3.1. Geometries of the Small- and Full-Scale FGD
A small-scale pilot FGD tower was used for validation first.
Figure 3a illustrates the details of the facility. All the spray nozzles and four sieve trays are set up in the right tower while the left tower is closed in this series of experiments. The height of the tower is 2.4 m, and the diameter is 0.6 m. The spacing between each tray is 0.4 m, and the spray system is placed above the highest tray by 0.2 m as shown in
Figure 3a,b. The liquid Mg(OH)
2 solution is injected downward without spray angle by 33 nozzles, as arranged in
Figure 3b from the top view. The array of nozzles has a radial distance of 0.05 m, and the diameter of each nozzle is 0.01 m. The pH value of liquid Mg(OH)
2 solution is 7.7 at the exit of nozzle. The gas with SO
2 enters the domain from a pipeline of a diameter 0.4 m in the rightmost face, as shown in
Figure 3a. With a series of chemical reactions shown in
Section 2.2, the desulfurization process reduces the concentration of SO
2, while the sulfurous process increases the acidity of the slurry. The liquid slurry then is discharged through the outlet under the bottom tank. Furthermore,
Figure 3b highlights the sampling locations to measure the SO
2 removal efficiency. Assuming point P in
Figure 3b is the origin in the
x–y plane, the locations of the sampling points from GT1 to GT3 are (−0.2, 0.93), (−0.2, 1.345), and (−0.263, 2.16), respectively, with meter as the unit.
Figure 4 illustrates the full-scale FGD tower. The height and diameter of the tower are 23 and 7 m. The tower has three sieve trays, and the gas is transported by a pipeline with diameter of 3.6 m and it leaves the domain from the outlet with a diameter of 3.6 m. There are two sets of nozzle arrays. One is above the highest tray by 1 m with 192 nozzles, and the other is below the lowest tray by 1.2 m with 29 nozzles. Both sets of nozzles have spray angle of 65°and diameter of 0.05 m. The experiments for both small- and large-scale towers have already been conducted by China Steel Cooperation [
34] with measured data for desulfurization and pressure at designated sampling points.
3.2. Geometries of the Perforated Sieve Trays of the Small- and Full-Scale FGD
The perforated hole structure on a sieve tray is illustrated in
Figure 5 from the top view (left) and side view (right). For the small-scale tower, the important parameters required to determine the inertial loss coefficient
C in Equation (16) are listed in
Table 1 for different cases and phases. The hole diameter
Dh is 20 mm, the tray thickness
th is 15 mm, and the pitch
Ph is 28.8 mm. With the aligned layout shown in
Figure 5, the hole diameter
Dh and pitch
Ph can determine the porosity
fh as 34.3%. The hole Reynolds number for gas phase
Reh,g =
ρgVgDh/
fhμg is 5130, where
ρg and
μg are the density and dynamic viscosity of the gas phase, and
Vg (1.4 m/s) is the cross-sectional average velocity of the gas phase within the tower.
L/
G is defined as the mass flow rate ratio of the total liquid to the exhaust gas. There are two setups for the small-scale tower, and this value varies as 4.9 or 3.2 for the small-scale tower, namely, Case 1 and 2. For Case 1, the velocity of the liquid solution is 0.766 m/s from each spray nozzle with a diameter of 0.01 m, and the velocity of Case 2 is 0.511 m/s. Similar to gas phase, the hole Reynolds number for liquid phase
Reh,l is 860 and 570, respectively.
Each sieve tray has 308 holes for the small-scale tower. By using the porous media model in Equation (16), these aforementioned parameters are used to determine the inertial loss coefficient to replace the detailed perforated structures. As for the tray of full-scale tower, its perforated hole is 8 mm. The porosity fh is 27.7%, th/Dh=0.75, the hole Reynolds numbers Reh for liquid and gas phase are 5500 and 940, respectively, which are all similar to those of Case 1 in the small-scale tower. As for the number of holes, there are 200,000 holes at each sieve tray for the large-scale tower.
3.3. Working Conditions of the Small- and Full-Scale FGD
For the small-scale tower, the inlet gas flow Reynolds number,
Reinle, is around 8 × 10
4 according to the gas mixture density (1.067 kg/m
3), velocity (3.2 m/s), and the diameter of the pipeline (0.4 m) at the inlet as shown in
Figure 3a. With different
L/
G values, the inlet Reynolds numbers for the liquid are about 1.6 × 10
4 for Case 1 and 1.07 × 10
4 for Case 2. These flow conditions of the gas and liquid inlets of the small-scale tower are highlighted in
Table 2 and
Table 3. Moreover, the concentration of SO
2 gas at inlet is 152 and 145 ppm, respectively.
As for the large-scale tower, the Reynolds number at inlets is 6.35 × 105, 1.35 × 105, and 1.44 × 105 for gas at inlet, liquid at the lower, and higher spray array, respectively. The corresponding value of L/G is 5, and the SO2 gas at inlet is 359 ppm.
3.4. Boundary Conditions, Grid Layouts, and Validations for the Small-Scale Tower
Figure 6a 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 6b. The velocities at inlets for both gas and liquid are prescribed according to
Table 2 and
Table 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
αg is 1. For Case 1, the concentration of SO
2 gas
YSO2 at this inlet is 3.42 × 10
−4, converting from the ppm value (152 ppm) and inlet densities. At the liquid inlets, the liquid volume fraction
αl and mass fraction
YM 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 3a 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 ε 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.
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 × 10
6 is chosen for the further simulations.
Table 4 and
Table 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%.
3.5. 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.
Table 6 presents the case name, flow condition, parameters in porous media model, and SO
2 removal efficiency at outlet for all the different cases.
