The wave equation with viscoelastic attenuation and its application in problems of shallow-sea acoustics

A suitable tool for the simulation of low frequency acoustic pulse signals propagating in a shallow sea is the numerical integration of the nonstationary wave equation. The main feature of such simulation problems is that in this case the sound waves propagate in the geoacoustic waveguide formed by the upper layers of the bottom and the water column. By this reason, the correct dependence of the attenuation of sound waves in the bottom on their frequency must be taken into account. In this paper we obtain an integro-differential equation for the sound waves in the viscoelastic fluid, which allows to simulate the arbitrary dependence of acoustic wave attenuation on frequency in the time domain computations. The procedure of numerical solution of this equation based on its approximation by a system of differential equations is then considered and the methods of artificial limitation of computational domain are described. We also construct a simple finite-difference scheme for the proposed equation suitable for the numerical solution of nonstationary problems arising in the shallow-sea acoustics.     

Noise simulation of aircraft engine fans by the boundary element method

Numerical simulation results of the civil aircraft engine fan stage noise in the far field are presented. Non-steady-state rotor–stator interaction is calculated the commercial software that solves the Navier–Stokes equations using differentturbulence models. Noise propagation to the far acoustic field is calculated by the boundary element method using acoustic Lighthill analogies without taking into account the mean current in the air inlet duct. The calculated sound pressure levels at points 50 m from the engine are presented, and the directional patterns of the acoustic radiation are shown. The use of the eddy resolving turbulence model to calculate rotor–stator interaction increases the accuracy in predicting fan stage noise.     

A note on the interaction of unsteady flow with an acoustic liner

The effects of a mean grazing flow on the energy exchanges involved in the interaction of a bias-flow acoustic liner with, respectively, incident sound and boundary layer turbulence are contrasted. The analysis of model problems which make use of a line vortex to simulate large scale, unsteady boundary layer structures indicates that, whereas acoustic waves may be effectively attenuated, dissipation caused by “jetting” in the apertures of the liner can result in a net transfer of energy from the mean flow to the turbulence in the boundary layer.     

新型大涡数值模拟亚格子模型及应用

基于湍流大小尺度间动量输运的结构函数方程，提出了一种新的湍流大涡模型(LES)亚格子涡粘模式．新亚格子涡粘系数正比于纵向速度增量的扭率，它表征大小尺度湍流间的能量输运和耗散之比．新模式通过各向同性湍流直接数值模拟数据库的检验，并用于槽道湍流的大涡模拟计算，将所得结果与DNS结果进行了比较．     

水下涡流场前向声散射特性分析

研究水下涡声散射特性,在目标探测和流场声成像领域具有重要意义。针对水下低马赫数涡流场前向声散射建立了数值计算方法,探究了其形态函数和指向性。首先,基于摄动声学理论给出了考虑流声耦合作用的涡声散射模型,采用时域有限差分结合完美匹配层构建了数值求解方法;随后,在算法验证的基础上,预报分析了高斯涡涡核尺寸在1~10 m,同时入射平面波无量纲波数在1~10范围内,涡流场强度对前向声散射特性的影响。结果表明,低马赫数下,声散射场具有对称性,且有明显的主瓣和指向性。其前向散射形态函数随入射波波数、涡核尺寸、涡流场强度增加而增大;主瓣方位角随波数增加而趋近入射波传播方向。      

Acoustic characteristics of composite materials as acoustic window at oblique incidence of sound waves

This paper described a method for estimating the acoustic characteristics of composite materials at oblique incidence of sound waves. Composite materials are used as acoustic windows of SONAR to protect the internal sensors and electronic parts from water. In this study the composite material of glass reinforced plastic and polyurethane was used as the specimen. As the acoustic characteristics the velocities and attenuation coefficients of sound waves through the composite material were measured in the high frequency range. The insertion loss was also measured as a function of incident angle at 200 and 76 kHz, respectively. The attenuation coefficients in the low frequency range were estimated by interpolating the measured attenuation in the high frequency range with power-law form fitting. A four-medium layer model was proposed to estimate the insertion loss of composite materials at oblique incidence of sound waves in the low frequency range. The four-medium layer model well described the experimentally measured insertion loss at the high frequency range. It suggests that the insertion loss of the composite materials can be well estimated as a function of incident angle in the low frequency range.     

