CFD Investigation of Bath Flow and Its Related Alumina Transmission in Aluminum Reduction Cells: Slotted Anodes and Busbar Designs

Alumina is an indispensable raw material for the modern aluminum electrolysis industry. The distribution and transmission of alumina within the bath is of great significance to maintain stable operation and reduce energy consumption. In this study, a computational fluid dynamics (CFD) model was developed to investigate the bath flow and its related alumina transmission in aluminum reduction cells. The bath flow driven by bubbles, electromagnetic force, and aluminum flow presented two different sized vortices in the horizontal plane of the anode–cathode distance (ACD). Both numerical results and industrial data show that the average alumina concentration in the half-cell at the duct end is slightly larger than that of the tap end. With the application of slotted anodes, the maximum velocity of the bath flow increased and the average velocity decreased slightly in the horizontal plane, resulting in a more uniform distribution of alumina than that in the use of unslotted anodes. The symmetrical nature of the bath flow vortices became more obvious with the upgrade of the busbar design and the alumina concentration gradient became smaller within the bath.


Introduction
The Hall-Héroult process was invented in 1886 and has been used as the only commercial method for aluminum smelting for over 120 years [1]. Alumina powder is used as the raw material and is added into the highly corrosive Na 3 AlF 6 molten salt at 950 • C, where carbon material is used as the anode and cathode. Under the action of strong direct current (up to 600 kA now), aluminum metal is extracted from alumina at the cathode and gas bubbles (primary CO 2 and CO) are produced in the electrochemical reaction occurring on the surface of the anode bottom.
Alumina is an indispensable raw material for the modern aluminum electrolysis industry. The physical properties of the Na 3 AlF 6 -Al 2 O 3 melt, such as super heat [2,3], density [4], and electrical conductivity [5,6], are impacted by the local concentration of alumina within the bath, which is a variable in determining the local anode-cathode distance (ACD) and regional stability. On the other hand, the alumina concentration is a critical parameter for aluminum reduction cells that the anode effect and current efficiency are closely related to the alumina concentration. However, due to the native characteristics of modern cells, it is very difficult to achieve a satisfactory and uniform alumina distribution at different locations. Rye et al. [7] and Dion et al. [8] measured the distribution of alumina concentration in aluminum reduction cells, and a clear gradient characteristic was presented in their works. According to Hydro research [9], a 1% alumina concentration difference could introduce a maximum of 8 mm deformation in the aluminum/bath interface. How to improve the uniformity of the alumina distribution in the cell is of great significance in maintaining stable operation and reducing energy consumption.
The dissolution and diffusion of alumina in aluminum reduction cells are closely related to the bath flow, thus, the modeling of alumina transmission is usually coupled with the calculation of the flow field. Early scholars believed that the gas release dominates the electrolyte flow field. Bilek et al. [10] developed a 3D computational model to predict the bulk turbulent flow and to assess the impact of bubbles, electromagnetic force, and the coupled effect. The presented case studies showed that the bubble driving force imparts significantly greater energy to the bath than the MHD (magneto-hydro-dynamics) forces. Zhou et al. [11] and Doheim et al. [12] have reached similar conclusions. However, very recent studies [13,14] found that bubbles promoted local circulation around anodes, especially in the vertical direction, and the electromagnetic force was the main reason for the horizontal flow of electrolyte to form large vortices. The drag effect of aluminum liquid cannot be ignored. Zhang et al. [15] also reached a similar conclusion and concluded that both bubbles and electromagnetic force should be taken into consideration in the modeling.
Feng et al. [16] developed a bubble-bath two-phase flow model and validated its accuracy by PIV (particle image velocimetry) measurements of a three-anode water model. Then the similarity and difference of the bath flow between the slotted anode case and the unslotted anode case were conducted. After that, the alumina transmission process was further coupled to carry out the numerical simulation of alumina concentration distribution [17]. This is a pioneering work; unfortunately the electromagnetic force and aluminum liquid drag force were not considered in their research. Zhang et al. [15] developed an alumina transmission model and studied the diffusion dynamics of alumina under the action of bubbles and electromagnetic forces. The study found that the transmission process of alumina was controlled by the electrolyte circulation flow. The bubble motion could promote the electrolyte movement in the vertical region around the anode, while the electromagnetic force drove alumina transmission in a larger and horizontal scale in the ACD region. Li et al. [18] and Jiang et al. [19] used a vorticity method to describe the state of the electrolyte flow, and the numerical simulation of the alumina concentration field was studied.
In the above studies, alumina mixing was modeled by solving a transient transmission equation for a scalar variable, which was more similar to the native properties of the electrolyte. Some scholars also developed another method in which the alumina was treated as particles. Zhan et al. [20] introduced the PBM (population balance model) into the CFD model to include the coalescence and breakage of alumina particles in the transmission process of alumina. This method was effective in simulating the early stage after alumina feeding. Liu et al. [21] also treated alumina as particles, and applied the DPM (discrete phase model) to investigate the movement characteristics of alumina particles from feeding points to the ACD region.
The scale and capacity of aluminum reduction cells increased rapidly in recent years, more and more scholars have realized that the transmission and diffusion of alumina is one of the insurmountable hot spots in this process. Although a large number of scholars have studied the transmission process of alumina, some detailed information has still not been clarified.
This paper established a simplified, more generic 3D computational fluid dynamic (CFD) model to access the circulating flow of electrolyte. The effects of bubbles, electromagnetic force, and aluminum drag force were considered in this model. Then the alumina transmission is coupled into the CFD model as a scalar. After verification by industrial measurement data of alumina concentration, some popular technologies in the aluminum electrolysis industry (slotted anodes, busbar design, and optimization) were investigated and evaluated.

