# 3D Numerical Study of the Impact of Macro-Roughnesses on a Tidal Turbine, on Its Performance and Hydrodynamic Wake

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Experimental Setups

**motionless blade experiment**chosen for the validation of the numerical model comes from [13]. Their experimental method is described hereafter. The tests were carried out in the Handley–Page wind tunnel with dimensions of 1.61 m high × 2.13 m wide × 2.74 m long. The air flow velocity was 45 m·s

^{−1}with 2.5% turbulence. The blade is made from a NACA 63-619 foil of 0.55 m chord. It passes completely through the height of the wind tunnel. The barnacle is represented by a solid cone with a radius of 20 mm at its base and 10 mm at its top and a height of 11 mm, dimensions nearby to the Balanus crenatus found in the Alderney Race [4]. A total of 25 pressure orifices are positioned on and around the barnacle in order to follow the evolution of the pressure field. Three angles of attack are studied: 5°, 10° and 15°. Sensor HDI series gauge sensors measured the dynamic stall while pressure transducers were used to sample the pressure evolution along the blade. The experimental setup also allowed blade oscillation, but unsteady tests were not used here.

**full rotor simulation**is built according to [18] and uses the IFREMER-LOMC1 horizontal axis turbine. The water velocity was fixed to 0.8 m·s

^{−1}with 3% of turbulence intensity. The rotor rotation was forced by a motor to fix the Tip Speed Ratio (TSR) to 4. TSR is defined as follows:

_{x}is the angular velocity, R is the radius of the tidal turbine and U

_{∞}is the inlet flow velocity. The rotor characteristics are presented in Table 1.

#### 2.2. Governing Equations

- (i)
- Air and water are considered as viscous fluids.
- (ii)
- Both fluids are considered incompressible. This hypothesis can be questioned in the case of air, but the validation cases in air have a Mach number of 0.14. It is generally accepted that for a flow with a Mach number below 0.3, the fluid can be considered incompressible.
- (iii)
- Gravity is neglected.
- (iv)
- The study is carried out in the middle of the water column, so wave and bottom effects are neglected.

^{−3}), p is the pressure, ${f}_{i}$ represents the volumetric forces in the i-direction, and $\nu $ is the kinematic viscosity.

#### 2.2.1. Reynolds-Averaged Navier-Stokes Turbulence Model

#### 2.2.2. Large Eddy Simulation Turbulence Model

#### 2.3. Boundary Conditions

#### 2.4. Geometries, Meshes and Numerical Setups

#### 2.4.1. Motionless Blade Simulation with a Single Barnacle

#### 2.4.2. Full Rotor Simulation with a Realistic Barnacle Colonisation

#### 2.5. Test Case Summary

## 3. Results

#### 3.1. Motionless Blade Simulation with One Barnacle

^{−1}) during the first time steps. Once the wake is stabilised, the biofouling blade releases vortexes that propagate “upwards” in a regular manner. The clean blade, on the other hand, shows a turbulence structure similar to Von Karman vortex streets.

