**3. Results**

## *3.1. Validation Dataset*

As part of the model validation process, the loading on the blades from our CFD results were computed considering the total pressure on each blade (static and dynamic pressure), which produces an axial net force on the blade surfaces. The validation presented in Figure 5 is a result of the axial induction exerted through the rotating frame, which induces an axial net force on the blade and consequently a velocity deficit in the wake. The tangential loads presented represent loading in the chord wise direction. The comparison between computational and experimental data shows acceptable agreemen<sup>t</sup> for the two velocity values (Figure 5a,b). Figures 6 and 7 present graphs of the pressure coefficient on the blade surface, showing acceptable agreemen<sup>t</sup> between CFD results and experimental data from the MEXICO experiment. The pressure coefficients presented in Figures 6 and 7 are normalized, setting up a value of one at the stagnation point. The radial locations at r/R = 0.25 and r/R = 0.35 show less accuracy than the others because of the airfoil extrapolated data for this blade location. Figures 8 and 9 show the validation based on data for the wake velocity flow field. Figure 8 shows the validation of the axial traverse (R=1.8m) considering the free stream velocity = 15 <sup>m</sup>·s<sup>−</sup><sup>1</sup> and 10 <sup>m</sup>·s<sup>−</sup><sup>1</sup> at one radial and one axial downstream position: R = 1.8 m (axial) and x=0.3 m (radial). Figure 9 shows the validation for the radial traverse at 0.3 m downstream of the rotor, while considering free stream velocity of 15 <sup>m</sup>·s<sup>−</sup><sup>1</sup> and 10 <sup>m</sup>·s<sup>−</sup>1. The computational results match the experimental data very well for the axial traverse at R = 1.8 m (Figure 8), and almost entirely match the radial traverse at x = 0.3 m (Figure 9). This demonstrates that this CFD model can accurately reflect the real rotor behavior. The computational results qualitatively agree with the experimental results; however, there are minor numerical discrepancies. Even though the velocity values do not completely overlap, the shape of the computational curve is very similar to the shape of the curve obtained with the experimental procedure.

**Figure 5.** Axial and tangential forces on the rotor, showing comparison between computational and experimental results for (**a**) 15 <sup>m</sup>·s<sup>−</sup><sup>1</sup> and TSR = 6.6; (**b**) 10 <sup>m</sup>·s<sup>−</sup><sup>1</sup> and TSR = 10.

**Figure 6.** Normalized pressure coefficient on the blades for U = 15 <sup>m</sup>·s<sup>−</sup>1, TSR = 6.6 and θ = <sup>−</sup>2.3◦.

**Figure 7.** *Cont.*

**Figure 7.** Normalized pressure coefficient on the blades for U = 10 <sup>m</sup>·s<sup>−</sup>1, TSR = 10 and θ = <sup>−</sup>2.3◦.

**Figure 8.** Validation dataset for an axial traverse at R = 1.8 m, showing comparison between computational and experimental data for (**a**) Free-Stream Velocity U = 15 <sup>m</sup>·s<sup>−</sup>1; (**b**) Free-Stream Velocity U = 10 <sup>m</sup>·s<sup>−</sup>1. The blue lines represent the computational data and the red lines represent experimental data.

**Figure 9.** Validation of the radial traverse at x = 0.30 m, showing comparison between computational and experimental data for (**a**) U = 15 <sup>m</sup>·s<sup>−</sup>1; (**b**) Free-Stream Velocity U = 10 <sup>m</sup>·s<sup>−</sup>1; (**c**) Free-Stream Velocity U = 10 <sup>m</sup>·s<sup>−</sup><sup>1</sup> for Azimuth = 100◦. The blue lines represent the computational data and the red lines represent MEXICO rotor experimental data.

A possible explanation for the minor discrepancies comes from the MRF approach utilized in the numerical method applied here, which assumes steady state behavior. This means that the Navier-Stokes equations are averaged by the Reynolds number. In spite of that, the simulation is suitable to determine how design parameters (such as TSR, velocity and pitch angle) affect the wake aerodynamic behavior.

#### *3.2. TSR (λ) Effect on the Near Wake*

#### 3.2.1. Velocity Profile at the Near Wake

The near wake aerodynamic behavior is dependent on the rotor loading, which is dependent on the TSR. The rotor loading increases as the TSR increases, leading to an increase of the velocity deficit at the wake. Figure 10 shows the streamwise velocity-deficit evolution at five downstream positions in intervals of 0.5D, under different loading (or TSR) and upstream velocity conditions. The x-axis

