Smoothed Particle Hydrodynamics with Unsteady Friction Model for Water Hammer Pipe Flow

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Abstract
Water hammer flows are almost simulated by using the Eulerian mesh methods including the most popular method of characteristics (MOC). In this paper, smoothed particle hydrodynamics (SPH) of the Lagrangian meshless method are introduced to simulate transient pipe flow considering the unsteady friction model (UFM). One special boundary treatment with virtual and mirror particles is proposed to improve the inherent boundary deficiency. Pressure results predicted by the SPH model are compared with those obtained from MOC scheme and experiments in a reservoir-pipe-valve system. The proposed model can accurately reproduce the experimental pressure histories. As the Courant number decreases (less than one), the SPH method is more accurate and more robust without numerical attenuation, whereas the Godunov scheme and MOC scheme produce obvious numerical damping. When the Courant number is less than one, for a similar level of accuracy, the SPH method could be more efficient than the Godunov scheme and MOC scheme. It is found that implicit and explicit solution schemes of the unsteady friction model, number of particles, artificial viscosity, smoothing length, and smoothing function significantly influence numerical stability and accuracy. Artificial viscosity can eliminate spurious numerical oscillations but may cause numerical dissipations. Cubic spline function and smoothing length close to the particle distance are suitable for the proposed model.

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