## 4 Discussion  
### Performance Analysis of the Optimized Profile  
To obtain a better estimate of the actual turbine performance, the simulation of the optimized rotor is performed using a larger scale simulation domain. A square domain whose side is 50 times the diameter of the rotor is used (blockage ratio of 2%), seeking to minimize the blockage effect produced by the rotor in the flow field. Rotors with the conventional semicircular profile and the split Bach type without secondary elements are also analyzed under the same conditions. In this way, the rotor with a conventional semicircular profile has a \(C_{P}\) of 0.195. Likewise, the geometry with the split Bach type profile without secondary elements allows reaching a \(C_{P}\) of 0.2661. In contrast, the rotor with the optimized multi-blade Bach profile develops a \(C_{P}\) of 0.2948, which represents an increase in its performance of 51.2% and 10.8%, respectively. To understand the aspects that led to this result, the variations in the aerodynamic behavior of the blade when implementing secondary elements are analyzed. To do this, the \(C_{T}\) in one of the blades of each rotor is determined as a function of \(\theta\), at a rotation velocity of 7 rps (\(TSR=1.0996\)), corresponding to the maximum performance of the Bach type profile for the 2% blockage ratio (optimal velocity decreases to convergence by reducing blockage effect). This is done under the simplification that the two blades that constitute each rotor have similar and counter-phase performances. In Figure 19, it can be seen that the maximum torque from the two types of blades is obtained at the beginning of the advancing phase, in a position close to 30\({}^{\circ}\), which allows to conclude that it is produced in contribution of drag force and lift force. In the same way, the minimum torque occurs during the returning phase when there is greater flow obstruction (close to 270\({}^{\circ}\)), which indicates that it is mainly caused by the parasitic drag force [19; 23]. When analyzing Figure 19 in detail, it can be seen that the advantage of the multi-blade profile presents when the advancing phase begins (Figure 20a), ascending to a medium height peak generated by the greater pressure that causes the flow deflected by the secondary element toward the most extreme zone of the concavity of the main element, where, as it has a greater eccentricity, a greater torque is generated (Figure 20b). This advantage continues until the blade is aligned with the flow on its way to the rear, where the drag force and its eccentricity decrease, causing a decrease in the torque generated. During this journey, in a position close to 115\({}^{\circ}\), the secondary element shows its greatest  
Figure 19: Difference between the torque coefficient (\(C_{T}\)) in one of the blades of each rotor, at a \(TSR\) of 1.0996.  
contribution by prolonging the drag force action and allowing the rotor in question to maintain a higher torque for a longer period (Figure 20c). Once the opposite blade overlaps, the flow that affects the reference blade becomes obstructed, causing it to decrease the positive torque and start to represent a load, since it requires to be moved through the fluid (Figure 20d). In this way, the reference blade travels a negative torque path that is asserted in the returning phase, when the flow incises the opposite way. While the secondary element remains hidden from the flow, it does not show any usefulness, but it does suppose a greater resistance by having to displace a greater mass of fluid in its movement, causing a detriment in performance compared to the base profile. This disadvantage reaches its lowest point at a position close to 225\({}^{\circ}\) (Figure 20e).