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Detection and monitoring of corrosion and erosion damage in pipe bends are open challenges due to the curvature of the elbow, the complex morphology of these defects, and their unpredictable location. Combining model based inversion with guided ultrasonic waves propagating along the elbow and inside its walls, offers the possibility of mapping wall-thickness losses over the entire bend and from a few permanently installed transducers under the realm of guided wave tomography (GWT). This paper provides the first experimental demonstration of GWT of pipe bends based on a novel curved ray tomography algorithm and an optimal transducer configuration consisting of two ring arrays mounted at the ends of the elbow and a line of transducers fixed to the elbow extrados. Using realistic, localized corrosion defects it is shown that detection of both the presence and progression of damage can be achieved with 100% sensitivity regardless of damage position around the bend. Importantly, this is possible for defects as shallow as 0.50% of wall thickness (WT) and for maximum depth increments of just 0.25% of WT. However, due to the highly irregular profile of corrosion defects, GWT generally underestimates maximum depth relative to the values obtained from 3-D laser scans of the same defects, leading in many cases to errors between 4 and 8% of WT.

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Ultrasonic guided wave tomography (GWT) methods for the detection of corrosion and erosion damage in straight pipe sections are now well advanced. However, successful application of GWT to pipe bends has not yet been demonstrated due to the computational burden associated with the complex forward model required to simulate guided wave propagation through the bend. In a previous paper [Brath et al., IEEE Trans. Ultrason., Ferroelectr., Freq. Control, vol. 61, pp. 815-829, 2014], we have shown that the speed of the forward model can be increased by replacing the 3-D pipe bend with a 2-D rectangular domain in which guided wave propagation is formulated based on an artificially inhomogeneous and elliptically anisotropic (INELAN) acoustic model. This paper provides further experimental validation of the INLEAN model by studying the traveltime shifts caused by the introduction of shallow defects on the elbow of a pipe bend. Comparison between experiments and simulations confirms that a defect can be modeled as a phase velocity perturbation to the INLEAN velocity field with accuracy that is within the experimental error of the measurements. In addition, it is found that the sensitivity of traveltime measurements to the presence of damage decreases as the damage position moves from the interior side of the bend (intrados) to the exterior one (extrados). This effect is due to the nonuniform ray coverage obtainable when transmitting the guided wave signals with one ring array of sources on one side of the elbow and receiving with a second array on the other side.

Recently, the use of guided wave technology in conjunction with tomographic techniques has provided the possibility of obtaining point-by-point maps of corrosion or erosion depth over the entire volume of a pipeline section between two ring arrays of ultrasonic transducers. However, current research has focused on straight pipes and little work has been done on pipe bends and other curved tubular structures which are also the most susceptible to developing damage. Tomography of curved tubes is challenging because of the complexity and computational cost of the 3-D elastic model required to accurately describe guided wave propagation. Based on the definition of travel-time-preserving orthogonal parametric representations of curved tubes, this paper demonstrates that guided wave propagation and scattering can be approximated by an equivalent 2-D acoustic model which is inhomogeneous and elliptically anisotropic. Numerical methods to solve the full wave equation and predict ray paths and travel times are introduced and applied to the case of a bend. Particular emphasis is given to the shortest-path ray tracing method, which is applied to the 2-D model to compute ray paths and predict travel times of the fundamental flexural mode, A0, propagating across a curved pipe. Good agreement is found between predictions and experiments performed on a 220-mm-diameter (8-in-diameter) (D) pipe with 1.5D bend radius. The 2-D model also reveals the existence of an acoustic lensing effect which leads to a focusing phenomenon also confirmed by the experiments. The computational efficiency of the 2-D model makes it ideally suited for tomographic algorithms.

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