Design of airfoils in unsteady viscous flows using Hierarchical Kriging model

In this paper, optimizations are carried out to determine an airfoil shape with the best aerodynamic performance in the unsteady low Reynolds flow. To capture the unsteady physics driving the design process, the time-accurate Navier-Stokes equations are solved for aerodynamic performance. The Hierarchical Kriging (HK) model is used due to its high efficiency in the process of building a model and ability in searching global optimal. The influence of different low-fidelity (L-F) models and infilling strategies on the optimization efficiency is investigated. It is found that an extremely coarse mesh would be an excellent L-F model, which is a suitable balance between accuracy and computational cost. By taking the advantage of the hybrid infilling strategy, the optimization converges rapidly without initial design of experiment for the high-fidelity (H-F) model. The design approach proposed in this paper allows highly efficient aerodynamic optimizations in unsteady low Reynolds number flow, at the same time global optimum can be surely guaranteed.