Investigation of water column separation induced by pressure pulsation based on critical cavitation rate model

Abstract

Significant pressure fluctuation may exists at the inlet of the draft pipe during load shedding of water pump and turbine sets. When the tail-water level is low, the minimum water hammer pressure at the inlet of the draft pipe set is higher than evaporation pressure; however, the overall pressure after superposition with pulsating pressure may reach the evaporation pressure in an instant. In these cases, it is unknown if a cavity is formed or water column separation is induced. It is also unknown how frequency and amplitude of the pulsating pressure affect the formation of cavity or water column separation. However, in terms of the physical formation of water column separation, liquid pressure reaching evaporation pressure is only the necessary condition of water column separation rather than a sufficient condition because the growth and aggregation of cavitations take time. In addition, water column separation could be induced only when the cavitation rate in the water reaches a specific value and gas-liquid relative motion occurs. In this study, based on the uniform cavitation distribution model, the critical of flow velocity gradients are calculated both in front and at the back of the section and are the sufficient condition of water column separation. This study uses the criterion of when the ratio of the vaporous cavitation volume to the volume of the pipe segment with a length of Δx exceeds a critical cavitation rate for classifying water column separation segments and non-water column separation segments. In water column separation segments, a concentrated vaporous cavitation model is used for calculation; however, dynamic meshes should be applied for tracking the change of vaporous cavitations. In the non-water column separation segments, the vaporous cavitation volume can be calculated according to the continuity equation but is converted into a cavitation rate in the pipe segment and substituted into gas-liquid two-phase equation to calculate wave velocity. Next, a case study was performed on a pipe-valve system. By taking into account the pulsating pressures with different frequencies and amplitudes on the downstream side in the valve closing process, water column separation and merging processes were analyzed and the change in flows, cavitation volumes and pressures on various sections and their laws during the transient process were concluded.