## 5 Results and Discussions
### Influence of Aperture Parameters  
It is known that turbulence kinetic energy and turbulent energy dissipation rate play crucial role in the mixing time and solid-liquid suspension quality. Figures 13 and 14 depict the distributions of the turbulence kinetic energy and the turbulent energy dissipation rate at different aperture diameters and aperture ratios, respectively. In all cases, the turbulenve kinetic energy and turbulent energy dissipation rate were highest near the impeller blade tip, but tended to be very low outside the sweep field by the impeller blades. The turbulence kinetic energy and turbulent energy dissipation rate profiles of the BCPBT presented increased values than those of the PBT for most of the positions and show multiple spikes, especially near the impeller (from \(r/R=0.3\) to \(r/R=0.6\)). The turbulent energy dissipation rate was higher for the BCPBT, which implies that smaller trailing vortices in the wake of the BCPBT blade dissipated over a shorter distance from the impeller. The turbulence kinetic energy and turbulent energy dissipation rate have an increasing trend with an increase in the aperture diameter; however, they decreased slightly when the aperture diameter was too large. Overall, the aperture diameter should not be too large, and 8 mm is more suitable. As shown in Figures 13b and 14b, the turbulence kinetic energy \begin{table}
\begin{tabular}{c c c} \hline \hline
**Impeller Type** & **Power Consumption (W)** & **Reduction of Power Consumption (\%)** \\ \hline PBT & 50.5 & — \\ PBPT & 46.9 & 7.1 \\ BCBT & 43.2 & 14.5 \\ BCPBT & 41.9 & 17.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Effect of impeller type on power consumption. Figure 14: Influence of aperture parameters on local radial turbulent kinetic energy dissipation rate profiles. (**a**) Influence of aperture diameter, (**b**) influence of aperture ratio. Figure 13: Influence of aperture parameters on local radial turbulence kinetic profiles. (**a**) Influence of aperture diameter, (**b**) influence of aperture ratio. and turbulent energy dissipation rate increased with the increase of the aperture ratio. Under conditions of an aperture ratio of 13%, the turbulence kinetic energy and turbulent energy dissipation rate were the largest, showing a downward trend when the aperture ratio as more than 13%. The vortex diffusion as weak due to the small aperture ratio. In the case of an oversized aperture ratio, the concurrent flow can emerge easily, thereby affecting the enhancement of eddy diffusion. Figure 15 depicts the axial solid concentration profile for different aperture parameters at \(r/R=0.5\). With the increase of aperture diameter, mixing effects were improved in the axial direction. When the aperture diameter reaches 8 mm, a better mixing performance forms in the tank, where particle deposition decreases significantly at the bottom. As the aperture diameter increases to 10 mm, owing to the fact that the axial pumping effects of impellers are weakened in the vertical direction, it has an adverse impact on particle axial motion. As a result, the solid hold-up is larger, and the deposition is more severe at the bottom of tank. It can be observed from Figure 15b that the \(C_{x}/C_{av}\) values of the BCPBT were higher than those of the PBT. The distribution of the solid particles of BCPBT was more uniform than that of PBT in the axial direction when the aperture ratio was 13%. An interface appears between the suspended solids and a clear liquid layer in the upper part of the tank. The height of this interface is the cloud height. In this research, the cloud height was analyzed by means of monitoring the average solid concentration iso-surface, which was defined as the maximum axial height of the iso-surface of the average solid concentration. The cloud height can be taken as a significant parameter for evaluating mixing degree. Figure 16 exhibits the change of cloud height in the stirred tank.