# Development of a CFD-Based Wind Turbine Rotor Optimization Tool in Considering Wake Effects
## 3 Results and Discussion
### Nibe Wind Turbine Case  
To validate the aerodynamic model accuracy, the full-scale measurements [52] of the Nibe wind turbines are shown in Figure 4 where the two turbines are seperated with an axial distance of 5D.  
Figure 3: (**a**) Sketch of the boundary conditions and turbine positions; (**b**) The mesh configuration. The horizontal and vertical directions are defined as x and y for later reference.  
The Nibe wind turbines operate at a rated power of 630 KW, and the wind turbine has a rotor diameter of D = 40 m, and the hub height is H = 45 m. The simulation is performed at an inflow wind speed of 8.55 m/s and a turbulence intensity of 10%.  
The comparisons between the measured and simulated wake velocity profiles are shown in Figure 5. The measurement data are available for a single wind turbine (Nibe B) at down-stream positions of 2.5D, 4.0D and 7.5D as depicted in Figure 4. It is worth noting that for the present single wake study, Nibe A is not operating during the measurement period. The detailed wake deficit is clearly observed from Figure 5a-c which ranges from the near wake to the far wake region. In terms of maximum wake deficit and turbulence intensity, the new model shown relatively better agreement with the measured data. At the near wake region, x = 2.5D, the new model does not produce a better velocity deficit than the original model. At x = 4D and 7.5D, the new model shows better results, which is also the normal spacing between wind turbines.  
For the double wake case, the streamwise velocity contour plot is presented in Figure 6. The axial velocity is largely reduced as the flow first passes through the Nibe B wind turbine and than the Nibe A wind turbine. The comparisons between the measured and simulated wake profiles for the two wind turbines at down-stream positions of 2.5D, 4.0D and 7.5D are shown in Figure 7. In this case, both Nibe A and Nibe B operate at a wind speed of 8.55 m/s. At the downstream locations 2.5D and 4D, the wake profiles are expected to be similar as that shown in Figure 6. As expected, only tiny differences are seen from the simulated results, which are due to the flow feedback from the Nibe A wind turbine, but the effect is very small. On the other hand, the experimental data showed a wider spread at 2.5D and 4D which is caused by different measurement conditions, Figure 7c shows the more complicated double wake case where the wake flow of two wind turbines are superimposed. At x = 7.5D, wake data are both measured behind the Nibe B and Nibe A wind turbines. The velocity deficit is seen to be relatively small as previously observed in Figure 5c. However, when the Nibe A wind turbine is operating, the x = 7.5D position is only 2.5D apart from the Nibe A wind turbine and thus it is considered to be the near wake position of turbine Nibe A. As seen from Figure 7a,c, wake profiles are similar at positions x = 2.5D and x = 7.5D. However, at x = 7.5D, a smaller velocity deficit is observed, which is due to the wake mixing effect introduced by the Nibe B wind turbine. At x = 7.5D, it is also seen that the fluctuation of turbulence intensity is quite large which cannot be captured by any RANS model.  
Figure 4: Sketch of the two Nibe wind turbines and the wake measurement locations.  
Figure 5: Comparisons between the measured and simulated wake data of a single wind turbine (Nibe B) at down-stream positions of 2.5D, 4.0D and 7.5D. (**a**) 2.5D; (**b**) 4D; (**c**) 7.5D.  
Figure 6: Contours of the time-averaged stream-wise velocity for two Nibe wind turbines.