## 4 Discussion
### Performance Analysis of the Optimized Profile
As the blade approaches the position of greatest resistance (Figure 20f), the secondary element begins perceiving a slight flow, which, when deflecting it toward the concavity of the main element, allows it to counteract the additional resistance that this means, and makes the difference between the performance of the two profiles remain close to zero. In this way, it once again achieves a position in which it gets to divert a sufficient part of the flow to replenish with profit the losses that will be generated during the next cycle (Figure 20a). Figure 21 shows the behavior of the \(C_{T}\) for each rotor, obtained from the performance sum of each of the blades that constitute them. Figure 20: Aerodynamic behavior diagram of the rotor with multi-blade profile at the significant points of performance: (**a**) azimuth angle (\(\theta\)) of 10\({}^{\circ}\), (**b**) 45\({}^{\circ}\), (**c**) 115\({}^{\circ}\), (**d**) 135\({}^{\circ}\), (**e**) 225\({}^{\circ}\) and (**f**) 270\({}^{\circ}\). As can be seen in Figure 21, the position in which the greatest performance advantage occurs between both rotors corresponds to a \(\theta\) close to 115\({}^{\circ}\) (and its homologous at 295\({}^{\circ}\)). Likewise, the position in which the greatest decrease in performance is revealed is close to 185\({}^{\circ}\) (and its homologous at 5\({}^{\circ}\)). When comparing the graphs of Figures 19 and 21, it is possible to conclude that the blades that are at the back, respecting the flow (90\({}^{\circ}\) to 270\({}^{\circ}\)), are the greatest contributors in the performance differences between both rotors. Similarly, in Figure 21, it can be seen that the addition of secondary elements allows reducing the fluctuation in torque, partially decreasing performance at the peaks, but almost completely canceling the negative torque. Thus, the standard deviation decreases from 0.31 to 0.23, which means a reduction of close to 35%. In the contour graphs, the states of pressure and flow velocity through the geometries being studied are presented. In Figure 22, it can be seen that the pressure on the concave side of the advancing blade is higher in the multi-element profile than in the profile without secondary elements, when the rotors are in the position of the greatest advantage in performance. This higher pressure also induces a slightly higher flow through the gap generated by the profile's splitting (Figure 23). In Figure 23, a region of higher velocity can be seen on the secondary element of the returning blade, generated by the flow that deflects this surface toward the concavity of the main element, which consequently can mitigate the depressurization that is generated in this area (Figure 22). This can help counteract the additional resistance that the secondary element surface supposes on said blade. Figure 21: Difference between the torque coefficient (\(C_{T}\)) of each rotor, at a \(TSR\) of 1.0996. Figure 22: Pressure contour graphs for the split Bach profile (**left**) and the multi-blade Bach profile (**right**) at a rotor azimuth angle (\(\theta\)) of 115\({}^{\circ}\) and a \(TSR\) of 1.0996. When the rotors are in the position with greatest decrease of performance (Figure 24), there are no relevant differences in the pressure on the reference blade that justifies their low performance, so it can be attributed to the greater resistance generated by pressure and friction from the additional surface. In the same way, an area of higher pressure can be evidenced on the secondary element of the opposite blade, which promotes the superior performance of the multi-element rotor in the following positions, by diverting a part of the flow toward the concavity of the main element (Figure 25). Figure 23: Velocity contour graphs for the split Bach profile (**left**) and the multi-blade Bach profile (**right**) at a rotor azimuth angle (\(\theta\)) of \(115^{\circ}\) and a \(TSR\) of 1.0996.