A stochastic approach for modeling incident gust effects on flow quantities

The uncertainty in gust loads on a rigid, flat-plate airfoil at zero angle-of-attack due to imprecise knowledge of the gust parameters is quantified. The loads are computed using the unsteady vortex lattice model, which includes temporal variations in wake vorticity and the associated downwash on the airfoil. The non-intrusive formulation of the polynomial chaos expansion in terms of the multivariate Hermite polynomials is employed to quantify the uncertainty in the predicted unsteady lift. The expansion coefficients were estimated through Latin hypercube sampling of the parameters in the vertical and streamwise gust spectra. The first-order chaos expansion in terms of the uncertain spectral parameters was found to be sufficient for representing the stochastic aerodynamic lift, which was found to be most sensitive to imprecision in the standard deviation of the vertical component of the gust. These conclusions were found to be unaffected by ignoring the effects of gusts on the locations of the shed vortices in the airfoil’s wake.