Two-step homogenization for the effective thermal conductivities of twisted multi-filamentary superconducting strand

For the accurate prediction of the effective thermal conductivities of the twisted multi-filamentary superconducting strand, a two-step homogenization method is adopted. Based on the distribution of filaments, the superconducting strand can be decomposed into a set of concentric cylinder layers. Each layer is a two-phase composite composed of the twisted filaments and copper matrix. In the first step of homogenization, the representative volume element (RVE) based finite element (FE) homogenization method with the periodic boundary condition (PBC) is adopted to evaluate the effective thermal conductivities of each layer. In the second step of homogenization, the generalized self-consistent method is used to obtain the effective thermal conductivities of all the concentric cylinder layers. The accuracy of the developed model is validated by comparing with the local and full-field FE simulation. Finally, the effects of the twist pitch on the effective thermal conductivities of twisted multi-filamentary superconducting strand are studied.