## 5 Results and Discussion
### Influence of Different Geometric Configurations on the Fluid Dynamic Behavior and Mixture Time
For those cases that achieved equilibrium more quickly (\(L/B=0.02\) and \(L/B=0.14\)), it was noted that the smallest standard deviation and consequently the best homogenization occurred when \(L/B=0.14\) (the baffles were shorter than the case with \(L/B=0.02\)). However, the case that presented the smallest standard deviation of all was when \(L/B=1.0\), which only required 0.5 s longer for homogenization than those mentioned above. In this case, the baffles had the shortest length; moreover, performance was nearly two times better than the unbaffled configuration when minimization of standard deviation was used as the  
Figure 18: Distribution of the fields of turbulence viscosity in the baffled tank for different ratios of \(L/B\) compared to the unbaffled tank. \begin{table}
\begin{tabular}{c c c} \hline  & **Time (s)** & **Relative Difference (\%)** \\ \hline Unbaffled & 5.0 & 4.82 \\ \hline \(L/B=1.00\) & 4.5 & 3.61 \\ \hline \(L/B=0.29\) & 4.5 & 1.18 \\ \hline \(L/B=0.14\) & 4.0 & 3.12 \\ \hline \(L/B=0.08\) & 4.5 & 3.01 \\ \hline \(L/B=0.05\) & 6.5 & 4.02 \\ \hline \(L/B=0.03\) & 5.0 & 3.95 \\ \hline \(L/B=0.02\) & 4.0 & 4.60 \\ \hline \end{tabular}
\end{table} 
Table 5: Maximum tracer mass fraction as a function of time in the tank domain. performance indicator. The largest standard deviation was seen in the case without baffles, and it required 5.0 s to reach equilibrium. Comparing the case without a baffle with the case where \(L/B=1.0\), it is easy to notice the influence of the baffles on the system, which changed the flow behavior as the length of the baffles increased towards the center of the tank. In Figure 21, the distribution of the tracer in the tank volume at \(t=7.0\) s is shown for all cases (\(L/B\) ratios). Figure 19: Illustration of the introduction of the tracer in the flow after achievement of the steady state. Figure 20: Standard deviation of the tracer mass fraction as a function of time for the different studied configurations. Although the case without baffles had the largest turbulence kinetic energy, this kinetic energy had the highest concentration in the region closest to the impeller without being distributed to the rest of the tank, so the standard deviation for this case was also the highest. For the case when \(L/B=1.0\), the presence of baffles assisted in the distribution of turbulence kinetic energy in the tank domain, increasing the homogenization capacity of the system and producing the smallest value for the tracer standard deviation. As the baffles grow in length in the tank domain (until they reach \(L/B=0.08\)), the turbulence kinetic energy decreases, and homogenization of the system is more difficult due to the generation of large regions of stagnation in the tank domain. In contrast, from \(L/B=0.05\) to \(L/B=0.02\), the turbulence kinetic energy begins to increase. However, this increase does not assist in homogenization of the system since the baffles are unable to distribute the turbulence kinetic energy and high concentrations develop close to the impeller. This behavior occurs because the baffles have become so long that the flow behaves as if it were in a tank without baffles but with a smaller radius (from the center to the tip of each baffle). Thus, from the analysis carried out, it can be concluded that the case with the best efficiency in terms of time and homogenization of the system was when \(L/B=1.0\). Figure 22 shows the evolution over time of tracer distribution for the case where \(L/B=1.0\). It is worth mentioning that the optimal case is the one that equilibrates the distribution of dead spots in the tank domain. In comparison with the unbaffled case, the optimal configuration prevents the concentration of dead spots in the peripheral region of the tank; and in comparison with the other extreme (\(L/B=0.02\)), it does not generate large regions of dead spots behind the baffles. Therefore, the results are in agreement with the constructal principle of \"optimal distribution of imperfections\".