孔隙介质包裹的充液管道结构中导波传播特性

研究孔隙介质包裹的充液管道中纵向导波传播特性,分析孔隙介质参数对频散曲线的影响。建立了孔隙介质包裹充液管道的结构模型,利用孔隙介质弹性波动理论,建立对应的频散方程,数值模拟计算得到该模型的频散曲线和时域波形,并分析了孔隙介质参数以及管壁厚度对频散曲线的影响。结果表明孔隙介质的渗透率对于导波频散的影响较小,孔隙度的改变对时域波形的位移幅度影响较大。同时,导波存在衰减,且衰减随孔隙度增大而增大。所得结论为埋地管道无损检测方面提供一定理论参考。      

被孔隙介质约束的弹性杆中的导波*

为了研究导波在被孔隙介质约束的弹性杆结构中的传播规律,分析孔隙参数对导波传播特性的影响,本文建立了无限大孔隙介质包裹圆柱体的理论模型,利用孔隙介质弹性波动理论,分析了导波的频散曲线,以及圆柱半径和孔隙参数对于导波传播特性的影响。结果表明,在该结构中传播的纵向导波存在频散特性。内部圆柱半径的改变影响波导结构,从而影响导波传播。外部孔隙介质的渗透率对于导波频散的影响较小,孔隙度的改变影响孔隙介质体波波速,从而影响导波频散曲线的截止频率。同时,导波存在较小的衰减,且衰减随孔隙度增大而增大。这些结果对于后续开展无限大介质包裹弹性杆结构的超声无损评价提供了一定的理论参考。     

Parallel capillary-tube-based extension of thermoacoustic theory for random porous media

Thermoacoustic theory is extended to stacks made of random bulk media. Characteristics of the porous stack such as the tortuosity and dynamic shape factors are introduced into the thermoacoustic wave equation in the low reduced frequency approximation. Basic thermoacoustic equations for a bulk porous medium are formulated analogously to the equations for a single pore. Use of different dynamic shape factors for the viscous and thermal effects is adopted and scaling using the dynamic shape factors and tortuosity is demonstrated. Comparisons of the calculated and experimentally derived thermoacoustic properties of reticulated vitreous carbon and aluminum foam show good agreement. A consistent mathematical model of sound propagation in a random porous medium with an imposed temperature is developed. This treatment leads to an expression for the coefficient of the temperature gradient in terms of scaled cylindrical thermoviscous functions.     

Propagation characteristics of guided waves in a liquid filled pipe embedded in a porous medium

A model of a liquid-filled pipe embedded in a porous medium is built to research its wave propagation characteristics,and to analyze the effect of the parameters of porous media on the dispersion.The dispersion equations are established on the basis of the elastic-dynamic theory of the liquid-saturated porous solid.The characteristic of dispersion and the time domain waveform in pipes of different thicknesses and with different porous-medium parameters are discussed theoretically and numerically.Results reveal that the porosity has little impact on dispersion,and the attenuation of guided wave increases with porosity,whilst the porosity influences the displacement amplitude of the time domain waveform.It is hard to detect the permeability variation of the media by the dispersion.The drawn conclusion can provide some theoretical instruction and guidance for the nondestructive testing of buried pipe.     

Propagation of ultrasonic waves in porous ceramics

Theoretical problems concerning the propagation of ultrasonic waves in a porous medium are outlined. The propagation velocity of longitudinal ultrasonic waves in an elastic medium with spherical gaseous inclusions is considered in detail. The calculation method adopted consists of determining equivalent elasticity moduli of the porous medium. The calculation of these moduli is based on the work of H. Mackenzie on media containing spherical gaseous inclusions of various diameters. The theoretical results obtained for the propagation velocity of ultrasonic waves, are compared with those measured on electrical porcelain, the latter constituting a model of a porous medium. Also a method allowing for the effect of composition of the porcelain mass to be taken into account, is described. The results of measurements of the propagation velocity of a longitudinal wave are found to be in good agreement with theoretical data. This conformity allows for non-destructive tests of products containing spherical gaseous inclusions.     

Low-frequency surface wave propagation along plane boundaries in fluid-saturated porous media

A method of the mechanics of a fluid-saturated porous medium is used to study the propagation of harmonic surface waves along the free boundary of such a medium, along the boundary between a porous medium and a fluid, and along the boundary between two porous half-spaces. It is shown that, at low frequencies (i.e., for waves with frequencies lower than the Biot characteristic frequency), the corresponding dispersion equations in zero-order approximation are reduced to the equations for an “equivalent” elastic medium. For the wave numbers of surface waves, corrections taking into account the generation of longitudinal waves of the second kind at the boundary are calculated. Examples of numerical solutions of dispersion equations for rock are presented.     

