Prediction of sound transmission through an annular cascade Using an analytical cascade response function

Abstract

The present study aims at developing and assessing an analytical model for the sound transmission through an annular blade row, by comparing with the Finite Element Method Solver of Virtual Lab Acoustics in a con guration without mean ow. The model reformulates a three-dimensional annular model dedicated to turbulence interaction noise to deal with the case of an incident acoustic mode of an annular duct. It is a strip theory approach based on a previously published analytical formulation for the unsteady blade loading in a rectilinear cascade. Three formulations are developed on the basis of two di erent de nitions of the incident gusts impinging on the rectilinear cascade. The latter are designed to match most of the properties of the incident mode in the annular case. The formulations are compared with the Finite Element Method Solver of Virtual Lab Acoustics and with a rectilinear cascade model in con gurations with no mean ow. The benchmarks consist in three annular ducts from very high to moderate hub-to-tip ratio containing a possibly staggered annular cascade. The radial mode order of the incident mode is varied. Both pressure eld and intensity coe cients are compared.