Propagation of sound waves through a blade row: I. Analysis based on the semi-actuator disk theory

Abstract

Propagation of sound waves through a single blade row in an axial-flow compressor duct is studied theoretically using the semi-actuator disk theory, which introduces a two-dimensional cascade model with finite chord length and infinitesimal blade spacing. Three flow fields—the upstream field, the downstream field and the field in the cascade—are combined properly to give the transmission and reflection coefficients as a function of flow Mach number, angle of incidence, wavelength and stagger angle of the cascade. Three kinds of incident wave are considered; a pressure wave from the downstream side, a pressure wave from the upstream side, and a vorticity wave from the upstream side of the cascade. The effects of flow Mach number, angle of incidence and stagger angle of the cascade on the transmission and reflection coefficients are shown to be significant. Wavelength of the incident wave has a minor effect on sound propagation through a cascade especiallyat higher Mach numbers. The effect of steady aerodynamicblade loading on sound propagation is also discussed.