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Linear and nonlinear analysis of the acoustic response of perforated plates traversed by a bias flow

Abstract : Thermo-acoustic instabilities are of primary concern in combustion chambers for a wide range of industrial applications, from domestic boiler to gas turbines or rocket engines. They are the consequence of a resonant coupling between the flame dynamics and the acoustic modes of the combustor, and can result in strong vibrations, early aging of combustor components and structural damage. The physical mechanisms involved are complex and difficult to model, thus thermo-acoustic oscillations are not easily predictable at the design stage of a combustor. In many combustors, passive dampers are implemented to increase the acoustic energy dissipation of the system and to hinder detrimental flame-acoustics interactions. In the present work, passive damping systems based on perforated screens backed by a resonant cavity and traversed by a bias flow are investigated. The main objectives are: (i) to improve and simplify the design of these dampers by maximizing their acoustic absorption properties in the linear regime, (ii) to analyze the effect of the sound wave amplitude on the acoustic response of these systems and (iii) to develop models capable of capturing absorption at high oscillation amplitudes. First, two interesting asymptotic regimes are identified where the plate operates at low and high Strouhal numbers respectively. In these regimes the design of a damper maximizing absorption is greatly simplified, since the choice of the optimal bias flow velocity and back cavity size can be decoupled. It is shown that at low Strouhal numbers the damper behaves as a quarter-wave resonator, and features a wide absorption bandwidth. At high Strouhal numbers, the system operates as a Helmholtz resonator, featuring shorter optimal back cavity sizes but narrower absorption bandwidths. These predictions are compared to measurements in a dedicated experimental setup for the different operating regimes identified. The dependence of the acoustic properties of a perforated plate on the forcing amplitude is then examined by means of direct numerical simulations. It is shown that transition from linear to nonlinear regimes occurs when the acoustic velocity amplitude in the orifice is comparable to the mean bias flow velocity. At high amplitudes, periodic flow reversal is observed within the perforation, vortex rings are alternatively shed upstream and downstream of the hole and convected away at a velocity which is increasing with the forcing amplitude. These mechanisms greatly influence the acoustic absorption of the perforate in the nonlinear regime. Two novel models capturing this nonlinear response are then inferred based on an analysis of the vortex trajectory (VC model), and on a quasi-steady description of the flow (IDF model). Their predictions are finally compared to measurements conducted in an impedance tube, and to results from numerical simulations. The results obtained in this work can be used to ease the design of robust dampers capable of operating in harsh environments with high sound levels, such as those found during self-sustained thermo-acoustic instabilities.
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Alessandro Scarpato. Linear and nonlinear analysis of the acoustic response of perforated plates traversed by a bias flow. Engineering Sciences [physics]. Ecole Centrale Paris, 2014. English. ⟨NNT : 2014ECAP0038⟩. ⟨tel-01126834⟩

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