Study on sound propagation in long enclosures with a vertical or inclined branch of different dimensions

As there may be some branches in long enclosures, such as high-speed railway and freeway tunnels, it will make a difference in the sound propagation in long enclosures if we give more consideration to different designs of the branches at the onset of their construction. However, most researches on the sound propagation in long enclosures available are concerned with straight long enclosures. In this paper, the sound pressure level (SPL) attenuation, early decay time (EDT), and reverberation time (RT30) of long enclosures with a vertical or inclined branch of different dimensions have been studied by comparing experimental results from physical scale models of such enclosures with those of the straight long enclosure. This experimental investigation gives interesting results on the behavior of sound propagation in long enclosures with a vertical or inclined branch of different dimensions. When conducting engineering design for long tunnels of the high-speed railway or freeway, it would be appropriate to consider designing the branch of the tunnels into a widened left inclined or right inclined one to provide a better relative SPL than that of other branches with different dimensions. This study further reveals that with an inclined branch of different dimensions, the EDT of the long enclosure will be different. At both 500 and 1000 Hz 1/3 octave bands, the EDT is the shortest when the long enclosure has a left inclined branch and an extended left inclined branch, while the EDT is the longest when the long enclosure has a widened vertical branch. Generally speaking, in the near field (i.e. the source-receiver distance is shorter than the threshold distance), the EDT measurements are similar, while in the far field (i.e. the source-receiver distance exceeds the threshold distance), the EDT is the longest for the straight long enclosure, second longest for the long enclosure with a widened inclined branch, third longest for the long enclosure with a vertical branch, and the shortest for the long enclosure with an extended inclined branch, which is similar to the trend with RT30.     

Sound propagation in long enclosures with a vertical or inclined branch

It is of interest to investigate the sound propagation in long enclosures with a vertical/inclined branch, since this may be relevant to long enclosures in practical applications, such as in high-speed railway tunnels. However, much research on sound propagation in long enclosures available is concerned with straight long enclosures. In this paper, the sound pressure level (SPL) attenuation, early decay time (EDT), and reverberation time (RT30) of long enclosures with vertical/inclined branches have been studied by comparing experimental results from physical scale models, of such enclosures with those for a straight long enclosure. It has been found that, compared with the straight long enclosure, the inclined branch makes more-difference to the SPL, EDT and RT30 of the long enclosure than the vertical branch, even though both kinds of branches have the equivalent volume.     

Sound field prediction in long enclosures with branches: A combined method

The propagation of sound in long enclosures with branches has been studied theoretically and experimentally, and an efficient combined method is proposed to predict the sound field in long enclosures with branches. Based on the wave-acoustics theory, the theoretical analysis of the sound field of the long enclosures with branches is performed. This paper also investigated the sound field prediction of long enclosures with branches, by using the acoustic modeling program, ODEON. The results obtained by the theoretical analysis and the numerical simulation ODEON are compared with the experimental measurements, and the characteristics of the two methods for predicting the sound field of long enclosures with branches are analyzed. Compared with the experimental results, it is found that: (1) the results predicted by the theoretical analysis fluctuate relatively large with respect to the source-receiver distance, and the sound pressure level (SPL) attenuation obtained is smaller than that measured; and (2) the results predicted by the numerical simulation is smoother, and the calculated SPL attenuation is larger than that measured. To effectively predict the sound field of long enclosures with branches, a combined numerical method is thus proposed. The effectiveness of the proposed combined method is demonstrated by the scale-model experiments.     

小尺度封闭空间声场的无网格数值算法

无网格法是一种新兴的数值计算方法,具有不需要网格支持的特点。本文将该方法引入室内声学建模,推导了无网格声场数值计算模型,并将其应用于典型小尺度封闭空间内部声场的数值分析。针对声传递函数,将本方法与理论解和SYSNOISE计算结果进行了比较,并将计算的混响时间与实验测量结果作了对比,表明本方法具有良好的精度。     

Parabolic equation for nonlinear acoustic wave propagation in inhomogeneous moving media

