A robust multi-fidelity design optimization methodology has been developed to integrate advantages of high- and low-fidelity analyses and alleviate their weaknesses. The aim of this methodology is to reach more efficient turbine runners with respect to different constraints, in reasonable computational time and cost. In such a framework, an inexpensive low-fidelity (inviscid) solver handles most of the computational burden by providing data for the optimizer to evaluate objective functions and constraint values in the low-fidelity phase. An open-source derivative-free optimizer, NOMAD, explores the search space. Promising candidates are selected among all feasible solutions using a filtering process. The proposed filtering process accounts for Pareto optimal solutions and considers solutions which are different in the design variable space and are dominant in their local territories. A high-fidelity (viscous) solver is used outside the optimization loop to accurately evaluate filtered solutions. Accurate information achieved by high-fidelity analyses is also employed to recalibrate the low-fidelity optimization.
The developed methodology demonstrated its ability to redesign a Francis turbine blade for a given best efficiency operating condition. The original and optimized cases were evaluated and compared for a complete range of operating conditions by calculating the efficiency curves and losses of different components. The optimal blade has provided an efficient runner for the given operating conditions considering the design constraints.