240 Ë 7 Numerical simulations of HTS Maglev
7.6 Three-dimensional modeling and simulations
7.6.1H-formulation [9]
We have developed a 3D-modeling numerical method using the dynamic boundary of
the H-formulation. The resolving code is compiled with FORTRAN language using the
FEM technique. It aims at simulating the electromagnetic properties of a HTS magnetic
levitation system. As shown in Fig. 7.15, the levitation system is composed of one HTSC
and one PMG, which generates the applied magnetic field for the HTSC. When the
HTSC is moved vertically from positionAto positionBand then moved back toA,
the levitation forces of the HTSC could be calculated with the 3D modeling numerical
method. The geometrical and material parameters of HTSC in the calculations of this
section is collected in Tab. 7.1.
7.6.1.1Mathematical fundamentals
In this section, we will give a 3D model and one PDE that is used to describe the
electromagnetic behavior in HTSC. The geometric configuration of this 3D model is
Fig. 7.15:Schematic sketch of levitation system composed of a bulk HTSC and PMG.
Tab. 7.1:Parameters of the levitation system used in the simulation.
Parameter Value
Dimension of HTSC (length×width×height) 30 mm×30 mm×15 mm
Magnetization of PMG (M 0 ) 96,000 A/m^2
Vertical moving height 50 mm
Velocity 1 mm/s
Mini gap between the HTSC and the PMG 3 mm
Critical current densityJc 8.0× 107 A/m^2
Material parameterEcof the HTSC 1.0× 10 −^4 V/m
Dimension of PMG n(length×height) 110 ×50 mm