GREEN’S FUNCTION OF THE CONVECTIVE GELMGOLTS EQUATION FOR THE FIRM-WALLED PIPE - Борисюк, А. (Science-based technologies, 2012)
Green’s function of the three-dimensional Helmholtz equation for an infinite straight rigid-walled pipe of circular cross-section with mean flow is found. This function is written in terms of series of the pipe acoustic modes, and is periodic in the azimuthal co-ordinate and symmetric about the pipe axial section of the point source location. Apart from this, the mean flow effects are directly reflected in the function. The effects become more significant as the flow Mach number increases, causing, in particular, the appearance and further growth of the Green’s function asymmetry about the pipe cross-section where the point source is located. And vice versa, the decrease of the Mach number results in the decrease of the effects 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.