# Current Limitations for Predicting Liquid Dispersion in Continuous Flow Bubble Columns Using CFD
## 3 Results
### Liquid Phase Dispersion in Single-Phase Water Flow  
First, CFD simulations were performed to identify the turbulence model that best predicted the experimental tracer dispersion in the single-phase water flow. The flow rate of water was fixed at the highest setting (\(Q_{w}\) = 3.2 m\({}^{3}\cdot\)h\({}^{-1}\), \(Re\) = 4.8 \(\times\) 10\({}^{3}\)). The temporal evolution of the CFD and experiment tracer responses was compared (Figure 4), corresponding to the centerline (r = 0 m) of the column at two different axial positions (z = 1.05 and 1.84 m). Although no single uncertainty estimate can be attributed to a pH measurement procedure, it has been shown that the pH measurement uncertainty for commercial glass electrodes is less than 0.05 pH units [34]. All data in Figure 4 were normalized using the highest measurement within a set for ease of comparison. Thus, the relative concentration of the tracer ranged between 0 and 1 (Figure 4). The experimental and simulated tracer responses at both axial positions followed a typical stimulus-response pattern characteristic of concurrent continuous flow: the tracer concentration rose rapidly to a peak value and then declined slowly to an equilibrium value.  
Figure 4: Comparison of the relative acid concentration (tracer) versus time in single-phase water flow (\(Q_{w}\) = 3.2 m\({}^{3}\) h\({}^{-1}\)) for the turbulence models evaluated and the experimental results. (**A**,**B**) tracer concentrations at 1.84 m above the column base at centerline for RANs and LES models, respectively. Mesh of 3.9 \(\times\) 10\({}^{5}\) elements; (**C**,**D**) tracer concentrations at 1.05 m above the column base at centerline for RANs and LES models, respectively. Mesh of 6.9 \(\times\) 10\({}^{5}\) elements.  
The standard, realizable, and RNG \(k\)-\(\varepsilon\) turbulence models reproduced the general trend but not the instabilities of tracer concentration (Figure 4A-C). In general, the three RANS models differed a little in their responses, for example, in their predictions of the time for the tracer to reach the measurement points. The model that best reproduced the trace peak width was the realizable \(k\)-\(\varepsilon\) model. As these are averaged models, they are not capable of capturing the finer details of the tracer response spectrum [20].  
Secondary peaks were observed between 50 and 100 s on the time axis (Figure 4) because of the previously mentioned recirculation zones near the walls. The secondary peaks were only correctly captured by SAS and SST-SAS (Figure 4B-D). The SAS model predicted a somewhat narrower peak at the lower probe location (z = 1.05 m) compared to experimental data but adjusted well to the peak width at the higher probe location (z = 1.84 m; Figure 4B) and also predicted well the time to reach the maximum tracer concentration.  
The problem with the SST model was that for both axial positions (z = 1.05 and 1.84 m), the tracer reached the measurement points quickly and also left these points rapidly (hence the narrow-predicted peaks) (Figure 4B-D). Overall, the SAS model and the SST-SAS model best reproduced the experimental responses, including some perturbation details, including the small secondary peak before the maximum tracer concentration.