Prediction of Sound Propagation in Ducted Potential Flows Using Green's Function Discretization

Abstract

The sound propagation in ducted mean potential flows is computed by using a Green’s function discretization (GFD) technique. Linear combinations of the free-space Green’s functions of the locally uniform convected Helmholtz problem are analytically differentiated to build shape functions for the derivatives of the acoustic potential. These are used to discretize both the field governing equation and the boundary conditions. The GFD approach is validated by computing the sound propagation in annular ducts with hard/soft walls and uniform flow. Acoustic modes of increasing wave number are computed without changing the computational mesh. A good level of accuracy is ensured up to three points per wavelength. As a first step toward relevant applications, the propagation in nonconstant annular ducts, with/without wall treatment and with/without flow, is computed. The numerical solutions compare favorably with the well-known analytical multiscale solutions.