Aerodynamic interactions of the model NREL 5 MW offshore horizontal axis wind turbines (HAWT) are investigated using a high-fidelity computational fluid dynamics (CFD) analysis. Four wind turbine configurations are considered; three-bladed upwind and downwind and two-bladed upwind and downwind configurations, which operate at two different rotor speeds of 12.1 and 16 RPM. In the present study, both steady and unsteady aerodynamic loads, such as the rotor torque, blade hub bending moment, and base the tower bending moment of the tower, are evaluated in detail to provide overall assessment of different wind turbine configurations. Aerodynamic interactions between the rotor and tower are analyzed, including the rotor wake development downstream. The computational analysis provides insight into aerodynamic performance of the upwind and downwind, two- and three-bladed horizontal axis wind turbines.

Wind turbines are designed to extract kinetic energy from the wind, usually to drive an electric generator. Almost all of the commercial wind turbines today are horizontal axis wind turbines (HAWT) [

When compared with the three-bladed design, the two-bladed wind turbine reduces the weight and cost by one rotor blade. Also, the three-bladed design requires more effort to transport assemble on site. In contrast, the two-bladed design is relatively easy to transport and may not require on-site assembly, thus lowering the cost. However, for the same rated power, the two-bladed turbines may increase the loading on individual rotor blade because of a larger chord, span, and/or rotational speed requirements. Due to the complexity of unsteady aerodynamics and structural response of large sized wind turbine blades, the wind turbine aeromechanic performance has been typically studied using a low-fidelity blade element momentum theory (BLMT) [

Many experimental investigations of the aerodynamic influences for traditional wind turbine configurations are reported by researchers at the National Renewable Energy Laboratory (NREL) such as by Robinson et al. [^{2}NCLE [

The unsteady Reynolds-averaged Navier-Stokes flow solver U^{2}NCLE [

In order to capture the unsteady relative motion between the rotating rotor and the tower, an efficient unstructured grid sliding interface method [

The NREL offshore 5 MW baseline wind turbine [

Upwind (a) and downwind (b) wind turbines.

Wind turbine blade shape with sketch view.

Four unstructured meshes corresponding to different wind turbine configurations were generated in the present study. Shown in Figure ^{+} value of one applied to all viscous surfaces. The boundary growth ratio of two is used in the anisentropic volume grid regions. The volume grid sizes range from 8.56 (two-bladed) to 11.73 (three-bladed) million points for the combination of rotor, tower, hub, and nacelle. The blade surface mesh resolution near the tip region is shown in Figure

Computational meshes of upwind (a) and (b) downwind configurations.

The blade surface grid resolution in the tip region.

All computations were performed at the sea level atmosphere temperature of 15°C and pressure of 1.013 × 10^{5} Pa. The rated wind speed of 11.4 m/s was chosen in all computations. The NREL 5 MW wind turbine has a diameter of 126 meters. Two rotational speeds of 12.1 RPM (rated) and 16 RPM were performed. The pitch angles are zero degree except negative 1.33 for the downwind two-bladed case with 16 PM at 75% span location from the center of rotation. The blade tip Mach number is 0.2346 for RPM 12.1 and 0.3102 for RPM 16. The corresponding Reynolds numbers are 689 million and 910 million based on the blade diameter and the rotor tip speed for RPM 12.1 and RPM 16, respectively.

In the wind turbine aerodynamic analysis, three important design parameters, the rotor orientation, the number of blades, and the rotor speed, are investigated in this study. Unsteady time-accurate simulations were performed using the high-fidelity CFD code U^{2}NCLE [

The rotor performance is investigated by evaluating the rotor power, torque, hub bending moment, and sectional loads. The computed rotor total power and mean and peak torque for different configurations are given in Table

Comparison of rotor power and torque.

Configuration | RPM | Power [MW] | Torque (mean)^{−6} |
Torque (peak)^{−6} |
(Peak − mean)/mean (%) |
---|---|---|---|---|---|

UW/3BLD | 12.1 | 5.29 | 4.17 | 3.91 | 6.23 |

DW/3BLD | 12.1 | 4.93 | 3.89 | 2.94 | 24.4 |

UW/2BLD | 12.1 | 4.47 | 3.55 | 3.15 | 11.3 |

DW/2BLD | 12.1 | 4.19 | 3.35 | 2.00 | 40.3 |

UW/2BLD | 16 | 4.85 | 2.89 | 2.54 | 12.1 |

DW/2BLD | 16 | 4.93 | 2.94 | 1.81 | 38.4 |

Perhaps more relevant comparisons should be made at the same rated power in order to develop relative merits among different wind turbine configurations. To match the rated power of 5 MW for the two-bladed turbines, the rotor speed has to be increased to 16 RPM. The pitch angle was slightly decreased by 1.33 degrees for the downwind case but remained the same for the upwind case. As shown in Table

The azimuthal distributions of the rotor total torque over one rotor revolution are shown in Figure

Rotor total torque variation over one rotor revolution.

