Presented here is the development of a predictive model for impedance of single-degree-of-freedom (SDOF) and two-degree-of-freedom (2DOF) acoustic linings that is suitable for the design stage of suppression of inlet noise for turbo-fan engines. It is required that over a probable range of lining physical parameters and operating conditions the impedance spectrum is predicted with accuracy sufficient to support a lining design process and assessment of achievable attenuation. The starting point is a published impedance model for SDOF linings that primarily focuses on the transfer impedance of conventional and micro-perforate face sheets with grazing flow. This is expanded here to include 2DOF linings, introducing new issues related to transfer impedance of the inserted septum. Problems addressed are related to the septum insertion process that can change thickness, hole diameter and open area ratio of the uninstalled septum, and introduce blockage. Required empiricism is discussed and models for face sheet and septum-in-core transfer impedance are derived, applicable to a specific range of sheet thickness, hole diameter, and open area ratio. Manufacturing processes considered are mechanical drilling in the case of the carbon fiber laminate face sheet that is conventional perforate, and laser drilling in the case of the epoxy film micro-perforate septum material. Benchmarking is carried out by comparison of acoustic field predictions, using the proposed lining model in an FEM propagation code, with measured data from a grazing flow duct facility. Test samples include SDOF and 2DOF linings, including cases with three segments, each with distinct physical properties. Example results of comparisons are shown to highlight the fidelity of the impedance model over a frequency range compatible with the grazing flow duct geometry.
A modified reciprocal equation to predict the complex transmission coefficient of a flow duct
