A 3‐D eddy current code, TRIFOU, has been used to simulate eddy currents flowing around cracks in very thick conductors, which is a fully 3‐D situation. The measurement set and…
Abstract
A 3‐D eddy current code, TRIFOU, has been used to simulate eddy currents flowing around cracks in very thick conductors, which is a fully 3‐D situation. The measurement set and the probe have also been simulated so that we can compare numerical and experimental output signals. Storage and CPU‐time requirements are detailed and the expectations of such a program in non‐destructive testing are discussed.
Problem 8 of the TEAM workshop comes from non‐destructive testing. A differential probe moves above a block with a crack. Three experimental and four numerical results are…
Abstract
Problem 8 of the TEAM workshop comes from non‐destructive testing. A differential probe moves above a block with a crack. Three experimental and four numerical results are presented and analysed. Some specific difficulties arising in this problem are discussed.
Z. REN, F. BOUILLAULT, A. RAZEK and J.C. VERITE
A semi‐analytical integration technique to evaluate the singular integration in 3‐D boundary element method for electromagnetic field computation is reported. The technique has…
Abstract
A semi‐analytical integration technique to evaluate the singular integration in 3‐D boundary element method for electromagnetic field computation is reported. The technique has been applied in a hybrid finite element—boundary integral model to evaluate the singular integral terms when constructing the “outside stiffness matrix” in the case of small air‐gaps, and it has also been used to calculate the exterior magnetic field in the proximity of the boundaries. The comparison with the conventional Gaussian quadrature has been carried out by modelling a 3‐D magnetostatic problem with a small air‐gap.
Two variational formulations of the three‐dimensional eddy‐current problem are discussed and compared. One is based on the use of h (the magnetic field) and the associated…
Abstract
Two variational formulations of the three‐dimensional eddy‐current problem are discussed and compared. One is based on the use of h (the magnetic field) and the associated magnetic potential as unknowns the other one is based on the use of a primitive of the electric field. They are found to be quite similar, suggesting some “duality” and, perhaps more importantly, that “mixed” finite elements, which were found efficient for the first case, could also be used for the second. This could alleviate some problems with the so‐called “modified vector potential approach” to the 3‐D eddy‐current problem.
The paper presents a new variant of the H-Φ field formulation for solving 3-D magnetostatic and frequency domain eddy current problems. The suggested formulation uses the vector…
Abstract
Purpose
The paper presents a new variant of the H-Φ field formulation for solving 3-D magnetostatic and frequency domain eddy current problems. The suggested formulation uses the vector and scalar tetrahedral elements within conducting and non-conducting domains, respectively. The presented numerical method is capable of solving multiply connected regions and eliminates the need for computing the source current density and the source magnetic field before the actual magnetostatic and eddy current simulations. The obtained magnetostatic results are verified by comparison against the corresponding results of the standard stationary current distribution analysis combined with the Biot-Savart integration. The accuracy of the eddy current results is demonstrated by comparison against the classical A-A-f approach in frequency domain.
Design/methodology/approach
The theory and implementation of the new H-Φ magnetostatic and eddy current solver is presented in detail. The method delivers reliable results without the need to compute the source current density and source magnetic field before the actual simulation.
Findings
The proposed H-Φ produce radically smaller and considerably better conditioned equation systems than the alternative A-A approach, which usually requires the unphysical regularization in terms of a low electric conductivity value within the nonconductive domain.
Originality/value
The presented numerical method is capable of solving multiply connected regions and eliminates the need for computing the source current density and the source magnetic field before the actual magnetostatic and eddy current simulations.
Details
Keywords
Takayoshi NAKATA and Koji FUJIWARA
Benchmark problem 13 of the TEAM Workshop consists of steel plates around a coil (a nonlinear magnetostatic problem). Seventeen computer codes developed by twelve groups are…
Abstract
Benchmark problem 13 of the TEAM Workshop consists of steel plates around a coil (a nonlinear magnetostatic problem). Seventeen computer codes developed by twelve groups are applied, and twenty‐five solutions are compared with each other and with experimental results. In addition to the numerical calculations, two theoretical presentations are given in order to explain discrepancies between the calculations and the experiment.
In the applications of FEM. a compromise between the accuracy and the computation cost is often required, especially when 3D cases are concerned Adaptive mesh refinement is a good…
Abstract
In the applications of FEM. a compromise between the accuracy and the computation cost is often required, especially when 3D cases are concerned Adaptive mesh refinement is a good answer to this demand.
Problem 6 of the International Workshop for Eddy Current Code Comparison is a hollow sphere in a uniform sinusoidal field. A total of 21 solutions, employing 17 different computer…
Abstract
Problem 6 of the International Workshop for Eddy Current Code Comparison is a hollow sphere in a uniform sinusoidal field. A total of 21 solutions, employing 17 different computer codes, are described and compared with analytic results. Several kinds of codes including 2‐D finite element, 3‐D finite element, and boundary element were found to give satisfactory solutions.
Koji FUJIWARA and Takayoshi NAKATA
Benchmark problem 7 of the TEAM workshop consists of an asymmetrical conductor with a hole. 17 computer codes are applied, and 25 solutions are compared with each other and with…
Abstract
Benchmark problem 7 of the TEAM workshop consists of an asymmetrical conductor with a hole. 17 computer codes are applied, and 25 solutions are compared with each other and with experimental results for eddy current densities and flux densities. Most of the codes were found to give satisfactory solutions.
Problem 5 of the International Workshops for Eddy Current Code Comparison consists of four aluminium blocks symmetrically located in an alternating magnetic field (the Bath Cube)…
Abstract
Problem 5 of the International Workshops for Eddy Current Code Comparison consists of four aluminium blocks symmetrically located in an alternating magnetic field (the Bath Cube). Five solutions employing five computer codes are described and compared with experimental results. In this, the most three‐dimensional of the six problems, with no 2‐D approximation to give insight, the results diverge about precisely those features of the field that computer simulations are expected to reveal.