# CFD in Wind Energy: The Virtual, Multiscale Wind Tunnel

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## Abstract

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## 1. Introduction

**S**is the mean strain rate tensor and ${\nu}_{t}$ must be modeled. The choice of turbulence model depends on the problem at hand and is a balance between desired accuracy and computational resources. Within this basic framework, a wide range of theoretical and practical problems can be investigated. As such, CFD has become a virtual, multiscale wind tunnel.

## 2. CFD at Small Scales: Aerodynamic Analysis of Wind Turbines

#### 2.1. Prediction of two-dimensional airfoil aerodynamics

#### 2.2. Prediction of three-dimensional rotor aerodynamics

#### 2.3. Simplified approaches to three-dimensional rotor aerodynamics

**Figure 2.**Isosurfaces of vorticity for the NREL Phase VI rotor using an actuator surface model [54].

## 3. CFD at Large Scales: Simulations in the Atmospheric Boundary Layer

#### 3.1. Simulation of the homogeneous neutral surface layer

Authors | ${C}_{\mu}$ | ${C}_{\epsilon 1}$ | ${C}_{\epsilon 2}$ | ${\sigma}_{k}$ | ${\sigma}_{\epsilon}$ | κ |
---|---|---|---|---|---|---|

Jones and Launder (1972) | 0.09 | 1.55 | 2.0 | 1.0 | 1.3 | 0.42 |

Launder et al. (1972) | 0.09 | 1.44 | 1.92 | 1.0 | 1.3 | 0.42 |

Crespo et al. (1985) | 0.0333 | 1.176 | 1.92 | 1.0 | 1.3 | 0.42 |

Richards and Hoxey (1993) | 0.013 | 1.44 | 1.92 | 1.0 | 3.22 | 0.42 |

Apsley and Castro (1997) | 0.09 | 1.44 | 1.92 | 1.0 | 1.11 | 0.40 |

Bechmann and Sørensen (2009) | 0.03 | 1.21 | 1.92 | 1.0 | 1.3 | 0.40 |

#### 3.2. Prediction of the flowfield over real terrain

**Flow over analytical shapes**Most current use of CFD for flow simulations in complex terrain entails the solution of the incompressible RANS equations with two-equation turbulence closure. Usually, thermal effects and the Coriolis force are neglected. Lower-order turbulence models are avoided as they appear to lack the sophistication to handle recirculation whereas higher-order methods require longer computing times. Presently, the $k-\epsilon $ model, and variants thereof, are the most popular.

**S**model and Ω model, respectively, and $\mathbf{S}-\Omega $ for their hybrid).

**Flow over real topography**Considering flow over real terrain, Kim and Patel [99] have investigated the performance of RNG $k-\epsilon $ by simulating neutral flow through the Sirhowy Valley in Wales, over an embankment on the Rhine in Germany, and over Askervein hill in Scotland. The choice of RNG was motivated by case studies involving flow over a triangular ridge and several two-equation closure schemes. In general, the RNG-based model best predicted mean velocity and turbulence characteristics, including the size and shape of recirculation zones. In a separate work, Kim et al. [100] presented further case studies using the RNG model for Cooper’s Ridge, Kettles Hill, Askervein hill, and the Sirhowy Valley. For Cooper’s Ridge, the simulation results for mean wind speed at 3 m AGL show good agreement with measurements on the windward slope and at the hill top. Similar conclusions can be made for the flow prediction over Kettles Hill. For Askervein, predicted 10-m velocities are in good agreement, even on the leeside, although hill top wind speeds are underestimated. Some problems predicting hill top and leeside turbulence are noted. The Sirhowy Valley simulations further demonstrated the ability of the RNG model to predict separation and reattachment. El Kasmi and Masson have also applied the RNG model for flow over Blashavel hill [70].

**Large eddy simulation**The vast majority of flow modeling over complex terrain to date employs a RANS approach. Considering wind resource assessment, it appears that the exact closure scheme has little impact on the predicted mean flow velocity for locations of interest for simple cases (i.e. an isolated hill top). The RNG variant seems best at dealing with flow recirculation and is recommended where such effects are important. Concerning the prediction of turbulent properties, there is much less agreement between closure schemes. Given the importance of turbulence predictions for the evaluation of turbine loads, the use of an additional transport equation for $\overline{uw}$ seems prudent.

#### 3.3. Analysis of wind turbine wakes

**Single wake analysis**Considering a single isolated rotor in a uniform flow, Sørensen et al. [132] have used the actuator disc concept to analyze wind turbine wake states for laminar conditions; however, most current analyses incorporate turbulence effects. Standard $k-\epsilon $ closure typically underestimates the velocity defect as turbulent diffusion is too high in the wake region. El Kasmi and Masson [131] have applied the Chen and Kim modified ε equation to a discrete volume around the rotor to correct this weakness and improve wake predictions for a single turbine. The Chen and Kim modification effectively limits the turbulent kinetic energy (and viscosity) in this region as the new ε source term is a function of the turbulence production rate.

**Multiple wakes**The objective of wake modeling, at the scale of wind farms, is to accurately predict the velocity defect and increase in turbulence to better model power variations and fatigue loading. Early approaches to accounting for the velocity defect in micro-siting relied on empirically-derived guidelines outlining minimum distances between turbines in an array [138]. Using an actuator disk approach to analyze a two-row array, Ammara and Masson [139] have shown these guidelines to be overly conservative. Barthelmie et al. [140] have carried out a comparison of wind farm models, ranging from engineering to full CFD models, for predicting power losses due to wake effects in the large Horns Rev wind park. Although models are not specifically identified in the presented results, the RANS/$k-\epsilon $ models tend to overpredict wake losses for narrow measurement sectors; wider sectors yield better agreement with data. Barthelmie et al. [141] have also published a good summary of developments in the field of AD applied to the study of wakes within a wind farm.

## 4. Conclusions

## Acknowledgements

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**MDPI and ACS Style**

Sumner, J.; Watters, C.S.; Masson, C.
CFD in Wind Energy: The Virtual, Multiscale Wind Tunnel. *Energies* **2010**, *3*, 989-1013.
https://doi.org/10.3390/en3050989

**AMA Style**

Sumner J, Watters CS, Masson C.
CFD in Wind Energy: The Virtual, Multiscale Wind Tunnel. *Energies*. 2010; 3(5):989-1013.
https://doi.org/10.3390/en3050989

**Chicago/Turabian Style**

Sumner, Jonathon, Christophe Sibuet Watters, and Christian Masson.
2010. "CFD in Wind Energy: The Virtual, Multiscale Wind Tunnel" *Energies* 3, no. 5: 989-1013.
https://doi.org/10.3390/en3050989