On the use of an analytical cascade response function to predict sound transmission through an annular cascade

The present study aims at developing and assessing an analytical model for the sound transmission through an annular stator row in a configuration without mean flow. 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 coupled with a previously published analytical formulation for the unsteady vane loading in a rectilinear cascade. Three formulations are developed on the basis of different definitions of the incident acoustic waves 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 a finite element method solution and with a rectilinear cascade model in configurations with no mean flow. The benchmarks consist in four annular ducts from very high (0.98) to moderate (0.5) hub-to-tip ratio containing a possibly staggered annular cascade. The frequency and the radial mode order of the incident mode are varied. Both pressure field and pressure coefficients are compared.