Model Description
Two demonstration cases were set up based on a 48 anode, 500 kA cell geometry and operating information: one has no slots in the anode (geometry and mesh shown in Figure 1a) and the other has different slot depths (geometry and mesh shown in Figure 1b). The slot parameters are listed in Table 1. Two inclined slots were pre-cut under anode surface in the longitudinal direction, with one depth near the side channel being 230 mm and the other near the center channel being 260 mm. The width of the slots was 14 mm due to mechanical reasons. In the aluminum reduction process, the slot depth shall be decreased day-by-day since the anode is consumed by about 1.5 cm/day. Table 1 lists the detailed slot configurations and parameters representing a period of real cell operating conditions.    .  24 23 22  21  20  19 18 17 16 15 14 13 12

Up-stream (Side A)
Due to the complexity of real cells, only the electrolyte layer was simplified here to focus on the bath flow dynamics and the alumina transmission in this model. The ACD and inter-anode gap are 40 mm, the bath height is 200 mm, and the anode slope is 0 • . Other parameters, such as anode size, and width of channels used in this model are typical of those in industrial Hall-Héroult cell.
Step 1: Bath Flow A multi-phase flow model was applied here, in which the bubbles were considered as a dispersed fluid with a fixed diameter and the bath was treated as a continuous fluid. Although the detailed bubbles dynamics (such as bubble growth, bubble coalescence) cannot be simulated in this model, the time-averaged bubble induced flow proved to be accurate by comparing experimental data [16] and the VOF (volume of fluid) model [22].
The gas (100% CO 2 ) injected from the anode surface, and the velocity of the gas corresponded to the chemical reaction, anode current density (0.8 A/cm 2 ), and Faraday's law. A degassing boundary was used on the top surface of the electrolyte which allows the gas to leave the flow domain while acting as a non-slip wall that prevents liquid from leaving the domain. The boundaries on the cell sides, anode sides, and anode slots were set as walls and used a turbulent wall-type boundary condition to account for steep velocity gradients in the boundary layer. A no-slip condition for the liquid bath and a free-slip condition for bubbles were used.
The electromagnetic force is generated from the coupling effect of the electric field and the magnetic field. An external force file [13] was applied as a body force in the computing domain. The drag effect of the metal flow was also considered in this model by applying external metal pad velocities [13] to the bath/metal interface as a moving wall boundary condition.
Both the governing equations and turbulence equations are well documented in a previous reference [16] and the ANSYS CFX User Manual: where γ α is the volume fraction of phase α (c for continuous phase and d for separated bubbles), ρ α and U α are the density and vector velocity of phase α, P is the pressure, Pa, µ is the effective viscosity, S Mα is the momentum sources due to body forces, and M α is the interfacial momentum transfer between phases. The effective viscosity of each phase is a critical in multi-phase modelling. The phase dependent turbulence modes have been used with k − ε model for liquid phase and zero equation model for gas bubbles. The turbulence eddy viscosity of liquid phase is calculated as: Metals 2020, 10, 805

