1. Semianalytical method for the identification of inclusions by air-cored coil interaction in ferromagnetic media
- Author
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Dominique Lesselier, Panayiotis Vafeas, Anastassios Skarlatos, Theodoros Theodoulidis, Department of Chemical Engineering, University of Patras, Laboratoire de Simulation et de Modélisation Électromagnetique (LSME), Département Imagerie et Simulation pour le Contrôle (DISC), Laboratoire d'Intégration des Systèmes et des Technologies (LIST (CEA)), Direction de Recherche Technologique (CEA) (DRT (CEA)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Direction de Recherche Technologique (CEA) (DRT (CEA)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Laboratoire d'Intégration des Systèmes et des Technologies (LIST (CEA)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay, MEANDER, Department of Mechanical Engineering, University of Western Macedonia [Kozani] (UoWM)-University of Western Macedonia [Kozani] (UoWM), Laboratoire des signaux et systèmes (L2S), Université Paris-Sud - Paris 11 (UP11)-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS), University of Patras [Greece], Laboratoire d'Intégration des Systèmes et des Technologies (LIST), and Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Laboratoire d'Intégration des Systèmes et des Technologies (LIST)
- Subjects
Primary field ,General Mathematics ,01 natural sciences ,Harmonic analysis ,[MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph] ,0103 physical sciences ,[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] ,Boundary value problem ,0101 mathematics ,Mathematics ,Parametric statistics ,010302 applied physics ,Generalized function ,ferromagnetic media ,Mathematical analysis ,General Engineering ,Eigenfunction ,Non-destructive evaluation ,semi–analytical methods ,010101 applied mathematics ,[SPI.ELEC]Engineering Sciences [physics]/Electromagnetism ,Electromagnetic coil ,air-cored coils ,magneto-statics ,harmonic analysis ,Vector field - Abstract
The magnetostatic vector fields in terms of harmonic scalar potentials scattered by near–surface air inclusion of arbitrary shape, embedded in a conductive ferromagnetic medium, are investigated. The hollow inclusion is illuminated by a current–carrying coil, which serves as the primary field. The do-main of interest is separated into homogeneous subdomains under the assumption of a suitable truncation of the region of magnetostatic activity at a long distance from the incident source. Therein, the field is considered negligible and consequently a perfect magnetic boundary condition is implied. On the other hand, the introduced methodology addresses the full coupling between the two interfaces, i.e. the plane that distinguishes the half–space ferromagnetic material from the open air and the arbitrary surface among the inclusion and the ferromagnetic region. To this end, continuity conditions are applied in a rigorous way, while the expected behavior of the fields, either as ascending or as descending are taken into account. The scattering problem is solved by means of a modal approach, where potentials associated with the half–space are expanded via cylindrical harmonic eigenfunctions, while those related with the inclusion’s arbitrary geometry admit a generalized–type formalism, being the key to our method. However, since the transmission conditions involve potentials with different eigenexpansions, we are obliged to rewrite cylindrical to generalized functions and vice versa, obtaining handy relationships in terms of easy–to–handle integrals, where orthogonality then would be feasible. Once done, the calculation of the exact solutions leads to infinite linear algebraic systems, whose solution is achieved trivially through standard cut–off techniques. Thus, we obtain the implicated fields in a general analytical and compact fashion, independent of the inclusion’s geometry. In order to demonstrate the efficiency of the analytical model approach, we assume the degenerate case of a spherical inclusion, whereas the air–cored coil simulation via a numerical procedure validates our generalized method. The calculation is very fast, rendering it suitable for use with parametric inversion algorithms.
- Published
- 2018