Three-dimensional analysis of blade force and sound generation for an annular cascade in distorted flows

An unsteady lifting-surface theory for a rotating subsonic annular cascade has been developed to predict the unsteady blade forces and the acoustic power generation caused by interaction of blades with inlet distortions or wakes. Disturbance pressure and velocity fields induced by the rotor blades with fluctuating blade force are expressed in terms of the blade force distribution and kernel functions. The spanwise distribution of the blade force is given as a sum of blade force modes, and the kernel functions are resolved into the corresponding modal components. The sound pressure and intensity are expressed as a sum of acoustic modes, the modal components of which are given in terms of the blade force mode components.Numerical computations have been conducted .for interaction with the external disturbance flows that are sinusoidal in the circumferential direction, but possess a phase skewing in the radial direction. Correlations among the acoustic modes, the blade force modes and the flow patterns of the external disturbance have been investigated. When the predominant acoustic mode is subresonant, the blade force amplitude is reduced by the three-dimensional effect, which is lessened as the frequency increases. At deeply superresonant states, however, the three-dimensional effect upon the spanwise average of the blade force amplitude is small. The generated sound power is effectively reduced by increasing the radial non-uniformity of the external disturbance.