Influence of the surrounding pressure on acoustic properties of slightly compressible porous media permeated with air-filled bubbles

The effective wave velocity, attenuation, and nonlinear properties of slightly compressible porous media permeated with air-filled bubbles are studied numerically by employing the nonlinear Hooke’s law for different surrounding pressures. Numerical simulations show that the acoustic properties of porous media are greatly affected by the surrounding pressure if the shear modulus of the elastic medium is very small due to the fact that the acoustic wave propagation in porous media are strongly influenced by the nonlinear oscillation of bubbles; moreover, the oscillation of a bubble depends on the equilibrium bubble radius, which is affected by the surrounding pressures. Published in Russian in Akusticheskiĭ Zhurnal, 2006, Vol. 52, No. 4, pp. 490–496. The text was submitted by the authors in English.     

Bessel驻波对椭球形液滴的声辐射转矩

在实际的声操控中,由于声辐射力、表面张力和重力的共同作用,液滴往往呈现出椭球的形状,在螺旋声场中会受到力矩的作用而发生转动。从声波的散射理论出发,根据部分波展开法求解得到了椭球形液滴在Bessel驻波场中的声散射系数,并给出了其受到的声辐射转矩的解析式。在此基础上,对椭球形不可压缩液滴和椭球形可压缩液滴分别进行数值计算。仿真结果表明,不可压缩液滴的声辐射转矩与声束半锥角的关系更密切,而可压缩液滴则更依赖于特定的频率;提升Bessel驻波场的阶数有利于增强声辐射转矩的峰值,但在中低频处较难对可压缩液滴产生明显的力矩。该研究结果预期对利用螺旋声场进行液滴的操控具有理论指导作用。      

Simultaneous effects of magnetic field and space porosity on compressible Maxwell fluid transport induced by a surface acoustic wave in a microchannel

Peristaltic motion induced by a surface acoustic wave of a viscous, compressible and electrically conducting Maxwell fluid in a confined parallel-plane microchannel through a porous medium is investigated in the presence of a constant magnetic field. The slip velocity is considered and the problem is discussed only for the free pumping case. A perturbation technique is employed to analyze the problem in terms of a small amplitude ratio. The phenomenon of a “backward flow” is found to exist in the center and at the boundaries of the channel. In the second order approximation, the net axial velocity is calculated for various values of the fluid parameters. Finally, the effects of the parameters of interest on the mean axial velocity, the reversal flow, and the perturbation function are discussed and shown graphically. We find that in the non-Newtonian regime, there is a possibility of a fluid flow in the direction opposite to the propagation of the traveling wave. This work is the most general model of peristalsis created to date with wide-ranging applications in biological, geophysical and industrial fluid dynamics.     

Experimental study on subharmonic and ultraharmonic acoustic waves in water-saturated sandy sediment

Experimental observations of the subharmonic and ultraharmonic acoustic waves in water-saturated sandy sediment are reported in this paper. Acoustic pressures of both nonlinear acoustic waves strongly depend on the driving acoustic pressure at a transducer. The first ultraharmonic wave reaches a saturation value as the driving acoustic pressure increases. The acoustic pressure levels of both nonlinear acoustic waves exhibit some fluctuations in comparison with that of the primary acoustic wave as the receiving distance of hydrophone increases in sediment. The subharmonic and the ultraharmonic phenomena in this study show close resemblance to those produced in bubbly water.     

鼓泡床中超声驻波的模拟及其对气泡的调制机理

采用计算流体动力学（CFD）的方法，数值生成了鼓泡床中一对声换能器以16kHz高频振动引发的超声场。数值计算是基于包括粘性影响的可压缩流体基本守恒方程，并耦合了水的状态方程。模拟结果表明，在本研究所用的几何布置和换能器与时间相关的速度入口边界条件下，反应器中形成了一个稳定的驻波声场；由于波的非线性以及水的粘性，压力波节点呈现出轻微的时间漂移性。模拟结果与前人的实验结果定性吻合。在模拟的声压分布的基础上，分析了驻波声场调制气泡的机理。如比较熟知，气泡在驻波声场作用下或者向压力波节点运动或者向压力波腹点运动，取决于气泡尺寸与共振尺寸的关系。     

