A non‐destructive testing application solved with A‐χ geometric eddy‐current formulation

Abstract

Purpose

The purpose of this paper is to introduce a perturbation method for the A‐χ geometric formulation to solve eddy‐current problems and apply it to the feasibility design of a non‐destructive evaluation device suitable to detect long‐longitudinal volumetric flaws in hot steel bars.

Design/methodology/approach

The effect of the flaw is accurately and efficiently computed by solving an eddy‐current problem over an hexahedral grid which gives directly the perturbation due to the flaw with respect to the unperturbed configuration.

Findings

The perturbation method, reducing the cancelation error, produces accurate results also for small variations between the solutions obtained in the perturbed and unperturbed configurations. This is especially required when the tool is used as a forward solver for an inverse problem. The method yields also to a considerable speedup: the mesh used in the perturbed problem can in fact be reduced at a small fraction of the initial mesh, considering only a limited region surrounding the flaw in which the mesh can be refined. Moreover, the full three‐dimensional unperturbed problem does not need to be solved, since the source term for computing the perturbation is evaluated by solving a two‐dimensional flawless configuration having revolution symmetry.

Originality/value

A perturbation method for the A‐χ geometric formulation to solve eddy‐current problems has been introduced. The advantages of the perturbation method for non‐destructive testing applications have been described.

Citation

Codecasa, L., Dular, P., Specogna, R. and Trevisan, F. (2010), "A non‐destructive testing application solved with A‐χ geometric eddy‐current formulation", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 29 No. 6, pp. 1606-1615. https://doi.org/10.1108/03321641011078670