**1. Introduction**

The necessity for improving wake models has become more apparent over the last decade with the continuous growth of the wind energy market. Literature shows several analytical wake models: Infinite wind farm boundary layer model, Jensen wake model, Larsen model, dynamic wake meandering model, FUGA (Linearized RANS Model), and EllipSys3D. All these models are excellent tools to estimate wake effects, but there is still room for improvement. Usually, analytical models do not consider wake characteristics according to variable operating conditions. However, Computational Fluid Dynamics (CFD) models have the capability to model wake velocity deficit and Turbulence Intensity (TI) according to variable operating conditions. Although computationally expensive, CFD models are powerful tools that can be applied to solve some of the most complex problems in engineering. This work describes how operational parameters affect the aerodynamic behavior of the near wake of a wind turbine up to 5 diameters downstream of the rotor. Moreover, this study proposes a CFD modeling technique to characterize three-dimensional far wake effects, and numerically quantify the influence of some important wind farm design parameters on the far wake aerodynamic behavior. The literature shows that there is a gap in attempting to solve the Wind Farm Layout Optimization Problem (WFLOP) while still considering a rigorous evaluation of the wake

effects. The objective of this work is to develop a CFD model with such capabilities, applicable for future applications related to the WFLOP.

#### *1.1. Review: Wind Farm Aerodynamics*

## 1.1.1. Wake Aerodynamics

Wake models are usually divided in literature [1–4] in two categories: (1) Analytical/empirical/ explicit wake models; and (2) computational/implicit wake models. The analytical models solve a set of equations based on the conservation of mass and empirical relations of wake decay, characterizing the energy content in the flow field, and ignoring the details of the exact nature of the flow field. Kinematic models such as Jensen, Larsen, and Frandsen's model assume self-similar velocity deficit profiles, not solving the turbulence field but only the momentum equation [2]. The velocity deficit is derived from global momentum conversation, using thrust coefficient of the turbine as an input [1]. The computational models solve the fluid flow equations for the wake velocity and turbulence field, whether simplified or not [2].

#### 1.1.2. Wind Energy Computational Fluid Dynamics (CFD) Review

Although there are many CFD studies in the literature approaching wind energy, this is a field of study still in development. CFD modeling techniques applicable for wind turbines significantly vary in literature, showing that there is no well-stablished standard approach. This section presents a comprehensive literature review in CFD models applicable to wind energy, providing an overview on what has been done prior to this work. In regards to CFD techniques for modeling wind turbine flow field, the goal is to investigate what possibilities have not been explored yet, seeking to develop a novel wind turbine CFD model capable of evaluating far wake aerodynamics characteristics. As previously mentioned, a correct evaluation of such characteristics can help to achieve better solutions for the WFLOP.

