Improved Rigid Water Column Formulation for Simulating Slow Transients and Controlled Operations
Publication: Journal of Hydraulic Engineering
Volume 142, Issue 9
Abstract
Rigid water column (RWC) models simulate the unsteady-incompressible hydraulics of pressurized pipe networks. They conceptually lie between water hammer and quasi-steady models, yet despite their intrinsic strengths, existing RWC formulations suffer efficiency-, stability-, and interpretation-related challenges; thus, they are typically overlooked as a modeling alternative. To address the aforementioned limitations, this article presents the RWC global gradient algorithm (GGA), a novel formulation for pipe networks that has greater efficiency and overcomes the numerical challenges. The RWC GGA extends the generalized GGA (G-GGA) to consider inertial effects in addition to variable-area tanks and mixed (i.e., demand and pressure-dependent) outflows. Two pipe networks of simple and moderate complexity are used to compare the new approach against two other RWC algorithms, the G-GGA, and a water hammer model: the current work is shown to have improved stability and efficiency relative to previous work. The RWC GGA is also found to have a computational cost only slightly greater than that of the G-GGA for the same time-step size. Overall, this work highlights the practical utility of RWC models to simulate slow transient events and controlled operations.
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Acknowledgments
The authors thank the three reviewers for their stimulating and insightful comments, which helped to elevate the quality of this article. We also acknowledge and thank the financial support received from the Natural Sciences and Engineering Research Council of Canada and FP&P HydraTek.
References
Abreu, J., Cabrera, E., Izquierdo, J., and Garcia-Serra, J. (1999). “Flow modeling in pressurized systems revisited.” J. Hydraul. Eng., 1154–1169.
Ahmed, I. (1997). “Application of the gradient method for the analysis of unsteady flow in water networks.” M.Sc. thesis, Univ. of Arizona, Tucson, AZ.
Ang, W. H., and Jowitt, P. W. (2006). “Solution for water distribution systems under pressure-deficient conditions.” J. Water Resour. Plann. Manage., 175–182.
Axworthy, D. H. (1997). “Water distribution network modelling: From steady state to waterhammer.” Ph.D. dissertation, Univ. of Toronto, Toronto.
Axworthy, D. H., and Karney, B. W. (2000). “Valve closure in graph-theoretical models for slow transient network analysis.” J. Hydraul. Eng., 304–309.
Berardi, L., Giustolisi, O., and Todini, E. (2011). “Accounting for uniformly distributed pipe demand in WDN analysis: Enhanced GGA.” Urban Water J., 7(4), 243–255.
Bhave, P. R. (1988). “Extended period simulation of water systems—Direct solution.” J. Environ. Eng., 1146–1159.
Cabrera, E., Garcia-Serra, J., and Iglesias, P. L. (1995). “Modelling water distribution networks: From steady flow to water hammer.” Improving efficiency and reliability in water distribution systems, E. Cabrera and A. Vela, eds., Kluwer, Dordrecht, the Netherlands, 3–32.
Chaudhry, M. H. (2014). “Transient flow equations” Chapter 2, Applied hydraulic transients, Springer, New York, 35–64.
Deuerlein, J., Elhay, S., and Simpson, A. (2015). “Fast graph matrix partitioning algorithm for solving the water distribution system equations.” J. Water Resour. Plann. Manage., 04015037.
Elhay, S., Piller, O., Deuerlein, J., and Simpson, A. (2015). “A robust, rapidly convergent method that solves the water distribution equations for pressure-dependent models.” J. Water Resour. Plann. Manage., 04015047.
Elhay, S., and Simpson, A. R. (2011). “Dealing with zero flows in solving the nonlinear equations for water distribution systems.” J. Hydraul. Eng., 1216–1224.
Giustolisi, O., Berardi, L., and Laucelli, D. (2012a). “Generalizing WDN simulation models to variable tank levels.” J. Hydroinf., 14(3), 562–573.
