Session: 01-04-01 Renewable Energy

Paper Number: 130904

130904 - Investigation on Design Parameters of a Francis Turbine Runner for Optimization Based on 3-D Inverse Design Method 

Hydroelectric power is expected to develop further as a stable and effective renewable energy source shortly. The installation of new small and medium-sized hydropower plants and the replacement of larger existing plants will increase the amount of power generated by hydroelectric plants. The design of hydraulic turbines is essentially made-to-order, involving a complex optimization process that demands sophisticated knowledge of the relationship between 3D internal flow and blade/passage configuration. Furthermore, the process often includes dozens of blade shape design and their evaluation, which leads to significant costs in both time and budget. Previous research presents optimization methods using the 3D inverse method to overcome those difficulties. However, important input parameters of the optimization method, such as the blade loading distribution and the lean angle at the runner inlet, known as the stacking condition, are difficult to determine because of their strong influence on the entire flow field. Therefore, in this paper, the effect of the blade loading distribution and the lean angle at the runner inlet are investigated to understand the internal flow in the turbine runner. Furthermore, a new Francis turbine runner is designed to improve the turbine performance by the optimization method using the 3D Inverse Design Method and Computational Fluid Dynamics (CFD). To evaluate the loss and analyze the internal flow, we apply the Reynolds-Averaged Navier-Stokes equation (RANS) with the SST k-ω turbulence model in CFD analysis. The validation of the CFD calculation is confirmed by a performance test of the directly optimized conventional turbine. For the blade loading distribution, we analyze the modified Rossby number's streamwise distributions obtained from the CFD results of 10 runners with different loading distributions. It confirms that the centrifugal force effect is dominant near the inlet of the runner. Since there is a pressure difference between the crown and band sides on the blade’s suction surface, it is expected that a secondary flow on the meridional plane is caused by both the centrifugal force effect and the pressure gradient. Thus, we conclude it is recommended to design a runner with the after-loading at both the crown and band sides to reduce the pressure gradient and minimize the meridional secondary flow. Brekke theoretically researched the effect of the lean angle on the internal flow. Considering his equation, we confirm that the positive blade lean angle, which is band side forward inclination in the direction of runner rotation, at the runner inlet is effective in reducing the pressure gradient on the meridional plane. Based on the above discussion, optimization of blade loading and the lean angle is achieved through a combination of the inverse method and the Genetic Algorithm (GA) to develop a new runner blade shape. The new turbine’s total loss at the design point is 4.8 [%] less than that of the conventional turbine, as confirmed by the full-domain CFD calculation. To conclude, this investigation of the blade loading and the lean angle helps to understand the complex internal flow in the Francis turbine runner. In addition, the optimization result confirms that designers can use the knowledge, control the secondary flow, and optimize the runner shapes by using the optimization process based on the 3D inverse design method. With the help of this knowledge and the optimization method, designers can now quickly and cost-effectively improve turbine performance.

Presenting Author: Shunsuke Nagata Department of Applied Mechanics and Aerospace Engineering, Waseda University