Multifidelity Physics-Based Method for Robust Optimization Applied to a Hovering Rotor Airfoil

The paper presents a multifidelity 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 lift-to-drag ratio 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 that exploits two aerodynamic models of different fidelity. The two models correspond to different physical descriptions of the flowfield around the airfoil; thus, the multifidelity 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 it 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 multifidelity approach is effective in reducing the sensitivity of the designed airfoils with respect to variation in the operating conditions.