The variation of the reflection coefficient of extensional guided waves in pipes from defects as a function of defect depth, axial extent, circumferential extent and frequency

Abstract

The reflection coefficients of extensional guided modes from notches of different axial, circumferential and through-thickness extent in pipes of different diameters have been studied using finite element analysis. A selection of the predictions has also been validated by experiments. For part-thickness notches of a given circumferential extent and minimal axial extent, the reflection coefficient increases monotonically with depth at all frequencies, and increases with frequency at a given depth. When the wavelength is long compared to the pipe wall thickness, the reflection coefficient from part-thickness notches of a given circumferential extent is a strong function of the defect axial extent, the reflection being a maximum at an axial extent of about 25 per cent of the wavelength and a minimum at 0 and 50 per cent. The reflection coefficient is a linear function of the defect circumferential extent at higher frequencies (with frequency-diameter products greater than about 3000 kHz mm) where a ray theory analysis explains the behaviour, while at low frequencies the reflection coefficient at a given circumferential extent is reduced. In the high-frequency regime, the axial extent of a through-thickness defect has little influence on the reflection coefficient, while it is important at lower frequencies. Three-dimensional, finite element predictions in the high-frequency regime have shown that the reflection coefficient from a part-thickness, part-circumferential defect can be predicted by multiplying the reflection coefficient for an axisymmetric defect of the same depth and axial extent by that for a through-thickness defect of the same circumferential extent.

The reflection of guided waves from notches in pipes: a guide for interpreting corrosion measurements

“…Only FE predictions are presented here because all of the model types used have already been validated with experiments in previous papers [1,2,16,20] (note that in this investigation, only square sided defects are considered). Then the frequency limits of this investigation are identified.…”

“…As already mentioned, the Finite Element (FE) tool is employed in this study in order to investigate new cases which were not documented in previous work on the same subject [1,2,14,16,19,20]. In general, a three-dimensional (3-D) solid model is required to perform a numerical analysis of the interaction between guided waves and discrete defects.…”

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

“…The advantage of limiting this study to the scattering of the T(0,1) mode from an axisymmetric defect is that one may then readily compare predictions against theoretical and experimental data reported in the literature for an uncoated pipe (see for example [26][27][28][29]). Furthermore, this also facilitates comparison with experimental measurements since it is relatively straightforward to generate and measure the T(0,1) mode and at the same time to minimise coherent noise.…”

Detecting pipe changes via acoustic matched field processing

“…Acoustic methods for the inspection of pipes to locate blockages and damage have been used extensively [1]- [4] with primary applications related to the quality control of pipes used in chemical engineering, the oil and gas industries, the water industry, and in the manufacturing of musical instruments. Unlike many other inspection methods, acoustic methods can be fast and non-invasive.…”

“…This approach can also be used to determine eigenvalue shifts [2]- [3] to detect finite duct blockages for one or two sets of termination conditions. Another application has been to model a pipe "notch" and its effects on low and high frequencies via finite element modelling of the duct and its defect [4]. The results for pulse reflectometry plus modelling are usually validated by comparison with test data and usually involve the assumption of idealized acoustic conditions.…”