# Using Experimentally Validated Navier-Stokes CFD to Minimize Tidal Stream Turbine Power Losses Due to Wake/Turbine Interactions

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## Abstract

**:**

## 1. Introduction

## 2. Numerical Method

#### 2.1. CFD Code

^{®}FLUENT

^{®}17.2, an unstructured finite-volume Navier-Stokes code. All simulations presented below are carried out solving the RANS equations, and the effects of turbulence on the mean flow are accounted for by using Menter’s k-ω shear stress transport (SST) turbulence model [20], a RANS turbulence closure successfully tested in other recent CFD studies of tidal arrays [21,22]. The incompressible flow equations are solved using a pressure-based solution approach. The Semi-Implicit Method for Pressure Linked Equations (SIMPLE) algorithm is used to solve the momentum and pressure equations in a segregated fashion. The space discretization is second order accurate and based on an upwind flux calculation, with the variable gradients being computed with a Green-Gauss cell-based approach. Calculation of the pressure in the cell faces is based on the Pressure Staggering Option (PRESTO) scheme. Further detail on the aforementioned numerical methods can be found in the FLUENT theory guide [23].

#### 2.2. Turbine Model

## 3. Validation

#### 3.1. Physical Domain and CFD Set-Up

#### 3.2. Mesh Refinement Analysis

_{c}based on the local chord and the estimated relative velocity along the blade for a TSR range between 2 and 7 varied between $7.00\times {10}^{4}$ and $1.85\times {10}^{5}$ in the XFoil analyses.

^{+}is about 1 in all cases. Table 3, in which M1 denotes the coarsest grid and M4 the finest one, provides the main parameters of all four grids, including the total number of elements ${N}_{E}$.

#### 3.3. Performance and Far-Wake Analysis of Isolated Rotor

#### 3.4. Performance and Wake Analysis of Two Longitudinally Aligned Rotors

## 4. Results

#### 4.1. Comparison of Measured and CFD Data

#### 4.2. Turbine/Wake Interactions and Optimal Array Layout

_{P}values for T < 2D are due to the interactions of the wakes of turbines t1, t2 and t3, as discussed below. The fact that for large values of T the value of this variable is larger than that of the tandem case is explained by the influence of the blockage of the tank cross section. To demonstrate this, simulations of the four-turbine array have been performed increasing W to reduce the blockage to 1.15%. The resulting curve is labeled ‘array BR 1.15%’ in Figure 17. It is seen that reducing the blockage, results in the power coefficient of turbine t4 achieving the value of the tandem case as T increases, as expected. This indicates that in an isolated four-turbine array the interactions of the wakes of turbines t1, t2 and t3 cannot be optimized to reduce the losses of turbine t4. However, future arrays will consist of more than four turbines. Therefore, to consider a more realistic future array scenario, the four array simulations have been repeated enforcing a periodicity BC, rather than a solid wall BC, on the lateral boundaries of the tank. In these periodic simulations, the distance between the two periodic boundaries is variable and set to 2T, which is, therefore, also the lateral spacing of the t1 and the t4 turbines. The result is the curve labeled ‘array periodic’ in Figure 17. This curve highlights the existence of a maximum C

_{P}of 0.199 of turbine t4 achieved at T = 3D. As discussed below, this power increase of about 19.16% over the tandem set-up and 6.7% over the BR = 4% wall-bounded four-turbine array is due to a beneficial interaction of the wakes of turbines t1, t2 and t3, and is an effect which may be exploited in the design of full-scale arrays. It is also seen that, as T increases above 3D, C

_{P}decreases again and tends towards the value of the tandem case, as expected.

## 5. Conclusions

^{®}FLUENT

^{®}Navier-Stokes computational fluid dynamics analyses, in which the turbines were modelled using a generalized actuator disk model. Validation of the numerical method was based on thorough and comprehensive analyses of two model turbine and model array flume tank experiments, one carried out at IFREMER, the other at Shanghai Jiao Tong University, and comparison of numerical results and measured data in terms of turbine power (IFREMER experiment) and wake velocity and turbulence intensity profiles (IFREMER and SJTU experiments). A very good agreement was found in most cases. Starting from the diamond-shaped layout of the four-turbine array layout of the SJTU experiments, a numerical study was undertaken with the aim of optimizing the spacing of the lateral turbines of this modular array pattern to minimize the power loss of the central downstream turbine and maximize the array mean power by increasing the recovery rate of the wake of the central upstream turbine. It was found that the optimal lateral spacing of three rotor diameters of the two side turbines maximizes the power coefficient of the array and the downstream turbine, enabling the power of this turbine to increase by nearly 20% with respect to the case in which the two side turbines are absent or positioned at larger lateral spacing.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 2.**Physical domain of CFD simulations of IFREMER flume tank experiments: (

**a**) front view; (

**b**) side view of physical domain for one-turbine simulation; (

**c**) side view of physical domain for two-turbine simulation.

**Figure 4.**Comparison of wake variables on horizontal line at rotor hub height at TSR λ = 3.67 obtained from measurements and simulations using grids M1 to M4: (

**a**) nondimensionalized velocity u* at 3D; (

**b**) nondimensionalized velocity u* at 5D; (

**c**) turbulence intensity I at 3D; (

**d**) turbulence intensity I at 5D.

**Figure 5.**Comparison of area-averaged wake variables obtained from measurements and simulations using grids M1 to M4: (

**a**) velocity deficit ${\gamma}_{R}$; (

**b**) turbulence intensity ${I}_{R}$.

**Figure 6.**Comparison of measured and computed power coefficient ${C}_{P}$ against TSR $\lambda $ of isolated turbine.

**Figure 7.**Comparison of nondimensionalized velocity u* on horizontal line at rotor hub height at TSR λ = 3.67 obtained from measurements and simulations 6D (

**left**), 8D (

**middle**), and 10D (

**right**) behind the rotor.

**Figure 8.**Comparison of turbulence intensity I on horizontal line at rotor hub height at TSR λ = 3.67 obtained from measurements and simulations 6D (

**left**), 8D (

**middle**), and 10D (

**right**) behind the rotor.

**Figure 9.**Comparison of measured and computed power coefficient C

_{P}against TSR λ of downstream turbine at 6D, 8D and 10D from upstream turbine in two-turbine set-up. Measured ${C}_{P}-\lambda $ curve of front turbine (t1) is also reported for reference.

