**3. Results**

#### *3.1. Wind Turbine Wake in the First and Second Rows*

#### 3.1.1. Velocity and Turbulence Intensity (TI) Contours

The intensity of the velocity-deficit decayed along the axial distance downstream of the rotor, however the velocity in the wake did not fully recover its free-stream value even after more than 10 diameters downstream of the rotor. Figure 3 shows time-averaged velocity contours for the two-turbine case when considering the designed aerodynamic condition for this specific wind turbine (U = 15 <sup>m</sup>·s<sup>−</sup>1, λ = 6.6, ω = 424.5 rpm, θ = −2.3◦). The region in red (15 <sup>m</sup>·s<sup>−</sup>1) represents the area where the velocity was not affected by wake effects. On the other hand, the velocity-deficit in the wake of the wind turbine is represented by green and yellow contours.

 **Figure 3.** Axial time-averaged velocity contours for the two-turbine case, representing the first row ofwindturbines.(**a**)Lateralviewofthewake;and (**b**)topviewofthewake.

(**b**)

Wind farms experience effects from the interaction between wakes from the different rows, which changes the velocity and turbulence flow field. The region free of wake effects became smaller after each row of turbines. Figure 4 shows the velocity contours for a hypothetical second row of wind turbines, while Figure 5 shows TI contours. These simulations considered the designed operational conditions (U = 15 <sup>m</sup>·s<sup>−</sup>1, θ = <sup>−</sup>2.3◦, and TSR = 6.6) for both the first and second row of turbines. Instead of simulating 4 turbines, the methodology applied used data from the previous simulation (Figure 3) for the velocity inlet. Basically, the pressure-outlet of Figure 3 became the velocity-inlet profile for the simulation from Figure 4. This procedure significantly improved the computational efficiency of the simulation with regards to computational time and convergence, since two turbines were simulated instead of four. The second row of wind turbines were not staggered from the first row of turbines, this way occupying a region affected by wake effects from the upstream first row. The wake velocity contours in Figure 4 show a smaller region of unaffected velocity in comparison with Figure 3, meaning that the region free of wake effects becomes smaller after each row of turbines.

 **Figure 4.** Time-averaged axial velocity contours for the two-turbine case in a hypothetical second row of wind turbines. (**a**) Lateral view of the wake; and (**b**) top view of the wake.

#### 3.1.2. Velocity and TI Plots

Wake data plots for the wake of the first and second turbine rows are shown in Figure 6, comparing the behavior of the velocity deficit (Figure 6a) and the TI (Figure 6b) at a radial traverse at 10 D (diameters) in the wake. The velocity deficit existing in the wake of the second row was slightly higher than the velocity deficit found in the wake of the first row (Figure 6a). The TI of the second row of turbines was considerably higher compared to the same downstream position (10 D) of the first row (Figure 6a). Moreover, interestingly there was an increase of the TI (Figure 6b) in the region between the two turbines (at r = 0), which can be attributed to wake expansion of the turbulence flow field. This can be extremely relevant in the context of wind farm layout optimization, since there is need for improving the turbine packing factor in a wind farm to take the highest benefit/output out of the windiest sites. For instance, the region between the two turbines would not be locally affected with reduced velocities, which could lead to a misleading decision of installing turbines at this position. However, the TI would have increased levels which could have an impact on the components (blades, tower, and turbine) fatigue lifetime. The increase in TI caused by wake interaction effects becomes much more significant as the lateral distance between turbines in the same row decreases. Figure 6b shows that there was a severe increase in TI for the first and second rows when the lateral spacing between turbines was too small (2 D), and Figure 6a shows that even the wake velocity profile was affected. Such effects tend to dissipate for larger lateral distances, as shown by Figure 6e,f which considered 4 D of lateral

spacing. Further studies on staggered wind farms should address the influence of the spacing between upstream turbines on turbulence flow field characteristics at the wake, aiming to determine the areas where the level of TI is reduced. If chosen correctly, the side by side distance (from upstream rows) could result in a wake region in which TI levels are reduced, consequently these spots would be more suitable to place downstream turbines.

**Figure 5.** Turbulence Intensity (TI) contours of a second row of turbines, using a profile from a simulation from a first row of turbines. (**a**) Lateral view of the wake; and (**b**) top view of the wake.

**Figure 6.** Wake interaction effect, showing wake data plots in the wake of the first and second rows for different lateral spacing in terms of rotor diameter (D): (**a**) Axial velocity for 2 D of lateral spacing; (**b**) TI for 2 D of lateral spacing; (**c**) axial velocity for 3 D of lateral spacing; (**d**) TI for 3 D of lateral spacing; (**e**) axial velocity for 4 D of lateral spacing; (**f**) TI for 4 D of lateral spacing. The spacing distances refer to hub rotor distances.

The evolution of the near wake (up to 6 D) of a single turbine is shown in Figures 7 and 8 for two different free-stream and TSR values (U = 10 <sup>m</sup>·s<sup>−</sup>1, U = 15 <sup>m</sup>·s<sup>−</sup>1, TSR = 4 and 6.6). The velocity-deficit increased as the TSR increased from 4 to 6.6 for all the positions considered in the wake (Figure 7).In regards to a TSR = 4 and considering U = 10 <sup>m</sup>·s<sup>−</sup>1, the wake velocity deficit had a peak of approximately 15% at x/D = 3 in the near wake, and the velocity deficit decreased at x/D = 6 to approximately 11%. The case of TSR = 6.6 and U = 10 <sup>m</sup>·s<sup>−</sup><sup>1</sup> presents a velocity deficit peak of 25% at x/D = 3 and 17.25% at x/D = 6, which was 9% and 6.25% smaller than the values for U = 10 <sup>m</sup>·s<sup>−</sup><sup>1</sup> and TSR = 4. The values of velocity deficit for the case of U = 15 <sup>m</sup>·s<sup>−</sup><sup>1</sup> and TSR = 4 were the same of the case U = 10 <sup>m</sup>·s-1 and TSR = 4, and so were the other two cases (U = 10 <sup>m</sup>·s<sup>−</sup><sup>1</sup> TSR = 6.6, and U = 15 <sup>m</sup>·s<sup>−</sup><sup>1</sup> and TSR = 6.6) as suggests the self-similar theory.

