A gPC-based approach to uncertain transonic aerodynamics

Date
2010
Authors
Simon F.
Guillen P.
Sagaut P.
Lucor, D.
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Source Title
Computer Methods in Applied Mechanics and Engineering
Print ISSN
0045-7825
Electronic ISSN
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Volume
199
Issue
17-20
Pages
1091 - 1099
Language
English
Type
Article
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Abstract

The present paper focus on the stochastic response of a two-dimensional transonic airfoil to parametric uncertainties. Both the freestream Mach number and the angle of attack are considered as random parameters and the generalized Polynomial Chaos (gPC) theory is coupled with standard deterministic numerical simulations through a spectral collocation projection methodology. The results allow for a better understanding of the flow sensitivity to such uncertainties and underline the coupling process between the stochastic parameters. Two kinds of non-linearities are critical with respect to the skin-friction uncertainties: on one hand, the leeward shock movement characteristic of the supercritical profile and on the other hand, the boundary-layer separation on the aft part of the airfoil downstream the shock. The sensitivity analysis, thanks to the Sobol' decomposition, shows that a strong non-linear coupling exists between the uncertain parameters. Comparisons with the one-dimensional cases demonstrate that the multi-dimensional parametric study is required to get the correct shape and magnitude of the standard deviation distributions of the flow quantities such as pressure and skin-friction. © 2009 Elsevier B.V.

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Book Title
Keywords
Polynomial chaos, Stochastic collocation, Transonic airfoil aerodynamics, Uncertain quantification, Boundary-layer separation, Coupling process, Flow quantities, Flow sensitivity, Freestream mach number, Generalized polynomial chaos (gPC), Movement characteristics, Nonlinear coupling, Nonlinearities, Numerical simulation, Parametric study, Parametric uncertainties, Polynomial chaos, Random parameters, Spectral collocation, Standard deviation, Stochastic collocation, Stochastic parameters, Stochastic response, Super-critical, Transonic airfoils, Two-dimensional transonic airfoil, Uncertain parameters, Uncertain quantification, Airfoils, Chaos theory, Friction, Mach number, Polynomials, Sensitivity analysis, Stochastic systems, Uncertainty analysis, Transonic aerodynamics
Citation
Published Version (Please cite this version)