颗粒介质中的粘滞系数

将颗粒介质看成是等效均匀介质, 其中的声衰减系数和声速等于该颗粒介质中的相应的量值(它们可由作者的理论给出), 等效静态密度可以用二元混合规则求得. 此外, 根据浓颗粒介质中相互作用的声传播理论, 当入射波为平面波时, 相互作用的次级波仍然是平面波. 在这样的情况下, 可以将三维非线性方程组简化为一维情况, 从而算得浓颗粒介质中的粘滞系数, 结果表明, 颗粒介质中的粘滞系数不仅依赖于颗粒的体积分数而且还与频率有关. 根据推导过程可知, 对比于爱因斯坦理论所能应用的限制, 本文的结果可以更广泛地应用于实际介质.     

Large eddy simulation of turbulent Taylor–Couette flow using isogeometric analysis and the residual-based variational multiscale method

We present an application of the residual-based variational multiscale turbulence modeling (RBVMS) methodology to the computation of turbulent Taylor–Couette flow at high Reynolds number. We show that the RBVMS formulation globally conserves angular momentum, a feature that is felt to be important for flows dominated by rotation, and that is not shared by standard stabilized formulations of fluid flow. Weak imposition of Dirichlet boundary conditions is employed to enhance the accuracy of the RBVMS framework in the presence of thin turbulent boundary layers near solid walls. Calculation of conservative boundary forces and torques is also presented for the case of weakly enforced boundary conditions. NURBS-based isogeometric analysis is employed for the spatial discretization, and mesh refinement is performed to assess the convergence characteristics of the proposed methodology. Numerical tests show that very accurate results are obtained on relatively coarse grids. To the best of the authors’ knowledge, this paper is the first to report large eddy simulation computations of this challenging test case.     

ANALYSIS AND MEASUREMENT OF SOUND TRANSMISSION THROUGH A DOUBLE-WALLED CYLINDRICAL SHELL

Sound transmission through a double-walled cylindrical shell is studied. The solution that describes the system response is obtained by combining the solutions of two different models of the system. The first model, which describes the sound transmission due to the interaction between the acoustic waves and the bending waves in the shells, is formulated by three acoustic wave equations and two shell vibration equations. The second model describes the sound transmission by one-dimensional waves propagating through the layers of the shells and the air-gap. The transmission losses calculated from the two models are combined to represent the system response in the entire frequency range. Analytical solutions are compared to corresponding measured results, which shows reasonable agreements if the extent of the simplifications used in the analytical model is considered. The effects of important design parameters such as the air-gap size and the thickness ratio are studied using analytical solutions.     

Acoustic velocity and attenuation coefficient of magnetorheological fluids under electromagnetic fields

Magnetorheological fluid (MRF) is a class of smart material whose acoustic properties can be varied rapidly and reversibly by the applied magnetic field. The MRF is proposed to be as actively sound barriers or acoustical metamaterial. This paper presents a theoretical model to study acoustic propagation in MRF under fields based on the Biot–Stoll model. The model considers the coupling interaction between ferro particle and base fluid. This paper investigated the acoustic velocity and attenuation of a commercial MRF dependence on the different parameters such as carrier fluid viscosity, permeability and intensity of magnetic field. The calculated results show that the attenuation is increased with small field strengths and independent on field strength when the magnetization begins to saturate.     

