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.     

Empirical model of the acoustic impedance of a circular orifice in grazing mean flow

Although there are many analytical and empirical models for orifice impedance, the predicted acoustical performance when adopting any one of them sometimes shows a large discrepancy with the measured result in some cases. In order to obtain a new practical and precise empirical impedance model under grazing flow conditions, the acoustic impedance of circular orifices has been measured with a variation of the involved parameters under very carefully tested and controlled measurement conditions. The parameters involved in determining the acoustic impedance of an orifice are comprised of the orifice diameter, orifice thickness, perforation ratio, mean flow velocity, and frequency. The range of involved parameters is chosen to cover the practical data span of perforates in typical exhaust systems of internal combustion engines. The empirical impedance model is obtained by using nonlinear regression analysis of the various results of the parametric tests. The proposed empirical model of orifice impedance, with a very high correlation coefficient, is applied to the prediction of the transmission loss of concentric resonators, which have geometric configurations typical of acoustically short and long through-flow resonators. By comparing the measured and predicted results, in which the predictions are made by employing many previous orifice impedance models as well as the present model, it is confirmed that the proposed orifice impedance model yields the most accurate prediction among all other existing impedance models.     

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.     

圆柱面上小孔的声阻抗率

本文根据严格的声学理论,分析了圆柱面上小孔端面由于辐射所产生的声阻抗率。对于声阻率导出了低频近似解。对于声抗率运用了一个分析技巧导出了简化的计算公式,从而得出结论:如果忽略高阶小量,圆柱面小孔的声抗率与无限大平面上相应小孔的声抗率是相等的。     

The influence of a stationary uniform axial flow on the propagation of acoustic modes of vibration in a cylindrical duct

The propagation, in a cylindrical duct, of acoustic modes of vibration whose wavelength is smaller than the damping length, is studied in the presence of a stationary uniform axial flow.     

The effect of a surface impedance load on the behavior of quasi-Rayleigh waves near a cylindrical cavity

The effect of a surface impedance load on the properties of axisymmetric quasi-Rayleigh waves propagating along the boundaries of a cylindrical cavity is investigated. By solving the problem by means of the impedance method, a dispersion equation for these waves is obtained. It is shown that the equation can be represented as the condition that the determinant of the sum of impedance matrices of the load and the medium is zero. Analysis of this equation allows one to investigate the effect of the surface load on the behavior of quasi-Rayleigh waves and on their critical frequencies. The conditions that should be met by the impedance load for quasi-Rayleigh waves to be absent near the cavity or for one or two such waves to exist are determined. The choice of the load is specified for the propagating quasi-Rayleigh wave to possess preset dispersion properties. The conclusions drawn on the basis of this study are illustrated by several examples of load models that can be implemented in practice.     

Geometrical perturbation of an inclined wall on decay times of acoustic modes in a trapezoidal cavity with an impedance surface

Decay times of acoustic modes of a trapezoidal cavity (TC modes) with an inclined wall are studied. Each cavity wall is successively assigned an impedance surface and the other five walls are rigid. The decay times are obtained from the coupling between rigid-walled modes of the rectangular cavity (RC modes) that bounds the trapezoidal cavity. Two coupling mechanisms are identified, namely, the damping coupling and the geometrical coupling. The former is related to the coupling of RC modes at the impedance surface, while the latter is related to the coupling of RC modes at the inclined wall. Both mechanisms include the same volume coupling where RC modes couple throughout the trapezoidal cavity. When the impedance surface is at either of the two trapezoidal walls, the grouping of TC modes with same decay times and the decay time variation with the wall inclination are determined only by the damping coupling. When the surface is at any of the other rectangular walls, both the damping and geometrical couplings are at work. This paper provides an understanding of how the inclined wall and the impedance surface location affect the TC-mode grouping, and what determines the decay time variation with the inclination.     

