Uncertainty Quantification for Airfoil Icing Using Polynomial Chaos Expansions

Abstract

The formation and accretion of ice on the leading edge of a wing can be detrimental to airplane performance. Complicating this reality is the fact that even a small amount of uncertainty in the shape of the accreted ice may result in a large amount of uncertainty in aerodynamic performance metrics (e.g., the stall angle of attack). The main focus of this work concerns using the techniques of polynomial chaos expansions to quantify icing uncertainty much more quickly than traditional methods (e.g., Monte Carlo). First, we present a brief survey of the literature concerning the physics of wing icing, with the intention of giving a certain amount of intuition for the physical process. Next, we give a brief overview of the background theory of polynomial chaos expansions. Finally, we compare the results of Monte Carlo simulations to polynomial-chaos-expansion-based uncertainty quantification for several different airfoil-icing scenarios. The results are in good agreement and confirm that polynomial chaos expansion methods are much more efficient for the canonical airfoil icing uncertainty quantification problem than Monte Carlo methods.