Development of the numerical method for calculating sound radiation from a rotating dipole source in an opened thin duct

Abstract

Sound radiation from a rotating dipole source in an opened thin duct is analyzed using the thin-body boundary element method in the frequency domain. The difficulty in describing the rotating source in the frequency domain is overcome by introducing a fixed Kirchhoff surface around the rotating source. Acoustic pressures generated from a rotating dipole source, a rotating point force, on the Kirchhoff surface are calculated using Lowson's equation. Normal derivatives on the Kirchhoff surface of acoustic pressures in the Helmholtz integral equation are derived analytically in this paper. Radiated acoustic pressure from the Kirchhoff source and that of the rotating original source in a free field are compared. Effects of the number of elements on the Kirchhoff surface are verified. The analytic solution for a dipole source in a duct is compared with the one obtained by the current Kirchhoff–Helmholtz thin-body boundary element method (K–H TBEM). Sound radiation from a ducted rotating force is calculated using K–H TBEM for selected rotating speeds. It is shown that wave propagation is strongly dependent on the cutoff frequency of the duct. Radiated acoustic pressure can be increased or decreased according to the relation between the cutoff frequency of the duct and the rotating frequency of the source.