#### 3.2. Full Rotor Simulation Simulation

#### 3.2.1. Impact of Biofouling on Tidal Turbine Performances

#### 3.2.2. Impact of Biofouling on Tidal Turbine Wake

## 4. Discussion and Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

Parameters | Definitions | Units |

D | Rotor diameter | $\mathrm{m}$ |

R | Rotor radius | $\mathrm{m}$ |

c | Blade chord | $\mathrm{m}$ |

$\delta {\Omega}_{1}$ | Computational domain inlet surface | - |

$\delta {\Omega}_{2}$ | Computational domain outlet surface | - |

$\delta {\Omega}_{3,4,5,6}$ | Computational domain side surfaces | - |

$\nu $ | Kinematic viscosity | ${\mathrm{m}}^{2}\xb7{\mathrm{s}}^{-1}$ |

$\omega $ | Rotor angular velocity | $\mathrm{rad}\xb7{\mathrm{s}}^{-1}$ |

p | Fluid pressure | $\mathrm{Pa}$ |

u | Fluid velocity | $\mathrm{m}\xb7{\mathrm{s}}^{-1}$ |

$\rho $ | Fluid density | $\mathrm{kg}\xb7{\mathrm{m}}^{-3}$ |

${U}_{\infty}$ | Inlet velocity magnitude | $\mathrm{m}\xb7{\mathrm{s}}^{-1}$ |

${p}_{\infty}$ | Undisturbed pressure | $\mathrm{m}\xb7{\mathrm{s}}^{-1}$ |

$\lambda $ | Tip speed ratio | $\mathrm{m}\xb7{\mathrm{s}}^{-1}$ |

$\overline{(\xb7)}$ | Mean values | - |

$\tilde{(\xb7)}$ | Filtered values | - |

$y+$ | Dimensionless wall distance | - |

${\Omega}_{R}$ | Rotor’s rotation speed | rad·s${}^{-1}$ |

${I}_{\infty}$ | Turbulence intensity | - |

${C}_{p}$ | Dimensionless pressure coefficient | - |

${C}_{P}^{*}$ | Corrected dimensionless power coefficient | - |

${C}_{d}$ | Dimensionless drag coefficient | - |

## Notes

1 | The French Research and Sea Exploitation Institute-Waves and Complex Environment Laboratory in Le Havre |

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**Figure 2.**3D geometry of the blade with one barnacle. The clean part of the blade is marked by the red arrow. The barnacle is in the middle of the section marked with the blue arrow.

**Figure 3.**3D geometry and mesh of the entire computational domain (

**a**), around the blade (

**b**), and around the conic barnacles (

**c**). Distored cells are due to the cutting plane and do not represent the 3D cells.

**Figure 4.**3D geometry of one of the three blades of the rotor with barnacles. Red lines are cut positions for post-processing.

**Figure 5.**Views of the X–Y (

**left**) and Y–Z (

**right**) planes of the computational domain including the rotor geometry. Green lines are the no-slip boundary conditions, the red line is the inlet with the velocity condition and the blue line is the pressure outlet condition.

**Figure 6.**Opposite of the pressure coefficient ($-{C}_{p}$) around barnacle for an angle of attack of 5° (

**a**), 10° (

**b**), 14° (

**c**) and 15° (

**d**) on the blade surface. Results are from LES simulation.

**Figure 7.**Opposite Pressure coefficient evolution ($-{C}_{p}$) according to the dimensionless x position (${x}^{*}$) along the chord-wise position on the centre-line for an angle of attack of 5° (

**a**) and 10° (

**b**). Numerical results with k-ω SST (blue line) and Smagoginsky (red line) are presented for the fouled blade. Experimental values for clean and fouled blades are shown in green and black squares, respectively, from [13] data.

**Figure 8.**Opposite Pressure coefficient ($-{C}_{p}$) evolution according to the dimensionless x position (${x}^{*}$) along the chord-wise position on the centre-line for an angle of attack of 15° (

**a**) and 14° (

**b**). Numerical results with k-ω SST (blue line) and Smagorinsky (red line) are presented for the fouled blade. Experimental values for clean and fouled blades are shown in green and black squares, respectively, (with an angle of attack of 15°) from [13] data.

**Figure 9.**$-{C}_{p}$ evolution against the dimensionless x-position profile (including the lower face) at a fixed time point for numerical modelling with fouling (blue line) and experimental mean values for a clean blade (green squares) and a fouled blade (black squares) for an angle of attack of 5° from [13] data.

**Figure 10.**Normal (

**Left**) and drag (

**Right**) coefficients measurements against the mean angle for clean (black squares) and fouled (green crosses) blades from [13] data. Numerical results for fouled blades are represented by red lozenges.

**Figure 11.**Magnitude of the vorticity around and behind the blade for the LES Smagorinsky (

**a**) and the RANS k-$\omega $ SST turbulence model (

**b**).

**Figure 12.**Magnitude of vorticity around and behind the blade at T = 0.04 s, T = 0.13 s, T = 0.26 s, and T = 1.14 s for cases without (

**a**) and with (

**b**) a barnacle.

**Figure 13.**Dimensionless wake thickness as a function of dimensionless position in the wake without (red diamonds) and with (black squares) a barnacle for angles of attack of 5° (

**left**) and 15° (

**right**).

**Figure 14.**Time evolution of the corrected power coefficient (${C}_{power}^{*}$). Measurements for a clean turbine are in black while numerical results for clean and fouled turbines are in blue and red, respectively.