**Figure 7.** Velocity deficit for two different values of Tip Speed Ratio (TSR) and free-stream velocity.

**Figure 8.** TI for several downstream radial positions and TSR, considering U = 10 <sup>m</sup>·s<sup>−</sup><sup>1</sup> and U = 15 <sup>m</sup>·s<sup>−</sup>1.

#### *3.2. Far Wake Aerodynamics: Influence of Operating Conditions*

The problem of optimizing a wind farm layout is very complex, therefore assumptions for the operational conditions are important to allow finding a solution to this type of problem. This explains the importance of this section; it is very important to verify the range of validity of the solution from the optimization routine. In this section, the influence of some important operating design parameters on the velocity deficit and the TI profile in the far-wake development was analyzed including: TSR, pitch angle (θ), and free-stream velocity (U).

#### 3.2.1. Influence of the Tip Speed Ratio (TSR)

The TSR (or λ) critically influenced the far wake behavior. The velocity deficit increased as the TSR increased from 4 to 10, according to the plots from Figure 9 for axial velocity for a radial traverse in the wake at 10 D (diameters) axial location downstream the rotor. Comparing the two values of TSR from Figure 9a, the highest TSR value (λ = 10) presented the highest velocity-deficit in the far wake behavior for the downstream position considered. Consequently, the TSR was a critical design parameter affecting the three-dimensional extension of the wake. This parameter must be considered to determine the minimal distances between rotors, since a wind farm experiences several different operational conditions with regards to TSR. The TSR (λ) also critically influences the TI in the far wake (Figure 9b), increasing the TSR means that the TI will increase too.

**Figure 9.** (**a**) Axial velocity profile at 10D (diameters) downstream the rotor in the wake of the first row; and (**b**) TI profile at 10D (diameters) downstream the rotor in the wake of the first row. Different line colors represent the TSR (or λ) of 4 (blue) or 10 (orange).

#### 3.2.2. Influence of the Pitch Angle

The pitch angle (θ) had little influence on the velocity and TI profiles in the far wake if the values were kept close to the designed condition. On the other hand, the wake profile was influenced by pitch angle values beyond the designed one. The MEXICO rotor designed condition (θ = <sup>−</sup>2.3◦, U = 15 <sup>m</sup>·s<sup>−</sup>1, and TSR = 6.6) would result in the best aerodynamic performance when the rotor operates under this specific condition. Part I of this research [56] simulated the MEXICO rotor for pitch angle values ranging from +2.3◦ to <sup>−</sup>3◦, showing that the velocity deficit in the near wake was significantly higher for pitch angle values close to the designed condition. Particularly, a pitch angle of −3◦ would result in a velocity deficit three times higher than a pitch angle of +2.3◦. These results are expected, since the axial induction of the rotor was higher for the designed condition because more energy was being extracted from the incident wind. For a value of +2.3◦, the near wake velocity deficit was lower because of the lower rotor axial induction. In this work, three different values of pitch angle were tested (Figure 10), considering the same free-stream velocity and TSR conditions for all of them. The idea was to check the effect of the variation of the pitch angle on the far wake profile. All three pitch angle values tested were close to the designed condition (θ = −2.3◦). The velocity profile (Figure 10a) remained the same at 10 diameters downstream the rotor for all the pitch angles values, whereas there was no significant variation between θ = −2.3◦ and θ = −3◦ for the TI profile (Figure 10b). Still considering the TI profile (Figure 10b), the case of θ = −1◦ showed little deviation from the designed condition θ = <sup>−</sup>2.3◦. This means that the pitch angle may be disregarded for an optimization routine. At least in a preliminary analysis, the pitch angle of individual rotors could be set to the designed condition in order to have the best aerodynamic performance. This could be very important tackling such a complex problem of optimizing wind farm layout, since it is desired to reduce the associated number of variables as much as possible. Figure 10a shows that the velocity wake profile would not be severely affected by doing that, and Figure 10b shows that the effect on the TI profile would be limited to less than a 10% increase. It is important to emphasize again that pitch angle values considerably different than the designed condition would severely affect the wake by altering the velocity and turbulence wake profiles, as shown in part I of this research [56].

**Figure 10.** Influence of the pitch angle (θ) on the: (**a**) velocity profile at 10D (diameters) downstream the rotor in the wake; and (**b**) TI profile at 10D (diameters) downstream the rotor in the wake.

#### 3.2.3. Influence of the Free-Stream Velocity

Increasing/decreasing the free-stream velocity value did not affect the magnitude (percentage) of the velocity deficit (Figure 11a). On the other hand, increasing the free-stream velocity value greatly affected the magnitude of the TI (Figure 11b). Consequently, it is important to consider variable free-stream velocity conditions to verify that the optimal wind farm layout solution is not sensitive to the variation of the velocity. Since the turbine components lifetime was closely related to the TI conditions, the variation of the free-stream velocity could be a critical factor to determine the payback of a wind farm.

**Figure 11.** Influence of the free-stream velocity on the: (**a**)velocity-deficit at 10D (diameters) downstream the rotor in the wake; and (**b**) TI at 10D (diameters) downstream the rotor in the wake.
