High frequency multimode radiation from ducts with flow

Sinayoko, S., Joseph, P.F. and McAlpine, A. (2008) High frequency multimode radiation from ducts with flow. Proceedings of the 14th AIAA/CEAS Aeroacoustics Conference (29th AIAA Aeroacoustics Conference), Vancouver, Canada. 04 - 06 May 2008. 12 pp .

Abstract

Multimode sound radiation from hard-walled semi-infinite ducts with uniform subsonic flow is investigated theoretically. An analytic expression, valid in the high frequency limit, is derived for the multimode directivity function in the forward arc for a general family of mode distribution functions. The multimode directivity depends on the amplitude and directivity function of each individual mode. The amplitude of each mode is expressed as a function of cut-off ratio for a uniform distribution of incoherent monopoles, a uniform distribution of incoherent axial dipoles and for equal power per mode. The modes' directivity functions are obtained analytically by applying a Lorentz transformation to the zero flow solution. The analytic formula for the multimode directivity with flow is derived assuming total transmission of power at the open-end of the duct. This formula is compared to the exact numerical result for an unflanged duct, computed utilizing a Wiener-Hopf solution.The agreement is shown to be excellent.

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Contributors

Author: A. McAlpine

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