The influence of grazing flow on the acoustic impedance of a cylindrical wall cavity

The acoustic impedance at low frequencies of a circular cylindrical cavity in the wall of a duct in the presence of a low Mach number mean flow is examined. A linearized theoretical model is proposed which involves the unsteady shedding of vorticity from the upstream edge of the cavity aperture. The shed vorticity causes a “potential difference” to be established across the aperture which modifies the reciprocating volume flux and results in the dissipation of acoustic energy. Comparison of theoretical predictions with preliminary experimental data obtained by Parrott (1978, private communication) at the NASA Langley Research Center provides tentative support for the present analysis. Certain difficulties associated with the linearized treatment of cavity oscillations are also discussed.     

掠过流作用下穿孔板的声阻抗

应用三维时域数值方法研究掠过流对穿孔板声阻抗的影响。建立了掠过流作用下穿孔板声阻抗计算的计算流体动力学(CFD)模型,通过时域计算得到掠过流作用下穿孔板的声阻抗,分析结构参数和掠过流马赫数对穿孔板声阻抗的影响。根据计算结果拟合掠过流作用下穿孔板声阻抗的近似表达式,利用获得的穿孔声阻抗新公式预测穿孔管消声器的传递损失,数值预测和实验结果吻合良好。计算结果表明,掠过流对穿孔板的声阻抗和穿孔管消声器的消声性能有明显影响。     

Ultrasonic flow measurement and wall acoustic impedance effects

An examination of the influence of wall acoustic impedance effects on sound propagation in flowing liquids confined by cylindrical walls is presented. Special focus is given to the importance of the wall acoustic impedance value for ultrasonic flow meter performance. The mathematical model presented allows any radially-dependent axial flow profile to be examined in the linear flow acoustics regime where fluid flow speed is much smaller than the fluid sound speed everywhere in the fluid medium.     

On the one-dimensional acoustic propagation in conical ducts with stationary mean flow

This paper proposes a direct time-domain calculation of the time-domain responses of anechoic conical tubes with steady weak mean flow. The starting point is the approximated linear one-dimensional wave equation governing the velocity potential for the case of steady flow with low Mach number. A traveling solution with general space-dependent propagation velocity is then proposed from which the inward and outward pressure and velocity impulse responses can be obtained. The results include the well-known responses of conical and cylindrical ducts with zero mean flow.     

Electrostatic interaction of a spherical particle in the vicinity of a circular orifice

The electrostatic interaction of a charged spherical particle in the vicinity of an orifice plane has been investigated in this paper.The particle can creep along the axis of the orifice and is immersed in a bulk electrolyte.By solving the Poisson-Boltzmann problem,we have obtained the effective electrostatic interaction for several values of reduced orifice radius h,including the cases of h > 1,h = 1 and h < 1.Two kinds of boundary conditions of the orifice plane are considered.One is the constant potential model corresponding to a conducting plane,the other is the constant charge model.In the constant potential model,there is an electrostatic attraction between the particle and the orifice plane when they get close to each other,while there is a pure electrostatic repulsion in the constant charge model.The interactions in both boundary models are sensitive to the parameters of the reduced orifice radius,the reduced particle-orifice distance,surface charge densities of the particle and orifice plane,and the reduced Debye screen constant corresponding to the salt-ion concentration and ion valence.     

On the acoustic performance of rectangular splitter silencers in the presence of mean flow

Dissipative splitter silencers are often used to reduce the noise emitted in ventilation and gas turbine systems. It is well known that the acoustic performance of a splitter silencer changes under the influence of the convective effects of a mean gas flow and so in this article a theoretical model is developed to include the effects of mean flow. The theoretical model is based on a hybrid finite element method which enables the inclusion of bull nose fairings and a perforated screen separating the mean gas flow from a bulk reacting porous material. Predictions are compared against experimental measurements obtained both with and without mean flow. Good agreement between prediction and measurement is generally observed in the absence of mean flow, although it is seen that for silencers with a low percentage open area the silencer insertion loss is over predicted at higher frequencies. When mean flow is present, problems with the experimental methodology are observed at relatively modest mean flow velocities, and so comparison between prediction and experiment is limited to relatively low face velocities. However, experiment and theory both show that the insertion loss reduces at low frequencies when mean flow is in the direction of sound propagation, and at high frequencies the influence of mean flow is generally much smaller. Following additional theoretical investigations it is concluded that the influence of mean flow on splitter silencer performance should be accounted for at low frequencies when silencer airway velocities are greater than about 20 m/s; however, at higher frequencies one may generally neglect the effect of mean flow, even at higher velocities. Predictions obtained using the hybrid method are also compared to a simplified point collocation approach and it is demonstrated that the computationally efficient point collocation method may be used to investigate the effects of mean flow in a splitter silencer without loss of accuracy.     

