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.     

Scattering and absorption of sound at flow duct expansions

The scattering of plane acoustic waves at area expansions in flow ducts is analysed using the vortex sheet model where the flow at the expansion is modelled as a jet, with a vortex sheet emanating from the edge. Of particular interest is the influence of the flow field on acoustic scattering and absorption.First, it is demonstrated that the stability properties of the shear layer can be simulated by modifying the edge condition within the vortex sheet model. To this end the accuracy for the region where the shear layer is changing from unstable to stable is improved by introducing a gradually relaxed Kutta edge condition with empirically derived coefficients. For low Strouhal numbers the vortex sheet model applies and for higher Strouhal numbers the two models converge.Second, it is demonstrated that the acoustic transmission through the jet expansion region can be determined by neglecting the scattering there. Incorporating this assumption, the vortex sheet model reproduces well the experimental results on transmission and absorption for an area expansion. This result supports the assumption that the main part of the scattering occurs at the area expansion at least for the low-frequency range. Furthermore, the influence of the flow field is particularly strong for small Strouhal numbers.     

Finite difference computation of acoustic scattering by small surface inhomogeneities and discontinuities

The use of finite difference schemes to compute the scattering of acoustic waves by surfaces made up of different materials with sharp surface discontinuities at the joints would, invariably, result in the generations of spurious reflected waves of numerical origin. Spurious scattered waves are produced even if a high-order scheme capable of resolving and supporting the propagation of the incident wave is used. This problem is of practical importance in jet engine duct acoustic computation. In this work, the basic reason for the generation of spurious numerical waves is first examined. It is known that when the governing partial differential equations of acoustics are discretized, one should only use the long waves of the computational scheme to represent or simulate the physical waves. The short waves of the computational scheme have entirely different propagation characteristics. They are the spurious numerical waves. A method by which high wave number components (short waves) in the wave scattering process is intentionally removed so as to minimize the scattering of spurious numerical waves is proposed. This method is implemented in several examples from computational aeroacoustics to illustrate its effectiveness, accuracy and efficiency. This method is also employed to compute the scattering of acoustic waves by scatterers, such as rigid wall acoustic liner splices, with width smaller than the computational mesh size. Good results are obtained when comparing with computed results using much smaller mesh size. The method is further extended for applications to computations of acoustic wave reflection and scattering by very small surface inhomogeneities with simple geometries.     

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.     

Flow-excited resonances in covered cavities

The results are presented of an investigation of flow-excited acoustic resonance in covered cavities. It is shown that energy is drawn from the mean flow entering a cavity and fed into the acoustic wavefield as a result of impingement of the inflowing jet against a solid boundary. Whether the oscillating wavefield consists of waves running transverse or longitudinal to the inflowing jet strongly depends upon whether the inflow is wall bounded on one side or free. It is also shown that if the exit duct has the characteristics of a diffuser it, too, can have an active influence on the resonance cycle. The conclusions reached are based upon fluctuating pressure measurements and visualization of the flow in a series of two-dimensional and axisymmetric cavity configurations.     

Identification of aero-acoustic scattering matrices from large eddy simulation. Application to a sudden area expansion of a duct

A methodology is presented which allows to determine the coefficients of transmission and reflection of plane acoustic waves at flow discontinuities in piping systems by combining large eddy simulation (LES) of turbulent compressible flows with system identification. The method works as follows. At first, an LES with external, broadband excitation of acoustic waves is carried out. Time series of acoustic data are extracted from the computed flow field and analyzed with system identification techniques in order to determine the acoustic scattering coefficients for a range of frequencies. The combination of broadband excitation with highly parallelized LES makes the overall approach quite efficient, despite the difficulties associated with simulation of low-Mach number compressible flows. The method is very general, here it is applied to study the scattering behavior of acoustic waves at a sudden change in cross-section in a duct system. The complex aero-acoustic interactions between acoustic waves and free shear layers are captured in detail by high resolution compressible LES, such that the scattering coefficients can be determined accurately from first principles. In order to demonstrate the reliability and accuracy of the method, the results for the scattering behavior and the acoustic impedance are presented and physically interpreted in combination with several analytical models and experimental data.     

