Modelling Water Hammer Effects in Rising Pipeline Systems Using the PKP Method and the MOC

Waldemar Sradomski, Aneta Nycz () and Marek Skowroński
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Waldemar Sradomski: Department of Technical Systems Operation and Maintenance, Faculty of Mechanical Engineering, Wrocław University of Science and Technology, Wyb. Wyspiańskiego 27, 50-370 Wrocław, Poland
Aneta Nycz: Department of Energy Conversion Engineering, Faculty of Mechanical and Power Engineering, Wrocław University of Science and Technology, Wyb. Wyspiańskiego 27, 50-370 Wrocław, Poland
Marek Skowroński: Department of Energy Conversion Engineering, Faculty of Mechanical and Power Engineering, Wrocław University of Science and Technology, Wyb. Wyspiańskiego 27, 50-370 Wrocław, Poland

Energies, 2025, vol. 18, issue 18, 1-21

Abstract: Water hammer is a critical transient phenomenon in pumping systems, occurring when a sudden change in flow velocity generates pressure waves propagating along the pipeline. This study focuses on the dynamic response of a long rising pipeline subjected to an emergency pump shutdown, with particular emphasis on the sudden release and propagation of hydraulic energy in the form of pressure waves. Such scenarios are typical for mine dewatering and water supply systems with high elevation differences. Two numerical approaches were investigated: the Method of Characteristics (MOC) implemented in TSNet as a reference model, and the Train Analogy Method (PKP) implemented in MATLAB R2024b/Simulink, where the fluid is represented as discrete masses connected by elastic links, enabling the inclusion of pump and motor dynamics. Simulations were performed for two configurations: first–with a check valve installed only at the pump discharge and second–with a check valve at the pump discharge and in the middle of the pipeline. The results demonstrate that both models capture the essential features of water hammer: a sharp initial pressure drop, the formation of transient waves, and pressure oscillations with decreasing amplitude. These oscillations reflect the propagation and gradual dissipation of hydraulic energy stored in the moving fluid, primarily due to frictional and elastic effects within the pipeline. The presence of a check valve accelerates the attenuation of oscillations, effectively reducing the impact of returning waves on the downstream pipeline. The novelty of this study lies in the use of the PKP method to simulate transient flow and energy exchange in long rising pipelines with dynamic pump behavior. The method offers a physically intuitive and modular approach that enables the modelling of local flow phenomena, pressure wave propagation, and system components such as pump–motor inertia and check valves. This makes PKP a valuable tool for investigating complex water hammer scenarios, as it enables the analysis of pressure wave propagation and damping, providing insight into the scale and evolution of energy released during sudden operational incidents, such as an emergency pump shutdown. The close agreement between the PKP and MOC results confirms that the PKP method implemented in Simulink is a reliable tool for predicting transient pressure behavior in hydraulic installations and supports its use for further validation and dynamic system analysis.

Keywords: water hammer; PKP method; MOC; MATLAB/Simulink; TSNet (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2025
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