Impedance modelling of acoustically treated circumferential grooves for over-tip-rotor fan noise suppression

Abstract

Experimental investigation of Over-Tip-Rotor circumferential groove liners has shown potential for fan noise suppression in turbofan engines whilst providing minimal penalty in fan aerodynamic performance. The validation of Over-Tip-Rotor liner analytical prediction models against published experimental data requires the modelling of an equivalent impedance for such acoustic treatments. This paper describes the formulation of two analytical groove impedance models as semi-locally reacting liners, that is locally reacting in the axial direction and non-locally reacting in the azimuthal direction. The models are cross-verified by comparison with high-order FEM simulations, and applied to a simplified Over-Tip-Rotor configuration consisting of multiple grooves excited by a monopole point source located close to the grooved surface.

Design of a single degree of freedom acoustic liner for a fan noise test rig

“…2 The acoustic liners are commonly employed at the nacelle internal walls, more specifically the inlet and bypass ducts, whereas over-the-rotor and external liners are currently under investigation. [4][5][6] The acoustic effectiveness of liners depends not only on its geometry, but also on the environmental conditions found in turbofan engines, namely high grazing flow velocity and high sound pressure levels. These two combined effects represent a striking challenge for liner modelling, predictive tools and experimental techniques.…”

Modeling of Over-Tip-Rotor Liners for the Suppression of Fan Noise

“…In this section an analytical Green's function model termed 'Green/FINF' is described for a Finite length liner Locally reacting in the axial direction and non-locally reacting in the azimuthal direction, as described in [11]. The acoustic field generated at x = ( , , ) by a distribution of dipoles ( ) located at y = ( , , ) on a 'blade' surface within the lined section of a duct is given by the non-dimensional version of the Goldstein acoustic analogy in the frequency domain [12]…”

“…It is noted that Eq. 6 is singular at the cut-on/cut-off frequency of each mode, which is considered in more detail in section V. This formulation is used for predicting the sound field for any locally reacting specific acoustic impedance (Z) but is also applied here to the case of a semi-locally reacting liner impedance such as the acoustically treated grooves described in [11] and addressed in this paper for the comparison with the W-8 data.…”

On the flow-acoustic coupling of fan blades with over-the-rotor liner

“…The decoupled assumption is also adopted in a recent analytical model of over-the-rotor acoustic treatment (Palleja-Cabre et al. 2019, 2020), where the sound attenuation by a circumferential groove liner was predicted using the tailored Green's function, with the rotor simplified as a point source of unit amplitude. On the other hand, the theoretical models for the prediction of aerodynamic sound sources in axial flow turbomachines usually consider highly simplified acoustic boundary conditions.…”

“…Examples of separate sound propagation analyses include the predictions based on the Wiener-Hopf technique (Noble 1958) of sound scatterings from flow ducts with semi-infinite acoustic linings (Liu et al 2016;Jiang, Lau & Huang 2018), the sound field predictions by the mode-matching technique (Zorumski 1974) and those by the commonly used finite element methods (Rienstra & Eversman 2001;Eversman 2003). The decoupled assumption is also adopted in a recent analytical model of over-the-rotor acoustic treatment (Palleja-Cabre et al 2019, 2020, where the sound attenuation by a circumferential groove liner was predicted using the tailored Green's function, with the rotor simplified as a point source of unit amplitude. On the other hand, the theoretical models for the prediction of aerodynamic sound sources in axial flow turbomachines usually consider highly simplified acoustic boundary conditions.…”