Uncertainty Quantification for the Trailing-Edge Noise of a Controlled-Diffusion Airfoil

Two deterministic incompressible flow solvers are coupled with a nonintrusive stochastic collocation method to propagate several aerodynamic uncertainties of the same type encountered in a standard trailing-edge noise experiment of a low-speed controlled-diffusion airfoil to predict the far-field noise. Reynolds-averaged Navier-Stokes and large-eddy simulations are applied to a common restricted domain surrounding the airfoil embedded in the potential core of the jet in the anechoic wind-tunnel experiment. Both simulation methods provide the wall-pressure fluctuations near the airfoil trailing edge, which are then used in Amiet's acoustic analogy for trailing-edge noise. In the Reynolds-averaged Navier-Stokes simulations, two different representative models are used to reconstruct the wall-pressure fluctuations: Rozenberg's deterministic model directly based on integral boundary-layer parameters, and Panton and Linebarger's statistical model based on the velocity field in the boundary layer. The nonintrusive stochastic model is solved in a stochastic collocation framework, with the inlet velocity profiles as random variables. This framework is found to be two orders of magnitude more efficient than a classical Monte Carlo simulation for the same accuracy. Comparisons of the mean and standard deviations of the wall-pressure spectra and the far-field acoustic pressure with experiment stress that Rozenberg's model is more accurate at low frequencies and has larger uncertainties at high frequencies because of the uncertainty on the wall shear stress and that Panton and Linerbarger's is less accurate at low frequencies because of the slow statistical convergence of the integration involved in the model.