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。     

声腔对电动式换能器工作特性的影响

传统的电动式换能器设计理论中,未考虑压力补偿系统等声腔结构对声学性能的影响,声源级理论设计结果与实测结果存在较大差别。研究中将电动式换能器内部的三段气腔视为突变截面声腔结构,给出了声腔的四端网络等效电路,将其作为辐射面的负载添加到电动式换能器的传统等效电路中,获得了电动式换能器改进的等效电路。基于改进的等效电路求解了带有声腔结构的电动式换能器声源级曲线,该曲线与有限元仿真分析结果基本一致,验证了该改进的等效电路在预报电动式换能器声源级方面的正确性。基于该等效电路研究了声腔的结构尺寸、末端声学边界及腔内气体声学参数对声源级起伏特征的影响。结果显示,在声腔末端敷设吸声材料或在声腔内充入特性阻抗较小的气体对于抑制或消除声源级起伏具有明显作用。     

声腔对电动式换能器工作特性的影响

传统的电动式换能器设计理论中,未考虑压力补偿系统等声腔结构对声学性能的影响,声源级理论设计结果与实测结果存在较大差别。研究中将电动式换能器内部的三段气腔视为突变截面声腔结构,给出了声腔的四端网络等效电路,将其作为辐射面的负载添加到电动式换能器的传统等效电路中,获得了电动式换能器改进的等效电路。基于改进的等效电路求解了带有声腔结构的电动式换能器声源级曲线,该曲线与有限元仿真分析结果基本一致,验证了该改进的等效电路在预报电动式换能器声源级方面的正确性。基于该等效电路研究了声腔的结构尺寸、末端声学边界及腔内气体声学参数对声源级起伏特征的影响。结果显示,在声腔末端敷设吸声材料或在声腔内充入特性阻抗较小的气体对于抑制或消除声源级起伏具有明显作用。     

Compton scattering of the accelerator radiation in cylindrical cavity wall

Starting from the Klein-Nishina relations describing Compton scattering there was calculated the intensity distribution of the radiation incoming from the cylindrical cavity wall. The calculations were carried out at first - as completely incoherent and next - assuming the possibility of the caustics arising. Its results, compared with the experimental ones, confirm the above supposition.     

The acoustical impedance of holes in the wall of flow ducts

The radiation impedance of circular and oblong holes in the wall of a flow duct has been measured as a function of the flow velocity. The boundary layer at the wall of the duct is thin compared to the dimensions of the orifices. At low Strouhal numbers (quasi-static case) and constant boundary layer thickness, the flow resistance of the orifice (real part of the impedance) increases in proportion to the flow velocity. The imaginary part of the impedance corresponds to a constant, negative attached mass above the orifice, i.e. the impedance is spring-like. In the transition range from air at rest to the quasi-static case (high Strouhal numbers) the impedance as a function of the flow velocity describes a spiral in the complex plane. The mechanism causing the flow dependence of the impedance is illustrated by a simple model of the flow above the orifice. As a practical example of the flow-dependent impedance of orifices, the flow-dependent sensitivity of a probe microphone used in flowing media is discussed.     

基于近场声全息的圆柱壳体内部声场重构效果的影响因素

在Neumann边界条件下基于近场声全息原理(NAH)重构了两端封闭的有限长圆柱壳体内部声场,计算出的结果与基于模态叠加法构建的内部声场进行比较,证明了重构方法的正确性,然后分别讨论了激励频率和全息面选择对NAH重构声场精度的影响以及重构面上不同位置的重构效果。     

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.     

Zonal flow induced by longitudinal librations of a rotating cylindrical cavity

Longitudinal librations represent oscillations about the axis of a rotating axisymmetric fluid filled cavity. An analytical theory is developed for the case of a cylindrical cavity in the limit when the libration frequency is small in comparison with the rotation rate, but large in comparison with the inverse of the spin-up time. It is shown that through the nonlinear advection in the Ekman layers the librations cause the fluid to rotate more slowly.     

