Linearized Solution for Rapid Filling of Horizontal Pipe with Entrapped Air
Publication: Journal of Engineering Mechanics
Volume 146, Issue 11
Abstract
Rapid filling of a horizontal pipe with an entrapped air pocket has attracted significant attention as overpressurization induced by air compression may cause safety concerns. This study developed a linearized model for a rapidly filling horizontal pipe, by using a Jacobian linearization around the equilibrium point of the nonlinear system. The analytical expressions explicitly show the relationship between the characteristics of pressure oscillation and parameters including the driving head, the length of the water column, the length of the entrapped air pocket, the location of the equilibrium point, and the polytropic exponent. The oscillation frequency increases with the driving head whereas it decreases with the length of the air pocket. The obtained analytical solution compares well with the rigid-column model for a limited range, and it is improved by means of introducing power-law fitting for general cases. The linearization method also can be used in other cases, such as rapid filling in a horizontal pipe with the entrapped air pocket above an initial water layer or in slope/vertical pipes.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
All of the data, models, or code generated or used during the study are available from the corresponding author by request.
Acknowledgments
This work was supported by the National Natural Science Foundation of China under Grant No. 51809240. The study was also partially funded by the Key Research and Development Program of Zhejiang Province (No. 2020C03082) and the Natural Sciences and Engineering Research Council (NSERC) of Canada.
References
Cabrera, E., J. Abreu, R. Perez, and A. Vela. 1994. “Influence of liquid length variation in hydraulic transients.” J. Hydraul. Eng. 120 (5): 663–666. https://doi.org/10.1061/(ASCE)0733-9429(1992)118:12(1639).
Cabrera, E., J. Abreu, R. Pérez, and A. Vela. 1992. “Influence of liquid length variation in hydraulic transients.” J. Hydraul. Eng. 118 (12): 1639–1650. https://doi.org/10.1061/(ASCE)0733-9429(1992)118:12(1639).
Huang, B., M. Fan, D. Z. Zhu, and S. Wu. 2018. “Numerical modeling of transient air–water flows within a riser downstream of a trunk sewer.” In Proc., 13th Int. Conf. on Hydroscience and Engineering (ICHE) 2018. Chongqing, China: Chongqing Jiaotong Univ.
Lee, N. H. 2005. “Effect of pressurization and expulsion of entrapped air in pipelines.” Ph.D. thesis, School of Civil and Environmental Engineering, Georgia Institute of Technology.
Li, L., D. Z. Zhu, and B. Huang. 2018. “Analysis of pressure transient following rapid filling of a vented horizontal pipe.” Water 10 (11): 1698. https://doi.org/10.3390/w10111698.
Malekpour, A., and B. W. Karney. 2014. “Pressure surges following sudden air pocket entrapment in storm-water tunnels.” J. Hydraul. Eng. 140 (4): 1081–1089. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000616.
Malekpour, A., B. W. Karney, and J. Nault. 2015. “Physical understanding of sudden pressurization of pipe systems with entrapped air: Energy auditing approach.” J. Hydraul. Eng. 142 (2): 04015044. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001067.
Martin, C. S. 1976. “Entrapped air in pipelines.” In Proc., 2nd Int. Conf. on Pressure Surges, 15–27. Bedford, UK: British Hydromechanics Research Association.
Tijsseling, A. S., Q. Hou, and Z. Bozkuş. 2015. “Analytical expressions for liquid-column velocities in pipelines with entrapped gas.” In Proc., ASME 2015 Pressure Vessels and Piping Conf. New York: ASME.
Zhou, F., F. Hicks, and P. Steffler. 2002. “Transient flow in a rapidly filling horizontal pipe containing trapped air.” J. Hydraul. Eng. 128 (6): 625–634. https://doi.org/10.1061/(ASCE)0733-9429(2002)128:6(625).
Zhou, L., D. Liu, B. Karney, and Q. Zhang. 2011. “Influence of entrapped air pockets on hydraulic transients in water pipelines.” J. Hydraul. Eng. 137 (12): 1686–1692. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000460.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 146 • Issue 11 • November 2020
Copyright
© 2020 American Society of Civil Engineers.
History
Received: Sep 25, 2019
Accepted: Jun 9, 2020
Published online: Aug 20, 2020
Published in print: Nov 1, 2020
Discussion open until: Jan 20, 2021
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.