Boundary-Integral method for calculating poloidal axisymmetric AC magnetic fields

Abstract

This paper presents a boundary-integral equation (BIE) method for the calculation of poloidal axisymmetric magnetic fields applicable in a wide range of ac frequencies. The method is based on the vector potential formulation, and it uses the Green's functions of Laplace and Helmholtz equations for the exterior and interior of conductors, respectively. The paper focuses on a calculation of axisymmetric Green's function for the Helmholtz equation which is both simpler and more accurate than previous approaches. We use three different techniques for calculation of Green's function, depending on the parameter range. For low and high ac frequencies, we use a power series expansion in terms of elliptical integrals and an asymptotic series in terms of modified Bessel functions of second kind, respectively. For the intermediate frequency range, we use Gauss-Chebyshev-Lobatto quadratures. We verify the accuracy of the method by comparing its results with the analytical solution for a sphere in a uniform external ac field. We illustrate the application of the method by analyzing a composite model inductor containing an external secondary circuit.

A modal boundary element method for axisymmetric acoustic problems in an arbitrary uniform mean flow

“…Precisely, the particular and convected operators increase the numbers of flow terms which allows the writing of the modal boundary integral representation with arbitrary uniform mean flow as the modal BIE formulation without flow. 42–45 This allows one to interpret the particular and convected normal derivatives of the modal acoustic field and the modal convected Green’s function as its first order normal derivatives. The simplified MBIE solution requires only the evaluation of four terms in the modal convected normal derivative equation (35).…”

“…A modal boundary element method for the acoustic modeling of poloidal axisymmetric magnetic fields using Laplace equation has been presented in literature. 42 It is based on an analytical method to calculate the modal Green’s function and its normal derivative. An advanced approach based on the boundary element/fast Fourier transform axisymmetric formulation for acoustic radiation and wave scattering problems with non-axisymmetric boundary conditions has been developed by Polyzos.…”

“…47 For non-axisymmetric flow cases, the non-axisymmetric free term can be used the three-dimensional convected free term for modeling particular acoustic domains. 42–45 For complex configurations, the convected terms not having a representation in non-axisymmetric cases and that the classical free terms not adapted to solving the complex acoustic domains. Generally, the main disadvantages of classical free terms 26,44 are represented by complex forms, validated for simple acoustic domains, and having high CPU times.…”

Magnetic field controlled single crystal growth and surface modification of titanium alloys exposed for biocompatibility

“…The fluid flow direction is thereby adjusted in a desired way for an optimum solid-liquid interface geometry formation. Important parameters for the adjustment of the desired melt pumping force are the gap between the coils, the capacitance and the resistance of the secondary circuit [14]. For optimum conditions, the phase shift between the coils has to be 901.…”

Experimental Investigation and Optimization of Permanent Magnet Motor Based on Coupling Boundary Element Method With Permeances Network

“…This allows a time stepping simulation in steady state operation. The motor is fed by trapezoidal three phase currents [9,10]. The reluctance network model is then fed by the real instantaneous MMF.…”