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Apr 2010

Volume 127, Issue 4, pp. EL121-2714

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Multimode radiation from an unflanged, semi-infinite circular duct with uniform flow

Samuel Sinayoko, Phillip Joseph, and Alan McAlpine

J. Acoust. Soc. Am. Volume 127, Issue 4, pp. 2159-2168 (2010); (10 pages) | Cited 3 times

Online Publication Date: 05 Apr 2010

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Multimode sound radiation from an unflanged, semi-infinite, rigid-walled circular duct with uniform subsonic mean flow everywhere is investigated theoretically. The multimode directivity depends on the amplitude and directivity function of each individual cut-on mode. The amplitude of each mode is expressed as a function of cut-on ratio for a uniform distribution of incoherent monopoles, a uniform distribution of incoherent axial dipoles, and for equal power per mode. The directivity function of each mode is obtained by applying a Lorentz transformation to the zero-flow directivity function, which is given by a Wiener–Hopf solution. This exact numerical result is compared to an analytic solution, valid in the high-frequency limit, for multimode directivity with uniform flow. The high-frequency asymptotic solution is derived assuming total transmission of power at the open end of the duct, and gives the multimode directivity function with flow in the forward arc for a general family of mode amplitude distribution functions. At high frequencies the agreement between the exact and asymptotic solutions is shown to be excellent.
Show PACS
43.28.Py Interaction of fluid motion and sound, Doppler effect, and sound in flow ducts
43.20.Mv Waveguides, wave propagation in tubes and ducts
43.50.Cb Noise spectra, determination of sound power
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