Lattice Boltzmann Methods for Metallurgical Process Simulation

"The Lattice Boltzmann Method (LBM) solves fluid dynamics problems based on a discrete mesoscopic approach. It is based on the Lattice Boltzmann equation which is a special discretisation of the continuous Boltzmann equation. Its principle advantage is that it can handle complex physical phenomena (like interaction between different components and surface effects), complicated boundary and initial conditions very well, free from many gridding and stability constraints that plague conventional numerical methods used for fluid flow simulations. Complex structures like porous media can be resolved directly. The LBM algorithm has a simple structure and acts locally, which is favourable for parallel computing. Its potential for metallurgical process simulation is demonstrated in the present study which is concerned with the simulation of the fluid flow in a copper winning electrolysis cell. The electrolyte is modelled as the carrier fluid and the oxygen is considered via a so called active scalar equation. The modelling of buoancy, momentum exchange and the free surface requires special effort. The results of the simulation are validated against experimental data obtained by Laser-Doppler-Anemometry. Despite the simplifications made, good agreement between the simulation and the experiments was found.IntroductionThe hydrodynamics in an electrometallurgical cell is a complex, highly non-linear phenomenon. It includes the simulation of a two component system with high density ratio, gravity driven flow and a free surface. A general solution to this problem is currently unknown.The flow field is a result of the combination of various hydrodynamic effects [18]. Metal deposition at the cathode yields in a decrease in the ion concentration, which reduces the density of the electrolyte. At the anode molecular oxygen is formed as a consequence of the oxidation of water molecules. The oxygen is solved in the electrolyte and again the electrolyte density is decreased. Both effects lead to a free upwards directed convective flow, refered to as natural convection."