CFD-based design and optimization of an elbow type draft tube for hydraulic turbines

Draft tube is an essential part of Francis type turbines. Its design is based not only on performance and efficiency (maximizing the recovery of the kinetic energy into the static head at the turbine runner exit with a minimum head loss), but also on other considerations, such as excavation depth and concreting. Optimization desigm process is used in order to obtain an optimum design which satisfy these conflicting requirements. In this work, a CFD-driven surrogate-based design optimization study is performed to optimize an elbow type draft tube. 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. Latin Hypercube Sampling method is used to construct four different types of surrogate models (standard second order polynomial response surface, Kriging, nonparametric regression and neural network). Two different multi-objective search algorithms (screening and multi-objective genetic algorithm) are utilized to find an optimized solution which maximizes the pressure recovery factor and minimizes the head loss. It is found that, pressure recovery factor can be increased by 4.3%, and head loss can be reduced by %20 reduction compared to the initial CFD aided design. Latin Hypercube Sampling design of experiment, standard second order polynomial response surface surrogate model and MOGA optimization algorithms are found to be the most suitable choices for an accurate CFD-driven surrogate-based design of the draft tube. A second order polinomial regression model is obtained for pressure recovery factor of elbow type draft tubes in terms of undimensional and independent parameters in specified limits. The model is verified and it can predict the pressure recovery factor with an error of 8%. A genetic optimization example is performed using this model. The regression model can predict the pressure recovery factor with an error of 7.2% when compared to CFD.