Multi-fidelity physics-based method for robust optimization with application to a hovering rotor airfoil

The paper presents a multi-fidelity robust optimization technique with application to the design of rotor blade airfoils in hover. A genetic algorithm is coupled with a non-intrusive uncertainty propagation technique based on Polynomial Chaos expansion to determine the robust optimal airfoils that maximize the mean value of the aerodynamic efficiency while minimizing the variance, under uncertain operating conditions. Uncertainties on the blade pitch angle and induced velocity are considered. To deal with the variable operating conditions induced by the considered uncertainties and to alleviate the computational cost of the optimization procedure, a multifidelity strategy is developed which exploits two aerodynamic models of different fidelity. The two models corresponds to different physical descrip-tions of the flowfield around the airfoil; thus, the multi-fidelity method employs the low-fidelity model in regions of the stochastic space where the physics of the problem is well-captured by the model, and switches to high-fidelity estimates only where needed. The proposed robust optimization technique is compared with the robust optimization based on the high-fidelity aerodynamic model and the deterministic optimization, to assess the capability of finding a consistent Pareto set, and to evaluate the numerical efficiency. The results obtained show how the robust multi-fidelity