Effect of Boundary on Water Hammer Wave Attenuation and Shape
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Volume 146, Issue 3
Abstract
The present study develops a refined water hammer model by postulating the presence of a water jet within the reservoir as the water hammer wave is reflected at the pipe inlet. The waterjet leads to a new boundary expression that induces a smoothing effect on the pressure wave front by introducing a smoothing factor, which is determined by minimizing the difference between pressure histories predicted numerically and those measured experimentally. The proposed boundary expression is applied in conjunction with the quasi-steady, the Brunone, and the Zielke friction water hammer models and is shown to more accurately replicate the peak pressure magnitudes, pressure wave shape, and the phase shifting when compared to experimental results for a variety of pipe systems and steady flow conditions. Using the quasi-steady and the Brunone models, the study shows that both the friction stresses and the proposed boundary expression attenuate the wave amplitude. However, only the proposed boundary expression smoothens the pressure distribution and delays the wave reflection in a manner consistent with experimental results. While the conventional Zielke model is shown to attenuate and smoothen the pressure distribution, the proposed boundary expression is shown to introduce additional damping and further phase shifting.
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Data Availability Statement
All code used during the study are available from the corresponding author by request, including the classical water hammer model with the quasi-steady, the Brunone, and the Zielke friction stresses using the classical and proposed boundary expressions.
Acknowledgments
The first author gratefully acknowledges funding from the China Scholarship Council (CSC) toward his Ph.D. program in the Department of Civil Engineering at the University of Ottawa, Canada.
References
Abani, N., and J. B. Ghandhi. 2012. “Behavior of unsteady turbulent starting round jets.” J. Fluids Eng. 134 (6): 061202. https://doi.org/10.1115/1.4006385.
Adamkowski, A., and M. Lewandowski. 2006. “Experimental examination of unsteady friction models for transient pipe flow simulation.” J. Fluids Eng. 128 (6): 1351–1363. https://doi.org/10.1115/1.2354521.
Afshar, M. H., and M. Rohani. 2008. “Water hammer simulation by implicit method of characteristic.” Int. J. Press. Vessel. Pip. 85 (12): 851–859. https://doi.org/10.1016/j.ijpvp.2008.08.006.
Alster, M. 1972. “Improved calculation of resonant frequencies of Helmholtz resonators.” J. Sound Vib. 24 (1): 63–85. https://doi.org/10.1016/0022-460X(72)90123-X.
Bergant, A., A. R. Simpson, and J. P. Vitkovsky. 1999. “Review of unsteady friction models in transient pipe flow.” In Proc., 9th Int. Meeting of the Work Group on the Behaviour of Hydraulic Machinery Unsteady Steady Oscillatory Conditions. Brno, Czech Republic: International Association of Hydraulic Research.
Bergant, A., A. R. Simpson, and J. Vítkovský. 2001. “Developments in unsteady pipe flow friction modeling.” J. Hydraul. Res. 39 (3): 249–257. https://doi.org/10.1080/00221680109499828.
Brunone, B., M. Ferrante, and F. Calabresi. 2002. “Discussion of ‘Evaluation of unsteady flow resistances by Quasi-2D or 1D models’ by Giuseppe Pezzinga.” J. Hydraul. Eng. 128 (6): 646–647. https://doi.org/10.1061/(ASCE)0733-9429(2002)128:6(646).
Brunone, B., U. M. Golia, and M. Greco. 1995. “Effects of two-dimensionality on pipe transients modeling.” J. Hydraul. Eng. 121 (12): 906–912. https://doi.org/10.1061/(ASCE)0733-9429(1995)121:12(906).
Brunone, B., B. W. Karney, M. Mecarelli, and M. Ferrante. 2000. “Velocity profiles and unsteady pipe friction in transient flow.” J. Water Resour. Plann. Manage. 126 (4): 236–244. https://doi.org/10.1061/(ASCE)0733-9496(2000)126:4(236).
Brunone, B., and L. Morelli. 1999. “Automatic control valve induced transients in an operative pipe system.” J. Hydraul. Eng. 125 (5): 534–542. https://doi.org/10.1061/(ASCE)0733-9429(1999)125:5(534).
Chaudhry, M. H. 2014. Applied hydraulic transients. New York: Springer.
Chaudry, M. H., and M. Y. Hussaini. 1985. “Second-order accurate explicit finite-difference schemes for waterhammer analysis.” J. Fluids Eng. 107 (4): 523–529. https://doi.org/10.1115/1.3242524.
Duan, H. F., M. S. Ghidaoui, P. J. Lee, and Y. K. Tung. 2012. “Relevance of unsteady friction to pipe size and length in pipe fluid transients.” J. Hydraul. Eng. 138 (2): 154–166. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000497.
Duan, H. F., M. S. Ghidaoui, and Y. K. Tung. 2009. “An efficient quasi-2D simulation of waterhammer in complex pipe systems.” J. Fluids Eng. 131 (8): 081105. https://doi.org/10.1115/1.3176978.
