# Gas-Liquid Mixability Study in a Jet-Stirred Tank for Mineral Flotation
## 4 Conclusions  
The flow dynamics and gas volume fraction distribution in a jet-stirred tank are investigated in this study through numerical simulation. The analysis involves computing and evaluating the flow field of the stirred vessel under varying slurry feeding rates and aeration volumes to assess the impact of operational parameters. Furthermore, optimizations and adjustments are conducted on the structural parameters of the jet-stirred tank to enhance its performance. Despite the focus on a specific case, the results of this study provide valuable insights into the performance of jet-stirring technology. However, it is important to consider the generalizability of these findings. The simulation of a single case \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **0.45** & **0.50** & **0.55** & **0.60** & **0.65** \\ \hline Average & \(1.82\times 10^{-2}\) & \(1.72\times 10^{-2}\) & \(1.62\times 10^{-2}\) & \(1.56\times 10^{-2}\) & \(1.53\times 10^{-2}\) \\ Variance & \(4.08\times 10^{-5}\) & \(3.86\times 10^{-5}\) & \(3.66\times 10^{-5}\) & \(3.89\times 10^{-5}\) & \(4.31\times 10^{-5}\) \\ DV & \(1.54\times 10^{-16}\) & \(1.45\times 10^{-16}\) & \(1.38\times 10^{-16}\) & \(1.47\times 10^{-16}\) & \(1.62\times 10^{-16}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Average and variance of different nozzle radius ratios. Figure 21: Gas volume fraction curve with height for different radius ratios; (**a**) all working conditions; (**b**) local zoom in grey area. Figure 20: The contour of gas volume fraction distribution for different radius ratios. may not fully capture the variability of different operational conditions and structural parameters in industrial applications. To address this, we used dimensionless numbers, such as the Reynolds number, to normalize our results. This approach enhances the applicability of our findings by allowing for comparisons across different scales and conditions. The principal findings are outlined as follows:  
1. In the jet-stirred tank, fluid flow rates decrease with increasing vessel height, leading to a notable velocity gradient and the formation of vortex phenomena. These vortices influence the aggregation of gas bubbles within the tank, resulting in a significantly higher internal gas volume fraction compared to the gas volume fraction near the tank walls. 2. When the inlet velocity is lower, the overall gas volume fraction remains low. Conversely, excessively high velocities exacerbate vortex effects, widening the disparity between the gas volume fraction within the vessel and that near the wall surface. Across varying filling volumes, gas movement ranges showed no significant differences, while the upward velocity of the liquid phase near the wall surface notably decreased from 0.49 m/s to 0.42 m/s, coinciding with an increased gas volume fraction. 3. During the optimization of the structural parameters, it was determined that the jet-stirred tank achieved optimal mixing homogeneity when employing circumferential jetting for the nozzles, with a nozzle height of 80 mm, a nozzle inner diameter of 5.0 mm, and a nozzle radius ratio of 0.55. Conceptualization, Y.H. and B.S. ; methodology, J.Y. and W.P. ; software, M.G. ; validation, Y.H., X.S. and D.M. ; formal analysis, B.S. ; investigation, M.G. ; resources, J.Y. ; data curation, Y.H. ; writing--original draft preparation, M.G. ; writing--review and editing, D.M. ; visualization, M.G. ; project administration, X.S. ; funding acquisition, Y.H. All authors have read and agreed to the published version of the manuscript. This research was funded by the National Key Research and Development Program of China (grant number 2020 YFC1908804) and the Science and Technology Research Projects in Henan Province in 2023 (grant number 232102320329). Not applicable. Not applicable. Not applicable. Data Availability Statement: The data presented in this study are available on request from the corresponding author. The data are not publicly available due to company privacy restrictions.