An empirical model to predict the wall-pressure fluctuations spectra beneath adverse pressure gradient flows is presented. It is based on Goody's model which already incorporates the effect of Reynolds number but is limited to zero-pressure gradient flows. The extension relies on 6 test-cases from 5 experimental or numerical studies covering a large range of Reynolds number, 5.6 × 10 2 < R θ < 1.72 × 10 4 , in both inter-

The paper is dealing with the experimental validation of an analytical trailing-edge noise model dedicated to low-speed fans operating in free field.The model is intrinsically related to the aerodynamics of the blades and should lead to a useful fast-running tool to be included in a blade design process in an industrial context. The investigations are made on a two- = distance between the fan axis and the mid-span network r 2 = distance between the fan axis and the tip network R = radial distance R 0 = distance between observer position and fan center R A = position vector of the middle of the trailing-edge segment in the moving reference frame R e = Reynolds number= corrected distance for convection effects S pp = acoustic pressure power spectral density S Ψ pp = acoustic pressure power spectral density due to one blade segment U = tangential velocity U c = convection velocity (x 1 , x 2 , x 3 ) = moving reference frame x = observer position in the moving reference frame (X, Y, Z) = fixed reference frame X = observer position in the fixed reference frame α g = airfoil angle of attack= cross spectral phase between signals i and j Φ pp = wall-pressure power spectral densitỹ Φ pp = normalized wall-pressure power spectral density Θ = azimuthal observer angle ρ = fluid density τ w = wall shear stress ω = radian frequency ω e = emission radian frequency Ω = fan angular velocity ξ = streamwise distance

An analytical model based on Paterson & Amiet's work dealing with the trailing-edge noise of a blade has been previously validated thanks to a dedicated experiment on a low speed axial fan. Wall-pressure spectra near the trailing-edge of the blade and at different radii are needed for an accurate prediction. Only experiments and LES simulations are able to provide them. In an industrial context, both methods can not be applied since they are too expensive and time-consuming. To overcome this difficulty, RANS simulations are combined with semi-empirical wall-pressure spectra to obtain the needed input data. The effect of the mean-pressure gradient is taken into account. The model is applied first to the noise radiated by an airfoil placed in the open-jet of an anechoic wind tunnel, then to an automotive cooling fan and finally to an aircraft engine fan. RANS simulations are post-processed to run the analytical model with appropriate input data. The noise predictions are then compared with experimental results.

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