For the small-scale tower of
L/
G = 4.9, the hole Reynolds number for gas phase
Reh, is 5130, porosity
fh is 34.3%, and
th/
Dh is 0.75 for Case 1, as shown in
Table 1. These values are used to tabulate in ref. [
28], and obtain values of
ξ1= 0.123,
ξ3 = 0.658,
ξ4 = 0.525, and
λ = 0.037 in Equation (16). The inertial loss coefficient in Equation (2) for gas flow in
y-direction
Cg,y is 11.33 after inserting these values into Equation (16). As for liquid phase in
Table 1, the hole Reynolds number for liquid phase
Reh,l is 860 for Case 1, corresponding to
ξ1 = 0.25,
ξ3 = 0.513,
ξ4 = 0.525, and
λ = 0.074. From Equation (16), the inertial loss coefficient for liquid phase
Cl,y is calculated as 10.31.
As the main direction of flow within the perforated hole aligns with the
y-direction, the inertial loss coefficients of these two phases in the
x- and
z-directions are amplified by 100 times from their corresponding values in the
y-direction [
4,
22]. From our preliminary results, based on the aforementioned setups (
Cg,y = 11.33 and
Cl,y = 10.31) for porous media model, the pressure drop within the right tower of the small-scale tower as
L/
G = 4.9 is 86.7 Pa, while that computed by real perforated structures (Case 1) is 104.6 Pa. This deficiency by using porous media model is caused by Equation (16) being calibrated based on experiments with single-phase flow [
4,
25,
28] and the two-phase flows within the tower have opposite direction.
As a result, it is reasonable to increase the inertial loss coefficients for the two-phase counterflow. Considering that gas flow occupies most of the domain within the tower, only the value of gas flow
Cg,y increases by 33% from 11.3 to 15 after a series of tests. The numerical results of Case A by
Cg,y = 15 and
Cl,y = 10.31 yields a pressure drop 103.5 Pa, which is exactly the same as that by Case 1 with perforated structures. As for Case B with a lower
L/
G, the information in
Table 1 yields original values of
Cg,y = 11.3 and
Cl,y = 10.48 from Equation (16). Similar to that for Case A,
Cg,y = 11.3 is increased by 33% to
Cg,y = 15 while
Cl,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
Cg,y by 33% and retain the original
Cl,y are applied to all the simulations by porous media model, as shown in
Table 6.
Figure 7 displays the liquid volume fraction (
αl), streamlines of gas phase, and the mass fraction of SO
2 (
YSO2) 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 (
ul,y) and gas flow velocity (
ug,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
Vg (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 8a, it tends to accumulate at each top surface of sieve tray, as shown in
Figure 7a. 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 7b. 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 7b for both cases. The radius of liquid column can be extracted from
Figure 7a, 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.
Since the two-phase flow structures are comparable for both cases, as shown in
Figure 7a,b,
Figure 8 and
Figure 9, the mass fraction of SO
2 (
YSO2) in
Figure 7c also has similar trends.
Table 4 and
Table 5 further compare the SO
2 removal efficiencies at different sampling points, which also displays similar trends and values between perforated structures (Case 1 and Case 2) and porous media models (Case A and B). Most important of all, the number of grid points after the sensitivity test for Case A and Case B is only 2 × 10
5, which is one-sixth that of Case 1 and Case 2. As a result, the computational time is reduced significantly from 8 days to 15 h (32 cores with 3.82 GHz processer), which makes it easier to conduct different designs as Case C–G for the small-scale FGD tower in
Table 6.
3.6. Numerical Results by Porous Media Model in a Large-Scale Tower
A mesh with number of grid points 1.2 × 106 is required for a small-scale tower that has 1200 holes at those four sieve trays. As for the large-scale tower, the number of holes becomes 600,000, and it could require a mesh of six hundred million grid points if their resolutions remain the same. The previous subsection validated the feasibility of the porous media model in a small-scale tower, which has also been utilized for the large-scale tower in this study to save computational costs. The number of grid points for the large-scale tower is 8 × 105 with the porous media model near the sieve trays.
The size and flow conditions of the large-scale tower were introduced in
Figure 4,
Section 3.1 and
Section 3.3. The setup of the boundary conditions is the same as that for the small-scale tower in
Section 3.4. The characteristics of perforated sieve trays used in the large-scale tower are
fh = 27.7%,
th/
Dh = 0.75,
Reh,g = 5500, and
Reh,l = 940, corresponding to
Cg,y = 18.41 and
Cl,y is 17.3 from Equation (16). By comparing with the measured pressure drop as 901 Pa in the experiment, the inertial loss coefficient of gas
Cg,y is adjusted 3 times from 18.41 to 73.3, while
Cl,y remains 17.3 to compensate the effects of two-phase counter flow as mentioned previously in
Section 3.5. After these treatments, the pressure drop calculated by the porous media model is 892 Pa, which is very close to the measured data. The simulation result displays unsteady flow structures, and is illustrated in
Figure 10a,b with time step size as 0.05 s. The two-phase mixing is very strong within the tray regions in
Figure 10a, resulting in a significant reduction of SO
2 mass fraction from the inlet, as shown in
Figure 10b.
Figure 11 shows the instantaneous variation of mass fraction of SO
2 (
YSO2) at outlet for the full-scale tower. The value of
YSO2 varies between 4 and 11 ppm, corresponding to SO
2 removal efficiency of 97–98.9%. The average efficiency is 98.3%. The experiment of this large-scale tower by China Steel Cooperation reports the efficiency as 96%. Therefore, this subsection further validates the porous media model in the full-scale tower.