## 1 Introduction  
In order to reduce the environmental acidification of sulfur dioxide (SO\({}_{2}\)) from the fossil fuel power plants or similar facilities, a flue gas desulfurization (FGD) tower is used to absorb the SO\({}_{2}\) component from the exhaust gas before it enters the environments [1, 2]. Downward alkaline solution injected from spray nozzles mixes with the upward exhaust gas within the tower [2, 3, 4]. During the desulfurization process, the gas SO\({}_{2}\) dissolves into alkaline solution in aqueous phase to form the sulfurrous acid (SO\({}_{2}\)-H\({}_{2}\)O), and the ensuing dissociation produces sulfurrous by-products, such as bisulfite (HSO\({}_{3}\)-) and sulfite (SO\({}_{3}\)\({}^{2-}\)). The sulfurrous species lead to the acidification of the alkaline solution. A higher pH value of the solution from the nozzles can neutralize the severity of acidification and absorb more SO\({}_{2}\) before its pH value eventually drops [5]. The setups of the nozzles, guide vane, direction of inlet exhaust gas can have tremendous impacts on the two-phase mixing, which can significantly influence the SO\({}_{2}\) removal efficiency. The ideal mathematical model that simplifies the flow conditions with uniform velocity [1, 6, 7, 8] could hardly capture these complex geometric effects within a facility, and hence, the Computational Fluid Dynamics (CFD) technique can provide more insightful information and benefit to optimal design. CFD has already been applied widely to solve the multiphase flow dynamics within the FGD tower [9, 10, 11, 12, 13, 14, 15, 16] and other facilities or processes with relevant fields, such as scrubbers of CO\({}_{2}\) emissions [11] and fine particle dust concentrators [17]. Depending on its approach to the interactions between liquid-solidand gas phase, the multiphase flow model can be categorized as an Eulerian-Lagrangian model [9; 11; 12; 13; 14] and an Eulerian-Eulerian model [5; 10]. The liquid droplets are usually regarded as a dispersed phase in the Eulerian-Lagrangian model with tracking of a large number of particles [18]. The droplet is usually regarded as a parcel which contains the same properties [11; 12; 19; 20; 21]. The drag coefficient of the particle is determined by the relative Reynolds number, which is based on the slip velocity between the liquid and solid phase. The drag force of a particle usually feeds back to the continuous phase as two-way coupling [9; 14]. The chemical reaction is modelled by dual-film theory, Henry's Law [11; 12; 13], and Chilton-Colburn analogy [8]. Under the aforementioned framework, Morocco and Inzoli [9] have simulated the hydrodynamics and chemical reaction for a dispersed liquid droplet within an open spray tower. Eight dissolved species from gas to liquid phase are considered during the desulfurization process, and the deposition and splashing of liquid particle as they hit the wall of tower are handled by an empirical droplet-wall interaction model. [PERSON] et al. [11] evaluated the effect of droplet diameter. A finer diameter benefits the mass transfer but could reduce the uniformity of the liquid-gas flow, and vice versa for a particle of larger diameter. An optimal diameter such as 200 \(\upmu\)m was selected based on their simulations. [PERSON] et al. [12] further investigated the flow structures at different region of the tower, and the two-phase mixing is stronger in the middle region that dominates the desulfurization process. The evaporation occurs at the inlet region of the gas phase, which only has minor influence on the desulfurization performance. [PERSON] et al. [13] investigated the CO\({}_{2}\) removal efficiency by NH\({}_{3}\) solution and the effect of the layout of the nozzle spray. A fraction of upward gas can be allowed to flow downward by the entrainment effect of the downward spraying liquid. An upward spray at a lower altitude can enhance 7% removal efficiency from a downward spray at a higher altitude because the former offers a longer residence time and increases the droplet volume fraction.