**4. Discussion**

Discrepancies between experimental and computational data were also verified in other studies. First of all, the type of experiment apparently plays an important role in regards to the discrepancies. Particle image velocimetry (PIV) is a technique very sensitive to experimental conditions. In the case of the MEXICO experiment, the light path close to the hub of the wind turbine can potentially disturb and induce the oscillations in the velocity profile observed in the traverse at R = 1.4 m. The problem with light reflection caused by the blade or the nacelle was also described by Carrión et al. [33], however the numerical discrepancies found in this study could be related to numerical reasons. Wimshurst and Willden [38] mentioned that the upstream axial free-stream velocity is lower in the MEXICO experiment than the computational simulation, arguing that the open tunnel configuration caused expansion of the streamtube between the wind tunnel nozzle and the collector, consequently causing smaller axial induction downstream of the rotor. The computed axial velocity was lower than the experimental axial velocity, which was explained by the greater force applied to the flow by the rotor. Shen et al. [35] observed that the computed axial free-stream velocity upstream of the rotor was 2.5% lower than the experimental (15 <sup>m</sup>·s<sup>−</sup>1), and the discrepancies in the near wake were attributed to smaller thrust prediction. A potential contribution to discrepancies is attributed to the type of experiment (PIV measurements), which does instantaneous measurements containing fluctuations. Additionally, the wake fluctuation caused by the tip vortex could not be captured by the computational physical model employed in that study. The type of mesh refinement from Shen's study was claimed to be dependent on the upstream velocity, where a coarse mesh causes excessive dissipation. The sudden drop in velocity for the radial traverse at x = 0.3 m was attributed to the vortex shedding from the transition between the airfoils DU and Riso, and the intensity of the vortex was related to the change of circulation on the blade. Nilsson et al. [37] attributed the slightly overestimated axial velocity to the thrust, which was underestimated for all flow configurations. Furthermore, the light in the tunnel might have reflected on the turbine hub, affecting the experimental PIV measurements at the blade inboard radial position 0.62R (closer to the hub). Garcia et al. [36] found under-prediction of the thrust close to the blade root, attributed to rotational Coriolis effects and centrifugal forces in the boundary layer. Sorensen [41] found that the size of the nacelle influenced the inboard blade flow for yawed cases, so that the nacelle must also be included for accurate CFD modeling at the inboard region.

Our work, unlike previous efforts in literature, simulated the near wake of the MEXICO rotor within an extended downstream region including three diameters, while considering other TSR, free-stream velocity and pitch angle operating conditions. The same trend between axial induction and rotor loading was observed in other studies [27,31], in which the axial induction significantly increased from TSR = 4.2 to TSR = 10. Furthermore, the rotor loading influences the shape of the velocity profile at several downstream positions (Figure 10, Figure 11). While little perturbation to the velocity curves is observed for lower rotor loading, unsteady behavior/oscillation is present for higher rotor loading. The dependence of the velocity deficit on the streamwise distance is clearly more significant for higher TSR. These results agree with other studies in literature [46]. Figure 11 shows the radial traverse in the wake immediately behind the MEXICO rotor at x = 0.3 m, confirming the trend between loading and velocity deficit, even immediately adjacent to the rotor. Moreover, the tip vortices cause the region close to the blade tip to present the highest velocity deficit in comparison to the other blade radial locations; this will determine the wake expansion. Tari et al. [47] also found that the axial induction of horizontal axis wind turbines increases with the TSR, in which a maximum axial velocity deficit occurs between 0.75 < r/R < 0.9.