Acoustic radiation from the submerged circular cylindrical shell treated with active constrained layer damping

Based on the transfer matrix method of exploring the circular cylindrical shell treated with active constrained layer damping(i.e., ACLD), combined with the analytical solution of the Helmholtz equation for a point source, a multi-point multipole virtual source simulation method is for the first time proposed for solving the acoustic radiation problem of a submerged ACLD shell. This approach, wherein some virtual point sources are assumed to be evenly distributed on the axial line of the cylindrical shell, and the sound pressure could be written in the form of the sum of the wave functions series with the undetermined coefficients, is demonstrated to be accurate to achieve the radiation acoustic pressure of the pulsating and oscillating spheres respectively. Meanwhile, this approach is proved to be accurate to obtain the radiation acoustic pressure for a stiffened cylindrical shell. Then, the chosen number of the virtual distributed point sources and truncated number of the wave functions series are discussed to achieve the approximate radiation acoustic pressure of an ACLD cylindrical shell. Applying this method, different radiation acoustic pressures of a submerged ACLD cylindrical shell with different boundary conditions, different thickness values of viscoelastic and piezoelectric layer, different feedback gains for the piezoelectric layer and coverage of ACLD are discussed in detail. Results show that a thicker thickness and larger velocity gain for the piezoelectric layer and larger coverage of the ACLD layer can obtain a better damping effect for the whole structure in general. Whereas, laying a thicker viscoelastic layer is not always a better treatment to achieve a better acoustic characteristic.     

Direct computation and aeroacoustic modelling of a subsonic axisymmetric jet

A numerical algorithm for acoustic noise predictions based on solving Lilley's third order wave equation in the time-space domain is developed for a subsonic axisymmetric jet. The sound field is simulated simultaneously with the source field calculation, which is based on a direct solution of the compressible Navier-Stokes equations. The computational domain includes both the nearfield and a portion of the acoustic farfield. In the simulation, the detailed sound source structure is provided by the nearfield direct numerical simulation (DNS), while the sound field is obtained from both the DNS and the numerical solution to the non-linear Lilley's equation. The source terms of Lilley's equation are used to identify the apparent sound source locations in the idealized axisymmetric low-Reynolds number jet. The sound field is mainly discussed in terms of instantaneous pressure fluctuations, frequency spectra, acoustic intensity and directivity. A good agreement is found between the predictions from the axisymmetric Lilley's equation and the DNS results for the sound field. Limitations and perspectives of the simulation are also discussed.     

Weak nonlinear propagation of sound in a finite exponential horn.

This article presents an approximate solution for weak nonlinear standing waves in the interior of an exponential acoustic horn. An analytical approach is chosen assuming one-dimensional plane-wave propagation in a lossless fluid within an exponential horn. The model developed for the propagation of finite-amplitude waves includes linear reflections at the throat and at the mouth of the horn, and neglects boundary layer effects. Starting from the one-dimensional continuity and momentum equations and an isentropic pressure-density relation in Eulerian coordinates, a perturbation analysis is used to obtain a hierarchy of wave equations with nonlinear source terms. Green's theorem is used to obtain a formal solution of the inhomogeneous equation which takes into account linear reflections at the ends of the horn, and the solution is applied to the nonlinear horn problem to yield the acoustic pressure for each order, first in the frequency and then in the time domain. In order to validate the model, an experimental setup for measuring fundamental and second harmonic pressures inside the horn has been developed. For an imposed throat fundamental level, good agreement is obtained between predicted and measured levels (fundamental and second harmonic) at the mouth of the horn.     

Achieving acoustic cloak by using compressible background flow

We propose a scheme of acoustic spherical cloaking by means of background irrotational flow in compressible fluid.The background flow forms a virtual curved spacetime and directs the sound waves to bypass the cloaked objects. To satisfy the laws of real fluid, we show that spatially distributed mass source and momentum source are necessary to supply. The propagation of sound waves in this system is studied via both geometric acoustics approximation and full wave approach.The analytic solution of sound fields is obtained for plane wave incidence. The results reveal the effect of phase retardation(or lead) in comparison with the ordinary transformation-acoustic cloak. In addition, the ability of cloaking is also evaluated for unideal background flows by analyzing the scattering cross section.     