#### NREL (National Renewable Energy Laboratory) Phase VI

Several studies utilized the NREL (National Renewable Energy Laboratory)/NASA (The National Aeronautics and Space Administration) Ames Phase VI experimental data campaign to validate their computational models, all of them using pressure coefficient on the blades and aerodynamic torque data for comparison. However, it is difficult to validate wake flow field since no wake measurements were performed in these experiments. Zhou et al. [5] performed Large-Eddy Simulation (LES) of the NREL phase VI, evaluating the effect of different inflow conditions (using user-defined functions) on aerodynamic loading and near wake characteristics. A structured multi-block mesh (with sliding mesh zone) was implemented with refinement on leading and trailing edges. They found that the wind shear and turbulence effects destroyed the uniform and symmetric wake profile in the far wake. Hsu et al. [6] validated a finite-element (Lagrangian–Eulerian) model of the NREL Phase VI using a non-structured rotating mesh. Wake characterization was not the focus of the study, which explains the wake made out of coarse non-structured cells with no refinement. Gundling et al. [7] evaluated low and high fidelity models using the NREL Phase VI for predicting wind turbine performance, aeroelastic behavior, and wakes: (1) The Blade Element Method (BEM) with a free-vortex wake; (2) the Actuator Disc Model (ADM); and (3) the Full Rotor Method (FRM). No specific information or sketch of the wake was provided or described. The FRM showed the largest wind deficits and the slowest dissipation rate for the far wake. Mo et al. [8] developed a study in more depth to understand wake aerodynamics performing a LES of the NREL Phase VI using the dynamic Smagorinsky model. Additionally, verification of the average TI was performed against an analytical model. They found that the downstream distance where instability and vortex breakdowns occur is dependent on wind free-stream inlet conditions: 7 <sup>m</sup>·s<sup>−</sup><sup>1</sup> happens at four rotor diameters, while 15.1 <sup>m</sup>·s<sup>−</sup><sup>1</sup> between 11 and 13 diameters. A decrease of the TI happened after instability and vortex breakdowns. The strategy for meshing the physical domain consisted of a virtual wind tunnel with the same dimensions of the NASA Ames with the rotor located at 2 diameters downstream of the inlet with a downstream domain of 20 rotor diameters in length. Choudhry et al. [9] performed a very similar CFD study of the NREL Phase VI using the same computational methods of the study conducted by Mo et al. [8], finding that regions of velocity deficit and high TI are within the high vorticity region. Choudry's study did not specify if the mesh is structured or unstructured.

## NREL 5 MW

Many studies have developed CFD models considering the NREL 5 MW wind turbine. Among these studies, Troldborg et al. [10] developed a wake CFD (EllipSys3D) study for the NREL 5MW considering three different models: (1) A fully resolved rotor geometry; (2) the Actuator Line Model (ALM); and (3) the ADM. A comparison for wake properties in uniform and turbulent inflows was performed. All the models correctly predict mean axial velocity within 4 radii downstream of the turbine for laminar inflow. The agreemen<sup>t</sup> between ADM and ALM methods is acceptable for the wake deficit. They found that the ADM/ALM model is sufficient to simulate turbines under Atmospheric Boundary Layer (ABL) conditions. Storey et al. [11] implemented a CFD model using a modified actuator technique to develop transient simulations, considering the NREL 5MW turbine. They achieved reduction in the computational time for the simulation while still keeping flow solution fidelity compared to the standard ADM. Seydel et al. [12] performed a Reynolds Averaged Navier-Stokes (RANS) k– ω simulation of the NREL 5 MW to study wake effects between two wind turbines. Réthoré et al. [13] investigated CFD techniques based on permeable body forces including: ADM, ALM, and the Actuator Surface Model (ASM). These approaches can potentially reduce the necessity for mesh refinement next to the rotor. Verification for the ADM in comparison with analytical solution for heavily-loaded turbines demonstrated that the ADM can be a cost-effective way to model wind turbine wake. The verification of the ADM showed that 10 cells per diameter are adequate to describe the near wake flow characteristics, and the cell size becomes less critical in the far wake. The computational domain extends 10 diameters laterally and 25 diameters horizontally, and the wake computational grid is uniformly spaced with cells of the same size. Heinz et al. [14] developed a fluid-structure interaction simulation using EllipSys3D and aero-elastic HAWC2 for the NREL 5 MW considering yaw and standard conditions. Miao et al. [15] developed an unsteady CFD (STAR-CCM+) model for the NREL 5 MW rotor considering yawed flow to investigate wake deviation. The full rotor geometry was modeled considering the NREL 5MW wind turbine, under neutral ABL conditions. Wilson et al. [16] developed a CFD model based on the RANS (OpenFoam and ANSYS Fluent) equations, considering k–ε and k– ω SST (Shear Stress Transport) turbulence model to investigate interactions between wind turbines in neutral ABL conditions. The ADM, the ALM, and the FRM were compared considering the NREL 5 MW. Weipao et al. [17] considered the tilt and cone angle to maximize the power generation of a wind farm for the NREL 5 MW.
