Analytical modeling of rotor-stator potential interaction for low-speed axial fans

This paper presents an analytical model to predict tonal noise of rotor-stator potential interaction for low-speed axial fans. The model is validated against high-fidelity lattice-Boltzmann (LBM) simulations for two fan configurations, varying the blades and vanes azimuthal spacing. The model couples Blade Element Momentum Theory, for steady blade loading, with an unsteady Sears-based formulation for unsteady blade loading. The latter is enhanced with a modification of the chordwise pressure distribution function to eliminate the leading edge singularity. The velocity field at the blade trailing edge is reconstructed via potential flow using two novel approaches: a Gaussian velocity deficit and a cascade representation of stator vanes. Results show that the modified pressure function improves the agreement with the surface pressure distribution obtained from LBM at the leading edge; moreover, the proposed flow-field reconstructions reproduce the dominant velocity features and the tonal noise trends reasonably compared with the LBM results. The model is found to capture the effect of blade-vane phasing on tonal noise generation and to reproduce the main characteristics of the acoustic directivity pattern. Remaining discrepancies in broadband noise indicate the need of including trailing edge and tip noise models.