Dynamic modeling of levitation of a superconducting bulk by coupled $H$-magnetic field and Arbitrary Lagrangian-Eulerian formulations

TL;DR

This paper introduces a new coupled $H$-formulation and Arbitrary Lagrangian-Eulerian model for simulating superconducting magnetic levitation, validated against existing models and used to analyze various configurations and conditions.

Contribution

The paper presents a novel moving mesh model combining $H$-formulation and ALE techniques for superconducting levitation, offering improved flexibility and ease of implementation.

Findings

Model accurately predicts levitation forces in various configurations.

Validated against a fixed mesh model and experimental data.

Effective in analyzing field-cooled and zero-field-cooled conditions.

Abstract

Intrinsically stable magnetic levitation between superconductors and permanent magnets can be exploited in a variety of applications of great technical interest in the field of transportation (rail transportation), energy (flywheels) and industry. In this contribution, we present a new model for the calculation of levitation forces between superconducting bulks and permanent magnet, based on the $H$-formulation of Maxwell's equations coupled with an Arbitrary Lagrangian-Eulerian formulation. The model uses a moving mesh that adapts at each time step based on the time-change of the distance between a superconductor bulk and a permanent magnet. The model is validated against a fixed mesh model (recently in turn validated against experiments) that uses an analytical approach for calculating the magnetic field generated by the moving permanent magnet. Then, it is used to analyze the magnetic field dynamics both in field-cooled and zero-field-cooled conditions and successively used to test different configurations of permanent magnets and to compare them in terms of levitation forces. The easiness of implementation of this model and its flexibility in handling different geometries, material properties, and application scenarios make the model an attractive tool for the analysis and optimization of magnetic levitation-based applications.