Available online at www.sciencedirect.com
ScienceDirect Procedia Engineering 119 (2015) 263 – 269
13th Computer Control for Water Industry Conference, CCWI 2015
Hydraulic characterization of PVC-O pipes by means of transient tests M. Ferrantea,∗, C. Capponia , B. Brunonea , S. Meniconia a Dipartimento
di Ingegneria Civile ed Ambientale, University of Perugia, Via G. Duranti, 93 - 06125 Perugia, Italy
Abstract Molecularly oriented PVC (known as PVC-O) was developed as an improvement to conventional unplasticized PVC (or PVC-u). For a given nominal pressure, the biaxial orientation of the pipe material allows to double the tensile strength and increase flexibility and resistance to cyclic fatigue, with a reduction in weight. Although the PVC-O pipes are produced and used since late 80s, the behavior of such pipes during transients is not well characterized in literature. In the paper we present the results of transient tests carried out on a PN16 DN110 pipe and generated by maneuvering an automatically controlled butterfly valve. The experimental setup has been installed at the Water Engineering Laboratory of the University of Perugia, Italy. Both time domain and frequency domain analyses are performed. The pressure wave speed is evaluated experimentally by means of pressure measurements. Information deriving from strain gauges is used to verify and characterize the actual viscoelastic behavior of PVC-O pipes. © Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license The Authors. Published by Elsevier Ltd. ©2015 2015The (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the Scientific Committee CCWI 2015. of CCWI of 2015 Peer-review under responsibility of the Scientific Committee
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1. Introduction Polyethylene (PE) and Polyvinyl Chloride (PVC) are the two most used plastic materials for pipes in water distribution systems. Molecularly oriented PVC (known as PVC-O) was developed as an improvement to conventional unplasticised PVC (sometimes referred to as PVC-U). Molecular orientation is achieved by increasing the diameter of the extruded pipes at a high temperature and cooling it rapidly, by means of water or air. Compared to PVC-U, PVC-O retains the characteristics that originated the massive use of plastic pipes in water distribution systems (no corrosion, low weight, easy to joint, . . . ); the increase to almost the double of the tensile strength yields larger internal diameters and reduces the weight for the same pipe nominal pressure. Since its introduction in the late seventies, PVC-O rheology has been studied and stress and fatigue tests on specimen can be found in literature (e.g., Campi et al. 2014; Kim and Gilbert 2004; Osry 2005; Robeyns and Vanspeybroeck 2005; West and Truss 2004,2012; Woods et al. 2003). In the framework of the investigations of the leak law, i.e. the pressure-discharge relationship, for pipes of different materials (Ferrante et al. 2011; Ferrante 2012; Massari ∗
Corresponding author. Tel: +39 075 5853618 ; Fax: +39 075 585 3892. E-mail address:
[email protected]
1877-7058 © 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the Scientific Committee of CCWI 2015
doi:10.1016/j.proeng.2015.08.884
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M. Ferrante et al. / Procedia Engineering 119 (2015) 263 – 269
consequence, the transversal strain gages were used as the active, i.e. variable resistance, of the Wheatstone quarter bridge configuration, while the longitudinal strain gages were used to compensate for the thermic effects, i.e. as compensating gages (Hoffman 1987). Four piezoresistive pressure transducers, with a 7 bar full scale (f.s.) and an accuracy of 0.1% f.s., were used to measure the pressure close to the reservoir (PTU ), upstream of the maneuver valve (PTD ) and 0.50 m downstream of the the strain gages SGU and SGD (PTSGU and PTSGD ). The data were acquired at 1000 Hz and down-sampled to 100 Hz. In the following, only a subset containing the most significative data is shown. 2.2. Results and discussion To characterize the viscoelastic behavior of the PVC-O pipe, transients were originated by means of complete closure maneuvers differing for two parameters: the valve initial opening degree, α, and the valve angular speed, β. By means of three values of α = π/4, π/9 and 2π/9 it was possible to have different ranges of pressure while by means of three values of β = (π/2) rad/s, 5(π/2) rad/s and 10(π/2) rad/s, the pressure gradients in time were varied. A resulting set of 9 tests was obtained. As a example, in Fig. 2 the variation in time of the measured pressures (pressure signals) is shown for α = π/9 and β = 5π/2 rad/s. The pressure wave originated by the valve closure reaches the transducer PD and then PTSGU and PTSGD causing an increase in the pressure signals. Once the wave is reflected by the upstream reservoir, it reaches the same transducers in the reverse order, causing a decrease in the measured pressure. Similar results can be seen in Figs. 3 and 4 where the pressure signals at PTD are shown for different values of α and β, respectively. By means of the measured wave arrival times and distances, it was possible to estimate a wave speed of about 370 m/s for the considered PVC-O pipe. Considering the value of the wave speed and the sampling frequency, the distance of 0.50 m from the pressure transducers PTSGU and PTSGD to the strain gages SGU and SGD can be considered as negligible and the pressure samples compared to the synchronous strain samples. Due to the high values of pressures, p, and low pipe thickness, e, compared to the pipe inner diameter, D, the transversal stresses on the outer surface of the pipe are given by the simplified expression: σ=
pD 2e
(1)
The stresses, σ, calculated by means of Eq. (1), can be compared to the measured strains, , to investigate the rheological behavior of the PVC-O. In Fig. 5, the same test of Fig. 2 is analyzed in the (,σ) domain. The stresses are in MPa while strains are in μ, i.e. 10−6 and both are referred to the initial values.
