Study of thermoviscous dissipation on axisymmetric wave propagating in a shear pipeline flow confined by rigid wall. Part II. Numerical study

Axisymmetric acoustic wave propagating in a shear pipeline flow confined by a rigid wall is studied in the two-part paper. The effects of viscous friction and thermal conduction on the acoustic wave propagating in the liquid and perfect gas are respectively analyzed under different configurations of acoustic frequency and shear mean flow. In Part 2 of this paper, comprehensive analysis of the effects of shear mean flow and acoustic frequency on the features (relative phase velocity and attenuation coefficient) of the acoustic wave are numerically addressed in cases of water and perfect gas respectively. Comparisons between the non-isentropic and isentropic models are provided in details. Meanwhile, discussions of the thermoviscous effects on the acoustic wave between water and perfect gas are given.     

Driving force of acoustic streaming caused by aperiodic sound beam in unbounded volumes

Instantaneous driving force of acoustic streaming in the thermoviscous medium is the subject of investigation. Dynamic equation of the Eulerian streaming velocity is a result of splitting the hydrodynamic equations into acoustic and non-acoustic parts. The acoustic force represents a sum of three parts, one is the classic one, which being averaged over the sound period coincides with the well-known expression. The second one is connected to the periodicity of the sound, it becomes exact zero after averaging for the strictly periodic sound but is not zero for other acoustic wave. The last term originates from the sound divergence. All terms are nonlinear and proportional to the overall attenuation. The consistent comparative analysis of both formula for quasi-periodic and modulated sound is proceeded.     

A k-space Green's function solution for acoustic initial value problems in homogeneous media with power law absorption

An efficient Green's function solution for acoustic initial value problems in homogeneous media with power law absorption is derived. The solution is based on the homogeneous wave equation for lossless media with two additional terms. These terms are dependent on the fractional Laplacian and separately account for power law absorption and dispersion. Given initial conditions for the pressure and its temporal derivative, the solution allows the pressure field for any time t>0 to be calculated in a single step using the Fourier transform and an exact k-space time propagator. For regularly spaced Cartesian grids, the former can be computed efficiently using the fast Fourier transform. Because no time stepping is required, the solution facilitates the efficient computation of the pressure field in one, two, or three dimensions without stability constraints. Several computational aspects of the solution are discussed, including the effect of using a truncated Fourier series to represent discrete initial conditions, the use of smoothing, and the properties of the encapsulated absorption and dispersion.     

基于分数导数研究高强度聚焦超声的非线性声场

在高强度聚焦超声(high intensity focused ultrasound, HIFU) 的研究中, 生物组织的衰减和色散性质会对声能量的空间分布产生影响. 本文提出应用分数导数修正非线性Khokhlov-Zabolotskaya-Kuznetsov (KZK)方程, 研究生物组织中非线性HIFU声场. 对三种生物仿体的衰减和声速色散的理论实验研究表明分数导数应用的可行性, 在此基础上通过数值仿真分析研究了衰减及声速随频率的变化对HIFU焦域分布的影响. 研究结果表明, 在计算强非线性聚焦超声时, 由于高次谐波的强色散作用, 引入分数导数来解决生物组织特殊的衰减以及色散问题可进一步提高HIFU治疗的安全性. 关键词： 分数导数 声衰减 色散 高强度聚焦超声     

Modified Szabo's wave equation models for lossy media obeying frequency power law

Szabo's models of acoustic attenuation [Szabo, J. Acoust. Soc. Am. 96(1), 491-500 (1994)] comply well with the empirical frequency power law involving noninteger and odd-integer exponent coefficients while guaranteeing causality, but nevertheless encounter the troublesome issues of hypersingular improper integral and obscurity in implementing initial conditions. The purpose of this paper is to ease or remove these drawbacks of the Szabo's models via the Caputo fractional derivative concept. The positive time-fractional derivative is also introduced to include the positivity of the attenuation processes.     

Series expansion solutions for the multi-term time and space fractional partial differential equations in two- and three-dimensions

Fractional partial differential equations with more than one fractional derivative in time describe some important physical phenomena, such as the telegraph equation, the power law wave equation, or the Szabo wave equation. In this paper, we consider two- and three-dimensional multi-term time and space fractional partial differential equations. The multi-term time-fractional derivative is defined in the Caputo sense, whose order belongs to the interval (1,2],(2,3],(3,4] or (0,m], and the space-fractional derivative is referred to as the fractional Laplacian form. We derive series expansion solutions based on a spectral representation of the Laplacian operator on a bounded region. Some applications are given for the two- and three-dimensional telegraph equation, power law wave equation and Szabo wave equation.     