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and for the gas phase as: The parameter σ = 1.0 is the turbulent Prandtl number relating the dispersed phase kinematic eddy viscosity to the continuous phase kinematic eddy viscosity. c µ = 0.09 is the k − ε turbulence model constant, and k and ε are the turbulence kinetic energy and turbulence dissipation rate respectively. The transmission equations for k and ε can be described as: where C ε1 = 1.44, C ε2 = 1.92, σ k = 1.0, and σ k = 1.3 are turbulence model constants, P α is the turbulence production due to viscous production, S K and S ε represent the inter-phase transfer for k and ε, and µ tα is the turbulent viscosity for phase α.
Bubbles rising in side channels will also increase the turbulence in the liquid phase, known as bubble-induced turbulence. This is still an active area of research. For the treatment of bubble-induced turbulence and turbulence dispersion, the same method, well documented in Feng's paper [16], was applied here.
Step 2: Alumina Transmission In the alumina transmission modeling, it was assumed that the hydrodynamic properties of cryolite are independent of the local concentration of alumina and the alumina is dissolved quickly in the cryolite. The predicted steady state bath flow was used for the following transient alumina transmission modeling, and only the scalar equation needs to be solved at each time step.
The distribution of the alumina concentration is controlled by three steps: feeding, consuming, and transmission. Two combinations of feeding points FP1-FP3-FP5 and FP2-FP4-FP6 were alternately fed in sequence by a feeding dose of each combination 3.6 kg (1.2 kg × 3) here.
A typical overfeeding and underfeeding cycle of the 500 kA electrolytic cell is shown in Figure 2, including 49 shots in underfeeding, 57 shots in overfeeding, and 4 shots in normal feeding. The alumina feeding was defined as a source term in specified locations. The alumina consumption was defined as a sink term in the ACD region, with the rate was obtained according to Faraday's law and current density. In addition to the bath flow, the alumina transmission was also determined by diffusion of which the coefficient was 1.5 × 10 −9 m 2 /s from [23]. The specific equation of alumina feeding is as follows: where is feeding rate, kg/s; m is feeding dose, 1.2 kg; n is number of feeding points, 6 is the designed feeding points in the 500 kA cell; t is the injecting time from alumina feeding start to feeding finished, 10 s here.
The consumption rate of alumina in a real electrolysis cell varies with different locations. The The specific equation of alumina feeding is as follows: Metals 2020, 10, 805 6 of 15 where M feed is feeding rate, kg/s; m is feeding dose, 1.2 kg; n is number of feeding points, 6 is the designed feeding points in the 500 kA cell; t is the injecting time from alumina feeding start to feeding finished, 10 s here. The consumption rate of alumina in a real electrolysis cell varies with different locations. The anode current distribution data was not introduced in this model, and a uniform alumina consumption rate was applied at each grid in the ACD region in the computing domain. According to the source term, the control equation of alumina consumption is as follows: where M consume is the alumina consuming rate, kg/s; I is the line current, 500 kA; η is the current efficiency, 0.92 here; and MW Al2O3 is the molar mass of alumina, g/mol.

Case Design
Three cases were conducted in this paper (see the list in Table 2). Case 0 is an unslotted anode with busbar design B as a base case for comparison. Case 1 represents a slot design currently running in smelters with busbar design B. The comparison of Case 0 and Case 1 is used to investigate the effect of slots on bath flow and alumina transmission. Case 2 has a similar basic setting with Case 0, and the only difference is under different busbar design A. The effect of busbar design on bath flow and alumina transmission is compared by Case 2 and Case 0. The above three cases have six feeding points. Table 2. Cases conducted in this paper.

