Three-Dimensional Modeling of Annular Cascade Trailing-Edge Noise

Abstract

The paper addresses various aspects of an analytical methodology for the modeling of the sound transmission through the outlet guide vanes of an axial-flow fan architecture, in view of predicting the trailing-edge noise with a proper account of the cascade effect. The first part extends a previous two-dimensional model by including the stagger and the curvature of the vanes. This is achieved by iteratively solving matching equations at the leadingedge and trailing-edge interfaces of the stator, with a multiple-scale analysis between two iterations, considering the inter-vane channels as bifurcated waveguides of slowly varying cross-section. The second part is aimed at extending a previous two-dimensional cascade trailing-edge noise model to an annular cascade described in cylindrical coordinates. For this the trailing-edge noise sources of a vane section are replaced by an equivalent lift dipole, the direct sound of which is expanded as a series of annular-duct modes. The scattering of each mode by the complete cascade is calculated by a three-dimensional mode-matching technique and the complete radiation of the trailing-edge source obtained by summing all modal contributions. The last part explains how the aforementioned two-dimensional model of curved-channel can be generalized in the three-dimensional annular geometry at the price of some approximations. Only preliminary results are given at each step, the paper being aimed at demonstrating the methodology but not yet at simulating a complete configuration. The objective is to formulate three-dimensional blade/vane row aeroacoustic problems without resorting to a strip-theory approach.