Acoustic attenuation in self-affine porous structures

As acoustic waves propagate through fluid-filled porous materials possessing heterogeneity in the elastic compressibility at scales less than wavelengths, the local wave-induced fluid-pressure response will also possess spatial heterogeneity that correlates with the compressibility structure. Such induced fluid-pressure gradients equilibrate via fluid-pressure diffusion causing wave energy to attenuate. This process is numerically simulated using finite-difference modeling. It is shown here, both numerically and analytically, that in the special case where the compressibility structure is a self-affine fractal characterized by a Hurst exponent H, the wave's quality factor Q (where Q(-1) is a measure of acoustic attenuation) is a power law in the wave's frequency omega given by Q proportional to omega(H) when /H/<1, and given by Q proportional to omega(tanhH) in general.     

A guided wave technique for the characterization of highly attenuative viscoelastic materials

The measurement of the acoustic properties of highly attenuative materials such as bitumen is very difficult. One possibility is to use measurements of the extent to which filling a cylindrical waveguide with the material affects the dispersion relationship of the cylinder. Torsional modes have been excited using piezoelectric transducers placed at one end of the cylinder, while the phase velocity and attenuation spectra have been measured by means of laser scanning. At each frequency, under the hypothesis of linear viscoelasticity, the phase velocity and attenuation of the fundamental torsional mode have been calculated as a function of the bulk shear velocity and the bulk shear attenuation of the inner core at that frequency. The resulting phase velocity and guided wave attenuation contour plots have been employed for deriving the unknown shear properties from the measured velocity and attenuation of the guided wave. The monochromaticity of the approach has not required a particular frequency dependence of the material properties to be assumed. Results for bitumen are given.     

A reflectivity equation for acoustic media with absorption

The wave equation which governs the propagation of dilatational stress (pressure) in viscoacoustic media can be reduced to the lossless acoustic wave equation by the introduction of a complex traveltime coordinate. An interesting property of this equation is that it contains a term which is proportional to the reflectivity function in its single scattering approximation.     

Nonlinear pulsed ultrasound beams radiated by rectangular focused diagnostic transducers

A numerical model for simulating nonlinear pulsed beams radiated by rectangular focused transducers, which are typical of diagnostic ultrasound systems, is presented. The model is based on a KZK-type nonlinear evolution equation generalized to an arbitrary frequency-dependent absorption. The method of fractional steps with an operator-splitting procedure is employed in the combined frequency-time domain algorithm. The diffraction is described using the implicit backward finite-difference scheme and the alternate direction implicit method. An analytic solution in the time domain is employed for the nonlinearity operator. The absorption and dispersion of the sound speed are also described using an analytic solution but in the frequency domain. Numerical solutions are obtained for the nonlinear acoustic field in a homogeneous tissue-like medium obeying a linear frequency law of absorption and in a thermoviscous fluid with a quadratic frequency law of absorption. The model is applied to study the spatial distributions of the fundamental and second harmonics for a typical diagnostic ultrasound source. The nonlinear distortion of pulses and their spectra due to the propagation in tissues are presented. A better understanding of nonlinear propagation in tissue may lead to improvements in nonlinear imaging and in specific tissue harmonic imaging. Published in Russian in Akusticheskiĭ Zhurnal, 2006, Vol. 52, No. 4, pp. 560–570. This article was translated by the authors.     

混凝土中的声发射波速特性及其在源定位中的应用*

利用声发射技术监测受载混凝土裂缝发展特征的首要任务是对声发射源的准确定位。为了解混凝土中声发射波速特性,提高声发射源定位精度,该文开展了一系列室内试验,构建了考虑衰减现象的声发射波速修正模型,优化建立了基于修正波速的区域穷举定位法。结果表明:水灰比越小,基准波速越大,波速随距离的衰减越大。骨料粒径越大,基准波速越大,波速随距离的衰减越大。直线距离小于500 mm时,可采用对数函数描述声发射波速与距离的定量关系,以此构建的波速修正模型满足工程精度要求。采用修正波速的区域穷举定位法对单轴压缩试验产生的裂缝进行定位时,定位点比时差定位法更接近裂缝实际位置,有效提高了定位精度。     