Cases No Slots Slots Busbar Net A Busbar Net B 6 Feeders
Case 0 The impact of mesh density on the calculation results was investigated by changing the mesh size. The detailed mesh information of three mesh sizes can be seen in Table 3. Mesh 1.00 was the base mesh size, and the two other meshes represented the division numbers of the base case multiplied by 1.11 and 1.25, respectively. The numbers of elements were 406,350, 545,589 and 725,760, respectively. Three cases with different mesh sizes produced a similar bath flow pattern, the differences in maximum velocity in the middle plane of the ACD were less than 0.005 m/s. The base mesh size of 1.00 was used as the mesh resolution in this study, considering that it has the shortest solution time among the above three mesh sizes.

Bath Flow
The bath flow was firstly investigated on a horizontal plane in the middle of the ACD in terms of velocity magnitude and flow pattern (shown in Figure 3). The model considered three factors, bubbles, electromagnetic force, and aluminum metal flow. It has been shown that the flow field presents two different-sized vortices, of which the vortex near to the duct end flows counterclockwise, occupying a larger region (anode 12 to anode 24, shown in Figure 1), while the vortex near to the tap end flows clockwise and covers a smaller area of anode 1 to anode 11. Feeding points 4, 5, and 6 are located in the larger vortex while feeding points 1 and 2 are located in the smaller vortex. Feeding point 3 is located on the boundary of the two vortices. The distribution of the feeding points may affect the alumina distribution within the cell. The flow velocity is larger at the outer boundary of the two vortices, and the maximum flow velocity is 20.3 cm/s in the up-stream side at the duct end.

Base Case
The bath flow was firstly investigated on a horizontal plane in the middle of the ACD in terms of velocity magnitude and flow pattern (shown in Figure 3). The model considered three factors, bubbles, electromagnetic force, and aluminum metal flow. It has been shown that the flow field presents two different-sized vortices, of which the vortex near to the duct end flows counterclockwise, occupying a larger region (anode 12 to anode 24, shown in Figure 1), while the vortex near to the tap end flows clockwise and covers a smaller area of anode 1 to anode 11. Feeding points 4, 5, and 6 are located in the larger vortex while feeding points 1 and 2 are located in the smaller vortex. Feeding point 3 is located on the boundary of the two vortices. The distribution of the feeding points may affect the alumina distribution within the cell. The flow velocity is larger at the outer boundary of the two vortices, and the maximum flow velocity is 20.3 cm/s in the up-stream side at the duct end.   Figure 4a represents the plane of Y = +70 mm and Figure 4b illustrates the flow pattern of Y = −70 mm. It can be seen that the maximum velocity presents at the cross-points of inter-anode gaps and center channel. This feature of the velocity distribution can be attributed to the gas pump effect. A very recent work [24] reported that more than 88.0% of gas escapes from the longer anode edge. These bubbles escaping from the ACD pump the bath upward and out of the inter-anode gaps and further into center channel. The large velocity or strong turbulence at the cross part would be beneficial to heat the added fresh alumina if it happens to be feeding there.
At the plane of Y = −70 mm, the velocity in the center area of the cell (anodes 4-21) is clearly larger than the duct end and tap end area (anodes 1-3 and anodes 22-24), while it shows a totally opposite trend at the plane of Y = +70 mm. This might be caused by the complex bath flow in the ACD region. turbulence at the cross part would be beneficial to heat the added fresh alumina if it happens to be feeding there.
At the plane of Y = −70 mm, the velocity in the center area of the cell (anodes 4-21) is clearly larger than the duct end and tap end area (anodes 1-3 and anodes [22][23][24], while it shows a totally opposite trend at the plane of Y = +70 mm. This might be caused by the complex bath flow in the ACD region.   Figure 5 shows the instantaneous alumina concentration in the middle plane of the ACD over one feeding cycle for the no-slot case. Following feeding, the alumina concentration under the feeding point quickly increases. Alumina is alternately fed by two groups of three feeders (out of the six total feeders), and it can be seen that the maximum alumina concentration occurs alternately under these two sets of three feeders. The maximum alumina concentration is lower than the saturation concentration [25]. This part of alumina (both undissolved solid alumina and dissolved alumina in real condition) transfer with the bath flow to the whole cell.

