A note on the interaction of unsteady flow with an acoustic liner

The effects of a mean grazing flow on the energy exchanges involved in the interaction of a bias-flow acoustic liner with, respectively, incident sound and boundary layer turbulence are contrasted. The analysis of model problems which make use of a line vortex to simulate large scale, unsteady boundary layer structures indicates that, whereas acoustic waves may be effectively attenuated, dissipation caused by “jetting” in the apertures of the liner can result in a net transfer of energy from the mean flow to the turbulence in the boundary layer.     

Measurements of energy exchange between acoustic fields and non-uniform steady flow fields

This paper describes an experimental investigation of interactions between acoustic waves and a non-uniform steady flow field. Data have been obtained for a resonance tube having a vent at the center in the lateral boundary, an average flow being introduced at the ends. Experiments have been done for both circular and slot vents, over ranges of both frequency and Mach number. According to the one- dimensional linear stability analysis, the interactions between the longitudinal acoustic field and the mean flow in the vicinity of the vent cause a net transfer of acoustic energy from the average flow to the acoustic field. This result has been verified by the experiments reported here. The gain of energy measured is less than that deduced from a one-dimensional analysis.     

Simulations of the scattering of sound waves at a sudden area expansion

The scattering of acoustic plane waves at a sudden area expansion in a flow duct is simulated using the linearized Navier–Stokes equations. The aim is to validate the numerical methodology for the flow duct area expansion, and to investigate the influence of the downstream mean flow on the acoustic scattering properties. A comparison of results from numerical simulations, analytical theory and experiments is presented. It is shown that the results for the acoustic scattering obtained by the different methods gives excellent agreement. For the end correction, the numerical approach is found superior to the analytical model at frequencies where coupling of acoustic and hydrodynamic waves is significant. A study with two additional flow profiles, representing a non-expanding jet with an infinitely thin shear layer, and an immediate expansion, shows that a realistic jet is needed to accurately capture the acoustic–hydrodynamic interaction. A study with several different artificial jet expansions concluded that the acoustic scattering is not significantly dependent on the mean flow profile below the area expansion. The constructed flow profiles give reasonable results although the reflection and transmission coefficients are underestimated, and this deviation seems to be rather independent of frequency for the parameter regime studied. The prediction of the end correction for the constructed mean flow profiles deviates significantly from that for the realistic profile in a Strouhal number regime representing strong coupling between acoustic and hydrodynamic waves. It is concluded that the constructed flow profiles lack the ability to predict the loss of energy to hydrodynamic waves, and that this effect increases with increasing Mach number.     

超声速层流/湍流压缩拐角流动结构的实验研究

在Ma=3.0的超声速风洞中, 分别对上游边界层为超声速层流和湍流, 压缩角度为25°和28°的压缩拐角流动进行了实验研究. 采用纳米粒子示踪平面激光散射(NPLS)技术获得了流场整体和局部区域的精细结构, 边界层、剪切层、分离激波、回流区和再附激波等典型结构清晰可见, 测量了超声速层流压缩拐角壁面的压力系数. 从时间平均的流场结构中测量出分离激波、再附激波的角度和再附后重新发展的边界层的增长情况, 通过分析时间相关的流场NPLS图像, 可以发现流场结构随时间的演化特性. 实验结果表明: 在25°的压缩角度下, 超声速层流压缩拐角流动发生了典型的分离, 边界层迅速增长失稳转捩, 并引起一道诱导激波, 流场中出现了K-H涡、剪切层和微弱压缩波结构, 而超声速湍流压缩拐角流动没有出现分离, 湍流边界层始终表现为附着状态; 在28° 的压缩角度下, 超声速层流压缩拐角流动进一步分离, 回流区范围明显扩大, 诱导激波、分离激波向上游移动, 再附激波向下游移动, 分离区流动结构复杂, 相比之下, 超声速湍流压缩拐角流动的回流区范围明显较小, 边界层增长缓慢, 流场中没有出现诱导激波、K-H涡和压缩波, 流动分离区域的结构也相对简单, 但分离激波的强度则明显更强. 关键词： 压缩拐角 层流 湍流 流动结构     

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.     

