Influence of runner blade number on hydraulic performance and flow control in draft tube of Francis turbine

As a widely used core component of hydropower generation, the stable and safe operation of the Francis turbine plays a very important role in engineering applications. Therefore, the effects of different rotor blade numbers on the hydraulic performance and flow control of the draft tube of the Francis turbine are of great research value. This paper focuses on the rotor blade number 13, 14, 15, 16, and 17 in the prohibited and stabilized operating zones, each of which is taken as a working condition point. (Condition alpha ref -HM and Condition 2 alpha ref -HM). Computational Fluid Dynamics (CFD) numerical simulations were performed and analyzed. In terms of hydraulic performance, the increase in the number of blades increases the efficiency and power of the turbine under Condition alpha ref -HM by 2.26% and 0.0021 MW respectively. The efficiency and power of the turbine under Condition alpha ref -HM is also elevated, with the efficiency reaching a maximum of 91.77% at blade number 15, and the power of the same turbine reaching a maximum of 0.182 MW at runner blade number 13. From the 3D flow analysis of the turbine, the increase in the number of blades does not significantly change the flow state of the turbine's draft tube. By defining the turbulence energy E, the fast Fourier transform of the turbulence energy signals on the two monitoring surfaces of the draft tube is used to obtain its main frequency, and the amplitude and phase at the typical main frequency are visualized, through which we can analyze the vortex band motion state on the two monitoring surfaces of the draft tube, and speculate the change of pressure pulsation of the draft tube. Such an analysis method has a guiding significance for us to improve the performance and stability of the turbine, which can be achieved by increasing or decreasing the number of blades.