Relevance of Pipe Period on Kelvin-Voigt Viscoelastic Parameters: 1D and 2D Inverse Transient Analysis
Publication: Journal of Hydraulic Engineering
Volume 142, Issue 12
Abstract
This paper presents the results of the calibration by means of a microgenetic algorithm, using Kelvin-Voigt viscoelastic parameters, to reproduce experimental unsteady flow tests in a polymeric pipe. During the tests, different pipe lengths—which give rise to different periods of the pressure oscillations—and initial discharges have been considered. The mechanical parameters of the viscoelastic models are estimated using both one-dimensional (1D) and quasi two-dimensional (2D) models. The calibration of Kelvin-Voigt models with 2, 3, 5, and 7 parameters, respectively, proves the substantial independence of the elastic modulus and the dependence of the retardation time on the pipe period (i.e., the pipe length). Moreover, in most cases, the increase in the number of mechanical parameters allows a better simulation of a single transient. However, the larger the number of parameters, the greater the risk of overfitting, and the more difficult the search for general laws of dependence of the parameters on the characteristics of the pipe—primarily of the retardation time on the period of the pressure oscillations.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
This research was funded by the University of Perugia, Italian Ministry of Education, University and Research (MIUR) under the following projects of relevant national interest: “Advanced Analysis Tools for the Management of Water Losses in Urban Aqueducts” and “Tools and Procedures for an Advanced and Sustainable Management of Water Distribution Systems”; and Fondazione Cassa Risparmio Perugia, under the project “Hydraulic and Microbiological Combined Approach Towards Water Quality Control (No. 2015.0383.021).” The help of Elisa Mazzetti in the laboratory experiments is really appreciated.
References
Aklonis, J. J., McKnight, W. J., and Shen, M. (1972). Introduction to polymer viscoelasticity, Wiley, New York.
Bergant, A., Simpson, A. R., and Vitkovsky, J. (2001). “Developments in unsteady pipe flow friction modelling.” J. Hydraul. Res., 39(3), 249–257.
Brunone, B., and Berni, A. (2010). “Wall shear stress in transient turbulent pipe flow by local velocity measurement.” J. Hydraul. Eng., 716–726.
Brunone, B., and Golia, U. M. (2008). “Discussion of ‘Systematic evaluation of one-dimensional unsteady friction models in simple pipelines’ by J.P. Vitkovsky, A. Bergant, A.R. Simpson, and M. F. Lambert.” J. Hydraul. Eng., 282–284.
Brunone, B., Golia, U. M., and Greco, M. (1995). “Effects of two-dimensionality on pipe transients modeling.” J. Hydraul. Eng., 906–912.
Brunone, B., Karney, B. W., Mecarelli, M., and Ferrante, M. (2000). “Velocity profiles and unsteady pipe friction in transient flow.” J. Water Resour. Plann. Manage., 236–244.
Carroll, D. L. (1996). “Genetic algorithms and optimizing chemical oxygen-iodine lasers.” Dev. Theor. Appl. Mech., 18(3), 411–424.
Covas, D., Stoianov, I., Mano, J. F., Ramos, H., Graham, N., and Maksimovic, C. (2004). “The dynamic effect of pipe-wall viscoelasticity in hydraulic transients. Part I: Experimental analysis and creep haracterization.” J. Hydraul. Res., 42(5), 517–532.
Covas, D., Stoianov, I., Mano, J. F., Ramos, H., Graham, N., and Maksimovic, C. (2005). “The dynamic effect of pipe-wall viscoelasticity in hydraulic transients. Part II: Model development, calibration and verification.” J. Hydraul. Res., 43(1), 56–70.
Darwin, C. (1859). On the origin of species by means of natural selection, Murray, London.
Duan, H.-F., Ghidaoui, M. S., Lee, P. J., and Tung, Y. K. (2010). “Unsteady friction and visco-elasticity in pipe fluid transients.” J. Hydraul. Res., 48(3), 354–362.
Duan, H.-F., Ghidaoui, M. S., Lee, P. J., and Tung, Y. K. (2012). “Relevance of unsteady friction to pipe size and length in pipe fluid transients.” J. Hydraul. Eng., 154–166.
Evangelista, S., Leopardi, A., Pignatelli, R., and de Marinis, G. (2015). “Hydraulic transients in viscoelastic branched pipelines.” J. Hydraul. Eng., 04015016.
Ferrante, M., Brunone, B., and Meniconi, S. (2009). “Leak detection in branched pipe systems coupling wavelet analysis and a Lagrangian model.” J. Water Supply: Res. Technol.– AQUA, 58(2), 95–106.
Ferry, J. D. (1980). Viscoelastic properties of polymers, Wiley, Chichester, U.K.
Franke, P. G., and Seyler, F. (1983). “Computation of unsteady pipe flow with respect to viscoelastic material properties.” J. Hydraul. Res., 21(5), 345–353.
