Influence of leading-edge cavitation on impeller blade axial force in the pump mode of reversible pump-turbine
Introduction
Reversible pump-turbine is widely used in pumped storage power station for electricity regulation. It is flexible in converting between generating (turbine) mode and storage (pump) mode [1,2]. However, internal flow stability becomes a problem in operation due to the high flexibility [3,4]. Cavitating flow is commonly seen in pump mode as unstable blade leading-edge cavitation. It also causes flow instability and has been received researches [[5], [6], [7]]. Recently, an important issue is found in the model test of pump-turbine in pump mode. The axial force of impeller strongly changes when blade leading-edge cavitation is happening and developing. It will increase the stability risk of the thrust bearing and shaft system of the pump-turbine unit [8,9].
As widely known, cavitation usually starts on blade leading-edge due to local pressure drop [10,11]. In pump mode, the impeller blade leading-edge is in low pressure because of both the impeller working mechanism and local flow striking. If cavitation number is high, cavitation scale may be small. Cavitation bubble will attach on the blade surface as stable cavity [12]. With the decreasing of cavitating number, cavitation scale gradually increases and covers larger and larger area on blade [13]. The backflow jet near wall will also break the stable cavity [14]. It makes cavitation bubble separate away from blade surface and move periodically with main flow [15,16]. The existence of cavitation on blade near leading-edge will change the blade loading [17]. For reversible pump turbines, the impeller is designed like centrifugal pump. For higher efficiency, blade is usually twisted and have large projection area in axial direction [18]. The axial force can be somehow affected by cavitation but still lack of investigation.
In the engineering standard of pumps and turbines, cavitation is commonly described using critical cavitation standard [19]. The change of energy performance like efficiency and head will be monitored when cavitation scale is changing. Usually, a specific proportion (0.5%, 1% or 3%) is used as the criterion of critical cavitation [20]. It means that cavitation bubbles exist before reaching critical cavitation. In actual pump cases and pump-turbine cases, the leading-edge cavitation is found covering at most 1/3 streamwise distance on blade in some specific channels [[21], [22], [23]]. Currently studies mainly care the influence of cavitation on efficiency, head, pressure fluctuation, noise and vibration [[24], [25], [26], [27]]. However, the influence of cavitation on axial force is not deeply studied.
For pumps and reversible pump-turbines, the impeller axial force has three main parts including the axial force on hub, axial force on shroud and axial force on blade [28,29]. The axial force on hub is because of the pressure difference between hub leakage and blade channel. Similarly, the axial force on shroud is because of the pressure difference between shroud leakage and blade channel [30]. These two force parts have not huge difference but there is another part that the axial force on blade which can be much bigger. It generates due to the pressure difference between blade suction surface and pressure surface. This pressure difference is also called blade loading and used for evaluating the performance of pump or pump-turbine [31]. The axial component of the blade loading will be the most important component of axial force and cannot be balanced without reducing the impeller performance [32]. If cavitation which may be in a small scale covers the blade leading-edge, the axial force will be influenced and need further consideration.
In this study, the influence of cavitation on impeller axial force of pump-turbine is qualitatively found in model test. However, it is very difficult to quantitatively measure it and compare model scale with prototype scale. Thus, using computational fluid dynamics (CFD) will be a good way in quantitatively evaluating this axial force problem under cavitating flow and understanding the mechanism [[33], [34], [35]]. This study will give a good reference for researchers and designers to avoid the over-loading of thrust bearing especially in pump-turbine’s pump mode. It will help enhancing the stability and security of the shaft-system of pump-turbine unit. It also helps researchers to build and adopt a better standard for cavitation in hydraulic turbomachinery.
Section snippets
Pump-turbine parameters
In this study, a pump-turbine model is taken as the research object. The design parameters and performance parameters of the model are shown in Table 1.
The specific speed of pump-turbine nq is defined as:
The specific speed nq of the pump-turbine model in this study is 40.41.
In order to compare with other similar specific speed pump-turbines, the hydraulic performance parameters are dimensionless. The flow rate coefficient Cϕ and head coefficient Cψ are calculated according to the
Experimental cavitation performance analysis
Experimental study is firstly conducted to understand the cavitation behavior of this model pump-turbine. Fig. 3 shows the measured cavitation performance curves including the inception and critical cavitation. For inception cavitation, the inception cavitation coefficient Cσi is smaller at design-load and bigger at partial and over load conditions. It means that cavitation is difficult to happen under design condition but easier to occur when condition is off-design. For critical cavitation,
Blade axial force characters
Based on numerical simulation, the variation of blade axial force with cavitation coefficient is got as shown in Fig. 4. The horizonal axis is the cavitation coefficient Cσ. The vertical axis is a relative value that Fz/Fz∗ where Fz∗ is the blade axial force in cavitation-free status. Seen from this figure, the simulated cavitation coefficients from inception to critical match the experimental data well. The variation law of axial force from inception to critical cavitation is similar at
Conclusions
By investigating the influence of leading-edge cavitation on impeller blade axial force in the pump mode of reversible pump-turbine, conclusions can be drawn as follows:
- (1)
The variation of impeller blade axial force is found in cavitation developing process. From cavitation-free to small scale cavitation, impeller blade axial force increases by at most 5%. From small scale to large scale or even critical cavitation, impeller blade axial force rapidly decreases by at most 13%.
- (2)
Cavitation on impeller
CRediT authorship contribution statement
Di Zhu: Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Validation, Visualization, Writing - original draft. Ruofu Xiao: Conceptualization, Formal analysis, Funding acquisition, Investigation, Methodology, Project administration, Software, Supervision, Writing - review & editing. Weichao Liu: Conceptualization, Funding acquisition, Investigation, Methodology, Project administration, Resources, Supervision, Writing - review & editing.
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgement
The authors would like to acknowledge the financial support of National Natural Science Foundation of China. This study is funded by National Natural Science Foundation of China grant number 51836010, National Natural Science Foundation of China grant number 51879265 and Open Research Fund Program of State Key Laboratory of Hydroscience and Engineering grant number sklhse-2019-E-01.
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