## 2 Materials and Methods
### Specification of the Experimental Setup  
To verify the results obtained numerically, an experimental study was carried out in which the conventional semicircular profile, the split Bach profile, and the multi-blade Bach profile were evaluated using a wind tunnel (Figure 8).  
The study was carried out in a closed test section of 50 cm \(\times\) 50 cm, with a rotor model of 200 mm in diameter and 200 mm in height, corresponding to a blockage ratio of 16% (Figure 9). Plates were installed at the ends of the rotor with a diameter of 220 mm made with 6 mm thick acrylic [41]. The blades on the models were made from 20-gauge aluminum sheet. The experiment was carried out in the city of Medellin, Colombia, with an approximate air density of 1.058 kg/m\({}^{3}\), corresponding to a height of 1500 meters above mean sea level (MAMSL) (ISO 2533).  
\begin{table}
\begin{tabular}{l l l l l l} \hline \hline
**Time Step** & **1** & **2** & **3** & **4** & **5** \\ \hline Number of elements [TS/rev] & 90 & 180 & 360 & 720 & 1440 \\ Averaged \(C_{T}\) & 0.2177 & 0.2851 & 0.3211 & 0.3405 & 0.3493 \\ Deviation & 37.68\% & 18.39\% & 8.08\% & 2.53\% & \\ Simulation time [h] & 3.73 & 6.10 & 10.52 & 19.87 & 33.42 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Temporal independence test results.  
Figure 8: Test rotors of the conventional semicircular profile (**right**) and multi-blade Bach (**left**) (the secondary blades were installed on the split Bach profile rotor model).  
Figure 9: Schematic of the experimental setup: (1) wind tunnel, (2) test section, (3) test model, (4) torque sensor, (5) couplings, and (6) braking electric motor.  
The test consisted of allowing an established air flow at a velocity of 4 m/s through the wind tunnel (Figure 10). The flow velocity was adjusted through an ultrasound anemometer located 0.5 m upstream of the rotor, before conducting each test. This was withdrawn again to avoid disturbance of the incident flow on the rotor.  
The flow inside the tunnel accelerated the rotor from zero velocity to its limit velocity without load. Once the rotation regime stabilized, a power signal was sent to an electric motor, which was constantly increasing its intensity. The load exerted by said motor made the test rotor brake until it was completely blocked (Figure 11).  
Measurements were made using a torque sensor with encoder and a control system that allowed modifying the load exerted by the electric motor from the pulse width modulation (PWM) in its power signal, regulated at 3.5 V.  
The purpose of the experimental study is to validate the results obtained from the numerical analysis rather than to approximate the real performance of the rotor. Therefore, in order to compare the results obtained experimentally with the numerically estimated data, it was necessary to replicate the experimental conditions within a three-dimensional numerical model formulated according to the system's degrees of freedom (6-DOF solver). In this regard, the blockage ratio within the wind tunnel does not represent a variation factor between both approaches.  
For this, the same conditions with which the two-dimensional models were studied were established, in addition to assigning the required degree of freedom to the turbine's axis of rotation (Figure 12. In the same way, the spatial and temporal discretization  
Figure 11: Velocity during tests histogram.  
Figure 10: Wind tunnel used for experimental development (**left**). Detail of the experimental setup and the measurement system (**right**).  
independence analysis was carried out, stabilizing the results, and obtaining an efficient discretization of 2,120,850 elements and a time step of 0.001 s (Figure 13).