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International Journal of Aerospace Engineering
Volume 2017 (2017), Article ID 8107190, 16 pages
Research Article

Uncertainty Quantification and Sensitivity Analysis of Transonic Aerodynamics with Geometric Uncertainty

School of Aeronautics, Northwestern Polytechnical University, Xi’an 710072, China

Correspondence should be addressed to Weiwei Zhang

Received 1 November 2016; Accepted 2 February 2017; Published 26 February 2017

Academic Editor: Hikmat Asadov

Copyright © 2017 Xiaojing Wu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Airfoil geometric uncertainty can generate aerodynamic characteristics fluctuations. Uncertainty quantification is applied to compute its impact on the aerodynamic characteristics. In addition, the contribution of each uncertainty variable to aerodynamic characteristics should be computed by the uncertainty sensitivity analysis. In the paper, Sobol’s analysis is used for uncertainty sensitivity analysis and a nonintrusive polynomial chaos method is used for uncertainty quantification and Sobol’s analysis. It is difficult to describe geometric uncertainty because it needs a lot of input parameters. In order to alleviate the contradiction between the variable dimension and computational cost, a principal component analysis is introduced to describe geometric uncertainty of airfoil. Through this technique, the number of input uncertainty variables can be reduced and typical global deformation modes can be obtained. By uncertainty quantification, we can learn that the flow characteristics of shock wave and boundary layer separation are sensitive to the geometric uncertainty in transonic region, which is the main reason that transonic drag is sensitive to the geometric uncertainty. The sensitivity analysis shows that the model can be simplified by eliminating unimportant geometric modes. Moreover, which are the most important geometric modes to transonic aerodynamics can be learnt. This is very helpful for airfoil design.