Acoustic power in non-uniform lined ducts

A definition of acoustic power in conservation form in lined infinitely long uniform ducts is extended to include axially symmetric non-uniform ducts with potential mean flow and finite length lining. The definition includes a contribution at the lined boundary. Benchmarking is accomplished by verification of acoustic power conservation in the case of a purely reactive lining. Calculations in the case of reactively lined ducts show that intense acoustic gradients near the lined surface can occur, and contributions to acoustic power from the boundary power term become relatively large. This observed behavior diminishes as the resistive component of lining impedance is increased. Power calculations for propagation and radiation from a typical turbo-fan inlet and equivalent calculations for an infinite duct propagation model of the same inlet contour are compared. Results are remarkably similar for the case considered, though it is noted that this conclusion is geometry dependent.