Uncertainty Analysis in Airfoil–Turbulence Interaction Noise Using Polynomial Chaos Expansion

Abstract

Airfoil–turbulence interaction noise is a known source of environmental disturbance and acoustic performance loss in aeroacoustics and hydroacoustics. This noise can be predicted using semi-analytical models that require input measurements of the incoming turbulent flow parameters. However, the turbulence parameters are inherently difficult to measure accurately. These parameters, which include the turbulence kinetic energy and its dissipation rate, have a stochastic nature. This study aims to investigate how small variations in the measurements of turbulence parameters affect the uncertainty of the predicted airfoil–turbulence interaction noise. This is achieved by applying polynomial chaos expansion (PCE) to the semi-analytical model of Amiet’s theory for airfoil-interaction noise. The validity of the deterministic and stochastic simulations is ensured by comparisons against available experimental data from the literature, and Monte Carlo simulations, respectively. Uncertainty quantification is then performed using a stochastic collocation technique, where the aerodynamic noise is evaluated at specific collocation points to estimate the coefficients required for PCE. Both the individual and combined effects of varying the uncertain input turbulence parameters are simulated to quantify the uncertainty of the output aerodynamic noise. The insights gained from the results suggest it is important to incorporate the stochastic behavior of the incoming turbulent flow in operational models for airfoil–turbulence interaction noise predictions.