Jet forking driven by pipe tone

The present work deals with an experimental investigation of flow of air through a square-edged circular orifice at the downstream end of a circular duct. Self-excited acoustic oscillations at the natural duct modes are observed for certain flow velocities when the orifice is sufficiently thick. For a specific Reynolds number based on the orifice diameter and the mean jet velocity (9150 < Re < 9850), the jet forks into two trains, with the alternating vortices falling into the same branch of the forked train. Whereas this phenomenon has been reported earlier to have occurred when the density ratio of the jet is less than 0.72, the present results show that it is possible for a jet having the same density as the ambient atmosphere. The jet forking is coincident with jump in the acoustic frequency from one natural acoustic mode to another with comparable amplitudes of both the modes.     

ON TRANSMISSION OF SOUND IN A NON-UNIFORM DUCT CARRYING A SUBSONIC COMPRESSIBLE FLOW

The differential equations governing the transmission of one-dimensional sound waves in a non-uniform duct carrying a subsonic compressible mean flow have been the subject of a recent debate [1, 2]. Of the two formulations presented, one is considered to be non-acoustical and the other as neglecting the spatial variation of the speed of sound. The present paper shows that both formulations are acoustical and represent valid approximations to correct conditions for isentropic sound propagation in a subsonic low Mach number duct. Each formulation is associated with an “error wave”, which is essentially a hydrodynamic wave when the mean flow Mach number is small. Three-port modelling is required, however, to capture this wave when the Mach number of the mean flow is relatively large and a numerical matrizant approach is described which can be used for this purpose.     

Acoustic control of instability waves in a turbulent jet

The possibility of acoustic control of instability waves formed in the mixing layer of a jet is experimentally investigated. The feasibility of suppressing a hydrodynamic instability wave in a subsonic turbulent jet by an external acoustic action is demonstrated. This result can be used in designing active control systems for jet noise suppression.     

Time-domain characterization of the acoustic damping of a perforated liner with bias flow

Combustion instabilities are caused by the interaction of unsteady heat releases and acoustic waves. To mitigate combustion instabilities, perforated liners, typically subjected to a low Mach number bias flow (a cooling flow through perforated holes), are fitted along the bounding walls of a combustor. They dissipate the acoustic waves by generating vorticity at the rims of perforated apertures. To investigate the absorption of plane waves by a perforated liner with bias flow, a time-domain numerical model of a cylindrical lined duct is developed. The liners' damping mechanism is characterized by using a time-domain "compliance." The development of such time-domain compliance is based on simplified or unsimplified Rayleigh conductivity. Numerical simulations of two different configurations of lined duct systems are performed by combining a 1D acoustic wave model with the compliance model. Comparison is then made between the results from the present models, and those from the experiment and the frequency-domain model of previous investigation [Eldredge and Dowling, J. Fluid Mech. 485, 307-335(2003)]. Good agreement is observed. This confirms that the present model can be used to simulate the propagation and dissipation of acoustic plane waves in a lined duct in real-time.     

管道后传声数值模拟的不稳定波抑制

在管道后传声的数值模拟中,必须考虑平均流剪切层的散射效应,然而在非均匀剪切流动下时域求解线化欧拉方程会面临Kelvin-Helmholtz不稳定波产生和放大的难题。已有的不稳定波抑制技术通常很难获得令人满意的结果。本文采用一种混合方法,首先引入有限时段的宽频声源波包将声波和不稳定波分离,进而采用声源滤波器技术对不稳定波进行抑制。数值验证算例选择半无限长轴对称环形硬壁直管道,采用计算气动声学方法时域求解2.5维线化欧拉方程,无背景流动的数值解与解析解符合很好,验证了程序的精度与可靠性,非均匀流动算例则表明所采用波包加声源滤波器混合方法对不稳定波抑制效果明显,对声场影响很小,充分显示了该方法的精度与可行性。     

High amplitude acoustic transmission through duct terminations: Theory

Recent experimental measurements have demonstrated that net acoustic energy dissipation can occur when sound waves interact with free shear layers, which are produced either by boundary layer separation in mean fluid flow at sharp edges, or by separation of the boundary layer in the acoustic flow at an edge in the absence of mean flow. This paper presents theoretical results which are offered in an attempt to explain these observations quantitatively. Comparison is made between the predicted and measured net energy loss which occurs upon transmission of high amplitude impulsive acoustic waves through various duct terminations, and also between calculated and measured reflection coefficients in the duct. The agreement is generally at least qualitatively good, and would appear to justify the physical assumptions on which the theoretical arguments are based.     

