# Current Limitations for Predicting Liquid Dispersion in Continuous Flow Bubble Columns Using CFD
## 4 Conclusions  
To our best knowledge, this is the first work assessing the abilities of CFD to describe tracer dispersion in a continuous flow column at industrial scale. LES-based models outperformed RANS. Moreover, LES models were qualitatively and quantitatively satisfactory for predicting the dispersion of tracer in a single-phase (water-only) continuous flow bubble column under all conditions. For two-phase air-water systems, these models could be used only in conjunction with VOF-type models in ANSYS Fluent(r), limiting their applicability. For the biphasic system, the turbulence models qualitatively predicted the time evolution  
Figure 6: Contours of tracer concentration (mole fraction of H\({}^{+}\)) for two-phase continuous flow bubble column, obtained using Fluent simulations. The time after tracer injection is shown beside each column. (**A**) \(Q_{w}=3.2\) m\({}^{3}\) h\({}^{-1}\), \(Q_{a}=4.5\) m\({}^{3}\) h\({}^{-1}\); (**B**) \(Q_{w}=1.98\) m\({}^{3}\) h\({}^{-1}\), \(Q_{a}=0.954\) m\({}^{3}\) h\({}^{-1}\). of the tracer concentration but lacked a quantitative prediction capacity. The biphasic VOF model appeared to have limited applicability if a fine mesh refinement was impractical. The following supporting information can be downloaded at: [[https://www.mdpi.com/article/10.3390/app13169250/s1](https://www.mdpi.com/article/10.3390/app13169250/s1)]([https://www.mdpi.com/article/10.3390/app13169250/s1](https://www.mdpi.com/article/10.3390/app13169250/s1)), Figure S1. Comparison of meshes: Simulated radial profiles of relative velocity (relative to maximum velocity) at different heights in the column with single phase flow (water only) (realizable \(k\)-\(e\); \(Q_{w}=1.98\) m\({}^{3}\) h\({}^{-1}\)). The number of elements in meshes 1, 2, 3, 4, and 5 were 325430, 394114, 613250, 694189, and 789452, respectively. Figure S2. Comparison meshes for air-water flow: Radial profiles of relative water velocity (relative to the maximum velocity) at different column heights (\(Q_{w}=1.98\) m\({}^{3}\) h\({}^{-1}\); \(Q_{d}=0.954\) m\({}^{3}\) h\({}^{-1}\)). The number of elements in meshes 2, 3, 4, 5 were 394114, 613250, 694189, and 789452, respectively. Figure S3. Comparison of meshes for air-water flow: Radial profiles of relative air velocity (relative to the maximum velocity) at different column heights (\(Q_{w}=1.98\) m\({}^{3}\) h\({}^{-1}\); \(Q_{d}=0.954\) m\({}^{3}\) h\({}^{-1}\)). The number of elements in meshes 2, 3, 4, 5 were 394114, 613250, 694189, and 789452, respectively. Figure S4. Values of \(10/\Delta\) calculated for air-water simulations (SAS-VOF model) 40 s after tracer injection: (A) \(Q_{w}=1.98\) m\({}^{3}\) h\({}^{-1}\), \(Q_{d}=0.954\) m\({}^{3}\) h\({}^{-1}\); (B) \(Q_{w}=3.2\) m\({}^{3}\) h\({}^{-1}\), \(Q_{d}=4.5\) m\({}^{3}\) h\({}^{-1}\). Figure S5. Contours of acid concentration (mole fraction) in air-water continuous flow bubble column (\(Q_{w}=3.2\) m\({}^{3}\) h\({}^{-1}\); \(Q_{d}=4.5\) m\({}^{3}\) h\({}^{-1}\)) obtained by Fluent simulations. Elapsed times after tracer injection are shown at the bottoms of the columns. (A) At the center of the column, parallel to flow; (B) At different heights (horizontal planes, normal to flow). Figure S6. Contours of acid concentration (mole fraction) in air-water continuous flow bubble column (\(Q_{w}=1.98\) m\({}^{3}\) h\({}^{-1}\); \(Q_{d}=0.954\) m\({}^{3}\) h\({}^{-1}\)) obtained by Fluent simulations. Elapsed times after tracer injection are shown at the bottoms of the columns. (A) At the center of the column, parallel to flow; (B) At different heights (horizontal planes, normal to flow). Table S1. Details of the meshes evaluated.