**4. Discussion**

The MEXICO experiment tested specific operating conditions, providing experimental PIV (Particle Image Velocimetry) measurements for the velocity flow field in the near wake. Far wake measurements in a controlled (wind tunnel) was not viable because of technical constraints, which explains why the MEXICO experiment did not provide such measurements. Although it is impossible to compare the far wake data from the simulations performed in this work against experimental data from the MEXICO rotor, the results of the velocity in the far wake can be verified by comparing other relevant works in the literature. Such comparisons show that the results of the CFD model developed in this work consistently agree with previous literature studies. It is worth mentioning that the following studies cited in this discussion neither computationally implemented the MEXICO rotor nor the exact same operating conditions than the ones implemented in this current work. Despite that, the comparisons presented in this discussion intend to verify an agreemen<sup>t</sup> with an acceptable range of consistency.

For instance, the range of velocity deficit found in this study agreed with other works in literature. Some of these studies specified operating conditions in which the results were obtained. Mittal et al. [54] analyzed operating conditions of TSR = 6 at x/D = 5, finding 40% of velocity deficit and a not completely symmetrical radial curve profile. Asymmetry was attributed to interaction with the tower. For the off-design condition of TSR = 3, the velocity deficit had a peak of 30% at x/D = 5. For the off-design condition of TSR = 10 showed a peak of 80% of the velocity deficit at x/D = 1, and 40% at x/D = 5. Although the velocity deficit values were slightly greater than the ones found in this work, there is consistency between the results found in this work (Figure 7), in which the estimated velocity deficit showed a value of approximately 25% for a TSR = 6.6 and 15% for a TSR = 4. Storey et al. [37] found that as the free-stream velocity increased and the TSR decreased (rpm maintained constant), the overall velocity deficit decreased. These results confirm the trend found in Figure 7, Figure 8, and Figure 9: A decrease of the TSR, results in a decrease of the velocity deficit. Additionally, Storey et al. [37] found that the shape and magnitude of the velocity deficit vary significantly with the wind speed and TSR. The expansion of the wake varies with wind speed, confirming the trend observed in this work in Figure 11b: The wake presents more pronounced expansion as the velocity varied from 10 <sup>m</sup>·s<sup>−</sup><sup>1</sup> to 15 <sup>m</sup>·s<sup>−</sup>1.

Moreover, even though some of the works in the literature did not specify operating conditions regarding TSR, their data consistently agree with the results for the velocity deficit found in this work. Prospathopoulos et al. [22] considered a downstream spacing of 5 D between the turbines, finding a

velocity deficit in the wake of 40% at 2.5 D and 30% at 3.5 D for the stable stratification case of the Energy Research Centre of the Netherlands (ECN) measurements. Those results are similar to the values found in this present work (Figure 7). Gundling et al. [7] modeled wake wind speed deficits for different wake models and compared them. The UWAKE (Free-vortex Wake with a BEM) model has a maximum velocity deficit of 67% at 4R for 5 <sup>m</sup>·s<sup>−</sup>1, and a maximum velocity deficit of 81% at 7R for 10 <sup>m</sup>·s<sup>−</sup>1. The FLOWYO (ALM and ADM) LES has a maximum velocity deficit of 70% at 3R for 5 <sup>m</sup>·s<sup>−</sup>1, and a maximum velocity deficit of 83% at 6R for 10 <sup>m</sup>·s<sup>−</sup>1. The wake deficit is similar for the FLOWYO and UWAKE, but little diffusion of the wake was found when using FLOWYO RANS. The diffusion in the wake is similar using UWAKE and FLOWYO LES, while the FLOWYO RANS had not enough turbulent eddy-viscosity produced by the ADM to result in a similar wake diffusion compared to FLOWYO LES and UWAKE. The HELIOS DES model has a velocity deficit of 58% at 4R for 5 <sup>m</sup>·s<sup>−</sup>1, and 65% at 9R for 10 <sup>m</sup>·s<sup>−</sup>1. All those values are within an acceptable range when compared to the values found in this work (Figures 7 and 8). Troldborg et al. [10] analyzed different turbulent inflow conditions for a FRM, an ALM, and an ADM approach. The ALM and the ADM showed the same results for velocity deficit in the wake. A maximum peak of approximately 60% was found at 2 R, which remained almost constant in the same value up to the 10 R analyzed. The FRM showed the same 60% velocity deficit at 2 R, but decreasing the peak value to approximately 50% at 10 R. Those results are similar to the ones found in this research for the wake characteristics (Figures 7 and 8).

