A numerical model is presented of the Rayleigh conductivity of a square-edged orie ce in the presence of e nite plate thickness and bias e ow. Particular attention is paid to the evaluation of the effect of e nite plate thickness on its acoustic impedance. In the presence of bias e ow, the acoustic impedance of a kind of perforated plate, which is constructed with square-edged orie ces in a plate of e nite thickness, is calculated from the Rayleigh conductivity on the assumption that the orie ces are well separated. The numerical analysis shows that, although the acoustic resistance increases with the increasing bias e ow speed on most occasions, it decreases in a certain range of low bias e ow speed, and it can even decrease to negative values for certain combinations of Strouhal number and plate thickness. When the bias e ow speed is near zero, increasing plate thickness leads to an increase of the acoustic reactance. However, the acoustic reactance decreases as the bias e ow speed is increasing. As a result, the effect of plate thickness on the acoustic reactance will disappear at high bias e ow speed. Experimental data are also presented. Qualitatively, the experimental and theoretical results are in good agreement.

Effect of Plate Thickness on Impedance of Perforated Plates with Bias Flow

https://www.cerfacs.fr/~cfdbib/repository/TR_CFD_09_8.pdf

Acoustic modeling of perforated plates with bias flow for Large-Eddy Simulations

The development of the advanced liner technology for aeroengine noise control necessitates the impedance measurement method under realistic flow conditions. Currently, the methods for this need are mainly based on the inverse impedance eduction principle, confronting with the problems of initial guess, high computation cost, and low convergence. In view of this, a new strategy is developed that straightforwardly educes the impedance from the sound pressure information measured on the duct wall opposing to the test acoustic liner embedded in a flow duct. Here, the key insight is that the modal nature of the duct acoustic field renders a summed-exponential representation of the measured sound pressure; thus, the characterizing axial wave number can be readily extracted by means of Prony’s method, and further the unknown impedance is calculated from the eigenvalue and dispersion relations based on the classical mode-decomposition analysis. This straightforward method is simple in its basic principle but rema...

A straightforward method for wall impedance eduction in a flow duct.

Effect of grazing–bias flow interaction on acoustic impedance of perforated plates

Resolved simulations of the sound-induced flow through a circular orifice with a 0.99 mm diameter are examined. The orifice is backed by a hexagonal cavity and is a local model for acoustic liners commonly used for aeroengine noise reduction. The simulation data identify the role the orifice wall boundary layers play in determining the orifice discharge coefficient which, in time-domain models, is an important indicator of nonlinearity. It is observed that when the liner behaviour is not well described by linear models, the orifice boundary layers contain secondary vorticity generated from its separation from the corner on the high-pressure side of the orifice. Quantitative comparisons of the simulation-predicted impedance match available data for incident sound of 130 dB amplitude at frequencies from 1.5 to 3.0 kHz. At amplitudes of 140–160 dB, the simulation impedance is in agreement with analytical predictions when using simulation-measured quantities, including the discharge coefficient and root-mean-square velocity through the orifice, although no experimental data for this liner exist at these conditions. The simulation data are used to develop two time-domain models for the acoustic impedance wherein the velocity profile through the orifice is modelled as the product of the fluid velocity and a presumed radial shape, . The models perform well, predicting the in-orifice velocity and pressure, and the impedance, except for the most nonlinear cases where it is seen that the assumed shape can affect the backplate pressure predictions. These results suggest that future time-domain models that take the velocity profile into account, by modelling the boundary layer thickness and assuming a velocity profile shape, may be successful in predicting the nonlinear response of the liner.

Numerical investigation and modelling of acoustically excited flow through a circular orifice backed by a hexagonal cavity

A linearized potential flow model is developed to study the effect of grazing flow on the acoustic behavior of an orifice. In accordance with the previous flow visualization and measurements, this model uses the particle velocity continuity boundary condition rather than the widely used displacement to match the flow-fields separated by the shear layer over the orifice. An experiment is also carried out to validate the present theory in the case of circular or rectangular orifices. The theory agrees well with the experiment. In addition, further comparison is made between the present and two existing impedance models. One major objective of the present investigation is to make a tentative judgement on the two boundary conditions for a sound wave transmitting through a turbulent boundary layer over an orifice. It is found that, compared to the particle displacement continuity boundary condition, the use of the particle velocity continuity boundary condition results in a much better agreement between the theoretical predictions and the experimental data. Finally, there is a discussion on the influence of plate thickness on orifice impedance in the presence of grazing flow.

Effect of Grazing Flow on the Acoustic Impedance of an Orifice

A linearized potential flow model is developed to study the effect of grazing flow on the acoustic behavior of an orifice. In accordance with the previous flow visualization and measurements, this model uses the particle velocity continuity boundary condition rather than the widely used displacement to match the flow fields separated by the shear layer over the orifice. An experiment is also carried out to validate the present theory in the case of circular or rectangular orifices. The theory agrees well with the experiment. In addition, further comparison is made between the present and two existing impedance models. One major objective of the present investigation is to make a tentative judgement on the two boundary conditions for a sound wave transmitting through a turbulent boundary layer over an orifice. It is found that, compared to the particle displacement continuity boundary condition, the use of the particle velocity continuity boundary condition results in a much better agreement between the theoretical predictions and the experimental data. Finally, a discussion is made on the influence of plate thickness on orifice impedance in the presence of grazing flow.

Jingshu Wu

Papers

Effect of Grazing Flow on the Acoustic Impedance of an Orifice

The effects of grazing flow on the acoustic behavior of orifices