Cascade trailing-edge noise modeling using a mode-matching technique and the edge-dipole theory

An original analytical approach is proposed to model the broadband trailing-edge noise produced by high-solidity outlet guide vanes in an axial turbomachine. The model is formulated in the frequency domain and first in two dimensions for a preliminary assessment of the method. In a first step the trailing-edge noise sources of a single vane are shown to be equivalent to the onset of a so-called edge dipole, the direct field of which is expanded in a series of plane-wave modes. A criterion for the distance of the dipole to the trailing-edge and a scaling of its amplitude is defined to yield a robust model. In a second step the diffraction of each plane-wave mode is derived considering the cascade as an array of bifurcated waveguides and using a mode-matching technique. The cascade response is finally synthesized by summing the diffracted fields of all cut-on modes to yield upstream and downstream sound power spectral densities. The obtained spectral shapes are physically consistent and the present results show that upstream radiation is typically 3 dB higher than downstream radiation, which has been experimentally observed previously. Even though the trailing-edge noise sources are not vane-to-vane correlated their radiation is strongly determined by a cascade effect that consequently must be accounted for. The interest of the approach is that it can be extended to a three-dimensional annular configuration without resorting to a strip theory approach. As such it is a promising and versatile alternative to previously published methods.