Models for Acoustically-Lined Turbofan Ducts

Abstract

Several models have recently been proposed for the impedance response of an acoustic lining; most recently, Rienstra's Enhanced Helmholtz Resonator model. All of these models have stability issues with nonzero mean flow, and there has been some debate over the existence of hydrodynamic instability waves over the surface of such acoustic linings. Mathematically, the standard proven Briggs-Bers stability analysis is not applicable. Computationally, the hydrodynamic modes are routinely ignored (in the frequency domain) and instabilities filtered out (in the time domain). This ambiguity causes significant problems for mode-matching and for scattering analysis. The inadequacies of the recently-proposed "Crighton-Leppington" stability criterion are demonstrated through a number of counterexamples. It is then shown that any impedance lining model not capable of being analysed using the Briggs-Bers criterion is illposed, in the true mathematical sense, and an explanation is given as to why such models should not be used in practice. Some commonly-used locally-reacting impedance boundaries (namely the mass-springdamper, three-parameter, Helmholtz Resonator, and Enhanced Helmholtz Resonator models) are shown to be illposed, and an empirical impedance model is suggested that is wellposed and stable, whilst maintaining mass-spring-damper-like behaviour for the propagating and first few cutoff modes. It is suggested that this model may well resolve the ambiguity caused by surface modes in scattering and mode-matching problems. A suggestion is also made for an additional fifth condition to be added to Rienstra's four conditions necessary for a locally-reacting impedance to be admissible.

Mean flow boundary layer effects of hydrodynamic instability of impedance wall

“…For a long time, however, there has been doubts [5,6,7] about a particular wave mode that exists along a lined wall with flow and the Ingard-Myers condition. This mode has some similarities with the Kelvin-Helmholtz instability of a free vortex sheet [8] and may therefore represent an instability, although the analysis is mathematically subtle [9,10,11,12].…”

Swirling mean flow effects on locally reacting interstage liner

“…Aurégan & Renou 25 experimentally evidenced the failure of Myers' boundary condition to retrieve proper impedance values in the context of impedance eduction. In parallel, Brambley 26 analytically highlighted some stability issues inherent to Myers' boundary condition. Consequently, several alternative models have been proposed to improve this boundary condition.…”