Geodesic equations for guided wave helical path separation for a pipe bend

Abstract

The sections of pipe bends are susceptible to wall thinning by flow-accelerated corrosion due to the sudden change in the fluid flow direction and velocity. Compared to existing screening approaches, Guided Wave Tomography (GWT) has been demonstrated to provide more accurate information about the defect. In GWT an inversion problem is solved, in which a forward model is used to predict a synthetic dataset for a given physical model. Two-dimensional (2D) forward models are preferred for the inversion scheme due to the feasibility of combining these with tomographic algorithms. Since 2D models resemble the GW propagation of a plate, they do not consider the cyclic nature of the pipe. To overcome this limitation, a robust helical path separation was introduced in Huthwaite and Seher (2015) for a straight pipe. However, it relies on time-reversing the measured wave field ϕ(t) as a function of the propagation distance xs,r from the source to the receiver. Although ray-tracing and grid-based methods are capable of computing the distance xs,r for complex geometries such as the pipe bend, they are complex and time-consuming. Hence, in this paper a straight forward approach is proposed to compute xs,r based on the pipe geometry and the geodesic equations of a torus. Then the computed distance xs,r is used for removing the helical path trajectories. Compared to the distance obtained by using the Hilbert envelope, the results show that the geodesic distances preserve the information of the wavefront of interest, including the focusing effect and the scattered wave field from a Hann-shaped defect. The technique is applied to experimental data and demonstrated to separate the wavefront of interest.