# Influence of Selected Model Parameters on the Electromagnetic Levitation Melting Efficiency
###### Abstract  
The article presents the results of multivariate calculations for the levitation metal melting system. The research had two main goals. The first goal of the multivariate calculations was to find the relationship between the basic electrical and geometric parameters of the selected calculation model and the maximum electromagnetic buoyancy force and the maximum power dissipated in the charge. The second goal was to find quasi-optimal conditions for levitation. The choice of the model with the highest melting efficiency is very important because electromagnetic levitation is essentially a low-efficiency process. Despite the low efficiency of this method, it is worth dealing with it because is one of the few methods that allow melting and obtaining alloys of refractory reactive metals. The research was limited to the analysis of the electromagnetic field modeled three-dimensionally. From among of 245 variants considered in the article, the most promising one was selected characterized by the highest efficiency. This variant will be a starting point for further work with the use of optimization methods. electromagnetic levitation; metal melting; electromagnetic field +
Footnote †: journal: Applied Sciences  
In the literature, the problem of levitation melting has been present for quite a long time [5; 18; 19; 20; 21]. Initially, it concerned practically implemented inductor systems, because analytical computational methods allowed for modelling of such a system in a very simplified manner. The use of numerical methods significantly accelerated and widened the scope of research [22] from simplified models covering only the analysis of the electromagnetic field, through models including coupled analysis of the electromagnetic field and temperature, to models taking into account the coupling of electromagnetic field temperature and fluid dynamics fields. Initially, of course, the models were created as two-dimensional models, followed by the advancement as 3D models. However, the necessity to couple the three types of field to this day causes computational problems to conduct a numerical analysis of electromagnetic levitation. Currently, progress is made especially in the area of flow modeling, where Reynolds Averaged Navier-Stokes Models are increasingly replaced by Scale Resolving Simulation models (e.g., LES). The complete levitation melting computational model includes the coupled analysis of the electromagnetic field, temperature and fluid dynamics fields. As a result of the effect of the electromagnetic field inside the batch, eddy currents are induced, which causes the appearance of electrodynamic forces and heating of the batch. If the direction and magnitude of the electrodynamic forces are \"correct\", the batch may begin to levitate. As the temperature of the batch changes, its material properties also change, which causes a change in the levitation conditions; if the batch melts, its shape changes, which also changes the calculation model. A sketch of the relationship between the fields is presented in Figure 1.  
As can be seen from the above description, the phenomenon of metal melting using electromagnetic levitation is very complex. The most obvious way of the electromagnetic levitation modelling is to compute the electromagnetic field, temperature and the flow field in the time domain, but the time step needed to calculate the EM field is much shorter than the time step needed to analyze the other fields. Performing calculations with such a short time step leads to a very large computational effort and a long calculation time. To avoid this, hybrid calculation models are often used, in which the analysis of the electromagnetic field is conducted as quasi-static (harmonic) and the analysis of the temperature field and flow field is already performed in the time domain. Such a calculation scheme allows one to extend the time step but leads to problems with the modeling of non-linearity of the electromagnetic field (B = f (H)).