Towards Analytical Modeling of Tonal and Broadband Sources of Axial Fan Noise

This work presents an analytical model for predicting tonal and broadband noise in low-speed axial fans coupled with of a statoric shroud. The model accounts for all the main dipolar noise sources, including unsteady loading tonal noise on both rotor and stator, trailing-edge broadband noise from boundary layer scattering on both rotor and stator, and leading-edge broadband noise from wake impingement on the stator. The mean blade loading is obtained through a modified blade element momentum theory, while the unsteady loading fluctuations are computed using an extended Sears' model coupled with potential flow theory. Broadband contributions are evaluated using Amiet's formulation for trailing-edge and leading-edge noise, including back-scattering corrections. The proposed approach is validated against high-fidelity lattice-Boltzmann simulations for two fan configurations, one with evenly spaced blades and vanes and one with random uneven spacing of blades and vanes, at both free blowing and maximum efficiency operating conditions. The model predicts well the mean aerodynamic loading, tonal components, and spectral variations induced by uneven spacing, while broadband noise levels are well captured except for underestimation at operating conditions where the tip vortex backflow dominates. Overall, the framework provides a computationally efficient tool for fan noise prediction and design optimization, bridging the gap between high-fidelity simulations and early stage analytical design.