The TI aerodynamic behavior in the near and far wake was also characterized in previous studies. For instance, Shives & Crawford [48] found that the oscillating /fluctuating behavior is less significant for x/D > 5 in comparison to the near wake, and the curve shape becomes more similar to a Gaussian distribution. This trend was different in comparison to the velocity curve behavior, where the velocity curve starts to define its shape at x/D > 3. Chamorro et al. [49] investigated the effect of the Reynolds number on the wake characteristics, finding that the TI profile in the near wake is dependent on the

Reynolds number, and independent at approximately x/D = 4. It is pointed that the non-uniformity of the boundary layer influences the TI profiles to present relatively asymmetric distribution, which could also explain the asymmetric shape of the velocity profile (Figure 10). Additionally, the effect of the TI could still be observed even up to 12 rotor diameters downstream. Xie and Archer [50] found that the streamwise component of the Turbulence Kinetic Energy (TKE) is dominant for horizontal axis wind turbines. Turbulence Intensity contours showed that the streamwise component of the TI reaches a maximum at 5D, which extends up to approximately 15D, when it starts decaying. A low TI region happens immediately behind the rotor, which contradicts the TI trend behavior found in our study (Figure 9). Zhou et al. [23] investigated the influence of the inflow characteristics on the near wake of the NREL Phase IV, finding that the combination of inflow turbulence and wind shear can also have an impact on the turbulence generation in the near wake.

The pitch angle is proven to have impact on wind farms and wind many researchers. Markou et al. [51] showed that individual-pitch controllers allowed fatigue load reductions for offshore applications, while not significantly influencing the far wake behavior. Tests for a wake compensator resulted in a minimal reduction in average output power of 0.05% for 10D downstream distance. Kanev et al. [52] showed the benefits of using a pitch-based system for wind farms with turbine distances from 6D to 7D, in which 1% to 4% of the wake losses were regained yearly. Additionally, a lifetime extension of 1% was achieved by reducing fatigue loads. In the referred study, the wake loss reduction was found to be insensitive to a particular farm layout. Even higher benefits could be achieved by combining pitch-based and yaw-based wind direction wise systems, in which a pitch-based system would be operated for wind directions well-aligned with the rows of turbines, while yaw system would act as the wind comes at an angle in respect to the rows. Symmetrical layouts combining both systems could achieve almost the sum of the power production benefits of the two separate strategies.

Wake characteristics are closely related to the aerodynamic behavior of the blades. In this research, a numerical CFD model was developed based on MRF approach, which is a CFD technique where a reference frame rotates instead of the body itself. The MRF technique models the blade loading effect by applying an axial induction through the central disc. As a consequence of the axial induction exerted on the central disc, the velocity in the wake has a deficit in comparison with the free-stream velocity. Essentially, this is the same effect that blade loading induces on the wake, producing a velocity-deficit by extracting kinetic energy from the free-stream wind. The order of magnitude of the loading on the blades is a function of the thickness of the moving reference frame (rotational central disc), meaning that a thicker frame will have higher axial induction.

There are many different CFD modelling techniques suitable to mimic experiments. In this work, the main objective is to implement a steady-state CFD model for a quick evaluation of wake effects, aiming to create a computational tool to propose further improvements on the design of wind farm layout. It is important to emphasize that a Fluid-Solid Interaction (FSI) model of the MEXICO rotor is out of the scope of this work. A FSI model would elevate the computational expenses to the point of preventing the applicability of the model to evaluate multiple operational conditions in a reduced time. As we previously stated, the main objective of this research is to develop a computational tool capable of simulating wind turbine operation under variable operating conditions. The MRF technique is capable of representing the axial induction of the wake, allowing the simulation of variable wind operating conditions in a faster way. However, an accurate computation of the torque (consequently mechanical power) would require a FSI model. In these cases when steady state models using MRF approach are implemented, it is recommended to use a hybrid approach: the validated CFD results are utilized to evaluate the wake in terms of velocity deficit and turbulence flow field, and a computational model based on a BEM code could be used to compute the output power.