shows a radial traverse downstream of the rotor, while the y-axis shows the velocity at the wake. First of all, the axial induction increases as the rotor loading/TSR increases. As a consequence, the velocity deficit in the near wake increases as the rotor loading (or TSR) increases. A TSR = 6.6 results in a higher rotor loading and more produced power compared to a TSR = 4, thus extracting more energy from the incident wind. The shape of the curves with the same TSR is very similar, regardless of the incident upstream velocity. For a TSR = 6.6 and U = 10 <sup>m</sup>·s<sup>−</sup><sup>1</sup> (Figure 10), the velocity increases from approximately 4 <sup>m</sup>·s<sup>−</sup><sup>1</sup> at 1D downstream of the rotor to 7 <sup>m</sup>·s<sup>−</sup><sup>1</sup> at 3D downstream of the rotor, showing an increased rate of 1.5 <sup>m</sup>·s<sup>−</sup><sup>1</sup> for each diameter or 15% of the free-stream velocity per rotor diameter at the wake. From the perspective of the same analysis, but considering the case of TSR = 6.6 and U = 15 <sup>m</sup>·s<sup>−</sup>1, the velocity increases from approximately 6 <sup>m</sup>·s<sup>−</sup><sup>1</sup> at 1D downstream of the rotor to approximately 11 <sup>m</sup>·s<sup>−</sup><sup>1</sup> at 3D downstream of the rotor. This corresponds to an increased ratio of 2.5 <sup>m</sup>·s<sup>−</sup><sup>1</sup> for each rotor diameter or approximately 15% of the free-stream velocity per rotor diameter at the wake. Moreover, the radial traverse right behind the rotor in Figure 11 shows an increase of 20% in the velocity deficit as the TSR varies from 6 to 10, corresponding to an increased ratio of approximately 5% <sup>m</sup>·s<sup>−</sup><sup>1</sup> per dimensionless unit of TSR.

**Figure 10.** Wake development for two different velocity and TSR (λ) values.

**Figure 11.** Axial Velocity profile for a radial traverse, and several TSR values.

#### 3.2.2. Turbulence Intensity Profile at the Near Wake

Figure 12a shows a plot of the TI profile in the y-axis as a function of the radial position in the x-axis, for three free-stream velocity values. The first thing to notice is that the TI profile is relatively more symmetric in comparison to the velocity profile, especially for the downstream positions corresponding to 2D and 3D. Moreover, the TI reaches a maximum peak at a location right behind the rotor in the wake at 1D, decreasing through the wake for the subsequent radial positions of 2D and 3D (Figure 12a). This trend is observed for all the three free-stream velocities analyzed in this work. Additionally, when comparing the TI profile between 1D and 2D/3D it is also possible to see the wake expansion effects as the fluid flow develops in the wake: the shape of the curves is slightly tighter for 1D than for 2D or 3D. Furthermore, the TI peak increases as the free-stream velocity increases. When considering a downstream position of 1D (Figure 12a): the TI reaches a maximum value of 0.35 for U = 10 <sup>m</sup>·s<sup>−</sup>1, while TI reaches a maximum peak of 0.65 for U = 15 <sup>m</sup>·s<sup>−</sup>1, and finally TI reaches 0.90 maximum peak for U = 24 <sup>m</sup>·s<sup>−</sup>1. This shows that there is a dependence of the TI behavior according to the free-stream velocity, and the same trend can be extended to the downstream positions of 2D and 3D. Figure 12b shows plots for the TKE as a function of the velocity and downstream distances (in rotor diameters) in the near wake. The TKE has some components: the advection by the mean flow, the transport by the vorticity, the TKE production, and the TKE dissipation. The TKE presents a similar trend observed in the TI, where the near wake immediately next to the rotor at 1D presents the TKE peak for all the velocities.

**Figure 12.** (**a**) Turbulence Intensity (TI) as a function of Velocity and downstream distances in the near wake; (**b**) Turbulence Kinetic Energy (TKE) as a function of Velocity and downstream distances in the near wake.

3.2.3. Pitch Angle (θ) Effect on the Near Wake

The Pitch Angle (θ) influences the near wake development in regards to the velocity deficit (Figure 13). The rotor design process aims to deliver the best aerodynamic performance according to

the blade geometry (chord length, airfoil, rotor diameter), and a specific set of operating conditions. It is important to point out that the designed pitch angle for the MEXICO rotor blade is θ = <sup>−</sup>2.3◦, corresponding to a TSR of λ = 6.6 for U = 15 <sup>m</sup>·s<sup>−</sup><sup>1</sup> and ω = 424.5 rpm. The pitch angle θ can significantly influence the near wake aerodynamic behavior. However, the far wake will not be significantly affected if the pitch angle is close to the designed condition. As can be seen by the axial velocity behavior (Figure 13), the velocity deficit is greater for negative pitch angle values than for positive values. This happens because in the case of the MEXICO rotor, negative pitch angle values are closer to the designed condition, thus extracting more energy from the incident wind. Consequently, the axial induction is greater for those pitch angle values close to the designed condition. Additionally, the velocity deficit increases as the pitch angle becomes more negative. This can be verified in Figure 13a,b, where a pitch angle of −1◦ resulted in a smaller velocity deficit in comparison to a pitch angle of −2.3◦ or <sup>−</sup>3◦.


**Figure 13.** Influence of the pitch angle (θ) in the wake for: (**a**) U = 10 <sup>m</sup>·s<sup>−</sup>1; (**b**) U = 15 <sup>m</sup>·s<sup>−</sup>1. The designed pitch angle is θ = <sup>−</sup>2.3◦.