Furthermore, a similarity in the shape/format of the wake profile was identified. Mo et al. [8] determined velocity profiles at the wake for several downstream positions. A near-symmetrical but not completely at the blades location, the vertical wake velocity profile had a clear W shape at 1 D and 2 D, and overall the velocity deficit decreased as the free-stream velocity increased from 5 <sup>m</sup>·s<sup>−</sup><sup>1</sup> to 15.1 <sup>m</sup>·s<sup>−</sup>1. This was attributed to the state of the completed attached flow in the turbine blade for smaller velocities, and not for more extracted power from the incident wind. Wake shape was not well defined for the further downstream positions. The W shape of the velocity deficit curves is similar to the curve shape found in this present work in Figure 9a for TSR = 4.

The TI behavior showed an increase of its peak value as the TSR increased (Figure 9b). For the cases of wake interaction (Figure 6a,b), there was a considerable increase of TI in the wake of the second row. A verification analysis consistently agrees with the literature results. Troldborg et al. [38] analyzed two turbines case for wake interaction and found that a spacing of 7 D was large enough to allow the wake profile to reach a steady state after the second turbine. AbdelSalam et al. [55] found 65% velocity deficit peak for x/D = 2, 60% velocity deficit peak at x/D = 4, 50% peak velocity deficit at x/D = 6, and 30% velocity deficit peak at x/D = 8. Those results are within an acceptable agreemen<sup>t</sup> with the results found in this work (Figures 9–11). Wilson et al. [16] modeled ADM, ALM, and FRM (full rotor). The wake interaction case showed a strong interaction of wakes when spacing 5 D, which is not easy to compare with our study because the downstream distance implemented is not the same. For a single turbine case, the velocity deficit found by Wilson et al. [16] was slightly higher for ADM than ALM, and MR presented the highest velocity deficit in the wake. The TI was significantly higher for ADM and ALM when compared with FRM.

In regards to field experimental data, Barthelmie et al. [62] studied the influence of the downstream spacing between the turbine rows in the normalized power for the case of the Horns Rev offshore wind farm. Considering 8 <sup>m</sup>·s<sup>−</sup><sup>1</sup> and the 2◦ sector and a downstream spacing of 7 D, the ratio between the output power of the second and first turbine row was approximately 58%. The output power ratio between the second and third row was 56%. For a downstream spacing of 9.4 D, the ratio between the output power of the second and first turbine row was approximately 70%. The output power ratio between the second and third row was 68%. For a downstream spacing of 10.5 D, the ratio between the output power of the second and first turbine row was approximately 75%. The output power ratio between the second and third row was 70%. Considering 8 <sup>m</sup>·s<sup>−</sup><sup>1</sup> and the 30-degree sector, the downstream spacing of 7 D had a ratio between the output power of the second and first turbine row of approximately 80%. The output power ratio between the second and third row was 79%. For a

downstream spacing of 9.4 D, the ratio between the output power of the second and first turbine row was approximately 85%. The output power ratio between the second and third row was 80%. For a downstream spacing of 10.5 D, the ratio between the output power of the second and first turbine row was approximately 88%. The output power ratio between the second and third row was 83%. As stated at the beginning of the discussion, operating conditions as well as turbines were not the same of the ones analyzed by Barthelmie et al. [62], such that no direct comparison can be made. However, all those results consistently agree within acceptable levels with the results found in this work (Figures 6 and 9–11). In this work, a downstream distance (spacing) between rows was 10 D, and the estimated ratio between output power of the first and second row was within the range of 73% (for a TSR = 4) and 35% (TSR = 10). A TSR = 4 was a more descriptive operating condition for commercial turbines than a TSR = 10, since turbines are more likely to operate in higher TSR conditions (such as TSR = 10) and only in extreme events such as a wind gust. Figure 6 allows a comparison between the second and third row for a TSR = 6.6, showing a power ratio estimate of 56%. The verification against Barthelmie et al. [62] results is especially important since these are wake field data, showing that the CFD model developed in this work is consistent even when compared against atmospheric measurements.

