar]
- Brito, M.; Teixeira, L.; Canelas, R.B.; Ferreira, R.M.L.; Neves, M.G. Experimental and Numerical Studies of Dynamic Behaviors of a Hydraulic Power Take-Off Cylinder Using Spectral Representation Method. J. Tribol.
**2017**, 140, 021102. [Google Scholar] [CrossRef] - Brito, M.; Ferreira, R.M.; Teixeira, L.; Neves, M.G.; Canelas, R.B. Experimental investigation on the power capture of an oscillating wave surge converter in unidirectional waves. Renew. Energy
**2020**, 151, 975–992. [Google Scholar] [CrossRef] - Gomes, R.; Lopes, M.; Henriques, J.; Gato, L.; Falcão, A. The dynamics and power extraction of bottom-hinged plate wave energy converters in regular and irregular waves. Ocean. Eng.
**2015**, 96, 86–99. [Google Scholar] [CrossRef] - Parsons, N.F.; Martin, P.A. Scattering of water waves by submerged plates using hypersingular integral equations. Appl. Ocean. Res.
**1992**, 14, 313–321. [Google Scholar] [CrossRef] - Parsons, N.F.; Martin, P.A. Scattering of water waves by submerged curved plates and by surface-piercing flat plates. Appl. Ocean. Res.
**1994**, 16, 129–139. [Google Scholar] [CrossRef] - Parsons, N.F.; Martin, P.A. Trapping of water waves by submerged plates using hypersingular integral equations. J. Fluid Mech.
**1995**, 284, 359. [Google Scholar] [CrossRef] [Green Version] - Evans, D.; Porter, R. Hydrodynamic characteristics of a thin rolling plate in finite depth of water. Appl. Ocean. Res.
**1996**, 18, 215–228. [Google Scholar] [CrossRef] - Renzi, E.; Dias, F. Resonant behavior of an oscillating wave energy converter in a channel. J. Fluid Mech.
**2012**, 701, 482–510. [Google Scholar] [CrossRef] [Green Version] - Renzi, E.; Dias, F. Relations for a periodic array of flap-type wave energy converters. Appl. Ocean. Res.
**2013**, 39, 31–39. [Google Scholar] [CrossRef] [Green Version] - Renzi, E.; Dias, F. Hydrodynamics of the oscillating wave surge converter in the open ocean. Eur. J. Mech.-B/Fluids
**2013**, 41, 1–10. [Google Scholar] [CrossRef] [Green Version] - Falcão, A.F. Wave energy utilization: A review of the technologies. Renew. Sustain. Energy Rev.
**2010**, 14, 899–918. [Google Scholar] [CrossRef] - Folley, M.; Whittaker, T.; Henry, A. The effect of water depth on the performance of a small surging wave energy converter. Ocean. Eng.
**2007**, 34, 1265–1274. [Google Scholar] [CrossRef] - Henry, A. The Hydrodynamics of Small Seabed Mounted Bottom Hinged Wave Energy Converters in Shallow Water. Ph.D. Thesis, Queen’s University Belfast, Belfast, UK, 2009. [Google Scholar]
- Henry, A.; Folley, M.; Whittaker, T. A conceptual model of the hydrodynamics of an oscillating wave surge converter. Renew. Energy
**2018**, 118, 965–972. [Google Scholar] [CrossRef] - Lin, C.C.; Chen, J.H.; Chow, Y.C.; Tzang, S.Y.; Hou, S.J.; Wang, F.Y. The Experimental Investigation of the Influencing Parameters of Flap Type Wave Energy Converters. In Proceedings of the 4th International Conference on Ocean Energy, Dublin, Ireland, 17–19 October 2012. [Google Scholar]
- Schmitt, P.; Bourdier, S.; Sarkar, D.; Renzi, E.; Dias, F.; Doherty, K.; Whittaker, T.; van’t Hoff, J. Hydrodynamic Loading on a Bottom Hinged Oscillating Wave Surge Converter. In Proceedings of the Twenty-second International Offshore and Polar Engineering Conference, Rhodes, Greece, 17–22 June 2012. [Google Scholar]
