Theoretical Investigation of Leak’s Impact on Normal Modes of a Water–Filled Pipe: Small to Large Leak Impedance
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Volume 145, Issue 6
Abstract
Recent research shows the potential of resonant frequency-based leakage detection methods. However, there is a disagreement in whether a leak shifts the normal modes (often called natural or resonant modes) and whether a leak introduces additional peaks to the frequency response function (FRF) of the pipeline. In this paper, the impact of a leak on the normal modes is investigated. The trajectories of normal modes in the frequency complex plane with varying leak size are studied. The key parameter that represents the leak size and controls the trajectories of the normal modes is the ratio of the acoustic impedance of the pipe to the resistance impedance of the leak. It is found that, as the impedance ratio increases from zero (i.e., no leak), each normal mode shifts toward the upper-half complex plane of frequency by a leak, where the imaginary part is a measure of the leak-induced damping of the wave. When the impedance ratio is less than the order of one, the leak-induced normal-mode frequency shift is negligible, which supports the theory put forward by proponents of the no-shift and no-additional-peak hypothesis. When the impedance ratio is of the order of one or larger, not only is the shift of the FRF’s peak significant, but also new peaks appear, which supports the theory raised by proponents of the leak-induced additional peaks hypothesis.
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Acknowledgments
This work has been supported by research grants from the Research Grant Council of the Hong Kong SAR, China (Project Nos. T21-602/15R and 612713). The authors would like to thank Dr. Andrei A. Kolyshkin for introducing the logarithmic residue-based quadrature method and thank Drs. Duncan A. McInnis, Arris S. Tijsseling, Jim C. P. Liou, Moez Louati, Bryan Karney, Hanif M. Chaudhry, Man Yue Lam, and Alireza Keramat for their helpful comments and discussions.
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Published In
Journal of Hydraulic Engineering
Volume 145 • Issue 6 • June 2019
Copyright
©2019 American Society of Civil Engineers.
History
Received: Apr 23, 2018
Accepted: Dec 6, 2018
Published online: Mar 26, 2019
Published in print: Jun 1, 2019
Discussion open until: Aug 26, 2019
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