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

Abstract

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 3dB 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.