Wave-Leak Interaction in a Simple Pipe System
Publication: Journal of Hydraulic Engineering
Volume 146, Issue 4
Abstract
In previous work, the authors have found that blockage-wave interaction relates to Bragg resonance effect, which is governed by the ratio of the wavelength to the length of the blockage. A direct extension of this work for the case of wave-leak interaction has led to a total failure. This is because, unlike blockages, a leak has a vanishingly small length (generally modeled as a point), and according to the blockage results, this would require an infinitesimal wavelength (i.e., infinite frequency). Yet, leak-imposed patterns are known to occur for finite wavelengths. Therefore, the motive of this work was to seek a novel mechanism that is responsible for leak-induced Bragg resonance. It was discovered that what matters in this case is the position of the leak point in relation to the node and antinode of the modes. It is shown that a leak located at an antinode of a given mode will induce Bragg-type resonance of maximum reflection, and the corresponding peak amplitude in the frequency response function (FRF) is a minimum. On the other hand, if a leak is located at a node of a given mode, it experiences Bragg-type resonance of maximum transmission, and the peak amplitude in the FRF is a maximum. The pattern induced by a leak on the FRF, used in many leak detection schemes, is attributable to the leak interaction with different modes. In fact, the closer the leak to a node is, the higher is the amplitude of the corresponding resonant peak, and vice versa for leaks closer to antinodes. A number of leak detection methods are discussed in light of the Bragg resonance mechanism. These insights are exploited for several distinguished leak detection methods showing how a leak-induced pattern is explained from a new point of view.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
This study was supported by the Hong Kong Research Grant Council (Project Nos. T21-602/15R and 16208618). The authors thank Dr. D. A. McInnis for the technical and editorial suggestions.
References
Bragg, W. H., and W. L. Bragg. 1913. “The reflection of X-rays by crystals.” Proc. R. Soc. London, Ser. A 88 (605): 428–438. https://doi.org/10.1098/rspa.1913.0040.
Brunone, B. 1999. “Transient test-based technique for leak detection in outfall pipes.” J. Water Resour. Plann. Manage. 125 (5): 302–306. https://doi.org/10.1061/(ASCE)0733-9496(1999)125:5(302).
Chaudhry, M. H. 2014. Applied hydraulic transients. 3rd ed. New York: Springer.
Covas, D., H. Ramos, and A. B. de Almeida. 2005. “Standing wave difference method for leak detection in pipeline systems.” J. Hydraul. Eng. 131 (12): 1106–1116. https://doi.org/10.1061/(ASCE)0733-9429(2005)131:12(1106).
Covas, D. I., H. M. Ramos, and A. B. de Almeida. 2008. “Closure to ‘Standing wave difference method for leak detection in pipeline systems’ by Dídia IC Covas, Helena M. Ramos, and António Betâmio de Almeida.” J. Hydraul. Eng. 134 (7): 1029–1033. https://doi.org/10.1061/(ASCE)0733-9429(2008)134:7(1029).
Ferrante, M., and B. Brunone. 2003a. “Pipe system diagnosis and leak detection by unsteady-state tests. I: Harmonic analysis.” Adv. Water Resour. 26 (1): 95–105. https://doi.org/10.1016/S0309-1708(02)00101-X.
Ferrante, M., and B. Brunone. 2003b. “Pipe system diagnosis and leak detection by unsteady-state tests. II: Wavelet analysis.” Adv. Water Resour. 26 (1): 107–116. https://doi.org/10.1016/S0309-1708(02)00102-1.
Ferrante, M., B. Brunone, and S. Meniconi. 2007. “Wavelets for the analysis of transient pressure signals for leak detection.” J. Hydraul. Eng. 133 (11): 1274–1282. https://doi.org/10.1061/(ASCE)0733-9429(2007)133:11(1274).
Ghidaoui, M. S. 2004. “On the fundamental equations of water hammer.” Urban Water J. 1 (2): 71–83. https://doi.org/10.1080/15730620412331290001.
Gong, J., M. F. Lambert, A. R. Simpson, and A. C. Zecchin. 2013. “Single-event leak detection in pipeline using first three resonant responses.” J. Hydraul. Eng. 139 (6): 645–655. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000720.
