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radiating spanwise aerodynamic wave number (!y=c 0 ) k x = chordwise aerodynamic wave number (!=U) k y = spanwise aerodynamic wave number L = aeroacoustic transfer function M = freestream Mach number n = number of airfoil strips T:I: = turbulence intensity U = freestream velocity x = observer coordinates x; y; z = compressibility parameter ( 1 M 2 p ) 0= density = far-field corrected distance [ x 2 2 y 2 z 2 p ] ww = two-dimensional wave number turbulence spectrum ! = circular frequency

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i n t r o d u c t i o nIn modern rotating machines, due to the significant effort put on reducing annoying discrete tones, the broadband noise is an important contribution to the overall noise level, as in fans, turboengines or wind turbines. A key source of broadband noise is the trailing-edge noise, caused by the scattering of boundary-layer pressure fluctuations into acoustic waves at the trailing-edge of any lifting surface. Numerical methods to evaluate this noise are more often using steady RANS computations for computational cost reasons, requiring modelling and introducing then uncertainties. The present study aims at assessing uncertainties associated with the prediction of trailing-edge noise, through an uncertainty quantification (UQ) framework, using RANS computations or conventional LES computations, in order to determine their respective robustness and accuracy. m e t h o d o l o g y f o r u qThe approach to uncertainty quantification (UQ) of airfoil trailing-edge noise is illustrated in Figure 1. The considered case is a Controlled-Diffusion airfoil of chord C placed in the large anechoic wind tunnel in Ecole Centrale de Lyon (LWT), and held by two horizontal side plates. The angle of attack (aoa) is 8o and the airfoil upstream velocity U0 is 16 m/s, which corresponds to a Reynolds number based on the airfoil chord ReC=1.6 x 105.As in previous studies (Moreau et al. 2006), a RANS computation of the complete experimental setup of the large anechoic wind tunnel in Ecole Centrale de Lyon (LWT), including the nozzle and part of the anechoic chamber has been done that captures the strong jet-airfoil interaction and its impact on airfoil loading. The boundary conditions are extracted (U and V profiles) for a smaller domain embedded in the je t potential core. This final result is obtained by two different procedures, both producing a wall frequency pressure spectrum @pp used in Amiet's theory (Amiet 1976) to predict the far-field sound spectrum Spp.In the first approach, an unsteady LES on the restricted domain with the above extracted velocity profiles, directly yields the trailing edge wall pressure spectrum. The second approach, less expensive but requiring more modeling, uses steady RANS computations on a two-dimensional slice of the restricted domain, with the same boundary condition profiles as for the LES. From this RANS computation, the primitive variables (Uj, U2, k and a> or s depending on the RANS turbulence model) are extracted through a boundary layer profile at the trailing-edge of the airfoil. Those The uncertainty is introduced at the inlet boundary of the restricted computational domain. The physical variations in the experimental flow measurements are taken into account by selecting a 2.5% error bound on the streamwise velocity U and a 10% error bound on the crosswise velocity V around the deterministic numerical solution. A set of 9 velocity inlet profiles are determined using a Clenshaw-Curtis quadrature and the corresponding RANS and LES computations are run. Both components U and V...