Multi-Objective Optimization for Francis Turbine Runner Using Genetic Algorithm

Abstract

A multi-objective optimization system for a Francis turbine runner that uses a genetic algorithm was developed. Francis turbine is widely used because of its flexibility of meriodinal geometry. However, since a runner of a Francis turbine consists of fixed blades, it can show a high performance in a narrower range of operating conditions compared with diagonal and axial hydraulic turbines. Thus, the design of a Francis turbine runner needs plentiful design experience. The aim of this study is to develop an automatic design system for a Francis turbine runner and evaluate its availability. This system optimizes six objective functions: runner efficiency, swirling losses at partial load point and over load point, minimum pressure coefficient on the blade surface, deviation of runner head, and area deviation of outlet opening from the baseline design. The runner head deviation represents the difference from the required specifications. The optimization procedures are as follows; first, an initial design population to create runner geometries was generated by Latin hypercube sampling method. Next, runner geometries were created in accordance with the design variables of the initial design population. Then, objective functions were evaluated. Since the area deviation of outlet opening has a strong correlation with the runner head deviation and can be calculated without computational fluid dynamics (CFD) analysis, we tried to reduce the number of CFD evaluations by using this correlation. For all runner geometries, the area deviation of outlet opening was calculated, and mesh generations and CFD analysis of those that exceeded a deviation threshold were skipped. The rest of the objective functions were evaluated by CFD analysis. Analysis models at design point, partial load point, and over load point were created. In the CFD stage, steady and single-phase analysis was executed to evaluate objective functions. Finally, the population of the next generation was created by using a multi-objective genetic algorithm. By iterating these procedures, optimized runners superior to the baseline design were obtained efficiently and automatically.