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      A gPC-based approach to uncertain transonic aerodynamics

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      Author(s)
      Simon F.
      Guillen P.
      Sagaut P.
      Lucor, D.
      Date
      2010
      Source Title
      Computer Methods in Applied Mechanics and Engineering
      Print ISSN
      0045-7825
      Volume
      199
      Issue
      17-20
      Pages
      1091 - 1099
      Language
      English
      Type
      Article
      Item Usage Stats
      133
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      128
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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.
      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
      Permalink
      http://hdl.handle.net/11693/22413
      Published Version (Please cite this version)
      http://dx.doi.org/10.1016/j.cma.2009.11.021
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