Analysis of Aeroelastic System Under Random Gust With Parametric Uncertainties Using Polynomial Chaos Expansion

In the design of wind turbine structures, aeroelastic stability is of utmost importance. It becomes even more crucial when there are uncertainties involved in it. A symmetric airfoil with its pitch-plunge flexibility is considered under potential flow. The potential flow model is justified as the classical flutter model involves unseparated flow over the body so that inviscid assumptions are valid. In the present study of aeroelastic system, nonlinear parameters have been considered as it can stabilize the diverging growth of a flutter oscillation. Quantification of aleatoric uncertainties present in the system has been done by modeling them as a Gaussian parameters. The epistemic uncertainty present in the system has also been reduced by considering unsteady vortex lattice method (UVLM) instead of the rigid wake model of Wagner. In this model, the wake is free to evolve and also the shape of airfoil has been considered. The present study involves usage of UVLM code on a NACA 0012 airfoil. The values of the linear flutter speed predicted by using UVLM code is in close agreement with that of the fixed wake model of Lee et al. When the structural nonlinearities are present, the system exhibits a self sustained oscillation of constant amplitude called as Limit Cycle Oscillation (LCO) even beyond the linear flutter speed. In the present study, a horizontal gust is modeled with a given spectra by superposition of a set of sinusoidal components which is a standard practice. This gust has then been applied on the airfoil along with the structural uncertainties. A spectral uncertainty quantification tool called Polynomial Chaos Expansion is used to quantify the effect of uncertainty propagation and calculate the response statistics. A non-intrusive version of the method using stochastic projection approach is used to capture the time histories and plot the PDFs at various time instants of all the realizations with Monte Carlo Simulation as a reference solution. The evolution of PCE coefficients in the time domain along with its ensemble variations has also been looked into in the present study.