The pumped-storage hydropower station is the most reliable, economic, long-term, large capacity, and mature energy storage technology in the power system, and it is an important component of renewable energy. Cavitation and water column separation of a pumped storage unit are important and widely researched factors in the safe and stable operation of a unit. This study focused on the evolution of water column separation of a pump turbine and its relationship with the pressure distribution of the cross section of a draft tube as well as the pressure pulsation characteristics of different measuring points in the cross section of the draft tube. A pumped storage experimental platform that can realize water column separation is established, and experiments with different opening angles are carried out. The results show that there are three factors that impact water column separation and cavitation: gas nucleus, vaporization pressure, and duration of vaporization pressure. Water column separation is the development and continuation of cavitation. The difference between the center pressure of the vortex rope and the wall pressure is large, reaching 2.23 m at a large opening. The pressure fluctuation amplitude of the wall measuring point is greater than that of the other measuring points in the same cross section, but the frequency characteristics are the same. In the transition process, the pressure pulsation amplitude of the liquid column bridging is the largest, and the largest pressure pulsation amplitude can reach 4.18 m at a small opening.

Pressure fluctuation characteristics of a pump turbine in a draft tube: New insight into water column separation

Investigation on multiscale features of cavitating flow in convergent-divergent test section using Eulerian-Lagrangian method

A water hammer is an important natural phenomenon that can be used to fracture rock with enhanced local water pressure. The oscillatory injection of a column of water can be used to make a pipe water hammer. However, the optimal injection frequency to create a water hammer has not yet been found. The main reason for this is that the distribution of fluid pressure and its variation are unclear inside a pipe. In this study, we demonstrate for the first time that there can be significant supercharging phenomena and a law governing their appearance in a water-filled pipe. We first find the optimal pulse frequency to reproduce the supercharging process. We also clarify the supercharging mechanism at an optimal frequency. First, a simplified pipe model is adopted, and weakly compressible Navier–Stokes equations are developed to simulate the flow of water in pulse hydraulic fracturing (PHF). The computation code is developed using the MacCormack method, which has second-order accuracy in time and space. The computation codes and program are validated using experimental data of weakly compressible flows. Then, the square pulse effects are studied inside a pipe, including the effects of pulse frequency, amplitude, pipe length, diameter, and wave speed. Finally, a new universal frequency model is built to describe the relationship among optimal pulse frequency, wave speed, and pipe length. The results show that in square PHF, there is a family of frequencies for which the fluid peak pressure can be significantly enhanced, and these frequencies include the optimal pulse frequency. The optimal frequency of a square pulse depends on the pipe length and wave speed. At the optimal pulse frequency, the maximum peak pressure of the fluid can be increased by 100% or more, and cavitation occurs. These new landmark findings are very valuable for understanding pulse supercharging in an internal water wave. In addition, a new universal frequency model is built to predict optimal pulse frequency. This study identifies an evolution law of peak pressure inside a pipe and proposes a practical frequency-control model for the first time, which can provide a theoretical guide for PHF design. 

Pulse supercharging phenomena in a water-filled pipe and a universal prediction model of optimal pulse frequency

Abstract Considering the discontinuous square pulse wave and continuous sine pulsating wave, we report a distinctive supercharging phenomenon of fluid in a water-filled semi-enclosed pipe and reveal the supercharging regularity. We demonstrate that there can be significant supercharging phenomena at the pipe end-face if the water is periodically injected at the pipe inlet with certain frequency. Compared to the traditional pulsating injection method, the present injection strategy can remarkably enhance the peak pressure of the water at the end face of the pipe. We explained this phenomenon by numerical simulations based on the computational fluid dynamic method. It’s found that there is a quantitative relationship between the optimal pulse frequency, pipe length and wave speed. The proposed frequency model is suitable for the multi-waveform, such as sine wave, square wave and arcuate wave. The fluid pressure at the pipe end-face intermittently increases and the end-face peak pressure is largest when the inlet injection frequency equals to the optimal frequency. 

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Pulse and pulsating supercharging phenomena in a semi-enclosed pipe

The transient process accompanied by extreme acceleration in the conical sections of hydraulic systems (e.g., draft tube, diffuser) can induce large cavitation bubbles both at the closed ends and in the bulk liquid. The collapses of the large cavitation bubbles can cause severe damage to the solid walls. We conduct experiments in the tubes with different conical-frustum shaped closed ends with the `tube-arrest' method and observe bubbles generated at these two locations. For the bubbles generated at the close end of the tube, we propose the onset criteria, consisting of two universal non-dimensional parameters Ca1 and Ca2, of large cavitation bubbles separating the water column. We investigate their dynamics including the collapse time and speed. The results indicate that the larger the conical angle, the faster the bubbles collapse. For the bubbles generated in the bulk liquid, we numerically study the collapse time, the jet characteristics and the pressure pulse at bubble collapse. We observe a much stronger jet and pressure pulse of bubbles in tubes, comparing with a bubble near an infinite plate. Our results can provide guidance in the design and safe operation of hydraulic machinery with complex geometries, considering the cavitation during the transient process.

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Large cavitation bubbles in the tube with a conical-frustum shaped closed end during a transient process

During the transient processes in load rejection in a pumped-storage system, water column separation (WCS) can occur in the draft tube when the local pressure is less than the vapor pressure. The reverse water hammer due to water column bridging affects the safety of the unit and the tailrace tunnel. However, what are the conditions that trigger WCS? What is the physical mechanism? These questions have not been elucidated experimentally. Therefore, it is necessary to investigate the conditions that lead to WCS and the impact of the reverse water hammer generated by WCS bridging on the stability of the unit. In this study, a semi-open test rig was modified by installing a variable-frequency pump to reduce the static pressure, resulting in a cavitation vortex in the draft tube. The static pressure and the water hammer pressure derived from load rejection cause the pressure at the draft tube wall to fall below the vapor pressure for some time, interrupting the flow in the draft tube. This is a typical case of WCS in a pump turbine. If the pressure in the draft tube does not remain at the minimum pressure for long enough, imperfect water column separation may occur with bubble groups. The amplitude of the pressure pulsations during the initial and development stages was (−0.2 m, 0.2 m). It was 4.96% of the initial static pressure. Thus, the pressure fluctuations have a negligible effect on WCS.

Experimental study of cavitating vortex rope and water column separation in a pump turbine

Evolution mechanism of water column separation in pump turbine: Model experiment and occurrence criterion

The occurrence of hump instability in pump mode within a pump turbine poses a significant challenge to the safe and stable operation of Pumped Storage Power Plants (PSPP). To achieve more precise numerical simulations, this paper establishes a weakly compressible model of water based on the Tait equation. Using this model, it is discovered that the onset of hump instability is closely linked to an increase in hydraulic losses induced by stalled rotation within the diffuser. Then, a flow control approach employing water injection into the guide vanes of a pump turbine is proposed in order to suppress flow instabilities and optimize the hump region. The findings reveal that the water injection approach can mitigate hydraulic losses, suppress unstable structures, and diminish the pulsation amplitude within the diffuser, ultimately delaying the emergence of the hump region to lower flow mass conditions. This study is helpful in widening the range of the safe and stable operation of pump turbines in pump mode.

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Tao Peng

Papers

Experimental study of cavitating vortex rope and water column separation in a pump turbine

Pressure fluctuation characteristics of a pump turbine in a draft tube: New insight into water column separation

Evolution mechanism of water column separation in pump turbine: Model experiment and occurrence criterion

The Suppression of Hump Instability inside a Pump Turbine in Pump Mode Using Water Injection Control