Oscillatory limited compressible fluid flow induced by the radial motion of a thick-walled piezoelectric tube

A simple oscillatory, slightly compressible, fluid flow model in a thick-walled piezoelectric tube used in a drop-on-demand inkjet print head is developed from the point of view of fluid-structure interaction to take account of pressure wave propagation and pressure loading opposing wall motion. A frequency sweep is performed computationally using the model revealing the first acoustic fluid-structure resonance frequency and the influence of fluid viscosity. The validity of the model, with given information on the speed of sound in a fluid, is evaluated by comparing the theoretically predicted resonance frequency to the experimentally measured resonance frequency. In addition, the intrinsic speed of sound can be easily computed using the measured acoustic resonance frequency and this computed speed of sound agrees closely with speeds of sound reported in the literature.     

Effect of the spectrum of a high-intensity sound source on the sound-absorbing properties of a resonance-type acoustic lining

Experimental results are presented on the effect of both the sound pressure level and the type of spectrum of a sound source on the impedance of an acoustic lining. The spectra under study include those of white noise, a narrow-band signal, and a signal with a preset waveform. It is found that, to obtain reliable data on the impedance of an acoustic lining from the results of interferometric measurements, the total sound pressure level of white noise or the maximal sound pressure level of a pure tone (at every oscillation frequency) needs to be identical to the total sound pressure level of the actual source at the site of acoustic lining on the channel wall.     

On the acoustic modes in a cylindrical duct with an arbitrary wall impedance distribution

The present paper considers the propagation of sound in a cylindrical duct, with a wall section of finite length covered by an acoustic liner whose impedance is an arbitrary function of position. The cases of (i) uniform wall impedance, and wall impedance varying along the (ii) circumference or (iii) axis of the duct, or (iv) both simultaneously, are explicitly considered. It is shown that a nonuniform wall impedance couples modes with distinct azimuthal l or axial m wave numbers, so that their radial wave numbers k can no longer be calculated separately for each pair (m,l). The radial wave numbers are the roots of an infinite determinant, in the case when the wall impedance varies either (i) circumferentially or (ii) radially. If the wall impedance varies (iv) both radially and circumferentially, then the radial wave numbers are the roots of a doubly infinite determinant, i.e., an infinite determinant in which each term is an infinite determinant. The infinite determinants specifying the radial wave numbers are written explicitly for sound in a cylindrical nozzle with a uniform axial flow, in which case the radial eigenfunctions are Bessel functions; the method of calculation of the radial wave numbers applies equally well to a cylindrical nozzle with shear flow and/or swirling flows, with the Bessel functions replaced by other eigenfunctions. The radial wave numbers are calculated by truncation of the infinite determinants, for several values of the aspect ratio, defined as the ratio of length to diameter. It is shown that a nonuniform wall impedance will give rise to additional modes compared with a uniform wall impedance. The radial wave numbers specify the eigenfrequencies for the acoustic modes in the duct; the imaginary parts of the eigenfrequencies specify the decay of the sound field with time, and thus the effectiveness of the acoustic liner.     

Measuring fluid and slurry density and solids concentration non-invasively

Staff at Pacific Northwest National Laboratory have developed a highly sensitive, non-invasive, self-calibrating, on-line sensor to measure the density, speed of sound, and attenuation of ultrasound for a liquid or slurry flowing through a pipeline; the approach can also be applied for measurements made in vessels. The sensor transducers are mounted directly upon the stainless steel wall and the pipeline wall becomes part of the measurement system. Multiple reflections within the stainless steel wall are used to determine the acoustic impedance of the liquid, where the acoustic impedance is defined as the product of the density and the speed of sound. The probe becomes self-calibrating because variations in the pulser voltage do not affect the measurements. This feature leads to the stability of the measurements and the instrument requires much less time and effort to calibrate. Further, the calibration remains constant in time, because it does not depend upon the pulser voltage remaining at a given value. By basing the measurement upon multiple reflections, the sensitivity of the measurement is significantly increased. For slurries with wt% solids concentration of 1% or less, high sensitivity is gained by analyzing attenuation measurements obtained from multiple paths through the slurry. For slurries with higher concentrations of solids, sufficient sensitivity is obtained by analyzing data from a simple transmission. Data are presented that show probe performance for each of these cases: very dilute and highly concentrated kaolin clay slurries.     

