On a mode-matching technique for acoustic scattering by a cascade of cambered vanes

A two-dimensional mode-matching technique is developed to compute the scattering of an acoustic wave by a cascade of staggered and cambered vanes in subsonic regime, such as those encountered in axial-flow fan stages. Apart from the need to reproduce a more realistic geometry in analytical modeling, introducing vane camber is a relevant way of retrieving the global evolution of the mean flow away from the vanes, simply by mass-flow conservation through the expanding inter-vane channels. This prevents mean-flow discontinuity and introduces a realistic variation of the equivalent dipole sources along the vane chord. The expansion of the cross-section along the inter-vane channels, induced by curvature, is taken into account by multiple-scale analysis, assuming slow variations of the geometry. The validity of the model is assessed by extensive comparisons with high-fidelity numerical results, with and without flow. The assumptions used in the analytical model are found to be suited to modern geometries of outlet guide vanes.