Modelling of non-uniform current diffusion coupled with thermohydraulic effects in superconducting cables

Abstract

Non-uniform current distributions in multistrand superconducting cables cooled by supercritical helium are often blamed for lower than expected performance relative to individual strands, both in steady-state and pulsed modes of operation. However, the lack of practical analysis tools has limited the quantification of such effects and the interpretation of experimental results. A resistive diffusion model for current redistribution between super and normal conducting strands has been coupled with a thermal model to allow simultaneous analysis of current distributions and stability in multistrand cables. The model is novel in that both resistive and superconducting strands can be analysed. Joint regions, current sharing lengths and normal conducting strands can be included simultaneously in the model so that a full current ramp up and development of non-uniformities from joint resistances can be simulated, as well as short time scale stability effects. The thermal model includes a stagnant boundary layer on the strand surfaces to simulate the heat transfer variation with fast heat inputs, as well as simple heat conduction in the transverse direction within the helium and a one-dimensional simplified fluid flow model along the cable. The calculation procedure is fast enough to be applied to 1000-strand cables although the calculation speed is improved using superstrands. It has been applied to a range of cables with different joint resistance distributions to investigate operating limits due to external heating and current ramps and the impact of transverse field gradients. A companion paper applies the procedure to the analysis and comparison with measured results in a large coil test with a 140 m long conductor.