An effective quiescent medium for sound propagating through an inhomogeneous,moving fluid

The idea of similarity between acoustic fields in a moving fluid and in a certain "effective" quiescent medium, first put forward by Lord Rayleigh, proved very helpful in understanding and modeling sound propagation in an atmosphere with winds and in an ocean with currents, as well as in other applications involving flows with small velocity compared to sound speed. Known as effective sound speed approximation, the idea is routinely utilized in the contexts of the ray theory, normal mode representation of the sound field, and the parabolic approximation. Despite the wide use of the concept of effective sound speed in acoustics of moving media, no theoretical justification of Rayleigh's idea was published that would be independent of the chosen representation of the sound field and uniformly apply to distinct propagation regimes. In this paper, we present such a justification by reducing boundary conditions and a wave equation governing sound fields in the inhomogeneous moving fluid with a slow flow to boundary conditions and a wave equation in a quiescent fluid with effective sound speed and density. The derivation provides insight into validity conditions of the concept of effective quiescent fluid. Introduction of effective density in conjunction with effective sound speed is essential to ensure accurate reproduction of acoustic pressure amplitude in the effective medium. Effective parameters depend on sound speed, flow velocity, and density of the moving fluid as well as on sound propagation direction. Conditions are discussed under which the dependence on the propagation direction can be avoided or relaxed.     

Inversion for acoustic impedance of a wall by using artificial neural network

A new approach for measuring acoustic impedance is developed by using artificial neural network (ANN) algorithm. Instead of using impedance tube, a rectangular room or a box is simulated with known boundary conditions at some boundaries and an unknown acoustic impedance at one side of the wall. A training data basis for the ANN algorithm is evaluated by similar source method which was developed earlier by Too and Su [Too G-PJ, Su T-K. Estimation of scattering sound field via nearfield measurement by source methods. Appl Acoust. 1999;58:261-81 (SCI) (EI)] for the estimation of interior and exterior sound field. The training data basis is constructed by evaluating of acoustic pressure at a field point with various acoustic impedance conditions at one side of the wall. Then, the inversion for unknown acoustic impedance of a wall is performed by measuring several field data and substituting these data into ANN algorithm. The simulation result indicates that the prediction of acoustic impedance is very accurate with error percentage under 1%. In addition, one field point measurement in the present approach for acoustic impedance provides more straightforward and easier evaluation than that in the two point measurement of impedance tube.     

Vocal tract resonances and the sound of the Australian didjeridu (yidaki) I. experiment

The didjeridu, or yidaki, is a simple tube about 1.5 m long, played with the lips, as in a tuba, but mostly producing just a tonal, rhythmic drone sound. The acoustic impedance spectra of performers' vocal tracts were measured while they played and compared with the radiated sound spectra. When the tongue is close to the hard palate, the vocal tract impedance has several maxima in the range 1-3 kHz. These maxima, if sufficiently large, produce minima in the spectral envelope of the sound because the corresponding frequency components of acoustic current in the flow entering the instrument are small. In the ranges between the impedance maxima, the lower impedance of the tract allows relatively large acoustic current components that correspond to strong formants in the radiated sound. Broad, weak formants can also be observed when groups of even or odd harmonics coincide with bore resonances. Schlieren photographs of the jet entering the instrument and high speed video images of the player's lips show that the lips are closed for about half of each cycle, thus generating high levels of upper harmonics of the lip frequency. Examples of the spectra of "circular breathing" and combined playing and vocalization are shown.     

流管实验装置中声传播计算的模态方法

流管实验装置是测量有流动情况下航空发动机消声短舱内声衬声阻抗的主要装置。本文发展了一种解析的模态匹配方法进行在平均流有声衬条件下矩形流管中声传播的计算。用同伦方法求解特征值问题,并与用环绕积分求解的结果进行比较。声场通过轴向阻抗间断面的声压和声质点速度积分相等计算。第一个算例是无流动、硬壁、有限长、考虑端口反射的情况,并与北航流管实验台测量数据进行了对比;第二个算例为有流动情况下有限长声衬管道不考虑端口反射的声场计算,它与文献中NASA流管实验结果和CAA计算结果符合得很好。     

Finite element simulation of an axisymmetric acoustic transmission system with a sound absorbing wall

A finite element formulation for the axisymmetric acoustic field problem with an arbitrary sound absorbing wall is developed on the true adjoint system approach. A triangular ring element with a second order polynomial trial function is used for discretization. As a first numerical example, the transmission characteristic of acoustic filters of expansion type is considered, in which the wall is partly treated with sound absorbing material. As a second example the effect of a temperature gradient in the chamber on the transmission characteristic is calculated. The third example is the calculation of the throat impedance of conical and exponential acoustic horns, for which the half sphere into which the radiation travels is assumed to be terminated at an appropriate radius by a hypothetical wall having the characteristic impedance of the acoustic medium. The calculated results are verified by comparison with measured results.     