A new parabolic equation is derived to describe the propagation of nonlinear sound waves in inhomogeneous moving media. The equation accounts for diffraction, nonlinearity, absorption, scalar inhomogeneities (density and sound speed), and vectorial inhomogeneities (flow). A numerical algorithm employed earlier to solve the KZK equation is adapted to this more general case. A two-dimensional version of the algorithm is used to investigate the propagation of nonlinear periodic waves in media with random inhomogeneities. For the case of scalar inhomogeneities, including the case of a flow parallel to the wave propagation direction, a complex acoustic field structure with multiple caustics is obtained. Inclusion of the transverse component of vectorial random inhomogeneities has little effect on the acoustic field. However, when a uniform transverse flow is present, the field structure is shifted without changing its morphology. The impact of nonlinearity is twofold: it produces strong shock waves in focal regions, while, outside the caustics, it produces higher harmonics without any shocks. When the intensity is averaged across the beam propagating through a random medium, it evolves similarly to the intensity of a plane nonlinear wave, indicating that the transverse redistribution of acoustic energy gives no considerable contribution to nonlinear absorption. Published in Russian in Akusticheskiĭ Zhurnal, 2006, Vol. 52, No. 6, pp. 725–735. This article was translated by the authors.     

Prediction of reverberation time and speech transmission index in long enclosures

It is known that the sound field in a long space is not diffuse, and that the classic theory of room acoustics is not applicable. A theoretical model is developed for the prediction of reverberation time and speech transmission index in rectangular long enclosures, such as corridors and train stations, where the acoustic quality is important for speech. The model is based on an image-source method, and both acoustically hard and impedance boundaries are investigated. An approximate analytical solution is used to predict the frequency response of the sound field. The reverberation time is determined from the decay curve which is computed by a reverse-time integration of the squared impulse response. The angle-dependence of reflection coefficients of the boundaries and the change of phase upon reflection are incorporated in this model. Due to the relatively long distance of sound propagation, the effect of atmospheric absorption is also considered. Measurements of reverberation time and speech transmission index taken from a real tunnel, a corridor, and a model tunnel are presented. The theoretical predictions are found to agree well with the experimental data. An application of the proposed model has been suggested.     

Modeling the propagation of nonlinear three-dimensional acoustic beams in inhomogeneous media

A three-dimensional model of the forward propagation of nonlinear sound beams in inhomogeneous media, a generalized Khokhlov-Zabolotskaya-Kuznetsov equation, is described. The Texas time-domain code (which accounts for paraxial diffraction, nonlinearity, thermoviscous absorption, and absorption and dispersion associated with multiple relaxation processes) was extended to solve for the propagation of nonlinear beams for the case where all medium properties vary in space. The code was validated with measurements of the nonlinear acoustic field generated by a phased array transducer operating at 2.5 MHz in water. A nonuniform layer of gel was employed to create an inhomogeneous medium. There was good agreement between the code and measurements in capturing the shift in the pressure distribution of both the fundamental and second harmonic due to the gel layer. The results indicate that the numerical tool described here is appropriate for propagation of nonlinear sound beams through weakly inhomogeneous media.     

Equations for finite-difference, time-domain simulation of sound propagation in moving inhomogeneous media and numerical implementation

Finite-difference, time-domain (FDTD) calculations are typically performed with partial differential equations that are first order in time. Equation sets appropriate for FDTD calculations in a moving inhomogeneous medium (with an emphasis on the atmosphere) are derived and discussed in this paper. Two candidate equation sets, both derived from linearized equations of fluid dynamics, are proposed. The first, which contains three coupled equations for the sound pressure, vector acoustic velocity, and acoustic density, is obtained without any approximations. The second, which contains two coupled equations for the sound pressure and vector acoustic velocity, is derived by ignoring terms proportional to the divergence of the medium velocity and the gradient of the ambient pressure. It is shown that the second set has the same or a wider range of applicability than equations for the sound pressure that have been previously used for analytical and numerical studies of sound propagation in a moving atmosphere. Practical FDTD implementation of the second set of equations is discussed. Results show good agreement with theoretical predictions of the sound pressure due to a point monochromatic source in a uniform, high Mach number flow and with Fast Field Program calculations of sound propagation in a stratified moving atmosphere.     

The prediction of speech intelligibility in underground stations of rectangular cross section

Long enclosures are spaces with nondiffuse sound fields, for which the classical theory of acoustics is not appropriate. Thus, the modeling of the sound field in a long enclosure is very different from the prediction of the behavior of sound in a diffuse space. Ray-tracing computer models have been developed for the prediction of the sound field in long enclosures, with particular reference to spaces such as underground stations which are generally long spaces of rectangular or curved cross section. This paper describes the development of a model for use in underground stations of rectangular cross section. The model predicts the sound-pressure level, early decay time, clarity index, and definition at receiver points along the enclosure. The model also calculates the value of the speech transmission index at individual points. Measurements of all parameters have been made in a station of rectangular cross section, and compared with the predicted values. The predictions of all parameters show good agreement with measurements at all frequencies, particularly in the far field of the sound source, and the trends in the behavior of the parameters along the enclosure have been correctly predicted.     

