Calculations of modes in circumferentially nonuniform lined ducts

This paper proposes a computationally efficient method of determining eigenfunctions and eigenvalues of acoustic modes propagating in circular lined ducts with zero or uniform flow. Linings with circumferentially nonuniform impedance, as found in nacelle acoustics, are the focus. The method of solution adapts in two important respects--the presence of flow and the imposition of impedance boundary conditions--the series expansion method first proposed by Pagneux et al. [J. Acoust. Soc. Am. 110, 1307-1314 (2001)] to calculate the eigenvalues of Lamb modes. The inclusion of flow, and a corresponding different method of solution leading to an improved convergence of eigenvalues (O(N(-5)), N is the truncation of radial basis of expansion), is the important new feature as compared to the previous adaptation by Bi et al. [J. Acoust. Soc. Am. 122, 280-291 (2007)]. As a result, it becomes possible to safely determine and in a simple manner the eigenvalues and eigenfunctions of circumferentially nonuniform lined ducts in the presence of uniform flow, up to relatively high frequencies (e.g., 30相似文献   

Sound propagation in acoustically lined elliptical ducts

Sound propagation in ducts with elliptical cross-sections can be described in terms of modes characterized by Mathieu functions of orders specified by the boundary conditions. For ducts with locally reacting liners there is coupling between modes because the admissible solutions are linear combinations of Mathieu functions of different orders and the eigenvalues are roots of an infinite determinant. The amount of mode coupling depends on the eccentricity of the duct. For the case of small eccentricity of the duct, approximate general solutions are derived and an example is discussed, where solutions are found.     

Non-linear attenuation of sound in circular lined ducts

The attenuation of high intensity sound in circular ducts lined with fibrous material has been investigated. With no mean flow, the sound pressure levels are varied to illustrate the linear and non-linear absorption characteristics of the liner. Effects of liner thickness, perforation ratio of the duct wall and the $\text{d}\text{t}$ ratio are analysed.Optimum combinations of the perforation geometry and liner thickness are found to be of stable attenuation characteristics over a wide frequency range and at high sound levels.     

Investigation of long-range sound propagation in surface ducts

Understanding the effect of source-receiver geometry on sound propagation in surface ducts can improve the performance of near-surface sonar in deep water. The Lloyd-mirror and normal mode theories are used to analyze the features of surface-duct propagation in this paper. Firstly, according to the Lloyd-mirror theory, a shallow point source generates directional lobes, whose grazing angles are determined by the source depth and frequency. By assuming a part of the first lobe to be just trapped in the surface duct, a method to calculate the minimum cutoff frequency （MCF） is obtained. The presented method is source depth dependent and thus is helpful for determining the working depth for sonar. Secondly, it is found that under certain environments there exists a layer of low transmission loss （TL） in the surface duct, whose thickness is related to the source geometry and can be calculated by the Lloyd-mirror method. The receiver should be placed in this layer to minimize the TL. Finally, the arrival angle on a vertical linear array （VLA） in the surface duct is analyzed based on normal mode theory, which provides a priori knowledge of the beam direction of passive sonar.     

具有声激波的跨音流管道中声传播的数值方法

本文采用四阶MacCormack格式和附加四阶粘性项方法,求解具有声激波的跨音流变差分格壁管中的声传播问题,比前人结果有明显改善。本文详细介绍了这种差分方法,特别是关于截面硬式,人工粘性项和计算可靠性判据。这种方法省内存,省机时,可以在微机上实现计算。     

Effect of wall shear layers on the sound attenuation in acoustically lined rectangular ducts

This paper deals with the manner in which a shear layer proximate to the wall of an acoustically treated rectangular duct modifies the attenuation spectra. The restriction of this shear layer to the region near the lined duct walls is aimed at simulating boundary layer effects on the attenuation. Theoretical results show that shear significantly changes the peak attenuation, causing a frequency shift of this peak. For the inlet mode, i.e. flow against the direction of sound propagation, both results are a strong function of Mach number and layer thickness. For the exhaust mode, i.e. flow in the direction of propagation, these effects are relatively weak.     

Attenuation of sound in multi-element acoustically lined rectangular ducts in the absence of mean flow

Extensions of the ordinary Wiener-Hopf technique are outlined and applied to the solution of sound attenuation in multi-element ducts with acoustically absorbing liners in series as well as in parallel combination. For demonstration purposes the simplest case of engineering interest is chosen: namely, a rectangular channel at zero convection velocity. Extensions to circular and annular geometries as well as to mean flow situations are possible. In the absence of a realistic source model acoustic power attenuation results are presented for an incoming fundamental mode only, to show the influence of major design parameters for point reacting liners. The broad band-width attenuation capacity of some liner configurations as well as the necessity to include wave reflections at liner discontinuities for multi-element liners is clearly demonstrated. For a given acoustic source a multi-mode solution can be found by summing the contributions of each incoming unattenuated mode.     