圆孔非线性声阻抗三维时域仿真与特性分析

为研究有限振幅声波作用下圆孔的非线性声学特性,提出了基于三维时域计算流体动力学(CFD)仿真的圆孔非线性声阻抗提取方法,通过求解层流方程来模拟声信号在圆孔及上下游的传播,以及采用横向周期性边界条件来考虑高穿孔率时圆孔之间相互作用的影响。研究了不同幅值声波作用下孔径、厚度和穿孔率对声阻抗的影响规律,通过对质点振速幅值、频率和板厚等组成的无量纲参量进行非线性回归分析,得到了圆孔非线性声阻抗的拟合公式,并将其转换为可考虑多频声波影响的时域模型。最后结合声阻抗时域模型和有限差分方法计算了直通穿孔管消声器在小振幅和有限振幅声波作用下的传递损失,通过与实验测量结果的比较,验证了拟合公式的准确性和实用性。     

Evaluation of the acoustic and non-acoustic properties of sound absorbing materials using a three-microphone impedance tube

This paper presents a straightforward application of an indirect method based on a three-microphone impedance tube setup to determine the non-acoustic properties of a sound absorbing porous material. First, a three-microphone impedance tube technique is used to measure some acoustic properties of the material (i.e., sound absorption coefficient, sound transmission loss, effective density and effective bulk modulus) regarded here as an equivalent fluid. Second, an indirect characterization allows one to extract its non-acoustic properties (i.e., static airflow resistivity, tortuosity, viscous and thermal characteristic lengths) from the measured effective properties and the material open porosity. The procedure is applied to four different sound absorbing materials and results of the characterization are compared with existing direct and inverse methods. Predictions of the acoustic behavior using an equivalent fluid model and the found non-acoustic properties are in good agreement with impedance tube measurements.     

A straightforward method for wall impedance eduction in a flow duct

The development of the advanced liner technology for aeroengine noise control necessitates the impedance measurement method under realistic flow conditions. Currently, the methods for this need are mainly based on the inverse impedance eduction principle, confronting with the problems of initial guess, high computation cost, and low convergence. In view of this, a new strategy is developed that straightforwardly educes the impedance from the sound pressure information measured on the duct wall opposing to the test acoustic liner embedded in a flow duct. Here, the key insight is that the modal nature of the duct acoustic field renders a summed-exponential representation of the measured sound pressure; thus, the characterizing axial wave number can be readily extracted by means of Prony's method, and further the unknown impedance is calculated from the eigenvalue and dispersion relations based on the classical mode-decomposition analysis. This straightforward method is simple in its basic principle but remarkably has the advantages of ultimately overcoming the drawbacks inherent to the inverse methods, incorporating the realistic multimode nonprogressive wave effects, high computational efficiency, possibly reducing the measurement points, and even avoiding the necessity of the duct exit impedance that bothers perhaps all the existing waveguide methods.     

Influence of viscosity on the diffraction of sound by a circular aperture in a plane screen

The linearized equations of viscous fluid flow are used to analyze the diffraction of a time-harmonic acoustic plane wave by a circular aperture in a rigid plane screen. Arbitrary aperture size and arbitrary angle of incidence are considered. Sets of dual integral equations are derived for the diffracted velocity and pressure fields, and are solved by analytic reduction to sets of linear algebraic equations. In the case of normal incidence, numerical results are presented for the fluid velocity in the aperture and the power absorption due to viscous dissipation. The theoretical results for power absorption are compared to previously obtained results from high amplitude acoustic experiments in air. The conditions under which the dissipation predicted by linear theory becomes significantare quantified in terms of the fluid viscosity and sound speed, the acoustic frequency, and the aperture radius.     

非对称阻抗插入管消声器的Chebyshev-变分法建模与求解

针对非对称阻抗插入管消声器三维理论建模与求解问题,提出了一种半解析变分建模和求解方法,试验及有限元结果验证了理论模型和求解结果的正确性,开展了模态频率、声压响应及传递损失等声场特性的预测分析。首先构建插入管消声器内部子声场拉格朗日泛函,基于声压与质点振速连续性条件,得到插入管消声器三维理论模型。随后,将子声场声压展开为切比雪夫-傅里叶级数组合形式,按里兹法求得消声器三维声场模态信息。搭建了消声器传递损失试验平台,进行了刚性壁面和阻抗壁面消声器传递损失测试试验,对理论模型和计算结果进行了验证。通过算例分析了壁面阻抗的大小、阻抗面积和分布形式以及插入管偏置对消声器消声性能的影响。结果表明,提出的变分建模求解方法是有效的,对消声器壁面阻抗位置和形式的合理设置可有效降低输出声压。      

