Characterising the Behaviour of an Electromagnetic Levitation Cell using Numerical Modelling

Abstract

Experimental investigations of high temperature industrial processes, for example the melting and smelting processes taking place inside furnaces, are complicated by the high temperatures and the chemically reactive environment in which they take place. Fortunately, mathematical models can be used in conjunction with the limited experimental results that are available to gain insight into these high temperature processes. However, mathematical models of high temperature processes require high temperature material properties, which are difficult to measure experimentally since container materials are often unable to withstand high enough temperatures, and sample contamination often occurs. These difficulties can be overcome by employing containerless processing techniques such as electromagnetic levitation melting to allow for characterisation of high temperature material properties. Efficient design of electromagnetic levitation cells is challenging since the effects of changes in coil design, sample size and sample material on levitation force and sample temperature are not yet well understood. In this work a numerical model of the electromagnetic levitation cell is implemented and used to investigate the sensitivity of levitation cell operation to variations in coil design, sample material and sample size. Various levitation cell modelling methods in literature are reviewed and a suitable model is chosen, adapted for the current application, and implemented in Python. The finite volume electromagnetic component of the model is derived from Maxwell’s equations, while heat transfer is modelled using a lumped parameter energy balance based on the first law of thermodynamics. The implemented model is verified for a simple case with a known analytical solution, and validated against published experimental results. It is found that a calibrated model can successfully predict the lifting force inside the levitation cell, as well as the sample temperature at low coil currents. The validated model is used to characterise the operation of a levitation cell for a number of different sample materials and sample sizes, and for variations in coil geometry and coil current. The model can be used in this way to investigate a variety of cases and hence to support experimental levitation cell design. Based on model results, a number of operating procedure recommendations are also made.