Characteristics of Alumina Distribution
At the end of the underfeeding period (about 2700 s), the overall alumina concentration reaches a low value except in locations under the feeding points. The overall concentration increases gradually during the overfeeding period (4860 s). As the feeding frequency is high, uniform alumina distribution cannot be reached before the next feeding cycle.  Figure 5 shows the instantaneous alumina concentration in the middle plane of the ACD over one feeding cycle for the no-slot case. Following feeding, the alumina concentration under the feeding point quickly increases. Alumina is alternately fed by two groups of three feeders (out of the six total feeders), and it can be seen that the maximum alumina concentration occurs alternately under these two sets of three feeders. The maximum alumina concentration is lower than the saturation concentration [25]. This part of alumina (both undissolved solid alumina and dissolved alumina in real condition) transfer with the bath flow to the whole cell.

Characteristics of Alumina Distribution
At the end of the underfeeding period (about 2700 s), the overall alumina concentration reaches a low value except in locations under the feeding points. The overall concentration increases gradually during the overfeeding period (4860 s). As the feeding frequency is high, uniform alumina distribution cannot be reached before the next feeding cycle.
It is interesting to see that the alumina concentration is higher in the half-cell near the duct end than that near the tap end during the overfeeding period. In order to obtain more accurate results, we ran this case for five cycles. Figure 6 shows the change trend of average concentration of alumina in the duct end half-cell (left half-cell) and the tap end half-cell (right half-cell) during five underfeeding and overfeeding cycles. The two curves in the first cycle do not reach stable state, and gradually stabilize after the second cycle. In the last three cycles, the average alumina concentration of the half-cell at the duct end is 2.41%, and the average concentration of the half-cell at tap end is 2.32%. This might involve the bath flow characteristics in the ACD and the locations of feeding points shown in Figure 3.  Figure 6 shows the change trend of average concentration of alumina in the duct end half-cell (left half-cell) and the tap end half-cell (right half-cell) during five underfeeding and overfeeding cycles. The two curves in the first cycle do not reach stable state, and gradually stabilize after the second cycle. In the last three cycles, the average alumina concentration of the half-cell at the duct end is 2.41%, and the average concentration of the half-cell at tap end is 2.32%. This might involve the bath flow characteristics in the ACD and the locations of feeding points shown in Figure 3.     Figure 6 shows the change trend of average concentration of alumina in the duct end half-cell (left half-cell) and the tap end half-cell (right half-cell) during five underfeeding and overfeeding cycles. The two curves in the first cycle do not reach stable state, and gradually stabilize after the second cycle. In the last three cycles, the average alumina concentration of the half-cell at the duct end is 2.41%, and the average concentration of the half-cell at tap end is 2.32%. This might involve the bath flow characteristics in the ACD and the locations of feeding points shown in Figure 3.  It is very difficult to validate the bath flow by industrial measurement in a real cell, and very limited information can be obtained during real operation. In order to characterize the alumina concentration at different locations within the cell and validate the model accuracy in this study 72 samples obtained from a running cell were analyzed in the laboratory. Table 4 lists the alumina concentration at different locations in an operating cell, SP1-SP6 (as shown in the sampling point in Figure 1a). The presented data is in a reasonable range, neither too high nor too low. Figure 7 shows the average alumina concentration in an overfeeding and underfeeding cycle, where the alumina concentration ranges from 1.6% to 2.1%, coinciding with the variation of cell voltage.
Based on the comparison of data in Table 4 and points location in Figure 1a, it can be found that SP3, SP4, and SP5 are located in the half-cell near the duct end with an average concentration of 2.09%, and SP1, SP2, and SP6 are located in the half-cell near the tap end with an average concentration of 1.68%. The concentration of the left half-cell is greater than that of the right half-cell. Several other industrial tests showed the same trends.

