Kinematic optimization of a flapping foil power generator using a multi-fidelity evolutionary algorithm

For hydrodynamic optimization using computational fluid dynamics methods, the high computational cost impedes the use of evolutionary algorithms since they require evaluation of numerous solutions. In this paper, a multi-fidelity evolutionary algorithm, implemented with a dynamic stall model and a modified discrete vortex method, is used to find values of kinematic parameters for high energy extraction performance from a flapping foil. A single objective problem with two variables is first used to illustrate the benefits of the multi fidelity optimization strategy. Then the efficiency and the power output characterized by five design variables are optimized by the multi-fidelity evolutionary algorithm. The nondominated solutions obtained from the exercise are evaluated by the lattice Boltzmann method for detailed analysis. The results show that despite the use of low fidelity models and limited budget of computational resources, the multi-fidelity strategy is capable of finding kinematic conditions suitable for high energy extraction performance from a flapping foil. In addition, detailed flow analysis reveals that high energy extraction performance is associated with the detachment of the leading edge vortex near stroke reversal, resulting in a horseshoe-shaped vorticity wake with a width approximating the swept distance of the foil behind the turbine plane.