Green's Functions for the Acoustic Field in Lined Ducts with Uniform Flow

• Published in: AIAA journal 2007-11, Vol.45 (11), p.2677-2687
• Main Authors: Alonso, Jose S, Burdisso, Ricardo A
• Format: Article
• Language: English
• Subjects: Acoustics; Aerodynamics; Aircraft; Exact sciences and technology; Flow velocity; Fundamental areas of phenomenology (including applications); Linear acoustics; Noise: its effects and control; Physics; Structural acoustics and vibration; Turbofan engines
• ISSN: 0001-1452; 1533-385X
• DOI: 10.2514/1.29872

This paper presents the analytical modeling of the radiation of sound from a moving boundary inside a lined circular duct containing uniform axial flow. This formulation can be used to model impedance discontinuities in the acoustic liners of turbofan-engine inlet ducts, such as the structural strips that separate liner panels, the liner splices near the fan, liner repair patches, and so forth. The model is based on finding a closed-form Green's function for the acoustic pressure inside the circular lined duct using a spectral expansion method, that is, using the duct modes. This method allows us to explicitly satisfy the continuity condition at the source location, which is strictly required by the Green's function. The solution is found for a point source and then extended to a finite piston by using the divergence theorem in the appropriate form to account for the effect of the soft wall. The Maxwell reciprocity principle used in this process is satisfied by using the adjoint Green's function, rather than the direct solution itself, because of the nonsymmetry introduced by the convective flow. As a consequence of the axial nonsymmetry, the expressions obtained for the radiated pressure depend on the direction of propagation of sound. The modeling of a circumferential array of rigid patches bonded to the surface of the liner is presented to illustrate the potential applications of this formulation. [PUBLICATION ABSTRACT]