Duct noise radiation through a jet flow

The radiation of internal (or core) noise for aircraft turbojet or turbofan engines is studied analytically. The geometry of a typical engine is simplified for analytical considerations to a hemispherical shell with a jet flow and internal sound emanating through a circular hole on the axis. A linearized theory is used to derive a flow modified spherical wave equation. A forced separation technique is used to produce a modified Legendre equation describing the angular variation of the acoustic radiation field. Then a numerical technique is described for obtaining a general field solution by progressively imposing continuity of pressure across hemispherical shells as the solution is marched from near field to the far field. In a companion paper, numerical results are presented and compared with experimental results from a test configuration identical to that described by the theory.