Propagation of sound waves through a blade row: II. Analysis based on the acceleration potential method

Abstract

Propagation of sound waves through a blade row with finite blade spacing is investigated theoretically. The main purpose of this study is to clarify the effect of blade spacing of the cascade on sound propagation through it, which is not settled by the preceding analysis based on the semi-actuator disk theory. A theory of cascading airfoils in a two-dimensional subsonic sound field is presented with use of the singular point method in a rigorous and general form, in which the kernel function of the aerodynamic integral equation is expressed by several series of the exponential functions. When the ratio of blade spacing to wavelength increases over the critical value the condition of the sound field becomes super-resonant, under which many circumferential modes propagate as the transmitted wave and the reflected wave for one mode of incident waves. The effect of blade spacing on sound propagation through a cascade is not considerable especially at higher Mach numbers. The other features of transmission and reflection dependent upon flow Mach number, angle of incidence and wavelength are almost the same as those deduced from the semi-actuator disk theory. In most cases of axial-flow compressors, if the condition of the sound field is not super-resonant, the semi-actuator disk theory is a useful one for the problem of sound propagation through blade rows.