Side-branch resonators modelling with Green׳s function methods

This paper deals with strategies for computing efficiently the propagation of sound waves in ducts containing passive components. In many cases of practical interest, these components are acoustic cavities which are connected to the duct. Though standard Finite Element software could be used for the numerical prediction of sound transmission through such a system, the method is known to be extremely demanding, both in terms of data preparation and computation, especially in the mid-frequency range. To alleviate this, a numerical technique that exploits the benefit of the FEM and the BEM approach has been devised. First, a set of eigenmodes is computed in the cavity to produce a numerical impedance matrix connecting the pressure and the acoustic velocity on the duct wall interface. Then an integral representation for the acoustic pressure in the main duct is used. By choosing an appropriate Green?s function for the duct, the integration procedure is limited to the duct–cavity interface only. This allows an accurate computation of the scattering matrix of such an acoustic system with a numerical complexity that grows very mildly with the frequency. Typical applications involving Helmholtz and Herschel–Quincke resonators are presented.     

Sound propagation through a subsonic jet due to a source near the duct exit

Matched asymptotic solutions are constructed for the acoustic potentials of a periodic point source located in a two-dimensional subsonic jet near the exit of the duct with the ratio of the duct thickness to the acoustic wave length as the small parameter. The leading term of the far field solution has the same directionality effect as that for an infinite jet without the duct and that when the plane at the duct exit is considered to be a plane of symmetry. However, the intensity is different because of the wave propagation into the duct and is dependent on the location of the source.     

Application of dual reciprocity boundary element method for prediction of acoustic characteristics of ducts and silencers with three-dimensional potential flow

The Dual Reciprocity Boundary Element Method （DRBEM） is applied to predict the acoustic characteristics of ducts and silencers with three-dimensional potential flow, and the basic principle and numerical procedure of the proposed method are introduced. Compared to the Conventional Boundary Element Method （CBEM）, the DRBEM takes into account the second order terms of flow Mach number in the acoustic governing equation, which is suitable for the situations with higher Mach number subsonic flow. The four-pole parameters of a duct and a varying cross-sectional area expansion chamber are predicted with the DRBEM, and the predictions are compared with the one-dimensional analytical solutions and the CBEM results. The comparisons demonstrated that the present method is valid. Transmission loss of silencers with different structures was also calculated with the DRBEM. The results showed that the influence of the three-dimensional flow on the acoustic characteristics of silencers with complex structures is not negligible.     

A new formalism for time-dependent wave scattering from a bounded obstacle

A time-dependent three-dimensional acoustic scattering problem is considered. An incoming wave packet is scattered by a bounded, simply connected obstacle with locally Lipschitz boundary. The obstacle is assumed to have a constant boundary acoustic impedance. The limit cases of acoustically soft and acoustically hard obstacles are considered. The scattered acoustic field is the solution of an exterior problem for the wave equation. A new numerical method to compute the scattered acoustic field is proposed. This numerical method obtains the time-dependent scattered field as a superposition of time-harmonic acoustic waves and computes the time-harmonic acoustic waves by a new "operator expansion method." That is, the time-harmonic acoustic waves are solutions of an exterior boundary value problem for the Helmholtz equation. The method used to compute the time-harmonic waves improves on the method proposed by Misici, Pacelli, and Zirilli [J. Acoust. Soc. Am. 103, 106-113 (1998)] and is based on a "perturbative series" of the type of the one proposed in the operator expansion method by Milder [J. Acoust. Soc. Am. 89, 529-541 (1991)]. Computationally, the method is highly parallelizable with respect to time and space variables. Some numerical experiments on test problems obtained with a parallel implementation of the numerical method proposed are shown and discussed from the numerical and the physical point of view. The website: http://www.econ.unian.it/recchioni/w1 shows four animations relative to the numerical experiments.     

FINITE ELEMENT AND BOUNDARY ELEMENT MODELLING FOR THE ACOUSTIC WAVE TRANSMISSION IN MEAN FLOW MEDIUM

The frequency characteristics of the acoustic wave transmission in a medium with mean flow are considered. One approach is to solve the Helmholtz equation with mean flow medium in original co-ordinates, which is directly discretized for the one-dimensional and the axisymmetric FEM. Another approach is to transform the equation into the standard Helmholtz equation, which is discretized for the axisymmetric FEM and the three-dimensional BEM. The numerical models are examined first for a straight circular duct. The solutions by the numerical approaches are compared with the analytical solution. The examination is then extended to the case when the mean flow is locally present in the muffler with expansion chamber. To model the spatial mean flow in the BEM model, the partitioned domain approach is also developed. No shear effect between the two regions are included.     

