Axisymmetric eddy current inspection of highly conducting thin layers via asymptotic models

Abstract

Thin copper deposits covering the steam generator tubes can blind eddy current probes in non-destructive testings of problematic faults and it is therefore important that they are identified. Existing methods based on shape reconstruction using eddy current signals encounter difficulties of high numerical costs due to the layer's small thickness and high conductivity. In this article, we approximate the axisymmetric eddy current problem with some appropriate asymptotic models using effective transmission conditions representing the thin deposits. In these models, the geometrical information related to the deposit is transformed into parameter coefficients on a fictitious interface. A standard iterative inversion algorithm is then applied to the asymptotic models to reconstruct the thickness of the thin copper layers. Numerical tests both validating the asymptotic model and showing the benefits of the inversion procedure are provided.

A finite element method with overlapping meshes for free-boundary axisymmetric plasma equilibria in realistic geometries

“…The result follows directly from combining those for non-linear magneto-statics in [51] with the results for non-linear problems in unbounded domains [23]. If in addition we had Ω Fe = ∅ we would end up with an even simpler linear elliptic 185 problem, for which existence and uniqueness are immediately available [31,30]. Rigorous existence and uniqueness assertion for the general case are still an open problem.…”

Equivalent Transmission Conditions for the Time-Harmonic Maxwell Equations in 3D for a Medium with a Highly Conductive Thin Sheet

“…As variation of the conditions by Levi-Civita the so called shielding element [22] has been introduced. Recently, conditions in the framework of Schmidt and Tordeux have been derived for the axis-symmetric setting and varying thickness [11].…”

Improved impedance conditions for a thin layer problem in a nonsmooth domain

“…In mechanical engineering, the study of the properties of composite materials is a critical issue (see Fakhrabadi and Khani and Gajjela et al) with the reinforcement by thin fibers or layers. Situations where two materials are glued together enter this scope as well; see, eg, Geymonat et al For electromagnetism, thin dielectric layers appear in many situations; see, for example, Haddar and Jiang for the eddy current problem in the context of copper deposits on tubes, or Zutter and Knockaert for the skin effect problem, which has strong connections with thin layers. Biological tissues often involve thin parts; see Perrussel and Poignard for a mathematical and numerical study of the electromagnetic field around and inside a biological cell, or Caubet et al for the description of the diffusion magnetic resonance imaging signal in biological tissues.…”