On the scattering of torsional elastic waves from axisymmetric defects in coated pipes

Abstract

Long range ultrasonic testing is now a well established method for examining in-service degradation in pipelines. In order to protect pipelines from the surrounding environment it is common for viscoelastic coatings to be applied to the outer surface. These coatings are, however, known to impact on the ability of long range ultrasonic techniques to locate degradation, or defects, within a coated pipe. The coating dissipates sound energy travelling along the pipe, attenuating both the incident and reflected signals making responses from defects difficult to detect. This article aims to investigate the influence of a viscoelastic coating on the ability of long range ultrasonic testing to detect a defect in an axisymmetric pipe. The article focuses on understanding the behaviour of the fundamental torsional mode and quantifying the effect of bitumen coatings on reflection coefficients generated by axisymmetric defects. Reflection coefficients are measured experimentally for coated and uncoated pipes and compared to theoretical predictions generated using numerical mode matching and a hybrid finite element technique. Good agreement between prediction and measurement is observed for uncoated pipes, and it is shown that the theoretical methods presented here are fast and efficient making them suitable for studying long pipe runs. However, when studying coated pipes agreement between theory and prediction is observed to be poor for predictions based on those bulk acoustic properties currently reported in the literature for bitumen. Good agreement is observed only after conducting a parametric study to identify more appropriate values for the bulk acoustic properties. Furthermore, the reflection coefficients obtained for the fundamental torsional mode in a coated pipe show that significant sound attenuation is present over relatively short lengths of coating, thus quantifying those problems commonly encountered with the use of long range ultrasonic testing on coated pipes in the field.3

A numerical model for the scattering of elastic waves from a non-axisymmetric defect in a pipe

“…The hybrid method implemented here follows the same general approach as that described by Kirby et al [21,22] for elastic waveguides, see also Kirby [18] and Duan and Kirby [19] for acoustic waveguides. Accordingly, a weak form of Eq.…”

“…The displacement continuity equations are weighted by an appropriate weighting function and then integrated over planes Γ and Γ respectively. The weighting function is chosen to take advantage of modal orthogonality where possible, see for example Gregory [28] for a discussion on orthogonality relations for elastic waves, and also Kirby et al [21,22] for implementation in axisymmetric problems.…”

“…This then provides a very rigorous test of the current model. The two dimensional results presented by Kirby et al [21,22] are chosen here and so this validation is carried out for a 3 inch Schedule 40 steel pipe and a square (uniform) axisymmetric defect with a 50% area reduction and a length of 15 mm. For the three dimensional model, six noded isoparametric elements are used for planes Γ A and Γ B , and ten noded tetrahedral isoparametric elements are used for Ω 2 .…”

“…This means that only those modes with a dominant displacement in the torsional direction will be picked up when the transducers are aligned to excite T(0,1), and similarly for axial displacements when exciting with L(0,2). Therefore, in order to enable direct comparison with the experimental measurements of Kirby et al [21,22] the reflection coefficient predictions must be designed to separate torsionally and axially dominant displacements. Accordingly, the reflection coefficient Λ for mode ( , ) is defined [in the frequency domain only] as Frequency (kHz)…”

“…Accordingly, this method removes the need for absorbing boundaries remote from the defect and/or separating three dimensional slices of the pipe for solving the eigenproblem. This makes the SAFE-FE hybrid method very efficient and so it has also been used, for example, to study axisymmetric defects in coated pipes [21,22]. The purpose of this article is the application of the SAFE-FE method to pipe in a way that permits the solution and separation of all propagating modes in the time domain.…”