Multilevel design optimization of hydraulic turbines based on hierarchical metamodel-assisted evolutionary algorithms

In this paper, an efficient hydraulic optimization procedure is presented and applied to the design of hydraulic turbines. For computationally expensive industrial design optimization problems, an advanced optimization tool (EASY software) and a fast CFD evaluation tool are required. EASY optimization software is a Hierarchical Metamodel-Assisted Evolutionary Algorithm (HMAEA) that can be used in both single- (SOO) and multi-objective optimization (MOO) problems. In order to minimize the CFD solver calls during the optimization design, the MAEA rely on local metamodels, trained on the fly, that are used to identify the most promising members in each population and then only these are to be re-evaluated by the CPU costly CFD solver. For additional economy in the CPU cost, the hierarchical (two-level) optimization scheme is used in this paper, where at each level, a different evaluation tool, a low and a high fidelity specific software, can be linked. The low level utilizes a low-CPU cost and low-accuracy tool to explore the design space with a minimum impact to the wall clock time and the high level, using the high fidelity, high-CPU cost tool is used to exploit the information from the low level. For the applications presented in this paper, the high fidelity model is an incompressible Navier-Stokes equation solver and the low fidelity model is based on the solution of the incompressible Euler equations. In order to optimize the geometry of hydraulic machines, an in-house automatic geometry and mesh generation tool has been integrated in the optimization tool chain. In what follows, 2 three-objective design optimization problems of 3D Francis hydraulic turbines are presented. The optimization objective functions concern the 'quality' of the runner outlet velocity profile, the cavitation behavior and efficiency of the runner. The optimization results of the hydraulic turbine components along with the performance of the presented optimization procedure are shown in the paper.