Investigation of Efficient Optimization Approach to the Modernization of Francis Turbine Draft Tube Geometry

Abstract

The installation of new and revitalization of existing hydropower requires the optimal design of hydraulic turbine parts, which were previously mostly based on simplified analytical methods and engineering practices. With the increase in computational power, optimization methods now present an effective approach to the improvement of the geometry of turbine parts, thus enabling fine geometry-tuning adjustments of site specifics. However, despite continually increasing computational power, such numerical optimizations still require substantial resources and time. Therefore, in the proposed paper, extensive analysis of different numerical simplifications was conducted to determine the best trade-off between accuracy and the required computational resources for draft tube optimization. Additionally, the influence of geometry parametrization in terms of greater geometry flexibility, different goal functions, and optimization parameters was investigated. Within the considered constraints, a novel draft tube geometry was obtained, with the elbow displacements toward the draft tube exit, a shape that could not be obtained with the usual draft tube parametrization. It was also observed that geometry improvements for a single operating point did not provide improvements for other operating points. The obtained findings regarding the numerical and optimization setup can be used as guidelines for future optimization research, where multiobjective optimization for multiple operating points should be further investigated.