Sparse grid-based polynomial chaos expansion for aerodynamics of an airfoil with uncertainties

Abstract

The uncertainties can generate fluctuations with aerodynamic characteristics. Uncertainty Quantification (UQ) is applied to compute its impact on the aerodynamic characteristics. In addition, the contribution of each uncertainty to aerodynamic characteristics should be computed by uncertainty sensitivity analysis. Non-Intrusive Polynomial Chaos (NIPC) has been successfully applied to uncertainty quantification and uncertainty sensitivity analysis. However, the non-intrusive polynomial chaos method becomes inefficient as the number of random variables adopted to describe uncertainties increases. This deficiency becomes significant in stochastic aerodynamic analysis considering the geometric uncertainty because the description of geometric uncertainty generally needs many parameters. To solve the deficiency, a Sparse Grid-based Polynomial Chaos (SGPC) expansion is used to do uncertainty quantification and sensitivity analysis for stochastic aerodynamic analysis considering geometric and operational uncertainties. It is proved that the method is more efficient than non-intrusive polynomial chaos and Monte Carlo Simulation (MSC) method for the stochastic aerodynamic analysis. By uncertainty quantification, it can be learnt that the flow characteristics of shock wave and boundary layer separation are sensitive to the geometric uncertainty in transonic region. The uncertainty sensitivity analysis reveals the individual and coupled effects among the uncertainty parameters.