Sound propagation in acoustically lined elliptical ducts

Sound propagation in ducts with elliptical cross-sections can be described in terms of modes characterized by Mathieu functions of orders specified by the boundary conditions. For ducts with locally reacting liners there is coupling between modes because the admissible solutions are linear combinations of Mathieu functions of different orders and the eigenvalues are roots of an infinite determinant. The amount of mode coupling depends on the eccentricity of the duct. For the case of small eccentricity of the duct, approximate general solutions are derived and an example is discussed, where solutions are found.     

Attenuation of sound in multi-element acoustically lined rectangular ducts in the absence of mean flow

Extensions of the ordinary Wiener-Hopf technique are outlined and applied to the solution of sound attenuation in multi-element ducts with acoustically absorbing liners in series as well as in parallel combination. For demonstration purposes the simplest case of engineering interest is chosen: namely, a rectangular channel at zero convection velocity. Extensions to circular and annular geometries as well as to mean flow situations are possible. In the absence of a realistic source model acoustic power attenuation results are presented for an incoming fundamental mode only, to show the influence of major design parameters for point reacting liners. The broad band-width attenuation capacity of some liner configurations as well as the necessity to include wave reflections at liner discontinuities for multi-element liners is clearly demonstrated. For a given acoustic source a multi-mode solution can be found by summing the contributions of each incoming unattenuated mode.     

Effect of wall shear layers on the sound attenuation in acoustically lined rectangular ducts

This paper deals with the manner in which a shear layer proximate to the wall of an acoustically treated rectangular duct modifies the attenuation spectra. The restriction of this shear layer to the region near the lined duct walls is aimed at simulating boundary layer effects on the attenuation. Theoretical results show that shear significantly changes the peak attenuation, causing a frequency shift of this peak. For the inlet mode, i.e. flow against the direction of sound propagation, both results are a strong function of Mach number and layer thickness. For the exhaust mode, i.e. flow in the direction of propagation, these effects are relatively weak.     

Non-linear attenuation of sound in circular lined ducts

The attenuation of high intensity sound in circular ducts lined with fibrous material has been investigated. With no mean flow, the sound pressure levels are varied to illustrate the linear and non-linear absorption characteristics of the liner. Effects of liner thickness, perforation ratio of the duct wall and the $\text{d}\text{t}$ ratio are analysed.Optimum combinations of the perforation geometry and liner thickness are found to be of stable attenuation characteristics over a wide frequency range and at high sound levels.     

On the prediction of “buzz-saw” noise in acoustically lined aero-engine inlet ducts

Aero-engines operating with supersonic fan tip speeds generate an acoustic signature containing energy spread over a range of harmonics of the engine shaft rotation frequency. These harmonics are commonly known as the “buzz-saw” tones. The pressure signature attached to a supersonic ducted fan will be a sawtooth waveform. The non-linear propagation of a high-amplitude irregular sawtooth upstream inside the inlet duct redistributes the energy amongst the buzz-saw tones. In most modern aero-engines the inlet duct contains an acoustic lining, whose properties will be dependent on the mode number and frequency of the sound, and the speed of the oncoming flow. Such effects may not easily be incorporated into a time-domain approach; hence the non-linear propagation of an irregular sawtooth is calculated in the frequency domain, which enables liner damping to be included in the numerical model. Results are presented comparing noise predictions in hard-walled and acoustically lined inlet ducts. These show the effect of an acoustic liner on the buzz-saw tones. These predictions compare favourably with previous experimental measurements of liner insertion loss (at blade passing frequency), and provide a plausible explanation for the observed reduction in this insertion loss at high fan operating speeds.     

气流管道有源降噪研究

如何消除气流的影响是管道有源降噪的难点之一，本文分析了湍流对有源降噪系统的影响，并开发了一种抗湍流传声器探管，最后在某种通风系统的进气管段进行了降噪试验，气流速度为２０ｍ／ｓ时，在６０－６３０Ｈｚ频带取得了１５ｄＢ（Ａ）的降噪效果。     

The attenuation of lined plenum chambers in ducts: I. Theoretical models

Two types of theory are described, with the purpose of predicting the acoustic transmission loss of lined plenum chambers (which are sometimes used as attenuators in air conditioning duct systems). The first kind of theory embodies a low frequency wave acoustic approach, and two separate models are evolved: one is for a single plenum chamber, and the second is for a plenum chamber incorporating one or more acoustically lined baffles. The other type of theory is valid at high frequencies, and is based upon geometrical (or “ray”) acoustics. This is applied to a single chamber and to chambers containing either one or two lined baffles. Both the high frequency and low frequency results are reasonably simple. A limited amount of experimental data is also presented, as justification for the validity of part of the theory.     

Comparison of measured broadband noise attenuation spectra from circular flow ducts and from lined engine intakes with predictions

Sound propagation in lined circular ducts is investigated in the presence of uniform and sheared flow. The modal solutions are obtained by solving an eigenvalue equation which, in the case of sheared flow, is derived by using finite differences and by matching the pressure and the radial component of the particle velocity at the interface of the regions of uniform and sheared flow. For the uniform flow region, standard Bessel function solutions are used. The attenuation of acoustic energy at a given frequency and for a given liner length is computed on the assumption that at the inlet to the lined duct, the acoustic energy is equally distributed among the propagating modes. The total number of propagating modes is determined from the hard wall “cut off” condition. The failure to find some of the modal solutions on the attenuation computed in this way is discussed. It is shown that the reliability of this method of computing liner attenuation depends on the ability to successfully compute most of the modal solutions over a large range of frequencies, flow conditions and duct wall impedance values. A numerical technique is developed which uses a fraction of the total number of solutions to compute the total attenuations without appreciable loss of accuracy. Measured attenuation spectra from a flow duct facility and from lined intake ducts of the RB.211 engine are compared with predictions. In general very good agreement between predictions and measurements is obtained.     

The attenuation of lined plenum chambers in ducts,II: Measurements and comparison with theory

Experimental measurements of the acoustic performance of single and three-pass lined plenum chambers are compared to calculations based on theoretical models described in a companion paper [1]. Generally, quite good agreement is obtained, subject to the limitations of the theories. For the sake of completeness, comparison is made between the performance of a single plenum chamber and that of an equivalent splitter silencer. The two are seen to differ somewhat in their attenuation characteristics. The aerodynamic pressure losses of all three silencers are compared, and observations are made concerning the relative mass, construction time, et cetera, of the single chamber and the splitter. A tentative design procedure for plena is suggested.