Stochastic Investigation of Flows About Airfoils at Transonic Speeds

In this study, a deterministic compressible solver is coupled to a nonintrusive stochastic spectral projection method to propagate several aerodynamic uncertainties through a transonic steady flow around a NACA0012 airfoil. The stochastic model is solved in a generalized polynomial chaos framework. This approach combines the advantage of not modifying the existing deterministic solver while maintaining accurate representations of the stochastic solution and its statistics. The major difficulty of this work is to deal with deterministic transonic flows for which aerodynamics nonlinearities are reported in the uncertain probabilistic space. The efficiency of the present methodology are evaluated for the propagation of random disturbances associated with the angle of attack and the freestream Mach number. An error analysis is carried out in order to determine appropriate physical and stochastic discretization levels. Different stochastic flow regimes are analyzed in details by means of various postprocessing procedures, including error bars, probabilistic density function of the aerodynamic field, and Sobol's coefficients.