The modelling technique implemented in this study is the MRF. The model itself is an adaptation of the actuator-surface method: even though the full blade geometry was resolved using the CFD model, the solid blade geometry was suppressed from the rotating disc centrally located at the physical

domain. The remaining model has the blade surface geometry represented as solid walls located in the central actuator disc, but the interior part of the blade (solid) was suppressed. A high number of cells (10 million) is necessary to achieve a validation within 5% agreemen<sup>t</sup> (see Appendix A) between computational and experimental data for the mesh layout designed for this simulation. Other studies in literature confirmed the necessity for a high number of cells to achieve validation within reasonable agreemen<sup>t</sup> [31,33,35,38,41,45]. When solving the full rotor blade geometry, the most efficient way of reducing computational expenses while still keeping a good level of agreemen<sup>t</sup> between computational and experimental data is to improve the layout of the mesh. For part I of this study, we focused on developing and validating a wind turbine CFD model, evaluating near wake characteristics under variable operating conditions other than the ones analyzed in the MEXICO experiment. In the second part of this research (Rodrigues and Lengsfeld [53] in review), the model from this study was adapted to analyze an extended wake region while still keeping a similar number of cells. The objective of part II is to develop a CFD model to analyze wind turbines interaction in wind farms. In order to do that, we broke the physical domain into smaller parts to locally design the mesh. This by itself represents an improvement of the mesh layout because there is a reduction in the number of cells relatively to the area analyzed. Further work could achieve an even better mesh layout design. Considering the extension of our analysis to a wind farm, a CFD technique was introduced in the second part of this research ([53], in review) in which a profile is created for the outlet of a first simulation (representing the first row of turbines), and then plugged into a new simulation (as an inlet) to model a hypothetical downstream row of turbines. Even though there is a need for running multiple simulations to analyze interaction effects, we eliminated the need for simulating two turbines rows at once. This could potentially allow users to simulate multiple rows of turbines while still using reduced resources in terms of computational capabilities. Therefore, to study wind farm layout, it would not be required an exorbitant number of cells, reducing the computational cost of these types of simulations.

Even though RANS model using kω SST is suitable for complex boundary layer flows under adverse pressure gradient and separation such as turbomachinery and external aerodynamics, separation is typically predicted to be excessive and early. This can reduce the suitability of the model for free shear flows, such as wakes. According to Sanderse et al. [22], RANS is more prevalent to engineering for modeling turbulence in the wake because of the computational expenses, even though eddy viscosity-based models are proved to be diffusive. A Reynolds-stress model based on LES would capture the rotational behavior of the wake, however a LES has to be run for a sufficiently long flow-time to obtain stable statistics of the flow being modeled. LES requires substantially finer meshes than those typically used for RANS models [54]. The computational cost with LES is typically orders of magnitude higher than the costs for steady RANS calculations in terms memory RAM and CPU time. Usually, high-performance computing (for instance, parallel computing) is necessary for LES applications. The main shortcomings of LES is the high resolution requirements for wall boundary layers, where the large eddies become relatively small, limiting LES for wall bounded flows to very ow Reynolds number (Re~104–105) ([54]).

The CFD technique implemented in this work considers kω SST to numerically model wake effects of the MEXICO rotor. The model does not take into consideration transient effects such as the LES model. Another distinctive capability of LES models is the possibility of introducing wind fluctuations for the inlet by using Reynolds Stress components. In despite of that, according to Rodrigo et al. [55] the application of CFD in wind resource assessment is still largely based on RANS models since LES or Detached Eddy Simulation (DES) models are still computationally expensive. According to Rodrigo et al. [55], the compromise between fidelity and cost for wind resource assessment is found with CFD models based on RANS simulations. Moriarty et al. [56] presented a comparison between several LES and RANS models in terms of accuracy on predicting wake deficit, considering the Sixberium and the Horns Rev and Lillgrund wind farms. The comparison showed that there is no apparent winner, as sometimes LES or RANS models have lower normalized average error than lower fidelity models, but often their error is higher. They concluded that more detailed

insight into individual models and more experimental observations are required to provide better information about model accuracy. Delineated observations of wind farms under different operating and atmospheric conditions are required for providing better validation data instead of using averaged data over long periods of time. Such information will give the best practices regarding wake modelling and wind farm design, helping to quantify uncertainty bounds for different modelling tools and to determine useful quantities for validation in order to guide future measurement campaigns.

