Guided Wave Propagation Mechanics Across a Pipe Elbow

[+] Author and Article Information
Takahiro Hayashi

Department of Mechanical Engineering,  Nagoya Institute of Technology, Nagoya, Japan

Koichiro Kawashima

 Ultrasonic Materials Diagnosis Laboratory, Nagoya, Japan

Zongqi Sun

 General Electric Global Research Center, Niskayuna, NY

Joseph L. Rose

Department of Engineering Science and Mechanics,  The Pennsylvania State University, University Park, PA

J. Pressure Vessel Technol 127(3), 322-327 (Jan 24, 2005) (6 pages) doi:10.1115/1.1990210 History: Received January 14, 2005; Revised January 24, 2005

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 useful. We have introduced a semianalytical 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 semianalytical 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.

Copyright © 2005 by American Society of Mechanical Engineers
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Figure 10

Snapshots of axisymmetric mode propagation in a pipe with two elbows. The shift value of grid points is the absolute value of displacements. Gray scale represents axisymmetric mode displacement in the longitudinal direction.

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Figure 11

Waveforms of axisymmetric modes at three different points A–C in Fig. 1

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Figure 12

Schematic of the two elbow pipe used in the calculation

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Figure 9

Pulse-echo signals obtained by the teletest unit in the configuration of Fig. 8

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Figure 8

Schematic of four elbow mock-up used in these experiments

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Figure 7

Transmission coefficient of axisymmetric modes in the case of the L(0,2) input

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Figure 6

Transmission coefficient of axisymmetric modes in the case of the L(0,1) input

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Figure 5

Energy ratio of transmission (ET) and reflection energy (ER) ratio and total energy (ET+ER) with respect to the incident energy EI at an elbow. Elbow curvature radius is 152.4mm, 90deg.

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Figure 4

Dispersion curves for a pipe of 4in. schedule 40. Longitudinal and flexural modes. (a) Phase velocity dispersion curves; (b) group velocity dispersion curves.

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Figure 3

Semianalytical FEM elements in quasicylindrical coordinate system

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Figure 2

Quasicylindrical coordinate system used in this study

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Figure 1

Subdiscritizations of the semianalytical finite element method for pipes. (a) 1D discretization model; (b) 2D discretization model.



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