Abstract
An innovative numerical model called the Modified Two-Component Pressure Approach (MTPA) is proposed to better capture the physics of column separation in conduit systems. Based on the Two-Component Pressure Approach (TPA), the MTPA calculates both cavitating and pressurized flow using a single set of equations that governs unsteady flow in open channel flow. As opposed to shock-fitting-based models, in which a complex algorithm is needed to keep track of the interfaces separating the cavitating and liquid zones, the proposed model can capture both flow phases automatically. The first-order Godunov type finite volume method is utilized to numerically solve the equations. A customized Harten, Lax and Van Leer (HLL) Riemann solver is employed to calculate the fluxes at the computational cell boundaries and to dissipate potential post-shock oscillations generated when the cavity is collapsed and the open channel flow beneath the cavity is switched back to pressurized flow. The numerical results are shown to be in good agreement with both experimental data and the results obtained from the Discrete Gas Cavity Model (DGCM). A hypothetical test case is also presented to demonstrate the unique feature of the proposed model, which is the ability to simultaneously account for waterhammer, cavitation, and open channel flow regimes, a feature making the model even superior to the DGCM.
Practical Applications
Several numerical approaches are available to successfully calculate the induced waterhammer pressures following column separation. Existing 1D models based on these numerical approaches can help engineers quantify the impacts of column separation and design measures to protect the pipe system against this phenomenon. Nevertheless, most of the existing models used in the industry exclusive work with pipe systems that remain fully pressurized during transient flow. However, column separation may occur in pipe systems carrying concurrent open channel and pressurized flows. Examples of such systems and operating conditions are sewer conveyance and pipe system collection, intermittent water distribution systems, pump power failure in self-draining pumped pipelines, and pipeline filling and draining. To fill part of this gap, this paper presents a numerical open channel-based 1D model that can treat concurrent transient open channel, pressurized flow, and column separation. The model is validated using experimental data, numerical results from other models, and a hypothetical example. The results reveal that the model is accurate enough to be used in practical applications. The model can also calculate the shape and spread of vapor cavities across the pipe system, a feature that makes the proposed model superior to counterpart models.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
Some data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request. This includes all numerical data obtained from the MTPA and DGCM models. Some models or code used during the study were provided by a third party. This includes the experimental data used for the validation of the model. Direct request for these materials may be made to the provider as indicated in the Acknowledgments.
Acknowledgments
The authors would like to thank Dr. Anton Bergant, who generously provided us with the experimental data utilized for the validation of the proposed model. The experimental data used in this paper are part of the research conducted by Bergant and Simpson (1999b, a). The authors are also thankful to the reviewers for their constructive comments. This research is supported by the US Geological Survey under Grant/Cooperative No. (G16AP00075) and North Dakota State Water Commission (NDSWC) through a fellowship award by the North Dakota Water Resources Research Institute (NDWRRI).
References
Adamkowski, A., and M. Lewandowski. 2012. “Investigation of hydraulic transients in a pipeline with column separation.” J. Hydraul. Eng. 138 (11): 935–944. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000596.
Autrique, R., and E. Rodal. 2013. “Laboratory studies of water column separation.” In Proc., IOP Conf. Series: Materials Science and Engineering, 022022. New York: IOP Publishing.
Baltzer, R. A. 1967a. “Column separation accompanying liquid transients in pipes.” J. Basic Eng. 1967 (1): 837–846. https://doi.org/10.1115/1.3609712.
Baltzer, R. A. 1967b. “A study of column separation accompanying transient flow of liquids in pipes.” Ph.D. thesis, Dept. of Civil Engineering, Univ. of Michigan.
Bergant, A., and A. R. Simpson. 1999a. “Cavitation inception in pipeline column separation.” In Proc., 28th IAHR Congress. Graz, Austria: CD-ROM.
Bergant, A., and A. R. Simpson. 1999b. “Pipeline column separation flow regimes.” J. Hydraul. Eng. 125 (8): 835–848. https://doi.org/10.1061/(ASCE)0733-9429(1999)125:8(835).