Boundary layer effects on sound in a circular duct

Boundary layer effects on an acoustic field in a unidirectional flow with transverse shear are studied. The acoustic pressure variation in the direction normal to that of the flow is governed in the boundary layer by a second order differential equation. The problem in the boundary layer is reduced from a two point boundary value problem to a one point boundary value problem by transforming the governing equation into the Riccati equation. The Riccati equation is easily integrated with standard numerical procedures. The integration process yields the effective admittance of the wall-boundary layer combination. The acoustic field in the uniform flow is then determined for this effective admittance. Further complications imposed by the boundary layer are thus eliminated. The simplicity of the technique allows calculation of the propagation and decay constants in a circular duct over a wide range of parameters and duct modes.     

In-duct identification of fluid-borne source with high spatial resolution

Source identification of acoustic characteristics of in-duct fluid machinery is required for coping with the fluid-borne noise. By knowing the acoustic pressure and particle velocity field at the source plane in detail, the sound generation mechanism of a fluid machine can be understood. The identified spatial distribution of the strength of major radiators would be useful for the low noise design. Conventional methods for measuring the source in a wide duct have not been very helpful in investigating the source properties in detail because their spatial resolution is improper for the design purpose. In this work, an inverse method to estimate the source parameters with a high spatial resolution is studied. The theoretical formulation including the evanescent modes and near-field measurement data is given for a wide duct. After validating the proposed method to a duct excited by an acoustic driver, an experiment on a duct system driven by an air blower is conducted in the presence of flow. A convergence test for the evanescent modes is performed to find the necessary number of modes to regenerate the measured pressure field precisely. By using the converged modal amplitudes, very-close near-field pressure to the source is regenerated and compared with the measured pressure, and the maximum error was −16.3 dB. The source parameters are restored from the converged modal amplitudes. Then, the distribution of source parameters on the driver and the blower is clearly revealed with a high spatial resolution for kR<1.84 in which range only plane waves can propagate to far field in a duct. Measurement using a flush mounted sensor array is discussed, and the removal of pure radial modes in the modeling is suggested.     

Stability and three-wave interaction of disturbances in supersonic boundary layer with mass exchange on the wall

The interaction of disturbances in a boundary layer of the compressible gas is considered in the linear and nonlinear approximation (the weakly nonlinear theory of stability) in the presence of mass exchange (gas blowing or suction) on the surface. The regimes of moderate (the Mach number M = 2) and high (M = 5.35) supersonic velocities of the flow are considered. The suction from the surface is shown to lead to a considerable variation of the linear evolution of disturbances: the vortex disturbances of the first mode and the acoustic disturbances of the second mode are stabilized, the rate of variation is determined by suction intensity. The nonlinear interactions in three-wave systems between the vortex waves in asymmetric triplets at M = 2 and between the waves of different nature (acoustic and vortex waves) ?? in the symmetric ones at M = 5.35 are considered. The planar acoustic wave is the excitation wave in the latter, which excites the three-dimensional subharmonic components of the vortex nature. It is shown that one can delay considerably the transition region with the aid of suction, thereby one can reduce the skin-friction drag. In the gas blowing regime, strong deformations of the mean fields of boundary layers occur, which lead to the destabilization of the vortex and acoustic waves in the linear region and activate the nonlinear processes in transition region. One can expect that this will lead to the acceleration of tripping in supersonic flow.     

Studying acoustic-wave fields in langasite-family crystals using the BESSY II synchrotron radiation source

The process of the excitation and propagation of pseudosurface acoustic waves in crystals of the langasite family is studied via X-ray diffractometry for the first time. The investigations are carried out using the BESSY II synchrotron radiation source in the double-crystal X-ray diffractometer scheme. The process of pseudosurface acoustic wave propagation is studied based on an analysis of the diffraction spectra of acoustically modulated crystals. Both the velocities of the pseudosurface acoustic waves and the power flow angles of the acoustic energy are measured for the first time. The pseudosurface acoustic wave is shown to be flowing. Surface and pseudosurface acoustic waves generated by an interdigital transducer in the Z cut of a La₃Ga_5.5Ta_0.5O₁₄ crystal are compared.     

