Estudo de modos acústicos em ramificação de duto cilíndrico utilizando funções de Green

Abstract

In this work, we investigate the propagation of sound in internal flows and the possibility of coupling between different modes in a side-branch of a hard walled duct. A convected wave equation for the pressure flutuation, including viscosity effects is developed. The Green function for the wave operator is obtained in the frequency domain. An expression for the interaction of modes in the side branch is developed, in terms of Bessel functions, as a result of a plane wave incident in the main duct, by considering a convolution integral between the Green function and the axial component of the velocity fluctuation. The interaction of radial modes is demonstrated through the resulting integral of product of Bessel functions.