Viscoelasticity of pipes and the effect of unsteady friction during water hammer using the Smoothed Particle Hydrodynamics (SPH) method

Abstract

A water hammer is a rapid pressure surge in pipelines caused by sudden flow velocity changes, such as when valves close. These surges can result in serious failures in fluid transport systems if not controlled. Traditional methods, like the Method of Characteristics (MOC), help predict water hammer but face challenges, including Courant number constraints and mass and momentum balance issues in complex geometries. The Smoothed Particle Hydrodynamics (SPH) method offers a promising alternative, enabling mesh-free modeling and improved flexibility for simulating these hydraulic transients. This study employs an in-house code based on the Corrected Smoothed Particle Hydrodynamics (CSPH) method that uses kernel function renormalization for boundary treatment. Unsteady friction models are included to enhance accuracy in modeling water-hammer in metal pipes. For plastic pipes, this approach is combined with a mechanical Kelvin-Voigtbased viscoelastic model. The numerical setup consists of a reservoir-tube-valve system to validate the SPH-based methods. Simulations assess the effects of unsteady friction and viscoelasticity on pressure wave propagation. Response Surface Methodology (RSM) is used to identify optimal configurations and how numerical parameters affect the simulations. Results show that CSPH effectively captures the wave pressure damping ratio but fails to estimate wave speed due to momentum loss from density reductions in renormalization. To correct this, one introduces the Compensated CSPH (CCSPH), which accurately simulates pressure wave damping ratios, wave speeds, and waveforms in elastic and viscoelastic pipes. One also validated an in-house Method of Characteristics (MOC) code for comparison with CCSPH. Both methods demonstrated similar accuracy and computational efficiency.