## 3 CFD Simulations
### CFD Setup  
The geometry used in CFD simulations corresponded to 1.4 m\({}^{3}\) cylindrical fish tank with inlet at the top close to the wall, and outlet at the bottom, operated at the Research Institute of Fish Culture and Hydrobiology, University of South Bohemia (see Figure 1). The same fish tank served for the validation of CFD analysis of the velocity flow field in the MSc thesis [19]. The mesh created in ANSYS Fluent Meshing had 420,000 mesh elements in total, using hexahedral mesh elements in the core of the geometry and polyhedral mesh elements between boundary layer mesh elements and the core of the geometry, see Figure 5 for illustration of the mesh in 3D fluid domain. This is a relatively new feature in ANSYS Fluent software package, which should deliver better efficiency and accuracy compared to purely tetrahedral or polyhedral meshes (see Mosaic technology for more details [20]). Grid convergency index based on average velocities in three horizontal planes was evaluated as 11.6% for this size of the mesh. The inlet flow rate was 0.5 L/s, representing 1.27 of the tank volume per hour and residence time 0.787 h. Corresponding mass flow rate boundary condition was set at the inlet pipe. Properties of the water inside the fish tank used in our simulations corresponded to 20 \({}^{\circ}\)C (density 998.2 kg/m\({}^{3}\) and kinematic viscosity \(1.004\times 10^{-6}\) m\({}^{2}\)/s). Turbulence modeling using ANSYS Fluent is rather technical; on the basis of our previous experimental measurements and subsequent studies [19; 21], the SST \(k-\omega\) intermittency turbulence model was used for the description of the turbulent flow. This model belongs to the family of transition RANS models, combining \(k-\omega\) model in the near-wall region and \(k-\epsilon\) further from the wall, along with another equation for intermittency variable, covering \begin{table}
\begin{tabular}{c c c c c c c} \hline  & **Char. Size (mm)** & **Time (s)** & **Velocity (cm/s)** & **Re** & \(C_{\rm d}\) & **Density (kg/m\({}^{3}\))** \\ \hline
1 & 3.9 & 5.2 & 4.308 & 167.331 & 0.9482 & 1032.6 \\
2 & 2.9 & 3.7 & 6.054 & 174.868 & 0.9351 & 1088.4 \\
3 & 3.5 & 3.9 & 5.744 & 200.225 & 0.8990 & 1062.9 \\
4 & 3.5 & 3.9 & 5.744 & 200.225 & 0.8990 & 1062.9 \\
5 & 3.0 & 3.367 & 6.653 & 198.789 & 0.9008 & 1099.6 \\
6 & 3.5 & 2.966 & 7.552 & 263.276 & 0.8434 & 1103.1 \\
7 & 3.0 & 5.067 & 4.421 & 132.094 & 1.0302 & 1049.4 \\
8 & 3.8 & 2.6 & 8.615 & 326.080 & 0.8148 & 1119.7 \\
9 & 3.9 & 3.667 & 6.109 & 237.284 & 0.8619 & 1061.1 \\
10 & 3.0 & 5.1 & 4.392 & 131.240 & 1.0328 & 1048.9 \\ \hline average & 3.4 & 3.947 & 5.959 & 203.141 & 0.9165 & 1072.9 \(\pm\) 1.9\% \\ \hline \end{tabular}
\end{table} 
Table 3: Experimental results of settling velocity for TM75 pellets [17]. The resulting effective density of particles expressed from Equation (9) is 1072.9 kg/m\({}^{3}\)\(\pm\) 1.9%. the laminar-turbulent transition process [22; 23]. This model should give better predictions of flow field in cases where the fully developed turbulent flow is not established in the whole fluid domain. After the developed steady-state velocity field in the tank was obtained (it took approx. 70 min on 3 cores of Intel i7-8700 processor), particle tracking followed. As one-way coupling between the solid and fluid phase was assumed, the particle tracking was part of post-processing procedure based on the steady-state solution. It took up to 20 min for the largest amount of feed pellets (42 thousand) injected at the liquid surface. Corresponding characteristic size (diameter), density and sphericity for the discrete phase (feed pellets) based on the experiments described in the previous section were used. One kilogram of particles were injected at the surface of the liquid (water) in the tank at the beginning of the simulation. The validation of the flow field obtained in CFD simulations with experimental data was done according to [19], where flow velocities in different positions of the tank were measured using acoustic doppler velocimeter (FlowTracker).