Two-Dimensional Features of Viscoelastic Models of Pipe Transients G. Pezzinga 1 ; B. Brunone, M.ASCE 2 ; D. Cannizzaro 3 ; M. Ferrante 4 ; S. Meniconi 5 ; and A. Berni 6 Abstract: Transients in pressurized polymeric pipes are analyzed by means of a two-dimensional (2D) Kelvin-Voigt viscoelastic model, calibrated by means of a microgenetic algorithm on the basis of pressure traces. The reliability of the proposed model is then tested by comparing numerical and experimental profiles of the axial component of the local velocity, the latter measured by means of an ultrasonic Doppler velocimeter. Differences between transients in viscoelastic and elastic pipes are pointed out by considering a 2D model in which an elastic behavior is assumed for pipe material. The comparison between the two 2D models allows attribution of the faster decay of pressure oscillations and velocity profiles to viscoelasticity because of the time-shift between pressure oscillation and retarded circumferential strain. The 2D analysis shows that the viscoelastic model generally presents flatter velocity profiles with respect to the elastic model. DOI: 10.1061/ (ASCE)HY.1943-7900.0000891. © 2014 American Society of Civil Engineers. Author keywords: Transients; Viscoelasticity; Two-dimensional models; Calibration; Velocity profile. Introduction Over the last few years, reliability of one-dimensional (1D) numeri- cal models to simulate transients in pressurized polymeric pipes has been tested by comparing experimental and numerical pressure traces. Specifically, attention has been focused, on one side, on the maximum overpressure, and on the other side, on the damping and smoothing of pressure oscillations within a long analysis period. Valuable contributions have been also offered with regard to the analysis of the fluid-structure interaction—see Keramat et al. (2012) for a thorough literature review—and water-column sepa- ration (Soares et al. 2012). The effect of the local head loss due to a partially closed in-line valve (Meniconi et al. 2011a, b, 2012a, 2014) and sudden changes of cross-section (Meniconi et al. 2011a, 2012b) has been investigated. In this frame of 1D modeling, great attention has been devoted to the parameter estimation procedure (Weinerowska-Bords 2007). When dealing with transients in polymeric pipes, the predominance of viscoelasticity (VE) with respect to unsteady friction (UF) has been shown (Pezzinga and Scandura 1995; Brunone et al. 2004, 2011; Covas et al. 2004, 2005; Pezzinga and Brunone 2006). This is the reason why unrealistic values of damping parameters in UF formulas have to be assumed when VE would be neglected as in classic water hammer models (Brunone et al. 2000; Pezzinga 2002a). Only recently—by means of local velocity measurements (Brunone and Berni 2010) and quasi–two-dimensional (2D) mod- els (Pezzinga 2002b; Duan et al. 2010a, b)—the peculiar character- istics of transients in polymeric pipes have been investigated in detail. Specifically, it has been shown quantitatively that UF is comparable with VE only in the first phases of transients, and VE plays an increasingly important role as time increases. In this paper, transients in polymeric pipes are analyzed from a different point of view with respect to the existing literature. That is, a quasi-2D model (Pezzinga 1999, 2000)—calibrated on the basis of pressure traces—is tested by considering velocity profiles acquired by an ultrasonic Doppler velocimeter (Brunone and Berni 2010). Then such a model is used to point out differences between transient flow field in elastic and viscoelastic pipes. Laboratory Setup Experiments were carried out at the Water Engineering Laboratory of the University of Perugia, Italy, on a high-density polyethylene (HDPE) pipe with length L ¼ 352 m, internal diameter D ¼ 93.3 mm, and wall thickness e ¼ 8.1 mm, supplied by a pressur- ized tank. Transients are generated by the fast and complete closure of an electromechanical butterfly valve placed at the downstream end section of the pipe and discharging in the air. Such a device assures the total repeatability of the maneuvers as well as the control of the valve closure time. During transients, both pressure and profile of the axial compo- nent, u, of the local velocity are measured at some selected loca- tions. Precisely, pressure values are acquired with an acquisition frequency f a ¼ 1,024 Hz by means of piezoresistive transducers placed at the supply tank and at a distance x ¼ 172 m from the maneuver valve. Local velocity measurements are carried out by means of an ultrasonic Doppler velocimeter (UDV) DOP1000 by Signal Processing S.A. (Willemetz 2000) at x ¼ 172 m, with 1 Professor, Dept. of Civil Engineering and Architecture, Univ. of Catania, Viale Andrea Doria 6, 95125 Catania, Italy (corresponding author). E-mail: gpezzinga@dica.unict.it 2 Professor, Dept. of Civil and Environmental Engineering, Univ. of Perugia, Via G. Duranti 93, 06125 Perugia, Italy. E-mail: bruno.brunone@ unipg.it 3 Civil Engineer, Idragest S.r.l., Via Santa Sofia 65, 95123 Catania, Italy. E-mail: donatella.cannizzaro@idragest.it 4 Associate Professor, Dept. of Civil and Environmental Engineering, Univ. of Perugia, Via G. Duranti 93, 06125 Perugia, Italy. E-mail: marco.ferrante@unipg.it 5 Assistant Professor, Dept. of Civil and Environmental Engineering, Univ. of Perugia, Via G. Duranti 93, 06125 Perugia, Italy. E-mail: silvia .meniconi@unipg.it 6 Civil Engineer, Studio Chiarini Associati–Ingegneria Civile e Ambien- tale, Via Galileo Ferraris 63, 52100 Arezzo, Italy. E-mail: alessandro .berni@alice.it Note. This manuscript was submitted on January 26, 2013; approved on February 13, 2014; published online on April 23, 2014. Discussion period open until September 23, 2014; separate discussions must be submitted for individual papers. This paper is part of the Journal of Hydraulic Engineer- ing, © ASCE, ISSN 0733-9429/04014036(9)/$25.00. © ASCE 04014036-1 J. Hydraul. Eng. J. Hydraul. Eng. 2014.140. Downloaded from ascelibrary.org by Bruno Brunone on 07/24/14. Copyright ASCE. For personal use only; all rights reserved.