Nonlinear asymptotic impedance model for a Helmholtz resonator liner

Numerical investigation of a honeycomb liner grazed by laminar and turbulent boundary layers

“…Under the assumption that the individual orifices do not interact (a point we will return to shortly) then a porosity-scaled impedance measure makes sense. Theoretical support for this scaling is given in Melling (1973), Hersh et al (2003) and in Singh & Rienstra (2014), for example, in the linear and weakly nonlinear sound amplitude regimes. Further support for the use of porosity-scaled impedance was given in Zhang & Bodony (2012) using normal impedance tube experimental data and more sophisticated semi-empirical models (Ingard 1953;Melling 1973;Jones et al 2004).…”

“…Marx & Aurégan (2013) performed linear stability normal mode analysis of a lined wall with flow and the effect of viscous dissipation while Fischer, Bake & Bassetti (2013) performed a comparison between the PIV and computational aeroacoustic results in the vicinity of an acoustic liner, with phase-locked results, with encouraging agreement between a linearized boundary condition and the experimental data. A recent theoretical nonlinear Helmholtz model was developed by Singh & Rienstra (2014) to be applicability in the weakly nonlinear sound amplitude regime. Ćosić et al (2015) investigated the effect of hot grazing flow over a Helmholtz resonator using PIV.…”

Dispersion, dissipation and refraction of shock waves in acoustically treated turbofan inlets

“…Under these conditions, the liner response to a single-frequency excitation would, in principle, consist of multiple harmonics. A detailed theoretical study carried out by Singh and Rienstra [21] reveals that the higher harmonic response is two orders of magnitude smaller than that of the fundamental away from liner cavity resonances and one order of magnitude smaller near resonances. Furthermore, although these results were derived in the weakly nonlinear limit, comparison with experimental data [21] indicates their validity for sound pressure levels as large as 150 dB.…”

“…A detailed theoretical study carried out by Singh and Rienstra [21] reveals that the higher harmonic response is two orders of magnitude smaller than that of the fundamental away from liner cavity resonances and one order of magnitude smaller near resonances. Furthermore, although these results were derived in the weakly nonlinear limit, comparison with experimental data [21] indicates their validity for sound pressure levels as large as 150 dB. This is also borne out in the detailed numerical simulations of Zhang [22], where it is shown that the response at the fundamental frequency is overwhelmingly dominant even at an excitation amplitude of 160 dB.…”

“…The present study employs a similar methodology, but the effects of nonlinearity, which are typically dominant only in the resistance component, are accounted for by assuming a linear dependence on the liner throughflow velocity [20]. With regard to the reactance, the effects of nonlinearity are small [20,21] so that the linear value of this quantity may be used.…”