Aside from the mean torque values, another important consideration in the wind turbine design is the unsteady loading. As illustrated in Figure

The azimuth distributions of the sectional normal force and torque on a single blade are illustrated in Figures

Three-bladed sectional normal force (Ft) and torque (Mq) distributions at 12.1 RPM.

Two-bladed sectional normal force (Ft) and torque (Mq) distributions at 12.1 RPM.

Two-bladed sectional normal force (Ft) and torque (Mq) distributions at 16 RPM.

The blade hub bending moment is a key consideration in the overall wind turbine design, because smaller bending moment means that less stiff design could be used to construct the rotor blades and reduce the overall costs. Both mean and peak bending moments are given in Table

Comparison of blade hub bending moments.

Configurations | RPM | Hub moment (mean)^{−7} |
Hub moment (peak)^{−7} |
(Peak − mean)/mean (%) |
---|---|---|---|---|

UW/3BLD | 12.1 | 1.32 | 1.26 | 4.5 |

DW/3BLD | 12.1 | 1.25 | 0.88 | 29.6 |

UW/2BLD | 12.1 | 1.43 | 1.35 | 5.6 |

DW/2BLD | 12.1 | 1.35 | 0.93 | 31.1 |

UW/2BLD | 16 | 1.94 | 1.85 | 4.6 |

DW/2BLD | 16 | 2.12 | 1.67 | 21.2 |

Similar to the rotor torque analysis, equally important is the blade unsteady load that affects the wind turbine structural load and dynamic response. The azimuthal distributions of the blade bending moments for all configurations are shown in Figure

Blade hub bending moment variation over one blade revolution.

To develop improved understanding of the blade hub bending moments, it is necessary to evaluate the blade sectional bending moment distributions from the hub to tip at different azimuthal positions, which are shown in Figure

Sectional bending moment distributions at different azimuthal positions.

In summary, the rotor performance was investigated for the upwind and downwind and three-bladed and two-bladed turbines at the same rotor RPM and the same rated power. The general finding here is that if the same rotor speed is maintained, changing the number of blades from three to two reduces the rotor total power and torque by around 17% in the upwind and downwind turbines. However, a slight higher torque is produced for the individual blade in the two-bladed turbines than in the three-bladed turbines, due to more uniform inflow in the two-bladed turbine operation. The blade hub bending moments are not significantly affected by different configurations, that is, three-bladed versus two-bladed or upwind versus downwind. However, to maintain the same rated power at a higher rotor RPM, two-bladed turbines have the blade hub bending moment increased significantly by 40% to 70% in the upwind and downwind cases, respectively. The increased blade bending moments in the two-bladed turbines should be further investigated using the structural analysis tool to evaluate the structural loads and dynamic responses to the wind turbine system.

Due to the large size and weight of the wind turbine blades, the fatigue and structural load on the supporting tower is an important consideration in the wind turbine design. Rotor rotation and wind cause periodic loading on the tower. Table

Comparison of the bending moment of the tower to the base center.

Wind turbine | RPM | Base moment (mean)^{−7} |
Base moment (peak)^{−7} |
(Mean − peak)/mean (%) |
---|---|---|---|---|

UW/3BLD | 12.1 | 8.58 | 8.36 | 2.6 |

DW/3BLD | 12.1 | 8.19 | 7.65 | 6.6 |

UW/2BLD | 12.1 | 6.24 | 5.99 | 4.0 |

DW/2BLD | 12.1 | 6.01 | 5.41 | 6.0 |

UW/2BLD | 16 | 8.14 | 7.79 | 9.9 |

DW/2BLD | 16 | 8.85 | 8.26 | 6.7 |

The unsteady loads of the base bending moment of different wind turbines are shown in Figure

Comparison of total base bending moments of the tower.

The sectional base bending moments of the tower are investigated and compared for all wind turbines at different blade azimuth positions, which are shown in Figure

Sectional bending moments to the tower base center.