Effect of Mean Flow on Acoustic Wave Propagation in a Duct with a Periodic Array of Helmholtz Resonators

Sound propagation properties of a duct system with Helmholtz resonators(HRs) are affected by mean flow.Previous studies have tended to focus on the effects of mean flows on acoustic response of a duct system with a finite number of HRs. Employing an empirical impedance model, we present a modified transfer matrix method for studying the effect of mean flow on the complex band structure of an air duct system with an infinite periodic array of HRs. The efficiency of the modified transfer matrix is demonstrated by comparison between an example of transmission response calculation for a finite single HR loaded duct and the finite element simulation result calculated using the COMSOL software. Numerical results are presented to analyze the effect of mean flow on the band structure and transmission loss of the sound wave in the duct system. It is hoped that this study will provide theoretical guidance for acoustic wave propagation of HR silencer in the presence of mean flow.     

Failure of the Ingard-Myers boundary condition for a lined duct: an experimental investigation

This paper deals with experimental investigation of the lined wall boundary condition in flow duct applications such as aircraft engine systems or automobile mufflers. A first experiment, based on a microphone array located in the liner test section, is carried out in order to extract the axial wavenumbers with the help of an "high-accurate" singular value decomposition Prony-like algorithm. The experimental axial wavenumbers are then used to provide the lined wall impedance for both downstream and upstream acoustic propagation by means of a straightforward impedance education method involving the classical Ingard-Myers boundary condition. The results show that the Ingard-Myers boundary condition fails to predict with accuracy the acoustic behavior in a lined duct with flow. An effective lined wall impedance, valid whatever the direction of acoustic propagation, can be suitably found from experimental axial wavenumbers and a modified version of the Ingard-Myers condition with the form inspired from a previous theoretical study [Aure?gan et al., J. Acoust. Soc. Am. 109, 59-64 (2001)]. In a second experiment, the scattering matrix of the liner test section is measured and is then compared to the predicted scattering matrix using the multimodal approach and the lined wall impedances previously deduced. A large discrepancy is observed between the measured and the predicted scattering coefficients that confirms the poor accuracy provided from the Ingard-Myers boundary condition widely used in lined duct applications.     

Reduction of fan noise by annulus boundary layer removal

Much of the noise produced by a fan is due to varying forces caused by the unsteady flow field through which it passes. In the absence of inlet guide vanes, support struts and other mechanical obstructions, the flow irregularities are caused by large scale intake turbulence and temporal and spatial variations in the annulus boundary layer. In many cases the most effective source is the annulus boundary layer, as this interacts with the blade tip which is the fastest part of the blade and is therefore the most effective noise source. This noise can be reduced if the annulus boundary layer is smoothly bled away from the rotor so that the blade tip sees a thin, uniform boundary layer. A one metre diameter ventilation fan has been run in a duct with and without a boundary layer bleed system and a reduction of far field sound power of approximately 5 dB has been obtained for a bleed of 5 % of the main flow with some far field tone reductions of more than 15 dB. Measurements of far field directivities, in-duct acoustic modes and aerodynamic distortions have confirmed the suggested explanation for this phenomenon. The tests have shown that great care must be taken in the design of a bleed system so that residual boundary layer distortions are not in the correct wavelength range to produce propagating acoustic waves at important blade passing harmonic frequencies. If such distortions are present, the far field noise can increase instead of decrease.     

