A.O.Borisyuk The Green's function of a tree-dimensional convective wave equation for a straight channel |
Acoustic bulletin, Vol. 17 ¹ 1, (2015) |
| The Green’s function of the three-dimensional convective wave equation for a straight channel of arbitrary (but constant along its length) cross-sectional shape, having either acoustically rigid or acoustically soft walls or the walls of a mixed type, is obtained by the method developed in this work. This function is represented by a series of the channel acoustic modes. Each term of the series is a superposition of the direct and reverse waves propagating in the corresponding mode downstream and upstream of the unit point impulse acoustic source, respectively. In the found Green’s function, the effects of a uniform mean flow in the channel are directly reflected. 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 channel cross-section in which the noted source is located. Vice versa, the decrease of the Mach number results in the decrease of flow effects and, in particular, decrease of the indicated function asymmetry. In the case of flow absence in the channel, the obtained Green’s function is symmetric about the noted cross-section. On the base of the above-mentioned method, the Green’s functions of the three-dimensional convective wave equation for straight channels of rectangular and circular cross-sectional shape are also obtained. Moreover, a transformation is suggested that allows the reduction of the one-dimensional convective Klein-Gordon equation to its classical one-dimensional counterpart having the known solution. |
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KEY WORDS: flow in the channel, the Green's function, the Mach number, the convective wave equation |
| TEXT LANGUAGE: Ukrainian |