.Modelica.Magnetic.QuasiStatic.FluxTubes.UsersGuide.FluxTubeConcept .Modelica.Magnetic.QuasiStatic.FluxTubes.UsersGuide.FluxTubeConceptFollowing below, the concept of magnetic flux tubes is outlined in short. For a detailed description of flux tube elements, please have a look at the listed literature. Magnetic flux tubes enable the modeling of magnetic fields with lumped equivalent circuit networks.
Since quasi-static conditions are assumed, each field quantity can be represented by a complex phasor -- which is indicated by underlining the respective variable:
The figure below and the following equations illustrate the relationships between
A flux tube confines the magnetic flux. Flied lines, and flux tubes, respectively are always closed. So there is no flux entering or leaving a flux tube. The total flux of a configuration can be represented by parallel flux tubes, representing different flux paths. This is considered by connecting the elements of a lumped circuit model, such that the sum of all fluxes of a connection is equivalent to zero.
For a section of a flux tube with length
the magnetic potential difference is determined by the length integral over the magnetic field strength:
The magnetic flux entering, and leaving a flux tube, respectively, is determined by the surface integral of the normal component of the magnetic field strength:
The magnetic potential difference and the magnetic flux have the same angle, so the reluctance a real (non complex) quantity:
For a
generic flux tube reluctance with constant
area of cross section,
,
and length,
,
the magnetic reluctance is:
The parameter and variable names are chosen as close as possible to the transient FluxTubes library, to avoid additional effort when converting transient into quasi-static flux tubes models.
A similar approach on quasi-static flux tube models is published in [Raabe2012].