Kelvin-Voigt 1-D models for simulating transients in viscoelastic pipes: influence of pipe lenght and limits

The attenuation of pressure peaks during transients in polymeric pressurized pipes or rather, its larger entity with respect to that given by the "classical" water-hammer models has been the main thrust of intense research activities with the aim of refining more reliable numerical models. This is the case of the wide literature on fluid-structure interaction, where the role of polymeric pipe materials is investigated in detail (e.g., Keramat et al., 2012) and gave rise to different viscoelastic models to simulate the pipe viscoelastic behavior (Ferry, 1980; Franke & Seyler, 1983). With respect to the elastic pipes, for polymeric ones the most important features to model are the retarded strain for a given applied load and its effects on the value of the pressure wave speed. One of the approaches that can be followed is the so-called Kelvin-Voigt (hereafter referred to as KV) model. The time-dependent strain behavior of the polymeric pipes – the so-called creep function – depends on the molecular structure, stress time-history, and temperature. In the KV models the creep function is simulated by considering a combination of elements such as springs – having an elastic response – and dashpots – with a linear viscous behaviour: the larger the number of such elements, the better the description of the pipe material behavior. As shown in Covas et al. (2004), the creep function obtained by mechanical tests on pipe samples does not represent the actual mechanical behavior of the material in the pipe system – but it provides an approximate trend – since it does not take into account the pipe constraints and stress time-history experienced during transients. Thus, to improve the reliability of the transient models, the KV parameters have been evaluated as the unknowns of an inverse transient analysis (ITA) (Covas et al., 2005; Weinerowska-Bords, 2015). The above brief discussion about the modeling of transients in polymeric pipes concerns simple pipes (i.e., pipes with a constant diameter and uniform geometrical characteristics). In literature less attention has been devoted to the analysis of the dependence of the KV parameters on the configuration of the pipe system and their evolution in time (Meniconi et al., 2012a, 2012b, 2013, 2014; Pezzinga, 2014; Evangelista et al., 2015). This paper explores the effect of the pipe length and then of its period for a reservoir-pipe-valve system. Particularly, within a ITA procedure by means of a 1-D model, the viscoelastic parameters for pipe systems with given geometrical characteristics but a different length are evaluated.