Effect of Slots
The slotted anode technology is the most exciting method that can be applied in industrial scale. Most researchers focused their attention on gas coverage [26,27], bubble-induced resistance [28], and bath flow [16], with very little literature reporting the alumina mixing in a slotted anode cell.    Although the overall difference trend measured in a commercial cell cannot be used as a quantitative verification for the accuracy of CFD models, the predicted trend shown here is consistent with the numerical simulation results, indicating that the model is an effective tool for the design and optimization of aluminum reduction cells. The following section would apply this model for two popular technologies of slotted anode and busbar designs.

Effect of Slots
The slotted anode technology is the most exciting method that can be applied in industrial scale. Most researchers focused their attention on gas coverage [26,27], bubble-induced resistance [28], and bath flow [16], with very little literature reporting the alumina mixing in a slotted anode cell.  Figure 3. There are two large vortices formed in the middle plane of the ACD, but more local re-circulations dominate in the side, end, and center channels, especially at the ends of reduction cell. With the application of slotted anodes, the maximum velocity on this plane increased from 20.3 cm/s of Case 0 to 22.0 cm/s of Case 1, and the average velocity decreased slightly from 7.89 cm/s to 7.67 cm/s. Figure 8 plots the overall bath flow in terms of velocity vector for the slotted case. The global flow patterns are very similar to the unslotted case in Figure 3. There are two large vortices formed in the middle plane of the ACD, but more local re-circulations dominate in the side, end, and center channels, especially at the ends of reduction cell. With the application of slotted anodes, the maximum velocity on this plane increased from 20.3 cm/s of Case 0 to 22.0 cm/s of Case 1, and the average velocity decreased slightly from 7.89 cm/s to 7.67 cm/s.  Figure 9 shows the velocity at two vertical planes of Y = +70 mm and Y = −70 mm. It can be seen that the direction of maximum velocity is clearly different with the unslotted Case 0. The maximum velocity vectors point from the unslotted anodes to the slotted anodes. Previous work [24] has illustrated that the gas escaping path is clearly different in the slotted case and unslotted case, especially at the stage where the slots are completely submerged in the bath when the anodes are consumed for a period of time. In the slotted anodes, about 40.0% of the gas escapes from the longer anode edge into the inter-anode gap, while the portion is twice that value for the unslotted anode (88%). The pump effect in the inter-anode gap is relatively smaller for the slotted anode, which dominates the flow direction from the unslotted anodes to the slotted anodes shown in this Figure 9. For the choosing of feeding location in the slotted case, we can reach a similar conclusion that the  Figure 9 shows the velocity at two vertical planes of Y = +70 mm and Y = −70 mm. It can be seen that the direction of maximum velocity is clearly different with the unslotted Case 0. The maximum velocity vectors point from the unslotted anodes to the slotted anodes. Previous work [24] has illustrated that the gas escaping path is clearly different in the slotted case and unslotted case, especially at the stage where the slots are completely submerged in the bath when the anodes are consumed for a period of time. In the slotted anodes, about 40.0% of the gas escapes from the longer anode edge into the inter-anode gap, while the portion is twice that value for the unslotted anode (88%). The pump effect in the inter-anode gap is relatively smaller for the slotted anode, which dominates the flow direction from the unslotted anodes to the slotted anodes shown in this Figure 9. For the choosing of feeding location in the slotted case, we can reach a similar conclusion that the cross-region of the inter-anode gap and center channel is perfect for cold alumina feeding due to the significant turbulence here [29].  Figure 10 shows the instantaneous alumina concentration on the middle plane of the ACD for the slotted case. The alumina distribution is very similar to the unslotted case shown in Figure 5 in whole scale. This indicates that the slots do not greatly impact the alumina distribution, and this feature also can be found in the bath flow in Figure 8. It can also be seen that the alumina concentration is more uniform than that of the unslotted case, which protrudes into another low concentration area. The alumina concentration is lower at the contacting area of the two re-circulation zones (near the anode 12 and 13). This might be caused by two reasons: Reason A is that the flow velocity is relatively low here, making the alumina diffuse from the feeding point to this area more  Figure 10 shows the instantaneous alumina concentration on the middle plane of the ACD for the slotted case. The alumina distribution is very similar to the unslotted case shown in Figure 5 in whole scale. This indicates that the slots do not greatly impact the alumina distribution, and this feature also can be found in the bath flow in Figure 8. It can also be seen that the alumina concentration is more uniform than that of the unslotted case, which protrudes into another low concentration area. The alumina concentration is lower at the contacting area of the two re-circulation zones (near the anode 12 and 13). This might be caused by two reasons: Reason A is that the flow velocity is relatively low here, making the alumina diffuse from the feeding point to this area more difficult; Reason B is that the alumina from feeding point 3 transfers into the right vortex with the bath flow, and the alumina from feeding point 4 flows into the left vortex with the bath. It is still unknown which is the dominate factor, and it will be determined in future work.  Figure 10 shows the instantaneous alumina concentration on the middle plane of the ACD for the slotted case. The alumina distribution is very similar to the unslotted case shown in Figure 5 in whole scale. This indicates that the slots do not greatly impact the alumina distribution, and this feature also can be found in the bath flow in Figure 8. It can also be seen that the alumina concentration is more uniform than that of the unslotted case, which protrudes into another low concentration area. The alumina concentration is lower at the contacting area of the two re-circulation zones (near the anode 12 and 13). This might be caused by two reasons: Reason A is that the flow velocity is relatively low here, making the alumina diffuse from the feeding point to this area more difficult; Reason B is that the alumina from feeding point 3 transfers into the right vortex with the bath flow, and the alumina from feeding point 4 flows into the left vortex with the bath. It is still unknown which is the dominate factor, and it will be determined in future work.

