Modelling alternating current effects in a submerged arc furnace

Abstract Modelling the production of silicon in a submerged arc furnace (SAF) requires accounting for wide range timescales different physical and chemical processes: electric current which is used to heat varies over timescale around $10^{-2}\,$ s, whereas flow consumption raw materials occurs several hours. Models generally either include only fast-timescale, or slow-timescale processes. In prior work, we developed model incorporating effects on both fast slow timescales, multiple-timescales analysis homogenise variations, deriving an averaged evolution materials. For simplicity, previous work focussed electrical behaviour base single electrode, prescribed this electrode be sinusoidal, with given amplitude. paper, extend our full system, modelled using equivalent circuit system. way, demonstrate how two furnace-modelling approaches (on timescales) may combined computationally efficient way. Our previously derived resistance based assumption that dominant loss from by radiation (we will refer as model). Alternative models empirical Cassie Mayr models, are commonly SAF literature. We compare these various explore dependence solution parameters solutions measurements operational furnace. particular, show has rising current-voltage characteristic at high currents. Simulations there upper limit length arc, above all bypasses flows through surrounding material.