Physics-based Surrogate Optimization of Francis Turbine Runner Blades, Using Mesh Adaptive Direct Search and Evolutionary Algorithms

Abstract

A robust multi-fidelity optimization methodology has been developed, focusing on efficiently handling industrial runner design of hydraulic Francis turbines. The computational task is split between low-and high-fidelity phases in order to properly balance the CFD cost and required accuracy in different design stages. In the low-fidelity phase, a physics-based surrogate optimization loop manages a large number of iterative optimization evaluations. Two derivative-free optimization methods use an inviscid flow solver as a physics-based surrogate to obtain the main characteristics of a good design in a relatively fast iterative process. The case study of a runner design for a low-head Francis turbine indicates advantages of integrating two derivative-free optimization algorithms with different local-and global search capabilities. Keywords:Physics-based surrogate optimization, Francis turbine runner blade, multi-fidelity algorithm Hydraulic Turbine Design Optimization ProcessBig changes in global energy demand, increasing environmental concerns, and growth potential of cost-efficient hydroelectric energy, have recently resulted in more demand to design hydraulic turbines which are more efficient and durable. As design challenges are getting more complex, runner designers rely more than ever on engineering and simulation tools, especially computational fluid dynamics (CFD), to obtain reliable designs with a competitive time and cost. Although runner designers already employ CFD tools to evaluate their designs, there is a strong need to integrate CFD analyses more tightly in the design chain using efficient optimization methods to obtain more efficient design processes.The full range of CFD methods have been utilized in the optimization of hydraulic turbine runner blades. Low-fidelity inviscid models (e.g. potential flow) have been employed by some researches such as Holmes and McNabb [1]. However, they are not accurate enough in their prediction of flow behavior, mainly due to lack of physics. High-fidelity viscous models have been used alone to optimize the runner as well (e.g. using turbulent RANS solvers, by Franco-Nava et al. [2] and Pilev et al. [3]); but they are too expensive and slow for iterative industrial runner design processes. To reduce high-fidelity analyses in the optimization loop, surrogatebased optimization approaches have been increasingly employed by researchers, using either mathematical surrogates or physic-based surrogates. Mathematical surrogates are computationally inexpensive approximation models constructed from a given number of highfidelity evaluations. For instance, artificial neural network was applied by Derakhshan et al. [4] to reduce Navier-Stokes solver calls during the optimization of a low-head axial hydro turbine by an evolutionary algorithm. Another popular mathematical surrogate, radial basis functions, was employed by Georgopoulou et al. [5].Although those mathematical surrogates have been used for blade shape optimizations, they still require a large number of high-