**Figure 10.**Comparison of nondimensionalized velocity u* on horizontal line at rotor hub height obtained from measurements and simulations at three distances behind downstream turbine in two-turbine experiment with downstream turbine at 8D from front turbine. Both turbines work at TSR λ = 3.67.

**Figure 11.**Comparison of turbulence intensity I on horizontal line at rotor hub height obtained from measurements and simulations at four distances behind downstream turbine in two-turbine experiment with downstream turbine at 8D from front turbine. Both turbines work at TSR λ = 3.67.

**Figure 12.**Computed and measured area-averaged profiles of (

**a**) velocity deficit behind downstream rotor, and (

**b**) turbulence intensity behind downstream rotor.

**Figure 13.**Physical domain of CFD simulations of SJTU flume tank experiments: (

**a**) side view; (

**b**) front view; (

**c**) 3D view.

**Figure 14.**Direct comparison of computed and measured profiles of wake centerline velocity deficit behind turbines t1 and t4 for array lateral spacing of 1.5D (

**left**), 2D (

**middle**), and 3D (

**right**).

**Figure 15.**Direct comparison of computed and measured profiles of wake centerline turbulence intensity behind turbines t1 and t4 for array lateral spacing of 1.5D (

**left**), 2D (

**middle**), and 3D (

**right**).

**Figure 16.**Measured (

**left**) and computed (

**right**) profiles of wake centerline velocity deficit behind turbines t1 and t4 for array lateral spacing of 1.5D, 2D, and 3D.

**Figure 18.**(

**a**) Radial profile of axial velocity component, and (

**b**) radial profile of turbulence intensity 1D upstream of turbine t4 for different array layouts.

**Figure 19.**Contour plot of nondimensionalized axial velocity u* for three periodic array modules: (

**a**) array L3T2, (

**b**) L3T3, and (

**c**) L3T4.

**Figure 20.**Contour plot of nondimensionalized axial velocity u* for three periodic array modules: (

**a**) array L3T2, (

**b**) L3T3, and (

**c**) L3T4.

Turbine Element | Geometry INFO |
---|---|

Hydrofoil | NACA 63418 |

Rotor radius (D/2) | 350 mm |

Hub radius | 46 mm |

Hub length | 720 mm |

**Table 2.**Boundary conditions on boundaries of physical domains of Figure 2.

Label | BC Type |
---|---|

Velocity inlet | b1 |

Inviscid wall | b2, b7 |

Pressure outlet | b3 |

Viscous wall | b4, b5, b6 |

Mesh | ${\mathit{N}}_{\mathit{R}}$ | ${\mathit{\Delta}}_{\mathit{R}}$ | ${\mathit{N}}_{\mathit{W}}$ | ${\mathit{\Delta}}_{\mathit{W}}$ | ${\mathit{N}}_{\mathit{E}}$ |
---|---|---|---|---|---|

M1 | 1660 | 0.0043 | 633,329 | 0.028 | 5,378,374 |

M2 | 5328 | 0.003 | 2,010,165 | 0.02 | 10,186,971 |

M3 | 13,509 | 0.0016 | 3,598,772 | 0.015 | 17,464,945 |

M4 | 13,509 | 0.0016 | 8,637,895 | 0.011 | 24,838,752 |

Mesh | ${\mathit{C}}_{\mathit{P}}$ | ${\mathit{C}}_{\mathit{T}}$ |
---|---|---|

M1 | 0.46 | 0.79 |

M2 | 0.442 | 0.78 |

M3 | 0.445 | 0.785 |

M4 | 0.447 | 0.786 |

Label | BC Type |
---|---|

Hydrofoil | NREL S814 |

Rotor radius | 140 mm |

Hub radius | 30 mm |

Hub length | 558 mm |

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**MDPI and ACS Style**

Attene, F.; Balduzzi, F.; Bianchini, A.; Campobasso, M.S.
Using Experimentally Validated Navier-Stokes CFD to Minimize Tidal Stream Turbine Power Losses Due to Wake/Turbine Interactions. *Sustainability* **2020**, *12*, 8768.
https://doi.org/10.3390/su12218768

**AMA Style**

Attene F, Balduzzi F, Bianchini A, Campobasso MS.
Using Experimentally Validated Navier-Stokes CFD to Minimize Tidal Stream Turbine Power Losses Due to Wake/Turbine Interactions. *Sustainability*. 2020; 12(21):8768.
https://doi.org/10.3390/su12218768

**Chicago/Turabian Style**

Attene, Federico, Francesco Balduzzi, Alessandro Bianchini, and M. Sergio Campobasso.
2020. "Using Experimentally Validated Navier-Stokes CFD to Minimize Tidal Stream Turbine Power Losses Due to Wake/Turbine Interactions" *Sustainability* 12, no. 21: 8768.
https://doi.org/10.3390/su12218768