Self-sustained oscillations in pipe systems with multiple deep side branches: Prediction and reduction by detuning

Flow-induced pulsations are frequently observed in pipe networks. In the present work we focus on the case of flow-induced pulsations in a pipe system composed of six equally spaced deep closed side branches. These pulsations are self-sustained aeroacoustic oscillations driven by the instability of the flow along the closed branches. The prediction of pulsations in such complex systems has not yet been proved to be possible, indeed the methods proposed in the literature have only been applied to relatively simple geometries, mainly single or double side branch systems. We propose a prediction model of the self-sustained oscillations in multiple deep side branch systems. This has been established by means of an analytical model for the acoustic wave propagation in which a semi-analytical source model is included. Detuning of the acoustic resonator is often considered as a possible remedial measure to suppress pulsations. Although this countermeasure appears to be very effective for double side branch systems in cross configuration, its effectiveness has never been assessed for different geometries. The effectiveness of the length-detuning on the six side branch system appear to be limited and depends on the upstream and downstream acoustic boundary conditions of the main pipe.     

Generalized acoustic energy density

The properties of acoustic kinetic energy density and total energy density of sound fields in lightly damped enclosures have been explored thoroughly in the literature. Their increased spatial uniformity makes them more favorable measurement quantities for various applications than acoustic potential energy density (or squared pressure), which is most often used. In this paper, a generalized acoustic energy density (GED), will be introduced. It is defined by introducing weighting factors into the formulation of total acoustic energy density. With an additional degree of freedom, the GED can conform to the traditional acoustic energy density quantities, or it can be optimized for different applications. The properties of the GED will be explored in this paper for individual room modes, a diffuse sound field, and a sound field below the Schroeder frequency.     

Sound Propagation in Shallow Water with an Inhomogeneous GAS-Saturated Bottom

We present the methods and results of numerical experiments studying the low-frequency sound propagation in one of the areas of the Arctic shelf with a randomly inhomogeneous gas-saturated bottom. The characteristics of the upper layer of bottom sedimentary rocks (sediments) used in calculations were obtained during a 3D seismic survey and trial drilling of the seafloor. We demonstrate the possibilities of substituting in numerical simulation a real bottom with a fluid homogeneous half-space where the effective value of the sound speed is equal to the average sound speed in the bottom, with averaging along the sound propagation path to a sediment depth of 0.6 wavelength in the bottom. An original technique is proposed for estimating the sound speed propagation in an upper inhomogeneous sediment layer. The technique is based on measurements of acoustic wave attenuation in water during waveguide propagation.     

Dependence of the Mean Intensity of a Low-Frequency Acoustic Field on the Bottom Parameters of a Shallow Sea with Random Volumetric Water-Layer Inhomogeneities

The study is devoted to statistical modeling of low-frequency acoustic signal propagation in a twodimensionally inhomogeneous random shallow sea with a thermocline and differing penetrability of the bottom. Calculations are performed using the local-mode representation of the solution in the one-way propagation approximation. Plots are presented for the behavior of the mean acoustic field intensity for different sound velocity and density values in the bottom. It is shown that the earlier described effect of a decrease in propagation losses in a model randomly inhomogeneous shallow sea with an absorbing bottom significantly depends on the parameters of bottom sediments and is more strongly manifested for bottom boundaries with greater penetrability.     

