Acoustic Power in 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 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 are made for FEM models of acoustic radiation to the far field and it is demonstrated that conclusions reached about lining performance based on acoustic power attenuation are not necessarily duplicated in comparisons of a non-uniform duct of infinite length and its equivalent finite length duct radiating to the far field.