*Article* **Hydraulic Transients in Viscoelastic Pipeline System with Sudden Cross-Section Changes**

**Michał Kubrak 1, Agnieszka Malesi ´nska 1, Apoloniusz Kodura 1,\*, Kamil Urbanowicz <sup>2</sup> and Michał Stosiak <sup>3</sup>**


**Abstract:** It is well known that the water hammer phenomenon can lead to pipeline system failures. For this reason, there is an increased need for simulation of hydraulic transients. High-density polyethylene (HDPE) pipes are commonly used in various pressurised pipeline systems. Most studies have only focused on water hammer events in a single pipe. However, typical fluid distribution networks are composed of serially connected pipes with various inner diameters. The present paper aims to investigate the influence of sudden cross-section changes in an HDPE pipeline system on pressure oscillations during the water hammer phenomenon. Numerical and experimental studies have been conducted. In order to include the viscoelastic behaviour of the HDPE pipe wall, the generalised Kelvin–Voigt model was introduced into the continuity equation. Transient equations were numerically solved using the explicit MacCormack method. A numerical model that involves assigning two values of flow velocity to the connection node was used. The aim of the conducted experiments was to record pressure changes downstream of the pipeline system during valve-induced water hammer. In order to validate the numerical model, the simulation results were compared with experimental data. A satisfactory compliance between the results of the numerical calculations and laboratory data was obtained.

**Keywords:** hydraulic transients; water hammer; viscoelasticity; cross-section change
