Multi-mode sound transmission in ducts with flow

Exhaust mufflers, large exhaust stacks, and turbofan engines are common examples of ducted noise. The most useful measure of the sound produced by these noise sources is the sound power transmitted along the duct. When airflow is present, sound power flow can no longer be uniquely determined from the usual measurements of acoustic pressure and particle velocity.One approach to sound power determination from in-duct pressure measurement, and the one discussed in this paper, is to predict the relationship between the sound power and pressure based upon an assumed mode amplitude distribution. This paper investigates the relationship between acoustic pressure and power for a family of idealized source distributions of arbitrary temporal and spatial order. Incoherent monopole and dipole sources uniformly distributed over a duct cross-section can be obtained as special cases. This paper covers the sensitivity of the pressure-power relationship to source multipole order, frequency and, in particular, flow speed. It is shown that the introduction of flow in a hard-walled duct can have a substantial effect on the behavior of the pressure-power relationship for certain source distributions. Preliminary experimental results in a no-flow facility are presented in order to verify some of the main results.     

Sound power flux measurements in strongly exited ducts with flow

This contribution describes new robust procedures for the measurement of sound power flux at appropriate axial positions along a duct with flow, using pairs of flush wall mounted microphones, or pressure transducers. The technology includes the application of selective averaging, order tracking, and optimized sampling rate methods to identify the small fraction of the total fluctuating wave energy that is being propagated along the flow path in a reverberent, or highly reactive duct system. Such measurements can also be used to quantify the local acoustic characteristics that govern the generation, transfer, and propagation of wave energy in the system. Illustrative examples include the determination of the acoustic characteristics of individual silencing elements installed in IC engine intakes and exhausts both on the flow bench and during controlled acceleration or run down on a test bed, where the wave component spectral levels approached 170 dB.     

Sound radiation from inflow turbulence in axial flow fans

The sound radiated when inflow turbulence is present in axial flow fans has been investigated. Theoretically, two noise radiating mechanisms can be identified: (i) interaction of turbulence with the rotor potential field results in a quadrupole-type volume source distribution, producing “flow-interaction” noise; (ii) impingement of turbulence on the blades results in a dipole-type (fluctuating force) surface source distribution, producing “fluctuating lift” noise. A theoretical expression for the flow interaction sound power in the upstream radiation field has been developed, in terms of parameters that can be experimentally determined by near field flow measurements involving spatial cross-correlations of the fluctuating axial velocity, with respect to both radial and circumferential position. Both these measurements and radiated sound pressure measurements have been made for eight- and ten-bladed rotors of relatively low tip Mach number (< 0·3). The sound pressure measurements revealed the occurrence of band-spreading of discrete tones at the blade passing frequency and its harmonics, as would be theoretically predicted for quadrupole-type sources here. The theoretical predictions and the measurements, respectively, of the sound power radiated upstream were compared. The results indicated that, for the fans tested, the “fluctuating lift” noise strongly predominated over the “flow-interaction” noise. The observed sound power levels were consistent with levels estimated from the theory.     

Attenuation of sound in wide ducts with flow at elevated pressure and temperature

At ambient conditions the acoustic losses within the fluid are two orders of magnitude smaller than those occurring at a duct wall, so that they are commonly neglected in duct acoustics. Recent measurements revealed an increasing sound attenuation at elevated pressure and temperature, which cannot be justified by the viscothermal losses at the wall alone. In the first part, this paper compiles available models to pursue a comprehensive treatment of the sound attenuation in a duct at elevated pressure and temperature. The second part presents an experimental study of the attenuation. The measurements have been performed at the Hot Acoustic Test Rig, where pressure and temperature can be independently adjusted from their ambient values up to 1100 kPa and 823 K, respectively. The theoretical prediction of the total losses matches the experimental data, thus confirming that the losses within the fluid cannot be neglected in ducts at elevated pressure and temperature.     

Sound transmission at low frequencies through the walls of distorted circular ducts

A theoretical treatment of sound transmission through the walls of distorted circular ducts is given, for plane mode transmission within the duct. The transmission mechanism is essentially that of “mode coupling”, whereby higher structural modes in the duct walls are excited, because of the wall distortion, by the internal sound field. The theory is in two parts: an approximate analytical model for the structural response of the walls to the internal sound field, and a structural radiation model. Computed results, based on the theory, are compared to measurements on “long-seam” air conditioning ducts. Where the duct geometry can be reliably specified, reasonably good agreement is obtained between theoretical and experimental data. It is concluded that mode coupling effects serve to account for the discrepancies between ideal and observed behaviour in sound transmission through duct walls.     

声在参数随距离变化的管道中的传播

本文对管道系统中声传播的一维理论作了推广。把管道系统看成由两种类型结构组成:一种是连续的管道结构,其中壁面声学参数、截面几何参数以及气体动力参数等可以沿管道随距离缓慢变化;另一种是突变的局部结构,在结构两侧的各种参数可以有不连续的跃变。文中从流体力学基本方程出发,在较普遍的情况下,对这两种类型结构作了分析研究,分别导出了反映其声传播特性的传递矩阵并作了讨论。     

Sound generation in a flow near a compliant wall

The generation of sound near an infinite compliant wall is studied, with account taken of a uniform mean flow. Stable and unstable configurations are looked at. It is shown that a possible influence of the wall on the sound generation occurs only via a modification of the turbulence if hydrodynamic non-linearities are responsible for the levelling-off of the instabilities. Then no fundamentally more efficient sound sources are found. An increase of the radiated sound may be possible because of the mirror sources and because of their possibly reduced compactness.     