Perturbation method for the second-order nonlinear effect of focused acoustic field around a scatterer in an ideal fluid

Two nonlinear models are proposed to investigate the focused acoustic waves that the nonlinear effects will be important inside the liquid around the scatterer. Firstly, the one dimensional solutions for the widely used Westervelt equation with different coordinates are obtained based on the perturbation method with the second order nonlinear terms. Then, by introducing the small parameter (Mach number), a dimensionless formulation and asymptotic perturbation expansion via the compressible potential flow theory is applied. This model permits the decoupling between the velocity potential and enthalpy to second order, with the first potential solutions satisfying the linear wave equation (Helmholtz equation), whereas the second order solutions are associated with the linear non-homogeneous equation. Based on the model, the local nonlinear effects of focused acoustic waves on certain volume are studied in which the findings may have important implications for bubble cavitation/initiation via focused ultrasound called HIFU (High Intensity Focused Ultrasound). The calculated results show that for the domain encompassing less than ten times the radius away from the center of the scatterer, the non-linear effect exerts a significant influence on the focused high intensity acoustic wave. Moreover, at the comparatively higher frequencies, for the model of spherical wave, a lower Mach number may result in stronger nonlinear effects.     

Erosive burning of a propellant in the field of a traveling acoustic wave

The response of the propellant burning rate to periodically varied pressure and the tangential mass flow of the combustion products is examined within the framework of the phenomenological theory of unsteady combustion. The effect of an elementary acoustic disturbance, a plane monochromatic traveling acoustic wave, is examined. The analytical and numerical results are obtained for the simplest propellant model with a minimum number of parameters. The roles of the steady and unsteady components of erosion at low and high values of the erosion ratio are established.     

Acoustic scattering by multiple elliptical cylinders using collocation multipole method

This paper presents the collocation multipole method for the acoustic scattering induced by multiple elliptical cylinders subjected to an incident plane sound wave. To satisfy the Helmholtz equation in the elliptical coordinate system, the scattered acoustic field is formulated in terms of angular and radial Mathieu functions which also satisfy the radiation condition at infinity. The sound-soft or sound-hard boundary condition is satisfied by uniformly collocating points on the boundaries. For the sound-hard or Neumann conditions, the normal derivative of the acoustic pressure is determined by using the appropriate directional derivative without requiring the addition theorem of Mathieu functions. By truncating the multipole expansion, a finite linear algebraic system is derived and the scattered field can then be determined according to the given incident acoustic wave. Once the total field is calculated as the sum of the incident field and the scattered field, the near field acoustic pressure along the scatterers and the far field scattering pattern can be determined. For the acoustic scattering of one elliptical cylinder, the proposed results match well with the analytical solutions. The proposed scattered fields induced by two and three elliptical–cylindrical scatterers are critically compared with those provided by the boundary element method to validate the present method. Finally, the effects of the convexity of an elliptical scatterer, the separation between scatterers and the incident wave number and angle on the acoustic scattering are investigated.     

Elastic response of an acoustic coating on a rib-stiffened plate

This paper develops a three-dimensional analytical model of a fluid-loaded acoustic coating affixed to a rib-stiffened plate. The system is loaded by a plane wave that is harmonic both spatially and temporally. The model begins with Navier-Cauchy equations of motion for an elastic solid, which produces displacement fields that have unknown wave propagation coefficients. These are inserted into stress equations at the boundaries of the plate and the acoustic coating. These stress fields are coupled to the fluid field and the rib stiffeners with force balances. Manipulation of these equations develops an infinite number of indexed equations that are truncated and incorporated into a global matrix equation. This global matrix equation can be solved to determine the wave propagation coefficients. This produces analytical solutions to the systems’ displacements, stresses, and scattered pressure field. This model, unlike previously developed analytical models, has elastic behavior and thus incorporates higher order wave motion that makes it accurate at higher wavenumbers and frequencies. An example problem is investigated for three specific model results: (1) the dynamic response, (2) a sonar array embedded in the acoustic coating, and (3) the scattered pressure field. An expression for the high frequency limitation of the model is derived. It is shown that the ribs can have a significant impact on the structural acoustic response of the system.     

