A new shear-layer growth-rate compressibility-scaling parameter is proposed as an alternative to the total convective Mach number, M c . This parameter derives from considerations of compressibility as a means of kinetic-to-thermal-energy conversion and can be significantly different from M c for flows with far-from-unity free-streamdensity and speed-of-sound ratios. Experimentally observed growth rates are wellrepresented by the new scaling.

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Two time-domain impedance models developed recently have been examined and tested numerically. One is based on the three-parameter model of Tam and Auriault augmented by a method to evaluate the effective impedance under flow conditions for a harmonic source. The other is Rienstra's extended Helmholtz resonator model. Its timedomain representation is fully based on the idea of Özyörük and Long to use a z transformation for an impedance function with periodic frequency response. The implementation of the models in a numerical simulation tool with the dispersion relation preserving scheme is discussed in detail. A filtering approach guarantees the stability of the Myers boundary condition. The results from both of the two models agree notably well with each other. The validation and verification of both models are carried out for the latest NASA impedance tube experiment. The adaptability to realistic inlet configurations is shown using a generic aeroengine geometry with available numerical results. Overall, both models give a similar physical behavior if limitations are carefully considered. The extended Helmholtz resonator is used as termination impedance. A broadband impedance eduction is successfully carried out, resulting in an extended Helmholtz resonator representation for a ceramic tubular liner. Nomenclature A, B, C, D = coefficient matrices (LEE) F 0 = flux vector (LEE) i = imaginary unit, e i!t convention m = face reactance (EHR) n = radial mode number n = wall normal vector p = pressure amplitude p 0 = pressure perturbation p 0 = mean pressure R = face resistance (EHR) R 0 0 = effective resistance parameter (EFI) s p = auxiliary variable (EFI and EHR) T l = period time (EHR) u n = normal velocity amplitude u 0 = mean velocity vector u 0 n = normal velocity perturbation u 0 = velocity perturbation X 0 1 = effective reactance parameter (EFI) X 0 1 = effective reactance parameter (EFI) Z= complex impedance = cavity reactance (EHR) = ratio of the specific heats "= cavity resistance (EHR) = correction coefficient (EFI and EHR) t = Myers term (EHR) = azimuthal mode number x = damping coefficient 0 = perturbation state vector ! = angular frequency % 0 = mean density % 0 = density perturbation

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