Effect of Busbar Design
In the design of modern aluminum reduction cells, the busbar design is an extremely important part [30]. Busbar design not only affects the electrical balance of the electrolytic cell, but also determines the magnetic field distribution and further determines the pattern and magnitude of the bath flow [31]. In this section, the bath flow and alumina transmission caused by the two busbar structures will be discussed. Figure 11 shows the velocity vectors of the bath flow in the middle horizontal plane of the ACD under busbar design A (busbar net A of Case 2). Comparing with Figure 3 of busbar design B (busbar net B of Case 0), it can be seen that the bath flow also exhibits two sizes of vortices, but the symmetry of the two vortices is not as obvious as that of the busbar net B. The velocity distribution in the center of the vortex is also more uneven than that of Figure 3. The maximum bath velocity in the middle plane of busbar net A is 24.3 cm/s, and the average velocity is about 7.76 cm/s. After the busbar structure is upgraded from A to B, the maximum flow velocity in the ACD plane is significantly reduced, especially at the ends of the reduction cell.

Effect of Busbar Design
In the design of modern aluminum reduction cells, the busbar design is an extremely important part [30]. Busbar design not only affects the electrical balance of the electrolytic cell, but also determines the magnetic field distribution and further determines the pattern and magnitude of the bath flow [31]. In this section, the bath flow and alumina transmission caused by the two busbar structures will be discussed. Figure 11 shows the velocity vectors of the bath flow in the middle horizontal plane of the ACD under busbar design A (busbar net A of Case 2). Comparing with Figure 3 of busbar design B (busbar net B of Case 0), it can be seen that the bath flow also exhibits two sizes of vortices, but the symmetry of the two vortices is not as obvious as that of the busbar net B. The velocity distribution in the center of the vortex is also more uneven than that of Figure 3. The maximum bath velocity in the middle plane of busbar net A is 24.3 cm/s, and the average velocity is about 7.76 cm/s. After the busbar structure is upgraded from A to B, the maximum flow velocity in the ACD plane is significantly reduced, especially at the ends of the reduction cell.

