# Experimental and Numerical Investigation of Wake Interactions of Marine Hydrokinetic Turbines

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Experimental Setup

#### 2.2. DES-BEM Model

## 3. Results and Discussion

#### 3.1. Flow Field Downstream of the Turbines

#### 3.2. Turbine Performance

#### 3.3. Turbine–Bathymetry Interactions

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

MHK | marine hydrokinetic |

BEM | blade element momentum |

ADM | actuator disk model |

ALM | actuator lines model |

DES | detached-eddy simulation |

HATT | horizontal-axis tidal turbines |

URANS | unsteady Reynolds-averaged Navier–Stokes |

DAQ | data acquisition |

TSR | tip-speed ratio |

ST | single turbine |

TT | two turbines |

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Sample Availability: All data is available from the authors. |

**Figure 1.**Flume setup for the TT case. Both turbines are aligned and centered. The side-looking Nortek ADV velocimeter is mounted on the DAQ Carriage.

**Figure 2.**(

**a**) Points measured for both cases. Black: hub height (${h}_{h}$) for the deficit at the centerline, green: long exposure for the energy spectrum, red: transverse profiles, blue: vertical profiles. The disk on this image represents primary turbine. (

**b**) Schematic view of the cylindrical volume V that represents turbines. Forces calculated from BEM theory are only applied over nodes inside this volume. (

**c**) Schematic view of the turbine rotor and differential radius $dr$ used on BEM.

**Figure 3.**Longitudinal mean velocity $\langle U\rangle $ deficit for both study cases normalized by upstream velocity. The ST deficit (

**top**) fits better to experiments than the TT case (

**bottom**). At $10D$ downstream, the wake recovered 80% of the mean streamwise velocity.

**Figure 4.**Transverse velocity profiles for the first three diameters of distance downstream of the primary turbine for the (

**top**) ST and (

**bottom**) TT cases. The DES-BEM model shows agreement with the experimental profiles, but the model is not capable of representing the asymmetry observed in the measurements.

**Figure 5.**Vertical longitudinal velocity profiles for the ST (

**top**) and TT (

**bottom**) cases. In this case, the model cannot reproduce the asymmetry of the experiments either.

**Figure 6.**Instantaneous q-iso surfaces from two different perspectives. Both cases show the annular vortex produced by the averaged blade tips and the high pressure point at the nacelle area. Wake vortical structures are shorter for the TT case due to the larger turbulent intensity that faces the primary turbine in that case. The dashed line indicates the position of the downstream turbine.

**Figure 7.**Voltage spectra for both study cases. The first peaks indicate the primary turbine rotational frequency for each case. At lower frequencies, surrounding flow effects are perceived.

**Figure 8.**Velocity spectrum upstream and downstream of the primary turbine for the ST (

**top**) and TT (

**bottom**) cases. Surrounding flow effects are perceived in the same frequency range of the voltage spectrum.

**Figure 9.**(

**a**) Experimental elevation after experiments and (

**b**) average shear stress calculated from the DES-BEM model. The DES-BEM model results show a similar low-shear zone after the turbines, which is coincident with experimental measurements.

Parameter | Definition | ST | TT | Unit |
---|---|---|---|---|

D | Diameter | 0.092 | 0.092 | m |

${D}_{h}$ | Hub diameter | 0.02 | 0.02 | m |

${h}_{h}$ | Hub height | 0.010 | 0.010 | m |

${N}_{b}$ | Number of blades | 6 | 6 | - |

$Re$ | Reynolds number | 1.26 × ${10}^{3}$ | 1.26 × ${10}^{3}$ | - |

$Fr$ | Froude number | 0.24 | 0.24 | - |

${U}_{\infty}$ | Upstream velocity | 0.42 | 0.42 | m·s${}^{-1}$ |

$\Omega $ | Rotor rotational velocity | 16.6 | 12.4 | rad·s${}^{-1}$ |

$TSR$ | Tip-speed ratio | 3.65 | 2.01 | - |

Parameter | Value |
---|---|

${N}_{x}\times {N}_{y}\times {N}_{z}$ | $282\times 325\times 101$ |

Total number of nodes | 9,256,650 |

Number of nodes inside turbine volume | 164,125 |

Inlet boundary condition | Random flow |

Outlet boundary condition | Zero gradient |

Wall boundary condition | Wall function |

Bottom boundary condition | Non-slip condition |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Gotelli, C.; Musa, M.; Guala, M.; Escauriaza, C. Experimental and Numerical Investigation of Wake Interactions of Marine Hydrokinetic Turbines. *Energies* **2019**, *12*, 3188.
https://doi.org/10.3390/en12163188

**AMA Style**

Gotelli C, Musa M, Guala M, Escauriaza C. Experimental and Numerical Investigation of Wake Interactions of Marine Hydrokinetic Turbines. *Energies*. 2019; 12(16):3188.
https://doi.org/10.3390/en12163188

**Chicago/Turabian Style**

Gotelli, Clemente, Mirko Musa, Michele Guala, and Cristián Escauriaza. 2019. "Experimental and Numerical Investigation of Wake Interactions of Marine Hydrokinetic Turbines" *Energies* 12, no. 16: 3188.
https://doi.org/10.3390/en12163188