| Clean energy sources such as wind and solar power are important ways to build a green and low-carbon new power system.However,their volatility,intermittency,and randomness pose significant challenges to real-time balancing of the power system.In this context,choosing the most flexible,mature,and cost-effective hydropower,wind,and solar power for multi-energy complementarity can effectively smooth the output fluctuations of wind and solar new energy generation and promote the high proportion of new energy generation consumption.However,it also puts more stringent requirements on the operational stability of hydropower units,and Francis Turbine will operate frequently under partial load conditions,and the resulting hydraulic instability will become a major bottleneck in the development of Francis Turbine,This paper focuses on the phenomenon of Inter-blade vortex of Francis Turbine under partial load conditions and proposes a multi-objective optimization design method based on geometric parameterization for multiple operating conditions to optimize the design of the impeller blades,improve the hydraulic efficiency of the unit,and suppress the inter-blade vortex structure and its induced unstable pressure pulsation.Finally,through data mining techniques,the impact of design variables on the performance of the Francis Turbine is identified,providing some guidance for future impeller blade design and optimization.(1)Based on the three-dimensional turbulent cavitation model and the time-frequency analysis method of bubble volume,the flow characteristics,spatiotemporal evolution characteristics,and pressure pulsation characteristics of the inter-blade vortex of the Francis turbine under partial load conditions were obtained.The results showed that the helical streamline of the inter-blade vortex mainly comes from the upper crown and flows out from the lower ring.The existence of the inter-blade vortex breaks the symmetry and continuity of the blade pressure distribution,leading to a sudden change in the suction side pressure of the blade,thus reducing the operating efficiency and stability of the water turbine.The spatiotemporal evolution characteristics of the inter-blade vortex show a dynamic cyclic process of birth,development,local collapse,and regeneration,with bubble volume pulsation frequencies of 1.0 times and 1.1 times the rotational frequency.At the same time,all overcurrent components of the water turbine captured low-frequency high-amplitude pressure pulsations,whose frequency is the same as that of the bubble volume pulsation frequency of the inter-blade vortex,indicating a close relationship between the low-frequency high-amplitude pressure pulsations and the bubble volume pulsations of the inter-blade vortex.Therefore,the influence of the inter-blade vortex on the operation of the water turbine is mainly manifested as low-frequency high-amplitude pressure pulsations of the water turbine caused by periodic evolution of the bubble volume,which will pose a serious threat to the long-term safe and stable operation of the water turbine.(2)A multi-objective and multi-operating condition optimization design method for Francis turbine was established based on Latin hypercube experimental design and Kriging approximation model.The inter-blade vortex structure was represented by the iso-surface of the cavitation inception pressure in the runner domain.In order to control the low-frequency and high-amplitude pressure pulsation caused by the periodic evolution of the inter-blade vortex cavity volume,the optimization design of the runner blades of the Francis turbine was carried out.The design variable was the circumferential angle of the runner blade spine,and the objective function was to maximize the hydraulic efficiency and the minimum pressure value in the runner domain under three operating conditions.The results showed that the hydraulic efficiency of the optimized Francis turbine was increased by 0.51%,4.34%and 3.57%respectively compared with that before optimization at the three operating points.The minimum pressure value in the runner domain was also significantly improved.Meanwhile,the optimized design significantly suppressed the inter-blade vortex structure,and the cavity volume was reduced by 88.58%and 78.99%respectively compared with the original design under two operating conditions.The lowfrequency and high-amplitude pressure pulsation of the Francis turbine was almost completely eliminated.The evolution of a small part of the cavity volume in the optimized design only had a local influence on the adjacent area with low amplitude,without spreading to the upstream or downstream flow components of the Francis turbine.(3)Based on the parallel coordinate visualization method and total variance analysis method of data mining technology,the information of the optimization design space of the Francis turbine rotor is explored to investigate the design variables and influence mechanism that significantly affect the performance of the Francis turbine and inter-blade vortex intensity.The results show that the design variables that significantly affect the inter-blade vortex are almost all from the 50%to 100%chord length of the rotor blade.Among them,the blade shape at 75%chord length plays an important role in both the performance of the Francis turbine and the suppression of the interblade vortex,while the blade shape at the outflow edge of 75%chord length plays a decisive role.Furthermore,it was found that when the design variables at the outflow edge of the rotor blade are optimized,the best suppression result of the inter-blade vortex can be obtained,and the outflow edge of the rotor blade is shifted towards the pressure side compared to the original design.Combining with the data mining results,this study verifies the effectiveness of the significant analysis of design variables based on the proposed data mining method,which provides reference for blade design and has certain engineering practical value. |
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