Abstract
Mathematical formulations of the unsteady three-dimensional flowfield induced by a rotating annular cascade interacting with an oncoming periodic gust and disturbances from an oscillating actuator surface composed as a part of the duct wall are presented on the basis of a linearized unsteady lifting surface theory. The problem of suppressing the tone noise due to interaction of the rotor with the gust by means of the actuator motion is studied. Theoretical analysis with numerical calculations is conducted for a simple harmonic sinusoidal gust, and a simple harmonic sinusoidal circumferential wave form of the actuator motion and optimum conditions of the actuator motion are investigated. There are substantial differences in the optimum phase and amplitude of the actuator motion between the conditions of suppressing the upstream and downstream acoustic powers. In the case of multiple cut-on duct modes, the actuator motions of the cut-off circumferential wave numbers are desirable to effectively suppress the total acoustic powers.
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