Bergant, A., A. R. Simpson, and A. S. Tijsseling. 2006. “Water hammer with column separation: A historical review.” J. Fluids Struct. 22 (Aug): 135–171. https://doi.org/10.1016/j.jfluidstructs.2005.08.008.
Boulos, P. F., B. W. Karney, D. J. Wood, and S. Lingireddy. 2005. “Hydraulic transient guidelines for protecting water distribution systems.” J. Am. Water Works Assoc. 97 (5): 111–124. https://doi.org/10.1002/j.1551-8833.2005.tb10892.x.
Chaiko, M. A. 2006. “A finite-volume approach for simulation of liquid-column separation in pipelines.” J. Fluids Eng. 128 (6): 1324–1335. https://doi.org/10.1115/1.2353271.
Chaudhry, M. H. 1987. Applied hydraulic transients. New York: Van Nostrana Reinhold Co.
Chaudhry, M. H. 1999. Open channel flow. Englewood Cliffs, NJ: Prentice-Hall.
Cunge, J. A., and M. Wegner. 1964. “Numerical integration of Bane de Saint-Venant’s flow equations by means of an implicit scheme of finite differences. Applications in the case of alternately free and pressurized flow in a tunnel.” Houille Blanche 50 (1): 33–39. https://doi.org/10.1051/lhb/1964002.
Daude, F., A. S. Tijsseling, and P. Galon. 2018. “Numerical investigations of water-hammer with column-separation induced by vaporous cavitation using a one-dimensional finite-volume approach.” J. Fluids Struct. 83 (4): 91–118. https://doi.org/10.1016/j.jfluidstructs.2018.08.014.
He, X., J. Y. Jiandong Yang, J. Hu, and T. Peng. 2022. “Experimental study of cavitating vortex rope and water column separation in a pump turbine.” Phys. Fluids 34 (4): 044101. https://doi.org/10.1063/5.0086509.
Kalkwijk, J. P., C. Kranenburg, C. B. Vreugdenhil, and A. H. De Vries. 1972. Cavitation caused by water hammer in horizontal. Delft, Netherlands: Delft Hydraulics Laboratory.
Karadžić, U., V. Bulatović, and A. Bergant. 2014. “Valve-induced water hammer and column separation in a pipeline apparatus.” Strojniški vestnik-J. Mech. Eng. 60 (11): 742–754. https://doi.org/10.5545/sv-jme.2014.1882.
Kerger, F., P. Archambeau, S. Erpicum, B. J. Dewals, and M. Pirotton. 2011. “An exact Riemann solver and a Godunov scheme for simulating highly transient mixed flows.” J. Comput. Appl. Math. 235 (May): 2030–2040. https://doi.org/10.1016/j.cam.2010.09.026.
Khani, D., Y. H. Lim, and A. Malekpour. 2020. “Hydraulic transient analysis of sewer pipe systems using a non-oscillatory two-component pressure approach.” Water 12 (10): 2896. https://doi.org/10.3390/w12102896.
Khani, D., Y. H. Lim, and A. Malekpour. 2021. “A mixed flow analysis of sewer pipes with different shapes using a non-oscillatory two-component pressure approach (TPA).” Modelling 2 (4): 467–481. https://doi.org/10.3390/modelling2040025.
Leon, A. S., M. S. Ghidaoui, A. R. Schmidt, and M. H. García. 2008. “Efficient second-order accurate shock-capturing scheme for modeling one-and two-phase water hammer flows.” J. Hydraul. Eng. 134 (7): 970–983. https://doi.org/10.1061/(ASCE)0733-9429(2008)134:7(970).
León, A. S., M. S. Ghidaoui, A. R. Schmidt, and M. H. García. 2009. “Application of Godunov-type schemes to transient mixed flows.” J. Hydraul. Res. 47 (2): 147–156. https://doi.org/10.3826/jhr.2009.3157.
LeVeque, R. J. 2002. Finite volume methods for hyperbolic problems. Cambridge, UK: Cambridge Press.
