## 3 CFD Simulations
### CFD Results  
CFD simulations were performed to obtain a description of particle distribution in the tank. Flow velocities in the tank are relatively small (maximum is around 0.8 m/s, but the average is 0.08 m/s), see Figure 7 illustrating contours of velocity magnitude in three horizontal planes (on the left). On the right, the vertical velocity components are depicted, and comparing with Table 2, we can see that their values are smaller than the measured settling velocities; therefore, they cannot simply prevent the pellets from settling down to the bottom relatively quickly. In some locations (near the wall and at the bottom central part near the outlet), the vertical velocity components are even negative, so they actually accelerate the pellets on their way down to the bottom there. So, if we wanted to increase the residence time of pellets in the tank for some reason, we should probably use a different configuration, for example a different position of the inlet or different inlet flow rate. Or, different properties of pellets (size and effective density) could affect the residence time as well, and they could be a part of the parameters (variables) to be optimized. Figure 8 shows the dependency of the mean residence time with respect to the pellet size for both types of pellets, TM0 and TM75, which were obtained with the created CFD model. A comparison for three different inlet volumetric flow rates, 0.33, 0.4, and 0.5 L/s, is depicted there. The pellets were uniformly injected at the whole surface of the tank. Figure 8: Dependency of mean residence time for pellets TM0 and TM75 with various diameters and inlet flow rates. Figure 7: **(left)** Contours of velocity magnitudes in three horizontal planes in the fish tank. (right) Contours of vertical velocity components (positive values represent upward direction). The mean residence time for pellets according to the identified Rosin-Rammler distribution parameters (see previous section) is 63.95 s \(\pm\) 0.21% for TM0, and 65.35 s \(\pm\) 0.25% for TM75, in the case of inlet flow rate 0.5 L/s. Figure 9 illustrates the normalized residence time distribution for TM0 pellets described by the identified parameters of the Rosin-Rammler distribution, Equation (3), with minimum and maximum diameters 1.9 and 4.74 mm, respectively. Table 4 presents the summary of mean residence times for three different inlet flow rates. Table 5 and Figure 10 describe the impact of the injection position on the mean residence time. Samples of 500 particles reflecting the Rosin-Rammler distribution parameters determined in the experimental part were injected at the liquid surface in a circular area with radius 7.5 cm around the corresponding points 0-8 depicted on the left of Figure 11. Points 1-8 were placed at the circle with 3/4 of tank radius \(R\). This dependency could help us to find out an optimum position with, for example, largest residence time; see Figure 10 describing the mean residence time dependency with respect to the angular coordinate. TM0 pellets have maximum mean residence time at point 5 (angle 180\({}^{\circ}\)), and TM75 pellets at point 6 (angle 225\({}^{\circ}\)), that is, they are situated on the opposite side of the inlet. \begin{table}
\begin{tabular}{c c c} \hline
**Inlet Volumetric Flow Rate (L/s)** & **Mean Residence Time for TM0 (s)** & **Mean Residence Time for TM75 (s)** \\ \hline
0.33 & \(131.40\pm 0.23\%\) & \(131.60\pm 0.28\%\) \\
0.40 & \(89.78\pm 0.22\%\) & \(90.05\pm 0.25\%\) \\
0.50 & \(63.95\pm 0.21\%\) & \(65.35\pm 0.25\%\) \\ \hline \end{tabular}
\end{table} 
Table 4: Summary of mean residence times for all inlet flow rates used in our CFD simulations. The confidence intervals are derived from standard deviations of residence times of the injected particle samples which were around 40 thousand in all three cases. Figure 9: Normalized residence time distribution of TM0 pellets in the fish tank. It is based on total number of particles around 42,000, injected at the surface. Inlet volumetric flow rate 0.5 L/s.