The discussion of Figure 6 gives a good sense on why to simulate two turbines instead of just one. Figure 6 shows the wake interaction effect that the two-turbine side-by-side case can cause on the TI profile in the wake region between these turbines. The simulation of only one turbine would not allow the detection in the increase in TI levels in the referred region. Moreover, a major objective of this research was to create a computational tool to be implemented in future research aiming to improve wind farm land use by investigating the ratio between output power and area for both aligned and staggered configurations. In such a study, TI effects caused by wake interaction need to be pointed out when proposing improvements for land use. This explains the need for simulating at least two turbines.

There are different approaches to model wind turbines, and some of the most common ones are ADM, ALM, and ASM. The ALM represents the blade by a line, and the ASM represents the blade by a planar surface. The ADM does not model the blades surface, and the rotor is modeled by an infinitesimal disc that represents a discontinuity in pressure. All the actuator approaches (ADM, ALM, and ASM) require knowledge of tabulated lift and drag on the blades, and they require corrections for Coriolis, centrifugal, and tip effects when 2D airfoil data are used [3]. According to Vermeer et al. [63], there are many reasons for 2D airfoil data to be corrected to better represent 3D cases. For instance, rotational effects limit the growth of the boundary layer at separation, resulting in increased lift for 3D cases in comparison with 2D cases. Moreover, the drag coefficient can largely differ for 3D cases in comparison with 2D because airfoil characteristics depend on the aspect ratio of the blade. Finally, airfoils under large temporal variations of the angle of attack present hysteresis that changes the static airfoil data. There are some critiques of actuator models. According to Sanderse et al. [3], the ASM requires more accurate airfoil data, as well as knowledge of pressure and skin-friction on the airfoil. According to Churchfield et al. [64], one critique of the ALM is that it does not model the surface of the blade, and in this way this technique is not capable of replicating finer flow features such as boundary layer and separation at high angle of attack. In spite of that, these techniques are still widely used because of the reduced required computational costs.

Previous works in the literature discussed the accuracy of ADM, ALM, and ASM models. Even though the referred models generally represent aerodynamic performance in a satisfactory way, there is a consensus about the need for improvements for properly representing wake flow field under more complex fluid flow configurations. Gundling et al. [7] found that the aerodynamic performance for the NREL Phase VI is well predicted at pre-stalling conditions by low complexity models (BEM and actuator approaches), presenting a similar level of accuracy as higher complexity methods (FRM CFD). The results for high and low fidelity models differ for stalled conditions, but they generally present a good agreemen<sup>t</sup> for other less complex situations. The aerodynamic performance at the transition regime was not well predicted by neither low complexity nor high complexity models, but high complexity models accurately predict performance at higher wind speeds when stalling is dominant at the blade surface. The use of a high complexity model (FRM CFD) with adaptative mesh accurately solved the far wake flow field up to a distance of 20 radii downstream of the rotor, but did not show remarkable benefits for performance prediction, in which only the near wake up to 1 radius downstream of the rotor was resolved. Troldborg et al. [10] found that the wake predicted by the ALM and the ADM have very close agreemen<sup>t</sup> for uniform inflow conditions, but there is a significant difference when compared with the full resolved rotor method. Additionally, the fully resolved rotor presented higher turbulence levels in the wake. At turbulent inflow, the three methods (ADM, ALM, and FRM) present a close agreement. Troldborg et al. [32] also found good agreemen<sup>t</sup> between computational and field data for the turbulence flow field and mean wake deficit. Réthoré et al. [13] compared improved ADM approaches with a CFD FRM, finding significant differences in the turbulence flow field at the wake. The blades and the nacelle from the FRM approach showed a production of turbulence several orders of magnitude higher than the turbulence produced by the ADM. Theunissen et al. [19] accurately performed power calculations using ADM but they found differences in comparison with experimental data for the wake velocity profiles. Storey et al. [37] showed that correct modeling of the ABL and turbulence inflow conditions are important to determine the stability of wind turbine wakes, which may sugges<sup>t</sup> that FRM approach is more suitable for more accuracy on wake prediction. Laan et al. [39] showed that there can be improvements to the actuator approaches by introducing new methodologies to better represent the forces on the rotor.

