title: Multimode radiation from an unflanged, semi-infinite circular duct with uniform flow.
abstract: 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.
authors.affiliation: Institute of Sound and Vibration Research, University of Southampton, Southampton SO17 1BJ, United Kingdom.
authors.forename: Samuel
authors.initials: S
authors.lastname: Sinayoko
authors.forename: Phillip
authors.initials: P
authors.lastname: Joseph
authors.forename: Alan
authors.initials: A
authors.lastname: McAlpine
mesh_terms: D000162:Acoustics; D003198:Computer Simulation; D004738:Engineering / Q000295:instrumentation*; D004867:Equipment Design; D008962:Models, Theoretical; D009038:Motion; D009622:Noise / Q000517:prevention & control*; D009716:Numerical Analysis, Computer-Assisted; D011312:Pressure