Bragg-Type Resonance in Blocked Pipe System and Its Effect on the Eigenfrequency Shift
Publication: Journal of Hydraulic Engineering
Volume 144, Issue 1
Abstract
Recent studies of measured transient pressure signals showed that eigenfrequencies shift with changes in cross-sectional area of the conduit and used this fact to develop blockage-detection algorithms. However, an understanding of the physical basis for eigenfrequency shift-based algorithms is currently lacking. This paper shows heuristically, analytically, and numerically that a blockage in either unbounded or bounded pipe systems interacts strongly with waves at specific frequencies. These specific interacting frequencies conform precisely to Bragg’s resonance condition. The frequency interval between consecutive Bragg frequencies is proportional to the wave speed divided by the blockage length. In addition, it is found that pipe blockage imposes a distinct signature through Bragg resonance phenomena on the unbounded and bounded pipe systems in exactly the same manner (i.e., they exhibit the same variation pattern). It is further shown that the eigenfrequency shift, currently used without physical basis or explanation in many published papers as a basis for blockage detection methods, is because of the Bragg resonance effect. Examples are used to show how this physical insight into the nature and cause of the eigenfrequency shifts can be advantageously used to design direct blockage detection techniques.
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Acknowledgments
This study is supported by the Hong Kong Research Grant Council (projects 612712 & 612713 & T21-602/15R), by the Postgraduate Studentship, the University of Perugia, the Italian Ministry of Education, University and Research (MIUR)—under the Projects of Relevant National Interest “Advanced analysis tools for the management of water losses in urban aqueducts” and “Tools and procedures for an advanced and sustainable management of water distribution systems”—and Fondazione Cassa Risparmio Perugia, under the project “Hydraulic and microbiological combined approach toward water quality control (No. 2015.0383.021)”. The authors thank Dr. D. A. McInnis for the technical and editorial suggestions.
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Published In
Journal of Hydraulic Engineering
Volume 144 • Issue 1 • January 2018
Copyright
©2017 American Society of Civil Engineers.
History
Received: Sep 13, 2016
Accepted: Jun 8, 2017
Published online: Oct 27, 2017
Published in print: Jan 1, 2018
Discussion open until: Mar 27, 2018
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