Opera’s Simulation Package Simplifies Computation for High Temperature Superconductor Coil Geometries

When developing class-leading simulation capabilities, we seek methods of correlating theory with the results from Opera simulations. In this excercise Opera demonstrates this by validating its methods against a highly challenging application – the simulation of Type II superconducting strips (specifically in the case outlined here; the latest generations of HTS superconductors). Opera has shown excellent agreement with analytic predictions (Brandt et al.[1]) for the induced current flow, fields and losses associated with the use of superconductors in AC applications paving the way for wider virtual investigation of devices utilizing this technology.

This success follows on from other pioneering efforts in the field, the most recent of which; the validation between simulation and measurement of a prototype superconducting generator developed in partnership with a leading global enterprise [2].

Some of the latest generation of HTS (high temperature superconductors) are now being investigated within a range of research establishments worldwide as potential candidates for use within AC systems. Examples include the stator side of an electric motor where the issue of coupling between stationary and moving parts of both the cooling system and power supply is removed.

The remainder of this study presents results obtained using the Opera Transient Electromagnetic Solver for a single piece of Type II HTS superconductor in free space. Reference to the original publication by Brandt et al. [1] is required in order for the comparison with analytic formulae to be drawn.

The simulation consists of an infinitely long superconducting strip of width 3 mm, thickness 0.1 mm in free space. Currents are induced in the strip using an oscillating 50 Hz background magnetic field, of amplitude 12000 A/m (the critical external field strength for this material and thickness of strip is 8594 A/m), applied perpendicular to the long axis of the strip (y-directed). Only a short section of the infinite strip needs to be modelled as the problem is effectively 2d and the rest is implied by tangential magnetic boundary conditions at z = 0 and z = 2e-4 mm. Additionally only a quarter of the plate/air cross section needs to be modelled as the remainder may be implied by symmetry (zx normal magnetic and zy tangential magnetic boundary conditions).

Figure 1 shows the 1/4 model including mesh with a close-up highlighting the uniform hexahedral mesh applied to the conducting region. The need for the use of a mesh of this type will be discussed within the results section.

Figure 1: Simulated section of the geometry, ¼ of the strip with implied symmetry in zx & zy planes and at z=0 and 2e-4 and zoomed in region of the conductor showing the mesh.

Results

Plots of the current density in the strip and the magnetic (H) field in all model space are shown in figures 2 & 3 respectively for the position of peak applied external field 12000 A/m achieved in the first cycle (at t = 0.005 s).

Figure 2: Distribution of current density (J) in the XY plane at peak applied field of 12000 A/m

Figure 3: Distribution of magnetic (H) field in the XY plane at peak applied field of 12000 A/m

It is necessary to model the conducting region with the fine and regular mesh because the induced current flow is not constrained simply to the edge as it is with external fields well below the critical field value. As the magnitude of the background field oscillates, the location of the transition between normal (resistive) and superconducting state (which has high field curvature) moves within the conductor. The location of this transition behaves like a new edge in the conductor where a skin effect forms with high amplitude and short wavelength due to the low resistance, hence the whole of the conducting region requires the granularity to capture this transition/skin effect.

The simulation data in the figures (4-5) is obtained from the line integral of the fields across the thickness of the plate at the peak applied external field (as above). The Opera results are compared with the analytic description proposed by Brandt et al. [2].

Figure 4: Comparison of normalised current distribution in simulation with analytic description [2].

Figure 5: Comparison of normalised magnetic field distribution in simulation with analytic description [2].

The volume integral for the losses in the strip with respect to time for a case where the peak applied field is equal to the critical applied field Hc is shown in figure 6.

Figure 6: Loss (W/m) in the conductor as a function of time

Simulation results for the loss per unit length of conductor with time, obtained for a range of working points are compared with the analytic description [2] in figure 7.

Figure 7: Loss (W/m) for a range of maximum external field amplitudes

This work demonstrates the power of the advanced edge variable method employed within the transient electromagnetic code originally developed within the prestigious Rutherford Appleton Laboratory. It can be combined with other tools incorporated in Opera, such as multiphysics simulation (thermal &/or structural including a tool design specifically to model superconducting quench), design optimization and automation to explore the design space for these challenging materials virtually. This opens the door to the production of devices incorporating this technology with far lower overheads in terms of physical prototyping.

References

 [1] Type-II-superconductor strip with current in a perpendicular magnetic field Brandt E H and Indenbohm M 1993 Phys. Rev. B 48 12893-906 [2] Simulation accuracy helps pioneering Superconducting Generator developments