The effect of grazing mean flow on acoustical characteristics of the micro-perforated panel absorber

There are three effects of grazing mean flow on acoustical characteristics of the micro-perforated panel absorber(1) on radiation impedance of the orifice,(2) on acoustical impedance of the construction at sound wave angle incidence,(3) on sound propagation property in a duct lined by absorber.Based on the acoustical fundamental principle,these effects were analyzed respectively,and relative formulas were derived. Some qualitative tendencies were shown that radiation impedance of an orifice,value ofξin function coth(ξ) which estimates cavity impedance,and transmission loss in a lined duct all will decrease with flow speed increases as well as the resonant frequency will move to lower frequency caused by Doppler Effect,when sound wave propagation direction is the same with flow direction. The discussion was also supported by a relative experimental study.     

Analytic mode matching for a circular dissipative silencer containing mean flow and a perforated pipe

An analytic mode matching scheme that includes higher order modes is developed for a straight-through circular dissipative silencer. Uniform mean flow is added to the central airway and a concentric perforated screen separates the mean flow from a bulk reacting porous material. Transmission loss predictions are compared with experimental measurements and good agreement is demonstrated for three different silencers. Furthermore, it is demonstrated that, when mean flow is present, the axial kinematic matching condition should equate to that chosen for the radial kinematic boundary condition over the interface between the airway and the material. Accordingly, if the radial matching conditions are continuity of pressure and displacement, then the axial matching conditions should also be continuity of pressure and displacement, rather than pressure and velocity as previously thought. When a perforated screen is present the radial pressure condition changes, but the radial kinematic condition should always remain equivalent to that chosen for the axial kinematic matching condition; here, results indicate that continuity of displacement should be retained when a perforated screen is present.     

切向流对微穿孔共振吸声结构声学性能的影响

切向流对微穿孔共振吸声结构声学性能的影响可以分成三类:(1)对小孔辐射声抗的影响;(2)对结构斜入射吸声性能的影响;(3)对消声通道消声性能的影响。根据声学基本理论,详细讨论这些影响,得到对应的理论分析公式。定性而言,若声波的传播方向与气流的运动方向一致,小孔外侧的辐射声抗、空腔声阻抗函数coth (ξ)的宗量ξ赋值和消声通道的消声系数都会减小;同时呈现多普勒效应,使得结构的吸声系数共振峰频率向低频移动。理论分析得到相应实验研究的支持。     

Towards a diffusion model of acoustic energy flow in large undamped structures

It is shown that energy transport parameters for vibrations in a complex structure may be extracted from the kind of data that might be obtained from limited and cost effective direct numerical simulations (DNS). A diffusion model is proposed which promises to avoid the requirement of statistical energy analysis (SEA)-like substructuring. The model is successfully fit to simulated data with an underlying nature which is unambiguously diffusive, as opposed to DNS data where the underlying nature is in question. The data is constructed with noise that mimics the sorts of fluctuations expected in practice. The algorithm's robustness depends heavily on the number of adjustable parameters.     

A study of the influence of mean flow on the acoustic performance of Herschel-Quincke tubes

In this paper, a simple flow model is used in order to assess the influence of mean flow and dissipation on the acoustic performance of the classical two-duct Herschel-Quincke tube. First, a transfer matrix is obtained for the system, which depends on the values of the Mach number in the two branches. These Mach numbers are then estimated separately by means of an incompressible flow calculation. Finally, both calculations are used to study the way in which mean flow affects the position and value of the characteristic attenuation and resonances of the system. The results indicate the nontrivial character of the influence observed.     