Alumina Transmission
Since the alumina concentration changing with time for busbar net A is similar with that of busbar net B in Figure 5, a no more detailed description is needed here. Figure 12 shows the tendency of standard deviation of alumina concentration in the underfeeding and overfeeding cycle. Both curves present saw-tooth patterns, which are closely consistent with the alumina concentration in Figure 5. The average value of the standard deviation decreases from 0.001868 for busbar net A to 0.001515 for busbar net B, which is about a 18.9% reduction. This indicates that busbar net B makes

Alumina Transmission
Since the alumina concentration changing with time for busbar net A is similar with that of busbar net B in Figure 5, a no more detailed description is needed here. Figure 12 shows the tendency of standard deviation of alumina concentration in the underfeeding and overfeeding cycle. Both curves present saw-tooth patterns, which are closely consistent with the alumina concentration in Figure 5. The average value of the standard deviation decreases from 0.001868 for busbar net A to 0.001515 for busbar net B, which is about a 18.9% reduction. This indicates that busbar net B makes the alumina concentration more uniform within the bath.

Alumina Transmission
Since the alumina concentration changing with time for busbar net A is similar with that of busbar net B in Figure 5, a no more detailed description is needed here. Figure 12 shows the tendency of standard deviation of alumina concentration in the underfeeding and overfeeding cycle. Both curves present saw-tooth patterns, which are closely consistent with the alumina concentration in Figure 5. The average value of the standard deviation decreases from 1.868×10 −3 for busbar net A to 1.515×10 −3 for busbar net B, which is about a 18.9% reduction. This indicates that busbar net B makes the alumina concentration more uniform within the bath.

Conclusions
A CFD model was used to simulate the bath flow and alumina transmission in aluminum reduction cells in this paper. The effect of slots and busbar design were investigated by this model.
The main findings from this study are summarized as follows: 1. The bath flow driven by bubbles, electromagnetic force, and aluminum drag force presents two different size vortices in the horizontal plane in the middle of the ACD region, of which the

Conclusions
A CFD model was used to simulate the bath flow and alumina transmission in aluminum reduction cells in this paper. The effect of slots and busbar design were investigated by this model.
The main findings from this study are summarized as follows: 1. The bath flow driven by bubbles, electromagnetic force, and aluminum drag force presents two different size vortices in the horizontal plane in the middle of the ACD region, of which the larger one at the duct end occupied the region of feeding points 4, 5, and 6, while the smaller one near to the tap end covered the area of feeding points 1 and 2. Feeding point 3 was located on the boundary of the two vortices.

2.
The larger velocity or stronger turbulence presented at the cross section of the inter-anode gaps and the center channel would be beneficial to heat the cold alumina added from the feeding points here.

3.
Both numerical results and industrial data show the average concentration of alumina within the half-cell at the duct end is larger than that at the tap end. This is possibly related to the bath flow characteristics and the locations of feeding points. 4.
In general, the global flow patterns and alumina distribution of the slotted case are very similar to the unslotted case. However, with the application of slotted anodes, the maximum velocity in the horizontal plane was increased, while the average velocity was decreased slightly. Therefore, the alumina distribution of the slotted case is more uniform than that of the unslotted case. 5.
Since the busbar structure was upgraded from A to B, the symmetry of the two vortices became more obvious and the maximum flow velocity was significantly reduced, especially at the ends of the aluminum reduction cell. Consequently, the alumina concentration is more uniform within the bath for busbar net B.
Author Contributions: J.Z. has conducted the study design and data analysis, developed the model, and written some parts of the manuscript. J.L. has provided valuable guidance. H.Z. has provided valuable guidance and written some parts of the manuscript. All authors have read and agreed to the published version of the manuscript.
Funding: This research received the financial support of the National Natural Science Foundation of China (51974373, 51874365, 51674300, 61751312, and 61621062), the Major Scientific and Technological Innovation Projects of Shandong Province(2019JZZY020123), and the Natural Science Foundation of Hunan Province, China (2018JJ2521).

Conflicts of Interest:
The authors declare no conflict of interest.