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。     

Analytical evaluation of the acoustic insulation provided by double infinite walls

The acoustic insulation provided by infinite double panel walls, when subjected to spatially sinusoidal line pressure loads, is computed analytically. The methodology used extends earlier work by the authors on the definition of the acoustic insulation conferred by a single panel wall. It does not entail any simplification other than the assumption that the panels are of infinite extent. The full interaction between the fluid (air) and the solid layers is thus taken into account and the calculation does not involve limiting the thickness of any layer, as the Kirchhoff or Mindlin theories require. The problem is first formulated in the frequency domain. Time domain solutions are then obtained by means of inverse Fourier transforms using complex frequencies.The model is first used to compute the sound reduction provided by a double homogeneous brick wall, with identical panels, when illuminated by plane sound waves. The results are then compared with those provided by the simplified method proposed by London, which was later extended by Beranek (London-Beranek method). The limitations of the simplified London-Beranek model, namely, its applicability only to double walls with identical mass, subjected to plane waves, and its failure to account for the coincidence effect, are overcome by the method proposed.Time signatures are produced to illustrate the different sound transmission mechanisms. Several types of body and guided waves are originated, giving rise to a complex dynamic system with multiple reflections within the solid and fluid layers and the global resonance of the system. The effect of the cavity absorption is considered by attributing a complex density to the air filling the space between the two wall panels. Absorption attenuates the dips of insulation controlled by the cavity resonances. Several simulations are then performed for different combinations of wall and air layer thickness to assess the influence of this variable on the final acoustic insulation. The influence of the air cavity on sound reduction was found to be dependent on the frequency. At low frequencies a better performance was achieved for thicker air layers, while at higher frequencies a thinner air layer is preferable. The use of wall panels with different mass resulted in the wall performing better, particularly for high frequencies.     

Numerical simulation of nonlinear acoustic attenuation of multi-component gas mixture

The direct simulation Monte Carlo （DSMC） method was introduced to model the acoustic propagation in multi-component gas mixtures. And a theoretical predictive model of acoustic attenuation was proposed, which does not rely on experiential parameters. The acoustic attenuation spectra of various multi-component gas mixtures, consisting of nitrogen, oxygen, carbon dioxide, methane and water, were estimated by the DSMC method. The sound frequency range of interest is from 8 MHz to 232 MHz. Compared with the result of the relaxation attenuation based on the DL model plus that of the classical attenuation calculated by the Stokes-Kirchhoff formula, the estimations of acoustic attenuation of our model agreed with them. The precision of the model depends upon the understanding of the physical mechanism of molecule collision from which the attenuation arises. In addition, the result of our model shows that the characters of the frequency-dependent acoustic attenuation rely on the composition of the gas mixtures. And this could lead to the development of smart acoustic gas sensors capable of quantitatively determining gas composition in various environments and processes.     

Acoustic wave dispersion in a cylindrical elastic tube filled with a viscous liquid

This paper deals with the study of the velocity and the attenuation of an acoustic wave propagating inside a cylindrical elastic tube filled with a viscous liquid. A theory describing the propagation of the axisymmetrical modes in such waveguides is presented, with special attention given to the absorption produced by the viscous mechanisms in the liquid. One of these mechanisms is related to the momentum transfer between the compression and rarefaction regions of a propagating wave. The other viscous mechanism is due to the momentum transport inside the viscous boundary layer, close to the tube wall. Numerical calculations were carried out to investigate the influence of different parameters (frequency, tube radii, viscosity coefficient) on the propagation of acoustic waves.     

The use of a hybrid model to compute the nonlinear acoustic performance of silencers for the finite amplitude acoustic wave

In the present study, a hybrid method is proposed for predicting the acoustic performance of a silencer for a nonlinear wave. This method is developed by combining two models: (i) a frequency-domain model for the computation of sound attenuation due to a silencer in a linear regime and (ii) a wavenumber space model for the prediction of the nonlinear time-evolution of finite amplitudes of the acoustic wave in a uniform duct of the same length as the silencer. The present method is proposed under the observation that the physical process of the nonlinear sound attenuation phenomenon of a silencer may be decoupled into two distinct mechanisms: (a) a linear acoustic energy loss that owes to the mismatch in the acoustic impedance between reactive elements and/or the sound absorption of acoustic liners in a silencer; (b) a nonlinear acoustic energy loss that is due to the energy-cascade phenomenon that arises from the nonlinear interaction between components of different frequencies. To establish the validity of the present model for predicting the acoustic performance of silencers, two model problems are considered. First, the performance of simple expansion mufflers with nonlinear incident waves has been predicted. Second, proposed method is applied for computing nonlinear acoustic wave propagation in the NASA Langley impedance duct configuration with ceramic tubular liner (CT57). Both results obtained from the hybrid models are compared with those from computational aero-acoustic techniques in a time-space domain that utilize a high-order finite-difference method. Through these comparisons, it is shown that there are good agreements between the two predictions. The main advantage of the present method is that it can effectively compute the nonlinear acoustic performance of silencers in nonlinear regimes without time-space domain calculations that generally entail a greater computational burden.     