声阻抗转换器的研究

描述不均匀传输线中的声反射系数可以归结为求解一种非线性微分方程（Riccati方程），本文探索一条寻找此类方程解析解的新方法，并利用此方法研究了声阻抗转换器，从而大大拓宽了声阻抗转换器阻抗分布的研究范围，作为例子，本文提出了几种阻抗变换形式，并把它们的功率传输效率与已有的均匀及指数型转换器作比较，计算结果表明：当转换器两端与传输介质的阻抗跃变很大时，某些阻抗转换器的传输效率比均匀及指数型转换器高得多．     

Exact solutions to one-dimensional acoustic fields with temperature gradient and mean flow

An exact solution for one-dimensional acoustic fields in ducts in the presence of an axial mean temperature gradient and mean flow is presented in this paper. The analysis is valid for mean Mach numbers such that the square of the mean Mach number is much less than one. The one-dimensional wave equation for ducts with axial mean temperature gradient and mean flow is derived. By appropriate transformations, the wave equation is reduced to an analytically solvable hypergeometric differential equation for the case of a linear mean temperature profile. The developed solution is applied to investigate the dependence of sound propagation in a duct on factors such as temperature gradient and mean flow. The results obtained using the analytical solution compare very well with the numerical results. The developed solution is also compared with an existing analytical solution.     

Reflection of an acoustic line source by an impedance surface with uniform flow

An exact analytic solution is derived for the 2D acoustic pressure field generated by a time-harmonic line mass source located above an impedance surface with uniform grazing flow. Closed-form asymptotic solutions in the far field are also provided. The analysis is valid for both locally-reacting and nonlocally-reacting impedances, as is demonstrated by analyzing a nonlocally reacting effective impedance representing the presence of a thin boundary layer over the surface. The analytic solution may be written in a form suggesting a generalization of the method of images to account for the impedance surface. The line source is found to excite surface waves on the impedance surface, some of which may be leaky waves which contradict the assumption of decay away from the surface predicted in previous analyses of surface waves with flow. The surface waves may be treated either (correctly) as unstable waves or (artificially) as stable waves, enabling comparison with previous numerical or mathematical studies which make either of these assumptions.     

A direct method for acoustic impedance measurement based on the measurement of electrical impedance of acoustic transmitter

A simple and straight forward method for acoustic impedance measurement is presented and evaluated. In this method a speaker is used as the signal source. The relationship between the electrical impedance of the speaker and its acoustical load is developed and studied. It is shown that the electrical current and voltage of the speaker relate to the acoustical pressure and volume velocity. The mechanical and acoustical impedances are therefore easily derived by measuring the electrical current and voltage of the circuit. The proposed method yield itself to the automatic computer measurement and can be used for the field and in situ measurements.Comparison of the measurement data with those from other methods proves the applicability and accuracy of the proposed method.     

Hydromagnetic flow in a circular pipe

This paper describes the flow of an electrically conducting liquid in a circular pipe when a uniform magnetic field is applied in a direction transverse to the direction of flow. It is found that the velocity profile of the liquid transforms itself from a parabola into a plateau as a magnetic field of greater strength is applied. This suggests that the induction drag is important in the central layers while the ordinary visosity is dominant near the wall of the channel. These findings support the earlier results obtained byHartmann andLazarus. It is also shown that the treatment, though elementary in nature, is quite rigorous and does not need correction for the electromagnetic shielding effect.     

A piecewise linear mean flow model for studying stability in a lined channel

Acoustic liners are used to reduce sound emission by turbofan engines. Under grazing flow they may sustain hydrodynamic instabilities and these are studied using a stability analysis, based on a simplified model: the liner is a mass–spring–damper system, the base channel flow is piecewise linear, and the inviscid, incompressible Rayleigh equation is used. The model is an extension to the channel case of a boundary layer model by Rienstra and Darau. The piecewise linear profile introduces a finite boundary layer thickness which ensures well-posedness, allowing an initial value problem to be conducted to investigate absolute stability. For typical values in aeronautics the flow above the liner is unstable. Absolute instability is obtained for somewhat extreme values of the mean flow (tiny boundary layer thickness), and under realistic conditions the flow is convectively unstable. The effect of finite channel height is investigated in both cases. In particular, for large boundary layer thicknesses associated with convective instability the channel height has little effect on the unstable mode. Favorable outcomes and failures of the model are shown by comparison to a published experimental work.