Multimodal far-field acoustic radiation pattern - An approximate equation

The far-field sound radiation theory for a circular duct was studied for both single mode and multimodal inputs. The investigation was intended to develop a method to determine the acoustic power produced by turbofans as a function of mode cut-off ratio. This information is essential for the design of acoustic suppressors in engine ducts. With reasonable simplifying assumptions the single mode radiation pattern was shown to be reducible to a function of mode cut-off ratio only (modal indices removed). With modal cut-off ratio as the dominant variable, multimodal radiation patterns can be reduced to a simple explicit expression. This approximate expression provides excellent agreement with an exact calculation of the sound radiation pattern using equal acoustic power per mode. Radiation patterns for cases other than equal modal power are presented using the approximate radiation equation. An approximate expression for the duct termination losses as a function of cut-off ratio is also included.