PD PSG
U
PSG
0.4
D
p [MPa]
0.3
0.2
0.1
0
−0.1
0
0.5
1
1.5
2
2.5
3
3.5
4
t [s]
Fig. 2: Variation in time of the measured pressures at the transducers PD , PTSGU and PTSGD , for α = π/9 and β = 5π/2 rad/s.
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β=π/2 rad/s β=5π/2 rad/s β=10π/2 rad/s 0.4
p [MPa]
0.3
0.2
0.1
0
−0.1
0
0.5
1
1.5
2
2.5
3
3.5
4
t [s]
Fig. 3: Variation in time of the measured pressures at the transducers PD for α = π/9 and β = π/2 , 5π/2 and 10π/2 rad/s.
α0=π/4 α0=π/9 α0=2 π/9
0.4
p [MPa]
0.3
0.2
0.1
0
−0.1
0
0.5
1
1.5
2
2.5
3
3.5
4
t [s]
Fig. 4: Variation in time of the measured pressure at the transducer PD , for α = π/4, π/9, and 2π/9 rad, and β = 5(π/2) rad/s.
For a linear elastic behavior, data in Fig. 5 should draw a straight line; although the drawn spiral is narrow and close to a line, the rheological behavior of the pipe material seems to depend on time, revealing a viscoelastic effect. To explore the time dependence on time of the σ- relationship, pressure signals of tests with different maneuver duration are considered (Fig. 4). The resulting variation in the (,σ) domain are shown in Fig. 6 where it can be seen that the lower the pressure signal gradients, the lower the spreading of the data around the elastic behavior line. When lower pressure gradient are considered, as for the tests of Fig. 4, the data are very close to the elastic behavior line and the viscoelastic effects become negligible. For all the considered cases, a linear fitting of the data provided values of the Young modulus, E, always higher than the literature value of about 4000 MPa. It is worth of noting that when the viscoelastic effects take place, the association of a single E value to the pipe material can be misleading since the viscoelastic rheological behavior requires more than one parameter.
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5
4
3
σ [MPa]
2
1
0
−1
−2
−3
−4 −800
−600
−400
−200
0
200
με
400
600
800
Fig. 5: Stresses and strains at SGD for Fig. 2 test. 6
4
σ [MPa]
2
0
−2
−4 β=π/2 rad/s β=5π/2 rad/s β=10π/2 rad/s −6 −800
−600
−400
−200
0
με
200
400
600
800
1000
Fig. 6: Stresses and strains at SGD for Fig. 3 tests.
3. Conclusions In this paper the preliminary results of transient tests on a PVC-O pipe are presented. The coupled measures of pressures and strains allow to investigate the viscoelastic effects straightforward in the strain-stress domain. Although these tests have to be considered as a first, preliminary attempt for an accurate rheological and hydraulic characterization, some conclusions can be derived. As an example, even though the considered pressure ranges concern about 1/6 of the pipe working pressures (0-2 bar compared to 0-12 bar), the viscoelastic effects are visible when a sharp transient pressure wave is generated. These effects are much less visible when the transient is originated by a maneuver that is slow in hydraulic terms, i.e. the duration is grater than the pipe characteristic time. What is sure is that further tests are needed to improve the knowledge about the implications of the rheological behavior of PVC-O pipes on the hydraulic characteristics of transients. Acknowledgements This research has been supported by the Italian Ministry of Education, University and Research (MIUR) — under the Projects of Relevant National Interest “Advanced analysis tools for the management of water losses in urban
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3
2
σ [MPa]
1
0
−1
−2 α0=π/4
−3
α0=π/9 α0=2 π/9
−4 −600
−400
−200
0
με
200
400
600
800
Fig. 7: Stresses and strains at SGD for Fig. 4 tests.
