Rainbow-trapping resonator array for high-level sound absorption

Sound absorbers designed for high sound pressure levels (SPLs) are ever more critical in aerospace industries. Traditional solutions with resonant absorbers exhibit useful damping properties, although they can struggle to maintain the intended behaviour at the high SPLs readily encountered during flight conditions.

By Adam A. Cavanagh, Acoustics Engineering Research MSc student, The University of Salford

Noise control methods in ducted aeroengines typically rely on perforated liners installed along engine intakes and exhausts. For example, single- and double-degree-of-freedom resonator arrays usually compose such liners by cavity- backing the perforations. Under linear acoustic conditions (120 dB), these resonators are efficient sound absorbers due to the thermoviscous losses inherent in their narrow dimensions. However, their performance can change significantly at sufficiently high SPLs due to the amplitude-dependent increase of perforates’ acoustic resistance.

Resonant absorbers generally have narrow band gaps, meaning that they interact with waves with frequencies near the structure’s resonance frequency, thus resulting in targeted sound absorption. The primary noise source in turbofan or electric ducted fan (EDF) engines is the fans and their spectra include both broadband and sharp tonal components that can exceed 150 dB during flight conditions. The noise’s high SPL and broadband nature make effective attenuation challenging. This and forecasted air travel trends highlight the need for effective sound absorbers. By analysing a 2D proof-of-concept absorber, we show that the rainbow-trapping effect can be used to design a compact and efficient high SPL broadband sound absorber.

Below: The 2D RTRA’s configuration. Five resonators are attached to a main duct, with the incident, transmitted and reflected wave icons

Acoustic rainbow-trapping
‘Rainbow-trapping’ refers to a spatial reduction in wave speed (slow sound). In this case, the reduction causes the energy of different frequency waves to become ‘trapped’ at differing points in space, where, once trapped, the inherent attenuation mechanisms efficiently dissipate that energy. We achieve this by tuning an array of ducted Helmholtz resonators (HRs) to cascade their resonance frequencies. Hence, they cover a broadband range when combined.

Design principles
The 2D rainbow-trapping resonator array (RTRA) comprises five HRs attached side-on to a duct of 29mm arbitrary height. The RTRA linear response (low SPL) was approximated using the transfer matrix method with equivalent properties obtained from the Johnson-Champoux-Allard model. We constrained the total length and width to 100mm and 30mm to represent realistic size restrictions.

The five HRs were tuned using an optimisation method (genetic algorithm) constrained to enhance absorption at high SPLs (e.g. > 130 dB). The paramount constraint was on the neck widths, ensuring a minimum height of 4mm. This way, the optimised design facilitates nonlinear loss mechanisms (e.g. vortex shedding) to dissipate high-amplitude wave energy more efficiently.

The HRs were tuned to the 1-2 kHz range to cover a typical aeroengine’s loudest fan noise harmonics (due to the blade passing frequency). These components are more noticeable than the broadband components so targeting them is a good way to reduce the perceived loudness and annoyance.

Performance
The RTRA’s nonlinear response (high SPL) was analysed numerically using the finite element method in COMSOL Multiphysics TM. The system was excited with plane waves at three SPLs, 80 dB, 130 dB and 155 dB, corresponding to the linear, weakly nonlinear and strongly nonlinear regimes. The RTRA shows reasonable broadband absorption at 80 dB. The four distinct peaks illustrate how each HR contributes to the combined response; their resonances overlap due to the moderate quality factors, causing maxima between each HR resonance frequency. The absorption grows substantially with SPL thanks to their relatively wide necks, contrasting a typical resonant absorber’s behaviour (usually with sub-millimetre-sized perforations), where the increased resistance reduces absorber-wave interaction and inhibits energy dissipation. Conversely, the RTRA design exploits the increasing resistance. Its absorption is approximately 0.8 or higher across the target range at 155 dB.

Above: Absorption plot: Frequency-dependent sound absorption of the RTRA at low, medium and high SPLs. Results were obtained numerically using FEM

Next steps
The conceptual RTRA highlights potential methods for high SPL broadband sound absorption. We plan to build on the summarised modelling work to represent realisable (axisymmetric) geometric configurations and experimentally validate the results with impedance tube measurements. The findings will help design compact and lightweight sound absorbers for small- and large-scale ducted fan engines.