Broadband noise suppression for turbofan inlet applications

Abstract

Broadband noise in turbofan inlets is represented in a frequency domain analysis by a statistical distribution of propagating duct modes. The required number of modes is estimated by Rice’s approximation method. A brief overview of essential results from the theory of acoustic propagation in ducts is given, providing a starting point for Rice’s estimation of the distribution of propagating modes in a uniform unlined duct required to represent a broadband noise source. The relationship between mode cut-off ratio and attenuation in lined ducts is examined to connect cut-off ratio to modal attenuation, and it is shown by example that for arbitrary impedance at a specified frequency, modes with similar cut-off ratios have similar attenuation. It is then shown by example that the attenuation of a low-order circumferential mode, specifically the axially symmetric circumferential mode, with a large range of propagating radial mode cut-off ratios, is insensitive to impedance variations near the optimum impedance. Two models for estimating achievable attenuation for broadband noise attenuation, based on equipartition of acoustic power among propagating modes, are considered. One uses only the axially symmetric circumferential mode, and the second uses all propagating circumferential modes and their associated propagating radial modes. A new parallel architecture version of an established propagation code, designed to include all propagating modes on a statistical basis, is described. Examples for prediction of acoustic power attenuation of broadband noise at low frequency and at moderate frequency are used to compare the performance of the axially symmetric circumferential mode and the all circumferential mode models. It is shown by example that a broadband noise model based on the axially symmetric circumferential mode predicts lower attenuation than a model with all propagating circumferential modes. Rice’s correlation of mode cut-off ratio with attenuation justifies this observation.