Coupled electromagnetic-fluid modelling of a bulk superconductor cooled by a cryogenic fluid

The electric and magnetic performance of a superconductor are strongly dependent of its temperature. For that reason, the cooling of the superconductor material is an important matter, especially for bulk superconductors, which favor low heat transfers because of their low thermal conductivity and the large volume to surface ratio.

Usually, heat transfers between a bulk superconductor and the cooling fluid is modelled by a simplified law depending on a convective coefficient and the temperature difference between the fluid and the bulk surface. In practice, however, the heat flux depends also on the geometry of the superconductor and its orientation. Its experimental determination can be difficult and requires considering realistic setups, as effectively used in applications.

The goal of this work is to model, in addition to the electromagnetic behaviour of the superconductor, the cooling fluid flow. We focus on the case of a bulk superconductor heated by induced AC losses. The hot surface of the superconductor initiates convective motion in the fluid, which will cool down the superconductor. This coupling effect is modelled using a finite element approach for both the fluid flow and the superconductor. The model is validated experimentally thanks to Particle Image Velocimetry (PIV) methods performs at room temperature with oil. The heat transfers are then estimated and compared with results from the conventional simplified model, in order to understand better its ranges of applicability.