Even though actuator approaches have still been widely applied in research because of its reduced computational costs, as Sanderse et al. [3] points out, there is need for a detailed study on the influence of exact blade geometry on far wake characteristics. In order to account for the influence of blades geometry on wake characteristics, the FRM CFD approach has been proved as a powerful tool for wind farm design. Unlike the ADM, ALM, or ASM, the CFD model of this work is a direct modeling approach of the rotor which considers the exact 3D blade geometry, including variable chord length, local twist angle, and pitch angle. The boundary layer was solved using 10 inflation layers with a ratio of 1.1 to ensure y+ < 1 next to the blade surface. Therefore, the CFD model of this work does not require the use of tabulated lift and drag data as does the ADM, ALM, and ASM. The capabilities of the model developed in this research allow the evaluation of wind turbine wakes interaction for multiple turbines while still using reduced computational resources. Even though further improvements of the modeling technique implemented in this research might be necessary to account the influence of downstream rows on the wake of upstream rows, the technique is promising towards reducing the computational costs for wind farms simulation. The model is a steady state approach (RANS) aiming to save computational time but can easily be improved to a transient simulation by using a sliding mesh. Moreover, the model of this work has been validated in part I [56] against experimental data for the near wake velocity field. This brings more confidence that the model can properly represent aerodynamics characteristics of the wake flow field. As pointed out by Rodrigo et al. [47], a more realistic description of the wake generation mechanisms in the near wake allows to understand and improve far wake models.

The method implemented in this work applied the outlet from upstream rows as the inlet of downstream rows, with the aim of studying wake interaction effects. This has been performed in this work in a one-way coupling, meaning that only the wake effects from an upstream row will be experienced by downstream rows. A possible effect on upstream rows coming from the interaction with a downstream row (e.g., a second row influencing the far wake of the first row) has not been considered in this work. This might be particularly important for the case of staggered wind farms, which are more densely packed than wind farms with aligned rows. In spite of that, the results presented in this manuscript considered spacing between rows (10 rotor diameters) large enough to dissipate the influence of downstream rows on the wake of an upstream row. A further improvement of the model developed in this research could include the development of a two-way coupling method capable of simulating the effects of downstream rows on the wake of an upstream row, which, as previously mentioned, might matter for the case of staggered farms. Aligned configurations will typically have greater spacing between rows, which potentially dissipates the referred wake interaction effects.

Inflation layers (Figure 2f) were implemented next to the blade surface, keeping y+ < 1 at this location for accurately characterizing boundary layer effects. In ANSYS Fluent, inflation layers can be automatically generated next to selected surfaces, regardless of the surface length (scaled or full-size blades). As specified in the methods section, 10 inflation layers were sufficient to keep y+ < 1 next to the prototype blade surface. In the case of a full-scale wind turbine which operate at higher Reynolds number in comparison with scaled prototypes, a different mesh resolution would be necessary to resolve boundary layer effects. The method implemented in this work would require a larger quantity of inflation layers to achieve mesh resolution small enough to keep y+ < 1 close to the blade surface of a full-scale turbine. The increase in the quantity of inflation layers would require an extra spent, making it more computationally expensive to keep a low y+ value for full-scale rotors. Even though the challenges previously discussed could require more computational costs, they would not prevent the method to be applicable for characterizing full-scale turbines. Moreover, wind turbine wake characteristics have been successfully studied using scaled prototypes such as the one implemented in this work (MEXICO rotor). Whale et al. [65] performed PIV measurements for an untwisted prototype with a flat plate airfoil profile, operating at TSR within 3 and 8 and Reynolds number within 6400 and 16,000. The study showed that wake behavior is insensitive to blade chord Reynolds number, as long as similarity of the TSR is maintained. This is the same hypothesis assumed in this current work (described in Section 2.4), where we assumed that wake similarity can be achieved by matching TSR values of scaled and full-scale turbines. Hossain et al. [61] performed wake measurements of a 500 mm four-bladed turbine using a PIV system, ultrasonic anemometers, and hot-wire anemometers. They performed the same measurements for a 1/10 scaled prototype aiming to study geometry similarity, finding that the wake decays at almost the same levels for the full-scale and the prototype turbines. Ivanell et al. [30] implemented an ADM model for a 0.2 m diameter turbine, showing that the power coefficient is independent of Reynolds number if the Reynolds number is greater than 1000. Additionally, they found that the Reynolds number does not affect the strength of the wake vortex, but only the radial vorticity distribution. Sturge et al. [60] performed an experiment using a wind turbine prototype in which the blade Reynolds number was two order of magnitude lower than the Reynolds number of common full-scale turbines. They presented an interesting discussion about scaled turbines, showing that the Reynolds number became less important for far wake modeling when the ADM was implemented. All these studies mentioned above are examples in the literature that sugges<sup>t</sup> that wake characteristics can be understood by using scaled turbines.
