Relation between source models and acoustic duct modes

The scope of this study is the noise generation by ducted axial fans. The work is chiefly concerned with the impact of source models on the excitation of the induct acoustic modes, and their eect on the total induct transfer function defined as the ratio of the induct to the free-field sound power. In the models, the sources are represented by static point sources (monopoles and dipoles) distributed along the stator vanes. These sources are assumed to be fully uncorrelated for broadband noise. Following Tyler and Sofrin, the sources are correlated and linear phase-shifted for the generation of rotor-stator interaction tones. The results show that the choice between monopole (volume) and dipole (force) sources does have a significant influence on the level of the excited induct modes. Whereas monopoles equally excite modes of positive and negative azimuthal order, the mode pattern generated by dipoles features a strong asymmetry between positive and negative modes. Based on the ray theory, it is shown that induct modes whose phase angle of propagations are perpendicular to the dipole axis are not excited. For both single and uncorrelated sources, the total induct transfer function tends asymptotically to one at high frequencies, which means that the influence of the duct on the total sound radiation can be neglected at high frequencies. This is not the case for correlated sources, as the total induct transfer function is proportional to 1/kR at high frequencies and independent of the nature of the source. This significantly diers from the radiation in free field.