Comparative study of different analytical approaches for modelling the transmission of sound waves through turbomachinery stators

The present study is dealing with the analytical modelling of sound transmission through turbomachinery stators. Two-dimensional cascade models are applied in combination with a newly proposed impedance model to account for the effect of flow deflection on the propagation of acoustic modes in annular flow ducts. Further, two different approaches for the calculation of the 3D mode transmission using 2D cascade models are used. The proposed methods allow the consideration of vane twist and mode scattering w.r.t. the radial mode order. The results obtained with the different approaches are compared with the outcome of numerical calculations for several flat plate cascades and a generic LPT vane geometry. The similarities and differences between the different analytical approaches are examined. It is shown, that the flow deflection through a stator row has a significant influence on the transmitted and reflected sound power. Furthermore, the occurrence of total transmission resp. zero reflection along with non-zero transmission is identified for particular mode orders and related to special conditions occurring in 2D cascade models.