Computing the sound power in non-uniform flow

An expression for the sound power in an annular duct with swirling mean flow is derived in the high-frequency limit relevant to fan aeroacoustics. The sound power is expressed in terms of the duct normal modes which are computed for several mean flows. It is shown that the mean flow non-uniformity modifies both the pressure-dominated modes and the expression for the sound power. The pressure-dominated modes are not orthogonal and thus one must account for interference between the different radial modes. The interference effects are small for the case of a potential mean flow. For a vortical mean flow interference terms may become significant.