Homogenised model for the electrical current distribution within a submerged arc furnace for silicon production. (English) Zbl 1504.78019
Summary: Silicon is produced in submerged arc furnaces which are heated by electric currents passing through the furnace. It is important to understand the distribution of heating within the furnace in order to accurately model the silicon production process, yet many existing studies neglect aspects of this current flow. In the present paper, we formulate a model that couples the electrical current to thermal, material flow and chemical processes in the furnace. We then exploit disparate timescales to homogenise the model over the timescale of the alternating current, deriving averaged equations for the slow evolution of the system. Our numerical simulations predict a minimum applied current that is required in order to obtain steady-state solutions of the homogenised model and show that for high enough applied currents, two spatially heterogeneous steady-state solutions exist, with distinct crater sizes. We show that the system evolves to the steady state with a larger crater radius and explain this behaviour in terms of the overall power balance typically found within a furnace. We find that the industrial practice of stoking furnaces increases the overall rate of material consumption in the furnace, thereby improving the efficiency of silicon production.
MSC:
| 78M40 | Homogenization in optics and electromagnetic theory |
| 78A35 | Motion of charged particles |
| 78A40 | Waves and radiation in optics and electromagnetic theory |
| 78A55 | Technical applications of optics and electromagnetic theory |
| 80A21 | Radiative heat transfer |
| 80A19 | Diffusive and convective heat and mass transfer, heat flow |
| 80A32 | Chemically reacting flows |
| 35R35 | Free boundary problems for PDEs |
Keywords:
homogenisation theory; submerged arc furnace; heat and mass transfer; endothermic chemical reaction; free boundary problemReferences:
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