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RESEARCH PAPERS

The Effect of Bends on the Propagation of Guided Waves in Pipes

[+] Author and Article Information
A. Demma, P. Cawley, M. Lowe

Department of Mechanical Engineering, Imperial College, London SW7 2AZ, UK

B. Pavlakovic

 Guided Ultrasonics Ltd., Nottingham NG15 9ER, UK

J. Pressure Vessel Technol 127(3), 328-335 (Feb 03, 2005) (8 pages) doi:10.1115/1.1990211 History: Received January 20, 2005; Revised February 03, 2005

The practical testing of pipes in a pipe network has shown that there are issues concerning the propagation of ultrasonic guided waves through bends. It is therefore desirable to improve the understanding of the reflection and transmission characteristics of the bend. First, the dispersion curves for toroidal structures have been calculated using a finite element method, as there is no available analytical solution. Then the factors affecting the transmission and reflection behavior have been identified by studying a straight-curved-straight structure both numerically and experimentally. The frequency dependent transmission behavior obtained is explained in terms of the modes propagating in the straight and curved sections of the pipe.

Copyright © 2005 by American Society of Mechanical Engineers
Topics: Waves , Pipes
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References

Figures

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Figure 3

Illustration of modal solution results (points) plotted onto frequency-phase velocity axes to construct dispersion curves

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Figure 4

Points obtained from the modal solution method for a 2in. pipe with 1.5m bend radius

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Figure 5

Mode shape example. Deformed mesh is for a circumferential order four mode.

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Figure 6

Comparison between dispersion curves obtained for a 2in. “almost” straight pipe using the FE modal analysis (points) and a 2in. perfectly straight pipe using the DISPERSE software (solid lines)

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Figure 7

Comparison between dispersion curves for (a) a straight pipe and (b) a curved pipe

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Figure 8

Antisymmetric (a) and symmetric (b) mode shape for F(1,3) in a toroidal structure

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Figure 9

Comparison between the L(0,2) mode in a straight pipe (a) and L(0,2)T mode in a curved pipe (b)

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Figure 10

Phase velocity dispersion curves for 8in. schedule 40 toroid (o.d.=219.07mmthickness=8.18mm) with k=1.5 (lines) and for a 3in. toroid defined as 3∕8 of the dimensions of the 8in. schedule 40 toroid (dots)

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Figure 11

Example of a road crossing application where it is necessary to inspect through bends

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Figure 12

Description of the geometry of the model (a) and schematic diagram of the setup used for the FE analysis (b)

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Figure 13

FE predicted amplitude of the axial displacement calculated from the displacement field at each node of the monitored lines displayed in Fig. 1 for the k=6 case. The mode extraction has been performed before the bend for the order 0 (a), 1 (b), and 2 (c) modes and after the bend for the order 0 (d), 1 (e), and 2 (f) modes.

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Figure 14

Predicted L(0,2) transmission coefficient for a series of 3in. schedule 40 (o.d.=88.9mmthickness=5.5mm) toroids with different bend radii RBM

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Figure 15

Predicted L(0,2) transmission coefficient for different bend lengths (k=10)

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Figure 16

Interpretation of mode propagation in pipe with bend

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Figure 17

Predicted amplitude of the torsional displacement calculated from the displacement field at each node of the monitored lines displayed in Fig. 1 for the k=6 case. The mode extraction has been performed before the bend for the order 0 (a), and 1 (b) modes and after the bend for the order 0 (c), and 1 (d) modes.

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Figure 18

Setup of single transmission experiment. The excitation ring was located at one end of the pipe and the laser interferometer was used to receive the signal.

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Figure 19

Comparison between single transmission coefficients obtained from experiments (highest and lowest value) and FE predicted. Results are for a 2in. schedule 40 pipe with a bend having a bend ratio k=6.

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Figure 1

Schematic of the toroid and coordinate axis

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Figure 2

Description of the geometry of the FE model used for the modal solution. Two-dimensional axisymmetric model of a cross section of the pipe (a) to calculate standing waves in a complete toroid (b).

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