Sound attenuation in acoustically lined curved ducts in the absence of fluid flow

A study has been made of the sound attenuation in a lined curved duct with rectangular cross-section. In this study, the derivation of the eigenvalue equation was based on the continuity of the normal component of the particle displacement and the matching of the acoustic pressure on the acoustic lining surface. The sound attenuation was calculated by using the acoustic energy expression for the waves propagating in a curved duct. For a given duct geometry and known acoustic lining impedances, a computer program was developed to solve for the eigenvalues and to obtain the sound attenuation of the propagating waves in the lined curved duct. It was found that in the case studied here the fundamental mode was least attenuated. The total sound attenuation was calculated on the assumption that the amplitudes for all propagating waves were equal at a given frequency. Effects of aspect ratio, bend angle and the acoustic impedance on the sound attenuation were investigated in the present work.     

Sound generation by steady flow through glottis-shaped orifices

Although the signature of human voice is mostly tonal, it also includes a significant broadband component. Quadrupolelike sources due to turbulence in the region downstream of the glottis, and dipolelike sources due to the force applied by the vocal folds onto the surrounding fluid are the two primary broadband sound generating mechanisms. In this study, experiments were conducted to characterize the broadband sound emissions of confined stationary jets through rubber orifices formed to imitate the approximate shape of the human glottis at different stages during one cycle of vocal fold vibrations. The radiated sound pressure spectra downstream of the orifices were measured for varying flow rates, orifice shapes, and gas mixtures. The nondimensional sound pressure spectra were decomposed into the product of three functions: a source function F, a radiation efficiency function M, and an acoustic response function G. The results show that, as for circular jets, the quadrupole source contributions dominated for straight and convergent orifices. For divergent jets, whistling tonal sounds were emitted at low flow rates. At high flow rates for the same geometry, dipole contributions dominated the sound radiated by free jets. However, possible source-load acoustic feedback may have hampered accurate source identification in confined flows.     

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.     

Acoustic transmission in non-uniform ducts with mean flow,part II: The finite element method

This second paper in a two part series describes the implementation of the finite element method for the solution of the problem of acoustic transmission through a non-uniform duct carrying a high speed subsonic compressible flow. A finite element scheme based on both the Galerkin method and the residual least squares method and with eight noded isoparametric elements is described. Multi-modal propagation is investigated by coupling of the solution in the duct non-uniform section to modal expansions in uniform sections. The accuracy of the finite element results for both the eigenvalue and transmission problems is assessed by comparison with exact solutions and with results from the method of weighted residuals in the form of a modified Galerkin method as introduced in Part I of this pair of papers. The results of calculations show that modal interactions, particularly in transmitted modes, become increasingly important with increasing duct flow Mach number. Power transmission coefficient calculations for the geometries studied reveal no indication of a linear basis for the phenomenon of subsonic acoustic choking.     

Sound transmission in pipes with porous walls

Pipes with porous (permeable) walls have received the attention of several authors as a noise control element in automotive intake systems; however, a closed theory of sound transmission including the effect of the coupling of the internal and external acoustic fields and the presence of mean flow does not appear to be available. The present paper proposes an integro-differential system for the propagation of plane sound waves in pipes with porous walls, and presents its general numerical solution, as well as an approximate analytical solution. The predicted effect of the coupling between the internal and external acoustic fields in a circular pipe made of reinforced woven fabric walls is shown, and the transmission loss predictions are compared with the existing experimental data in the literature.     

Acoustic transmission in non-uniform ducts with mean flow,part I: The method of weighted residuals

3n this and a companion paper the problem of transmission of sound through non-uniform ducts carrying a high speed subsonic compressible flow is approached using the method of weighted residuals (MWR) in the form of a modified Galerkin method and the finite element method (FEM). The intent of the investigation is to carry out a careful evaluation of these methods in this computationally difficult problem. To this end both MWR and FEM have been limited to in-core computer implementations to generate useful results with relatively modest computational requirements. This paper (Part I) details the MWR formulation and presents numerical results establishing the degree of accuracy of MWR as compared to exact eigenvalue calculations and approximate one dimensional transmission calculations. The comparison of MWR and FEM results is carried out in the companion paper (Part II).     

Sound radiation from ducts: Theory and experiment

The paper deals with a method of prediction of noise radiated from finite length ducts with arbitrary shape. The computation of the internal and external acoustic field is based upon a new variational formulation by integral equations. Numerical results of far and near field radiation patterns are compared with experimental data for various higher order mode source conditions.     

Absorption of sound at a surface exposed to flow and temperature gradients

In noise abatement using porous or fibrous materials, accurate determination of the surface impedance representing the absorber is decisive for simulation quality. The presence of grazing flow and non-homogeneous ambient temperature influence the reaction of the absorber and may suitably be included in a modified “effective” surface impedance. In this paper, this approach is applied to a generic case representative for the engine bay of a heavy truck, where porous shields suppress the radiated noise, e.g. during a pass-by noise test. The change in the absorption is determined numerically by solving the wave propagation through a layer of varying temperature and flow adjacent to the impedance surface for different angles of incidence. The study shows significant impact of both flow and temperature, especially for materials with low absorption. The diffuse field absorption coefficient is also derived and although the effect is less pronounced in this case, it is still important in lower frequencies and in the frequency range typical for IC engine noise. The proposed numerical method is shown to be accurate and efficient for determination of the effective impedance and moreover not limited to thin boundary layers.