A Frequency-Domain Formulation for Predicting Multi-Frequency Noise Generated by Flows with Periodically Moving Boundaries

A frequency-domain formulation is proposed to compute the far-field noise generated by flows with periodically oscillating or rotating boundaries. The proposed formulation significantly enhances the efficiency of the frequency-domain method in handling the multi-frequency sources with nonrectilinear motion. The novelty of the proposed method is that the frequency- and time-dependent components of the Ffowcs Williams and Hawkings (FW-H) integral are separated by using the far-field asymptotic Green’s function. The separation of the frequency- and time-dependent components avoids the need for an expensive time integration in computing the multi-frequency noise generated by flows with periodically moving boundaries. They proposed only one Fourier transform computation in obtaining the noise at different frequencies. The efficiency of the proposed formulation is investigated by analyzing the required number of floating-point operations. Its validity is examined by computing the noise from rotating or oscillating permeable boundaries around composite monopoles and a flapping wing. The proposed formulation is applicable to the FW-H integral with periodically oscillating or rotating boundaries when the maximum velocity on the moving boundary is subsonic.