次声波在非均匀运动大气中非线性传播特性的研究

基于有限时域差分方法将大气中近似到二阶的非线性波动方程进行离散化,得到了数值模拟所采用的差分方程. 在此基础上,对线阵列辐射的脉冲声波在非均匀运动大气中的垂直和斜向传播进行了二维数值模拟,模拟了武汉地区(114:20°E, 30:37°N)在夏季和冬季UT=29000 s时开始传播的脉冲声波在不同时刻的声压分布. 模拟时通过采用Msise00和HWM93 两个大气模型,考虑了由于大气温度和密度变化以及大气风场存在所引起的大气不均匀性和运动性. 通过研究上述两季有风与无风条件下的声压差值p_r,可以发现:风场对次声波在传播中声压分布的影响较大;由于不同季节和不同传播距离上"有效声速"的不同,导致了两季p_r分布波形存在差异;风场对声波非线性传播的影响要远大于其对线性传播的影响. 关键词： 次声波传播 非均匀运动大气 有效声速     

复等效深度耦合简正波模型

为了考虑海底地形随距离变化的非水平分层介质中割线积分对声场的贡献,提出了复等效深度耦合简正波模型。该耦合简正波模型由介质运动方程和连续性方程推导得到了耦合微分方程组,此方程组满足海底地形随距离变化情况下的边界条件且仅包含一个耦合矩阵,并通过引入复等效深度理论处理连续谱和离散谱之间的相互耦合。仿真计算表明,复等效深度耦合简正波模型提高了波导简正波本征值位于割线枝点附近情况下声传播损失的计算精度,充分考虑了波导简正波、非波导简正波和割线积分对声场的贡献,可快速而准确地计算非水平分层介质中的声场。      

Real-time near-field acoustic holography for continuously visualizing nonstationary acoustic fields

Near-field acoustic holography (NAH) is an effective tool for visualizing acoustic sources from pressure measurements made in the near-field of sources using a microphone array. The method involving the Fourier transform and some processing in the frequency-wavenumber domain is suitable for the study of stationary acoustic sources, providing an image of the spatial acoustic field for one frequency. When the behavior of acoustic sources fluctuates in time, NAH may not be used. Unlike time domain holography or transient method, the method proposed in the paper needs no transformation in the frequency domain or any assumption about local stationary properties. It is based on a time formulation of forward sound prediction or backward sound radiation in the time-wavenumber domain. The propagation is described by an analytic impulse response used to define a digital filter. The implementation of one filter in forward propagation and its inverse to recover the acoustic field on the source plane implies by simulations that real-time NAH is viable. Since a numerical filter is used rather than a Fourier transform of the time-signal, the emission on a point of the source may be rebuilt continuously and used for other post-processing applications.     

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.     

含气泡液体中的非线性声传播

考虑到分布在液体中的气泡是声波在含气泡液体中传播时引起非线性的一个很重要的因素,本文研究了声波在含气泡液体中的非线性传播.将气体含量的影响引入到声波在液体中传播的方程中,从而得到声波在气液混合物中传播的数学模型.通过对该模型进行数值模拟发现,气体含量、驱动声场声压幅值及驱动声场作用时间均会影响到气液混合物中的声场分布及声压幅值大小.液体中的气泡会"阻滞"液体中声场的传播并将能量"聚集"在声源附近.对于连续大功率的驱动声场来说,液体中的气泡会"阻滞"气液混合物中声场及其能量的传播.     

Features of the energy structure of acoustic fields in the ocean with two-dimensional random inhomogeneities

The paper is devoted to the analytic study and numerical simulation of mid-frequency acoustic signal propagation in a two-dimensional inhomogeneous random shallow-water medium. The study was carried out by the cross section method (local modes). We present original theoretical estimates for the behavior of the average acoustic field intensity and show that at different distances, the features of propagation loss behavior are determined by the intensity of fluctuations and their horizontal scale and depend on the initial regular parameters, such as the emission frequency and size of sound losses in the bottom. We establish analytically that for the considered waveguide and sound frequency parameters, mode coupling effect has a local character and weakly influences the statistics. We establish that the specific form of the spatial spectrum of sound velocity inhomogeneities for the statistical patterns of the field intensity is insignificant during observations in the range of shallow-water distances of practical interest.     

A coupled-mode sound propagation model with complex effective depth

A coupled-mode sound propagation model with complex effective depth is presented,in order to involve the effect of branch line integral for acoustic field in a range-dependent waveguide.The equations of motion and continuity are used to obtain the coupled equations,which satisfy boundary conditions in the waveguide with varying topography and contain one coupling matrix.Meanwhile,the couplings between discrete and continuous spectrum are dealt with based on complex effective depth theory.Numerical simulations show that the accuracy of transmission loss is improved by the coupled mode model when eigenvalues of trapped modes are located near the branch point.The acoustic field in a non-horizontally stratified waveguide can be calculated efficiently and accurately by this model,and the energy corresponding to trapped modes,leaky modes and branch line integral can be considered adequately.