The above analyses showed relative merits of the rotor and tower for different wind turbine designs, which may have contradicting features as desired. For example, the downwind turbines in general produced the smallest average and dynamic bending moments at the tower base but produced higher mean and maximum hub bending moments on the individual blades than the three-bladed turbines. In addition, in the downwind turbines, the magnitude variation of the hub bending moments was significantly higher than that in the three-bladed upwind turbine, which can have adverse effects on the wind turbine structural and fatigue loads. To make the final determination on how important a given factor is for the fatigue and what impact that has on cost, a structural dynamic analysis needs to be performed.

Because the wind turbine extracts kinetic energy from the wind, the air velocity decreases as air passes through the rotor. The wind turbine rotor also generates wake vortices lasting as far as several rotor diameters downstream, which will affect the inflow of the wind turbine placed in the near downstream, and its operation and performance. The wind speed gradually recovers to the undisturbed state when the wake effectively disappears because of mixing several rotor diameters away. In order to reduce the wake interference in a wind farm, the downstream wind turbine must be placed at a certain distance from the upstream one. Therefore, a correct estimation of the wind turbine spacing distance is essential to an optimal wind farm design.

The predicted instantaneous vorticity contours generated by upwind and downwind turbines as the blade one moves to the top position are exhibited in Figures

Instantaneous vorticity of three-bladed upwind and downwind turbines at 12.1 RPM.

Instantaneous vorticity of two-bladed upwind and downwind turbines at 12.1 RPM.

Instantaneous vorticity of two-bladed upwind and downwind turbines at 16 RPM.

The circumferentially averaged axial velocity variations along the vertical centerline parallel to the tower axis at several downstream locations up to five diameters downstream are shown in Figures

Downstream wake deficit of three-bladed upwind and downwind turbines at 12.1 RPM.

Downstream wake deficit of two-bladed upwind and downwind turbines at 12.1 RPM.

Downstream wake deficit of two-bladed upwind and downwind turbines at 16 RPM.

NREL 5 MW offshore wind turbine configurations were numerically investigated in the present study using a high-fidelity Navier-Stokes CFD code U^{2}NCLE, which included the three-bladed upwind and downwind turbines and two-bladed upwind and downwind turbines. Detailed aerodynamic analyses were performed on the rotor power and blade hub bending moment, the tower base bending moment, and the turbine wake flow. The relative merits of different wind turbine designs were discussed, as well as their implications on the structural loads and dynamic response. The following conclusions can be drawn from the current work.

Both the blade number and rotor speed have the largest impact on the mean aerodynamic loading of the rotor power, blade hub bending moment, and base bending moment of the tower. The effect of the rotor orientation, that is, the upwind or downwind turbine, is secondary on the mean rotor aerodynamic loads but has a dominating impact on the unsteady loads of the wind turbine system.

For the same rotor speed of 12.1 RPM and blade pitch angle, two-bladed wind turbines reduced the rotor power by roughly 17% but increased the blade mean bending moment by 9% approximately, compared with the three-bladed counterparts. However, there was a 27% reduction of the base bending moment of the tower, due to the reduction of the power generated by two-bladed wind turbines.

For two-bladed turbines operating at a rotor speed of 16 RPM or the rated power of 5 MW, there was a 17% reduction of the rotor torque compared with the three-bladed turbines operating at 12.1 RPM. However, the blade mean hub bending moment was increased significantly by 47% in the upwind case, and 70% in the downwind case, in comparison with the three-bladed counterparts, respectively. The base bending moment of the tower remained at the same level if the same rotor power was maintained.

The unsteady loading was generally higher in the downwind turbines than in the upwind turbines. Excluding the weight, the two-bladed downwind turbine experienced the largest variation of the unsteady rotor torque, about 40% from the peak to the mean values, and about 21% to 30% of the blade bending moment variation comparing to roughly 5% variation in the upwind turbines. However, the tower unsteady load of the base bending moment was not significantly affected by the upwind and downwind turbine designs.

Three-bladed wind turbines generated stronger rotor tip vortices than the two-bladed turbines did at the same rotor RPM. Two-bladed wind turbines generated stronger tip vortices at a higher rotor speed of 16 RPM, with the wake deficit recovered within a short distance downstream of the rotor. In general, a distance of five rotor diameters downstream is needed for the deficit velocity to recover to the uniform state.

The authors declare that there is no conflict of interests regarding the publication of this paper.

The authors gratefully acknowledge the financial support for this project from the U.S. Department of Energy, Grant nos. DE-FG36-06GO86096 and DE-EE0003540.