
Conductive cylinder in rotating magnetic field.
Problem Type:
A plane problem of transient magnetics.
Geometry:
Given:
Relative magnetic permeability of air μ = 1;
Relative magnetic permeability of conductor μ = 1;
Conductivity of conductor σ = 6.3·10^{7} S/m;
Magnitude of external field B_{0} = 1 T;
Number of poles 2p = 6;
Frequency f = 50 Hz.
Solution:
To specify rotating magnetic field on the outer boundary of the region, B_{n} = B_{0} sin (ωt  pφ), we apply the Dirichlet boundary condition, using the formula: A = cos (18000*t  3*atan2 (y/x)) / 60
The coefficient A_{0} = 1/60 arises from consideration
B_{n} = (1/r)(∂A/∂φ) = A_{0}p·sin(ωt  pφ) / r
and
A_{0} = B_{0}·r/p
Due to periodicity of the problem, only half of the model is presented, and odd periodic boundary condition A_{1} = A_{2} is applied on the cut. In fact, it would be enough to simulate just 60° sector of the model. In time domain, problem is simulated with automatic adaptive time step, up to 0.05 seconds (approx. 2.5 periods).
Results:
t = 0.0002 sec:
t = 0.048 sec:
t = 0.05 sec:
See the Dirich1.pbm problem in the Examples folder.