GREEN'S FUNCTION OF THE CONVECTIVE WAVE EQUATION FOR THE RIGIDWALLED PIPE

Abstract

Green’s function of the three-dimensional wave equation for an infinite straight rigid-walled pipe of circular cross-section with mean flow is found. This function is written in terms of the series of the pipe acoustic modes, and is periodic in the azimuthal coordinate and symmetric about the pipe axial section of the unit point impulse source location. Each term of the series is a sum of the direct and reverse waves propagating in the corresponding pipe mode downstream and upstream of the noted source. In the found Green’s function, the mean flow effects are reflected in the direct manner. The effects become more significant as the flow Mach number increases, causing, in particular, the appearance and further growth of the function asymmetry about the pipe cross-section of the source location. And vice versa, the decrease of the Mach number results in the decrease of the ef-fects and, in particular, the decrease of the indicated asymmetry of the function. In the case of mean flow absence the obtained Green’s function is symmetric about the indicated cross-section and coincides with the corresponding Green’s function for the investigated pipe, which is available in the scientific literature.