A.O.Borisyuk The Green's function of the tree-dimensional convective Helmholtz equation for a straight channel |
Acoustic bulletin, Vol. 17 ¹ 2, (2015) |
| This paper deals with developing of method for obtaining the Green's function of a three-dimensional convective Helmholtz equation for an infinite straight channel of arbitrary (but constant along its length) cross-sectional shape and area, having either acoustically rigid or acoustically soft walls, or the walls of a mixed type. This function admits a representation by the series of the channel acoustic modes. In the obtained Green's function, the effects of a uniform mean flow in the channel are explicitly reflected. They become more significant with the increase of the flow Mach number causing, in particular, the appearance and further growth of the function asymmetry about the cross-section where the acoustic source is located. In the case of flow absence, the obtained Green's function is symmetric about this cross-section. On the based of the above mentioned method, the Green's functions of a three-dimensional convective Helmholtz equation are obtained for the infinite straight channels of circular and rectangular cross-section and various wall types. |
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KEY WORDS: flow in the channel, the Green's function, the Mach number, the convective wave equation, acoustic modes |
| TEXT LANGUAGE: Ukrainian |