Electromagnetic induction in non-uniform domains

Numerical simulations of the electromagnetic induction equation are carried out applying a grid based finite volume method where insulating boundaries are treated by the boundary element method. A prescribed flow of liquid sodium provides the energy source for self-generation of a magnetic field and the influences of non-uniform material properties on the induction process are examined by means of internal assemblies and outer container walls with high conductivity or high permeability.

High permeability material even if localized in a small volume like the flow driving impellers in the French VKS dynamo experiment, essentially determines the field generation process (decrease of the effective critical magnetic Reynolds number and enforcing of internal boundary conditions on material interfaces). Permeability caused facilitation of dynamo action might be important as well for the helical flow in cooling circuits of fast breeders. Preliminary simulations for a model flow in and around soft-iron sub-assemblies (that comprise the nuclear fuel pins) show a reduction of the critical magnetic Reynolds number for the onset of dynamo action by a factor of 2.

The third examined configuration is motivated by an application of the contactless inductive flow tomography (CIFT) in a continuous casting model experiment. Consideration of the finite conductivity of the copper container walls results in a quantitative modification of the current distribution within the solid material. An enhanced current yields an amplified induced magnetic field outside of the container which must be considered in the reconstruction of the fluid velocity field.