The numerical study of the defined parameter k 0 is a first study of its kind. The electric conductivity is implemented in the finite element model (FEM) as an orthotropic inhomogeneous material property with the proposed six-parameter equation. In the second part of the article, a two-dimensional (2D) numerical model is developed to determine a typical variation in k 0 for some realistic anode geometries and anode conductivity gradients. The anode conductivity gradients are also parameterized with linear and nonlinear parameters by a six-parameter equation to study how different conductivity gradients can affect the ACD through the k 0 parameter. The parameter is coupled even more by a proposed analytical equation to the ACD to explain how the k 0 parameter affects the ACD. The first section of the article defines the k 0 parameter to describe the degree of initial inhomogeneous current densities in the anode. This article will focus on one special effect on the ACD variation, that is, the initial electric current distribution (the anode in an initial state in the bath as explained previously). It is emphasized that each slot implementation must be treated individually for each plant to avoid pitfalls. The actions for reducing the noise in the ACD resistance by slots in the anode have led to negative effects on other parameters, like current efficiency and increased inhomogeneous anode consumptions. In normal situations, it is reported that the standard deviation in the current load on individual anodes in the same cell often are more than 10 pct of the average current. Still, variations exist in the ACD resistance. This gives motivation for alumina distribution to the cell through individual feeder control to reduce the density differences in the bath. There is also a focus on how the inhomogeneous density of the bath creates inhomogeneous ACDs. The low-frequency noise components in the liquid metal have also been studied in a magnetohydrodynamic (MHD) aspect that has influenced design optimizations of the cell and also the bus bar system. The produced carbon dioxide creates bubbles in the bath and the slots function as an escape route for the bubbles. One of the major improvements of reducing the noise was the implementation of slots in the wear surface as illustrated in Figure 1. Over the last 10 years, there has been focus on current increase actions and also on reducing the noise in the ACD resistance in the aluminum industry. If not, the process will be directed toward an unstable state with reduced current efficiency and higher probability for dynamic short circuiting, which is caused by magneto hydrodynamic waves and the risk of growing spikes at the anodes wear surface. When the average of the ACD is reduced by current increase actions, it is important to reduce the variation/noise in the ACD resistance. This is preferred to make sure that the pots stay inside an operational resistance load window where sufficient frozen side ledge is retained. The electrical power loss from the bath resistance as a result of the current increase can be reduced by decreasing the anode-to-cathode distance (ACD). T he metal capacity from the aluminum reduction cell increases proportionally with a current increase as long as the current efficiency (CE) is constant. The lowest degree of initial inhomogeneous current in the anode is achieved with deeper slots closer to each other and with an electrical current entering the anode in the bottom of the anode stub hole. To avoid a variation in the ACD for this case, the defined bath conductivity relation n should be within certain limits for the analyzed industrial reduction cell.
The degree of initial inhomogeneous anode current density, which is expressed with a defined parameter k 0, can reach values to cause variations in the ACD typically measured in the aluminum industry.
The anode is implemented as an inhomogeneous orthotropic material with a defined six-parameter equation. The slot positioning, slot depths, and stub hole dimensions have been considered in the FEM. The electrical power loss in the anode has also been studied at different anode geometries and material properties. The numerical results of the initial state of the anode electrical current were used to describe analytically how this will affect the variation in the anode-to-cathode distance (ACD) in a steady-state scenario after several hours in the electrolysis bath. A two-dimensional (2D) finite element model (FEM) of an anode immersed in an aluminum reduction cell was developed to study the initial current distribution in the anode as a function of anode geometry and electrical anode conductivity gradients.
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