Electromagnetic Processing from AC to DC Field : Modeling Approach with COMSOL Multiphysics®
Electromagnetic (EM) processes are good candidates for energy saving and CO2 reduction demand. In metallurgy industry, it leads to productivity improvement, maintenance reduction and safety integration. These processes can be classified by their frequency range from several hundred kHz to 0 Hz mining AC to DC field. The choice depends on the wished action on the electro-conductive materials: heating, melting, flow, shape, solidification control.... A transverse approach by using Multiphysics modeling, analytical approach and experiments leads to development of innovative processes with integration and optimization of specific EM configuration.
Several modeling approaches are presented and illustrated through four different EM devices: (1) Induction heating of thin layers with transverse magnetic flux (2) Melting alloys with Cold crucible, (3) EM Pumping, (4) EM wiping with DC magnets to control the zinc coating on galvanizing lines. Application fields are respectively packaging, electronics, aeronautic, nuclear, automotive….
COMSOL® AC/DC Module with magnetic field interface (to solve for potential vector A) and a frequency domain formulation are used. Weak or strong Multiphysics coupling are studied with heat transfer or Navier-Stokes interface for induction heating or fluid flow control. An Arbitrary Lagrange Eulerian (ALE) deformed mesh technique is also set up which allows the deformation of the free surface.
The choice of the modeling approach is dependent on the frequency range, physical properties of the conductive materials and complexity of the system. To minimize computing time and mesh size a simplified approach is needed.
A surface description with an imposed current density is in many cases sufficient to describe properly the coil (multi-turn coil description). Besides, it’s also possible to consider only the external surface of the electro-conductive material which interacts with the electromagnetic field. This is the case if the skin depth δ (penetration depth of the electromagnetic field inside the material) is very small compared to the characteristic dimension (e). A surface Impedance Boundary Condition (IBC) is set up and we do not need to resolve in detail the interior volume. For a thin conductive layer (e < δ), the layer is described only by a surface with a two way boundary condition (Transition Boundary Condition). An extension to multilayered materials was also developed and coupled with heat transfer in shells.
For magnetic materials, a non-linear relation that connects the magnetic field H and the magnetic flux density B needs to be introduced. A specific effective HB Curve can be used in frequency domain formulation. With some adaptation of the physical description, it’s also possible to combine this with surface description (IBC).
Magnetic materials (FeSi laminations, soft magnetic materials, ferrite…) are also used to optimize and localize induction heating. It acts like a magnetic flux concentrator and leads to global power efficiency improvement by reducing the current in the coil for a same power injected in the metallic charge. For a good definition of the processes, all losses need to taking into account: induced current, magnetic losses…. The evaluation is done by analytical Steinmetz law or introduction of complex magnetic permeability description.
