This paper describes a coupled boundary and finite element analysis of electromagnetic, free surface deformation and thermal problems in magnetic levitation systems under both normal and microgravity conditions. A computer code is developed, which involves the use of finite elements in the regions of interest and boundary elements in other regions for electromagnetic field calculations, along with an iterative and remeshing scheme for free surface deformation calculations. The code is tested against available analytical solutions and experimental measurements, and then applied to study the free surface deformation and temperature distribution in magnetically levitated droplets on earth and in microgravity. It is found that an accurate assessment of the thermal behavior of a droplet must be made along with its deformation, including the bulk movement, for magnetic levitation systems. In normal gravity, a magnetically levitated droplet assumes a conical shape with its apex pointing downward, and higher temperature occurs in the lower portion of the droplet. In microgravity, on the other hand, surface deformation is primarily attributed to the heating coils and the deformation is symmetric, with the droplet squeezed at the equator plane and bulged out along the axis of symmetry. Positioning coils give rise to a smaller deformation force and a lower Joule heating rate under normal operation conditions. The temperature profiles and free surface shapes induced by the positioning coils, though symmetric, are different from those induced by heating coils.
Finite Element Analysis of Stationary Magnetic Field