Light propagation in porous ceramics: porosity and optical property studies using tunable diode laser spectroscopy

By integrating gas in scattering media absorption spectroscopy and frequency domain photon migration a new method is developed for the study of optical porosity and optical properties of porous media, in our case ceramics. The optical porosity is defined as the ratio of the path length through the gas-filled pores and the physical path length through the whole medium. The effective refractive index of the porous ceramics is also retrieved based on the optical porosity, which is then used to evaluate the reduced scattering coefficients of the porous ceramics. The combined method provides a new way to study light propagation in porous media. A modified Looyenga model is proposed to study the relationship between the physical porosity and the effective refractive index of the porous medium, which also connects the optical and physical porosities, and provides the possibility to use the present method for porosimetry analysis.     

Interface wave propagation characteristics of liquid-immersed porous cylinder

This paper devotes to investigate the propagation characteristics of the interface wave on the liquid-immersed porous cylinder, and special emphasis is paid on the dependence of the dispersion relation on the porous media parameters. A model of liquid-immersed porous cylinder is established theoretically. Based on the elastic-dynamic theory of liquid-saturated porous solid and wave theory, the dispersion curves and transient response of open-pores and sealed-pores are simulated numerically, and their dependence on the cylinder radius and porous medium parameters are analyzed. The results show that the Stoneley-Scholte wave can be clearly distinguished with other waves in the time domain, and the Stoneley-Scholte wave dispersion relates intimately with the porosity of the porous medium and cylinder radius, whilst the permeability of the media has little effect on the dispersion property.     

Reflection and transmission of acoustic waves on multilayered porous media

Based on the Boit theory of acoustic wave propagation in fluid-satu-rated porous medium we have studied in this paper the acoustic reflection andtransmission on multilayered porous media,in which the adequate boundaryconditions across the interfaces are taken into account.Numerical calculationsof the reflection and transmission coefficients at different incident angles andfrequencies of the fast compressional wave incident on porous media with threeor four layers are presented.The results indicate that the maximum or mini-mum reflection and transmission coefficients appear at certain ratios of thewavelength to the thickness.The acoustic incident angle and porous mediumproperties are shown to affect significantly these coefficients.As an example,the measured transmission coefficients in a water-saturated fused glass beadsample are in good agreement with theoretical prediction.     

Theoretical analysis of porous radiant burners under 2-D radiation field using discrete ordinates method

This paper describes a theoretical study to investigate the heat transfer characteristics of porous radiant burners (PRBs). In the present work, a 2-D rectangular model is used to solve the governing equations for porous medium and gas flow before the premixed flame to the exhaust gas. The gas and the solid phases are considered in non-local thermal equilibrium and combustion in the porous medium is modeled by considering a non-uniform heat generation zone. The homogeneous porous media, in addition to its convective heat exchange with the gas, may absorb, emit and scatter thermal radiation. The radiation effect in the gas flow is neglected but the conductive heat transfer is taken into account. In order to analyze the thermal characteristics of porous burners, the coupled energy equations for the gas and porous medium in steady condition are solved numerically and the discrete ordinates method (DOM) is used to obtain the distribution of radiative heat flux in the porous media. Finally, the effects of various parameters on the performance of porous radiant burners are examined. The present results are compared with some reported theoretical and experimental results by other investigators and good agreement is found.     

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.     

各向异性渗流条件下弹性波的传播特征

研究了弹性波在非均匀裂纹孔隙介质中的传播特性,建立了各向异性喷射流模型.当弹性波通过裂纹孔隙介质时,由于波的扰动及裂纹和孔隙几何结构的不一致,导致在裂纹内部及裂纹与周边孔隙之间同时存在着流体压力梯度.此时的弹性波波动响应中包含着裂纹内连通性特征和背景孔隙渗透率信息.流体的动态流动过程使得介质的等效弹性参数为复数(非完全弹性),并且具有频率依赖性.当弹性波为低频和高频极限时,介质为完全弹性;当处于中间频段时,波有衰减和频率依赖.裂纹孔隙介质的各向异性连通性(渗透率)对应着各向异性特征频率(当渗流长度等于非均匀尺度时的弹性波频率),波的传播受到裂纹内连通性的影响.在一定频段内,随着裂纹厚度的增加,将出现第二峰值,峰值大小同时受到裂纹厚度和半径的影响.     