Reducing computational requirements for wake simulations is a tremendously demanding topic for wind energy research applicable for wind farms. The physical modeling implemented in this work essentially represents the forces using a rotating central disc, but careful work has been taken to correctly represent these forces. The model validation process is described throughout Section 3.1, including blade loading and near wake flow field. The full blade surface geometry was modeled, including twist angle, pitch angle and variable chord. This approach is similar to the actuator surface method. According to Sanderse et al. [22], the actuator surface approach is more accurate than the actuator disc and actuator line models. Still according to the same reference, even though the actuator disc method still remains the most widely used method for multiple wake simulation because of its reduced computational requirements, current research approaching the use of actuator surface technique has been evolved because of its relatively higher accuracy on wake modeling.

Extremely valuable work has already been carried out in literature to solve validation of near wake flow field using the MEXICO experimental dataset. In this current research, an extensive numerical effort has been performed to provide new insights related to near wake aerodynamics, which are crucial to understand wake characteristics and consequently to propose improvements to wind farm layout. The influence of some important design parameters on near wake aerodynamics has been determined, providing numerical estimates of wake profile. Such an extensive numerical effort specifically on near wake modeling had not been addressed in literature yet. The simulation of a range of pitch angle values provided a numerical estimate on the influence of this design parameter on the velocity deficit in the near wake. Additionally, a detailed study provided numerical estimates on the impact of TSR on velocity deficit and turbulence intensity/turbulent kinetic energy on the near wake. Furthermore, the near wake analysis in this work considered an extended near wake region: the original MEXICO experiment covered a near wake region up to 1.33 rotor diameters behind the rotor, while in this work the near wake analysis considers a length up to three rotor diameters. A previous work carried out by Bechmann et al. [31] considered an extended near wake region up to three diameters downstream of the MEXICO rotor, simulating the same operating conditions of the original experiment (one TSR value for each of the three velocities tested). Here in this work, the analysis considered different loading and pitch angle conditions, not only analyzing velocity flow field but additionally evaluating turbulent characteristics of the wake. Furthermore, the validation in this work implemented a particular type of lateral boundary condition never before applied for wind turbine CFD analysis: pressure-far-field. The implementation of pressure-far-field boundaries prevent the need for modeling tunnel lateral wall effects, allowing for coarse mesh at lateral boundaries, which are not meaningful for modeling experiments such as the MEXICO rotor (performed in open jet wind tunnel) or even to model turbines in natural field.

In part II of this work [53], an adaptation of CFD model validated in part I was carried out by extending the wake region to numerically model far wake effects. One of the novel aspects of part II is the application of a validated wind turbine CFD model to propose improvements for wind farm layout. The majority of previous works in this topic (wind farm layout optimization) rely on analytical models or non-validated CFD models. As pointed out by Rodrigo et al. [55], "Wind turbine wake aerodynamics is a topic of study that has attracted many researchers, which are divided into the ones studying rotor aerodynamics (near wake) and wind farm array efficiency (far wake). It is common sense that a more realistic description of the wake generation mechanisms in the near wake allows to understand and improve far wake models." In part II, a CFD technique that has never been applied before to solve wind turbine wakes interaction is introduced: we separately implement each wind farm

row, creating a profile from each outlet. This profile is implemented as the inlet of a new simulation, allowing to simulate wake interaction effects. The technique allows to simulate multiple wind turbine rows with relatively reduced computational resources in terms of processers, since there is no need to simulate multiple turbines at once. Researchers may take benefit by using this technique to model wind farm rows while still considering wake interaction effects.
