## 2 Materials and Methods
### Specification of the Numerical Analysis  
In this study, the geometries are analyzed under two-dimensional models, assuming that the rotor aspect ratio (\(H/D\)) is greater than or equal to the unit [31]. All geometries are analyzed in transient regime, under the same algorithms, parameters, and models of computational fluid dynamics (CFD) through the \(ANSYS\)_Fluent_ software. The turbulence model \(k-\omega~{}SST\) is proposed for its good performance in predicting free flows and adverse pressure gradients [32; 33; 34]. A _coupled_ scheme was selected for the pressure-velocity coupling algorithm and an implicit transient first-order formulation was used. The analysis domain is made up of two parts: a rotating circular region and a stationary rectangular region. The circular region contains the profile under study and rotates constantly at the determined velocity (\(TSR=1.2566\)). The rotating circular region is divided by a sliding interface, whose diameter does not significantly influence the results. However, a prudent distance is sought with respect to the walls of the geometry so that the high gradients that occur there due to the boundary layer phenomenon do not have to be divided into different regions. An air inlet is established at a velocity of 4 m/s (class 1 wind) [35], corresponding to a flow regime with a Reynolds number of \(6\times 10^{4}\). Similarly, an output to atmospheric conditions is set and the lateral field is simulated under symmetry conditions since there are low-scale gradients [32; 36] (Figure 3). However, established boundary conditions can make it difficult to deflect flow around the turbine as opposed to the restriction produced by the turbine, thus generating a blockage effect [37]. This produces an acceleration of the flow around the obstacle and means an over-prediction of the rotor's performance [38]. Figure 2: Reference system used for the analysis of geometries. In a two-dimensional analysis, the blockage ratio is defined as the ratio of the rotor diameter to the flow's domain width (\(D/W\)), so the blockage effect can be minimized by increasing the simulation domain scale with respect to rotor size [38]. Despite this, given that within the experimental designs the same boundary conditions and the same domain size will be used for all geometries studied, this does not represent a significant variation factor, so in spite of producing altered results, these will largely preserve their relationship to each other [37]. To know the value and trend of said alteration, an independence analysis is carried out for the computational domain, under the same conditions with which the experimental designs geometries are studied. The center dimensions profile is used as a test model. The results obtained in this analysis describe the behavior of \(C_{T}\) according to \(\theta\), for each tested domains (Figure 4). When estimating the average \(C_{T}\) for each computational domain, it is evidenced that the size of the domain has a notable effect on it and that its variation becomes smaller compared with the value corresponding to the larger-scale domain (domain 5). The asymptotic convergence indicator for the domain independence analysis according to [PERSON]'s extrapolation is 0.9521; whose closeness to unity indicates the existence of a convergence value [39]. Table 2 shows the results obtained when testing the different computational domains. Seeking a shorter simulation time, the general dimensions of the analysis domain are established for a blockage ratio of 20% (Figure 3), similar to the study carried out by [40], so its respective deviation must be taken into account. Figure 4: Torque coefficient (\(C_{T}\)) according to azimuth (\(\theta\)) for each domain. Figure 3: Analysis domain and boundary conditions. Similarly, to obtain an efficient number of partitions into which both the analysis geometry and the period to be simulated must be divided, it is necessary to perform a spatial and temporal discretization independence analysis, seeking to obtain a convergence in the result.