Ghidaoui, M. S., Mansour, G. S., and Zhao, M. (2002). “Applicability of quasi-steady and axisymmetric turbulence models in water- hammer models.” J. Hydraul. Eng., 917–924.
Goldberg, D. E. (1989a). Genetic algorithm in search, optimization, and machine learning, Addison Wesley, Reading, MA.
Goldberg, D. E. (1989b). “Sizing populations for serial and parallel genetic algorithms.” Proc., 3rd Int. Conf. on Genetic Algorithms, Morgan Kaufmann Publishers, San Francisco, 70–79.
Holland, J. H. (1975). Adaptation in natural and artificial systems, University of Michigan Press, Ann Arbor, MI.
Keramat, A., and Haghighi, A. (2014). “Straightforward transient-based approach for the creep function determination in viscoelastic pipes.” J. Hydraul. Eng., 04014058.
Meniconi, S., Brunone, B., and Ferrante, M. (2012a). “Water hammer pressure waves interaction at cross-section changes in series in viscoelastic pipes.” J. Fluids Struct., 33(1), 44–58.
Meniconi, S., Brunone, B., Ferrante, M., and Massari, C. (2012b). “Transient hydrodynamics of in-line valves in viscoelastic pressurised pipes. Long period analysis.” Exp. Fluids, 53(1), 265–275.
Meniconi, S., Brunone, B., Ferrante, M., and Massari, C. (2014a). “Energy dissipation and pressure decay during transients in viscoelastic pipes with an in-line valve.” J. Fluids Struct., 45, 235–249.
Meniconi, S., Duan, H. F., Brunone, B., Ghidaoui, M. S., Lee, P. J., and Ferrante, M. (2014b). “Further developments in rapidly decelerating turbulent pipe flow modeling.” J. Hydraul. Eng., 04014028-1–04014028-9.
Mitosek, M., and Chorzelski, M. (2003). “Influence of visco-elasticity on pressure wave velocity in polyethylene MDPE pipe.” Archit. Hydro. Eng. Environ. Mech., 50(2), 127–140.
Pezzinga, G. (1999). “Quasi-2D model for unsteady flow in pipe networks.” J. Hydraul. Eng., 676–685.
Pezzinga, G. (2000). “Evaluation of unsteady flow resistances by quasi-2D or 1D models.” J. Hydraul. Eng., 778–785.
Pezzinga, G. (2009). “Local balance unsteady friction model.” J. Hydraul. Eng., 45–56.
Pezzinga, G. (2014). “Evaluation of time evolution of mechanical parameters of polymeric pipes by unsteady flow runs.” J. Hydraul. Eng., 04014057.
Pezzinga, G., Brunone, B., Cannizzaro, D., Ferrante, M., Meniconi, S., and Berni, A. (2014). “Two-dimensional features of viscoelastic models of pipe transients.” J. Hydraul. Eng., 04014036.
Shamloo, H., and Mousavifard, M. (2015). “Turbulence behaviour investigation in transient flows.” J. Hydraul. Res., 53(1), 83–92.
Soares, A. K., Covas, D. I. C., and Reis, L. F. R. (2008). “Analysis of PVC pipe-wall viscoelasticity during water hammer.” J. Hydraul. Eng., 1389–1394.
Vardy, A. E., and Brown, J. M. B. (2003). “Transient turbulent friction in smooth pipe flows.” J. Sound Vib., 259(5), 1011–1036.
Vardy, A. E., and Brown, J. M. B. (2004). “Transient turbulent friction in fully rough pipe flows.” J. Sound Vib., 270(1–2), 233–257.
Weinerowska-Bords, K. (2006). “Viscoelastic model of waterhammer in single pipeline—Problems and questions.” Archit. Hydro. Eng. Environ. Mech., 53(4), 331–351.
Weinerowska-Bords, K. (2007). “Accuracy and parameter estimation of elastic and viscoelastic models of the water hammer.” Task Q., 11(4), 383–395.
Weinerowska-Bords, K. (2015). “Alternative approach to convolution term of viscoelasticity in equations of unsteady pipe flow.” J. Fluids Eng., 137(5), 054501.
Yao, E., Kember, G., and Hansen, D. (2016). “Water hammer analysis and parameter estimation in polymer pipes with weak strain-rate feedback.” J. Eng. Mech., 04016052.
Zielke, W. (1968). “Frequency-dependent friction in transient pipe flow.” J. Basic Eng., 90(1), 109–115.
Information & Authors
Information
Published In
Journal of Hydraulic Engineering
Volume 142 • Issue 12 • December 2016
Copyright
© 2016 American Society of Civil Engineers.
History
Received: Jan 13, 2016
Accepted: Jun 1, 2016
Published online: Jul 26, 2016
Published in print: Dec 1, 2016
Discussion open until: Dec 26, 2016
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.