Multifidelity kinematic parameter optimization of a flapping airfoil.

We construct a multifidelity framework for the kinematic parameter optimization of flapping airfoil. We employ multifidelity Gaussian process regression and Bayesian optimization to effectively synthesize the aerodynamic performance of the flapping airfoil with the kinematic parameters under multiresolution numerical simulations. The objective of this work is to demonstrate that the multifidelity framework can efficiently discover the optimal kinematic parameters of the flapping airfoil with specific aerodynamic performance using a limited number of expensive high-fidelity simulations combined with a larger number of inexpensive low-fidelity simulations. We efficiently identify the optimal kinematic parameters of an asymmetrically flapping airfoil with various target aerodynamic forces in the design space of heaving amplitude, flapping frequency, angle of attack amplitude, and stroke angle. Notably, it is found that the angle of attack can significantly affect the magnitude of aerodynamic forces by facilitating the generation of the leading-edge vortex. In the meanwhile, its combination effect with the stroke angle can determine the attitude and trajectory of the flapping airfoil, thus further affect the direction of the aerodynamic forces. With the influence of the streamwise in-line motion, the asymmetrical vortex structures emerge in the wake fields because the streamwise velocities of shedding vortices are different in the upstroke and downstroke. Furthermore, we conduct the kinematic parameter optimization for a three-dimensional asymmetrically flapping wing. Compared to the two-dimensional simulations, we further investigate the flow induced by the vortex ring and its unsteady effects on the vortex structure and aerodynamic performance.