Combination of a Particle Swarm Optimization and Nelder–Mead Algorithm in a Diffuser Shape Optimization

Abstract

This work focuses on the optimization of a hydraulic turbine diffuser, which is located behind the runner of the swirl turbine. The present paper extends our work in shape optimization using direct methods (namely Nelder–Mead method) and stochastic methods (namely Particle swarm optimization) coupled with CFD simulations. Both methods have their own advantages and disadvantages. Present work focuses on a combination of particle swarm optimization (at the beginning of the algorithm) and Nelder–Mead algorithm (NMA) (at the end of the algorithm). The diffuser will serve as the test case to demonstrate efficient coupling of the mathematical optimization procedure and CFD simulation. The main goal of this test problem is set to maximize the coefficient of pressure recovery c p, which is the main parameter to judge the proper design of the draft tube. Results obtained with this new method will be discussed and their advantages/disadvantages summarized.