Analytical formulation of the radiation of sound from a rectangular lined duct
Keywords:Acoustic impedance, Approximation theory, Ducts, Mathematical models, Modal analysis, Directivity pattern, Impedance discontinuity junction
AbstractThis paper deals with the radiation of sound from the open-end of a flanged rectangular lined duct. The duct model consists of a semi-infinite rectangular duct with a lined section of length L. The efficiency of the acoustic treatment for the radiated sound is evaluated by comparing the total power radiated from a duct with and without the lined section. This procedure also allows evaluation of the directivity patterns. The transmitted modal coefficients at the impedance discontinuity junction for a propagating mode (plane wave or higher order mode), incident from the rigid duct, are calculated. Simple analytical tools to predict the radiation of sound have been developed by using `baffled membrane' approximation method. This model cannot handle reflections from the end, nor radiation to the back, nor an eventual outside flow. However, it is well adapted to the case of a lined duct treated with an arbitrary acoustic impedance, where an exact solution for even a two-dimensional duct is difficult. This method can be applied to turbofan noise and to HVAC systems for possible altering of the radiation pattern by either modifying the radiation field or the types of propagating modes.
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