## 3 Results
### Flow Patterns and Dead Agitation Zones
In this case, the maximum \(E_{ca}\) to which the microalgal cells will be exposed is estimated to be 1.6618 \(\times\) 10\({}^{-5}\), 2.1705 \(\times\) 10\({}^{-5}\), and 2.7470 \(\times\) 10\({}^{-5}\) J, at 35, 40, and 45 rpm, respectively. The collisions between the cells and the stirrer are those that cause the most damage to the culture since, in this area, there is greater turbulence, fluid velocity, and suction and discharge of the stirrer. It is important to note that in Raceway systems, this parameter has not been determined, so there are no values in the literature to compare. In contrast, [PERSON] et al. [28] carried out cultures of _Xanthomonas campestris_ under different hydrodynamic conditions in a stirred tank bioreactor, in which they reported \(E_{ca}\) values of 1.3 \(\times\) 10\({}^{16}\) J, 5.5 \(\times\) 10\({}^{16}\) J and 16 \(\times\) 10\({}^{16}\) J at typical stirrer speeds of 0.246 m/s, 0.517 m/s, and 0.821 m/s respectively. Although the geometric configuration of the bioreactor of [PERSON] et al. [28] is different from that of the present study, the typical speeds of the stirrer are in a similar range (Table 3). The \(E_{ca}\) values of the present work are much lower, which causes the cellular damage to be minimal. This is thanks to the sign of the curved agitator (turbine type), which decreases cavitation in the agitator zone when it drives the fluid, creating a laminar underlayer at the solid-liquid interface, which leads the cells to move parallel to the flow lines, as indicated [PERSON] [29]. The values of the parameters in Table 3 increase by the increase in angular velocity, except for the Power Number (\(N_{P}\)), which decreases with increasing power consumption (\(P\)). These values are expected to be the maximums presented in the cultivation of the microalgae consortium. In all cases, the Reynolds number corresponds to the turbulent regime in the stirrer (\(Re_{st}\)) and the channel (\(Re_{ch}\)). The difference observed in these two zones is that the first depends on the annular velocity and the second on the flow velocity [11; 30]. [PERSON] et al. [7] state that in the Raceway bioreactor, the flow remains turbulent with \(Re\) values > 1000. However, this criterion is not always met since the Raceway bioreactor is composed of channels, and the flow in these can be considered laminar with \(Re\) values < 10,000 [15]. On the other hand, the hydrodynamic stress (\(\tau\)) was 0.3576, 0.3834, and 0.4072 Pa at 35, 40, and 45 rpm, respectively, which was maintained when the microalgae were cultivated. These stress values are lower than those found by [PERSON] et al. [16] in a simulation with CFD, who reported \(\tau\) of up to 8 Pa with velocities of 0.6 m/s, which would cause greater cellular damage. Given that \(\tau\) provides a significant contribution to cell damage, the values shown in Table 3 represent less damage compared to the values reported by [PERSON] et al. [16]. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \(\omega\) (rpm) & \(v\) (m/s) & \(v_{tip}\) (m/s) & \(E_{ca}\) (J) & \(Re_{st}\) & \(Re_{ch}\) & \(Fr\) & \(P\) (W) & \(N_{p}\) & \(\tau\) (Pa) & \%\(dz\) \\ \hline
35 & 0.3949 & 0.3115 & 1.6618 \(\times\) 10\({}^{-5}\) & 21,325 & 35,900 & 0.7974 & 0.4743 & 7.1489 & 0.3576 & 13.48 \\
40 & 0.4494 & 0.356 & 2.1705 \(\times\) 10\({}^{-5}\) & 24,371 & 40,855 & 0.9075 & 0.542 & 5.4734 & 0.3834 & 7.93 \\
45 & 0.4903 & 0.4006 & 2.7470 \(\times\) 10\({}^{-5}\) & 27,418 & 44,573 & 0.9901 & 0.6098 & 4.3247 & 0.4072 & 4.61 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Hydrodynamic parameters in abiotic media.