Effect of Local Impedance Variation and Non-Linearity on Multiple Tone Attenuation

An iterative model based on an FEM propagation code is introduced for prediction of attenuation in a duct in the presence of a two degree of freedom acoustic lining for which impedance depends on local grazing flow speed and overall local sound pressure level. A general approach is described with emphasis on the case of a source spectrum dominated by several tones characteristic of multiple pure tones. Each tone is specified by its frequency, circumferential mode, and a statistically represented radial mode amplitude distribution. Lining impedance is computed locally dependent on local grazing flow Mach number and local sound pressure level spectrum and is described by an iterative model imbedded in the FEM propagation code. The propagation code is run sequentially within an iteration loop at frequencies of the targeted tones. A rapidly convergent iteration is used in which the source spectrum initially determines lining impedance locally. In successive iterations the local sound pressure level spectrum on the lining from the previous iteration determines the local impedance. The result is a method for prediction of the suppression of a multiple tone spectrum including the effect of lining non-linearity related to local sound pressure level. The iterative model is implemented in the context of the assessment of performance of a two degree of freedom lining that has been designed by conventional means not accounting for local impedance variation due to non-linearity and assuming that the source spectrum drives the impedance model. It is found that the effect of local lining non-linearity is to reduce realized attenuation in the targeted tones. An additional step in the lining design process is introduced in which spectrum levels used in determination of lining parameters to achieve required impedances are adjusted to reflect the reduction of sound pressure level along the lining. This results in reduced sensitivity of lining attenuation performance to local non-linearity. © 2010 by the American Institute of Aeronautics and Astronautics, Inc