Stochastic aerodynamics and aeroelasticity of a flat plate via generalised Polynomial Chaos

This paper deals with the characterisation of the aerodynamic and aeroelastic behaviour of a flat plate under uncertain flow conditions. The incoming mean flow velocity is described in terms of its probabilistic distribution, and the Reynolds number is consequently treated as a random variable. The objective of the study is to give a probabilistic description of the quantities which characterise the aerodynamics and aeroelasticity of a flat plate, i.e., steady forces, friction coefficient and velocity in the wake for the first and flutter derivatives for the second. Classical techniques such as Monte Carlo and quasi-Monte Carlo methods seem to be too expensive, in that they require many costly wind tunnel tests or numerical simulations of the steady and unsteady flow field around the motionless and moving plate. An efficient Multi-Element generalised Polynomial Chaos approach allows a significant reduction of the required number of realisations, making its cost affordable for real-world applications. The proposed method gives sufficiently accurate approximations of the probabilistic distributions of the desired quantities. Several examples of different representations of the stochastic outputs are given.