Fluid dynamics of a flow excited resonance,Part II: Flow acoustic interaction

This is the second of two companion papers in which the physics and detailed fluid dynamics of a flow excited resonance are examined. The approach is rather different from those previously used, in which stability theory has been applied to small wavelike disturbances in a linearly unstable shear layer, with an equivalent source driving the sound field which provides the feedback. In the approach used here, the physics of the flow acoustic interaction is explained in terms of the detailed momentum and energy exchanges occurring inside the fluid. Gross properties of the flow and resonance are described in terms of the parameters necessary to determine the behaviour of the feedback system. In this second paper it is shown that two relatively distinct momentum balances can be considered in the resonator neck region. One can be identified with the vortically induced pressure and velocity fluctuations and the other with the reciprocating potential flow. The fluctuating Coriolis force caused by the interaction of the potential and vortical flows is shown to be the only term in the linearized momentum equation which is not directly balanced by a fluctuating pressure gradient. This force provides the mechanism for the exchange of the mean energies associated with the mean and fluctuating momenta, respectively. A source and sink of energy are identified in which mean energy associated with fluctuating momentum is extracted from and returned to the mean flow, respectively. The imbalance between the source and sink is responsible for both the radiated acoustic power and the power carried away by the vortices as they convect downstream. This radiated acoustic power and vortically convected power, and the source and sink powers, are all of the same order of magnitude. With the vortex shedding and reciprocating potential flow “phase locked” the amplitude of the steady state oscillations is determined by the condition that the net power produced in the resonator neck (the source power less the sink power) is equal to the sum of the radiated acoustic power and that carried by the vortices.     

Accounting for convective effects in zero-Mach-number thermoacoustic models

This paper presents a methodology to account for some mean-flow effects on thermoacoustic instabilities when using the zero-Mach-number assumption. It is shown that when a computational domain is represented under the M=0 assumption, a nonzero-Mach-number element can simply be taken into account by imposing a proper acoustic impedance at the boundaries so as to mimic the mean flow effects in the outer, not computed flow domain. A model that accounts for the coupling between acoustic and entropy waves is presented. It relies on a “delayed entropy coupled boundary condition” (DECBC) for the Helmholtz equation satisfied by the acoustic pressure. The model proves able to capture low-frequency entropic modes even without mean-flow terms in the fluctuating-pressure equation.     

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.     

The displacement-thickness theory of trailing edge noise

The problem of estimating the sound generated by turbulent boundary layer flow over the edge of a rigid half-plane is re-examined. A theory is proposed which is strictly valid at low Strouhal numbers based on boundary layer width, wherein the flow inhomogeneities are specified in terms of the fluctuations in the boundary layer displacement thickness. This enables account to be taken of changes in the properties of the turbulence as it translates past the edge, which are shown to result in the appearance of an acoustic dipole whose axis is aligned with the mean flow, and which supplements the radiation field predicted by conventional methods [1,2]. Detailed comparison is made with acoustic and surface pressures which are calculated according to the evanescent wave theory of edge noise [3–5].     

Mixed convection boundary layer flow over a vertical surface embedded in a thermally stratified porous medium

The mixed convection boundary layer flow through a stable stratified porous medium bounded by a vertical surface is investigated. The external velocity and the surface temperature are assumed to vary as xm, where x is measured from the leading edge of the vertical surface and m is a constant. Numerical solutions for the governing Darcy and energy equations are obtained. The results indicate that the thermal stratification significantly affects the surface shear stress as well as the surface heat transfer, besides delays the boundary layer separation.     

Propagation of acoustic waves in a medium with the Rayleigh energy release mechanism

This research continues theoretical studies of propagation of acoustic waves in a plasma considering it in the context of a Rayleigh medium. For the first time, the solution to the problem with the boundary and not the initial conditions is examined. It is shown that for small values of the parameter characterizing the energy input in the plasma, the amplification coefficients of a harmonic acoustic wave in the problem of propagation of the initial perturbation and in the problem with the boundary conditions are close. However, if the energy input increases, the amplification of the wave propagating from the source is larger than in the problem of the initial perturbation propagation. The same concerns the amplification of waves with different frequencies for fixed parameters of the plasma; i.e., the difference between the amplification coefficients is larger, the lower the wave frequency. The resultant analytic dependences make it possible to determine exactly which of the problems (with the initial or boundary conditions) should be solved to compute the amplification coefficient of acoustic waves under specific experimental conditions.     

Thermoacoustic separation of a He-Ar mixture

We report observation of a new mixture-separation process: an insonified mixture of helium and argon in a narrow duct spatially separates along the acoustic-propagation axis. We measure mole-fraction differences across the ends of the duct as large as 7%. We measure initial separation flux densities as high as 10(-3) M2 c, where M is the acoustic Mach number and c is the sound speed. This initial separation flux, as a function of both the amplitudes and the relative phasing of the pressure and velocity oscillations in the duct, agrees well with a recent theory involving oscillating thermal diffusion in the acoustic boundary layer.