Reflection of sound at area expansions in a flow duct

An analytical model for scattering at area discontinuities and sharp edges in flow ducts and pipes is presented. The application we have in mind is large industrial duct systems, where sound attenuation by reactive and absorptive baffle silencers is of great importance. Such devices commonly have a rectangular cross-section, so the model is chosen as two-dimensional. Earlier solutions to this problem are reviewed in the paper. The modelling of the flow conditions downstream of the area expansion, with and without extended edges, and its implications for the resulting acoustic modes are discussed. Here, the scattering problem is solved with the Wiener-Hopf technique, and a Kutta condition is applied at the edge. The solution of the wave equation downstream of the expansion includes hydrodynamic waves, of which one is a growing wave. Theoretical results are compared with experimental data for the reflection coefficient for the plane wave, at frequencies below the cut-on for higher order modes. Influence of the interaction between the sound field and the flow field is discussed. A region where the reflection coefficient is strongly Strouhal number dependent is found.     

Scattering of sound by an elastic plate with flow

An elastic plate, set in an infinite baffle and immersed in a fluid moving with a uniform subsonic velocity, is excited by an acoustic source. The scattered sound field is analyzed when fluid-plate coupling is large, and a solution is found by the use of matched asymptotic expansions. The far field is found to approximate to the solution obtained when the elastic plate is absent. At a plate resonance, however, the outer field must include eigensolutions with singularities at the plate edges, and close to the plate the dominant terms are travelling plate waves. These plate waves are found to have a wavelength independent of the frequency of the source. It is also shown that a plate resonance corresponds to a divergence instability of aerodynamic flutter theory and that the stability results found in this paper are in agreement with those obtained by using modal expansions. The limit as the Mach number goes to zero is found to be singular, suggesting an analysis of the model for small flow velocity. This calculation is performed and the results match smoothly to the respective solutions for a stationary fluid and for a large subsonic flow.     

Scattering of sound by sound

The previous results for the scattered field of two plane monochromatic sound waves is shown to possess a singularity as the wave vectors become equal. A new solution which removes this singularity is presented.     

Self-induced sound generation by flow over perforated duct liners

An adverse “singing” phenomenon due to flow over perforated liners in a duct was studied experimentally. The liners consisted of honeycomb structures bonded to and sandwiched between two flat aluminum skins. The inner skin in contact with the flow had holes (perforations) with pitch distances either equal to or different from those of the honeycomb structures, forming, respectively, narrow-band or broadband liners. The shedding of vortices in the flow over these holes induced excitation of acoustic modes within the duct, and under the condition whereby the cut-on frequency of an excited mode coincided with, or was very near to, the shedding frequency a very strong tone corresponding to that particular modal cut-on frequency resulted. For narrow-band liners, the “singing” phenomenon could also be induced by cavity resonance. The shedding frequency increased with increase in flow velocities and thus higher order acoustic modes were excited consecutively in a similar manner. The Strouhal number calculated from the observed shedding frequency and the flow velocity was found to vary directly with the hole diameter of the perforate. The high signal to noise ratio during the peak of self-excitation presents a new method in the determination of the wall admittance under the flow conditions.     

Experimental investigations of sound reflection from hot and subsonic flow duct termination

The knowledge of the reflection properties of open end jet ducts is important for different applications, where the flow and high temperature conditions are involved and add complexity to the problem. In this paper, the magnitude of the reflection coefficients together with the respective end-corrections is experimentally determined for hot flow duct openings. A Mach number range up to 0.3 for cold jets and up to 0.12 for a jet temperature of 200 °C is treated. The experimental results are compared with the numerical model proposed by Munt (Acoustic transmission properties of a jet duct with subsonic jet flow: 1. The cold jet reflection coefficient, Journal of Sound and Vibration 142 (1990) 413–436) and a good correlation in plane-wave region is demonstrated. To reduce experimental uncertainty, the sound reflection properties at the duct opening are obtained by using an overdetermined two-microphone technique with the implementation of a three pressure transducer array. By introducing a modified multistep version of the stepped sine excitation, the accuracy of data acquisition process is improved without compromising the measurement time.     

有流条件下环形管道中的声传播特性

本文从线性波动方程出发,根据界面处声压连续和质点位移连续的条件,导得有流条件下无限长环形吸声管道中声传播的特征方程,并且具体分析了管道衰减系数与气流速度、壁面特性、截面几何尺寸和声波频率等参量的相互关系。研究表明,管道衰减系数随着气流流速的增加,管壁吸声系数的减小、管道截面几何尺寸的增加而减小。同时,随着声波频率从低频到高频的变化,衰减系数从小到大,再从大到小地变化,存在一个最佳峰值。     

Influence of mean flow profile and geometrical ratios on scattering of sound at a sudden area expansion in a duct

