Application of state-of-the-art FEM techniques to magnetostatic NDE

A typical example of the complexities involved in the numerical modeling of electromagnetic phenomena is that of modeling the magnetic flux leakage inspection of gas transmission pipelines. The problem calls for three-dimensional modeling of motionally induced currents (using transient analysis), modeling nonlinearity of the ferromagnetic parts, and accurate modeling of the permanent magnet used in the magnetizer. Researchers, have thus far simplified the problem using several assumptions, including that of axisymmetry, and modeling velocity effects using steady-state analysis. However, there has been no attempt to quantify the errors introduced by these assumptions. Also, due to the unavailability of commercial codes to solve three-dimensional motion-related problems using transient analysis, a detailed study of the true nature of velocity effects has not been possible;This dissertation implements and evaluates state-of-the-art finite element modeling techniques applied to the specific problem of modeling magnetic flux leakage inspection of gas pipelines. This provides the basis from which conclusions can be drawn on the general problem of modeling magnetostatic phenomena. Axisymmetric and three-dimensional models are developed capable of modeling velocity effects. A detailed analysis of the differences between axisymmetric and three-dimensional geometries, based on a study of permeability variations in the vicinity of defects is presented. Also, the need for transient analysis is argued based on results generated. As part of this study, serious problems (including spurious solutions and corner singularities) associated with the traditional node-based finite-element techniques, when applied to the three-dimensional modeling, are discussed. In this work, new and efficient numerical modeling concepts, using the edge-based finite-element technique are employed to overcome these problems;This study demonstrates the need for accurate modeling of the full three-dimensional geometry, incorporating velocity effects and nonlinear permeability, for realistic predictions of flux leakage inspection tools. Major contributions of this work include: (1) detailed analysis of the physical processes associated with the magnetic flux leakage tool, (2) design ideas to improve the performance of the tool, and (3) development of an edge-based finite element code for modeling magnetostatic nondestructive testing applications in three-dimensions incorporating velocity effects. This is the first study of this nature, applied to pipeline inspection, and, many of the conclusions presented can be applied to nondestructive testing techniques in general