An analysis of three-dimensional unsteady subsonic flow through rectilinear cascades

A finite-pitch, finite-chordlength cascade theory is constructed with elementary wave solutions of an actuator-disk analysis of a three-dimensional unsteady subsonic flow. The theory is applied to the analyses of unsteady forces due to blade vibration or sinusoidal gusts, taking into account the effects of spanwise phase shifts of the disturbances. By comparing the fluctuating pressure in the flow passage between the blades with fluctuating lift curves in a complex plane, it is shown that an acoustic resonance in the space between the blades may enlarge lift fluctuation on the blades. Three-dimensionality of the disturbances decreases the lift fluctuation in the case of incompressible flow, but it has the opposite effect if acoustic resonance occurs.