Duan, H. F., P. J. Lee, T. C. Che, M. S. Ghidaoui, B. W. Karney, and A. A. Kolyshkin. 2017a. “The influence of non-uniform blockages on transient wave behavior and blockage detection in pressurized water pipelines.” J. Hydro-environ. Res. 17 (Dec): 1–7. https://doi.org/10.1016/j.jher.2017.08.002.
Duan, H. F., S. Meniconi, P. J. Lee, B. Brunone, and M. S. Ghidaoui. 2017b. “Local and integral energy-based evaluation for the unsteady friction relevance in transient pipe flows.” J. Hydraul. Eng. 143 (7): 04017015. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001304.
Ghidaoui, M. S., B. W. Karney, and D. A. Mclnnis. 1998. “Energy estimates for discretization errors in water hammer problems.” J. Hydraul. Eng. 124 (4): 384–393. https://doi.org/10.1061/(ASCE)0733-9429(1998)124:4(384).
Ghidaoui, M. S., M. Zhao, D. A. Mclnnis, and D. H. Axworthy. 2005. “A review of water hammer theory and practice.” Appl. Mech. Rev. 58 (1): 49–76. https://doi.org/10.1115/1.1828050.
Haaland, S. E. 1983. “Simple and explicit formulas for the friction factor in turbulent pipe flow.” J. Fluids Eng. 105 (1): 89–90. https://doi.org/10.1115/1.3240948.
Holmboe, E. L., and W. T. Rouleau. 1967. “The effect of viscous shear on transients in liquid lines.” J. Basic Eng. 89 (1): 174–180. https://doi.org/10.1115/1.3609549.
Jang, T. U., Y. Wu, Y. Xu, J. Newman, and Q. Sun. 2016. “Efficient quasi-two-dimensional water hammer model on a characteristic grid.” J. Hydraul. Eng. 142 (12): 06016019. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001219.
Karney, B. W., and D. Mclnnis. 1992. “Efficient calculation of transient flow in simple pipe networks.” J. Hydraul. Eng. 118 (7): 1014–1030. https://doi.org/10.1061/(ASCE)0733-9429(1992)118:7(1014).
Karney, W. B. 1990. “Energy relations in transient closed-conduit flow.” J. Hydraul. Eng. 116 (10): 1180–1196. https://doi.org/10.1061/(ASCE)0733-9429(1990)116:10(1180).
Louati, M., and M. S. Ghidaoui. 2017. “Eigenfrequency shift mechanism due to variation in the cross sectional area of a conduit.” J. Hydraul. Res. 55 (6): 829–846. https://doi.org/10.1080/00221686.2017.1394373.
Martins, N. M. C., B. Brunone, S. Meniconi, H. M. Ramos, and D. I. C. Covas. 2017. “CFD and 1D approaches for the unsteady friction analysis of low Reynolds number turbulent flows.” J. Hydraul. Eng. 143 (12): 04017050. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001372.
Martins, N. M. C., A. K. Soares, H. M. Ramos, and D. I. C. Covas. 2016. “CFD modeling of transient flow in pressurized pipes.” Comput. Fluids 126 (Mar): 129–140. https://doi.org/10.1016/j.compfluid.2015.12.002.
Mitosek, M., and R. Szymkiewicz. 2016. “Reservoir influence on pressure wave propagation in steel pipes.” J. Hydraul. Eng. 142 (8): 6016007. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001140.
Nikpour, M. R., A. H. Nazemi, A. H. Dalir, F. Shoja, and P. Varjavand. 2014. “Experimental and numerical simulation of water hammer.” Arabian J. Sci. Eng. 39 (4): 2669–2675. https://doi.org/10.1007/s13369-013-0942-1.
Pezzinga, G. 1999. “Quasi-2D model for unsteady flow in pipe networks.” J. Hydraul. Eng. 125 (7): 676–685. https://doi.org/10.1061/(ASCE)0733-9429(1999)125:7(676).
Pezzinga, G. 2000. “Evaluation of unsteady flow resistances by quasi-2D or 1D models.” J. Hydraul. Eng. 126 (10): 778–785. https://doi.org/10.1061/(ASCE)0733-9429(2000)126:10(778).
Pezzinga, G. 2009. “Local balance unsteady friction model.” J. Hydraul. Eng. 135 (1): 45–56. https://doi.org/10.1061/(ASCE)0733-9429(2009)135:1(45).
Reddy, H. P., W. F. Silva-Araya, and M. H. Chaudhry. 2012. “Estimation of decay coefficients for unsteady friction for instantaneous, acceleration-based models.” J. Hydraul. Eng. 138 (3): 260–271. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000508.
Shimada, M., J. M. Brown, and A. E. Vardy. 2008. “Interpolation errors in rectangular and diamond characteristic grids.” J. Hydraul. Eng. 134 (10): 1480–1490. https://doi.org/10.1061/(ASCE)0733-9429(2008)134:10(1480).
Soares, A. K., D. I. C. Covas, and H. M. Ramos. 2013. “Damping analysis of hydraulic transients in pump-rising main systems.” J. Hydraul. Eng. 139 (2): 233–243. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000663.
