# Hydrodynamics of an Airlift Column for Aeration in Molten Sulfur
## 4 Results and Discussion  
### Gas Holdup  
The area-averaged value of the gas holdup at a cross section of the riser is defined as \(\epsilon_{a}\). The total gas holdup is the volume-averaged gas holdup in the riser zone. Figure 4 shows the contours of the gas holdup with \(U_{Gr}\) at a total column height of 15 m. The gas holdup increases with the superficial gas velocity \(U_{Gr}\). Apparently, the gas holdup at the center of the riser is larger than the sidewalls of the riser. The growth of gas volume increases the gas holdup difference between the riser and the downcomer, accelerates the liquid circulation, and brings more bubbles into the annulus. With the increase of \(U_{Gr}\), a small amount of bubbles gradually circulates from the downcomer into the riser. Figure 5 shows the gas holdup distribution with the total column height \(H\) at a constant \(U_{Gr}\) of 0.0389 m/s. The gas holdup exhibits similar distributions at different values of column heights. It can be seen that even if the column height is 5 m, a large number of bubbles cannot circulate through the annular gap into the riser, indicating that the column height is not a leading factor of bubble circulation. Figure 3: Variation of average gas holdup at the cross section with different grid numbers. Figure 2: Schematic diagram of model grid. The gas is enriched at the top region of the downcomer, and the bottom region of the downcomer contains a negligible amount of the gas. This is in agreement with flow regime II according to [PERSON] et al. (2012). The bubble-enriched zone in the downcomer in the column with a height of 5 m is smaller than the column with a height of 25 m. The displacement of the bubbles in the downcomer tends to increase with the total column height. Figure 6 shows the variation of the area-averaged gas holdup at different cross sections (local heights) of the riser when the total column height is 15 m. It is interesting that there is a downturn region when the gas holdup increases with the increment of local height in a global trend. Moreover, the area-averaged gas holdup is almost constant in the riser region  
Figure 4: Evolution of gas holdup distribution with \(U_{Gr}\) at a total column height of 15 m.  
Figure 5: Gas holdup distribution at different total column heights with \(U_{Gr}\) of 0.0389 m/s. between the second and sixth cross sections. It shows that the bubbles were ejected from the bubble generator, after full development and uniformity, it belongs to the homogeneous flow, with only a small amount of bubble coalescence and breakup. Figure 7 shows the area-averaged gas holdup at the cross sections of the riser at different total column heights with a fixed \(U_{Gr}\) of 0.0389 m/s. The area-averaged gas holdup increases with the \(U_{Gr}\), demonstrating a similar trend for different total column heights. Figures 6 and 7 show that the gas holdup is the lowest at the first cross section, which indicates the undeveloped multiphase flow at this location. Figures 8 and 9 show the comparison of the total gas holdup calculated by the Chisti correlation [23], the newly proposed correlation, and the CFD simulation results in the present study. Figure 8 implies that the total gas holdup calculated by the simulation is lower than the gas holdup calculated by the Chisti correlation, while the proposed correlation is higher. Figure 9 shows the results for different total column heights at a constant \(U_{Gr}\) of 0.0389 m/s. The total gas holdup calculated by the simulation is slightly lower than the two correlations. The simulation results exhibit a good agreement. Although the proposed correlation considers the bubble diameter to extend the validity of the calculation results, the assumption that bubbles enter from the downcomer into the riser at the bottom of the column may cause some deviations, therefore, the value is larger.