适用于任意形状封闭空间的声场预测相干模型

针对现有几何声学的方法对封闭空间内声场进行预测时在中低频段出现较大误差的问题,该文提出一种近似圆锥声束追踪法和相干反射场理论相结合的声场预测新模型。在近似圆锥声束追踪法基础上,考虑声束轴线在边界多次反射时声压和相位的改变,最后计算不同声波之间的干涉效应,建立一种适用于任意形状封闭空间的声场预测相干模型。利用该模型对某一矩形封闭空间进行声场预测,通过对边界元法、Raynoise软件相干和非相干算法的预测结果和本模型的数值模拟结果对比。结果表明,文中提出的方法和边界元法的计算结果在中低频段非常吻合,两者的计算结果平均绝对误差为1.1 d B。本模型在中低频率下与同样考虑了相位的Raynoise相干算法相比有更好的准确性,在较高频率上,本模型计算结果与Raynoise相干算法计算结果非常吻合。     

Effects of nonlocal hydromechanics in a flow in thin channels

An approach to viscous friction is described as nonlocal momentum exchange between different layers of a fluid. The Navier?Stokes equations are replaced by pseudo-differential equations hyperbolic in time. In this case, instead of zero velocity on the boundary, a nonlocal nonlinear boundary condition is set in the form of the velocity dependence of the coefficient before the intensity of the momentum exchange with the boundary. The non-newtonian character of the viscosity of water is shown in experiments with thin insulin needles and explained by the nonlinear character of the momentum exchange of water with the boundary. The calculations agree very well both with our experiments and with the experiments of other authors. Calculations show that the flow decreases more than one-and-a-half times in comparison with the Poiseuille flow for channels with a diameter of 360?390 μm, which is confirmed in experiments.     

A simple model of ultrasound propagation in a cavitating liquid. Part II: Primary Bjerknes force and bubble structures

In a companion paper, a reduced model for propagation of acoustic waves in a cloud of inertial cavitation bubbles was proposed. The wave attenuation was calculated directly from the energy dissipated by a single bubble, the latter being estimated directly from the fully nonlinear radial dynamics. The use of this model in a mono-dimensional configuration has shown that the attenuation near the vibrating emitter was much higher than predictions obtained from linear theory, and that this strong attenuation creates a large traveling wave contribution, even for closed domain where standing waves are normally expected. In this paper, we show that, owing to the appearance of traveling waves, the primary Bjerknes force near the emitter becomes very large and tends to expel the bubbles up to a stagnation point. Two-dimensional axi-symmetric computations of the acoustic field created by a large area immersed sonotrode are also performed, and the paths of the bubbles in the resulting Bjerknes force field are sketched. Cone bubble structures are recovered and compare reasonably well to reported experimental results. The underlying mechanisms yielding such structures is examined, and it is found that the conical structure is generic and results from the appearance a sound velocity gradient along the transducer area. Finally, a more complex system, similar to an ultrasonic bath, in which the sound field results from the flexural vibrations of a thin plate, is also simulated. The calculated bubble paths reveal the appearance of other commonly observed structures in such configurations, such as streamers and flare structures.     

Nonlinear wave interactions in porous media filled with a quantum fluid

The problem of the nonlinear interaction between the fourth sound and an acoustic wave propagating in a porous medium filled with superfluid helium is solved. Based on the Landau equations of quantum fluid dynamics and on the Biot theory of mechanical waves in a porous medium, nonlinear wave equations are derived for studying the aforementioned interaction. An expression is obtained for the vertex that determines the excitation of an acoustic wave by two waves of the fourth sound. The possibility of an experimental observation of this process is estimated.