Finite difference modelling of bulk high temperature superconducting cylindrical hysteresis machines

Abstract

A mathematical model of the critical state based on averaged fluxon motion has been implemented to solve for the current and field distributions inside a high temperature superconducting hysteresis machine. The machine consists of a rotor made from a solid cylindrical single domain HTS placed in a perpendicular rotating field. The solution technique uses the finite difference approximation for a two-dimensional domain, discretized in cylindrical polar co-ordinates. The torque generated or equivalently the hysteresis loss in such a machine has been investigated using the model. It was found that to maximize the efficiency, the field needs to penetrate the rotor such that B 0 /µ 0 J c R = 0.56, where B 0 is the applied field amplitude, J c is the critical current density and R is the rotor radius. This corresponds to a penetration that is 27% greater than that which reaches the centre of the rotor. An examination of the torque density distributions across the rotor reveal that for situations where the field is less than optimal, a significant increase in the performance can be achieved by removing an inner cylinder from the rotor.

A Hierarchy of Models for Type-II Superconductors

“…In fact vortices will be generated whenever |J | > J nucl on the boundary, but as we have seen, will not move if J nucl < J c until |J | = J c on the boundary 6 . Hence the generation of vortices at the boundary is controlled by the constraint…”

“…The colour indicates the current density (blue coming out of the paper, red moving into the paper), while the contour lines indicate the direction of the magnetic field. (Numerical solution due to G. Barnes [6,5].) An example of the numerical solution of the two-dimensional Bean critical-state model (equations (205)-(206) coupled with Maxwell's equations) describing the magnetic field and electric current in a cross-section of the superconducting cylinder (assuming the cylinder has a large aspect ratio) is shown in Figure 1b [5].…”

“…An example of the numerical solution of the two-dimensional Bean critical-state model (equations (205)-(206) coupled with Maxwell's equations) describing the magnetic field and electric current in a cross-section of the superconducting cylinder (assuming the cylinder has a large aspect ratio) is shown in Figure 1b [5]. This can be used to determine the torque on the superconducting rotor, and hence the power of the motor [6,5].…”

Reluctance machines incorporating high temperature superconducting materials on the rotor

“…The ceramic YBCO is a type-II HTS with a critical temperature T c of 94 K. This compound is achievable with dimensions of centimetres and when cooled with cheap and readily available liquid nitrogen (77 K), can carry large current densities in the region of 10 4 A/ cm 2 [5] without any dissipation to provide high magnetic flux density. It can be shown [6] that HTS machines can be 2-5 times smaller in volume compared with conventional electrical machines for the same power.…”

Experimental Characterization of a Conventional (Aluminum) and of a Superconducting (YBCO) Axial Flux Disc Motor

“…However flux density is limited due to magnetic saturation. HTS materials can carry large current within smaller sections, presenting higher specific torque (torque per volume) than their conventional counterparts, providing also some interesting and benefic levitation phenomena [26], [34]- [36]. Several types of machinery were optimized based on HTS materials (hysteresis [11]- [15], variable reluctance [16]- [19] and trapped flux [20]).…”