## 3 Validations of the Two-Phase and Porous Media Model
### Boundary Conditions, Grid Layouts, and Validations for the Small-Scale Tower
As for Case B with a lower \(L/G\), the information in Table 1 yields original values of \(C_{g,y}=11.3\) and \(C_{l,y}=10.48\) from Equation (16). Similar to that for Case A, \(C_{g,y}=11.3\) is increased by 33% to \(C_{g,y}=15\) while \(C_{l,y}\) is maintained as 10.48. The corresponding pressure drop is 96.8 Pa, which is very consistent to 95.5 Pa of Case 2 by real perforated structures. Therefore, these treatments that increase \(C_{g,y}\) by 33% and retain the original \(C_{l,y}\) are applied to all the simulations by porous media model, as shown in Table 6.  
Figure 7 displays the liquid volume fraction (\(\alpha_{l}\)), streamlines of gas phase, and the mass fraction of SO\({}_{2}\) (\(Y_{\text{SO2}}\)) within the right tower of small-scale FGD facility for Case 1 and Case A at \(L/G=4.9\). Both cases of perforated structures and porous media model have similar flow patterns. Figure 8 presents the liquid flow velocity (\(u_{i,y}\)) and gas flow velocity (\(u_{g,y}\)) in the \(y\)-direction along the centerline of the small-scale tower for Case 1 and Case A, and the velocity is normalized by average gas velocity \(V_{g}\) (1.4 m/s). The dashed lines display the positions of sieve trays. It is clear that the downward liquid flow in Figure 8a accelerates between each sieve tray and decelerates as the liquid flow approaches the sieve tray. For Case A, the porous media model can also obtain a strong deceleration as that in Case 1 with real perforated structures. Since the sieve tray is not regarded as a no-slip boundary condition in the porous media model, the liquid flow cannot decelerate to zero velocity when it impacts the porous-based sieve tray, as shown in Figure 8a. Moreover, the sudden reduction of the cross section within the real perforated sieve tray leads to a very strong acceleration. However, the porous media model regards the sieve tray as an interior flow domain, and hence, the strong acceleration cannot be displayed by Case A in Figure 8a. As a result, the liquid velocity between two sieve trays is slower by using the porous media model in Figure 8a. Considering the extremely large liquid-to-gas density ratio, the gas flow inside the liquid column travels downward with the liquid flow instead of rising, which is illustrated in Figure 8b for gas flow at the centerline of the tower for both cases. Since the liquid flow of Case 1 is faster, as mentioned previously in Figure 8a, it can accelerate the gas flow into a faster velocity. Correspondingly, the gas flow velocity between two sieve trays is made slower by using the porous media model in Figure 8b. Since the liquid flow decelerates to zero as it approaches the sieve trays for Case 1 as shown in Figure 7(a), it tends to accumulate at each top surface of sieve tray, as shown in Figure 7(a). As for the porous media model of Case A, although the liquid flow cannot decelerate to zero velocity onto the sieve tray, it remains sufficient to hold the liquid flow and produce accumulation near the locations of sieve trays. In contrast with the downward gas flow within the liquid column, the gas flow outside it moves upward, which can be seen in the streamlines in Figure 7(b). As a result, the liquid column serves as a boundary to separate the upward and downward gas flow, and hence, a pair of counter vortexes between two neighboring sieve trays can be seen in Figure 7(b) for both cases. The radius of liquid column can be extracted from Figure 7(a), which defines the size occupied by liquid flow. Figure 9 illustrates the radius as function of \(y\)-direction for Case 1 and Case A. The trend is comparable with average deficiency as 15% between Case 1 with perforated structure and Case A by porous media model.