Eddy current power dissipation at sharp corners: a numerical right-angle conducting wedge solution and simple function fit

Abstract

A numerical solution using the rotated real integral equations for the right angle wedge is carried out. Point matching or collocation, using triangular basis functions for the difference magnetic field, is carried out on both the perfectly conducting difference and impedance difference integral equations. By means of this solution, the real corner constant, axial electric field at the origin, and the rotated and scaled fields are determined for arbitrary ratios of the internal to external magnetic permeabilities. A simple fit function is given which accurately represents the real corner constant over the full range of ratios of internal to external magnetic permeabilities. Furthermore, construction of this fit function only requires knowledge of the real corner constant for unit ratio of internal to external magnetic permeabilities (along with the small and large limits which have been given analytically in previous papers). Comparisons are given of the scaled and rotated fields with approximations, such as the external surface impedance boundary condition solution, given in previous papers. A Galerkin method, using triangular basis functions, is also used for the case of unit ratio of internal to external magnetic permeabilities. The moments computed in the Galerkin method enable the variational principle, discussed in a previous paper, to be implemented with respect to both the collocation and Galerkin solutions of the impedance difference integral equation. By means of this implementation, and a comparison with the point matching results, the real comer constant value for unit ratio of internal to external magnetic permeabilities is ascertained to three significant figures.