**1. Introduction**

High-density polyethylene (HDPE) pipes are widely used in various pressurised pipeline systems. This is due to the excellent mechanical and chemical properties of polymers. Almost without exception, polymeric materials are known to exhibit timedependent viscoelastic mechanical behaviour [1]. This property is particularly visible in the case of hydraulic transients, as it induces major dissipation and dispersion of the pressure waves [2]. In many practical applications, accurate computational models predicting pressure oscillations in pipeline systems are required [3]. For this reason, several studies investigating pipe wall behaviour during the water hammer phenomenon have been conducted. Most of the papers on this topic refer to single-pipe systems [4–9]. However, typical fluid distribution networks are composed of serially connected pipes with various inner diameters. Transients in viscoelastic pipes with sudden contractions and expansions have seldom been addressed in the literature. To the authors' knowledge, only [10] investigated the influence of cross-section changes on pressure waves, and [11] studied transients in a series of two polymeric pipes. Recently, in order to numerically simulate water hammer in steel pipe series, an improved junction boundary condition was established [12]. It involves assigning two sets of values, which describe flow parameters, to the connection node, thus causing it to act as two separate nodes. The present paper aims to

**Citation:** Kubrak, M.; Malesi ´nska, A.; Kodura, A.; Urbanowicz, K.; Stosiak, M. Hydraulic Transients in Viscoelastic Pipeline System with Sudden Cross-Section Changes. *Energies* **2021**, *14*, 4071. https:// doi.org/10.3390/en14144071

Academic Editor: Mehdi Esmaeilpour

Received: 2 June 2021 Accepted: 2 July 2021 Published: 6 July 2021

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confirm this method for HDPE pipes. As part of the study, laboratory tests were conducted, designed to record pressure changes at the downstream end of a serially connected HDPE pipeline system. To numerically solve the transient flow equations, the MacCormack explicit scheme was used. The results of the numerical calculations were compared with the experimental data.

This article is organised as follows. After this introduction, the second section gives a brief overview of the theoretical aspects of the viscoelastic behaviour of the pipe structure. In the third section, a one-dimensional numerical model of the water hammer phenomenon in serially connected viscoelastic pipes is presented. The next section looks at the experimental study. Analysis of the experimental data and numerical model validation are presented in the fifth section, and some conclusions are drawn in the final section.