Malekpour, A., and B. Karney. 2015. Spurious numerical oscillations in the preissmann slot method: Origin and suppression. Reston, VA: ASCE.
Malekpour, A., and B. W. Karney. 2014a. “Column separation and rejoinder during rapid pipeline filling induced by a partial flow blockage.” J. Hydraul. Res. 52 (5): 693–704. https://doi.org/10.1080/00221686.2014.905502.
Malekpour, A., and B. W. Karney. 2014b. “Profile-induced column separation and rejoining during rapid pipeline filling.” J. Hydraul. Eng. 140 (11): 04014054. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000918.
Marsden, N. J., and J. A. Fox. 1976. “An alternative approach to the problem of column separation in an elevated section of pipeline.” In Proc., 2nd Int. Conf. on Pressure Surges. London: BHRA.
Martin, C. S. 1983. “Experimental investigation of column separation with rapid closure of downstream valve.” In Proc., 4th Int. Conf. on Pressure Surges. Cranfield, UK: BHRA Fluid Engineering.
Provoost, G. A., and E. B. Wylie. 1981. “Discrete gas model to represent distributed free gas in liquids.” In Proc., 5th Int. Symp. on Water Column Separation. Bedford, UK: BHRA Fluid Engineering.
Siemons, J. 1967. “The phenomenon of cavitation in a horizontal pipe-line due to a sudden pump-failure.” J. Hydraul. Res. 5 (2): 135–152. https://doi.org/10.1080/00221686709500198.
Simpson, A. R., and A. Bergant. 1994. “Numerical comparison of pipe column-separation models.” J. Hydraul. Eng. 120 (3): 361–377. https://doi.org/10.1061/(ASCE)0733-9429(1994)120:3(361).
Simpson, A. R., and E. B. Wylie. 1991. “Large water-hammer pressures for column separation in pipelines.” J. Hydraul. Eng. 117 (10): 1310–1316. https://doi.org/10.1061/(ASCE)0733-9429(1991)117:10(1310).
Toro, E. F. 2001. Shock-capturing methods for free-surface shallow flows. New York: Wiley.
Vasconcelos, G. J., and T. B. D. Marwell. 2011. “Innovative simulation of unsteady low-pressure flows in water mains.” J. Hydraul. Eng. 137 (11): 1490–1499. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000440.
Vasconcelos, J. G., S. J. Wright, and P. L. Roe. 2006. Current Issues on modeling extreme inflows in stormwater systems in intelligent modeling of urban water systems. Guelph, ON: CHI.
Vasconcelos, J. G., S. J. Wright, and P. L. Roe. 2009. “Numerical oscillations in pipe-filling bore predictions by shock-capturing models.” J. Hydraul. Eng. 135 (4): 296–305. https://doi.org/10.1061/(ASCE)0733-9429(2009)135:4(296).
Warda, H. A., E. M. Wahba, and M. Salah El-Din. 2020. “Computational fluid dynamics (CFD) simulation of liquid column separation in pipe transients.” Alexandria Eng. J. 59 (5): 3451–3462. https://doi.org/10.1016/j.aej.2020.05.025.
Zhou, L., H. Wang, D. Liu, J. Ma, P. Wang, and L. Xia. 2017. “A second-order finite volume method for pipe flow with water column separation.” J. Hydro-environ. Res. 17 (Nov): 47–55. https://doi.org/10.1016/j.jher.2016.11.004.
Information & Authors
Information
Published In
Journal of Hydraulic Engineering
Volume 149 • Issue 2 • February 2023
Copyright
© 2022 American Society of Civil Engineers.
History
Received: Jan 5, 2022
Accepted: Sep 8, 2022
Published online: Nov 23, 2022
Published in print: Feb 1, 2023
Discussion open until: Apr 23, 2023
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.
Cited by
- Zijian Xue, Ling Zhou, Deyou Liu, Tong-Chuan Che, A Random Choice Scheme for Transient Mixed Flows, Journal of Hydraulic Engineering, 10.1061/JHEND8.HYENG-13605, 149, 8, (2023).