谐振管内非线性驻波的有限体积数值算法

为了扩展谐振管内非线性驻波在工程中的应用, 以及克服现有数值计算方法仅局限于求解直圆柱形和指数形谐振管内非线性驻波的问题. 根据变截面的非稳态可压缩热黏性流体Navier-Stokes方程和空间守恒方程, 并基于求解压力速度耦合方程的半隐式算法和交错网格技术, 构建一种能够计算任意形状轴对称谐振管受活塞驱动时内部非线性驻波的有限体积算法. 分别对圆柱形、指数形和圆锥形谐振管内的非线性驻波进行仿真计算. 通过与现有试验结果以及数值仿真结果的对比, 验证了该方法的正确性.并获得除驻波声压之外的另外一些新的物理结果, 包括速度、密度、温度的瞬时变化.在直圆柱形谐振管内产生冲击声压波, 速度波形中出现钉状结构.而在指数形和圆锥形谐振管内产生高声压幅值的驻波, 没有出现冲击波, 速度波形中均未发现钉状结构. 计算结果表明谐振管内非线性驻波的物理属性与谐振管形状之间有密切关系.     

含少量气泡流体饱和孔隙介质中的弹性波

考虑孔隙流体中含有少量气泡,且气泡在声波作用下线性振动,研究声波在这种孔隙介质中的传播特性.本文先由流体质量守恒方程和孔隙度微分与流体压力微分的关系推导出了含有气泡形式的渗流连续性方程;在处理渗流连续性方程中的气体体积分数时间导数时,应用Commander气泡线性振动理论导出气体体积分数时间导数与流体压强时间导数的关系,进而得到了修正的Biot形式的渗流连续性方程;最后结合Biot动力学方程求得了含气泡形式的位移场方程,便可得到两类纵波及一类横波的声学特性.通过对快、慢纵波的频散、衰减及两类波引起的流体位移与固体位移关系的考察,发现少量气泡的存在对快纵波和慢纵波的传播特性影响较大.     

基于分数阶最大相关熵算法的混沌时间序列预测

为提高最大相关熵算法对混沌时间序列的预测速度和精度,提出了一种新的分数阶最大相关熵算法.在采用最大相关熵准则的基础上,利用分数阶微分设计了一种新的权重更新方法.在alpha噪声环境下,采用新的分数阶最大相关熵算法对Mackey-Glass和Lorenz两类具有代表性的混沌时间序列进行预测,并分析了分数阶的阶数对混沌时间序列预测性能的影响.仿真结果表明:与最小均方算法、最大相关熵算法以及分数阶最小均方算法三类自适应滤波算法相比,所提分数阶最大相关熵算法在混沌时间序列预测中能够有效地抑制非高斯脉冲噪声干扰的影响,具有较快收的敛速度和较低的稳态误差.     

Modeling power law absorption and dispersion for acoustic propagation using the fractional Laplacian

The efficient simulation of wave propagation through lossy media in which the absorption follows a frequency power law has many important applications in biomedical ultrasonics. Previous wave equations which use time-domain fractional operators require the storage of the complete pressure field at previous time steps (such operators are convolution based). This makes them unsuitable for many three-dimensional problems of interest. Here, a wave equation that utilizes two lossy derivative operators based on the fractional Laplacian is derived. These operators account separately for the required power law absorption and dispersion and can be efficiently incorporated into Fourier based pseudospectral and k-space methods without the increase in memory required by their time-domain fractional counterparts. A framework for encoding the developed wave equation using three coupled first-order constitutive equations is discussed, and the model is demonstrated through several one-, two-, and three-dimensional simulations.     

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.     

Acoustic streaming in a rotating fluid

Acoustic streaming theory is derived that is applicable to a fluid that is slow moving in a reference frame that rotates with a constant angular velocity omega. A simplified streaming equation is obtained for the special case in which the acoustic angular frequency omega is large relative to omega, and the change in fluid density due to rotation alone is negligible. For this special case it is shown that the "driving force" for the acoustic streaming is independent of omega. Thus, if no acoustic streaming is present in a fluid system that is stationary, then no steady-state acoustic streaming is predicted for a similar system that rotates with constant angular velocity. For a system in which acoustic streaming is present, the flow behavior depends on the relative magnitudes of the Coriolis forces and the viscous forces. If the Ekman number is large (that is, the viscous force dominates) then the predicted flow is identical to that which would exist in a stationary system. If, on the other hand, the Ekman number is small then the Coriolis force dominates and the component of flow in the direction of the axis of rotation can be much smaller in the rotating system than in a similar system at rest.