Exploring Stochastic Models for Fast Analysis of Unsteady Wing Aerodynamics

摘要

Wings, hydrofoils, and other 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 a stochastic process. For fluid dynamics practitioners, this leads to a challenge: how can the long term, random design loads (e.g. fatigue or 20-year return extreme) be quantified efficiently? The conventional approach to this challenge 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 solving many simulations separately. This is computationally expensive and presents a handicap, especially in early design stages (optimization), where rapid evaluations of candidate designs and their gradients with respect to design variables are required. To tackle this problem, we introduce two alternative stochastic methods, one based on a Galerkin projection onto a set of Fourier modes, and the other based on a Polynomial Chaos Expansion. These stochastic approaches 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.