- Henry, A.; Kimmoun, O.; Nicholson, J.; Dupont, G.; Wei, Y.; Dias, F. A Two Dimensional Experimental Investigation of Slamming of an Oscillating Wave Surge Converter. In Proceedings of the Twenty-fourth International Ocean and Polar Engineering Conference, Busan, Korea, 15–20 June 2014. [Google Scholar]
- Henry, A.; Rafiee, A.; Schmitt, P.; Dias, F.; Whittaker, T. The Characteristics of Wave Impacts on an Oscillating Wave Surge Converter. J. Ocean. Wind. Energy
**2014**, 1, 101–110. [Google Scholar] - Andersen, T.L.; Frigaard, P. Wave Generation in Physical Models: Technical Documentation for AwaSys 6; Department of Civil Engineering, Aalborg University: Aalborg, Denmark, 2014. [Google Scholar]
- Count, B.M.; Evans, D.V. The influence of projecting sidewalls on the hydrodynamic performance of wave-energy devices. J. Fluid Mech.
**1984**, 145, 361–376. [Google Scholar] [CrossRef] - Mansard, E.; Funke, E. The Measurement of Incident and Reflected Spectra Using a Least Squares Method. In Coastal Engineering; American Society of Civil Engineers (ASCE): Reston, VA, USA, 1980. [Google Scholar] [CrossRef] [Green Version]
- Sarmento, A.J.N.A. Wave flume experiments on two-dimensional oscillating water column wave energy devices. Exp. Fluids
**1992**, 12, 286–292. [Google Scholar] [CrossRef] - Met-Flow. UVP Monitor User’s Guide; Met-Flow S.A.: Lausanne, Switzerland, 2002. [Google Scholar]
- Lemmin, U.; Rolland, T. Acoustic Velocity Profiler for Laboratory and Field Studies. J. Hydraul. Eng.
**1997**, 123, 1089–1098. [Google Scholar] [CrossRef] - Ting, F.C.; Kirby, J.T. Observation of undertow and turbulence in a laboratory surf zone. Coast. Eng.
**1994**, 24, 51–80. [Google Scholar] [CrossRef] - Dimas, A.A.; Galani, K.A. Turbulent Flow Induced by Regular and Irregular Waves above a Steep Rock-Armored Slope. J. Waterw. Port Coastal Ocean. Eng.
**2016**, 142, 04016004. [Google Scholar] [CrossRef] - Alonso, R.; Solari, S.; Teixeira, L. Wave energy resource assessment in Uruguay. Energy
**2015**, 93, 683–696. [Google Scholar] [CrossRef] - Ting, F.C. Laboratory study of wave and turbulence velocities in a broad-banded irregular wave surf zone. Coast. Eng.
**2001**, 43, 183–208. [Google Scholar] [CrossRef] - Van der A, D.A.; O’Donoghue, T.; Davies, A.G.; Ribberink, J.S. Experimental study of the turbulent boundary layer in acceleration-skewed oscillatory flow. J. Fluid Mech.
**2011**, 684, 251–283. [Google Scholar] [CrossRef] [Green Version] - Monin, A.S.; Yaglom, A.M. Statistical Fluid Mechanics: Mechanics of Turbulence; MIT Press: Boston, MA, USA, 1971; Volume 1. [Google Scholar]
- Umeyama, M. Changes in Turbulent Flow Structure under Combined Wave-Current Motions. J. Waterw. Port Coastal Ocean. Eng.
**2009**, 135, 213–227. [Google Scholar] [CrossRef] - Singh, S.K.; Debnath, K.; Mazumder, B.S. Turbulence Statistics of Wave-Current Flow over a Submerged Cube. J. Waterw. Port Coastal Ocean. Eng.
**2016**, 142, 04015027. [Google Scholar] [CrossRef] - Yanada, H.; Sekikawa, Y. Modeling of dynamic behaviors of friction. Mechatronics
**2008**, 18, 330–339. [Google Scholar] [CrossRef] - Tran, X.B.; Hafizah, N.; Yanada, H. Modeling of dynamic friction behaviors of hydraulic cylinders. Mechatronics
**2012**, 22, 65–75. [Google Scholar] [CrossRef]