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 support of F. Mazzetti to the laboratory activity was highly appreciated. References F. Campi, M. Casagrande, G. Franzoni, C. Minelli, A. Porta, G. Ramella, A study of the behavior of bi-oriented PVC exposed to ionizing radiation and its possible use in nuclear applications, Radiation Physics and Chemistry 99 (2014) 86–91. H. C. Kim, M. Gilbert, Characterisation and properties of oriented PVC fibres, Polymer 45 (2004) 7293–7301. M. A. Osry, Modern developments and design criteria for unmodified, modified and oriented PVC pipes, Plastics, Rubber and Composites 34 (2005) 9–14. J. Robeyns, P. Vanspeybroeck, Molecular-oriented PVC (MOPVC) and PVC-U pipes for pressure applications in the water industry, Plastics, Rubber and Composites 34 (2005) 318–323. D. B. West, R. W. Truss, Mode II delamination testing in uniaxially oriented PVC pipes, Journal of materials science 39 (2004) 2789–2794. D. B. West, R. W. Truss, Stochastic fatigue limits and fatigue life variability in oriented–PVC pipe, Polymer Testing 31 (2012) 304–311. D. W. Woods, T. Marti, S. Ferry, Pipeline rehabilitation with expanded andoriented PVC, in: Underground Infrastructure Advanced Technology Conference, 2003. M. Ferrante, C. Massari, B. Brunone, S. Meniconi, Experimental evidence of hysteresis in the head-discharge relationship for a leak in a polyethylene pipe, Journal of Hydraulic Engineering, ASCE 137 (2011) 775–780. M. Ferrante, Experimental Investigation of the Effects of Pipe Material on the Leak Head-Discharge Relationship, Journal of Hydraulic Engineering, ASCE 138 (2012) 736–743. C. Massari, M. Ferrante, B. Brunone, S. Meniconi, Is the leak head–discharge relationship in polyethylene pipes a bijective function?, Journal of Hydraulic Research, IAHR 50 (2012) 409–417. M. Ferrante, C. Massari, B. Brunone, S. Meniconi, Leak behaviour in pressurized PVC pipes, Water Science & Technology: Water Supply 13 (2013) 987. D. Covas, I. Stoianov, J. Mano, H. Ramos, N. Graham, C. Maksimovic, The dynamic effect of pipe-wall viscoelasticity in hydraulic transients. Part I - experimental analysis and creep characterization, Journal of Hydraulic Research, IAHR 42 (2004) 517–532. D. Covas, I. Stoianov, J. Mano, H. Ramos, N. Graham, C. Maksimovic, The dynamic effect of pipe-wall viscoelasticity in hydraulic transients. Part II - model development, calibration and verification, Journal of Hydraulic Research, IAHR 43 (2005) 56–70. H.-F. Duan, P. J. Lee, M. S. Ghidaoui, Y.-K. Tung, System response function–based leak detection in viscoelastic pipelines, Journal of Hydraulic Engineering, ASCE 138 (2012) 143–153. C. Massari, T.-C. J. Yeh, M. Ferrante, B. Brunone, S. Meniconi, A stochastic tool for determining the presence of partial blockages in viscoelastic pipelines: first experimental results, Procedia Engineering 70 (2014) 1112–1120. S. Meniconi, B. Brunone, M. Ferrante, C. Massari, Transient hydrodynamics of in-line valves in viscoelastic pressurized pipes: long-period analysis, Experiments in Fluids 53 (2012a) 265–275. S. Meniconi, B. Brunone, M. Ferrante, Water-hammer pressure waves interaction at cross-section changes in series in viscoelastic pipes, Journal of Fluids and Structures 33 (2012b) 44–58.
M. Ferrante et al. / Procedia Engineering 119 (2015) 263 – 269 S. Meniconi, B. Brunone, M. Ferrante, C. Massari, Numerical and experimental investigation of leaks in viscoelastic pressurized pipe flow, Drinking Water Engineering and Science 6 (2013) 11–16. S. Meniconi, B. Brunone, M. Ferrante, C. Massari, Energy dissipation and pressure decay during transients in viscoelastic pipes with an in-line valve, Journal of Fluids and Structures 45 (2014) 235–249. G. Pezzinga, B. Brunone, D. Cannizzaro, M. Ferrante, S. Meniconi, A. Berni, Two-dimensional features of viscoelastic models of pipe transients, Journal of Hydraulic Engineering, ASCE (2014) 04014036–1–04014036–9. K. Hoffman, An introduction to stress analysis and transducer design using strain gauges, Eine einf¨uhrung in die technik des messens mit dehnungsmeßstreifen, Pfungstadt, 1987.
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