Geometrical Uncertainties—Accuracy of Parametrization and Its Influence on UQ and RDO Results

Abstract

A large number of geometrical uncertainties of a transonic RAE2822 airfoil are parameterized by a truncated Karhunen–Loève expansion (KLE), and the influence of the truncation on the statistics of aerodynamic quantities is investigated both in terms of efficiency and accuracy. Direct integration of a very large number of quasi-Monte Carlo samples computed with CFD is used to compute the mean and standard deviation for different levels of truncation, i.e., for different numbers of uncertain parameters. We show that a parameterization based on a well-truncated KLE can efficiently reduce the number of geometrical uncertainties while maintaining accuracy. Excessive truncation will not improve the efficiency of surrogate-based statistics integration and will inevitably lead to a loss of accuracy of the estimated statistics. This is attributed to the use of a gradient-enhanced surrogate model that employs an adjoint flow solver to compute the gradient of the aerodynamic coefficients with respect to the uncertain parameters. All partial gradients can be computed at the cost of one adjoint solution; i.e., the cost of computing all partial gradients is independent of the number of uncertain parameters. It is also shown that a loss of accuracy due to an improper truncation may influence the results of robust design optimization.