Multi-objective shape optimization of Francis runner using metamodel assisted genetic algorithm

Abstract

Nowadays evolutionary optimization techniques become an integral part of the design process of hydraulic turbine runners. For optimization the shape of the runner is parameterized by a set of geometrical parameters. The objective functions of each runner geometry, being the efficiency and cavitation performance, are evaluated through CFD analysis of 3D flow-field. As usual, some kind of genetic algorithm is used for searching the Pareto front, due to its inherent possibility of parallel evaluation of different runner variants within one generation. This approach requires extensive CFD computations of hundreds and thousands of runner variants. In order to speed up the optimization process a metamodel (approximate, surrogate model) can be utilized. The metamodel provides an approximation of true dependency of the objective functions on the design parameters. The metamodel is built based on the known objective functions for some initial set of points randomly taken form the design space. Once built, it can be used to replace time consuming CFD computations during the optimization process. In the present paper a metamodel, based on Gaussian processes, is implemented and integrated into a multi-objective genetic algorithm. The obtained algorithm is applied for shape optimization of the Francis turbine runner. The number of the design parameters varied from 4 to 24. The objective functions are multi-point efficiency and cavitation characteristics. True values of the objective functions are evaluated using Reynolds averaged Navier-Stokes computations of the flow field in a reduced turbine domain, including wicket gate, runner and draft tube. These values are used to train the initial metamodel. In order to enhance predictive capabilities of the metamodel, it is retrained periodically during the optimization loop. The results of metamodel-assisted optimization runs are compared to that obtained without metamodel. It is shown that application of metamodel significantly reduces the number of actual CFD computations even for high number of design parameters and thus speeds up the overall optimization process.