Polynomial Chaos Expansion Applied to Airfoil Limit Cycle Oscillations

Monte Carlo simulation was used to analyze the aeroelastic response of a typicalsection airfoil subject to uncertainties in key aerodynamic and structural dynamic parameters. When the Monte Carlo results were used to compute the coe‐cients of a Hermite-chaos expansion, di‐culties arose at large times in modeling the probabilistic response of the system in limit-cycle oscillation; in particular, the simulated time histories consistently decayed to zero at large times. A sinusoidal model problem was analyzed to clarify the issues responsible for these di‐culties, which do not appear to have been formally previously in the literature. The projected solution coe‐cients were found to successively gain and lose dominance over other coe‐cients as time increases in a manner that causes any flxed expansion to fail over a simulation time of su‐cient duration. An intuitive explanation of this behavior is ofiered, and a waveletbased stochastic expansion is proposed for future efiorts to improve the convergence of the expansion at large times.

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