# Blade-Resolved CFD Simulations of a Periodic Array of NREL 5 MW Rotors with and without Towers

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## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Turbine and Domain Geometries

#### 2.2. Meshing

#### 2.3. RANS Setup

#### 2.3.1. AD Simulations

#### 2.3.2. FR Simulations

#### 2.4. DDES Setup

#### 2.5. Postprocessing of URANS Results

## 3. Results and Discussion

#### 3.1. URANS

#### 3.2. DDES

#### 3.3. Comparison with Theoretical Model

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 7.**Convergence history of revolution-averaged power output (FR-URANS model with and without tower).

**Figure 8.**Contours of instantaneous streamwise velocity (m/s) at the vertical centre plane (taken at 100th revolution from FR-URANS): (

**a**) no tower; (

**b**) with tower.

**Figure 9.**Contours of instantaneous streamwise velocity (m/s) at the rotor hub height (taken at 100th revolution from FR-URANS): (

**a**) no tower; (

**b**) with tower.

**Figure 10.**Streamwise velocity profiles at different locations behind the turbine: (

**a**) $x/D=0.5$, (

**b**) $x/D=1.5$, (

**c**) $x/D=2.5$, (

**d**) $x/D=5$. The dotted horizontal line indicates the top position of the turbine.

**Figure 11.**(

**a**) Time history of instantaneous and revolution-averaged power outputs; (

**b**) time history of streamwise velocity measured at hub height ($z=90\mathrm{m}$) and $2.5D$ upstream of the turbine ($x=-315\mathrm{m}$ ).

**Figure 12.**Instantaneous streamwise velocity contours (m/s) on the streamwise vertical plane across the centre of a turbine and the horizontal plane at the turbine hub-height (taken at the 154th revolution).

**Figure 13.**Contours of instantaneous streamwise velocity (m/s) at vertical centre plane (taken at the 154th revolution).

**Figure 14.**Contours of instantaneous streamwise velocity (m/s) at rotor hub height (taken at the 154th revolution).

**Figure 15.**Vortical flow structures over a staggered array of turbines, obtained from the FR-URANS simulation with tower (visualised using iso-surfaces of Q-Criterion).

**Figure 16.**Vortical flow structures over a staggered array of turbines, obtained from FR-DDES with tower (visualised using iso-surfaces of Q-Criterion, taken at the 154th revolution).

FR + Tower | FR | AD + Tower | AD | |
---|---|---|---|---|

Rotor subdomain | $5.8\times {10}^{6}$ | $5.8\times {10}^{6}$ | $0.9\times {10}^{6}$ | N/A |

Outer domain | $11.3\times {10}^{6}$ | $6.8\times {10}^{6}$ | $11.3\times {10}^{6}$ | N/A |

Total | $17.1\times {10}^{6}$ | $12.6\times {10}^{6}$ | $12.2\times {10}^{6}$ | $0.8\times {10}^{6}$ |

${\mathit{C}}_{\mathit{P}}$ | ${\mathit{C}}_{\mathit{P}}^{*}$ | ${\mathit{C}}_{\mathit{T}}$ | ${\mathit{C}}_{\mathit{T}}^{*}$ | ||
---|---|---|---|---|---|

AD-RANS | No Tower | 0.0651 | 0.414 | 0.176 | 0.603 |

Tower | 0.0641 | 0.412 | 0.174 | 0.601 | |

Diff.% | 1.55% | 0.52% | 1.04% | 0.35% | |

FR-URANS | No Tower | 0.0495 | 0.303 | 0.167 | 0.561 |

Tower | 0.0469 | 0.306 | 0.163 | 0.570 | |

Diff.% | 5.21% | −0.90% | 2.48% | −1.67% | |

Theoretical model [22] | No Tower | 0.0622 | 0.380 | 0.198 | 0.570 |

Tower | 0.0607 | 0.380 | 0.195 | 0.570 | |

Diff.% | 2.50% | 0.00% | 1.68% | 0.00% |

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**MDPI and ACS Style**

Ma, L.; Delafin, P.-L.; Tsoutsanis, P.; Antoniadis, A.; Nishino, T.
Blade-Resolved CFD Simulations of a Periodic Array of NREL 5 MW Rotors with and without Towers. *Wind* **2022**, *2*, 51-67.
https://doi.org/10.3390/wind2010004

**AMA Style**

Ma L, Delafin P-L, Tsoutsanis P, Antoniadis A, Nishino T.
Blade-Resolved CFD Simulations of a Periodic Array of NREL 5 MW Rotors with and without Towers. *Wind*. 2022; 2(1):51-67.
https://doi.org/10.3390/wind2010004

**Chicago/Turabian Style**

Ma, Lun, Pierre-Luc Delafin, Panagiotis Tsoutsanis, Antonis Antoniadis, and Takafumi Nishino.
2022. "Blade-Resolved CFD Simulations of a Periodic Array of NREL 5 MW Rotors with and without Towers" *Wind* 2, no. 1: 51-67.
https://doi.org/10.3390/wind2010004