Guided wave propagation mechanics across a pipe elbow

Wave propagation across a pipe elbow region is complex. Subsequent reflected and transmitted waves are largely deformed due to mode conversions at the elbow, This prevents us to date from applying guided waves to the nondestructive evaluation of meandering pipeworks. Since theoretical development of guided wave propagation in a pipe is difficult, numerical modeling techniques are used. We have introduced a semi-analytical finite element method, a special modeling technique for guided wave propagation, because ordinary finite element methods require extremely long computational times and memory for such a long-range guided wave calculation. In this study, the semi-analytical finite element method for curved pipes is developed. A curved cylindrical coordinate system is used for the curved pipe region, where a curved center axis of the pipe elbow region is an axis (z' axis) of the coordinate system, instead of the straight axis (z axis) of the cylindrical coordinate system. Guided waves in the z' direction are described as a superposition of orthogonal functions. The calculation region is divided only in the thickness and circumferential directions. Using this calculation technique, echoes from the back wall beyond up to four elbows are discussed.