Large Water Hammer Pressures Due to Column Separation in Sloping Pipes (Transients, Cavitation).

Abstract

Liquid transients involving column separation occur in pipelines when the pressure drops to liquid vapor pressure. Consequently, localized vapor cavities or distributed vaporous cavitation may occur. Cavity collapse may result in short duration pressure pulses superimposed on water hammer waves, which exceed the Joukowsky pressure rise. Most previous experimental studies exhibit pressure traces with maximum pressures due to cavity collapse that attenuate with time. Additionally, existing numerical models exhibit deficiencies in modeling column separation. The primary objective of this study is to provide a better underst and ing of the occurrence of short duration pressure pulses associated with column separation. An experimental apparatus has been constructed comprising an upstream reservoir, a 36.0 meter pipe, and a downstream fast-closing ball valve. A set of experimental results are presented that exhibit short duration pulses of various magnitudes and widths. The results show the change in characteristics of the short duration pressure pulses as the velocity increases. With higher velocities, which produce extensive distributed vaporous cavitation, the nature of the transient changes. Pressure pulses are no longer present. Pressure traces exhibit much sharper high frequency and low amplitude variations in the form of spikes, following the elimination of a vaporous region. There is also attenuation of the peak at the pressure rise. The analytical development of an improved mathematical model describing water hammer regions, vaporous cavitation regions, and intermediate vapor cavities is presented. The incorporation of intermediate vapor cavities that may form due to the interaction of two low pressure waves is an important addition to the analytical development. A numerical model has been developed to implement the theory. The results compare favorably with the experimental results. Short duration pressure pulses are faithfully reproduced for low velocities, and attenuation of the pressure rise at the valve is predicted for the higher velocity case. The physical high frequency, low amplitude spikes are reproduced in the model. For comparison, the results from two commonly used numerical models are also presented. These models predict the smaller velocity cases quite well, however, the attenuation of the first pressure rise for the higher velocity case is not predicted.