Stability of supersonic boundary layer on a porous plate with a flexible coating

The development of disturbances in the boundary layer of compressible gas on a flexible surface has been investigated in the linear and nonlinear approximations (the weakly nonlinear stability theory). The regimes of moderate (the Mach number M = 2) and high (M = 5.35) supersonic velocities as well as a model of a porous wall, on which a flexible film is spanned, have been considered. The boundary conditions for disturbances with regard for their transformation by a flexible porous coating have been derived. The character of the variation of the coefficients of the stream-wise growth of linear oscillations of different nature (the vortex waves of the first mode and the acoustic waves of the second mode) is shown. The direction and the degree of their deformations are determined by the flexible coating parameters. It is found that at moderate Mach numbers, the stabilization of disturbances and the diminution of increments occur, whereas at high M on a surface with a film, the acoustic components are destabilized, which may lead to an earlier onset of nonlinear processes. The nonlinear interactions in three-wave symmetric triplets between the vortex waves at M = 2 and between the waves of different nature at M = 5.35 are considered. In the latter case, the plane acoustic wave is the pumping wave, which excites the three-dimensional subharmonic components of vortex nature.     

Existence of traveling wave solutions of a high-order nonlinear acoustic wave equation

In this Letter, we present an analytical study of a high-order acoustic wave equation in one dimension, and reformulate a previously given equation in terms of an expansion of the acoustic Mach number. We search for non-trivial traveling wave solutions to this equation, and also discuss the accuracy of acoustic wave equations in terms of the range of Mach numbers for which they are valid.     

Identification of aero-acoustic scattering matrices from large eddy simulation. Application to a sudden area expansion of a duct

A methodology is presented which allows to determine the coefficients of transmission and reflection of plane acoustic waves at flow discontinuities in piping systems by combining large eddy simulation (LES) of turbulent compressible flows with system identification. The method works as follows. At first, an LES with external, broadband excitation of acoustic waves is carried out. Time series of acoustic data are extracted from the computed flow field and analyzed with system identification techniques in order to determine the acoustic scattering coefficients for a range of frequencies. The combination of broadband excitation with highly parallelized LES makes the overall approach quite efficient, despite the difficulties associated with simulation of low-Mach number compressible flows. The method is very general, here it is applied to study the scattering behavior of acoustic waves at a sudden change in cross-section in a duct system. The complex aero-acoustic interactions between acoustic waves and free shear layers are captured in detail by high resolution compressible LES, such that the scattering coefficients can be determined accurately from first principles. In order to demonstrate the reliability and accuracy of the method, the results for the scattering behavior and the acoustic impedance are presented and physically interpreted in combination with several analytical models and experimental data.     

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.     

基于声源预估的波叠加组合全息声源识别方法

为解决声源识别中旁瓣效应等因素引起的虚假识别结果问题,提出了基于声源位置预估的波叠加组合全息算法。应用波束形成算法进行声源位置的预估,将预估声压峰值点作为假定声源点,通过波叠加原理建立方程组,利用声源强度求解结果构造完整全息平面,通过声全息方法重新计算重建面声压。进行了仿真和实验验证,经该算法重构后,波束形成算法产生的虚假声源处的声压得以明显降低。表明该算法可以抑制旁瓣效应等因素的影响,提高声源识别的准确率。      

Spatial filtering of wall pressure fluctuations beneath a turbulent boundary layer

Methods of experimental spatial filtering of wall pressure fluctuations beneath a turbulent boundary layer are developed with the aim of obtaining information on the wave number-frequency spectrum. The spatial filtering of the pressure field components by wave-vector filters is studied. The method of spatial filtering of pressure fluctuations by an acoustic array, i.e., a periodic structure with a finite number of elementary transducers, is analyzed. The relation between the wave number characteristic of the acoustic array and the wave number spectrum of the amplitude distribution of transducer’s local sensitivity is determined. Quantitative estimates are obtained for the sensitivity of the array to the wave number spectrum of turbulent boundary-layer pressures, which is necessary for measuring the wall pressure fluctuations in a turbulent boundary layer by wave-vector filters.