Green’s Functions Of A Non-Self Adjoint Operator Applied To Sound Radiation In A Circular Duct With Axial Flow.

Abstract

This paper presents a mathematical model to simulate the sound radiation from a
moving boundary of a lined circular duct in the presence of a convective axial flow. The
model is based on finding a new closed form solution for the Green’s functions of the
convected wave equation inside a soft wall duct, using the eigenfunctions method. Using the
Divergence Theorem, this closed form solution allows to find expressions for the sound field
generated by a rectangular shaped piston source with uniform velocity. This formulation can
be applied to model discontinuities in acoustic liners for turban engines such as embedded
actuators used in active noise control, the scattering effects of liner splices near the fan and
so forth. By properly selecting the piston velocity or strength, the different discontinuities in
the liner can be modeled. An example consisting of a circumferential array of rigid patches
mounted on the wall of the lined duct is described.