Giustolisi, O., and Laucelli, D. (2011). “Water distribution network pressure-driven analysis using the enhanced global gradient algorithm (EGGA).” J. Water Resour. Plann. Manage., 498–510.
Giustolisi, O., Laucelli, D., Berardi, L., and Savić, D. (2012b). “Computationally efficient modeling method for large water network analysis.” J. Hydraul. Eng., 313–326.
Giustolisi, O., Savic, D., and Kapelan, Z. (2008). “Pressure-driven demand and leakage simulation for water distribution networks.” J. Hydraul. Eng., 626–635.
Giustolisi, O., and Todini, E. (2009). “Pipe hydraulic resistance correction in WDN analysis.” Urban Water J., 6(1), 39–52.
Holloway, M. B. (1985). “Dynamic pipe network computer model.” Ph.D. dissertation, Washington State Univ., Pullman, WA.
Islam, M. R., and Chaudhry, M. H. (1998). “Modeling of constituent transport in unsteady flows in pipe networks.” J. Hydraul. Eng., 1115–1124.
Karney, B. (1990). “Energy relations in transient closed-conduit flow.” J. Hydraul. Eng., 1180–1196.
Kesavan, H. K., and Chandrashekar, M. (1972). “Graph-theoretic models for pipe network analysis.” J. Hydraul. Div., 98(HY2), 345–363.
Nahavandi, A. N., and Catanzaro, G. V. (1973). “Matrix method for analysis of hydraulic networks.” J. Hydraul. Div., 99(HY1), 47–63.
Onizuka, K. (1986). “System dynamics approach to pipe network analysis.” J. Hydraul. Eng., 728–749.
Ormsbee, L. E. (2006). “The history of water distribution network analysis: The computer age.” Water Distribution Systems Analysis Symp., ASCE, Reston, VA.
Rao, H. S., and Bree, D. W. (1977). “Extended period simulation of water systems—Part A.” J. Hydraul. Div., 103(2), 97–108.
Rao, H. S., Markel, L., and Bree, D. J. (1977). “Extended period simulation of water systems—Part B.” J. Hydraul. Div., 103(3), 281–294.
Rossman, L. A. (2000). “EPANET 2 user’s manual.” Water Supply and Water Resources Division, National Risk Management Laboratory, Cincinnati.
Shimada, M. (1989). “Graph-theoretical model for slow transient analysis of pipe networks.” J. Hydraul. Eng., 1165–1183.
Shimada, M. (1992). “State-space analysis and control of slow transients in pipes.” J. Hydraul. Eng., 1287–1304.
Simpson, A., and Elhay, S. (2011). “Jacobian matrix for solving water distribution system equations with the Darcy-Weisbach head-loss model.” J. Hydraul. Eng., 696–700.
Todini, E. (2011). “Extending the global gradient algorithm to unsteady flow extended period simulations of water distribution systems.” J. Hydroinform., 13(2), 167–180.
Todini, E., and Pilati, S. (1988). “A gradient method for the solution of looped pipe networks.” Computer applications in water supply, Vol. 1 (system analysis and simulation), B. Coulbeck and C. H. Orr, eds., Wiley, London, 1–20.
Todini, E., and Rossman, L. A. (2013). “Unified framework for deriving simultaneous equation algorithms for water distribution networks.” J. Hydraul. Eng., 511–526.
Wylie, E. B., and Streeter, V. L. (1978). “Basic differential equations for transient flow.” Chapter 2, Fluid transients, McGraw-Hill, New York.
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Published In
Journal of Hydraulic Engineering
Volume 142 • Issue 9 • September 2016
Copyright
© 2016 American Society of Civil Engineers.
History
Received: Jan 15, 2015
Accepted: Jan 12, 2016
Published online: May 9, 2016
Published in print: Sep 1, 2016
Discussion open until: Oct 9, 2016
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