The scattering of sound at a sudden area expansion in a duct with subsonic mean flow has been modelled with a multimodal method. Technological applications are for instance internal combustion engine exhaust silencers and silencers in industrial duct systems. Both 2D rectangular and 2D cylindrical geometries are considered.The influence of the mean flow profile, and the—in this method—associated application of an acoustic Kutta condition at the edge of the area discontinuity, is investigated. The scattering coefficients for the plane waves are found to change smoothly as the flow profile is changed gradually from one, where the acoustic Kutta condition is applied to one where it is not applied. Furthermore, for high Strouhal numbers no difference is observed in the results for the scattering coefficients obtained for different flow profiles. Also, at low Strouhal numbers the magnitudes of the scattering coefficients are the same for different profiles.The influence of the ratio of the heights (in 2D rectangular geometry), respectively, radii (in 2D cylindrical geometry), of the ducts upstream and downstream of the area expansion on the scattering coefficients is examined. Around a certain Strouhal number, a specific feature in the scattering coefficients is observed when the ratio of the duct heights or radii is less than 0.5. This is found to be connected to a strong interaction between the first evanescent acoustic mode and the hydrodynamic instability mode. For non-uniform flow even an apparent jump between the first evanescent acoustic mode and the hydrodynamic unstable mode and a corresponding jump in scattering coefficients is observed, when employing causality analysis according to the Briggs-Bers or Crighton-Leppington procedure. This implies that in fact an absolute instability occurs.     

Nonlinear absorption of sound by sound at the interaction of waves with multiple frequencies

The role of the phase-dependent nonlinear processes that accompany the interaction of a weak signal wave with an intense pump wave is investigated for the case of the pump frequency being a multiple of the signal frequency. Phase relations that provide the maximum absorption of sound by sound are determined. It is shown that, as the frequency ratio of the waves increases, the role of the phase-dependent absorption rapidly decreases and becomes negligible.     

Scattering of sound in industrial spaces

A rigorous solution is derived for the steady state sound field of a point source in a space randomly filled with absorptive scatterers. With use of approximations for fields in bounded spaces, sound distributions are calculated for shallow industrial work rooms accounting for effects of scattering, specular reflections from floor and ceiling, and shielding by barriers. Theoretical results are compared with data from model and field measurements.     

高声压级时多孔金属板的吸声特性研究

针对高声压级下有限厚度多孔金属板在线性阻抗背衬条件下(背衬表面声压与声质点速度为线性关系)的吸声问题,提出了一个描述不同声压级下材料层法向吸声性能的一维模型,并给出求解材料层内部声质点速度的线化与差分方法,以预测多孔金属板在高声压级下的非线性吸声特性。在阻抗管中对两块多孔金属板进行了声学测试,得到了材料层法向表面阻抗和吸声系数随入射声压级变化的实验结果。研究表明:实验与理论预测符合良好,验证了模型与数值方法的正确性。本文所提原理和方法,可用于一般硬质多孔材料。     

Series expansions of rotating two and three dimensional sound fields

The cylindrical and spherical harmonic expansions of oscillating sound fields rotating at a constant rate are derived. These expansions are a generalized form of the stationary sound field expansions. The derivations are based on the representation of interior and exterior sound fields using the simple source approach and determination of the simple source solutions with uniform rotation. Numerical simulations of rotating sound fields are presented to verify the theory.     

Spectral analysis of the flow sound interaction at a bias flow liner

The interaction between the flow field and the sound field is responsible for the sound absorption at perforated acoustic liners with bias flow and has to be investigated contactlessly. Based on the optically measured flow velocity spectrum, an energy analysis was performed. As a result, the generation of broadband flow velocity fluctuations in the shear layer surrounding the bias flow caused by the flow sound interaction has been observed. In addition, the magnitude of this acoustically induced flow velocity oscillation exhibits a correlation with the acoustic dissipation coefficient of the bias flow liner. This supports the assumption that an energy transfer between the flow field and the sound field is responsible for the acoustic damping.     

声波的吸收与反射

测量声波幅度随传播距离变化的实验曲线,用波动学的观点分析实验数据,考虑到吸收和反射等耗散因素,计算出空气的吸收系数和换能器的反射系数.     

Scattering of sound in a moving viscous microinhomogeneous medium at large Reynolds numbers

A generalization of the Rayleigh law of a low-frequency sound attenuation in a microinhomogeneous medium to the case of scattering particles moving in a viscous liquid at a large Reynolds numbers is proposed. It is shown that, under these conditions, the attenuation may be independent of the scattering by the moving particles themselves but be only determined by the flow caused by these particles, the maximum attenuation being observed in the direction across the particle motion. The corresponding corrections proportional to the first power of the hydrodynamic Mach number are compared with the corrections lying at the basis of the modified Rayleigh law, which was proposed earlier for the potential flow of an ideal liquid around inhomogeneities, and also with the laws of scattering in a moving viscous microinhomogeneous medium at a small Reynolds numbers. As an example of the operation of the generalized law, characteristics of the sound scattering by rain are refined.     

Reduction of sound in a low velocity flow duct by the use of Bragg reflections

This paper presents the results of some experiments on the use of structures of aerodynamically-shaped elements as narrow-band sound reflectors in a duct. The structures are tuned to give maximum attenuation for frequencies determined by the Bragg reflection condition, and are thought to be of special value where space considerations prohibit the use of conventional acoustic wave filters.