Daniel Mazzoni

Finite Difference Method for the Acoustic Radiation of an Elastic Plate Excited by a Turbulent Boundary Layer: A Spectral Domain Solution

A finite difference method is developed to study, on a two-dimensional model, the acoustic pressure radiated when a thin elastic plate, clamped at its boundaries, is excited by a turbulent boundary layer.Consider a homogeneous thin elastic plate clamped at its boundaries and extended to infinity by a plane, perfectly rigid, baffle. This plate closes a rectangular cavity. Both the cavity and the outside domain contain a perfect fluid. The fluid in the cavity is at rest. The fluid in the outside domain moves in the direction parallel to the system plate/baffle with a constant speed. A turbulent boundary layer develops at the interface baffle/plate. The wall pressure fluctuations in this boundary layer generates a vibration of the plate and an acoustic radiation in the two fluid domains.Modeling the wall pressure fluctuations spectrum in a turbulent boundary layer developed over a vibrating surface is a very complex and unresolved task. Ducan and Sirkis [1] proposed a model for the two-way interactions between a membrane and a turbulent flow of fluid. The excitation of the membrane is modeled by a potential flow randomly perturbed. This potential flow is modified by the displacement of the membrane. Howe [2] proposed a model for the turbulent wall pressure fluctuations power spectrum over an elastomeric material. The model presented in this article is based on a hypothesis of one-way interaction between the flow and the structure: the flow generates wall pressure fluctuations which are at the origin of the vibration of the plate, but the vibration of the plate does not modify the characteristics of the flow.A finite difference scheme that incorporates the vibration of the plate and the acoustic pressure inside the fluid cavity has been developed and coupled with a boundary element method that ensures the outside domain coupling. In this paper, we focus on the resolution of the coupled vibration/interior acoustic problem. We compare the results obtained with three numerical methods: (a) a finite difference representation for both the plate displacement and the acoustic pressure inside the cavity; (b) a coupled method involving a finite difference representation for the displacement of the plate and a boundary element method for the interior acoustic pressure; (c) a boundary element method for both the vibration of the plate and the interior acoustic pressure.A comparison of the numerical results obtained with two models of turbulent wall pressure fluctuations spectrums - the Corcos model [3] and the Chase model [4] - is proposed. A difference of 20 dB is found in the vibro-acoustic response of the structure. In [3], this difference is explained by calculating a wavenumber transfer function of the plate. In [6], coupled beam-cavity modes for similar geometry are calculated by the finite difference method.

Reducing the generation of discrete-tones by micro-perforating the back of an open shallow cavity under a subsonic flow

An experimental and numerical study has been carried out to investigate the effect of micro-perforating the back of an open shallow cavity under a low-speed air flow in order to reduce the amplitudes of the discrete tones due to the shear layer-cavity interaction. Open shallow cavities with length-to-depth ratio of 10 and 17 have been considered flush-mounted on the test section of a low-speed wind-tunnel with mean flow velocity 30 m/s. The bottom plate of the cavity was either a plain or an unbacked micro-perforated panel (MPP). A set of wall-pressure measurements over the bottom wall showed that the MPP was able to reduce by up to 8 dB the amplitude of the discrete tones, mostly noticeable beneath the upstream edge of the cavity within the recirculation bubble where the acoustic components dominate over the broadband components. However, the MPP may enhance the broadband components over and beyond the reattachment zone, thereby suggesting to micro-perforate the back wall only in the attenuation zone. Th...

Reducing discrete-tones generation by micro-perforating the base of an open shallow cavity under a subsonic flow

Experimental and numerical studies have been carried out to investigate the effect of micro-perforating the base of an open shallow cavity under a low-speed air flow in order to reduce the amplitudes of the discrete tones due to the shear layer-cavity interaction. An open shallow transitional cavity with a length-to-depth ratio of 10.6 has been considered flush-mounted on the test section of a low-speed wind-tunnel with mean flow velocity 30.7 m/s. The bottom wall of the cavity was either a plain or an unbacked micro-perforated panel (MPP). A set of wall-pressure measurements over the base showed that the MPP was able to reduce by up to 8 dB the amplitude of the discrete tones, mostly noticeable beneath the upstream edge of the cavity within the recirculation bubble where the acoustic components dominate over the broadband components. The streamwise and spanwise cavity resonance frequencies were identified from a simple model. These results were assessed against aeroacoustic numerical simulations performe...

Controlling the Acoustic Resonance in a Corrugated Flow Pipe

A new experimental study, aimed at investigating the coupling between the flow in a corrugated pipe, the acoustically generated flow oscillations, and the emitted resulting noise is carried out. Hot-wire anemometry, Particle Image Velocimetry, and microphone measurements are associated to characterize the flow. The flow response to the corrugation is shown to fit to the sixth to ninth acoustic modes of the pipe according to the flow rate. When low frequency acoustically generated oscillations interfere with this, one checks that they either significantly reduce the noise level or modify the peak frequencies. In addition, theoretical/numerical works are also performed, in order to provide an analytical framework describing the acoustical properties of such corrugated pipe flows.