## 3 Validations of the Two-Phase and Porous Media Model
### Boundary Conditions, Grid Layouts, and Validations for the Small-Scale Tower  
Figure 6(a) illustrates the grid layouts by cut-cell technique [5,22] for the small-scale tower at the symmetric plane at z = 0. Its computational domain is discretized by hexahedral elements with finer resolution around the spray nozzles and sieve trays in Figure 6(b). The velocities at inlets for both gas and liquid are prescribed according to Tables 2 and 3, while the pressure is extrapolated. The turbulent quantities are specified as eddy-to-laminar viscosity ratio equal to 1000. At the gas inlet, the volume fraction of gas phase \(\alpha_{g}\) is 1. For Case 1, the concentration of SO\({}_{2}\) gas \(Y_{\text{SO2}}\) at this inlet is 3.42 \(\times\) 10\({}^{-4}\), converting from the ppm value (152 ppm) and inlet densities. At the liquid inlets, the liquid volume fraction \(\alpha_{l}\) and mass fraction \(Y_{\text{M}}\) for the Mg(OH)\({}_{2}\) are all set up as 1. The pressure at gas outlet is maintained as 1 atm, while remaining variables are extrapolated. The liquid outlet at the bottom surface of Figure 3(a) is set up as 1.1 atm, in order to maintain the height of the free surface of the bottom tank by 1 m.  
For the simulation by real perforated sieve tray, the no-slip boundary condition is applied to the surface of the sieve tray and wall of the tower. The turbulent quantity \(k\) is zero, while \(\varepsilon\) is calculated by wall function. In this study, the y+ value for the first grid away from the no-slip wall is around 60. As for the porous media model, the tray region becomes an interior flow domain without solid boundary and retains the same grid resolution as that outside the tray. Figure 6: The figure displays the grid distributions of the small-scale FGD tower at the symmetric plane (z = 0) in (**a**) and the detailed layouts for the right tower near the sieve trays and nozzles in (**b**). \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Mixture** & **Velocity** & **Mixture Viscosity** & \(Re_{\text{inlet}}\) \\ \hline Gas inlet & 1.066 kg/m\({}^{3}\) & 3.2 m/s & 1.72 \(\times\) 10\({}^{-5}\) N\(\cdot\)S/m\({}^{2}\) & 8 \(\times\) 10\({}^{4}\) \\ \hline Liquid & 983 kg/m\({}^{3}\) & 0.511 m/s & 4.68 \(\times\) 10\({}^{-4}\) N\(\cdot\)S/m\({}^{2}\) & 1.07 \(\times\) 10\({}^{4}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: This table lists the important parameters of inlet flow of Case 2 (L/G=3.2). for the small-scale tower. The nonlinear sets of equations from Equations (1)-(5) are solved by Phase Coupled SIMPLE (PC-SIMPLE) [22; 35], which is based on an extension of the SIMPLE algorithm to multiphase flows. The Second Order Upwind scheme (SOU) [22; 30] is used for the convective nonlinear terms, and the central difference is applied to diffusion terms. The time step size for small-scale tower is 0.01 s. Although the time-dependent computation is considered, the solution finally reaches a steady state for a small-scale tower. After a series of grid dependency test, the mesh with number of grid points as 1.2 \(\times\) 10\({}^{6}\) is chosen for the further simulations. Tables 4 and 5 list the simulated SO\({}_{2}\) removal efficiencies at three sampling locations for Case 1 (\(L/G\) = 4.9) and Case 2 (\(L/G\) = 3.2) by real perforated structures. The measured values [36] have also been compared, and the results are consistent with most of discrepancies less than 10%. Comparisons between Numerical Results by Perforated Structures and Porous Media Model in a Small-Scale Tower  
After validation in a small-scale tower, this subsection discusses the feasibility of using porous media model for saving computational cost. Case 1 and Case A have the same flow conditions, except the latter applies the porous media model, and the same situation applies to Case 2 and Case B. Different setups for number of sieve trays and inlet gas flow rate will further be discussed by using the porous media model in Section 4.