A PIV study of a supersonic impinging jet

The characteristics of supersonic impinging jets are investigated using Particle Image Velocimetry (PIV). The purpose of the experiments is to understand the jet induced forces on STOVL aircraft while hovering close to the ground. For this purpose, a large diameter circular plate was attached at the nozzle exit. The oscillations of the impinging jet generated due to a feedback loop are captured in the PIV images. The instantaneous velocity field measurements are used to describe flow characteristics of the impinging jet. The important flow features such as oscillating shock waves, slipstream shear layers and large scale structures are captured clearly by the PIV. The presence of large scale structures in the impinging jet induced high entrainment velocity in the near hydrodynamic field, which resulted in lift plate suction pressures. A passive control device is used to interfere with the acoustic waves travelling in the ambient medium to suppress the feedback loop. As a consequence, the large scale vortical structures disappeared completely leading to a corresponding reduction in the entrainment.     

Scattering of wavepackets by a flat plate in the vicinity of a turbulent jet

We present an investigation of the acoustic scattering due to the presence of a flat plate in the vicinity of a turbulent subsonic jet. Experiments have been performed to measure changes in the velocity and sound fields for Mach numbers ranging from 0.4 to 0.6, and for distances between the plate and the jet axis ranging from 1 to 2 jet diameters. Results show only very slight changes in the mean flow induced by the plate, and no differences in the velocity fluctuation amplitudes on the jet centreline, suggesting that wave-packet models derived for jets without installation effects may be representative of the installed case, at least for the jet–plate distances considered here. The acoustic results, on the other hand, include a significant increase in the low-frequency sound radiation, and phase opposition between the shielded and unshielded sides of the plate. There is an exponential decay of the scattered sound with increasing jet–plate distance, suggesting that low-frequency radiation is due to the scattering of evanescent hydrodynamic wavepackets in the jet near field. To model this phenomenon, we calculate sound generation from wave-packet sources in two ways: on one hand we use a tailored Green?s function that accounts for the presence of a semi-infinite, rigid flat plate; and, on the other, we solve numerically the Helmholtz equation, with boundary conditions representative of a finite flat plate, using a fast multipole boundary element method. In agreement with the experimental measurements, numerical calculations capture the phase opposition between shielded and unshielded sides, and the scattered sound depends exponentially on the position of the plate. This exponential dependence is related to non-compact effects associated with wavepackets, as compact sources would lead to an algebraic dependence. Acoustic pressure directivities computed for the finite and semi-infinite flat plates agree well where acoustic reflection and diffraction from the trailing edge of the plates are concerned. However, additional diffraction effects associated with the leading and lateral edges of the finite plate, and which take the form of multiple lobes in the directivity, are illustrated by the comparison. As the plate dimensions are increased, i.e. the Helmholtz number is increased, the solution approaches that obtained for the semi-infinite plate.     

Noise Prediction in Subsonic Flow Using Seventh-Order Dissipative Compact Scheme on Curvilinear Mesh

In this paper, we investigate the performance of the seventh-order hybrid cell-edge and cell-node dissipative compact scheme (HDCS-E8T7) on curvilinear mesh for noise prediction in subsonic flow. In order to eliminate the errors due to surface conservation law (SCL) is dissatisfied with curvilinear meshes, the symmetrical conservative metric method (SCMM) is adopted to calculate the grid metric derivatives for the HDCS-E8T7. For the simulation of turbulence flow which may have main responsibility for the noise radiation, the new high-order implicit large eddy simulation (HILES) based on the HDCS-E8T7 is employed. Three typical cases, i.e., scattering of acoustic waves by multiple cylinder, sound radiated from a rod-airfoil and subsonic jet noise from nozzle, are chosen to investigate the performance of the new scheme for predicting aeroacoustic problem. The results of scattering of acoustic waves by multiple cylinder indicate that the HDCS-E8T7 satisfying the SCL has high resolution for the aeroacoustic prediction. The potential of the HDCS-E8T7 for aeroacoustic problems on complex geometry is shown by the predicting sound radiated from a rod-airfoil configuration. Moreover, the subsonic jet noise from nozzle has been successfully predicted by the HDCS-E8T7.