Suzuki, K., T. Taketomi, and S. Sato. 1991. “Improving Zielke’s method of simulating frequency-dependent friction in laminar liquid pipe flow.” J. Fluids Eng. 113 (4): 569–573. https://doi.org/10.1115/1.2926516.
Szymkiewicz, R., and M. Mitosek. 2007. “Numerical aspects of improvement of the unsteady pipe flow equations.” Int. J. Numer. Methods Fluids. 55 (11): 1039–1058. https://doi.org/10.1002/fld.1507.
Szymkiewicz, R., and M. Mitosek. 2014. “Alternative convolution approach to friction in unsteady pipe flow.” J. Fluids Eng. 136 (1): 011202. https://doi.org/10.1115/1.4025509.
Tijsseling, A. S., Q. Hou, B. Svingen, and A. Bergant. 2010. “Acoustic resonance in a reservoir-pipeline-orifice system.” In Proc. ASME 2010 Pressure Vessels and Piping Division/K-PVP Conf., PVP2010–25083. Bellevue, WA: ASME.
Tiselj, I., and J. Gale. 2008. “Integration of unsteady friction models in pipe flow simulations.” J. Hydraul. Res. 46 (4): 526–535. https://doi.org/10.3826/jhr.2008.3326.
Trikha, A. K. 1975. “An efficient method for simulating frequency-dependent friction in transient liquid flow.” J. Fluids Eng. 97 (1): 97–105. https://doi.org/10.1115/1.3447224.
Vardy, A. E., and J. M. B. Brown. 1995. “Transient, turbulent, smooth pipe friction.” J. Hydraul. Res. 33 (4): 435–456. https://doi.org/10.1080/00221689509498654.
Vardy, A. E., and J. M. B. Brown. 2003. “Transient turbulent friction in smooth pipe flows.” J. Sound Vib. 259 (5): 1011–1036. https://doi.org/10.1006/jsvi.2002.5160.
Vardy, A. E., and J. M. B. Brown. 2004. “Transient turbulent friction in fully rough pipe flows.” J. Sound Vib. 270 (1–2): 233–257. https://doi.org/10.1016/S0022-460X(03)00492-9.
Vardy, A. E., and K. L. Hwang. 1991. “A characteristics model of transient friction in pipes.” J. Hydraul. Res. 29 (5): 669–684. https://doi.org/10.1080/00221689109498983.
Vitkovský, J., M. Stephens, A. Bergant, M. Lambert, and A. Simpson. 2004. “Efficient and accurate calculation of Zielke and Vardy-Brown unsteady friction in pipe transients.” In Proc., 9th Int. Conf. on Pressure Surges, 405–420. Chester, UK: BHR Group.
Vítkovský, J., M. Lambert, A. R. Simpson, and A. Bergant. 2000. “Advances in unsteady friction modelling in transient pipe flow.” In Proc., 8th Int. Conf. on Pressure Surges–Safe Design and Operation of Industrial Pipe System, 471–482. The Hague, Netherlands: BHR Group.
Vítkovský, J. P., A. Bergant, A. R. Simpson, and M. F. Lambert. 2006. “Systematic evaluation of one-dimensional unsteady friction models in simple pipelines.” J. Hydraul. Eng. 132 (7): 696–708. https://doi.org/10.1061/(ASCE)0733-9429(2006)132:7(696).
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.
Watters, G. Z. 1979. Modern analysis and control of unsteady flow in pipelines. Ann Arbor, MI: Ann Arbor Science Publishers.
Wylie, E. B. 1997. “Frictional effects in unsteady turbulent pipe flows.” Supplement, Appl. Mech. Rev. 50 (S11): S241–S244. https://doi.org/10.1115/1.3101843.
Zhang, C., J. Gong, A. Zecchin, M. Lambert, and A. Simpson. 2018. “Faster inverse transient analysis with a head-based method of characteristics and a flexible computational grid for pipeline condition assessment.” J. Hydraul. Eng. 144 (4): 04018007. https://doi.org/10.1061/(ASCE)HY.1943-7900.0001438.
Zhao, M., and M. Ghidaoui. 2004. “Godunov-type solutions for water hammer flows.” J. Hydraul. Eng. 130 (4): 341–348. https://doi.org/10.1061/(ASCE)0733-9429(2004)130:4(341).
Zhao, M., and M. S. Ghidaoui. 2003. “Efficient quasi-two-dimensional model for water hammer problems.” J. Hydraul. Eng. 129 (12): 1007–1013. https://doi.org/10.1061/(ASCE)0733-9429(2003)129:12(1007).
Zielke, W. 1968. “Frequency-dependent friction in transient pipe flow.” J. Basic Eng. 90 (1): 109–115. https://doi.org/10.1115/1.3605049.
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Published In
Journal of Hydraulic Engineering
Volume 146 • Issue 3 • March 2020
Copyright
©2020 American Society of Civil Engineers.
History
Received: Dec 31, 2018
Accepted: Aug 2, 2019
Published online: Jan 3, 2020
Published in print: Mar 1, 2020
Discussion open until: Jun 3, 2020
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