Suppression of Helmholtz resonance using inside acoustic liner

When a Helmholtz resonator is exposed to grazing flow, an unstable shear layer at the opening can cause the occurrence of acoustic resonance under appropriate conditions. In this paper, in order to suppress the flow-induced resonance, the effects of inside acoustic liners placed on the side wall or the bottom of a Helmholtz resonator are investigated. Based on the one-dimensional sound propagation theory, the time domain impedance model of a Helmholtz resonator with inside acoustic liner is derived, and then combined with a discrete vortex model the resonant behavior of the resonator under grazing flow is simulated. Besides, an experiment is conducted to validate the present model, showing significant reduction of the peak sound pressure level achieved by the use of the side-wall liners. And the simulation results match reasonably well with the experimental data. The present results reveal that the inside acoustic liner can not only absorb the resonant sound pressure, but also suppress the fluctuation motion of the shear layer over the opening of the resonator. In all, the impact of the acoustic liners is to dampen the instability of the flow-acoustic coupled system. This demonstrates that it is a convenient and effective method for suppressing Helmholtz resonance by using inside acoustic liner.     

Temperature dependence of acoustic impedance for specific fluorocarbon liquids

Recent studies by our group have demonstrated the efficacy of perfluorocarbon liquid nanoparticles for enhancing the reflectivity of tissuelike surfaces to which they are bound. The magnitude of this enhancement depends in large part on the difference in impedances of the perfluorocarbon, the bound substrate, and the propagating medium. The impedance varies directly with temperature because both the speed of sound and the mass density of perfluorocarbon liquids are highly temperature dependent. However, there are relatively little data in the literature pertaining to the temperature dependence of the acoustic impedance of these compounds. In this study, the speed of sound and density of seven different fluorocarbon liquids were measured at specific temperatures between 20 degrees C and 45 degrees C. All of the samples demonstrated negative, linear dependencies on temperature for both speed of sound and density and, consequently, for the acoustic impedance. The slope of sound speed was greatest for perfluorohexane (-278 +/- 1.5 cm/s-degrees C) and lowest for perfluorodichlorooctane (-222 +/- 0.9 cm/s-degrees C). Of the compounds measured, perfluorohexane exhibited the lowest acoustic impedance at all temperatures, and perfluorodecalin the highest at all temperatures. Computations from a simple transmission-line model used to predict reflectivity enhancement from surface-bound nanoparticles are discussed in light of these results.     

Recovering the acoustic Green's function from ambient noise cross correlation in an inhomogeneous moving medium

We study long-range correlation of diffuse acoustic noise fields in an arbitrary inhomogeneous, moving fluid. The flow reversal theorem is used to show that the cross-correlation function of ambient noise provides an estimate of a combination of the Green's functions corresponding to sound propagation in opposite directions between the two receivers. Measurements of the noise cross correlation allow one to quantify flow-induced acoustic nonreciprocity and evaluate both spatially averaged flow velocity and sound speed between the two points.     

A revisit to imperfect acoustic cloak of multi-layered shell structures considering sound speed and impedance matching

An imperfect multi-layered acoustic cloak is proposed for a two-dimensional cloaking zone based on feasible material properties. In this model, the matching of sound speed and acoustic impedance has been investigated, and the effects of material and geometric properties on the imperfect cloak have been studied for better design of the imperfect cloak. The imperfect cloak could be improved using appropriate changes in the design parameters. By increasing the thickness of the high density layer and with some changes in the sound speeds between the high density and the low density layers, the imperfect cloaking model showed better cloaking performance than Cummer–Schurig cloak. Also, present results show that the sound speed matching is more important for acoustic cloaking than the impedance matching. These results can be applied as a practical design guide for two-dimensional cloaks using multilayered structures composed of naturally existing materials.     

Sound decay in a rectangular room with impedance walls

The problem of sound decay in a rectangular room is considered for the case of a room with walls the acoustic properties of which are described by the impedance, which implies a dependence of the absorption coefficient on the angle of incidence of sound waves. The ray approximation is used to determine the sound decay laws for different distributions of wall absorption. It is shown that, in a room with impedance walls, the sound decay is slower than in the conventional reverberation model, in which the wall absorption coefficient is independent of the angle of incidence. The problem is also solved in the wave approximation to determine the decay law for a preset frequency band.