Overview

Test Case

A long hollow aluminum cylinder is placed in a uniform magnetic field. The magnetic field is perpendicular to the axis of the cylinder and varies sinusoidally with time. Determine the magnetic flux density at the center of the cylinder and the average power loss in the cylinder.

Figure 235: Long Cylinder Problem Sketch

Material Properties	Geometric Properties	Loading
σ = 2.5380711 x 107 S/m	ri = 0.05715 m ro = 0.06985 m = 0.84 m	B = B(y) = B0 cos ωt where Bo = 0.1T, ω = 60 Hz

Analysis Assumptions and Modeling Notes

The external radial boundary is set at   = 0.84 m. The applied external field is calculated as B(y) = - δA / δx, so at  θ = 0 and r = , A = -B_or = -.084. The vector potential A varies along as A_θ = -B_or cos θ.

The cylinder is assumed to be infinitely long, thus end effects are ignored allowing for a two-dimensional planar analysis. The problem can be modeled in quarter symmetry with the flux-parallel (A = 0) boundary condition at x = 0, and the flux-normal (natural) boundary condition at y = 0. The average power loss in the cylinder is calculated from the real and imaginary power loss density (JHEAT) terms available in the database:

when n is the number of elements in the aluminum cylinder, V_i is the element volume (per-unit-depth). A fine mesh is defined in the cylinder for accurate calculation of the power loss.

Results Comparison