**Figure 16.**Discrete Fourier Transform of the vorticity numerical magnitude took one diameter behind the rotor at the tip of the blade position for a clean (blue line) and fouled (red line) tidal turbine. The probe appears on Figure 5.

**Figure 17.**Zoomed view of two sections of one blade of the tidal turbine in the X–Z plan. The left refers to (1) and the right section refers to (2) on Figure 5.

Turbine | IFREMER-LOMC | Unit |
---|---|---|

Profile | NACA 63418 | |

Rotor Radius (R) | 350 | mm |

Hub Radius | 46 | mm |

Pitch | 0 | degrees |

TSR | 4 | - |

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

ρ | 1.177 | kg·m^{−3} |

ν | 1.57 × 10^{−5} | m^{2}·s^{−1} |

U_{∞} | 45 | m·s^{−1} |

p_{∞} | 1.013 × 10^{6} | Pa |

k | 1.898 | m^{2}·s^{−2} |

ω | 4.574 | s^{−1} |

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

ρ | 1025 | kg·m^{−3} |

ν | 1.3 × 10^{−6} | m^{2}·s^{−1} |

U_{∞} | 0.8 | m·s^{−1} |

p_{∞} | 0 | Pa |

Ω_{R} | 9.143 | rad·s^{−1} |

I_{∞} | 0.03 | - |

Case Name | Fluid | Rotation | Barnacle | Angle of Attack |
---|---|---|---|---|

Blade 5° | Air | No | Only one | 5° |

Blade 10° | Air | No | Only one | 10° |

Blade 14° | Air | No | Only one | 14° |

Blade 15° | Air | No | Only one | 15° |

Rotor clean | Water | Yes | Realistic | 0° |

Rotor colonised | Water | Yes | Realistic | 0° |

Case Name | ΔT_{min} (s) | ΔT_{min} (s) | ΔX_{min} (m) | Total Running Time |
---|---|---|---|---|

Blade 5° | ∼10^{−7} | ∼10^{−4} | $2.2\times {10}^{-4}$ | 1.26 |

Blade 10° | ∼10^{−7} | ∼10^{−4} | $2.2\times {10}^{-4}$ | 1.21 |

Blade 14° | ∼10^{−7} | ∼10^{−4} | $2.2\times {10}^{-4}$ | 1.16 |

Blade 15° | ∼10^{−7} | ∼10^{−4} | $2.2\times {10}^{-4}$ | 1.15 |

Rotor clean | ∼10^{−9} | ∼10^{−4} | $4.4\times {10}^{-4}$ | 2.41 |

Rotor colonised | ∼10^{−12} | ∼10^{−4} | $2.6\times {10}^{-4}$ | 1.505 |

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**MDPI and ACS Style**

Robin, I.; Bennis, A.-C.; Dauvin, J.-C.
3D Numerical Study of the Impact of Macro-Roughnesses on a Tidal Turbine, on Its Performance and Hydrodynamic Wake. *J. Mar. Sci. Eng.* **2021**, *9*, 1288.
https://doi.org/10.3390/jmse9111288

**AMA Style**

Robin I, Bennis A-C, Dauvin J-C.
3D Numerical Study of the Impact of Macro-Roughnesses on a Tidal Turbine, on Its Performance and Hydrodynamic Wake. *Journal of Marine Science and Engineering*. 2021; 9(11):1288.
https://doi.org/10.3390/jmse9111288

**Chicago/Turabian Style**

Robin, Ilan, Anne-Claire Bennis, and Jean-Claude Dauvin.
2021. "3D Numerical Study of the Impact of Macro-Roughnesses on a Tidal Turbine, on Its Performance and Hydrodynamic Wake" *Journal of Marine Science and Engineering* 9, no. 11: 1288.
https://doi.org/10.3390/jmse9111288