Source effects on attenuation in lined ducts. Part II: Statistical properties

Statistical models for acoustic attenuation in non-uniform ducts with mean flow are developed. With source descriptions based on random distributions of input modal powers and modal phase, numerical experimentation has revealed that statistical metrics of lining performance can be generated. These include probability density functions for transmitted acoustic power and attenuation, expected (mean) attenuation, and standard deviation from the mean. An important result is that for a broadband source represented by many acoustic modes, the transmitted power appears to be described by a Gaussian distribution. In the present investigation it is shown that based on arguments involving the duct transmission model and the Central Limit Theorem, the Gaussian distribution of transmitted power observed by numerical experiment is expected. For all cases, including tonal noise represented with relatively few modes, it is shown that statistical characteristics can be described by common probability density functions and conclusions about mean attenuation, deviation from the mean, and cumulative distributions are drawn. The statistical approach described has application for design of acoustic treatment in cases where knowledge of the details of the source is minimal or non-existent.