Impedance models for single and two degree of freedom linings with an improved data base and local non-linearity

Abstract

Previously developed predictive models for impedance of single-degree-of-freedom and two-degree-of-freedom acoustic linings driven by a broad band acoustic source are reexamined. Two issues are addressed, the first being improvement of the conventional perforate face sheet impedance model. Data correlations based on flow bench measurements of steady flow pressure drop are reevaluated with emphasis on low flow velocity to improve the consistency of the prediction of linear resistance. In addition, for two-degree-of-freedom linings, face sheet mass reactance is modified to account for the presence of the septum. The second issue addresses the implication that for a non-linear lining, with impedance a function of the local sound pressure level, the installed performance of the lining depends on the local impedance, as opposed to impedance based on the source sound pressure level. This is investigated in the benchmarking of the impedance models by comparison of the acoustic transfer function predicted by a propagation code with the imbedded impedance model and transfer function measurements made in a grazing flow duct test facility. The propagation code is extended to make the non-linear behavior of the lining model dependent on the local acoustic spectrum, introducing an additional level of non-linearity and an iterative application of the propagation code. A principal conclusion is that with no grazing flow both the lining model and grazing flow duct transfer function measurements show a significant effect of local variation of the acoustic spectrum. With increasing grazing flow Mach number, this effect is reduced and effectively disappears at the highest Mach number. With increasing grazing flow Mach number the grazing flow contribution to face sheet resistance dominates and tends to mask the non-linear behavior of the component of resistance not related to grazing flow.