An improved gridding method for spiral MRI using nonuniform fast Fourier transform

The algorithm of Liu and Nguyen [IEEE Microw. Guided Wave Lett. 8 (1) (1998) 18; SIAM J. Sci. Comput. 21 (1) (1999) 283] for nonuniform fast Fourier transform (NUFFT) has been extended to two dimensions to reconstruct images using spiral MRI. The new gridding method, called LS_NUFFT, minimizes the reconstruction approximation error in the Least Square sense by generated convolution kernels that fit for the spiral k-space trajectories. For analytical comparison, the LS_NUFFT has been fitted into a consistent framework with the conventional gridding methods using Kaiser-Bessel gridding and a recently proposed generalized FFT (GFFT) approach. Experimental comparison was made by assessing the performance of the LS_NUFFT with that of the standard direct summation method and the Kaiser-Bessel gridding method, using both digital phantom data and in vivo experimental data. Because of the explicitly optimized convolution kernel in LS_NUFFT, reconstruction results showed that the LS_NUFFT yields smaller reconstruction approximation error than the Kaiser-Bessel gridding method, but with the same computation complexity.     

Ray dynamics of the propagation of sound in nonuniform moving media

This paper presents a new ray theory for the propagation of sound waves in nonuniformly moving media. It is found that the ray equations in weakly inhomogeneous and slowly moving media are analogous to the equations of motion of charged particles in nonuniform electric and magnetic fields. The adiabatic approximation is used to study the problem of the propagation of sound rays in a model of near-ocean-bottom waveguide with horizontal flow and slowly varying parameters along the direction of propagation of the wave. A general formula is derived that describes the transverse displacement of the trajectory of the ray relative to the direction of propagation of the wave.     

A comparison of experiment and theory for sound propagation in variable area ducts

An experimental and analytical program has been carried out to evaluate sound suppression techniques in ducts that produce refraction effects due to axial velocity gradients. The analytical program employs a computer code based on the method of multiple scales to calculate the influence of axial variations due to slow changes in the cross-sectional area as well as transverse gradients due to the wall boundary layers. Detailed comparisons between the analytical predictions and the experimental measurements have been made. The circumferential variations of pressure amplitudes and phases at several axial positions have been examined in straight and variable area ducts, with hard walls and lined sections, and with and without a mean flow. Reasonable agreement between the theoretical and experimental results has been found.     

An improved method for determination of radiated sound power and sound transmission from large sources

The proposed method is an improvement of the methods for measurement of sound power level, in which the real sound source is represented by an equivalent monopole. It is based on a new concept, the equivalent acoustical centre, which is introduced and defined in the paper. The main assets of the method in comparison with the existing monopole-methods are a higher accuracy, a possibility of measuring at considerably shorter distances from the noise source, and a certain freedom in the choise of the measuring points around the source. Moreover, since the position of the equivalent monopole is obtained, it can be used for more accurate calculations of the sound transmission to the surroundings of the source. The method is particularly suitable for determination of sound power levels and sound transmission of noise radiated from large areas, such as industrial complexes, installations of petrochemical industries and the like. It can be especially useful in disputable cases of industrial plants that produce noise close to the legally permissible limit. The new method was first reported at the meeting of the Dutch Acoustical Society which took place in Utrecht on 22 November 1978.     

一种水平变化波导中声传播问题的耦合模态法

针对介质参数及海底边界水平变化波导中的声传播问题,本文基于多模态导纳法提出一种能量守恒且便于数值稳定求解的耦合模态方法.将声压表示为一组正交完备的本地本征函数之和,对声压满足的Helmholtz方程在本地本征函数上作投影,推导出关于声压模态系数的二阶耦合模态方程组.耦合矩阵直观描述水平变化因素对模态耦合的贡献.为避免直接求解二阶耦合模态方程组可能遇到的数值发散问题,将其重构为两个耦合的一阶演化方程组,引入导纳矩阵并使用Magnus数值积分方法获得稳定的声场解.利用该耦合模态方法数值计算水平变化波导中的声场,并与COMSOL参考解比较,结果表明该耦合模态理论能够精确求解水平变化波导中的点源及分布源传播问题.