**12. Turbulence and stirring model selection**

Standard, RNG and realizable *k*- were compared in terms of the convergence time. Global residual tolerances for all variables (velocity, continuity, *k*- ) were kept constant at 1 × 10−3. Realizable *k*- was selected due to its reduced convergence time (1305 iterations), this being compatible with the literature recommendation for high-velocity rotational flows [25, 26].

Various simulations with liquid water were performed at 100 rpm (Re=11,739) to select a stirring model (ROT, MRF, or SM). All simulations were run using a 3D no-stationary solver. Cross-sections, as shown in **Figure 11**, were used to visualize velocity profiles in the stirred tank. **Figures 7**–**9** show a typical velocity behavior of stirred tanks: a mixing zone in the upper section, high velocity gradients close to the moving blades, and a dead recirculation zone below the impeller. The mathematical model was validated by comparing the mixing time obtained against experimental data.

**Figure 7.** MRF, colored vectors by velocity magnitude in m/s (Scale/Omission relation of 50/1).

**Figure 8.** SM, colored vectors by velocity magnitude in m/s (Scale/Omission relation of 50/1).

**Figure 9.** ROT, colored vectors by velocity magnitude in m/s (Scale/Omission relation of 50/1).

**Figure 10.** Cross-section for analysis of simulated data.

The graphics presented in **Figures 7**–**9** were taken from the cross-section defined in **Fig‐ ures 10** and **11**. **Figures 7**–**9** show the velocity profiles of MRF, SM, and ROT models. The color scale indicates the magnitude of each vector view from two planes: Y-Z and X-Y. All images enclosed in red squares are radial cross-sections near the blades.

**Figure 11.** Cross-section defined in the Y-Z plane.

**Figure 8.** SM, colored vectors by velocity magnitude in m/s (Scale/Omission relation of 50/1).

282 Modeling and Simulation in Engineering Sciences

**Figure 9.** ROT, colored vectors by velocity magnitude in m/s (Scale/Omission relation of 50/1).

The graphics presented in **Figures 7**–**9** were taken from the cross-section defined in **Fig‐ ures 10** and **11**. **Figures 7**–**9** show the velocity profiles of MRF, SM, and ROT models. The color

**Figure 10.** Cross-section for analysis of simulated data.