Experimental studies on perturbed acoustic resonant spectroscopy by a small rock sample in a cylindrical cavity

A measurement system for acoustic resonant spectroscopy (ARS) is established, and the effects of resonant cavity geometry, inner perturbation samples and environmental temperature on the ARS are investigated. The ARSs of the small samples with various sizes and acoustic properties are measured. The results show that at the normal pressure, the resonant frequency decreases gradually with the increase of liquid temperature in the cylindrical cavity, while the resonant amplitude increases. At certain pressure and temperature, both the resonant frequency and the amplitude decrease greatly when there exist air bubbles inside the cavity fluid. The ARS is apparently affected by the sample porosity and the sample location in the resonant cavity. At the middle of the cavity, the resonant frequencies reach their maximum values for all of the measurement samples. The resonant frequencies of the porous rock samples are smaller than those of the compacted samples if other acoustic parameters are the same. As the sample is moved from the top to the middle of the cavity along its axis, the resonant amplitude increases gradually for the compacted rocks while decreases for the unconsolidated rocks. Furthermore, the resonant amplitude increases firstly and then decreases if the porosity of the rock sample is relatively small. In addition, through the comparisons between the experimental and theoretical results, it is found that the effects of the acoustic parameters and sizes of the samples and the size of the cylindrical cavity on the laboratory results agree well with the theoretical ones qualitatively. These results may provide basic reference for the experiment study of rock acoustic properties in a low frequency using ARS.     

Investigation of flow features and acoustic radiation of a round cavity

In this work, the interaction between a boundary layer and a circular cylindrical cavity is studied. Experimental pressure and velocity results for a cavity of diameter 10 cm and depth ranging from 10 to 15 cm are described, for flow velocities between 50 and 110 m s^?1. This flow configuration is found to generate intense discrete depth- and flow-dependent tones, resulting in modes similar in appearance to Rossiter modes found in shallow rectangular cavities. Differences between the cylindrical cavity's mean flow and that of a similarly sized rectangular cavity are highlighted. The development of the shear layer is quantified, in terms of thickening and of velocity statistics profiles. Radial and azimuthal acoustic modes are observed in the acoustic field inside the cavity. A feedback model based on the coupled behaviour of the fundamental acoustic depth mode of the cavity and the large scale dynamics of the shear layer is constructed, and its response is compared to experimental data. A good qualitative agreement between available data and modeled behaviour is observed, allowing the two acoustic modes found in this work to be attributed to the interaction of the shear layer with the cavity's fundamental depth mode.     

腔壁弹性对充水亥姆霍兹共振器声学特性的影响:圆柱形腔等效集中参数模型

研究了充水亥姆霍兹共振器的弹性壁对其声学特性的影响。建立了考虑壁面弹性的圆柱形共振器的等效集中参数理论模型,并在静水管路上进行了实验验证。从共振器的共振频率、激励声压与腔内声压的传递函数以及共振器的传递损失等方面阐述了弹性壁的影响,并对刚性壁假设和弹性壁结果进行了比较。理论和实验都证明了腔壁弹性对亥姆霍兹共振器的声学特性有很大的影响。     

Radiation of cylindrical duct acoustic modes with flow mismatch

An analysis is presented for the radiation of spinning acoustic modes from a round duct. The model, based on a plug flow exhaust jet, allows for a flow temperature and velocity mismatch. Solutions to the convected wave equations within and outside the jet are devised, the continuity of acoustic pressure and particle displacement match at the jet interface being used. Formal solution is obtained by applying Fourier transforms, inversion being accomplished by using the Wiener-Hopf technique coupled with the Carrier-Koiter approximations. The analysis also is extended formally to include the inlet problem, but with a plug type inlet flow.The calculations suggest that the influence of the Mach number discontinuity is to offer a conflict between the effects of convection and refraction, the former becoming increasingly more significant at high subsonic Mach numbers by the presence of a strong lobe in the shadow zone. Effects of flight conditions are to weaken such conflicts so that in the limit of uniform Mach number, one recovers Carrier's well-known solution.The effect of a temperature mismatch is rather more dramatic, resulting in a sharp beaming of sound off to the side. This is consistent with the kinematic picture of a plane wave impinging on a temperature discontinuity.