**Figure 2.**Layout of the OWSC model, illustrating: the position of the experimental setup; the configuration of the UVP probes (UP1, UP2 and UP3); and the geometry of the OWSC.

**Figure 5.**Full time series of normalized (

**a**) free-surface elevation and (

**b**) rotation angle of the flap. The dash-dotted line represents the amplitude scales. The vertical line at $t/T=35$ indicates the beginning of the quasi-steady condition.

**Figure 6.**Time series for $65<t/T<75$ of normalized (

**a**) free-surface elevation, (

**b**) rotation angle of the flap, (

**c**) pressure in the cylinder chamber, and (

**d**) angular velocity of the flap. Dash-dotted lines represent the amplitude scale.

**Figure 7.**Comparison between measured and fitted torque due to the pressure force of the hydraulic cylinder for (

**a**) $T=3.5$ s and $H=0.25$ m, (

**b**) $T=2.5$ s and $H=0.2$ m.

**Figure 8.**Comparison between experimental and analytical variations of the amplitude of hydrodynamic torque with a wave period.

**Figure 9.**Comparison between experimental and analytical variation of (

**a**) amplitude of rotation angle of the flap and (

**b**) power capture factor with the wave period.

**Figure 10.**Comparison between experimental and analytical phase-averaged of normalized (

**a**) free-surface elevation, (

**b**) rotation, (

**c**) power capture, and (

**d**) angular velocity of the flap.

**Figure 11.**Experimental phase-averaged velocity vector field and contour of longitudinal velocity normalized by ${U}_{0}$ at (

**a**) $t/T=0$, (

**b**) $t/T=0.06$, (

**c**) $t/T=0.15$, (

**d**) $t/T=0.27$, (

**e**) $t/T=0.38$, and (

**f**) $t/T=0.44$.

**Figure 12.**Longitudinal and vertical phase-averaged velocity profiles normalized by ${U}_{0}$ at $x/h=-0.11$ and (

**a**) $t/T=0$, (

**b**) $t/T=0.06$, (

**c**) $t/T=0.15$, (

**d**) $t/T=0.27$, (

**e**) $t/T=0.38$, and (

**f**) $t/T=0.44$.

T (s) | H (m) | ${\mathit{x}}_{12}$ (m) | ${\mathit{x}}_{23}$ (m) |
---|---|---|---|

2 | [0.15; 0.175; 0.2; 0.225; 0.25; 0.275; 0.3] | 0.49 | 1.23 |

2.25 | [0.15; 0.175; 0.2; 0.225; 0.25; 0.275; 0.3] | 0.57 | 1.42 |

2.5 | [0.15; 0.175; 0.2; 0.225; 0.25; 0.275; 0.3] | 0.65 | 1.62 |

2.75 | [0.15; 0.175; 0.2; 0.225; 0.25; 0.275; 0.3] | 0.72 | 1.81 |

3 | [0.15; 0.175; 0.2; 0.225; 0.25; 0.275; 0.3] | 0.8 | 2 |

3.25 | [0.15; 0.175; 0.2; 0.225; 0.25; 0.275; 0.3] | 0.88 | 2.19 |

3.5 | [0.15; 0.175; 0.2; 0.225; 0.25; 0.275; 0.3] | 0.95 | 2.38 |

3.75 | [0.15; 0.175; 0.2; 0.225; 0.25; 0.275; 0.3] | 1.02 | 2.56 |

4 | [0.15; 0.175; 0.2; 0.225; 0.25; 0.275; 0.3] | 1.1 | 2.75 |

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**MDPI and ACS Style**

Brito, M.; Ferreira, R.M.L.; Teixeira, L.; Neves, M.G.; Gil, L.
Experimental Investigation of the Flow Field in the Vicinity of an Oscillating Wave Surge Converter. *J. Mar. Sci. Eng.* **2020**, *8*, 976.
https://doi.org/10.3390/jmse8120976

**AMA Style**

Brito M, Ferreira RML, Teixeira L, Neves MG, Gil L.
Experimental Investigation of the Flow Field in the Vicinity of an Oscillating Wave Surge Converter. *Journal of Marine Science and Engineering*. 2020; 8(12):976.
https://doi.org/10.3390/jmse8120976

**Chicago/Turabian Style**

Brito, Moisés, Rui M. L. Ferreira, Luis Teixeira, Maria G. Neves, and Luís Gil.
2020. "Experimental Investigation of the Flow Field in the Vicinity of an Oscillating Wave Surge Converter" *Journal of Marine Science and Engineering* 8, no. 12: 976.
https://doi.org/10.3390/jmse8120976