Effect of Boundary on Water Hammer Wave Attenuation and Shape

Abstract

The present study develops a refined water hammer model by postulating the presence of a water jet within the reservoir as the water hammer wave is reflected at the pipe inlet. The waterjet leads to a new boundary expression that induces a smoothing effect on the pressure wave front by introducing a smoothing factor, which is determined by minimizing the difference between pressure histories predicted numerically and those measured experimentally. The proposed boundary expression is applied in conjunction with the quasi-steady, the Brunone, and the Zielke friction water hammer models and is shown to more accurately replicate the peak pressure magnitudes, pressure wave shape, and the phase shifting when compared to experimental results for a variety of pipe systems and steady flow conditions. Using the quasi-steady and the Brunone models, the study shows that both the friction stresses and the proposed boundary expression attenuate the wave amplitude. However, only the proposed boundary expression smoothens the pressure distribution and delays the wave reflection in a manner consistent with experimental results. While the conventional Zielke model is shown to attenuate and smoothen the pressure distribution, the proposed boundary expression is shown to introduce additional damping and further phase shifting.