This paper presents the results of insertion loss measurements and numerical impedance eduction of three different liner samples. An overview of the test rig and methodology is given, and preprocessed results in terms of reflection and transmission coefficients as well as the energy dissipation are discussed. These coefficients are calculated for discrete frequencies within the investigated frequency range. Subsequently, a numerical postprocessing is performed in the time domain, and the educed impedance function for each sample and flow Mach number is presented. This postprocessing in the time domain uses an impedance model based on the extended Helmholtz resonator with five free parameters. The parameters of the model are fitted via an optimization, which determines the whole frequency response in one optimization process. The comparison of measured and numerically evaluated energy coefficients proves the reliability of the tools for impedance evaluation under flow conditions. Finally, the impedance results of the different samples are discussed, including a comparative study with Aermacchi data of the National Aerospace Laboratory (The Netherlands) flow tube and Aermacchi impedance tube experiments. NomenclatureA Facesheet = area of the liner facesheet A Hole = area of one hole c = speed of sound d = spacing between two holes e r = radial vector, pointing from the source to the boundary point f = frequency f R;H = Helmholtz resonance frequency f R;L = =4-resonance frequency F = objective function ImfZg = reactive part of the impedance l Cell = cell depth l Neck = thickness of the perforated facesheet/neck length l corr: Neck = neck length with correction M = mean Mach number in the duct m = facesheet reactance (extended Helmholtz resonator model) n Hole = number of holes in the liner facesheet p = pressure R = reflection (energy value) RefZg = resistive part of the impedance R f = facesheet resistance (extended Helmholtz resonator model) r = reflection (amplitude ratio)/radius r Hole = radius of one hole T = transmission (energy value) T l = time delay (extended Helmholtz resonator model) t = transmission (amplitude ratio)/time u = velocity field V Cell = volume of one cell behind a hole v g = group velocity = cavity reactance (extended Helmholtz resonator model) = ratio of specific heats = energy dissipation " = cavity resistance (extended Helmholtz resonator model) = wave length % = density of the fluid c = characteristic impedance of the fluid = open-area-ratio of the liner = porosity of the liner facesheet ! = angular frequency Superscripts = in downstream direction = in upstream direction 0 = perturbation 0 = mean value

The design of acoustic liners with complex cavities for a wide frequency range of attenuation using numerical method is investigated in this paper. Three novel liner concepts are presented, demonstrating predicted improvements in broadband sound absorption when compared with that for conventional designs. The liners include a slanted septum core, a slanted septum core with varying percentage open area, and a MultiFOCAL concept. A finite element model of a normal incidence impedance tube is developed using COMSOL Multiphysics modeling software to predict the acoustic properties (resistance and reactance) of liners at medium and high sound pressure levels, and to study the impact of variations in the liner design parameters. The impedance tube finite element model incorporates non-linear semi-empirical impedance equations, validated by comparing numerical results with measurements performed on a single-degree-of-freedom liner, with a perforated face sheet, at high sound pressure level. The design variables of the novel liner concepts are optimized using a hybrid automated optimisation procedure. The low-frequency optimum slanted septum core concept with an open area of 4.5% for the face sheet and 18% for the short slanted septum is predicted to have an absorption level of at least 14 dB in the frequency range of 400–1000 Hz for normally incident pure tone excitations at 150 dB. The slanted septum core concept with varying percentage open area, with broadband optimum design variables, is predicted to have good broadband sound absorption levels of at least 10 dB in the frequency range of 570–3800 Hz. Finally, the MultiFOCAL liner concept with optimised percentage open areas is predicted to have an excellent broadband sound absorption levels of at least 14 dB, for pure tone excitations at 150 dB, in the frequency range of 900–5300 Hz. This work will be followed by optimisation of the face sheet geometries of these novel liner designs in order to maximise lined duct attenuation for aircraft engine applications.