A comparison of the damping properties of perforated plates backed by a cavity operating at low and high Strouhal numbers

Alessandro Scarpato; Sébastien Ducruix; Thierry Schuller

doi:10.1016/j.crme.2012.10.016

Combustion, flow and spray dynamics for aerospace propulsion

A comparison of the damping properties of perforated plates backed by a cavity operating at low and high Strouhal numbers

Alessandro Scarpato ^1,² ; Sébastien Ducruix ^1,² ; Thierry Schuller ^1,²

¹ CNRS, UPR 288, Laboratoire dʼÉnergétique Moléculaire et Macroscopique, Combustion (EM2C), 92295 Châtenay-Malabry, France
² École Centrale Paris, 92295 Châtenay-Malabry, France

Comptes Rendus. Mécanique, Volume 341 (2013) no. 1-2, pp. 161-170.

Résumé
Abstract

Les plaques perforées couplées à une cavité résonante et traversées par un écoulement axial sont souvent utilisées pour augmenter lʼamortissement acoustique dans les moteurs aéronautiques. Leur conception repose sur une procédure dʼoptimisation complexe, avec un jeu important de paramètres à examiner. Dans cette étude nous montrons comment réduire ce nombre de paramètres en maximisant lʼabsorption dans deux régimes asymptotiques où les choix de la vitesse optimale dans les trous et de la taille de la cavité résonante peuvent être découplés. Des expressions analytiques utiles lors de la conception sont indiquées pour ces deux régimes de fonctionnement caractérisés par des bandes dʼabsorption étroite à fort Strouhal et large à faible Strouhal. Ces développements sont valides pour des plaques perforées de différentes porosités et épaisseurs en absence dʼécoulement rasant. Ils peuvent contribuer à améliorer la conception de systèmes robustes dʼatténuation dʼinstabilités de combustion lorsque la fréquence de lʼinstabilité varie.

Liners backed by a resonant cavity and traversed by a bias flow are widely used for acoustic damping in aeronautical engines. Their design relies on a relatively complex optimization procedure with a large number of parameters to examine. It is shown in this study how to reduce this number by maximizing absorption in two limit regimes where the choice of the optimal bias flow velocity and size of the back cavity can be decoupled. These developments apply for perforated plates of different porosity and thickness in the absence of grazing flow. In these regimes, the optimal bias flow velocity is only controlled by the plate porosity while the size of the back cavity fixes the peak absorption frequency. The first absorption regime reached at high Strouhal numbers is characterized by a Helmholtz resonance ( $He ≪ 1$ ) and a narrow frequency absorption bandwidth. The Mach number associated to the optimal bias flow velocity is then given by $M_{c} = (2 / π) σ$ , where σ is the plate porosity. This regime minimizes the size of the resonant back cavity, but the absorption bandwidth narrows also with the Strouhal number. The second absorption regime reached at low Strouhal numbers operates with a quarter-wave resonator ( $He ≃ π / 2$ ) and a bias flow velocity fixed by $M_{c} = σ / 2$ . This regime offers a wide absorption bandwidth around the peak absorption frequency well suited for low frequency dampers when the bias flow velocity may vary within the system. Theoretical expressions derived in this study are validated against experimental data in the two regimes identified. They may be used to ease the design of robust dampers to hinder self-sustained thermo-acoustic instabilities when the instability frequency varies.

Publié le : 2013-01-01

DOI : 10.1016/j.crme.2012.10.016

Keywords: Robust control, Perforated plate, Acoustic damping, Thermo-acoustic instabilities, Sound absorption
Mots clés : Contrôle robuste, Plaque perforée, Amortissement acoustique, Instabilités de combustion, Absorption sonore

Affiliations des auteurs :

Alessandro Scarpato ^{1, 2} ; Sébastien Ducruix ^{1, 2} ; Thierry Schuller ^{1, 2}

¹ CNRS, UPR 288, Laboratoire dʼÉnergétique Moléculaire et Macroscopique, Combustion (EM2C), 92295 Châtenay-Malabry, France
² École Centrale Paris, 92295 Châtenay-Malabry, France

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Alessandro Scarpato; Sébastien Ducruix; Thierry Schuller. A comparison of the damping properties of perforated plates backed by a cavity operating at low and high Strouhal numbers. Comptes Rendus. Mécanique, Volume 341 (2013) no. 1-2, pp. 161-170. doi : 10.1016/j.crme.2012.10.016. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2012.10.016/

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