Denis Prémel

Dyad-based model of the electric field in a conductive cylinder at eddy-current frequencies

We propose a rigorous model of the electromagnetic field in a conductive circular cylinder illuminated by an arbitrarily shaped and oriented current-carrying coil placed nearby for nondestructive evaluation at eddy-current frequencies. The model is based on a dyadic field formulation, and its modularity enables handy generalizations to a multilayered cylindrical structure that might be affected by various defects. We give a variety of numerical results about the primary electric field within the cylinder in both canonical and practical cases in order to illustrate pros and cons of the solution method. The results agree quite well with known analytical results (which are available only in highly symmetrical cases), and fairly well with results yielded at high computational cost by an industrial finite-element code in more general cases. We discuss in detail the conditions for reaching a good numerical accuracy (involving some suitable regularization) while preserving both generality and small computational burden of the resulting computer code.

Fast Computation of the Fields Diffracted by a Multi-Layered Conductor With Non-Parallel Rough Interfaces. Application to Eddy-Current Non-Destructive Testing Simulation

This paper deals with the computation of quasi-static fields induced in a conductor by a 3-D eddy-current probe. The shape of the slab is locally distorted and constituted by several homogeneous layers with non-parallel interfaces. The approach is based on writing Maxwell equations in a curvilinear system, leading to a simple analytical expression of boundary conditions. Near every interface, the fields are expanded as sums of eigenfunctions depending on the analytical expression of the 1-D profile describing each interface. Finally, a global S-matrix is computed using a stable recursive algorithm which includes the local change of basis needed for a modal description of the fields in layers presenting non-parallel interfaces. Numerical results are presented and compared with other numerical data.

Recent Advances in Simulation of Eddy Current Testing of Tubes and Experimental Validations

Eddy current testing (ECT) is widely used in iron and steel industry for the inspection of tubes during manufacturing. A collaboration between CEA and the Vallourec Research Center led to the development of new numerical functionalities dedicated to the simulation of ECT of non‐magnetic tubes by external probes. The achievement of experimental validations led us to the integration of these models into the CIVA platform. Modeling approach and validation results are discussed here. A new numerical scheme is also proposed in order to improve the accuracy of the model.

New discretisation scheme based on splines for volume integral method: Application to eddy current testing of tubes

Purpose - A numerical model dedicated to external eddy current inspection of tubes has been developed using the volume integral method (VIM). The purpose of this paper is to suggest new discretization schemes based on non-uniform B-splines for the solution of the state equation with the method of moments (MoM). Design/methodology/approach - VIM is a semi-analytical approach providing fast and accurate results for the simulation of eddy current testing (ECT) of pieces with canonical geometries. The state equation derived with this formalism is solved using the Galerkin variant of the well-known MoM. Findings - This paper shows that an accuracy improvement is achieved in MoM by using B-splines with degree 1 or 2 as projection functions in MoM instead of pulse functions. Moreover, comparisons between simulation results show that, for all ECT configurations tested, the use of degree 1 B-splines is sufficient to get this improvement. Originality/value - The use of B-splines functions has already been proposed for MoM in the literature, but not in the framework of the Galerkin variant of MoM. This paper also shows quantitative comparisons between experiment and simulation as well as a study of the minimal degree required to get an accuracy improvement in MoM.

Eddy‐Current Modeling of Ferrite‐Cored Probes

The CEA has developed a fast code for the simulation of eddy‐current probes. It is based on the Volume Integral (VIM) approach. Within the framework of an EADS partnership, this code has been extended to the simulation of different kinds of ferrite‐cored probes with for example I, C or E shapes. The model gives the response of the probe to a parallelepiped 3D flaw included in a conductive slab. It has been benchmarked with experimental data for several configurations and an excellent agreement has been achieved.

Hybridization of volumetric and surface models for the computation of the T/R EC probe response due to a thin opening flaw

The purpose of this paper is to describe the development of simulation tools dedicated to eddy current non destructive testing (ECNDT) on planar structures implying planar defects. Two integral approaches using the Green dyadic formalism are considered. The surface integral model (SIM) is dedicated to ideal cracks, whereas the volume integral method is adapted to general volumetric defects. The authors observed that SIM provides satisfactory results, except in some critical transmitting/receiving (T/R) configurations. This led us to propose a hybrid method based on the combination of the two previous ones. This method enables to simulate ECNDT on planar structures implying defects with a small opening using T/R probes.