Lee, P., J. Tuck, M. Davidson, and R. May. 2017. “Piezoelectric wave generation system for condition assessment of field water pipelines.” J. Hydraul. Res. 55 (5): 721–730. https://doi.org/10.1080/00221686.2017.1323805.
Lee, P. J., M. F. Lambert, A. R. Simpson, J. P. Vítkovský, and J. Liggett. 2006. “Experimental verification of the frequency response method for pipeline leak detection.” J. Hydraul. Res. 44 (5): 693–707. https://doi.org/10.1080/00221686.2006.9521718.
Lee, P. J., J. P. Vítkovský, M. F. Lambert, A. R. Simpson, and J. A. Liggett. 2005a. “Frequency domain analysis for detecting pipeline leaks.” J. Hydraul. Eng. 131 (7): 596–604. https://doi.org/10.1061/(ASCE)0733-9429(2005)131:7(596).
Lee, P. J., J. P. Vítkovský, M. F. Lambert, A. R. Simpson, and J. A. Liggett. 2005b. “Leak location using the pattern of the frequency response diagram in pipelines: A numerical study.” J. Sound Vib. 284 (3–5): 1051–1073. https://doi.org/10.1016/j.jsv.2004.07.023.
Louati, M., M. S. Ghidaoui, S. Meniconi, and B. Brunone. 2018. “Bragg-type resonance in blocked pipe system and its effect on the eigenfrequency shift.” J. Hydraul. Eng. 144 (1): 04017056. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001383.
Louati, M., S. Meniconi, M. S. Ghidaoui, and B. Brunone. 2017. “Experimental study of the eigenfrequency shift mechanism in a blocked pipe system.” J. Hydraul. Eng. 143 (10): 04017044. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001347.
Maloney, C. A. 1973. “Locating cable faults.” IEEE Trans. Ind. Appl. IA-9 (4): 380–394. https://doi.org/10.1109/TIA.1973.349965.
Mei, C. C. 1985. “Resonant reflection of surface water waves by periodic sandbars.” J. Fluid Mech. 152 (3): 315–335. https://doi.org/10.1017/S0022112085000714.
Nixon, W., and M. S. Ghidaoui. 2007. “Numerical sensitivity study of unsteady friction in simple systems with external flows.” J. Hydraul. Eng. 133 (7): 736–749. https://doi.org/10.1061/(ASCE)0733-9429(2007)133:7(736).
Nixon, W., M. S. Ghidaoui, and A. A. Kolyshkin. 2006. “Range of validity of the transient damping leakage detection method.” J. Hydraul. Eng. 132 (9): 944–957. https://doi.org/10.1061/(ASCE)0733-9429(2006)132:9(944).
Sattar, A. M., and M. H. Chaudhry. 2010. “Leak detection in pipelines by frequency response method.” Supplement, J. Hydraul. Res. 46 (S1): 138–151. https://doi.org/10.1080/00221686.2008.9521948.
Tijsseling, A. S., and A. Vardy. 2017. “Some intriguing aspects of boundary conditions in water hammer.” In E-Proc., 37th IAHR World Congress. London: Taylor and Francis.
Vítkovský, J. P., and P. J. Lee. 2008. “Discussion of ‘Standing wave difference method for leak detection in pipeline systems’ by Dídia IC Covas, Helena M. Ramos, and António Betâmio de Almeida.” J. Hydraul. Eng. 134 (7): 1027–1029. https://doi.org/10.1061/(ASCE)0733-9429(2008)134:7(1027).
Wang, X., and M. S. Ghidaoui. 2018. “Pipeline leak detection using the matched-field processing method.” J. Hydraul. Eng. 144 (6): 04018030. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001476.
Wang, X. J., M. F. Lambert, A. R. Simpson, J. A. Liggett, and J. P. Vítkovský. 2002. “Leak detection in pipelines using the damping of fluid transients.” J. Hydraul. Eng. 128 (7): 697–711. https://doi.org/10.1061/(ASCE)0733-9429(2002)128:7(697).
Wylie, E. B., and V. L. Streeter. 1993. Fluid transients in systems. Englewood Cliffs, NJ: Prentice Hall.
Information & Authors
Information
Published In
Copyright
©2020 American Society of Civil Engineers.
History
Received: Jul 27, 2018
Accepted: Aug 29, 2019
Published online: Jan 27, 2020
Published in print: Apr 1, 2020
Discussion open until: Jun 27, 2020
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.