Numerical Modelling of Transient Flow in Viscoelastic Pipe Network

Document Type : Original Article

Authors

1 Professor of faculty of Water Science Engineering of Ahvaz Chamran University

2 Assistant Professor, Department of Hydraulic Structures, Faculty of Water Science Engineering, Shahid Chamran University of Ahvaz, Ahvaz

3 Associate Professor, Civil Engineering Department, Faculty of Engineering, Shahid Chamran University of Ahvaz, Ahvaz, Iran,

Abstract

The present research deals with the introduction and simulation of viscoelastic effects in transient flows in polymeric pipes widely used in pipe network. The viscoelastic properties result in appearing new terms in transient flow governing equations which are generally absent in available models. In this study, the governing equations are rewritten and manipulated for considering the viscoelastic properties. The equations are then solved using the method of characteristics coupled with the finite difference method. In order to calibrate the unknown parameters including the unsteady friction and creep coefficients as well as to verify the model, a model of viscoelastic pipe network was made at the hydraulics laboratory of Water Sciences Engineering department of Shahid Chamran University. The configuration of the experimental set-up consists of a pipe network with six square loops, having each loop 3m×3m. The pipes are made of PE with 50 mm nominal diameter and 5.5 mm of wall thickness. The data of dynamic pressure oscillation during these transient events were collected by Pressure transducers. Appling the inverse transient analysis method and with the aid of a genetic algorithm, the friction and creep coefficients of the experimental pipe are determined. The results show that the classical water hammer solver cannot accurately analyze the transient flows in polyethylene pipes. In fact, modeling both dynamic effects of unsteady friction losses and viscoelasticity for such pipes is quite necessary. However, it is also found that the viscoelasticity is obviously more effective than the unsteady friction effects in formation and attenuation of transient signals so that, considering onlyviscoelastic effects would result in acceptable responses

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منابع
کوچک­زاده، ص. و ع. پرورش­ریزی. 1392. مقدمه­ای بر هیدرولیک جریان ناپایدار. انتشارات دانشگاه تهران.
Aklonis, J. J., W. J. MacKnight and M. Shen. 1972. Introduction to Polymer Viscoelasticity. John Wiley & Sons, NewYork.
Apollonio, C., D. I. C. Covas, G. de Marinis, A. Leopardi and H. M. Ramos. 2013. Creep functions for transients in HDPE pipes. Urban Water Journal, 11(2): 160-166.
Brunone, B., U. M. Golia and M. Greco. 1991. Modelling of fast transients by numerical methods. In Proc. Int. Conf. on Hydraulic Transients with Water Column Separation, pp. 273-280.
Brunone, B., U. M. Golia and M. Greco. 1995. Effects of two-dimensionality on pipe transients modeling. Journal of Hydraulic Engineering, 121(12): 906-912.
Carriço, N. J. G., A. K. Soares and D. I. C. Covas. 2016. Uncertainties of inverse transient modelling with unsteady friction and pipe-wall viscoelasticity. Journal of Water Supply: Research and Technology, 65(4): 342-353.
Chaudhry, M. H. 2014. Applied Hydraulic Transients. Springer New York, pp. 503.
Covas, D., I. Stoianov, J. Mano, H. Ramos, N. Graham and C. Maksimovic. 2004. The dynamic effect of pipe-wall viscoelasticity in hydraulic transients. Part I—Experimental analysis and creep characterization. Journal of Hydraulic Engineering, 42(5): 516–530.
Covas, D., I. Stoianov, J. Mano, H. Ramos, N. Graham and C. Maksimovic. 2005. The dynamic effect of pipe-wall viscoelasticity in hydraulic transients. Part II— Model development, calibration and verification. Journal of Hydraulic Engineering, 43(1): 56–70.
Daily, J. W., W. L. Hankey, R. W. Olive and J. M. Jordaan. 1956. Resistance Coefficients for Accelerated and Decelerated Flows through Smooth Tubes and Orifices. Trans. ASME, 78: 1071–1077.
Duan, H. F., M. S. Ghidaoui, P. J. Lee and Y. K. Tung. 2010. Unsteady friction and viscoelasticity in pipe fluid transients. Journal of Hydraulic Engineering, 48(3): 354–362.
Evangelista, S., A. Leopardi, R. Pignatelli and G. Marinis. 2015. Hydraulic Transients in Viscoelastic Branched Pipelines. Journal of Hydraulic Engineering, ASCE, 141(8): 1-9.
Ghidaoui, M. S., S. G. S. Mansour and M. Zhao. 2002. Applicability of Quasi Steady and Axisymmetric Turbulence Models in Water Hammer. Journal of Hydraulic Engineering, 128(10): 917–924.
Holmboe, E. L. and W. T. Rouleau. 1967. The effect of viscous shear on transients in liquid lines. Journal of Basic Engineering, 89(1): 174-180.
Karney, B. W. and D. McInnis. 1992. Efficient calculation of transient flow in simple pipe networks. Journal of hydraulic engineering, 118(7): 1014-1030.
Keramat, A., A. Ahmadi and A. Majd. 2009. Transient caveating pipe flow due to a pump failure: Proceedings of the 3rd IAHR International Meeting of the Work Group on Cavitation and Dynamic Problems in Hydraulic Machinery and Systems, Brno, Czech Republic.
Pezzinga, G., B. Brunone, D. Cannizzaro, M. Ferrante, S. Meniconi and A. Berni. 2014. Two-Dimensional Features of Viscoelastic Models of Pipe Transients. Journal of Hydraulic Engineering, 140(8):04014036.
Reddy, H. P., W. F. Silva-Araya and M. H. Chaudhry. 2012. Estimation of Decay Coefficients for Unsteady Friction for Instantaneous, Acceleration-Based Models. Journal of Hydraulic Engineering, 138(3): 260-271.
Soares, A. K., D. I. C., Covas and F. R. Reis. 2008. Analysis of PVC pipe-wall viscoelasticity during water hammer. Journal of Hydraulic Engineering, ASCE, 134(9): 1389-1394.
Vardy, A. E., K. L. Hwang and J. M. B. Brown. 1993. A weighting function model of transient turbulent pipe friction. Journal of Hydraulics Research, 31: 533-544.
White, F. M. 1999. Fluid Mechanics (4th Edition). McGraw-Hill.
Zielke, W. 1968. Frequency-dependent friction in transient pipe flow. Journal of Fluids Engineering, 90(1): 109-115.