# Current Limitations for Predicting Liquid Dispersion in Continuous Flow Bubble Columns Using CFD
## 3 Results  
### Velocity Profiles for Mono- and Biphasic Simulations  
CFD predictions of the relative water velocities (relative to the maximum value at the specified height of the column) as functions of radial position are shown in Figure 2 for a single-phase flow of water. The simulations used the \(k\)-\(\epsilon\) turbulence model and an imposed water flow rate (\(Q_{w}\)) of 1.98 m\({}^{3}\cdot\)h\({}^{-1}\). The computed velocity profiles depended on the mesh size used for the simulations (Supplementary Materials, Figure S1), especially in the lower entry region of the column. As was expected, biphasic simulations required finer meshes. Except in the vicinity of the column inlet, the radial velocity profiles had a parabolic shape consistent with expectations [25]. The flow velocity was maximum at the centerline of the column and minimum at the walls (Figure 2). The sole exception was the M-shaped radial velocity profile at a column height of 0.25 m (Figure 2). This shape was due to velocity distortions associated with the location of the liquid distributor below the air sparger (Figure 1A). Although there was no flow of gas, the liquid lost velocity as it impacted the sparger. The M-shaped profile was essentially an entrance effect that disappeared above 0.5 m (Figure 2). Over a column height of 1.0-1.5 m, the radial velocity profile had a plug-flow character and had not fully developed into the parabolic profile seen at a column height of 1.95 m (Figure 2). The parabolic shape of the profile (noticeably higher flow at the centerline than elsewhere) close to the outlet (column height of 1.95 m; Figure 2) was also contributed by the end effect of the flow exit tubes near the top of the column: more flow exited through the central tube compared to the peripheral ones. The negative relative velocities close to the walls (Figure 2) indicated downflow or recirculation of the liquid. The cause of the recirculation was a significant resistance to flow at the outlet tubes near the top of the column. As the flow could not exit through the entire cross section of the column because of the narrowing of the cross section into the exit tubes (Figure 1A), some of the flow descended near the walls. The relative radial velocity profiles predicted for air (\(Q_{a}\) = 0.954 m\({}^{3}\cdot\)h\({}^{-1}\)) and water (\(Q_{w}\) = 1.98 m\({}^{3}\cdot\)h\({}^{-1}\)) in two-phase flow are shown in Figure 3. The gas phase was simulated using the dispersed Eulerian two-phase model. The radial velocity profiles (Figure 3) were markedly different compared to the profiles observed for single-phase water flow (Figure 2). The two-phase profiles had a relatively sharp peak in the central axial region, indicating a substantially faster flow of both phases in the core zone of the column compared to the flow in the peripheral zone of the cross section (Figure 3). \begin{table}
\begin{tabular}{c c c} \hline
**Flow** & **Low** & **High** \\ \hline \(t_{i}\) & 2.5 & 2.5 \\ (s) & 0.2246 & 0.2246 \\ \hline \(Q_{w}\) & 1.98 & 3.2 \\ (m\({}^{3}\) h\({}^{-1}\)) & 0.0128 & 0.0207 \\ \hline \(m_{w}\) & 0.549 & 0.887 \\ (kg s\({}^{-1}\)) & 0.954 & 4.5 \\ \hline \(u_{\epsilon}\) & 0.0612 & 0.0291 \\ (m s\({}^{-1}\)) & 0.185 & 0.872 \\ \hline \(m_{u}\) & 32.46 \(\times\) 10\({}^{-5}\) & 153.13 \(\times\) 10\({}^{-5}\) \\ \hline \end{tabular}
\end{table} 
Table 3: Flow settings. Figure 3: Radial profile of relative velocity (relative to the maximum velocity) at different heights in the column simulated for water-air flow (\(Q_{w}\) = 1.98 m\({}^{3}\) h\({}^{-1}\), \(Q_{a}\) = 0.954 m\({}^{3}\) h\({}^{-1}\)) using the realizable \(k\)-\(\varepsilon\)/dispersed Eulerian biphasic model. (**A**) velocities for the water phase; (**B**) velocities for air phase. Mesh of 3.9 \(\times\) 10\({}^{5}\) elements.