流体-孔隙介质圆柱界面波传播特性

研究流体-孔隙介质圆柱界面波传播特性,分析孔隙介质孔隙率等参数对频散曲线的影响。理论上建立了无限大流体包裹孔隙介质圆柱界面波的模型,利用孔隙介质弹性波动理论,通过数值模拟计算得到流体-孔隙介质圆柱的频散曲线及时域波形,并分析了孔隙介质为开孔和闭孔状态下孔隙介质圆柱半径、孔隙率及渗透率对频散曲线的影响。结果表明,时域上斯通利波可以被明显区分开,孔隙介质圆柱半径的变化改变了圆柱尺度,孔隙率的变化改变了孔隙介质的纵、横波波速,因此对于斯通利波频散曲线的影响较大。而渗透率的变化既不改变圆柱的尺度也不改变孔隙层的纵、横波速度,因此对斯通利波频散曲线影响较小。      

The role of surface tension in elastic wave scattering in an inhomogeneous poroelastic medium

It is well known that many porous media such as rocks have heterogeneities at nearly all scales. We applied Biot's poroelastic theory to study the propagation of elastic waves in isotropic porous matrix with spherical inclusions. It is assumed that the heterogeneity dimension exceeds significantly the pore size. Modified boundary conditions on poroelastic interface are used to take into account the surface tension effects. The effective wavenumber is calculated using the Waterman and Truell multiple scattering theory, which relates the effective wave number to the amplitude of the wave field scattered by a single inclusion. The calculations were performed for a medium containing fluid-filled cavities or porous inclusions contrasting in saturating fluid elastic properties. The results obtained show that when we consider elastic wave propagation in poroelastic medium containing soft inclusions, it is necessary to take into account the capillary pressure. The influence of the surface tension depends on the diffraction parameter and it is a maximum in the low frequency range.     

The role of surface tension in elastic wave scattering in an inhomogeneous poroelastic medium

It is well known that many porous media such as rocks have heterogeneities at nearly all scales. We applied Biot's poroelastic theory to study the propagation of elastic waves in isotropic porous matrix with spherical inclusions. It is assumed that the heterogeneity dimension exceeds significantly the pore size. Modified boundary conditions on poroelastic interface are used to take into account the surface tension effects. The effective wavenumber is calculated using the Waterman and Truell multiple scattering theory, which relates the effective wave number to the amplitude of the wave field scattered by a single inclusion. The calculations were performed for a medium containing fluid-filled cavities or porous inclusions contrasting in saturating fluid elastic properties. The results obtained show that when we consider elastic wave propagation in poroelastic medium containing soft inclusions, it is necessary to take into account the capillary pressure. The influence of the surface tension depends on the diffraction parameter and it is a maximum in the low frequency range.     

流体/准饱和多孔介质中伪Scholte波的传播特性

研究流体/多孔介质界面Scholte波的传播特性对于水下勘探、地震工程等领域具有重要意义.本文基于Biot理论和等效流体模型,采用势函数方法,推导了描述有限厚度流体/准饱和多孔半空间远场界面波的特征方程和位移、孔压计算公式.在此基础上,分别以砂岩和松散沉积土为例,研究了流体/硬多孔介质和流体/软多孔介质两种情况下,可压缩流体层厚度和多孔介质饱和度对伪Scholte波传播特性的影响.结果表明：多孔介质软硬程度显著影响界面波的种类、相速度、位移和水压力分布;有限厚度流体/饱和多孔半空间界面处伪Scholte波相速度与界面波波长和流体厚度的比值有关;孔隙水中溶解的少量气体对剪切波的相速度的影响不大,对压缩波相速度、伪Scholte波相速度和孔隙水压力分布影响显著.     

Validity of the permeability Carman-Kozeny equation: A volume averaging approach

A volume averaging approach is used to estimate the porous media permeability. Contrary to traditional methods that rely on solving the Navier-Stokes equations for laminar flow, this approach has the advantage that it does not require the specification of some physical conditions and parameters (pressure drop and viscosity). Numerical results on synthetic models of porous media showed that (i) the local porous medium configuration has an important effect on the permeability value, and (ii) the Carman-Kozeny equation cannot describe the permeability behavior as a function of porosity and characteristic lengths. In turn, our results indicate that simple empirical equations, commonly used in practice, are unable to describe the permeability functionalities over a broad range of porous media configurations.     

弹性介质的Lagrange动力学与地震波方程

本文将地球介质看作是弹性介质, 从弹性体的Navier方程出发, 建立均匀弹性介质和非均匀弹性介质的分析动力学方程——Lagrange方程, 利用弹性介质的Lagrange方程导出匀弹性介质和非均匀弹性介质的地震波方程, 为用Lagrange分析动力学研究地球介质中地震波传播规律和解决地震勘探中的有关问题提供基础. 关键词： 地震勘探 弹性介质 Lagrange 方程 地震波方程