Fast Analysis of Unsteady Wing Aerodynamics via Stochastic Models

Abstract

Lifting surfaces often operate in highly unsteady inflow conditions, such as gusty wind or waves. These inflows are unsteady on many time scales and have to be considered stochastic processes. For fluid dynamics practitioners, this leads to a challenge: how can long-term, random design loads (e.g., fatigue or 20 year return extreme) be quantified efficiently? The conventional approach involves analysis of a large set of short-term inflow realizations and extrapolates the results to long-term loads via their assumed probability distributions. However, this requires separately solving many simulations. This is computationally expensive and presents a handicap, especially in early design stages (optimization), where rapid evaluations of candidate designs and performance gradients are required. To tackle this problem, we introduce two alternative stochastic methods: one based on a Galerkin projection onto Fourier modes, and the other based on a polynomial chaos expansion. This approach enables us to carry the randomness though the solution process to directly obtain a stochastic result. Thus, long-term loads can be directly constructed from the stochastic solution, without having to analyze specific realizations of the inflow inputs. The new processes are illustrated and discussed with an example based on a rectangular wing lifting-line model.