Numerical modelling of high-temperature superconducting dynamos: A review

•Summarises recent developments in the numerical modelling of HTS dynamos.•Describes modelling techniques in 2D and 3D to analyse open-circuit behaviour.•Details how models can be used to characterise HTS dynamos & explore key parameters.•Describes modelling dynamic coil charging behaviour & calculating dynamo losses.•Outlines outstanding challenges & developments required to address these. The high-temperature superconducting (HTS) dynamo enables injection of large DC currents into a superconducting coil, without the need for thermally-inefficient current leads. Because of this important advantage, there is significant interest in using such technology to energise superconducting coils in superconducting rotating machines and NMR/MRI magnets. Despite the extensive experimental work carried out over the past decade, there was – until very recently – considerable confusion and debate regarding the physical origin of the HTS dynamo’s DC output voltage. Numerical modelling has played a key role in elucidating the underlying physics of such devices and several different numerical models have now been developed as useful and cost-effective tools to not only explain and further examine experimental results, but also optimise and improve dynamo designs. This review summarises all of the developments in this important area over recent years, including modelling the open-circuit voltage behaviour in 2D and 3D, the definition of a new benchmark problem for the HTS modelling community, investigating key dynamo parameters, modelling dynamic coil charging behaviour and calculating losses. A view towards the future is provided, including the outstanding challenges and the developments required to address these.