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

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 zerofield-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. arXiv:1807.00329v2 [cond-mat.supr-con]

Mechanism of the High- Tc Superconducting Dynamo: Models and Experiment

“…To solve the problem of representing a moving magnet in the H -formulation formalism [49,50], we represent the field of the magnet as a sheet current J m along the boundary ∂ R . To enforce this condition, we add a weak formulation condition to the finite-element problem,…”

Overview of H-Formulation: A Versatile Tool for Modeling Electromagnetics in High-Temperature Superconductor Applications

“…where S T is the surface of all superconducting regions. Grilli et al used H-formulation and the Arbitrary Lagrangian-Eulerian formulations to model the levitation phenomena of superconducting bulks and permanent magnets with a dynamic mesh approach [121], and Zheng et al used a similar method to investigate the electromagnetic characteristics of superconducting maglev devices [122]. Ta and Gao built a 3D electromagnetic-mechanical H-formulation FEM model to study the current density, the magnetic field distribution and the Lorentz force of a Nb 3 Sn superconducting strand [123].…”

Study and Design of a Magnetic Levitator System

“…Sets of dynamic equations (Newton's and Kirchhoff's equations) that provide theory to the system are given by the following set of equations using equation (4) we have the equation of mechanical system and the differential equation of the circuit.…”

“…A current flow through the wound coils of the electromagnet generating a magnetic field, being that the ferromagnetic core provides a path of reluctance in which the magnetic field is concentrated which induces an attractive force on the object to be levitated. Now, if we understand the theory of Superconductivity [4], we know that cooling an object at sufficiently low temperatures causes a distance to be separated from its initial base by positioning itself at a height that we can call a gap, until the temperature again decays. There is levitation by repulsion and suspension, in both cases a study of field forces must be performed, because positioning the object at the midpoint that will be the equilibrium-stable point to levitate, will depend a lot on the circuit, the coils and the distance between them, how to calibrate until the objective is achieved.…”