CFD-driven surrogate-based multi-objective shape optimization of an elbow type draft tube

Abstract Draft tube is the part of Francis turbines which is used to both discharge water and recover kinetic energy at the exit of the runner. A design optimization study of an elbow type draft tube based on the combined use of Computational Fluid Dynamics (CFD), design of experiments, surrogate models and multi-objective optimization is presented in this study. The geometric variables that specify the shape of the draft tube are chosen as input variables for surrogate models and the pressure recovery factor and the head loss are selected as output responses. It is determined that, pressure recovery factor, which is the main performance parameter, can be increased by 4.3%, and head loss can be reduced by %20 compared to the initial CFD aided design. Pressure recovery factor, is represented with a second order polynomial regression model in terms of the geometrical parameters based on the optimization results. The verification of the model is also provided by comparison with CFD results for different draft tubes other than that are used in the development of the model. The model is verified using 30 different design points and it can predict the pressure recovery factor with an error of less than 8%. This model allows the fast and correct design and optimization of elbow type draft tubes, without the need for further CFD simulations.