Refinement of Impedance Models for Single and Two Degree of Freedom Linings based on Grazing Flow Duct Predictions and Measurements

A previously developed predictive model for impedance of single-degree-of-freedom and two-degree-of-freedom acoustic linings is extended to examine the effect of non-linearity on the assessment of fidelity of the model. Non-linearity was originally included in the impedance model via dependence of face sheet and septum flow resistance on acoustic particle velocity. Benchmarking was done by comparison of the acoustic field predicted by a propagation code with the imbedded impedance model and measurements made in a grazing flow duct test facility. The non-linear behavior of the lining model in the propagation code depended on the acoustic spectrum of the source. In this investigation the propagation code is extended to make the non-linear behavior of the lining model dependent on the local acoustic spectrum seen by the lining, accounting for the possibly significant local variation of sound pressure level created by the lining. This introduces an additional level of non-linearity that is approached by an iterative application of the propagation model. The principal conclusion drawn is that the significance of local variation of SPL is dependent on the increase of grazing flow resistance with grazing flow Mach number that tends to mask the flow resistance related to perforate flow resistance. The present study also reexamines the face sheet impedance model with the goal to improve the consistency of the linear resistance component. The septum impedance model is repeated for completeness, as is the grazing flow resistance model.