Transient Wave Propagation and Reflection in Long Penstocks with Delay Effects and Boundary Layer Damping
DOI:
https://doi.org/10.37134/jsml.vol14.1.11.2026Keywords:
Transient flow, Water hammer, Viscous damping, Wavefront dispersion, Surge protectionAbstract
This study examined wave propagation and reflection in long, pressurised penstocks, ranging from 3 to 4 km, within high-head hydropower systems in Albania to address challenges in transient flow dynamics for enhanced design and operational safety. A modified one-dimensional model based on the Method of Characteristics (MOC) was developed, incorporating wall elasticity, unsteady friction, and wave travel delays, with analytical and numerical simulations conducted to assess their impacts. The results indicated a wave travel delay of 11.7% (3.44 s versus 3.08 s predicted by the classical model), accompanied by a phase shift of 0.33 rad at 0.13 Hz. Peak surge pressures were also reduced by 17.8% (176 m instead of 214 m), with cumulative attenuation reaching up to 26% over an 85 s interval. This damping effect was attributed to the progressive growth of the viscous boundary layer, reaching a thickness of ~0.057 m within 12 s, as well as the influence of unsteady friction. In pumped-storage operating scenarios, the model further showed that negative pressures were alleviated by 20% (-43 m compared with -54 m), highlighting the combined role of delay and damping mechanisms in surge wave mitigation. The study concludes that integrating these factors is essential for optimising surge protection, improving turbine regulation, and ensuring structural integrity in Albania’s high-head hydropower systems. Hydropower engineers and system designers in Albania can use the research results to optimise surge protection, enhance turbine regulation, and improve the structural safety of long penstock systems in high-head hydropower plants.
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